# Properties

 Label 784.2.i.m.177.2 Level $784$ Weight $2$ Character 784.177 Analytic conductor $6.260$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$784 = 2^{4} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 784.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.26027151847$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 98) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 177.2 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 784.177 Dual form 784.2.i.m.753.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 + 1.22474i) q^{3} +(1.41421 - 2.44949i) q^{5} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.707107 + 1.22474i) q^{3} +(1.41421 - 2.44949i) q^{5} +(0.500000 - 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} +4.00000 q^{15} +(-0.707107 - 1.22474i) q^{17} +(3.53553 - 6.12372i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-1.50000 - 2.59808i) q^{25} +5.65685 q^{27} +2.00000 q^{29} +(-4.24264 - 7.34847i) q^{31} +(1.41421 - 2.44949i) q^{33} +(-5.00000 + 8.66025i) q^{37} +9.89949 q^{41} -2.00000 q^{43} +(-1.41421 - 2.44949i) q^{45} +(-1.41421 + 2.44949i) q^{47} +(1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{53} -5.65685 q^{55} +10.0000 q^{57} +(0.707107 + 1.22474i) q^{59} +(1.41421 - 2.44949i) q^{61} +(6.00000 + 10.3923i) q^{67} -5.65685 q^{69} +12.0000 q^{71} +(-0.707107 - 1.22474i) q^{73} +(2.12132 - 3.67423i) q^{75} +(-2.00000 + 3.46410i) q^{79} +(2.50000 + 4.33013i) q^{81} +9.89949 q^{83} -4.00000 q^{85} +(1.41421 + 2.44949i) q^{87} +(-3.53553 + 6.12372i) q^{89} +(6.00000 - 10.3923i) q^{93} +(-10.0000 - 17.3205i) q^{95} -9.89949 q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{9} + O(q^{10})$$ $$4 q + 2 q^{9} - 4 q^{11} + 16 q^{15} - 8 q^{23} - 6 q^{25} + 8 q^{29} - 20 q^{37} - 8 q^{43} + 4 q^{51} + 4 q^{53} + 40 q^{57} + 24 q^{67} + 48 q^{71} - 8 q^{79} + 10 q^{81} - 16 q^{85} + 24 q^{93} - 40 q^{95} - 8 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$687$$ $$689$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$3$$ 0.707107 + 1.22474i 0.408248 + 0.707107i 0.994694 0.102882i $$-0.0328064\pi$$
−0.586445 + 0.809989i $$0.699473\pi$$
$$4$$ 0 0
$$5$$ 1.41421 2.44949i 0.632456 1.09545i −0.354593 0.935021i $$-0.615380\pi$$
0.987048 0.160424i $$-0.0512862\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0.500000 0.866025i 0.166667 0.288675i
$$10$$ 0 0
$$11$$ −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i $$-0.264158\pi$$
−0.976478 + 0.215615i $$0.930824\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 4.00000 1.03280
$$16$$ 0 0
$$17$$ −0.707107 1.22474i −0.171499 0.297044i 0.767445 0.641114i $$-0.221528\pi$$
−0.938944 + 0.344070i $$0.888194\pi$$
$$18$$ 0 0
$$19$$ 3.53553 6.12372i 0.811107 1.40488i −0.100983 0.994888i $$-0.532199\pi$$
0.912090 0.409991i $$-0.134468\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ 0 0
$$25$$ −1.50000 2.59808i −0.300000 0.519615i
$$26$$ 0 0
$$27$$ 5.65685 1.08866
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ −4.24264 7.34847i −0.762001 1.31982i −0.941818 0.336124i $$-0.890884\pi$$
0.179817 0.983700i $$-0.442449\pi$$
$$32$$ 0 0
$$33$$ 1.41421 2.44949i 0.246183 0.426401i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.00000 + 8.66025i −0.821995 + 1.42374i 0.0821995 + 0.996616i $$0.473806\pi$$
−0.904194 + 0.427121i $$0.859528\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 9.89949 1.54604 0.773021 0.634381i $$-0.218745\pi$$
0.773021 + 0.634381i $$0.218745\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 0 0
