# Properties

 Label 930.2.d.a.559.2 Level $930$ Weight $2$ Character 930.559 Analytic conductor $7.426$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.42608738798$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 559.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 930.559 Dual form 930.2.d.a.559.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -3.00000 q^{11} -1.00000i q^{12} +4.00000i q^{13} -1.00000 q^{14} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{18} +1.00000 q^{19} +(1.00000 - 2.00000i) q^{20} -1.00000 q^{21} -3.00000i q^{22} -5.00000i q^{23} +1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} -4.00000 q^{26} -1.00000i q^{27} -1.00000i q^{28} -2.00000 q^{29} +(1.00000 - 2.00000i) q^{30} -1.00000 q^{31} +1.00000i q^{32} -3.00000i q^{33} +(-2.00000 - 1.00000i) q^{35} +1.00000 q^{36} +4.00000i q^{37} +1.00000i q^{38} -4.00000 q^{39} +(2.00000 + 1.00000i) q^{40} -10.0000 q^{41} -1.00000i q^{42} +5.00000i q^{43} +3.00000 q^{44} +(1.00000 - 2.00000i) q^{45} +5.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} +6.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -4.00000i q^{52} -5.00000i q^{53} +1.00000 q^{54} +(3.00000 - 6.00000i) q^{55} +1.00000 q^{56} +1.00000i q^{57} -2.00000i q^{58} +6.00000 q^{59} +(2.00000 + 1.00000i) q^{60} -2.00000 q^{61} -1.00000i q^{62} -1.00000i q^{63} -1.00000 q^{64} +(-8.00000 - 4.00000i) q^{65} +3.00000 q^{66} +2.00000i q^{67} +5.00000 q^{69} +(1.00000 - 2.00000i) q^{70} -5.00000 q^{71} +1.00000i q^{72} +7.00000i q^{73} -4.00000 q^{74} +(4.00000 - 3.00000i) q^{75} -1.00000 q^{76} -3.00000i q^{77} -4.00000i q^{78} -3.00000 q^{79} +(-1.00000 + 2.00000i) q^{80} +1.00000 q^{81} -10.0000i q^{82} +2.00000i q^{83} +1.00000 q^{84} -5.00000 q^{86} -2.00000i q^{87} +3.00000i q^{88} -1.00000 q^{89} +(2.00000 + 1.00000i) q^{90} -4.00000 q^{91} +5.00000i q^{92} -1.00000i q^{93} +8.00000 q^{94} +(-1.00000 + 2.00000i) q^{95} -1.00000 q^{96} -10.0000i q^{97} +6.00000i q^{98} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^9 $$2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9} - 4 q^{10} - 6 q^{11} - 2 q^{14} - 4 q^{15} + 2 q^{16} + 2 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{24} - 6 q^{25} - 8 q^{26} - 4 q^{29} + 2 q^{30} - 2 q^{31} - 4 q^{35} + 2 q^{36} - 8 q^{39} + 4 q^{40} - 20 q^{41} + 6 q^{44} + 2 q^{45} + 10 q^{46} + 12 q^{49} + 8 q^{50} + 2 q^{54} + 6 q^{55} + 2 q^{56} + 12 q^{59} + 4 q^{60} - 4 q^{61} - 2 q^{64} - 16 q^{65} + 6 q^{66} + 10 q^{69} + 2 q^{70} - 10 q^{71} - 8 q^{74} + 8 q^{75} - 2 q^{76} - 6 q^{79} - 2 q^{80} + 2 q^{81} + 2 q^{84} - 10 q^{86} - 2 q^{89} + 4 q^{90} - 8 q^{91} + 16 q^{94} - 2 q^{95} - 2 q^{96} + 6 q^{99}+O(q^{100})$$ 2 * q - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^9 - 4 * q^10 - 6 * q^11 - 2 * q^14 - 4 * q^15 + 2 * q^16 + 2 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^24 - 6 * q^25 - 8 * q^26 - 4 * q^29 + 2 * q^30 - 2 * q^31 - 4 * q^35 + 2 * q^36 - 8 * q^39 + 4 * q^40 - 20 * q^41 + 6 * q^44 + 2 * q^45 + 10 * q^46 + 12 * q^49 + 8 * q^50 + 2 * q^54 + 6 * q^55 + 2 * q^56 + 12 * q^59 + 4 * q^60 - 4 * q^61 - 2 * q^64 - 16 * q^65 + 6 * q^66 + 10 * q^69 + 2 * q^70 - 10 * q^71 - 8 * q^74 + 8 * q^75 - 2 * q^76 - 6 * q^79 - 2 * q^80 + 2 * q^81 + 2 * q^84 - 10 * q^86 - 2 * q^89 + 4 * q^90 - 8 * q^91 + 16 * q^94 - 2 * q^95 - 2 * q^96 + 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$$.

 $$n$$ $$187$$ $$311$$ $$871$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 1.00000i 0.577350i
$$4$$ −1.00000 −0.500000
$$5$$ −1.00000 + 2.00000i −0.447214 + 0.894427i
$$6$$ −1.00000 −0.408248
$$7$$ 1.00000i 0.377964i 0.981981 + 0.188982i $$0.0605189\pi$$
−0.981981 + 0.188982i $$0.939481\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −1.00000 −0.333333
$$10$$ −2.00000 1.00000i −0.632456 0.316228i
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 4.00000i 1.10940i 0.832050 + 0.554700i $$0.187167\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ −2.00000 1.00000i −0.516398 0.258199i
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 1.00000 0.229416 0.114708 0.993399i $$-0.463407\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 1.00000 2.00000i 0.223607 0.447214i
$$21$$ −1.00000 −0.218218
$$22$$ 3.00000i 0.639602i
$$23$$ 5.00000i 1.04257i −0.853382 0.521286i $$-0.825452\pi$$
0.853382 0.521286i $$-0.174548\pi$$
$$24$$ 1.00000 0.204124
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ −4.00000 −0.784465
$$27$$ 1.00000i 0.192450i
