# Properties

 Label 1078.2.i.d.901.9 Level $1078$ Weight $2$ Character 1078.901 Analytic conductor $8.608$ Analytic rank $0$ Dimension $32$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.i (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.60787333789$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 901.9 Character $$\chi$$ $$=$$ 1078.901 Dual form 1078.2.i.d.1011.9

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})$$ $$q+(0.866025 + 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} -1.84776 q^{6} +1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +(-1.23576 - 2.14039i) q^{10} +(-1.30225 + 3.05027i) q^{11} +(-1.60021 - 0.923880i) q^{12} +1.96452 q^{13} +4.56676 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.82487 - 4.89282i) q^{17} +(0.358719 - 0.207107i) q^{18} +(-0.453489 + 0.785466i) q^{19} -2.47151i q^{20} +(-2.65291 + 1.99049i) q^{22} +(0.468406 - 0.811303i) q^{23} +(-0.923880 - 1.60021i) q^{24} +(0.554192 + 0.959889i) q^{25} +(1.70132 + 0.982258i) q^{26} -4.77791i q^{27} -7.50358i q^{29} +(3.95493 + 2.28338i) q^{30} +(-4.08699 + 2.35963i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.734219 - 6.08418i) q^{33} -5.64974i q^{34} +0.414214 q^{36} +(4.81498 - 8.33978i) q^{37} +(-0.785466 + 0.453489i) q^{38} +(-3.14363 + 1.81498i) q^{39} +(1.23576 - 2.14039i) q^{40} +6.93240 q^{41} -6.80940i q^{43} +(-3.29274 + 0.397356i) q^{44} +(-0.886580 + 0.511867i) q^{45} +(0.811303 - 0.468406i) q^{46} +(-3.46605 - 2.00112i) q^{47} -1.84776i q^{48} +1.10838i q^{50} +(9.04075 + 5.21968i) q^{51} +(0.982258 + 1.70132i) q^{52} +(-3.28338 - 5.68698i) q^{53} +(2.38896 - 4.13779i) q^{54} +(6.55672 - 4.91952i) q^{55} -1.67588i q^{57} +(3.75179 - 6.49829i) q^{58} +(0.836265 - 0.482818i) q^{59} +(2.28338 + 3.95493i) q^{60} +(-5.95014 + 10.3059i) q^{61} -4.71925 q^{62} -1.00000 q^{64} +(-4.20484 - 2.42766i) q^{65} +(2.40624 - 5.63617i) q^{66} +(-3.36002 - 5.81973i) q^{67} +(2.82487 - 4.89282i) q^{68} +1.73100i q^{69} -11.5485 q^{71} +(0.358719 + 0.207107i) q^{72} +(5.43072 + 9.40628i) q^{73} +(8.33978 - 4.81498i) q^{74} +(-1.77364 - 1.02401i) q^{75} -0.906978 q^{76} -3.62995 q^{78} +(7.34847 + 4.24264i) q^{79} +(2.14039 - 1.23576i) q^{80} +(5.03553 + 8.72180i) q^{81} +(6.00363 + 3.46620i) q^{82} +4.83601 q^{83} +13.9634i q^{85} +(3.40470 - 5.89712i) q^{86} +(6.93240 + 12.0073i) q^{87} +(-3.05027 - 1.30225i) q^{88} +(-11.0280 - 6.36702i) q^{89} -1.02373 q^{90} +0.936812 q^{92} +(4.36002 - 7.55178i) q^{93} +(-2.00112 - 3.46605i) q^{94} +(1.94129 - 1.12080i) q^{95} +(0.923880 - 1.60021i) q^{96} -3.82683i q^{97} +(0.824487 + 1.09887i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32 q + 16 q^{4} - 16 q^{9} + O(q^{10})$$ $$32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 + 0.500000i 0.612372 + 0.353553i
$$3$$ −1.60021 + 0.923880i −0.923880 + 0.533402i −0.884871 0.465837i $$-0.845753\pi$$
−0.0390089 + 0.999239i $$0.512420\pi$$
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ −2.14039 1.23576i −0.957214 0.552647i −0.0618992 0.998082i $$-0.519716\pi$$
−0.895314 + 0.445435i $$0.853049\pi$$
$$6$$ −1.84776 −0.754344
$$7$$ 0 0
$$8$$ 1.00000i 0.353553i
$$9$$ 0.207107 0.358719i 0.0690356 0.119573i
$$10$$ −1.23576 2.14039i −0.390781 0.676852i
$$11$$ −1.30225 + 3.05027i −0.392642 + 0.919691i
$$12$$ −1.60021 0.923880i −0.461940 0.266701i
$$13$$ 1.96452 0.544859 0.272429 0.962176i $$-0.412173\pi$$
0.272429 + 0.962176i $$0.412173\pi$$
$$14$$ 0 0
$$15$$ 4.56676 1.17913
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.82487 4.89282i −0.685131 1.18668i −0.973395 0.229132i $$-0.926411\pi$$
0.288264 0.957551i $$-0.406922\pi$$
$$18$$ 0.358719 0.207107i 0.0845510 0.0488155i
$$19$$ −0.453489 + 0.785466i −0.104038 + 0.180198i −0.913345 0.407188i $$-0.866510\pi$$
0.809307 + 0.587386i $$0.199843\pi$$
$$20$$ 2.47151i 0.552647i
$$21$$ 0 0
$$22$$ −2.65291 + 1.99049i −0.565603 + 0.424374i
$$23$$ 0.468406 0.811303i 0.0976694 0.169168i −0.813050 0.582194i $$-0.802195\pi$$
0.910720 + 0.413025i $$0.135528\pi$$
$$24$$ −0.923880 1.60021i −0.188586 0.326641i
$$25$$ 0.554192 + 0.959889i 0.110838 + 0.191978i
$$26$$ 1.70132 + 0.982258i 0.333656 + 0.192637i
$$27$$ 4.77791i 0.919509i
$$28$$ 0 0
$$29$$ 7.50358i 1.39338i −0.717373 0.696689i $$-0.754656\pi$$
0.717373 0.696689i $$-0.245344\pi$$
$$30$$ 3.95493 + 2.28338i 0.722069 + 0.416887i
$$31$$ −4.08699 + 2.35963i −0.734046 + 0.423801i −0.819900 0.572506i $$-0.805971\pi$$
0.0858548 + 0.996308i $$0.472638\pi$$
$$32$$ −0.866025 + 0.500000i −0.153093 + 0.0883883i
$$33$$ −0.734219 6.08418i −0.127811 1.05912i
$$34$$ 5.64974i 0.968922i
$$35$$ 0 0
$$36$$ 0.414214 0.0690356
$$37$$ 4.81498 8.33978i 0.791577 1.37105i −0.133413 0.991061i $$-0.542594\pi$$
0.924990 0.379991i $$-0.124073\pi$$
$$38$$ −0.785466 + 0.453489i −0.127419 + 0.0735656i
$$39$$ −3.14363 + 1.81498i −0.503384 + 0.290629i
$$40$$ 1.23576 2.14039i 0.195390 0.338426i
$$41$$ 6.93240 1.08266 0.541329 0.840811i $$-0.317921\pi$$
0.541329 + 0.840811i $$0.317921\pi$$
$$42$$ 0 0
$$43$$ 6.80940i 1.03842i −0.854645 0.519212i $$-0.826225\pi$$
0.854645 0.519212i $$-0.173775\pi$$
$$44$$ −3.29274 + 0.397356i −0.496399 + 0.0599037i
$$45$$ −0.886580 + 0.511867i −0.132164 + 0.0763047i
$$46$$ 0.811303 0.468406i 0.119620 0.0690627i