$$45$$ −1.41421 2.44949i −0.210819 0.365148i
$$46$$ 0 0
$$47$$ −1.41421 + 2.44949i −0.206284 + 0.357295i −0.950541 0.310599i $$-0.899470\pi$$
0.744257 + 0.667893i $$0.232804\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 1.00000 1.73205i 0.140028 0.242536i
$$52$$ 0 0
$$53$$ 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i $$-0.122805\pi$$
−0.789136 + 0.614218i $$0.789471\pi$$
$$54$$ 0 0
$$55$$ −5.65685 −0.762770
$$56$$ 0 0
$$57$$ 10.0000 1.32453
$$58$$ 0 0
$$59$$ 0.707107 + 1.22474i 0.0920575 + 0.159448i 0.908377 0.418153i $$-0.137322\pi$$
−0.816319 + 0.577601i $$0.803989\pi$$
$$60$$ 0 0
$$61$$ 1.41421 2.44949i 0.181071 0.313625i −0.761174 0.648547i $$-0.775377\pi$$
0.942246 + 0.334922i $$0.108710\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i $$0.0952216\pi$$
−0.222571 + 0.974916i $$0.571445\pi$$
$$68$$ 0 0
$$69$$ −5.65685 −0.681005
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ −0.707107 1.22474i −0.0827606 0.143346i 0.821674 0.569958i $$-0.193040\pi$$
−0.904435 + 0.426612i $$0.859707\pi$$
$$74$$ 0 0
$$75$$ 2.12132 3.67423i 0.244949 0.424264i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i $$-0.905577\pi$$
0.731307 + 0.682048i $$0.238911\pi$$
$$80$$ 0 0
$$81$$ 2.50000 + 4.33013i 0.277778 + 0.481125i
$$82$$ 0 0
$$83$$ 9.89949 1.08661 0.543305 0.839535i $$-0.317173\pi$$
0.543305 + 0.839535i $$0.317173\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ 0 0
$$87$$ 1.41421 + 2.44949i 0.151620 + 0.262613i
$$88$$ 0 0
$$89$$ −3.53553 + 6.12372i −0.374766 + 0.649113i −0.990292 0.139003i $$-0.955610\pi$$
0.615526 + 0.788116i $$0.288944\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 6.00000 10.3923i 0.622171 1.07763i
$$94$$ 0 0
$$95$$ −10.0000 17.3205i −1.02598 1.77705i
$$96$$ 0 0
$$97$$ −9.89949 −1.00514 −0.502571 0.864536i $$-0.667612\pi$$
−0.502571 + 0.864536i $$0.667612\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ 4.24264 + 7.34847i 0.422159 + 0.731200i 0.996150 0.0876610i $$-0.0279392\pi$$
−0.573992 + 0.818861i $$0.694606\pi$$
$$102$$ 0 0
$$103$$ −1.41421 + 2.44949i −0.139347 + 0.241355i −0.927249 0.374444i $$-0.877834\pi$$
0.787903 + 0.615800i $$0.211167\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.00000 + 3.46410i −0.193347 + 0.334887i −0.946357 0.323122i $$-0.895268\pi$$
0.753010 + 0.658009i $$0.228601\pi$$
$$108$$ 0 0
$$109$$ 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i $$-0.136131\pi$$
−0.814152 + 0.580651i $$0.802798\pi$$
$$110$$ 0 0
$$111$$ −14.1421 −1.34231
$$112$$ 0 0
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ 0 0
$$115$$ 5.65685 + 9.79796i 0.527504 + 0.913664i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 0 0
$$123$$ 7.00000 + 12.1244i 0.631169 + 1.09322i
$$124$$ 0 0
$$125$$ 5.65685 0.505964
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ 0 0
$$129$$ −1.41421 2.44949i −0.124515 0.215666i
$$130$$ 0 0
$$131$$ −6.36396 + 11.0227i −0.556022 + 0.963058i 0.441801 + 0.897113i $$0.354340\pi$$
−0.997823 + 0.0659452i $$0.978994\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 8.00000 13.8564i 0.688530 1.19257i
$$136$$ 0 0
$$137$$ −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i $$-0.995344\pi$$
0.487278 0.873247i $$-0.337990\pi$$
$$138$$ 0 0
$$139$$ 9.89949 0.839664 0.419832 0.907602i $$-0.362089\pi$$
0.419832 + 0.907602i $$0.362089\pi$$
$$140$$ 0 0
$$141$$ −4.00000 −0.336861
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 2.82843 4.89898i 0.234888 0.406838i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i $$-0.967671\pi$$
