# Properties

 Label 1024.2.e.b.257.1 Level $1024$ Weight $2$ Character 1024.257 Analytic conductor $8.177$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1024 = 2^{10}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1024.e (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.17668116698$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 512) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 257.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1024.257 Dual form 1024.2.e.b.769.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 2.00000i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +O(q^{10})$$ $$q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 2.00000i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +(-1.00000 + 1.00000i) q^{11} +(2.00000 + 2.00000i) q^{13} +4.00000 q^{15} +4.00000 q^{17} +(-5.00000 - 5.00000i) q^{19} +(4.00000 - 4.00000i) q^{21} -4.00000i q^{23} -3.00000i q^{25} +(-4.00000 + 4.00000i) q^{27} +(-6.00000 - 6.00000i) q^{29} -8.00000 q^{31} +2.00000 q^{33} +(-8.00000 - 8.00000i) q^{35} +(2.00000 - 2.00000i) q^{37} -4.00000i q^{39} +2.00000i q^{41} +(-3.00000 + 3.00000i) q^{43} +(2.00000 + 2.00000i) q^{45} -9.00000 q^{49} +(-4.00000 - 4.00000i) q^{51} +(-2.00000 + 2.00000i) q^{53} -4.00000i q^{55} +10.0000i q^{57} +(3.00000 - 3.00000i) q^{59} +(6.00000 + 6.00000i) q^{61} +4.00000 q^{63} -8.00000 q^{65} +(-3.00000 - 3.00000i) q^{67} +(-4.00000 + 4.00000i) q^{69} -4.00000i q^{71} -4.00000i q^{73} +(-3.00000 + 3.00000i) q^{75} +(-4.00000 - 4.00000i) q^{77} -8.00000 q^{79} +5.00000 q^{81} +(-7.00000 - 7.00000i) q^{83} +(-8.00000 + 8.00000i) q^{85} +12.0000i q^{87} -12.0000i q^{89} +(-8.00000 + 8.00000i) q^{91} +(8.00000 + 8.00000i) q^{93} +20.0000 q^{95} -4.00000 q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} - 4 q^{5} + O(q^{10})$$ $$2 q - 2 q^{3} - 4 q^{5} - 2 q^{11} + 4 q^{13} + 8 q^{15} + 8 q^{17} - 10 q^{19} + 8 q^{21} - 8 q^{27} - 12 q^{29} - 16 q^{31} + 4 q^{33} - 16 q^{35} + 4 q^{37} - 6 q^{43} + 4 q^{45} - 18 q^{49} - 8 q^{51} - 4 q^{53} + 6 q^{59} + 12 q^{61} + 8 q^{63} - 16 q^{65} - 6 q^{67} - 8 q^{69} - 6 q^{75} - 8 q^{77} - 16 q^{79} + 10 q^{81} - 14 q^{83} - 16 q^{85} - 16 q^{91} + 16 q^{93} + 40 q^{95} - 8 q^{97} + 2 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$1023$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$1$$

## 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 0
$$3$$ −1.00000 1.00000i −0.577350 0.577350i 0.356822 0.934172i $$-0.383860\pi$$
−0.934172 + 0.356822i $$0.883860\pi$$
$$4$$ 0 0
$$5$$ −2.00000 + 2.00000i −0.894427 + 0.894427i −0.994936 0.100509i $$-0.967953\pi$$
0.100509 + 0.994936i $$0.467953\pi$$
$$6$$ 0 0
$$7$$ 4.00000i 1.51186i 0.654654 + 0.755929i $$0.272814\pi$$
−0.654654 + 0.755929i $$0.727186\pi$$
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ −1.00000 + 1.00000i −0.301511 + 0.301511i −0.841605 0.540094i $$-0.818389\pi$$
0.540094 + 0.841605i $$0.318389\pi$$
$$12$$ 0 0
$$13$$ 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i $$-0.121703\pi$$
−0.373094 + 0.927794i $$0.621703\pi$$
$$14$$ 0 0
$$15$$ 4.00000 1.03280
$$16$$ 0 0
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ 0 0
$$19$$ −5.00000 5.00000i −1.14708 1.14708i −0.987124 0.159954i $$-0.948865\pi$$
−0.159954 0.987124i $$-0.551135\pi$$
$$20$$ 0 0
$$21$$ 4.00000 4.00000i 0.872872 0.872872i
$$22$$ 0 0
$$23$$ 4.00000i 0.834058i −0.908893 0.417029i $$-0.863071\pi$$
0.908893 0.417029i $$-0.136929\pi$$
$$24$$ 0 0
$$25$$ 3.00000i 0.600000i
$$26$$ 0 0
$$27$$ −4.00000 + 4.00000i −0.769800 + 0.769800i
$$28$$ 0 0
$$29$$ −6.00000 6.00000i −1.11417 1.11417i −0.992580 0.121592i $$-0.961200\pi$$
−0.121592 0.992580i $$-0.538800\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 0 0
$$33$$ 2.00000 0.348155
$$34$$ 0 0
$$35$$ −8.00000 8.00000i −1.35225 1.35225i
$$36$$ 0 0