$$47$$ −3.46605 2.00112i −0.505575 0.291894i 0.225438 0.974258i $$-0.427619\pi$$
−0.731013 + 0.682364i $$0.760952\pi$$
$$48$$ 1.84776i 0.266701i
$$49$$ 0 0
$$50$$ 1.10838i 0.156749i
$$51$$ 9.04075 + 5.21968i 1.26596 + 0.730901i
$$52$$ 0.982258 + 1.70132i 0.136215 + 0.235931i
$$53$$ −3.28338 5.68698i −0.451007 0.781167i 0.547442 0.836844i $$-0.315602\pi$$
−0.998449 + 0.0556765i $$0.982268\pi$$
$$54$$ 2.38896 4.13779i 0.325096 0.563082i
$$55$$ 6.55672 4.91952i 0.884108 0.663348i
$$56$$ 0 0
$$57$$ 1.67588i 0.221975i
$$58$$ 3.75179 6.49829i 0.492634 0.853267i
$$59$$ 0.836265 0.482818i 0.108872 0.0628575i −0.444575 0.895742i $$-0.646645\pi$$
0.553447 + 0.832884i $$0.313312\pi$$
$$60$$ 2.28338 + 3.95493i 0.294783 + 0.510580i
$$61$$ −5.95014 + 10.3059i −0.761838 + 1.31954i 0.180065 + 0.983655i $$0.442369\pi$$
−0.941902 + 0.335887i $$0.890964\pi$$
$$62$$ −4.71925 −0.599346
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −4.20484 2.42766i −0.521546 0.301115i
$$66$$ 2.40624 5.63617i 0.296188 0.693764i
$$67$$ −3.36002 5.81973i −0.410492 0.710993i 0.584452 0.811429i $$-0.301310\pi$$
−0.994944 + 0.100436i $$0.967976\pi$$
$$68$$ 2.82487 4.89282i 0.342566 0.593341i
$$69$$ 1.73100i 0.208388i
$$70$$ 0 0
$$71$$ −11.5485 −1.37055 −0.685276 0.728284i $$-0.740318\pi$$
−0.685276 + 0.728284i $$0.740318\pi$$
$$72$$ 0.358719 + 0.207107i 0.0422755 + 0.0244078i
$$73$$ 5.43072 + 9.40628i 0.635617 + 1.10092i 0.986384 + 0.164458i $$0.0525876\pi$$
−0.350767 + 0.936463i $$0.614079\pi$$
$$74$$ 8.33978 4.81498i 0.969480 0.559730i
$$75$$ −1.77364 1.02401i −0.204803 0.118243i
$$76$$ −0.906978 −0.104038
$$77$$ 0 0
$$78$$ −3.62995 −0.411011
$$79$$ 7.34847 + 4.24264i 0.826767 + 0.477334i 0.852745 0.522328i $$-0.174936\pi$$
−0.0259772 + 0.999663i $$0.508270\pi$$
$$80$$ 2.14039 1.23576i 0.239303 0.138162i
$$81$$ 5.03553 + 8.72180i 0.559504 + 0.969089i
$$82$$ 6.00363 + 3.46620i 0.662990 + 0.382778i
$$83$$ 4.83601 0.530821 0.265411 0.964135i $$-0.414493\pi$$
0.265411 + 0.964135i $$0.414493\pi$$
$$84$$ 0 0
$$85$$ 13.9634i 1.51454i
$$86$$ 3.40470 5.89712i 0.367138 0.635902i
$$87$$ 6.93240 + 12.0073i 0.743231 + 1.28731i
$$88$$ −3.05027 1.30225i −0.325160 0.138820i
$$89$$ −11.0280 6.36702i −1.16897 0.674903i −0.215530 0.976497i $$-0.569148\pi$$
−0.953436 + 0.301594i $$0.902481\pi$$
$$90$$ −1.02373 −0.107911
$$91$$ 0 0
$$92$$ 0.936812 0.0976694
$$93$$ 4.36002 7.55178i 0.452113 0.783083i
$$94$$ −2.00112 3.46605i −0.206400 0.357496i
$$95$$ 1.94129 1.12080i 0.199172 0.114992i
$$96$$ 0.923880 1.60021i 0.0942931 0.163320i
$$97$$ 3.82683i 0.388556i −0.980946 0.194278i $$-0.937764\pi$$
0.980946 0.194278i $$-0.0622364\pi$$
$$98$$ 0 0
$$99$$ 0.824487 + 1.09887i 0.0828641 + 0.110441i
$$100$$ −0.554192 + 0.959889i −0.0554192 + 0.0959889i
$$101$$ −7.91466 13.7086i −0.787538 1.36406i −0.927471 0.373895i $$-0.878022\pi$$
0.139933 0.990161i $$-0.455311\pi$$
$$102$$ 5.21968 + 9.04075i 0.516825 + 0.895167i
$$103$$ 0.684352 + 0.395111i 0.0674312 + 0.0389314i 0.533337 0.845903i $$-0.320938\pi$$
−0.465905 + 0.884835i $$0.654271\pi$$
$$104$$ 1.96452i 0.192637i
$$105$$ 0 0
$$106$$ 6.56676i 0.637820i
$$107$$ 14.3861 + 8.30583i 1.39076 + 0.802955i 0.993399 0.114708i $$-0.0365933\pi$$
0.397359 + 0.917663i $$0.369927\pi$$
$$108$$ 4.13779 2.38896i 0.398159 0.229877i
$$109$$ −5.19615 + 3.00000i −0.497701 + 0.287348i −0.727764 0.685828i $$-0.759440\pi$$
0.230063 + 0.973176i $$0.426107\pi$$
$$110$$ 8.13804 0.982072i 0.775932 0.0936369i
$$111$$ 17.7938i 1.68892i
$$112$$ 0 0
$$113$$ −5.76421 −0.542251 −0.271126 0.962544i $$-0.587396\pi$$
−0.271126 + 0.962544i $$0.587396\pi$$
$$114$$ 0.837939 1.45135i 0.0784801 0.135932i
$$115$$ −2.00515 + 1.15767i −0.186981 + 0.107953i
$$116$$ 6.49829 3.75179i 0.603351 0.348345i
$$117$$ 0.406865 0.704710i 0.0376146 0.0651505i
$$118$$ 0.965635 0.0888940
$$119$$ 0 0
$$120$$ 4.56676i 0.416887i
$$121$$ −7.60831 7.94441i −0.691664 0.722219i
$$122$$ −10.3059 + 5.95014i −0.933057 + 0.538701i
$$123$$ −11.0933 + 6.40470i −1.00025 + 0.577493i
$$124$$ −4.08699 2.35963i −0.367023 0.211901i
$$125$$ 9.61818i 0.860277i
$$126$$ 0 0
$$127$$ 18.6371i 1.65378i 0.562367 + 0.826888i $$0.309891\pi$$
−0.562367 + 0.826888i $$0.690109\pi$$
$$128$$ −0.866025 0.500000i −0.0765466 0.0441942i
$$129$$ 6.29107 + 10.8965i 0.553898 + 0.959379i
$$130$$ −2.42766 4.20484i −0.212920 0.368789i
$$131$$ 9.99173 17.3062i 0.872982 1.51205i 0.0140849 0.999901i $$-0.495516\pi$$
0.858897 0.512148i $$-0.171150\pi$$
$$132$$ 4.90195 3.67794i 0.426660 0.320124i
$$133$$ 0 0
$$134$$ 6.72004i 0.580523i
$$135$$ −5.90434 + 10.2266i −0.508164 + 0.880167i
$$136$$ 4.89282 2.82487i 0.419556 0.242231i
$$137$$ −8.21968 14.2369i −0.702254 1.21634i −0.967673 0.252207i $$-0.918844\pi$$
0.265419 0.964133i $$-0.414490\pi$$
$$138$$ −0.865501 + 1.49909i −0.0736764 + 0.127611i
$$139$$ −10.7109 −0.908484 −0.454242 0.890878i $$-0.650090\pi$$
−0.454242 + 0.890878i $$0.650090\pi$$
$$140$$ 0 0
$$141$$ 7.39519 0.622787
$$142$$ −10.0013 5.77423i −0.839288 0.484563i
$$143$$ −2.55828 + 5.99231i −0.213935 + 0.501102i
$$144$$ 0.207107 + 0.358719i 0.0172589 + 0.0298933i
$$145$$ −9.27260 + 16.0606i −0.770047 + 1.33376i
$$146$$ 10.8614i 0.898898i
$$147$$ 0 0
$$148$$ 9.62995 0.791577