0.585231 + 0.810867i $$0.301004\pi$$
$$150$$ 0 0
$$151$$ −8.00000 13.8564i −0.651031 1.12762i −0.982873 0.184284i $$-0.941004\pi$$
0.331842 0.943335i $$-0.392330\pi$$
$$152$$ 0 0
$$153$$ −1.41421 −0.114332
$$154$$ 0 0
$$155$$ −24.0000 −1.92773
$$156$$ 0 0
$$157$$ −5.65685 9.79796i −0.451466 0.781962i 0.547011 0.837125i $$-0.315765\pi$$
−0.998477 + 0.0551630i $$0.982432\pi$$
$$158$$ 0 0
$$159$$ −1.41421 + 2.44949i −0.112154 + 0.194257i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 5.00000 8.66025i 0.391630 0.678323i −0.601035 0.799223i $$-0.705245\pi$$
0.992665 + 0.120900i $$0.0385779\pi$$
$$164$$ 0 0
$$165$$ −4.00000 6.92820i −0.311400 0.539360i
$$166$$ 0 0
$$167$$ −19.7990 −1.53209 −0.766046 0.642786i $$-0.777779\pi$$
−0.766046 + 0.642786i $$0.777779\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ −3.53553 6.12372i −0.270369 0.468293i
$$172$$ 0 0
$$173$$ −8.48528 + 14.6969i −0.645124 + 1.11739i 0.339149 + 0.940733i $$0.389861\pi$$
−0.984273 + 0.176655i $$0.943472\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −1.00000 + 1.73205i −0.0751646 + 0.130189i
$$178$$ 0 0
$$179$$ 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i $$-0.0186389\pi$$
−0.549825 + 0.835280i $$0.685306\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 4.00000 0.295689
$$184$$ 0 0
$$185$$ 14.1421 + 24.4949i 1.03975 + 1.80090i
$$186$$ 0 0
$$187$$ −1.41421 + 2.44949i −0.103418 + 0.179124i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i $$-0.879560\pi$$
0.784552 + 0.620063i $$0.212893\pi$$
$$192$$ 0 0
$$193$$ 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i $$0.0286631\pi$$
−0.420096 + 0.907480i $$0.638004\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ −4.24264 7.34847i −0.300753 0.520919i 0.675554 0.737311i $$-0.263905\pi$$
−0.976307 + 0.216391i $$0.930571\pi$$
$$200$$ 0 0
$$201$$ −8.48528 + 14.6969i −0.598506 + 1.03664i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 14.0000 24.2487i 0.977802 1.69360i
$$206$$ 0 0
$$207$$ 2.00000 + 3.46410i 0.139010 + 0.240772i
$$208$$ 0 0
$$209$$ −14.1421 −0.978232
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 0 0
$$213$$ 8.48528 + 14.6969i 0.581402 + 1.00702i
$$214$$ 0 0
$$215$$ −2.82843 + 4.89898i −0.192897 + 0.334108i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 1.00000 1.73205i 0.0675737 0.117041i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ −3.00000 −0.200000
$$226$$ 0 0
$$227$$ 10.6066 + 18.3712i 0.703985 + 1.21934i 0.967057 + 0.254561i $$0.0819311\pi$$
−0.263072 + 0.964776i $$0.584736\pi$$
$$228$$ 0 0
$$229$$ −8.48528 + 14.6969i −0.560723 + 0.971201i 0.436710 + 0.899602i $$0.356143\pi$$
−0.997434 + 0.0715988i $$0.977190\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −12.0000 + 20.7846i −0.786146 + 1.36165i 0.142166 + 0.989843i $$0.454593\pi$$
−0.928312 + 0.371802i $$0.878740\pi$$
$$234$$ 0 0
$$235$$ 4.00000 + 6.92820i 0.260931 + 0.451946i
$$236$$ 0 0
$$237$$ −5.65685 −0.367452
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −10.6066 18.3712i −0.683231 1.18339i −0.973989 0.226595i $$-0.927241\pi$$
0.290758 0.956797i $$-0.406093\pi$$
$$242$$ 0 0
$$243$$ 4.94975 8.57321i 0.317526 0.549972i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 7.00000 + 12.1244i 0.443607 + 0.768350i
$$250$$ 0 0
$$251$$ 9.89949 0.624851 0.312425 0.949942i $$-0.398859\pi$$
0.312425 + 0.949942i $$0.398859\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ 0 0
$$255$$ −2.82843 4.89898i −0.177123 0.306786i
$$256$$ 0 0
$$257$$ 6.36396 11.0227i 0.396973 0.687577i −0.596378 0.802704i $$-0.703394\pi$$
