Properties

 Label 1805.2.b.d.1084.1 Level $1805$ Weight $2$ Character 1805.1084 Analytic conductor $14.413$ Analytic rank $0$ Dimension $2$ CM discriminant -19 Inner twists $4$

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Newspace parameters

 Level: $$N$$ $$=$$ $$1805 = 5 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1805.b (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$14.4129975648$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-19})$$ Defining polynomial: $$x^{2} - x + 5$$ x^2 - x + 5 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

 Embedding label 1084.1 Root $$0.500000 - 2.17945i$$ of defining polynomial Character $$\chi$$ $$=$$ 1805.1084 Dual form 1805.2.b.d.1084.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{4} +(-0.500000 - 2.17945i) q^{5} -4.35890i q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{4} +(-0.500000 - 2.17945i) q^{5} -4.35890i q^{7} +3.00000 q^{9} +5.00000 q^{11} +4.00000 q^{16} -4.35890i q^{17} +(-1.00000 - 4.35890i) q^{20} +8.71780i q^{23} +(-4.50000 + 2.17945i) q^{25} -8.71780i q^{28} +(-9.50000 + 2.17945i) q^{35} +6.00000 q^{36} +13.0767i q^{43} +10.0000 q^{44} +(-1.50000 - 6.53835i) q^{45} -4.35890i q^{47} -12.0000 q^{49} +(-2.50000 - 10.8972i) q^{55} -15.0000 q^{61} -13.0767i q^{63} +8.00000 q^{64} -8.71780i q^{68} +13.0767i q^{73} -21.7945i q^{77} +(-2.00000 - 8.71780i) q^{80} +9.00000 q^{81} -8.71780i q^{83} +(-9.50000 + 2.17945i) q^{85} +17.4356i q^{92} +15.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{4} - q^{5} + 6 q^{9}+O(q^{10})$$ 2 * q + 4 * q^4 - q^5 + 6 * q^9 $$2 q + 4 q^{4} - q^{5} + 6 q^{9} + 10 q^{11} + 8 q^{16} - 2 q^{20} - 9 q^{25} - 19 q^{35} + 12 q^{36} + 20 q^{44} - 3 q^{45} - 24 q^{49} - 5 q^{55} - 30 q^{61} + 16 q^{64} - 4 q^{80} + 18 q^{81} - 19 q^{85} + 30 q^{99}+O(q^{100})$$ 2 * q + 4 * q^4 - q^5 + 6 * q^9 + 10 * q^11 + 8 * q^16 - 2 * q^20 - 9 * q^25 - 19 * q^35 + 12 * q^36 + 20 * q^44 - 3 * q^45 - 24 * q^49 - 5 * q^55 - 30 * q^61 + 16 * q^64 - 4 * q^80 + 18 * q^81 - 19 * q^85 + 30 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$$.

