# Properties

 Label 1050.2.d.b.1049.2 Level $1050$ Weight $2$ Character 1050.1049 Analytic conductor $8.384$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1050.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.38429221223$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1049.2 Root $$-1.22474 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.1049 Dual form 1050.2.d.b.1049.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +(-1.22474 + 1.22474i) q^{3} +1.00000 q^{4} +(1.22474 - 1.22474i) q^{6} +(-2.44949 + 1.00000i) q^{7} -1.00000 q^{8} -3.00000i q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +(-1.22474 + 1.22474i) q^{3} +1.00000 q^{4} +(1.22474 - 1.22474i) q^{6} +(-2.44949 + 1.00000i) q^{7} -1.00000 q^{8} -3.00000i q^{9} +(-1.22474 + 1.22474i) q^{12} -2.44949 q^{13} +(2.44949 - 1.00000i) q^{14} +1.00000 q^{16} -4.89898i q^{17} +3.00000i q^{18} +2.44949i q^{19} +(1.77526 - 4.22474i) q^{21} +6.00000 q^{23} +(1.22474 - 1.22474i) q^{24} +2.44949 q^{26} +(3.67423 + 3.67423i) q^{27} +(-2.44949 + 1.00000i) q^{28} -6.00000i q^{29} -1.00000 q^{32} +4.89898i q^{34} -3.00000i q^{36} +2.00000i q^{37} -2.44949i q^{38} +(3.00000 - 3.00000i) q^{39} -4.89898 q^{41} +(-1.77526 + 4.22474i) q^{42} +4.00000i q^{43} -6.00000 q^{46} -4.89898i q^{47} +(-1.22474 + 1.22474i) q^{48} +(5.00000 - 4.89898i) q^{49} +(6.00000 + 6.00000i) q^{51} -2.44949 q^{52} +6.00000 q^{53} +(-3.67423 - 3.67423i) q^{54} +(2.44949 - 1.00000i) q^{56} +(-3.00000 - 3.00000i) q^{57} +6.00000i q^{58} +12.2474 q^{59} +12.2474i q^{61} +(3.00000 + 7.34847i) q^{63} +1.00000 q^{64} -8.00000i q^{67} -4.89898i q^{68} +(-7.34847 + 7.34847i) q^{69} +3.00000i q^{72} +9.79796 q^{73} -2.00000i q^{74} +2.44949i q^{76} +(-3.00000 + 3.00000i) q^{78} +10.0000 q^{79} -9.00000 q^{81} +4.89898 q^{82} +2.44949i q^{83} +(1.77526 - 4.22474i) q^{84} -4.00000i q^{86} +(7.34847 + 7.34847i) q^{87} +(6.00000 - 2.44949i) q^{91} +6.00000 q^{92} +4.89898i q^{94} +(1.22474 - 1.22474i) q^{96} -4.89898 q^{97} +(-5.00000 + 4.89898i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{2} + 4q^{4} - 4q^{8} + O(q^{10})$$ $$4q - 4q^{2} + 4q^{4} - 4q^{8} + 4q^{16} + 12q^{21} + 24q^{23} - 4q^{32} + 12q^{39} - 12q^{42} - 24q^{46} + 20q^{49} + 24q^{51} + 24q^{53} - 12q^{57} + 12q^{63} + 4q^{64} - 12q^{78} + 40q^{79} - 36q^{81} + 12q^{84} + 24q^{91} + 24q^{92} - 20q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ −1.22474 + 1.22474i −0.707107 + 0.707107i
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 1.22474 1.22474i 0.500000 0.500000i
$$7$$ −2.44949 + 1.00000i −0.925820 + 0.377964i
$$8$$ −1.00000 −0.353553
$$9$$ 3.00000i 1.00000i
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ −1.22474 + 1.22474i −0.353553 + 0.353553i
$$13$$ −2.44949 −0.679366 −0.339683 0.940540i $$-0.610320\pi$$
−0.339683 + 0.940540i $$0.610320\pi$$
$$14$$ 2.44949 1.00000i 0.654654 0.267261i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.89898i 1.18818i −0.804400 0.594089i $$-0.797513\pi$$
0.804400 0.594089i $$-0.202487\pi$$
$$18$$ 3.00000i 0.707107i
$$19$$ 2.44949i 0.561951i 0.959715 + 0.280976i $$0.0906580\pi$$
−0.959715 + 0.280976i $$0.909342\pi$$
$$20$$ 0 0
$$21$$ 1.77526 4.22474i 0.387392 0.921915i
$$22$$ 0 0
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 1.22474 1.22474i 0.250000 0.250000i
$$25$$ 0 0
$$26$$ 2.44949 0.480384
$$27$$ 3.67423 + 3.67423i 0.707107 + 0.707107i
$$28$$ −2.44949 + 1.00000i −0.462910 + 0.188982i
$$29$$ 6.00000i 1.11417i −0.830455 0.557086i $$-0.811919\pi$$
0.830455 0.557086i $$-0.188081\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 4.89898i 0.840168i
$$35$$ 0 0
$$36$$ 3.00000i 0.500000i
$$37$$ 2.00000i 0.328798i 0.986394 + 0.164399i $$0.0525685\pi$$
−0.986394 + 0.164399i $$0.947432\pi$$
$$38$$ 2.44949i 0.397360i
$$39$$ 3.00000 3.00000i 0.480384 0.480384i
$$40$$ 0 0
$$41$$ −4.89898 −0.765092 −0.382546 0.923936i $$-0.624953\pi$$
−0.382546 + 0.923936i $$0.624953\pi$$
$$42$$ −1.77526 + 4.22474i −0.273928 + 0.651892i