0.993351 + 0.115126i $$0.0367273\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 1.00000 1.73205i 0.0618984 0.107211i
$$262$$ 0 0
$$263$$ 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i $$-0.0460326\pi$$
−0.619586 + 0.784929i $$0.712699\pi$$
$$264$$ 0 0
$$265$$ 5.65685 0.347498
$$266$$ 0 0
$$267$$ −10.0000 −0.611990
$$268$$ 0 0
$$269$$ −5.65685 9.79796i −0.344904 0.597392i 0.640432 0.768015i $$-0.278755\pi$$
−0.985336 + 0.170623i $$0.945422\pi$$
$$270$$ 0 0
$$271$$ −11.3137 + 19.5959i −0.687259 + 1.19037i 0.285462 + 0.958390i $$0.407853\pi$$
−0.972721 + 0.231977i $$0.925480\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −3.00000 + 5.19615i −0.180907 + 0.313340i
$$276$$ 0 0
$$277$$ 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i $$-0.147530\pi$$
−0.834419 + 0.551131i $$0.814196\pi$$
$$278$$ 0 0
$$279$$ −8.48528 −0.508001
$$280$$ 0 0
$$281$$ 16.0000 0.954480 0.477240 0.878773i $$-0.341637\pi$$
0.477240 + 0.878773i $$0.341637\pi$$
$$282$$ 0 0
$$283$$ 0.707107 + 1.22474i 0.0420331 + 0.0728035i 0.886277 0.463156i $$-0.153283\pi$$
−0.844243 + 0.535960i $$0.819950\pi$$
$$284$$ 0 0
$$285$$ 14.1421 24.4949i 0.837708 1.45095i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 7.50000 12.9904i 0.441176 0.764140i
$$290$$ 0 0
$$291$$ −7.00000 12.1244i −0.410347 0.710742i
$$292$$ 0 0
$$293$$ 19.7990 1.15667 0.578335 0.815800i $$-0.303703\pi$$
0.578335 + 0.815800i $$0.303703\pi$$
$$294$$ 0 0
$$295$$ 4.00000 0.232889
$$296$$ 0 0
$$297$$ −5.65685 9.79796i −0.328244 0.568535i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −6.00000 + 10.3923i −0.344691 + 0.597022i
$$304$$ 0 0
$$305$$ −4.00000 6.92820i −0.229039 0.396708i
$$306$$ 0 0
$$307$$ −9.89949 −0.564994 −0.282497 0.959268i $$-0.591163\pi$$
−0.282497 + 0.959268i $$0.591163\pi$$
$$308$$ 0 0
$$309$$ −4.00000 −0.227552
$$310$$ 0 0
$$311$$ 5.65685 + 9.79796i 0.320771 + 0.555591i 0.980647 0.195783i $$-0.0627248\pi$$
−0.659877 + 0.751374i $$0.729391\pi$$
$$312$$ 0 0
$$313$$ 6.36396 11.0227i 0.359712 0.623040i −0.628200 0.778052i $$-0.716208\pi$$
0.987913 + 0.155012i $$0.0495415\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i $$-0.923942\pi$$
0.690761 + 0.723083i $$0.257276\pi$$
$$318$$ 0 0
$$319$$ −2.00000 3.46410i −0.111979 0.193952i
$$320$$ 0 0
$$321$$ −5.65685 −0.315735
$$322$$ 0 0
$$323$$ −10.0000 −0.556415
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −1.41421 + 2.44949i −0.0782062 + 0.135457i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i $$-0.744713\pi$$
0.970091 + 0.242742i $$0.0780468\pi$$
$$332$$ 0 0
$$333$$ 5.00000 + 8.66025i 0.273998 + 0.474579i
$$334$$ 0 0
$$335$$ 33.9411 1.85440
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 0 0
$$339$$ −8.48528 14.6969i −0.460857 0.798228i
$$340$$ 0 0
$$341$$ −8.48528 + 14.6969i −0.459504 + 0.795884i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −8.00000 + 13.8564i −0.430706 + 0.746004i
$$346$$ 0 0
$$347$$ −15.0000 25.9808i −0.805242 1.39472i −0.916127 0.400887i $$-0.868702\pi$$
0.110885 0.993833i $$-0.464631\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −0.707107 1.22474i −0.0376355 0.0651866i 0.846594 0.532239i $$-0.178649\pi$$
−0.884230 + 0.467052i $$0.845316\pi$$
$$354$$ 0 0
$$355$$ 16.9706 29.3939i 0.900704 1.56007i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −16.0000 + 27.7128i −0.844448 + 1.46263i 0.0416523 + 0.999132i $$0.486738\pi$$
−0.886100 + 0.463494i $$0.846596\pi$$
$$360$$ 0 0
$$361$$ −15.5000 26.8468i −0.815789 1.41299i
$$362$$ 0 0
