# Properties

 Label 546.2.c.b.337.2 Level $546$ Weight $2$ Character 546.337 Analytic conductor $4.360$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ 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 337.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.337 Dual form 546.2.c.b.337.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +2.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} -2.00000 q^{10} -1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -1.00000 q^{14} +2.00000i q^{15} +1.00000 q^{16} -2.00000 q^{17} +1.00000i q^{18} +4.00000i q^{19} -2.00000i q^{20} +1.00000i q^{21} -6.00000 q^{23} -1.00000i q^{24} +1.00000 q^{25} +(-3.00000 + 2.00000i) q^{26} +1.00000 q^{27} -1.00000i q^{28} -2.00000 q^{30} +1.00000i q^{32} -2.00000i q^{34} -2.00000 q^{35} -1.00000 q^{36} -2.00000i q^{37} -4.00000 q^{38} +(2.00000 + 3.00000i) q^{39} +2.00000 q^{40} -1.00000 q^{42} +4.00000 q^{43} +2.00000i q^{45} -6.00000i q^{46} +8.00000i q^{47} +1.00000 q^{48} -1.00000 q^{49} +1.00000i q^{50} -2.00000 q^{51} +(-2.00000 - 3.00000i) q^{52} +4.00000 q^{53} +1.00000i q^{54} +1.00000 q^{56} +4.00000i q^{57} -6.00000i q^{59} -2.00000i q^{60} +12.0000 q^{61} +1.00000i q^{63} -1.00000 q^{64} +(-6.00000 + 4.00000i) q^{65} -2.00000i q^{67} +2.00000 q^{68} -6.00000 q^{69} -2.00000i q^{70} -1.00000i q^{72} -14.0000i q^{73} +2.00000 q^{74} +1.00000 q^{75} -4.00000i q^{76} +(-3.00000 + 2.00000i) q^{78} +2.00000i q^{80} +1.00000 q^{81} -14.0000i q^{83} -1.00000i q^{84} -4.00000i q^{85} +4.00000i q^{86} +4.00000i q^{89} -2.00000 q^{90} +(-3.00000 + 2.00000i) q^{91} +6.00000 q^{92} -8.00000 q^{94} -8.00000 q^{95} +1.00000i q^{96} -2.00000i q^{97} -1.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10})$$ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 $$2 q + 2 q^{3} - 2 q^{4} + 2 q^{9} - 4 q^{10} - 2 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 12 q^{23} + 2 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{30} - 4 q^{35} - 2 q^{36} - 8 q^{38} + 4 q^{39} + 4 q^{40} - 2 q^{42} + 8 q^{43} + 2 q^{48} - 2 q^{49} - 4 q^{51} - 4 q^{52} + 8 q^{53} + 2 q^{56} + 24 q^{61} - 2 q^{64} - 12 q^{65} + 4 q^{68} - 12 q^{69} + 4 q^{74} + 2 q^{75} - 6 q^{78} + 2 q^{81} - 4 q^{90} - 6 q^{91} + 12 q^{92} - 16 q^{94} - 16 q^{95}+O(q^{100})$$ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 - 4 * q^10 - 2 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 12 * q^23 + 2 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^30 - 4 * q^35 - 2 * q^36 - 8 * q^38 + 4 * q^39 + 4 * q^40 - 2 * q^42 + 8 * q^43 + 2 * q^48 - 2 * q^49 - 4 * q^51 - 4 * q^52 + 8 * q^53 + 2 * q^56 + 24 * q^61 - 2 * q^64 - 12 * q^65 + 4 * q^68 - 12 * q^69 + 4 * q^74 + 2 * q^75 - 6 * q^78 + 2 * q^81 - 4 * q^90 - 6 * q^91 + 12 * q^92 - 16 * q^94 - 16 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 1.00000 0.577350
$$4$$ −1.00000 −0.500000
$$5$$ 2.00000i 0.894427i 0.894427 + 0.447214i $$0.147584\pi$$
−0.894427 + 0.447214i $$0.852416\pi$$
$$6$$ 1.00000i 0.408248i
$$7$$ 1.00000i 0.377964i
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000 0.333333
$$10$$ −2.00000 −0.632456
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 2.00000 + 3.00000i 0.554700 + 0.832050i
$$14$$ −1.00000 −0.267261
$$15$$ 2.00000i 0.516398i
$$16$$ 1.00000 0.250000
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 4.00000i 0.917663i 0.888523 + 0.458831i $$0.151732\pi$$
−0.888523 + 0.458831i $$0.848268\pi$$
$$20$$ 2.00000i 0.447214i
$$21$$ 1.00000i 0.218218i
$$22$$ 0 0
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ 1.00000 0.200000
$$26$$ −3.00000 + 2.00000i −0.588348 + 0.392232i
$$27$$ 1.00000 0.192450
$$28$$ 1.00000i 0.188982i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ −2.00000 −0.365148
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 2.00000i 0.342997i
$$35$$ −2.00000 −0.338062
$$36$$ −1.00000 −0.166667