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 4.89898i 0.714590i −0.933992 0.357295i $$-0.883699\pi$$
0.933992 0.357295i $$-0.116301\pi$$
$$48$$ −1.22474 + 1.22474i −0.176777 + 0.176777i
$$49$$ 5.00000 4.89898i 0.714286 0.699854i
$$50$$ 0 0
$$51$$ 6.00000 + 6.00000i 0.840168 + 0.840168i
$$52$$ −2.44949 −0.339683
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ −3.67423 3.67423i −0.500000 0.500000i
$$55$$ 0 0
$$56$$ 2.44949 1.00000i 0.327327 0.133631i
$$57$$ −3.00000 3.00000i −0.397360 0.397360i
$$58$$ 6.00000i 0.787839i
$$59$$ 12.2474 1.59448 0.797241 0.603661i $$-0.206292\pi$$
0.797241 + 0.603661i $$0.206292\pi$$
$$60$$ 0 0
$$61$$ 12.2474i 1.56813i 0.620682 + 0.784063i $$0.286856\pi$$
−0.620682 + 0.784063i $$0.713144\pi$$
$$62$$ 0 0
$$63$$ 3.00000 + 7.34847i 0.377964 + 0.925820i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 4.89898i 0.594089i
$$69$$ −7.34847 + 7.34847i −0.884652 + 0.884652i
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 3.00000i 0.353553i
$$73$$ 9.79796 1.14676 0.573382 0.819288i $$-0.305631\pi$$
0.573382 + 0.819288i $$0.305631\pi$$
$$74$$ 2.00000i 0.232495i
$$75$$ 0 0
$$76$$ 2.44949i 0.280976i
$$77$$ 0 0
$$78$$ −3.00000 + 3.00000i −0.339683 + 0.339683i
$$79$$ 10.0000 1.12509 0.562544 0.826767i $$-0.309823\pi$$
0.562544 + 0.826767i $$0.309823\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 4.89898 0.541002
$$83$$ 2.44949i 0.268866i 0.990923 + 0.134433i $$0.0429214\pi$$
−0.990923 + 0.134433i $$0.957079\pi$$
$$84$$ 1.77526 4.22474i 0.193696 0.460957i
$$85$$ 0 0
$$86$$ 4.00000i 0.431331i
$$87$$ 7.34847 + 7.34847i 0.787839 + 0.787839i
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 6.00000 2.44949i 0.628971 0.256776i
$$92$$ 6.00000 0.625543
$$93$$ 0 0
$$94$$ 4.89898i 0.505291i
$$95$$ 0 0
$$96$$ 1.22474 1.22474i 0.125000 0.125000i
$$97$$ −4.89898 −0.497416 −0.248708 0.968579i $$-0.580006\pi$$
−0.248708 + 0.968579i $$0.580006\pi$$
$$98$$ −5.00000 + 4.89898i −0.505076 + 0.494872i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 7.34847 0.731200 0.365600 0.930772i $$-0.380864\pi$$
0.365600 + 0.930772i $$0.380864\pi$$
$$102$$ −6.00000 6.00000i −0.594089 0.594089i
$$103$$ 9.79796 0.965422 0.482711 0.875780i $$-0.339652\pi$$
0.482711 + 0.875780i $$0.339652\pi$$
$$104$$ 2.44949 0.240192
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 3.67423 + 3.67423i 0.353553 + 0.353553i
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 0 0
$$111$$ −2.44949 2.44949i −0.232495 0.232495i
$$112$$ −2.44949 + 1.00000i −0.231455 + 0.0944911i
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 3.00000 + 3.00000i 0.280976 + 0.280976i
$$115$$ 0 0
$$116$$ 6.00000i 0.557086i
$$117$$ 7.34847i 0.679366i
$$118$$ −12.2474 −1.12747
$$119$$ 4.89898 + 12.0000i 0.449089 + 1.10004i
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 12.2474i 1.10883i
$$123$$ 6.00000 6.00000i 0.541002 0.541002i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ −3.00000 7.34847i −0.267261 0.654654i
$$127$$ 8.00000i 0.709885i −0.934888 0.354943i $$-0.884500\pi$$
0.934888 0.354943i $$-0.115500\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −4.89898 4.89898i −0.431331 0.431331i
$$130$$ 0 0
$$131$$ 7.34847 0.642039 0.321019 0.947073i $$-0.395975\pi$$
0.321019 + 0.947073i $$0.395975\pi$$
$$132$$ 0 0
$$133$$ −2.44949 6.00000i −0.212398 0.520266i
$$134$$ 8.00000i 0.691095i
$$135$$ 0 0
$$136$$ 4.89898i 0.420084i
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ 7.34847 7.34847i 0.625543 0.625543i
$$139$$ 2.44949i 0.207763i 0.994590 + 0.103882i $$0.0331263\pi$$
−0.994590 + 0.103882i $$0.966874\pi$$
$$140$$ 0 0
$$141$$ 6.00000 + 6.00000i 0.505291 + 0.505291i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 3.00000i 0.250000i
$$145$$ 0 0
$$146$$ −9.79796 −0.810885
$$147$$ −0.123724 + 12.1237i −0.0102046 + 0.999948i
$$148$$ 2.00000i 0.164399i
$$149$$ 6.00000i 0.491539i −0.969328 0.245770i $$-0.920959\pi$$
0.969328 0.245770i $$-0.0790407\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 2.44949i 0.198680i
$$153$$ −14.6969 −1.18818
