Properties

 Label 1470.2.n.i.79.1 Level $1470$ Weight $2$ Character 1470.79 Analytic conductor $11.738$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1470.n (of order $$6$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$11.7380090971$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 210) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 79.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1470.79 Dual form 1470.2.n.i.949.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.23205 + 1.86603i) q^{10} +(2.50000 + 4.33013i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(2.00000 - 1.00000i) q^{20} -5.00000i q^{22} +(-2.59808 - 1.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.96410 - 0.598076i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000i q^{27} +(0.133975 - 2.23205i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.33013 - 2.50000i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-4.33013 - 2.50000i) q^{37} +(6.06218 - 3.50000i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-2.23205 - 0.133975i) q^{40} +9.00000 q^{41} +10.0000i q^{43} +(-2.50000 + 4.33013i) q^{44} +(-1.86603 - 1.23205i) q^{45} +(1.50000 + 2.59808i) q^{46} +(11.2583 + 6.50000i) q^{47} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(1.00000 - 1.73205i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-0.866025 + 0.500000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +(-2.00000 - 3.46410i) q^{59} +(-1.23205 + 1.86603i) q^{60} +(-1.00000 + 1.73205i) q^{61} +6.00000i q^{62} -1.00000 q^{64} +(-2.23205 - 0.133975i) q^{65} +(2.50000 + 4.33013i) q^{66} +(-5.19615 + 3.00000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(2.50000 + 4.33013i) q^{74} +(4.59808 - 1.96410i) q^{75} -7.00000 q^{76} -1.00000i q^{78} +(-7.00000 + 12.1244i) q^{79} +(1.86603 + 1.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.79423 - 4.50000i) q^{82} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.00000 - 8.66025i) q^{86} +(4.33013 - 2.50000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(1.00000 + 2.00000i) q^{90} -3.00000i q^{92} +(5.19615 + 3.00000i) q^{93} +(-6.50000 - 11.2583i) q^{94} +(13.0622 + 8.62436i) q^{95} +(-0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +5.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} + 4q^{5} + 4q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} + 4q^{5} + 4q^{6} + 2q^{9} + 2q^{10} + 10q^{11} + 4q^{15} - 2q^{16} - 14q^{19} + 8q^{20} + 2q^{24} - 6q^{25} - 2q^{26} + 4q^{30} - 12q^{31} + 8q^{34} + 4q^{36} + 2q^{39} - 2q^{40} + 36q^{41} - 10q^{44} - 4q^{45} + 6q^{46} + 16q^{50} + 4q^{51} + 2q^{54} + 40q^{55} - 8q^{59} + 2q^{60} - 4q^{61} - 4q^{64} - 2q^{65} + 10q^{66} + 12q^{69} - 8q^{71} + 10q^{74} + 8q^{75} - 28q^{76} - 28q^{79} + 4q^{80} - 2q^{81} + 8q^{85} + 20q^{86} - 20q^{89} + 4q^{90} - 26q^{94} + 28q^{95} - 2q^{96} + 20q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$$.

 $$n$$ $$491$$ $$1081$$ $$1177$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$

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
$$3$$ −0.866025 + 0.500000i −0.500000 + 0.288675i
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ 0.133975 2.23205i 0.0599153 0.998203i
$$6$$ 1.00000 0.408248
$$7$$ 0 0
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 0.866025i 0.166667 0.288675i
$$10$$ −1.23205 + 1.86603i −0.389609 + 0.590089i
$$11$$ 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i $$0.105104\pi$$
−0.192201 + 0.981356i $$0.561563\pi$$
$$12$$ −0.866025 0.500000i −0.250000 0.144338i
$$13$$ 1.00000i 0.277350i −0.990338 0.138675i $$-0.955716\pi$$
0.990338 0.138675i $$-0.0442844\pi$$
$$14$$ 0 0
$$15$$ 1.00000 + 2.00000i 0.258199 + 0.516398i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.73205 + 1.00000i −0.420084 + 0.242536i −0.695113 0.718900i $$-0.744646\pi$$
0.275029 + 0.961436i $$0.411312\pi$$
$$18$$ −0.866025 + 0.500000i −0.204124 + 0.117851i
$$19$$ −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i $$0.463407\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 2.00000 1.00000i 0.447214 0.223607i
$$21$$ 0 0
$$22$$ 5.00000i 1.06600i
$$23$$ −2.59808 1.50000i −0.541736 0.312772i 0.204046 0.978961i $$-0.434591\pi$$
−0.745782 + 0.666190i $$0.767924\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ −4.96410 0.598076i −0.992820 0.119615i
$$26$$ −0.500000 + 0.866025i −0.0980581 + 0.169842i
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0.133975 2.23205i 0.0244603 0.407515i
$$31$$ −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i $$-0.985539\pi$$
0.460152 0.887840i $$-0.347795\pi$$
$$32$$ 0.866025 0.500000i 0.153093 0.0883883i
$$33$$ −4.33013 2.50000i −0.753778 0.435194i
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −4.33013 2.50000i −0.711868 0.410997i 0.0998840 0.994999i $$-0.468153\pi$$
−0.811752 + 0.584002i $$0.801486\pi$$
$$38$$ 6.06218 3.50000i 0.983415 0.567775i
$$39$$ 0.500000 + 0.866025i 0.0800641 + 0.138675i
$$40$$ −2.23205 0.133975i −0.352918 0.0211832i
$$41$$ 9.00000 1.40556 0.702782 0.711405i $$-0.251941\pi$$
0.702782 + 0.711405i $$0.251941\pi$$
$$42$$ 0 0
