# Properties

 Label 756.2.ba.a.71.10 Level $756$ Weight $2$ Character 756.71 Analytic conductor $6.037$ Analytic rank $0$ Dimension $72$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$756 = 2^{2} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 756.ba (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.03669039281$$ Analytic rank: $$0$$ Dimension: $$72$$ Relative dimension: $$36$$ over $$\Q(\zeta_{6})$$ Twist minimal: no (minimal twist has level 252) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 71.10 Character $$\chi$$ $$=$$ 756.71 Dual form 756.2.ba.a.575.10

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +O(q^{10})$$ $$q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +(0.635018 + 3.60669i) q^{10} +(0.124825 + 0.216204i) q^{11} +(-0.0646102 + 0.111908i) q^{13} +(1.32880 + 0.484025i) q^{14} +(-3.75739 - 1.37188i) q^{16} -0.554691i q^{17} +3.58986i q^{19} +(3.33106 - 3.96573i) q^{20} +(0.120837 - 0.331737i) q^{22} +(-3.94814 + 6.83839i) q^{23} +(0.852871 + 1.47722i) q^{25} +(0.179977 - 0.0316879i) q^{26} +(-0.683091 - 1.87973i) q^{28} +(5.90477 - 3.40912i) q^{29} +(6.96683 + 4.02230i) q^{31} +(1.92804 + 5.31814i) q^{32} +(-0.601052 + 0.504084i) q^{34} +2.58954 q^{35} +9.96519 q^{37} +(3.88991 - 3.26234i) q^{38} +(-7.32434 - 0.00555133i) q^{40} +(-4.25964 - 2.45930i) q^{41} +(3.78791 - 2.18695i) q^{43} +(-0.469276 + 0.170534i) q^{44} +(10.9979 - 1.93636i) q^{46} +(2.41916 + 4.19011i) q^{47} +(0.500000 - 0.866025i) q^{49} +(0.825622 - 2.26660i) q^{50} +(-0.197893 - 0.166223i) q^{52} +9.00057i q^{53} -0.646482i q^{55} +(-1.41607 + 2.44842i) q^{56} +(-9.06010 - 3.30020i) q^{58} +(-3.71629 + 6.43680i) q^{59} +(6.42524 + 11.1288i) q^{61} +(-1.97273 - 11.2045i) q^{62} +(4.01050 - 6.92213i) q^{64} +(0.289791 - 0.167311i) q^{65} +(5.23554 + 3.02274i) q^{67} +(1.09243 + 0.193194i) q^{68} +(-2.35329 - 2.80598i) q^{70} +15.7820 q^{71} -14.1020 q^{73} +(-9.05602 - 10.7981i) q^{74} +(-7.07002 - 1.25032i) q^{76} +(-0.216204 - 0.124825i) q^{77} +(2.04035 - 1.17800i) q^{79} +(6.65009 + 7.94155i) q^{80} +(1.20616 + 6.85059i) q^{82} +(2.36518 + 4.09661i) q^{83} +(-0.718199 + 1.24396i) q^{85} +(-5.81205 - 2.11708i) q^{86} +(0.611249 + 0.353523i) q^{88} -7.82233i q^{89} -0.129220i q^{91} +(-12.0927 - 10.1574i) q^{92} +(2.34187 - 6.42918i) q^{94} +(4.64806 - 8.05067i) q^{95} +(-5.67078 - 9.82208i) q^{97} +(-1.39279 + 0.245224i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$72 q+O(q^{10})$$ 72 * q $$72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100})$$ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$325$$ $$379$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.908765 1.08358i −0.642594 0.766207i
$$3$$ 0 0
$$4$$ −0.348292 + 1.96944i −0.174146 + 0.984720i
$$5$$ −2.24261 1.29477i −1.00293 0.579040i −0.0938136 0.995590i $$-0.529906\pi$$
−0.909113 + 0.416550i $$0.863239\pi$$
$$6$$ 0 0
$$7$$ −0.866025 + 0.500000i −0.327327 + 0.188982i
$$8$$ 2.45056 1.41236i 0.866404 0.499343i
$$9$$ 0 0
$$10$$ 0.635018 + 3.60669i 0.200810 + 1.14054i
$$11$$ 0.124825 + 0.216204i 0.0376363 + 0.0651879i 0.884230 0.467052i $$-0.154684\pi$$
−0.846594 + 0.532240i $$0.821351\pi$$
$$12$$ 0 0
$$13$$ −0.0646102 + 0.111908i −0.0179197 + 0.0310377i −0.874846 0.484401i $$-0.839038\pi$$
0.856927 + 0.515439i $$0.172371\pi$$
$$14$$ 1.32880 + 0.484025i 0.355138 + 0.129361i
$$15$$ 0 0
$$16$$ −3.75739 1.37188i −0.939347 0.342970i
$$17$$ 0.554691i 0.134532i −0.997735 0.0672662i $$-0.978572\pi$$
0.997735 0.0672662i $$-0.0214277\pi$$
$$18$$ 0 0
$$19$$ 3.58986i 0.823571i 0.911281 + 0.411786i $$0.135095\pi$$
−0.911281 + 0.411786i $$0.864905\pi$$
$$20$$ 3.33106 3.96573i 0.744847 0.886764i
$$21$$ 0 0
$$22$$ 0.120837 0.331737i 0.0257626 0.0707265i
$$23$$ −3.94814 + 6.83839i −0.823245 + 1.42590i 0.0800083 + 0.996794i $$0.474505\pi$$
−0.903253 + 0.429108i $$0.858828\pi$$
$$24$$ 0 0
$$25$$ 0.852871 + 1.47722i 0.170574 + 0.295443i
$$26$$ 0.179977 0.0316879i 0.0352964 0.00621451i
$$27$$ 0 0
$$28$$ −0.683091 1.87973i −0.129092 0.355236i
$$29$$ 5.90477 3.40912i 1.09649 0.633058i 0.161192 0.986923i $$-0.448466\pi$$
0.935296 + 0.353865i $$0.115133\pi$$
$$30$$ 0 0
$$31$$ 6.96683 + 4.02230i 1.25128 + 0.722427i 0.971364 0.237597i $$-0.0763598\pi$$
0.279917 + 0.960024i $$0.409693\pi$$
$$32$$ 1.92804 + 5.31814i 0.340833 + 0.940124i
$$33$$ 0 0
$$34$$ −0.601052 + 0.504084i −0.103080 + 0.0864497i
$$35$$ 2.58954 0.437713
$$36$$ 0 0
$$37$$ 9.96519 1.63827 0.819134 0.573603i $$-0.194455\pi$$
0.819134 + 0.573603i $$0.194455\pi$$
$$38$$ 3.88991 3.26234i 0.631026 0.529222i
$$39$$ 0 0
$$40$$ −7.32434 0.00555133i −1.15808 0.000877742i
$$41$$ −4.25964 2.45930i −0.665244 0.384079i 0.129028 0.991641i $$-0.458814\pi$$
−0.794272 + 0.607562i $$0.792148\pi$$
$$42$$ 0 0
$$43$$ 3.78791 2.18695i 0.577651 0.333507i −0.182549 0.983197i $$-0.558435\pi$$
0.760199 + 0.649690i $$0.225101\pi$$
$$44$$ −0.469276 + 0.170534i −0.0707460 + 0.0257090i