$$37$$ 2.00000 2.00000i 0.328798 0.328798i −0.523331 0.852129i $$-0.675311\pi$$
0.852129 + 0.523331i $$0.175311\pi$$
$$38$$ 0 0
$$39$$ 4.00000i 0.640513i
$$40$$ 0 0
$$41$$ 2.00000i 0.312348i 0.987730 + 0.156174i $$0.0499160\pi$$
−0.987730 + 0.156174i $$0.950084\pi$$
$$42$$ 0 0
$$43$$ −3.00000 + 3.00000i −0.457496 + 0.457496i −0.897833 0.440337i $$-0.854859\pi$$
0.440337 + 0.897833i $$0.354859\pi$$
$$44$$ 0 0
$$45$$ 2.00000 + 2.00000i 0.298142 + 0.298142i
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −9.00000 −1.28571
$$50$$ 0 0
$$51$$ −4.00000 4.00000i −0.560112 0.560112i
$$52$$ 0 0
$$53$$ −2.00000 + 2.00000i −0.274721 + 0.274721i −0.830997 0.556276i $$-0.812230\pi$$
0.556276 + 0.830997i $$0.312230\pi$$
$$54$$ 0 0
$$55$$ 4.00000i 0.539360i
$$56$$ 0 0
$$57$$ 10.0000i 1.32453i
$$58$$ 0 0
$$59$$ 3.00000 3.00000i 0.390567 0.390567i −0.484323 0.874889i $$-0.660934\pi$$
0.874889 + 0.484323i $$0.160934\pi$$
$$60$$ 0 0
$$61$$ 6.00000 + 6.00000i 0.768221 + 0.768221i 0.977793 0.209572i $$-0.0672070\pi$$
−0.209572 + 0.977793i $$0.567207\pi$$
$$62$$ 0 0
$$63$$ 4.00000 0.503953
$$64$$ 0 0
$$65$$ −8.00000 −0.992278
$$66$$ 0 0
$$67$$ −3.00000 3.00000i −0.366508 0.366508i 0.499694 0.866202i $$-0.333446\pi$$
−0.866202 + 0.499694i $$0.833446\pi$$
$$68$$ 0 0
$$69$$ −4.00000 + 4.00000i −0.481543 + 0.481543i
$$70$$ 0 0
$$71$$ 4.00000i 0.474713i −0.971423 0.237356i $$-0.923719\pi$$
0.971423 0.237356i $$-0.0762809\pi$$
$$72$$ 0 0
$$73$$ 4.00000i 0.468165i −0.972217 0.234082i $$-0.924791\pi$$
0.972217 0.234082i $$-0.0752085\pi$$
$$74$$ 0 0
$$75$$ −3.00000 + 3.00000i −0.346410 + 0.346410i
$$76$$ 0 0
$$77$$ −4.00000 4.00000i −0.455842 0.455842i
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 5.00000 0.555556
$$82$$ 0 0
$$83$$ −7.00000 7.00000i −0.768350 0.768350i 0.209466 0.977816i $$-0.432827\pi$$
−0.977816 + 0.209466i $$0.932827\pi$$
$$84$$ 0 0
$$85$$ −8.00000 + 8.00000i −0.867722 + 0.867722i
$$86$$ 0 0
$$87$$ 12.0000i 1.28654i
$$88$$ 0 0
$$89$$ 12.0000i 1.27200i −0.771690 0.635999i $$-0.780588\pi$$
0.771690 0.635999i $$-0.219412\pi$$
$$90$$ 0 0
$$91$$ −8.00000 + 8.00000i −0.838628 + 0.838628i
$$92$$ 0 0
$$93$$ 8.00000 + 8.00000i 0.829561 + 0.829561i
$$94$$ 0 0
$$95$$ 20.0000 2.05196
$$96$$ 0 0
$$97$$ −4.00000 −0.406138 −0.203069 0.979164i $$-0.565092\pi$$
−0.203069 + 0.979164i $$0.565092\pi$$
$$98$$ 0 0
$$99$$ 1.00000 + 1.00000i 0.100504 + 0.100504i
$$100$$ 0 0
$$101$$ 2.00000 2.00000i 0.199007 0.199007i −0.600567 0.799574i $$-0.705058\pi$$
0.799574 + 0.600567i $$0.205058\pi$$
$$102$$ 0 0
$$103$$ 12.0000i 1.18240i 0.806527 + 0.591198i $$0.201345\pi$$
−0.806527 + 0.591198i $$0.798655\pi$$
$$104$$ 0 0
$$105$$ 16.0000i 1.56144i
$$106$$ 0 0
$$107$$ 7.00000 7.00000i 0.676716 0.676716i −0.282540 0.959256i $$-0.591177\pi$$
0.959256 + 0.282540i $$0.0911770\pi$$
$$108$$ 0 0
$$109$$ −10.0000 10.0000i −0.957826 0.957826i 0.0413197 0.999146i $$-0.486844\pi$$
−0.999146 + 0.0413197i $$0.986844\pi$$
$$110$$ 0 0
$$111$$ −4.00000 −0.379663
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ 8.00000 + 8.00000i 0.746004 + 0.746004i
$$116$$ 0 0
$$117$$ 2.00000 2.00000i 0.184900 0.184900i
$$118$$ 0 0
$$119$$ 16.0000i 1.46672i
$$120$$ 0 0
$$121$$ 9.00000i 0.818182i
$$122$$ 0 0
$$123$$ 2.00000 2.00000i 0.180334 0.180334i
$$124$$ 0 0
$$125$$ −4.00000 4.00000i −0.357771 0.357771i
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ 6.00000 0.528271
$$130$$ 0 0
$$131$$ 5.00000 + 5.00000i 0.436852 + 0.436852i 0.890951 0.454099i $$-0.150039\pi$$
−0.454099 + 0.890951i $$0.650039\pi$$
$$132$$ 0 0
$$133$$ 20.0000 20.0000i 1.73422 1.73422i
$$134$$ 0 0
$$135$$ 16.0000i 1.37706i
$$136$$ 0 0
$$137$$ 18.0000i 1.53784i −0.639343 0.768922i $$-0.720793\pi$$
0.639343 0.768922i $$-0.279207\pi$$
$$138$$ 0 0
$$139$$ −3.00000 + 3.00000i −0.254457 + 0.254457i −0.822795 0.568338i $$-0.807586\pi$$
