# Properties

 Label 370.2.e.c.211.1 Level $370$ Weight $2$ Character 370.211 Analytic conductor $2.954$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$370 = 2 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 370.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.95446487479$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 211.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 370.211 Dual form 370.2.e.c.121.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(1.50000 + 2.59808i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(3.00000 - 5.19615i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -6.00000 q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} -9.00000 q^{27} +6.00000 q^{29} +(1.50000 - 2.59808i) q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +(-1.00000 + 1.73205i) q^{34} +6.00000 q^{36} +(-5.50000 + 2.59808i) q^{37} -2.00000 q^{38} +(-1.50000 - 2.59808i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} +7.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} -6.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} -8.00000 q^{47} -3.00000 q^{48} +(3.50000 + 6.06218i) q^{49} +(0.500000 - 0.866025i) q^{50} +6.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(5.50000 + 9.52628i) q^{53} +(-4.50000 - 7.79423i) q^{54} +(1.00000 - 1.73205i) q^{55} +(3.00000 + 5.19615i) q^{57} +(3.00000 + 5.19615i) q^{58} +(1.00000 + 1.73205i) q^{59} +3.00000 q^{60} +(-5.00000 + 8.66025i) q^{61} +(2.50000 + 4.33013i) q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +6.00000 q^{66} +(-2.00000 + 3.46410i) q^{67} -2.00000 q^{68} +(-9.00000 + 15.5885i) q^{69} +(3.00000 + 5.19615i) q^{72} -2.00000 q^{73} +(-5.00000 - 3.46410i) q^{74} -3.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(1.50000 - 2.59808i) q^{78} +(2.00000 - 3.46410i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -3.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} +2.00000 q^{85} +(3.50000 + 6.06218i) q^{86} +(9.00000 - 15.5885i) q^{87} -2.00000 q^{88} +(-1.00000 - 1.73205i) q^{89} +(-3.00000 - 5.19615i) q^{90} +(3.00000 - 5.19615i) q^{92} +(7.50000 - 12.9904i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-1.50000 - 2.59808i) q^{96} +18.0000 q^{97} +(-3.50000 + 6.06218i) q^{98} +(-6.00000 - 10.3923i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} + 3q^{3} - q^{4} + q^{5} + 6q^{6} - 2q^{8} - 6q^{9} + O(q^{10})$$ $$2q + q^{2} + 3q^{3} - q^{4} + q^{5} + 6q^{6} - 2q^{8} - 6q^{9} + 2q^{10} + 4q^{11} + 3q^{12} + q^{13} - 3q^{15} - q^{16} + 2q^{17} + 6q^{18} - 2q^{19} + q^{20} + 2q^{22} - 12q^{23} - 3q^{24} - q^{25} + 2q^{26} - 18q^{27} + 12q^{29} + 3q^{30} + 10q^{31} + q^{32} + 6q^{33} - 2q^{34} + 12q^{36} - 11q^{37} - 4q^{38} - 3q^{39} - q^{40} - 3q^{41} + 14q^{43} - 2q^{44} - 12q^{45} - 6q^{46} - 16q^{47} - 6q^{48} + 7q^{49} + q^{50} + 12q^{51} + q^{52} + 11q^{53} - 9q^{54} + 2q^{55} + 6q^{57} + 6q^{58} + 2q^{59} + 6q^{60} - 10q^{61} + 5q^{62} + 2q^{64} - q^{65} + 12q^{66} - 4q^{67} - 4q^{68} - 18q^{69} + 6q^{72} - 4q^{73} - 10q^{74} - 6q^{75} - 2q^{76} + 3q^{78} + 4q^{79} - 2q^{80} - 9q^{81} - 6q^{82} - 12q^{83} + 4q^{85} + 7q^{86} + 18q^{87} - 4q^{88} - 2q^{89} - 6q^{90} + 6q^{92} + 15q^{93} - 8q^{94} + 2q^{95} - 3q^{96} + 36q^{97} - 7q^{98} - 12q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$297$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 1.50000 2.59808i 0.866025 1.50000i 1.00000i $$-0.5\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 3.00000 1.22474
$$7$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −3.00000 5.19615i −1.00000 1.73205i
$$10$$ 1.00000 0.316228
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 1.50000 + 2.59808i 0.433013 + 0.750000i
$$13$$ 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i $$-0.789049\pi$$
0.926995 + 0.375073i $$0.122382\pi$$
$$14$$ 0 0
$$15$$ −1.50000 2.59808i −0.387298 0.670820i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i $$-0.0886875\pi$$
−0.718900 + 0.695113i $$0.755354\pi$$
$$18$$ 3.00000 5.19615i 0.707107 1.22474i
$$19$$ −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i $$-0.907015\pi$$
0.728219 + 0.685344i $$0.240348\pi$$
$$20$$ 0.500000 + 0.866025i 0.111803 + 0.193649i
$$21$$ 0 0
$$22$$ 1.00000 + 1.73205i 0.213201 + 0.369274i
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ −1.50000 + 2.59808i −0.306186 + 0.530330i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 1.00000 0.196116
$$27$$ −9.00000 −1.73205
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 1.50000 2.59808i 0.273861 0.474342i
$$31$$ 5.00000 0.898027 0.449013 0.893525i $$-0.351776\pi$$
0.449013 + 0.893525i $$0.351776\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 3.00000 5.19615i 0.522233 0.904534i
$$34$$ −1.00000 + 1.73205i −0.171499 + 0.297044i
$$35$$ 0 0
$$36$$ 6.00000 1.00000
$$37$$ −5.50000 + 2.59808i −0.904194 + 0.427121i
$$38$$ −2.00000 −0.324443
$$39$$ −1.50000 2.59808i −0.240192 0.416025i
$$40$$ −0.500000 + 0.866025i −0.0790569 + 0.136931i
$$41$$ −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i $$-0.908600\pi$$
0.724797 + 0.688963i $$0.241934\pi$$
