# Properties

 Label 1078.2.i.d.1011.7 Level $1078$ Weight $2$ Character 1078.1011 Analytic conductor $8.608$ Analytic rank $0$ Dimension $32$ CM no Inner twists $8$

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## 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 1011.7 Character $$\chi$$ $$=$$ 1078.1011 Dual form 1078.2.i.d.901.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} +0.765367 q^{6} +1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} +0.765367 q^{6} +1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +(-1.02581 + 1.77675i) q^{10} +(0.649042 + 3.25250i) q^{11} +(-0.662827 + 0.382683i) q^{12} -6.59694 q^{13} -1.57024 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.80554 + 3.12729i) q^{17} +(2.09077 + 1.20711i) q^{18} +(-0.439269 - 0.760837i) q^{19} -2.05161i q^{20} +(-2.18834 - 2.49222i) q^{22} +(-3.30966 - 5.73249i) q^{23} +(0.382683 - 0.662827i) q^{24} +(-0.395443 + 0.684927i) q^{25} +(5.71311 - 3.29847i) q^{26} +4.14386i q^{27} +6.18955i q^{29} +(1.35986 - 0.785118i) q^{30} +(-5.61510 - 3.24188i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.814474 - 2.40422i) q^{33} -3.61108i q^{34} -2.41421 q^{36} +(5.52454 + 9.56878i) q^{37} +(0.760837 + 0.439269i) q^{38} +(4.37263 + 2.52454i) q^{39} +(1.02581 + 1.77675i) q^{40} +2.36864 q^{41} +7.81288i q^{43} +(3.14127 + 1.06416i) q^{44} +(-4.28945 - 2.47652i) q^{45} +(5.73249 + 3.30966i) q^{46} +(4.97716 - 2.87357i) q^{47} +0.765367i q^{48} -0.790886i q^{50} +(2.39352 - 1.38190i) q^{51} +(-3.29847 + 5.71311i) q^{52} +(-0.214882 + 0.372186i) q^{53} +(-2.07193 - 3.58869i) q^{54} +(4.48962 + 5.11308i) q^{55} +0.672404i q^{57} +(-3.09477 - 5.36031i) q^{58} +(-2.78725 - 1.60922i) q^{59} +(-0.785118 + 1.35986i) q^{60} +(-5.66711 - 9.81572i) q^{61} +6.48376 q^{62} -1.00000 q^{64} +(-11.7211 + 6.76718i) q^{65} +(0.496755 + 2.48935i) q^{66} +(-1.48123 + 2.56556i) q^{67} +(1.80554 + 3.12729i) q^{68} +5.06620i q^{69} -2.13403 q^{71} +(2.09077 - 1.20711i) q^{72} +(-5.41262 + 9.37493i) q^{73} +(-9.56878 - 5.52454i) q^{74} +(0.524221 - 0.302659i) q^{75} -0.878539 q^{76} -5.04908 q^{78} +(7.34847 - 4.24264i) q^{79} +(-1.77675 - 1.02581i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(-2.05130 + 1.18432i) q^{82} -12.3153 q^{83} +7.40854i q^{85} +(-3.90644 - 6.76615i) q^{86} +(2.36864 - 4.10260i) q^{87} +(-3.25250 + 0.649042i) q^{88} +(-5.82684 + 3.36413i) q^{89} +4.95303 q^{90} -6.61931 q^{92} +(2.48123 + 4.29762i) q^{93} +(-2.87357 + 4.97716i) q^{94} +(-1.56094 - 0.901211i) q^{95} +(-0.382683 - 0.662827i) q^{96} -9.23880i q^{97} +(6.01676 - 5.28311i) 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 $$32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100})$$ 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

## Character values

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

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

## 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
$$3$$ −0.662827 0.382683i −0.382683 0.220942i 0.296302 0.955094i $$-0.404247\pi$$
−0.678985 + 0.734152i $$0.737580\pi$$
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 1.77675 1.02581i 0.794586 0.458755i −0.0469885 0.998895i $$-0.514962\pi$$
0.841575 + 0.540141i $$0.181629\pi$$
$$6$$ 0.765367 0.312460
$$7$$ 0 0
$$8$$ 1.00000i 0.353553i
$$9$$ −1.20711 2.09077i −0.402369 0.696923i
$$10$$ −1.02581 + 1.77675i −0.324388 + 0.561857i
$$11$$ 0.649042 + 3.25250i 0.195694 + 0.980665i
$$12$$ −0.662827 + 0.382683i −0.191342 + 0.110471i
$$13$$ −6.59694 −1.82966 −0.914830 0.403838i $$-0.867676\pi$$
−0.914830 + 0.403838i $$0.867676\pi$$
$$14$$ 0 0
$$15$$ −1.57024 −0.405433
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.80554 + 3.12729i −0.437908 + 0.758478i −0.997528 0.0702708i $$-0.977614\pi$$
0.559620 + 0.828749i $$0.310947\pi$$
$$18$$ 2.09077 + 1.20711i 0.492799 + 0.284518i
$$19$$ −0.439269 0.760837i −0.100775 0.174548i 0.811229 0.584729i $$-0.198799\pi$$
−0.912004 + 0.410181i $$0.865466\pi$$
$$20$$ 2.05161i 0.458755i
$$21$$ 0 0
$$22$$ −2.18834 2.49222i −0.466555 0.531344i
$$23$$ −3.30966 5.73249i −0.690111 1.19531i −0.971801 0.235802i $$-0.924228\pi$$
0.281690 0.959505i $$-0.409105\pi$$
$$24$$ 0.382683 0.662827i 0.0781149 0.135299i
$$25$$ −0.395443 + 0.684927i −0.0790886 + 0.136985i
$$26$$ 5.71311 3.29847i 1.12043 0.646883i
$$27$$ 4.14386i 0.797486i
$$28$$ 0 0
$$29$$ 6.18955i 1.14937i 0.818375 + 0.574685i $$0.194876\pi$$
−0.818375 + 0.574685i $$0.805124\pi$$
$$30$$ 1.35986 0.785118i 0.248276 0.143342i
$$31$$ −5.61510 3.24188i −1.00850 0.582259i −0.0977497 0.995211i $$-0.531164\pi$$
−0.910753 + 0.412952i $$0.864498\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 0.814474 2.40422i 0.141782 0.418521i
$$34$$ 3.61108i 0.619295i
$$35$$ 0 0
$$36$$ −2.41421 −0.402369
$$37$$ 5.52454 + 9.56878i 0.908229 + 1.57310i 0.816524 + 0.577312i $$0.195898\pi$$
0.0917046 + 0.995786i $$0.470768\pi$$
$$38$$ 0.760837 + 0.439269i 0.123424 + 0.0712589i
$$39$$ 4.37263 + 2.52454i 0.700181 + 0.404250i
$$40$$ 1.02581 + 1.77675i 0.162194 + 0.280929i
$$41$$ 2.36864 0.369919 0.184960 0.982746i $$-0.440785\pi$$
0.184960 + 0.982746i $$0.440785\pi$$
$$42$$ 0 0
$$43$$ 7.81288i 1.19145i 0.803188 + 0.595726i $$0.203136\pi$$
−0.803188 + 0.595726i $$0.796864\pi$$
