Properties

 Label 1386.2.k.e.793.1 Level $1386$ Weight $2$ Character 1386.793 Analytic conductor $11.067$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.k (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$11.0672657201$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 793.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1386.793 Dual form 1386.2.k.e.991.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} -9.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} -5.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-5.50000 - 9.52628i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.00000 - 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(-3.00000 + 5.19615i) q^{82} +6.00000 q^{83} +(2.00000 - 3.46410i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-9.00000 + 15.5885i) q^{89} +(0.500000 + 2.59808i) q^{91} +6.00000 q^{92} +(-3.00000 - 5.19615i) q^{94} -13.0000 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{4} - q^{7} + 2q^{8} + O(q^{10})$$ $$2q - q^{2} - q^{4} - q^{7} + 2q^{8} - q^{11} - 2q^{13} + 5q^{14} - q^{16} - 6q^{17} - 2q^{19} + 2q^{22} - 6q^{23} + 5q^{25} + q^{26} - 4q^{28} - 18q^{29} + 4q^{31} - q^{32} + 12q^{34} - 2q^{37} - 2q^{38} + 12q^{41} - 8q^{43} - q^{44} - 6q^{46} - 6q^{47} - 13q^{49} - 10q^{50} + q^{52} - q^{56} + 9q^{58} - 3q^{59} - 11q^{61} - 8q^{62} + 2q^{64} - 11q^{67} - 6q^{68} - 2q^{73} - 2q^{74} + 4q^{76} - 4q^{77} - 5q^{79} - 6q^{82} + 12q^{83} + 4q^{86} - q^{88} - 18q^{89} + q^{91} + 12q^{92} - 6q^{94} - 26q^{97} + 2q^{98} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$$.

 $$n$$ $$155$$ $$199$$ $$1135$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ 0 0
$$7$$ −0.500000 2.59808i −0.188982 0.981981i
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ 0 0
$$13$$ −1.00000 −0.277350 −0.138675 0.990338i $$-0.544284\pi$$
−0.138675 + 0.990338i $$0.544284\pi$$
$$14$$ 2.50000 + 0.866025i 0.668153 + 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i $$-0.907299\pi$$
0.230285 0.973123i $$-0.426034\pi$$
$$18$$ 0 0
$$19$$ −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i $$-0.907015\pi$$
0.728219 + 0.685344i $$0.240348\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i $$0.381789\pi$$
−0.988436 + 0.151642i $$0.951544\pi$$
$$24$$ 0 0
$$25$$ 2.50000 + 4.33013i 0.500000 + 0.866025i
$$26$$ 0.500000 0.866025i 0.0980581 0.169842i
$$27$$ 0 0
$$28$$ −2.00000 + 1.73205i −0.377964 + 0.327327i
$$29$$ −9.00000 −1.67126 −0.835629 0.549294i $$-0.814897\pi$$
−0.835629 + 0.549294i $$0.814897\pi$$
$$30$$ 0 0
$$31$$ 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i $$-0.0497126\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i $$-0.885902\pi$$
0.772043 + 0.635571i $$0.219235\pi$$
$$38$$ −1.00000 1.73205i −0.162221 0.280976i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ 0 0
$$46$$ −3.00000 5.19615i −0.442326 0.766131i
$$47$$ −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i $$-0.977503\pi$$
0.559908 + 0.828554i $$0.310836\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ −5.00000 −0.707107
$$51$$ 0 0
$$52$$ 0.500000 + 0.866025i 0.0693375 + 0.120096i
$$53$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −0.500000 2.59808i −0.0668153 0.347183i
$$57$$ 0 0
$$58$$ 4.50000 7.79423i 0.590879 1.02343i
$$59$$ −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i $$-0.229229\pi$$
−0.946993 + 0.321253i $$0.895896\pi$$
$$60$$ 0 0
$$61$$ −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i $$0.415362\pi$$
−0.966978 + 0.254858i $$0.917971\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i $$-0.932131\pi$$
0.305424 0.952217i $$-0.401202\pi$$
$$68$$ −3.00000 + 5.19615i −0.363803 + 0.630126i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i $$-0.204008\pi$$
−0.918594 + 0.395203i $$0.870674\pi$$
$$74$$ −1.00000 1.73205i −0.116248 0.201347i
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ −2.00000 + 1.73205i −0.227921 + 0.197386i
$$78$$ 0 0