$$28$$ 1.00000i 0.188982i
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 1.00000 2.00000i 0.182574 0.365148i
$$31$$ −1.00000 −0.179605
$$32$$ 1.00000i 0.176777i
$$33$$ 3.00000i 0.522233i
$$34$$ 0 0
$$35$$ −2.00000 1.00000i −0.338062 0.169031i
$$36$$ 1.00000 0.166667
$$37$$ 4.00000i 0.657596i 0.944400 + 0.328798i $$0.106644\pi$$
−0.944400 + 0.328798i $$0.893356\pi$$
$$38$$ 1.00000i 0.162221i
$$39$$ −4.00000 −0.640513
$$40$$ 2.00000 + 1.00000i 0.316228 + 0.158114i
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 1.00000i 0.154303i
$$43$$ 5.00000i 0.762493i 0.924473 + 0.381246i $$0.124505\pi$$
−0.924473 + 0.381246i $$0.875495\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 1.00000 2.00000i 0.149071 0.298142i
$$46$$ 5.00000 0.737210
$$47$$ 8.00000i 1.16692i −0.812142 0.583460i $$-0.801699\pi$$
0.812142 0.583460i $$-0.198301\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 6.00000 0.857143
$$50$$ 4.00000 3.00000i 0.565685 0.424264i
$$51$$ 0 0
$$52$$ 4.00000i 0.554700i
$$53$$ 5.00000i 0.686803i −0.939189 0.343401i $$-0.888421\pi$$
0.939189 0.343401i $$-0.111579\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 3.00000 6.00000i 0.404520 0.809040i
$$56$$ 1.00000 0.133631
$$57$$ 1.00000i 0.132453i
$$58$$ 2.00000i 0.262613i
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ 2.00000 + 1.00000i 0.258199 + 0.129099i
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 1.00000i 0.127000i
$$63$$ 1.00000i 0.125988i
$$64$$ −1.00000 −0.125000
$$65$$ −8.00000 4.00000i −0.992278 0.496139i
$$66$$ 3.00000 0.369274
$$67$$ 2.00000i 0.244339i 0.992509 + 0.122169i $$0.0389851\pi$$
−0.992509 + 0.122169i $$0.961015\pi$$
$$68$$ 0 0
$$69$$ 5.00000 0.601929
$$70$$ 1.00000 2.00000i 0.119523 0.239046i
$$71$$ −5.00000 −0.593391 −0.296695 0.954972i $$-0.595885\pi$$
−0.296695 + 0.954972i $$0.595885\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 7.00000i 0.819288i 0.912245 + 0.409644i $$0.134347\pi$$
−0.912245 + 0.409644i $$0.865653\pi$$
$$74$$ −4.00000 −0.464991
$$75$$ 4.00000 3.00000i 0.461880 0.346410i
$$76$$ −1.00000 −0.114708
$$77$$ 3.00000i 0.341882i
$$78$$ 4.00000i 0.452911i
$$79$$ −3.00000 −0.337526 −0.168763 0.985657i $$-0.553977\pi$$
−0.168763 + 0.985657i $$0.553977\pi$$
$$80$$ −1.00000 + 2.00000i −0.111803 + 0.223607i
$$81$$ 1.00000 0.111111
$$82$$ 10.0000i 1.10432i
$$83$$ 2.00000i 0.219529i 0.993958 + 0.109764i $$0.0350096\pi$$
−0.993958 + 0.109764i $$0.964990\pi$$
$$84$$ 1.00000 0.109109
$$85$$ 0 0
$$86$$ −5.00000 −0.539164
$$87$$ 2.00000i 0.214423i
$$88$$ 3.00000i 0.319801i
$$89$$ −1.00000 −0.106000 −0.0529999 0.998595i $$-0.516878\pi$$
−0.0529999 + 0.998595i $$0.516878\pi$$
$$90$$ 2.00000 + 1.00000i 0.210819 + 0.105409i
$$91$$ −4.00000 −0.419314
$$92$$ 5.00000i 0.521286i
$$93$$ 1.00000i 0.103695i
$$94$$ 8.00000 0.825137
$$95$$ −1.00000 + 2.00000i −0.102598 + 0.205196i
$$96$$ −1.00000 −0.102062
$$97$$ 10.0000i 1.01535i −0.861550 0.507673i $$-0.830506\pi$$
0.861550 0.507673i $$-0.169494\pi$$
$$98$$ 6.00000i 0.606092i
$$99$$ 3.00000 0.301511
$$100$$ 3.00000 + 4.00000i 0.300000 + 0.400000i
$$101$$ −15.0000 −1.49256 −0.746278 0.665635i $$-0.768161\pi$$
−0.746278 + 0.665635i $$0.768161\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 1.00000 2.00000i 0.0975900 0.195180i
$$106$$ 5.00000 0.485643
$$107$$ 19.0000i 1.83680i 0.395654 + 0.918400i $$0.370518\pi$$
−0.395654 + 0.918400i $$0.629482\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 6.00000 + 3.00000i 0.572078 + 0.286039i
$$111$$ −4.00000 −0.379663
$$112$$ 1.00000i 0.0944911i
$$113$$ 15.0000i 1.41108i 0.708669 + 0.705541i $$0.249296\pi$$
−0.708669 + 0.705541i $$0.750704\pi$$
$$114$$ −1.00000 −0.0936586
$$115$$ 10.0000 + 5.00000i 0.932505 + 0.466252i
$$116$$ 2.00000 0.185695
$$117$$ 4.00000i 0.369800i
$$118$$ 6.00000i 0.552345i
$$119$$ 0 0
$$120$$ −1.00000 + 2.00000i −0.0912871 + 0.182574i
$$121$$ −2.00000 −0.181818
$$122$$ 2.00000i 0.181071i
$$123$$ 10.0000i 0.901670i
$$124$$ 1.00000 0.0898027
$$125$$ 11.0000 2.00000i 0.983870 0.178885i
$$126$$ 1.00000 0.0890871
$$127$$ 8.00000i 0.709885i 0.934888 + 0.354943i $$0.115500\pi$$
−0.934888 + 0.354943i $$0.884500\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −5.00000 −0.440225
$$130$$ 4.00000 8.00000i 0.350823 0.701646i
$$131$$ −2.00000 −0.174741 −0.0873704 0.996176i $$-0.527846\pi$$
−0.0873704 + 0.996176i $$0.527846\pi$$
$$132$$ 3.00000i 0.261116i
$$133$$ 1.00000i 0.0867110i
$$134$$ −2.00000 −0.172774
$$135$$ 2.00000 + 1.00000i 0.172133 + 0.0860663i