$$44$$ 3.14127 + 1.06416i 0.473564 + 0.160428i
$$45$$ −4.28945 2.47652i −0.639434 0.369177i
$$46$$ 5.73249 + 3.30966i 0.845210 + 0.487982i
$$47$$ 4.97716 2.87357i 0.725994 0.419153i −0.0909611 0.995854i $$-0.528994\pi$$
0.816955 + 0.576702i $$0.195661\pi$$
$$48$$ 0.765367i 0.110471i
$$49$$ 0 0
$$50$$ 0.790886i 0.111848i
$$51$$ 2.39352 1.38190i 0.335160 0.193505i
$$52$$ −3.29847 + 5.71311i −0.457415 + 0.792266i
$$53$$ −0.214882 + 0.372186i −0.0295163 + 0.0511237i −0.880406 0.474220i $$-0.842730\pi$$
0.850890 + 0.525344i $$0.176063\pi$$
$$54$$ −2.07193 3.58869i −0.281954 0.488359i
$$55$$ 4.48962 + 5.11308i 0.605380 + 0.689448i
$$56$$ 0 0
$$57$$ 0.672404i 0.0890621i
$$58$$ −3.09477 5.36031i −0.406364 0.703843i
$$59$$ −2.78725 1.60922i −0.362870 0.209503i 0.307469 0.951558i $$-0.400518\pi$$
−0.670339 + 0.742055i $$0.733851\pi$$
$$60$$ −0.785118 + 1.35986i −0.101358 + 0.175558i
$$61$$ −5.66711 9.81572i −0.725599 1.25677i −0.958727 0.284328i $$-0.908230\pi$$
0.233129 0.972446i $$-0.425104\pi$$
$$62$$ 6.48376 0.823439
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −11.7211 + 6.76718i −1.45382 + 0.839365i
$$66$$ 0.496755 + 2.48935i 0.0611464 + 0.306418i
$$67$$ −1.48123 + 2.56556i −0.180961 + 0.313434i −0.942208 0.335028i $$-0.891254\pi$$
0.761247 + 0.648462i $$0.224587\pi$$
$$68$$ 1.80554 + 3.12729i 0.218954 + 0.379239i
$$69$$ 5.06620i 0.609899i
$$70$$ 0 0
$$71$$ −2.13403 −0.253263 −0.126631 0.991950i $$-0.540417\pi$$
−0.126631 + 0.991950i $$0.540417\pi$$
$$72$$ 2.09077 1.20711i 0.246400 0.142259i
$$73$$ −5.41262 + 9.37493i −0.633499 + 1.09725i 0.353332 + 0.935498i $$0.385049\pi$$
−0.986831 + 0.161754i $$0.948285\pi$$
$$74$$ −9.56878 5.52454i −1.11235 0.642215i
$$75$$ 0.524221 0.302659i 0.0605318 0.0349480i
$$76$$ −0.878539 −0.100775
$$77$$ 0 0
$$78$$ −5.04908 −0.571695
$$79$$ 7.34847 4.24264i 0.826767 0.477334i −0.0259772 0.999663i $$-0.508270\pi$$
0.852745 + 0.522328i $$0.174936\pi$$
$$80$$ −1.77675 1.02581i −0.198647 0.114689i
$$81$$ −2.03553 + 3.52565i −0.226170 + 0.391739i
$$82$$ −2.05130 + 1.18432i −0.226528 + 0.130786i
$$83$$ −12.3153 −1.35178 −0.675892 0.737001i $$-0.736241\pi$$
−0.675892 + 0.737001i $$0.736241\pi$$
$$84$$ 0 0
$$85$$ 7.40854i 0.803569i
$$86$$ −3.90644 6.76615i −0.421242 0.729613i
$$87$$ 2.36864 4.10260i 0.253945 0.439845i
$$88$$ −3.25250 + 0.649042i −0.346717 + 0.0691881i
$$89$$ −5.82684 + 3.36413i −0.617644 + 0.356597i −0.775951 0.630793i $$-0.782730\pi$$
0.158307 + 0.987390i $$0.449396\pi$$
$$90$$ 4.95303 0.522095
$$91$$ 0 0
$$92$$ −6.61931 −0.690111
$$93$$ 2.48123 + 4.29762i 0.257291 + 0.445642i
$$94$$ −2.87357 + 4.97716i −0.296386 + 0.513355i
$$95$$ −1.56094 0.901211i −0.160149 0.0924622i
$$96$$ −0.382683 0.662827i −0.0390575 0.0676495i
$$97$$ 9.23880i 0.938058i −0.883183 0.469029i $$-0.844604\pi$$
0.883183 0.469029i $$-0.155396\pi$$
$$98$$ 0 0
$$99$$ 6.01676 5.28311i 0.604707 0.530973i
$$100$$ 0.395443 + 0.684927i 0.0395443 + 0.0684927i
$$101$$ 0.929830 1.61051i 0.0925216 0.160252i −0.816050 0.577981i $$-0.803841\pi$$
0.908572 + 0.417729i $$0.137174\pi$$
$$102$$ −1.38190 + 2.39352i −0.136829 + 0.236994i
$$103$$ −5.81112 + 3.35505i −0.572587 + 0.330583i −0.758182 0.652043i $$-0.773912\pi$$
0.185595 + 0.982626i $$0.440579\pi$$
$$104$$ 6.59694i 0.646883i
$$105$$ 0 0
$$106$$ 0.429764i 0.0417423i
$$107$$ −12.7768 + 7.37667i −1.23518 + 0.713130i −0.968105 0.250547i $$-0.919390\pi$$
−0.267073 + 0.963676i $$0.586056\pi$$
$$108$$ 3.58869 + 2.07193i 0.345322 + 0.199372i
$$109$$ 5.19615 + 3.00000i 0.497701 + 0.287348i 0.727764 0.685828i $$-0.240560\pi$$
−0.230063 + 0.973176i $$0.573893\pi$$
$$110$$ −6.44466 2.18325i −0.614475 0.208165i
$$111$$ 8.45660i 0.802665i
$$112$$ 0 0
$$113$$ −0.597322 −0.0561913 −0.0280956 0.999605i $$-0.508944\pi$$
−0.0280956 + 0.999605i $$0.508944\pi$$
$$114$$ −0.336202 0.582319i −0.0314882 0.0545392i
$$115$$ −11.7609 6.79013i −1.09671 0.633183i
$$116$$ 5.36031 + 3.09477i 0.497692 + 0.287343i
$$117$$ 7.96321 + 13.7927i 0.736199 + 1.27513i
$$118$$ 3.21844 0.296282
$$119$$ 0 0
$$120$$ 1.57024i 0.143342i
$$121$$ −10.1575 + 4.22202i −0.923408 + 0.383820i
$$122$$ 9.81572 + 5.66711i 0.888673 + 0.513076i
$$123$$ −1.57000 0.906438i −0.141562 0.0817308i
$$124$$ −5.61510 + 3.24188i −0.504251 + 0.291130i
$$125$$ 11.8807i 1.06264i
$$126$$ 0 0
$$127$$ 7.33002i 0.650434i −0.945639 0.325217i $$-0.894563\pi$$
0.945639 0.325217i $$-0.105437\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ 2.98986 5.17859i 0.263242 0.455949i
$$130$$ 6.76718 11.7211i 0.593521 1.02801i
$$131$$ −4.41025 7.63878i −0.385325 0.667403i 0.606489 0.795092i $$-0.292577\pi$$
−0.991814 + 0.127689i $$0.959244\pi$$
$$132$$ −1.67488 1.90747i −0.145780 0.166024i
$$133$$ 0 0
$$134$$ 2.96246i 0.255917i
$$135$$ 4.25080 + 7.36260i 0.365850 + 0.633671i
$$136$$ −3.12729 1.80554i −0.268163 0.154824i
$$137$$ −1.61810 + 2.80263i −0.138244 + 0.239445i −0.926832 0.375477i $$-0.877479\pi$$
0.788588 + 0.614922i $$0.210812\pi$$
$$138$$ −2.53310 4.38746i −0.215632 0.373485i
$$139$$ 2.47122 0.209606 0.104803 0.994493i $$-0.466579\pi$$
0.104803 + 0.994493i $$0.466579\pi$$
$$140$$ 0 0
$$141$$ −4.39866 −0.370434
$$142$$ 1.84813 1.06702i 0.155091 0.0895420i
$$143$$ −4.28169 21.4565i −0.358053 1.79428i
$$144$$ −1.20711 + 2.09077i −0.100592 + 0.174231i