$$363$$ 9.89949 0.519589
$$364$$ 0 0
$$365$$ −4.00000 −0.209370
$$366$$ 0 0
$$367$$ −14.1421 24.4949i −0.738213 1.27862i −0.953299 0.302028i $$-0.902336\pi$$
0.215086 0.976595i $$-0.430997\pi$$
$$368$$ 0 0
$$369$$ 4.94975 8.57321i 0.257674 0.446304i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i $$-0.916690\pi$$
0.707055 + 0.707159i $$0.250023\pi$$
$$374$$ 0 0
$$375$$ 4.00000 + 6.92820i 0.206559 + 0.357771i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 26.0000 1.33553 0.667765 0.744372i $$-0.267251\pi$$
0.667765 + 0.744372i $$0.267251\pi$$
$$380$$ 0 0
$$381$$ −11.3137 19.5959i −0.579619 1.00393i
$$382$$ 0 0
$$383$$ 18.3848 31.8434i 0.939418 1.62712i 0.172859 0.984947i $$-0.444700\pi$$
0.766559 0.642173i $$-0.221967\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −1.00000 + 1.73205i −0.0508329 + 0.0880451i
$$388$$ 0 0
$$389$$ −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i $$-0.937593\pi$$
0.321716 0.946836i $$-0.395740\pi$$
$$390$$ 0 0
$$391$$ 5.65685 0.286079
$$392$$ 0 0
$$393$$ −18.0000 −0.907980
$$394$$ 0 0
$$395$$ 5.65685 + 9.79796i 0.284627 + 0.492989i
$$396$$ 0 0
$$397$$ 11.3137 19.5959i 0.567819 0.983491i −0.428963 0.903322i $$-0.641121\pi$$
0.996781 0.0801687i $$-0.0255459\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i $$-0.684957\pi$$
0.998350 + 0.0574304i $$0.0182907\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 14.1421 0.702728
$$406$$ 0 0
$$407$$ 20.0000 0.991363
$$408$$ 0 0
$$409$$ 19.0919 + 33.0681i 0.944033 + 1.63511i 0.757676 + 0.652631i $$0.226335\pi$$
0.186357 + 0.982482i $$0.440332\pi$$
$$410$$ 0 0
$$411$$ 8.48528 14.6969i 0.418548 0.724947i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 14.0000 24.2487i 0.687233 1.19032i
$$416$$ 0 0
$$417$$ 7.00000 + 12.1244i 0.342791 + 0.593732i
$$418$$ 0 0
$$419$$ −9.89949 −0.483622 −0.241811 0.970323i $$-0.577741\pi$$
−0.241811 + 0.970323i $$0.577741\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ 1.41421 + 2.44949i 0.0687614 + 0.119098i
$$424$$ 0 0
$$425$$ −2.12132 + 3.67423i −0.102899 + 0.178227i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i $$-0.0733406\pi$$
−0.684564 + 0.728953i $$0.740007\pi$$
$$432$$ 0 0
$$433$$ 29.6985 1.42722 0.713609 0.700544i $$-0.247059\pi$$
0.713609 + 0.700544i $$0.247059\pi$$
$$434$$ 0 0
$$435$$ 8.00000 0.383571
$$436$$ 0 0
$$437$$ 14.1421 + 24.4949i 0.676510 + 1.17175i
$$438$$ 0 0
$$439$$ 8.48528 14.6969i 0.404980 0.701447i −0.589339 0.807886i $$-0.700612\pi$$
0.994319 + 0.106439i $$0.0339450\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i $$-0.863626\pi$$
0.814595 + 0.580030i $$0.196959\pi$$
$$444$$ 0 0
$$445$$ 10.0000 + 17.3205i 0.474045 + 0.821071i
$$446$$ 0 0
$$447$$ −14.1421 −0.668900
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ −9.89949 17.1464i −0.466149 0.807394i
$$452$$ 0 0
$$453$$ 11.3137 19.5959i 0.531564 0.920697i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −12.0000 + 20.7846i −0.561336 + 0.972263i 0.436044 + 0.899925i $$0.356379\pi$$
−0.997380 + 0.0723376i $$0.976954\pi$$
$$458$$ 0 0
$$459$$ −4.00000 6.92820i −0.186704 0.323381i
$$460$$ 0 0
$$461$$ −39.5980 −1.84426 −0.922131 0.386878i $$-0.873553\pi$$
−0.922131 + 0.386878i $$0.873553\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ −16.9706 29.3939i −0.786991 1.36311i
$$466$$ 0 0
$$467$$ −16.2635 + 28.1691i −0.752583 + 1.30351i 0.193984 + 0.981005i $$0.437859\pi$$
−0.946567 + 0.322507i $$0.895474\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 8.00000 13.8564i 0.368621 0.638470i
$$472$$ 0 0