$$37$$ 2.00000i 0.328798i −0.986394 0.164399i $$-0.947432\pi$$
0.986394 0.164399i $$-0.0525685\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ 2.00000 + 3.00000i 0.320256 + 0.480384i
$$40$$ 2.00000 0.316228
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ −1.00000 −0.154303
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 2.00000i 0.298142i
$$46$$ 6.00000i 0.884652i
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −1.00000 −0.142857
$$50$$ 1.00000i 0.141421i
$$51$$ −2.00000 −0.280056
$$52$$ −2.00000 3.00000i −0.277350 0.416025i
$$53$$ 4.00000 0.549442 0.274721 0.961524i $$-0.411414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 4.00000i 0.529813i
$$58$$ 0 0
$$59$$ 6.00000i 0.781133i −0.920575 0.390567i $$-0.872279\pi$$
0.920575 0.390567i $$-0.127721\pi$$
$$60$$ 2.00000i 0.258199i
$$61$$ 12.0000 1.53644 0.768221 0.640184i $$-0.221142\pi$$
0.768221 + 0.640184i $$0.221142\pi$$
$$62$$ 0 0
$$63$$ 1.00000i 0.125988i
$$64$$ −1.00000 −0.125000
$$65$$ −6.00000 + 4.00000i −0.744208 + 0.496139i
$$66$$ 0 0
$$67$$ 2.00000i 0.244339i −0.992509 0.122169i $$-0.961015\pi$$
0.992509 0.122169i $$-0.0389851\pi$$
$$68$$ 2.00000 0.242536
$$69$$ −6.00000 −0.722315
$$70$$ 2.00000i 0.239046i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 14.0000i 1.63858i −0.573382 0.819288i $$-0.694369\pi$$
0.573382 0.819288i $$-0.305631\pi$$
$$74$$ 2.00000 0.232495
$$75$$ 1.00000 0.115470
$$76$$ 4.00000i 0.458831i
$$77$$ 0 0
$$78$$ −3.00000 + 2.00000i −0.339683 + 0.226455i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 2.00000i 0.223607i
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 14.0000i 1.53670i −0.640030 0.768350i $$-0.721078\pi$$
0.640030 0.768350i $$-0.278922\pi$$
$$84$$ 1.00000i 0.109109i
$$85$$ 4.00000i 0.433861i
$$86$$ 4.00000i 0.431331i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 4.00000i 0.423999i 0.977270 + 0.212000i $$0.0679975\pi$$
−0.977270 + 0.212000i $$0.932002\pi$$
$$90$$ −2.00000 −0.210819
$$91$$ −3.00000 + 2.00000i −0.314485 + 0.209657i
$$92$$ 6.00000 0.625543
$$93$$ 0 0
$$94$$ −8.00000 −0.825137
$$95$$ −8.00000 −0.820783
$$96$$ 1.00000i 0.102062i
$$97$$ 2.00000i 0.203069i −0.994832 0.101535i $$-0.967625\pi$$
0.994832 0.101535i $$-0.0323753\pi$$
$$98$$ 1.00000i 0.101015i
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ 2.00000 0.199007 0.0995037 0.995037i $$-0.468274\pi$$
0.0995037 + 0.995037i $$0.468274\pi$$
$$102$$ 2.00000i 0.198030i
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 3.00000 2.00000i 0.294174 0.196116i
$$105$$ −2.00000 −0.195180
$$106$$ 4.00000i 0.388514i
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ 6.00000i 0.574696i −0.957826 0.287348i $$-0.907226\pi$$
0.957826 0.287348i $$-0.0927736\pi$$
$$110$$ 0 0
$$111$$ 2.00000i 0.189832i
$$112$$ 1.00000i 0.0944911i
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ −4.00000 −0.374634
$$115$$ 12.0000i 1.11901i
$$116$$ 0 0
$$117$$ 2.00000 + 3.00000i 0.184900 + 0.277350i
$$118$$ 6.00000 0.552345
$$119$$ 2.00000i 0.183340i
$$120$$ 2.00000 0.182574
$$121$$ 11.0000 1.00000
$$122$$ 12.0000i 1.08643i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000i 1.07331i
$$126$$ −1.00000 −0.0890871
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 4.00000 0.352180
$$130$$ −4.00000 6.00000i −0.350823 0.526235i
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 0 0
$$133$$ −4.00000 −0.346844
$$134$$ 2.00000 0.172774
$$135$$ 2.00000i 0.172133i
$$136$$ 2.00000i 0.171499i
$$137$$ 2.00000i 0.170872i −0.996344 0.0854358i $$-0.972772\pi$$
0.996344 0.0854358i $$-0.0272282\pi$$
$$138$$ 6.00000i 0.510754i
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 2.00000 0.169031
$$141$$ 8.00000i 0.673722i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 14.0000 1.15865
$$147$$ −1.00000 −0.0824786
$$148$$ 2.00000i 0.164399i
$$149$$ 6.00000i 0.491539i −0.969328 0.245770i $$-0.920959\pi$$
0.969328 0.245770i $$-0.0790407\pi$$