$$43$$ 10.0000i 1.52499i 0.646997 + 0.762493i $$0.276025\pi$$
−0.646997 + 0.762493i $$0.723975\pi$$
$$44$$ −2.50000 + 4.33013i −0.376889 + 0.652791i
$$45$$ −1.86603 1.23205i −0.278171 0.183663i
$$46$$ 1.50000 + 2.59808i 0.221163 + 0.383065i
$$47$$ 11.2583 + 6.50000i 1.64220 + 0.948122i 0.980051 + 0.198747i $$0.0636872\pi$$
0.662145 + 0.749375i $$0.269646\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 0 0
$$50$$ 4.00000 + 3.00000i 0.565685 + 0.424264i
$$51$$ 1.00000 1.73205i 0.140028 0.242536i
$$52$$ 0.866025 0.500000i 0.120096 0.0693375i
$$53$$ −0.866025 + 0.500000i −0.118958 + 0.0686803i −0.558298 0.829640i $$-0.688546\pi$$
0.439340 + 0.898321i $$0.355212\pi$$
$$54$$ 0.500000 0.866025i 0.0680414 0.117851i
$$55$$ 10.0000 5.00000i 1.34840 0.674200i
$$56$$ 0 0
$$57$$ 7.00000i 0.927173i
$$58$$ 0 0
$$59$$ −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i $$-0.250514\pi$$
−0.966342 + 0.257260i $$0.917180\pi$$
$$60$$ −1.23205 + 1.86603i −0.159057 + 0.240903i
$$61$$ −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i $$-0.874201\pi$$
0.794879 + 0.606768i $$0.207534\pi$$
$$62$$ 6.00000i 0.762001i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −2.23205 0.133975i −0.276852 0.0166175i
$$66$$ 2.50000 + 4.33013i 0.307729 + 0.533002i
$$67$$ −5.19615 + 3.00000i −0.634811 + 0.366508i −0.782613 0.622509i $$-0.786114\pi$$
0.147802 + 0.989017i $$0.452780\pi$$
$$68$$ −1.73205 1.00000i −0.210042 0.121268i
$$69$$ 3.00000 0.361158
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ −0.866025 0.500000i −0.102062 0.0589256i
$$73$$ −3.46410 + 2.00000i −0.405442 + 0.234082i −0.688830 0.724923i $$-0.741875\pi$$
0.283387 + 0.959006i $$0.408542\pi$$
$$74$$ 2.50000 + 4.33013i 0.290619 + 0.503367i
$$75$$ 4.59808 1.96410i 0.530940 0.226795i
$$76$$ −7.00000 −0.802955
$$77$$ 0 0
$$78$$ 1.00000i 0.113228i
$$79$$ −7.00000 + 12.1244i −0.787562 + 1.36410i 0.139895 + 0.990166i $$0.455323\pi$$
−0.927457 + 0.373930i $$0.878010\pi$$
$$80$$ 1.86603 + 1.23205i 0.208628 + 0.137747i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −7.79423 4.50000i −0.860729 0.496942i
$$83$$ 10.0000i 1.09764i 0.835940 + 0.548821i $$0.184923\pi$$
−0.835940 + 0.548821i $$0.815077\pi$$
$$84$$ 0 0
$$85$$ 2.00000 + 4.00000i 0.216930 + 0.433861i
$$86$$ 5.00000 8.66025i 0.539164 0.933859i
$$87$$ 0 0
$$88$$ 4.33013 2.50000i 0.461593 0.266501i
$$89$$ −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i $$0.344474\pi$$
−0.999388 + 0.0349934i $$0.988859\pi$$
$$90$$ 1.00000 + 2.00000i 0.105409 + 0.210819i
$$91$$ 0 0
$$92$$ 3.00000i 0.312772i
$$93$$ 5.19615 + 3.00000i 0.538816 + 0.311086i
$$94$$ −6.50000 11.2583i −0.670424 1.16121i
$$95$$ 13.0622 + 8.62436i 1.34015 + 0.884840i
$$96$$ −0.500000 + 0.866025i −0.0510310 + 0.0883883i
$$97$$ 8.00000i 0.812277i 0.913812 + 0.406138i $$0.133125\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 0 0
$$99$$ 5.00000 0.502519
$$100$$ −1.96410 4.59808i −0.196410 0.459808i
$$101$$ 4.00000 + 6.92820i 0.398015 + 0.689382i 0.993481 0.113998i $$-0.0363659\pi$$
−0.595466 + 0.803380i $$0.703033\pi$$
$$102$$ −1.73205 + 1.00000i −0.171499 + 0.0990148i
$$103$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 1.00000 0.0971286
$$107$$ 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i $$-0.136370\pi$$
0.0950377 + 0.995474i $$0.469703\pi$$
$$108$$ −0.866025 + 0.500000i −0.0833333 + 0.0481125i
$$109$$ −9.00000 15.5885i −0.862044 1.49310i −0.869953 0.493135i $$-0.835851\pi$$
0.00790932 0.999969i $$-0.497482\pi$$
$$110$$ −11.1603 0.669873i −1.06409 0.0638699i
$$111$$ 5.00000 0.474579
$$112$$ 0 0
$$113$$ 6.00000i 0.564433i 0.959351 + 0.282216i $$0.0910696\pi$$
−0.959351 + 0.282216i $$0.908930\pi$$
$$114$$ −3.50000 + 6.06218i −0.327805 + 0.567775i
$$115$$ −3.69615 + 5.59808i −0.344668 + 0.522023i
$$116$$ 0 0
$$117$$ −0.866025 0.500000i −0.0800641 0.0462250i
$$118$$ 4.00000i 0.368230i
$$119$$ 0 0
$$120$$ 2.00000 1.00000i 0.182574 0.0912871i
$$121$$ −7.00000 + 12.1244i −0.636364 + 1.10221i
$$122$$ 1.73205 1.00000i 0.156813 0.0905357i
$$123$$ −7.79423 + 4.50000i −0.702782 + 0.405751i
$$124$$ 3.00000 5.19615i 0.269408 0.466628i
$$125$$ −2.00000 + 11.0000i −0.178885 + 0.983870i
$$126$$ 0 0
$$127$$ 9.00000i 0.798621i −0.916816 0.399310i $$-0.869250\pi$$
0.916816 0.399310i $$-0.130750\pi$$
$$128$$ 0.866025 + 0.500000i 0.0765466 + 0.0441942i
$$129$$ −5.00000 8.66025i −0.440225 0.762493i
$$130$$ 1.86603 + 1.23205i 0.163661 + 0.108058i
$$131$$ −8.50000 + 14.7224i −0.742648 + 1.28630i 0.208637 + 0.977993i $$0.433097\pi$$
−0.951285 + 0.308312i $$0.900236\pi$$
$$132$$ 5.00000i 0.435194i
$$133$$ 0 0
$$134$$ 6.00000 0.518321
$$135$$ 2.23205 + 0.133975i 0.192104 + 0.0115307i
$$136$$ 1.00000 + 1.73205i 0.0857493 + 0.148522i
$$137$$ 3.46410 2.00000i 0.295958 0.170872i −0.344668 0.938725i $$-0.612008\pi$$
0.640626 + 0.767853i $$0.278675\pi$$
$$138$$ −2.59808 1.50000i −0.221163 0.127688i
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ 0 0
$$141$$ −13.0000 −1.09480
$$142$$ 1.73205 + 1.00000i 0.145350 + 0.0839181i
$$143$$ 4.33013 2.50000i 0.362103 0.209061i
$$144$$ 0.500000 + 0.866025i 0.0416667 + 0.0721688i
$$145$$ 0 0
$$146$$ 4.00000 0.331042