0.568338 + 0.822795i $$0.307586\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −4.00000 −0.334497
$$144$$ 0 0
$$145$$ 24.0000 1.99309
$$146$$ 0 0
$$147$$ 9.00000 + 9.00000i 0.742307 + 0.742307i
$$148$$ 0 0
$$149$$ 2.00000 2.00000i 0.163846 0.163846i −0.620422 0.784268i $$-0.713039\pi$$
0.784268 + 0.620422i $$0.213039\pi$$
$$150$$ 0 0
$$151$$ 4.00000i 0.325515i −0.986666 0.162758i $$-0.947961\pi$$
0.986666 0.162758i $$-0.0520389\pi$$
$$152$$ 0 0
$$153$$ 4.00000i 0.323381i
$$154$$ 0 0
$$155$$ 16.0000 16.0000i 1.28515 1.28515i
$$156$$ 0 0
$$157$$ 6.00000 + 6.00000i 0.478852 + 0.478852i 0.904764 0.425912i $$-0.140047\pi$$
−0.425912 + 0.904764i $$0.640047\pi$$
$$158$$ 0 0
$$159$$ 4.00000 0.317221
$$160$$ 0 0
$$161$$ 16.0000 1.26098
$$162$$ 0 0
$$163$$ 7.00000 + 7.00000i 0.548282 + 0.548282i 0.925944 0.377661i $$-0.123272\pi$$
−0.377661 + 0.925944i $$0.623272\pi$$
$$164$$ 0 0
$$165$$ −4.00000 + 4.00000i −0.311400 + 0.311400i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i −0.885681 0.464294i $$-0.846308\pi$$
0.885681 0.464294i $$-0.153692\pi$$
$$168$$ 0 0
$$169$$ 5.00000i 0.384615i
$$170$$ 0 0
$$171$$ −5.00000 + 5.00000i −0.382360 + 0.382360i
$$172$$ 0 0
$$173$$ 10.0000 + 10.0000i 0.760286 + 0.760286i 0.976374 0.216088i $$-0.0693298\pi$$
−0.216088 + 0.976374i $$0.569330\pi$$
$$174$$ 0 0
$$175$$ 12.0000 0.907115
$$176$$ 0 0
$$177$$ −6.00000 −0.450988
$$178$$ 0 0
$$179$$ 1.00000 + 1.00000i 0.0747435 + 0.0747435i 0.743490 0.668747i $$-0.233169\pi$$
−0.668747 + 0.743490i $$0.733169\pi$$
$$180$$ 0 0
$$181$$ −6.00000 + 6.00000i −0.445976 + 0.445976i −0.894015 0.448038i $$-0.852123\pi$$
0.448038 + 0.894015i $$0.352123\pi$$
$$182$$ 0 0
$$183$$ 12.0000i 0.887066i
$$184$$ 0 0
$$185$$ 8.00000i 0.588172i
$$186$$ 0 0
$$187$$ −4.00000 + 4.00000i −0.292509 + 0.292509i
$$188$$ 0 0
$$189$$ −16.0000 16.0000i −1.16383 1.16383i
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 0 0
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 0 0
$$195$$ 8.00000 + 8.00000i 0.572892 + 0.572892i
$$196$$ 0 0
$$197$$ −10.0000 + 10.0000i −0.712470 + 0.712470i −0.967051 0.254581i $$-0.918062\pi$$
0.254581 + 0.967051i $$0.418062\pi$$
$$198$$ 0 0
$$199$$ 4.00000i 0.283552i 0.989899 + 0.141776i $$0.0452813\pi$$
−0.989899 + 0.141776i $$0.954719\pi$$
$$200$$ 0 0
$$201$$ 6.00000i 0.423207i
$$202$$ 0 0
$$203$$ 24.0000 24.0000i 1.68447 1.68447i
$$204$$ 0 0
$$205$$ −4.00000 4.00000i −0.279372 0.279372i
$$206$$ 0 0
$$207$$ −4.00000 −0.278019
$$208$$ 0 0
$$209$$ 10.0000 0.691714
$$210$$ 0 0
$$211$$ 17.0000 + 17.0000i 1.17033 + 1.17033i 0.982131 + 0.188197i $$0.0602643\pi$$
0.188197 + 0.982131i $$0.439736\pi$$
$$212$$ 0 0
$$213$$ −4.00000 + 4.00000i −0.274075 + 0.274075i
$$214$$ 0 0
$$215$$ 12.0000i 0.818393i
$$216$$ 0 0
$$217$$ 32.0000i 2.17230i
$$218$$ 0 0
$$219$$ −4.00000 + 4.00000i −0.270295 + 0.270295i
$$220$$ 0 0
$$221$$ 8.00000 + 8.00000i 0.538138 + 0.538138i
$$222$$ 0 0
$$223$$ −24.0000 −1.60716 −0.803579 0.595198i $$-0.797074\pi$$
−0.803579 + 0.595198i $$0.797074\pi$$
$$224$$ 0 0
$$225$$ −3.00000 −0.200000
$$226$$ 0 0
$$227$$ 15.0000 + 15.0000i 0.995585 + 0.995585i 0.999990 0.00440533i $$-0.00140226\pi$$
−0.00440533 + 0.999990i $$0.501402\pi$$
$$228$$ 0 0
$$229$$ −18.0000 + 18.0000i −1.18947 + 1.18947i −0.212260 + 0.977213i $$0.568082\pi$$
−0.977213 + 0.212260i $$0.931918\pi$$
$$230$$ 0 0
$$231$$ 8.00000i 0.526361i
$$232$$ 0 0
$$233$$ 12.0000i 0.786146i 0.919507 + 0.393073i $$0.128588\pi$$
−0.919507 + 0.393073i $$0.871412\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 8.00000 + 8.00000i 0.519656 + 0.519656i
$$238$$ 0 0
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ −12.0000 −0.772988 −0.386494 0.922292i $$-0.626314\pi$$
−0.386494 + 0.922292i $$0.626314\pi$$
$$242$$ 0 0
$$243$$ 7.00000 + 7.00000i 0.449050 + 0.449050i
$$244$$ 0 0
$$245$$ 18.0000 18.0000i 1.14998 1.14998i
$$246$$ 0 0
$$247$$ 20.0000i 1.27257i
$$248$$ 0 0