$$150$$ 1.00000i 0.0816497i
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 4.00000 0.324443
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −2.00000 3.00000i −0.160128 0.240192i
$$157$$ 8.00000 0.638470 0.319235 0.947676i $$-0.396574\pi$$
0.319235 + 0.947676i $$0.396574\pi$$
$$158$$ 0 0
$$159$$ 4.00000 0.317221
$$160$$ −2.00000 −0.158114
$$161$$ 6.00000i 0.472866i
$$162$$ 1.00000i 0.0785674i
$$163$$ 14.0000i 1.09656i −0.836293 0.548282i $$-0.815282\pi$$
0.836293 0.548282i $$-0.184718\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 14.0000 1.08661
$$167$$ 12.0000i 0.928588i −0.885681 0.464294i $$-0.846308\pi$$
0.885681 0.464294i $$-0.153692\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ −5.00000 + 12.0000i −0.384615 + 0.923077i
$$170$$ 4.00000 0.306786
$$171$$ 4.00000i 0.305888i
$$172$$ −4.00000 −0.304997
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 0 0
$$175$$ 1.00000i 0.0755929i
$$176$$ 0 0
$$177$$ 6.00000i 0.450988i
$$178$$ −4.00000 −0.299813
$$179$$ −20.0000 −1.49487 −0.747435 0.664335i $$-0.768715\pi$$
−0.747435 + 0.664335i $$0.768715\pi$$
$$180$$ 2.00000i 0.149071i
$$181$$ 12.0000 0.891953 0.445976 0.895045i $$-0.352856\pi$$
0.445976 + 0.895045i $$0.352856\pi$$
$$182$$ −2.00000 3.00000i −0.148250 0.222375i
$$183$$ 12.0000 0.887066
$$184$$ 6.00000i 0.442326i
$$185$$ 4.00000 0.294086
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 8.00000i 0.583460i
$$189$$ 1.00000i 0.0727393i
$$190$$ 8.00000i 0.580381i
$$191$$ 2.00000 0.144715 0.0723575 0.997379i $$-0.476948\pi$$
0.0723575 + 0.997379i $$0.476948\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 4.00000i 0.287926i −0.989583 0.143963i $$-0.954015\pi$$
0.989583 0.143963i $$-0.0459847\pi$$
$$194$$ 2.00000 0.143592
$$195$$ −6.00000 + 4.00000i −0.429669 + 0.286446i
$$196$$ 1.00000 0.0714286
$$197$$ 18.0000i 1.28245i 0.767354 + 0.641223i $$0.221573\pi$$
−0.767354 + 0.641223i $$0.778427\pi$$
$$198$$ 0 0
$$199$$ −10.0000 −0.708881 −0.354441 0.935079i $$-0.615329\pi$$
−0.354441 + 0.935079i $$0.615329\pi$$
$$200$$ 1.00000i 0.0707107i
$$201$$ 2.00000i 0.141069i
$$202$$ 2.00000i 0.140720i
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ 0 0
$$206$$ 14.0000i 0.975426i
$$207$$ −6.00000 −0.417029
$$208$$ 2.00000 + 3.00000i 0.138675 + 0.208013i
$$209$$ 0 0
$$210$$ 2.00000i 0.138013i
$$211$$ −28.0000 −1.92760 −0.963800 0.266627i $$-0.914091\pi$$
−0.963800 + 0.266627i $$0.914091\pi$$
$$212$$ −4.00000 −0.274721
$$213$$ 0 0
$$214$$ 12.0000i 0.820303i
$$215$$ 8.00000i 0.545595i
$$216$$ 1.00000i 0.0680414i
$$217$$ 0 0
$$218$$ 6.00000 0.406371
$$219$$ 14.0000i 0.946032i
$$220$$ 0 0
$$221$$ −4.00000 6.00000i −0.269069 0.403604i
$$222$$ 2.00000 0.134231
$$223$$ 16.0000i 1.07144i 0.844396 + 0.535720i $$0.179960\pi$$
−0.844396 + 0.535720i $$0.820040\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 1.00000 0.0666667
$$226$$ 14.0000i 0.931266i
$$227$$ 22.0000i 1.46019i −0.683345 0.730096i $$-0.739475\pi$$
0.683345 0.730096i $$-0.260525\pi$$
$$228$$ 4.00000i 0.264906i
$$229$$ 14.0000i 0.925146i 0.886581 + 0.462573i $$0.153074\pi$$
−0.886581 + 0.462573i $$0.846926\pi$$
$$230$$ 12.0000 0.791257
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ −3.00000 + 2.00000i −0.196116 + 0.130744i
$$235$$ −16.0000 −1.04372
$$236$$ 6.00000i 0.390567i
$$237$$ 0 0
$$238$$ 2.00000 0.129641
$$239$$ 16.0000i 1.03495i −0.855697 0.517477i $$-0.826871\pi$$
0.855697 0.517477i $$-0.173129\pi$$
$$240$$ 2.00000i 0.129099i
$$241$$ 10.0000i 0.644157i 0.946713 + 0.322078i $$0.104381\pi$$
−0.946713 + 0.322078i $$0.895619\pi$$
$$242$$ 11.0000i 0.707107i
$$243$$ 1.00000 0.0641500
$$244$$ −12.0000 −0.768221
$$245$$ 2.00000i 0.127775i
$$246$$ 0 0
$$247$$ −12.0000 + 8.00000i −0.763542 + 0.509028i
$$248$$ 0 0
$$249$$ 14.0000i 0.887214i
$$250$$ −12.0000 −0.758947
$$251$$ −28.0000 −1.76734 −0.883672 0.468106i $$-0.844936\pi$$
−0.883672 + 0.468106i $$0.844936\pi$$
