Properties

 Label 252.2.w.a.5.6 Level $252$ Weight $2$ Character 252.5 Analytic conductor $2.012$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 252.w (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$2.01223013094$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$3^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 5.6 Root $$1.68124 - 0.416458i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.5 Dual form 252.2.w.a.101.6

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.06740 - 1.36406i) q^{3} +(0.349828 + 0.605920i) q^{5} +(2.48683 + 0.903137i) q^{7} +(-0.721326 - 2.91199i) q^{9} +O(q^{10})$$ $$q+(1.06740 - 1.36406i) q^{3} +(0.349828 + 0.605920i) q^{5} +(2.48683 + 0.903137i) q^{7} +(-0.721326 - 2.91199i) q^{9} +(0.229685 + 0.132608i) q^{11} +(1.13823 + 0.657156i) q^{13} +(1.19992 + 0.169570i) q^{15} +(-1.86392 - 3.22840i) q^{17} +(-0.382449 - 0.220807i) q^{19} +(3.88637 - 2.42819i) q^{21} +(-4.29949 + 2.48231i) q^{23} +(2.25524 - 3.90619i) q^{25} +(-4.74208 - 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} +5.60632i q^{31} +(0.426051 - 0.171758i) q^{33} +(0.322736 + 1.82276i) q^{35} +(-0.351124 + 0.608164i) q^{37} +(2.11134 - 0.851166i) q^{39} +(-5.39354 + 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(1.51209 - 1.45576i) q^{45} -7.00570 q^{47} +(5.36869 + 4.49190i) q^{49} +(-6.39328 - 0.903488i) q^{51} +(8.51919 - 4.91856i) q^{53} +0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} -13.4636 q^{59} -5.65207i q^{61} +(0.836106 - 7.89309i) q^{63} +0.919566i q^{65} -5.94120 q^{67} +(-1.20324 + 8.51439i) q^{69} +13.4323i q^{71} +(-6.66182 + 3.84620i) q^{73} +(-2.92105 - 7.24575i) q^{75} +(0.451424 + 0.537212i) q^{77} +1.39672 q^{79} +(-7.95938 + 4.20099i) q^{81} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(-0.0764809 + 0.541196i) q^{87} +(5.59261 - 9.68668i) q^{89} +(2.23708 + 2.66221i) q^{91} +(7.64736 + 5.98417i) q^{93} -0.308978i q^{95} +(-9.18225 + 5.30138i) q^{97} +(0.220477 - 0.764493i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - q^{7} + 6q^{9} + O(q^{10})$$ $$16q - q^{7} + 6q^{9} - 6q^{11} - 3q^{13} - 3q^{15} + 9q^{17} + 6q^{21} + 21q^{23} - 8q^{25} + 9q^{27} + 6q^{29} - 15q^{35} + q^{37} - 3q^{39} - 6q^{41} - 2q^{43} - 30q^{45} - 36q^{47} - 5q^{49} - 33q^{51} + 15q^{57} - 30q^{59} - 15q^{63} + 14q^{67} + 21q^{69} - 57q^{75} + 3q^{77} + 2q^{79} + 18q^{81} + 6q^{85} + 48q^{87} + 21q^{89} + 9q^{91} + 21q^{93} - 3q^{97} - 9q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

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 0
$$3$$ 1.06740 1.36406i 0.616262 0.787541i
$$4$$ 0 0
$$5$$ 0.349828 + 0.605920i 0.156448 + 0.270975i 0.933585 0.358355i $$-0.116662\pi$$
−0.777137 + 0.629331i $$0.783329\pi$$
$$6$$ 0 0
$$7$$ 2.48683 + 0.903137i 0.939935 + 0.341354i
$$8$$ 0 0
$$9$$ −0.721326 2.91199i −0.240442 0.970663i
$$10$$ 0 0
$$11$$ 0.229685 + 0.132608i 0.0692525 + 0.0399829i 0.534226 0.845341i $$-0.320603\pi$$
−0.464974 + 0.885324i $$0.653936\pi$$
$$12$$ 0 0
$$13$$ 1.13823 + 0.657156i 0.315688 + 0.182262i 0.649469 0.760388i $$-0.274991\pi$$
−0.333781 + 0.942651i $$0.608325\pi$$
$$14$$ 0 0
$$15$$ 1.19992 + 0.169570i 0.309817 + 0.0437829i
$$16$$ 0 0
$$17$$ −1.86392 3.22840i −0.452067 0.783003i 0.546447 0.837493i $$-0.315980\pi$$
−0.998514 + 0.0544906i $$0.982646\pi$$
$$18$$ 0 0
$$19$$ −0.382449 0.220807i −0.0877398 0.0506566i 0.455488 0.890242i $$-0.349465\pi$$
−0.543228 + 0.839585i $$0.682798\pi$$
$$20$$ 0 0
$$21$$ 3.88637 2.42819i 0.848076 0.529874i
$$22$$ 0 0
$$23$$ −4.29949 + 2.48231i −0.896507 + 0.517598i −0.876065 0.482193i $$-0.839840\pi$$
−0.0204414 + 0.999791i $$0.506507\pi$$
$$24$$ 0 0
$$25$$ 2.25524 3.90619i 0.451048 0.781238i
$$26$$ 0 0
$$27$$ −4.74208 2.12432i −0.912613 0.408825i
$$28$$ 0 0
$$29$$ −0.273287 + 0.157782i −0.0507480 + 0.0292994i −0.525159 0.851004i $$-0.675994\pi$$
0.474411 + 0.880303i $$0.342661\pi$$
$$30$$ 0 0
$$31$$ 5.60632i 1.00692i 0.864017 + 0.503462i $$0.167941\pi$$
−0.864017 + 0.503462i $$0.832059\pi$$
$$32$$ 0 0
$$33$$ 0.426051 0.171758i 0.0741659 0.0298992i
$$34$$ 0 0
$$35$$ 0.322736 + 1.82276i 0.0545523 + 0.308103i
$$36$$ 0 0
$$37$$ −0.351124 + 0.608164i −0.0577244 + 0.0999816i −0.893444 0.449175i $$-0.851718\pi$$
0.835719 + 0.549157i $$0.185051\pi$$
$$38$$ 0 0
$$39$$ 2.11134 0.851166i 0.338085 0.136296i
$$40$$ 0 0