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 3.00000 3.00000i 0.240192 0.240192i
$$157$$ 7.34847 0.586472 0.293236 0.956040i $$-0.405268\pi$$
0.293236 + 0.956040i $$0.405268\pi$$
$$158$$ −10.0000 −0.795557
$$159$$ −7.34847 + 7.34847i −0.582772 + 0.582772i
$$160$$ 0 0
$$161$$ −14.6969 + 6.00000i −1.15828 + 0.472866i
$$162$$ 9.00000 0.707107
$$163$$ 16.0000i 1.25322i −0.779334 0.626608i $$-0.784443\pi$$
0.779334 0.626608i $$-0.215557\pi$$
$$164$$ −4.89898 −0.382546
$$165$$ 0 0
$$166$$ 2.44949i 0.190117i
$$167$$ 4.89898i 0.379094i −0.981872 0.189547i $$-0.939298\pi$$
0.981872 0.189547i $$-0.0607020\pi$$
$$168$$ −1.77526 + 4.22474i −0.136964 + 0.325946i
$$169$$ −7.00000 −0.538462
$$170$$ 0 0
$$171$$ 7.34847 0.561951
$$172$$ 4.00000i 0.304997i
$$173$$ 22.0454i 1.67608i −0.545608 0.838041i $$-0.683701\pi$$
0.545608 0.838041i $$-0.316299\pi$$
$$174$$ −7.34847 7.34847i −0.557086 0.557086i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −15.0000 + 15.0000i −1.12747 + 1.12747i
$$178$$ 0 0
$$179$$ 24.0000i 1.79384i 0.442189 + 0.896922i $$0.354202\pi$$
−0.442189 + 0.896922i $$0.645798\pi$$
$$180$$ 0 0
$$181$$ 12.2474i 0.910346i −0.890403 0.455173i $$-0.849577\pi$$
0.890403 0.455173i $$-0.150423\pi$$
$$182$$ −6.00000 + 2.44949i −0.444750 + 0.181568i
$$183$$ −15.0000 15.0000i −1.10883 1.10883i
$$184$$ −6.00000 −0.442326
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 4.89898i 0.357295i
$$189$$ −12.6742 5.32577i −0.921915 0.387392i
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ −1.22474 + 1.22474i −0.0883883 + 0.0883883i
$$193$$ 4.00000i 0.287926i 0.989583 + 0.143963i $$0.0459847\pi$$
−0.989583 + 0.143963i $$0.954015\pi$$
$$194$$ 4.89898 0.351726
$$195$$ 0 0
$$196$$ 5.00000 4.89898i 0.357143 0.349927i
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 9.79796i 0.694559i −0.937762 0.347279i $$-0.887106\pi$$
0.937762 0.347279i $$-0.112894\pi$$
$$200$$ 0 0
$$201$$ 9.79796 + 9.79796i 0.691095 + 0.691095i
$$202$$ −7.34847 −0.517036
$$203$$ 6.00000 + 14.6969i 0.421117 + 1.03152i
$$204$$ 6.00000 + 6.00000i 0.420084 + 0.420084i
$$205$$ 0 0
$$206$$ −9.79796 −0.682656
$$207$$ 18.0000i 1.25109i
$$208$$ −2.44949 −0.169842
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ 6.00000 0.412082
$$213$$ 0 0
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ −3.67423 3.67423i −0.250000 0.250000i
$$217$$ 0 0
$$218$$ 10.0000 0.677285
$$219$$ −12.0000 + 12.0000i −0.810885 + 0.810885i
$$220$$ 0 0
$$221$$ 12.0000i 0.807207i
$$222$$ 2.44949 + 2.44949i 0.164399 + 0.164399i
$$223$$ −14.6969 −0.984180 −0.492090 0.870544i $$-0.663767\pi$$
−0.492090 + 0.870544i $$0.663767\pi$$
$$224$$ 2.44949 1.00000i 0.163663 0.0668153i
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ 7.34847i 0.487735i 0.969809 + 0.243868i $$0.0784162\pi$$
−0.969809 + 0.243868i $$0.921584\pi$$
$$228$$ −3.00000 3.00000i −0.198680 0.198680i
$$229$$ 22.0454i 1.45680i −0.685151 0.728401i $$-0.740264\pi$$
0.685151 0.728401i $$-0.259736\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 6.00000i 0.393919i
$$233$$ −24.0000 −1.57229 −0.786146 0.618041i $$-0.787927\pi$$
−0.786146 + 0.618041i $$0.787927\pi$$
$$234$$ 7.34847i 0.480384i
$$235$$ 0 0
$$236$$ 12.2474 0.797241
$$237$$ −12.2474 + 12.2474i −0.795557 + 0.795557i
$$238$$ −4.89898 12.0000i −0.317554 0.777844i
$$239$$ 6.00000i 0.388108i −0.980991 0.194054i $$-0.937836\pi$$
0.980991 0.194054i $$-0.0621637\pi$$
$$240$$ 0 0
$$241$$ 24.4949i 1.57786i −0.614486 0.788928i $$-0.710637\pi$$
0.614486 0.788928i $$-0.289363\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ 11.0227 11.0227i 0.707107 0.707107i
$$244$$ 12.2474i 0.784063i
$$245$$ 0 0
$$246$$ −6.00000 + 6.00000i −0.382546 + 0.382546i
$$247$$ 6.00000i 0.381771i
$$248$$ 0 0
$$249$$ −3.00000 3.00000i −0.190117 0.190117i
$$250$$ 0 0
$$251$$ −17.1464 −1.08227 −0.541136 0.840935i $$-0.682006\pi$$
−0.541136 + 0.840935i $$0.682006\pi$$
$$252$$ 3.00000 + 7.34847i 0.188982 + 0.462910i
$$253$$ 0 0
$$254$$ 8.00000i 0.501965i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 29.3939i 1.83354i −0.399416 0.916770i $$-0.630787\pi$$
