# Properties

 Label 1950.2.i.d.601.1 Level $1950$ Weight $2$ Character 1950.601 Analytic conductor $15.571$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ 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: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 601.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.601 Dual form 1950.2.i.d.451.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(2.50000 - 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-2.50000 - 4.33013i) q^{29} -11.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} -2.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} +(1.00000 + 1.73205i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-5.50000 + 9.52628i) q^{43} -5.00000 q^{44} +(-0.500000 + 0.866025i) q^{46} -9.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +2.00000 q^{51} +(2.50000 + 2.59808i) q^{52} -6.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(5.50000 + 9.52628i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -5.00000 q^{66} +(8.00000 + 13.8564i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-0.500000 + 0.866025i) q^{69} +(-0.500000 + 0.866025i) q^{72} +6.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{76} -10.0000 q^{77} +(2.50000 + 2.59808i) q^{78} -11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +11.0000 q^{86} +(-2.50000 + 4.33013i) q^{87} +(2.50000 + 4.33013i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(5.00000 + 5.19615i) q^{91} +1.00000 q^{92} +(5.50000 + 9.52628i) q^{93} +(4.50000 + 7.79423i) q^{94} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{3} - q^{4} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + O(q^{10})$$ $$2q - q^{2} - q^{3} - q^{4} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + 5q^{11} + 2q^{12} + 2q^{13} + 4q^{14} - q^{16} - 2q^{17} + 2q^{18} + 2q^{19} + 4q^{21} + 5q^{22} - q^{23} - q^{24} - 7q^{26} + 2q^{27} - 2q^{28} - 5q^{29} - 22q^{31} - q^{32} + 5q^{33} + 4q^{34} - q^{36} + 3q^{37} - 4q^{38} - 7q^{39} + 2q^{41} - 2q^{42} - 11q^{43} - 10q^{44} - q^{46} - 18q^{47} - q^{48} + 3q^{49} + 4q^{51} + 5q^{52} - 12q^{53} - q^{54} - 2q^{56} - 4q^{57} - 5q^{58} + 15q^{59} - 10q^{61} + 11q^{62} - 2q^{63} + 2q^{64} - 10q^{66} + 16q^{67} - 2q^{68} - q^{69} - q^{72} + 12q^{73} + 3q^{74} + 2q^{76} - 20q^{77} + 5q^{78} - 22q^{79} - q^{81} + 2q^{82} - 12q^{83} - 2q^{84} + 22q^{86} - 5q^{87} + 5q^{88} - 2q^{89} + 10q^{91} + 2q^{92} + 11q^{93} + 9q^{94} + 2q^{96} - 2q^{97} + 3q^{98} - 10q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

## 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
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ −0.500000 + 0.866025i −0.204124 + 0.353553i
$$7$$ −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i $$-0.956709\pi$$
0.612801 + 0.790237i $$0.290043\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i $$0.105104\pi$$
−0.192201 + 0.981356i $$0.561563\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 1.00000 3.46410i 0.277350 0.960769i
$$14$$ 2.00000 0.534522
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i $$-0.911312\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i $$-0.759652\pi$$
0.957635 + 0.287984i $$0.0929851\pi$$
$$20$$ 0 0
$$21$$ 2.00000 0.436436
$$22$$ 2.50000 4.33013i 0.533002 0.923186i
$$23$$ −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i $$-0.199913\pi$$
−0.913434 + 0.406986i $$0.866580\pi$$
$$24$$ −0.500000 0.866025i −0.102062 0.176777i
$$25$$ 0 0
$$26$$ −3.50000 + 0.866025i −0.686406 + 0.169842i
$$27$$ 1.00000 0.192450
$$28$$ −1.00000 1.73205i −0.188982 0.327327i
$$29$$ −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i $$-0.320339\pi$$
−0.999167 + 0.0408130i $$0.987005\pi$$
$$30$$ 0 0
$$31$$ −11.0000 −1.97566 −0.987829 0.155543i $$-0.950287\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 2.50000 4.33013i 0.435194 0.753778i
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i $$-0.0873538\pi$$
−0.715981 + 0.698119i $$0.754020\pi$$
$$38$$ −2.00000 −0.324443
$$39$$ −3.50000 + 0.866025i −0.560449 + 0.138675i
$$40$$ 0 0
$$41$$ 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i $$-0.116751\pi$$
−0.777312 + 0.629115i $$0.783417\pi$$
$$42$$ −1.00000 1.73205i −0.154303 0.267261i
$$43$$ −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i $$0.483375\pi$$
−0.890947 + 0.454108i $$0.849958\pi$$
$$44$$ −5.00000 −0.753778
$$45$$ 0 0
$$46$$ −0.500000 + 0.866025i −0.0737210 + 0.127688i
$$47$$ −9.00000 −1.31278 −0.656392 0.754420i $$-0.727918\pi$$
−0.656392 + 0.754420i $$0.727918\pi$$
$$48$$ −0.500000 + 0.866025i −0.0721688 + 0.125000i
$$49$$ 1.50000 + 2.59808i 0.214286 + 0.371154i
$$50$$ 0 0
$$51$$ 2.00000 0.280056
$$52$$ 2.50000 + 2.59808i 0.346688 + 0.360288i
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ 0 0