$$42$$ 0 0
$$43$$ 7.00000 1.06749 0.533745 0.845645i $$-0.320784\pi$$
0.533745 + 0.845645i $$0.320784\pi$$
$$44$$ −1.00000 + 1.73205i −0.150756 + 0.261116i
$$45$$ −6.00000 −0.894427
$$46$$ −3.00000 5.19615i −0.442326 0.766131i
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ −3.00000 −0.433013
$$49$$ 3.50000 + 6.06218i 0.500000 + 0.866025i
$$50$$ 0.500000 0.866025i 0.0707107 0.122474i
$$51$$ 6.00000 0.840168
$$52$$ 0.500000 + 0.866025i 0.0693375 + 0.120096i
$$53$$ 5.50000 + 9.52628i 0.755483 + 1.30854i 0.945134 + 0.326683i $$0.105931\pi$$
−0.189651 + 0.981852i $$0.560736\pi$$
$$54$$ −4.50000 7.79423i −0.612372 1.06066i
$$55$$ 1.00000 1.73205i 0.134840 0.233550i
$$56$$ 0 0
$$57$$ 3.00000 + 5.19615i 0.397360 + 0.688247i
$$58$$ 3.00000 + 5.19615i 0.393919 + 0.682288i
$$59$$ 1.00000 + 1.73205i 0.130189 + 0.225494i 0.923749 0.382998i $$-0.125108\pi$$
−0.793560 + 0.608492i $$0.791775\pi$$
$$60$$ 3.00000 0.387298
$$61$$ −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i $$0.387809\pi$$
−0.985391 + 0.170305i $$0.945525\pi$$
$$62$$ 2.50000 + 4.33013i 0.317500 + 0.549927i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −0.500000 0.866025i −0.0620174 0.107417i
$$66$$ 6.00000 0.738549
$$67$$ −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i $$-0.911904\pi$$
0.717607 + 0.696449i $$0.245238\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ −9.00000 + 15.5885i −1.08347 + 1.87663i
$$70$$ 0 0
$$71$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ 3.00000 + 5.19615i 0.353553 + 0.612372i
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ −5.00000 3.46410i −0.581238 0.402694i
$$75$$ −3.00000 −0.346410
$$76$$ −1.00000 1.73205i −0.114708 0.198680i
$$77$$ 0 0
$$78$$ 1.50000 2.59808i 0.169842 0.294174i
$$79$$ 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i $$-0.761089\pi$$
0.956325 + 0.292306i $$0.0944227\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ −3.00000 −0.331295
$$83$$ −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i $$-0.937822\pi$$
0.322396 0.946605i $$-0.395512\pi$$
$$84$$ 0 0
$$85$$ 2.00000 0.216930
$$86$$ 3.50000 + 6.06218i 0.377415 + 0.653701i
$$87$$ 9.00000 15.5885i 0.964901 1.67126i
$$88$$ −2.00000 −0.213201
$$89$$ −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i $$-0.200471\pi$$
−0.914146 + 0.405385i $$0.867138\pi$$
$$90$$ −3.00000 5.19615i −0.316228 0.547723i
$$91$$ 0 0
$$92$$ 3.00000 5.19615i 0.312772 0.541736i
$$93$$ 7.50000 12.9904i 0.777714 1.34704i
$$94$$ −4.00000 6.92820i −0.412568 0.714590i
$$95$$ 1.00000 + 1.73205i 0.102598 + 0.177705i
$$96$$ −1.50000 2.59808i −0.153093 0.265165i
$$97$$ 18.0000 1.82762 0.913812 0.406138i $$-0.133125\pi$$
0.913812 + 0.406138i $$0.133125\pi$$
$$98$$ −3.50000 + 6.06218i −0.353553 + 0.612372i
$$99$$ −6.00000 10.3923i −0.603023 1.04447i
$$100$$ 1.00000 0.100000
$$101$$ −18.0000 −1.79107 −0.895533 0.444994i $$-0.853206\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 3.00000 + 5.19615i 0.297044 + 0.514496i
$$103$$ −18.0000 −1.77359 −0.886796 0.462160i $$-0.847074\pi$$
−0.886796 + 0.462160i $$0.847074\pi$$
$$104$$ −0.500000 + 0.866025i −0.0490290 + 0.0849208i
$$105$$ 0 0
$$106$$ −5.50000 + 9.52628i −0.534207 + 0.925274i
$$107$$ 8.50000 14.7224i 0.821726 1.42327i −0.0826699 0.996577i $$-0.526345\pi$$
0.904396 0.426694i $$-0.140322\pi$$
$$108$$ 4.50000 7.79423i 0.433013 0.750000i
$$109$$ 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i $$0.164149\pi$$
−0.00790932 + 0.999969i $$0.502518\pi$$
$$110$$ 2.00000 0.190693
$$111$$ −1.50000 + 18.1865i −0.142374 + 1.72619i
$$112$$ 0 0
$$113$$ −10.0000 17.3205i −0.940721 1.62938i −0.764100 0.645097i $$-0.776817\pi$$
−0.176620 0.984279i $$-0.556517\pi$$
$$114$$ −3.00000 + 5.19615i −0.280976 + 0.486664i
$$115$$ −3.00000 + 5.19615i −0.279751 + 0.484544i
$$116$$ −3.00000 + 5.19615i −0.278543 + 0.482451i
$$117$$ −6.00000 −0.554700
$$118$$ −1.00000 + 1.73205i −0.0920575 + 0.159448i
$$119$$ 0 0
$$120$$ 1.50000 + 2.59808i 0.136931 + 0.237171i
$$121$$ −7.00000 −0.636364
$$122$$ −10.0000 −0.905357
$$123$$ 4.50000 + 7.79423i 0.405751 + 0.702782i
$$124$$ −2.50000 + 4.33013i −0.224507 + 0.388857i
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 2.00000 + 3.46410i 0.177471 + 0.307389i 0.941014 0.338368i $$-0.109875\pi$$
−0.763542 + 0.645758i $$0.776542\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 10.5000 18.1865i 0.924473 1.60123i
$$130$$ 0.500000 0.866025i 0.0438529 0.0759555i
$$131$$ 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i $$-0.0822479\pi$$
−0.704692 + 0.709514i $$0.748915\pi$$
$$132$$ 3.00000 + 5.19615i 0.261116 + 0.452267i
$$133$$ 0 0
$$134$$ −4.00000 −0.345547
$$135$$ −4.50000 + 7.79423i −0.387298 + 0.670820i
$$136$$ −1.00000 1.73205i −0.0857493 0.148522i
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ −18.0000 −1.53226
$$139$$ −7.00000 12.1244i −0.593732 1.02837i −0.993724 0.111856i $$-0.964321\pi$$
0.399992 0.916519i $$-0.369013\pi$$
$$140$$ 0 0
$$141$$ −12.0000 + 20.7846i −1.01058 + 1.75038i
$$142$$ 0 0
$$143$$ 1.00000 1.73205i 0.0836242 0.144841i
$$144$$ −3.00000 + 5.19615i −0.250000 + 0.433013i