$$45$$ 0 0
$$46$$ 10.9979 1.93636i 1.62155 0.285500i
$$47$$ 2.41916 + 4.19011i 0.352871 + 0.611190i 0.986751 0.162241i $$-0.0518721\pi$$
−0.633880 + 0.773431i $$0.718539\pi$$
$$48$$ 0 0
$$49$$ 0.500000 0.866025i 0.0714286 0.123718i
$$50$$ 0.825622 2.26660i 0.116761 0.320545i
$$51$$ 0 0
$$52$$ −0.197893 0.166223i −0.0274429 0.0230509i
$$53$$ 9.00057i 1.23632i 0.786051 + 0.618162i $$0.212122\pi$$
−0.786051 + 0.618162i $$0.787878\pi$$
$$54$$ 0 0
$$55$$ 0.646482i 0.0871715i
$$56$$ −1.41607 + 2.44842i −0.189230 + 0.327184i
$$57$$ 0 0
$$58$$ −9.06010 3.30020i −1.18965 0.433338i
$$59$$ −3.71629 + 6.43680i −0.483820 + 0.838001i −0.999827 0.0185836i $$-0.994084\pi$$
0.516007 + 0.856584i $$0.327418\pi$$
$$60$$ 0 0
$$61$$ 6.42524 + 11.1288i 0.822667 + 1.42490i 0.903689 + 0.428189i $$0.140848\pi$$
−0.0810220 + 0.996712i $$0.525818\pi$$
$$62$$ −1.97273 11.2045i −0.250537 1.42297i
$$63$$ 0 0
$$64$$ 4.01050 6.92213i 0.501312 0.865266i
$$65$$ 0.289791 0.167311i 0.0359442 0.0207524i
$$66$$ 0 0
$$67$$ 5.23554 + 3.02274i 0.639623 + 0.369287i 0.784469 0.620167i $$-0.212935\pi$$
−0.144846 + 0.989454i $$0.546269\pi$$
$$68$$ 1.09243 + 0.193194i 0.132477 + 0.0234282i
$$69$$ 0 0
$$70$$ −2.35329 2.80598i −0.281272 0.335379i
$$71$$ 15.7820 1.87298 0.936489 0.350697i $$-0.114055\pi$$
0.936489 + 0.350697i $$0.114055\pi$$
$$72$$ 0 0
$$73$$ −14.1020 −1.65051 −0.825256 0.564759i $$-0.808969\pi$$
−0.825256 + 0.564759i $$0.808969\pi$$
$$74$$ −9.05602 10.7981i −1.05274 1.25525i
$$75$$ 0 0
$$76$$ −7.07002 1.25032i −0.810987 0.143421i
$$77$$ −0.216204 0.124825i −0.0246387 0.0142252i
$$78$$ 0 0
$$79$$ 2.04035 1.17800i 0.229558 0.132535i −0.380810 0.924653i $$-0.624355\pi$$
0.610368 + 0.792118i $$0.291022\pi$$
$$80$$ 6.65009 + 7.94155i 0.743502 + 0.887892i
$$81$$ 0 0
$$82$$ 1.20616 + 6.85059i 0.133198 + 0.756521i
$$83$$ 2.36518 + 4.09661i 0.259612 + 0.449662i 0.966138 0.258026i $$-0.0830719\pi$$
−0.706526 + 0.707687i $$0.749739\pi$$
$$84$$ 0 0
$$85$$ −0.718199 + 1.24396i −0.0778996 + 0.134926i
$$86$$ −5.81205 2.11708i −0.626730 0.228290i
$$87$$ 0 0
$$88$$ 0.611249 + 0.353523i 0.0651594 + 0.0376856i
$$89$$ 7.82233i 0.829165i −0.910012 0.414582i $$-0.863928\pi$$
0.910012 0.414582i $$-0.136072\pi$$
$$90$$ 0 0
$$91$$ 0.129220i 0.0135460i
$$92$$ −12.0927 10.1574i −1.26075 1.05898i
$$93$$ 0 0
$$94$$ 2.34187 6.42918i 0.241545 0.663119i
$$95$$ 4.64806 8.05067i 0.476881 0.825981i
$$96$$ 0 0
$$97$$ −5.67078 9.82208i −0.575780 0.997281i −0.995956 0.0898382i $$-0.971365\pi$$
0.420176 0.907443i $$-0.361968\pi$$
$$98$$ −1.39279 + 0.245224i −0.140693 + 0.0247713i
$$99$$ 0 0
$$100$$ −3.20634 + 1.16518i −0.320634 + 0.116518i
$$101$$ 3.16980 1.83009i 0.315407 0.182100i −0.333936 0.942596i $$-0.608377\pi$$
0.649344 + 0.760495i $$0.275044\pi$$
$$102$$ 0 0
$$103$$ −5.95960 3.44077i −0.587216 0.339030i 0.176780 0.984250i $$-0.443432\pi$$
−0.763996 + 0.645221i $$0.776765\pi$$
$$104$$ −0.000277016 0.365490i −2.71637e−5 0.0358393i
$$105$$ 0 0
$$106$$ 9.75284 8.17941i 0.947280 0.794454i
$$107$$ −7.43669 −0.718932 −0.359466 0.933158i $$-0.617041\pi$$
−0.359466 + 0.933158i $$0.617041\pi$$
$$108$$ 0 0
$$109$$ −8.23684 −0.788947 −0.394473 0.918907i $$-0.629073\pi$$
−0.394473 + 0.918907i $$0.629073\pi$$
$$110$$ −0.700514 + 0.587500i −0.0667914 + 0.0560159i
$$111$$ 0 0
$$112$$ 3.93993 0.690611i 0.372288 0.0652567i
$$113$$ 7.42933 + 4.28933i 0.698893 + 0.403506i 0.806935 0.590640i $$-0.201125\pi$$
−0.108042 + 0.994146i $$0.534458\pi$$
$$114$$ 0 0
$$115$$ 17.7083 10.2239i 1.65131 0.953383i
$$116$$ 4.65748 + 12.8165i 0.432436 + 1.18998i
$$117$$ 0 0
$$118$$ 10.3520 1.82265i 0.952981 0.167788i
$$119$$ 0.277346 + 0.480377i 0.0254242 + 0.0440361i
$$120$$ 0 0
$$121$$ 5.46884 9.47230i 0.497167 0.861119i
$$122$$ 6.21995 17.0758i 0.563128 1.54597i
$$123$$ 0 0
$$124$$ −10.3482 + 12.3198i −0.929294 + 1.10635i
$$125$$ 8.53063i 0.763003i
$$126$$ 0 0
$$127$$ 4.71023i 0.417965i 0.977919 + 0.208982i $$0.0670152\pi$$
−0.977919 + 0.208982i $$0.932985\pi$$
$$128$$ −11.1453 + 1.94490i −0.985113 + 0.171906i
$$129$$ 0 0
$$130$$ −0.444647 0.161966i −0.0389981 0.0142053i
$$131$$ −4.97136 + 8.61065i −0.434350 + 0.752316i −0.997242 0.0742144i $$-0.976355\pi$$
0.562893 + 0.826530i $$0.309688\pi$$
$$132$$ 0 0
$$133$$ −1.79493 3.10891i −0.155640 0.269577i
$$134$$ −1.48250 8.42009i −0.128068 0.727385i
$$135$$ 0 0
$$136$$ −0.783422 1.35930i −0.0671779 0.116559i
$$137$$ −13.1903 + 7.61545i −1.12693 + 0.650632i −0.943160 0.332338i $$-0.892162\pi$$
−0.183767 + 0.982970i $$0.558829\pi$$
$$138$$ 0 0
$$139$$ −1.53695 0.887356i −0.130362 0.0752645i 0.433401 0.901201i $$-0.357313\pi$$
−0.563763 + 0.825937i $$0.690647\pi$$
$$140$$ −0.901917 + 5.09995i −0.0762259 + 0.431025i
$$141$$ 0 0
$$142$$ −14.3421 17.1011i −1.20356 1.43509i
$$143$$ −0.0322600 −0.00269771
$$144$$ 0 0
$$145$$ −17.6561 −1.46626
$$146$$ 12.8154 + 15.2806i 1.06061 + 1.26463i
$$147$$ 0 0
$$148$$ −3.47079 + 19.6258i −0.285297 + 1.61323i
