# Properties

 Label 672.2.q.a.193.1 Level $672$ Weight $2$ Character 672.193 Analytic conductor $5.366$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.36594701583$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 193.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 672.193 Dual form 672.2.q.a.289.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{17} +(-2.50000 - 0.866025i) q^{21} +(-4.00000 - 6.92820i) q^{23} +(-2.00000 + 3.46410i) q^{25} +1.00000 q^{27} -7.00000 q^{29} +(-5.50000 + 9.52628i) q^{31} +(0.500000 + 0.866025i) q^{33} +(6.00000 - 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{37} +(2.00000 - 3.46410i) q^{39} -4.00000 q^{41} -2.00000 q^{43} +(-1.50000 + 2.59808i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(5.50000 - 9.52628i) q^{53} -3.00000 q^{55} +(-3.50000 + 6.06218i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(2.00000 - 1.73205i) q^{63} +(6.00000 + 10.3923i) q^{65} +(-5.00000 + 8.66025i) q^{67} +8.00000 q^{69} +6.00000 q^{71} +(3.00000 - 5.19615i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(2.50000 + 0.866025i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +11.0000 q^{83} +12.0000 q^{85} +(3.50000 - 6.06218i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-2.00000 - 10.3923i) q^{91} +(-5.50000 - 9.52628i) q^{93} +7.00000 q^{97} -1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} - 3q^{5} + q^{7} - q^{9} + O(q^{10})$$ $$2q - q^{3} - 3q^{5} + q^{7} - q^{9} + q^{11} - 8q^{13} + 6q^{15} - 4q^{17} - 5q^{21} - 8q^{23} - 4q^{25} + 2q^{27} - 14q^{29} - 11q^{31} + q^{33} + 12q^{35} - 4q^{37} + 4q^{39} - 8q^{41} - 4q^{43} - 3q^{45} + 2q^{47} - 13q^{49} - 4q^{51} + 11q^{53} - 6q^{55} - 7q^{59} - 10q^{61} + 4q^{63} + 12q^{65} - 10q^{67} + 16q^{69} + 12q^{71} + 6q^{73} - 4q^{75} + 5q^{77} - 11q^{79} - q^{81} + 22q^{83} + 24q^{85} + 7q^{87} - 6q^{89} - 4q^{91} - 11q^{93} + 14q^{97} - 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$421$$ $$449$$ $$577$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i $$-0.932609\pi$$
0.306851 0.951757i $$-0.400725\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i $$-0.785163\pi$$
0.931505 + 0.363727i $$0.118496\pi$$
$$12$$ 0 0
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ 3.00000 0.774597
$$16$$ 0 0
$$17$$ −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i $$-0.994540\pi$$
0.514782 + 0.857321i $$0.327873\pi$$
$$18$$ 0 0
$$19$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$20$$ 0 0
$$21$$ −2.50000 0.866025i −0.545545 0.188982i
$$22$$ 0 0
$$23$$ −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i $$-0.852679\pi$$
0.0607377 0.998154i $$-0.480655\pi$$
$$24$$ 0 0
$$25$$ −2.00000 + 3.46410i −0.400000 + 0.692820i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −7.00000 −1.29987 −0.649934 0.759991i $$-0.725203\pi$$
−0.649934 + 0.759991i $$0.725203\pi$$
$$30$$ 0 0
$$31$$ −5.50000 + 9.52628i −0.987829 + 1.71097i −0.359211 + 0.933257i $$0.616954\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ 0 0
$$33$$ 0.500000 + 0.866025i 0.0870388 + 0.150756i
$$34$$ 0 0
$$35$$ 6.00000 5.19615i 1.01419 0.878310i
$$36$$ 0 0
$$37$$ −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i $$-0.273310\pi$$
−0.982274 + 0.187453i $$0.939977\pi$$
$$38$$ 0 0
$$39$$ 2.00000 3.46410i 0.320256 0.554700i
$$40$$ 0 0
$$41$$ −4.00000 −0.624695 −0.312348 0.949968i $$-0.601115\pi$$
−0.312348 + 0.949968i $$0.601115\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 0 0
$$45$$ −1.50000 + 2.59808i −0.223607 + 0.387298i
$$46$$ 0 0
$$47$$ 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i $$-0.120070\pi$$
−0.783830 + 0.620975i $$0.786737\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ −2.00000 3.46410i −0.280056 0.485071i
$$52$$ 0 0
$$53$$ 5.50000 9.52628i 0.755483 1.30854i −0.189651 0.981852i $$-0.560736\pi$$
0.945134 0.326683i $$-0.105931\pi$$
$$54$$ 0 0