$$147$$ 0 0
$$148$$ 5.00000i 0.410997i
$$149$$ −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i $$-0.912374\pi$$
0.716578 + 0.697507i $$0.245707\pi$$
$$150$$ −4.96410 0.598076i −0.405317 0.0488327i
$$151$$ 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i $$0.186277\pi$$
0.0615699 + 0.998103i $$0.480389\pi$$
$$152$$ 6.06218 + 3.50000i 0.491708 + 0.283887i
$$153$$ 2.00000i 0.161690i
$$154$$ 0 0
$$155$$ −12.0000 + 6.00000i −0.963863 + 0.481932i
$$156$$ −0.500000 + 0.866025i −0.0400320 + 0.0693375i
$$157$$ 11.2583 6.50000i 0.898513 0.518756i 0.0217953 0.999762i $$-0.493062\pi$$
0.876717 + 0.481006i $$0.159728\pi$$
$$158$$ 12.1244 7.00000i 0.964562 0.556890i
$$159$$ 0.500000 0.866025i 0.0396526 0.0686803i
$$160$$ −1.00000 2.00000i −0.0790569 0.158114i
$$161$$ 0 0
$$162$$ 1.00000i 0.0785674i
$$163$$ 10.3923 + 6.00000i 0.813988 + 0.469956i 0.848339 0.529454i $$-0.177603\pi$$
−0.0343508 + 0.999410i $$0.510936\pi$$
$$164$$ 4.50000 + 7.79423i 0.351391 + 0.608627i
$$165$$ −6.16025 + 9.33013i −0.479575 + 0.726349i
$$166$$ 5.00000 8.66025i 0.388075 0.672166i
$$167$$ 19.0000i 1.47026i −0.677924 0.735132i $$-0.737120\pi$$
0.677924 0.735132i $$-0.262880\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0.267949 4.46410i 0.0205508 0.342381i
$$171$$ 3.50000 + 6.06218i 0.267652 + 0.463586i
$$172$$ −8.66025 + 5.00000i −0.660338 + 0.381246i
$$173$$ 6.06218 + 3.50000i 0.460899 + 0.266100i 0.712422 0.701751i $$-0.247598\pi$$
−0.251523 + 0.967851i $$0.580932\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −5.00000 −0.376889
$$177$$ 3.46410 + 2.00000i 0.260378 + 0.150329i
$$178$$ 8.66025 5.00000i 0.649113 0.374766i
$$179$$ −5.50000 9.52628i −0.411089 0.712028i 0.583920 0.811811i $$-0.301518\pi$$
−0.995009 + 0.0997838i $$0.968185\pi$$
$$180$$ 0.133975 2.23205i 0.00998588 0.166367i
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 2.00000i 0.147844i
$$184$$ −1.50000 + 2.59808i −0.110581 + 0.191533i
$$185$$ −6.16025 + 9.33013i −0.452911 + 0.685965i
$$186$$ −3.00000 5.19615i −0.219971 0.381000i
$$187$$ −8.66025 5.00000i −0.633300 0.365636i
$$188$$ 13.0000i 0.948122i
$$189$$ 0 0
$$190$$ −7.00000 14.0000i −0.507833 1.01567i
$$191$$ 8.00000 13.8564i 0.578860 1.00261i −0.416751 0.909021i $$-0.636831\pi$$
0.995610 0.0935936i $$-0.0298354\pi$$
$$192$$ 0.866025 0.500000i 0.0625000 0.0360844i
$$193$$ −15.5885 + 9.00000i −1.12208 + 0.647834i −0.941932 0.335805i $$-0.890992\pi$$
−0.180150 + 0.983639i $$0.557658\pi$$
$$194$$ 4.00000 6.92820i 0.287183 0.497416i
$$195$$ 2.00000 1.00000i 0.143223 0.0716115i
$$196$$ 0 0
$$197$$ 27.0000i 1.92367i 0.273629 + 0.961835i $$0.411776\pi$$
−0.273629 + 0.961835i $$0.588224\pi$$
$$198$$ −4.33013 2.50000i −0.307729 0.177667i
$$199$$ 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i $$-0.00138876\pi$$
−0.503774 + 0.863836i $$0.668055\pi$$
$$200$$ −0.598076 + 4.96410i −0.0422904 + 0.351015i
$$201$$ 3.00000 5.19615i 0.211604 0.366508i
$$202$$ 8.00000i 0.562878i
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ 1.20577 20.0885i 0.0842147 1.40304i
$$206$$ 0 0
$$207$$ −2.59808 + 1.50000i −0.180579 + 0.104257i
$$208$$ 0.866025 + 0.500000i 0.0600481 + 0.0346688i
$$209$$ −35.0000 −2.42100
$$210$$ 0 0
$$211$$ 19.0000 1.30801 0.654007 0.756489i $$-0.273087\pi$$
0.654007 + 0.756489i $$0.273087\pi$$
$$212$$ −0.866025 0.500000i −0.0594789 0.0343401i
$$213$$ 1.73205 1.00000i 0.118678 0.0685189i
$$214$$ −6.00000 10.3923i −0.410152 0.710403i
$$215$$ 22.3205 + 1.33975i 1.52225 + 0.0913699i
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ 18.0000i 1.21911i
$$219$$ 2.00000 3.46410i 0.135147 0.234082i
$$220$$ 9.33013 + 6.16025i 0.629037 + 0.415324i
$$221$$ 1.00000 + 1.73205i 0.0672673 + 0.116510i
$$222$$ −4.33013 2.50000i −0.290619 0.167789i
$$223$$ 16.0000i 1.07144i −0.844396 0.535720i $$-0.820040\pi$$
0.844396 0.535720i $$-0.179960\pi$$
$$224$$ 0 0
$$225$$ −3.00000 + 4.00000i −0.200000 + 0.266667i
$$226$$ 3.00000 5.19615i 0.199557 0.345643i
$$227$$ 12.1244 7.00000i 0.804722 0.464606i −0.0403978 0.999184i $$-0.512863\pi$$
0.845120 + 0.534577i $$0.179529\pi$$
$$228$$ 6.06218 3.50000i 0.401478 0.231793i
$$229$$ 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i $$-0.791141\pi$$
0.924510 + 0.381157i $$0.124474\pi$$
$$230$$ 6.00000 3.00000i 0.395628 0.197814i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$234$$ 0.500000 + 0.866025i 0.0326860 + 0.0566139i
$$235$$ 16.0167 24.2583i 1.04481 1.58244i
$$236$$ 2.00000 3.46410i 0.130189 0.225494i
$$237$$ 14.0000i 0.909398i
$$238$$ 0 0
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ −2.23205 0.133975i −0.144078 0.00864802i
$$241$$ −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i $$-0.176921\pi$$
−0.881680 + 0.471848i $$0.843587\pi$$
$$242$$ 12.1244 7.00000i 0.779383 0.449977i
$$243$$ 0.866025 + 0.500000i 0.0555556 + 0.0320750i
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ 9.00000 0.573819
$$247$$ 6.06218 + 3.50000i 0.385727 + 0.222700i
$$248$$ −5.19615 + 3.00000i −0.329956 + 0.190500i
$$249$$ −5.00000 8.66025i −0.316862 0.548821i
$$250$$ 7.23205 8.52628i 0.457395 0.539249i