$$79$$ −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i $$-0.924090\pi$$
0.690426 + 0.723403i $$0.257423\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −3.00000 + 5.19615i −0.331295 + 0.573819i
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 2.00000 3.46410i 0.215666 0.373544i
$$87$$ 0 0
$$88$$ −0.500000 0.866025i −0.0533002 0.0923186i
$$89$$ −9.00000 + 15.5885i −0.953998 + 1.65237i −0.217354 + 0.976093i $$0.569742\pi$$
−0.736644 + 0.676280i $$0.763591\pi$$
$$90$$ 0 0
$$91$$ 0.500000 + 2.59808i 0.0524142 + 0.272352i
$$92$$ 6.00000 0.625543
$$93$$ 0 0
$$94$$ −3.00000 5.19615i −0.309426 0.535942i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −13.0000 −1.31995 −0.659975 0.751288i $$-0.729433\pi$$
−0.659975 + 0.751288i $$0.729433\pi$$
$$98$$ 1.00000 6.92820i 0.101015 0.699854i
$$99$$ 0 0
$$100$$ 2.50000 4.33013i 0.250000 0.433013i
$$101$$ −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i $$-0.898506\pi$$
0.203317 0.979113i $$-0.434828\pi$$
$$102$$ 0 0
$$103$$ 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i $$-0.544314\pi$$
0.927030 0.374987i $$-0.122353\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i $$-0.636370\pi$$
0.995474 0.0950377i $$-0.0302972\pi$$
$$108$$ 0 0
$$109$$ −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i $$-0.197202\pi$$
−0.909935 + 0.414751i $$0.863869\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 2.50000 + 0.866025i 0.236228 + 0.0818317i
$$113$$ −9.00000 −0.846649 −0.423324 0.905978i $$-0.639137\pi$$
−0.423324 + 0.905978i $$0.639137\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 4.50000 + 7.79423i 0.417815 + 0.723676i
$$117$$ 0 0
$$118$$ 3.00000 0.276172
$$119$$ −12.0000 + 10.3923i −1.10004 + 0.952661i
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ −5.50000 9.52628i −0.497947 0.862469i
$$123$$ 0 0
$$124$$ 2.00000 3.46410i 0.179605 0.311086i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −7.00000 −0.621150 −0.310575 0.950549i $$-0.600522\pi$$
−0.310575 + 0.950549i $$0.600522\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i $$-0.545310\pi$$
0.928199 0.372084i $$-0.121357\pi$$
$$132$$ 0 0
$$133$$ 5.00000 + 1.73205i 0.433555 + 0.150188i
$$134$$ 11.0000 0.950255
$$135$$ 0 0
$$136$$ −3.00000 5.19615i −0.257248 0.445566i
$$137$$ −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i $$-0.292279\pi$$
−0.991694 + 0.128618i $$0.958946\pi$$
$$138$$ 0 0
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0.500000 + 0.866025i 0.0418121 + 0.0724207i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 2.00000 0.165521
$$147$$ 0 0
$$148$$ 2.00000 0.164399
$$149$$ 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i $$-0.754293\pi$$
0.962348 + 0.271821i $$0.0876260\pi$$
$$150$$ 0 0
$$151$$ 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i $$0.114628\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ −1.00000 + 1.73205i −0.0811107 + 0.140488i
$$153$$ 0 0
$$154$$ −0.500000 2.59808i −0.0402911 0.209359i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i $$-0.115641\pi$$
−0.775113 + 0.631822i $$0.782307\pi$$
$$158$$ −2.50000 4.33013i −0.198889 0.344486i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 15.0000 + 5.19615i 1.18217 + 0.409514i
$$162$$ 0 0
$$163$$ −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i $$0.398564\pi$$
−0.979076 + 0.203497i $$0.934769\pi$$
$$164$$ −3.00000 5.19615i −0.234261 0.405751i
$$165$$ 0 0
$$166$$ −3.00000 + 5.19615i −0.232845 + 0.403300i
$$167$$ −3.00000 −0.232147 −0.116073 0.993241i $$-0.537031\pi$$
−0.116073 + 0.993241i $$0.537031\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i $$0.460934\pi$$
−0.920722 + 0.390218i $$0.872399\pi$$
$$174$$ 0 0
$$175$$ 10.0000 8.66025i 0.755929 0.654654i
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ −9.00000 15.5885i −0.674579 1.16840i
$$179$$ −7.50000 12.9904i −0.560576 0.970947i −0.997446 0.0714220i $$-0.977246\pi$$