$$41$$ −5.39354 + 9.34189i −0.842330 + 1.45896i 0.0455900 + 0.998960i $$0.485483\pi$$
−0.887920 + 0.459998i $$0.847850\pi$$
$$42$$ 0 0
$$43$$ 3.73131 + 6.46283i 0.569020 + 0.985572i 0.996663 + 0.0816240i $$0.0260106\pi$$
−0.427643 + 0.903948i $$0.640656\pi$$
$$44$$ 0 0
$$45$$ 1.51209 1.45576i 0.225409 0.217012i
$$46$$ 0 0
$$47$$ −7.00570 −1.02189 −0.510943 0.859614i $$-0.670704\pi$$
−0.510943 + 0.859614i $$0.670704\pi$$
$$48$$ 0 0
$$49$$ 5.36869 + 4.49190i 0.766955 + 0.641700i
$$50$$ 0 0
$$51$$ −6.39328 0.903488i −0.895239 0.126514i
$$52$$ 0 0
$$53$$ 8.51919 4.91856i 1.17020 0.675616i 0.216474 0.976288i $$-0.430544\pi$$
0.953727 + 0.300672i $$0.0972111\pi$$
$$54$$ 0 0
$$55$$ 0.185561i 0.0250210i
$$56$$ 0 0
$$57$$ −0.709419 + 0.285995i −0.0939648 + 0.0378809i
$$58$$ 0 0
$$59$$ −13.4636 −1.75282 −0.876408 0.481570i $$-0.840067\pi$$
−0.876408 + 0.481570i $$0.840067\pi$$
$$60$$ 0 0
$$61$$ 5.65207i 0.723674i −0.932241 0.361837i $$-0.882150\pi$$
0.932241 0.361837i $$-0.117850\pi$$
$$62$$ 0 0
$$63$$ 0.836106 7.89309i 0.105340 0.994436i
$$64$$ 0 0
$$65$$ 0.919566i 0.114058i
$$66$$ 0 0
$$67$$ −5.94120 −0.725833 −0.362916 0.931822i $$-0.618219\pi$$
−0.362916 + 0.931822i $$0.618219\pi$$
$$68$$ 0 0
$$69$$ −1.20324 + 8.51439i −0.144853 + 1.02501i
$$70$$ 0 0
$$71$$ 13.4323i 1.59412i 0.603900 + 0.797060i $$0.293613\pi$$
−0.603900 + 0.797060i $$0.706387\pi$$
$$72$$ 0 0
$$73$$ −6.66182 + 3.84620i −0.779707 + 0.450164i −0.836326 0.548232i $$-0.815301\pi$$
0.0566194 + 0.998396i $$0.481968\pi$$
$$74$$ 0 0
$$75$$ −2.92105 7.24575i −0.337293 0.836667i
$$76$$ 0 0
$$77$$ 0.451424 + 0.537212i 0.0514445 + 0.0612210i
$$78$$ 0 0
$$79$$ 1.39672 0.157143 0.0785716 0.996908i $$-0.474964\pi$$
0.0785716 + 0.996908i $$0.474964\pi$$
$$80$$ 0 0
$$81$$ −7.95938 + 4.20099i −0.884375 + 0.466777i
$$82$$ 0 0
$$83$$ −3.72399 6.45014i −0.408761 0.707995i 0.585990 0.810318i $$-0.300706\pi$$
−0.994751 + 0.102323i $$0.967372\pi$$
$$84$$ 0 0
$$85$$ 1.30410 2.25877i 0.141450 0.244998i
$$86$$ 0 0
$$87$$ −0.0764809 + 0.541196i −0.00819961 + 0.0580223i
$$88$$ 0 0
$$89$$ 5.59261 9.68668i 0.592815 1.02679i −0.401036 0.916062i $$-0.631350\pi$$
0.993851 0.110724i $$-0.0353168\pi$$
$$90$$ 0 0
$$91$$ 2.23708 + 2.66221i 0.234510 + 0.279076i
$$92$$ 0 0
$$93$$ 7.64736 + 5.98417i 0.792995 + 0.620529i
$$94$$ 0 0
$$95$$ 0.308978i 0.0317004i
$$96$$ 0 0
$$97$$ −9.18225 + 5.30138i −0.932316 + 0.538273i −0.887543 0.460724i $$-0.847590\pi$$
−0.0447729 + 0.998997i $$0.514256\pi$$
$$98$$ 0 0
$$99$$ 0.220477 0.764493i 0.0221588 0.0768345i
$$100$$ 0 0
$$101$$ 8.75357 15.1616i 0.871013 1.50864i 0.0100634 0.999949i $$-0.496797\pi$$
0.860950 0.508690i $$-0.169870\pi$$
$$102$$ 0 0
$$103$$ 7.39775 4.27110i 0.728922 0.420844i −0.0891054 0.996022i $$-0.528401\pi$$
0.818028 + 0.575179i $$0.195067\pi$$
$$104$$ 0 0
$$105$$ 2.83085 + 1.50538i 0.276263 + 0.146910i
$$106$$ 0 0
$$107$$ 9.09489 + 5.25093i 0.879236 + 0.507627i 0.870406 0.492334i $$-0.163856\pi$$
0.00882940 + 0.999961i $$0.497189\pi$$
$$108$$ 0 0
$$109$$ −7.12110 12.3341i −0.682078 1.18139i −0.974346 0.225057i $$-0.927743\pi$$
0.292268 0.956337i $$-0.405590\pi$$
$$110$$ 0 0
$$111$$ 0.454785 + 1.12811i 0.0431663 + 0.107075i
$$112$$ 0 0
$$113$$ 13.3783 + 7.72396i 1.25852 + 0.726609i 0.972788 0.231699i $$-0.0744284\pi$$
0.285737 + 0.958308i $$0.407762\pi$$
$$114$$ 0 0
$$115$$ −3.00817 1.73677i −0.280513 0.161954i
$$116$$ 0 0
$$117$$ 1.09260 3.78853i 0.101011 0.350250i
$$118$$ 0 0
$$119$$ −1.71957 9.71188i −0.157633 0.890286i
$$120$$ 0 0
$$121$$ −5.46483 9.46536i −0.496803 0.860488i
$$122$$ 0 0
$$123$$ 6.98586 + 17.3286i 0.629894 + 1.56247i
$$124$$ 0 0
$$125$$ 6.65406 0.595157
$$126$$ 0 0
$$127$$ 21.8304 1.93713 0.968566 0.248758i $$-0.0800225\pi$$
0.968566 + 0.248758i $$0.0800225\pi$$
$$128$$ 0 0
$$129$$ 12.7985 + 1.80866i 1.12684 + 0.159244i
$$130$$ 0 0
$$131$$ 2.60461 + 4.51132i 0.227566 + 0.394156i 0.957086 0.289803i $$-0.0935899\pi$$
−0.729520 + 0.683959i $$0.760257\pi$$
$$132$$ 0 0
$$133$$ −0.751668 0.894514i −0.0651779 0.0775642i
$$134$$ 0 0
$$135$$ −0.371744 3.61646i −0.0319947 0.311255i
$$136$$ 0 0
$$137$$ −2.33589 1.34863i −0.199568 0.115221i 0.396886 0.917868i $$-0.370091\pi$$
−0.596454 + 0.802647i $$0.703424\pi$$
$$138$$ 0 0
$$139$$ −10.1448 5.85710i −0.860470 0.496793i 0.00369951 0.999993i $$-0.498822\pi$$
−0.864170 + 0.503200i $$0.832156\pi$$
$$140$$ 0 0
$$141$$ −7.47787 + 9.55621i −0.629750 + 0.804778i