$$252$$ 1.00000i 0.0629941i
$$253$$ 0 0
$$254$$ 12.0000i 0.752947i
$$255$$ 4.00000i 0.250490i
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 4.00000i 0.249029i
$$259$$ 2.00000 0.124274
$$260$$ 6.00000 4.00000i 0.372104 0.248069i
$$261$$ 0 0
$$262$$ 12.0000i 0.741362i
$$263$$ −6.00000 −0.369976 −0.184988 0.982741i $$-0.559225\pi$$
−0.184988 + 0.982741i $$0.559225\pi$$
$$264$$ 0 0
$$265$$ 8.00000i 0.491436i
$$266$$ 4.00000i 0.245256i
$$267$$ 4.00000i 0.244796i
$$268$$ 2.00000i 0.122169i
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ −2.00000 −0.121716
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ −3.00000 + 2.00000i −0.181568 + 0.121046i
$$274$$ 2.00000 0.120824
$$275$$ 0 0
$$276$$ 6.00000 0.361158
$$277$$ −22.0000 −1.32185 −0.660926 0.750451i $$-0.729836\pi$$
−0.660926 + 0.750451i $$0.729836\pi$$
$$278$$ 20.0000i 1.19952i
$$279$$ 0 0
$$280$$ 2.00000i 0.119523i
$$281$$ 30.0000i 1.78965i 0.446417 + 0.894825i $$0.352700\pi$$
−0.446417 + 0.894825i $$0.647300\pi$$
$$282$$ −8.00000 −0.476393
$$283$$ −16.0000 −0.951101 −0.475551 0.879688i $$-0.657751\pi$$
−0.475551 + 0.879688i $$0.657751\pi$$
$$284$$ 0 0
$$285$$ −8.00000 −0.473879
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000i 0.0589256i
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 2.00000i 0.117242i
$$292$$ 14.0000i 0.819288i
$$293$$ 6.00000i 0.350524i 0.984522 + 0.175262i $$0.0560772\pi$$
−0.984522 + 0.175262i $$0.943923\pi$$
$$294$$ 1.00000i 0.0583212i
$$295$$ 12.0000 0.698667
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ −12.0000 18.0000i −0.693978 1.04097i
$$300$$ −1.00000 −0.0577350
$$301$$ 4.00000i 0.230556i
$$302$$ 0 0
$$303$$ 2.00000 0.114897
$$304$$ 4.00000i 0.229416i
$$305$$ 24.0000i 1.37424i
$$306$$ 2.00000i 0.114332i
$$307$$ 28.0000i 1.59804i 0.601302 + 0.799022i $$0.294649\pi$$
−0.601302 + 0.799022i $$0.705351\pi$$
$$308$$ 0 0
$$309$$ 14.0000 0.796432
$$310$$ 0 0
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 3.00000 2.00000i 0.169842 0.113228i
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ 8.00000i 0.451466i
$$315$$ −2.00000 −0.112687
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i −0.998421 0.0561656i $$-0.982113\pi$$
0.998421 0.0561656i $$-0.0178875\pi$$
$$318$$ 4.00000i 0.224309i
$$319$$ 0 0
$$320$$ 2.00000i 0.111803i
$$321$$ −12.0000 −0.669775
$$322$$ 6.00000 0.334367
$$323$$ 8.00000i 0.445132i
$$324$$ −1.00000 −0.0555556
$$325$$ 2.00000 + 3.00000i 0.110940 + 0.166410i
$$326$$ 14.0000 0.775388
$$327$$ 6.00000i 0.331801i
$$328$$ 0 0
$$329$$ −8.00000 −0.441054
$$330$$ 0 0
$$331$$ 10.0000i 0.549650i −0.961494 0.274825i $$-0.911380\pi$$
0.961494 0.274825i $$-0.0886199\pi$$
$$332$$ 14.0000i 0.768350i
$$333$$ 2.00000i 0.109599i
$$334$$ 12.0000 0.656611
$$335$$ 4.00000 0.218543
$$336$$ 1.00000i 0.0545545i
$$337$$ −22.0000 −1.19842 −0.599208 0.800593i $$-0.704518\pi$$
−0.599208 + 0.800593i $$0.704518\pi$$
$$338$$ −12.0000 5.00000i −0.652714 0.271964i
$$339$$ 14.0000 0.760376
$$340$$ 4.00000i 0.216930i
$$341$$ 0 0
$$342$$ −4.00000 −0.216295
$$343$$ 1.00000i 0.0539949i
$$344$$ 4.00000i 0.215666i
$$345$$ 12.0000i 0.646058i
$$346$$ 6.00000i 0.322562i
$$347$$ −32.0000 −1.71785 −0.858925 0.512101i $$-0.828867\pi$$
−0.858925 + 0.512101i $$0.828867\pi$$
$$348$$ 0 0
$$349$$ 14.0000i 0.749403i 0.927146 + 0.374701i $$0.122255\pi$$
−0.927146 + 0.374701i $$0.877745\pi$$
$$350$$ −1.00000 −0.0534522
$$351$$ 2.00000 + 3.00000i 0.106752 + 0.160128i
$$352$$ 0 0
$$353$$ 24.0000i 1.27739i −0.769460 0.638696i $$-0.779474\pi$$
0.769460 0.638696i $$-0.220526\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ 4.00000i 0.212000i
$$357$$ 2.00000i 0.105851i
$$358$$ 20.0000i 1.05703i
$$359$$ 24.0000i 1.26667i 0.773877 + 0.633336i $$0.218315\pi$$
−0.773877 + 0.633336i $$0.781685\pi$$
$$360$$ 2.00000 0.105409
$$361$$ 3.00000 0.157895
$$362$$ 12.0000i 0.630706i
$$363$$ 11.0000 0.577350