$$149$$ −12.7855 7.38174i −1.04743 0.604736i −0.125503 0.992093i $$-0.540055\pi$$
−0.921930 + 0.387358i $$0.873388\pi$$
$$150$$ −1.02401 1.77364i −0.0836104 0.144817i
$$151$$ 9.09017 5.24821i 0.739748 0.427093i −0.0822300 0.996613i $$-0.526204\pi$$
0.821978 + 0.569520i $$0.192871\pi$$
$$152$$ −0.785466 0.453489i −0.0637097 0.0367828i
$$153$$ −2.34020 −0.189194
$$154$$ 0 0
$$155$$ 11.6637 0.936851
$$156$$ −3.14363 1.81498i −0.251692 0.145314i
$$157$$ −3.99732 + 2.30785i −0.319021 + 0.184187i −0.650956 0.759115i $$-0.725632\pi$$
0.331935 + 0.943302i $$0.392298\pi$$
$$158$$ 4.24264 + 7.34847i 0.337526 + 0.584613i
$$159$$ 10.5082 + 6.06690i 0.833353 + 0.481136i
$$160$$ 2.47151 0.195390
$$161$$ 0 0
$$162$$ 10.0711i 0.791258i
$$163$$ −7.28732 + 12.6220i −0.570787 + 0.988632i 0.425698 + 0.904865i $$0.360028\pi$$
−0.996485 + 0.0837671i $$0.973305\pi$$
$$164$$ 3.46620 + 6.00363i 0.270665 + 0.468805i
$$165$$ −5.94705 + 13.9299i −0.462978 + 1.08444i
$$166$$ 4.18811 + 2.41800i 0.325060 + 0.187674i
$$167$$ −7.37045 −0.570342 −0.285171 0.958477i $$-0.592050\pi$$
−0.285171 + 0.958477i $$0.592050\pi$$
$$168$$ 0 0
$$169$$ −9.14068 −0.703129
$$170$$ −6.98171 + 12.0927i −0.535472 + 0.927465i
$$171$$ 0.187841 + 0.325351i 0.0143646 + 0.0248802i
$$172$$ 5.89712 3.40470i 0.449651 0.259606i
$$173$$ −5.57446 + 9.65525i −0.423818 + 0.734075i −0.996309 0.0858362i $$-0.972644\pi$$
0.572491 + 0.819911i $$0.305977\pi$$
$$174$$ 13.8648i 1.05109i
$$175$$ 0 0
$$176$$ −1.99049 2.65291i −0.150039 0.199971i
$$177$$ −0.892131 + 1.54522i −0.0670567 + 0.116146i
$$178$$ −6.36702 11.0280i −0.477229 0.826584i
$$179$$ −7.90434 13.6907i −0.590798 1.02329i −0.994125 0.108236i $$-0.965480\pi$$
0.403327 0.915056i $$-0.367854\pi$$
$$180$$ −0.886580 0.511867i −0.0660818 0.0381523i
$$181$$ 16.6528i 1.23779i −0.785473 0.618896i $$-0.787580\pi$$
0.785473 0.618896i $$-0.212420\pi$$
$$182$$ 0 0
$$183$$ 21.9889i 1.62546i
$$184$$ 0.811303 + 0.468406i 0.0598100 + 0.0345313i
$$185$$ −20.6119 + 11.9003i −1.51542 + 0.874926i
$$186$$ 7.55178 4.36002i 0.553723 0.319692i
$$187$$ 18.6031 2.24496i 1.36039 0.164168i
$$188$$ 4.00225i 0.291894i
$$189$$ 0 0
$$190$$ 2.24161 0.162623
$$191$$ −13.1784 + 22.8257i −0.953557 + 1.65161i −0.215921 + 0.976411i $$0.569275\pi$$
−0.737636 + 0.675199i $$0.764058\pi$$
$$192$$ 1.60021 0.923880i 0.115485 0.0666753i
$$193$$ 0.601170 0.347086i 0.0432731 0.0249838i −0.478207 0.878247i $$-0.658713\pi$$
0.521481 + 0.853263i $$0.325380\pi$$
$$194$$ 1.91342 3.31414i 0.137375 0.237941i
$$195$$ 8.97148 0.642461
$$196$$ 0 0
$$197$$ 9.74519i 0.694316i 0.937807 + 0.347158i $$0.112853\pi$$
−0.937807 + 0.347158i $$0.887147\pi$$
$$198$$ 0.164590 + 1.36390i 0.0116969 + 0.0969279i
$$199$$ 6.09214 3.51730i 0.431860 0.249335i −0.268279 0.963341i $$-0.586455\pi$$
0.700139 + 0.714007i $$0.253121\pi$$
$$200$$ −0.959889 + 0.554192i −0.0678744 + 0.0391873i
$$201$$ 10.7535 + 6.20851i 0.758490 + 0.437915i
$$202$$ 15.8293i 1.11375i
$$203$$ 0 0
$$204$$ 10.4394i 0.730901i
$$205$$ −14.8381 8.56676i −1.03634 0.598329i
$$206$$ 0.395111 + 0.684352i 0.0275287 + 0.0476811i
$$207$$ −0.194020 0.336053i −0.0134853 0.0233573i
$$208$$ −0.982258 + 1.70132i −0.0681073 + 0.117965i
$$209$$ −1.80533 2.40614i −0.124877 0.166436i
$$210$$ 0 0
$$211$$ 24.1152i 1.66016i −0.557643 0.830081i $$-0.688294\pi$$
0.557643 0.830081i $$-0.311706\pi$$
$$212$$ 3.28338 5.68698i 0.225504 0.390584i
$$213$$ 18.4799 10.6694i 1.26622 0.731055i
$$214$$ 8.30583 + 14.3861i 0.567775 + 0.983415i
$$215$$ −8.41477 + 14.5748i −0.573883 + 0.993994i
$$216$$ 4.77791 0.325096
$$217$$ 0 0
$$218$$ −6.00000 −0.406371
$$219$$ −17.3805 10.0347i −1.17447 0.678079i
$$220$$ 7.53879 + 3.21852i 0.508265 + 0.216993i
$$221$$ −5.54950 9.61202i −0.373300 0.646574i
$$222$$ −8.89692 + 15.4099i −0.597122 + 1.03425i
$$223$$ 2.90530i 0.194553i −0.995257 0.0972765i $$-0.968987\pi$$
0.995257 0.0972765i $$-0.0310131\pi$$
$$224$$ 0 0
$$225$$ 0.459108 0.0306072
$$226$$ −4.99195 2.88210i −0.332060 0.191715i
$$227$$ −7.21349 12.4941i −0.478776 0.829265i 0.520928 0.853601i $$-0.325586\pi$$
−0.999704 + 0.0243362i $$0.992253\pi$$
$$228$$ 1.45135 0.837939i 0.0961181 0.0554938i
$$229$$ −6.14615 3.54848i −0.406149 0.234490i 0.282985 0.959124i $$-0.408675\pi$$
−0.689134 + 0.724634i $$0.742009\pi$$
$$230$$ −2.31534 −0.152669
$$231$$ 0 0
$$232$$ 7.50358 0.492634
$$233$$ 3.60367 + 2.08058i 0.236084 + 0.136303i 0.613376 0.789791i $$-0.289811\pi$$
−0.377291 + 0.926095i $$0.623145\pi$$
$$234$$ 0.704710 0.406865i 0.0460683 0.0265976i
$$235$$ 4.94581 + 8.56639i 0.322629 + 0.558810i
$$236$$ 0.836265 + 0.482818i 0.0544362 + 0.0314288i
$$237$$ −15.6788 −1.01844
$$238$$ 0 0
$$239$$ 19.8625i 1.28480i 0.766371 + 0.642399i $$0.222061\pi$$
−0.766371 + 0.642399i $$0.777939\pi$$
$$240$$ −2.28338 + 3.95493i −0.147392 + 0.255290i
$$241$$ 7.24467 + 12.5481i 0.466670 + 0.808297i 0.999275 0.0380673i $$-0.0121201\pi$$
−0.532605 + 0.846364i $$0.678787\pi$$
$$242$$ −2.61678 10.6842i −0.168213 0.686807i
$$243$$ −3.70241 2.13759i −0.237510 0.137126i
$$244$$ −11.9003 −0.761838
$$245$$ 0 0
$$246$$ −12.8094 −0.816698
$$247$$ −0.890886 + 1.54306i −0.0566857 + 0.0981826i
$$248$$ −2.35963 4.08699i −0.149836 0.259524i
$$249$$ −7.73861 + 4.46789i −0.490415 + 0.283141i