$$142$$ 0 0
$$143$$ 0.174289 + 0.301877i 0.0145748 + 0.0252442i
$$144$$ 0 0
$$145$$ −0.191206 0.110393i −0.0158788 0.00916765i
$$146$$ 0 0
$$147$$ 11.8578 2.52858i 0.978011 0.208553i
$$148$$ 0 0
$$149$$ 16.3055 9.41399i 1.33580 0.771224i 0.349618 0.936892i $$-0.386311\pi$$
0.986182 + 0.165668i $$0.0529781\pi$$
$$150$$ 0 0
$$151$$ −5.00143 + 8.66273i −0.407010 + 0.704963i −0.994553 0.104230i $$-0.966762\pi$$
0.587543 + 0.809193i $$0.300095\pi$$
$$152$$ 0 0
$$153$$ −8.05659 + 7.75645i −0.651336 + 0.627072i
$$154$$ 0 0
$$155$$ −3.39698 + 1.96125i −0.272852 + 0.157531i
$$156$$ 0 0
$$157$$ 0.252063i 0.0201168i 0.999949 + 0.0100584i $$0.00320175\pi$$
−0.999949 + 0.0100584i $$0.996798\pi$$
$$158$$ 0 0
$$159$$ 2.38415 16.8708i 0.189075 1.33794i
$$160$$ 0 0
$$161$$ −12.9340 + 2.29007i −1.01934 + 0.180483i
$$162$$ 0 0
$$163$$ 4.29780 7.44400i 0.336629 0.583059i −0.647167 0.762348i $$-0.724046\pi$$
0.983796 + 0.179289i $$0.0573797\pi$$
$$164$$ 0 0
$$165$$ 0.253116 + 0.198067i 0.0197050 + 0.0154195i
$$166$$ 0 0
$$167$$ 2.24437 3.88736i 0.173674 0.300813i −0.766027 0.642808i $$-0.777769\pi$$
0.939702 + 0.341995i $$0.111103\pi$$
$$168$$ 0 0
$$169$$ −5.63629 9.76234i −0.433561 0.750949i
$$170$$ 0 0
$$171$$ −0.367117 + 1.27296i −0.0280742 + 0.0973457i
$$172$$ 0 0
$$173$$ −7.12145 −0.541434 −0.270717 0.962659i $$-0.587261\pi$$
−0.270717 + 0.962659i $$0.587261\pi$$
$$174$$ 0 0
$$175$$ 9.13624 7.67726i 0.690634 0.580346i
$$176$$ 0 0
$$177$$ −14.3710 + 18.3652i −1.08019 + 1.38041i
$$178$$ 0 0
$$179$$ 22.1270 12.7750i 1.65385 0.954848i 0.678376 0.734715i $$-0.262684\pi$$
0.975470 0.220134i $$-0.0706494\pi$$
$$180$$ 0 0
$$181$$ 0.943175i 0.0701057i 0.999385 + 0.0350528i $$0.0111599\pi$$
−0.999385 + 0.0350528i $$0.988840\pi$$
$$182$$ 0 0
$$183$$ −7.70977 6.03301i −0.569923 0.445973i
$$184$$ 0 0
$$185$$ −0.491332 −0.0361234
$$186$$ 0 0
$$187$$ 0.988686i 0.0722999i
$$188$$ 0 0
$$189$$ −9.87421 9.56557i −0.718243 0.695793i
$$190$$ 0 0
$$191$$ 2.97235i 0.215072i 0.994201 + 0.107536i $$0.0342960\pi$$
−0.994201 + 0.107536i $$0.965704\pi$$
$$192$$ 0 0
$$193$$ −18.5144 −1.33270 −0.666348 0.745641i $$-0.732144\pi$$
−0.666348 + 0.745641i $$0.732144\pi$$
$$194$$ 0 0
$$195$$ 1.25434 + 0.981542i 0.0898255 + 0.0702897i
$$196$$ 0 0
$$197$$ 14.1774i 1.01010i 0.863091 + 0.505048i $$0.168525\pi$$
−0.863091 + 0.505048i $$0.831475\pi$$
$$198$$ 0 0
$$199$$ −20.5293 + 11.8526i −1.45529 + 0.840209i −0.998774 0.0495081i $$-0.984235\pi$$
−0.456512 + 0.889717i $$0.650901\pi$$
$$200$$ 0 0
$$201$$ −6.34162 + 8.10416i −0.447303 + 0.571623i
$$202$$ 0 0
$$203$$ −0.822117 + 0.145563i −0.0577013 + 0.0102165i
$$204$$ 0 0
$$205$$ −7.54725 −0.527123
$$206$$ 0 0
$$207$$ 10.3298 + 10.7295i 0.717972 + 0.745754i
$$208$$ 0 0
$$209$$ −0.0585617 0.101432i −0.00405080 0.00701619i
$$210$$ 0 0
$$211$$ 3.04004 5.26550i 0.209285 0.362492i −0.742205 0.670173i $$-0.766220\pi$$
0.951489 + 0.307681i $$0.0995531\pi$$
$$212$$ 0 0
$$213$$ 18.3225 + 14.3376i 1.25544 + 0.982396i
$$214$$ 0 0
$$215$$ −2.61063 + 4.52175i −0.178044 + 0.308381i
$$216$$ 0 0
$$217$$ −5.06327 + 13.9420i −0.343717 + 0.946444i
$$218$$ 0 0
$$219$$ −1.86435 + 13.1926i −0.125981 + 0.891470i
$$220$$ 0 0
$$221$$ 4.89954i 0.329579i
$$222$$ 0 0
$$223$$ 0.796137 0.459650i 0.0533133 0.0307804i −0.473106 0.881005i $$-0.656867\pi$$
0.526420 + 0.850225i $$0.323534\pi$$
$$224$$ 0 0
$$225$$ −13.0016 3.74960i −0.866771 0.249973i
$$226$$ 0 0
$$227$$ 5.00297 8.66540i 0.332059 0.575143i −0.650857 0.759201i $$-0.725590\pi$$
0.982915 + 0.184058i $$0.0589234\pi$$
$$228$$ 0 0
$$229$$ −2.38179 + 1.37513i −0.157393 + 0.0908710i −0.576628 0.817007i $$-0.695632\pi$$
0.419235 + 0.907878i $$0.362298\pi$$
$$230$$ 0 0
$$231$$ 1.21464 0.0423515i 0.0799173 0.00278652i
$$232$$ 0 0
$$233$$ −5.55513 3.20725i −0.363928 0.210114i 0.306874 0.951750i $$-0.400717\pi$$
−0.670803 + 0.741636i $$0.734050\pi$$
$$234$$ 0 0
$$235$$ −2.45079 4.24489i −0.159872 0.276906i
$$236$$ 0 0
$$237$$ 1.49085 1.90521i 0.0968414 0.123757i
$$238$$ 0 0
$$239$$ −11.4288 6.59844i −0.739270 0.426818i 0.0825337 0.996588i $$-0.473699\pi$$
−0.821804 + 0.569770i $$0.807032\pi$$
$$240$$ 0 0
$$241$$ −2.20722 1.27434i −0.142180 0.0820874i 0.427223 0.904146i $$-0.359492\pi$$
−0.569402 + 0.822059i $$0.692825\pi$$
$$242$$ 0 0
$$243$$ −2.76541 + 15.3412i −0.177401 + 0.984139i
$$244$$ 0 0
$$245$$ −0.843615 + 4.82439i −0.0538966 + 0.308219i