$$56$$ −1.00000 + 1.73205i −0.133631 + 0.231455i
$$57$$ −2.00000 −0.264906
$$58$$ −2.50000 + 4.33013i −0.328266 + 0.568574i
$$59$$ 7.50000 12.9904i 0.976417 1.69120i 0.301239 0.953549i $$-0.402600\pi$$
0.675178 0.737655i $$-0.264067\pi$$
$$60$$ 0 0
$$61$$ −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i $$0.387809\pi$$
−0.985391 + 0.170305i $$0.945525\pi$$
$$62$$ 5.50000 + 9.52628i 0.698501 + 1.20984i
$$63$$ −1.00000 1.73205i −0.125988 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −5.00000 −0.615457
$$67$$ 8.00000 + 13.8564i 0.977356 + 1.69283i 0.671932 + 0.740613i $$0.265465\pi$$
0.305424 + 0.952217i $$0.401202\pi$$
$$68$$ −1.00000 1.73205i −0.121268 0.210042i
$$69$$ −0.500000 + 0.866025i −0.0601929 + 0.104257i
$$70$$ 0 0
$$71$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ −0.500000 + 0.866025i −0.0589256 + 0.102062i
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 1.50000 2.59808i 0.174371 0.302020i
$$75$$ 0 0
$$76$$ 1.00000 + 1.73205i 0.114708 + 0.198680i
$$77$$ −10.0000 −1.13961
$$78$$ 2.50000 + 2.59808i 0.283069 + 0.294174i
$$79$$ −11.0000 −1.23760 −0.618798 0.785550i $$-0.712380\pi$$
−0.618798 + 0.785550i $$0.712380\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 1.00000 1.73205i 0.110432 0.191273i
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ −1.00000 + 1.73205i −0.109109 + 0.188982i
$$85$$ 0 0
$$86$$ 11.0000 1.18616
$$87$$ −2.50000 + 4.33013i −0.268028 + 0.464238i
$$88$$ 2.50000 + 4.33013i 0.266501 + 0.461593i
$$89$$ −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i $$-0.200471\pi$$
−0.914146 + 0.405385i $$0.867138\pi$$
$$90$$ 0 0
$$91$$ 5.00000 + 5.19615i 0.524142 + 0.544705i
$$92$$ 1.00000 0.104257
$$93$$ 5.50000 + 9.52628i 0.570323 + 0.987829i
$$94$$ 4.50000 + 7.79423i 0.464140 + 0.803913i
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i $$-0.865709\pi$$
0.810782 + 0.585348i $$0.199042\pi$$
$$98$$ 1.50000 2.59808i 0.151523 0.262445i
$$99$$ −5.00000 −0.502519
$$100$$ 0 0
$$101$$ −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i $$-0.198392\pi$$
−0.911479 + 0.411346i $$0.865059\pi$$
$$102$$ −1.00000 1.73205i −0.0990148 0.171499i
$$103$$ −10.0000 −0.985329 −0.492665 0.870219i $$-0.663977\pi$$
−0.492665 + 0.870219i $$0.663977\pi$$
$$104$$ 1.00000 3.46410i 0.0980581 0.339683i
$$105$$ 0 0
$$106$$ 3.00000 + 5.19615i 0.291386 + 0.504695i
$$107$$ 5.00000 + 8.66025i 0.483368 + 0.837218i 0.999818 0.0190994i $$-0.00607989\pi$$
−0.516449 + 0.856318i $$0.672747\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ 1.50000 2.59808i 0.142374 0.246598i
$$112$$ 2.00000 0.188982
$$113$$ 5.50000 9.52628i 0.517396 0.896157i −0.482399 0.875951i $$-0.660235\pi$$
0.999796 0.0202056i $$-0.00643208\pi$$
$$114$$ 1.00000 + 1.73205i 0.0936586 + 0.162221i
$$115$$ 0 0
$$116$$ 5.00000 0.464238
$$117$$ 2.50000 + 2.59808i 0.231125 + 0.240192i
$$118$$ −15.0000 −1.38086
$$119$$ −2.00000 3.46410i −0.183340 0.317554i
$$120$$ 0 0
$$121$$ −7.00000 + 12.1244i −0.636364 + 1.10221i
$$122$$ 10.0000 0.905357
$$123$$ 1.00000 1.73205i 0.0901670 0.156174i
$$124$$ 5.50000 9.52628i 0.493915 0.855485i
$$125$$ 0 0
$$126$$ −1.00000 + 1.73205i −0.0890871 + 0.154303i
$$127$$ 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i $$-0.138384\pi$$
−0.818241 + 0.574875i $$0.805051\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 11.0000 0.968496
$$130$$ 0 0
$$131$$ −1.00000 −0.0873704 −0.0436852 0.999045i $$-0.513910\pi$$
−0.0436852 + 0.999045i $$0.513910\pi$$
$$132$$ 2.50000 + 4.33013i 0.217597 + 0.376889i
$$133$$ 2.00000 + 3.46410i 0.173422 + 0.300376i
$$134$$ 8.00000 13.8564i 0.691095 1.19701i
$$135$$ 0 0
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ −5.50000 + 9.52628i −0.469897 + 0.813885i −0.999408 0.0344182i $$-0.989042\pi$$
0.529511 + 0.848303i $$0.322376\pi$$
$$138$$ 1.00000 0.0851257
$$139$$ −1.00000 + 1.73205i −0.0848189 + 0.146911i −0.905314 0.424743i $$-0.860365\pi$$
0.820495 + 0.571654i $$0.193698\pi$$
$$140$$ 0 0
$$141$$ 4.50000 + 7.79423i 0.378968 + 0.656392i
$$142$$ 0 0
$$143$$ 17.5000 4.33013i 1.46342 0.362103i
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −3.00000 5.19615i −0.248282 0.430037i
$$147$$ 1.50000 2.59808i 0.123718 0.214286i
$$148$$ −3.00000 −0.246598
$$149$$ −8.50000 + 14.7224i −0.696347 + 1.20611i 0.273377 + 0.961907i $$0.411859\pi$$
−0.969724 + 0.244202i $$0.921474\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 1.00000 1.73205i 0.0811107 0.140488i
$$153$$ −1.00000 1.73205i −0.0808452 0.140028i
$$154$$ 5.00000 + 8.66025i 0.402911 + 0.697863i
$$155$$ 0 0
$$156$$ 1.00000 3.46410i 0.0800641 0.277350i
$$157$$ 7.00000 0.558661 0.279330 0.960195i $$-0.409888\pi$$
0.279330 + 0.960195i $$0.409888\pi$$
$$158$$ 5.50000 + 9.52628i 0.437557 + 0.757870i
$$159$$ 3.00000 + 5.19615i 0.237915 + 0.412082i