$$364$$ 3.00000 2.00000i 0.157243 0.104828i
$$365$$ 28.0000 1.46559
$$366$$ 12.0000i 0.627250i
$$367$$ −22.0000 −1.14839 −0.574195 0.818718i $$-0.694685\pi$$
−0.574195 + 0.818718i $$0.694685\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 0 0
$$370$$ 4.00000i 0.207950i
$$371$$ 4.00000i 0.207670i
$$372$$ 0 0
$$373$$ 34.0000 1.76045 0.880227 0.474554i $$-0.157390\pi$$
0.880227 + 0.474554i $$0.157390\pi$$
$$374$$ 0 0
$$375$$ 12.0000i 0.619677i
$$376$$ 8.00000 0.412568
$$377$$ 0 0
$$378$$ −1.00000 −0.0514344
$$379$$ 26.0000i 1.33553i −0.744372 0.667765i $$-0.767251\pi$$
0.744372 0.667765i $$-0.232749\pi$$
$$380$$ 8.00000 0.410391
$$381$$ −12.0000 −0.614779
$$382$$ 2.00000i 0.102329i
$$383$$ 24.0000i 1.22634i −0.789950 0.613171i $$-0.789894\pi$$
0.789950 0.613171i $$-0.210106\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ 0 0
$$386$$ 4.00000 0.203595
$$387$$ 4.00000 0.203331
$$388$$ 2.00000i 0.101535i
$$389$$ 20.0000 1.01404 0.507020 0.861934i $$-0.330747\pi$$
0.507020 + 0.861934i $$0.330747\pi$$
$$390$$ −4.00000 6.00000i −0.202548 0.303822i
$$391$$ 12.0000 0.606866
$$392$$ 1.00000i 0.0505076i
$$393$$ 12.0000 0.605320
$$394$$ −18.0000 −0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 18.0000i 0.903394i 0.892171 + 0.451697i $$0.149181\pi$$
−0.892171 + 0.451697i $$0.850819\pi$$
$$398$$ 10.0000i 0.501255i
$$399$$ −4.00000 −0.200250
$$400$$ 1.00000 0.0500000
$$401$$ 30.0000i 1.49813i −0.662497 0.749064i $$-0.730503\pi$$
0.662497 0.749064i $$-0.269497\pi$$
$$402$$ 2.00000 0.0997509
$$403$$ 0 0
$$404$$ −2.00000 −0.0995037
$$405$$ 2.00000i 0.0993808i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 2.00000i 0.0990148i
$$409$$ 14.0000i 0.692255i 0.938187 + 0.346128i $$0.112504\pi$$
−0.938187 + 0.346128i $$0.887496\pi$$
$$410$$ 0 0
$$411$$ 2.00000i 0.0986527i
$$412$$ −14.0000 −0.689730
$$413$$ 6.00000 0.295241
$$414$$ 6.00000i 0.294884i
$$415$$ 28.0000 1.37447
$$416$$ −3.00000 + 2.00000i −0.147087 + 0.0980581i
$$417$$ 20.0000 0.979404
$$418$$ 0 0
$$419$$ 20.0000 0.977064 0.488532 0.872546i $$-0.337533\pi$$
0.488532 + 0.872546i $$0.337533\pi$$
$$420$$ 2.00000 0.0975900
$$421$$ 30.0000i 1.46211i −0.682318 0.731055i $$-0.739028\pi$$
0.682318 0.731055i $$-0.260972\pi$$
$$422$$ 28.0000i 1.36302i
$$423$$ 8.00000i 0.388973i
$$424$$ 4.00000i 0.194257i
$$425$$ −2.00000 −0.0970143
$$426$$ 0 0
$$427$$ 12.0000i 0.580721i
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ −8.00000 −0.385794
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −26.0000 −1.24948 −0.624740 0.780833i $$-0.714795\pi$$
−0.624740 + 0.780833i $$0.714795\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 6.00000i 0.287348i
$$437$$ 24.0000i 1.14808i
$$438$$ 14.0000 0.668946
$$439$$ 30.0000 1.43182 0.715911 0.698192i $$-0.246012\pi$$
0.715911 + 0.698192i $$0.246012\pi$$
$$440$$ 0 0
$$441$$ −1.00000 −0.0476190
$$442$$ 6.00000 4.00000i 0.285391 0.190261i
$$443$$ 4.00000 0.190046 0.0950229 0.995475i $$-0.469708\pi$$
0.0950229 + 0.995475i $$0.469708\pi$$
$$444$$ 2.00000i 0.0949158i
$$445$$ −8.00000 −0.379236
$$446$$ −16.0000 −0.757622
$$447$$ 6.00000i 0.283790i
$$448$$ 1.00000i 0.0472456i
$$449$$ 14.0000i 0.660701i 0.943858 + 0.330350i $$0.107167\pi$$
−0.943858 + 0.330350i $$0.892833\pi$$
$$450$$ 1.00000i 0.0471405i
$$451$$ 0 0
$$452$$ −14.0000 −0.658505
$$453$$ 0 0
$$454$$ 22.0000 1.03251
$$455$$ −4.00000 6.00000i −0.187523 0.281284i
$$456$$ 4.00000 0.187317
$$457$$ 8.00000i 0.374224i 0.982339 + 0.187112i $$0.0599128\pi$$
−0.982339 + 0.187112i $$0.940087\pi$$
$$458$$ −14.0000 −0.654177
$$459$$ −2.00000 −0.0933520
$$460$$ 12.0000i 0.559503i
$$461$$ 10.0000i 0.465746i 0.972507 + 0.232873i $$0.0748127\pi$$
−0.972507 + 0.232873i $$0.925187\pi$$
$$462$$ 0 0
$$463$$ 16.0000i 0.743583i 0.928316 + 0.371792i $$0.121256\pi$$
−0.928316 + 0.371792i $$0.878744\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 6.00000i 0.277945i