$$145$$ 3.00000 5.19615i 0.249136 0.431517i
$$146$$ −1.00000 1.73205i −0.0827606 0.143346i
$$147$$ 21.0000 1.73205
$$148$$ 0.500000 6.06218i 0.0410997 0.498308i
$$149$$ −4.00000 −0.327693 −0.163846 0.986486i $$-0.552390\pi$$
−0.163846 + 0.986486i $$0.552390\pi$$
$$150$$ −1.50000 2.59808i −0.122474 0.212132i
$$151$$ 4.50000 7.79423i 0.366205 0.634285i −0.622764 0.782410i $$-0.713990\pi$$
0.988969 + 0.148124i $$0.0473236\pi$$
$$152$$ 1.00000 1.73205i 0.0811107 0.140488i
$$153$$ 6.00000 10.3923i 0.485071 0.840168i
$$154$$ 0 0
$$155$$ 2.50000 4.33013i 0.200805 0.347804i
$$156$$ 3.00000 0.240192
$$157$$ −1.50000 2.59808i −0.119713 0.207349i 0.799941 0.600079i $$-0.204864\pi$$
−0.919654 + 0.392730i $$0.871531\pi$$
$$158$$ 4.00000 0.318223
$$159$$ 33.0000 2.61707
$$160$$ −0.500000 0.866025i −0.0395285 0.0684653i
$$161$$ 0 0
$$162$$ −9.00000 −0.707107
$$163$$ 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i $$-0.154198\pi$$
−0.845780 + 0.533533i $$0.820864\pi$$
$$164$$ −1.50000 2.59808i −0.117130 0.202876i
$$165$$ −3.00000 5.19615i −0.233550 0.404520i
$$166$$ 6.00000 10.3923i 0.465690 0.806599i
$$167$$ 5.00000 8.66025i 0.386912 0.670151i −0.605121 0.796134i $$-0.706875\pi$$
0.992032 + 0.125983i $$0.0402085\pi$$
$$168$$ 0 0
$$169$$ 6.00000 + 10.3923i 0.461538 + 0.799408i
$$170$$ 1.00000 + 1.73205i 0.0766965 + 0.132842i
$$171$$ 12.0000 0.917663
$$172$$ −3.50000 + 6.06218i −0.266872 + 0.462237i
$$173$$ −11.0000 19.0526i −0.836315 1.44854i −0.892956 0.450145i $$-0.851372\pi$$
0.0566411 0.998395i $$-0.481961\pi$$
$$174$$ 18.0000 1.36458
$$175$$ 0 0
$$176$$ −1.00000 1.73205i −0.0753778 0.130558i
$$177$$ 6.00000 0.450988
$$178$$ 1.00000 1.73205i 0.0749532 0.129823i
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 3.00000 5.19615i 0.223607 0.387298i
$$181$$ −8.00000 + 13.8564i −0.594635 + 1.02994i 0.398963 + 0.916967i $$0.369370\pi$$
−0.993598 + 0.112972i $$0.963963\pi$$
$$182$$ 0 0
$$183$$ 15.0000 + 25.9808i 1.10883 + 1.92055i
$$184$$ 6.00000 0.442326
$$185$$ −0.500000 + 6.06218i −0.0367607 + 0.445700i
$$186$$ 15.0000 1.09985
$$187$$ 2.00000 + 3.46410i 0.146254 + 0.253320i
$$188$$ 4.00000 6.92820i 0.291730 0.505291i
$$189$$ 0 0
$$190$$ −1.00000 + 1.73205i −0.0725476 + 0.125656i
$$191$$ −3.00000 −0.217072 −0.108536 0.994092i $$-0.534616\pi$$
−0.108536 + 0.994092i $$0.534616\pi$$
$$192$$ 1.50000 2.59808i 0.108253 0.187500i
$$193$$ 26.0000 1.87152 0.935760 0.352636i $$-0.114715\pi$$
0.935760 + 0.352636i $$0.114715\pi$$
$$194$$ 9.00000 + 15.5885i 0.646162 + 1.11919i
$$195$$ −3.00000 −0.214834
$$196$$ −7.00000 −0.500000
$$197$$ −5.50000 9.52628i −0.391859 0.678719i 0.600836 0.799372i $$-0.294834\pi$$
−0.992695 + 0.120653i $$0.961501\pi$$
$$198$$ 6.00000 10.3923i 0.426401 0.738549i
$$199$$ 25.0000 1.77220 0.886102 0.463491i $$-0.153403\pi$$
0.886102 + 0.463491i $$0.153403\pi$$
$$200$$ 0.500000 + 0.866025i 0.0353553 + 0.0612372i
$$201$$ 6.00000 + 10.3923i 0.423207 + 0.733017i
$$202$$ −9.00000 15.5885i −0.633238 1.09680i
$$203$$ 0 0
$$204$$ −3.00000 + 5.19615i −0.210042 + 0.363803i
$$205$$ 1.50000 + 2.59808i 0.104765 + 0.181458i
$$206$$ −9.00000 15.5885i −0.627060 1.08610i
$$207$$ 18.0000 + 31.1769i 1.25109 + 2.16695i
$$208$$ −1.00000 −0.0693375
$$209$$ −2.00000 + 3.46410i −0.138343 + 0.239617i
$$210$$ 0 0
$$211$$ −2.00000 −0.137686 −0.0688428 0.997628i $$-0.521931\pi$$
−0.0688428 + 0.997628i $$0.521931\pi$$
$$212$$ −11.0000 −0.755483
$$213$$ 0 0
$$214$$ 17.0000 1.16210
$$215$$ 3.50000 6.06218i 0.238698 0.413437i
$$216$$ 9.00000 0.612372
$$217$$ 0 0
$$218$$ −9.00000 + 15.5885i −0.609557 + 1.05578i
$$219$$ −3.00000 + 5.19615i −0.202721 + 0.351123i
$$220$$ 1.00000 + 1.73205i 0.0674200 + 0.116775i
$$221$$ 2.00000 0.134535
$$222$$ −16.5000 + 7.79423i −1.10741 + 0.523114i
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ 0 0
$$225$$ −3.00000 + 5.19615i −0.200000 + 0.346410i
$$226$$ 10.0000 17.3205i 0.665190 1.15214i
$$227$$ 12.5000 21.6506i 0.829654 1.43700i −0.0686556 0.997640i $$-0.521871\pi$$
0.898310 0.439363i $$-0.144796\pi$$
$$228$$ −6.00000 −0.397360
$$229$$ 6.00000 10.3923i 0.396491 0.686743i −0.596799 0.802391i $$-0.703561\pi$$
0.993290 + 0.115648i $$0.0368944\pi$$
$$230$$ −6.00000 −0.395628
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ −16.0000 −1.04819 −0.524097 0.851658i $$-0.675597\pi$$
−0.524097 + 0.851658i $$0.675597\pi$$
$$234$$ −3.00000 5.19615i −0.196116 0.339683i
$$235$$ −4.00000 + 6.92820i −0.260931 + 0.451946i
$$236$$ −2.00000 −0.130189
$$237$$ −6.00000 10.3923i −0.389742 0.675053i
$$238$$ 0 0
$$239$$ −12.0000 20.7846i −0.776215 1.34444i −0.934109 0.356988i $$-0.883804\pi$$
0.157893 0.987456i $$-0.449530\pi$$
$$240$$ −1.50000 + 2.59808i −0.0968246 + 0.167705i
$$241$$ 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i $$-0.728952\pi$$
0.980917 + 0.194429i $$0.0622852\pi$$
$$242$$ −3.50000 6.06218i −0.224989 0.389692i
$$243$$ 0 0
$$244$$ −5.00000 8.66025i −0.320092 0.554416i
$$245$$ 7.00000 0.447214
$$246$$ −4.50000 + 7.79423i −0.286910 + 0.496942i
$$247$$ 1.00000 + 1.73205i 0.0636285 + 0.110208i
$$248$$ −5.00000 −0.317500
$$249$$ −36.0000 −2.28141
