# Properties

 Label 1050.2.b.b.251.4 Level $1050$ Weight $2$ Character 1050.251 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.b (of order $$2$$, degree $$1$$, 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 251.4 Root $$1.22474 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.251 Dual form 1050.2.b.b.251.2

## $q$-expansion

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

## 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
<
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 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
$$7$$ 1.00000 2.44949i 0.377964 0.925820i
$$8$$ 1.00000i 0.353553i
$$9$$ 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
$$13$$ 2.44949i 0.679366i 0.940540 + 0.339683i $$0.110320\pi$$
−0.940540 + 0.339683i $$0.889680\pi$$
$$14$$ 2.44949 + 1.00000i 0.654654 + 0.267261i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.89898 1.18818 0.594089 0.804400i $$-0.297513\pi$$
0.594089 + 0.804400i $$0.297513\pi$$
$$18$$ −3.00000 −0.707107
$$19$$ 2.44949i 0.561951i 0.959715 + 0.280976i $$0.0906580\pi$$
−0.959715 + 0.280976i $$0.909342\pi$$
$$20$$ 0 0
$$21$$ 4.22474 1.77526i 0.921915 0.387392i
$$22$$ 0 0
$$23$$ 6.00000i 1.25109i 0.780189 + 0.625543i $$0.215123\pi$$
−0.780189 + 0.625543i $$0.784877\pi$$
$$24$$ 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
$$28$$ −1.00000 + 2.44949i −0.188982 + 0.462910i
$$29$$ 6.00000i 1.11417i 0.830455 + 0.557086i $$0.188081\pi$$
−0.830455 + 0.557086i $$0.811919\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 4.89898i 0.840168i
$$35$$ 0 0
$$36$$ 3.00000i 0.500000i
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ −2.44949 −0.397360
$$39$$ −3.00000 + 3.00000i −0.480384 + 0.480384i
$$40$$ 0 0
$$41$$ 4.89898 0.765092 0.382546 0.923936i $$-0.375047\pi$$
0.382546 + 0.923936i $$0.375047\pi$$
$$42$$ 1.77526 + 4.22474i 0.273928 + 0.651892i
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 4.89898 0.714590 0.357295 0.933992i $$-0.383699\pi$$
0.357295 + 0.933992i $$0.383699\pi$$
$$48$$ 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
$$52$$ 2.44949i 0.339683i
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ −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
$$58$$ −6.00000 −0.787839
$$59$$ 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 $$-0.713144\pi$$
0.620682 0.784063i $$-0.286856\pi$$
$$62$$ 0 0
$$63$$ 7.34847 + 3.00000i 0.925820 + 0.377964i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −8.00000 −0.977356 −0.488678 0.872464i $$-0.662521\pi$$
−0.488678 + 0.872464i $$0.662521\pi$$
$$68$$ −4.89898 −0.594089
$$69$$ −7.34847 + 7.34847i −0.884652 + 0.884652i
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 3.00000 0.353553
$$73$$ 9.79796i 1.14676i −0.819288 0.573382i $$-0.805631\pi$$
0.819288 0.573382i $$-0.194369\pi$$
$$74$$ 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 $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 4.89898i 0.541002i
$$83$$ 2.44949 0.268866 0.134433 0.990923i $$-0.457079\pi$$
0.134433 + 0.990923i $$0.457079\pi$$
$$84$$ −4.22474 + 1.77526i −0.460957 + 0.193696i
$$85$$ 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
$$92$$ 6.00000i 0.625543i
$$93$$ 0 0
$$94$$ 4.89898i 0.505291i
$$95$$ 0 0