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ −2.00000 3.00000i −0.0924500 0.138675i
$$469$$ 2.00000 0.0923514
$$470$$ 16.0000i 0.738025i
$$471$$ 8.00000 0.368621
$$472$$ −6.00000 −0.276172
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 4.00000i 0.183533i
$$476$$ 2.00000i 0.0916698i
$$477$$ 4.00000 0.183147
$$478$$ 16.0000 0.731823
$$479$$ 16.0000i 0.731059i −0.930800 0.365529i $$-0.880888\pi$$
0.930800 0.365529i $$-0.119112\pi$$
$$480$$ −2.00000 −0.0912871
$$481$$ 6.00000 4.00000i 0.273576 0.182384i
$$482$$ −10.0000 −0.455488
$$483$$ 6.00000i 0.273009i
$$484$$ −11.0000 −0.500000
$$485$$ 4.00000 0.181631
$$486$$ 1.00000i 0.0453609i
$$487$$ 28.0000i 1.26880i 0.773004 + 0.634401i $$0.218753\pi$$
−0.773004 + 0.634401i $$0.781247\pi$$
$$488$$ 12.0000i 0.543214i
$$489$$ 14.0000i 0.633102i
$$490$$ 2.00000 0.0903508
$$491$$ −8.00000 −0.361035 −0.180517 0.983572i $$-0.557777\pi$$
−0.180517 + 0.983572i $$0.557777\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −8.00000 12.0000i −0.359937 0.539906i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 14.0000 0.627355
$$499$$ 14.0000i 0.626726i 0.949633 + 0.313363i $$0.101456\pi$$
−0.949633 + 0.313363i $$0.898544\pi$$
$$500$$ 12.0000i 0.536656i
$$501$$ 12.0000i 0.536120i
$$502$$ 28.0000i 1.24970i
$$503$$ −36.0000 −1.60516 −0.802580 0.596544i $$-0.796540\pi$$
−0.802580 + 0.596544i $$0.796540\pi$$
$$504$$ 1.00000 0.0445435
$$505$$ 4.00000i 0.177998i
$$506$$ 0 0
$$507$$ −5.00000 + 12.0000i −0.222058 + 0.532939i
$$508$$ 12.0000 0.532414
$$509$$ 26.0000i 1.15243i −0.817298 0.576215i $$-0.804529\pi$$
0.817298 0.576215i $$-0.195471\pi$$
$$510$$ 4.00000 0.177123
$$511$$ 14.0000 0.619324
$$512$$ 1.00000i 0.0441942i
$$513$$ 4.00000i 0.176604i
$$514$$ 18.0000i 0.793946i
$$515$$ 28.0000i 1.23383i
$$516$$ −4.00000 −0.176090
$$517$$ 0 0
$$518$$ 2.00000i 0.0878750i
$$519$$ −6.00000 −0.263371
$$520$$ 4.00000 + 6.00000i 0.175412 + 0.263117i
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ 0 0
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 1.00000i 0.0436436i
$$526$$ 6.00000i 0.261612i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ −8.00000 −0.347498
$$531$$ 6.00000i 0.260378i
$$532$$ 4.00000 0.173422
$$533$$ 0 0
$$534$$ −4.00000 −0.173097
$$535$$ 24.0000i 1.03761i
$$536$$ −2.00000 −0.0863868
$$537$$ −20.0000 −0.863064
$$538$$ 10.0000i 0.431131i
$$539$$ 0 0
$$540$$ 2.00000i 0.0860663i
$$541$$ 30.0000i 1.28980i −0.764267 0.644900i $$-0.776899\pi$$
0.764267 0.644900i $$-0.223101\pi$$
$$542$$ 0 0
$$543$$ 12.0000 0.514969
$$544$$ 2.00000i 0.0857493i
$$545$$ 12.0000 0.514024
$$546$$ −2.00000 3.00000i −0.0855921 0.128388i
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 2.00000i 0.0854358i
$$549$$ 12.0000 0.512148
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 6.00000i 0.255377i
$$553$$ 0 0
$$554$$ 22.0000i 0.934690i
$$555$$ 4.00000 0.169791
$$556$$ −20.0000 −0.848189
$$557$$ 18.0000i 0.762684i 0.924434 + 0.381342i $$0.124538\pi$$
−0.924434 + 0.381342i $$0.875462\pi$$
$$558$$ 0 0
$$559$$ 8.00000 + 12.0000i 0.338364 + 0.507546i
$$560$$ −2.00000 −0.0845154
$$561$$ 0 0
$$562$$ −30.0000 −1.26547
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ 8.00000i 0.336861i
$$565$$ 28.0000i 1.17797i
$$566$$ 16.0000i 0.672530i
$$567$$ 1.00000i 0.0419961i
$$568$$ 0 0
$$569$$ 30.0000 1.25767 0.628833 0.777541i $$-0.283533\pi$$
0.628833 + 0.777541i $$0.283533\pi$$
$$570$$ 8.00000i 0.335083i
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ 0 0
$$573$$ 2.00000 0.0835512
$$574$$ 0 0
$$575$$ −6.00000 −0.250217
$$576$$ −1.00000 −0.0416667
$$577$$ 22.0000i 0.915872i −0.888985 0.457936i $$-0.848589\pi$$
0.888985 0.457936i $$-0.151411\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 4.00000i 0.166234i
$$580$$ 0 0
$$581$$ 14.0000 0.580818
$$582$$ 2.00000 0.0829027
$$583$$ 0 0
$$584$$ −14.0000 −0.579324
$$585$$ −6.00000 + 4.00000i −0.248069 + 0.165380i