$$160$$ 0 0
$$161$$ 2.00000 0.157622
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ −7.50000 + 12.9904i −0.587445 + 1.01749i 0.407120 + 0.913375i $$0.366533\pi$$
−0.994566 + 0.104111i $$0.966800\pi$$
$$164$$ −2.00000 −0.156174
$$165$$ 0 0
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ 1.50000 + 2.59808i 0.116073 + 0.201045i 0.918208 0.396098i $$-0.129636\pi$$
−0.802135 + 0.597143i $$0.796303\pi$$
$$168$$ 2.00000 0.154303
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ 0 0
$$171$$ 1.00000 + 1.73205i 0.0764719 + 0.132453i
$$172$$ −5.50000 9.52628i −0.419371 0.726372i
$$173$$ 10.0000 17.3205i 0.760286 1.31685i −0.182417 0.983221i $$-0.558392\pi$$
0.942703 0.333633i $$-0.108275\pi$$
$$174$$ 5.00000 0.379049
$$175$$ 0 0
$$176$$ 2.50000 4.33013i 0.188445 0.326396i
$$177$$ −15.0000 −1.12747
$$178$$ −1.00000 + 1.73205i −0.0749532 + 0.129823i
$$179$$ 6.50000 + 11.2583i 0.485833 + 0.841487i 0.999867 0.0162823i $$-0.00518305\pi$$
−0.514035 + 0.857769i $$0.671850\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 2.00000 6.92820i 0.148250 0.513553i
$$183$$ 10.0000 0.739221
$$184$$ −0.500000 0.866025i −0.0368605 0.0638442i
$$185$$ 0 0
$$186$$ 5.50000 9.52628i 0.403280 0.698501i
$$187$$ −10.0000 −0.731272
$$188$$ 4.50000 7.79423i 0.328196 0.568453i
$$189$$ −1.00000 + 1.73205i −0.0727393 + 0.125988i
$$190$$ 0 0
$$191$$ −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i $$-0.879560\pi$$
0.784552 + 0.620063i $$0.212893\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ −12.0000 20.7846i −0.863779 1.49611i −0.868255 0.496119i $$-0.834758\pi$$
0.00447566 0.999990i $$-0.498575\pi$$
$$194$$ 2.00000 0.143592
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ −4.00000 6.92820i −0.284988 0.493614i 0.687618 0.726073i $$-0.258656\pi$$
−0.972606 + 0.232458i $$0.925323\pi$$
$$198$$ 2.50000 + 4.33013i 0.177667 + 0.307729i
$$199$$ −12.0000 + 20.7846i −0.850657 + 1.47338i 0.0299585 + 0.999551i $$0.490462\pi$$
−0.880616 + 0.473831i $$0.842871\pi$$
$$200$$ 0 0
$$201$$ 8.00000 13.8564i 0.564276 0.977356i
$$202$$ −1.00000 + 1.73205i −0.0703598 + 0.121867i
$$203$$ 10.0000 0.701862
$$204$$ −1.00000 + 1.73205i −0.0700140 + 0.121268i
$$205$$ 0 0
$$206$$ 5.00000 + 8.66025i 0.348367 + 0.603388i
$$207$$ 1.00000 0.0695048
$$208$$ −3.50000 + 0.866025i −0.242681 + 0.0600481i
$$209$$ 10.0000 0.691714
$$210$$ 0 0
$$211$$ 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i $$-0.122700\pi$$
−0.788935 + 0.614477i $$0.789367\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ 0 0
$$214$$ 5.00000 8.66025i 0.341793 0.592003i
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 11.0000 19.0526i 0.746729 1.29337i
$$218$$ 1.00000 + 1.73205i 0.0677285 + 0.117309i
$$219$$ −3.00000 5.19615i −0.202721 0.351123i
$$220$$ 0 0
$$221$$ 5.00000 + 5.19615i 0.336336 + 0.349531i
$$222$$ −3.00000 −0.201347
$$223$$ 13.0000 + 22.5167i 0.870544 + 1.50783i 0.861435 + 0.507869i $$0.169566\pi$$
0.00910984 + 0.999959i $$0.497100\pi$$
$$224$$ −1.00000 1.73205i −0.0668153 0.115728i
$$225$$ 0 0
$$226$$ −11.0000 −0.731709
$$227$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$228$$ 1.00000 1.73205i 0.0662266 0.114708i
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 5.00000 + 8.66025i 0.328976 + 0.569803i
$$232$$ −2.50000 4.33013i −0.164133 0.284287i
$$233$$ −1.00000 −0.0655122 −0.0327561 0.999463i $$-0.510428\pi$$
−0.0327561 + 0.999463i $$0.510428\pi$$
$$234$$ 1.00000 3.46410i 0.0653720 0.226455i
$$235$$ 0 0
$$236$$ 7.50000 + 12.9904i 0.488208 + 0.845602i
$$237$$ 5.50000 + 9.52628i 0.357263 + 0.618798i
$$238$$ −2.00000 + 3.46410i −0.129641 + 0.224544i
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 0 0
$$241$$ 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i $$-0.760947\pi$$
0.956456 + 0.291877i $$0.0942799\pi$$
$$242$$ 14.0000 0.899954
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ −5.00000 8.66025i −0.320092 0.554416i
$$245$$ 0 0
$$246$$ −2.00000 −0.127515
$$247$$ −5.00000 5.19615i −0.318142 0.330623i
$$248$$ −11.0000 −0.698501
$$249$$ 3.00000 + 5.19615i 0.190117 + 0.329293i
$$250$$ 0 0
$$251$$ −12.5000 + 21.6506i −0.788993 + 1.36658i 0.137591 + 0.990489i $$0.456064\pi$$
−0.926584 + 0.376087i $$0.877269\pi$$
$$252$$ 2.00000 0.125988
$$253$$ 2.50000 4.33013i 0.157174 0.272233i
$$254$$ 1.00000 1.73205i 0.0627456 0.108679i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −8.50000 14.7224i −0.530215 0.918360i −0.999379 0.0352486i $$-0.988778\pi$$
0.469163 0.883112i $$-0.344556\pi$$
$$258$$ −5.50000 9.52628i −0.342415 0.593080i
$$259$$ −6.00000 −0.372822
$$260$$ 0 0
$$261$$ 5.00000 0.309492
$$262$$ 0.500000 + 0.866025i 0.0308901 + 0.0535032i
$$263$$ 10.5000 + 18.1865i 0.647458 + 1.12143i 0.983728 + 0.179664i $$0.0575011\pi$$
−0.336270 + 0.941766i $$0.609166\pi$$