 $$n$$ $$362$$ $$1446$$ $$\chi(n)$$ $$-1$$ $$1$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 2.00000 1.00000
$$5$$ −0.500000 2.17945i −0.223607 0.974679i
$$6$$ 0 0
$$7$$ 4.35890i 1.64751i −0.566947 0.823754i $$-0.691875\pi$$
0.566947 0.823754i $$-0.308125\pi$$
$$8$$ 0 0
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ 5.00000 1.50756 0.753778 0.657129i $$-0.228229\pi$$
0.753778 + 0.657129i $$0.228229\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4.00000 1.00000
$$17$$ 4.35890i 1.05719i −0.848875 0.528594i $$-0.822719\pi$$
0.848875 0.528594i $$-0.177281\pi$$
$$18$$ 0 0
$$19$$ 0 0
$$20$$ −1.00000 4.35890i −0.223607 0.974679i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 8.71780i 1.81779i 0.417029 + 0.908893i $$0.363071\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ 0 0
$$25$$ −4.50000 + 2.17945i −0.900000 + 0.435890i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 8.71780i 1.64751i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −9.50000 + 2.17945i −1.60579 + 0.368394i
$$36$$ 6.00000 1.00000
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 13.0767i 1.99418i 0.0762493 + 0.997089i $$0.475706\pi$$
−0.0762493 + 0.997089i $$0.524294\pi$$
$$44$$ 10.0000 1.50756
$$45$$ −1.50000 6.53835i −0.223607 0.974679i
$$46$$ 0 0
$$47$$ 4.35890i 0.635811i −0.948122 0.317905i $$-0.897021\pi$$
0.948122 0.317905i $$-0.102979\pi$$
$$48$$ 0 0
$$49$$ −12.0000 −1.71429
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ −2.50000 10.8972i −0.337100 1.46938i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −15.0000 −1.92055 −0.960277 0.279050i $$-0.909981\pi$$
−0.960277 + 0.279050i $$0.909981\pi$$
$$62$$ 0 0
$$63$$ 13.0767i 1.64751i
$$64$$ 8.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 8.71780i 1.05719i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 13.0767i 1.53051i 0.643726 + 0.765256i $$0.277388\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 21.7945i 2.48371i
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −2.00000 8.71780i −0.223607 0.974679i
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 8.71780i 0.956903i −0.878114 0.478451i $$-0.841198\pi$$
0.878114 0.478451i $$-0.158802\pi$$
$$84$$ 0 0
$$85$$ −9.50000 + 2.17945i −1.03042 + 0.236394i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 17.4356i 1.81779i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 15.0000 1.50756
$$100$$ −9.00000 + 4.35890i −0.900000 + 0.435890i
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 17.4356i 1.64751i
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 19.0000 4.35890i 1.77176 0.406469i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −19.0000 −1.74173
$$120$$ 0 0
$$121$$ 14.0000 1.27273
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 7.00000 + 8.71780i 0.626099 + 0.779744i
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −7.00000 −0.611593 −0.305796 0.952097i $$-0.598923\pi$$
−0.305796 + 0.952097i $$0.598923\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 4.35890i 0.372406i 0.982511 + 0.186203i $$0.0596182\pi$$
−0.982511 + 0.186203i $$0.940382\pi$$
$$138$$ 0 0
$$139$$ 9.00000 0.763370 0.381685 0.924292i $$-0.375344\pi$$
0.381685 + 0.924292i $$0.375344\pi$$
$$140$$ −19.0000 + 4.35890i −1.60579 + 0.368394i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 12.0000 1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 11.0000 0.901155 0.450578 0.892737i $$-0.351218\pi$$
0.450578 + 0.892737i $$0.351218\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 13.0767i 1.05719i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 17.4356i 1.39151i 0.718278 + 0.695756i $$0.244931\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 38.0000 2.99482
$$162$$ 0 0
$$163$$ 8.71780i 0.682831i 0.939913 + 0.341415i $$0.110906\pi$$
−0.939913 + 0.341415i $$0.889094\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 26.1534i 1.99418i
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 9.50000 + 19.6150i 0.718132 + 1.48276i
$$176$$ 20.0000 1.50756
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ −3.00000 13.0767i −0.223607 0.974679i
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 21.7945i 1.59377i
$$188$$ 8.71780i 0.635811i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −17.0000 −1.23008 −0.615038 0.788497i $$-0.710860\pi$$