$$246$$ 0 0
$$247$$ −0.290209 0.502657i −0.0184656 0.0319833i
$$248$$ 0 0
$$249$$ −12.7734 1.80511i −0.809479 0.114394i
$$250$$ 0 0
$$251$$ 18.7893 1.18597 0.592986 0.805213i $$-0.297949\pi$$
0.592986 + 0.805213i $$0.297949\pi$$
$$252$$ 0 0
$$253$$ −1.31670 −0.0827804
$$254$$ 0 0
$$255$$ −1.68911 4.18988i −0.105776 0.262380i
$$256$$ 0 0
$$257$$ 7.19727 + 12.4660i 0.448953 + 0.777610i 0.998318 0.0579725i $$-0.0184636\pi$$
−0.549365 + 0.835583i $$0.685130\pi$$
$$258$$ 0 0
$$259$$ −1.42244 + 1.19529i −0.0883863 + 0.0742718i
$$260$$ 0 0
$$261$$ 0.656589 + 0.681995i 0.0406418 + 0.0422145i
$$262$$ 0 0
$$263$$ 6.79810 + 3.92488i 0.419189 + 0.242019i 0.694730 0.719271i $$-0.255524\pi$$
−0.275542 + 0.961289i $$0.588857\pi$$
$$264$$ 0 0
$$265$$ 5.96050 + 3.44130i 0.366151 + 0.211397i
$$266$$ 0 0
$$267$$ −7.24369 17.9682i −0.443307 1.09964i
$$268$$ 0 0
$$269$$ −7.72267 13.3760i −0.470859 0.815552i 0.528585 0.848880i $$-0.322723\pi$$
−0.999444 + 0.0333281i $$0.989389\pi$$
$$270$$ 0 0
$$271$$ 10.9476 + 6.32057i 0.665016 + 0.383947i 0.794186 0.607675i $$-0.207898\pi$$
−0.129169 + 0.991623i $$0.541231\pi$$
$$272$$ 0 0
$$273$$ 6.01928 0.209878i 0.364303 0.0127024i
$$274$$ 0 0
$$275$$ 1.03599 0.598128i 0.0624724 0.0360685i
$$276$$ 0 0
$$277$$ 5.94531 10.2976i 0.357219 0.618722i −0.630276 0.776371i $$-0.717058\pi$$
0.987495 + 0.157649i $$0.0503915\pi$$
$$278$$ 0 0
$$279$$ 16.3255 4.04399i 0.977385 0.242107i
$$280$$ 0 0
$$281$$ −2.75411 + 1.59009i −0.164297 + 0.0948568i −0.579894 0.814692i $$-0.696906\pi$$
0.415597 + 0.909549i $$0.363573\pi$$
$$282$$ 0 0
$$283$$ 18.4978i 1.09958i 0.835303 + 0.549789i $$0.185292\pi$$
−0.835303 + 0.549789i $$0.814708\pi$$
$$284$$ 0 0
$$285$$ −0.421464 0.329802i −0.0249654 0.0195358i
$$286$$ 0 0
$$287$$ −21.8499 + 18.3606i −1.28976 + 1.08379i
$$288$$ 0 0
$$289$$ 1.55161 2.68746i 0.0912711 0.158086i
$$290$$ 0 0
$$291$$ −2.56971 + 18.1838i −0.150639 + 1.06595i
$$292$$ 0 0
$$293$$ −1.42975 + 2.47639i −0.0835266 + 0.144672i −0.904762 0.425917i $$-0.859952\pi$$
0.821236 + 0.570589i $$0.193285\pi$$
$$294$$ 0 0
$$295$$ −4.70995 8.15788i −0.274224 0.474970i
$$296$$ 0 0
$$297$$ −0.807479 1.11676i −0.0468547 0.0648011i
$$298$$ 0 0
$$299$$ −6.52507 −0.377355
$$300$$ 0 0
$$301$$ 3.44234 + 19.4419i 0.198413 + 1.12061i
$$302$$ 0 0
$$303$$ −11.3379 28.1239i −0.651343 1.61568i
$$304$$ 0 0
$$305$$ 3.42470 1.97725i 0.196098 0.113217i
$$306$$ 0 0
$$307$$ 21.6746i 1.23704i −0.785771 0.618518i $$-0.787734\pi$$
0.785771 0.618518i $$-0.212266\pi$$
$$308$$ 0 0
$$309$$ 2.07031 14.6499i 0.117776 0.833406i
$$310$$ 0 0
$$311$$ −23.6925 −1.34348 −0.671738 0.740789i $$-0.734452\pi$$
−0.671738 + 0.740789i $$0.734452\pi$$
$$312$$ 0 0
$$313$$ 27.2836i 1.54216i 0.636737 + 0.771081i $$0.280284\pi$$
−0.636737 + 0.771081i $$0.719716\pi$$
$$314$$ 0 0
$$315$$ 5.07507 2.25461i 0.285948 0.127033i
$$316$$ 0 0
$$317$$ 24.5544i 1.37911i 0.724232 + 0.689556i $$0.242194\pi$$
−0.724232 + 0.689556i $$0.757806\pi$$
$$318$$ 0 0
$$319$$ −0.0836929 −0.00468590
$$320$$ 0 0
$$321$$ 16.8705 6.80115i 0.941617 0.379603i
$$322$$ 0 0
$$323$$ 1.64626i 0.0916006i
$$324$$ 0 0
$$325$$ 5.13396 2.96409i 0.284781 0.164418i
$$326$$ 0 0
$$327$$ −24.4255 3.45178i −1.35074 0.190884i
$$328$$ 0 0
$$329$$ −17.4220 6.32711i −0.960507 0.348825i
$$330$$ 0 0
$$331$$ 16.3116 0.896566 0.448283 0.893892i $$-0.352036\pi$$
0.448283 + 0.893892i $$0.352036\pi$$
$$332$$ 0 0
$$333$$ 2.02424 + 0.583784i 0.110928 + 0.0319912i
$$334$$ 0 0
$$335$$ −2.07840 3.59989i −0.113555 0.196683i
$$336$$ 0 0
$$337$$ 13.6580 23.6563i 0.743998 1.28864i −0.206663 0.978412i $$-0.566261\pi$$
0.950661 0.310230i $$-0.100406\pi$$
$$338$$ 0 0
$$339$$ 24.8159 10.0043i 1.34782 0.543358i
$$340$$ 0 0
$$341$$ −0.743445 + 1.28768i −0.0402598 + 0.0697320i
$$342$$ 0 0
$$343$$ 9.29424 + 16.0193i 0.501842 + 0.864960i
$$344$$ 0 0
$$345$$ −5.57996 + 2.24950i −0.300415 + 0.121109i
$$346$$ 0 0
$$347$$ 6.21213i 0.333485i −0.986001 0.166742i $$-0.946675\pi$$
0.986001 0.166742i $$-0.0533248\pi$$
$$348$$ 0 0
$$349$$ 24.6529 14.2334i 1.31964 0.761896i 0.335971 0.941872i $$-0.390936\pi$$
0.983671 + 0.179977i $$0.0576023\pi$$
$$350$$ 0 0
$$351$$ −4.00155 5.53424i −0.213587 0.295396i
$$352$$ 0 0
$$353$$ 1.49346 2.58674i 0.0794887 0.137678i −0.823541 0.567257i $$-0.808005\pi$$
0.903029 + 0.429579i $$0.141338\pi$$
$$354$$ 0 0