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ −10.0000 −0.631194 −0.315597 0.948893i $$-0.602205\pi$$
−0.315597 + 0.948893i $$0.602205\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ −2.00000 + 3.46410i −0.125491 + 0.217357i
$$255$$ 3.00000 5.19615i 0.187867 0.325396i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 8.00000 + 13.8564i 0.499026 + 0.864339i 0.999999 0.00112398i $$-0.000357774\pi$$
−0.500973 + 0.865463i $$0.667024\pi$$
$$258$$ 21.0000 1.30740
$$259$$ 0 0
$$260$$ 1.00000 0.0620174
$$261$$ −18.0000 31.1769i −1.11417 1.92980i
$$262$$ −3.00000 + 5.19615i −0.185341 + 0.321019i
$$263$$ −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i $$-0.997543\pi$$
0.506669 + 0.862141i $$0.330877\pi$$
$$264$$ −3.00000 + 5.19615i −0.184637 + 0.319801i
$$265$$ 11.0000 0.675725
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ −2.00000 3.46410i −0.122169 0.211604i
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ −9.00000 −0.547723
$$271$$ −0.500000 0.866025i −0.0303728 0.0526073i 0.850439 0.526073i $$-0.176336\pi$$
−0.880812 + 0.473466i $$0.843003\pi$$
$$272$$ 1.00000 1.73205i 0.0606339 0.105021i
$$273$$ 0 0
$$274$$ −3.00000 5.19615i −0.181237 0.313911i
$$275$$ −1.00000 1.73205i −0.0603023 0.104447i
$$276$$ −9.00000 15.5885i −0.541736 0.938315i
$$277$$ −14.5000 + 25.1147i −0.871221 + 1.50900i −0.0104855 + 0.999945i $$0.503338\pi$$
−0.860735 + 0.509053i $$0.829996\pi$$
$$278$$ 7.00000 12.1244i 0.419832 0.727171i
$$279$$ −15.0000 25.9808i −0.898027 1.55543i
$$280$$ 0 0
$$281$$ 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i $$0.0251222\pi$$
−0.430165 + 0.902750i $$0.641545\pi$$
$$282$$ −24.0000 −1.42918
$$283$$ 5.50000 9.52628i 0.326941 0.566279i −0.654962 0.755662i $$-0.727315\pi$$
0.981903 + 0.189383i $$0.0606488\pi$$
$$284$$ 0 0
$$285$$ 6.00000 0.355409
$$286$$ 2.00000 0.118262
$$287$$ 0 0
$$288$$ −6.00000 −0.353553
$$289$$ 6.50000 11.2583i 0.382353 0.662255i
$$290$$ 6.00000 0.352332
$$291$$ 27.0000 46.7654i 1.58277 2.74143i
$$292$$ 1.00000 1.73205i 0.0585206 0.101361i
$$293$$ −13.5000 + 23.3827i −0.788678 + 1.36603i 0.138098 + 0.990419i $$0.455901\pi$$
−0.926777 + 0.375613i $$0.877432\pi$$
$$294$$ 10.5000 + 18.1865i 0.612372 + 1.06066i
$$295$$ 2.00000 0.116445
$$296$$ 5.50000 2.59808i 0.319681 0.151010i
$$297$$ −18.0000 −1.04447
$$298$$ −2.00000 3.46410i −0.115857 0.200670i
$$299$$ −3.00000 + 5.19615i −0.173494 + 0.300501i
$$300$$ 1.50000 2.59808i 0.0866025 0.150000i
$$301$$ 0 0
$$302$$ 9.00000 0.517892
$$303$$ −27.0000 + 46.7654i −1.55111 + 2.68660i
$$304$$ 2.00000 0.114708
$$305$$ 5.00000 + 8.66025i 0.286299 + 0.495885i
$$306$$ 12.0000 0.685994
$$307$$ −23.0000 −1.31268 −0.656340 0.754466i $$-0.727896\pi$$
−0.656340 + 0.754466i $$0.727896\pi$$
$$308$$ 0 0
$$309$$ −27.0000 + 46.7654i −1.53598 + 2.66039i
$$310$$ 5.00000 0.283981
$$311$$ −1.50000 2.59808i −0.0850572 0.147323i 0.820358 0.571850i $$-0.193774\pi$$
−0.905416 + 0.424526i $$0.860441\pi$$
$$312$$ 1.50000 + 2.59808i 0.0849208 + 0.147087i
$$313$$ −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i $$-0.296152\pi$$
−0.993186 + 0.116543i $$0.962819\pi$$
$$314$$ 1.50000 2.59808i 0.0846499 0.146618i
$$315$$ 0 0
$$316$$ 2.00000 + 3.46410i 0.112509 + 0.194871i
$$317$$ −8.50000 14.7224i −0.477408 0.826894i 0.522257 0.852788i $$-0.325090\pi$$
−0.999665 + 0.0258939i $$0.991757\pi$$
$$318$$ 16.5000 + 28.5788i 0.925274 + 1.60262i
$$319$$ 12.0000 0.671871
$$320$$ 0.500000 0.866025i 0.0279508 0.0484123i
$$321$$ −25.5000 44.1673i −1.42327 2.46518i
$$322$$ 0 0
$$323$$ −4.00000 −0.222566
$$324$$ −4.50000 7.79423i −0.250000 0.433013i
$$325$$ −1.00000 −0.0554700
$$326$$ −0.500000 + 0.866025i −0.0276924 + 0.0479647i
$$327$$ 54.0000 2.98621
$$328$$ 1.50000 2.59808i 0.0828236 0.143455i
$$329$$ 0 0
$$330$$ 3.00000 5.19615i 0.165145 0.286039i
$$331$$ −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i $$-0.981428\pi$$
0.448649 0.893708i $$-0.351905\pi$$
$$332$$ 12.0000 0.658586
$$333$$ 30.0000 + 20.7846i 1.64399 + 1.13899i
$$334$$ 10.0000 0.547176
$$335$$ 2.00000 + 3.46410i 0.109272 + 0.189264i
$$336$$ 0 0
$$337$$ −5.00000 + 8.66025i −0.272367 + 0.471754i −0.969468 0.245220i $$-0.921140\pi$$
0.697100 + 0.716974i $$0.254473\pi$$
$$338$$ −6.00000 + 10.3923i −0.326357 + 0.565267i
$$339$$ −60.0000 −3.25875
$$340$$ −1.00000 + 1.73205i −0.0542326 + 0.0939336i
$$341$$ 10.0000 0.541530
$$342$$ 6.00000 + 10.3923i 0.324443 + 0.561951i
$$343$$ 0 0
$$344$$ −7.00000 −0.377415
$$345$$ 9.00000 + 15.5885i 0.484544 + 0.839254i
$$346$$ 11.0000 19.0526i 0.591364 1.02427i
$$347$$ 4.00000 0.214731 0.107366 0.994220i $$-0.465758\pi$$
0.107366 + 0.994220i $$0.465758\pi$$
$$348$$ 9.00000 + 15.5885i 0.482451 + 0.835629i
$$349$$ 3.00000 + 5.19615i 0.160586 + 0.278144i 0.935079 0.354439i $$-0.115328\pi$$
−0.774493 + 0.632583i $$0.781995\pi$$
$$350$$ 0 0
$$351$$ −4.50000 + 7.79423i −0.240192 + 0.416025i
$$352$$ 1.00000 1.73205i 0.0533002 0.0923186i
$$353$$ −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i $$-0.946141\pi$$
0.347024 0.937856i $$-0.387192\pi$$
$$354$$ 3.00000 + 5.19615i 0.159448 + 0.276172i
$$355$$ 0 0
$$356$$ 2.00000 0.106000