$$96$$ −1.22474 + 1.22474i −0.125000 + 0.125000i
$$97$$ 4.89898i 0.497416i −0.968579 0.248708i $$-0.919994\pi$$
0.968579 0.248708i $$-0.0800060\pi$$
$$98$$ 4.89898 5.00000i 0.494872 0.505076i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −7.34847 −0.731200 −0.365600 0.930772i $$-0.619136\pi$$
−0.365600 + 0.930772i $$0.619136\pi$$
$$102$$ −6.00000 + 6.00000i −0.594089 + 0.594089i
$$103$$ 9.79796i 0.965422i −0.875780 0.482711i $$-0.839652\pi$$
0.875780 0.482711i $$-0.160348\pi$$
$$104$$ 2.44949 0.240192
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000i 1.16008i −0.814587 0.580042i $$-0.803036\pi$$
0.814587 0.580042i $$-0.196964\pi$$
$$108$$ 3.67423 3.67423i 0.353553 0.353553i
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 0 0
$$111$$ 2.44949 + 2.44949i 0.232495 + 0.232495i
$$112$$ 1.00000 2.44949i 0.0944911 0.231455i
$$113$$ 6.00000i 0.564433i 0.959351 + 0.282216i $$0.0910696\pi$$
−0.959351 + 0.282216i $$0.908930\pi$$
$$114$$ −3.00000 3.00000i −0.280976 0.280976i
$$115$$ 0 0
$$116$$ 6.00000i 0.557086i
$$117$$ −7.34847 −0.679366
$$118$$ 12.2474i 1.12747i
$$119$$ 4.89898 12.0000i 0.449089 1.10004i
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 12.2474 1.10883
$$123$$ 6.00000 + 6.00000i 0.541002 + 0.541002i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ −3.00000 + 7.34847i −0.267261 + 0.654654i
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −4.89898 4.89898i −0.431331 0.431331i
$$130$$ 0 0
$$131$$ −7.34847 −0.642039 −0.321019 0.947073i $$-0.604025\pi$$
−0.321019 + 0.947073i $$0.604025\pi$$
$$132$$ 0 0
$$133$$ 6.00000 + 2.44949i 0.520266 + 0.212398i
$$134$$ 8.00000i 0.691095i
$$135$$ 0 0
$$136$$ 4.89898i 0.420084i
$$137$$ 12.0000i 1.02523i −0.858619 0.512615i $$-0.828677\pi$$
0.858619 0.512615i $$-0.171323\pi$$
$$138$$ −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
$$148$$ −2.00000 −0.164399
$$149$$ 6.00000i 0.491539i 0.969328 + 0.245770i $$0.0790407\pi$$
−0.969328 + 0.245770i $$0.920959\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 2.44949 0.198680
$$153$$ 14.6969i 1.18818i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 3.00000 3.00000i 0.240192 0.240192i
$$157$$ 7.34847i 0.586472i 0.956040 + 0.293236i $$0.0947321\pi$$
−0.956040 + 0.293236i $$0.905268\pi$$
$$158$$ 10.0000i 0.795557i
$$159$$ −7.34847 + 7.34847i −0.582772 + 0.582772i
$$160$$ 0 0
$$161$$ 14.6969 + 6.00000i 1.15828 + 0.472866i
$$162$$ 9.00000i 0.707107i
$$163$$ 16.0000 1.25322 0.626608 0.779334i $$-0.284443\pi$$
0.626608 + 0.779334i $$0.284443\pi$$
$$164$$ −4.89898 −0.382546
$$165$$ 0 0
$$166$$ 2.44949i 0.190117i
$$167$$ 4.89898 0.379094 0.189547 0.981872i $$-0.439298\pi$$
0.189547 + 0.981872i $$0.439298\pi$$
$$168$$ −1.77526 4.22474i −0.136964 0.325946i
$$169$$ 7.00000 0.538462
$$170$$ 0 0
$$171$$ −7.34847 −0.561951
$$172$$ 4.00000 0.304997
$$173$$ −22.0454 −1.67608 −0.838041 0.545608i $$-0.816299\pi$$
−0.838041 + 0.545608i $$0.816299\pi$$
$$174$$ −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 $$-0.645798\pi$$
0.442189 0.896922i $$-0.354202\pi$$
$$180$$ 0 0
$$181$$ 12.2474i 0.910346i 0.890403 + 0.455173i $$0.150423\pi$$
−0.890403 + 0.455173i $$0.849577\pi$$
$$182$$ −2.44949 + 6.00000i −0.181568 + 0.444750i
$$183$$ 15.0000 15.0000i 1.10883 1.10883i
$$184$$ 6.00000 0.442326