0.436870 0.899525i $$-0.356087\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ −2.50000 0.866025i −0.185312 0.0641941i
$$183$$ 0 0
$$184$$ −3.00000 + 5.19615i −0.221163 + 0.383065i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −3.00000 + 5.19615i −0.219382 + 0.379980i
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i $$-0.763683\pi$$
0.953912 + 0.300088i $$0.0970159\pi$$
$$192$$ 0 0
$$193$$ −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i $$-0.998575\pi$$
0.496119 0.868255i $$-0.334758\pi$$
$$194$$ 6.50000 11.2583i 0.466673 0.808301i
$$195$$ 0 0
$$196$$ 5.50000 + 4.33013i 0.392857 + 0.309295i
$$197$$ 3.00000 0.213741 0.106871 0.994273i $$-0.465917\pi$$
0.106871 + 0.994273i $$0.465917\pi$$
$$198$$ 0 0
$$199$$ −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i $$-0.331945\pi$$
−0.999990 + 0.00436292i $$0.998611\pi$$
$$200$$ 2.50000 + 4.33013i 0.176777 + 0.306186i
$$201$$ 0 0
$$202$$ 15.0000 1.05540
$$203$$ 4.50000 + 23.3827i 0.315838 + 1.64114i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 8.00000 + 13.8564i 0.557386 + 0.965422i
$$207$$ 0 0
$$208$$ 0.500000 0.866025i 0.0346688 0.0600481i
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ −10.0000 −0.688428 −0.344214 0.938891i $$-0.611855\pi$$
−0.344214 + 0.938891i $$0.611855\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 6.00000 + 10.3923i 0.410152 + 0.710403i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 8.00000 6.92820i 0.543075 0.470317i
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 3.00000 + 5.19615i 0.201802 + 0.349531i
$$222$$ 0 0
$$223$$ 26.0000 1.74109 0.870544 0.492090i $$-0.163767\pi$$
0.870544 + 0.492090i $$0.163767\pi$$
$$224$$ −2.00000 + 1.73205i −0.133631 + 0.115728i
$$225$$ 0 0
$$226$$ 4.50000 7.79423i 0.299336 0.518464i
$$227$$ 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i $$0.0371134\pi$$
−0.395860 + 0.918311i $$0.629553\pi$$
$$228$$ 0 0
$$229$$ 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i $$-0.656030\pi$$
0.999442 0.0334101i $$-0.0106368\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −9.00000 −0.590879
$$233$$ −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i $$-0.896303\pi$$
0.750867 + 0.660454i $$0.229636\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −1.50000 + 2.59808i −0.0976417 + 0.169120i
$$237$$ 0 0
$$238$$ −3.00000 15.5885i −0.194461 1.01045i
$$239$$ 9.00000 0.582162 0.291081 0.956698i $$-0.405985\pi$$
0.291081 + 0.956698i $$0.405985\pi$$
$$240$$ 0 0
$$241$$ −13.0000 22.5167i −0.837404 1.45043i −0.892058 0.451920i $$-0.850739\pi$$
0.0546547 0.998505i $$-0.482594\pi$$
$$242$$ −0.500000 0.866025i −0.0321412 0.0556702i
$$243$$ 0 0
$$244$$ 11.0000 0.704203
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.00000 1.73205i 0.0636285 0.110208i
$$248$$ 2.00000 + 3.46410i 0.127000 + 0.219971i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 6.00000 0.377217
$$254$$ 3.50000 6.06218i 0.219610 0.380375i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i $$-0.803506\pi$$
0.909010 + 0.416775i $$0.136840\pi$$
$$258$$ 0 0
$$259$$ 5.00000 + 1.73205i 0.310685 + 0.107624i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 9.00000 + 15.5885i 0.556022 + 0.963058i
$$263$$ −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i $$-0.256167\pi$$
−0.970758 + 0.240059i $$0.922833\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −4.00000 + 3.46410i −0.245256 + 0.212398i
$$267$$ 0 0
$$268$$ −5.50000 + 9.52628i −0.335966 + 0.581910i
$$269$$ 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i $$-0.0474530\pi$$
−0.623082 + 0.782157i $$0.714120\pi$$
$$270$$ 0 0
$$271$$ −14.5000 + 25.1147i −0.880812 + 1.52561i −0.0303728 + 0.999539i $$0.509669\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ 9.00000 0.543710
$$275$$ 2.50000 4.33013i 0.150756 0.261116i
$$276$$ 0 0
$$277$$ −14.5000 25.1147i −0.871221 1.50900i −0.860735 0.509053i $$-0.829996\pi$$
−0.0104855 0.999945i $$-0.503338\pi$$
$$278$$ −4.00000 + 6.92820i −0.239904 + 0.415526i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i $$-0.0706075\pi$$