$$145$$ 6.34928 + 10.9973i 0.527279 + 0.913274i
$$146$$ 10.8252i 0.895903i
$$147$$ 0 0
$$148$$ 11.0491 0.908229
$$149$$ 3.38495 1.95430i 0.277306 0.160103i −0.354897 0.934905i $$-0.615484\pi$$
0.632203 + 0.774803i $$0.282151\pi$$
$$150$$ −0.302659 + 0.524221i −0.0247120 + 0.0428024i
$$151$$ −20.9488 12.0948i −1.70479 0.984259i −0.940760 0.339074i $$-0.889886\pi$$
−0.764027 0.645185i $$-0.776780\pi$$
$$152$$ 0.760837 0.439269i 0.0617120 0.0356294i
$$153$$ 8.71792 0.704802
$$154$$ 0 0
$$155$$ −13.3022 −1.06846
$$156$$ 4.37263 2.52454i 0.350090 0.202125i
$$157$$ 17.5828 + 10.1514i 1.40326 + 0.810172i 0.994726 0.102571i $$-0.0327068\pi$$
0.408534 + 0.912743i $$0.366040\pi$$
$$158$$ −4.24264 + 7.34847i −0.337526 + 0.584613i
$$159$$ 0.284859 0.164463i 0.0225908 0.0130428i
$$160$$ 2.05161 0.162194
$$161$$ 0 0
$$162$$ 4.07107i 0.319853i
$$163$$ 6.63031 + 11.4840i 0.519326 + 0.899499i 0.999748 + 0.0224612i $$0.00715023\pi$$
−0.480422 + 0.877038i $$0.659516\pi$$
$$164$$ 1.18432 2.05130i 0.0924798 0.160180i
$$165$$ −1.01915 5.10719i −0.0793407 0.397594i
$$166$$ 10.6654 6.15767i 0.827795 0.477928i
$$167$$ −20.4160 −1.57984 −0.789920 0.613210i $$-0.789878\pi$$
−0.789920 + 0.613210i $$0.789878\pi$$
$$168$$ 0 0
$$169$$ 30.5196 2.34766
$$170$$ −3.70427 6.41598i −0.284104 0.492083i
$$171$$ −1.06049 + 1.83682i −0.0810977 + 0.140465i
$$172$$ 6.76615 + 3.90644i 0.515914 + 0.297863i
$$173$$ −7.78809 13.4894i −0.592117 1.02558i −0.993947 0.109863i $$-0.964959\pi$$
0.401830 0.915714i $$-0.368374\pi$$
$$174$$ 4.73728i 0.359132i
$$175$$ 0 0
$$176$$ 2.49222 2.18834i 0.187859 0.164952i
$$177$$ 1.23165 + 2.13327i 0.0925761 + 0.160347i
$$178$$ 3.36413 5.82684i 0.252152 0.436740i
$$179$$ 2.25080 3.89850i 0.168232 0.291387i −0.769566 0.638567i $$-0.779527\pi$$
0.937798 + 0.347180i $$0.112861\pi$$
$$180$$ −4.28945 + 2.47652i −0.319717 + 0.184589i
$$181$$ 8.18338i 0.608266i 0.952630 + 0.304133i $$0.0983667\pi$$
−0.952630 + 0.304133i $$0.901633\pi$$
$$182$$ 0 0
$$183$$ 8.67483i 0.641262i
$$184$$ 5.73249 3.30966i 0.422605 0.243991i
$$185$$ 19.6314 + 11.3342i 1.44333 + 0.833308i
$$186$$ −4.29762 2.48123i −0.315116 0.181933i
$$187$$ −11.3434 3.84277i −0.829509 0.281011i
$$188$$ 5.74713i 0.419153i
$$189$$ 0 0
$$190$$ 1.80242 0.130761
$$191$$ −5.18311 8.97741i −0.375037 0.649582i 0.615296 0.788296i $$-0.289037\pi$$
−0.990333 + 0.138714i $$0.955703\pi$$
$$192$$ 0.662827 + 0.382683i 0.0478354 + 0.0276178i
$$193$$ −1.40584 0.811664i −0.101195 0.0584248i 0.448549 0.893758i $$-0.351941\pi$$
−0.549743 + 0.835334i $$0.685274\pi$$
$$194$$ 4.61940 + 8.00103i 0.331653 + 0.574441i
$$195$$ 10.3587 0.741805
$$196$$ 0 0
$$197$$ 4.38713i 0.312570i −0.987712 0.156285i $$-0.950048\pi$$
0.987712 0.156285i $$-0.0499518\pi$$
$$198$$ −2.56911 + 7.58369i −0.182579 + 0.538949i
$$199$$ 17.3760 + 10.0320i 1.23175 + 0.711151i 0.967394 0.253275i $$-0.0815077\pi$$
0.264355 + 0.964426i $$0.414841\pi$$
$$200$$ −0.684927 0.395443i −0.0484317 0.0279620i
$$201$$ 1.96360 1.13368i 0.138502 0.0799639i
$$202$$ 1.85966i 0.130845i
$$203$$ 0 0
$$204$$ 2.76380i 0.193505i
$$205$$ 4.20847 2.42976i 0.293933 0.169702i
$$206$$ 3.35505 5.81112i 0.233758 0.404880i
$$207$$ −7.99022 + 13.8395i −0.555359 + 0.961909i
$$208$$ 3.29847 + 5.71311i 0.228708 + 0.396133i
$$209$$ 2.18952 1.92254i 0.151452 0.132985i
$$210$$ 0 0
$$211$$ 8.56380i 0.589556i −0.955566 0.294778i $$-0.904754\pi$$
0.955566 0.294778i $$-0.0952457\pi$$
$$212$$ 0.214882 + 0.372186i 0.0147581 + 0.0255619i
$$213$$ 1.41449 + 0.816659i 0.0969195 + 0.0559565i
$$214$$ 7.37667 12.7768i 0.504259 0.873402i
$$215$$ 8.01450 + 13.8815i 0.546584 + 0.946712i
$$216$$ −4.14386 −0.281954
$$217$$ 0 0
$$218$$ −6.00000 −0.406371
$$219$$ 7.17526 4.14264i 0.484859 0.279934i
$$220$$ 6.67287 1.33158i 0.449885 0.0897753i
$$221$$ 11.9110 20.6305i 0.801223 1.38776i
$$222$$ 4.22830 + 7.32363i 0.283785 + 0.491530i
$$223$$ 8.24084i 0.551848i 0.961180 + 0.275924i $$0.0889837\pi$$
−0.961180 + 0.275924i $$0.911016\pi$$
$$224$$ 0 0
$$225$$ 1.90937 0.127291
$$226$$ 0.517296 0.298661i 0.0344100 0.0198666i
$$227$$ 13.7397 23.7979i 0.911938 1.57952i 0.100614 0.994926i $$-0.467919\pi$$
0.811324 0.584597i $$-0.198747\pi$$
$$228$$ 0.582319 + 0.336202i 0.0385650 + 0.0222655i
$$229$$ 0.0903638 0.0521716i 0.00597141 0.00344759i −0.497011 0.867744i $$-0.665569\pi$$
0.502983 + 0.864296i $$0.332236\pi$$
$$230$$ 13.5803 0.895456
$$231$$ 0 0
$$232$$ −6.18955 −0.406364
$$233$$ 13.1269 7.57884i 0.859974 0.496507i −0.00402925 0.999992i $$-0.501283\pi$$
0.864004 + 0.503485i $$0.167949\pi$$
$$234$$ −13.7927 7.96321i −0.901656 0.520571i
$$235$$ 5.89544 10.2112i 0.384576 0.666106i
$$236$$ −2.78725 + 1.60922i −0.181435 + 0.104751i
$$237$$ −6.49435 −0.421854
$$238$$ 0 0
$$239$$ 25.9135i 1.67620i −0.545515 0.838101i $$-0.683666\pi$$
0.545515 0.838101i $$-0.316334\pi$$
$$240$$ 0.785118 + 1.35986i 0.0506792 + 0.0877789i
$$241$$ −3.65554 + 6.33158i −0.235474 + 0.407853i −0.959410 0.282014i $$-0.908998\pi$$
0.723936 + 0.689867i $$0.242331\pi$$
$$242$$ 6.68563 8.73512i 0.429769 0.561515i
$$243$$ 13.4645 7.77372i 0.863747 0.498684i
$$244$$ −11.3342 −0.725599
$$245$$ 0 0
$$246$$ 1.81288 0.115585
$$247$$ 2.89783 + 5.01919i 0.184385 + 0.319364i
$$248$$ 3.24188 5.61510i 0.205860 0.356560i