$$136$$ 0 0
$$137$$ 2.00000i 0.170872i 0.996344 + 0.0854358i $$0.0272282\pi$$
−0.996344 + 0.0854358i $$0.972772\pi$$
$$138$$ 5.00000i 0.425628i
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 2.00000 + 1.00000i 0.169031 + 0.0845154i
$$141$$ 8.00000 0.673722
$$142$$ 5.00000i 0.419591i
$$143$$ 12.0000i 1.00349i
$$144$$ −1.00000 −0.0833333
$$145$$ 2.00000 4.00000i 0.166091 0.332182i
$$146$$ −7.00000 −0.579324
$$147$$ 6.00000i 0.494872i
$$148$$ 4.00000i 0.328798i
$$149$$ −15.0000 −1.22885 −0.614424 0.788976i $$-0.710612\pi$$
−0.614424 + 0.788976i $$0.710612\pi$$
$$150$$ 3.00000 + 4.00000i 0.244949 + 0.326599i
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 1.00000i 0.0811107i
$$153$$ 0 0
$$154$$ 3.00000 0.241747
$$155$$ 1.00000 2.00000i 0.0803219 0.160644i
$$156$$ 4.00000 0.320256
$$157$$ 9.00000i 0.718278i 0.933284 + 0.359139i $$0.116930\pi$$
−0.933284 + 0.359139i $$0.883070\pi$$
$$158$$ 3.00000i 0.238667i
$$159$$ 5.00000 0.396526
$$160$$ −2.00000 1.00000i −0.158114 0.0790569i
$$161$$ 5.00000 0.394055
$$162$$ 1.00000i 0.0785674i
$$163$$ 4.00000i 0.313304i 0.987654 + 0.156652i $$0.0500701\pi$$
−0.987654 + 0.156652i $$0.949930\pi$$
$$164$$ 10.0000 0.780869
$$165$$ 6.00000 + 3.00000i 0.467099 + 0.233550i
$$166$$ −2.00000 −0.155230
$$167$$ 21.0000i 1.62503i 0.582941 + 0.812514i $$0.301902\pi$$
−0.582941 + 0.812514i $$0.698098\pi$$
$$168$$ 1.00000i 0.0771517i
$$169$$ −3.00000 −0.230769
$$170$$ 0 0
$$171$$ −1.00000 −0.0764719
$$172$$ 5.00000i 0.381246i
$$173$$ 2.00000i 0.152057i 0.997106 + 0.0760286i $$0.0242240\pi$$
−0.997106 + 0.0760286i $$0.975776\pi$$
$$174$$ 2.00000 0.151620
$$175$$ 4.00000 3.00000i 0.302372 0.226779i
$$176$$ −3.00000 −0.226134
$$177$$ 6.00000i 0.450988i
$$178$$ 1.00000i 0.0749532i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ −1.00000 + 2.00000i −0.0745356 + 0.149071i
$$181$$ −5.00000 −0.371647 −0.185824 0.982583i $$-0.559495\pi$$
−0.185824 + 0.982583i $$0.559495\pi$$
$$182$$ 4.00000i 0.296500i
$$183$$ 2.00000i 0.147844i
$$184$$ −5.00000 −0.368605
$$185$$ −8.00000 4.00000i −0.588172 0.294086i
$$186$$ 1.00000 0.0733236
$$187$$ 0 0
$$188$$ 8.00000i 0.583460i
$$189$$ 1.00000 0.0727393
$$190$$ −2.00000 1.00000i −0.145095 0.0725476i
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ 10.0000i 0.719816i 0.932988 + 0.359908i $$0.117192\pi$$
−0.932988 + 0.359908i $$0.882808\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 4.00000 8.00000i 0.286446 0.572892i
$$196$$ −6.00000 −0.428571
$$197$$ 18.0000i 1.28245i 0.767354 + 0.641223i $$0.221573\pi$$
−0.767354 + 0.641223i $$0.778427\pi$$
$$198$$ 3.00000i 0.213201i
$$199$$ 21.0000 1.48865 0.744325 0.667817i $$-0.232771\pi$$
0.744325 + 0.667817i $$0.232771\pi$$
$$200$$ −4.00000 + 3.00000i −0.282843 + 0.212132i
$$201$$ −2.00000 −0.141069
$$202$$ 15.0000i 1.05540i
$$203$$ 2.00000i 0.140372i
$$204$$ 0 0
$$205$$ 10.0000 20.0000i 0.698430 1.39686i
$$206$$ 0 0
$$207$$ 5.00000i 0.347524i
$$208$$ 4.00000i 0.277350i
$$209$$ −3.00000 −0.207514
$$210$$ 2.00000 + 1.00000i 0.138013 + 0.0690066i
$$211$$ 7.00000 0.481900 0.240950 0.970538i $$-0.422541\pi$$
0.240950 + 0.970538i $$0.422541\pi$$
$$212$$ 5.00000i 0.343401i
$$213$$ 5.00000i 0.342594i
$$214$$ −19.0000 −1.29881
$$215$$ −10.0000 5.00000i −0.681994 0.340997i
$$216$$ −1.00000 −0.0680414
$$217$$ 1.00000i 0.0678844i
$$218$$ 2.00000i 0.135457i
$$219$$ −7.00000 −0.473016
$$220$$ −3.00000 + 6.00000i −0.202260 + 0.404520i
$$221$$ 0 0
$$222$$ 4.00000i 0.268462i
$$223$$ 20.0000i 1.33930i 0.742677 + 0.669650i $$0.233556\pi$$
−0.742677 + 0.669650i $$0.766444\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 3.00000 + 4.00000i 0.200000 + 0.266667i
$$226$$ −15.0000 −0.997785
$$227$$ 9.00000i 0.597351i −0.954355 0.298675i $$-0.903455\pi$$
0.954355 0.298675i $$-0.0965448\pi$$
$$228$$ 1.00000i 0.0662266i
$$229$$ −15.0000 −0.991228 −0.495614 0.868543i $$-0.665057\pi$$
−0.495614 + 0.868543i $$0.665057\pi$$
$$230$$ −5.00000 + 10.0000i −0.329690 + 0.659380i
$$231$$ 3.00000 0.197386
$$232$$ 2.00000i 0.131306i
$$233$$ 21.0000i 1.37576i 0.725826 + 0.687878i $$0.241458\pi$$
−0.725826 + 0.687878i $$0.758542\pi$$
$$234$$ 4.00000 0.261488
$$235$$ 16.0000 + 8.00000i 1.04372 + 0.521862i
$$236$$ −6.00000 −0.390567
$$237$$ 3.00000i 0.194871i
$$238$$ 0 0
$$239$$ 14.0000 0.905585 0.452792 0.891616i $$-0.350428\pi$$
0.452792 + 0.891616i $$0.350428\pi$$
$$240$$ −2.00000 1.00000i −0.129099 0.0645497i
$$241$$ −12.0000 −0.772988 −0.386494 0.922292i $$-0.626314\pi$$