−0.678280 + 0.734804i $$0.737274\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −1.00000 −0.0591312
$$287$$ −3.00000 15.5885i −0.177084 0.920158i
$$288$$ 0 0
$$289$$ −9.50000 + 16.4545i −0.558824 + 0.967911i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −1.00000 + 1.73205i −0.0585206 + 0.101361i
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −1.00000 + 1.73205i −0.0581238 + 0.100673i
$$297$$ 0 0
$$298$$ 3.00000 + 5.19615i 0.173785 + 0.301005i
$$299$$ 3.00000 5.19615i 0.173494 0.300501i
$$300$$ 0 0
$$301$$ 2.00000 + 10.3923i 0.115278 + 0.599002i
$$302$$ −19.0000 −1.09333
$$303$$ 0 0
$$304$$ −1.00000 1.73205i −0.0573539 0.0993399i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 20.0000 1.14146 0.570730 0.821138i $$-0.306660\pi$$
0.570730 + 0.821138i $$0.306660\pi$$
$$308$$ 2.50000 + 0.866025i 0.142451 + 0.0493464i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i $$0.0715523\pi$$
−0.294384 + 0.955687i $$0.595114\pi$$
$$312$$ 0 0
$$313$$ −8.50000 + 14.7224i −0.480448 + 0.832161i −0.999748 0.0224310i $$-0.992859\pi$$
0.519300 + 0.854592i $$0.326193\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 0 0
$$316$$ 5.00000 0.281272
$$317$$ 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i $$-0.723923\pi$$
0.983866 + 0.178908i $$0.0572566\pi$$
$$318$$ 0 0
$$319$$ 4.50000 + 7.79423i 0.251952 + 0.436393i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −12.0000 + 10.3923i −0.668734 + 0.579141i
$$323$$ 12.0000 0.667698
$$324$$ 0 0
$$325$$ −2.50000 4.33013i −0.138675 0.240192i
$$326$$ −8.50000 14.7224i −0.470771 0.815400i
$$327$$ 0 0
$$328$$ 6.00000 0.331295
$$329$$ 15.0000 + 5.19615i 0.826977 + 0.286473i
$$330$$ 0 0
$$331$$ −17.5000 + 30.3109i −0.961887 + 1.66604i −0.244131 + 0.969742i $$0.578503\pi$$
−0.717756 + 0.696295i $$0.754831\pi$$
$$332$$ −3.00000 5.19615i −0.164646 0.285176i
$$333$$ 0 0
$$334$$ 1.50000 2.59808i 0.0820763 0.142160i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 6.00000 10.3923i 0.326357 0.565267i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 2.00000 3.46410i 0.108306 0.187592i
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ −4.00000 −0.215666
$$345$$ 0 0
$$346$$ −10.5000 18.1865i −0.564483 0.977714i
$$347$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 2.50000 + 12.9904i 0.133631 + 0.694365i
$$351$$ 0 0
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i $$-0.325675\pi$$
−0.999711 + 0.0240566i $$0.992342\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 18.0000 0.953998
$$357$$ 0 0
$$358$$ 15.0000 0.792775
$$359$$ −1.50000 + 2.59808i −0.0791670 + 0.137121i −0.902891 0.429870i $$-0.858559\pi$$
0.823724 + 0.566991i $$0.191893\pi$$
$$360$$ 0 0
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ −1.00000 + 1.73205i −0.0525588 + 0.0910346i
$$363$$ 0 0
$$364$$ 2.00000 1.73205i 0.104828 0.0907841i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 5.00000 + 8.66025i 0.260998 + 0.452062i 0.966507 0.256639i $$-0.0826151\pi$$
−0.705509 + 0.708700i $$0.749282\pi$$
$$368$$ −3.00000 5.19615i −0.156386 0.270868i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 15.5000 26.8468i 0.802560 1.39007i −0.115367 0.993323i $$-0.536804\pi$$
0.917926 0.396751i $$-0.129862\pi$$
$$374$$ −3.00000 5.19615i −0.155126 0.268687i
$$375$$ 0 0
$$376$$ −3.00000 + 5.19615i −0.154713 + 0.267971i
$$377$$ 9.00000 0.463524
$$378$$ 0 0
$$379$$ 23.0000 1.18143 0.590715 0.806880i $$-0.298846\pi$$
0.590715 + 0.806880i $$0.298846\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 3.00000 + 5.19615i 0.153493 + 0.265858i
$$383$$ −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i $$0.538281\pi$$
−0.799783 + 0.600289i $$0.795052\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 14.0000 0.712581
$$387$$ 0 0
$$388$$ 6.50000 + 11.2583i 0.329988 + 0.571555i
$$389$$ 6.00000 + 10.3923i 0.304212 + 0.526911i 0.977086 0.212847i $$-0.0682735\pi$$