$$357$$ 0 0
$$358$$ 2.00000 + 3.46410i 0.105703 + 0.183083i
$$359$$ 21.0000 1.10834 0.554169 0.832404i $$-0.313036\pi$$
0.554169 + 0.832404i $$0.313036\pi$$
$$360$$ 6.00000 0.316228
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ −16.0000 −0.840941
$$363$$ −10.5000 + 18.1865i −0.551107 + 0.954545i
$$364$$ 0 0
$$365$$ −1.00000 + 1.73205i −0.0523424 + 0.0906597i
$$366$$ −15.0000 + 25.9808i −0.784063 + 1.35804i
$$367$$ −13.0000 + 22.5167i −0.678594 + 1.17536i 0.296810 + 0.954937i $$0.404077\pi$$
−0.975404 + 0.220423i $$0.929256\pi$$
$$368$$ 3.00000 + 5.19615i 0.156386 + 0.270868i
$$369$$ 18.0000 0.937043
$$370$$ −5.50000 + 2.59808i −0.285931 + 0.135068i
$$371$$ 0 0
$$372$$ 7.50000 + 12.9904i 0.388857 + 0.673520i
$$373$$ 8.50000 14.7224i 0.440113 0.762299i −0.557584 0.830120i $$-0.688272\pi$$
0.997697 + 0.0678218i $$0.0216049\pi$$
$$374$$ −2.00000 + 3.46410i −0.103418 + 0.179124i
$$375$$ −1.50000 + 2.59808i −0.0774597 + 0.134164i
$$376$$ 8.00000 0.412568
$$377$$ 3.00000 5.19615i 0.154508 0.267615i
$$378$$ 0 0
$$379$$ 5.00000 + 8.66025i 0.256833 + 0.444847i 0.965392 0.260804i $$-0.0839877\pi$$
−0.708559 + 0.705652i $$0.750654\pi$$
$$380$$ −2.00000 −0.102598
$$381$$ 12.0000 0.614779
$$382$$ −1.50000 2.59808i −0.0767467 0.132929i
$$383$$ 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i $$-0.734147\pi$$
0.977613 + 0.210411i $$0.0674801\pi$$
$$384$$ 3.00000 0.153093
$$385$$ 0 0
$$386$$ 13.0000 + 22.5167i 0.661683 + 1.14607i
$$387$$ −21.0000 36.3731i −1.06749 1.84895i
$$388$$ −9.00000 + 15.5885i −0.456906 + 0.791384i
$$389$$ −8.00000 + 13.8564i −0.405616 + 0.702548i −0.994393 0.105748i $$-0.966276\pi$$
0.588777 + 0.808296i $$0.299610\pi$$
$$390$$ −1.50000 2.59808i −0.0759555 0.131559i
$$391$$ −6.00000 10.3923i −0.303433 0.525561i
$$392$$ −3.50000 6.06218i −0.176777 0.306186i
$$393$$ 18.0000 0.907980
$$394$$ 5.50000 9.52628i 0.277086 0.479927i
$$395$$ −2.00000 3.46410i −0.100631 0.174298i
$$396$$ 12.0000 0.603023
$$397$$ 25.0000 1.25471 0.627357 0.778732i $$-0.284137\pi$$
0.627357 + 0.778732i $$0.284137\pi$$
$$398$$ 12.5000 + 21.6506i 0.626568 + 1.08525i
$$399$$ 0 0
$$400$$ −0.500000 + 0.866025i −0.0250000 + 0.0433013i
$$401$$ 2.00000 0.0998752 0.0499376 0.998752i $$-0.484098\pi$$
0.0499376 + 0.998752i $$0.484098\pi$$
$$402$$ −6.00000 + 10.3923i −0.299253 + 0.518321i
$$403$$ 2.50000 4.33013i 0.124534 0.215699i
$$404$$ 9.00000 15.5885i 0.447767 0.775555i
$$405$$ 4.50000 + 7.79423i 0.223607 + 0.387298i
$$406$$ 0 0
$$407$$ −11.0000 + 5.19615i −0.545250 + 0.257564i
$$408$$ −6.00000 −0.297044
$$409$$ −14.5000 25.1147i −0.716979 1.24184i −0.962191 0.272374i $$-0.912191\pi$$
0.245212 0.969469i $$-0.421142\pi$$
$$410$$ −1.50000 + 2.59808i −0.0740797 + 0.128310i
$$411$$ −9.00000 + 15.5885i −0.443937 + 0.768922i
$$412$$ 9.00000 15.5885i 0.443398 0.767988i
$$413$$ 0 0
$$414$$ −18.0000 + 31.1769i −0.884652 + 1.53226i
$$415$$ −12.0000 −0.589057
$$416$$ −0.500000 0.866025i −0.0245145 0.0424604i
$$417$$ −42.0000 −2.05675
$$418$$ −4.00000 −0.195646
$$419$$ 7.00000 + 12.1244i 0.341972 + 0.592314i 0.984799 0.173698i $$-0.0555717\pi$$
−0.642827 + 0.766012i $$0.722238\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ −1.00000 1.73205i −0.0486792 0.0843149i
$$423$$ 24.0000 + 41.5692i 1.16692 + 2.02116i
$$424$$ −5.50000 9.52628i −0.267104 0.462637i
$$425$$ 1.00000 1.73205i 0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 8.50000 + 14.7224i 0.410863 + 0.711636i
$$429$$ −3.00000 5.19615i −0.144841 0.250873i
$$430$$ 7.00000 0.337570
$$431$$ −6.50000 + 11.2583i −0.313094 + 0.542295i −0.979030 0.203714i $$-0.934699\pi$$
0.665937 + 0.746008i $$0.268032\pi$$
$$432$$ 4.50000 + 7.79423i 0.216506 + 0.375000i
$$433$$ 16.0000 0.768911 0.384455 0.923144i $$-0.374389\pi$$
0.384455 + 0.923144i $$0.374389\pi$$
$$434$$ 0 0
$$435$$ −9.00000 15.5885i −0.431517 0.747409i
$$436$$ −18.0000 −0.862044
$$437$$ 6.00000 10.3923i 0.287019 0.497131i
$$438$$ −6.00000 −0.286691
$$439$$ −3.50000 + 6.06218i −0.167046 + 0.289332i −0.937380 0.348309i $$-0.886756\pi$$
0.770334 + 0.637641i $$0.220089\pi$$
$$440$$ −1.00000 + 1.73205i −0.0476731 + 0.0825723i
$$441$$ 21.0000 36.3731i 1.00000 1.73205i
$$442$$ 1.00000 + 1.73205i 0.0475651 + 0.0823853i
$$443$$ −21.0000 −0.997740 −0.498870 0.866677i $$-0.666252\pi$$
−0.498870 + 0.866677i $$0.666252\pi$$
$$444$$ −15.0000 10.3923i −0.711868 0.493197i
$$445$$ −2.00000 −0.0948091
$$446$$ 1.00000 + 1.73205i 0.0473514 + 0.0820150i
$$447$$ −6.00000 + 10.3923i −0.283790 + 0.491539i
$$448$$ 0 0
$$449$$ −10.5000 + 18.1865i −0.495526 + 0.858276i −0.999987 0.00515887i $$-0.998358\pi$$
0.504461 + 0.863434i $$0.331691\pi$$
$$450$$ −6.00000 −0.282843
$$451$$ −3.00000 + 5.19615i −0.141264 + 0.244677i
$$452$$ 20.0000 0.940721
$$453$$ −13.5000 23.3827i −0.634285 1.09861i
$$454$$ 25.0000 1.17331
$$455$$ 0 0
$$456$$ −3.00000 5.19615i −0.140488 0.243332i
$$457$$ −6.00000 + 10.3923i −0.280668 + 0.486132i −0.971549 0.236837i $$-0.923889\pi$$
0.690881 + 0.722968i $$0.257223\pi$$
$$458$$ 12.0000 0.560723
$$459$$ −9.00000 15.5885i −0.420084 0.727607i
$$460$$ −3.00000 5.19615i −0.139876 0.242272i