$$586$$ −6.00000 −0.247858
$$587$$ 18.0000i 0.742940i 0.928445 + 0.371470i $$0.121146\pi$$
−0.928445 + 0.371470i $$0.878854\pi$$
$$588$$ 1.00000 0.0412393
$$589$$ 0 0
$$590$$ 12.0000i 0.494032i
$$591$$ 18.0000i 0.740421i
$$592$$ 2.00000i 0.0821995i
$$593$$ 24.0000i 0.985562i −0.870153 0.492781i $$-0.835980\pi$$
0.870153 0.492781i $$-0.164020\pi$$
$$594$$ 0 0
$$595$$ 4.00000 0.163984
$$596$$ 6.00000i 0.245770i
$$597$$ −10.0000 −0.409273
$$598$$ 18.0000 12.0000i 0.736075 0.490716i
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 1.00000i 0.0408248i
$$601$$ −18.0000 −0.734235 −0.367118 0.930175i $$-0.619655\pi$$
−0.367118 + 0.930175i $$0.619655\pi$$
$$602$$ −4.00000 −0.163028
$$603$$ 2.00000i 0.0814463i
$$604$$ 0 0
$$605$$ 22.0000i 0.894427i
$$606$$ 2.00000i 0.0812444i
$$607$$ 18.0000 0.730597 0.365299 0.930890i $$-0.380967\pi$$
0.365299 + 0.930890i $$0.380967\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ −24.0000 −0.971732
$$611$$ −24.0000 + 16.0000i −0.970936 + 0.647291i
$$612$$ 2.00000 0.0808452
$$613$$ 34.0000i 1.37325i −0.727013 0.686624i $$-0.759092\pi$$
0.727013 0.686624i $$-0.240908\pi$$
$$614$$ −28.0000 −1.12999
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000i 0.724653i 0.932051 + 0.362326i $$0.118017\pi$$
−0.932051 + 0.362326i $$0.881983\pi$$
$$618$$ 14.0000i 0.563163i
$$619$$ 16.0000i 0.643094i −0.946894 0.321547i $$-0.895797\pi$$
0.946894 0.321547i $$-0.104203\pi$$
$$620$$ 0 0
$$621$$ −6.00000 −0.240772
$$622$$ 12.0000i 0.481156i
$$623$$ −4.00000 −0.160257
$$624$$ 2.00000 + 3.00000i 0.0800641 + 0.120096i
$$625$$ −19.0000 −0.760000
$$626$$ 6.00000i 0.239808i
$$627$$ 0 0
$$628$$ −8.00000 −0.319235
$$629$$ 4.00000i 0.159490i
$$630$$ 2.00000i 0.0796819i
$$631$$ 20.0000i 0.796187i −0.917345 0.398094i $$-0.869672\pi$$
0.917345 0.398094i $$-0.130328\pi$$
$$632$$ 0 0
$$633$$ −28.0000 −1.11290
$$634$$ 2.00000 0.0794301
$$635$$ 24.0000i 0.952411i
$$636$$ −4.00000 −0.158610
$$637$$ −2.00000 3.00000i −0.0792429 0.118864i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 2.00000 0.0790569
$$641$$ 42.0000 1.65890 0.829450 0.558581i $$-0.188654\pi$$
0.829450 + 0.558581i $$0.188654\pi$$
$$642$$ 12.0000i 0.473602i
$$643$$ 44.0000i 1.73519i −0.497271 0.867595i $$-0.665665\pi$$
0.497271 0.867595i $$-0.334335\pi$$
$$644$$ 6.00000i 0.236433i
$$645$$ 8.00000i 0.315000i
$$646$$ 8.00000 0.314756
$$647$$ 28.0000 1.10079 0.550397 0.834903i $$-0.314476\pi$$
0.550397 + 0.834903i $$0.314476\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ 0 0
$$650$$ −3.00000 + 2.00000i −0.117670 + 0.0784465i
$$651$$ 0 0
$$652$$ 14.0000i 0.548282i
$$653$$ 4.00000 0.156532 0.0782660 0.996933i $$-0.475062\pi$$
0.0782660 + 0.996933i $$0.475062\pi$$
$$654$$ 6.00000 0.234619
$$655$$ 24.0000i 0.937758i
$$656$$ 0 0
$$657$$ 14.0000i 0.546192i
$$658$$ 8.00000i 0.311872i
$$659$$ 20.0000 0.779089 0.389545 0.921008i $$-0.372632\pi$$
0.389545 + 0.921008i $$0.372632\pi$$
$$660$$ 0 0
$$661$$ 10.0000i 0.388955i 0.980907 + 0.194477i $$0.0623011\pi$$
−0.980907 + 0.194477i $$0.937699\pi$$
$$662$$ 10.0000 0.388661
$$663$$ −4.00000 6.00000i −0.155347 0.233021i
$$664$$ −14.0000 −0.543305
$$665$$ 8.00000i 0.310227i
$$666$$ 2.00000 0.0774984
$$667$$ 0 0
$$668$$ 12.0000i 0.464294i
$$669$$ 16.0000i 0.618596i
$$670$$ 4.00000i 0.154533i
$$671$$ 0 0
$$672$$ −1.00000 −0.0385758
$$673$$ −46.0000 −1.77317 −0.886585 0.462566i $$-0.846929\pi$$
−0.886585 + 0.462566i $$0.846929\pi$$
$$674$$ 22.0000i 0.847408i
$$675$$ 1.00000 0.0384900
$$676$$ 5.00000 12.0000i 0.192308 0.461538i
$$677$$ −22.0000 −0.845529 −0.422764 0.906240i $$-0.638940\pi$$
−0.422764 + 0.906240i $$0.638940\pi$$
$$678$$ 14.0000i 0.537667i
$$679$$ 2.00000 0.0767530
$$680$$ −4.00000 −0.153393
$$681$$ 22.0000i 0.843042i
$$682$$ 0 0
$$683$$ 16.0000i 0.612223i 0.951996 + 0.306111i $$0.0990280\pi$$
−0.951996 + 0.306111i $$0.900972\pi$$
$$684$$ 4.00000i 0.152944i
$$685$$ 4.00000 0.152832