−0.615038 + 0.788497i $$0.710860\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −24.0000 −1.71429
$$197$$ 17.4356i 1.24223i −0.783718 0.621117i $$-0.786679\pi$$
0.783718 0.621117i $$-0.213321\pi$$
$$198$$ 0 0
$$199$$ −25.0000 −1.77220 −0.886102 0.463491i $$-0.846597\pi$$
−0.886102 + 0.463491i $$0.846597\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 26.1534i 1.81779i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 28.5000 6.53835i 1.94368 0.445912i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −5.00000 21.7945i −0.337100 1.46938i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ −13.5000 + 6.53835i −0.900000 + 0.435890i
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ −21.0000 −1.38772 −0.693860 0.720110i $$-0.744091\pi$$
−0.693860 + 0.720110i $$0.744091\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 30.5123i 1.99893i −0.0327561 0.999463i $$-0.510428\pi$$
0.0327561 0.999463i $$-0.489572\pi$$
$$234$$ 0 0
$$235$$ −9.50000 + 2.17945i −0.619712 + 0.142172i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −5.00000 −0.323423 −0.161712 0.986838i $$-0.551701\pi$$
−0.161712 + 0.986838i $$0.551701\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ −30.0000 −1.92055
$$245$$ 6.00000 + 26.1534i 0.383326 + 1.67088i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −23.0000 −1.45175 −0.725874 0.687828i $$-0.758564\pi$$
−0.725874 + 0.687828i $$0.758564\pi$$
$$252$$ 26.1534i 1.64751i
$$253$$ 43.5890i 2.74042i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 30.5123i 1.88147i −0.339145 0.940734i $$-0.610138\pi$$
0.339145 0.940734i $$-0.389862\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 17.4356i 1.05719i
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −22.5000 + 10.8972i −1.35680 + 0.657129i
$$276$$ 0 0
$$277$$ 4.35890i 0.261901i −0.991389 0.130950i $$-0.958197\pi$$
0.991389 0.130950i $$-0.0418029\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ 13.0767i 0.777329i −0.921379 0.388664i $$-0.872937\pi$$
0.921379 0.388664i $$-0.127063\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −2.00000 −0.117647
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 26.1534i 1.53051i
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 57.0000 3.28543
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 7.50000 + 32.6917i 0.429449 + 1.87192i
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 43.5890i 2.48371i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 35.0000 1.98467 0.992334 0.123585i $$-0.0394392\pi$$
0.992334 + 0.123585i $$0.0394392\pi$$
$$312$$ 0 0
$$313$$ 34.8712i 1.97104i 0.169570 + 0.985518i $$0.445762\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ 0 0
$$315$$ −28.5000 + 6.53835i −1.60579 + 0.368394i
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −4.00000 17.4356i −0.223607 0.974679i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 18.0000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −19.0000 −1.04750
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 17.4356i 0.956903i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ −19.0000 + 4.35890i −1.03042 + 0.236394i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 21.7945i 1.17679i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4.35890i 0.233998i 0.993132 + 0.116999i $$0.0373274\pi$$
−0.993132 + 0.116999i $$0.962673\pi$$
$$348$$ 0 0
$$349$$ −35.0000 −1.87351 −0.936754 0.349990i $$-0.886185\pi$$
−0.936754 + 0.349990i $$0.886185\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 34.8712i 1.85601i 0.372572 + 0.928003i $$0.378476\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −31.0000 −1.63612 −0.818059 0.575135i $$-0.804950\pi$$
−0.818059 + 0.575135i $$0.804950\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 28.5000 6.53835i 1.49176 0.342233i
$$366$$ 0 0
$$367$$ 26.1534i 1.36520i 0.730794 + 0.682598i $$0.239150\pi$$
−0.730794 + 0.682598i $$0.760850\pi$$
$$368$$ 34.8712i 1.81779i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ −47.5000 + 10.8972i −2.42082 + 0.555375i
$$386$$ 0 0
$$387$$ 39.2301i 1.99418i
$$388$$ 0 0
$$389$$ −25.0000 −1.26755 −0.633775 0.773517i $$-0.718496\pi$$
−0.633775 + 0.773517i $$0.718496\pi$$