$$251$$ 3.00000 0.189358 0.0946792 0.995508i $$-0.469817\pi$$
0.0946792 + 0.995508i $$0.469817\pi$$
$$252$$ 0 0
$$253$$ 15.0000i 0.943042i
$$254$$ −4.50000 + 7.79423i −0.282355 + 0.489053i
$$255$$ −3.73205 2.46410i −0.233710 0.154308i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 8.66025 + 5.00000i 0.540212 + 0.311891i 0.745165 0.666880i $$-0.232371\pi$$
−0.204953 + 0.978772i $$0.565704\pi$$
$$258$$ 10.0000i 0.622573i
$$259$$ 0 0
$$260$$ −1.00000 2.00000i −0.0620174 0.124035i
$$261$$ 0 0
$$262$$ 14.7224 8.50000i 0.909555 0.525132i
$$263$$ 20.7846 12.0000i 1.28163 0.739952i 0.304487 0.952517i $$-0.401515\pi$$
0.977147 + 0.212565i $$0.0681817\pi$$
$$264$$ −2.50000 + 4.33013i −0.153864 + 0.266501i
$$265$$ 1.00000 + 2.00000i 0.0614295 + 0.122859i
$$266$$ 0 0
$$267$$ 10.0000i 0.611990i
$$268$$ −5.19615 3.00000i −0.317406 0.183254i
$$269$$ −7.00000 12.1244i −0.426798 0.739235i 0.569789 0.821791i $$-0.307025\pi$$
−0.996586 + 0.0825561i $$0.973692\pi$$
$$270$$ −1.86603 1.23205i −0.113563 0.0749802i
$$271$$ 4.00000 6.92820i 0.242983 0.420858i −0.718580 0.695444i $$-0.755208\pi$$
0.961563 + 0.274586i $$0.0885408\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 0 0
$$274$$ −4.00000 −0.241649
$$275$$ −9.82051 22.9904i −0.592199 1.38637i
$$276$$ 1.50000 + 2.59808i 0.0902894 + 0.156386i
$$277$$ −1.73205 + 1.00000i −0.104069 + 0.0600842i −0.551131 0.834419i $$-0.685804\pi$$
0.447062 + 0.894503i $$0.352470\pi$$
$$278$$ 6.92820 + 4.00000i 0.415526 + 0.239904i
$$279$$ −6.00000 −0.359211
$$280$$ 0 0
$$281$$ −11.0000 −0.656205 −0.328102 0.944642i $$-0.606409\pi$$
−0.328102 + 0.944642i $$0.606409\pi$$
$$282$$ 11.2583 + 6.50000i 0.670424 + 0.387069i
$$283$$ −22.5167 + 13.0000i −1.33848 + 0.772770i −0.986581 0.163270i $$-0.947796\pi$$
−0.351895 + 0.936039i $$0.614463\pi$$
$$284$$ −1.00000 1.73205i −0.0593391 0.102778i
$$285$$ −15.6244 0.937822i −0.925507 0.0555518i
$$286$$ −5.00000 −0.295656
$$287$$ 0 0
$$288$$ 1.00000i 0.0589256i
$$289$$ −6.50000 + 11.2583i −0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ −4.00000 6.92820i −0.234484 0.406138i
$$292$$ −3.46410 2.00000i −0.202721 0.117041i
$$293$$ 1.00000i 0.0584206i −0.999573 0.0292103i $$-0.990701\pi$$
0.999573 0.0292103i $$-0.00929925\pi$$
$$294$$ 0 0
$$295$$ −8.00000 + 4.00000i −0.465778 + 0.232889i
$$296$$ −2.50000 + 4.33013i −0.145310 + 0.251684i
$$297$$ −4.33013 + 2.50000i −0.251259 + 0.145065i
$$298$$ 5.19615 3.00000i 0.301005 0.173785i
$$299$$ −1.50000 + 2.59808i −0.0867472 + 0.150251i
$$300$$ 4.00000 + 3.00000i 0.230940 + 0.173205i
$$301$$ 0 0
$$302$$ 22.0000i 1.26596i
$$303$$ −6.92820 4.00000i −0.398015 0.229794i
$$304$$ −3.50000 6.06218i −0.200739 0.347690i
$$305$$ 3.73205 + 2.46410i 0.213697 + 0.141094i
$$306$$ 1.00000 1.73205i 0.0571662 0.0990148i
$$307$$ 2.00000i 0.114146i 0.998370 + 0.0570730i $$0.0181768\pi$$
−0.998370 + 0.0570730i $$0.981823\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 13.3923 + 0.803848i 0.760632 + 0.0456555i
$$311$$ −13.0000 22.5167i −0.737162 1.27680i −0.953768 0.300544i $$-0.902832\pi$$
0.216606 0.976259i $$-0.430501\pi$$
$$312$$ 0.866025 0.500000i 0.0490290 0.0283069i
$$313$$ −8.66025 5.00000i −0.489506 0.282617i 0.234863 0.972028i $$-0.424536\pi$$
−0.724370 + 0.689412i $$0.757869\pi$$
$$314$$ −13.0000 −0.733632
$$315$$ 0 0
$$316$$ −14.0000 −0.787562
$$317$$ 1.73205 + 1.00000i 0.0972817 + 0.0561656i 0.547852 0.836576i $$-0.315446\pi$$
−0.450570 + 0.892741i $$0.648779\pi$$
$$318$$ −0.866025 + 0.500000i −0.0485643 + 0.0280386i
$$319$$ 0 0
$$320$$ −0.133975 + 2.23205i −0.00748941 + 0.124775i
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ 14.0000i 0.778981i
$$324$$ 0.500000 0.866025i 0.0277778 0.0481125i
$$325$$ −0.598076 + 4.96410i −0.0331753 + 0.275359i
$$326$$ −6.00000 10.3923i −0.332309 0.575577i
$$327$$ 15.5885 + 9.00000i 0.862044 + 0.497701i
$$328$$ 9.00000i 0.496942i
$$329$$ 0 0
$$330$$ 10.0000 5.00000i 0.550482 0.275241i
$$331$$ 7.50000 12.9904i 0.412237 0.714016i −0.582897 0.812546i $$-0.698081\pi$$
0.995134 + 0.0985303i $$0.0314141\pi$$
$$332$$ −8.66025 + 5.00000i −0.475293 + 0.274411i
$$333$$ −4.33013 + 2.50000i −0.237289 + 0.136999i
$$334$$ −9.50000 + 16.4545i −0.519817 + 0.900349i
$$335$$ 6.00000 + 12.0000i 0.327815 + 0.655630i
$$336$$ 0 0
$$337$$ 14.0000i 0.762629i 0.924445 + 0.381314i $$0.124528\pi$$
−0.924445 + 0.381314i $$0.875472\pi$$
$$338$$ −10.3923 6.00000i −0.565267 0.326357i
$$339$$ −3.00000 5.19615i −0.162938 0.282216i
$$340$$ −2.46410 + 3.73205i −0.133635 + 0.202399i
$$341$$ 15.0000 25.9808i 0.812296 1.40694i
$$342$$ 7.00000i 0.378517i
$$343$$ 0 0
$$344$$ 10.0000 0.539164
$$345$$ 0.401924 6.69615i 0.0216388 0.360509i
$$346$$ −3.50000 6.06218i −0.188161 0.325905i
$$347$$ 13.8564 8.00000i 0.743851 0.429463i −0.0796169 0.996826i $$-0.525370\pi$$
0.823468 + 0.567363i $$0.192036\pi$$
$$348$$ 0 0
$$349$$ −24.0000 −1.28469 −0.642345 0.766415i $$-0.722038\pi$$
−0.642345 + 0.766415i $$0.722038\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ 4.33013 + 2.50000i 0.230797 + 0.133250i
$$353$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$354$$ −2.00000 3.46410i −0.106299 0.184115i