$$264$$ 2.50000 4.33013i 0.153864 0.266501i
$$265$$ 0 0
$$266$$ 2.00000 3.46410i 0.122628 0.212398i
$$267$$ −1.00000 + 1.73205i −0.0611990 + 0.106000i
$$268$$ −16.0000 −0.977356
$$269$$ −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i $$-0.973692\pi$$
0.569789 + 0.821791i $$0.307025\pi$$
$$270$$ 0 0
$$271$$ 6.50000 + 11.2583i 0.394847 + 0.683895i 0.993082 0.117426i $$-0.0374643\pi$$
−0.598235 + 0.801321i $$0.704131\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 2.00000 6.92820i 0.121046 0.419314i
$$274$$ 11.0000 0.664534
$$275$$ 0 0
$$276$$ −0.500000 0.866025i −0.0300965 0.0521286i
$$277$$ −5.50000 + 9.52628i −0.330463 + 0.572379i −0.982603 0.185720i $$-0.940538\pi$$
0.652140 + 0.758099i $$0.273872\pi$$
$$278$$ 2.00000 0.119952
$$279$$ 5.50000 9.52628i 0.329276 0.570323i
$$280$$ 0 0
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ 4.50000 7.79423i 0.267971 0.464140i
$$283$$ 9.50000 + 16.4545i 0.564716 + 0.978117i 0.997076 + 0.0764162i $$0.0243478\pi$$
−0.432360 + 0.901701i $$0.642319\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −12.5000 12.9904i −0.739140 0.768137i
$$287$$ −4.00000 −0.236113
$$288$$ −0.500000 0.866025i −0.0294628 0.0510310i
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ 2.00000 0.117242
$$292$$ −3.00000 + 5.19615i −0.175562 + 0.304082i
$$293$$ 3.00000 5.19615i 0.175262 0.303562i −0.764990 0.644042i $$-0.777256\pi$$
0.940252 + 0.340480i $$0.110589\pi$$
$$294$$ −3.00000 −0.174964
$$295$$ 0 0
$$296$$ 1.50000 + 2.59808i 0.0871857 + 0.151010i
$$297$$ 2.50000 + 4.33013i 0.145065 + 0.251259i
$$298$$ 17.0000 0.984784
$$299$$ −3.50000 + 0.866025i −0.202410 + 0.0500835i
$$300$$ 0 0
$$301$$ −11.0000 19.0526i −0.634029 1.09817i
$$302$$ −4.00000 6.92820i −0.230174 0.398673i
$$303$$ −1.00000 + 1.73205i −0.0574485 + 0.0995037i
$$304$$ −2.00000 −0.114708
$$305$$ 0 0
$$306$$ −1.00000 + 1.73205i −0.0571662 + 0.0990148i
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 5.00000 8.66025i 0.284901 0.493464i
$$309$$ 5.00000 + 8.66025i 0.284440 + 0.492665i
$$310$$ 0 0
$$311$$ 20.0000 1.13410 0.567048 0.823685i $$-0.308085\pi$$
0.567048 + 0.823685i $$0.308085\pi$$
$$312$$ −3.50000 + 0.866025i −0.198148 + 0.0490290i
$$313$$ −20.0000 −1.13047 −0.565233 0.824931i $$-0.691214\pi$$
−0.565233 + 0.824931i $$0.691214\pi$$
$$314$$ −3.50000 6.06218i −0.197516 0.342108i
$$315$$ 0 0
$$316$$ 5.50000 9.52628i 0.309399 0.535895i
$$317$$ −16.0000 −0.898650 −0.449325 0.893368i $$-0.648335\pi$$
−0.449325 + 0.893368i $$0.648335\pi$$
$$318$$ 3.00000 5.19615i 0.168232 0.291386i
$$319$$ 12.5000 21.6506i 0.699866 1.21220i
$$320$$ 0 0
$$321$$ 5.00000 8.66025i 0.279073 0.483368i
$$322$$ −1.00000 1.73205i −0.0557278 0.0965234i
$$323$$ 2.00000 + 3.46410i 0.111283 + 0.192748i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 15.0000 0.830773
$$327$$ 1.00000 + 1.73205i 0.0553001 + 0.0957826i
$$328$$ 1.00000 + 1.73205i 0.0552158 + 0.0956365i
$$329$$ 9.00000 15.5885i 0.496186 0.859419i
$$330$$ 0 0
$$331$$ 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i $$-0.553834\pi$$
0.937829 0.347097i $$-0.112833\pi$$
$$332$$ 3.00000 5.19615i 0.164646 0.285176i
$$333$$ −3.00000 −0.164399
$$334$$ 1.50000 2.59808i 0.0820763 0.142160i
$$335$$ 0 0
$$336$$ −1.00000 1.73205i −0.0545545 0.0944911i
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ −0.500000 + 12.9904i −0.0271964 + 0.706584i
$$339$$ −11.0000 −0.597438
$$340$$ 0 0
$$341$$ −27.5000 47.6314i −1.48921 2.57938i
$$342$$ 1.00000 1.73205i 0.0540738 0.0936586i
$$343$$ −20.0000 −1.07990
$$344$$ −5.50000 + 9.52628i −0.296540 + 0.513623i
$$345$$ 0 0
$$346$$ −20.0000 −1.07521
$$347$$ 17.0000 29.4449i 0.912608 1.58068i 0.102241 0.994760i $$-0.467399\pi$$
0.810366 0.585923i $$-0.199268\pi$$
$$348$$ −2.50000 4.33013i −0.134014 0.232119i
$$349$$ −10.0000 17.3205i −0.535288 0.927146i −0.999149 0.0412379i $$-0.986870\pi$$
0.463862 0.885908i $$-0.346463\pi$$
$$350$$ 0 0
$$351$$ 1.00000 3.46410i 0.0533761 0.184900i
$$352$$ −5.00000 −0.266501
$$353$$ −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i $$-0.325675\pi$$
−0.999711 + 0.0240566i $$0.992342\pi$$
$$354$$ 7.50000 + 12.9904i 0.398621 + 0.690431i
$$355$$ 0 0
$$356$$ 2.00000 0.106000
$$357$$ −2.00000 + 3.46410i −0.105851 + 0.183340i
$$358$$ 6.50000 11.2583i 0.343536 0.595021i
$$359$$ 12.0000 0.633336 0.316668 0.948536i $$-0.397436\pi$$
0.316668 + 0.948536i $$0.397436\pi$$
$$360$$ 0 0
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ 8.00000 + 13.8564i 0.420471 + 0.728277i
$$363$$ 14.0000 0.734809
$$364$$ −7.00000 + 1.73205i −0.366900 + 0.0907841i
$$365$$ 0 0
$$366$$ −5.00000 8.66025i −0.261354 0.452679i
$$367$$ −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i $$-0.303794\pi$$
−0.995697 + 0.0926670i $$0.970461\pi$$