$$149$$ 14.3488 + 8.28427i 1.17550 + 0.678674i 0.954969 0.296706i $$-0.0958882\pi$$
0.220529 + 0.975380i $$0.429222\pi$$
$$150$$ 0 0
$$151$$ −15.2363 + 8.79668i −1.23991 + 0.715864i −0.969076 0.246761i $$-0.920634\pi$$
−0.270836 + 0.962625i $$0.587300\pi$$
$$152$$ 5.07017 + 8.79718i 0.411245 + 0.713546i
$$153$$ 0 0
$$154$$ 0.0612203 + 0.347711i 0.00493327 + 0.0280194i
$$155$$ −10.4159 18.0409i −0.836628 1.44908i
$$156$$ 0 0
$$157$$ 1.12675 1.95160i 0.0899248 0.155754i −0.817554 0.575851i $$-0.804671\pi$$
0.907479 + 0.420097i $$0.138004\pi$$
$$158$$ −3.13066 1.14036i −0.249062 0.0907223i
$$159$$ 0 0
$$160$$ 2.56194 14.4229i 0.202539 1.14023i
$$161$$ 7.89629i 0.622315i
$$162$$ 0 0
$$163$$ 6.99511i 0.547899i 0.961744 + 0.273950i $$0.0883302\pi$$
−0.961744 + 0.273950i $$0.911670\pi$$
$$164$$ 6.32705 7.53255i 0.494060 0.588193i
$$165$$ 0 0
$$166$$ 2.28961 6.28572i 0.177709 0.487867i
$$167$$ −5.40220 + 9.35689i −0.418035 + 0.724058i −0.995742 0.0921866i $$-0.970614\pi$$
0.577707 + 0.816244i $$0.303948\pi$$
$$168$$ 0 0
$$169$$ 6.49165 + 11.2439i 0.499358 + 0.864913i
$$170$$ 2.00060 0.352239i 0.153439 0.0270155i
$$171$$ 0 0
$$172$$ 2.98777 + 8.22175i 0.227815 + 0.626903i
$$173$$ −4.01988 + 2.32088i −0.305626 + 0.176453i −0.644968 0.764210i $$-0.723129\pi$$
0.339341 + 0.940663i $$0.389796\pi$$
$$174$$ 0 0
$$175$$ −1.47722 0.852871i −0.111667 0.0644710i
$$176$$ −0.172412 0.983606i −0.0129960 0.0741421i
$$177$$ 0 0
$$178$$ −8.47612 + 7.10866i −0.635312 + 0.532816i
$$179$$ −6.66668 −0.498291 −0.249145 0.968466i $$-0.580150\pi$$
−0.249145 + 0.968466i $$0.580150\pi$$
$$180$$ 0 0
$$181$$ −7.61248 −0.565831 −0.282916 0.959145i $$-0.591302\pi$$
−0.282916 + 0.959145i $$0.591302\pi$$
$$182$$ −0.140021 + 0.117431i −0.0103790 + 0.00870457i
$$183$$ 0 0
$$184$$ −0.0169276 + 22.3341i −0.00124792 + 1.64649i
$$185$$ −22.3481 12.9027i −1.64306 0.948622i
$$186$$ 0 0
$$187$$ 0.119926 0.0692395i 0.00876988 0.00506329i
$$188$$ −9.09474 + 3.30501i −0.663302 + 0.241043i
$$189$$ 0 0
$$190$$ −12.9475 + 2.27963i −0.939313 + 0.165382i
$$191$$ 2.15506 + 3.73268i 0.155935 + 0.270087i 0.933399 0.358840i $$-0.116828\pi$$
−0.777464 + 0.628927i $$0.783494\pi$$
$$192$$ 0 0
$$193$$ −0.690908 + 1.19669i −0.0497327 + 0.0861395i −0.889820 0.456312i $$-0.849170\pi$$
0.840087 + 0.542451i $$0.182504\pi$$
$$194$$ −5.48960 + 15.0707i −0.394130 + 1.08201i
$$195$$ 0 0
$$196$$ 1.53144 + 1.28635i 0.109389 + 0.0918821i
$$197$$ 9.26481i 0.660091i −0.943965 0.330045i $$-0.892936\pi$$
0.943965 0.330045i $$-0.107064\pi$$
$$198$$ 0 0
$$199$$ 24.5989i 1.74377i −0.489712 0.871884i $$-0.662898\pi$$
0.489712 0.871884i $$-0.337102\pi$$
$$200$$ 4.17637 + 2.41545i 0.295314 + 0.170798i
$$201$$ 0 0
$$202$$ −4.86365 1.77162i −0.342205 0.124650i
$$203$$ −3.40912 + 5.90477i −0.239273 + 0.414434i
$$204$$ 0 0
$$205$$ 6.36848 + 11.0305i 0.444794 + 0.770406i
$$206$$ 1.68752 + 9.58456i 0.117575 + 0.667788i
$$207$$ 0 0
$$208$$ 0.396290 0.331845i 0.0274778 0.0230093i
$$209$$ −0.776142 + 0.448106i −0.0536869 + 0.0309961i
$$210$$ 0 0
$$211$$ 8.98731 + 5.18882i 0.618712 + 0.357213i 0.776367 0.630281i $$-0.217060\pi$$
−0.157655 + 0.987494i $$0.550394\pi$$
$$212$$ −17.7261 3.13482i −1.21743 0.215301i
$$213$$ 0 0
$$214$$ 6.75820 + 8.05824i 0.461981 + 0.550850i
$$215$$ −11.3264 −0.772455
$$216$$ 0 0
$$217$$ −8.04461 −0.546104
$$218$$ 7.48536 + 8.92528i 0.506972 + 0.604496i
$$219$$ 0 0
$$220$$ 1.27321 + 0.225164i 0.0858396 + 0.0151806i
$$221$$ 0.0620745 + 0.0358387i 0.00417558 + 0.00241077i
$$222$$ 0 0
$$223$$ −22.3502 + 12.9039i −1.49668 + 0.864109i −0.999993 0.00382012i $$-0.998784\pi$$
−0.496688 + 0.867929i $$0.665451\pi$$
$$224$$ −4.32881 3.64163i −0.289230 0.243316i
$$225$$ 0 0
$$226$$ −2.10369 11.9483i −0.139935 0.794787i
$$227$$ −6.74196 11.6774i −0.447480 0.775057i 0.550742 0.834676i $$-0.314345\pi$$
−0.998221 + 0.0596183i $$0.981012\pi$$
$$228$$ 0 0
$$229$$ 6.49974 11.2579i 0.429515 0.743941i −0.567315 0.823501i $$-0.692018\pi$$
0.996830 + 0.0795594i $$0.0253513\pi$$
$$230$$ −27.1711 9.89725i −1.79161 0.652605i
$$231$$ 0 0
$$232$$ 9.65510 16.6939i 0.633889 1.09601i
$$233$$ 22.7845i 1.49266i 0.665575 + 0.746331i $$0.268186\pi$$
−0.665575 + 0.746331i $$0.731814\pi$$
$$234$$ 0 0
$$235$$ 12.5291i 0.817305i
$$236$$ −11.3825 9.56089i −0.740941 0.622361i
$$237$$ 0 0
$$238$$ 0.268485 0.737076i 0.0174033 0.0477775i
$$239$$ 10.1962 17.6603i 0.659537 1.14235i −0.321198 0.947012i $$-0.604086\pi$$
0.980736 0.195340i $$-0.0625810\pi$$
$$240$$ 0 0
$$241$$ 3.27539 + 5.67314i 0.210986 + 0.365439i 0.952024 0.306025i $$-0.0989991\pi$$
−0.741037 + 0.671464i $$0.765666\pi$$
$$242$$ −15.2339 + 2.68218i −0.979271 + 0.172417i
$$243$$ 0 0
$$244$$ −24.1554 + 8.77804i −1.54639 + 0.561956i
$$245$$ −2.24261 + 1.29477i −0.143275 + 0.0827200i
$$246$$ 0 0
$$247$$ −0.401735 0.231942i −0.0255618 0.0147581i
$$248$$ 22.7536 + 0.0172456i 1.44485 + 0.00109510i
$$249$$ 0 0
$$250$$ 9.24362 7.75234i 0.584618 0.490301i