$$473$$ 2.00000 + 3.46410i 0.0919601 + 0.159280i
$$474$$ 0 0
$$475$$ −21.2132 −0.973329
$$476$$ 0 0
$$477$$ 2.00000 0.0915737
$$478$$ 0 0
$$479$$ 15.5563 + 26.9444i 0.710788 + 1.23112i 0.964562 + 0.263857i $$0.0849947\pi$$
−0.253774 + 0.967264i $$0.581672\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −14.0000 + 24.2487i −0.635707 + 1.10108i
$$486$$ 0 0
$$487$$ 6.00000 + 10.3923i 0.271886 + 0.470920i 0.969345 0.245705i $$-0.0790193\pi$$
−0.697459 + 0.716625i $$0.745686\pi$$
$$488$$ 0 0
$$489$$ 14.1421 0.639529
$$490$$ 0 0
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ 0 0
$$493$$ −1.41421 2.44949i −0.0636930 0.110319i
$$494$$ 0 0
$$495$$ −2.82843 + 4.89898i −0.127128 + 0.220193i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2.00000 + 3.46410i −0.0895323 + 0.155074i −0.907314 0.420455i $$-0.861871\pi$$
0.817781 + 0.575529i $$0.195204\pi$$
$$500$$ 0 0
$$501$$ −14.0000 24.2487i −0.625474 1.08335i
$$502$$ 0 0
$$503$$ 39.5980 1.76559 0.882793 0.469762i $$-0.155660\pi$$
0.882793 + 0.469762i $$0.155660\pi$$
$$504$$ 0 0
$$505$$ 24.0000 1.06799
$$506$$ 0 0
$$507$$ −9.19239 15.9217i −0.408248 0.707107i
$$508$$ 0 0
$$509$$ 11.3137 19.5959i 0.501471 0.868574i −0.498527 0.866874i $$-0.666126\pi$$
0.999999 0.00169976i $$-0.000541051\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 20.0000 34.6410i 0.883022 1.52944i
$$514$$ 0 0
$$515$$ 4.00000 + 6.92820i 0.176261 + 0.305293i
$$516$$ 0 0
$$517$$ 5.65685 0.248788
$$518$$ 0 0
$$519$$ −24.0000 −1.05348
$$520$$ 0 0
$$521$$ −0.707107 1.22474i −0.0309789 0.0536570i 0.850120 0.526589i $$-0.176529\pi$$
−0.881099 + 0.472931i $$0.843196\pi$$
$$522$$ 0 0
$$523$$ −6.36396 + 11.0227i −0.278277 + 0.481989i −0.970957 0.239256i $$-0.923097\pi$$
0.692680 + 0.721245i $$0.256430\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −6.00000 + 10.3923i −0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ 0 0
$$531$$ 1.41421 0.0613716
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 5.65685 + 9.79796i 0.244567 + 0.423603i
$$536$$ 0 0
$$537$$ −8.48528 + 14.6969i −0.366167 + 0.634220i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −5.00000 + 8.66025i −0.214967 + 0.372333i −0.953262 0.302144i $$-0.902298\pi$$
0.738296 + 0.674477i $$0.235631\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 5.65685 0.242313
$$546$$ 0 0
$$547$$ 26.0000 1.11168 0.555840 0.831289i $$-0.312397\pi$$
0.555840 + 0.831289i $$0.312397\pi$$
$$548$$ 0 0
$$549$$ −1.41421 2.44949i −0.0603572 0.104542i
$$550$$ 0 0
$$551$$ 7.07107 12.2474i 0.301238 0.521759i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −20.0000 + 34.6410i −0.848953 + 1.47043i
$$556$$ 0 0
$$557$$ 15.0000 + 25.9808i 0.635570 + 1.10084i 0.986394 + 0.164399i $$0.0525683\pi$$
−0.350824 + 0.936442i $$0.614098\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ 0 0
$$563$$ 0.707107 + 1.22474i 0.0298010 + 0.0516168i 0.880541 0.473970i $$-0.157179\pi$$
−0.850740 + 0.525586i $$0.823846\pi$$
$$564$$ 0 0
$$565$$ −16.9706 + 29.3939i −0.713957 + 1.23661i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i $$-0.900553\pi$$
0.741981 + 0.670421i $$0.233886\pi$$
$$570$$ 0 0
$$571$$ −1.00000 1.73205i −0.0418487 0.0724841i 0.844342 0.535804i $$-0.179991\pi$$
−0.886191 + 0.463320i $$0.846658\pi$$
$$572$$ 0 0
$$573$$ −5.65685 −0.236318
$$574$$ 0 0
$$575$$ 12.0000 0.500435
$$576$$ 0 0
$$577$$ −10.6066 18.3712i −0.441559 0.764802i 0.556247 0.831017i $$-0.312241\pi$$
−0.997805 + 0.0662152i $$0.978908\pi$$
$$578$$ 0 0