$$368$$ −0.500000 + 0.866025i −0.0260643 + 0.0451447i
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ 6.00000 10.3923i 0.311504 0.539542i
$$372$$ −11.0000 −0.570323
$$373$$ −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i $$-0.997028\pi$$
0.508065 + 0.861319i $$0.330361\pi$$
$$374$$ 5.00000 + 8.66025i 0.258544 + 0.447811i
$$375$$ 0 0
$$376$$ −9.00000 −0.464140
$$377$$ −17.5000 + 4.33013i −0.901296 + 0.223013i
$$378$$ 2.00000 0.102869
$$379$$ 1.00000 + 1.73205i 0.0513665 + 0.0889695i 0.890565 0.454855i $$-0.150309\pi$$
−0.839199 + 0.543825i $$0.816976\pi$$
$$380$$ 0 0
$$381$$ 1.00000 1.73205i 0.0512316 0.0887357i
$$382$$ 4.00000 0.204658
$$383$$ 15.5000 26.8468i 0.792013 1.37181i −0.132706 0.991155i $$-0.542367\pi$$
0.924719 0.380651i $$-0.124300\pi$$
$$384$$ −0.500000 + 0.866025i −0.0255155 + 0.0441942i
$$385$$ 0 0
$$386$$ −12.0000 + 20.7846i −0.610784 + 1.05791i
$$387$$ −5.50000 9.52628i −0.279581 0.484248i
$$388$$ −1.00000 1.73205i −0.0507673 0.0879316i
$$389$$ 5.00000 0.253510 0.126755 0.991934i $$-0.459544\pi$$
0.126755 + 0.991934i $$0.459544\pi$$
$$390$$ 0 0
$$391$$ 2.00000 0.101144
$$392$$ 1.50000 + 2.59808i 0.0757614 + 0.131223i
$$393$$ 0.500000 + 0.866025i 0.0252217 + 0.0436852i
$$394$$ −4.00000 + 6.92820i −0.201517 + 0.349038i
$$395$$ 0 0
$$396$$ 2.50000 4.33013i 0.125630 0.217597i
$$397$$ 1.50000 2.59808i 0.0752828 0.130394i −0.825926 0.563778i $$-0.809347\pi$$
0.901209 + 0.433384i $$0.142681\pi$$
$$398$$ 24.0000 1.20301
$$399$$ 2.00000 3.46410i 0.100125 0.173422i
$$400$$ 0 0
$$401$$ −18.0000 31.1769i −0.898877 1.55690i −0.828932 0.559350i $$-0.811051\pi$$
−0.0699455 0.997551i $$-0.522283\pi$$
$$402$$ −16.0000 −0.798007
$$403$$ −11.0000 + 38.1051i −0.547949 + 1.89815i
$$404$$ 2.00000 0.0995037
$$405$$ 0 0
$$406$$ −5.00000 8.66025i −0.248146 0.429801i
$$407$$ −7.50000 + 12.9904i −0.371761 + 0.643909i
$$408$$ 2.00000 0.0990148
$$409$$ −15.0000 + 25.9808i −0.741702 + 1.28467i 0.210017 + 0.977698i $$0.432648\pi$$
−0.951720 + 0.306968i $$0.900685\pi$$
$$410$$ 0 0
$$411$$ 11.0000 0.542590
$$412$$ 5.00000 8.66025i 0.246332 0.426660i
$$413$$ 15.0000 + 25.9808i 0.738102 + 1.27843i
$$414$$ −0.500000 0.866025i −0.0245737 0.0425628i
$$415$$ 0 0
$$416$$ 2.50000 + 2.59808i 0.122573 + 0.127381i
$$417$$ 2.00000 0.0979404
$$418$$ −5.00000 8.66025i −0.244558 0.423587i
$$419$$ 2.00000 + 3.46410i 0.0977064 + 0.169232i 0.910735 0.412991i $$-0.135516\pi$$
−0.813029 + 0.582224i $$0.802183\pi$$
$$420$$ 0 0
$$421$$ −16.0000 −0.779792 −0.389896 0.920859i $$-0.627489\pi$$
−0.389896 + 0.920859i $$0.627489\pi$$
$$422$$ 2.00000 3.46410i 0.0973585 0.168630i
$$423$$ 4.50000 7.79423i 0.218797 0.378968i
$$424$$ −6.00000 −0.291386
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −10.0000 17.3205i −0.483934 0.838198i
$$428$$ −10.0000 −0.483368
$$429$$ −12.5000 12.9904i −0.603506 0.627182i
$$430$$ 0 0
$$431$$ −20.0000 34.6410i −0.963366 1.66860i −0.713942 0.700205i $$-0.753092\pi$$
−0.249424 0.968394i $$-0.580241\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ 14.0000 24.2487i 0.672797 1.16532i −0.304311 0.952573i $$-0.598426\pi$$
0.977108 0.212746i $$-0.0682406\pi$$
$$434$$ −22.0000 −1.05603
$$435$$ 0 0
$$436$$ 1.00000 1.73205i 0.0478913 0.0829502i
$$437$$ −2.00000 −0.0956730
$$438$$ −3.00000 + 5.19615i −0.143346 + 0.248282i
$$439$$ 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i $$-0.136236\pi$$
−0.814344 + 0.580383i $$0.802903\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 2.00000 6.92820i 0.0951303 0.329541i
$$443$$ −20.0000 −0.950229 −0.475114 0.879924i $$-0.657593\pi$$
−0.475114 + 0.879924i $$0.657593\pi$$
$$444$$ 1.50000 + 2.59808i 0.0711868 + 0.123299i
$$445$$ 0 0
$$446$$ 13.0000 22.5167i 0.615568 1.06619i
$$447$$ 17.0000 0.804072
$$448$$ −1.00000 + 1.73205i −0.0472456 + 0.0818317i
$$449$$ −6.00000 + 10.3923i −0.283158 + 0.490443i −0.972161 0.234315i $$-0.924715\pi$$
0.689003 + 0.724758i $$0.258049\pi$$
$$450$$ 0 0
$$451$$ −5.00000 + 8.66025i −0.235441 + 0.407795i
$$452$$ 5.50000 + 9.52628i 0.258698 + 0.448078i
$$453$$ −4.00000 6.92820i −0.187936 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ 19.0000 + 32.9090i 0.888783 + 1.53942i 0.841316 + 0.540544i $$0.181781\pi$$
0.0474665 + 0.998873i $$0.484885\pi$$
$$458$$ −5.00000 8.66025i −0.233635 0.404667i
$$459$$ −1.00000 + 1.73205i −0.0466760 + 0.0808452i
$$460$$ 0 0
$$461$$ 19.5000 33.7750i 0.908206 1.57306i 0.0916500 0.995791i $$-0.470786\pi$$
0.816556 0.577267i $$-0.195881\pi$$
$$462$$ 5.00000 8.66025i 0.232621 0.402911i
$$463$$ −14.0000 −0.650635 −0.325318 0.945605i $$-0.605471\pi$$
−0.325318 + 0.945605i $$0.605471\pi$$
$$464$$ −2.50000 + 4.33013i −0.116060 + 0.201021i
$$465$$ 0 0
$$466$$ 0.500000 + 0.866025i 0.0231621 + 0.0401179i
$$467$$ −6.00000 −0.277647 −0.138823 0.990317i $$-0.544332\pi$$