$$686$$ 1.00000 0.0381802
$$687$$ 14.0000i 0.534133i
$$688$$ 4.00000 0.152499
$$689$$ 8.00000 + 12.0000i 0.304776 + 0.457164i
$$690$$ 12.0000 0.456832
$$691$$ 40.0000i 1.52167i −0.648944 0.760836i $$-0.724789\pi$$
0.648944 0.760836i $$-0.275211\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ 32.0000i 1.21470i
$$695$$ 40.0000i 1.51729i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −14.0000 −0.529908
$$699$$ −6.00000 −0.226941
$$700$$ 1.00000i 0.0377964i
$$701$$ −48.0000 −1.81293 −0.906467 0.422276i $$-0.861231\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ −3.00000 + 2.00000i −0.113228 + 0.0754851i
$$703$$ 8.00000 0.301726
$$704$$ 0 0
$$705$$ −16.0000 −0.602595
$$706$$ 24.0000 0.903252
$$707$$ 2.00000i 0.0752177i
$$708$$ 6.00000i 0.225494i
$$709$$ 46.0000i 1.72757i −0.503864 0.863783i $$-0.668089\pi$$
0.503864 0.863783i $$-0.331911\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 4.00000 0.149906
$$713$$ 0 0
$$714$$ 2.00000 0.0748481
$$715$$ 0 0
$$716$$ 20.0000 0.747435
$$717$$ 16.0000i 0.597531i
$$718$$ −24.0000 −0.895672
$$719$$ 20.0000 0.745874 0.372937 0.927857i $$-0.378351\pi$$
0.372937 + 0.927857i $$0.378351\pi$$
$$720$$ 2.00000i 0.0745356i
$$721$$ 14.0000i 0.521387i
$$722$$ 3.00000i 0.111648i
$$723$$ 10.0000i 0.371904i
$$724$$ −12.0000 −0.445976
$$725$$ 0 0
$$726$$ 11.0000i 0.408248i
$$727$$ 38.0000 1.40934 0.704671 0.709534i $$-0.251095\pi$$
0.704671 + 0.709534i $$0.251095\pi$$
$$728$$ 2.00000 + 3.00000i 0.0741249 + 0.111187i
$$729$$ 1.00000 0.0370370
$$730$$ 28.0000i 1.03633i
$$731$$ −8.00000 −0.295891
$$732$$ −12.0000 −0.443533
$$733$$ 14.0000i 0.517102i −0.965998 0.258551i $$-0.916755\pi$$
0.965998 0.258551i $$-0.0832450\pi$$
$$734$$ 22.0000i 0.812035i
$$735$$ 2.00000i 0.0737711i
$$736$$ 6.00000i 0.221163i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 34.0000i 1.25071i 0.780340 + 0.625355i $$0.215046\pi$$
−0.780340 + 0.625355i $$0.784954\pi$$
$$740$$ −4.00000 −0.147043
$$741$$ −12.0000 + 8.00000i −0.440831 + 0.293887i
$$742$$ −4.00000 −0.146845
$$743$$ 16.0000i 0.586983i 0.955962 + 0.293492i $$0.0948173\pi$$
−0.955962 + 0.293492i $$0.905183\pi$$
$$744$$ 0 0
$$745$$ 12.0000 0.439646
$$746$$ 34.0000i 1.24483i
$$747$$ 14.0000i 0.512233i
$$748$$ 0 0
$$749$$ 12.0000i 0.438470i
$$750$$ −12.0000 −0.438178
$$751$$ 12.0000 0.437886 0.218943 0.975738i $$-0.429739\pi$$
0.218943 + 0.975738i $$0.429739\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ −28.0000 −1.02038
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 1.00000i 0.0363696i
$$757$$ −42.0000 −1.52652 −0.763258 0.646094i $$-0.776401\pi$$
−0.763258 + 0.646094i $$0.776401\pi$$
$$758$$ 26.0000 0.944363
$$759$$ 0 0
$$760$$ 8.00000i 0.290191i
$$761$$ 40.0000i 1.45000i 0.688749 + 0.724999i $$0.258160\pi$$
−0.688749 + 0.724999i $$0.741840\pi$$
$$762$$ 12.0000i 0.434714i
$$763$$ 6.00000 0.217215
$$764$$ −2.00000 −0.0723575
$$765$$ 4.00000i 0.144620i
$$766$$ 24.0000 0.867155
$$767$$ 18.0000 12.0000i 0.649942 0.433295i
$$768$$ 1.00000 0.0360844
$$769$$ 26.0000i 0.937584i −0.883309 0.468792i $$-0.844689\pi$$
0.883309 0.468792i $$-0.155311\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 4.00000i 0.143963i
$$773$$ 26.0000i 0.935155i 0.883952 + 0.467578i $$0.154873\pi$$
−0.883952 + 0.467578i $$0.845127\pi$$
$$774$$ 4.00000i 0.143777i
$$775$$ 0 0
$$776$$ −2.00000 −0.0717958
$$777$$ 2.00000 0.0717496
$$778$$ 20.0000i 0.717035i
$$779$$ 0 0
$$780$$ 6.00000 4.00000i 0.214834 0.143223i
$$781$$ 0 0
$$782$$ 12.0000i 0.429119i
$$783$$ 0 0
$$784$$ −1.00000 −0.0357143
$$785$$ 16.0000i 0.571064i
$$786$$ 12.0000i 0.428026i
$$787$$ 48.0000i 1.71102i 0.517790 + 0.855508i $$0.326755\pi$$
−0.517790 + 0.855508i $$0.673245\pi$$
$$788$$ 18.0000i 0.641223i
$$789$$ −6.00000 −0.213606
$$790$$ 0 0
$$791$$ 14.0000i 0.497783i
$$792$$ 0 0
$$793$$ 24.0000 + 36.0000i 0.852265 + 1.27840i
$$794$$ −18.0000 −0.638796
$$795$$ 8.00000i 0.283731i