$$390$$ 0 0
$$391$$ 38.0000 1.92174
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 30.0000 1.50756
$$397$$ 39.2301i 1.96890i 0.175660 + 0.984451i $$0.443794\pi$$
−0.175660 + 0.984451i $$0.556206\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −18.0000 + 8.71780i −0.900000 + 0.435890i
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −20.0000 −0.995037
$$405$$ −4.50000 19.6150i −0.223607 0.974679i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −19.0000 + 4.35890i −0.932673 + 0.213970i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 40.0000 1.95413 0.977064 0.212946i $$-0.0683059\pi$$
0.977064 + 0.212946i $$0.0683059\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 0 0
$$423$$ 13.0767i 0.635811i
$$424$$ 0 0
$$425$$ 9.50000 + 19.6150i 0.460818 + 0.951469i
$$426$$ 0 0
$$427$$ 65.3835i 3.16413i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ −36.0000 −1.71429
$$442$$ 0 0
$$443$$ 30.5123i 1.44968i −0.688916 0.724841i $$-0.741913\pi$$
0.688916 0.724841i $$-0.258087\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 34.8712i 1.64751i
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 39.2301i 1.83511i 0.397613 + 0.917553i $$0.369839\pi$$
−0.397613 + 0.917553i $$0.630161\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 38.0000 8.71780i 1.77176 0.406469i
$$461$$ 37.0000 1.72326 0.861631 0.507535i $$-0.169443\pi$$
0.861631 + 0.507535i $$0.169443\pi$$
$$462$$ 0 0
$$463$$ 13.0767i 0.607726i −0.952716 0.303863i $$-0.901724\pi$$
0.952716 0.303863i $$-0.0982765\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 4.35890i 0.201706i 0.994901 + 0.100853i $$0.0321571\pi$$
−0.994901 + 0.100853i $$0.967843\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 65.3835i 3.00634i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −38.0000 −1.74173
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 4.00000 0.182765 0.0913823 0.995816i $$-0.470871\pi$$
0.0913823 + 0.995816i $$0.470871\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 28.0000 1.27273
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 8.00000 0.361035 0.180517 0.983572i $$-0.442223\pi$$
0.180517 + 0.983572i $$0.442223\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −7.50000 32.6917i −0.337100 1.46938i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 39.0000 1.74588 0.872940 0.487828i $$-0.162211\pi$$
0.872940 + 0.487828i $$0.162211\pi$$
$$500$$ 14.0000 + 17.4356i 0.626099 + 0.779744i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 8.71780i 0.388707i 0.980932 + 0.194354i $$0.0622609\pi$$
−0.980932 + 0.194354i $$0.937739\pi$$
$$504$$ 0 0
$$505$$ 5.00000 + 21.7945i 0.222497 + 0.969842i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 57.0000 2.52153
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 21.7945i 0.958521i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ −14.0000 −0.611593
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −53.0000 −2.30435
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −60.0000 −2.58438
$$540$$ 0 0
$$541$$ 25.0000 1.07483 0.537417 0.843317i $$-0.319400\pi$$
0.537417 + 0.843317i $$0.319400\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 8.71780i 0.372406i
$$549$$ −45.0000 −1.92055
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 18.0000 0.763370
$$557$$ 4.35890i 0.184692i −0.995727 0.0923462i $$-0.970563\pi$$
0.995727 0.0923462i $$-0.0294367\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −38.0000 + 8.71780i −1.60579 + 0.368394i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 39.2301i 1.64751i
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −19.0000 39.2301i −0.792355 1.63601i
$$576$$ 24.0000 1.00000
$$577$$ 47.9479i 1.99610i −0.0624458 0.998048i $$-0.519890\pi$$
0.0624458 0.998048i $$-0.480110\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −38.0000 −1.57651
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 47.9479i 1.97902i −0.144460 0.989511i $$-0.546145\pi$$
0.144460 0.989511i $$-0.453855\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 34.8712i 1.43199i 0.698106 + 0.715994i $$0.254026\pi$$
−0.698106 + 0.715994i $$0.745974\pi$$
$$594$$ 0 0
$$595$$ 9.50000 + 41.4095i 0.389462 + 1.69763i
$$596$$ 22.0000 0.901155