−0.386494 + 0.922292i $$0.626314\pi$$
$$242$$ 2.00000i 0.128565i
$$243$$ 1.00000i 0.0641500i
$$244$$ 2.00000 0.128037
$$245$$ −6.00000 + 12.0000i −0.383326 + 0.766652i
$$246$$ 10.0000 0.637577
$$247$$ 4.00000i 0.254514i
$$248$$ 1.00000i 0.0635001i
$$249$$ −2.00000 −0.126745
$$250$$ 2.00000 + 11.0000i 0.126491 + 0.695701i
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 1.00000i 0.0629941i
$$253$$ 15.0000i 0.943042i
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 5.00000i 0.311891i 0.987766 + 0.155946i $$0.0498425\pi$$
−0.987766 + 0.155946i $$0.950158\pi$$
$$258$$ 5.00000i 0.311286i
$$259$$ −4.00000 −0.248548
$$260$$ 8.00000 + 4.00000i 0.496139 + 0.248069i
$$261$$ 2.00000 0.123797
$$262$$ 2.00000i 0.123560i
$$263$$ 24.0000i 1.47990i −0.672660 0.739952i $$-0.734848\pi$$
0.672660 0.739952i $$-0.265152\pi$$
$$264$$ −3.00000 −0.184637
$$265$$ 10.0000 + 5.00000i 0.614295 + 0.307148i
$$266$$ −1.00000 −0.0613139
$$267$$ 1.00000i 0.0611990i
$$268$$ 2.00000i 0.122169i
$$269$$ −2.00000 −0.121942 −0.0609711 0.998140i $$-0.519420\pi$$
−0.0609711 + 0.998140i $$0.519420\pi$$
$$270$$ −1.00000 + 2.00000i −0.0608581 + 0.121716i
$$271$$ 9.00000 0.546711 0.273356 0.961913i $$-0.411866\pi$$
0.273356 + 0.961913i $$0.411866\pi$$
$$272$$ 0 0
$$273$$ 4.00000i 0.242091i
$$274$$ −2.00000 −0.120824
$$275$$ 9.00000 + 12.0000i 0.542720 + 0.723627i
$$276$$ −5.00000 −0.300965
$$277$$ 2.00000i 0.120168i 0.998193 + 0.0600842i $$0.0191369\pi$$
−0.998193 + 0.0600842i $$0.980863\pi$$
$$278$$ 20.0000i 1.19952i
$$279$$ 1.00000 0.0598684
$$280$$ −1.00000 + 2.00000i −0.0597614 + 0.119523i
$$281$$ −32.0000 −1.90896 −0.954480 0.298275i $$-0.903589\pi$$
−0.954480 + 0.298275i $$0.903589\pi$$
$$282$$ 8.00000i 0.476393i
$$283$$ 14.0000i 0.832214i −0.909316 0.416107i $$-0.863394\pi$$
0.909316 0.416107i $$-0.136606\pi$$
$$284$$ 5.00000 0.296695
$$285$$ −2.00000 1.00000i −0.118470 0.0592349i
$$286$$ 12.0000 0.709575
$$287$$ 10.0000i 0.590281i
$$288$$ 1.00000i 0.0589256i
$$289$$ 17.0000 1.00000
$$290$$ 4.00000 + 2.00000i 0.234888 + 0.117444i
$$291$$ 10.0000 0.586210
$$292$$ 7.00000i 0.409644i
$$293$$ 18.0000i 1.05157i 0.850617 + 0.525786i $$0.176229\pi$$
−0.850617 + 0.525786i $$0.823771\pi$$
$$294$$ −6.00000 −0.349927
$$295$$ −6.00000 + 12.0000i −0.349334 + 0.698667i
$$296$$ 4.00000 0.232495
$$297$$ 3.00000i 0.174078i
$$298$$ 15.0000i 0.868927i
$$299$$ 20.0000 1.15663
$$300$$ −4.00000 + 3.00000i −0.230940 + 0.173205i
$$301$$ −5.00000 −0.288195
$$302$$ 16.0000i 0.920697i
$$303$$ 15.0000i 0.861727i
$$304$$ 1.00000 0.0573539
$$305$$ 2.00000 4.00000i 0.114520 0.229039i
$$306$$ 0 0
$$307$$ 4.00000i 0.228292i −0.993464 0.114146i $$-0.963587\pi$$
0.993464 0.114146i $$-0.0364132\pi$$
$$308$$ 3.00000i 0.170941i
$$309$$ 0 0
$$310$$ 2.00000 + 1.00000i 0.113592 + 0.0567962i
$$311$$ 16.0000 0.907277 0.453638 0.891186i $$-0.350126\pi$$
0.453638 + 0.891186i $$0.350126\pi$$
$$312$$ 4.00000i 0.226455i
$$313$$ 6.00000i 0.339140i 0.985518 + 0.169570i $$0.0542379\pi$$
−0.985518 + 0.169570i $$0.945762\pi$$
$$314$$ −9.00000 −0.507899
$$315$$ 2.00000 + 1.00000i 0.112687 + 0.0563436i
$$316$$ 3.00000 0.168763
$$317$$ 18.0000i 1.01098i 0.862832 + 0.505490i $$0.168688\pi$$
−0.862832 + 0.505490i $$0.831312\pi$$
$$318$$ 5.00000i 0.280386i
$$319$$ 6.00000 0.335936
$$320$$ 1.00000 2.00000i 0.0559017 0.111803i
$$321$$ −19.0000 −1.06048
$$322$$ 5.00000i 0.278639i
$$323$$ 0 0
$$324$$ −1.00000 −0.0555556
$$325$$ 16.0000 12.0000i 0.887520 0.665640i
$$326$$ −4.00000 −0.221540
$$327$$ 2.00000i 0.110600i
$$328$$ 10.0000i 0.552158i
$$329$$ 8.00000 0.441054
$$330$$ −3.00000 + 6.00000i −0.165145 + 0.330289i
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ 2.00000i 0.109764i
$$333$$ 4.00000i 0.219199i
$$334$$ −21.0000 −1.14907
$$335$$ −4.00000 2.00000i −0.218543 0.109272i
$$336$$ −1.00000 −0.0545545
$$337$$ 34.0000i 1.85210i −0.377403 0.926049i $$-0.623183\pi$$
0.377403 0.926049i $$-0.376817\pi$$
$$338$$ 3.00000i 0.163178i
$$339$$ −15.0000 −0.814688
$$340$$ 0 0
$$341$$ 3.00000 0.162459
$$342$$ 1.00000i 0.0540738i
$$343$$ 13.0000i 0.701934i
$$344$$ 5.00000 0.269582
$$345$$ −5.00000 + 10.0000i −0.269191 + 0.538382i
$$346$$ −2.00000 −0.107521
$$347$$ 22.0000i 1.18102i −0.807030 0.590511i $$-0.798926\pi$$
0.807030 0.590511i $$-0.201074\pi$$
$$348$$ 2.00000i 0.107211i
$$349$$ −20.0000 −1.07058 −0.535288 0.844670i $$-0.679797\pi$$
−0.535288 + 0.844670i $$0.679797\pi$$
$$350$$ 3.00000 + 4.00000i 0.160357 + 0.213809i
$$351$$ 4.00000 0.213504