$$251$$ 18.3086 1.15563 0.577814 0.816169i $$-0.303906\pi$$
0.577814 + 0.816169i $$0.303906\pi$$
$$252$$ 0 0
$$253$$ −1.97131 −0.123935
$$254$$ 5.10391 4.28049i 0.320248 0.268582i
$$255$$ 0 0
$$256$$ 12.2359 + 10.3094i 0.764744 + 0.644335i
$$257$$ −13.8378 7.98924i −0.863176 0.498355i 0.00189858 0.999998i $$-0.499396\pi$$
−0.865075 + 0.501643i $$0.832729\pi$$
$$258$$ 0 0
$$259$$ −8.63011 + 4.98260i −0.536249 + 0.309603i
$$260$$ 0.228577 + 0.628999i 0.0141758 + 0.0390089i
$$261$$ 0 0
$$262$$ 13.8481 2.43819i 0.855540 0.150632i
$$263$$ 1.92259 + 3.33002i 0.118552 + 0.205338i 0.919194 0.393805i $$-0.128841\pi$$
−0.800642 + 0.599143i $$0.795508\pi$$
$$264$$ 0 0
$$265$$ 11.6537 20.1848i 0.715881 1.23994i
$$266$$ −1.73758 + 4.77022i −0.106538 + 0.292481i
$$267$$ 0 0
$$268$$ −7.77660 + 9.25829i −0.475032 + 0.565540i
$$269$$ 3.59531i 0.219210i 0.993975 + 0.109605i $$0.0349585\pi$$
−0.993975 + 0.109605i $$0.965041\pi$$
$$270$$ 0 0
$$271$$ 4.24361i 0.257781i 0.991659 + 0.128891i $$0.0411416\pi$$
−0.991659 + 0.128891i $$0.958858\pi$$
$$272$$ −0.760969 + 2.08419i −0.0461405 + 0.126373i
$$273$$ 0 0
$$274$$ 20.2389 + 7.37214i 1.22267 + 0.445367i
$$275$$ −0.212920 + 0.368788i −0.0128395 + 0.0222387i
$$276$$ 0 0
$$277$$ 4.88987 + 8.46950i 0.293804 + 0.508883i 0.974706 0.223491i $$-0.0717454\pi$$
−0.680902 + 0.732374i $$0.738412\pi$$
$$278$$ 0.435201 + 2.47180i 0.0261016 + 0.148249i
$$279$$ 0 0
$$280$$ 6.34584 3.65736i 0.379236 0.218569i
$$281$$ −20.3980 + 11.7768i −1.21684 + 0.702544i −0.964241 0.265027i $$-0.914619\pi$$
−0.252600 + 0.967571i $$0.581286\pi$$
$$282$$ 0 0
$$283$$ 4.19988 + 2.42480i 0.249657 + 0.144139i 0.619607 0.784912i $$-0.287292\pi$$
−0.369950 + 0.929052i $$0.620625\pi$$
$$284$$ −5.49673 + 31.0817i −0.326171 + 1.84436i
$$285$$ 0 0
$$286$$ 0.0293167 + 0.0349563i 0.00173353 + 0.00206701i
$$287$$ 4.91861 0.290336
$$288$$ 0 0
$$289$$ 16.6923 0.981901
$$290$$ 16.0453 + 19.1318i 0.942212 + 1.12346i
$$291$$ 0 0
$$292$$ 4.91160 27.7730i 0.287430 1.62529i
$$293$$ 16.8856 + 9.74890i 0.986467 + 0.569537i 0.904216 0.427075i $$-0.140456\pi$$
0.0822504 + 0.996612i $$0.473789\pi$$
$$294$$ 0 0
$$295$$ 16.6684 9.62350i 0.970471 0.560302i
$$296$$ 24.4203 14.0744i 1.41940 0.818058i
$$297$$ 0 0
$$298$$ −4.06300 23.0765i −0.235363 1.33679i
$$299$$ −0.510181 0.883659i −0.0295045 0.0511033i
$$300$$ 0 0
$$301$$ −2.18695 + 3.78791i −0.126054 + 0.218331i
$$302$$ 23.3781 + 8.51563i 1.34526 + 0.490020i
$$303$$ 0 0
$$304$$ 4.92486 13.4885i 0.282460 0.773619i
$$305$$ 33.2769i 1.90543i
$$306$$ 0 0
$$307$$ 6.21611i 0.354772i −0.984141 0.177386i $$-0.943236\pi$$
0.984141 0.177386i $$-0.0567642\pi$$
$$308$$ 0.321138 0.382325i 0.0182985 0.0217850i
$$309$$ 0 0
$$310$$ −10.0832 + 27.6815i −0.572685 + 1.57220i
$$311$$ 11.2742 19.5275i 0.639303 1.10731i −0.346283 0.938130i $$-0.612556\pi$$
0.985586 0.169176i $$-0.0541105\pi$$
$$312$$ 0 0
$$313$$ −7.53213 13.0460i −0.425741 0.737405i 0.570748 0.821125i $$-0.306653\pi$$
−0.996489 + 0.0837201i $$0.973320\pi$$
$$314$$ −3.13867 + 0.552614i −0.177125 + 0.0311858i
$$315$$ 0 0
$$316$$ 1.60936 + 4.42864i 0.0905335 + 0.249130i
$$317$$ 9.34442 5.39500i 0.524835 0.303013i −0.214076 0.976817i $$-0.568674\pi$$
0.738911 + 0.673804i $$0.235341\pi$$
$$318$$ 0 0
$$319$$ 1.47413 + 0.851089i 0.0825354 + 0.0476518i
$$320$$ −17.9566 + 10.3310i −1.00380 + 0.577519i
$$321$$ 0 0
$$322$$ −8.55626 + 7.17587i −0.476822 + 0.399896i
$$323$$ 1.99127 0.110797
$$324$$ 0 0
$$325$$ −0.220417 −0.0122265
$$326$$ 7.57976 6.35691i 0.419804 0.352077i
$$327$$ 0 0
$$328$$ −13.9119 0.0105443i −0.768158 0.000582209i
$$329$$ −4.19011 2.41916i −0.231008 0.133373i
$$330$$ 0 0
$$331$$ −9.03466 + 5.21616i −0.496590 + 0.286706i −0.727304 0.686315i $$-0.759227\pi$$
0.230714 + 0.973021i $$0.425894\pi$$
$$332$$ −8.89181 + 3.23127i −0.488001 + 0.177339i
$$333$$ 0 0
$$334$$ 15.0483 2.64950i 0.823405 0.144974i
$$335$$ −7.82753 13.5577i −0.427663 0.740735i
$$336$$ 0 0
$$337$$ 15.0986 26.1516i 0.822475 1.42457i −0.0813590 0.996685i $$-0.525926\pi$$
0.903834 0.427883i $$-0.140741\pi$$
$$338$$ 6.28425 17.2523i 0.341818 0.938399i
$$339$$ 0 0
$$340$$ −2.19976 1.84771i −0.119299 0.100206i
$$341$$ 2.00834i 0.108758i
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 6.19375 10.7091i 0.333944 0.577398i
$$345$$ 0 0
$$346$$ 6.16799 + 2.24673i 0.331593 + 0.120785i
$$347$$ 12.7498 22.0832i 0.684443 1.18549i −0.289169 0.957278i $$-0.593379\pi$$
0.973612 0.228212i $$-0.0732878\pi$$
$$348$$ 0 0
$$349$$ 15.4421 + 26.7465i 0.826597 + 1.43171i 0.900692 + 0.434457i $$0.143060\pi$$
−0.0740953 + 0.997251i $$0.523607\pi$$
$$350$$ 0.418288 + 2.37574i 0.0223585 + 0.126989i
$$351$$ 0 0
$$352$$ −0.909134 + 1.08069i −0.0484570 + 0.0576009i
$$353$$ 30.2542 17.4672i 1.61027 0.929688i 0.620958 0.783843i $$-0.286744\pi$$
0.989308 0.145844i $$-0.0465898\pi$$
$$354$$ 0 0
$$355$$ −35.3929 20.4341i −1.87846 1.08453i