$$250$$ −4.80909 + 8.32959i −0.304154 + 0.526810i
$$251$$ 14.6156i 0.922529i 0.887263 + 0.461264i $$0.152604\pi$$
−0.887263 + 0.461264i $$0.847396\pi$$
$$252$$ 0 0
$$253$$ 1.86471 + 2.48528i 0.117234 + 0.156248i
$$254$$ −9.31855 + 16.1402i −0.584698 + 1.01273i
$$255$$ −12.9005 22.3443i −0.807861 1.39926i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 20.0209 + 11.5591i 1.24887 + 0.721035i 0.970884 0.239550i $$-0.0769998\pi$$
0.277986 + 0.960585i $$0.410333\pi$$
$$258$$ 12.5821i 0.783330i
$$259$$ 0 0
$$260$$ 4.85533i 0.301115i
$$261$$ −2.69168 1.55404i −0.166611 0.0961927i
$$262$$ 17.3062 9.99173i 1.06918 0.617291i
$$263$$ −7.34847 + 4.24264i −0.453126 + 0.261612i −0.709150 0.705058i $$-0.750921\pi$$
0.256023 + 0.966671i $$0.417588\pi$$
$$264$$ 6.08418 0.734219i 0.374456 0.0451881i
$$265$$ 16.2299i 0.996992i
$$266$$ 0 0
$$267$$ 23.5294 1.43998
$$268$$ 3.36002 5.81973i 0.205246 0.355496i
$$269$$ 26.5008 15.3003i 1.61578 0.932874i 0.627791 0.778382i $$-0.283959\pi$$
0.987994 0.154492i $$-0.0493739\pi$$
$$270$$ −10.2266 + 5.90434i −0.622372 + 0.359327i
$$271$$ −6.60081 + 11.4329i −0.400971 + 0.694502i −0.993843 0.110794i $$-0.964661\pi$$
0.592872 + 0.805296i $$0.297994\pi$$
$$272$$ 5.64974 0.342566
$$273$$ 0 0
$$274$$ 16.4394i 0.993138i
$$275$$ −3.64962 + 0.440424i −0.220080 + 0.0265586i
$$276$$ −1.49909 + 0.865501i −0.0902347 + 0.0520970i
$$277$$ 3.45445 1.99443i 0.207558 0.119834i −0.392618 0.919702i $$-0.628431\pi$$
0.600176 + 0.799868i $$0.295097\pi$$
$$278$$ −9.27589 5.35544i −0.556331 0.321198i
$$279$$ 1.95478i 0.117030i
$$280$$ 0 0
$$281$$ 5.94293i 0.354526i −0.984164 0.177263i $$-0.943276\pi$$
0.984164 0.177263i $$-0.0567243\pi$$
$$282$$ 6.40442 + 3.69760i 0.381378 + 0.220189i
$$283$$ 10.6331 + 18.4170i 0.632070 + 1.09478i 0.987128 + 0.159933i $$0.0511279\pi$$
−0.355058 + 0.934844i $$0.615539\pi$$
$$284$$ −5.77423 10.0013i −0.342638 0.593466i
$$285$$ −2.07098 + 3.58704i −0.122674 + 0.212478i
$$286$$ −5.21169 + 3.91035i −0.308174 + 0.231224i
$$287$$ 0 0
$$288$$ 0.414214i 0.0244078i
$$289$$ −7.45977 + 12.9207i −0.438810 + 0.760042i
$$290$$ −16.0606 + 9.27260i −0.943112 + 0.544506i
$$291$$ 3.53553 + 6.12372i 0.207257 + 0.358979i
$$292$$ −5.43072 + 9.40628i −0.317809 + 0.550461i
$$293$$ −27.7920 −1.62362 −0.811812 0.583919i $$-0.801519\pi$$
−0.811812 + 0.583919i $$0.801519\pi$$
$$294$$ 0 0
$$295$$ −2.38658 −0.138952
$$296$$ 8.33978 + 4.81498i 0.484740 + 0.279865i
$$297$$ 14.5739 + 6.22202i 0.845665 + 0.361038i
$$298$$ −7.38174 12.7855i −0.427613 0.740647i
$$299$$ 0.920191 1.59382i 0.0532160 0.0921728i
$$300$$ 2.04803i 0.118243i
$$301$$ 0 0
$$302$$ 10.4964 0.604001
$$303$$ 25.3302 + 14.6244i 1.45518 + 0.840149i
$$304$$ −0.453489 0.785466i −0.0260094 0.0450496i
$$305$$ 25.4713 14.7059i 1.45848 0.842055i
$$306$$ −2.02667 1.17010i −0.115857 0.0668901i
$$307$$ 16.2674 0.928427 0.464214 0.885723i $$-0.346337\pi$$
0.464214 + 0.885723i $$0.346337\pi$$
$$308$$ 0 0
$$309$$ −1.46014 −0.0830644
$$310$$ 10.1011 + 5.83185i 0.573702 + 0.331227i
$$311$$ 9.34656 5.39624i 0.529995 0.305993i −0.211020 0.977482i $$-0.567678\pi$$
0.741014 + 0.671489i $$0.234345\pi$$
$$312$$ −1.81498 3.14363i −0.102753 0.177973i
$$313$$ −15.8579 9.15556i −0.896341 0.517503i −0.0203300 0.999793i $$-0.506472\pi$$
−0.876011 + 0.482290i $$0.839805\pi$$
$$314$$ −4.61571 −0.260480
$$315$$ 0 0
$$316$$ 8.48528i 0.477334i
$$317$$ 0.179452 0.310821i 0.0100791 0.0174574i −0.860942 0.508703i $$-0.830125\pi$$
0.871021 + 0.491246i $$0.163458\pi$$
$$318$$ 6.06690 + 10.5082i 0.340215 + 0.589269i
$$319$$ 22.8879 + 9.77151i 1.28148 + 0.547099i
$$320$$ 2.14039 + 1.23576i 0.119652 + 0.0690809i
$$321$$ −30.6943 −1.71319
$$322$$ 0 0
$$323$$ 5.12419 0.285118
$$324$$ −5.03553 + 8.72180i −0.279752 + 0.484544i
$$325$$ 1.08872 + 1.88572i 0.0603913 + 0.104601i
$$326$$ −12.6220 + 7.28732i −0.699069 + 0.403607i
$$327$$ 5.54328 9.60124i 0.306544 0.530950i
$$328$$ 6.93240i 0.382778i
$$329$$ 0 0
$$330$$ −12.1152 + 9.09009i −0.666922 + 0.500393i
$$331$$ 14.4567 25.0398i 0.794615 1.37631i −0.128469 0.991714i $$-0.541006\pi$$
0.923084 0.384599i $$-0.125660\pi$$
$$332$$ 2.41800 + 4.18811i 0.132705 + 0.229852i
$$333$$ −1.99443 3.45445i −0.109294 0.189303i
$$334$$ −6.38299 3.68522i −0.349262 0.201646i
$$335$$ 16.6087i 0.907429i
$$336$$ 0 0
$$337$$ 7.96341i 0.433795i −0.976194 0.216897i $$-0.930406\pi$$
0.976194 0.216897i $$-0.0695937\pi$$
$$338$$ −7.91606 4.57034i −0.430577 0.248594i
$$339$$ 9.22392 5.32543i 0.500975 0.289238i
$$340$$ −12.0927 + 6.98171i −0.655817 + 0.378636i
$$341$$ −1.87523 15.5393i −0.101549 0.841498i
$$342$$ 0.375683i 0.0203146i
$$343$$ 0 0
$$344$$ 6.80940 0.367138
$$345$$ 2.13910 3.70503i 0.115165 0.199472i
$$346$$ −9.65525 + 5.57446i −0.519069 + 0.299685i
$$347$$ 21.3743 12.3405i 1.14743 0.662472i 0.199174 0.979964i $$-0.436174\pi$$
0.948261 + 0.317492i $$0.102841\pi$$
$$348$$ −6.93240 + 12.0073i −0.371616 + 0.643657i
$$349$$ 11.1489 0.596788 0.298394 0.954443i $$-0.403549\pi$$
0.298394 + 0.954443i $$0.403549\pi$$
$$350$$ 0 0
$$351$$ 9.38628i 0.501003i
$$352$$ −0.397356 3.29274i −0.0211792 0.175503i
$$353$$ −18.5202 + 10.6926i −0.985729 + 0.569111i −0.903995 0.427543i $$-0.859379\pi$$
−0.0817341 + 0.996654i $$0.526046\pi$$