$$249$$ 8.16294 + 4.71287i 0.517305 + 0.298666i
$$250$$ −5.94033 10.2889i −0.375699 0.650730i
$$251$$ 10.0161i 0.632208i −0.948724 0.316104i $$-0.897625\pi$$
0.948724 0.316104i $$-0.102375\pi$$
$$252$$ 0 0
$$253$$ 16.4968 14.4853i 1.03715 0.910682i
$$254$$ 3.66501 + 6.34799i 0.229963 + 0.398308i
$$255$$ 2.83512 4.91058i 0.177542 0.307512i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −15.1654 + 8.75577i −0.945994 + 0.546170i −0.891834 0.452362i $$-0.850581\pi$$
−0.0541598 + 0.998532i $$0.517248\pi$$
$$258$$ 5.97972i 0.372281i
$$259$$ 0 0
$$260$$ 13.5344i 0.839365i
$$261$$ 12.9409 7.47145i 0.801023 0.462471i
$$262$$ 7.63878 + 4.41025i 0.471925 + 0.272466i
$$263$$ −7.34847 4.24264i −0.453126 0.261612i 0.256023 0.966671i $$-0.417588\pi$$
−0.709150 + 0.705058i $$0.750921\pi$$
$$264$$ 2.40422 + 0.814474i 0.147970 + 0.0501274i
$$265$$ 0.881709i 0.0541629i
$$266$$ 0 0
$$267$$ 5.14958 0.315149
$$268$$ 1.48123 + 2.56556i 0.0904805 + 0.156717i
$$269$$ 5.85020 + 3.37761i 0.356693 + 0.205937i 0.667629 0.744494i $$-0.267309\pi$$
−0.310936 + 0.950431i $$0.600643\pi$$
$$270$$ −7.36260 4.25080i −0.448073 0.258695i
$$271$$ 9.77158 + 16.9249i 0.593581 + 1.02811i 0.993745 + 0.111669i $$0.0356197\pi$$
−0.400164 + 0.916443i $$0.631047\pi$$
$$272$$ 3.61108 0.218954
$$273$$ 0 0
$$274$$ 3.23620i 0.195506i
$$275$$ −2.48438 0.841631i −0.149814 0.0507522i
$$276$$ 4.38746 + 2.53310i 0.264094 + 0.152475i
$$277$$ 23.1011 + 13.3374i 1.38801 + 0.801368i 0.993091 0.117348i $$-0.0374394\pi$$
0.394919 + 0.918716i $$0.370773\pi$$
$$278$$ −2.14014 + 1.23561i −0.128357 + 0.0741070i
$$279$$ 15.6532i 0.937132i
$$280$$ 0 0
$$281$$ 20.9533i 1.24997i 0.780636 + 0.624986i $$0.214895\pi$$
−0.780636 + 0.624986i $$0.785105\pi$$
$$282$$ 3.80935 2.19933i 0.226844 0.130968i
$$283$$ −5.03147 + 8.71476i −0.299090 + 0.518039i −0.975928 0.218093i $$-0.930016\pi$$
0.676838 + 0.736132i $$0.263350\pi$$
$$284$$ −1.06702 + 1.84813i −0.0633157 + 0.109666i
$$285$$ 0.689757 + 1.19469i 0.0408577 + 0.0707675i
$$286$$ 14.4363 + 16.4410i 0.853637 + 0.972180i
$$287$$ 0 0
$$288$$ 2.41421i 0.142259i
$$289$$ 1.98005 + 3.42955i 0.116474 + 0.201738i
$$290$$ −10.9973 6.34928i −0.645782 0.372842i
$$291$$ −3.53553 + 6.12372i −0.207257 + 0.358979i
$$292$$ 5.41262 + 9.37493i 0.316749 + 0.548626i
$$293$$ −29.6429 −1.73176 −0.865879 0.500253i $$-0.833240\pi$$
−0.865879 + 0.500253i $$0.833240\pi$$
$$294$$ 0 0
$$295$$ −6.60300 −0.384442
$$296$$ −9.56878 + 5.52454i −0.556174 + 0.321107i
$$297$$ −13.4779 + 2.68954i −0.782067 + 0.156063i
$$298$$ −1.95430 + 3.38495i −0.113210 + 0.196085i
$$299$$ 21.8336 + 37.8169i 1.26267 + 2.18701i
$$300$$ 0.605318i 0.0349480i
$$301$$ 0 0
$$302$$ 24.1895 1.39195
$$303$$ −1.23263 + 0.711661i −0.0708129 + 0.0408839i
$$304$$ −0.439269 + 0.760837i −0.0251938 + 0.0436370i
$$305$$ −20.1380 11.6267i −1.15310 0.665743i
$$306$$ −7.54994 + 4.35896i −0.431601 + 0.249185i
$$307$$ 16.1877 0.923883 0.461941 0.886910i $$-0.347153\pi$$
0.461941 + 0.886910i $$0.347153\pi$$
$$308$$ 0 0
$$309$$ 5.13569 0.292159
$$310$$ 11.5200 6.65109i 0.654293 0.377756i
$$311$$ 1.23529 + 0.713195i 0.0700469 + 0.0404416i 0.534614 0.845096i $$-0.320457\pi$$
−0.464568 + 0.885538i $$0.653790\pi$$
$$312$$ −2.52454 + 4.37263i −0.142924 + 0.247551i
$$313$$ −9.99982 + 5.77340i −0.565223 + 0.326332i −0.755239 0.655449i $$-0.772479\pi$$
0.190016 + 0.981781i $$0.439146\pi$$
$$314$$ −20.3029 −1.14576
$$315$$ 0 0
$$316$$ 8.48528i 0.477334i
$$317$$ −15.8620 27.4737i −0.890896 1.54308i −0.838803 0.544435i $$-0.816744\pi$$
−0.0520931 0.998642i $$-0.516589\pi$$
$$318$$ −0.164463 + 0.284859i −0.00922265 + 0.0159741i
$$319$$ −20.1315 + 4.01728i −1.12715 + 0.224924i
$$320$$ −1.77675 + 1.02581i −0.0993233 + 0.0573443i
$$321$$ 11.2917 0.630242
$$322$$ 0 0
$$323$$ 3.17247 0.176521
$$324$$ 2.03553 + 3.52565i 0.113085 + 0.195869i
$$325$$ 2.60871 4.51842i 0.144705 0.250637i
$$326$$ −11.4840 6.63031i −0.636042 0.367219i
$$327$$ −2.29610 3.97696i −0.126975 0.219927i
$$328$$ 2.36864i 0.130786i
$$329$$ 0 0
$$330$$ 3.43620 + 3.91338i 0.189157 + 0.215425i
$$331$$ −15.9620 27.6469i −0.877348 1.51961i −0.854240 0.519879i $$-0.825977\pi$$
−0.0231086 0.999733i $$-0.507356\pi$$
$$332$$ −6.15767 + 10.6654i −0.337946 + 0.585339i
$$333$$ 13.3374 23.1011i 0.730886 1.26593i
$$334$$ 17.6808 10.2080i 0.967450 0.558558i
$$335$$ 6.07782i 0.332067i
$$336$$ 0 0
$$337$$ 1.40854i 0.0767278i −0.999264 0.0383639i $$-0.987785\pi$$
0.999264 0.0383639i $$-0.0122146\pi$$
$$338$$ −26.4307 + 15.2598i −1.43764 + 0.830023i
$$339$$ 0.395921 + 0.228585i 0.0215035 + 0.0124150i
$$340$$ 6.41598 + 3.70427i 0.347955 + 0.200892i
$$341$$ 6.89978 20.3672i 0.373644 1.10295i
$$342$$ 2.12098i 0.114689i
$$343$$ 0 0
$$344$$ −7.81288 −0.421242
$$345$$ 5.19694 + 9.00137i 0.279794 + 0.484617i
$$346$$ 13.4894 + 7.78809i 0.725193 + 0.418690i
$$347$$ −9.55973 5.51931i −0.513193 0.296292i 0.220952 0.975285i $$-0.429084\pi$$
−0.734145 + 0.678993i $$0.762417\pi$$
$$348$$ −2.36864 4.10260i −0.126972 0.219923i
$$349$$ 15.5762 0.833773 0.416887 0.908958i $$-0.363121\pi$$
0.416887 + 0.908958i $$0.363121\pi$$
$$350$$ 0 0
$$351$$ 27.3368i 1.45913i
$$352$$ −1.06416 + 3.14127i −0.0567200 + 0.167430i
$$353$$ 5.44549 + 3.14396i 0.289834 + 0.167336i 0.637867 0.770146i $$-0.279817\pi$$