$$355$$ −8.13889 + 4.69899i −0.431968 + 0.249397i
$$356$$ 0 0
$$357$$ −15.0831 8.02083i −0.798280 0.424508i
$$358$$ 0 0
$$359$$ −26.5977 15.3562i −1.40377 0.810468i −0.408994 0.912537i $$-0.634120\pi$$
−0.994777 + 0.102070i $$0.967454\pi$$
$$360$$ 0 0
$$361$$ −9.40249 16.2856i −0.494868 0.857136i
$$362$$ 0 0
$$363$$ −18.7445 2.64894i −0.983830 0.139033i
$$364$$ 0 0
$$365$$ −4.66098 2.69102i −0.243967 0.140854i
$$366$$ 0 0
$$367$$ 16.4877 + 9.51918i 0.860651 + 0.496897i 0.864230 0.503096i $$-0.167806\pi$$
−0.00357920 + 0.999994i $$0.501139\pi$$
$$368$$ 0 0
$$369$$ 31.0940 + 8.96739i 1.61869 + 0.466824i
$$370$$ 0 0
$$371$$ 25.6280 4.53764i 1.33054 0.235583i
$$372$$ 0 0
$$373$$ −2.05869 3.56576i −0.106595 0.184628i 0.807794 0.589465i $$-0.200661\pi$$
−0.914389 + 0.404837i $$0.867328\pi$$
$$374$$ 0 0
$$375$$ 7.10253 9.07655i 0.366773 0.468711i
$$376$$ 0 0
$$377$$ −0.414750 −0.0213607
$$378$$ 0 0
$$379$$ −11.2436 −0.577546 −0.288773 0.957398i $$-0.593247\pi$$
−0.288773 + 0.957398i $$0.593247\pi$$
$$380$$ 0 0
$$381$$ 23.3017 29.7779i 1.19378 1.52557i
$$382$$ 0 0
$$383$$ 15.8046 + 27.3745i 0.807580 + 1.39877i 0.914536 + 0.404505i $$0.132556\pi$$
−0.106956 + 0.994264i $$0.534110\pi$$
$$384$$ 0 0
$$385$$ −0.167586 + 0.461458i −0.00854100 + 0.0235181i
$$386$$ 0 0
$$387$$ 16.1282 15.5274i 0.819842 0.789300i
$$388$$ 0 0
$$389$$ 18.4018 + 10.6243i 0.933007 + 0.538672i 0.887761 0.460304i $$-0.152260\pi$$
0.0452458 + 0.998976i $$0.485593\pi$$
$$390$$ 0 0
$$391$$ 16.0278 + 9.25367i 0.810562 + 0.467978i
$$392$$ 0 0
$$393$$ 8.93387 + 1.26252i 0.450654 + 0.0636857i
$$394$$ 0 0
$$395$$ 0.488611 + 0.846300i 0.0245847 + 0.0425820i
$$396$$ 0 0
$$397$$ 20.6927 + 11.9469i 1.03854 + 0.599599i 0.919419 0.393281i $$-0.128660\pi$$
0.119118 + 0.992880i $$0.461993\pi$$
$$398$$ 0 0
$$399$$ −2.02250 + 0.0705196i −0.101252 + 0.00353040i
$$400$$ 0 0
$$401$$ 22.0121 12.7087i 1.09923 0.634642i 0.163213 0.986591i $$-0.447814\pi$$
0.936019 + 0.351948i $$0.114481\pi$$
$$402$$ 0 0
$$403$$ −3.68423 + 6.38127i −0.183524 + 0.317874i
$$404$$ 0 0
$$405$$ −5.32987 3.35312i −0.264844 0.166618i
$$406$$ 0 0
$$407$$ −0.161295 + 0.0931240i −0.00799512 + 0.00461598i
$$408$$ 0 0
$$409$$ 22.3817i 1.10670i 0.832948 + 0.553351i $$0.186651\pi$$
−0.832948 + 0.553351i $$0.813349\pi$$
$$410$$ 0 0
$$411$$ −4.33293 + 1.74678i −0.213728 + 0.0861621i
$$412$$ 0 0
$$413$$ −33.4818 12.1595i −1.64753 0.598330i
$$414$$ 0 0
$$415$$ 2.60551 4.51288i 0.127900 0.221528i
$$416$$ 0 0
$$417$$ −18.8180 + 7.58627i −0.921520 + 0.371501i
$$418$$ 0 0
$$419$$ 7.04181 12.1968i 0.344015 0.595851i −0.641159 0.767408i $$-0.721546\pi$$
0.985174 + 0.171556i $$0.0548796\pi$$
$$420$$ 0 0
$$421$$ 8.07639 + 13.9887i 0.393619 + 0.681768i 0.992924 0.118753i $$-0.0378896\pi$$
−0.599305 + 0.800521i $$0.704556\pi$$
$$422$$ 0 0
$$423$$ 5.05340 + 20.4005i 0.245705 + 0.991908i
$$424$$ 0 0
$$425$$ −16.8143 −0.815616
$$426$$ 0 0
$$427$$ 5.10459 14.0558i 0.247029 0.680206i
$$428$$ 0 0
$$429$$ 0.597815 + 0.0844822i 0.0288628 + 0.00407884i
$$430$$ 0 0
$$431$$ −7.16179 + 4.13486i −0.344971 + 0.199169i −0.662468 0.749090i $$-0.730491\pi$$
0.317497 + 0.948259i $$0.397158\pi$$
$$432$$ 0 0
$$433$$ 4.35102i 0.209097i 0.994520 + 0.104548i $$0.0333397\pi$$
−0.994520 + 0.104548i $$0.966660\pi$$
$$434$$ 0 0
$$435$$ −0.354676 + 0.142984i −0.0170054 + 0.00685556i
$$436$$ 0 0
$$437$$ 2.19245 0.104879
$$438$$ 0 0
$$439$$ 20.8077i 0.993098i −0.868009 0.496549i $$-0.834600\pi$$
0.868009 0.496549i $$-0.165400\pi$$
$$440$$ 0 0
$$441$$ 9.20780 18.8737i 0.438467 0.898747i
$$442$$ 0 0
$$443$$ 30.9376i 1.46989i 0.678127 + 0.734945i $$0.262792\pi$$
−0.678127 + 0.734945i $$0.737208\pi$$
$$444$$ 0 0
$$445$$ 7.82580 0.370978
$$446$$ 0 0
$$447$$ 4.56320 32.2902i 0.215832 1.52727i
$$448$$ 0 0
$$449$$ 20.9215i 0.987346i −0.869648 0.493673i $$-0.835654\pi$$
0.869648 0.493673i $$-0.164346\pi$$
$$450$$ 0 0
$$451$$ −2.47763 + 1.43046i −0.116667 + 0.0673577i
$$452$$ 0 0
$$453$$ 6.47798 + 16.0688i 0.304362 + 0.754979i
$$454$$ 0 0
$$455$$ −0.830494 + 2.28681i −0.0389342 + 0.107207i
$$456$$ 0 0
$$457$$ 2.30115 0.107643 0.0538217 0.998551i $$-0.482860\pi$$
0.0538217 + 0.998551i $$0.482860\pi$$
$$458$$ 0 0
$$459$$ 1.98069 + 19.2689i 0.0924509 + 0.899395i
$$460$$ 0 0
$$461$$ 8.92497 + 15.4585i 0.415677 + 0.719974i 0.995499 0.0947688i $$-0.0302112\pi$$
−0.579822 + 0.814743i $$0.696878\pi$$
$$462$$ 0 0