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −4.89898 −0.357295
$$189$$ 5.32577 + 12.6742i 0.387392 + 0.921915i
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ −1.22474 1.22474i −0.0883883 0.0883883i
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 4.89898 0.351726
$$195$$ 0 0
$$196$$ 5.00000 + 4.89898i 0.357143 + 0.349927i
$$197$$ 18.0000i 1.28245i 0.767354 + 0.641223i $$0.221573\pi$$
−0.767354 + 0.641223i $$0.778427\pi$$
$$198$$ 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
$$202$$ 7.34847i 0.517036i
$$203$$ 14.6969 + 6.00000i 1.03152 + 0.421117i
$$204$$ −6.00000 6.00000i −0.420084 0.420084i
$$205$$ 0 0
$$206$$ 9.79796 0.682656
$$207$$ −18.0000 −1.25109
$$208$$ 2.44949i 0.169842i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ 0 0
$$216$$ 3.67423 + 3.67423i 0.250000 + 0.250000i
$$217$$ 0 0
$$218$$ 10.0000i 0.677285i
$$219$$ 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
$$223$$ 14.6969i 0.984180i 0.870544 + 0.492090i $$0.163767\pi$$
−0.870544 + 0.492090i $$0.836233\pi$$
$$224$$ 2.44949 + 1.00000i 0.163663 + 0.0668153i
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −7.34847 −0.487735 −0.243868 0.969809i $$-0.578416\pi$$
−0.243868 + 0.969809i $$0.578416\pi$$
$$228$$ 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
$$232$$ 6.00000 0.393919
$$233$$ 24.0000i 1.57229i −0.618041 0.786146i $$-0.712073\pi$$
0.618041 0.786146i $$-0.287927\pi$$
$$234$$ 7.34847i 0.480384i
$$235$$ 0 0
$$236$$ −12.2474 −0.797241
$$237$$ −12.2474 12.2474i −0.795557 0.795557i
$$238$$ 12.0000 + 4.89898i 0.777844 + 0.317554i
$$239$$ 6.00000i 0.388108i 0.980991 + 0.194054i $$0.0621637\pi$$
−0.980991 + 0.194054i $$0.937836\pi$$
$$240$$ 0 0
$$241$$ 24.4949i 1.57786i 0.614486 + 0.788928i $$0.289363\pi$$
−0.614486 + 0.788928i $$0.710637\pi$$
$$242$$ 11.0000i 0.707107i
$$243$$ −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
$$247$$ −6.00000 −0.381771
$$248$$ 0 0
$$249$$ 3.00000 + 3.00000i 0.190117 + 0.190117i
$$250$$ 0 0
$$251$$ 17.1464 1.08227 0.541136 0.840935i $$-0.317994\pi$$
0.541136 + 0.840935i $$0.317994\pi$$
$$252$$ −7.34847 3.00000i −0.462910 0.188982i
$$253$$ 0 0
$$254$$ 8.00000i 0.501965i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 29.3939 1.83354 0.916770 0.399416i $$-0.130787\pi$$
0.916770 + 0.399416i $$0.130787\pi$$
$$258$$ 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
$$262$$ 7.34847i 0.453990i
$$263$$ 24.0000i 1.47990i −0.672660 0.739952i $$-0.734848\pi$$
0.672660 0.739952i $$-0.265152\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −2.44949 + 6.00000i −0.150188 + 0.367884i
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ 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 $$-0.732936\pi$$
0.668202 0.743980i $$-0.267064\pi$$
$$272$$ 4.89898 0.297044
$$273$$ 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
$$277$$ 22.0000 1.32185 0.660926 0.750451i $$-0.270164\pi$$
0.660926 + 0.750451i $$0.270164\pi$$
$$278$$ −2.44949 −0.146911
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ −6.00000 + 6.00000i −0.357295 + 0.357295i
$$283$$ 22.0454i 1.31046i −0.755428 0.655232i $$-0.772571\pi$$
0.755428 0.655232i $$-0.227429\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 4.89898 12.0000i 0.289178 0.708338i