−0.672874 + 0.739758i $$0.734940\pi$$
$$390$$ 0 0
$$391$$ 36.0000 1.82060
$$392$$ −6.50000 + 2.59808i −0.328300 + 0.131223i
$$393$$ 0 0
$$394$$ −1.50000 + 2.59808i −0.0755689 + 0.130889i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i $$-0.647170\pi$$
0.998125 0.0612128i $$-0.0194968\pi$$
$$398$$ 14.0000 0.701757
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ −16.5000 + 28.5788i −0.823971 + 1.42716i 0.0787327 + 0.996896i $$0.474913\pi$$
−0.902703 + 0.430263i $$0.858421\pi$$
$$402$$ 0 0
$$403$$ −2.00000 3.46410i −0.0996271 0.172559i
$$404$$ −7.50000 + 12.9904i −0.373139 + 0.646296i
$$405$$ 0 0
$$406$$ −22.5000 7.79423i −1.11666 0.386821i
$$407$$ 2.00000 0.0991363
$$408$$ 0 0
$$409$$ 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i $$-0.135136\pi$$
−0.812333 + 0.583193i $$0.801803\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −16.0000 −0.788263
$$413$$ −6.00000 + 5.19615i −0.295241 + 0.255686i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0.500000 + 0.866025i 0.0245145 + 0.0424604i
$$417$$ 0 0
$$418$$ −1.00000 + 1.73205i −0.0489116 + 0.0847174i
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −28.0000 −1.36464 −0.682318 0.731055i $$-0.739028\pi$$
−0.682318 + 0.731055i $$0.739028\pi$$
$$422$$ 5.00000 8.66025i 0.243396 0.421575i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 15.0000 25.9808i 0.727607 1.26025i
$$426$$ 0 0
$$427$$ 27.5000 + 9.52628i 1.33082 + 0.461009i
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.50000 2.59808i −0.0722525 0.125145i 0.827636 0.561266i $$-0.189685\pi$$
−0.899888 + 0.436121i $$0.856352\pi$$
$$432$$ 0 0
$$433$$ −34.0000 −1.63394 −0.816968 0.576683i $$-0.804347\pi$$
−0.816968 + 0.576683i $$0.804347\pi$$
$$434$$ 2.00000 + 10.3923i 0.0960031 + 0.498847i
$$435$$ 0 0
$$436$$ −1.00000 + 1.73205i −0.0478913 + 0.0829502i
$$437$$ −6.00000 10.3923i −0.287019 0.497131i
$$438$$ 0 0
$$439$$ 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i $$-0.825737\pi$$
0.877711 + 0.479191i $$0.159070\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −6.00000 −0.285391
$$443$$ 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i $$-0.741317\pi$$
0.972626 + 0.232377i $$0.0746503\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −13.0000 + 22.5167i −0.615568 + 1.06619i
$$447$$ 0 0
$$448$$ −0.500000 2.59808i −0.0236228 0.122748i
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ −3.00000 5.19615i −0.141264 0.244677i
$$452$$ 4.50000 + 7.79423i 0.211662 + 0.366610i
$$453$$ 0 0
$$454$$ −18.0000 −0.844782
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i $$-0.661289\pi$$
0.999857 0.0168929i $$-0.00537742\pi$$
$$458$$ 8.00000 + 13.8564i 0.373815 + 0.647467i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −21.0000 −0.978068 −0.489034 0.872265i $$-0.662651\pi$$
−0.489034 + 0.872265i $$0.662651\pi$$
$$462$$ 0 0
$$463$$ −22.0000 −1.02243 −0.511213 0.859454i $$-0.670804\pi$$
−0.511213 + 0.859454i $$0.670804\pi$$
$$464$$ 4.50000 7.79423i 0.208907 0.361838i
$$465$$ 0 0
$$466$$ −3.00000 5.19615i −0.138972 0.240707i
$$467$$ 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i $$-0.743779\pi$$
0.970799 + 0.239892i $$0.0771121\pi$$
$$468$$ 0 0
$$469$$ −22.0000 + 19.0526i −1.01587 + 0.879765i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −1.50000 2.59808i −0.0690431 0.119586i
$$473$$ 2.00000 + 3.46410i 0.0919601 + 0.159280i
$$474$$ 0 0
$$475$$ −10.0000 −0.458831
$$476$$ 15.0000 + 5.19615i 0.687524 + 0.238165i
$$477$$ 0 0
$$478$$ −4.50000 + 7.79423i −0.205825 + 0.356500i
$$479$$ 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i $$-0.0553307\pi$$
−0.642246 + 0.766498i $$0.721997\pi$$
$$480$$ 0 0
$$481$$ 1.00000 1.73205i 0.0455961 0.0789747i
$$482$$ 26.0000 1.18427
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −10.0000 17.3205i −0.453143 0.784867i 0.545436 0.838152i $$-0.316364\pi$$
−0.998579 + 0.0532853i $$0.983031\pi$$