−0.348033 + 0.937482i $$0.613150\pi$$
$$354$$ −2.13327 1.23165i −0.113382 0.0654612i
$$355$$ −3.79164 + 2.18910i −0.201239 + 0.116186i
$$356$$ 6.72825i 0.356597i
$$357$$ 0 0
$$358$$ 4.50159i 0.237917i
$$359$$ 8.90941 5.14385i 0.470221 0.271482i −0.246111 0.969242i $$-0.579153\pi$$
0.716332 + 0.697759i $$0.245820\pi$$
$$360$$ 2.47652 4.28945i 0.130524 0.226074i
$$361$$ 9.11408 15.7861i 0.479689 0.830845i
$$362$$ −4.09169 7.08701i −0.215054 0.372485i
$$363$$ 8.34836 + 1.08864i 0.438175 + 0.0571385i
$$364$$ 0 0
$$365$$ 22.2092i 1.16248i
$$366$$ −4.33742 7.51262i −0.226720 0.392691i
$$367$$ −3.91575 2.26076i −0.204401 0.118011i 0.394306 0.918979i $$-0.370985\pi$$
−0.598706 + 0.800969i $$0.704318\pi$$
$$368$$ −3.30966 + 5.73249i −0.172528 + 0.298827i
$$369$$ −2.85920 4.95228i −0.148844 0.257805i
$$370$$ −22.6684 −1.17848
$$371$$ 0 0
$$372$$ 4.96246 0.257291
$$373$$ −17.0814 + 9.86195i −0.884442 + 0.510633i −0.872120 0.489291i $$-0.837255\pi$$
−0.0123213 + 0.999924i $$0.503922\pi$$
$$374$$ 11.7450 2.34374i 0.607321 0.121192i
$$375$$ 4.54653 7.87482i 0.234782 0.406654i
$$376$$ 2.87357 + 4.97716i 0.148193 + 0.256677i
$$377$$ 40.8321i 2.10296i
$$378$$ 0 0
$$379$$ −35.6268 −1.83003 −0.915014 0.403423i $$-0.867820\pi$$
−0.915014 + 0.403423i $$0.867820\pi$$
$$380$$ −1.56094 + 0.901211i −0.0800747 + 0.0462311i
$$381$$ −2.80508 + 4.85854i −0.143708 + 0.248910i
$$382$$ 8.97741 + 5.18311i 0.459324 + 0.265191i
$$383$$ 18.7384 10.8186i 0.957488 0.552806i 0.0620891 0.998071i $$-0.480224\pi$$
0.895399 + 0.445265i $$0.146890\pi$$
$$384$$ −0.765367 −0.0390575
$$385$$ 0 0
$$386$$ 1.62333 0.0826252
$$387$$ 16.3349 9.43098i 0.830351 0.479403i
$$388$$ −8.00103 4.61940i −0.406191 0.234514i
$$389$$ 4.32349 7.48851i 0.219210 0.379682i −0.735357 0.677680i $$-0.762985\pi$$
0.954567 + 0.297998i $$0.0963188\pi$$
$$390$$ −8.97094 + 5.17937i −0.454261 + 0.262268i
$$391$$ 23.9029 1.20882
$$392$$ 0 0
$$393$$ 6.75092i 0.340539i
$$394$$ 2.19356 + 3.79936i 0.110510 + 0.191409i
$$395$$ 8.70426 15.0762i 0.437959 0.758567i
$$396$$ −1.56693 7.85223i −0.0787410 0.394589i
$$397$$ −31.3257 + 18.0859i −1.57219 + 0.907705i −0.576292 + 0.817244i $$0.695501\pi$$
−0.995900 + 0.0904617i $$0.971166\pi$$
$$398$$ −20.0640 −1.00572
$$399$$ 0 0
$$400$$ 0.790886 0.0395443
$$401$$ 4.49678 + 7.78865i 0.224558 + 0.388947i 0.956187 0.292757i $$-0.0945727\pi$$
−0.731628 + 0.681704i $$0.761239\pi$$
$$402$$ −1.13368 + 1.96360i −0.0565430 + 0.0979354i
$$403$$ 37.0425 + 21.3865i 1.84522 + 1.06534i
$$404$$ −0.929830 1.61051i −0.0462608 0.0801260i
$$405$$ 8.35225i 0.415027i
$$406$$ 0 0
$$407$$ −27.5368 + 24.1791i −1.36495 + 1.19851i
$$408$$ 1.38190 + 2.39352i 0.0684143 + 0.118497i
$$409$$ −4.79140 + 8.29894i −0.236919 + 0.410356i −0.959829 0.280587i $$-0.909471\pi$$
0.722909 + 0.690943i $$0.242804\pi$$
$$410$$ −2.42976 + 4.20847i −0.119997 + 0.207842i
$$411$$ 2.14504 1.23844i 0.105807 0.0610877i
$$412$$ 6.71011i 0.330583i
$$413$$ 0 0
$$414$$ 15.9804i 0.785396i
$$415$$ −21.8813 + 12.6331i −1.07411 + 0.620137i
$$416$$ −5.71311 3.29847i −0.280108 0.161721i
$$417$$ −1.63799 0.945695i −0.0802128 0.0463109i
$$418$$ −0.934908 + 2.75972i −0.0457278 + 0.134983i
$$419$$ 37.9064i 1.85185i −0.377709 0.925924i $$-0.623288\pi$$
0.377709 0.925924i $$-0.376712\pi$$
$$420$$ 0 0
$$421$$ 2.88394 0.140555 0.0702774 0.997527i $$-0.477612\pi$$
0.0702774 + 0.997527i $$0.477612\pi$$
$$422$$ 4.28190 + 7.41646i 0.208440 + 0.361028i
$$423$$ −12.0159 6.93740i −0.584235 0.337308i
$$424$$ −0.372186 0.214882i −0.0180750 0.0104356i
$$425$$ −1.42798 2.47333i −0.0692670 0.119974i
$$426$$ −1.63332 −0.0791345
$$427$$ 0 0
$$428$$ 14.7533i 0.713130i
$$429$$ −5.37304 + 15.8605i −0.259413 + 0.765752i
$$430$$ −13.8815 8.01450i −0.669426 0.386493i
$$431$$ 28.0651 + 16.2034i 1.35185 + 0.780490i 0.988508 0.151167i $$-0.0483032\pi$$
0.363339 + 0.931657i $$0.381637\pi$$
$$432$$ 3.58869 2.07193i 0.172661 0.0996858i
$$433$$ 10.2319i 0.491714i −0.969306 0.245857i $$-0.920931\pi$$
0.969306 0.245857i $$-0.0790694\pi$$
$$434$$ 0 0
$$435$$ 9.71905i 0.465993i
$$436$$ 5.19615 3.00000i 0.248851 0.143674i
$$437$$ −2.90766 + 5.03622i −0.139092 + 0.240915i
$$438$$ −4.14264 + 7.17526i −0.197943 + 0.342847i
$$439$$ −14.4363 25.0044i −0.689008 1.19340i −0.972159 0.234321i $$-0.924713\pi$$
0.283152 0.959075i $$-0.408620\pi$$
$$440$$ −5.11308 + 4.48962i −0.243757 + 0.214034i
$$441$$ 0 0
$$442$$ 23.8221i 1.13310i
$$443$$ 4.28018 + 7.41349i 0.203358 + 0.352226i 0.949608 0.313439i $$-0.101481\pi$$
−0.746251 + 0.665665i $$0.768148\pi$$
$$444$$ −7.32363 4.22830i −0.347564 0.200666i
$$445$$ −6.90188 + 11.9544i −0.327181 + 0.566694i
$$446$$ −4.12042 7.13678i −0.195108 0.337936i
$$447$$ −2.99152 −0.141494
$$448$$ 0 0
$$449$$ −10.8089 −0.510102 −0.255051 0.966928i $$-0.582092\pi$$
−0.255051 + 0.966928i $$0.582092\pi$$
$$450$$ −1.65356 + 0.954684i −0.0779496 + 0.0450042i
$$451$$ 1.53735 + 7.70399i 0.0723908 + 0.362767i
$$452$$ −0.298661 + 0.517296i −0.0140478 + 0.0243315i
$$453$$ 9.25694 + 16.0335i 0.434929 + 0.753319i
$$454$$ 27.4795i 1.28967i
$$455$$ 0 0
$$456$$ −0.672404 −0.0314882
$$457$$ 21.1220 12.1948i 0.988044 0.570448i 0.0833551 0.996520i $$-0.473436\pi$$
0.904689 + 0.426072i $$0.140103\pi$$
$$458$$ −0.0521716 + 0.0903638i −0.00243782 + 0.00422242i