$$355$$ −0.267949 + 4.46410i −0.0142213 + 0.236930i
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ 11.0000i 0.581368i
$$359$$ −14.0000 + 24.2487i −0.738892 + 1.27980i 0.214103 + 0.976811i $$0.431317\pi$$
−0.952995 + 0.302987i $$0.902016\pi$$
$$360$$ −1.23205 + 1.86603i −0.0649348 + 0.0983482i
$$361$$ −15.0000 25.9808i −0.789474 1.36741i
$$362$$ −1.73205 1.00000i −0.0910346 0.0525588i
$$363$$ 14.0000i 0.734809i
$$364$$ 0 0
$$365$$ 4.00000 + 8.00000i 0.209370 + 0.418739i
$$366$$ −1.00000 + 1.73205i −0.0522708 + 0.0905357i
$$367$$ −32.0429 + 18.5000i −1.67263 + 0.965692i −0.706469 + 0.707744i $$0.749713\pi$$
−0.966159 + 0.257948i $$0.916954\pi$$
$$368$$ 2.59808 1.50000i 0.135434 0.0781929i
$$369$$ 4.50000 7.79423i 0.234261 0.405751i
$$370$$ 10.0000 5.00000i 0.519875 0.259938i
$$371$$ 0 0
$$372$$ 6.00000i 0.311086i
$$373$$ −5.19615 3.00000i −0.269047 0.155334i 0.359408 0.933181i $$-0.382979\pi$$
−0.628454 + 0.777847i $$0.716312\pi$$
$$374$$ 5.00000 + 8.66025i 0.258544 + 0.447811i
$$375$$ −3.76795 10.5263i −0.194576 0.543575i
$$376$$ 6.50000 11.2583i 0.335212 0.580604i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.00000 0.0513665 0.0256833 0.999670i $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ −0.937822 + 15.6244i −0.0481093 + 0.801513i
$$381$$ 4.50000 + 7.79423i 0.230542 + 0.399310i
$$382$$ −13.8564 + 8.00000i −0.708955 + 0.409316i
$$383$$ −7.79423 4.50000i −0.398266 0.229939i 0.287469 0.957790i $$-0.407186\pi$$
−0.685736 + 0.727851i $$0.740519\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ 18.0000 0.916176
$$387$$ 8.66025 + 5.00000i 0.440225 + 0.254164i
$$388$$ −6.92820 + 4.00000i −0.351726 + 0.203069i
$$389$$ 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i $$-0.118061\pi$$
−0.779895 + 0.625910i $$0.784728\pi$$
$$390$$ −2.23205 0.133975i −0.113024 0.00678407i
$$391$$ 6.00000 0.303433
$$392$$ 0 0
$$393$$ 17.0000i 0.857537i
$$394$$ 13.5000 23.3827i 0.680120 1.17800i
$$395$$ 26.1244 + 17.2487i 1.31446 + 0.867877i
$$396$$ 2.50000 + 4.33013i 0.125630 + 0.217597i
$$397$$ 1.73205 + 1.00000i 0.0869291 + 0.0501886i 0.542834 0.839840i $$-0.317351\pi$$
−0.455905 + 0.890028i $$0.650684\pi$$
$$398$$ 14.0000i 0.701757i
$$399$$ 0 0
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i $$-0.597840\pi$$
0.976714 0.214544i $$-0.0688266\pi$$
$$402$$ −5.19615 + 3.00000i −0.259161 + 0.149626i
$$403$$ −5.19615 + 3.00000i −0.258839 + 0.149441i
$$404$$ −4.00000 + 6.92820i −0.199007 + 0.344691i
$$405$$ −2.00000 + 1.00000i −0.0993808 + 0.0496904i
$$406$$ 0 0
$$407$$ 25.0000i 1.23920i
$$408$$ −1.73205 1.00000i −0.0857493 0.0495074i
$$409$$ −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i $$-0.246188\pi$$
−0.962757 + 0.270367i $$0.912855\pi$$
$$410$$ −11.0885 + 16.7942i −0.547620 + 0.829408i
$$411$$ −2.00000 + 3.46410i −0.0986527 + 0.170872i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 3.00000 0.147442
$$415$$ 22.3205 + 1.33975i 1.09567 + 0.0657655i
$$416$$ −0.500000 0.866025i −0.0245145 0.0424604i
$$417$$ 6.92820 4.00000i 0.339276 0.195881i
$$418$$ 30.3109 + 17.5000i 1.48255 + 0.855953i
$$419$$ 3.00000 0.146560 0.0732798 0.997311i $$-0.476653\pi$$
0.0732798 + 0.997311i $$0.476653\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ −16.4545 9.50000i −0.800992 0.462453i
$$423$$ 11.2583 6.50000i 0.547399 0.316041i
$$424$$ 0.500000 + 0.866025i 0.0242821 + 0.0420579i
$$425$$ 9.19615 3.92820i 0.446079 0.190546i
$$426$$ −2.00000 −0.0969003
$$427$$ 0 0
$$428$$ 12.0000i 0.580042i
$$429$$ −2.50000 + 4.33013i −0.120701 + 0.209061i
$$430$$ −18.6603 12.3205i −0.899877 0.594148i
$$431$$ −9.00000 15.5885i −0.433515 0.750870i 0.563658 0.826008i $$-0.309393\pi$$
−0.997173 + 0.0751385i $$0.976060\pi$$
$$432$$ −0.866025 0.500000i −0.0416667 0.0240563i
$$433$$ 4.00000i 0.192228i −0.995370 0.0961139i $$-0.969359\pi$$
0.995370 0.0961139i $$-0.0306413\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 9.00000 15.5885i 0.431022 0.746552i
$$437$$ 18.1865 10.5000i 0.869980 0.502283i
$$438$$ −3.46410 + 2.00000i −0.165521 + 0.0955637i
$$439$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$440$$ −5.00000 10.0000i −0.238366 0.476731i
$$441$$ 0 0
$$442$$ 2.00000i 0.0951303i
$$443$$ 5.19615 + 3.00000i 0.246877 + 0.142534i 0.618333 0.785916i $$-0.287808\pi$$
−0.371457 + 0.928450i $$0.621142\pi$$
$$444$$ 2.50000 + 4.33013i 0.118645 + 0.205499i
$$445$$ 18.6603 + 12.3205i 0.884581 + 0.584048i
$$446$$ −8.00000 + 13.8564i −0.378811 + 0.656120i
$$447$$ 6.00000i 0.283790i
$$448$$ 0 0
$$449$$ −9.00000 −0.424736 −0.212368 0.977190i $$-0.568118\pi$$
−0.212368 + 0.977190i $$0.568118\pi$$
$$450$$ 4.59808 1.96410i 0.216755 0.0925886i
$$451$$ 22.5000 + 38.9711i 1.05948 + 1.83508i
$$452$$ −5.19615 + 3.00000i −0.244406 + 0.141108i
$$453$$ −19.0526 11.0000i −0.895167 0.516825i
$$454$$ −14.0000 −0.657053
$$455$$ 0 0
$$456$$ −7.00000 −0.327805
$$457$$ −32.9090 19.0000i −1.53942 0.888783i −0.998873 0.0474665i $$-0.984885\pi$$
−0.540544 0.841316i $$-0.681781\pi$$
$$458$$ −3.46410 + 2.00000i −0.161867 + 0.0934539i
$$459$$ −1.00000 1.73205i −0.0466760 0.0808452i
$$460$$ −6.69615 0.401924i −0.312210 0.0187398i