$$288$$ −3.00000 −0.176777
$$289$$ 7.00000 0.411765
$$290$$ 0 0
$$291$$ 6.00000 6.00000i 0.351726 0.351726i
$$292$$ 9.79796i 0.573382i
$$293$$ 2.44949 0.143101 0.0715504 0.997437i $$-0.477205\pi$$
0.0715504 + 0.997437i $$0.477205\pi$$
$$294$$ 12.1237 0.123724i 0.707070 0.00721575i
$$295$$ 0 0
$$296$$ 2.00000i 0.116248i
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ −14.6969 −0.849946
$$300$$ 0 0
$$301$$ −4.00000 + 9.79796i −0.230556 + 0.564745i
$$302$$ 8.00000i 0.460348i
$$303$$ −9.00000 9.00000i −0.517036 0.517036i
$$304$$ 2.44949i 0.140488i
$$305$$ 0 0
$$306$$ −14.6969 −0.840168
$$307$$ 7.34847i 0.419399i 0.977766 + 0.209700i $$0.0672486\pi$$
−0.977766 + 0.209700i $$0.932751\pi$$
$$308$$ 0 0
$$309$$ 12.0000 12.0000i 0.682656 0.682656i
$$310$$ 0 0
$$311$$ −19.5959 −1.11118 −0.555591 0.831456i $$-0.687508\pi$$
−0.555591 + 0.831456i $$0.687508\pi$$
$$312$$ 3.00000 + 3.00000i 0.169842 + 0.169842i
$$313$$ 34.2929i 1.93835i −0.246380 0.969173i $$-0.579241\pi$$
0.246380 0.969173i $$-0.420759\pi$$
$$314$$ −7.34847 −0.414698
$$315$$ 0 0
$$316$$ 10.0000 0.562544
$$317$$ 18.0000i 1.01098i 0.862832 + 0.505490i $$0.168688\pi$$
−0.862832 + 0.505490i $$0.831312\pi$$
$$318$$ −7.34847 7.34847i −0.412082 0.412082i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 14.6969 14.6969i 0.820303 0.820303i
$$322$$ −6.00000 + 14.6969i −0.334367 + 0.819028i
$$323$$ 12.0000i 0.667698i
$$324$$ 9.00000 0.500000
$$325$$ 0 0
$$326$$ 16.0000i 0.886158i
$$327$$ 12.2474 + 12.2474i 0.677285 + 0.677285i
$$328$$ 4.89898i 0.270501i
$$329$$ 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 $$0.570560\pi$$
$$332$$ −2.44949 −0.134433
$$333$$ 6.00000i 0.328798i
$$334$$ 4.89898i 0.268060i
$$335$$ 0 0
$$336$$ 4.22474 1.77526i 0.230479 0.0968481i
$$337$$ 32.0000 1.74315 0.871576 0.490261i $$-0.163099\pi$$
0.871576 + 0.490261i $$0.163099\pi$$
$$338$$ 7.00000i 0.380750i
$$339$$ −7.34847 + 7.34847i −0.399114 + 0.399114i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 7.34847i 0.397360i
$$343$$ −17.0000 + 7.34847i −0.917914 + 0.396780i
$$344$$ 4.00000i 0.215666i
$$345$$ 0 0
$$346$$ 22.0454i 1.18517i
$$347$$ 12.0000i 0.644194i −0.946707 0.322097i $$-0.895612\pi$$
0.946707 0.322097i $$-0.104388\pi$$
$$348$$ 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
$$353$$ −9.79796 −0.521493 −0.260746 0.965407i $$-0.583969\pi$$
−0.260746 + 0.965407i $$0.583969\pi$$
$$354$$ −15.0000 + 15.0000i −0.797241 + 0.797241i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 20.6969 8.69694i 1.09540 0.460291i
$$358$$ 24.0000 1.26844
$$359$$ 6.00000i 0.316668i 0.987386 + 0.158334i $$0.0506123\pi$$
−0.987386 + 0.158334i $$0.949388\pi$$
$$360$$ 0 0
$$361$$ 13.0000 0.684211
$$362$$ −12.2474 −0.643712
$$363$$ 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
$$367$$ 4.89898i 0.255725i −0.991792 0.127862i $$-0.959188\pi$$
0.991792 0.127862i $$-0.0408116\pi$$
$$368$$ 6.00000i 0.312772i
$$369$$ 14.6969i 0.765092i
$$370$$ 0 0
$$371$$ 14.6969 + 6.00000i 0.763027 + 0.311504i
$$372$$ 0 0
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 4.89898i 0.252646i
$$377$$ −14.6969 −0.756931
$$378$$ −12.6742 + 5.32577i −0.651892 + 0.273928i
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ −9.79796 9.79796i −0.501965 0.501965i