$$461$$ 7.00000 + 12.1244i 0.326023 + 0.564688i 0.981719 0.190337i $$-0.0609581\pi$$
−0.655696 + 0.755025i $$0.727625\pi$$
$$462$$ 0 0
$$463$$ −10.0000 + 17.3205i −0.464739 + 0.804952i −0.999190 0.0402476i $$-0.987185\pi$$
0.534450 + 0.845200i $$0.320519\pi$$
$$464$$ −3.00000 5.19615i −0.139272 0.241225i
$$465$$ −7.50000 12.9904i −0.347804 0.602414i
$$466$$ −8.00000 13.8564i −0.370593 0.641886i
$$467$$ −23.0000 −1.06431 −0.532157 0.846646i $$-0.678618\pi$$
−0.532157 + 0.846646i $$0.678618\pi$$
$$468$$ 3.00000 5.19615i 0.138675 0.240192i
$$469$$ 0 0
$$470$$ −8.00000 −0.369012
$$471$$ −9.00000 −0.414698
$$472$$ −1.00000 1.73205i −0.0460287 0.0797241i
$$473$$ 14.0000 0.643721
$$474$$ 6.00000 10.3923i 0.275589 0.477334i
$$475$$ 2.00000 0.0917663
$$476$$ 0 0
$$477$$ 33.0000 57.1577i 1.51097 2.61707i
$$478$$ 12.0000 20.7846i 0.548867 0.950666i
$$479$$ −3.50000 6.06218i −0.159919 0.276988i 0.774920 0.632059i $$-0.217790\pi$$
−0.934839 + 0.355071i $$0.884457\pi$$
$$480$$ −3.00000 −0.136931
$$481$$ −0.500000 + 6.06218i −0.0227980 + 0.276412i
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ 3.50000 6.06218i 0.159091 0.275554i
$$485$$ 9.00000 15.5885i 0.408669 0.707835i
$$486$$ 0 0
$$487$$ −22.0000 −0.996915 −0.498458 0.866914i $$-0.666100\pi$$
−0.498458 + 0.866914i $$0.666100\pi$$
$$488$$ 5.00000 8.66025i 0.226339 0.392031i
$$489$$ 3.00000 0.135665
$$490$$ 3.50000 + 6.06218i 0.158114 + 0.273861i
$$491$$ 2.00000 0.0902587 0.0451294 0.998981i $$-0.485630\pi$$
0.0451294 + 0.998981i $$0.485630\pi$$
$$492$$ −9.00000 −0.405751
$$493$$ 6.00000 + 10.3923i 0.270226 + 0.468046i
$$494$$ −1.00000 + 1.73205i −0.0449921 + 0.0779287i
$$495$$ −12.0000 −0.539360
$$496$$ −2.50000 4.33013i −0.112253 0.194428i
$$497$$ 0 0
$$498$$ −18.0000 31.1769i −0.806599 1.39707i
$$499$$ 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i $$-0.685590\pi$$
0.998233 + 0.0594153i $$0.0189236\pi$$
$$500$$ 0.500000 0.866025i 0.0223607 0.0387298i
$$501$$ −15.0000 25.9808i −0.670151 1.16073i
$$502$$ −5.00000 8.66025i −0.223161 0.386526i
$$503$$ −12.0000 20.7846i −0.535054 0.926740i −0.999161 0.0409609i $$-0.986958\pi$$
0.464107 0.885779i $$-0.346375\pi$$
$$504$$ 0 0
$$505$$ −9.00000 + 15.5885i −0.400495 + 0.693677i
$$506$$ −6.00000 10.3923i −0.266733 0.461994i
$$507$$ 36.0000 1.59882
$$508$$ −4.00000 −0.177471
$$509$$ 12.0000 + 20.7846i 0.531891 + 0.921262i 0.999307 + 0.0372243i $$0.0118516\pi$$
−0.467416 + 0.884037i $$0.654815\pi$$
$$510$$ 6.00000 0.265684
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 9.00000 15.5885i 0.397360 0.688247i
$$514$$ −8.00000 + 13.8564i −0.352865 + 0.611180i
$$515$$ −9.00000 + 15.5885i −0.396587 + 0.686909i
$$516$$ 10.5000 + 18.1865i 0.462237 + 0.800617i
$$517$$ −16.0000 −0.703679
$$518$$ 0 0
$$519$$ −66.0000 −2.89708
$$520$$ 0.500000 + 0.866025i 0.0219265 + 0.0379777i
$$521$$ −12.5000 + 21.6506i −0.547635 + 0.948532i 0.450801 + 0.892624i $$0.351138\pi$$
−0.998436 + 0.0559071i $$0.982195\pi$$
$$522$$ 18.0000 31.1769i 0.787839 1.36458i
$$523$$ 4.50000 7.79423i 0.196771 0.340818i −0.750708 0.660634i $$-0.770288\pi$$
0.947480 + 0.319816i $$0.103621\pi$$
$$524$$ −6.00000 −0.262111
$$525$$ 0 0
$$526$$ −16.0000 −0.697633
$$527$$ 5.00000 + 8.66025i 0.217803 + 0.377247i
$$528$$ −6.00000 −0.261116
$$529$$ 13.0000 0.565217
$$530$$ 5.50000 + 9.52628i 0.238905 + 0.413795i
$$531$$ 6.00000 10.3923i 0.260378 0.450988i
$$532$$ 0 0
$$533$$ 1.50000 + 2.59808i 0.0649722 + 0.112535i
$$534$$ −3.00000 5.19615i −0.129823 0.224860i
$$535$$ −8.50000 14.7224i −0.367487 0.636506i
$$536$$ 2.00000 3.46410i 0.0863868 0.149626i
$$537$$ 6.00000 10.3923i 0.258919 0.448461i
$$538$$ 1.00000 + 1.73205i 0.0431131 + 0.0746740i
$$539$$ 7.00000 + 12.1244i 0.301511 + 0.522233i
$$540$$ −4.50000 7.79423i −0.193649 0.335410i
$$541$$ 6.00000 0.257960 0.128980 0.991647i $$-0.458830\pi$$
0.128980 + 0.991647i $$0.458830\pi$$
$$542$$ 0.500000 0.866025i 0.0214768 0.0371990i
$$543$$ 24.0000 + 41.5692i 1.02994 + 1.78391i
$$544$$ 2.00000 0.0857493
$$545$$ 18.0000 0.771035
$$546$$ 0 0
$$547$$ −11.0000 −0.470326 −0.235163 0.971956i $$-0.575562\pi$$
−0.235163 + 0.971956i $$0.575562\pi$$
$$548$$ 3.00000 5.19615i 0.128154 0.221969i
$$549$$ 60.0000 2.56074
$$550$$ 1.00000 1.73205i 0.0426401 0.0738549i
$$551$$ −6.00000 + 10.3923i −0.255609 + 0.442727i
$$552$$ 9.00000 15.5885i 0.383065 0.663489i
$$553$$ 0 0
$$554$$ −29.0000 −1.23209
$$555$$ 15.0000 + 10.3923i 0.636715 + 0.441129i
$$556$$ 14.0000 0.593732
$$557$$ 12.5000 + 21.6506i 0.529642 + 0.917367i 0.999402 + 0.0345728i $$0.0110071\pi$$
−0.469760 + 0.882794i $$0.655660\pi$$
$$558$$ 15.0000 25.9808i 0.635001 1.09985i
$$559$$ 3.50000 6.06218i 0.148034 0.256403i
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ −9.50000 + 16.4545i −0.400733 + 0.694090i
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ −12.0000 20.7846i −0.505291 0.875190i
$$565$$ −20.0000 −0.841406
$$566$$ 11.0000 0.462364
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 21.0000 0.880366 0.440183 0.897908i $$-0.354914\pi$$
0.440183 + 0.897908i $$0.354914\pi$$
$$570$$ 3.00000 + 5.19615i 0.125656 + 0.217643i