$$352$$ 3.00000i 0.159901i
$$353$$ 24.0000i 1.27739i −0.769460 0.638696i $$-0.779474\pi$$
0.769460 0.638696i $$-0.220526\pi$$
$$354$$ −6.00000 −0.318896
$$355$$ 5.00000 10.0000i 0.265372 0.530745i
$$356$$ 1.00000 0.0529999
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −3.00000 −0.158334 −0.0791670 0.996861i $$-0.525226\pi$$
−0.0791670 + 0.996861i $$0.525226\pi$$
$$360$$ −2.00000 1.00000i −0.105409 0.0527046i
$$361$$ −18.0000 −0.947368
$$362$$ 5.00000i 0.262794i
$$363$$ 2.00000i 0.104973i
$$364$$ 4.00000 0.209657
$$365$$ −14.0000 7.00000i −0.732793 0.366397i
$$366$$ 2.00000 0.104542
$$367$$ 14.0000i 0.730794i 0.930852 + 0.365397i $$0.119067\pi$$
−0.930852 + 0.365397i $$0.880933\pi$$
$$368$$ 5.00000i 0.260643i
$$369$$ 10.0000 0.520579
$$370$$ 4.00000 8.00000i 0.207950 0.415900i
$$371$$ 5.00000 0.259587
$$372$$ 1.00000i 0.0518476i
$$373$$ 11.0000i 0.569558i 0.958593 + 0.284779i $$0.0919203\pi$$
−0.958593 + 0.284779i $$0.908080\pi$$
$$374$$ 0 0
$$375$$ 2.00000 + 11.0000i 0.103280 + 0.568038i
$$376$$ −8.00000 −0.412568
$$377$$ 8.00000i 0.412021i
$$378$$ 1.00000i 0.0514344i
$$379$$ 15.0000 0.770498 0.385249 0.922813i $$-0.374116\pi$$
0.385249 + 0.922813i $$0.374116\pi$$
$$380$$ 1.00000 2.00000i 0.0512989 0.102598i
$$381$$ −8.00000 −0.409852
$$382$$ 16.0000i 0.818631i
$$383$$ 28.0000i 1.43073i −0.698749 0.715367i $$-0.746260\pi$$
0.698749 0.715367i $$-0.253740\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 6.00000 + 3.00000i 0.305788 + 0.152894i
$$386$$ −10.0000 −0.508987
$$387$$ 5.00000i 0.254164i
$$388$$ 10.0000i 0.507673i
$$389$$ 28.0000 1.41966 0.709828 0.704375i $$-0.248773\pi$$
0.709828 + 0.704375i $$0.248773\pi$$
$$390$$ 8.00000 + 4.00000i 0.405096 + 0.202548i
$$391$$ 0 0
$$392$$ 6.00000i 0.303046i
$$393$$ 2.00000i 0.100887i
$$394$$ −18.0000 −0.906827
$$395$$ 3.00000 6.00000i 0.150946 0.301893i
$$396$$ −3.00000 −0.150756
$$397$$ 31.0000i 1.55585i −0.628360 0.777923i $$-0.716273\pi$$
0.628360 0.777923i $$-0.283727\pi$$
$$398$$ 21.0000i 1.05263i
$$399$$ −1.00000 −0.0500626
$$400$$ −3.00000 4.00000i −0.150000 0.200000i
$$401$$ 5.00000 0.249688 0.124844 0.992176i $$-0.460157\pi$$
0.124844 + 0.992176i $$0.460157\pi$$
$$402$$ 2.00000i 0.0997509i
$$403$$ 4.00000i 0.199254i
$$404$$ 15.0000 0.746278
$$405$$ −1.00000 + 2.00000i −0.0496904 + 0.0993808i
$$406$$ 2.00000 0.0992583
$$407$$ 12.0000i 0.594818i
$$408$$ 0 0
$$409$$ −4.00000 −0.197787 −0.0988936 0.995098i $$-0.531530\pi$$
−0.0988936 + 0.995098i $$0.531530\pi$$
$$410$$ 20.0000 + 10.0000i 0.987730 + 0.493865i
$$411$$ −2.00000 −0.0986527
$$412$$ 0 0
$$413$$ 6.00000i 0.295241i
$$414$$ −5.00000 −0.245737
$$415$$ −4.00000 2.00000i −0.196352 0.0981761i
$$416$$ −4.00000 −0.196116
$$417$$ 20.0000i 0.979404i
$$418$$ 3.00000i 0.146735i
$$419$$ 18.0000 0.879358 0.439679 0.898155i $$-0.355092\pi$$
0.439679 + 0.898155i $$0.355092\pi$$
$$420$$ −1.00000 + 2.00000i −0.0487950 + 0.0975900i
$$421$$ −14.0000 −0.682318 −0.341159 0.940006i $$-0.610819\pi$$
−0.341159 + 0.940006i $$0.610819\pi$$
$$422$$ 7.00000i 0.340755i
$$423$$ 8.00000i 0.388973i
$$424$$ −5.00000 −0.242821
$$425$$ 0 0
$$426$$ 5.00000 0.242251
$$427$$ 2.00000i 0.0967868i
$$428$$ 19.0000i 0.918400i
$$429$$ 12.0000 0.579365
$$430$$ 5.00000 10.0000i 0.241121 0.482243i
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 19.0000i 0.913082i −0.889702 0.456541i $$-0.849088\pi$$
0.889702 0.456541i $$-0.150912\pi$$
$$434$$ 1.00000 0.0480015
$$435$$ 4.00000 + 2.00000i 0.191785 + 0.0958927i
$$436$$ 2.00000 0.0957826
$$437$$ 5.00000i 0.239182i
$$438$$ 7.00000i 0.334473i
$$439$$ −20.0000 −0.954548 −0.477274 0.878755i $$-0.658375\pi$$
−0.477274 + 0.878755i $$0.658375\pi$$
$$440$$ −6.00000 3.00000i −0.286039 0.143019i
$$441$$ −6.00000 −0.285714
$$442$$ 0 0
$$443$$ 29.0000i 1.37783i −0.724841 0.688916i $$-0.758087\pi$$
0.724841 0.688916i $$-0.241913\pi$$
$$444$$ 4.00000 0.189832
$$445$$ 1.00000 2.00000i 0.0474045 0.0948091i
$$446$$ −20.0000 −0.947027
$$447$$ 15.0000i 0.709476i
$$448$$ 1.00000i 0.0472456i
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ −4.00000 + 3.00000i −0.188562 + 0.141421i
$$451$$ 30.0000 1.41264
$$452$$ 15.0000i 0.705541i
$$453$$ 16.0000i 0.751746i
$$454$$ 9.00000 0.422391
$$455$$ 4.00000 8.00000i 0.187523 0.375046i
$$456$$ 1.00000 0.0468293
$$457$$ 30.0000i 1.40334i 0.712502 + 0.701670i $$0.247562\pi$$
−0.712502 + 0.701670i $$0.752438\pi$$
$$458$$ 15.0000i 0.700904i
$$459$$ 0 0
$$460$$ −10.0000 5.00000i −0.466252 0.233126i