$$249$$ 14.0000i 0.887214i
$$250$$ 0 0
$$251$$ 3.00000 3.00000i 0.189358 0.189358i −0.606060 0.795419i $$-0.707251\pi$$
0.795419 + 0.606060i $$0.207251\pi$$
$$252$$ 0 0
$$253$$ 4.00000 + 4.00000i 0.251478 + 0.251478i
$$254$$ 0 0
$$255$$ 16.0000 1.00196
$$256$$ 0 0
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 0 0
$$259$$ 8.00000 + 8.00000i 0.497096 + 0.497096i
$$260$$ 0 0
$$261$$ −6.00000 + 6.00000i −0.371391 + 0.371391i
$$262$$ 0 0
$$263$$ 28.0000i 1.72655i 0.504730 + 0.863277i $$0.331592\pi$$
−0.504730 + 0.863277i $$0.668408\pi$$
$$264$$ 0 0
$$265$$ 8.00000i 0.491436i
$$266$$ 0 0
$$267$$ −12.0000 + 12.0000i −0.734388 + 0.734388i
$$268$$ 0 0
$$269$$ 14.0000 + 14.0000i 0.853595 + 0.853595i 0.990574 0.136979i $$-0.0437393\pi$$
−0.136979 + 0.990574i $$0.543739\pi$$
$$270$$ 0 0
$$271$$ 32.0000 1.94386 0.971931 0.235267i $$-0.0755965\pi$$
0.971931 + 0.235267i $$0.0755965\pi$$
$$272$$ 0 0
$$273$$ 16.0000 0.968364
$$274$$ 0 0
$$275$$ 3.00000 + 3.00000i 0.180907 + 0.180907i
$$276$$ 0 0
$$277$$ 6.00000 6.00000i 0.360505 0.360505i −0.503494 0.863999i $$-0.667952\pi$$
0.863999 + 0.503494i $$0.167952\pi$$
$$278$$ 0 0
$$279$$ 8.00000i 0.478947i
$$280$$ 0 0
$$281$$ 20.0000i 1.19310i 0.802576 + 0.596550i $$0.203462\pi$$
−0.802576 + 0.596550i $$0.796538\pi$$
$$282$$ 0 0
$$283$$ 17.0000 17.0000i 1.01055 1.01055i 0.0106013 0.999944i $$-0.496625\pi$$
0.999944 0.0106013i $$-0.00337456\pi$$
$$284$$ 0 0
$$285$$ −20.0000 20.0000i −1.18470 1.18470i
$$286$$ 0 0
$$287$$ −8.00000 −0.472225
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 4.00000 + 4.00000i 0.234484 + 0.234484i
$$292$$ 0 0
$$293$$ 6.00000 6.00000i 0.350524 0.350524i −0.509781 0.860304i $$-0.670273\pi$$
0.860304 + 0.509781i $$0.170273\pi$$
$$294$$ 0 0
$$295$$ 12.0000i 0.698667i
$$296$$ 0 0
$$297$$ 8.00000i 0.464207i
$$298$$ 0 0
$$299$$ 8.00000 8.00000i 0.462652 0.462652i
$$300$$ 0 0
$$301$$ −12.0000 12.0000i −0.691669 0.691669i
$$302$$ 0 0
$$303$$ −4.00000 −0.229794
$$304$$ 0 0
$$305$$ −24.0000 −1.37424
$$306$$ 0 0
$$307$$ −5.00000 5.00000i −0.285365 0.285365i 0.549879 0.835244i $$-0.314674\pi$$
−0.835244 + 0.549879i $$0.814674\pi$$
$$308$$ 0 0
$$309$$ 12.0000 12.0000i 0.682656 0.682656i
$$310$$ 0 0
$$311$$ 20.0000i 1.13410i 0.823685 + 0.567048i $$0.191915\pi$$
−0.823685 + 0.567048i $$0.808085\pi$$
$$312$$ 0 0
$$313$$ 14.0000i 0.791327i 0.918396 + 0.395663i $$0.129485\pi$$
−0.918396 + 0.395663i $$0.870515\pi$$
$$314$$ 0 0
$$315$$ −8.00000 + 8.00000i −0.450749 + 0.450749i
$$316$$ 0 0
$$317$$ 2.00000 + 2.00000i 0.112331 + 0.112331i 0.761038 0.648707i $$-0.224690\pi$$
−0.648707 + 0.761038i $$0.724690\pi$$
$$318$$ 0 0
$$319$$ 12.0000 0.671871
$$320$$ 0 0
$$321$$ −14.0000 −0.781404
$$322$$ 0 0
$$323$$ −20.0000 20.0000i −1.11283 1.11283i
$$324$$ 0 0
$$325$$ 6.00000 6.00000i 0.332820 0.332820i
$$326$$ 0 0
$$327$$ 20.0000i 1.10600i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −9.00000 + 9.00000i −0.494685 + 0.494685i −0.909779 0.415094i $$-0.863749\pi$$
0.415094 + 0.909779i $$0.363749\pi$$
$$332$$ 0 0
$$333$$ −2.00000 2.00000i −0.109599 0.109599i
$$334$$ 0 0
$$335$$ 12.0000 0.655630
$$336$$ 0 0
$$337$$ −30.0000 −1.63420 −0.817102 0.576493i $$-0.804421\pi$$
−0.817102 + 0.576493i $$0.804421\pi$$
$$338$$ 0 0
$$339$$ 14.0000 + 14.0000i 0.760376 + 0.760376i
$$340$$ 0 0
$$341$$ 8.00000 8.00000i 0.433224 0.433224i
$$342$$ 0 0
$$343$$ 8.00000i 0.431959i
$$344$$ 0 0
$$345$$ 16.0000i 0.861411i
$$346$$ 0 0
$$347$$ 11.0000 11.0000i 0.590511 0.590511i −0.347259 0.937769i $$-0.612887\pi$$
0.937769 + 0.347259i $$0.112887\pi$$
$$348$$ 0 0
$$349$$ −14.0000 14.0000i −0.749403 0.749403i 0.224964 0.974367i $$-0.427773\pi$$
−0.974367 + 0.224964i $$0.927773\pi$$
$$350$$ 0 0
$$351$$ −16.0000 −0.854017
$$352$$ 0 0
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 0 0
$$355$$ 8.00000 + 8.00000i 0.424596 + 0.424596i
$$356$$ 0 0