$$463$$ −6.24034 + 10.8086i −0.290013 + 0.502318i −0.973813 0.227353i $$-0.926993\pi$$
0.683799 + 0.729670i $$0.260326\pi$$
$$464$$ 0 0
$$465$$ −0.950665 + 6.72712i −0.0440860 + 0.311963i
$$466$$ 0 0
$$467$$ −2.42799 + 4.20541i −0.112354 + 0.194603i −0.916719 0.399533i $$-0.869172\pi$$
0.804365 + 0.594136i $$0.202506\pi$$
$$468$$ 0 0
$$469$$ −14.7748 5.36571i −0.682236 0.247766i
$$470$$ 0 0
$$471$$ 0.343830 + 0.269052i 0.0158428 + 0.0123972i
$$472$$ 0 0
$$473$$ 1.97921i 0.0910044i
$$474$$ 0 0
$$475$$ −1.72503 + 0.995945i −0.0791497 + 0.0456971i
$$476$$ 0 0
$$477$$ −20.4679 21.2599i −0.937161 0.973425i
$$478$$ 0 0
$$479$$ 4.40542 7.63041i 0.201289 0.348642i −0.747655 0.664087i $$-0.768820\pi$$
0.948944 + 0.315445i $$0.102154\pi$$
$$480$$ 0 0
$$481$$ −0.799318 + 0.461486i −0.0364458 + 0.0210420i
$$482$$ 0 0
$$483$$ −10.6819 + 20.0872i −0.486044 + 0.913999i
$$484$$ 0 0
$$485$$ −6.42441 3.70914i −0.291718 0.168423i
$$486$$ 0 0
$$487$$ 4.66185 + 8.07456i 0.211249 + 0.365893i 0.952106 0.305770i $$-0.0989137\pi$$
−0.740857 + 0.671663i $$0.765580\pi$$
$$488$$ 0 0
$$489$$ −5.56662 13.8082i −0.251731 0.624427i
$$490$$ 0 0
$$491$$ −26.9192 15.5418i −1.21485 0.701391i −0.251034 0.967978i $$-0.580771\pi$$
−0.963811 + 0.266587i $$0.914104\pi$$
$$492$$ 0 0
$$493$$ 1.01877 + 0.588186i 0.0458830 + 0.0264906i
$$494$$ 0 0
$$495$$ 0.540350 0.133850i 0.0242869 0.00601610i
$$496$$ 0 0
$$497$$ −12.1312 + 33.4039i −0.544159 + 1.49837i
$$498$$ 0 0
$$499$$ 11.1694 + 19.3459i 0.500010 + 0.866043i 1.00000 1.16519e-5i $$3.70891e-6\pi$$
−0.499990 + 0.866031i $$0.666663\pi$$
$$500$$ 0 0
$$501$$ −2.90697 7.21081i −0.129874 0.322155i
$$502$$ 0 0
$$503$$ −12.2396 −0.545738 −0.272869 0.962051i $$-0.587973\pi$$
−0.272869 + 0.962051i $$0.587973\pi$$
$$504$$ 0 0
$$505$$ 12.2490 0.545072
$$506$$ 0 0
$$507$$ −19.3326 2.73205i −0.858591 0.121335i
$$508$$ 0 0
$$509$$ −7.05496 12.2195i −0.312706 0.541622i 0.666242 0.745736i $$-0.267902\pi$$
−0.978947 + 0.204114i $$0.934569\pi$$
$$510$$ 0 0
$$511$$ −20.0405 + 3.54834i −0.886539 + 0.156969i
$$512$$ 0 0
$$513$$ 1.34454 + 1.85953i 0.0593627 + 0.0821000i
$$514$$ 0 0
$$515$$ 5.17588 + 2.98830i 0.228077 + 0.131680i
$$516$$ 0 0
$$517$$ −1.60910 0.929015i −0.0707682 0.0408580i
$$518$$ 0 0
$$519$$ −7.60141 + 9.71409i −0.333665 + 0.426401i
$$520$$ 0 0
$$521$$ 2.81632 + 4.87800i 0.123385 + 0.213709i 0.921101 0.389325i $$-0.127292\pi$$
−0.797715 + 0.603034i $$0.793958\pi$$
$$522$$ 0 0
$$523$$ −33.2293 19.1849i −1.45302 0.838899i −0.454364 0.890816i $$-0.650133\pi$$
−0.998651 + 0.0519176i $$0.983467\pi$$
$$524$$ 0 0
$$525$$ −0.720262 20.6571i −0.0314348 0.901549i
$$526$$ 0 0
$$527$$ 18.0995 10.4497i 0.788425 0.455197i
$$528$$ 0 0
$$529$$ 0.823769 1.42681i 0.0358161 0.0620352i
$$530$$ 0 0
$$531$$ 9.71167 + 39.2060i 0.421451 + 1.70139i
$$532$$ 0 0
$$533$$ −12.2782 + 7.08880i −0.531826 + 0.307050i
$$534$$ 0 0
$$535$$ 7.34769i 0.317668i
$$536$$ 0 0
$$537$$ 6.19236 43.8185i 0.267220 1.89091i
$$538$$ 0 0
$$539$$ 0.637441 + 1.74365i 0.0274565 + 0.0751045i
$$540$$ 0 0
$$541$$ −3.21673 + 5.57154i −0.138298 + 0.239539i −0.926852 0.375426i $$-0.877496\pi$$
0.788555 + 0.614965i $$0.210830\pi$$
$$542$$ 0 0
$$543$$ 1.28655 + 1.00674i 0.0552111 + 0.0432035i
$$544$$ 0 0
$$545$$ 4.98232 8.62963i 0.213419 0.369653i
$$546$$ 0 0
$$547$$ −6.52889 11.3084i −0.279155 0.483511i 0.692020 0.721878i $$-0.256721\pi$$
−0.971175 + 0.238368i $$0.923388\pi$$
$$548$$ 0 0
$$549$$ −16.4588 + 4.07699i −0.702444 + 0.174002i
$$550$$ 0 0
$$551$$ 0.139357 0.00593683
$$552$$ 0 0
$$553$$ 3.47341 + 1.26143i 0.147704 + 0.0536414i
$$554$$ 0 0
$$555$$ −0.524446 + 0.670206i −0.0222615 + 0.0284487i
$$556$$ 0 0
$$557$$ −25.5409 + 14.7460i −1.08220 + 0.624809i −0.931489 0.363769i $$-0.881490\pi$$
−0.150712 + 0.988578i $$0.548157\pi$$
$$558$$ 0 0
$$559$$ 9.80822i 0.414844i
$$560$$ 0 0
$$561$$ −1.34863 1.05532i −0.0569391 0.0445557i
$$562$$ 0 0
$$563$$ −10.5187 −0.443310 −0.221655 0.975125i $$-0.571146\pi$$
−0.221655 + 0.975125i $$0.571146\pi$$
$$564$$ 0 0
$$565$$ 10.8082i 0.454706i
$$566$$ 0 0
$$567$$ −23.5877 + 3.25876i −0.990591 + 0.136855i
$$568$$ 0 0
$$569$$ 26.3334i 1.10395i 0.833859 + 0.551977i $$0.186126\pi$$
−0.833859 + 0.551977i $$0.813874\pi$$
$$570$$ 0 0
$$571$$ −44.0590 −1.84381 −0.921906 0.387413i $$-0.873369\pi$$
−0.921906 + 0.387413i $$0.873369\pi$$
$$572$$ 0 0
$$573$$ 4.05447 + 3.17268i 0.169378 + 0.132540i