$$579$$ −11.3137 + 19.5959i −0.470182 + 0.814379i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 2.00000 3.46410i 0.0828315 0.143468i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −29.6985 −1.22579 −0.612894 0.790165i $$-0.709995\pi$$
−0.612894 + 0.790165i $$0.709995\pi$$
$$588$$ 0 0
$$589$$ −60.0000 −2.47226
$$590$$ 0 0
$$591$$ 1.41421 + 2.44949i 0.0581730 + 0.100759i
$$592$$ 0 0
$$593$$ −3.53553 + 6.12372i −0.145187 + 0.251471i −0.929443 0.368967i $$-0.879712\pi$$
0.784256 + 0.620438i $$0.213045\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 6.00000 10.3923i 0.245564 0.425329i
$$598$$ 0 0
$$599$$ −8.00000 13.8564i −0.326871 0.566157i 0.655018 0.755613i $$-0.272661\pi$$
−0.981889 + 0.189456i $$0.939328\pi$$
$$600$$ 0 0
$$601$$ −29.6985 −1.21143 −0.605713 0.795683i $$-0.707112\pi$$
−0.605713 + 0.795683i $$0.707112\pi$$
$$602$$ 0 0
$$603$$ 12.0000 0.488678
$$604$$ 0 0
$$605$$ −9.89949 17.1464i −0.402472 0.697101i
$$606$$ 0 0
$$607$$ 8.48528 14.6969i 0.344407 0.596530i −0.640839 0.767675i $$-0.721413\pi$$
0.985246 + 0.171145i $$0.0547467\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i $$0.0404979\pi$$
−0.386073 + 0.922468i $$0.626169\pi$$
$$614$$ 0 0
$$615$$ 39.5980 1.59674
$$616$$ 0 0
$$617$$ −26.0000 −1.04672 −0.523360 0.852111i $$-0.675322\pi$$
−0.523360 + 0.852111i $$0.675322\pi$$
$$618$$ 0 0
$$619$$ −9.19239 15.9217i −0.369473 0.639946i 0.620010 0.784594i $$-0.287129\pi$$
−0.989483 + 0.144647i $$0.953795\pi$$
$$620$$ 0 0
$$621$$ −11.3137 + 19.5959i −0.454003 + 0.786357i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 15.5000 26.8468i 0.620000 1.07387i
$$626$$ 0 0
$$627$$ −10.0000 17.3205i −0.399362 0.691714i
$$628$$ 0 0
$$629$$ 14.1421 0.563884
$$630$$ 0 0
$$631$$ −44.0000 −1.75161 −0.875806 0.482663i $$-0.839670\pi$$
−0.875806 + 0.482663i $$0.839670\pi$$
$$632$$ 0 0
$$633$$ 8.48528 + 14.6969i 0.337260 + 0.584151i
$$634$$ 0 0
$$635$$ −22.6274 + 39.1918i −0.897942 + 1.55528i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 6.00000 10.3923i 0.237356 0.411113i
$$640$$ 0 0
$$641$$ −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i $$-0.995027\pi$$
0.486409 0.873731i $$-0.338307\pi$$
$$642$$ 0 0
$$643$$ 9.89949 0.390398 0.195199 0.980764i $$-0.437465\pi$$
0.195199 + 0.980764i $$0.437465\pi$$
$$644$$ 0 0
$$645$$ −8.00000 −0.315000
$$646$$ 0 0
$$647$$ −4.24264 7.34847i −0.166795 0.288898i 0.770496 0.637445i $$-0.220009\pi$$
−0.937291 + 0.348547i $$0.886675\pi$$
$$648$$ 0 0
$$649$$ 1.41421 2.44949i 0.0555127 0.0961509i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i $$-0.718768\pi$$
0.986634 + 0.162951i $$0.0521013\pi$$
$$654$$ 0 0
$$655$$ 18.0000 + 31.1769i 0.703318 + 1.21818i
$$656$$ 0 0
$$657$$ −1.41421 −0.0551737
$$658$$ 0 0
$$659$$ −30.0000 −1.16863 −0.584317 0.811525i $$-0.698638\pi$$
−0.584317 + 0.811525i $$0.698638\pi$$
$$660$$ 0 0
$$661$$ 4.24264 + 7.34847i 0.165020 + 0.285822i 0.936662 0.350234i $$-0.113898\pi$$
−0.771643 + 0.636056i $$0.780565\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −4.00000 + 6.92820i −0.154881 + 0.268261i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −5.65685 −0.218380
$$672$$ 0 0
$$673$$ −12.0000 −0.462566 −0.231283 0.972887i $$-0.574292\pi$$
−0.231283 + 0.972887i $$0.574292\pi$$
$$674$$ 0 0
$$675$$ −8.48528 14.6969i −0.326599 0.565685i
$$676$$ 0 0
$$677$$ −8.48528 + 14.6969i −0.326116 + 0.564849i −0.981738 0.190240i $$-0.939073\pi$$
0.655622 + 0.755090i $$0.272407\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −15.0000 + 25.9808i −0.574801 + 0.995585i
$$682$$ 0 0
$$683$$ 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i $$-0.0929302\pi$$