$$357$$ 16.0000 16.0000i 0.846810 0.846810i
$$358$$ 0 0
$$359$$ 36.0000i 1.90001i −0.312239 0.950004i $$-0.601079\pi$$
0.312239 0.950004i $$-0.398921\pi$$
$$360$$ 0 0
$$361$$ 31.0000i 1.63158i
$$362$$ 0 0
$$363$$ 9.00000 9.00000i 0.472377 0.472377i
$$364$$ 0 0
$$365$$ 8.00000 + 8.00000i 0.418739 + 0.418739i
$$366$$ 0 0
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ 0 0
$$369$$ 2.00000 0.104116
$$370$$ 0 0
$$371$$ −8.00000 8.00000i −0.415339 0.415339i
$$372$$ 0 0
$$373$$ −26.0000 + 26.0000i −1.34623 + 1.34623i −0.456511 + 0.889718i $$0.650901\pi$$
−0.889718 + 0.456511i $$0.849099\pi$$
$$374$$ 0 0
$$375$$ 8.00000i 0.413118i
$$376$$ 0 0
$$377$$ 24.0000i 1.23606i
$$378$$ 0 0
$$379$$ −21.0000 + 21.0000i −1.07870 + 1.07870i −0.0820711 + 0.996626i $$0.526153\pi$$
−0.996626 + 0.0820711i $$0.973847\pi$$
$$380$$ 0 0
$$381$$ 8.00000 + 8.00000i 0.409852 + 0.409852i
$$382$$ 0 0
$$383$$ −16.0000 −0.817562 −0.408781 0.912633i $$-0.634046\pi$$
−0.408781 + 0.912633i $$0.634046\pi$$
$$384$$ 0 0
$$385$$ 16.0000 0.815436
$$386$$ 0 0
$$387$$ 3.00000 + 3.00000i 0.152499 + 0.152499i
$$388$$ 0 0
$$389$$ −14.0000 + 14.0000i −0.709828 + 0.709828i −0.966499 0.256671i $$-0.917374\pi$$
0.256671 + 0.966499i $$0.417374\pi$$
$$390$$ 0 0
$$391$$ 16.0000i 0.809155i
$$392$$ 0 0
$$393$$ 10.0000i 0.504433i
$$394$$ 0 0
$$395$$ 16.0000 16.0000i 0.805047 0.805047i
$$396$$ 0 0
$$397$$ −2.00000 2.00000i −0.100377 0.100377i 0.655135 0.755512i $$-0.272612\pi$$
−0.755512 + 0.655135i $$0.772612\pi$$
$$398$$ 0 0
$$399$$ −40.0000 −2.00250
$$400$$ 0 0
$$401$$ 36.0000 1.79775 0.898877 0.438201i $$-0.144384\pi$$
0.898877 + 0.438201i $$0.144384\pi$$
$$402$$ 0 0
$$403$$ −16.0000 16.0000i −0.797017 0.797017i
$$404$$ 0 0
$$405$$ −10.0000 + 10.0000i −0.496904 + 0.496904i
$$406$$ 0 0
$$407$$ 4.00000i 0.198273i
$$408$$ 0 0
$$409$$ 14.0000i 0.692255i 0.938187 + 0.346128i $$0.112504\pi$$
−0.938187 + 0.346128i $$0.887496\pi$$
$$410$$ 0 0
$$411$$ −18.0000 + 18.0000i −0.887875 + 0.887875i
$$412$$ 0 0
$$413$$ 12.0000 + 12.0000i 0.590481 + 0.590481i
$$414$$ 0 0
$$415$$ 28.0000 1.37447
$$416$$ 0 0
$$417$$ 6.00000 0.293821
$$418$$ 0 0
$$419$$ −19.0000 19.0000i −0.928211 0.928211i 0.0693796 0.997590i $$-0.477898\pi$$
−0.997590 + 0.0693796i $$0.977898\pi$$
$$420$$ 0 0
$$421$$ 6.00000 6.00000i 0.292422 0.292422i −0.545614 0.838036i $$-0.683704\pi$$
0.838036 + 0.545614i $$0.183704\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 12.0000i 0.582086i
$$426$$ 0 0
$$427$$ −24.0000 + 24.0000i −1.16144 + 1.16144i
$$428$$ 0 0
$$429$$ 4.00000 + 4.00000i 0.193122 + 0.193122i
$$430$$ 0 0
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 0 0
$$433$$ 20.0000 0.961139 0.480569 0.876957i $$-0.340430\pi$$
0.480569 + 0.876957i $$0.340430\pi$$
$$434$$ 0 0
$$435$$ −24.0000 24.0000i −1.15071 1.15071i
$$436$$ 0 0
$$437$$ −20.0000 + 20.0000i −0.956730 + 0.956730i
$$438$$ 0 0
$$439$$ 4.00000i 0.190910i 0.995434 + 0.0954548i $$0.0304305\pi$$
−0.995434 + 0.0954548i $$0.969569\pi$$
$$440$$ 0 0
$$441$$ 9.00000i 0.428571i
$$442$$ 0 0
$$443$$ 25.0000 25.0000i 1.18779 1.18779i 0.210108 0.977678i $$-0.432619\pi$$
0.977678 0.210108i $$-0.0673814\pi$$
$$444$$ 0 0
$$445$$ 24.0000 + 24.0000i 1.13771 + 1.13771i
$$446$$ 0 0
$$447$$ −4.00000 −0.189194
$$448$$ 0 0
$$449$$ −20.0000 −0.943858 −0.471929 0.881636i $$-0.656442\pi$$
−0.471929 + 0.881636i $$0.656442\pi$$
$$450$$ 0 0
$$451$$ −2.00000 2.00000i −0.0941763 0.0941763i
$$452$$ 0 0
$$453$$ −4.00000 + 4.00000i −0.187936 + 0.187936i
$$454$$ 0 0
$$455$$ 32.0000i 1.50018i
$$456$$ 0 0
$$457$$ 2.00000i 0.0935561i 0.998905 + 0.0467780i $$0.0148953\pi$$
−0.998905 + 0.0467780i $$0.985105\pi$$
$$458$$ 0 0
$$459$$ −16.0000 + 16.0000i −0.746816 + 0.746816i
$$460$$ 0 0
$$461$$ −10.0000 10.0000i −0.465746 0.465746i 0.434787 0.900533i $$-0.356824\pi$$
−0.900533 + 0.434787i $$0.856824\pi$$
$$462$$ 0 0