$$574$$ 0 0
$$575$$ 22.3929i 0.933847i
$$576$$ 0 0
$$577$$ 12.1535 7.01684i 0.505957 0.292115i −0.225213 0.974310i $$-0.572308\pi$$
0.731170 + 0.682195i $$0.238974\pi$$
$$578$$ 0 0
$$579$$ −19.7622 + 25.2548i −0.821290 + 1.04955i
$$580$$ 0 0
$$581$$ −3.43559 19.4037i −0.142532 0.805001i
$$582$$ 0 0
$$583$$ 2.60897 0.108052
$$584$$ 0 0
$$585$$ 2.67777 0.663307i 0.110712 0.0274244i
$$586$$ 0 0
$$587$$ 1.52469 + 2.64085i 0.0629308 + 0.108999i 0.895774 0.444509i $$-0.146622\pi$$
−0.832843 + 0.553509i $$0.813289\pi$$
$$588$$ 0 0
$$589$$ 1.23791 2.14413i 0.0510073 0.0883473i
$$590$$ 0 0
$$591$$ 19.3388 + 15.1329i 0.795493 + 0.622484i
$$592$$ 0 0
$$593$$ 13.3041 23.0434i 0.546334 0.946278i −0.452188 0.891923i $$-0.649356\pi$$
0.998522 0.0543552i $$-0.0173103\pi$$
$$594$$ 0 0
$$595$$ 5.28306 4.43941i 0.216585 0.181998i
$$596$$ 0 0
$$597$$ −5.74526 + 40.6547i −0.235138 + 1.66389i
$$598$$ 0 0
$$599$$ 4.46099i 0.182271i −0.995838 0.0911356i $$-0.970950\pi$$
0.995838 0.0911356i $$-0.0290497\pi$$
$$600$$ 0 0
$$601$$ 5.25019 3.03120i 0.214160 0.123645i −0.389083 0.921203i $$-0.627208\pi$$
0.603243 + 0.797557i $$0.293875\pi$$
$$602$$ 0 0
$$603$$ 4.28554 + 17.3007i 0.174521 + 0.704539i
$$604$$ 0 0
$$605$$ 3.82350 6.62250i 0.155447 0.269243i
$$606$$ 0 0
$$607$$ 39.2581 22.6657i 1.59344 0.919971i 0.600725 0.799455i $$-0.294879\pi$$
0.992711 0.120516i $$-0.0384548\pi$$
$$608$$ 0 0
$$609$$ −0.678969 + 1.27679i −0.0275132 + 0.0517382i
$$610$$ 0 0
$$611$$ −7.97409 4.60384i −0.322597 0.186251i
$$612$$ 0 0
$$613$$ 16.6294 + 28.8029i 0.671654 + 1.16334i 0.977435 + 0.211237i $$0.0677492\pi$$
−0.305781 + 0.952102i $$0.598917\pi$$
$$614$$ 0 0
$$615$$ −8.05591 + 10.2949i −0.324846 + 0.415131i
$$616$$ 0 0
$$617$$ 31.3001 + 18.0711i 1.26010 + 0.727516i 0.973093 0.230414i $$-0.0740079\pi$$
0.287002 + 0.957930i $$0.407341\pi$$
$$618$$ 0 0
$$619$$ −22.9031 13.2231i −0.920554 0.531482i −0.0367423 0.999325i $$-0.511698\pi$$
−0.883812 + 0.467843i $$0.845031\pi$$
$$620$$ 0 0
$$621$$ 25.6617 2.63783i 1.02977 0.105852i
$$622$$ 0 0
$$623$$ 22.6563 19.0383i 0.907705 0.762752i
$$624$$ 0 0
$$625$$ −8.94843 15.4991i −0.357937 0.619965i
$$626$$ 0 0
$$627$$ −0.200868 0.0283863i −0.00802189 0.00113364i
$$628$$ 0 0
$$629$$ 2.61787 0.104381
$$630$$ 0 0
$$631$$ −32.0484 −1.27583 −0.637914 0.770107i $$-0.720203\pi$$
−0.637914 + 0.770107i $$0.720203\pi$$
$$632$$ 0 0
$$633$$ −3.93754 9.76717i −0.156503 0.388210i
$$634$$ 0 0
$$635$$ 7.63687 + 13.2274i 0.303060 + 0.524915i
$$636$$ 0 0
$$637$$ 3.15891 + 8.64088i 0.125161 + 0.342364i
$$638$$ 0 0
$$639$$ 39.1147 9.68907i 1.54735 0.383294i
$$640$$ 0 0
$$641$$ −21.1444 12.2077i −0.835153 0.482176i 0.0204610 0.999791i $$-0.493487\pi$$
−0.855614 + 0.517615i $$0.826820\pi$$
$$642$$ 0 0
$$643$$ −31.9014 18.4183i −1.25807 0.726346i −0.285370 0.958418i $$-0.592116\pi$$
−0.972699 + 0.232071i $$0.925450\pi$$
$$644$$ 0 0
$$645$$ 3.38136 + 8.38757i 0.133141 + 0.330260i
$$646$$ 0 0
$$647$$ 13.2847 + 23.0098i 0.522276 + 0.904608i 0.999664 + 0.0259155i $$0.00825009\pi$$
−0.477389 + 0.878692i $$0.658417\pi$$
$$648$$ 0 0
$$649$$ −3.09239 1.78539i −0.121387 0.0700827i
$$650$$ 0 0
$$651$$ 13.6132 + 21.7883i 0.533543 + 0.853949i
$$652$$ 0 0
$$653$$ 26.2767 15.1709i 1.02829 0.593683i 0.111794 0.993731i $$-0.464340\pi$$
0.916494 + 0.400049i $$0.131007\pi$$
$$654$$ 0 0
$$655$$ −1.82233 + 3.15637i −0.0712044 + 0.123330i
$$656$$ 0 0
$$657$$ 16.0055 + 16.6248i 0.624432 + 0.648595i
$$658$$ 0 0
$$659$$ 40.9873 23.6640i 1.59664 0.921820i 0.604511 0.796597i $$-0.293369\pi$$
0.992129 0.125223i $$-0.0399647\pi$$
$$660$$ 0 0
$$661$$ 35.1245i 1.36618i −0.730332 0.683092i $$-0.760635\pi$$
0.730332 0.683092i $$-0.239365\pi$$
$$662$$ 0 0
$$663$$ −6.68328 5.22976i −0.259557 0.203107i
$$664$$ 0 0
$$665$$ 0.279049 0.768376i 0.0108211 0.0297963i
$$666$$ 0 0
$$667$$ 0.783329 1.35677i 0.0303306 0.0525342i
$$668$$ 0 0
$$669$$ 0.222804 1.57661i 0.00861409 0.0609552i
$$670$$ 0 0
$$671$$ 0.749513 1.29819i 0.0289346 0.0501162i
$$672$$ 0 0
$$673$$ −2.54758 4.41254i −0.0982020 0.170091i 0.812738 0.582629i $$-0.197976\pi$$
−0.910940 + 0.412538i $$0.864642\pi$$
$$674$$ 0 0
$$675$$ −18.9925 + 13.7326i −0.731022 + 0.528568i
$$676$$ 0 0
$$677$$ −16.8414 −0.647269 −0.323635 0.946182i $$-0.604905\pi$$
−0.323635 + 0.946182i $$0.604905\pi$$
$$678$$ 0 0
$$679$$ −27.6226 + 4.89081i −1.06006 + 0.187692i
$$680$$ 0 0