$$356$$ 15.4056 + 2.72445i 0.816495 + 0.144396i
$$357$$ 0 0
$$358$$ 6.05844 + 7.22388i 0.320199 + 0.381794i
$$359$$ −5.92966 −0.312956 −0.156478 0.987681i $$-0.550014\pi$$
−0.156478 + 0.987681i $$0.550014\pi$$
$$360$$ 0 0
$$361$$ 6.11288 0.321730
$$362$$ 6.91796 + 8.24873i 0.363600 + 0.433544i
$$363$$ 0 0
$$364$$ 0.254492 + 0.0450064i 0.0133390 + 0.00235898i
$$365$$ 31.6253 + 18.2589i 1.65534 + 0.955712i
$$366$$ 0 0
$$367$$ −26.1820 + 15.1162i −1.36669 + 0.789059i −0.990504 0.137485i $$-0.956098\pi$$
−0.376187 + 0.926544i $$0.622765\pi$$
$$368$$ 24.2161 20.2781i 1.26235 1.05707i
$$369$$ 0 0
$$370$$ 6.32807 + 35.9414i 0.328981 + 1.86850i
$$371$$ −4.50029 7.79472i −0.233643 0.404682i
$$372$$ 0 0
$$373$$ 2.54373 4.40588i 0.131710 0.228128i −0.792626 0.609708i $$-0.791287\pi$$
0.924336 + 0.381580i $$0.124620\pi$$
$$374$$ −0.184011 0.0670273i −0.00951501 0.00346590i
$$375$$ 0 0
$$376$$ 11.8462 + 6.85140i 0.610923 + 0.353334i
$$377$$ 0.881056i 0.0453767i
$$378$$ 0 0
$$379$$ 18.6036i 0.955600i 0.878469 + 0.477800i $$0.158566\pi$$
−0.878469 + 0.477800i $$0.841434\pi$$
$$380$$ 14.2364 + 11.9580i 0.730314 + 0.613435i
$$381$$ 0 0
$$382$$ 2.08621 5.72731i 0.106740 0.293035i
$$383$$ 5.98305 10.3630i 0.305720 0.529522i −0.671702 0.740822i $$-0.734436\pi$$
0.977421 + 0.211300i $$0.0677696\pi$$
$$384$$ 0 0
$$385$$ 0.323241 + 0.559869i 0.0164739 + 0.0285336i
$$386$$ 1.92458 0.338854i 0.0979586 0.0172472i
$$387$$ 0 0
$$388$$ 21.3191 7.74731i 1.08231 0.393310i
$$389$$ 16.3655 9.44864i 0.829765 0.479065i −0.0240072 0.999712i $$-0.507642\pi$$
0.853772 + 0.520647i $$0.174309\pi$$
$$390$$ 0 0
$$391$$ 3.79319 + 2.19000i 0.191830 + 0.110753i
$$392$$ 0.00214375 2.82843i 0.000108276 0.142857i
$$393$$ 0 0
$$394$$ −10.0392 + 8.41954i −0.505766 + 0.424170i
$$395$$ −6.10096 −0.306973
$$396$$ 0 0
$$397$$ −26.3234 −1.32113 −0.660566 0.750768i $$-0.729684\pi$$
−0.660566 + 0.750768i $$0.729684\pi$$
$$398$$ −26.6549 + 22.3546i −1.33609 + 1.12054i
$$399$$ 0 0
$$400$$ −1.17801 6.72051i −0.0589003 0.336025i
$$401$$ 7.64521 + 4.41396i 0.381783 + 0.220423i 0.678594 0.734514i $$-0.262590\pi$$
−0.296811 + 0.954936i $$0.595923\pi$$
$$402$$ 0 0
$$403$$ −0.900257 + 0.519764i −0.0448450 + 0.0258913i
$$404$$ 2.50023 + 6.88014i 0.124391 + 0.342300i
$$405$$ 0 0
$$406$$ 9.49638 1.67199i 0.471297 0.0829797i
$$407$$ 1.24391 + 2.15451i 0.0616582 + 0.106795i
$$408$$ 0 0
$$409$$ −11.4524 + 19.8361i −0.566283 + 0.980831i 0.430646 + 0.902521i $$0.358286\pi$$
−0.996929 + 0.0783100i $$0.975048\pi$$
$$410$$ 6.16501 16.9249i 0.304468 0.835862i
$$411$$ 0 0
$$412$$ 8.85207 10.5387i 0.436110 0.519203i
$$413$$ 7.43258i 0.365733i
$$414$$ 0 0
$$415$$ 12.2495i 0.601304i
$$416$$ −0.719715 0.127843i −0.0352869 0.00626801i
$$417$$ 0 0
$$418$$ 1.19089 + 0.433789i 0.0582483 + 0.0212173i
$$419$$ −5.10769 + 8.84679i −0.249527 + 0.432194i −0.963395 0.268087i $$-0.913609\pi$$
0.713868 + 0.700281i $$0.246942\pi$$
$$420$$ 0 0
$$421$$ 5.95328 + 10.3114i 0.290145 + 0.502546i 0.973844 0.227218i $$-0.0729630\pi$$
−0.683699 + 0.729765i $$0.739630\pi$$
$$422$$ −2.54485 14.4539i −0.123881 0.703604i
$$423$$ 0 0
$$424$$ 12.7120 + 22.0565i 0.617350 + 1.07116i
$$425$$ 0.819399 0.473080i 0.0397467 0.0229478i
$$426$$ 0 0
$$427$$ −11.1288 6.42524i −0.538562 0.310939i
$$428$$ 2.59013 14.6461i 0.125199 0.707946i
$$429$$ 0 0
$$430$$ 10.2930 + 12.2731i 0.496375 + 0.591860i
$$431$$ −4.26567 −0.205470 −0.102735 0.994709i $$-0.532759\pi$$
−0.102735 + 0.994709i $$0.532759\pi$$
$$432$$ 0 0
$$433$$ 36.7838 1.76772 0.883858 0.467756i $$-0.154937\pi$$
0.883858 + 0.467756i $$0.154937\pi$$
$$434$$ 7.31066 + 8.71698i 0.350923 + 0.418428i
$$435$$ 0 0
$$436$$ 2.86882 16.2220i 0.137392 0.776891i
$$437$$ −24.5489 14.1733i −1.17433 0.678001i
$$438$$ 0 0
$$439$$ 13.2806 7.66755i 0.633848 0.365952i −0.148393 0.988928i $$-0.547410\pi$$
0.782241 + 0.622976i $$0.214077\pi$$
$$440$$ −0.913062 1.58424i −0.0435285 0.0755258i
$$441$$ 0 0
$$442$$ −0.0175770 0.0998317i −0.000836053 0.00474851i
$$443$$ 5.27986 + 9.14498i 0.250854 + 0.434491i 0.963761 0.266767i $$-0.0859554\pi$$
−0.712907 + 0.701258i $$0.752622\pi$$
$$444$$ 0 0
$$445$$ −10.1281 + 17.5424i −0.480119 + 0.831591i
$$446$$ 34.2935 + 12.4916i 1.62384 + 0.591496i
$$447$$ 0 0
$$448$$ −0.0121269 + 7.99999i −0.000572940 + 0.377964i
$$449$$ 16.5280i 0.780006i 0.920813 + 0.390003i $$0.127526\pi$$
−0.920813 + 0.390003i $$0.872474\pi$$
$$450$$ 0 0
$$451$$ 1.22793i 0.0578212i
$$452$$ −11.0351 + 13.1377i −0.519050 + 0.617945i
$$453$$ 0 0
$$454$$ −6.52656 + 17.9175i −0.306307 + 0.840909i
$$455$$ −0.167311 + 0.289791i −0.00784366 + 0.0135856i
$$456$$ 0 0
$$457$$ −5.27095 9.12955i −0.246564 0.427062i 0.716006 0.698094i $$-0.245968\pi$$
−0.962570 + 0.271032i $$0.912635\pi$$
$$458$$ −18.1055 + 3.18778i −0.846016 + 0.148955i
$$459$$ 0 0
$$460$$ 13.9677 + 38.4363i 0.651247 + 1.79210i
$$461$$ 21.5838 12.4614i 1.00526 0.580387i 0.0954593 0.995433i $$-0.469568\pi$$
0.909800 + 0.415046i $$0.136235\pi$$