$$463$$ 8.00000 0.371792 0.185896 0.982569i $$-0.440481\pi$$
0.185896 + 0.982569i $$0.440481\pi$$
$$464$$ 0 0
$$465$$ −32.0000 −1.48396
$$466$$ 0 0
$$467$$ −13.0000 13.0000i −0.601568 0.601568i 0.339160 0.940729i $$-0.389857\pi$$
−0.940729 + 0.339160i $$0.889857\pi$$
$$468$$ 0 0
$$469$$ 12.0000 12.0000i 0.554109 0.554109i
$$470$$ 0 0
$$471$$ 12.0000i 0.552931i
$$472$$ 0 0
$$473$$ 6.00000i 0.275880i
$$474$$ 0 0
$$475$$ −15.0000 + 15.0000i −0.688247 + 0.688247i
$$476$$ 0 0
$$477$$ 2.00000 + 2.00000i 0.0915737 + 0.0915737i
$$478$$ 0 0
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 8.00000 0.364769
$$482$$ 0 0
$$483$$ −16.0000 16.0000i −0.728025 0.728025i
$$484$$ 0 0
$$485$$ 8.00000 8.00000i 0.363261 0.363261i
$$486$$ 0 0
$$487$$ 12.0000i 0.543772i −0.962329 0.271886i $$-0.912353\pi$$
0.962329 0.271886i $$-0.0876473\pi$$
$$488$$ 0 0
$$489$$ 14.0000i 0.633102i
$$490$$ 0 0
$$491$$ −11.0000 + 11.0000i −0.496423 + 0.496423i −0.910323 0.413900i $$-0.864166\pi$$
0.413900 + 0.910323i $$0.364166\pi$$
$$492$$ 0 0
$$493$$ −24.0000 24.0000i −1.08091 1.08091i
$$494$$ 0 0
$$495$$ −4.00000 −0.179787
$$496$$ 0 0
$$497$$ 16.0000 0.717698
$$498$$ 0 0
$$499$$ 9.00000 + 9.00000i 0.402895 + 0.402895i 0.879252 0.476357i $$-0.158043\pi$$
−0.476357 + 0.879252i $$0.658043\pi$$
$$500$$ 0 0
$$501$$ −12.0000 + 12.0000i −0.536120 + 0.536120i
$$502$$ 0 0
$$503$$ 20.0000i 0.891756i −0.895094 0.445878i $$-0.852892\pi$$
0.895094 0.445878i $$-0.147108\pi$$
$$504$$ 0 0
$$505$$ 8.00000i 0.355995i
$$506$$ 0 0
$$507$$ −5.00000 + 5.00000i −0.222058 + 0.222058i
$$508$$ 0 0
$$509$$ −2.00000 2.00000i −0.0886484 0.0886484i 0.661392 0.750040i $$-0.269966\pi$$
−0.750040 + 0.661392i $$0.769966\pi$$
$$510$$ 0 0
$$511$$ 16.0000 0.707798
$$512$$ 0 0
$$513$$ 40.0000 1.76604
$$514$$ 0 0
$$515$$ −24.0000 24.0000i −1.05757 1.05757i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 20.0000i 0.877903i
$$520$$ 0 0
$$521$$ 14.0000i 0.613351i 0.951814 + 0.306676i $$0.0992167\pi$$
−0.951814 + 0.306676i $$0.900783\pi$$
$$522$$ 0 0
$$523$$ 7.00000 7.00000i 0.306089 0.306089i −0.537302 0.843390i $$-0.680556\pi$$
0.843390 + 0.537302i $$0.180556\pi$$
$$524$$ 0 0
$$525$$ −12.0000 12.0000i −0.523723 0.523723i
$$526$$ 0 0
$$527$$ −32.0000 −1.39394
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ 0 0
$$531$$ −3.00000 3.00000i −0.130189 0.130189i
$$532$$ 0 0
$$533$$ −4.00000 + 4.00000i −0.173259 + 0.173259i
$$534$$ 0 0
$$535$$ 28.0000i 1.21055i
$$536$$ 0 0
$$537$$ 2.00000i 0.0863064i
$$538$$ 0 0
$$539$$ 9.00000 9.00000i 0.387657 0.387657i
$$540$$ 0 0
$$541$$ 6.00000 + 6.00000i 0.257960 + 0.257960i 0.824224 0.566264i $$-0.191612\pi$$
−0.566264 + 0.824224i $$0.691612\pi$$
$$542$$ 0 0
$$543$$ 12.0000 0.514969
$$544$$ 0 0
$$545$$ 40.0000 1.71341
$$546$$ 0 0
$$547$$ −19.0000 19.0000i −0.812381 0.812381i 0.172609 0.984990i $$-0.444780\pi$$
−0.984990 + 0.172609i $$0.944780\pi$$
$$548$$ 0 0
$$549$$ 6.00000 6.00000i 0.256074 0.256074i
$$550$$ 0 0
$$551$$ 60.0000i 2.55609i
$$552$$ 0 0
$$553$$ 32.0000i 1.36078i
$$554$$ 0 0
$$555$$ 8.00000 8.00000i 0.339581 0.339581i
$$556$$ 0 0
$$557$$ −22.0000 22.0000i −0.932170 0.932170i 0.0656714 0.997841i $$-0.479081\pi$$
−0.997841 + 0.0656714i $$0.979081\pi$$
$$558$$ 0 0
$$559$$ −12.0000 −0.507546
$$560$$ 0 0
$$561$$ 8.00000 0.337760
$$562$$ 0 0
$$563$$ −5.00000 5.00000i −0.210725 0.210725i 0.593851 0.804575i $$-0.297607\pi$$
−0.804575 + 0.593851i $$0.797607\pi$$
$$564$$ 0 0
$$565$$ 28.0000 28.0000i 1.17797 1.17797i
$$566$$ 0 0
$$567$$ 20.0000i 0.839921i
$$568$$ 0 0
$$569$$ 30.0000i 1.25767i −0.777541 0.628833i $$-0.783533\pi$$
0.777541 0.628833i $$-0.216467\pi$$
$$570$$ 0 0
$$571$$ −23.0000 + 23.0000i −0.962520 + 0.962520i −0.999323 0.0368025i $$-0.988283\pi$$
0.0368025 + 0.999323i $$0.488283\pi$$
$$572$$ 0 0
$$573$$ 8.00000 + 8.00000i 0.334205 + 0.334205i
$$574$$ 0 0
$$575$$ −12.0000 −0.500435
$$576$$ 0 0