$$382$$ 0 0
$$383$$ −34.2929 −1.75228 −0.876142 0.482054i $$-0.839891\pi$$
−0.876142 + 0.482054i $$0.839891\pi$$
$$384$$ 1.22474 1.22474i 0.0625000 0.0625000i
$$385$$ 0 0
$$386$$ 4.00000i 0.203595i
$$387$$ 12.0000i 0.609994i
$$388$$ 4.89898i 0.248708i
$$389$$ 6.00000i 0.304212i 0.988364 + 0.152106i $$0.0486055\pi$$
−0.988364 + 0.152106i $$0.951394\pi$$
$$390$$ 0 0
$$391$$ 29.3939i 1.48651i
$$392$$ −4.89898 + 5.00000i −0.247436 + 0.252538i
$$393$$ −9.00000 9.00000i −0.453990 0.453990i
$$394$$ −18.0000 −0.906827
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 7.34847i 0.368809i 0.982850 + 0.184405i $$0.0590357\pi$$
−0.982850 + 0.184405i $$0.940964\pi$$
$$398$$ 9.79796 0.491127
$$399$$ 4.34847 + 10.3485i 0.217696 + 0.518071i
$$400$$ 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
$$412$$ 9.79796i 0.482711i
$$413$$ 12.2474 30.0000i 0.602658 1.47620i
$$414$$ 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 $$0.484480\pi$$
$$422$$ 8.00000i 0.389434i
$$423$$ 14.6969i 0.714590i
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −30.0000 12.2474i −1.45180 0.592696i
$$428$$ 12.0000i 0.580042i
$$429$$ 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
$$433$$ 14.6969i 0.706290i 0.935569 + 0.353145i $$0.114888\pi$$
−0.935569 + 0.353145i $$0.885112\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −10.0000 −0.478913
$$437$$ −14.6969 −0.703050
$$438$$ 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
$$442$$ −12.0000 −0.570782
$$443$$ 36.0000i 1.71041i 0.518289 + 0.855206i $$0.326569\pi$$
−0.518289 + 0.855206i $$0.673431\pi$$
$$444$$ −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
$$448$$ −1.00000 + 2.44949i −0.0472456 + 0.115728i
$$449$$ 36.0000i 1.69895i 0.527633 + 0.849473i $$0.323080\pi$$
−0.527633 + 0.849473i $$0.676920\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 6.00000i 0.282216i
$$453$$ −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
$$457$$ −28.0000 −1.30978 −0.654892 0.755722i $$-0.727286\pi$$
−0.654892 + 0.755722i $$0.727286\pi$$
$$458$$ 22.0454 1.03011
$$459$$ −18.0000 + 18.0000i −0.840168 + 0.840168i
$$460$$ 0 0
$$461$$ −31.8434 −1.48309 −0.741547 0.670901i $$-0.765907\pi$$
−0.741547 + 0.670901i $$0.765907\pi$$
$$462$$ 0 0
$$463$$ −14.0000 −0.650635 −0.325318 0.945605i $$-0.605471\pi$$
−0.325318 + 0.945605i $$0.605471\pi$$
$$464$$ 6.00000i 0.278543i
$$465$$ 0 0
$$466$$ 24.0000 1.11178
$$467$$ −7.34847 −0.340047 −0.170023 0.985440i $$-0.554384\pi$$
−0.170023 + 0.985440i $$0.554384\pi$$
$$468$$ 7.34847 0.339683
$$469$$ −8.00000 + 19.5959i −0.369406 + 0.904855i
$$470$$ 0 0
$$471$$ −9.00000 + 9.00000i −0.414698 + 0.414698i
$$472$$ 12.2474i 0.563735i
$$473$$ 0 0
$$474$$ 12.2474 12.2474i 0.562544 0.562544i
$$475$$ 0 0
$$476$$ −4.89898 + 12.0000i −0.224544 + 0.550019i
$$477$$ −18.0000 −0.824163
$$478$$ −6.00000 −0.274434
$$479$$ −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
$$482$$ −24.4949 −1.11571
$$483$$ 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
$$487$$ 32.0000 1.45006 0.725029 0.688718i $$-0.241826\pi$$
0.725029 + 0.688718i $$0.241826\pi$$
$$488$$ −12.2474 −0.554416
$$489$$ 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
$$493$$ 29.3939i 1.32383i