0.399416 0.916770i $$-0.369213\pi$$
$$258$$ 4.89898 + 4.89898i 0.304997 + 0.304997i
$$259$$ −2.00000 4.89898i −0.124274 0.304408i
$$260$$ 0 0
$$261$$ −18.0000 −1.11417
$$262$$ −7.34847 −0.453990
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 2.44949 + 6.00000i 0.150188 + 0.367884i
$$267$$ 0 0
$$268$$ 8.00000i 0.488678i
$$269$$ 12.2474 0.746740 0.373370 0.927682i $$-0.378202\pi$$
0.373370 + 0.927682i $$0.378202\pi$$
$$270$$ 0 0
$$271$$ 24.4949i 1.48796i 0.668202 + 0.743980i $$0.267064\pi$$
−0.668202 + 0.743980i $$0.732936\pi$$
$$272$$ 4.89898i 0.297044i
$$273$$ −4.34847 + 10.3485i −0.263181 + 0.626318i
$$274$$ −12.0000 −0.724947
$$275$$ 0 0
$$276$$ −7.34847 + 7.34847i −0.442326 + 0.442326i
$$277$$ 22.0000i 1.32185i 0.750451 + 0.660926i $$0.229836\pi$$
−0.750451 + 0.660926i $$0.770164\pi$$
$$278$$ 2.44949i 0.146911i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ −6.00000 6.00000i −0.357295 0.357295i
$$283$$ 22.0454 1.31046 0.655232 0.755428i $$-0.272571\pi$$
0.655232 + 0.755428i $$0.272571\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 12.0000 4.89898i 0.708338 0.289178i
$$288$$ 3.00000i 0.176777i
$$289$$ −7.00000 −0.411765
$$290$$ 0 0
$$291$$ 6.00000 6.00000i 0.351726 0.351726i
$$292$$ 9.79796 0.573382
$$293$$ 2.44949i 0.143101i 0.997437 + 0.0715504i $$0.0227947\pi$$
−0.997437 + 0.0715504i $$0.977205\pi$$
$$294$$ 0.123724 12.1237i 0.00721575 0.707070i
$$295$$ 0 0
$$296$$ 2.00000i 0.116248i
$$297$$ 0 0
$$298$$ 6.00000i 0.347571i
$$299$$ −14.6969 −0.849946
$$300$$ 0 0
$$301$$ −4.00000 9.79796i −0.230556 0.564745i
$$302$$ 8.00000 0.460348
$$303$$ −9.00000 + 9.00000i −0.517036 + 0.517036i
$$304$$ 2.44949i 0.140488i
$$305$$ 0 0
$$306$$ 14.6969 0.840168
$$307$$ 7.34847 0.419399 0.209700 0.977766i $$-0.432751\pi$$
0.209700 + 0.977766i $$0.432751\pi$$
$$308$$ 0 0
$$309$$ −12.0000 + 12.0000i −0.682656 + 0.682656i
$$310$$ 0 0
$$311$$ 19.5959 1.11118 0.555591 0.831456i $$-0.312492\pi$$
0.555591 + 0.831456i $$0.312492\pi$$
$$312$$ −3.00000 + 3.00000i −0.169842 + 0.169842i
$$313$$ 34.2929 1.93835 0.969173 0.246380i $$-0.0792410\pi$$
0.969173 + 0.246380i $$0.0792410\pi$$
$$314$$ −7.34847 −0.414698
$$315$$ 0 0
$$316$$ 10.0000 0.562544
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 7.34847 7.34847i 0.412082 0.412082i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −14.6969 + 14.6969i −0.820303 + 0.820303i
$$322$$ 14.6969 6.00000i 0.819028 0.334367i
$$323$$ 12.0000 0.667698
$$324$$ −9.00000 −0.500000
$$325$$ 0 0
$$326$$ 16.0000i 0.886158i
$$327$$ 12.2474 12.2474i 0.677285 0.677285i
$$328$$ 4.89898 0.270501
$$329$$ 4.89898 + 12.0000i 0.270089 + 0.661581i
$$330$$ 0 0
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ 2.44949i 0.134433i
$$333$$ 6.00000 0.328798
$$334$$ 4.89898i 0.268060i
$$335$$ 0 0
$$336$$ 1.77526 4.22474i 0.0968481 0.230479i
$$337$$ 32.0000i 1.74315i 0.490261 + 0.871576i $$0.336901\pi$$
−0.490261 + 0.871576i $$0.663099\pi$$
$$338$$ 7.00000 0.380750
$$339$$ −7.34847 + 7.34847i −0.399114 + 0.399114i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −7.34847 −0.397360
$$343$$ −7.34847 + 17.0000i −0.396780 + 0.917914i
$$344$$ 4.00000i 0.215666i
$$345$$ 0 0
$$346$$ 22.0454i 1.18517i
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ 7.34847 + 7.34847i 0.393919 + 0.393919i
$$349$$ 2.44949i 0.131118i 0.997849 + 0.0655591i $$0.0208831\pi$$
−0.997849 + 0.0655591i $$0.979117\pi$$
$$350$$ 0 0
$$351$$ −9.00000 9.00000i −0.480384 0.480384i
$$352$$ 0 0
$$353$$ 9.79796i 0.521493i −0.965407 0.260746i $$-0.916031\pi$$
0.965407 0.260746i $$-0.0839686\pi$$
$$354$$ 15.0000 15.0000i 0.797241 0.797241i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −20.6969 8.69694i −1.09540 0.460291i
$$358$$ 24.0000i 1.26844i
$$359$$ 6.00000i 0.316668i −0.987386 0.158334i $$-0.949388\pi$$
0.987386 0.158334i $$-0.0506123\pi$$
$$360$$ 0 0
$$361$$ 13.0000 0.684211
$$362$$ 12.2474i 0.643712i
$$363$$ −13.4722 + 13.4722i −0.707107 + 0.707107i
$$364$$ 6.00000 2.44949i 0.314485 0.128388i
$$365$$ 0 0