$$55$$ −3.00000 −0.404520
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.50000 + 6.06218i −0.455661 + 0.789228i −0.998726 0.0504625i $$-0.983930\pi$$
0.543065 + 0.839691i $$0.317264\pi$$
$$60$$ 0 0
$$61$$ −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i $$-0.945525\pi$$
0.345207 0.938527i $$-0.387809\pi$$
$$62$$ 0 0
$$63$$ 2.00000 1.73205i 0.251976 0.218218i
$$64$$ 0 0
$$65$$ 6.00000 + 10.3923i 0.744208 + 1.28901i
$$66$$ 0 0
$$67$$ −5.00000 + 8.66025i −0.610847 + 1.05802i 0.380251 + 0.924883i $$0.375838\pi$$
−0.991098 + 0.133135i $$0.957496\pi$$
$$68$$ 0 0
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ 3.00000 5.19615i 0.351123 0.608164i −0.635323 0.772246i $$-0.719133\pi$$
0.986447 + 0.164083i $$0.0524664\pi$$
$$74$$ 0 0
$$75$$ −2.00000 3.46410i −0.230940 0.400000i
$$76$$ 0 0
$$77$$ 2.50000 + 0.866025i 0.284901 + 0.0986928i
$$78$$ 0 0
$$79$$ −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i $$-0.954286\pi$$
0.370907 0.928670i $$-0.379047\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 11.0000 1.20741 0.603703 0.797209i $$-0.293691\pi$$
0.603703 + 0.797209i $$0.293691\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 0 0
$$87$$ 3.50000 6.06218i 0.375239 0.649934i
$$88$$ 0 0
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 0 0
$$91$$ −2.00000 10.3923i −0.209657 1.08941i
$$92$$ 0 0
$$93$$ −5.50000 9.52628i −0.570323 0.987829i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ 0 0
$$99$$ −1.00000 −0.100504
$$100$$ 0 0
$$101$$ −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i $$-0.929823\pi$$
0.677284 + 0.735721i $$0.263157\pi$$
$$102$$ 0 0
$$103$$ 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i $$0.122353\pi$$
−0.138767 + 0.990325i $$0.544314\pi$$
$$104$$ 0 0
$$105$$ 1.50000 + 7.79423i 0.146385 + 0.760639i
$$106$$ 0 0
$$107$$ 3.50000 + 6.06218i 0.338358 + 0.586053i 0.984124 0.177482i $$-0.0567953\pi$$
−0.645766 + 0.763535i $$0.723462\pi$$
$$108$$ 0 0
$$109$$ −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i $$-0.992302\pi$$
0.520794 + 0.853682i $$0.325636\pi$$
$$110$$ 0 0
$$111$$ 4.00000 0.379663
$$112$$ 0 0
$$113$$ 12.0000 1.12887 0.564433 0.825479i $$-0.309095\pi$$
0.564433 + 0.825479i $$0.309095\pi$$
$$114$$ 0 0
$$115$$ −12.0000 + 20.7846i −1.11901 + 1.93817i
$$116$$ 0 0
$$117$$ 2.00000 + 3.46410i 0.184900 + 0.320256i
$$118$$ 0 0
$$119$$ −10.0000 3.46410i −0.916698 0.317554i
$$120$$ 0 0
$$121$$ 5.00000 + 8.66025i 0.454545 + 0.787296i
$$122$$ 0 0
$$123$$ 2.00000 3.46410i 0.180334 0.312348i
$$124$$ 0 0
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 17.0000 1.50851 0.754253 0.656584i $$-0.227999\pi$$
0.754253 + 0.656584i $$0.227999\pi$$
$$128$$ 0 0
$$129$$ 1.00000 1.73205i 0.0880451 0.152499i
$$130$$ 0 0
$$131$$ −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i $$-0.208503\pi$$
−0.924084 + 0.382190i $$0.875170\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −1.50000 2.59808i −0.129099 0.223607i
$$136$$ 0 0
$$137$$ 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i $$-0.806105\pi$$
0.905577 + 0.424182i $$0.139438\pi$$
$$138$$ 0 0
$$139$$ −22.0000 −1.86602 −0.933008 0.359856i $$-0.882826\pi$$
−0.933008 + 0.359856i $$0.882826\pi$$
$$140$$ 0 0
$$141$$ −2.00000 −0.168430
$$142$$ 0 0
$$143$$ −2.00000 + 3.46410i −0.167248 + 0.289683i
$$144$$ 0 0
$$145$$ 10.5000 + 18.1865i 0.871978 + 1.51031i
$$146$$ 0 0
$$147$$ 1.00000 6.92820i 0.0824786 0.571429i
$$148$$ 0 0
$$149$$ 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i $$-0.0876260\pi$$
−0.716578 + 0.697507i $$0.754293\pi$$
$$150$$ 0 0
$$151$$ −5.50000 + 9.52628i −0.447584 + 0.775238i −0.998228 0.0595022i $$-0.981049\pi$$
0.550645 + 0.834740i $$0.314382\pi$$
$$152$$ 0 0
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 33.0000 2.65062
$$156$$ 0 0
$$157$$ 6.00000 10.3923i 0.478852 0.829396i −0.520854 0.853646i $$-0.674386\pi$$
0.999706 + 0.0242497i $$0.00771967\pi$$