$$461$$ 12.0000 0.558896 0.279448 0.960161i $$-0.409849\pi$$
0.279448 + 0.960161i $$0.409849\pi$$
$$462$$ 0 0
$$463$$ 15.0000i 0.697109i −0.937288 0.348555i $$-0.886673\pi$$
0.937288 0.348555i $$-0.113327\pi$$
$$464$$ 0 0
$$465$$ 7.39230 11.1962i 0.342810 0.519209i
$$466$$ 0 0
$$467$$ −1.73205 1.00000i −0.0801498 0.0462745i 0.459390 0.888235i $$-0.348068\pi$$
−0.539539 + 0.841960i $$0.681402\pi$$
$$468$$ 1.00000i 0.0462250i
$$469$$ 0 0
$$470$$ −26.0000 + 13.0000i −1.19929 + 0.599645i
$$471$$ −6.50000 + 11.2583i −0.299504 + 0.518756i
$$472$$ −3.46410 + 2.00000i −0.159448 + 0.0920575i
$$473$$ −43.3013 + 25.0000i −1.99099 + 1.14950i
$$474$$ −7.00000 + 12.1244i −0.321521 + 0.556890i
$$475$$ 21.0000 28.0000i 0.963546 1.28473i
$$476$$ 0 0
$$477$$ 1.00000i 0.0457869i
$$478$$ 17.3205 + 10.0000i 0.792222 + 0.457389i
$$479$$ −4.00000 6.92820i −0.182765 0.316558i 0.760056 0.649857i $$-0.225171\pi$$
−0.942821 + 0.333300i $$0.891838\pi$$
$$480$$ 1.86603 + 1.23205i 0.0851720 + 0.0562352i
$$481$$ −2.50000 + 4.33013i −0.113990 + 0.197437i
$$482$$ 1.00000i 0.0455488i
$$483$$ 0 0
$$484$$ −14.0000 −0.636364
$$485$$ 17.8564 + 1.07180i 0.810818 + 0.0486678i
$$486$$ −0.500000 0.866025i −0.0226805 0.0392837i
$$487$$ −20.7846 + 12.0000i −0.941841 + 0.543772i −0.890537 0.454911i $$-0.849671\pi$$
−0.0513038 + 0.998683i $$0.516338\pi$$
$$488$$ 1.73205 + 1.00000i 0.0784063 + 0.0452679i
$$489$$ −12.0000 −0.542659
$$490$$ 0 0
$$491$$ 24.0000 1.08310 0.541552 0.840667i $$-0.317837\pi$$
0.541552 + 0.840667i $$0.317837\pi$$
$$492$$ −7.79423 4.50000i −0.351391 0.202876i
$$493$$ 0 0
$$494$$ −3.50000 6.06218i −0.157472 0.272750i
$$495$$ 0.669873 11.1603i 0.0301086 0.501616i
$$496$$ 6.00000 0.269408
$$497$$ 0 0
$$498$$ 10.0000i 0.448111i
$$499$$ −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i $$0.382272\pi$$
−0.988204 + 0.153141i $$0.951061\pi$$
$$500$$ −10.5263 + 3.76795i −0.470750 + 0.168508i
$$501$$ 9.50000 + 16.4545i 0.424429 + 0.735132i
$$502$$ −2.59808 1.50000i −0.115958 0.0669483i
$$503$$ 24.0000i 1.07011i −0.844818 0.535054i $$-0.820291\pi$$
0.844818 0.535054i $$-0.179709\pi$$
$$504$$ 0 0
$$505$$ 16.0000 8.00000i 0.711991 0.355995i
$$506$$ −7.50000 + 12.9904i −0.333416 + 0.577493i
$$507$$ −10.3923 + 6.00000i −0.461538 + 0.266469i
$$508$$ 7.79423 4.50000i 0.345813 0.199655i
$$509$$ −7.00000 + 12.1244i −0.310270 + 0.537403i −0.978421 0.206623i $$-0.933753\pi$$
0.668151 + 0.744026i $$0.267086\pi$$
$$510$$ 2.00000 + 4.00000i 0.0885615 + 0.177123i
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ −6.06218 3.50000i −0.267652 0.154529i
$$514$$ −5.00000 8.66025i −0.220541 0.381987i
$$515$$ 0 0
$$516$$ 5.00000 8.66025i 0.220113 0.381246i
$$517$$ 65.0000i 2.85870i
$$518$$ 0 0
$$519$$ −7.00000 −0.307266
$$520$$ −0.133975 + 2.23205i −0.00587517 + 0.0978819i
$$521$$ −7.50000 12.9904i −0.328581 0.569119i 0.653650 0.756797i $$-0.273237\pi$$
−0.982231 + 0.187678i $$0.939904\pi$$
$$522$$ 0 0
$$523$$ 10.3923 + 6.00000i 0.454424 + 0.262362i 0.709697 0.704507i $$-0.248832\pi$$
−0.255273 + 0.966869i $$0.582165\pi$$
$$524$$ −17.0000 −0.742648
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ 10.3923 + 6.00000i 0.452696 + 0.261364i
$$528$$ 4.33013 2.50000i 0.188445 0.108799i
$$529$$ −7.00000 12.1244i −0.304348 0.527146i
$$530$$ 0.133975 2.23205i 0.00581948 0.0969541i
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ 9.00000i 0.389833i
$$534$$ −5.00000 + 8.66025i −0.216371 + 0.374766i
$$535$$ 14.7846 22.3923i 0.639194 0.968104i
$$536$$ 3.00000 + 5.19615i 0.129580 + 0.224440i
$$537$$ 9.52628 + 5.50000i 0.411089 + 0.237343i
$$538$$ 14.0000i 0.603583i
$$539$$ 0 0
$$540$$ 1.00000 + 2.00000i 0.0430331 + 0.0860663i
$$541$$ −2.00000 + 3.46410i −0.0859867 + 0.148933i −0.905811 0.423681i $$-0.860738\pi$$
0.819825 + 0.572615i $$0.194071\pi$$
$$542$$ −6.92820 + 4.00000i −0.297592 + 0.171815i
$$543$$ −1.73205 + 1.00000i −0.0743294 + 0.0429141i
$$544$$ −1.00000 + 1.73205i −0.0428746 + 0.0742611i
$$545$$ −36.0000 + 18.0000i −1.54207 + 0.771035i
$$546$$ 0 0
$$547$$ 14.0000i 0.598597i 0.954160 + 0.299298i $$0.0967526\pi$$
−0.954160 + 0.299298i $$0.903247\pi$$
$$548$$ 3.46410 + 2.00000i 0.147979 + 0.0854358i
$$549$$ 1.00000 + 1.73205i 0.0426790 + 0.0739221i
$$550$$ −2.99038 + 24.8205i −0.127510 + 1.05835i
$$551$$ 0 0
$$552$$ 3.00000i 0.127688i
$$553$$ 0 0
$$554$$ 2.00000 0.0849719
$$555$$ 0.669873 11.1603i 0.0284345 0.473726i
$$556$$ −4.00000 6.92820i −0.169638 0.293821i
$$557$$ 33.7750 19.5000i 1.43109 0.826242i 0.433888 0.900967i $$-0.357141\pi$$
0.997204 + 0.0747252i $$0.0238080\pi$$
$$558$$ 5.19615 + 3.00000i 0.219971 + 0.127000i
$$559$$ 10.0000 0.422955
$$560$$ 0 0
$$561$$ 10.0000 0.422200
$$562$$ 9.52628 + 5.50000i 0.401842 + 0.232003i
$$563$$ −25.9808 + 15.0000i −1.09496 + 0.632175i −0.934892 0.354932i $$-0.884504\pi$$
−0.160066 + 0.987106i $$0.551171\pi$$
$$564$$ −6.50000 11.2583i −0.273699 0.474061i
$$565$$ 13.3923 + 0.803848i 0.563418 + 0.0338181i
$$566$$ 26.0000 1.09286
$$567$$ 0 0
$$568$$ 2.00000i 0.0839181i
$$569$$ −1.50000 + 2.59808i −0.0628833 + 0.108917i −0.895753 0.444552i $$-0.853363\pi$$
0.832870 + 0.553469i $$0.186696\pi$$