$$354$$ −1.54522 + 0.892131i −0.0821273 + 0.0474162i
$$355$$ 24.7183 + 14.2711i 1.31191 + 0.757432i
$$356$$ 12.7340i 0.674903i
$$357$$ 0 0
$$358$$ 15.8087i 0.835514i
$$359$$ 5.40718 + 3.12184i 0.285380 + 0.164764i 0.635856 0.771807i $$-0.280647\pi$$
−0.350477 + 0.936572i $$0.613980\pi$$
$$360$$ −0.511867 0.886580i −0.0269778 0.0467269i
$$361$$ 9.08870 + 15.7421i 0.478352 + 0.828531i
$$362$$ 8.32639 14.4217i 0.437625 0.757989i
$$363$$ 19.5145 + 5.68354i 1.02425 + 0.298309i
$$364$$ 0 0
$$365$$ 26.8442i 1.40509i
$$366$$ 10.9944 19.0429i 0.574688 0.995389i
$$367$$ 24.9011 14.3767i 1.29983 0.750456i 0.319454 0.947602i $$-0.396501\pi$$
0.980374 + 0.197146i $$0.0631673\pi$$
$$368$$ 0.468406 + 0.811303i 0.0244173 + 0.0422921i
$$369$$ 1.43575 2.48679i 0.0747420 0.129457i
$$370$$ −23.8006 −1.23733
$$371$$ 0 0
$$372$$ 8.72004 0.452113
$$373$$ −10.7031 6.17945i −0.554187 0.319960i 0.196622 0.980479i $$-0.437003\pi$$
−0.750809 + 0.660519i $$0.770336\pi$$
$$374$$ 17.2332 + 7.35736i 0.891109 + 0.380440i
$$375$$ −8.88604 15.3911i −0.458873 0.794792i
$$376$$ 2.00112 3.46605i 0.103200 0.178748i
$$377$$ 14.7409i 0.759195i
$$378$$ 0 0
$$379$$ −23.7822 −1.22161 −0.610805 0.791781i $$-0.709154\pi$$
−0.610805 + 0.791781i $$0.709154\pi$$
$$380$$ 1.94129 + 1.12080i 0.0995861 + 0.0574961i
$$381$$ −17.2184 29.8232i −0.882127 1.52789i
$$382$$ −22.8257 + 13.1784i −1.16786 + 0.674267i
$$383$$ −27.5955 15.9323i −1.41006 0.814100i −0.414669 0.909972i $$-0.636103\pi$$
−0.995394 + 0.0958720i $$0.969436\pi$$
$$384$$ 1.84776 0.0942931
$$385$$ 0 0
$$386$$ 0.694171 0.0353324
$$387$$ −2.44267 1.41027i −0.124168 0.0716882i
$$388$$ 3.31414 1.91342i 0.168250 0.0971390i
$$389$$ −10.5077 18.1999i −0.532763 0.922773i −0.999268 0.0382540i $$-0.987820\pi$$
0.466505 0.884519i $$-0.345513\pi$$
$$390$$ 7.76953 + 4.48574i 0.393425 + 0.227144i
$$391$$ −5.29274 −0.267665
$$392$$ 0 0
$$393$$ 36.9246i 1.86260i
$$394$$ −4.87259 + 8.43958i −0.245478 + 0.425180i
$$395$$ −10.4857 18.1618i −0.527595 0.913822i
$$396$$ −0.539408 + 1.26346i −0.0271063 + 0.0634914i
$$397$$ −7.20364 4.15902i −0.361540 0.208735i 0.308216 0.951316i $$-0.400268\pi$$
−0.669756 + 0.742581i $$0.733601\pi$$
$$398$$ 7.03460 0.352612
$$399$$ 0 0
$$400$$ −1.10838 −0.0554192
$$401$$ 15.3410 26.5714i 0.766093 1.32691i −0.173574 0.984821i $$-0.555532\pi$$
0.939667 0.342091i $$-0.111135\pi$$
$$402$$ 6.20851 + 10.7535i 0.309652 + 0.536334i
$$403$$ −8.02896 + 4.63552i −0.399951 + 0.230912i
$$404$$ 7.91466 13.7086i 0.393769 0.682028i
$$405$$ 24.8908i 1.23683i
$$406$$ 0 0
$$407$$ 19.1683 + 25.5474i 0.950138 + 1.26634i
$$408$$ −5.21968 + 9.04075i −0.258413 + 0.447584i
$$409$$ 4.78939 + 8.29546i 0.236820 + 0.410184i 0.959800 0.280685i $$-0.0905615\pi$$
−0.722980 + 0.690869i $$0.757228\pi$$
$$410$$ −8.56676 14.8381i −0.423082 0.732800i
$$411$$ 26.3064 + 15.1880i 1.29760 + 0.749168i
$$412$$ 0.790221i 0.0389314i
$$413$$ 0 0
$$414$$ 0.388040i 0.0190711i
$$415$$ −10.3510 5.97613i −0.508109 0.293357i
$$416$$ −1.70132 + 0.982258i −0.0834141 + 0.0481592i
$$417$$ 17.1396 9.89556i 0.839330 0.484587i
$$418$$ −0.360394 2.98644i −0.0176274 0.146072i
$$419$$ 10.3074i 0.503550i 0.967786 + 0.251775i $$0.0810143\pi$$
−0.967786 + 0.251775i $$0.918986\pi$$
$$420$$ 0 0
$$421$$ −25.8805 −1.26134 −0.630669 0.776052i $$-0.717219\pi$$
−0.630669 + 0.776052i $$0.717219\pi$$
$$422$$ 12.0576 20.8844i 0.586956 1.01664i
$$423$$ −1.43568 + 0.828893i −0.0698054 + 0.0403021i
$$424$$ 5.68698 3.28338i 0.276184 0.159455i
$$425$$ 3.13104 5.42312i 0.151878 0.263060i
$$426$$ 21.3388 1.03387
$$427$$ 0 0
$$428$$ 16.6117i 0.802955i
$$429$$ −1.44238 11.9525i −0.0696390 0.577071i
$$430$$ −14.5748 + 8.41477i −0.702860 + 0.405796i
$$431$$ 14.7967 8.54290i 0.712734 0.411497i −0.0993388 0.995054i $$-0.531673\pi$$
0.812072 + 0.583557i $$0.198339\pi$$
$$432$$ 4.13779 + 2.38896i 0.199080 + 0.114939i
$$433$$ 1.92881i 0.0926926i 0.998925 + 0.0463463i $$0.0147578\pi$$
−0.998925 + 0.0463463i $$0.985242\pi$$
$$434$$ 0 0
$$435$$ 34.2671i 1.64298i
$$436$$ −5.19615 3.00000i −0.248851 0.143674i
$$437$$ 0.424834 + 0.735834i 0.0203226 + 0.0351997i
$$438$$ −10.0347 17.3805i −0.479474 0.830474i
$$439$$ 5.21169 9.02692i 0.248741 0.430831i −0.714436 0.699701i $$-0.753317\pi$$
0.963177 + 0.268869i $$0.0866500\pi$$
$$440$$ 4.91952 + 6.55672i 0.234529 + 0.312579i
$$441$$ 0 0
$$442$$ 11.0990i 0.527926i
$$443$$ −7.96268 + 13.7918i −0.378318 + 0.655267i −0.990818 0.135204i $$-0.956831\pi$$
0.612499 + 0.790471i $$0.290164\pi$$
$$444$$ −15.4099 + 8.89692i −0.731322 + 0.422229i
$$445$$ 15.7362 + 27.2559i 0.745967 + 1.29205i
$$446$$ 1.45265 2.51606i 0.0687849 0.119139i
$$447$$ 27.2794 1.29027
$$448$$ 0 0
$$449$$ 10.4404 0.492712 0.246356 0.969179i $$-0.420767\pi$$
0.246356 + 0.969179i $$0.420767\pi$$
$$450$$ 0.397599 + 0.229554i 0.0187430 + 0.0108213i
$$451$$ −9.02770 + 21.1457i −0.425098 + 0.995712i
$$452$$ −2.88210 4.99195i −0.135563 0.234802i
$$453$$ −9.69743 + 16.7964i −0.455625 + 0.789166i
$$454$$ 14.4270i 0.677092i
$$455$$ 0 0
$$456$$ 1.67588 0.0784801
$$457$$ 15.6388 + 9.02908i 0.731554 + 0.422363i 0.818990 0.573807i $$-0.194534\pi$$
−0.0874367 + 0.996170i $$0.527868\pi$$
$$458$$ −3.54848 6.14615i −0.165810 0.287191i
$$459$$ −23.3774 + 13.4970i −1.09117 + 0.629985i