$$158$$ 0 0
$$159$$ 5.50000 + 9.52628i 0.436178 + 0.755483i
$$160$$ 0 0
$$161$$ 16.0000 13.8564i 1.26098 1.09204i
$$162$$ 0 0
$$163$$ 4.00000 + 6.92820i 0.313304 + 0.542659i 0.979076 0.203497i $$-0.0652307\pi$$
−0.665771 + 0.746156i $$0.731897\pi$$
$$164$$ 0 0
$$165$$ 1.50000 2.59808i 0.116775 0.202260i
$$166$$ 0 0
$$167$$ −22.0000 −1.70241 −0.851206 0.524832i $$-0.824128\pi$$
−0.851206 + 0.524832i $$0.824128\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i $$-0.0934200\pi$$
−0.729155 + 0.684349i $$0.760087\pi$$
$$174$$ 0 0
$$175$$ −10.0000 3.46410i −0.755929 0.261861i
$$176$$ 0 0
$$177$$ −3.50000 6.06218i −0.263076 0.455661i
$$178$$ 0 0
$$179$$ 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i $$-0.685306\pi$$
0.998286 + 0.0585225i $$0.0186389\pi$$
$$180$$ 0 0
$$181$$ 12.0000 0.891953 0.445976 0.895045i $$-0.352856\pi$$
0.445976 + 0.895045i $$0.352856\pi$$
$$182$$ 0 0
$$183$$ 10.0000 0.739221
$$184$$ 0 0
$$185$$ −6.00000 + 10.3923i −0.441129 + 0.764057i
$$186$$ 0 0
$$187$$ 2.00000 + 3.46410i 0.146254 + 0.253320i
$$188$$ 0 0
$$189$$ 0.500000 + 2.59808i 0.0363696 + 0.188982i
$$190$$ 0 0
$$191$$ −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i $$-0.831886\pi$$
−0.00454614 0.999990i $$-0.501447\pi$$
$$192$$ 0 0
$$193$$ 9.50000 16.4545i 0.683825 1.18442i −0.289980 0.957033i $$-0.593649\pi$$
0.973805 0.227387i $$-0.0730182\pi$$
$$194$$ 0 0
$$195$$ −12.0000 −0.859338
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i $$-0.582534\pi$$
0.965272 0.261245i $$-0.0841331\pi$$
$$200$$ 0 0
$$201$$ −5.00000 8.66025i −0.352673 0.610847i
$$202$$ 0 0
$$203$$ −3.50000 18.1865i −0.245652 1.27644i
$$204$$ 0 0
$$205$$ 6.00000 + 10.3923i 0.419058 + 0.725830i
$$206$$ 0 0
$$207$$ −4.00000 + 6.92820i −0.278019 + 0.481543i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 2.00000 0.137686 0.0688428 0.997628i $$-0.478069\pi$$
0.0688428 + 0.997628i $$0.478069\pi$$
$$212$$ 0 0
$$213$$ −3.00000 + 5.19615i −0.205557 + 0.356034i
$$214$$ 0 0
$$215$$ 3.00000 + 5.19615i 0.204598 + 0.354375i
$$216$$ 0 0
$$217$$ −27.5000 9.52628i −1.86682 0.646686i
$$218$$ 0 0
$$219$$ 3.00000 + 5.19615i 0.202721 + 0.351123i
$$220$$ 0 0
$$221$$ 8.00000 13.8564i 0.538138 0.932083i
$$222$$ 0 0
$$223$$ 9.00000 0.602685 0.301342 0.953516i $$-0.402565\pi$$
0.301342 + 0.953516i $$0.402565\pi$$
$$224$$ 0 0
$$225$$ 4.00000 0.266667
$$226$$ 0 0
$$227$$ 3.50000 6.06218i 0.232303 0.402361i −0.726182 0.687502i $$-0.758707\pi$$
0.958485 + 0.285141i $$0.0920405\pi$$
$$228$$ 0 0
$$229$$ 4.00000 + 6.92820i 0.264327 + 0.457829i 0.967387 0.253302i $$-0.0815167\pi$$
−0.703060 + 0.711131i $$0.748183\pi$$
$$230$$ 0 0
$$231$$ −2.00000 + 1.73205i −0.131590 + 0.113961i
$$232$$ 0 0
$$233$$ −6.00000 10.3923i −0.393073 0.680823i 0.599780 0.800165i $$-0.295255\pi$$
−0.992853 + 0.119342i $$0.961921\pi$$
$$234$$ 0 0
$$235$$ 3.00000 5.19615i 0.195698 0.338960i
$$236$$ 0 0
$$237$$ 11.0000 0.714527
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i $$-0.535394\pi$$
0.916159 0.400815i $$-0.131273\pi$$
$$242$$ 0 0
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 16.5000 + 12.9904i 1.05415 + 0.829925i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −5.50000 + 9.52628i −0.348548 + 0.603703i
$$250$$ 0 0
$$251$$ −25.0000 −1.57799 −0.788993 0.614402i $$-0.789397\pi$$
−0.788993 + 0.614402i $$0.789397\pi$$
$$252$$ 0 0
$$253$$ −8.00000 −0.502956
$$254$$ 0 0
$$255$$ −6.00000 + 10.3923i −0.375735 + 0.650791i
$$256$$ 0 0
$$257$$ −7.00000 12.1244i −0.436648 0.756297i 0.560781 0.827964i $$-0.310501\pi$$
−0.997429 + 0.0716680i $$0.977168\pi$$
$$258$$ 0 0
$$259$$ 8.00000 6.92820i 0.497096 0.430498i
$$260$$ 0 0
$$261$$ 3.50000 + 6.06218i 0.216645 + 0.375239i
$$262$$ 0 0
$$263$$ −13.0000 + 22.5167i −0.801614 + 1.38844i 0.116939 + 0.993139i $$0.462692\pi$$
−0.918553 + 0.395298i $$0.870641\pi$$
$$264$$ 0 0
$$265$$ −33.0000 −2.02717