$$681$$ −6.47998 16.0738i −0.248313 0.615949i
$$682$$ 0 0
$$683$$ 15.7555 9.09645i 0.602868 0.348066i −0.167301 0.985906i $$-0.553505\pi$$
0.770169 + 0.637840i $$0.220172\pi$$
$$684$$ 0 0
$$685$$ 1.88715i 0.0721042i
$$686$$ 0 0
$$687$$ −0.666559 + 4.71672i −0.0254308 + 0.179954i
$$688$$ 0 0
$$689$$ 12.9290 0.492557
$$690$$ 0 0
$$691$$ 3.52652i 0.134155i −0.997748 0.0670775i $$-0.978633\pi$$
0.997748 0.0670775i $$-0.0213675\pi$$
$$692$$ 0 0
$$693$$ 1.23873 1.70205i 0.0470555 0.0646554i
$$694$$ 0 0
$$695$$ 8.19591i 0.310888i
$$696$$ 0 0
$$697$$ 40.2125 1.52316
$$698$$ 0 0
$$699$$ −10.3044 + 4.15412i −0.389749 + 0.157123i
$$700$$ 0 0
$$701$$ 13.3502i 0.504229i 0.967697 + 0.252114i $$0.0811259\pi$$
−0.967697 + 0.252114i $$0.918874\pi$$
$$702$$ 0 0
$$703$$ 0.268574 0.155061i 0.0101295 0.00584824i
$$704$$ 0 0
$$705$$ −8.40626 1.18796i −0.316598 0.0447411i
$$706$$ 0 0
$$707$$ 35.4617 29.7988i 1.33368 1.12070i
$$708$$ 0 0
$$709$$ −42.2894 −1.58821 −0.794107 0.607779i $$-0.792061\pi$$
−0.794107 + 0.607779i $$0.792061\pi$$
$$710$$ 0 0
$$711$$ −1.00749 4.06723i −0.0377838 0.152533i
$$712$$ 0 0
$$713$$ −13.9166 24.1043i −0.521182 0.902715i
$$714$$ 0 0
$$715$$ −0.121942 + 0.211210i −0.00456038 + 0.00789881i
$$716$$ 0 0
$$717$$ −21.1998 + 8.54648i −0.791721 + 0.319174i
$$718$$ 0 0
$$719$$ 15.2035 26.3332i 0.566994 0.982062i −0.429868 0.902892i $$-0.641440\pi$$
0.996861 0.0791697i $$-0.0252269\pi$$
$$720$$ 0 0
$$721$$ 22.2544 3.94032i 0.828796 0.146745i
$$722$$ 0 0
$$723$$ −4.09426 + 1.65056i −0.152267 + 0.0613849i
$$724$$ 0 0
$$725$$ 1.42335i 0.0528617i
$$726$$ 0 0
$$727$$ −11.3671 + 6.56280i −0.421583 + 0.243401i −0.695754 0.718280i $$-0.744930\pi$$
0.274171 + 0.961681i $$0.411596\pi$$
$$728$$ 0 0
$$729$$ 17.9746 + 20.1473i 0.665724 + 0.746198i
$$730$$ 0 0
$$731$$ 13.9097 24.0924i 0.514470 0.891089i
$$732$$ 0 0
$$733$$ −32.7001 + 18.8794i −1.20781 + 0.697327i −0.962280 0.272063i $$-0.912294\pi$$
−0.245527 + 0.969390i $$0.578961\pi$$
$$734$$ 0 0
$$735$$ 5.68029 + 6.30028i 0.209521 + 0.232389i
$$736$$ 0 0
$$737$$ −1.36460 0.787853i −0.0502657 0.0290209i
$$738$$ 0 0
$$739$$ −13.1215 22.7271i −0.482683 0.836031i 0.517119 0.855913i $$-0.327004\pi$$
−0.999802 + 0.0198820i $$0.993671\pi$$
$$740$$ 0 0
$$741$$ −0.995424 0.140672i −0.0365678 0.00516770i
$$742$$ 0 0
$$743$$ −8.78379 5.07132i −0.322246 0.186049i 0.330147 0.943929i $$-0.392902\pi$$
−0.652393 + 0.757881i $$0.726235\pi$$
$$744$$ 0 0
$$745$$ 11.4082 + 6.58655i 0.417966 + 0.241313i
$$746$$ 0 0
$$747$$ −16.0965 + 15.4969i −0.588941 + 0.567001i
$$748$$ 0 0
$$749$$ 17.8752 + 21.2721i 0.653144 + 0.777267i
$$750$$ 0 0
$$751$$ −3.95369 6.84798i −0.144272 0.249886i 0.784829 0.619712i $$-0.212751\pi$$
−0.929101 + 0.369826i $$0.879417\pi$$
$$752$$ 0 0
$$753$$ 20.0557 25.6298i 0.730870 0.934002i
$$754$$ 0 0
$$755$$ −6.99855 −0.254703
$$756$$ 0 0
$$757$$ 29.8903 1.08638 0.543191 0.839609i $$-0.317216\pi$$
0.543191 + 0.839609i $$0.317216\pi$$
$$758$$ 0 0
$$759$$ −1.40545 + 1.79606i −0.0510144 + 0.0651930i
$$760$$ 0 0
$$761$$ −3.05687 5.29465i −0.110811 0.191931i 0.805286 0.592886i $$-0.202012\pi$$
−0.916098 + 0.400955i $$0.868678\pi$$
$$762$$ 0 0
$$763$$ −6.56961 37.1042i −0.237836 1.34326i
$$764$$ 0 0
$$765$$ −7.51820 2.16822i −0.271821 0.0783922i
$$766$$ 0 0
$$767$$ −15.3247 8.84771i −0.553342 0.319472i
$$768$$ 0 0
$$769$$ −9.79863 5.65724i −0.353348 0.204005i 0.312811 0.949815i $$-0.398729\pi$$
−0.666159 + 0.745810i $$0.732063\pi$$
$$770$$ 0 0
$$771$$ 24.6868 + 3.48870i 0.889073 + 0.125642i
$$772$$ 0 0
$$773$$ 19.2106 + 33.2737i 0.690956 + 1.19677i 0.971525 + 0.236937i $$0.0761437\pi$$
−0.280569 + 0.959834i $$0.590523\pi$$
$$774$$ 0 0
$$775$$ 21.8994 + 12.6436i 0.786648 + 0.454172i
$$776$$ 0 0
$$777$$ 0.112139 + 3.21615i 0.00402297 + 0.115379i
$$778$$ 0 0
$$779$$ 4.12551 2.38186i 0.147812 0.0853391i
$$780$$ 0 0
$$781$$ −1.78124 + 3.08519i −0.0637376 + 0.110397i
$$782$$ 0 0
$$783$$ 1.63112 0.167667i 0.0582916 0.00599193i
$$784$$ 0 0
$$785$$ −0.152730 + 0.0881788i −0.00545117 + 0.00314723i
$$786$$ 0 0
$$787$$ 47.6600i 1.69889i −0.527674 0.849447i $$-0.676936\pi$$
0.527674 0.849447i $$-0.323064\pi$$
$$788$$ 0 0
$$789$$ 12.6100 5.08361i 0.448930 0.180981i
$$790$$ 0 0
$$791$$ 26.2938 + 31.2906i 0.934900 + 1.11257i
$$792$$ 0 0
$$793$$ 3.71430 6.43335i 0.131898 0.228455i
$$794$$ 0 0
$$795$$ 11.0564 4.45726i 0.392129 0.158083i