$$488$$ −5.50000 + 9.52628i −0.248973 + 0.431234i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −42.0000 −1.89543 −0.947717 0.319113i $$-0.896615\pi$$
−0.947717 + 0.319113i $$0.896615\pi$$
$$492$$ 0 0
$$493$$ 27.0000 + 46.7654i 1.21602 + 2.10621i
$$494$$ 1.00000 + 1.73205i 0.0449921 + 0.0779287i
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 20.0000 34.6410i 0.895323 1.55074i 0.0619186 0.998081i $$-0.480278\pi$$
0.833404 0.552664i $$-0.186389\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −6.00000 + 10.3923i −0.267793 + 0.463831i
$$503$$ 33.0000 1.47140 0.735699 0.677309i $$-0.236854\pi$$
0.735699 + 0.677309i $$0.236854\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −3.00000 + 5.19615i −0.133366 + 0.230997i
$$507$$ 0 0
$$508$$ 3.50000 + 6.06218i 0.155287 + 0.268966i
$$509$$ −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i $$-0.875786\pi$$
0.791849 + 0.610718i $$0.209119\pi$$
$$510$$ 0 0
$$511$$ −4.00000 + 3.46410i −0.176950 + 0.153243i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 1.50000 + 2.59808i 0.0661622 + 0.114596i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 6.00000 0.263880
$$518$$ −4.00000 + 3.46410i −0.175750 + 0.152204i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −21.0000 36.3731i −0.920027 1.59353i −0.799370 0.600839i $$-0.794833\pi$$
−0.120656 0.992694i $$-0.538500\pi$$
$$522$$ 0 0
$$523$$ 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i $$-0.719578\pi$$
0.986216 + 0.165460i $$0.0529109\pi$$
$$524$$ −18.0000 −0.786334
$$525$$ 0 0
$$526$$ 9.00000 0.392419
$$527$$ 12.0000 20.7846i 0.522728 0.905392i
$$528$$ 0 0
$$529$$ −6.50000 11.2583i −0.282609 0.489493i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −1.00000 5.19615i −0.0433555 0.225282i
$$533$$ −6.00000 −0.259889
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −5.50000 9.52628i −0.237564 0.411473i
$$537$$ 0 0
$$538$$ −12.0000 −0.517357
$$539$$ 5.50000 + 4.33013i 0.236902 + 0.186512i
$$540$$ 0 0
$$541$$ 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i $$-0.652733\pi$$
0.999042 0.0437584i $$-0.0139332\pi$$
$$542$$ −14.5000 25.1147i −0.622828 1.07877i
$$543$$ 0 0
$$544$$ −3.00000 + 5.19615i −0.128624 + 0.222783i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ −4.50000 + 7.79423i −0.192230 + 0.332953i
$$549$$ 0 0
$$550$$ 2.50000 + 4.33013i 0.106600 + 0.184637i
$$551$$ 9.00000 15.5885i 0.383413 0.664091i
$$552$$ 0 0
$$553$$ 12.5000 + 4.33013i 0.531554 + 0.184136i
$$554$$ 29.0000 1.23209
$$555$$ 0 0
$$556$$ −4.00000 6.92820i −0.169638 0.293821i
$$557$$ −9.00000 15.5885i −0.381342 0.660504i 0.609912 0.792469i $$-0.291205\pi$$
−0.991254 + 0.131965i $$0.957871\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 9.00000 15.5885i 0.379642 0.657559i
$$563$$ −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i $$-0.290503\pi$$
−0.990961 + 0.134148i $$0.957170\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −10.0000 −0.420331
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −18.0000 + 31.1769i −0.754599 + 1.30700i 0.190974 + 0.981595i $$0.438835\pi$$
−0.945573 + 0.325409i $$0.894498\pi$$
$$570$$ 0 0
$$571$$ −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i $$-0.933141\pi$$
0.308443 0.951243i $$-0.400192\pi$$
$$572$$ 0.500000 0.866025i 0.0209061 0.0362103i
$$573$$ 0 0
$$574$$ 15.0000 + 5.19615i 0.626088 + 0.216883i
$$575$$ −30.0000 −1.25109
$$576$$ 0 0
$$577$$ 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i $$-0.120121\pi$$
−0.783930 + 0.620850i $$0.786788\pi$$
$$578$$ −9.50000 16.4545i −0.395148 0.684416i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3.00000 15.5885i −0.124461 0.646718i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −1.00000 1.73205i −0.0413803 0.0716728i
$$585$$ 0 0
$$586$$ −15.0000 + 25.9808i −0.619644 + 1.07326i
$$587$$ −9.00000 −0.371470 −0.185735 0.982600i $$-0.559467\pi$$
−0.185735 + 0.982600i $$0.559467\pi$$
$$588$$ 0 0
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.00000 1.73205i −0.0410997 0.0711868i