$$459$$ −12.9590 7.48190i −0.604876 0.349225i
$$460$$ −11.7609 + 6.79013i −0.548353 + 0.316592i
$$461$$ 1.13186 0.0527158 0.0263579 0.999653i $$-0.491609\pi$$
0.0263579 + 0.999653i $$0.491609\pi$$
$$462$$ 0 0
$$463$$ 6.38388 0.296684 0.148342 0.988936i $$-0.452606\pi$$
0.148342 + 0.988936i $$0.452606\pi$$
$$464$$ 5.36031 3.09477i 0.248846 0.143671i
$$465$$ 8.81704 + 5.09052i 0.408881 + 0.236067i
$$466$$ −7.57884 + 13.1269i −0.351083 + 0.608094i
$$467$$ 30.9033 17.8420i 1.43003 0.825629i 0.432910 0.901437i $$-0.357487\pi$$
0.997122 + 0.0758078i $$0.0241536\pi$$
$$468$$ 15.9264 0.736199
$$469$$ 0 0
$$470$$ 11.7909i 0.543873i
$$471$$ −7.76957 13.4573i −0.358003 0.620079i
$$472$$ 1.60922 2.78725i 0.0740704 0.128294i
$$473$$ −25.4114 + 5.07089i −1.16842 + 0.233160i
$$474$$ 5.62427 3.24718i 0.258331 0.149148i
$$475$$ 0.694824 0.0318807
$$476$$ 0 0
$$477$$ 1.03754 0.0475058
$$478$$ 12.9567 + 22.4417i 0.592627 + 1.02646i
$$479$$ −5.79094 + 10.0302i −0.264595 + 0.458291i −0.967457 0.253034i $$-0.918571\pi$$
0.702863 + 0.711325i $$0.251905\pi$$
$$480$$ −1.35986 0.785118i −0.0620690 0.0358356i
$$481$$ −36.4450 63.1246i −1.66175 2.87824i
$$482$$ 7.31108i 0.333011i
$$483$$ 0 0
$$484$$ −1.42237 + 10.9077i −0.0646532 + 0.495802i
$$485$$ −9.47721 16.4150i −0.430338 0.745368i
$$486$$ −7.77372 + 13.4645i −0.352623 + 0.610761i
$$487$$ −20.0319 + 34.6963i −0.907732 + 1.57224i −0.0905248 + 0.995894i $$0.528854\pi$$
−0.817207 + 0.576344i $$0.804479\pi$$
$$488$$ 9.81572 5.66711i 0.444337 0.256538i
$$489$$ 10.1492i 0.458964i
$$490$$ 0 0
$$491$$ 19.7876i 0.893003i −0.894783 0.446502i $$-0.852670\pi$$
0.894783 0.446502i $$-0.147330\pi$$
$$492$$ −1.57000 + 0.906438i −0.0707810 + 0.0408654i
$$493$$ −19.3565 11.1755i −0.871773 0.503318i
$$494$$ −5.01919 2.89783i −0.225824 0.130380i
$$495$$ 5.27083 15.5588i 0.236906 0.699316i
$$496$$ 6.48376i 0.291130i
$$497$$ 0 0
$$498$$ −9.42575 −0.422378
$$499$$ 13.3276 + 23.0841i 0.596627 + 1.03339i 0.993315 + 0.115435i $$0.0368260\pi$$
−0.396688 + 0.917953i $$0.629841\pi$$
$$500$$ 10.2889 + 5.94033i 0.460136 + 0.265660i
$$501$$ 13.5323 + 7.81288i 0.604579 + 0.349054i
$$502$$ 5.00803 + 8.67417i 0.223519 + 0.387147i
$$503$$ −10.9142 −0.486638 −0.243319 0.969946i $$-0.578236\pi$$
−0.243319 + 0.969946i $$0.578236\pi$$
$$504$$ 0 0
$$505$$ 3.81530i 0.169779i
$$506$$ −7.04402 + 20.7930i −0.313145 + 0.924363i
$$507$$ −20.2292 11.6793i −0.898410 0.518697i
$$508$$ −6.34799 3.66501i −0.281646 0.162609i
$$509$$ −19.4284 + 11.2170i −0.861149 + 0.497184i −0.864397 0.502810i $$-0.832299\pi$$
0.00324816 + 0.999995i $$0.498966\pi$$
$$510$$ 5.67025i 0.251083i
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ 3.15280 1.82027i 0.139200 0.0803669i
$$514$$ 8.75577 15.1654i 0.386200 0.668919i
$$515$$ −6.88327 + 11.9222i −0.303313 + 0.525354i
$$516$$ −2.98986 5.17859i −0.131621 0.227975i
$$517$$ 12.5767 + 14.3231i 0.553121 + 0.629931i
$$518$$ 0 0
$$519$$ 11.9215i 0.523295i
$$520$$ −6.76718 11.7211i −0.296760 0.514004i
$$521$$ 33.9574 + 19.6053i 1.48770 + 0.858925i 0.999902 0.0140307i $$-0.00446624\pi$$
0.487800 + 0.872955i $$0.337800\pi$$
$$522$$ −7.47145 + 12.9409i −0.327016 + 0.566409i
$$523$$ 9.04494 + 15.6663i 0.395508 + 0.685039i 0.993166 0.116712i $$-0.0372353\pi$$
−0.597658 + 0.801751i $$0.703902\pi$$
$$524$$ −8.82050 −0.385325
$$525$$ 0 0
$$526$$ 8.48528 0.369976
$$527$$ 20.2766 11.7067i 0.883262 0.509952i
$$528$$ −2.48935 + 0.496755i −0.108335 + 0.0216185i
$$529$$ −10.4077 + 18.0266i −0.452507 + 0.783764i
$$530$$ −0.440854 0.763582i −0.0191495 0.0331679i
$$531$$ 7.77001i 0.337190i
$$532$$ 0 0
$$533$$ −15.6258 −0.676827
$$534$$ −4.45967 + 2.57479i −0.192989 + 0.111422i
$$535$$ −15.1341 + 26.2130i −0.654303 + 1.13329i
$$536$$ −2.56556 1.48123i −0.110816 0.0639794i
$$537$$ −2.98378 + 1.72269i −0.128760 + 0.0743394i
$$538$$ −6.75523 −0.291238
$$539$$ 0 0
$$540$$ 8.50159 0.365850
$$541$$ 8.33615 4.81288i 0.358399 0.206922i −0.309979 0.950743i $$-0.600322\pi$$
0.668378 + 0.743822i $$0.266989\pi$$
$$542$$ −16.9249 9.77158i −0.726985 0.419725i
$$543$$ 3.13164 5.42416i 0.134392 0.232773i
$$544$$ −3.12729 + 1.80554i −0.134081 + 0.0774119i
$$545$$ 12.3097 0.527289
$$546$$ 0 0
$$547$$ 10.2834i 0.439685i −0.975535 0.219843i $$-0.929446\pi$$
0.975535 0.219843i $$-0.0705544\pi$$
$$548$$ 1.61810 + 2.80263i 0.0691218 + 0.119722i
$$549$$ −13.6816 + 23.6972i −0.583917 + 1.01137i
$$550$$ 2.57235 0.513318i 0.109686 0.0218880i
$$551$$ 4.70924 2.71888i 0.200620 0.115828i
$$552$$ −5.06620 −0.215632
$$553$$ 0 0
$$554$$ −26.6748 −1.13330
$$555$$ −8.67483 15.0252i −0.368226 0.637786i
$$556$$ 1.23561 2.14014i 0.0524016 0.0907622i
$$557$$ 32.2426 + 18.6153i 1.36616 + 0.788755i 0.990436 0.137974i $$-0.0440591\pi$$
0.375729 + 0.926730i $$0.377392\pi$$
$$558$$ −7.82660 13.5561i −0.331326 0.573874i
$$559$$ 51.5411i 2.17995i
$$560$$ 0 0
$$561$$ 6.04812 + 6.88801i 0.255352 + 0.290812i
$$562$$ −10.4767 18.1461i −0.441932 0.765448i
$$563$$ −8.09387 + 14.0190i −0.341116 + 0.590830i −0.984640 0.174596i $$-0.944138\pi$$
0.643524 + 0.765426i $$0.277471\pi$$
$$564$$ −2.19933 + 3.80935i −0.0926086 + 0.160403i
$$565$$ −1.06129 + 0.612736i −0.0446488 + 0.0257780i
$$566$$ 10.0629i 0.422977i
$$567$$ 0 0
$$568$$ 2.13403i 0.0895420i