$$494$$ 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 $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ 0 0
$$501$$ 6.00000 + 6.00000i 0.268060 + 0.268060i
$$502$$ 17.1464i 0.765283i
$$503$$ 39.1918 1.74748 0.873739 0.486395i $$-0.161689\pi$$
0.873739 + 0.486395i $$0.161689\pi$$
$$504$$ 3.00000 7.34847i 0.133631 0.327327i
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 8.57321 + 8.57321i 0.380750 + 0.380750i
$$508$$ 8.00000 0.354943
$$509$$ 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
$$512$$ 1.00000i 0.0441942i
$$513$$ −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
$$518$$ 4.89898 + 2.00000i 0.215249 + 0.0878750i
$$519$$ −27.0000 27.0000i −1.18517 1.18517i
$$520$$ 0 0
$$521$$ 4.89898 0.214628 0.107314 0.994225i $$-0.465775\pi$$
0.107314 + 0.994225i $$0.465775\pi$$
$$522$$ 18.0000i 0.787839i
$$523$$ 2.44949i 0.107109i 0.998565 + 0.0535544i $$0.0170550\pi$$
−0.998565 + 0.0535544i $$0.982945\pi$$
$$524$$ 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
$$532$$ −6.00000 2.44949i −0.260133 0.106199i
$$533$$ 12.0000i 0.519778i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 8.00000i 0.345547i
$$537$$ 29.3939 29.3939i 1.26844 1.26844i
$$538$$ 12.2474i 0.528025i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 2.00000 0.0859867 0.0429934 0.999075i $$-0.486311\pi$$
0.0429934 + 0.999075i $$0.486311\pi$$
$$542$$ 24.4949 1.05215
$$543$$ −15.0000 + 15.0000i −0.643712 + 0.643712i
$$544$$ 4.89898i 0.210042i
$$545$$ 0 0
$$546$$ −10.3485 + 4.34847i −0.442874 + 0.186097i
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ 12.0000i 0.512615i
$$549$$ 36.7423 1.56813
$$550$$ 0 0
$$551$$ −14.6969 −0.626111
$$552$$ 7.34847 + 7.34847i 0.312772 + 0.312772i
$$553$$ −10.0000 + 24.4949i −0.425243 + 1.04163i
$$554$$ 22.0000i 0.934690i
$$555$$ 0 0
$$556$$ 2.44949i 0.103882i
$$557$$ 18.0000i 0.762684i 0.924434 + 0.381342i $$0.124538\pi$$
−0.924434 + 0.381342i $$0.875462\pi$$
$$558$$ 0 0
$$559$$ 9.79796i 0.414410i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −22.0454 −0.929103 −0.464552 0.885546i $$-0.653784\pi$$
−0.464552 + 0.885546i $$0.653784\pi$$
$$564$$ −6.00000 6.00000i −0.252646 0.252646i
$$565$$ 0 0
$$566$$ 22.0454 0.926638
$$567$$ −9.00000 + 22.0454i −0.377964 + 0.925820i
$$568$$ 0 0
$$569$$ 6.00000i 0.251533i 0.992060 + 0.125767i $$0.0401390\pi$$
−0.992060 + 0.125767i $$0.959861\pi$$
$$570$$ 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
$$577$$ 19.5959i 0.815789i 0.913029 + 0.407894i $$0.133737\pi$$
−0.913029 + 0.407894i $$0.866263\pi$$
$$578$$ 7.00000i 0.291162i
$$579$$ −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
$$587$$ −7.34847 −0.303304 −0.151652 0.988434i $$-0.548459\pi$$
−0.151652 + 0.988434i $$0.548459\pi$$
$$588$$ 0.123724 + 12.1237i 0.00510231 + 0.499974i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −22.0454 + 22.0454i −0.906827 + 0.906827i
$$592$$ 2.00000 0.0821995
$$593$$ 39.1918 1.60942 0.804708 0.593671i $$-0.202322\pi$$
0.804708 + 0.593671i $$0.202322\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000i 0.245770i
$$597$$ 12.0000 12.0000i 0.491127 0.491127i
$$598$$ 14.6969i 0.601003i
$$599$$ 24.0000i 0.980613i −0.871550 0.490307i $$-0.836885\pi$$
0.871550 0.490307i $$-0.163115\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ −9.79796 4.00000i −0.399335 0.163028i