$$577$$ −18.0000 −0.749350 −0.374675 0.927156i $$-0.622246\pi$$
−0.374675 + 0.927156i $$0.622246\pi$$
$$578$$ 0 0
$$579$$ 4.00000 + 4.00000i 0.166234 + 0.166234i
$$580$$ 0 0
$$581$$ 28.0000 28.0000i 1.16164 1.16164i
$$582$$ 0 0
$$583$$ 4.00000i 0.165663i
$$584$$ 0 0
$$585$$ 8.00000i 0.330759i
$$586$$ 0 0
$$587$$ −1.00000 + 1.00000i −0.0412744 + 0.0412744i −0.727443 0.686168i $$-0.759291\pi$$
0.686168 + 0.727443i $$0.259291\pi$$
$$588$$ 0 0
$$589$$ 40.0000 + 40.0000i 1.64817 + 1.64817i
$$590$$ 0 0
$$591$$ 20.0000 0.822690
$$592$$ 0 0
$$593$$ −18.0000 −0.739171 −0.369586 0.929197i $$-0.620500\pi$$
−0.369586 + 0.929197i $$0.620500\pi$$
$$594$$ 0 0
$$595$$ −32.0000 32.0000i −1.31187 1.31187i
$$596$$ 0 0
$$597$$ 4.00000 4.00000i 0.163709 0.163709i
$$598$$ 0 0
$$599$$ 36.0000i 1.47092i 0.677568 + 0.735460i $$0.263034\pi$$
−0.677568 + 0.735460i $$0.736966\pi$$
$$600$$ 0 0
$$601$$ 4.00000i 0.163163i 0.996667 + 0.0815817i $$0.0259972\pi$$
−0.996667 + 0.0815817i $$0.974003\pi$$
$$602$$ 0 0
$$603$$ −3.00000 + 3.00000i −0.122169 + 0.122169i
$$604$$ 0 0
$$605$$ −18.0000 18.0000i −0.731804 0.731804i
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ −48.0000 −1.94506
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 6.00000 6.00000i 0.242338 0.242338i −0.575479 0.817817i $$-0.695184\pi$$
0.817817 + 0.575479i $$0.195184\pi$$
$$614$$ 0 0
$$615$$ 8.00000i 0.322591i
$$616$$ 0 0
$$617$$ 28.0000i 1.12724i 0.826035 + 0.563619i $$0.190591\pi$$
−0.826035 + 0.563619i $$0.809409\pi$$
$$618$$ 0 0
$$619$$ −1.00000 + 1.00000i −0.0401934 + 0.0401934i −0.726918 0.686724i $$-0.759048\pi$$
0.686724 + 0.726918i $$0.259048\pi$$
$$620$$ 0 0
$$621$$ 16.0000 + 16.0000i 0.642058 + 0.642058i
$$622$$ 0 0
$$623$$ 48.0000 1.92308
$$624$$ 0 0
$$625$$ 31.0000 1.24000
$$626$$ 0 0
$$627$$ −10.0000 10.0000i −0.399362 0.399362i
$$628$$ 0 0
$$629$$ 8.00000 8.00000i 0.318981 0.318981i
$$630$$ 0 0
$$631$$ 4.00000i 0.159237i −0.996825 0.0796187i $$-0.974630\pi$$
0.996825 0.0796187i $$-0.0253703\pi$$
$$632$$ 0 0
$$633$$ 34.0000i 1.35138i
$$634$$ 0 0
$$635$$ 16.0000 16.0000i 0.634941 0.634941i
$$636$$ 0 0
$$637$$ −18.0000 18.0000i −0.713186 0.713186i
$$638$$ 0 0
$$639$$ −4.00000 −0.158238
$$640$$ 0 0
$$641$$ −4.00000 −0.157991 −0.0789953 0.996875i $$-0.525171\pi$$
−0.0789953 + 0.996875i $$0.525171\pi$$
$$642$$ 0 0
$$643$$ −3.00000 3.00000i −0.118308 0.118308i 0.645474 0.763782i $$-0.276660\pi$$
−0.763782 + 0.645474i $$0.776660\pi$$
$$644$$ 0 0
$$645$$ −12.0000 + 12.0000i −0.472500 + 0.472500i
$$646$$ 0 0
$$647$$ 12.0000i 0.471769i 0.971781 + 0.235884i $$0.0757987\pi$$
−0.971781 + 0.235884i $$0.924201\pi$$
$$648$$ 0 0
$$649$$ 6.00000i 0.235521i
$$650$$ 0 0
$$651$$ −32.0000 + 32.0000i −1.25418 + 1.25418i
$$652$$ 0 0
$$653$$ −34.0000 34.0000i −1.33052 1.33052i −0.904901 0.425622i $$-0.860055\pi$$
−0.425622 0.904901i $$-0.639945\pi$$
$$654$$ 0 0
$$655$$ −20.0000 −0.781465
$$656$$ 0 0
$$657$$ −4.00000 −0.156055
$$658$$ 0 0
$$659$$ −23.0000 23.0000i −0.895953 0.895953i 0.0991224 0.995075i $$-0.468396\pi$$
−0.995075 + 0.0991224i $$0.968396\pi$$
$$660$$ 0 0
$$661$$ −22.0000 + 22.0000i −0.855701 + 0.855701i −0.990828 0.135127i $$-0.956856\pi$$
0.135127 + 0.990828i $$0.456856\pi$$
$$662$$ 0 0
$$663$$ 16.0000i 0.621389i
$$664$$ 0 0
$$665$$ 80.0000i 3.10227i
$$666$$ 0 0
$$667$$ −24.0000 + 24.0000i −0.929284 + 0.929284i
$$668$$ 0 0
$$669$$ 24.0000 + 24.0000i 0.927894 + 0.927894i
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ −20.0000 −0.770943 −0.385472 0.922720i $$-0.625961\pi$$
−0.385472 + 0.922720i $$0.625961\pi$$
$$674$$ 0 0
$$675$$ 12.0000 + 12.0000i 0.461880 + 0.461880i
$$676$$ 0 0
$$677$$ −30.0000 + 30.0000i −1.15299 + 1.15299i −0.167044 + 0.985949i $$0.553422\pi$$
−0.985949 + 0.167044i $$0.946578\pi$$
$$678$$ 0 0
$$679$$ 16.0000i 0.614024i
$$680$$ 0 0
$$681$$ 30.0000i 1.14960i
$$682$$ 0 0