$$593$$ 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i $$-0.568551\pi$$
0.952869 0.303383i $$-0.0981160\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 0 0
$$598$$ 3.00000 + 5.19615i 0.122679 + 0.212486i
$$599$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$600$$ 0 0
$$601$$ 2.00000 0.0815817 0.0407909 0.999168i $$-0.487012\pi$$
0.0407909 + 0.999168i $$0.487012\pi$$
$$602$$ −10.0000 3.46410i −0.407570 0.141186i
$$603$$ 0 0
$$604$$ 9.50000 16.4545i 0.386550 0.669523i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 20.0000 34.6410i 0.811775 1.40604i −0.0998457 0.995003i $$-0.531835\pi$$
0.911621 0.411033i $$-0.134832\pi$$
$$608$$ 2.00000 0.0811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 3.00000 5.19615i 0.121367 0.210214i
$$612$$ 0 0
$$613$$ 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i $$-0.101939\pi$$
−0.747208 + 0.664590i $$0.768606\pi$$
$$614$$ −10.0000 + 17.3205i −0.403567 + 0.698999i
$$615$$ 0 0
$$616$$ −2.00000 + 1.73205i −0.0805823 + 0.0697863i
$$617$$ −21.0000 −0.845428 −0.422714 0.906263i $$-0.638923\pi$$
−0.422714 + 0.906263i $$0.638923\pi$$
$$618$$ 0 0
$$619$$ −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i $$-0.298329\pi$$
−0.993959 + 0.109749i $$0.964995\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −24.0000 −0.962312
$$623$$ 45.0000 + 15.5885i 1.80289 + 0.624538i
$$624$$ 0 0
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ −8.50000 14.7224i −0.339728 0.588427i
$$627$$ 0 0
$$628$$ 2.00000 3.46410i 0.0798087 0.138233i
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ −2.50000 + 4.33013i −0.0994447 + 0.172243i
$$633$$ 0 0
$$634$$ 6.00000 + 10.3923i 0.238290 + 0.412731i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.50000 2.59808i 0.257539 0.102940i
$$638$$ −9.00000 −0.356313
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i $$-0.109788\pi$$
−0.763367 + 0.645966i $$0.776455\pi$$
$$642$$ 0 0
$$643$$ 5.00000 0.197181 0.0985904 0.995128i $$-0.468567\pi$$
0.0985904 + 0.995128i $$0.468567\pi$$
$$644$$ −3.00000 15.5885i −0.118217 0.614271i
$$645$$ 0 0
$$646$$ −6.00000 + 10.3923i −0.236067 + 0.408880i
$$647$$ −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i $$-0.242465\pi$$
−0.959529 + 0.281609i $$0.909132\pi$$
$$648$$ 0 0
$$649$$ −1.50000 + 2.59808i −0.0588802 + 0.101983i
$$650$$ 5.00000 0.196116
$$651$$ 0 0
$$652$$ 17.0000 0.665771
$$653$$ 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i $$-0.718768\pi$$
0.986634 + 0.162951i $$0.0521013\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −3.00000 + 5.19615i −0.117130 + 0.202876i
$$657$$ 0 0
$$658$$ −12.0000 + 10.3923i −0.467809 + 0.405134i
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i $$-0.254441\pi$$
−0.969442 + 0.245319i $$0.921107\pi$$
$$662$$ −17.5000 30.3109i −0.680157 1.17807i
$$663$$ 0 0
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 27.0000 46.7654i 1.04544 1.81076i
$$668$$ 1.50000 + 2.59808i 0.0580367 + 0.100523i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 11.0000 0.424650
$$672$$ 0 0
$$673$$ −28.0000 −1.07932 −0.539660 0.841883i $$-0.681447\pi$$
−0.539660 + 0.841883i $$0.681447\pi$$
$$674$$ −7.00000 + 12.1244i −0.269630 + 0.467013i
$$675$$ 0 0
$$676$$ 6.00000 + 10.3923i 0.230769 + 0.399704i
$$677$$ 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i $$-0.796551\pi$$
0.917899 + 0.396813i $$0.129884\pi$$
$$678$$ 0 0
$$679$$ 6.50000 + 33.7750i 0.249447 + 1.29617i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 2.00000 + 3.46410i 0.0765840 + 0.132647i
$$683$$ −10.5000 18.1865i −0.401771 0.695888i 0.592168 0.805814i $$-0.298272\pi$$
−0.993940 + 0.109926i $$0.964939\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −18.5000 + 0.866025i −0.706333 + 0.0330650i
$$687$$ 0 0
$$688$$ 2.00000 3.46410i 0.0762493 0.132068i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −5.50000 + 9.52628i −0.209230 + 0.362397i −0.951472 0.307735i $$-0.900429\pi$$
0.742242 + 0.670132i $$0.233762\pi$$