$$571$$ 6.00000 + 10.3923i 0.251092 + 0.434904i 0.963827 0.266529i $$-0.0858769\pi$$
−0.712735 + 0.701434i $$0.752544\pi$$
$$572$$ 1.00000 + 1.73205i 0.0418121 + 0.0724207i
$$573$$ −4.50000 + 7.79423i −0.187990 + 0.325609i
$$574$$ 0 0
$$575$$ 3.00000 + 5.19615i 0.125109 + 0.216695i
$$576$$ −3.00000 5.19615i −0.125000 0.216506i
$$577$$ 16.0000 + 27.7128i 0.666089 + 1.15370i 0.978989 + 0.203913i $$0.0653661\pi$$
−0.312900 + 0.949786i $$0.601301\pi$$
$$578$$ 13.0000 0.540729
$$579$$ 39.0000 67.5500i 1.62078 2.80728i
$$580$$ 3.00000 + 5.19615i 0.124568 + 0.215758i
$$581$$ 0 0
$$582$$ 54.0000 2.23837
$$583$$ 11.0000 + 19.0526i 0.455573 + 0.789076i
$$584$$ 2.00000 0.0827606
$$585$$ −3.00000 + 5.19615i −0.124035 + 0.214834i
$$586$$ −27.0000 −1.11536
$$587$$ 7.50000 12.9904i 0.309558 0.536170i −0.668708 0.743525i $$-0.733152\pi$$
0.978266 + 0.207355i $$0.0664855\pi$$
$$588$$ −10.5000 + 18.1865i −0.433013 + 0.750000i
$$589$$ −5.00000 + 8.66025i −0.206021 + 0.356840i
$$590$$ 1.00000 + 1.73205i 0.0411693 + 0.0713074i
$$591$$ −33.0000 −1.35744
$$592$$ 5.00000 + 3.46410i 0.205499 + 0.142374i
$$593$$ 34.0000 1.39621 0.698106 0.715994i $$-0.254026\pi$$
0.698106 + 0.715994i $$0.254026\pi$$
$$594$$ −9.00000 15.5885i −0.369274 0.639602i
$$595$$ 0 0
$$596$$ 2.00000 3.46410i 0.0819232 0.141895i
$$597$$ 37.5000 64.9519i 1.53477 2.65830i
$$598$$ −6.00000 −0.245358
$$599$$ 7.50000 12.9904i 0.306442 0.530773i −0.671140 0.741331i $$-0.734195\pi$$
0.977581 + 0.210558i $$0.0675282\pi$$
$$600$$ 3.00000 0.122474
$$601$$ 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i $$0.0863789\pi$$
−0.249565 + 0.968358i $$0.580288\pi$$
$$602$$ 0 0
$$603$$ 24.0000 0.977356
$$604$$ 4.50000 + 7.79423i 0.183102 + 0.317143i
$$605$$ −3.50000 + 6.06218i −0.142295 + 0.246463i
$$606$$ −54.0000 −2.19360
$$607$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$608$$ 1.00000 + 1.73205i 0.0405554 + 0.0702439i
$$609$$ 0 0
$$610$$ −5.00000 + 8.66025i −0.202444 + 0.350643i
$$611$$ −4.00000 + 6.92820i −0.161823 + 0.280285i
$$612$$ 6.00000 + 10.3923i 0.242536 + 0.420084i
$$613$$ −3.00000 5.19615i −0.121169 0.209871i 0.799060 0.601251i $$-0.205331\pi$$
−0.920229 + 0.391381i $$0.871998\pi$$
$$614$$ −11.5000 19.9186i −0.464102 0.803849i
$$615$$ 9.00000 0.362915
$$616$$ 0 0
$$617$$ 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i $$-0.128129\pi$$
−0.799298 + 0.600935i $$0.794795\pi$$
$$618$$ −54.0000 −2.17220
$$619$$ −26.0000 −1.04503 −0.522514 0.852631i $$-0.675006\pi$$
−0.522514 + 0.852631i $$0.675006\pi$$
$$620$$ 2.50000 + 4.33013i 0.100402 + 0.173902i
$$621$$ 54.0000 2.16695
$$622$$ 1.50000 2.59808i 0.0601445 0.104173i
$$623$$ 0 0
$$624$$ −1.50000 + 2.59808i −0.0600481 + 0.104006i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 7.00000 12.1244i 0.279776 0.484587i
$$627$$ 6.00000 + 10.3923i 0.239617 + 0.415029i
$$628$$ 3.00000 0.119713
$$629$$ −10.0000 6.92820i −0.398726 0.276246i
$$630$$ 0 0
$$631$$ −7.50000 12.9904i −0.298570 0.517139i 0.677239 0.735763i $$-0.263176\pi$$
−0.975809 + 0.218624i $$0.929843\pi$$
$$632$$ −2.00000 + 3.46410i −0.0795557 + 0.137795i
$$633$$ −3.00000 + 5.19615i −0.119239 + 0.206529i
$$634$$ 8.50000 14.7224i 0.337578 0.584702i
$$635$$ 4.00000 0.158735
$$636$$ −16.5000 + 28.5788i −0.654268 + 1.13322i
$$637$$ 7.00000 0.277350
$$638$$ 6.00000 + 10.3923i 0.237542 + 0.411435i
$$639$$ 0 0
$$640$$ 1.00000 0.0395285
$$641$$ 0.500000 + 0.866025i 0.0197488 + 0.0342059i 0.875731 0.482800i $$-0.160380\pi$$
−0.855982 + 0.517005i $$0.827047\pi$$
$$642$$ 25.5000 44.1673i 1.00640 1.74314i
$$643$$ 1.00000 0.0394362 0.0197181 0.999806i $$-0.493723\pi$$
0.0197181 + 0.999806i $$0.493723\pi$$
$$644$$ 0 0
$$645$$ −10.5000 18.1865i −0.413437 0.716094i
$$646$$ −2.00000 3.46410i −0.0786889 0.136293i
$$647$$ 8.00000 13.8564i 0.314512 0.544752i −0.664821 0.747002i $$-0.731492\pi$$
0.979334 + 0.202251i $$0.0648256\pi$$
$$648$$ 4.50000 7.79423i 0.176777 0.306186i
$$649$$ 2.00000 + 3.46410i 0.0785069 + 0.135978i
$$650$$ −0.500000 0.866025i −0.0196116 0.0339683i
$$651$$ 0 0
$$652$$ −1.00000 −0.0391630
$$653$$ 2.50000 4.33013i 0.0978326 0.169451i −0.812955 0.582327i $$-0.802142\pi$$
0.910787 + 0.412876i $$0.135476\pi$$
$$654$$ 27.0000 + 46.7654i 1.05578 + 1.82867i
$$655$$ 6.00000 0.234439
$$656$$ 3.00000 0.117130
$$657$$ 6.00000 + 10.3923i 0.234082 + 0.405442i
$$658$$ 0 0
$$659$$ 20.0000 34.6410i 0.779089 1.34942i −0.153378 0.988168i $$-0.549015\pi$$
0.932467 0.361255i $$-0.117652\pi$$
$$660$$ 6.00000 0.233550
$$661$$ 14.0000 24.2487i 0.544537 0.943166i −0.454099 0.890951i $$-0.650039\pi$$
0.998636 0.0522143i $$-0.0166279\pi$$
$$662$$ 10.0000 17.3205i 0.388661 0.673181i
$$663$$ 3.00000 5.19615i 0.116510 0.201802i
$$664$$ 6.00000 + 10.3923i 0.232845 + 0.403300i
$$665$$ 0 0
$$666$$ −3.00000 + 36.3731i −0.116248 + 1.40943i
$$667$$ −36.0000 −1.39393
$$668$$ 5.00000 + 8.66025i 0.193456 + 0.335075i
$$669$$ 3.00000 5.19615i 0.115987 0.200895i
$$670$$ −2.00000 + 3.46410i −0.0772667 + 0.133830i
$$671$$ −10.0000 + 17.3205i −0.386046 + 0.668651i
$$672$$ 0 0
$$673$$ −14.0000 + 24.2487i −0.539660 + 0.934719i 0.459262 + 0.888301i $$0.348114\pi$$