$$462$$ 0 0
$$463$$ −27.8446 16.0761i −1.29405 0.747119i −0.314679 0.949198i $$-0.601897\pi$$
−0.979369 + 0.202079i $$0.935230\pi$$
$$464$$ −26.8634 + 4.70876i −1.24710 + 0.218598i
$$465$$ 0 0
$$466$$ 24.6888 20.7058i 1.14369 0.959176i
$$467$$ −8.54957 −0.395627 −0.197813 0.980240i $$-0.563384\pi$$
−0.197813 + 0.980240i $$0.563384\pi$$
$$468$$ 0 0
$$469$$ −6.04548 −0.279155
$$470$$ −13.5762 + 11.3860i −0.626225 + 0.525195i
$$471$$ 0 0
$$472$$ −0.0159336 + 21.0225i −0.000733402 + 0.967639i
$$473$$ 0.945654 + 0.545973i 0.0434812 + 0.0251039i
$$474$$ 0 0
$$475$$ −5.30300 + 3.06169i −0.243319 + 0.140480i
$$476$$ −1.04267 + 0.378904i −0.0477907 + 0.0173671i
$$477$$ 0 0
$$478$$ −28.4023 + 5.00070i −1.29909 + 0.228727i
$$479$$ 8.25859 + 14.3043i 0.377345 + 0.653580i 0.990675 0.136247i $$-0.0435039\pi$$
−0.613330 + 0.789826i $$0.710171\pi$$
$$480$$ 0 0
$$481$$ −0.643853 + 1.11519i −0.0293572 + 0.0508481i
$$482$$ 3.17074 8.70470i 0.144423 0.396488i
$$483$$ 0 0
$$484$$ 16.7504 + 14.0697i 0.761381 + 0.639530i
$$485$$ 29.3695i 1.33360i
$$486$$ 0 0
$$487$$ 7.93519i 0.359578i −0.983705 0.179789i $$-0.942459\pi$$
0.983705 0.179789i $$-0.0575415\pi$$
$$488$$ 31.4633 + 18.1972i 1.42428 + 0.823747i
$$489$$ 0 0
$$490$$ 3.44100 + 1.25341i 0.155448 + 0.0566231i
$$491$$ −1.83003 + 3.16970i −0.0825880 + 0.143047i −0.904361 0.426769i $$-0.859652\pi$$
0.821773 + 0.569815i $$0.192985\pi$$
$$492$$ 0 0
$$493$$ −1.89101 3.27532i −0.0851668 0.147513i
$$494$$ 0.113755 + 0.646093i 0.00511809 + 0.0290691i
$$495$$ 0 0
$$496$$ −20.6590 24.6710i −0.927615 1.10776i
$$497$$ −13.6676 + 7.89100i −0.613076 + 0.353960i
$$498$$ 0 0
$$499$$ −7.46689 4.31101i −0.334264 0.192987i 0.323469 0.946239i $$-0.395151\pi$$
−0.657733 + 0.753252i $$0.728484\pi$$
$$500$$ −16.8006 2.97115i −0.751344 0.132874i
$$501$$ 0 0
$$502$$ −16.6382 19.8388i −0.742599 0.885449i
$$503$$ −44.0191 −1.96271 −0.981357 0.192194i $$-0.938440\pi$$
−0.981357 + 0.192194i $$0.938440\pi$$
$$504$$ 0 0
$$505$$ −9.47818 −0.421773
$$506$$ 1.79146 + 2.13608i 0.0796402 + 0.0949602i
$$507$$ 0 0
$$508$$ −9.27651 1.64053i −0.411578 0.0727868i
$$509$$ −9.48279 5.47489i −0.420317 0.242670i 0.274896 0.961474i $$-0.411357\pi$$
−0.695213 + 0.718804i $$0.744690\pi$$
$$510$$ 0 0
$$511$$ 12.2127 7.05099i 0.540257 0.311917i
$$512$$ 0.0514499 22.6274i 0.00227379 0.999997i
$$513$$ 0 0
$$514$$ 3.91830 + 22.2547i 0.172829 + 0.981611i
$$515$$ 8.91004 + 15.4326i 0.392623 + 0.680043i
$$516$$ 0 0
$$517$$ −0.603945 + 1.04606i −0.0265615 + 0.0460058i
$$518$$ 13.2418 + 4.82340i 0.581811 + 0.211928i
$$519$$ 0 0
$$520$$ 0.473848 0.819295i 0.0207796 0.0359284i
$$521$$ 6.26841i 0.274624i −0.990528 0.137312i $$-0.956154\pi$$
0.990528 0.137312i $$-0.0438463\pi$$
$$522$$ 0 0
$$523$$ 18.7279i 0.818913i 0.912330 + 0.409456i $$0.134282\pi$$
−0.912330 + 0.409456i $$0.865718\pi$$
$$524$$ −15.2267 12.7898i −0.665180 0.558725i
$$525$$ 0 0
$$526$$ 1.86116 5.10948i 0.0811505 0.222784i
$$527$$ 2.23114 3.86444i 0.0971898 0.168338i
$$528$$ 0 0
$$529$$ −19.6757 34.0793i −0.855465 1.48171i
$$530$$ −32.4623 + 5.71552i −1.41007 + 0.248267i
$$531$$ 0 0
$$532$$ 6.74798 2.45220i 0.292562 0.106316i
$$533$$ 0.550433 0.317792i 0.0238419 0.0137651i
$$534$$ 0 0
$$535$$ 16.6776 + 9.62882i 0.721035 + 0.416290i
$$536$$ 17.0992 + 0.0129600i 0.738573 + 0.000559786i
$$537$$ 0 0
$$538$$ 3.89580 3.26729i 0.167960 0.140863i
$$539$$ 0.249651 0.0107532
$$540$$ 0 0
$$541$$ 24.7122 1.06246 0.531230 0.847228i $$-0.321730\pi$$
0.531230 + 0.847228i $$0.321730\pi$$
$$542$$ 4.59830 3.85645i 0.197514 0.165649i
$$543$$ 0 0
$$544$$ 2.94993 1.06947i 0.126477 0.0458531i
$$545$$ 18.4720 + 10.6648i 0.791255 + 0.456832i
$$546$$ 0 0
$$547$$ 23.9787 13.8441i 1.02525 0.591930i 0.109632 0.993972i $$-0.465033\pi$$
0.915621 + 0.402042i $$0.131699\pi$$
$$548$$ −10.4041 28.6300i −0.444440 1.22301i
$$549$$ 0 0
$$550$$ 0.593105 0.104426i 0.0252901 0.00445274i
$$551$$ 12.2383 + 21.1973i 0.521368 + 0.903036i
$$552$$ 0 0
$$553$$ −1.17800 + 2.04035i −0.0500936 + 0.0867646i
$$554$$ 4.73364 12.9954i 0.201113 0.552120i
$$555$$ 0 0
$$556$$ 2.28290 2.71786i 0.0968165 0.115263i
$$557$$ 43.5015i 1.84322i −0.388119 0.921609i $$-0.626875\pi$$
0.388119 0.921609i $$-0.373125\pi$$
$$558$$ 0 0
$$559$$ 0.565197i 0.0239053i
$$560$$ −9.72992 3.55254i −0.411164 0.150122i
$$561$$ 0 0
$$562$$ 31.2981 + 11.4005i 1.32023 + 0.480902i
$$563$$ 0.525773 0.910665i 0.0221587 0.0383800i −0.854733 0.519067i $$-0.826279\pi$$
0.876892 + 0.480687i $$0.159613\pi$$
$$564$$ 0 0
$$565$$ −11.1074 19.2386i −0.467292 0.809374i
$$566$$ −1.18924 6.75448i −0.0499874 0.283912i
$$567$$ 0 0
$$568$$ 38.6747 22.2898i 1.62276 0.935259i
$$569$$ 4.94731 2.85633i 0.207402 0.119744i −0.392701 0.919666i $$-0.628459\pi$$
0.600103 + 0.799922i $$0.295126\pi$$
$$570$$ 0 0
$$571$$ 15.2710 + 8.81671i 0.639071 + 0.368968i 0.784257 0.620436i $$-0.213045\pi$$
−0.145185 + 0.989404i $$0.546378\pi$$