$$460$$ −2.00515 1.15767i −0.0934904 0.0539767i
$$461$$ −11.4500 −0.533281 −0.266641 0.963796i $$-0.585914\pi$$
−0.266641 + 0.963796i $$0.585914\pi$$
$$462$$ 0 0
$$463$$ −26.6805 −1.23995 −0.619975 0.784622i $$-0.712857\pi$$
−0.619975 + 0.784622i $$0.712857\pi$$
$$464$$ 6.49829 + 3.75179i 0.301675 + 0.174172i
$$465$$ −18.6643 + 10.7759i −0.865538 + 0.499718i
$$466$$ 2.08058 + 3.60367i 0.0963810 + 0.166937i
$$467$$ −8.41452 4.85813i −0.389378 0.224807i 0.292513 0.956262i $$-0.405509\pi$$
−0.681890 + 0.731454i $$0.738842\pi$$
$$468$$ 0.813729 0.0376146
$$469$$ 0 0
$$470$$ 9.89162i 0.456266i
$$471$$ 4.26436 7.38609i 0.196491 0.340333i
$$472$$ 0.482818 + 0.836265i 0.0222235 + 0.0384922i
$$473$$ 20.7705 + 8.86753i 0.955030 + 0.407729i
$$474$$ −13.5782 7.83938i −0.623667 0.360075i
$$475$$ −1.00528 −0.0461254
$$476$$ 0 0
$$477$$ −2.72004 −0.124542
$$478$$ −9.93124 + 17.2014i −0.454244 + 0.786774i
$$479$$ −9.60418 16.6349i −0.438826 0.760069i 0.558773 0.829321i $$-0.311272\pi$$
−0.997599 + 0.0692512i $$0.977939\pi$$
$$480$$ −3.95493 + 2.28338i −0.180517 + 0.104222i
$$481$$ 9.45910 16.3836i 0.431298 0.747029i
$$482$$ 14.4893i 0.659972i
$$483$$ 0 0
$$484$$ 3.07591 10.5612i 0.139814 0.480054i
$$485$$ −4.72904 + 8.19093i −0.214735 + 0.371931i
$$486$$ −2.13759 3.70241i −0.0969630 0.167945i
$$487$$ −0.181298 0.314017i −0.00821539 0.0142295i 0.861888 0.507098i $$-0.169282\pi$$
−0.870104 + 0.492868i $$0.835948\pi$$
$$488$$ −10.3059 5.95014i −0.466528 0.269350i
$$489$$ 26.9304i 1.21784i
$$490$$ 0 0
$$491$$ 1.04374i 0.0471033i 0.999723 + 0.0235516i $$0.00749741\pi$$
−0.999723 + 0.0235516i $$0.992503\pi$$
$$492$$ −11.0933 6.40470i −0.500123 0.288746i
$$493$$ −36.7136 + 21.1966i −1.65350 + 0.954648i
$$494$$ −1.54306 + 0.890886i −0.0694256 + 0.0400829i
$$495$$ −0.406788 3.37089i −0.0182837 0.151510i
$$496$$ 4.71925i 0.211901i
$$497$$ 0 0
$$498$$ −8.93578 −0.400422
$$499$$ −9.80041 + 16.9748i −0.438727 + 0.759897i −0.997592 0.0693620i $$-0.977904\pi$$
0.558865 + 0.829259i $$0.311237\pi$$
$$500$$ −8.32959 + 4.80909i −0.372511 + 0.215069i
$$501$$ 11.7942 6.80940i 0.526928 0.304222i
$$502$$ −7.30780 + 12.6575i −0.326163 + 0.564931i
$$503$$ 36.6503 1.63415 0.817077 0.576529i $$-0.195593\pi$$
0.817077 + 0.576529i $$0.195593\pi$$
$$504$$ 0 0
$$505$$ 39.1224i 1.74092i
$$506$$ 0.372248 + 3.08467i 0.0165484 + 0.137130i
$$507$$ 14.6270 8.44489i 0.649607 0.375051i
$$508$$ −16.1402 + 9.31855i −0.716106 + 0.413444i
$$509$$ −32.1251 18.5474i −1.42392 0.822101i −0.427290 0.904115i $$-0.640531\pi$$
−0.996631 + 0.0820139i $$0.973865\pi$$
$$510$$ 25.8010i 1.14249i
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ 3.75289 + 2.16673i 0.165694 + 0.0956635i
$$514$$ 11.5591 + 20.0209i 0.509849 + 0.883084i
$$515$$ −0.976522 1.69139i −0.0430307 0.0745314i
$$516$$ −6.29107 + 10.8965i −0.276949 + 0.479690i
$$517$$ 10.6176 7.96643i 0.466963 0.350363i
$$518$$ 0 0
$$519$$ 20.6005i 0.904262i
$$520$$ 2.42766 4.20484i 0.106460 0.184394i
$$521$$ −16.8745 + 9.74250i −0.739285 + 0.426827i −0.821809 0.569762i $$-0.807035\pi$$
0.0825240 + 0.996589i $$0.473702\pi$$
$$522$$ −1.55404 2.69168i −0.0680185 0.117812i
$$523$$ 21.5163 37.2674i 0.940844 1.62959i 0.176977 0.984215i $$-0.443368\pi$$
0.763867 0.645374i $$-0.223298\pi$$
$$524$$ 19.9835 0.872982
$$525$$ 0 0
$$526$$ −8.48528 −0.369976
$$527$$ 23.0904 + 13.3313i 1.00584 + 0.580719i
$$528$$ 5.63617 + 2.40624i 0.245283 + 0.104718i
$$529$$ 11.0612 + 19.1585i 0.480921 + 0.832980i
$$530$$ −8.11493 + 14.0555i −0.352490 + 0.610530i
$$531$$ 0.399979i 0.0173576i
$$532$$ 0 0
$$533$$ 13.6188 0.589896
$$534$$ 20.3771 + 11.7647i 0.881803 + 0.509109i
$$535$$ −20.5280 35.5555i −0.887502 1.53720i
$$536$$ 5.81973 3.36002i 0.251374 0.145131i
$$537$$ 25.2971 + 14.6053i 1.09165 + 0.630266i
$$538$$ 30.6005 1.31928
$$539$$ 0 0
$$540$$ −11.8087 −0.508164
$$541$$ 16.9904 + 9.80940i 0.730474 + 0.421739i 0.818595 0.574370i $$-0.194753\pi$$
−0.0881217 + 0.996110i $$0.528086\pi$$
$$542$$ −11.4329 + 6.60081i −0.491087 + 0.283529i
$$543$$ 15.3852 + 26.6479i 0.660241 + 1.14357i
$$544$$ 4.89282 + 2.82487i 0.209778 + 0.121115i
$$545$$ 14.8291 0.635208
$$546$$ 0 0
$$547$$ 42.5800i 1.82059i 0.413959 + 0.910295i $$0.364146\pi$$
−0.413959 + 0.910295i $$0.635854\pi$$
$$548$$ 8.21968 14.2369i 0.351127 0.608170i
$$549$$ 2.46463 + 4.26886i 0.105188 + 0.182191i
$$550$$ −3.38087 1.44339i −0.144161 0.0615464i
$$551$$ 5.89380 + 3.40279i 0.251085 + 0.144964i
$$552$$ −1.73100 −0.0736764
$$553$$ 0 0
$$554$$ 3.98886 0.169470
$$555$$ 21.9889 38.0858i 0.933375 1.61665i
$$556$$ −5.35544 9.27589i −0.227121 0.393385i
$$557$$ −7.67681 + 4.43221i −0.325277 + 0.187799i −0.653742 0.756717i $$-0.726802\pi$$
0.328465 + 0.944516i $$0.393469\pi$$
$$558$$ −0.977389 + 1.69289i −0.0413762 + 0.0716657i
$$559$$ 13.3772i 0.565795i
$$560$$ 0 0
$$561$$ −27.6947 + 20.7794i −1.16927 + 0.877308i
$$562$$ 2.97147 5.14673i 0.125344 0.217102i
$$563$$ −8.13368 14.0879i −0.342794 0.593736i 0.642157 0.766573i $$-0.278040\pi$$
−0.984950 + 0.172837i $$0.944707\pi$$
$$564$$ 3.69760 + 6.40442i 0.155697 + 0.269675i
$$565$$ 12.3377 + 7.12316i 0.519050 + 0.299674i
$$566$$ 21.2661i 0.893882i
$$567$$ 0 0
$$568$$ 11.5485i 0.484563i
$$569$$ −37.3354 21.5556i −1.56518 0.903659i −0.996718 0.0809508i $$-0.974204\pi$$