$$603$$ 24.0000i 0.977356i
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ 9.00000 9.00000i 0.365600 0.365600i
$$607$$ 4.89898i 0.198843i −0.995045 0.0994217i $$-0.968301\pi$$
0.995045 0.0994217i $$-0.0316993\pi$$
$$608$$ −2.44949 −0.0993399
$$609$$ 10.6515 + 25.3485i 0.431622 + 1.02717i
$$610$$ 0 0
$$611$$ 12.0000i 0.485468i
$$612$$ 14.6969i 0.594089i
$$613$$ −14.0000 −0.565455 −0.282727 0.959200i $$-0.591239\pi$$
−0.282727 + 0.959200i $$0.591239\pi$$
$$614$$ −7.34847 −0.296560
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000i 0.724653i 0.932051 + 0.362326i $$0.118017\pi$$
−0.932051 + 0.362326i $$0.881983\pi$$
$$618$$ 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
$$622$$ 19.5959i 0.785725i
$$623$$ 0 0
$$624$$ −3.00000 + 3.00000i −0.120096 + 0.120096i
$$625$$ 0 0
$$626$$ 34.2929 1.37062
$$627$$ 0 0
$$628$$ 7.34847i 0.293236i
$$629$$ 9.79796 0.390670
$$630$$ 0 0
$$631$$ 2.00000 0.0796187 0.0398094 0.999207i $$-0.487325\pi$$
0.0398094 + 0.999207i $$0.487325\pi$$
$$632$$ 10.0000i 0.397779i
$$633$$ −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
$$637$$ 12.0000 12.2474i 0.475457 0.485262i
$$638$$ 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
$$643$$ 22.0454i 0.869386i −0.900579 0.434693i $$-0.856857\pi$$
0.900579 0.434693i $$-0.143143\pi$$
$$644$$ −14.6969 6.00000i −0.579141 0.236433i
$$645$$ 0 0
$$646$$ −12.0000 −0.472134
$$647$$ −44.0908 −1.73339 −0.866694 0.498839i $$-0.833760\pi$$
−0.866694 + 0.498839i $$0.833760\pi$$
$$648$$ 9.00000i 0.353553i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −16.0000 −0.626608
$$653$$ 6.00000i 0.234798i 0.993085 + 0.117399i $$0.0374557\pi$$
−0.993085 + 0.117399i $$0.962544\pi$$
$$654$$ −12.2474 + 12.2474i −0.478913 + 0.478913i
$$655$$ 0 0
$$656$$ 4.89898 0.191273
$$657$$ 29.3939 1.14676
$$658$$ 12.0000 + 4.89898i 0.467809 + 0.190982i
$$659$$ 36.0000i 1.40236i 0.712984 + 0.701180i $$0.247343\pi$$
−0.712984 + 0.701180i $$0.752657\pi$$
$$660$$ 0 0
$$661$$ 12.2474i 0.476371i 0.971220 + 0.238185i $$0.0765525\pi$$
−0.971220 + 0.238185i $$0.923447\pi$$
$$662$$ 8.00000i 0.310929i
$$663$$ −14.6969 + 14.6969i −0.570782 + 0.570782i
$$664$$ 2.44949i 0.0950586i
$$665$$ 0 0
$$666$$ −6.00000 −0.232495
$$667$$ −36.0000 −1.39393
$$668$$ −4.89898 −0.189547
$$669$$ −18.0000 + 18.0000i −0.695920 + 0.695920i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.77526 + 4.22474i 0.0684820 + 0.162973i
$$673$$ −34.0000 −1.31060 −0.655302 0.755367i $$-0.727459\pi$$
−0.655302 + 0.755367i $$0.727459\pi$$
$$674$$ 32.0000i 1.23259i
$$675$$ 0 0
$$676$$ −7.00000 −0.269231
$$677$$ −7.34847 −0.282425 −0.141212 0.989979i $$-0.545100\pi$$
−0.141212 + 0.989979i $$0.545100\pi$$
$$678$$ −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
$$683$$ 24.0000i 0.918334i −0.888350 0.459167i $$-0.848148\pi$$
0.888350 0.459167i $$-0.151852\pi$$
$$684$$ 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
$$688$$ −4.00000 −0.152499
$$689$$ −14.6969 −0.559909
$$690$$ 0 0
$$691$$ 36.7423i 1.39774i −0.715246 0.698872i $$-0.753686\pi$$
0.715246 0.698872i $$-0.246314\pi$$
$$692$$ 22.0454 0.838041
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 0 0
$$696$$ 7.34847 + 7.34847i 0.278543 + 0.278543i
$$697$$ 24.0000 0.909065