$$572$$ 0.0112359 0.0635341i 0.000469795 0.00265649i
$$573$$ 0 0
$$574$$ −4.46986 5.32971i −0.186568 0.222458i
$$575$$ −13.4690 −0.561697
$$576$$ 0 0
$$577$$ −18.3399 −0.763501 −0.381751 0.924265i $$-0.624679\pi$$
−0.381751 + 0.924265i $$0.624679\pi$$
$$578$$ −15.1694 18.0875i −0.630964 0.752339i
$$579$$ 0 0
$$580$$ 6.14948 34.7727i 0.255343 1.44386i
$$581$$ −4.09661 2.36518i −0.169956 0.0981243i
$$582$$ 0 0
$$583$$ −1.94596 + 1.12350i −0.0805933 + 0.0465306i
$$584$$ −34.5578 + 19.9170i −1.43001 + 0.824172i
$$585$$ 0 0
$$586$$ −4.78132 27.1563i −0.197515 1.12182i
$$587$$ 8.18823 + 14.1824i 0.337965 + 0.585372i 0.984050 0.177893i $$-0.0569282\pi$$
−0.646085 + 0.763265i $$0.723595\pi$$
$$588$$ 0 0
$$589$$ −14.4395 + 25.0100i −0.594970 + 1.03052i
$$590$$ −25.5755 9.31603i −1.05293 0.383535i
$$591$$ 0 0
$$592$$ −37.4431 13.6710i −1.53890 0.561876i
$$593$$ 2.86950i 0.117836i −0.998263 0.0589181i $$-0.981235\pi$$
0.998263 0.0589181i $$-0.0187651\pi$$
$$594$$ 0 0
$$595$$ 1.43640i 0.0588866i
$$596$$ −21.3129 + 25.3737i −0.873012 + 1.03935i
$$597$$ 0 0
$$598$$ −0.493881 + 1.35586i −0.0201963 + 0.0554453i
$$599$$ −0.530101 + 0.918163i −0.0216594 + 0.0375151i −0.876652 0.481125i $$-0.840228\pi$$
0.854993 + 0.518640i $$0.173562\pi$$
$$600$$ 0 0
$$601$$ 6.48648 + 11.2349i 0.264589 + 0.458282i 0.967456 0.253040i $$-0.0814303\pi$$
−0.702867 + 0.711322i $$0.748097\pi$$
$$602$$ 6.09192 1.07258i 0.248288 0.0437153i
$$603$$ 0 0
$$604$$ −12.0179 33.0708i −0.489000 1.34563i
$$605$$ −24.5290 + 14.1618i −0.997244 + 0.575759i
$$606$$ 0 0
$$607$$ 24.3945 + 14.0842i 0.990144 + 0.571660i 0.905317 0.424736i $$-0.139633\pi$$
0.0848266 + 0.996396i $$0.472966\pi$$
$$608$$ −19.0914 + 6.92141i −0.774259 + 0.280700i
$$609$$ 0 0
$$610$$ −36.0582 + 30.2409i −1.45995 + 1.22442i
$$611$$ −0.625210 −0.0252933
$$612$$ 0 0
$$613$$ −22.1934 −0.896381 −0.448191 0.893938i $$-0.647931\pi$$
−0.448191 + 0.893938i $$0.647931\pi$$
$$614$$ −6.73566 + 5.64899i −0.271829 + 0.227975i
$$615$$ 0 0
$$616$$ −0.706118 0.000535188i −0.0284503 2.15633e-5i
$$617$$ −12.7221 7.34512i −0.512173 0.295703i 0.221553 0.975148i $$-0.428887\pi$$
−0.733726 + 0.679445i $$0.762221\pi$$
$$618$$ 0 0
$$619$$ −14.2161 + 8.20765i −0.571392 + 0.329893i −0.757705 0.652597i $$-0.773679\pi$$
0.186313 + 0.982490i $$0.440346\pi$$
$$620$$ 39.1583 14.2301i 1.57264 0.571493i
$$621$$ 0 0
$$622$$ −31.4053 + 5.52942i −1.25924 + 0.221710i
$$623$$ 3.91116 + 6.77433i 0.156697 + 0.271408i
$$624$$ 0 0
$$625$$ 15.3096 26.5170i 0.612383 1.06068i
$$626$$ −7.29148 + 20.0174i −0.291426 + 0.800058i
$$627$$ 0 0
$$628$$ 3.45111 + 2.89880i 0.137714 + 0.115675i
$$629$$ 5.52760i 0.220400i
$$630$$ 0 0
$$631$$ 12.7711i 0.508411i −0.967150 0.254205i $$-0.918186\pi$$
0.967150 0.254205i $$-0.0818139\pi$$
$$632$$ 3.33626 5.76846i 0.132709 0.229457i
$$633$$ 0 0
$$634$$ −14.3378 5.22263i −0.569427 0.207417i
$$635$$ 6.09867 10.5632i 0.242018 0.419188i
$$636$$ 0 0
$$637$$ 0.0646102 + 0.111908i 0.00255995 + 0.00443396i
$$638$$ −0.417414 2.37078i −0.0165256 0.0938600i
$$639$$ 0 0
$$640$$ 27.5127 + 10.0690i 1.08754 + 0.398010i
$$641$$ −13.2162 + 7.63040i −0.522010 + 0.301383i −0.737757 0.675067i $$-0.764115\pi$$
0.215746 + 0.976449i $$0.430782\pi$$
$$642$$ 0 0
$$643$$ 33.5137 + 19.3492i 1.32165 + 0.763057i 0.983992 0.178211i $$-0.0570311\pi$$
0.337661 + 0.941268i $$0.390364\pi$$
$$644$$ 15.5513 + 2.75021i 0.612806 + 0.108373i
$$645$$ 0 0
$$646$$ −1.80959 2.15770i −0.0711975 0.0848934i
$$647$$ 0.564326 0.0221860 0.0110930 0.999938i $$-0.496469\pi$$
0.0110930 + 0.999938i $$0.496469\pi$$
$$648$$ 0 0
$$649$$ −1.85555 −0.0728367
$$650$$ 0.200307 + 0.238839i 0.00785669 + 0.00936804i
$$651$$ 0 0
$$652$$ −13.7765 2.43634i −0.539527 0.0954144i
$$653$$ 3.90030 + 2.25184i 0.152631 + 0.0881214i 0.574370 0.818596i $$-0.305247\pi$$
−0.421740 + 0.906717i $$0.638580\pi$$
$$654$$ 0 0
$$655$$ 22.2977 12.8736i 0.871241 0.503011i
$$656$$ 12.6312 + 15.0843i 0.493167 + 0.588942i
$$657$$ 0 0
$$658$$ 1.18647 + 6.73877i 0.0462535 + 0.262705i
$$659$$ −7.02737 12.1718i −0.273747 0.474144i 0.696071 0.717973i $$-0.254930\pi$$
−0.969818 + 0.243829i $$0.921597\pi$$
$$660$$ 0 0
$$661$$ −17.4242 + 30.1797i −0.677724 + 1.17385i 0.297940 + 0.954585i $$0.403700\pi$$
−0.975665 + 0.219269i $$0.929633\pi$$
$$662$$ 13.8625 + 5.04951i 0.538782 + 0.196255i
$$663$$ 0 0
$$664$$ 11.5819 + 6.69852i 0.449465 + 0.259953i
$$665$$ 9.29611i 0.360488i
$$666$$ 0 0
$$667$$ 53.8388i 2.08465i
$$668$$ −16.5463 13.8982i −0.640195 0.537739i
$$669$$ 0 0
$$670$$ −7.57744 + 20.8025i −0.292742 + 0.803670i
$$671$$ −1.60406 + 2.77832i −0.0619242 + 0.107256i
$$672$$ 0 0
$$673$$ −9.76133 16.9071i −0.376272 0.651722i 0.614245 0.789115i $$-0.289461\pi$$
−0.990516 + 0.137394i $$0.956127\pi$$
$$674$$ −42.0585 + 7.40509i −1.62003 + 0.285233i
$$675$$ 0 0
$$676$$ −24.4051 + 8.86877i −0.938658 + 0.341107i
$$677$$ −7.35277 + 4.24512i −0.282590 + 0.163153i −0.634595 0.772845i $$-0.718833\pi$$