$$570$$ 13.0622 + 8.62436i 0.547114 + 0.361235i
$$571$$ 4.00000 + 6.92820i 0.167395 + 0.289936i 0.937503 0.347977i $$-0.113131\pi$$
−0.770108 + 0.637913i $$0.779798\pi$$
$$572$$ 4.33013 + 2.50000i 0.181052 + 0.104530i
$$573$$ 16.0000i 0.668410i
$$574$$ 0 0
$$575$$ 12.0000 + 9.00000i 0.500435 + 0.375326i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 20.7846 12.0000i 0.865275 0.499567i −0.000500448 1.00000i $$-0.500159\pi$$
0.865775 + 0.500433i $$0.166826\pi$$
$$578$$ 11.2583 6.50000i 0.468285 0.270364i
$$579$$ 9.00000 15.5885i 0.374027 0.647834i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 8.00000i 0.331611i
$$583$$ −4.33013 2.50000i −0.179336 0.103539i
$$584$$ 2.00000 + 3.46410i 0.0827606 + 0.143346i
$$585$$ −1.23205 + 1.86603i −0.0509390 + 0.0771507i
$$586$$ −0.500000 + 0.866025i −0.0206548 + 0.0357752i
$$587$$ 2.00000i 0.0825488i 0.999148 + 0.0412744i $$0.0131418\pi$$
−0.999148 + 0.0412744i $$0.986858\pi$$
$$588$$ 0 0
$$589$$ 42.0000 1.73058
$$590$$ 8.92820 + 0.535898i 0.367568 + 0.0220626i
$$591$$ −13.5000 23.3827i −0.555316 0.961835i
$$592$$ 4.33013 2.50000i 0.177967 0.102749i
$$593$$ −29.4449 17.0000i −1.20916 0.698106i −0.246581 0.969122i $$-0.579307\pi$$
−0.962575 + 0.271016i $$0.912640\pi$$
$$594$$ 5.00000 0.205152
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −12.1244 7.00000i −0.496217 0.286491i
$$598$$ 2.59808 1.50000i 0.106243 0.0613396i
$$599$$ −14.0000 24.2487i −0.572024 0.990775i −0.996358 0.0852695i $$-0.972825\pi$$
0.424333 0.905506i $$-0.360508\pi$$
$$600$$ −1.96410 4.59808i −0.0801841 0.187716i
$$601$$ 30.0000 1.22373 0.611863 0.790964i $$-0.290420\pi$$
0.611863 + 0.790964i $$0.290420\pi$$
$$602$$ 0 0
$$603$$ 6.00000i 0.244339i
$$604$$ −11.0000 + 19.0526i −0.447584 + 0.775238i
$$605$$ 26.1244 + 17.2487i 1.06211 + 0.701260i
$$606$$ 4.00000 + 6.92820i 0.162489 + 0.281439i
$$607$$ −11.2583 6.50000i −0.456962 0.263827i 0.253804 0.967256i $$-0.418318\pi$$
−0.710766 + 0.703429i $$0.751651\pi$$
$$608$$ 7.00000i 0.283887i
$$609$$ 0 0
$$610$$ −2.00000 4.00000i −0.0809776 0.161955i
$$611$$ 6.50000 11.2583i 0.262962 0.455463i
$$612$$ −1.73205 + 1.00000i −0.0700140 + 0.0404226i
$$613$$ 16.4545 9.50000i 0.664590 0.383701i −0.129433 0.991588i $$-0.541316\pi$$
0.794024 + 0.607887i $$0.207983\pi$$
$$614$$ 1.00000 1.73205i 0.0403567 0.0698999i
$$615$$ 9.00000 + 18.0000i 0.362915 + 0.725830i
$$616$$ 0 0
$$617$$ 30.0000i 1.20775i −0.797077 0.603877i $$-0.793622\pi$$
0.797077 0.603877i $$-0.206378\pi$$
$$618$$ 0 0
$$619$$ −7.50000 12.9904i −0.301450 0.522127i 0.675014 0.737805i $$-0.264137\pi$$
−0.976465 + 0.215677i $$0.930804\pi$$
$$620$$ −11.1962 7.39230i −0.449648 0.296882i
$$621$$ 1.50000 2.59808i 0.0601929 0.104257i
$$622$$ 26.0000i 1.04251i
$$623$$ 0 0
$$624$$ −1.00000 −0.0400320
$$625$$ 24.2846 + 5.93782i 0.971384 + 0.237513i
$$626$$ 5.00000 + 8.66025i 0.199840 + 0.346133i
$$627$$ 30.3109 17.5000i 1.21050 0.698883i
$$628$$ 11.2583 + 6.50000i 0.449256 + 0.259378i
$$629$$ 10.0000 0.398726
$$630$$ 0 0
$$631$$ 18.0000 0.716569 0.358284 0.933613i $$-0.383362\pi$$
0.358284 + 0.933613i $$0.383362\pi$$
$$632$$ 12.1244 + 7.00000i 0.482281 + 0.278445i
$$633$$ −16.4545 + 9.50000i −0.654007 + 0.377591i
$$634$$ −1.00000 1.73205i −0.0397151 0.0687885i
$$635$$ −20.0885 1.20577i −0.797186 0.0478496i
$$636$$ 1.00000 0.0396526
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −1.00000 + 1.73205i −0.0395594 + 0.0685189i
$$640$$ 1.23205 1.86603i 0.0487011 0.0737611i
$$641$$ 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i $$0.0592817\pi$$
−0.330997 + 0.943632i $$0.607385\pi$$
$$642$$ 10.3923 + 6.00000i 0.410152 + 0.236801i
$$643$$ 38.0000i 1.49857i −0.662246 0.749287i $$-0.730396\pi$$
0.662246 0.749287i $$-0.269604\pi$$
$$644$$ 0 0
$$645$$ −20.0000 + 10.0000i −0.787499 + 0.393750i
$$646$$ −7.00000 + 12.1244i −0.275411 + 0.477026i
$$647$$ −0.866025 + 0.500000i −0.0340470 + 0.0196570i −0.516927 0.856030i $$-0.672924\pi$$
0.482880 + 0.875687i $$0.339591\pi$$
$$648$$ −0.866025 + 0.500000i −0.0340207 + 0.0196419i
$$649$$ 10.0000 17.3205i 0.392534 0.679889i
$$650$$ 3.00000 4.00000i 0.117670 0.156893i
$$651$$ 0 0
$$652$$ 12.0000i 0.469956i
$$653$$ −4.33013 2.50000i −0.169451 0.0978326i 0.412876 0.910787i $$-0.364524\pi$$
−0.582327 + 0.812955i $$0.697858\pi$$
$$654$$ −9.00000 15.5885i −0.351928 0.609557i
$$655$$ 31.7224 + 20.9449i 1.23950 + 0.818384i
$$656$$ −4.50000 + 7.79423i −0.175695 + 0.304314i
$$657$$ 4.00000i 0.156055i
$$658$$ 0 0
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ −11.1603 0.669873i −0.434412 0.0260748i
$$661$$ 20.0000 + 34.6410i 0.777910 + 1.34738i 0.933144 + 0.359502i $$0.117053\pi$$
−0.155235 + 0.987878i $$0.549613\pi$$
$$662$$ −12.9904 + 7.50000i −0.504885 + 0.291496i
$$663$$ −1.73205 1.00000i −0.0672673 0.0388368i
$$664$$ 10.0000 0.388075
$$665$$ 0 0
$$666$$ 5.00000 0.193746
$$667$$ 0 0
$$668$$ 16.4545 9.50000i 0.636643 0.367566i
$$669$$ 8.00000 + 13.8564i 0.309298 + 0.535720i
$$670$$ 0.803848 13.3923i 0.0310553 0.517390i
$$671$$ −10.0000 −0.386046
$$672$$ 0 0
$$673$$ 36.0000i 1.38770i 0.720121 + 0.693849i $$0.244086\pi$$
−0.720121 + 0.693849i $$0.755914\pi$$