$$366$$ 15.0000 + 15.0000i 0.784063 + 0.784063i
$$367$$ −4.89898 −0.255725 −0.127862 0.991792i $$-0.540812\pi$$
−0.127862 + 0.991792i $$0.540812\pi$$
$$368$$ 6.00000 0.312772
$$369$$ 14.6969i 0.765092i
$$370$$ 0 0
$$371$$ −14.6969 + 6.00000i −0.763027 + 0.311504i
$$372$$ 0 0
$$373$$ 14.0000i 0.724893i 0.932005 + 0.362446i $$0.118058\pi$$
−0.932005 + 0.362446i $$0.881942\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 4.89898i 0.252646i
$$377$$ 14.6969i 0.756931i
$$378$$ 12.6742 + 5.32577i 0.651892 + 0.273928i
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ 9.79796 + 9.79796i 0.501965 + 0.501965i
$$382$$ 0 0
$$383$$ 34.2929i 1.75228i −0.482054 0.876142i $$-0.660109\pi$$
0.482054 0.876142i $$-0.339891\pi$$
$$384$$ 1.22474 1.22474i 0.0625000 0.0625000i
$$385$$ 0 0
$$386$$ 4.00000i 0.203595i
$$387$$ 12.0000 0.609994
$$388$$ −4.89898 −0.248708
$$389$$ 6.00000i 0.304212i −0.988364 0.152106i $$-0.951394\pi$$
0.988364 0.152106i $$-0.0486055\pi$$
$$390$$ 0 0
$$391$$ 29.3939i 1.48651i
$$392$$ −5.00000 + 4.89898i −0.252538 + 0.247436i
$$393$$ −9.00000 + 9.00000i −0.453990 + 0.453990i
$$394$$ 18.0000 0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 7.34847 0.368809 0.184405 0.982850i $$-0.440964\pi$$
0.184405 + 0.982850i $$0.440964\pi$$
$$398$$ 9.79796i 0.491127i
$$399$$ 10.3485 + 4.34847i 0.518071 + 0.217696i
$$400$$ 0 0
$$401$$ 30.0000i 1.49813i −0.662497 0.749064i $$-0.730503\pi$$
0.662497 0.749064i $$-0.269497\pi$$
$$402$$ −9.79796 9.79796i −0.488678 0.488678i
$$403$$ 0 0
$$404$$ 7.34847 0.365600
$$405$$ 0 0
$$406$$ −6.00000 14.6969i −0.297775 0.729397i
$$407$$ 0 0
$$408$$ −6.00000 6.00000i −0.297044 0.297044i
$$409$$ 34.2929i 1.69567i −0.530258 0.847836i $$-0.677905\pi$$
0.530258 0.847836i $$-0.322095\pi$$
$$410$$ 0 0
$$411$$ −14.6969 + 14.6969i −0.724947 + 0.724947i
$$412$$ 9.79796 0.482711
$$413$$ −30.0000 + 12.2474i −1.47620 + 0.602658i
$$414$$ 18.0000i 0.884652i
$$415$$ 0 0
$$416$$ 2.44949 0.120096
$$417$$ −3.00000 3.00000i −0.146911 0.146911i
$$418$$ 0 0
$$419$$ −12.2474 −0.598327 −0.299164 0.954202i $$-0.596708\pi$$
−0.299164 + 0.954202i $$0.596708\pi$$
$$420$$ 0 0
$$421$$ 2.00000 0.0974740 0.0487370 0.998812i $$-0.484480\pi$$
0.0487370 + 0.998812i $$0.484480\pi$$
$$422$$ 8.00000 0.389434
$$423$$ −14.6969 −0.714590
$$424$$ −6.00000 −0.291386
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −12.2474 30.0000i −0.592696 1.45180i
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 30.0000i 1.44505i −0.691345 0.722525i $$-0.742982\pi$$
0.691345 0.722525i $$-0.257018\pi$$
$$432$$ 3.67423 + 3.67423i 0.176777 + 0.176777i
$$433$$ −14.6969 −0.706290 −0.353145 0.935569i $$-0.614888\pi$$
−0.353145 + 0.935569i $$0.614888\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −10.0000 −0.478913
$$437$$ 14.6969i 0.703050i
$$438$$ 12.0000 12.0000i 0.573382 0.573382i
$$439$$ 14.6969i 0.701447i 0.936479 + 0.350723i $$0.114064\pi$$
−0.936479 + 0.350723i $$0.885936\pi$$
$$440$$ 0 0
$$441$$ −14.6969 15.0000i −0.699854 0.714286i
$$442$$ 12.0000i 0.570782i
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ −2.44949 2.44949i −0.116248 0.116248i
$$445$$ 0 0
$$446$$ 14.6969 0.695920
$$447$$ 7.34847 + 7.34847i 0.347571 + 0.347571i
$$448$$ −2.44949 + 1.00000i −0.115728 + 0.0472456i
$$449$$ 36.0000i 1.69895i −0.527633 0.849473i $$-0.676920\pi$$
0.527633 0.849473i $$-0.323080\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 6.00000 0.282216
$$453$$ 9.79796 9.79796i 0.460348 0.460348i
$$454$$ 7.34847i 0.344881i
$$455$$ 0 0
$$456$$ 3.00000 + 3.00000i 0.140488 + 0.140488i
$$457$$ 28.0000i 1.30978i −0.755722 0.654892i $$-0.772714\pi$$
0.755722 0.654892i $$-0.227286\pi$$
$$458$$ 22.0454i 1.03011i
$$459$$ 18.0000 18.0000i 0.840168 0.840168i
$$460$$ 0 0
$$461$$ 31.8434 1.48309 0.741547 0.670901i $$-0.234093\pi$$
0.741547 + 0.670901i $$0.234093\pi$$
$$462$$ 0 0
$$463$$ 14.0000i 0.650635i 0.945605 + 0.325318i $$0.105471\pi$$
−0.945605 + 0.325318i $$0.894529\pi$$
$$464$$ 6.00000i 0.278543i
$$465$$ 0 0
$$466$$ 24.0000 1.11178
$$467$$ 7.34847i 0.340047i 0.985440 + 0.170023i $$0.0543843\pi$$