$$461$$ 16.0000 0.745194 0.372597 0.927993i $$-0.378467\pi$$
0.372597 + 0.927993i $$0.378467\pi$$
$$462$$ 3.00000i 0.139573i
$$463$$ 14.0000i 0.650635i 0.945605 + 0.325318i $$0.105471\pi$$
−0.945605 + 0.325318i $$0.894529\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 2.00000 + 1.00000i 0.0927478 + 0.0463739i
$$466$$ −21.0000 −0.972806
$$467$$ 28.0000i 1.29569i 0.761774 + 0.647843i $$0.224329\pi$$
−0.761774 + 0.647843i $$0.775671\pi$$
$$468$$ 4.00000i 0.184900i
$$469$$ −2.00000 −0.0923514
$$470$$ −8.00000 + 16.0000i −0.369012 + 0.738025i
$$471$$ −9.00000 −0.414698
$$472$$ 6.00000i 0.276172i
$$473$$ 15.0000i 0.689701i
$$474$$ 3.00000 0.137795
$$475$$ −3.00000 4.00000i −0.137649 0.183533i
$$476$$ 0 0
$$477$$ 5.00000i 0.228934i
$$478$$ 14.0000i 0.640345i
$$479$$ 25.0000 1.14228 0.571140 0.820853i $$-0.306501\pi$$
0.571140 + 0.820853i $$0.306501\pi$$
$$480$$ 1.00000 2.00000i 0.0456435 0.0912871i
$$481$$ −16.0000 −0.729537
$$482$$ 12.0000i 0.546585i
$$483$$ 5.00000i 0.227508i
$$484$$ 2.00000 0.0909091
$$485$$ 20.0000 + 10.0000i 0.908153 + 0.454077i
$$486$$ −1.00000 −0.0453609
$$487$$ 4.00000i 0.181257i −0.995885 0.0906287i $$-0.971112\pi$$
0.995885 0.0906287i $$-0.0288876\pi$$
$$488$$ 2.00000i 0.0905357i
$$489$$ −4.00000 −0.180886
$$490$$ −12.0000 6.00000i −0.542105 0.271052i
$$491$$ 33.0000 1.48927 0.744635 0.667472i $$-0.232624\pi$$
0.744635 + 0.667472i $$0.232624\pi$$
$$492$$ 10.0000i 0.450835i
$$493$$ 0 0
$$494$$ −4.00000 −0.179969
$$495$$ −3.00000 + 6.00000i −0.134840 + 0.269680i
$$496$$ −1.00000 −0.0449013
$$497$$ 5.00000i 0.224281i
$$498$$ 2.00000i 0.0896221i
$$499$$ −22.0000 −0.984855 −0.492428 0.870353i $$-0.663890\pi$$
−0.492428 + 0.870353i $$0.663890\pi$$
$$500$$ −11.0000 + 2.00000i −0.491935 + 0.0894427i
$$501$$ −21.0000 −0.938211
$$502$$ 12.0000i 0.535586i
$$503$$ 14.0000i 0.624229i −0.950044 0.312115i $$-0.898963\pi$$
0.950044 0.312115i $$-0.101037\pi$$
$$504$$ −1.00000 −0.0445435
$$505$$ 15.0000 30.0000i 0.667491 1.33498i
$$506$$ −15.0000 −0.666831
$$507$$ 3.00000i 0.133235i
$$508$$ 8.00000i 0.354943i
$$509$$ −32.0000 −1.41838 −0.709188 0.705020i $$-0.750938\pi$$
−0.709188 + 0.705020i $$0.750938\pi$$
$$510$$ 0 0
$$511$$ −7.00000 −0.309662
$$512$$ 1.00000i 0.0441942i
$$513$$ 1.00000i 0.0441511i
$$514$$ −5.00000 −0.220541
$$515$$ 0 0
$$516$$ 5.00000 0.220113
$$517$$ 24.0000i 1.05552i
$$518$$ 4.00000i 0.175750i
$$519$$ −2.00000 −0.0877903
$$520$$ −4.00000 + 8.00000i −0.175412 + 0.350823i
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 2.00000i 0.0875376i
$$523$$ 19.0000i 0.830812i −0.909636 0.415406i $$-0.863640\pi$$
0.909636 0.415406i $$-0.136360\pi$$
$$524$$ 2.00000 0.0873704
$$525$$ 3.00000 + 4.00000i 0.130931 + 0.174574i
$$526$$ 24.0000 1.04645
$$527$$ 0 0
$$528$$ 3.00000i 0.130558i
$$529$$ −2.00000 −0.0869565
$$530$$ −5.00000 + 10.0000i −0.217186 + 0.434372i
$$531$$ −6.00000 −0.260378
$$532$$ 1.00000i 0.0433555i
$$533$$ 40.0000i 1.73259i
$$534$$ 1.00000 0.0432742
$$535$$ −38.0000 19.0000i −1.64288 0.821442i
$$536$$ 2.00000 0.0863868
$$537$$ 0 0
$$538$$ 2.00000i 0.0862261i
$$539$$ −18.0000 −0.775315
$$540$$ −2.00000 1.00000i −0.0860663 0.0430331i
$$541$$ 24.0000 1.03184 0.515920 0.856637i $$-0.327450\pi$$
0.515920 + 0.856637i $$0.327450\pi$$
$$542$$ 9.00000i 0.386583i
$$543$$ 5.00000i 0.214571i
$$544$$ 0 0
$$545$$ 2.00000 4.00000i 0.0856706 0.171341i
$$546$$ 4.00000 0.171184
$$547$$ 28.0000i 1.19719i 0.801050 + 0.598597i $$0.204275\pi$$
−0.801050 + 0.598597i $$0.795725\pi$$
$$548$$ 2.00000i 0.0854358i
$$549$$ 2.00000 0.0853579
$$550$$ −12.0000 + 9.00000i −0.511682 + 0.383761i
$$551$$ −2.00000 −0.0852029
$$552$$ 5.00000i 0.212814i
$$553$$ 3.00000i 0.127573i
$$554$$ −2.00000 −0.0849719
$$555$$ 4.00000 8.00000i 0.169791 0.339581i
$$556$$ −20.0000 −0.848189
$$557$$ 9.00000i 0.381342i 0.981654 + 0.190671i $$0.0610664\pi$$
−0.981654 + 0.190671i $$0.938934\pi$$
$$558$$ 1.00000i 0.0423334i
$$559$$ −20.0000 −0.845910
$$560$$ −2.00000 1.00000i −0.0845154 0.0422577i
$$561$$ 0 0
$$562$$ 32.0000i 1.34984i
$$563$$ 36.0000i 1.51722i −0.651546 0.758610i $$-0.725879\pi$$
0.651546 0.758610i $$-0.274121\pi$$
$$564$$ −8.00000 −0.336861
$$565$$ −30.0000 15.0000i −1.26211 0.631055i
$$566$$ 14.0000 0.588464
$$567$$ 1.00000i 0.0419961i
$$568$$ 5.00000i 0.209795i
$$569$$ 39.0000 1.63497 0.817483 0.575953i $$-0.195369\pi$$
0.817483 + 0.575953i $$0.195369\pi$$
$$570$$ 1.00000 2.00000i 0.0418854 0.0837708i
$$571$$ 26.0000 1.08807 0.544033 0.839064i $$-0.316897\pi$$
