# Properties

 Label 672.2.q.i.193.1 Level $672$ Weight $2$ Character 672.193 Analytic conductor $5.366$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.36594701583$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 193.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 672.193 Dual form 672.2.q.i.289.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +5.00000 q^{13} +(1.00000 - 1.73205i) q^{17} +(1.50000 + 2.59808i) q^{19} +(2.00000 + 1.73205i) q^{21} +(1.00000 + 1.73205i) q^{23} +(2.50000 - 4.33013i) q^{25} -1.00000 q^{27} +8.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(2.50000 + 4.33013i) q^{37} +(2.50000 - 4.33013i) q^{39} +2.00000 q^{41} -7.00000 q^{43} +(-4.00000 - 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{53} +3.00000 q^{57} +(5.00000 - 8.66025i) q^{59} +(1.00000 + 1.73205i) q^{61} +(2.50000 - 0.866025i) q^{63} +(-5.50000 + 9.52628i) q^{67} +2.00000 q^{69} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{73} +(-2.50000 - 4.33013i) q^{75} +(4.00000 + 3.46410i) q^{77} +(8.50000 + 14.7224i) q^{79} +(-0.500000 + 0.866025i) q^{81} +16.0000 q^{83} +(4.00000 - 6.92820i) q^{87} +(-6.00000 - 10.3923i) q^{89} +(-2.50000 + 12.9904i) q^{91} +(0.500000 + 0.866025i) q^{93} -14.0000 q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{3} - q^{7} - q^{9} + O(q^{10})$$ $$2q + q^{3} - q^{7} - q^{9} + 2q^{11} + 10q^{13} + 2q^{17} + 3q^{19} + 4q^{21} + 2q^{23} + 5q^{25} - 2q^{27} + 16q^{29} - q^{31} - 2q^{33} + 5q^{37} + 5q^{39} + 4q^{41} - 14q^{43} - 8q^{47} - 13q^{49} - 2q^{51} + 2q^{53} + 6q^{57} + 10q^{59} + 2q^{61} + 5q^{63} - 11q^{67} + 4q^{69} - 24q^{71} + 3q^{73} - 5q^{75} + 8q^{77} + 17q^{79} - q^{81} + 32q^{83} + 8q^{87} - 12q^{89} - 5q^{91} + q^{93} - 28q^{97} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$421$$ $$449$$ $$577$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ 0 0
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 2.59808i −0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i $$-0.735842\pi$$
0.976478 + 0.215615i $$0.0691756\pi$$
$$12$$ 0 0
$$13$$ 5.00000 1.38675 0.693375 0.720577i $$-0.256123\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i $$-0.755354\pi$$
0.961436 + 0.275029i $$0.0886875\pi$$
$$18$$ 0 0
$$19$$ 1.50000 + 2.59808i 0.344124 + 0.596040i 0.985194 0.171442i $$-0.0548427\pi$$
−0.641071 + 0.767482i $$0.721509\pi$$
$$20$$ 0 0
$$21$$ 2.00000 + 1.73205i 0.436436 + 0.377964i
$$22$$ 0 0
$$23$$ 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i $$-0.0998038\pi$$
−0.742732 + 0.669588i $$0.766471\pi$$
$$24$$ 0 0
$$25$$ 2.50000 4.33013i 0.500000 0.866025i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 8.00000 1.48556 0.742781 0.669534i $$-0.233506\pi$$
0.742781 + 0.669534i $$0.233506\pi$$
$$30$$ 0 0
$$31$$ −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i $$-0.861957\pi$$
0.817625 + 0.575751i $$0.195290\pi$$
$$32$$ 0 0
$$33$$ −1.00000 1.73205i −0.174078 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.50000 + 4.33013i 0.410997 + 0.711868i 0.994999 0.0998840i $$-0.0318472\pi$$
−0.584002 + 0.811752i $$0.698514\pi$$
$$38$$ 0 0
$$39$$ 2.50000 4.33013i 0.400320 0.693375i
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ −7.00000 −1.06749 −0.533745 0.845645i $$-0.679216\pi$$
−0.533745 + 0.845645i $$0.679216\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i $$-0.968365\pi$$
0.411606 0.911362i $$-0.364968\pi$$
$$48$$ 0 0
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ 0 0
$$51$$ −1.00000 1.73205i −0.140028 0.242536i
$$52$$ 0 0
$$53$$ 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i $$-0.789471\pi$$
0.926497 + 0.376303i $$0.122805\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ 5.00000 8.66025i 0.650945 1.12747i −0.331949 0.943297i $$-0.607706\pi$$
0.982894 0.184172i $$-0.0589603\pi$$
$$60$$ 0 0
$$61$$ 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i $$-0.125799\pi$$
−0.794879 + 0.606768i $$0.792466\pi$$
$$62$$ 0 0
$$63$$ 2.50000 0.866025i 0.314970 0.109109i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −5.50000 + 9.52628i −0.671932 + 1.16382i 0.305424 + 0.952217i $$0.401202\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 0 0
$$69$$ 2.00000 0.240772