$$683$$ 21.0000 21.0000i 0.803543 0.803543i −0.180105 0.983647i $$-0.557644\pi$$
0.983647 + 0.180105i $$0.0576437\pi$$
$$684$$ 0 0
$$685$$ 36.0000 + 36.0000i 1.37549 + 1.37549i
$$686$$ 0 0
$$687$$ 36.0000 1.37349
$$688$$ 0 0
$$689$$ −8.00000 −0.304776
$$690$$ 0 0
$$691$$ 33.0000 + 33.0000i 1.25538 + 1.25538i 0.953275 + 0.302104i $$0.0976891\pi$$
0.302104 + 0.953275i $$0.402311\pi$$
$$692$$ 0 0
$$693$$ −4.00000 + 4.00000i −0.151947 + 0.151947i
$$694$$ 0 0
$$695$$ 12.0000i 0.455186i
$$696$$ 0 0
$$697$$ 8.00000i 0.303022i
$$698$$ 0 0
$$699$$ 12.0000 12.0000i 0.453882 0.453882i
$$700$$ 0 0
$$701$$ −34.0000 34.0000i −1.28416 1.28416i −0.938277 0.345886i $$-0.887579\pi$$
−0.345886 0.938277i $$-0.612421\pi$$
$$702$$ 0 0
$$703$$ −20.0000 −0.754314
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 8.00000 + 8.00000i 0.300871 + 0.300871i
$$708$$ 0 0
$$709$$ −6.00000 + 6.00000i −0.225335 + 0.225335i −0.810740 0.585406i $$-0.800935\pi$$
0.585406 + 0.810740i $$0.300935\pi$$
$$710$$ 0 0
$$711$$ 8.00000i 0.300023i
$$712$$ 0 0
$$713$$ 32.0000i 1.19841i
$$714$$ 0 0
$$715$$ 8.00000 8.00000i 0.299183 0.299183i
$$716$$ 0 0
$$717$$ 8.00000 + 8.00000i 0.298765 + 0.298765i
$$718$$ 0 0
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ −48.0000 −1.78761
$$722$$ 0 0
$$723$$ 12.0000 + 12.0000i 0.446285 + 0.446285i
$$724$$ 0 0
$$725$$ −18.0000 + 18.0000i −0.668503 + 0.668503i
$$726$$ 0 0
$$727$$ 28.0000i 1.03846i −0.854634 0.519231i $$-0.826218\pi$$
0.854634 0.519231i $$-0.173782\pi$$
$$728$$ 0 0
$$729$$ 29.0000i 1.07407i
$$730$$ 0 0
$$731$$ −12.0000 + 12.0000i −0.443836 + 0.443836i
$$732$$ 0 0
$$733$$ −14.0000 14.0000i −0.517102 0.517102i 0.399592 0.916693i $$-0.369152\pi$$
−0.916693 + 0.399592i $$0.869152\pi$$
$$734$$ 0 0
$$735$$ −36.0000 −1.32788
$$736$$ 0 0
$$737$$ 6.00000 0.221013
$$738$$ 0 0
$$739$$ −17.0000 17.0000i −0.625355 0.625355i 0.321541 0.946896i $$-0.395799\pi$$
−0.946896 + 0.321541i $$0.895799\pi$$
$$740$$ 0 0
$$741$$ −20.0000 + 20.0000i −0.734718 + 0.734718i
$$742$$ 0 0
$$743$$ 4.00000i 0.146746i 0.997305 + 0.0733729i $$0.0233763\pi$$
−0.997305 + 0.0733729i $$0.976624\pi$$
$$744$$ 0 0
$$745$$ 8.00000i 0.293097i
$$746$$ 0 0
$$747$$ −7.00000 + 7.00000i −0.256117 + 0.256117i
$$748$$ 0 0
$$749$$ 28.0000 + 28.0000i 1.02310 + 1.02310i
$$750$$ 0 0
$$751$$ −40.0000 −1.45962 −0.729810 0.683650i $$-0.760392\pi$$
−0.729810 + 0.683650i $$0.760392\pi$$
$$752$$ 0 0
$$753$$ −6.00000 −0.218652
$$754$$ 0 0
$$755$$ 8.00000 + 8.00000i 0.291150 + 0.291150i
$$756$$ 0 0
$$757$$ 18.0000 18.0000i 0.654221 0.654221i −0.299786 0.954007i $$-0.596915\pi$$
0.954007 + 0.299786i $$0.0969151\pi$$
$$758$$ 0 0
$$759$$ 8.00000i 0.290382i
$$760$$ 0 0
$$761$$ 18.0000i 0.652499i −0.945284 0.326250i $$-0.894215\pi$$
0.945284 0.326250i $$-0.105785\pi$$
$$762$$ 0 0
$$763$$ 40.0000 40.0000i 1.44810 1.44810i
$$764$$ 0 0
$$765$$ 8.00000 + 8.00000i 0.289241 + 0.289241i
$$766$$ 0 0
$$767$$ 12.0000 0.433295
$$768$$ 0 0
$$769$$ 44.0000 1.58668 0.793340 0.608778i $$-0.208340\pi$$
0.793340 + 0.608778i $$0.208340\pi$$
$$770$$ 0 0
$$771$$ 2.00000 + 2.00000i 0.0720282 + 0.0720282i
$$772$$ 0 0
$$773$$ −6.00000 + 6.00000i −0.215805 + 0.215805i −0.806728 0.590923i $$-0.798764\pi$$
0.590923 + 0.806728i $$0.298764\pi$$
$$774$$ 0 0
$$775$$ 24.0000i 0.862105i
$$776$$ 0 0
$$777$$ 16.0000i 0.573997i
$$778$$ 0 0
$$779$$ 10.0000 10.0000i 0.358287 0.358287i
$$780$$ 0 0
$$781$$ 4.00000 + 4.00000i 0.143131 + 0.143131i
$$782$$ 0 0
$$783$$ 48.0000 1.71538
$$784$$ 0 0
$$785$$ −24.0000 −0.856597
$$786$$ 0 0
$$787$$ 33.0000 + 33.0000i 1.17632 + 1.17632i 0.980674 + 0.195649i $$0.0626813\pi$$
0.195649 + 0.980674i $$0.437319\pi$$
$$788$$ 0 0
$$789$$ 28.0000 28.0000i 0.996826 0.996826i
$$790$$ 0 0
$$791$$ 56.0000i 1.99113i
$$792$$ 0 0
$$793$$ 24.0000i 0.852265i
$$794$$ 0 0
$$795$$ −8.00000 + 8.00000i −0.283731 + 0.283731i
$$796$$ 0 0
$$797$$ 14.0000 + 14.0000i 0.495905