−0.568465 0.822708i $$-0.692462\pi$$
$$570$$ −3.58704 + 2.07098i −0.150244 + 0.0867437i
$$571$$ −4.15542 + 2.39913i −0.173899 + 0.100400i −0.584423 0.811449i $$-0.698679\pi$$
0.410524 + 0.911850i $$0.365346\pi$$
$$572$$ −6.46863 + 0.780613i −0.270467 + 0.0326391i
$$573$$ 48.7011i 2.03452i
$$574$$ 0 0
$$575$$ 1.03835 0.0433021
$$576$$ −0.207107 + 0.358719i −0.00862945 + 0.0149466i
$$577$$ 1.65586 0.956014i 0.0689345 0.0397994i −0.465137 0.885239i $$-0.653995\pi$$
0.534071 + 0.845440i $$0.320661\pi$$
$$578$$ −12.9207 + 7.45977i −0.537431 + 0.310286i
$$579$$ −0.641330 + 1.11082i −0.0266528 + 0.0461640i
$$580$$ −18.5452 −0.770047
$$581$$ 0 0
$$582$$ 7.07107i 0.293105i
$$583$$ 21.6226 2.60935i 0.895517 0.108068i
$$584$$ −9.40628 + 5.43072i −0.389234 + 0.224725i
$$585$$ −1.74170 + 1.00557i −0.0720105 + 0.0415753i
$$586$$ −24.0685 13.8960i −0.994262 0.574038i
$$587$$ 1.71510i 0.0707896i −0.999373 0.0353948i $$-0.988731\pi$$
0.999373 0.0353948i $$-0.0112689\pi$$
$$588$$ 0 0
$$589$$ 4.28026i 0.176365i
$$590$$ −2.06684 1.19329i −0.0850905 0.0491270i
$$591$$ −9.00338 15.5943i −0.370349 0.641464i
$$592$$ 4.81498 + 8.33978i 0.197894 + 0.342763i
$$593$$ 7.01955 12.1582i 0.288258 0.499278i −0.685136 0.728415i $$-0.740257\pi$$
0.973394 + 0.229137i $$0.0735905\pi$$
$$594$$ 9.51038 + 12.6754i 0.390215 + 0.520077i
$$595$$ 0 0
$$596$$ 14.7635i 0.604736i
$$597$$ −6.49912 + 11.2568i −0.265991 + 0.460710i
$$598$$ 1.59382 0.920191i 0.0651760 0.0376294i
$$599$$ −3.03517 5.25707i −0.124014 0.214798i 0.797333 0.603539i $$-0.206243\pi$$
−0.921347 + 0.388741i $$0.872910\pi$$
$$600$$ 1.02401 1.77364i 0.0418052 0.0724087i
$$601$$ −18.3373 −0.747995 −0.373998 0.927430i $$-0.622013\pi$$
−0.373998 + 0.927430i $$0.622013\pi$$
$$602$$ 0 0
$$603$$ −2.78353 −0.113354
$$604$$ 9.09017 + 5.24821i 0.369874 + 0.213547i
$$605$$ 6.46741 + 26.4062i 0.262938 + 1.07356i
$$606$$ 14.6244 + 25.3302i 0.594075 + 1.02897i
$$607$$ 0.106462 0.184397i 0.00432114 0.00748444i −0.863857 0.503738i $$-0.831958\pi$$
0.868178 + 0.496253i $$0.165291\pi$$
$$608$$ 0.906978i 0.0367828i
$$609$$ 0 0
$$610$$ 29.4117 1.19085
$$611$$ −6.80911 3.93124i −0.275467 0.159041i
$$612$$ −1.17010 2.02667i −0.0472985 0.0819233i
$$613$$ −14.6270 + 8.44493i −0.590781 + 0.341087i −0.765406 0.643548i $$-0.777462\pi$$
0.174625 + 0.984635i $$0.444129\pi$$
$$614$$ 14.0879 + 8.13368i 0.568543 + 0.328249i
$$615$$ 31.6586 1.27660
$$616$$ 0 0
$$617$$ 33.0864 1.33201 0.666004 0.745948i $$-0.268003\pi$$
0.666004 + 0.745948i $$0.268003\pi$$
$$618$$ −1.26452 0.730069i −0.0508663 0.0293677i
$$619$$ 12.3404 7.12472i 0.496001 0.286366i −0.231059 0.972940i $$-0.574219\pi$$
0.727061 + 0.686573i $$0.240886\pi$$
$$620$$ 5.83185 + 10.1011i 0.234213 + 0.405668i
$$621$$ −3.87633 2.23800i −0.155552 0.0898079i
$$622$$ 10.7925 0.432739
$$623$$ 0 0
$$624$$ 3.62995i 0.145314i
$$625$$ 14.6567 25.3862i 0.586268 1.01545i
$$626$$ −9.15556 15.8579i −0.365930 0.633809i
$$627$$ 5.11188 + 2.18241i 0.204149 + 0.0871569i
$$628$$ −3.99732 2.30785i −0.159510 0.0920934i
$$629$$ −54.4067 −2.16934
$$630$$ 0 0
$$631$$ −19.3751 −0.771312 −0.385656 0.922643i $$-0.626025\pi$$
−0.385656 + 0.922643i $$0.626025\pi$$
$$632$$ −4.24264 + 7.34847i −0.168763 + 0.292306i
$$633$$ 22.2796 + 38.5893i 0.885533 + 1.53379i
$$634$$ 0.310821 0.179452i 0.0123443 0.00712697i
$$635$$ 23.0309 39.8908i 0.913955 1.58302i
$$636$$ 12.1338i 0.481136i
$$637$$ 0 0
$$638$$ 14.9358 + 19.9063i 0.591313 + 0.788100i
$$639$$ −2.39177 + 4.14266i −0.0946168 + 0.163881i
$$640$$ 1.23576 + 2.14039i 0.0488476 + 0.0846065i
$$641$$ 18.2543 + 31.6174i 0.721003 + 1.24881i 0.960598 + 0.277941i $$0.0896518\pi$$
−0.239595 + 0.970873i $$0.577015\pi$$
$$642$$ −26.5821 15.3472i −1.04911 0.605705i
$$643$$ 2.49558i 0.0984161i 0.998789 + 0.0492080i $$0.0156697\pi$$
−0.998789 + 0.0492080i $$0.984330\pi$$
$$644$$ 0 0
$$645$$ 31.0969i 1.22444i
$$646$$ 4.43768 + 2.56209i 0.174598 + 0.100804i
$$647$$ 3.65045 2.10759i 0.143514 0.0828577i −0.426524 0.904476i $$-0.640262\pi$$
0.570038 + 0.821619i $$0.306929\pi$$
$$648$$ −8.72180 + 5.03553i −0.342625 + 0.197814i
$$649$$ 0.383701 + 3.17958i 0.0150616 + 0.124810i
$$650$$ 2.17744i 0.0854062i
$$651$$ 0 0
$$652$$ −14.5746 −0.570787
$$653$$ 5.39862 9.35068i 0.211264 0.365920i −0.740846 0.671675i $$-0.765575\pi$$
0.952110 + 0.305754i $$0.0989086\pi$$
$$654$$ 9.60124 5.54328i 0.375438 0.216759i
$$655$$ −42.7725 + 24.6947i −1.67126 + 0.964903i
$$656$$ −3.46620 + 6.00363i −0.135332 + 0.234403i
$$657$$ 4.49895 0.175521
$$658$$ 0 0
$$659$$ 42.1591i 1.64229i 0.570723 + 0.821143i $$0.306663\pi$$
−0.570723 + 0.821143i $$0.693337\pi$$
$$660$$ −15.0371 + 1.81463i −0.585320 + 0.0706345i
$$661$$ 7.77796 4.49061i 0.302528 0.174664i −0.341050 0.940045i $$-0.610783\pi$$
0.643578 + 0.765381i $$0.277449\pi$$
$$662$$ 25.0398 14.4567i 0.973200 0.561877i
$$663$$ 17.7607 + 10.2541i 0.689768 + 0.398238i
$$664$$ 4.83601i 0.187674i
$$665$$ 0 0
$$666$$ 3.98886i 0.154565i
$$667$$ −6.08767 3.51472i −0.235716 0.136090i
$$668$$ −3.68522 6.38299i −0.142586 0.246965i
$$669$$ 2.68414 + 4.64907i 0.103775 + 0.179744i
$$670$$ −8.30434 + 14.3835i −0.320825 + 0.555685i
$$671$$ −23.6874 31.5704i −0.914441 1.21876i
$$672$$ 0 0
$$673$$ 26.4282i 1.01873i −0.860550 0.509366i $$-0.829880\pi$$