−0.138823 + 0.990317i $$0.544332\pi$$
$$468$$ −3.50000 + 0.866025i −0.161788 + 0.0400320i
$$469$$ −32.0000 −1.47762
$$470$$ 0 0
$$471$$ −3.50000 6.06218i −0.161271 0.279330i
$$472$$ 7.50000 12.9904i 0.345215 0.597931i
$$473$$ −55.0000 −2.52890
$$474$$ 5.50000 9.52628i 0.252623 0.437557i
$$475$$ 0 0
$$476$$ 4.00000 0.183340
$$477$$ 3.00000 5.19615i 0.137361 0.237915i
$$478$$ 10.0000 + 17.3205i 0.457389 + 0.792222i
$$479$$ 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i $$0.0180558\pi$$
−0.450098 + 0.892979i $$0.648611\pi$$
$$480$$ 0 0
$$481$$ 10.5000 2.59808i 0.478759 0.118462i
$$482$$ −7.00000 −0.318841
$$483$$ −1.00000 1.73205i −0.0455016 0.0788110i
$$484$$ −7.00000 12.1244i −0.318182 0.551107i
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ 1.00000 1.73205i 0.0453143 0.0784867i −0.842479 0.538730i $$-0.818904\pi$$
0.887793 + 0.460243i $$0.152238\pi$$
$$488$$ −5.00000 + 8.66025i −0.226339 + 0.392031i
$$489$$ 15.0000 0.678323
$$490$$ 0 0
$$491$$ 8.00000 + 13.8564i 0.361035 + 0.625331i 0.988131 0.153611i $$-0.0490902\pi$$
−0.627096 + 0.778942i $$0.715757\pi$$
$$492$$ 1.00000 + 1.73205i 0.0450835 + 0.0780869i
$$493$$ 10.0000 0.450377
$$494$$ −2.00000 + 6.92820i −0.0899843 + 0.311715i
$$495$$ 0 0
$$496$$ 5.50000 + 9.52628i 0.246957 + 0.427743i
$$497$$ 0 0
$$498$$ 3.00000 5.19615i 0.134433 0.232845i
$$499$$ 28.0000 1.25345 0.626726 0.779240i $$-0.284395\pi$$
0.626726 + 0.779240i $$0.284395\pi$$
$$500$$ 0 0
$$501$$ 1.50000 2.59808i 0.0670151 0.116073i
$$502$$ 25.0000 1.11580
$$503$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$504$$ −1.00000 1.73205i −0.0445435 0.0771517i
$$505$$ 0 0
$$506$$ −5.00000 −0.222277
$$507$$ −0.500000 + 12.9904i −0.0222058 + 0.576923i
$$508$$ −2.00000 −0.0887357
$$509$$ −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i $$-0.944480\pi$$
0.342126 0.939654i $$-0.388853\pi$$
$$510$$ 0 0
$$511$$ −6.00000 + 10.3923i −0.265424 + 0.459728i
$$512$$ 1.00000 0.0441942
$$513$$ 1.00000 1.73205i 0.0441511 0.0764719i
$$514$$ −8.50000 + 14.7224i −0.374919 + 0.649379i
$$515$$ 0 0
$$516$$ −5.50000 + 9.52628i −0.242124 + 0.419371i
$$517$$ −22.5000 38.9711i −0.989549 1.71395i
$$518$$ 3.00000 + 5.19615i 0.131812 + 0.228306i
$$519$$ −20.0000 −0.877903
$$520$$ 0 0
$$521$$ 18.0000 0.788594 0.394297 0.918983i $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ −2.50000 4.33013i −0.109422 0.189525i
$$523$$ −15.5000 26.8468i −0.677768 1.17393i −0.975652 0.219326i $$-0.929614\pi$$
0.297884 0.954602i $$-0.403719\pi$$
$$524$$ 0.500000 0.866025i 0.0218426 0.0378325i
$$525$$ 0 0
$$526$$ 10.5000 18.1865i 0.457822 0.792971i
$$527$$ 11.0000 19.0526i 0.479168 0.829943i
$$528$$ −5.00000 −0.217597
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ 0 0
$$531$$ 7.50000 + 12.9904i 0.325472 + 0.563735i
$$532$$ −4.00000 −0.173422
$$533$$ 7.00000 1.73205i 0.303204 0.0750234i
$$534$$ 2.00000 0.0865485
$$535$$ 0 0
$$536$$ 8.00000 + 13.8564i 0.345547 + 0.598506i
$$537$$ 6.50000 11.2583i 0.280496 0.485833i
$$538$$ 14.0000 0.603583
$$539$$ −7.50000 + 12.9904i −0.323048 + 0.559535i
$$540$$ 0 0
$$541$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$542$$ 6.50000 11.2583i 0.279199 0.483587i
$$543$$ 8.00000 + 13.8564i 0.343313 + 0.594635i
$$544$$ −1.00000 1.73205i −0.0428746 0.0742611i
$$545$$ 0 0
$$546$$ −7.00000 + 1.73205i −0.299572 + 0.0741249i
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ −5.50000 9.52628i −0.234948 0.406942i
$$549$$ −5.00000 8.66025i −0.213395 0.369611i
$$550$$ 0 0
$$551$$ −10.0000 −0.426014
$$552$$ −0.500000 + 0.866025i −0.0212814 + 0.0368605i
$$553$$ 11.0000 19.0526i 0.467768 0.810197i
$$554$$ 11.0000 0.467345
$$555$$ 0 0
$$556$$ −1.00000 1.73205i −0.0424094 0.0734553i
$$557$$ 13.0000 + 22.5167i 0.550828 + 0.954062i 0.998215 + 0.0597213i $$0.0190212\pi$$
−0.447387 + 0.894340i $$0.647645\pi$$
$$558$$ −11.0000 −0.465667
$$559$$ 27.5000 + 28.5788i 1.16313 + 1.20876i
$$560$$ 0 0
$$561$$ 5.00000 + 8.66025i 0.211100 + 0.365636i
$$562$$ 5.00000 + 8.66025i 0.210912 + 0.365311i
$$563$$ 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i $$-0.751959\pi$$
0.964315 + 0.264758i $$0.0852922\pi$$
$$564$$ −9.00000 −0.378968
$$565$$ 0 0
$$566$$ 9.50000 16.4545i 0.399315 0.691633i
$$567$$ 2.00000 0.0839921
$$568$$ 0 0
$$569$$ 11.0000 + 19.0526i 0.461144 + 0.798725i 0.999018 0.0443003i $$-0.0141058\pi$$
−0.537874 + 0.843025i $$0.680772\pi$$
$$570$$ 0 0
$$571$$ −16.0000 −0.669579 −0.334790 0.942293i $$-0.608665\pi$$
−0.334790 + 0.942293i $$0.608665\pi$$
$$572$$ −5.00000 + 17.3205i −0.209061 + 0.724207i
$$573$$ 4.00000 0.167102
$$574$$ 2.00000 + 3.46410i 0.0834784 + 0.144589i
$$575$$ 0 0
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 22.0000 0.915872 0.457936 0.888985i $$-0.348589\pi$$