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ 0 0
$$269$$ −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i $$0.387814\pi$$
−0.985389 + 0.170321i $$0.945520\pi$$
$$270$$ 0 0
$$271$$ 0.500000 + 0.866025i 0.0303728 + 0.0526073i 0.880812 0.473466i $$-0.156997\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ 0 0
$$273$$ 10.0000 + 3.46410i 0.605228 + 0.209657i
$$274$$ 0 0
$$275$$ 2.00000 + 3.46410i 0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ −16.0000 + 27.7128i −0.961347 + 1.66510i −0.242222 + 0.970221i $$0.577876\pi$$
−0.719125 + 0.694881i $$0.755457\pi$$
$$278$$ 0 0
$$279$$ 11.0000 0.658553
$$280$$ 0 0
$$281$$ −30.0000 −1.78965 −0.894825 0.446417i $$-0.852700\pi$$
−0.894825 + 0.446417i $$0.852700\pi$$
$$282$$ 0 0
$$283$$ 1.00000 1.73205i 0.0594438 0.102960i −0.834772 0.550596i $$-0.814401\pi$$
0.894216 + 0.447636i $$0.147734\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −2.00000 10.3923i −0.118056 0.613438i
$$288$$ 0 0
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ −3.50000 + 6.06218i −0.205174 + 0.355371i
$$292$$ 0 0
$$293$$ −7.00000 −0.408944 −0.204472 0.978872i $$-0.565548\pi$$
−0.204472 + 0.978872i $$0.565548\pi$$
$$294$$ 0 0
$$295$$ 21.0000 1.22267
$$296$$ 0 0
$$297$$ 0.500000 0.866025i 0.0290129 0.0502519i
$$298$$ 0 0
$$299$$ 16.0000 + 27.7128i 0.925304 + 1.60267i
$$300$$ 0 0
$$301$$ −1.00000 5.19615i −0.0576390 0.299501i
$$302$$ 0 0
$$303$$ −3.00000 5.19615i −0.172345 0.298511i
$$304$$ 0 0
$$305$$ −15.0000 + 25.9808i −0.858898 + 1.48765i
$$306$$ 0 0
$$307$$ −8.00000 −0.456584 −0.228292 0.973593i $$-0.573314\pi$$
−0.228292 + 0.973593i $$0.573314\pi$$
$$308$$ 0 0
$$309$$ −16.0000 −0.910208
$$310$$ 0 0
$$311$$ −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i $$-0.943838\pi$$
0.644246 + 0.764818i $$0.277171\pi$$
$$312$$ 0 0
$$313$$ −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i $$-0.175664\pi$$
−0.879810 + 0.475325i $$0.842331\pi$$
$$314$$ 0 0
$$315$$ −7.50000 2.59808i −0.422577 0.146385i
$$316$$ 0 0
$$317$$ −8.50000 14.7224i −0.477408 0.826894i 0.522257 0.852788i $$-0.325090\pi$$
−0.999665 + 0.0258939i $$0.991757\pi$$
$$318$$ 0 0
$$319$$ −3.50000 + 6.06218i −0.195962 + 0.339417i
$$320$$ 0 0
$$321$$ −7.00000 −0.390702
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 8.00000 13.8564i 0.443760 0.768615i
$$326$$ 0 0
$$327$$ −5.00000 8.66025i −0.276501 0.478913i
$$328$$ 0 0
$$329$$ −4.00000 + 3.46410i −0.220527 + 0.190982i
$$330$$ 0 0
$$331$$ −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i $$-0.273645\pi$$
−0.982470 + 0.186421i $$0.940311\pi$$
$$332$$ 0 0
$$333$$ −2.00000 + 3.46410i −0.109599 + 0.189832i
$$334$$ 0 0
$$335$$ 30.0000 1.63908
$$336$$ 0 0
$$337$$ −15.0000 −0.817102 −0.408551 0.912735i $$-0.633966\pi$$
−0.408551 + 0.912735i $$0.633966\pi$$
$$338$$ 0 0
$$339$$ −6.00000 + 10.3923i −0.325875 + 0.564433i
$$340$$ 0 0
$$341$$ 5.50000 + 9.52628i 0.297842 + 0.515877i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 0 0
$$345$$ −12.0000 20.7846i −0.646058 1.11901i
$$346$$ 0 0
$$347$$ −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i $$-0.937721\pi$$
0.658824 + 0.752297i $$0.271054\pi$$
$$348$$ 0 0
$$349$$ −34.0000 −1.81998 −0.909989 0.414632i $$-0.863910\pi$$
−0.909989 + 0.414632i $$0.863910\pi$$
$$350$$ 0 0
$$351$$ −4.00000 −0.213504
$$352$$ 0 0
$$353$$ 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i $$-0.612808\pi$$
0.985719 0.168397i $$-0.0538590\pi$$
$$354$$ 0 0
$$355$$ −9.00000 15.5885i −0.477670 0.827349i
$$356$$ 0 0
$$357$$ 8.00000 6.92820i 0.423405 0.366679i
$$358$$ 0 0
$$359$$ −1.00000 1.73205i −0.0527780 0.0914141i 0.838429 0.545010i $$-0.183474\pi$$
−0.891207 + 0.453596i $$0.850141\pi$$
$$360$$ 0 0
$$361$$ 9.50000 16.4545i 0.500000 0.866025i
$$362$$ 0 0
$$363$$ −10.0000 −0.524864
$$364$$ 0 0
$$365$$ −18.0000 −0.942163
$$366$$ 0 0
$$367$$ −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i $$-0.979666\pi$$