0.860550 0.509366i $$-0.170120\pi$$
$$674$$ 3.98171 6.89652i 0.153370 0.265644i
$$675$$ 4.58626 2.64788i 0.176525 0.101917i
$$676$$ −4.57034 7.91606i −0.175782 0.304464i
$$677$$ 5.85689 10.1444i 0.225099 0.389882i −0.731250 0.682109i $$-0.761063\pi$$
0.956349 + 0.292227i $$0.0943962\pi$$
$$678$$ 10.6509 0.409044
$$679$$ 0 0
$$680$$ −13.9634 −0.535472
$$681$$ 23.0861 + 13.3288i 0.884663 + 0.510760i
$$682$$ 6.14563 14.3950i 0.235328 0.551213i
$$683$$ −17.9934 31.1655i −0.688498 1.19251i −0.972324 0.233638i $$-0.924937\pi$$
0.283825 0.958876i $$-0.408396\pi$$
$$684$$ −0.187841 + 0.325351i −0.00718229 + 0.0124401i
$$685$$ 40.6301i 1.55240i
$$686$$ 0 0
$$687$$ 13.1135 0.500310
$$688$$ 5.89712 + 3.40470i 0.224825 + 0.129803i
$$689$$ −6.45026 11.1722i −0.245735 0.425626i
$$690$$ 3.70503 2.13910i 0.141048 0.0814341i
$$691$$ −5.11870 2.95528i −0.194725 0.112424i 0.399468 0.916747i $$-0.369195\pi$$
−0.594192 + 0.804323i $$0.702528\pi$$
$$692$$ −11.1489 −0.423818
$$693$$ 0 0
$$694$$ 24.6810 0.936877
$$695$$ 22.9255 + 13.2360i 0.869613 + 0.502072i
$$696$$ −12.0073 + 6.93240i −0.455134 + 0.262772i
$$697$$ −19.5831 33.9190i −0.741764 1.28477i
$$698$$ 9.65525 + 5.57446i 0.365456 + 0.210996i
$$699$$ −7.68882 −0.290818
$$700$$ 0 0
$$701$$ 39.6167i 1.49630i −0.663527 0.748152i $$-0.730941\pi$$
0.663527 0.748152i $$-0.269059\pi$$
$$702$$ 4.69314 8.12876i 0.177131 0.306800i
$$703$$ 4.36708 + 7.56400i 0.164707 + 0.285282i
$$704$$ 1.30225 3.05027i 0.0490803 0.114961i
$$705$$ −15.8286 9.13866i −0.596141 0.344182i
$$706$$ −21.3852 −0.804844
$$707$$ 0 0
$$708$$ −1.78426 −0.0670567
$$709$$ 10.2012 17.6689i 0.383113 0.663571i −0.608392 0.793636i $$-0.708185\pi$$
0.991505 + 0.130065i $$0.0415186\pi$$
$$710$$ 14.2711 + 24.7183i 0.535585 + 0.927661i
$$711$$ 3.04384 1.75736i 0.114153 0.0659061i
$$712$$ 6.36702 11.0280i 0.238614 0.413292i
$$713$$ 4.42105i 0.165570i
$$714$$ 0 0
$$715$$ 12.8808 9.66448i 0.481714 0.361431i
$$716$$ 7.90434 13.6907i 0.295399 0.511646i
$$717$$ −18.3505 31.7841i −0.685313 1.18700i
$$718$$ 3.12184 + 5.40718i 0.116506 + 0.201794i
$$719$$ −24.8714 14.3595i −0.927545 0.535518i −0.0415109 0.999138i $$-0.513217\pi$$
−0.886034 + 0.463620i $$0.846550\pi$$
$$720$$ 1.02373i 0.0381523i
$$721$$ 0 0
$$722$$ 18.1774i 0.676492i
$$723$$ −23.1859 13.3864i −0.862294 0.497846i
$$724$$ 14.4217 8.32639i 0.535979 0.309448i
$$725$$ 7.20260 4.15842i 0.267498 0.154440i
$$726$$ 14.0583 + 14.6794i 0.521753 + 0.544802i
$$727$$ 9.15820i 0.339659i 0.985473 + 0.169829i $$0.0543217\pi$$
−0.985473 + 0.169829i $$0.945678\pi$$
$$728$$ 0 0
$$729$$ −22.3137 −0.826434
$$730$$ 13.4221 23.2477i 0.496774 0.860438i
$$731$$ −33.3172 + 19.2357i −1.23228 + 0.711457i
$$732$$ 19.0429 10.9944i 0.703846 0.406366i
$$733$$ −22.3549 + 38.7197i −0.825695 + 1.43015i 0.0756916 + 0.997131i $$0.475884\pi$$
−0.901387 + 0.433015i $$0.857450\pi$$
$$734$$ 28.7533 1.06130
$$735$$ 0 0
$$736$$ 0.936812i 0.0345313i
$$737$$ 22.1273 2.67025i 0.815070 0.0983600i
$$738$$ 2.48679 1.43575i 0.0915399 0.0528506i
$$739$$ −18.7939 + 10.8507i −0.691345 + 0.399148i −0.804116 0.594473i $$-0.797361\pi$$
0.112771 + 0.993621i $$0.464027\pi$$
$$740$$ −20.6119 11.9003i −0.757708 0.437463i
$$741$$ 3.29229i 0.120945i
$$742$$ 0 0
$$743$$ 8.20708i 0.301089i −0.988603 0.150544i $$-0.951897\pi$$
0.988603 0.150544i $$-0.0481026\pi$$
$$744$$ 7.55178 + 4.36002i 0.276862 + 0.159846i
$$745$$ 18.2441 + 31.5997i 0.668411 + 1.15772i
$$746$$ −6.17945 10.7031i −0.226246 0.391869i
$$747$$ 1.00157 1.73477i 0.0366455 0.0634719i
$$748$$ 11.2457 + 14.9883i 0.411185 + 0.548026i
$$749$$ 0 0
$$750$$ 17.7721i 0.648945i
$$751$$ 9.71032 16.8188i 0.354335 0.613725i −0.632669 0.774422i $$-0.718041\pi$$
0.987004 + 0.160697i $$0.0513741\pi$$
$$752$$ 3.46605 2.00112i 0.126394 0.0729735i
$$753$$ −13.5031 23.3880i −0.492079 0.852306i
$$754$$ 7.37045 12.7660i 0.268416 0.464910i
$$755$$ −25.9421 −0.944128
$$756$$ 0 0
$$757$$ 44.7958 1.62813 0.814065 0.580774i $$-0.197250\pi$$
0.814065 + 0.580774i $$0.197250\pi$$
$$758$$ −20.5960 11.8911i −0.748080 0.431904i
$$759$$ −5.28003 2.25419i −0.191653 0.0818220i
$$760$$ 1.12080 + 1.94129i 0.0406559 + 0.0704180i
$$761$$ −1.91789 + 3.32189i −0.0695235 + 0.120418i −0.898692 0.438581i $$-0.855481\pi$$
0.829168 + 0.558999i $$0.188815\pi$$
$$762$$ 34.4369i 1.24752i
$$763$$ 0 0
$$764$$ −26.3568 −0.953557
$$765$$ 5.00895 + 2.89192i 0.181099 + 0.104557i
$$766$$ −15.9323 27.5955i −0.575656 0.997065i
$$767$$ 1.64286 0.948503i 0.0593201 0.0342485i
$$768$$ 1.60021 + 0.923880i 0.0577425 + 0.0333376i
$$769$$ 37.6267 1.35685 0.678427 0.734667i $$-0.262662\pi$$
0.678427 + 0.734667i $$0.262662\pi$$
$$770$$ 0 0
$$771$$ −42.7168 −1.53841
$$772$$ 0.601170 + 0.347086i 0.0216366 + 0.0124919i
$$773$$ 24.7455 14.2868i 0.890034 0.513861i 0.0160805 0.999871i $$-0.494881\pi$$
0.873954 + 0.486009i $$0.161548\pi$$
$$774$$ −1.41027 2.44267i −0.0506912 0.0877998i
$$775$$ −4.52996 2.61537i −0.162721 0.0939470i
$$776$$ 3.82683 0.137375
$$777$$ 0 0
$$778$$ 21.0155i 0.753441i
$$779$$ −3.14377 + 5.44517i −0.112637 + 0.195093i
$$780$$ 4.48574 + 7.76953i 0.160615 + 0.278194i
$$781$$ 15.0390 35.2260i 0.538136 1.26048i
$$782$$ −4.58365 2.64637i −0.163911 0.0946340i
$$783$$ −35.8514 −1.28122