0.457936 + 0.888985i $$0.348589\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ −12.0000 + 20.7846i −0.498703 + 0.863779i
$$580$$ 0 0
$$581$$ 6.00000 10.3923i 0.248922 0.431145i
$$582$$ −1.00000 1.73205i −0.0414513 0.0717958i
$$583$$ −15.0000 25.9808i −0.621237 1.07601i
$$584$$ 6.00000 0.248282
$$585$$ 0 0
$$586$$ −6.00000 −0.247858
$$587$$ −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i $$-0.287813\pi$$
−0.989792 + 0.142520i $$0.954479\pi$$
$$588$$ 1.50000 + 2.59808i 0.0618590 + 0.107143i
$$589$$ −11.0000 + 19.0526i −0.453247 + 0.785047i
$$590$$ 0 0
$$591$$ −4.00000 + 6.92820i −0.164538 + 0.284988i
$$592$$ 1.50000 2.59808i 0.0616496 0.106780i
$$593$$ −31.0000 −1.27302 −0.636509 0.771270i $$-0.719622\pi$$
−0.636509 + 0.771270i $$0.719622\pi$$
$$594$$ 2.50000 4.33013i 0.102576 0.177667i
$$595$$ 0 0
$$596$$ −8.50000 14.7224i −0.348174 0.603054i
$$597$$ 24.0000 0.982255
$$598$$ 2.50000 + 2.59808i 0.102233 + 0.106243i
$$599$$ 42.0000 1.71607 0.858037 0.513588i $$-0.171684\pi$$
0.858037 + 0.513588i $$0.171684\pi$$
$$600$$ 0 0
$$601$$ 1.50000 + 2.59808i 0.0611863 + 0.105978i 0.894996 0.446074i $$-0.147178\pi$$
−0.833810 + 0.552052i $$0.813845\pi$$
$$602$$ −11.0000 + 19.0526i −0.448327 + 0.776524i
$$603$$ −16.0000 −0.651570
$$604$$ −4.00000 + 6.92820i −0.162758 + 0.281905i
$$605$$ 0 0
$$606$$ 2.00000 0.0812444
$$607$$ 9.00000 15.5885i 0.365299 0.632716i −0.623525 0.781803i $$-0.714300\pi$$
0.988824 + 0.149087i $$0.0476335\pi$$
$$608$$ 1.00000 + 1.73205i 0.0405554 + 0.0702439i
$$609$$ −5.00000 8.66025i −0.202610 0.350931i
$$610$$ 0 0
$$611$$ −9.00000 + 31.1769i −0.364101 + 1.26128i
$$612$$ 2.00000 0.0808452
$$613$$ −14.5000 25.1147i −0.585649 1.01437i −0.994794 0.101905i $$-0.967506\pi$$
0.409145 0.912470i $$-0.365827\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ −10.0000 −0.402911
$$617$$ 20.5000 35.5070i 0.825299 1.42946i −0.0763917 0.997078i $$-0.524340\pi$$
0.901691 0.432382i $$-0.142327\pi$$
$$618$$ 5.00000 8.66025i 0.201129 0.348367i
$$619$$ −10.0000 −0.401934 −0.200967 0.979598i $$-0.564408\pi$$
−0.200967 + 0.979598i $$0.564408\pi$$
$$620$$ 0 0
$$621$$ −0.500000 0.866025i −0.0200643 0.0347524i
$$622$$ −10.0000 17.3205i −0.400963 0.694489i
$$623$$ 4.00000 0.160257
$$624$$ 2.50000 + 2.59808i 0.100080 + 0.104006i
$$625$$ 0 0
$$626$$ 10.0000 + 17.3205i 0.399680 + 0.692267i
$$627$$ −5.00000 8.66025i −0.199681 0.345857i
$$628$$ −3.50000 + 6.06218i −0.139665 + 0.241907i
$$629$$ −6.00000 −0.239236
$$630$$ 0 0
$$631$$ −20.0000 + 34.6410i −0.796187 + 1.37904i 0.125895 + 0.992044i $$0.459820\pi$$
−0.922082 + 0.386994i $$0.873514\pi$$
$$632$$ −11.0000 −0.437557
$$633$$ 2.00000 3.46410i 0.0794929 0.137686i
$$634$$ 8.00000 + 13.8564i 0.317721 + 0.550308i
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 10.5000 2.59808i 0.416025 0.102940i
$$638$$ −25.0000 −0.989759
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i $$-0.631488\pi$$
0.993899 0.110291i $$-0.0351782\pi$$
$$642$$ −10.0000 −0.394669
$$643$$ 4.00000 6.92820i 0.157745 0.273222i −0.776310 0.630351i $$-0.782911\pi$$
0.934055 + 0.357129i $$0.116244\pi$$
$$644$$ −1.00000 + 1.73205i −0.0394055 + 0.0682524i
$$645$$ 0 0
$$646$$ 2.00000 3.46410i 0.0786889 0.136293i
$$647$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ 75.0000 2.94401
$$650$$ 0 0
$$651$$ −22.0000 −0.862248
$$652$$ −7.50000 12.9904i −0.293723 0.508743i
$$653$$ 17.0000 + 29.4449i 0.665261 + 1.15227i 0.979214 + 0.202828i $$0.0650132\pi$$
−0.313953 + 0.949439i $$0.601653\pi$$
$$654$$ 1.00000 1.73205i 0.0391031 0.0677285i
$$655$$ 0 0
$$656$$ 1.00000 1.73205i 0.0390434 0.0676252i
$$657$$ −3.00000 + 5.19615i −0.117041 + 0.202721i
$$658$$ −18.0000 −0.701713
$$659$$ 19.5000 33.7750i 0.759612 1.31569i −0.183436 0.983032i $$-0.558722\pi$$
0.943049 0.332655i $$-0.107945\pi$$
$$660$$ 0 0
$$661$$ −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i $$-0.952854\pi$$
0.366723 0.930330i $$-0.380480\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 2.00000 6.92820i 0.0776736 0.269069i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 1.50000 + 2.59808i 0.0581238 + 0.100673i
$$667$$ −2.50000 + 4.33013i −0.0968004 + 0.167663i
$$668$$ −3.00000 −0.116073
$$669$$ 13.0000 22.5167i 0.502609 0.870544i
$$670$$ 0 0
$$671$$ −50.0000 −1.93023
$$672$$ −1.00000 + 1.73205i −0.0385758 + 0.0668153i
$$673$$ 4.00000 + 6.92820i 0.154189 + 0.267063i 0.932763 0.360489i $$-0.117390\pi$$
−0.778575 + 0.627552i $$0.784057\pi$$
$$674$$ −1.00000 1.73205i −0.0385186 0.0667161i
$$675$$ 0 0
$$676$$ 11.5000 6.06218i 0.442308 0.233161i
$$677$$ 4.00000 0.153732 0.0768662 0.997041i $$-0.475509\pi$$
0.0768662 + 0.997041i $$0.475509\pi$$
$$678$$ 5.50000 + 9.52628i 0.211226 + 0.365855i
$$679$$ −2.00000 3.46410i −0.0767530 0.132940i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −27.5000 + 47.6314i −1.05303 + 1.82390i