0.554264 + 0.832341i $$0.313000\pi$$
$$368$$ 0 0
$$369$$ 2.00000 + 3.46410i 0.104116 + 0.180334i
$$370$$ 0 0
$$371$$ 27.5000 + 9.52628i 1.42773 + 0.494580i
$$372$$ 0 0
$$373$$ 6.00000 + 10.3923i 0.310668 + 0.538093i 0.978507 0.206213i $$-0.0661139\pi$$
−0.667839 + 0.744306i $$0.732781\pi$$
$$374$$ 0 0
$$375$$ 1.50000 2.59808i 0.0774597 0.134164i
$$376$$ 0 0
$$377$$ 28.0000 1.44207
$$378$$ 0 0
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ 0 0
$$381$$ −8.50000 + 14.7224i −0.435468 + 0.754253i
$$382$$ 0 0
$$383$$ −1.00000 1.73205i −0.0510976 0.0885037i 0.839345 0.543599i $$-0.182939\pi$$
−0.890443 + 0.455095i $$0.849605\pi$$
$$384$$ 0 0
$$385$$ −1.50000 7.79423i −0.0764471 0.397231i
$$386$$ 0 0
$$387$$ 1.00000 + 1.73205i 0.0508329 + 0.0880451i
$$388$$ 0 0
$$389$$ 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i $$-0.784728\pi$$
0.932002 + 0.362454i $$0.118061\pi$$
$$390$$ 0 0
$$391$$ 32.0000 1.61831
$$392$$ 0 0
$$393$$ 3.00000 0.151330
$$394$$ 0 0
$$395$$ −16.5000 + 28.5788i −0.830205 + 1.43796i
$$396$$ 0 0
$$397$$ 2.00000 + 3.46410i 0.100377 + 0.173858i 0.911840 0.410546i $$-0.134662\pi$$
−0.811463 + 0.584404i $$0.801328\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −8.00000 13.8564i −0.399501 0.691956i 0.594163 0.804344i $$-0.297483\pi$$
−0.993664 + 0.112388i $$0.964150\pi$$
$$402$$ 0 0
$$403$$ 22.0000 38.1051i 1.09590 1.89815i
$$404$$ 0 0
$$405$$ 3.00000 0.149071
$$406$$ 0 0
$$407$$ −4.00000 −0.198273
$$408$$ 0 0
$$409$$ −3.50000 + 6.06218i −0.173064 + 0.299755i −0.939490 0.342578i $$-0.888700\pi$$
0.766426 + 0.642333i $$0.222033\pi$$
$$410$$ 0 0
$$411$$ 1.00000 + 1.73205i 0.0493264 + 0.0854358i
$$412$$ 0 0
$$413$$ −17.5000 6.06218i −0.861119 0.298300i
$$414$$ 0 0
$$415$$ −16.5000 28.5788i −0.809953 1.40288i
$$416$$ 0 0
$$417$$ 11.0000 19.0526i 0.538672 0.933008i
$$418$$ 0 0
$$419$$ −24.0000 −1.17248 −0.586238 0.810139i $$-0.699392\pi$$
−0.586238 + 0.810139i $$0.699392\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ 1.00000 1.73205i 0.0486217 0.0842152i
$$424$$ 0 0
$$425$$ −8.00000 13.8564i −0.388057 0.672134i
$$426$$ 0 0
$$427$$ 20.0000 17.3205i 0.967868 0.838198i
$$428$$ 0 0
$$429$$ −2.00000 3.46410i −0.0965609 0.167248i
$$430$$ 0 0
$$431$$ −4.00000 + 6.92820i −0.192673 + 0.333720i −0.946135 0.323772i $$-0.895049\pi$$
0.753462 + 0.657491i $$0.228382\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ −21.0000 −1.00687
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −7.50000 12.9904i −0.357955 0.619997i 0.629664 0.776868i $$-0.283193\pi$$
−0.987619 + 0.156871i $$0.949859\pi$$
$$440$$ 0 0
$$441$$ 5.50000 + 4.33013i 0.261905 + 0.206197i
$$442$$ 0 0
$$443$$ 10.5000 + 18.1865i 0.498870 + 0.864068i 0.999999 0.00130426i $$-0.000415158\pi$$
−0.501129 + 0.865373i $$0.667082\pi$$
$$444$$ 0 0
$$445$$ −9.00000 + 15.5885i −0.426641 + 0.738964i
$$446$$ 0 0
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ −12.0000 −0.566315 −0.283158 0.959073i $$-0.591382\pi$$
−0.283158 + 0.959073i $$0.591382\pi$$
$$450$$ 0 0
$$451$$ −2.00000 + 3.46410i −0.0941763 + 0.163118i
$$452$$ 0 0
$$453$$ −5.50000 9.52628i −0.258413 0.447584i
$$454$$ 0 0
$$455$$ −24.0000 + 20.7846i −1.12514 + 0.974398i
$$456$$ 0 0
$$457$$ 8.50000 + 14.7224i 0.397613 + 0.688686i 0.993431 0.114433i $$-0.0365053\pi$$
−0.595818 + 0.803120i $$0.703172\pi$$
$$458$$ 0 0
$$459$$ −2.00000 + 3.46410i −0.0933520 + 0.161690i
$$460$$ 0 0
$$461$$ −2.00000 −0.0931493 −0.0465746 0.998915i $$-0.514831\pi$$
−0.0465746 + 0.998915i $$0.514831\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ −16.5000 + 28.5788i −0.765169 + 1.32531i
$$466$$ 0 0
$$467$$ −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i $$-0.256221\pi$$
−0.970799 + 0.239892i $$0.922888\pi$$
$$468$$ 0 0
$$469$$ −25.0000 8.66025i −1.15439 0.399893i
$$470$$ 0 0
$$471$$ 6.00000 + 10.3923i 0.276465 + 0.478852i