−0.728101 + 0.685470i $$0.759597\pi$$
$$684$$ 0 0
$$685$$ −33.9411 −1.29682
$$686$$ 0 0
$$687$$ −24.0000 −0.915657
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −6.36396 + 11.0227i −0.242096 + 0.419323i −0.961311 0.275464i $$-0.911168\pi$$
0.719215 + 0.694788i $$0.244502\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 14.0000 24.2487i 0.531050 0.919806i
$$696$$ 0 0
$$697$$ −7.00000 12.1244i −0.265144 0.459243i
$$698$$ 0 0
$$699$$ −33.9411 −1.28377
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 35.3553 + 61.2372i 1.33345 + 2.30961i
$$704$$ 0 0
$$705$$ −5.65685 + 9.79796i −0.213049 + 0.369012i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i $$-0.893462\pi$$
0.756730 + 0.653727i $$0.226796\pi$$
$$710$$ 0 0
$$711$$ 2.00000 + 3.46410i 0.0750059 + 0.129914i
$$712$$ 0 0
$$713$$ 33.9411 1.27111
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 8.48528 + 14.6969i 0.316889 + 0.548867i
$$718$$ 0 0
$$719$$ −1.41421 + 2.44949i −0.0527413 + 0.0913506i −0.891191 0.453629i $$-0.850129\pi$$
0.838449 + 0.544979i $$0.183463\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 15.0000 25.9808i 0.557856 0.966235i
$$724$$ 0 0
$$725$$ −3.00000 5.19615i −0.111417 0.192980i
$$726$$ 0 0
$$727$$ −19.7990 −0.734304 −0.367152 0.930161i $$-0.619667\pi$$
−0.367152 + 0.930161i $$0.619667\pi$$
$$728$$ 0 0
$$729$$ 29.0000 1.07407
$$730$$ 0 0
$$731$$ 1.41421 + 2.44949i 0.0523066 + 0.0905977i
$$732$$ 0 0
$$733$$ 21.2132 36.7423i 0.783528 1.35711i −0.146347 0.989233i $$-0.546752\pi$$
0.929875 0.367876i $$-0.119915\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 12.0000 20.7846i 0.442026 0.765611i
$$738$$ 0 0
$$739$$ −15.0000 25.9808i −0.551784 0.955718i −0.998146 0.0608653i $$-0.980614\pi$$
0.446362 0.894852i $$-0.352719\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ 0 0
$$745$$ 14.1421 + 24.4949i 0.518128 + 0.897424i
$$746$$ 0 0
$$747$$ 4.94975 8.57321i 0.181102 0.313678i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i $$-0.856585\pi$$
0.827225 + 0.561870i $$0.189918\pi$$
$$752$$ 0 0
$$753$$ 7.00000 + 12.1244i 0.255094 + 0.441836i
$$754$$ 0 0
$$755$$ −45.2548 −1.64699
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 5.65685 + 9.79796i 0.205331 + 0.355643i
$$760$$ 0 0
$$761$$ −3.53553 + 6.12372i −0.128163 + 0.221985i −0.922965 0.384884i $$-0.874241\pi$$
0.794802 + 0.606869i $$0.207575\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −2.00000 + 3.46410i −0.0723102 + 0.125245i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −29.6985 −1.07095 −0.535477 0.844550i $$-0.679868\pi$$
−0.535477 + 0.844550i $$0.679868\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 0 0
$$773$$ 24.0416 + 41.6413i 0.864717 + 1.49773i 0.867328 + 0.497738i $$0.165836\pi$$
−0.00261021 + 0.999997i $$0.500831\pi$$
$$774$$ 0 0
$$775$$ −12.7279 + 22.0454i −0.457200 + 0.791894i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 35.0000 60.6218i 1.25401 2.17200i
$$780$$ 0 0
$$781$$ −12.0000 20.7846i −0.429394 0.743732i
$$782$$ 0 0
$$783$$ 11.3137 0.404319
$$784$$ 0 0
$$785$$ −32.0000 −1.14213
$$786$$ 0 0
$$787$$ 0.707107 + 1.22474i 0.0252056 + 0.0436574i 0.878353 0.478012i $$-0.158643\pi$$
−0.853147 + 0.521670i $$0.825309\pi$$
$$788$$ 0 0
$$789$$ −8.48528 + 14.6969i −0.302084 + 0.523225i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 4.00000 + 6.92820i 0.141865 + 0.245718i
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 4.00000 0.141510
$$800$$ 0 0
$$801$$ 3.53553 + 6.12372i 0.124922 + 0.216371i