$$674$$ 7.00000 12.1244i 0.269630 0.467013i
$$675$$ 0.598076 4.96410i 0.0230200 0.191068i
$$676$$ 6.00000 + 10.3923i 0.230769 + 0.399704i
$$677$$ −28.5788 16.5000i −1.09837 0.634147i −0.162581 0.986695i $$-0.551982\pi$$
−0.935793 + 0.352549i $$0.885315\pi$$
$$678$$ 6.00000i 0.230429i
$$679$$ 0 0
$$680$$ 4.00000 2.00000i 0.153393 0.0766965i
$$681$$ −7.00000 + 12.1244i −0.268241 + 0.464606i
$$682$$ −25.9808 + 15.0000i −0.994855 + 0.574380i
$$683$$ −3.46410 + 2.00000i −0.132550 + 0.0765279i −0.564809 0.825222i $$-0.691050\pi$$
0.432259 + 0.901750i $$0.357717\pi$$
$$684$$ −3.50000 + 6.06218i −0.133826 + 0.231793i
$$685$$ −4.00000 8.00000i −0.152832 0.305664i
$$686$$ 0 0
$$687$$ 4.00000i 0.152610i
$$688$$ −8.66025 5.00000i −0.330169 0.190623i
$$689$$ 0.500000 + 0.866025i 0.0190485 + 0.0329929i
$$690$$ −3.69615 + 5.59808i −0.140710 + 0.213115i
$$691$$ −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i $$-0.957553\pi$$
0.610704 + 0.791859i $$0.290887\pi$$
$$692$$ 7.00000i 0.266100i
$$693$$ 0 0
$$694$$ −16.0000 −0.607352
$$695$$ −1.07180 + 17.8564i −0.0406556 + 0.677332i
$$696$$ 0 0
$$697$$ −15.5885 + 9.00000i −0.590455 + 0.340899i
$$698$$ 20.7846 + 12.0000i 0.786709 + 0.454207i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ −0.866025 0.500000i −0.0326860 0.0188713i
$$703$$ 30.3109 17.5000i 1.14320 0.660025i
$$704$$ −2.50000 4.33013i −0.0942223 0.163198i
$$705$$ −1.74167 + 29.0167i −0.0655951 + 1.09283i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 4.00000i 0.150329i
$$709$$ 8.00000 13.8564i 0.300446 0.520388i −0.675791 0.737093i $$-0.736198\pi$$
0.976237 + 0.216705i $$0.0695310\pi$$
$$710$$ 2.46410 3.73205i 0.0924761 0.140061i
$$711$$ 7.00000 + 12.1244i 0.262521 + 0.454699i
$$712$$ 8.66025 + 5.00000i 0.324557 + 0.187383i
$$713$$ 18.0000i 0.674105i
$$714$$ 0 0
$$715$$ −5.00000 10.0000i −0.186989 0.373979i
$$716$$ 5.50000 9.52628i 0.205545 0.356014i
$$717$$ 17.3205 10.0000i 0.646846 0.373457i
$$718$$ 24.2487 14.0000i 0.904954 0.522475i
$$719$$ 1.00000 1.73205i 0.0372937 0.0645946i −0.846776 0.531949i $$-0.821460\pi$$
0.884070 + 0.467355i $$0.154793\pi$$
$$720$$ 2.00000 1.00000i 0.0745356 0.0372678i
$$721$$ 0 0
$$722$$ 30.0000i 1.11648i
$$723$$ 0.866025 + 0.500000i 0.0322078 + 0.0185952i
$$724$$ 1.00000 + 1.73205i 0.0371647 + 0.0643712i
$$725$$ 0 0
$$726$$ −7.00000 + 12.1244i −0.259794 + 0.449977i
$$727$$ 53.0000i 1.96566i 0.184510 + 0.982831i $$0.440930\pi$$
−0.184510 + 0.982831i $$0.559070\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0.535898 8.92820i 0.0198345 0.330448i
$$731$$ −10.0000 17.3205i −0.369863 0.640622i
$$732$$ 1.73205 1.00000i 0.0640184 0.0369611i
$$733$$ −18.1865 10.5000i −0.671735 0.387826i 0.124999 0.992157i $$-0.460107\pi$$
−0.796734 + 0.604331i $$0.793441\pi$$
$$734$$ 37.0000 1.36569
$$735$$ 0 0
$$736$$ −3.00000 −0.110581
$$737$$ −25.9808 15.0000i −0.957014 0.552532i
$$738$$ −7.79423 + 4.50000i −0.286910 + 0.165647i
$$739$$ 23.5000 + 40.7032i 0.864461 + 1.49729i 0.867581 + 0.497296i $$0.165674\pi$$
−0.00311943 + 0.999995i $$0.500993\pi$$
$$740$$ −11.1603 0.669873i −0.410259 0.0246250i
$$741$$ −7.00000 −0.257151
$$742$$ 0 0
$$743$$ 31.0000i 1.13728i −0.822587 0.568640i $$-0.807470\pi$$
0.822587 0.568640i $$-0.192530\pi$$
$$744$$ 3.00000 5.19615i 0.109985 0.190500i
$$745$$ 11.1962 + 7.39230i 0.410195 + 0.270833i
$$746$$ 3.00000 + 5.19615i 0.109838 + 0.190245i
$$747$$ 8.66025 + 5.00000i 0.316862 + 0.182940i
$$748$$ 10.0000i 0.365636i
$$749$$ 0 0
$$750$$ −2.00000 + 11.0000i −0.0730297 + 0.401663i
$$751$$ −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i $$-0.856585\pi$$
0.827225 + 0.561870i $$0.189918\pi$$
$$752$$ −11.2583 + 6.50000i −0.410549 + 0.237031i
$$753$$ −2.59808 + 1.50000i −0.0946792 + 0.0546630i
$$754$$ 0 0
$$755$$ 44.0000 22.0000i 1.60132 0.800662i
$$756$$ 0 0
$$757$$ 26.0000i 0.944986i 0.881334 + 0.472493i $$0.156646\pi$$
−0.881334 + 0.472493i $$0.843354\pi$$
$$758$$ −0.866025 0.500000i −0.0314555 0.0181608i
$$759$$ 7.50000 + 12.9904i 0.272233 + 0.471521i
$$760$$ 8.62436 13.0622i 0.312838 0.473815i
$$761$$ −1.50000 + 2.59808i −0.0543750 + 0.0941802i −0.891932 0.452170i $$-0.850650\pi$$
0.837557 + 0.546350i $$0.183983\pi$$
$$762$$ 9.00000i 0.326036i
$$763$$ 0 0
$$764$$ 16.0000 0.578860
$$765$$ 4.46410 + 0.267949i 0.161400 + 0.00968772i
$$766$$ 4.50000 + 7.79423i 0.162592 + 0.281617i
$$767$$ −3.46410 + 2.00000i −0.125081 + 0.0722158i
$$768$$ 0.866025 + 0.500000i 0.0312500 + 0.0180422i
$$769$$ 51.0000 1.83911 0.919554 0.392965i $$-0.128551\pi$$
0.919554 + 0.392965i $$0.128551\pi$$
$$770$$ 0 0
$$771$$ −10.0000 −0.360141
$$772$$ −15.5885 9.00000i −0.561041 0.323917i
$$773$$ 32.0429 18.5000i 1.15250 0.665399i 0.203008 0.979177i $$-0.434928\pi$$
0.949496 + 0.313778i $$0.101595\pi$$
$$774$$ −5.00000 8.66025i −0.179721 0.311286i
$$775$$ 11.7846 + 27.5885i 0.423316 + 0.991007i
$$776$$ 8.00000 0.287183
$$777$$ 0 0
$$778$$ 6.00000i 0.215110i
$$779$$ −31.5000 + 54.5596i −1.12860 + 1.95480i
$$780$$ 1.86603 + 1.23205i 0.0668144 + 0.0441145i
$$781$$ −5.00000 8.66025i −0.178914 0.309888i
$$782$$ −5.19615 3.00000i −0.185814 0.107280i