−0.998922 + 0.0464181i $$0.985219\pi$$
$$674$$ −10.0000 −0.385186
$$675$$ 4.50000 + 7.79423i 0.173205 + 0.300000i
$$676$$ −12.0000 −0.461538
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ −30.0000 51.9615i −1.15214 1.99557i
$$679$$ 0 0
$$680$$ −2.00000 −0.0766965
$$681$$ −37.5000 64.9519i −1.43700 2.48896i
$$682$$ 5.00000 + 8.66025i 0.191460 + 0.331618i
$$683$$ 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i $$0.101432\pi$$
−0.203510 + 0.979073i $$0.565235\pi$$
$$684$$ −6.00000 + 10.3923i −0.229416 + 0.397360i
$$685$$ −3.00000 + 5.19615i −0.114624 + 0.198535i
$$686$$ 0 0
$$687$$ −18.0000 31.1769i −0.686743 1.18947i
$$688$$ −3.50000 6.06218i −0.133436 0.231118i
$$689$$ 11.0000 0.419067
$$690$$ −9.00000 + 15.5885i −0.342624 + 0.593442i
$$691$$ 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i $$-0.0424468\pi$$
−0.610704 + 0.791859i $$0.709113\pi$$
$$692$$ 22.0000 0.836315
$$693$$ 0 0
$$694$$ 2.00000 + 3.46410i 0.0759190 + 0.131495i
$$695$$ −14.0000 −0.531050
$$696$$ −9.00000 + 15.5885i −0.341144 + 0.590879i
$$697$$ −6.00000 −0.227266
$$698$$ −3.00000 + 5.19615i −0.113552 + 0.196677i
$$699$$ −24.0000 + 41.5692i −0.907763 + 1.57229i
$$700$$ 0 0
$$701$$ 11.0000 + 19.0526i 0.415464 + 0.719605i 0.995477 0.0950021i $$-0.0302858\pi$$
−0.580013 + 0.814607i $$0.696952\pi$$
$$702$$ −9.00000 −0.339683
$$703$$ 1.00000 12.1244i 0.0377157 0.457279i
$$704$$ 2.00000 0.0753778
$$705$$ 12.0000 + 20.7846i 0.451946 + 0.782794i
$$706$$ 12.0000 20.7846i 0.451626 0.782239i
$$707$$ 0 0
$$708$$ −3.00000 + 5.19615i −0.112747 + 0.195283i
$$709$$ 24.0000 0.901339 0.450669 0.892691i $$-0.351185\pi$$
0.450669 + 0.892691i $$0.351185\pi$$
$$710$$ 0 0
$$711$$ −24.0000 −0.900070
$$712$$ 1.00000 + 1.73205i 0.0374766 + 0.0649113i
$$713$$ −30.0000 −1.12351
$$714$$ 0 0
$$715$$ −1.00000 1.73205i −0.0373979 0.0647750i
$$716$$ −2.00000 + 3.46410i −0.0747435 + 0.129460i
$$717$$ −72.0000 −2.68889
$$718$$ 10.5000 + 18.1865i 0.391857 + 0.678715i
$$719$$ 18.5000 + 32.0429i 0.689934 + 1.19500i 0.971859 + 0.235564i $$0.0756936\pi$$
−0.281925 + 0.959436i $$0.590973\pi$$
$$720$$ 3.00000 + 5.19615i 0.111803 + 0.193649i
$$721$$ 0 0
$$722$$ −7.50000 + 12.9904i −0.279121 + 0.483452i
$$723$$ −15.0000 25.9808i −0.557856 0.966235i
$$724$$ −8.00000 13.8564i −0.297318 0.514969i
$$725$$ −3.00000 5.19615i −0.111417 0.192980i
$$726$$ −21.0000 −0.779383
$$727$$ −26.0000 + 45.0333i −0.964287 + 1.67019i −0.252767 + 0.967527i $$0.581341\pi$$
−0.711520 + 0.702666i $$0.751993\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ −2.00000 −0.0740233
$$731$$ 7.00000 + 12.1244i 0.258904 + 0.448435i
$$732$$ −30.0000 −1.10883
$$733$$ 7.00000 12.1244i 0.258551 0.447823i −0.707303 0.706910i $$-0.750088\pi$$
0.965854 + 0.259087i $$0.0834217\pi$$
$$734$$ −26.0000 −0.959678
$$735$$ 10.5000 18.1865i 0.387298 0.670820i
$$736$$ −3.00000 + 5.19615i −0.110581 + 0.191533i
$$737$$ −4.00000 + 6.92820i −0.147342 + 0.255204i
$$738$$ 9.00000 + 15.5885i 0.331295 + 0.573819i
$$739$$ −6.00000 −0.220714 −0.110357 0.993892i $$-0.535199\pi$$
−0.110357 + 0.993892i $$0.535199\pi$$
$$740$$ −5.00000 3.46410i −0.183804 0.127343i
$$741$$ 6.00000 0.220416
$$742$$ 0 0
$$743$$ 21.0000 36.3731i 0.770415 1.33440i −0.166920 0.985970i $$-0.553382\pi$$
0.937336 0.348428i $$-0.113284\pi$$
$$744$$ −7.50000 + 12.9904i −0.274963 + 0.476250i
$$745$$ −2.00000 + 3.46410i −0.0732743 + 0.126915i
$$746$$ 17.0000 0.622414
$$747$$ −36.0000 + 62.3538i −1.31717 + 2.28141i
$$748$$ −4.00000 −0.146254
$$749$$ 0 0
$$750$$ −3.00000 −0.109545
$$751$$ 11.0000 0.401396 0.200698 0.979653i $$-0.435679\pi$$
0.200698 + 0.979653i $$0.435679\pi$$
$$752$$ 4.00000 + 6.92820i 0.145865 + 0.252646i
$$753$$ −15.0000 + 25.9808i −0.546630 + 0.946792i
$$754$$ 6.00000 0.218507
$$755$$ −4.50000 7.79423i −0.163772 0.283661i
$$756$$ 0 0
$$757$$ 23.5000 + 40.7032i 0.854122 + 1.47938i 0.877457 + 0.479655i $$0.159238\pi$$
−0.0233351 + 0.999728i $$0.507428\pi$$
$$758$$ −5.00000 + 8.66025i −0.181608 + 0.314555i
$$759$$ −18.0000 + 31.1769i −0.653359 + 1.13165i
$$760$$ −1.00000 1.73205i −0.0362738 0.0628281i
$$761$$ −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i $$-0.891253\pi$$
0.180957 0.983491i $$-0.442080\pi$$
$$762$$ 6.00000 + 10.3923i 0.217357 + 0.376473i
$$763$$ 0 0
$$764$$ 1.50000 2.59808i 0.0542681 0.0939951i
$$765$$ −6.00000 10.3923i −0.216930 0.375735i
$$766$$ 12.0000 0.433578
$$767$$ 2.00000 0.0722158
$$768$$ 1.50000 + 2.59808i 0.0541266 + 0.0937500i
$$769$$ 30.0000 1.08183 0.540914 0.841078i $$-0.318079\pi$$
0.540914 + 0.841078i $$0.318079\pi$$
$$770$$ 0 0
$$771$$ 48.0000 1.72868
$$772$$ −13.0000 + 22.5167i −0.467880 + 0.810392i
$$773$$ 3.50000 6.06218i 0.125886 0.218041i −0.796193 0.605043i $$-0.793156\pi$$
0.922079 + 0.387002i $$0.126489\pi$$
$$774$$ 21.0000 36.3731i 0.754829 1.30740i
$$775$$ −2.50000 4.33013i −0.0898027 0.155543i
$$776$$ −18.0000 −0.646162
$$777$$ 0 0
$$778$$ −16.0000 −0.573628
$$779$$ −3.00000 5.19615i −0.107486 0.186171i
$$780$$ 1.50000 2.59808i 0.0537086 0.0930261i
$$781$$ 0 0
$$782$$ 6.00000 10.3923i 0.214560 0.371628i
$$783$$ −54.0000 −1.92980