$$692$$ 21.0000 0.798300
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −18.0000 31.1769i −0.681799 1.18091i
$$698$$ −1.00000 + 1.73205i −0.0378506 + 0.0655591i
$$699$$ 0 0
$$700$$ −12.5000 4.33013i −0.472456 0.163663i
$$701$$ −39.0000 −1.47301 −0.736505 0.676432i $$-0.763525\pi$$
−0.736505 + 0.676432i $$0.763525\pi$$
$$702$$ 0 0
$$703$$ −2.00000 3.46410i −0.0754314 0.130651i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ −30.0000 + 25.9808i −1.12827 + 0.977107i
$$708$$ 0 0
$$709$$ −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i $$-0.995689\pi$$
0.511683 + 0.859174i $$0.329022\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −9.00000 + 15.5885i −0.337289 + 0.584202i
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −7.50000 + 12.9904i −0.280288 + 0.485473i
$$717$$ 0 0
$$718$$ −1.50000 2.59808i −0.0559795 0.0969593i
$$719$$ −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i $$0.453064\pi$$
−0.930087 + 0.367338i $$0.880269\pi$$
$$720$$ 0 0
$$721$$ −40.0000 13.8564i −1.48968 0.516040i
$$722$$ −15.0000 −0.558242
$$723$$ 0 0
$$724$$ −1.00000 1.73205i −0.0371647 0.0643712i
$$725$$ −22.5000 38.9711i −0.835629 1.44735i
$$726$$ 0 0
$$727$$ 14.0000 0.519231 0.259616 0.965712i $$-0.416404\pi$$
0.259616 + 0.965712i $$0.416404\pi$$
$$728$$ 0.500000 + 2.59808i 0.0185312 + 0.0962911i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 12.0000 + 20.7846i 0.443836 + 0.768747i
$$732$$ 0 0
$$733$$ 12.5000 21.6506i 0.461698 0.799684i −0.537348 0.843361i $$-0.680574\pi$$
0.999046 + 0.0436764i $$0.0139070\pi$$
$$734$$ −10.0000 −0.369107
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ −5.50000 + 9.52628i −0.202595 + 0.350905i
$$738$$ 0 0
$$739$$ −25.0000 43.3013i −0.919640 1.59286i −0.799962 0.600050i $$-0.795147\pi$$
−0.119677 0.992813i $$-0.538186\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 36.0000 1.32071 0.660356 0.750953i $$-0.270405\pi$$
0.660356 + 0.750953i $$0.270405\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 15.5000 + 26.8468i 0.567495 + 0.982931i
$$747$$ 0 0
$$748$$ 6.00000 0.219382
$$749$$ −30.0000 10.3923i −1.09618 0.379727i
$$750$$ 0 0
$$751$$ 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i $$-0.810082\pi$$
0.900207 + 0.435463i $$0.143415\pi$$
$$752$$ −3.00000 5.19615i −0.109399 0.189484i
$$753$$ 0 0
$$754$$ −4.50000 + 7.79423i −0.163880 + 0.283849i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −46.0000 −1.67190 −0.835949 0.548807i $$-0.815082\pi$$
−0.835949 + 0.548807i $$0.815082\pi$$
$$758$$ −11.5000 + 19.9186i −0.417699 + 0.723476i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i $$-0.939118\pi$$
0.655515 + 0.755182i $$0.272452\pi$$
$$762$$ 0 0
$$763$$ −4.00000 + 3.46410i −0.144810 + 0.125409i
$$764$$ −6.00000 −0.217072
$$765$$ 0 0
$$766$$ −18.0000 31.1769i −0.650366 1.12647i
$$767$$ 1.50000 + 2.59808i 0.0541619 + 0.0938111i
$$768$$ 0 0
$$769$$ −22.0000 −0.793340 −0.396670 0.917961i $$-0.629834\pi$$
−0.396670 + 0.917961i $$0.629834\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −7.00000 + 12.1244i −0.251936 + 0.436365i
$$773$$ 12.0000 + 20.7846i 0.431610 + 0.747570i 0.997012 0.0772449i $$-0.0246123\pi$$
−0.565402 + 0.824815i $$0.691279\pi$$
$$774$$ 0 0
$$775$$ −10.0000 + 17.3205i −0.359211 + 0.622171i
$$776$$ −13.0000 −0.466673
$$777$$ 0 0
$$778$$ −12.0000 −0.430221
$$779$$ −6.00000 + 10.3923i −0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −18.0000 + 31.1769i −0.643679 + 1.11488i
$$783$$ 0 0
$$784$$ 1.00000 6.92820i 0.0357143 0.247436i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −7.00000 12.1244i −0.249523 0.432187i 0.713871 0.700278i $$-0.246941\pi$$
−0.963394 + 0.268091i $$0.913607\pi$$
$$788$$ −1.50000 2.59808i −0.0534353 0.0925526i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 4.50000 + 23.3827i 0.160002 + 0.831393i
$$792$$ 0 0
$$793$$ 5.50000 9.52628i 0.195311 0.338288i
$$794$$ 11.0000 + 19.0526i 0.390375 + 0.676150i
$$795$$ 0 0