0.544033 + 0.839064i $$0.316897\pi$$
$$572$$ 12.0000i 0.501745i
$$573$$ 16.0000i 0.668410i
$$574$$ 10.0000 0.417392
$$575$$ −20.0000 + 15.0000i −0.834058 + 0.625543i
$$576$$ 1.00000 0.0416667
$$577$$ 34.0000i 1.41544i −0.706494 0.707719i $$-0.749724\pi$$
0.706494 0.707719i $$-0.250276\pi$$
$$578$$ 17.0000i 0.707107i
$$579$$ −10.0000 −0.415586
$$580$$ −2.00000 + 4.00000i −0.0830455 + 0.166091i
$$581$$ −2.00000 −0.0829740
$$582$$ 10.0000i 0.414513i
$$583$$ 15.0000i 0.621237i
$$584$$ 7.00000 0.289662
$$585$$ 8.00000 + 4.00000i 0.330759 + 0.165380i
$$586$$ −18.0000 −0.743573
$$587$$ 6.00000i 0.247647i 0.992304 + 0.123823i $$0.0395156\pi$$
−0.992304 + 0.123823i $$0.960484\pi$$
$$588$$ 6.00000i 0.247436i
$$589$$ −1.00000 −0.0412043
$$590$$ −12.0000 6.00000i −0.494032 0.247016i
$$591$$ −18.0000 −0.740421
$$592$$ 4.00000i 0.164399i
$$593$$ 6.00000i 0.246390i −0.992382 0.123195i $$-0.960686\pi$$
0.992382 0.123195i $$-0.0393141\pi$$
$$594$$ −3.00000 −0.123091
$$595$$ 0 0
$$596$$ 15.0000 0.614424
$$597$$ 21.0000i 0.859473i
$$598$$ 20.0000i 0.817861i
$$599$$ −13.0000 −0.531166 −0.265583 0.964088i $$-0.585564\pi$$
−0.265583 + 0.964088i $$0.585564\pi$$
$$600$$ −3.00000 4.00000i −0.122474 0.163299i
$$601$$ −44.0000 −1.79480 −0.897399 0.441221i $$-0.854546\pi$$
−0.897399 + 0.441221i $$0.854546\pi$$
$$602$$ 5.00000i 0.203785i
$$603$$ 2.00000i 0.0814463i
$$604$$ 16.0000 0.651031
$$605$$ 2.00000 4.00000i 0.0813116 0.162623i
$$606$$ 15.0000 0.609333
$$607$$ 27.0000i 1.09590i −0.836512 0.547948i $$-0.815409\pi$$
0.836512 0.547948i $$-0.184591\pi$$
$$608$$ 1.00000i 0.0405554i
$$609$$ 2.00000 0.0810441
$$610$$ 4.00000 + 2.00000i 0.161955 + 0.0809776i
$$611$$ 32.0000 1.29458
$$612$$ 0 0
$$613$$ 24.0000i 0.969351i −0.874694 0.484675i $$-0.838938\pi$$
0.874694 0.484675i $$-0.161062\pi$$
$$614$$ 4.00000 0.161427
$$615$$ 20.0000 + 10.0000i 0.806478 + 0.403239i
$$616$$ −3.00000 −0.120873
$$617$$ 5.00000i 0.201292i 0.994922 + 0.100646i $$0.0320910\pi$$
−0.994922 + 0.100646i $$0.967909\pi$$
$$618$$ 0 0
$$619$$ 12.0000 0.482321 0.241160 0.970485i $$-0.422472\pi$$
0.241160 + 0.970485i $$0.422472\pi$$
$$620$$ −1.00000 + 2.00000i −0.0401610 + 0.0803219i
$$621$$ −5.00000 −0.200643
$$622$$ 16.0000i 0.641542i
$$623$$ 1.00000i 0.0400642i
$$624$$ −4.00000 −0.160128
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ −6.00000 −0.239808
$$627$$ 3.00000i 0.119808i
$$628$$ 9.00000i 0.359139i
$$629$$ 0 0
$$630$$ −1.00000 + 2.00000i −0.0398410 + 0.0796819i
$$631$$ 25.0000 0.995234 0.497617 0.867397i $$-0.334208\pi$$
0.497617 + 0.867397i $$0.334208\pi$$
$$632$$ 3.00000i 0.119334i
$$633$$ 7.00000i 0.278225i
$$634$$ −18.0000 −0.714871
$$635$$ −16.0000 8.00000i −0.634941 0.317470i
$$636$$ −5.00000 −0.198263
$$637$$ 24.0000i 0.950915i
$$638$$ 6.00000i 0.237542i
$$639$$ 5.00000 0.197797
$$640$$ 2.00000 + 1.00000i 0.0790569 + 0.0395285i
$$641$$ 50.0000 1.97488 0.987441 0.157991i $$-0.0505015\pi$$
0.987441 + 0.157991i $$0.0505015\pi$$
$$642$$ 19.0000i 0.749870i
$$643$$ 7.00000i 0.276053i 0.990429 + 0.138027i $$0.0440759\pi$$
−0.990429 + 0.138027i $$0.955924\pi$$
$$644$$ −5.00000 −0.197028
$$645$$ 5.00000 10.0000i 0.196875 0.393750i
$$646$$ 0 0
$$647$$ 7.00000i 0.275198i 0.990488 + 0.137599i $$0.0439386\pi$$
−0.990488 + 0.137599i $$0.956061\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ −18.0000 −0.706562
$$650$$ 12.0000 + 16.0000i 0.470679 + 0.627572i
$$651$$ 1.00000 0.0391931
$$652$$ 4.00000i 0.156652i
$$653$$ 42.0000i 1.64359i 0.569785 + 0.821794i $$0.307026\pi$$
−0.569785 + 0.821794i $$0.692974\pi$$
$$654$$ 2.00000 0.0782062
$$655$$ 2.00000 4.00000i 0.0781465 0.156293i
$$656$$ −10.0000 −0.390434
$$657$$ 7.00000i 0.273096i
$$658$$ 8.00000i 0.311872i
$$659$$ −6.00000 −0.233727 −0.116863 0.993148i $$-0.537284\pi$$
−0.116863 + 0.993148i $$0.537284\pi$$
$$660$$ −6.00000 3.00000i −0.233550 0.116775i
$$661$$ 36.0000 1.40024 0.700119 0.714026i $$-0.253130\pi$$
0.700119 + 0.714026i $$0.253130\pi$$
$$662$$ 8.00000i 0.310929i
$$663$$ 0 0
$$664$$ 2.00000 0.0776151
$$665$$ −2.00000 1.00000i −0.0775567 0.0387783i
$$666$$ 4.00000 0.154997
$$667$$ 10.0000i 0.387202i
$$668$$ 21.0000i 0.812514i
$$669$$ −20.0000 −0.773245
$$670$$ 2.00000 4.00000i 0.0772667 0.154533i
$$671$$ 6.00000 0.231627
$$672$$ 1.00000i 0.0385758i
$$673$$ 30.0000i 1.15642i 0.815890 + 0.578208i $$0.196248\pi$$
−0.815890 + 0.578208i $$0.803752\pi$$
$$674$$ 34.0000 1.30963
$$675$$ −4.00000 + 3.00000i −0.153960 + 0.115470i
$$676$$ 3.00000 0.115385