$$683$$ −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i $$-0.907070\pi$$
0.728101 + 0.685470i $$0.240403\pi$$
$$684$$ −2.00000 −0.0764719
$$685$$ 0 0
$$686$$ 10.0000 + 17.3205i 0.381802 + 0.661300i
$$687$$ −5.00000 8.66025i −0.190762 0.330409i
$$688$$ 11.0000 0.419371
$$689$$ −6.00000 + 20.7846i −0.228582 + 0.791831i
$$690$$ 0 0
$$691$$ 15.0000 + 25.9808i 0.570627 + 0.988355i 0.996502 + 0.0835727i $$0.0266331\pi$$
−0.425875 + 0.904782i $$0.640034\pi$$
$$692$$ 10.0000 + 17.3205i 0.380143 + 0.658427i
$$693$$ 5.00000 8.66025i 0.189934 0.328976i
$$694$$ −34.0000 −1.29062
$$695$$ 0 0
$$696$$ −2.50000 + 4.33013i −0.0947623 + 0.164133i
$$697$$ −4.00000 −0.151511
$$698$$ −10.0000 + 17.3205i −0.378506 + 0.655591i
$$699$$ 0.500000 + 0.866025i 0.0189117 + 0.0327561i
$$700$$ 0 0
$$701$$ 13.0000 0.491003 0.245502 0.969396i $$-0.421047\pi$$
0.245502 + 0.969396i $$0.421047\pi$$
$$702$$ −3.50000 + 0.866025i −0.132099 + 0.0326860i
$$703$$ 6.00000 0.226294
$$704$$ 2.50000 + 4.33013i 0.0942223 + 0.163198i
$$705$$ 0 0
$$706$$ −9.00000 + 15.5885i −0.338719 + 0.586679i
$$707$$ 4.00000 0.150435
$$708$$ 7.50000 12.9904i 0.281867 0.488208i
$$709$$ 4.00000 6.92820i 0.150223 0.260194i −0.781086 0.624423i $$-0.785334\pi$$
0.931309 + 0.364229i $$0.118667\pi$$
$$710$$ 0 0
$$711$$ 5.50000 9.52628i 0.206266 0.357263i
$$712$$ −1.00000 1.73205i −0.0374766 0.0649113i
$$713$$ 5.50000 + 9.52628i 0.205977 + 0.356762i
$$714$$ 4.00000 0.149696
$$715$$ 0 0
$$716$$ −13.0000 −0.485833
$$717$$ 10.0000 + 17.3205i 0.373457 + 0.646846i
$$718$$ −6.00000 10.3923i −0.223918 0.387837i
$$719$$ −12.0000 + 20.7846i −0.447524 + 0.775135i −0.998224 0.0595683i $$-0.981028\pi$$
0.550700 + 0.834703i $$0.314361\pi$$
$$720$$ 0 0
$$721$$ 10.0000 17.3205i 0.372419 0.645049i
$$722$$ 7.50000 12.9904i 0.279121 0.483452i
$$723$$ −7.00000 −0.260333
$$724$$ 8.00000 13.8564i 0.297318 0.514969i
$$725$$ 0 0
$$726$$ −7.00000 12.1244i −0.259794 0.449977i
$$727$$ 40.0000 1.48352 0.741759 0.670667i $$-0.233992\pi$$
0.741759 + 0.670667i $$0.233992\pi$$
$$728$$ 5.00000 + 5.19615i 0.185312 + 0.192582i
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −11.0000 19.0526i −0.406850 0.704684i
$$732$$ −5.00000 + 8.66025i −0.184805 + 0.320092i
$$733$$ −6.00000 −0.221615 −0.110808 0.993842i $$-0.535344\pi$$
−0.110808 + 0.993842i $$0.535344\pi$$
$$734$$ −8.00000 + 13.8564i −0.295285 + 0.511449i
$$735$$ 0 0
$$736$$ 1.00000 0.0368605
$$737$$ −40.0000 + 69.2820i −1.47342 + 2.55204i
$$738$$ 1.00000 + 1.73205i 0.0368105 + 0.0637577i
$$739$$ −22.0000 38.1051i −0.809283 1.40172i −0.913361 0.407150i $$-0.866523\pi$$
0.104078 0.994569i $$-0.466811\pi$$
$$740$$ 0 0
$$741$$ −2.00000 + 6.92820i −0.0734718 + 0.254514i
$$742$$ −12.0000 −0.440534
$$743$$ 25.5000 + 44.1673i 0.935504 + 1.62034i 0.773732 + 0.633513i $$0.218388\pi$$
0.161772 + 0.986828i $$0.448279\pi$$
$$744$$ 5.50000 + 9.52628i 0.201640 + 0.349250i
$$745$$ 0 0
$$746$$ 19.0000 0.695639
$$747$$ 3.00000 5.19615i 0.109764 0.190117i
$$748$$ 5.00000 8.66025i 0.182818 0.316650i
$$749$$ −20.0000 −0.730784
$$750$$ 0 0
$$751$$ 11.5000 + 19.9186i 0.419641 + 0.726839i 0.995903 0.0904254i $$-0.0288227\pi$$
−0.576262 + 0.817265i $$0.695489\pi$$
$$752$$ 4.50000 + 7.79423i 0.164098 + 0.284226i
$$753$$ 25.0000 0.911051
$$754$$ 12.5000 + 12.9904i 0.455223 + 0.473082i
$$755$$ 0 0
$$756$$ −1.00000 1.73205i −0.0363696 0.0629941i
$$757$$ 5.00000 + 8.66025i 0.181728 + 0.314762i 0.942469 0.334293i $$-0.108498\pi$$
−0.760741 + 0.649056i $$0.775164\pi$$
$$758$$ 1.00000 1.73205i 0.0363216 0.0629109i
$$759$$ −5.00000 −0.181489
$$760$$ 0 0
$$761$$ −10.0000 + 17.3205i −0.362500 + 0.627868i −0.988372 0.152058i $$-0.951410\pi$$
0.625872 + 0.779926i $$0.284743\pi$$
$$762$$ −2.00000 −0.0724524
$$763$$ 2.00000 3.46410i 0.0724049 0.125409i
$$764$$ −2.00000 3.46410i −0.0723575 0.125327i
$$765$$ 0 0
$$766$$ −31.0000 −1.12008
$$767$$ −37.5000 38.9711i −1.35405 1.40717i
$$768$$ 1.00000 0.0360844
$$769$$ −21.5000 37.2391i −0.775310 1.34288i −0.934620 0.355647i $$-0.884260\pi$$
0.159310 0.987229i $$-0.449073\pi$$
$$770$$ 0 0
$$771$$ −8.50000 + 14.7224i −0.306120 + 0.530215i
$$772$$ 24.0000 0.863779
$$773$$ 16.0000 27.7128i 0.575480 0.996761i −0.420509 0.907288i $$-0.638149\pi$$
0.995989 0.0894724i $$-0.0285181\pi$$
$$774$$ −5.50000 + 9.52628i −0.197693 + 0.342415i
$$775$$ 0 0
$$776$$ −1.00000 + 1.73205i −0.0358979 + 0.0621770i
$$777$$ 3.00000 + 5.19615i 0.107624 + 0.186411i
$$778$$ −2.50000 4.33013i −0.0896293 0.155243i
$$779$$ 4.00000 0.143315
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −1.00000 1.73205i −0.0357599 0.0619380i
$$783$$ −2.50000 4.33013i −0.0893427 0.154746i
$$784$$ 1.50000 2.59808i 0.0535714 0.0927884i
$$785$$ 0 0
$$786$$ 0.500000