$$569$$ −26.4052 + 15.2451i −1.10696 + 0.639106i −0.938042 0.346523i $$-0.887362\pi$$
−0.168923 + 0.985629i $$0.554029\pi$$
$$570$$ −1.19469 0.689757i −0.0500402 0.0288907i
$$571$$ −35.0634 20.2439i −1.46736 0.847179i −0.468025 0.883715i $$-0.655034\pi$$
−0.999332 + 0.0365365i $$0.988367\pi$$
$$572$$ −20.7227 7.02021i −0.866461 0.293530i
$$573$$ 7.93396i 0.331446i
$$574$$ 0 0
$$575$$ 5.23512 0.218320
$$576$$ 1.20711 + 2.09077i 0.0502961 + 0.0871154i
$$577$$ −22.1360 12.7802i −0.921533 0.532047i −0.0374092 0.999300i $$-0.511910\pi$$
−0.884124 + 0.467253i $$0.845244\pi$$
$$578$$ −3.42955 1.98005i −0.142651 0.0823594i
$$579$$ 0.621221 + 1.07599i 0.0258170 + 0.0447164i
$$580$$ 12.6986 0.527279
$$581$$ 0 0
$$582$$ 7.07107i 0.293105i
$$583$$ −1.35000 0.457338i −0.0559114 0.0189410i
$$584$$ −9.37493 5.41262i −0.387937 0.223976i
$$585$$ 28.2972 + 16.3374i 1.16995 + 0.675469i
$$586$$ 25.6715 14.8215i 1.06048 0.612269i
$$587$$ 7.18094i 0.296389i 0.988958 + 0.148195i $$0.0473462\pi$$
−0.988958 + 0.148195i $$0.952654\pi$$
$$588$$ 0 0
$$589$$ 5.69624i 0.234709i
$$590$$ 5.71837 3.30150i 0.235421 0.135921i
$$591$$ −1.67888 + 2.90791i −0.0690599 + 0.119615i
$$592$$ 5.52454 9.56878i 0.227057 0.393274i
$$593$$ −9.88857 17.1275i −0.406075 0.703343i 0.588371 0.808591i $$-0.299770\pi$$
−0.994446 + 0.105249i $$0.966436\pi$$
$$594$$ 10.3274 9.06816i 0.423740 0.372071i
$$595$$ 0 0
$$596$$ 3.90860i 0.160103i
$$597$$ −7.67817 13.2990i −0.314247 0.544291i
$$598$$ −37.8169 21.8336i −1.54645 0.892842i
$$599$$ 6.87989 11.9163i 0.281105 0.486888i −0.690552 0.723282i $$-0.742632\pi$$
0.971657 + 0.236395i $$0.0759658\pi$$
$$600$$ 0.302659 + 0.524221i 0.0123560 + 0.0214012i
$$601$$ 11.0384 0.450266 0.225133 0.974328i $$-0.427718\pi$$
0.225133 + 0.974328i $$0.427718\pi$$
$$602$$ 0 0
$$603$$ 7.15201 0.291252
$$604$$ −20.9488 + 12.0948i −0.852393 + 0.492129i
$$605$$ −13.7163 + 17.9211i −0.557648 + 0.728595i
$$606$$ 0.711661 1.23263i 0.0289093 0.0500723i
$$607$$ 5.90718 + 10.2315i 0.239765 + 0.415285i 0.960647 0.277773i $$-0.0895963\pi$$
−0.720882 + 0.693058i $$0.756263\pi$$
$$608$$ 0.878539i 0.0356294i
$$609$$ 0 0
$$610$$ 23.2534 0.941503
$$611$$ −32.8340 + 18.9567i −1.32832 + 0.766907i
$$612$$ 4.35896 7.54994i 0.176200 0.305188i
$$613$$ 18.3140 + 10.5736i 0.739697 + 0.427064i 0.821959 0.569546i $$-0.192881\pi$$
−0.0822621 + 0.996611i $$0.526214\pi$$
$$614$$ −14.0190 + 8.09387i −0.565760 + 0.326642i
$$615$$ −3.71932 −0.149978
$$616$$ 0 0
$$617$$ −43.8743 −1.76631 −0.883157 0.469078i $$-0.844586\pi$$
−0.883157 + 0.469078i $$0.844586\pi$$
$$618$$ −4.44764 + 2.56785i −0.178910 + 0.103294i
$$619$$ 4.12964 + 2.38425i 0.165984 + 0.0958310i 0.580691 0.814124i $$-0.302782\pi$$
−0.414707 + 0.909955i $$0.636116\pi$$
$$620$$ −6.65109 + 11.5200i −0.267114 + 0.462655i
$$621$$ 23.7546 13.7148i 0.953241 0.550354i
$$622$$ −1.42639 −0.0571931
$$623$$ 0 0
$$624$$ 5.04908i 0.202125i
$$625$$ 10.2100 + 17.6843i 0.408401 + 0.707372i
$$626$$ 5.77340 9.99982i 0.230751 0.399673i
$$627$$ −2.18699 + 0.436419i −0.0873401 + 0.0174289i
$$628$$ 17.5828 10.1514i 0.701630 0.405086i
$$629$$ −39.8991 −1.59088
$$630$$ 0 0
$$631$$ −6.66195 −0.265208 −0.132604 0.991169i $$-0.542334\pi$$
−0.132604 + 0.991169i $$0.542334\pi$$
$$632$$ 4.24264 + 7.34847i 0.168763 + 0.292306i
$$633$$ −3.27722 + 5.67632i −0.130258 + 0.225613i
$$634$$ 27.4737 + 15.8620i 1.09112 + 0.629959i
$$635$$ −7.51918 13.0236i −0.298390 0.516826i
$$636$$ 0.328927i 0.0130428i
$$637$$ 0 0
$$638$$ 15.4257 13.5448i 0.610711 0.536244i
$$639$$ 2.57600 + 4.46177i 0.101905 + 0.176505i
$$640$$ 1.02581 1.77675i 0.0405486 0.0702322i
$$641$$ 5.76074 9.97789i 0.227535 0.394103i −0.729542 0.683936i $$-0.760267\pi$$
0.957077 + 0.289833i $$0.0935999\pi$$
$$642$$ −9.77892 + 5.64586i −0.385943 + 0.222824i
$$643$$ 21.7793i 0.858892i 0.903093 + 0.429446i $$0.141291\pi$$
−0.903093 + 0.429446i $$0.858709\pi$$
$$644$$ 0 0
$$645$$ 12.2681i 0.483055i
$$646$$ −2.74744 + 1.58624i −0.108097 + 0.0624096i
$$647$$ −15.2087 8.78075i −0.597916 0.345207i 0.170306 0.985391i $$-0.445525\pi$$
−0.768221 + 0.640185i $$0.778858\pi$$
$$648$$ −3.52565 2.03553i −0.138501 0.0799633i
$$649$$ 3.42495 10.1100i 0.134441 0.396852i
$$650$$ 5.21742i 0.204644i
$$651$$ 0 0
$$652$$ 13.2606 0.519326
$$653$$ −13.2213 22.9000i −0.517390 0.896146i −0.999796 0.0201984i $$-0.993570\pi$$
0.482406 0.875948i $$-0.339763\pi$$
$$654$$ 3.97696 + 2.29610i 0.155512 + 0.0897846i
$$655$$ −15.6718 9.04812i −0.612348 0.353539i
$$656$$ −1.18432 2.05130i −0.0462399 0.0800898i
$$657$$ 26.1344 1.01960
$$658$$ 0 0
$$659$$ 38.9324i 1.51659i 0.651910 + 0.758296i $$0.273968\pi$$
−0.651910 + 0.758296i $$0.726032\pi$$
$$660$$ −4.93253 1.67099i −0.191999 0.0650430i
$$661$$ 10.2982 + 5.94569i 0.400555 + 0.231261i 0.686723 0.726919i $$-0.259048\pi$$
−0.286168 + 0.958179i $$0.592382\pi$$
$$662$$ 27.6469 + 15.9620i 1.07453 + 0.620379i
$$663$$ −15.7899 + 9.11631i −0.613229 + 0.354048i
$$664$$ 12.3153i 0.477928i
$$665$$ 0 0
$$666$$ 26.6748i 1.03363i
$$667$$ 35.4815 20.4853i 1.37385 0.793193i
$$668$$ −10.2080 + 17.6808i −0.394960 + 0.684091i
$$669$$ 3.15363 5.46225i 0.121927 0.211183i
$$670$$ −3.03891 5.26354i −0.117403 0.203348i
$$671$$ 28.2474 24.8031i 1.09048 0.957512i
$$672$$ 0 0
$$673$$ 17.4386i 0.672210i 0.941825 + 0.336105i $$0.109110\pi$$