$$472$$ 0 0
$$473$$ −1.00000 + 1.73205i −0.0459800 + 0.0796398i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −11.0000 −0.503655
$$478$$ 0 0
$$479$$ −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i $$-0.877103\pi$$
0.789314 + 0.613990i $$0.210436\pi$$
$$480$$ 0 0
$$481$$ 8.00000 + 13.8564i 0.364769 + 0.631798i
$$482$$ 0 0
$$483$$ 4.00000 + 20.7846i 0.182006 + 0.945732i
$$484$$ 0 0
$$485$$ −10.5000 18.1865i −0.476780 0.825808i
$$486$$ 0 0
$$487$$ 1.50000 2.59808i 0.0679715 0.117730i −0.830037 0.557709i $$-0.811681\pi$$
0.898008 + 0.439979i $$0.145014\pi$$
$$488$$ 0 0
$$489$$ −8.00000 −0.361773
$$490$$ 0 0
$$491$$ −37.0000 −1.66979 −0.834893 0.550412i $$-0.814471\pi$$
−0.834893 + 0.550412i $$0.814471\pi$$
$$492$$ 0 0
$$493$$ 14.0000 24.2487i 0.630528 1.09211i
$$494$$ 0 0
$$495$$ 1.50000 + 2.59808i 0.0674200 + 0.116775i
$$496$$ 0 0
$$497$$ 3.00000 + 15.5885i 0.134568 + 0.699238i
$$498$$ 0 0
$$499$$ −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i $$-0.238523\pi$$
−0.955968 + 0.293471i $$0.905190\pi$$
$$500$$ 0 0
$$501$$ 11.0000 19.0526i 0.491444 0.851206i
$$502$$ 0 0
$$503$$ 32.0000 1.42681 0.713405 0.700752i $$-0.247152\pi$$
0.713405 + 0.700752i $$0.247152\pi$$
$$504$$ 0 0
$$505$$ 18.0000 0.800989
$$506$$ 0 0
$$507$$ −1.50000 + 2.59808i −0.0666173 + 0.115385i
$$508$$ 0 0
$$509$$ 21.5000 + 37.2391i 0.952971 + 1.65059i 0.738945 + 0.673766i $$0.235324\pi$$
0.214026 + 0.976828i $$0.431342\pi$$
$$510$$ 0 0
$$511$$ 15.0000 + 5.19615i 0.663561 + 0.229864i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 24.0000 41.5692i 1.05757 1.83176i
$$516$$ 0 0
$$517$$ 2.00000 0.0879599
$$518$$ 0 0
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ −7.00000 + 12.1244i −0.306676 + 0.531178i −0.977633 0.210318i $$-0.932550\pi$$
0.670957 + 0.741496i $$0.265883\pi$$
$$522$$ 0 0
$$523$$ 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i $$-0.0226123\pi$$
−0.560208 + 0.828352i $$0.689279\pi$$
$$524$$ 0 0
$$525$$ 8.00000 6.92820i 0.349149 0.302372i
$$526$$ 0 0
$$527$$ −22.0000 38.1051i −0.958335 1.65989i
$$528$$ 0 0
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ 0 0
$$531$$ 7.00000 0.303774
$$532$$ 0 0
$$533$$ 16.0000 0.693037
$$534$$ 0 0
$$535$$ 10.5000 18.1865i 0.453955 0.786272i
$$536$$ 0 0
$$537$$ 6.00000 + 10.3923i 0.258919 + 0.448461i
$$538$$ 0 0
$$539$$ −1.00000 + 6.92820i −0.0430730 + 0.298419i
$$540$$ 0 0
$$541$$ 15.0000 + 25.9808i 0.644900 + 1.11700i 0.984325 + 0.176367i $$0.0564345\pi$$
−0.339424 + 0.940633i $$0.610232\pi$$
$$542$$ 0 0
$$543$$ −6.00000 + 10.3923i −0.257485 + 0.445976i
$$544$$ 0 0
$$545$$ 30.0000 1.28506
$$546$$ 0 0
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ 0 0
$$549$$ −5.00000 + 8.66025i −0.213395 + 0.369611i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 22.0000 19.0526i 0.935535 0.810197i
$$554$$ 0 0
$$555$$ −6.00000 10.3923i −0.254686 0.441129i
$$556$$ 0 0
$$557$$ −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i $$-0.853578\pi$$
0.832496 + 0.554031i $$0.186911\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ 0 0
$$563$$ −9.50000 + 16.4545i −0.400377 + 0.693474i −0.993771 0.111438i $$-0.964454\pi$$
0.593394 + 0.804912i $$0.297788\pi$$
$$564$$ 0 0
$$565$$ −18.0000 31.1769i −0.757266 1.31162i
$$566$$ 0 0
$$567$$ −2.50000 0.866025i −0.104990 0.0363696i
$$568$$ 0 0
$$569$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$570$$ 0 0
$$571$$ 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i $$-0.681062\pi$$
0.998978 + 0.0452101i $$0.0143957\pi$$
$$572$$ 0 0
$$573$$ 24.0000 1.00261
$$574$$ 0 0
$$575$$ 32.0000 1.33449
$$576$$ 0 0
$$577$$ 8.50000 14.7224i 0.353860 0.612903i −0.633062 0.774101i $$-0.718202\pi$$
0.986922 + 0.161198i $$0.0515357\pi$$
$$578$$ 0 0
$$579$$ 9.50000 + 16.4545i 0.394807 + 0.683825i
$$580$$ 0 0
$$581$$ 5.50000 + 28.5788i 0.228178 + 1.18565i
$$582$$ 0 0
$$583$$ −5.50000 9.52628i −0.227787 0.394538i