−0.985440 + 0.170023i $$0.945616\pi$$
$$468$$ 7.34847i 0.339683i
$$469$$ 8.00000 + 19.5959i 0.369406 + 0.904855i
$$470$$ 0 0
$$471$$ −9.00000 + 9.00000i −0.414698 + 0.414698i
$$472$$ −12.2474 −0.563735
$$473$$ 0 0
$$474$$ 12.2474 12.2474i 0.562544 0.562544i
$$475$$ 0 0
$$476$$ 4.89898 + 12.0000i 0.224544 + 0.550019i
$$477$$ 18.0000i 0.824163i
$$478$$ 6.00000i 0.274434i
$$479$$ −24.4949 −1.11920 −0.559600 0.828763i $$-0.689045\pi$$
−0.559600 + 0.828763i $$0.689045\pi$$
$$480$$ 0 0
$$481$$ 4.89898i 0.223374i
$$482$$ 24.4949i 1.11571i
$$483$$ 10.6515 25.3485i 0.484661 1.15340i
$$484$$ 11.0000 0.500000
$$485$$ 0 0
$$486$$ −11.0227 + 11.0227i −0.500000 + 0.500000i
$$487$$ 32.0000i 1.45006i 0.688718 + 0.725029i $$0.258174\pi$$
−0.688718 + 0.725029i $$0.741826\pi$$
$$488$$ 12.2474i 0.554416i
$$489$$ 19.5959 + 19.5959i 0.886158 + 0.886158i
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 6.00000 6.00000i 0.270501 0.270501i
$$493$$ −29.3939 −1.32383
$$494$$ 6.00000i 0.269953i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 3.00000 + 3.00000i 0.134433 + 0.134433i
$$499$$ 20.0000 0.895323 0.447661 0.894203i $$-0.352257\pi$$
0.447661 + 0.894203i $$0.352257\pi$$
$$500$$ 0 0
$$501$$ 6.00000 + 6.00000i 0.268060 + 0.268060i
$$502$$ 17.1464 0.765283
$$503$$ 39.1918i 1.74748i 0.486395 + 0.873739i $$0.338311\pi$$
−0.486395 + 0.873739i $$0.661689\pi$$
$$504$$ −3.00000 7.34847i −0.133631 0.327327i
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 8.57321 8.57321i 0.380750 0.380750i
$$508$$ 8.00000i 0.354943i
$$509$$ 12.2474 0.542859 0.271429 0.962458i $$-0.412504\pi$$
0.271429 + 0.962458i $$0.412504\pi$$
$$510$$ 0 0
$$511$$ −24.0000 + 9.79796i −1.06170 + 0.433436i
$$512$$ −1.00000 −0.0441942
$$513$$ −9.00000 + 9.00000i −0.397360 + 0.397360i
$$514$$ 29.3939i 1.29651i
$$515$$ 0 0
$$516$$ −4.89898 4.89898i −0.215666 0.215666i
$$517$$ 0 0
$$518$$ 2.00000 + 4.89898i 0.0878750 + 0.215249i
$$519$$ 27.0000 + 27.0000i 1.18517 + 1.18517i
$$520$$ 0 0
$$521$$ −4.89898 −0.214628 −0.107314 0.994225i $$-0.534225\pi$$
−0.107314 + 0.994225i $$0.534225\pi$$
$$522$$ 18.0000 0.787839
$$523$$ −2.44949 −0.107109 −0.0535544 0.998565i $$-0.517055\pi$$
−0.0535544 + 0.998565i $$0.517055\pi$$
$$524$$ 7.34847 0.321019
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 36.7423i 1.59448i
$$532$$ −2.44949 6.00000i −0.106199 0.260133i
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 8.00000i 0.345547i
$$537$$ −29.3939 29.3939i −1.26844 1.26844i
$$538$$ −12.2474 −0.528025
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 2.00000 0.0859867 0.0429934 0.999075i $$-0.486311\pi$$
0.0429934 + 0.999075i $$0.486311\pi$$
$$542$$ 24.4949i 1.05215i
$$543$$ 15.0000 + 15.0000i 0.643712 + 0.643712i
$$544$$ 4.89898i 0.210042i
$$545$$ 0 0
$$546$$ 4.34847 10.3485i 0.186097 0.442874i
$$547$$ 8.00000i 0.342055i −0.985266 0.171028i $$-0.945291\pi$$
0.985266 0.171028i $$-0.0547087\pi$$
$$548$$ 12.0000 0.512615
$$549$$ 36.7423 1.56813
$$550$$ 0 0
$$551$$ 14.6969 0.626111
$$552$$ 7.34847 7.34847i 0.312772 0.312772i
$$553$$ −24.4949 + 10.0000i −1.04163 + 0.425243i
$$554$$ 22.0000i 0.934690i
$$555$$ 0 0
$$556$$ 2.44949i 0.103882i
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 0 0
$$559$$ 9.79796i 0.414410i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 22.0454i 0.929103i −0.885546 0.464552i $$-0.846216\pi$$
0.885546 0.464552i $$-0.153784\pi$$
$$564$$ 6.00000 + 6.00000i 0.252646 + 0.252646i
$$565$$ 0 0
$$566$$ −22.0454 −0.926638
$$567$$ 22.0454 9.00000i 0.925820 0.377964i
$$568$$ 0 0
$$569$$ 6.00000i 0.251533i −0.992060 0.125767i $$-0.959861\pi$$
0.992060 0.125767i $$-0.0401390\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −12.0000 + 4.89898i −0.500870 + 0.204479i
$$575$$ 0 0
$$576$$ 3.00000i 0.125000i
$$577$$ 19.5959 0.815789 0.407894 0.913029i $$-0.366263\pi$$
0.407894 + 0.913029i $$0.366263\pi$$
$$578$$ 7.00000 0.291162
$$579$$ −4.89898 4.89898i −0.203595 0.203595i
$$580$$ 0 0
$$581$$ −2.44949 6.00000i −0.101622 0.248922i