$$698$$ −2.44949 −0.0927146
$$699$$ 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
$$703$$ 4.89898i 0.184769i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 9.79796i 0.368751i
$$707$$ −7.34847 + 18.0000i −0.276368 + 0.676960i
$$708$$ −15.0000 15.0000i −0.563735 0.563735i
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ 30.0000i 1.12509i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 8.69694 + 20.6969i 0.325475 + 0.774563i
$$715$$ 0 0
$$716$$ 24.0000i 0.896922i
$$717$$ −7.34847 + 7.34847i −0.274434 + 0.274434i
$$718$$ −6.00000 −0.223918
$$719$$ −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
$$722$$ 13.0000i 0.483810i
$$723$$ −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
$$727$$ 29.3939i 1.09016i −0.838385 0.545079i $$-0.816500\pi$$
0.838385 0.545079i $$-0.183500\pi$$
$$728$$ 2.44949 6.00000i 0.0907841 0.222375i
$$729$$ 27.0000i 1.00000i
$$730$$ 0 0
$$731$$ −19.5959 −0.724781
$$732$$ −15.0000 + 15.0000i −0.554416 + 0.554416i
$$733$$ 22.0454i 0.814266i −0.913369 0.407133i $$-0.866529\pi$$
0.913369 0.407133i $$-0.133471\pi$$
$$734$$ 4.89898 0.180825
$$735$$ 0 0
$$736$$ −6.00000 −0.221163
$$737$$ 0 0
$$738$$ −14.6969 −0.541002
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ −7.34847 7.34847i −0.269953 0.269953i
$$742$$ −6.00000 + 14.6969i −0.220267 + 0.539542i
$$743$$ 6.00000i 0.220119i 0.993925 + 0.110059i $$0.0351041\pi$$
−0.993925 + 0.110059i $$0.964896\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 14.0000i 0.512576i
$$747$$ 7.34847i 0.268866i
$$748$$ 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 $$0.546628\pi$$
$$752$$ 4.89898 0.178647
$$753$$ 21.0000 + 21.0000i 0.765283 + 0.765283i
$$754$$ 14.6969i 0.535231i
$$755$$ 0 0
$$756$$ −5.32577 12.6742i −0.193696 0.460957i
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 20.0000i 0.726433i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 4.89898 0.177588 0.0887939 0.996050i $$-0.471699\pi$$
0.0887939 + 0.996050i $$0.471699\pi$$
$$762$$ 9.79796 9.79796i 0.354943 0.354943i
$$763$$ 10.0000 24.4949i 0.362024 0.886775i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 34.2929i 1.23905i
$$767$$ 30.0000i 1.08324i
$$768$$ 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
$$772$$ 4.00000 0.143963
$$773$$ 26.9444 0.969122 0.484561 0.874757i $$-0.338979\pi$$
0.484561 + 0.874757i $$0.338979\pi$$
$$774$$ 12.0000 0.431331
$$775$$ 0 0
$$776$$ −4.89898 −0.175863
$$777$$ 8.44949 3.55051i 0.303124 0.127374i
$$778$$ −6.00000 −0.215110
$$779$$ 12.0000i 0.429945i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −29.3939 −1.05112
$$783$$ −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
$$787$$ 31.8434i 1.13509i 0.823341 + 0.567547i $$0.192107\pi$$
−0.823341 + 0.567547i $$0.807893\pi$$
$$788$$ 18.0000i 0.641223i
$$789$$ 29.3939 29.3939i 1.04645 1.04645i
$$790$$ 0 0
$$791$$ 14.6969 + 6.00000i 0.522563 + 0.213335i
$$792$$ 0 0
$$793$$ 30.0000 1.06533
$$794$$ −7.34847 −0.260787
$$795$$ 0 0
$$796$$ 9.79796i 0.347279i
$$797$$ −7.34847 −0.260296 −0.130148 0.991495i $$-0.541545\pi$$
−0.130148 + 0.991495i $$0.541545\pi$$
$$798$$ −10.3485 + 4.34847i −0.366332 + 0.153934i
$$799$$ 24.0000 0.849059
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 30.0000 1.05934
$$803$$ 0 0
$$804$$ 9.79796