$$677$$ 13.0000i 0.499631i 0.968294 + 0.249815i $$0.0803699\pi$$
−0.968294 + 0.249815i $$0.919630\pi$$
$$678$$ 15.0000i 0.576072i
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ 9.00000 0.344881
$$682$$ 3.00000i 0.114876i
$$683$$ 35.0000i 1.33924i −0.742705 0.669619i $$-0.766457\pi$$
0.742705 0.669619i $$-0.233543\pi$$
$$684$$ 1.00000 0.0382360
$$685$$ −4.00000 2.00000i −0.152832 0.0764161i
$$686$$ −13.0000 −0.496342
$$687$$ 15.0000i 0.572286i
$$688$$ 5.00000i 0.190623i
$$689$$ 20.0000 0.761939
$$690$$ −10.0000 5.00000i −0.380693 0.190347i
$$691$$ −41.0000 −1.55971 −0.779857 0.625958i $$-0.784708\pi$$
−0.779857 + 0.625958i $$0.784708\pi$$
$$692$$ 2.00000i 0.0760286i
$$693$$ 3.00000i 0.113961i
$$694$$ 22.0000 0.835109
$$695$$ −20.0000 + 40.0000i −0.758643 + 1.51729i
$$696$$ −2.00000 −0.0758098
$$697$$ 0 0
$$698$$ 20.0000i 0.757011i
$$699$$ −21.0000 −0.794293
$$700$$ −4.00000 + 3.00000i −0.151186 + 0.113389i
$$701$$ −35.0000 −1.32193 −0.660966 0.750416i $$-0.729853\pi$$
−0.660966 + 0.750416i $$0.729853\pi$$
$$702$$ 4.00000i 0.150970i
$$703$$ 4.00000i 0.150863i
$$704$$ 3.00000 0.113067
$$705$$ −8.00000 + 16.0000i −0.301297 + 0.602595i
$$706$$ 24.0000 0.903252
$$707$$ 15.0000i 0.564133i
$$708$$ 6.00000i 0.225494i
$$709$$ −5.00000 −0.187779 −0.0938895 0.995583i $$-0.529930\pi$$
−0.0938895 + 0.995583i $$0.529930\pi$$
$$710$$ 10.0000 + 5.00000i 0.375293 + 0.187647i
$$711$$ 3.00000 0.112509
$$712$$ 1.00000i 0.0374766i
$$713$$ 5.00000i 0.187251i
$$714$$ 0 0
$$715$$ 24.0000 + 12.0000i 0.897549 + 0.448775i
$$716$$ 0 0
$$717$$ 14.0000i 0.522840i
$$718$$ 3.00000i 0.111959i
$$719$$ −10.0000 −0.372937 −0.186469 0.982461i $$-0.559704\pi$$
−0.186469 + 0.982461i $$0.559704\pi$$
$$720$$ 1.00000 2.00000i 0.0372678 0.0745356i
$$721$$ 0 0
$$722$$ 18.0000i 0.669891i
$$723$$ 12.0000i 0.446285i
$$724$$ 5.00000 0.185824
$$725$$ 6.00000 + 8.00000i 0.222834 + 0.297113i
$$726$$ 2.00000 0.0742270
$$727$$ 49.0000i 1.81731i 0.417548 + 0.908655i $$0.362889\pi$$
−0.417548 + 0.908655i $$0.637111\pi$$
$$728$$ 4.00000i 0.148250i
$$729$$ −1.00000 −0.0370370
$$730$$ 7.00000 14.0000i 0.259082 0.518163i
$$731$$ 0 0
$$732$$ 2.00000i 0.0739221i
$$733$$ 22.0000i 0.812589i 0.913742 + 0.406294i $$0.133179\pi$$
−0.913742 + 0.406294i $$0.866821\pi$$
$$734$$ −14.0000 −0.516749
$$735$$ −12.0000 6.00000i −0.442627 0.221313i
$$736$$ 5.00000 0.184302
$$737$$ 6.00000i 0.221013i
$$738$$ 10.0000i 0.368105i
$$739$$ 18.0000 0.662141 0.331070 0.943606i $$-0.392590\pi$$
0.331070 + 0.943606i $$0.392590\pi$$
$$740$$ 8.00000 + 4.00000i 0.294086 + 0.147043i
$$741$$ −4.00000 −0.146944
$$742$$ 5.00000i 0.183556i
$$743$$ 15.0000i 0.550297i −0.961402 0.275148i $$-0.911273\pi$$
0.961402 0.275148i $$-0.0887270\pi$$
$$744$$ −1.00000 −0.0366618
$$745$$ 15.0000 30.0000i 0.549557 1.09911i
$$746$$ −11.0000 −0.402739
$$747$$ 2.00000i 0.0731762i
$$748$$ 0 0
$$749$$ −19.0000 −0.694245
$$750$$ −11.0000 + 2.00000i −0.401663 + 0.0730297i
$$751$$ 22.0000 0.802791 0.401396 0.915905i $$-0.368525\pi$$
0.401396 + 0.915905i $$0.368525\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 12.0000i 0.437304i
$$754$$ 8.00000 0.291343
$$755$$ 16.0000 32.0000i 0.582300 1.16460i
$$756$$ −1.00000 −0.0363696
$$757$$ 20.0000i 0.726912i 0.931611 + 0.363456i $$0.118403\pi$$
−0.931611 + 0.363456i $$0.881597\pi$$
$$758$$ 15.0000i 0.544825i
$$759$$ −15.0000 −0.544466
$$760$$ 2.00000 + 1.00000i 0.0725476 + 0.0362738i
$$761$$ 21.0000 0.761249 0.380625 0.924730i $$-0.375709\pi$$
0.380625 + 0.924730i $$0.375709\pi$$
$$762$$ 8.00000i 0.289809i
$$763$$ 2.00000i 0.0724049i
$$764$$ 16.0000 0.578860
$$765$$ 0 0
$$766$$ 28.0000 1.01168
$$767$$ 24.0000i 0.866590i
$$768$$ 1.00000i 0.0360844i
$$769$$ −45.0000 −1.62274 −0.811371 0.584532i $$-0.801278\pi$$
−0.811371 + 0.584532i $$0.801278\pi$$
$$770$$ −3.00000 + 6.00000i −0.108112 + 0.216225i
$$771$$ −5.00000 −0.180071
$$772$$ 10.0000i 0.359908i
$$773$$ 29.0000i 1.04306i 0.853234 + 0.521529i $$0.174638\pi$$
−0.853234 + 0.521529i $$0.825362\pi$$
$$774$$ 5.00000 0.179721
$$775$$ 3.00000 + 4.00000i 0.107763 + 0.143684i
$$776$$ −10.0000 −0.358979
$$777$$ 4.00000i 0.143499i
$$778$$ 28.0000i 1.00385i
$$779$$ −10.0000 −0.358287
$$780$$ −4.00000 + 8.00000i −0.143223 + 0.286446i
$$781$$ 15.0000 0.536742
$$782$$ 0 0
$$783$$ 2.00000i 0.0714742i
$$784$$ 6.00000 0.214286
$$785$$ −18.0000 9.00000i −0.642448 0.321224i
$$786$$ 2.00000 0.0713376
$$787$$ 27.0000i 0.962446i 0.876598 + 0.481223i $$0.159807\pi$$
−0.876598 + 0.481223i $$0.840193\pi$$
$$788$$ 18.0000i