0.352005 + 0.935998i $$0.385500\pi$$
$$678$$ 0 0
$$679$$ 9.82208 + 5.67078i 0.376937 + 0.217625i
$$680$$ −0.00307927 + 4.06275i −0.000118085 + 0.155799i
$$681$$ 0 0
$$682$$ 2.17620 1.82511i 0.0833310 0.0698871i
$$683$$ 16.0399 0.613751 0.306876 0.951750i $$-0.400716\pi$$
0.306876 + 0.951750i $$0.400716\pi$$
$$684$$ 0 0
$$685$$ 39.4411 1.50697
$$686$$ 1.08358 0.908765i 0.0413713 0.0346968i
$$687$$ 0 0
$$688$$ −17.2329 + 3.02066i −0.656997 + 0.115162i
$$689$$ −1.00724 0.581529i −0.0383727 0.0221545i
$$690$$ 0 0
$$691$$ 17.7036 10.2212i 0.673476 0.388831i −0.123917 0.992293i $$-0.539546\pi$$
0.797392 + 0.603461i $$0.206212\pi$$
$$692$$ −3.17074 8.72526i −0.120534 0.331685i
$$693$$ 0 0
$$694$$ −35.5155 + 6.25309i −1.34815 + 0.237364i
$$695$$ 2.29785 + 3.97999i 0.0871623 + 0.150970i
$$696$$ 0 0
$$697$$ −1.36415 + 2.36279i −0.0516710 + 0.0894969i
$$698$$ 14.9487 41.0391i 0.565818 1.55335i
$$699$$ 0 0
$$700$$ 2.19418 2.61224i 0.0829322 0.0987334i
$$701$$ 11.4242i 0.431488i 0.976450 + 0.215744i $$0.0692176\pi$$
−0.976450 + 0.215744i $$0.930782\pi$$
$$702$$ 0 0
$$703$$ 35.7737i 1.34923i
$$704$$ 1.99720 + 0.00302748i 0.0752724 + 0.000114102i
$$705$$ 0 0
$$706$$ −46.4211 16.9092i −1.74708 0.636385i
$$707$$ −1.83009 + 3.16980i −0.0688275 + 0.119213i
$$708$$ 0 0
$$709$$ 5.08955 + 8.81537i 0.191142 + 0.331068i 0.945629 0.325247i $$-0.105447\pi$$
−0.754487 + 0.656315i $$0.772114\pi$$
$$710$$ 10.0218 + 56.9208i 0.376113 + 2.13620i
$$711$$ 0 0
$$712$$ −11.0479 19.1691i −0.414038 0.718392i
$$713$$ −55.0121 + 31.7613i −2.06022 + 1.18947i
$$714$$ 0 0
$$715$$ 0.0723466 + 0.0417693i 0.00270561 + 0.00156208i
$$716$$ 2.32195 13.1296i 0.0867752 0.490677i
$$717$$ 0 0
$$718$$ 5.38867 + 6.42526i 0.201103 + 0.239789i
$$719$$ 25.4397 0.948741 0.474370 0.880325i $$-0.342676\pi$$
0.474370 + 0.880325i $$0.342676\pi$$
$$720$$ 0 0
$$721$$ 6.88155 0.256282
$$722$$ −5.55517 6.62379i −0.206742 0.246512i
$$723$$ 0 0
$$724$$ 2.65136 14.9923i 0.0985371 0.557185i
$$725$$ 10.0720 + 5.81508i 0.374065 + 0.215967i
$$726$$ 0 0
$$727$$ −14.2142 + 8.20655i −0.527174 + 0.304364i −0.739865 0.672756i $$-0.765111\pi$$
0.212691 + 0.977120i $$0.431777\pi$$
$$728$$ −0.182505 0.316663i −0.00676410 0.0117363i
$$729$$ 0 0
$$730$$ −8.95501 50.8615i −0.331440 1.88247i
$$731$$ −1.21308 2.10112i −0.0448674 0.0777127i
$$732$$ 0 0
$$733$$ −18.2362 + 31.5859i −0.673568 + 1.16665i 0.303318 + 0.952889i $$0.401906\pi$$
−0.976885 + 0.213764i $$0.931428\pi$$
$$734$$ 40.1729 + 14.6332i 1.48281 + 0.540123i
$$735$$ 0 0
$$736$$ −43.9797 7.81211i −1.62111 0.287958i
$$737$$ 1.50926i 0.0555943i
$$738$$ 0 0
$$739$$ 43.0747i 1.58453i −0.610177 0.792265i $$-0.708902\pi$$
0.610177 0.792265i $$-0.291098\pi$$
$$740$$ 33.1946 39.5193i 1.22026 1.45276i
$$741$$ 0 0
$$742$$ −4.35650 + 11.9600i −0.159932 + 0.439065i
$$743$$ −21.0352 + 36.4340i −0.771705 + 1.33663i 0.164922 + 0.986307i $$0.447263\pi$$
−0.936628 + 0.350326i $$0.886071\pi$$
$$744$$ 0 0
$$745$$ −21.4525 37.1568i −0.785959 1.36132i
$$746$$ −7.08578 + 1.24757i −0.259429 + 0.0456767i
$$747$$ 0 0
$$748$$ 0.0945937 + 0.260303i 0.00345869 + 0.00951763i
$$749$$ 6.44036 3.71834i 0.235326 0.135865i
$$750$$ 0 0
$$751$$ −3.20236 1.84888i −0.116856 0.0674667i 0.440433 0.897786i $$-0.354825\pi$$
−0.557289 + 0.830319i $$0.688158\pi$$
$$752$$ −3.34140 19.0627i −0.121848 0.695144i
$$753$$ 0 0
$$754$$ 0.954695 0.800673i 0.0347679 0.0291588i
$$755$$ 45.5588 1.65805
$$756$$ 0 0
$$757$$ 12.8240 0.466097 0.233048 0.972465i $$-0.425130\pi$$
0.233048 + 0.972465i $$0.425130\pi$$
$$758$$ 20.1584 16.9063i 0.732188 0.614063i
$$759$$ 0 0
$$760$$ 0.0199285 26.2934i 0.000722883 0.953761i
$$761$$ −30.7741 17.7674i −1.11556 0.644069i −0.175296 0.984516i $$-0.556088\pi$$
−0.940264 + 0.340447i $$0.889422\pi$$
$$762$$ 0 0
$$763$$ 7.13332 4.11842i 0.258243 0.149097i
$$764$$ −8.10188 + 2.94421i −0.293116 + 0.106518i
$$765$$ 0 0
$$766$$ −16.6663 + 2.93437i −0.602177 + 0.106023i
$$767$$ −0.480221 0.831767i −0.0173398 0.0300334i
$$768$$ 0 0
$$769$$ −3.57085 + 6.18489i −0.128768 + 0.223033i −0.923200 0.384321i $$-0.874436\pi$$
0.794431 + 0.607354i $$0.207769\pi$$
$$770$$ 0.312913 0.859047i 0.0112766 0.0309579i
$$771$$ 0 0
$$772$$ −2.11617 1.77750i −0.0761626 0.0639736i
$$773$$ 39.5269i 1.42168i 0.703351 + 0.710842i $$0.251686\pi$$
−0.703351 + 0.710842i $$0.748314\pi$$
$$774$$ 0 0
$$775$$ 13.7220i 0.492910i
$$776$$ −27.7689 16.0604i −0.996844 0.576536i
$$777$$ 0 0
$$778$$ −25.1108 9.14676i −0.900265 0.327927i
$$779$$ 8.82857 15.2915i 0.316316 0.547876i
$$780$$ 0 0
$$781$$ 1.96999 + 3.41213i 0.0704919 + 0.122095i
$$782$$ −1.07408 6.10042i −0.0384090 0.218151i
$$783$$ 0 0
$$784$$ −3.06677 + 2.56805i −0.109528 + 0.0917162i
$$785$$ −5.05375 + 2.91778i −0.180376 + 0.104140i
$$786$$ 0 0
$$787$$ −37.4865 21.6428i −1.33625 0.771484i −0.350000 0.936750i $$-0.613818\pi$$
−0.986249 + 0.165266i $$0.947152\pi$$
$$788$$ 18.2465 + 3.22686i 0.650004 + 0.114952i
$$789$$