−0.941825 + 0.336105i $$0.890890\pi$$
$$674$$ 0.704268 + 1.21983i 0.0271274 + 0.0469860i
$$675$$ −2.83824 1.63866i −0.109244 0.0630720i
$$676$$ 15.2598 26.4307i 0.586915 1.01657i
$$677$$ 20.7150 + 35.8794i 0.796141 + 1.37896i 0.922112 + 0.386923i $$0.126462\pi$$
−0.125970 + 0.992034i $$0.540204\pi$$
$$678$$ −0.457170 −0.0175575
$$679$$ 0 0
$$680$$ −7.40854 −0.284104
$$681$$ −18.2141 + 10.5159i −0.697967 + 0.402971i
$$682$$ 4.20824 + 21.0884i 0.161142 + 0.807518i
$$683$$ −10.7076 + 18.5462i −0.409717 + 0.709650i −0.994858 0.101281i $$-0.967706\pi$$
0.585141 + 0.810931i $$0.301039\pi$$
$$684$$ 1.06049 + 1.83682i 0.0405488 + 0.0702327i
$$685$$ 6.63943i 0.253679i
$$686$$ 0 0
$$687$$ −0.0798608 −0.00304688
$$688$$ 6.76615 3.90644i 0.257957 0.148932i
$$689$$ 1.41756 2.45529i 0.0540048 0.0935391i
$$690$$ −9.00137 5.19694i −0.342676 0.197844i
$$691$$ 11.6732 6.73955i 0.444071 0.256384i −0.261252 0.965271i $$-0.584135\pi$$
0.705323 + 0.708886i $$0.250802\pi$$
$$692$$ −15.5762 −0.592117
$$693$$ 0 0
$$694$$ 11.0386 0.419020
$$695$$ 4.39074 2.53499i 0.166550 0.0961578i
$$696$$ 4.10260 + 2.36864i 0.155509 + 0.0897830i
$$697$$ −4.27667 + 7.40741i −0.161990 + 0.280576i
$$698$$ −13.4894 + 7.78809i −0.510580 + 0.294783i
$$699$$ −11.6012 −0.438797
$$700$$ 0 0
$$701$$ 26.4644i 0.999545i −0.866157 0.499773i $$-0.833417\pi$$
0.866157 0.499773i $$-0.166583\pi$$
$$702$$ 13.6684 + 23.6743i 0.515880 + 0.893531i
$$703$$ 4.85352 8.40654i 0.183054 0.317059i
$$704$$ −0.649042 3.25250i −0.0244617 0.122583i
$$705$$ −7.81532 + 4.51218i −0.294342 + 0.169938i
$$706$$ −6.28791 −0.236649
$$707$$ 0 0
$$708$$ 2.46329 0.0925761
$$709$$ −9.38888 16.2620i −0.352607 0.610733i 0.634099 0.773252i $$-0.281371\pi$$
−0.986705 + 0.162519i $$0.948038\pi$$
$$710$$ 2.18910 3.79164i 0.0821556 0.142298i
$$711$$ −17.7408 10.2426i −0.665331 0.384129i
$$712$$ −3.36413 5.82684i −0.126076 0.218370i
$$713$$ 42.9181i 1.60729i
$$714$$ 0 0
$$715$$ −29.6177 33.7307i −1.10764 1.26146i
$$716$$ −2.25080 3.89850i −0.0841162 0.145694i
$$717$$ −9.91665 + 17.1761i −0.370344 + 0.641455i
$$718$$ −5.14385 + 8.90941i −0.191967 + 0.332496i
$$719$$ −3.00287 + 1.73371i −0.111988 + 0.0646564i −0.554948 0.831885i $$-0.687262\pi$$
0.442960 + 0.896542i $$0.353928\pi$$
$$720$$ 4.95303i 0.184589i
$$721$$ 0 0
$$722$$ 18.2282i 0.678382i
$$723$$ 4.84598 2.79783i 0.180224 0.104052i
$$724$$ 7.08701 + 4.09169i 0.263387 + 0.152066i
$$725$$ −4.23939 2.44761i −0.157447 0.0909021i
$$726$$ −7.77421 + 3.23139i −0.288528 + 0.119928i
$$727$$ 21.6647i 0.803500i 0.915749 + 0.401750i $$0.131598\pi$$
−0.915749 + 0.401750i $$0.868402\pi$$
$$728$$ 0 0
$$729$$ 0.313708 0.0116188
$$730$$ −11.1046 19.2337i −0.410999 0.711872i
$$731$$ −24.4331 14.1065i −0.903691 0.521746i
$$732$$ 7.51262 + 4.33742i 0.277675 + 0.160315i
$$733$$ 7.45423 + 12.9111i 0.275328 + 0.476883i 0.970218 0.242234i $$-0.0778801\pi$$
−0.694890 + 0.719116i $$0.744547\pi$$
$$734$$ 4.52152 0.166892
$$735$$ 0 0
$$736$$ 6.61931i 0.243991i
$$737$$ −9.30587 3.15254i −0.342786 0.116125i
$$738$$ 4.95228 + 2.85920i 0.182296 + 0.105249i
$$739$$ −4.11862 2.37789i −0.151506 0.0874719i 0.422331 0.906442i $$-0.361212\pi$$
−0.573836 + 0.818970i $$0.694545\pi$$
$$740$$ 19.6314 11.3342i 0.721666 0.416654i
$$741$$ 4.43581i 0.162954i
$$742$$ 0 0
$$743$$ 14.8792i 0.545864i 0.962033 + 0.272932i $$0.0879934\pi$$
−0.962033 + 0.272932i $$0.912007\pi$$
$$744$$ −4.29762 + 2.48123i −0.157558 + 0.0909663i
$$745$$ 4.00947 6.94461i 0.146896 0.254431i
$$746$$ 9.86195 17.0814i 0.361072 0.625395i
$$747$$ 14.8659 + 25.7485i 0.543916 + 0.942090i
$$748$$ −8.99962 + 7.90226i −0.329059 + 0.288935i
$$749$$ 0 0
$$750$$ 9.09306i 0.332032i
$$751$$ −8.24101 14.2739i −0.300719 0.520860i 0.675580 0.737287i $$-0.263893\pi$$
−0.976299 + 0.216426i $$0.930560\pi$$
$$752$$ −4.97716 2.87357i −0.181498 0.104788i
$$753$$ −3.83298 + 6.63892i −0.139682 + 0.241936i
$$754$$ 20.4160 + 35.3616i 0.743508 + 1.28779i
$$755$$ −49.6276 −1.80613
$$756$$ 0 0
$$757$$ −3.82008 −0.138843 −0.0694216 0.997587i $$-0.522115\pi$$
−0.0694216 + 0.997587i $$0.522115\pi$$
$$758$$ 30.8537 17.8134i 1.12066 0.647012i
$$759$$ −16.4778 + 3.28818i −0.598107 + 0.119353i
$$760$$ 0.901211 1.56094i 0.0326903 0.0566213i
$$761$$ −0.927001 1.60561i −0.0336038 0.0582034i 0.848734 0.528819i $$-0.177365\pi$$
−0.882338 + 0.470616i $$0.844032\pi$$
$$762$$ 5.61016i 0.203235i
$$763$$ 0 0
$$764$$ −10.3662 −0.375037
$$765$$ 15.4895 8.94289i 0.560026 0.323331i
$$766$$ −10.8186 + 18.7384i −0.390893 + 0.677046i
$$767$$ 18.3873 + 10.6159i 0.663928 + 0.383319i
$$768$$ 0.662827 0.382683i 0.0239177 0.0138089i
$$769$$ −8.92308 −0.321775 −0.160887 0.986973i $$-0.551436\pi$$
−0.160887 + 0.986973i $$0.551436\pi$$
$$770$$ 0 0
$$771$$ 13.4028 0.482688
$$772$$ −1.40584 + 0.811664i −0.0505974 + 0.0292124i
$$773$$ 17.6034 + 10.1633i 0.633151 + 0.365550i 0.781971 0.623315i $$-0.214214\pi$$
−0.148821 + 0.988864i $$0.547548\pi$$
$$774$$ −9.43098 + 16.3349i −0.338989 + 0.587147i
$$775$$ 4.44091 2.56396i 0.159522 0.0921001i
$$776$$ 9.23880 0.331653
$$777$$ 0 0
$$778$$ 8.64698i 0.310009i
$$779$$ −1.04047 1.80215i −0.0372787 0.0645686i
$$780$$ 5.17937 8.97094i 0.185451 0.321211i
$$781$$ −1.38508 6.94093i −0.0495619 0.248366i
$$782$$ −20.7005 + 11.9514i −0.740248 + 0.427382i