$$582$$ −6.00000 + 6.00000i −0.248708 + 0.248708i
$$583$$ 0 0
$$584$$ −9.79796 −0.405442
$$585$$ 0 0
$$586$$ 2.44949i 0.101187i
$$587$$ 7.34847i 0.303304i 0.988434 + 0.151652i $$0.0484593\pi$$
−0.988434 + 0.151652i $$0.951541\pi$$
$$588$$ −0.123724 + 12.1237i −0.00510231 + 0.499974i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 22.0454 22.0454i 0.906827 0.906827i
$$592$$ 2.00000i 0.0821995i
$$593$$ 39.1918i 1.60942i 0.593671 + 0.804708i $$0.297678\pi$$
−0.593671 + 0.804708i $$0.702322\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000i 0.245770i
$$597$$ 12.0000 + 12.0000i 0.491127 + 0.491127i
$$598$$ 14.6969 0.601003
$$599$$ 24.0000i 0.980613i 0.871550 + 0.490307i $$0.163115\pi$$
−0.871550 + 0.490307i $$0.836885\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 4.00000 + 9.79796i 0.163028 + 0.399335i
$$603$$ −24.0000 −0.977356
$$604$$ −8.00000 −0.325515
$$605$$ 0 0
$$606$$ 9.00000 9.00000i 0.365600 0.365600i
$$607$$ −4.89898 −0.198843 −0.0994217 0.995045i $$-0.531699\pi$$
−0.0994217 + 0.995045i $$0.531699\pi$$
$$608$$ 2.44949i 0.0993399i
$$609$$ −25.3485 10.6515i −1.02717 0.431622i
$$610$$ 0 0
$$611$$ 12.0000i 0.485468i
$$612$$ −14.6969 −0.594089
$$613$$ 14.0000i 0.565455i 0.959200 + 0.282727i $$0.0912392\pi$$
−0.959200 + 0.282727i $$0.908761\pi$$
$$614$$ −7.34847 −0.296560
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ 12.0000 12.0000i 0.482711 0.482711i
$$619$$ 26.9444i 1.08299i 0.840705 + 0.541493i $$0.182141\pi$$
−0.840705 + 0.541493i $$0.817859\pi$$
$$620$$ 0 0
$$621$$ 22.0454 + 22.0454i 0.884652 + 0.884652i
$$622$$ −19.5959 −0.785725
$$623$$ 0 0
$$624$$ 3.00000 3.00000i 0.120096 0.120096i
$$625$$ 0 0
$$626$$ −34.2929 −1.37062
$$627$$ 0 0
$$628$$ 7.34847 0.293236
$$629$$ 9.79796 0.390670
$$630$$ 0 0
$$631$$ 2.00000 0.0796187 0.0398094 0.999207i $$-0.487325\pi$$
0.0398094 + 0.999207i $$0.487325\pi$$
$$632$$ −10.0000 −0.397779
$$633$$ 9.79796 9.79796i 0.389434 0.389434i
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ −7.34847 + 7.34847i −0.291386 + 0.291386i
$$637$$ −12.2474 + 12.0000i −0.485262 + 0.475457i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 30.0000i 1.18493i 0.805597 + 0.592464i $$0.201845\pi$$
−0.805597 + 0.592464i $$0.798155\pi$$
$$642$$ 14.6969 14.6969i 0.580042 0.580042i
$$643$$ 22.0454 0.869386 0.434693 0.900579i $$-0.356857\pi$$
0.434693 + 0.900579i $$0.356857\pi$$
$$644$$ −14.6969 + 6.00000i −0.579141 + 0.236433i
$$645$$ 0 0
$$646$$ −12.0000 −0.472134
$$647$$ 44.0908i 1.73339i 0.498839 + 0.866694i $$0.333760\pi$$
−0.498839 + 0.866694i $$0.666240\pi$$
$$648$$ 9.00000 0.353553
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 16.0000i 0.626608i
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ −12.2474 + 12.2474i −0.478913 + 0.478913i
$$655$$ 0 0
$$656$$ −4.89898 −0.191273
$$657$$ 29.3939i 1.14676i
$$658$$ −4.89898 12.0000i −0.190982 0.467809i
$$659$$ 36.0000i 1.40236i −0.712984 0.701180i $$-0.752657\pi$$
0.712984 0.701180i $$-0.247343\pi$$
$$660$$ 0 0
$$661$$ 12.2474i 0.476371i −0.971220 0.238185i $$-0.923447\pi$$
0.971220 0.238185i $$-0.0765525\pi$$
$$662$$ 8.00000 0.310929
$$663$$ −14.6969 14.6969i −0.570782 0.570782i
$$664$$ 2.44949i 0.0950586i
$$665$$ 0 0
$$666$$ −6.00000 −0.232495
$$667$$ 36.0000i 1.39393i
$$668$$ 4.89898i 0.189547i
$$669$$ 18.0000 18.0000i 0.695920 0.695920i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ −1.77526 + 4.22474i −0.0684820 + 0.162973i
$$673$$ 34.0000i 1.31060i 0.755367 + 0.655302i $$0.227459\pi$$
−0.755367 + 0.655302i $$0.772541\pi$$
$$674$$ 32.0000i 1.23259i
$$675$$ 0 0
$$676$$ −7.00000 −0.269231
$$677$$ 7.34847i 0.282425i 0.989979 + 0.141212i $$0.0451000\pi$$
−0.989979 + 0.141212i $$0.954900\pi$$
$$678$$ 7.34847 7.34847i 0.282216 0.282216i
$$679$$ 12.0000 4.89898i 0.460518 0.188006i
$$680$$ 0 0
$$681$$ −9.00000 9.00000i −0.344881 0.344881i
$$682$$ 0 0
$$683$$ −24.0000 −0.918334 −0.459167 0.888350i $$-0.651852\pi$$
−0.459167 + 0.888350i $$0.651852\pi$$
$$684$$ 7.34847 0.280976
$$685$$ 0 0
$$686$$ 7.34847 17.0000i 0.280566 0.649063i