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −7.00000 30.5123i −0.284590 1.24050i
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 26.1534i 1.05719i
$$613$$ 30.5123i 1.23238i 0.787598 + 0.616190i $$0.211325\pi$$
−0.787598 + 0.616190i $$0.788675\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 47.9479i 1.93031i −0.261680 0.965155i $$-0.584277\pi$$
0.261680 0.965155i $$-0.415723\pi$$
$$618$$ 0 0
$$619$$ 24.0000 0.964641 0.482321 0.875995i $$-0.339794\pi$$
0.482321 + 0.875995i $$0.339794\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 15.5000 19.6150i 0.620000 0.784602i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 34.8712i 1.39151i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −15.0000 −0.597141 −0.298570 0.954388i $$-0.596510\pi$$
−0.298570 + 0.954388i $$0.596510\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$642$$ 0 0
$$643$$ 13.0767i 0.515695i −0.966186 0.257847i $$-0.916987\pi$$
0.966186 0.257847i $$-0.0830131\pi$$
$$644$$ 76.0000 2.99482
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 47.9479i 1.88503i −0.334169 0.942513i $$-0.608456\pi$$
0.334169 0.942513i $$-0.391544\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 17.4356i 0.682831i
$$653$$ 30.5123i 1.19404i 0.802227 + 0.597019i $$0.203648\pi$$
−0.802227 + 0.597019i $$0.796352\pi$$
$$654$$ 0 0
$$655$$ 3.50000 + 15.2561i 0.136756 + 0.596107i
$$656$$ 0 0
$$657$$ 39.2301i 1.53051i
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −75.0000 −2.89534
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 26.0000 1.00000
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 9.50000 2.17945i 0.362976 0.0832725i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 52.3068i 1.99418i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 35.0000 1.33146 0.665731 0.746191i $$-0.268120\pi$$
0.665731 + 0.746191i $$0.268120\pi$$
$$692$$ 0 0
$$693$$ 65.3835i 2.48371i
$$694$$ 0 0
$$695$$ −4.50000 19.6150i −0.170695 0.744041i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 19.0000 + 39.2301i 0.718132 + 1.48276i
$$701$$ −50.0000 −1.88847 −0.944237 0.329267i $$-0.893198\pi$$
−0.944237 + 0.329267i $$0.893198\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 40.0000 1.50756
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 43.5890i 1.63933i
$$708$$ 0 0
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 49.0000 1.82739 0.913696 0.406399i $$-0.133216\pi$$
0.913696 + 0.406399i $$0.133216\pi$$
$$720$$ −6.00000 26.1534i −0.223607 0.974679i
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 39.2301i 1.45496i −0.686127 0.727482i $$-0.740691\pi$$
0.686127 0.727482i $$-0.259309\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 57.0000 2.10822
$$732$$ 0 0
$$733$$ 52.3068i 1.93200i −0.258551 0.965998i $$-0.583245\pi$$
0.258551 0.965998i $$-0.416755\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −45.0000 −1.65535 −0.827676 0.561206i $$-0.810337\pi$$
−0.827676 + 0.561206i $$0.810337\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ −5.50000 23.9739i −0.201504 0.878337i
$$746$$ 0 0
$$747$$ 26.1534i 0.956903i
$$748$$ 43.5890i 1.59377i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 17.4356i 0.635811i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 47.9479i 1.74270i 0.490666 + 0.871348i $$0.336754\pi$$
−0.490666 + 0.871348i $$0.663246\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 55.0000 1.99375 0.996874 0.0790050i $$-0.0251743\pi$$
0.996874 + 0.0790050i $$0.0251743\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −34.0000 −1.23008
$$765$$ −28.5000 + 6.53835i −1.03042 + 0.236394i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −51.0000 −1.83911 −0.919554 0.392965i $$-0.871449\pi$$
−0.919554 + 0.392965i $$0.871449\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −48.0000 −1.71429
$$785$$ 38.0000 8.71780i 1.35628 0.311152i
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 34.8712i 1.24223i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −50.0000 −1.77220
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ −19.0000 −0.672172
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 65.3835i 2.30733i
$$804$$ 0 0
$$805$$ −19.0000 82.8191i −0.669662 2.91899i
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −5.00000 −0.175791