$$584$$ 0 0
$$585$$ 6.00000 10.3923i 0.248069 0.429669i
$$586$$ 0 0
$$587$$ −15.0000 −0.619116 −0.309558 0.950881i $$-0.600181\pi$$
−0.309558 + 0.950881i $$0.600181\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −3.00000 + 5.19615i −0.123404 + 0.213741i
$$592$$ 0 0
$$593$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$594$$ 0 0
$$595$$ 6.00000 + 31.1769i 0.245976 + 1.27813i
$$596$$ 0 0
$$597$$ 10.0000 + 17.3205i 0.409273 + 0.708881i
$$598$$ 0 0
$$599$$ −9.00000 + 15.5885i −0.367730 + 0.636927i −0.989210 0.146503i $$-0.953198\pi$$
0.621480 + 0.783430i $$0.286532\pi$$
$$600$$ 0 0
$$601$$ −37.0000 −1.50926 −0.754631 0.656150i $$-0.772184\pi$$
−0.754631 + 0.656150i $$0.772184\pi$$
$$602$$ 0 0
$$603$$ 10.0000 0.407231
$$604$$ 0 0
$$605$$ 15.0000 25.9808i 0.609837 1.05627i
$$606$$ 0 0
$$607$$ 13.5000 + 23.3827i 0.547948 + 0.949074i 0.998415 + 0.0562808i $$0.0179242\pi$$
−0.450467 + 0.892793i $$0.648742\pi$$
$$608$$ 0 0
$$609$$ 17.5000 + 6.06218i 0.709136 + 0.245652i
$$610$$ 0 0
$$611$$ −4.00000 6.92820i −0.161823 0.280285i
$$612$$ 0 0
$$613$$ 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i $$-0.728603\pi$$
0.981129 + 0.193352i $$0.0619359\pi$$
$$614$$ 0 0
$$615$$ −12.0000 −0.483887
$$616$$ 0 0
$$617$$ 22.0000 0.885687 0.442843 0.896599i $$-0.353970\pi$$
0.442843 + 0.896599i $$0.353970\pi$$
$$618$$ 0 0
$$619$$ 11.0000 19.0526i 0.442127 0.765787i −0.555720 0.831370i $$-0.687557\pi$$
0.997847 + 0.0655827i $$0.0208906\pi$$
$$620$$ 0 0
$$621$$ −4.00000 6.92820i −0.160514 0.278019i
$$622$$ 0 0
$$623$$ 12.0000 10.3923i 0.480770 0.416359i
$$624$$ 0 0
$$625$$ 14.5000 + 25.1147i 0.580000 + 1.00459i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ −43.0000 −1.71180 −0.855901 0.517139i $$-0.826997\pi$$
−0.855901 + 0.517139i $$0.826997\pi$$
$$632$$ 0 0
$$633$$ −1.00000 + 1.73205i −0.0397464 + 0.0688428i
$$634$$ 0 0
$$635$$ −25.5000 44.1673i −1.01194 1.75273i
$$636$$ 0 0
$$637$$ 26.0000 10.3923i 1.03016 0.411758i
$$638$$ 0 0
$$639$$ −3.00000 5.19615i −0.118678 0.205557i
$$640$$ 0 0
$$641$$ 5.00000 8.66025i 0.197488 0.342059i −0.750225 0.661182i $$-0.770055\pi$$
0.947713 + 0.319123i $$0.103388\pi$$
$$642$$ 0 0
$$643$$ 2.00000 0.0788723 0.0394362 0.999222i $$-0.487444\pi$$
0.0394362 + 0.999222i $$0.487444\pi$$
$$644$$ 0 0
$$645$$ −6.00000 −0.236250
$$646$$ 0 0
$$647$$ 15.0000 25.9808i 0.589711 1.02141i −0.404559 0.914512i $$-0.632575\pi$$
0.994270 0.106897i $$-0.0340916\pi$$
$$648$$ 0 0
$$649$$ 3.50000 + 6.06218i 0.137387 + 0.237961i
$$650$$ 0 0
$$651$$ 22.0000 19.0526i 0.862248 0.746729i
$$652$$ 0 0
$$653$$ −21.5000 37.2391i −0.841360 1.45728i −0.888745 0.458402i $$-0.848422\pi$$
0.0473852 0.998877i $$-0.484911\pi$$
$$654$$ 0 0
$$655$$ −4.50000 + 7.79423i −0.175830 + 0.304546i
$$656$$ 0 0
$$657$$ −6.00000 −0.234082
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 21.0000 36.3731i 0.816805 1.41475i −0.0912190 0.995831i $$-0.529076\pi$$
0.908024 0.418917i $$-0.137590\pi$$
$$662$$ 0 0
$$663$$ 8.00000 + 13.8564i 0.310694 + 0.538138i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 28.0000 + 48.4974i 1.08416 + 1.87783i
$$668$$ 0 0
$$669$$ −4.50000 + 7.79423i −0.173980 + 0.301342i
$$670$$ 0 0
$$671$$ −10.0000 −0.386046
$$672$$ 0 0
$$673$$ 45.0000 1.73462 0.867311 0.497766i $$-0.165846\pi$$
0.867311 + 0.497766i $$0.165846\pi$$
$$674$$ 0 0
$$675$$ −2.00000 + 3.46410i −0.0769800 + 0.133333i
$$676$$ 0 0
$$677$$ −7.50000 12.9904i −0.288248 0.499261i 0.685143 0.728408i $$-0.259740\pi$$
−0.973392 + 0.229147i $$0.926406\pi$$
$$678$$ 0 0
$$679$$ 3.50000 + 18.1865i 0.134318 + 0.697935i
$$680$$ 0 0
$$681$$ 3.50000 + 6.06218i 0.134120 + 0.232303i
$$682$$ 0 0
$$683$$ −10.5000 + 18.1865i −0.401771 + 0.695888i −0.993940 0.109926i $$-0.964939\pi$$
0.592168 + 0.805814i $$0.298272\pi$$
$$684$$ 0 0
$$685$$ −6.00000 −0.229248
$$686$$ 0 0
$$687$$ −8.00000 −0.305219