$$687$$ 27.0000 + 27.0000i 1.03011 + 1.03011i
$$688$$ 4.00000i 0.152499i
$$689$$ −14.6969 −0.559909
$$690$$ 0 0
$$691$$ 36.7423i 1.39774i 0.715246 + 0.698872i $$0.246314\pi$$
−0.715246 + 0.698872i $$0.753686\pi$$
$$692$$ 22.0454i 0.838041i
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 0 0
$$696$$ −7.34847 7.34847i −0.278543 0.278543i
$$697$$ 24.0000i 0.909065i
$$698$$ 2.44949i 0.0927146i
$$699$$ 29.3939 29.3939i 1.11178 1.11178i
$$700$$ 0 0
$$701$$ 30.0000i 1.13308i −0.824033 0.566542i $$-0.808281\pi$$
0.824033 0.566542i $$-0.191719\pi$$
$$702$$ 9.00000 + 9.00000i 0.339683 + 0.339683i
$$703$$ −4.89898 −0.184769
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 9.79796i 0.368751i
$$707$$ −18.0000 + 7.34847i −0.676960 + 0.276368i
$$708$$ −15.0000 + 15.0000i −0.563735 + 0.563735i
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ 0 0
$$711$$ 30.0000i 1.12509i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 20.6969 + 8.69694i 0.774563 + 0.325475i
$$715$$ 0 0
$$716$$ 24.0000i 0.896922i
$$717$$ 7.34847 + 7.34847i 0.274434 + 0.274434i
$$718$$ 6.00000i 0.223918i
$$719$$ −24.4949 −0.913506 −0.456753 0.889594i $$-0.650988\pi$$
−0.456753 + 0.889594i $$0.650988\pi$$
$$720$$ 0 0
$$721$$ −24.0000 + 9.79796i −0.893807 + 0.364895i
$$722$$ −13.0000 −0.483810
$$723$$ 30.0000 + 30.0000i 1.11571 + 1.11571i
$$724$$ 12.2474i 0.455173i
$$725$$ 0 0
$$726$$ 13.4722 13.4722i 0.500000 0.500000i
$$727$$ −29.3939 −1.09016 −0.545079 0.838385i $$-0.683500\pi$$
−0.545079 + 0.838385i $$0.683500\pi$$
$$728$$ −6.00000 + 2.44949i −0.222375 + 0.0907841i
$$729$$ 27.0000i 1.00000i
$$730$$ 0 0
$$731$$ 19.5959 0.724781
$$732$$ −15.0000 15.0000i −0.554416 0.554416i
$$733$$ 22.0454 0.814266 0.407133 0.913369i $$-0.366529\pi$$
0.407133 + 0.913369i $$0.366529\pi$$
$$734$$ 4.89898 0.180825
$$735$$ 0 0
$$736$$ −6.00000 −0.221163
$$737$$ 0 0
$$738$$ 14.6969i 0.541002i
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ 0 0
$$741$$ 7.34847 + 7.34847i 0.269953 + 0.269953i
$$742$$ 14.6969 6.00000i 0.539542 0.220267i
$$743$$ 6.00000 0.220119 0.110059 0.993925i $$-0.464896\pi$$
0.110059 + 0.993925i $$0.464896\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 14.0000i 0.512576i
$$747$$ 7.34847 0.268866
$$748$$ 0 0
$$749$$ −29.3939 + 12.0000i −1.07403 + 0.438470i
$$750$$ 0 0
$$751$$ −8.00000 −0.291924 −0.145962 0.989290i $$-0.546628\pi$$
−0.145962 + 0.989290i $$0.546628\pi$$
$$752$$ 4.89898i 0.178647i
$$753$$ 21.0000 21.0000i 0.765283 0.765283i
$$754$$ 14.6969i 0.535231i
$$755$$ 0 0
$$756$$ −12.6742 5.32577i −0.460957 0.193696i
$$757$$ 2.00000i 0.0726912i 0.999339 + 0.0363456i $$0.0115717\pi$$
−0.999339 + 0.0363456i $$0.988428\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −4.89898 −0.177588 −0.0887939 0.996050i $$-0.528301\pi$$
−0.0887939 + 0.996050i $$0.528301\pi$$
$$762$$ −9.79796 9.79796i −0.354943 0.354943i
$$763$$ 24.4949 10.0000i 0.886775 0.362024i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 34.2929i 1.23905i
$$767$$ −30.0000 −1.08324
$$768$$ −1.22474 + 1.22474i −0.0441942 + 0.0441942i
$$769$$ 34.2929i 1.23663i −0.785930 0.618316i $$-0.787815\pi$$
0.785930 0.618316i $$-0.212185\pi$$
$$770$$ 0 0
$$771$$ 36.0000 + 36.0000i 1.29651 + 1.29651i
$$772$$ 4.00000i 0.143963i
$$773$$ 26.9444i 0.969122i 0.874757 + 0.484561i $$0.161021\pi$$
−0.874757 + 0.484561i $$0.838979\pi$$
$$774$$ −12.0000 −0.431331
$$775$$ 0 0
$$776$$ 4.89898 0.175863
$$777$$ 8.44949 + 3.55051i 0.303124 + 0.127374i
$$778$$ 6.00000i 0.215110i
$$779$$ 12.0000i 0.429945i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 29.3939i 1.05112i
$$783$$ 22.0454 22.0454i 0.787839 0.787839i
$$784$$ 5.00000 4.89898i 0.178571 0.174964i
$$785$$ 0 0
$$786$$ 9.00000 9.00000i 0.321019 0.321019i
$$787$$ 31.8434 1.13509 0.567547 0.823341i $$-0.307893\pi$$
0.567547 + 0.823341i $$0.307893\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 29.3939 29.3939i 1.04645 1.04645i
$$790$$ 0 0
$$791$$ −14.6969 + 6.00000i −0.522563 + 0.213335i
$$792$$ 0 0
$$793$$ 30.0000i 1.06533i
$$794$$ −7.34847 −0.260787
$$795$$ 0 0