$$688$$ 0 0
$$689$$ −22.0000 + 38.1051i −0.838133 + 1.45169i
$$690$$ 0 0
$$691$$ −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i $$-0.290887\pi$$
−0.991122 + 0.132956i $$0.957553\pi$$
$$692$$ 0 0
$$693$$ −0.500000 2.59808i −0.0189934 0.0986928i
$$694$$ 0 0
$$695$$ 33.0000 + 57.1577i 1.25176 + 2.16811i
$$696$$ 0 0
$$697$$ 8.00000 13.8564i 0.303022 0.524849i
$$698$$ 0 0
$$699$$ 12.0000 0.453882
$$700$$ 0 0
$$701$$ 33.0000 1.24639 0.623196 0.782065i $$-0.285834\pi$$
0.623196 + 0.782065i $$0.285834\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 3.00000 + 5.19615i 0.112987 + 0.195698i
$$706$$ 0 0
$$707$$ −15.0000 5.19615i −0.564133 0.195421i
$$708$$ 0 0
$$709$$ 17.0000 + 29.4449i 0.638448 + 1.10583i 0.985773 + 0.168080i $$0.0537568\pi$$
−0.347325 + 0.937745i $$0.612910\pi$$
$$710$$ 0 0
$$711$$ −5.50000 + 9.52628i −0.206266 + 0.357263i
$$712$$ 0 0
$$713$$ 88.0000 3.29563
$$714$$ 0 0
$$715$$ 12.0000 0.448775
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 9.00000 + 15.5885i 0.335643 + 0.581351i 0.983608 0.180319i $$-0.0577130\pi$$
−0.647965 + 0.761670i $$0.724380\pi$$
$$720$$ 0 0
$$721$$ −32.0000 + 27.7128i −1.19174 + 1.03208i
$$722$$ 0 0
$$723$$ 12.5000 + 21.6506i 0.464880 + 0.805196i
$$724$$ 0 0
$$725$$ 14.0000 24.2487i 0.519947 0.900575i
$$726$$ 0 0
$$727$$ 7.00000 0.259616 0.129808 0.991539i $$-0.458564\pi$$
0.129808 + 0.991539i $$0.458564\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 4.00000 6.92820i 0.147945 0.256249i
$$732$$ 0 0
$$733$$ −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i $$-0.249912\pi$$
−0.965854 + 0.259087i $$0.916578\pi$$
$$734$$ 0 0
$$735$$ −19.5000 + 7.79423i −0.719268 + 0.287494i
$$736$$ 0 0
$$737$$ 5.00000 + 8.66025i 0.184177 + 0.319005i
$$738$$ 0 0
$$739$$ −17.0000 + 29.4449i −0.625355 + 1.08315i 0.363117 + 0.931744i $$0.381713\pi$$
−0.988472 + 0.151403i $$0.951621\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −50.0000 −1.83432 −0.917161 0.398517i $$-0.869525\pi$$
−0.917161 + 0.398517i $$0.869525\pi$$
$$744$$ 0 0
$$745$$ 9.00000 15.5885i 0.329734 0.571117i
$$746$$ 0 0
$$747$$ −5.50000 9.52628i −0.201234 0.348548i
$$748$$ 0 0
$$749$$ −14.0000 + 12.1244i −0.511549 + 0.443014i
$$750$$ 0 0
$$751$$ 1.50000 + 2.59808i 0.0547358 + 0.0948051i 0.892095 0.451848i $$-0.149235\pi$$
−0.837359 + 0.546653i $$0.815902\pi$$
$$752$$ 0 0
$$753$$ 12.5000 21.6506i 0.455525 0.788993i
$$754$$ 0 0
$$755$$ 33.0000 1.20099
$$756$$ 0 0
$$757$$ −14.0000 −0.508839 −0.254419 0.967094i $$-0.581884\pi$$
−0.254419 + 0.967094i $$0.581884\pi$$
$$758$$ 0 0
$$759$$ 4.00000 6.92820i 0.145191 0.251478i
$$760$$ 0 0
$$761$$ 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i $$-0.0968765\pi$$
−0.736543 + 0.676391i $$0.763543\pi$$
$$762$$ 0 0
$$763$$ −25.0000 8.66025i −0.905061 0.313522i
$$764$$ 0 0
$$765$$ −6.00000 10.3923i −0.216930 0.375735i
$$766$$ 0 0
$$767$$ 14.0000 24.2487i 0.505511 0.875570i
$$768$$ 0 0
$$769$$ −3.00000 −0.108183 −0.0540914 0.998536i $$-0.517226\pi$$
−0.0540914 + 0.998536i $$0.517226\pi$$
$$770$$ 0 0
$$771$$ 14.0000 0.504198
$$772$$ 0 0
$$773$$ −15.0000 + 25.9808i −0.539513 + 0.934463i 0.459418 + 0.888220i $$0.348058\pi$$
−0.998930 + 0.0462427i $$0.985275\pi$$
$$774$$ 0 0
$$775$$ −22.0000 38.1051i −0.790263 1.36878i
$$776$$ 0 0
$$777$$ 2.00000 + 10.3923i 0.0717496 + 0.372822i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 3.00000 5.19615i 0.107348 0.185933i
$$782$$ 0 0
$$783$$ −7.00000 −0.250160
$$784$$ 0 0
$$785$$ −36.0000 −1.28490
$$786$$ 0 0
$$787$$ 17.0000 29.4449i 0.605985 1.04960i −0.385911 0.922536i $$-0.626113\pi$$
0.991895 0.127060i $$-0.0405540\pi$$
$$788$$ 0 0
$$789$$ −13.0000 22.5167i −0.462812 0.801614i
$$790$$ 0 0
$$791$$ 6.00000 + 31.1769i 0.213335 + 1.10852i
$$792$$ 0 0
$$793$$ 20.0000 + 34.6410i 0.710221 + 1.23014i
$$794$$ 0 0
$$795$$ 16.5000 28.5788i 0.585195 1.01359i
$$796$$ 0 0
$$797$$ −25.0000 −0.885545