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i $$-0.777159\pi$$
0.940356 + 0.340193i $$0.110493\pi$$
$$74$$ 0 0
$$75$$ −2.50000 4.33013i −0.288675 0.500000i
$$76$$ 0 0
$$77$$ 4.00000 + 3.46410i 0.455842 + 0.394771i
$$78$$ 0 0
$$79$$ 8.50000 + 14.7224i 0.956325 + 1.65640i 0.731307 + 0.682048i $$0.238911\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 16.0000 1.75623 0.878114 0.478451i $$-0.158802\pi$$
0.878114 + 0.478451i $$0.158802\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 4.00000 6.92820i 0.428845 0.742781i
$$88$$ 0 0
$$89$$ −6.00000 10.3923i −0.635999 1.10158i −0.986303 0.164946i $$-0.947255\pi$$
0.350304 0.936636i $$-0.386078\pi$$
$$90$$ 0 0
$$91$$ −2.50000 + 12.9904i −0.262071 + 1.36176i
$$92$$ 0 0
$$93$$ 0.500000 + 0.866025i 0.0518476 + 0.0898027i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i $$0.519872\pi$$
−0.833143 + 0.553058i $$0.813461\pi$$
$$102$$ 0 0
$$103$$ −0.500000 0.866025i −0.0492665 0.0853320i 0.840341 0.542059i $$-0.182355\pi$$
−0.889607 + 0.456727i $$0.849022\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1.00000 + 1.73205i 0.0966736 + 0.167444i 0.910306 0.413936i $$-0.135846\pi$$
−0.813632 + 0.581380i $$0.802513\pi$$
$$108$$ 0 0
$$109$$ −0.500000 + 0.866025i −0.0478913 + 0.0829502i −0.888977 0.457951i $$-0.848583\pi$$
0.841086 + 0.540901i $$0.181917\pi$$
$$110$$ 0 0
$$111$$ 5.00000 0.474579
$$112$$ 0 0
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −2.50000 4.33013i −0.231125 0.400320i
$$118$$ 0 0
$$119$$ 4.00000 + 3.46410i 0.366679 + 0.317554i
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ 0 0
$$123$$ 1.00000 1.73205i 0.0901670 0.156174i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −11.0000 −0.976092 −0.488046 0.872818i $$-0.662290\pi$$
−0.488046 + 0.872818i $$0.662290\pi$$
$$128$$ 0 0
$$129$$ −3.50000 + 6.06218i −0.308158 + 0.533745i
$$130$$ 0 0
$$131$$ −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i $$-0.251085\pi$$
−0.966803 + 0.255524i $$0.917752\pi$$
$$132$$ 0 0
$$133$$ −7.50000 + 2.59808i −0.650332 + 0.225282i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i $$-0.887992\pi$$
0.767853 + 0.640626i $$0.221325\pi$$
$$138$$ 0 0
$$139$$ 1.00000 0.0848189 0.0424094 0.999100i $$-0.486497\pi$$
0.0424094 + 0.999100i $$0.486497\pi$$
$$140$$ 0 0
$$141$$ −8.00000 −0.673722
$$142$$ 0 0
$$143$$ 5.00000 8.66025i 0.418121 0.724207i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −5.50000 + 4.33013i −0.453632 + 0.357143i
$$148$$ 0 0
$$149$$ −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i $$-0.330232\pi$$
−0.999953 + 0.00974235i $$0.996899\pi$$
$$150$$ 0 0
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 0 0
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 3.00000 5.19615i 0.239426 0.414698i −0.721124 0.692806i $$-0.756374\pi$$
0.960550 + 0.278108i $$0.0897074\pi$$
$$158$$ 0 0
$$159$$ −1.00000 1.73205i −0.0793052 0.137361i
$$160$$ 0 0
$$161$$ −5.00000 + 1.73205i −0.394055 + 0.136505i
$$162$$ 0 0
$$163$$ 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i $$-0.116597\pi$$
−0.777007 + 0.629492i $$0.783263\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −20.0000 −1.54765 −0.773823 0.633402i $$-0.781658\pi$$
−0.773823 + 0.633402i $$0.781658\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ 1.50000 2.59808i 0.114708 0.198680i
$$172$$ 0 0
$$173$$ 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i $$-0.0934200\pi$$
−0.729155 + 0.684349i $$0.760087\pi$$
$$174$$ 0 0
$$175$$ 10.0000 + 8.66025i 0.755929 + 0.654654i
$$176$$ 0 0
$$177$$ −5.00000 8.66025i −0.375823 0.650945i
$$178$$ 0 0
$$179$$ 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i $$-0.685306\pi$$
0.998286 + 0.0585225i $$0.0186389\pi$$
$$180$$ 0 0
$$181$$ −15.0000 −1.11494 −0.557471 0.830197i $$-0.688228\pi$$
−0.557471 + 0.830197i $$0.688228\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −2.00000 3.46410i −0.146254 0.253320i
$$188$$ 0 0
$$189$$ 0.500000 2.59808i 0.0363696 0.188982i
$$190$$ 0 0
$$191$$ 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i $$-0.0237173\pi$$
−0.563081 + 0.826402i $$0.690384\pi$$
$$192$$ 0 0
$$193$$ −11.5000 + 19.9186i −0.827788 + 1.43377i 0.0719816 + 0.997406i $$0.477068\pi$$
−0.899770 + 0.436365i $$0.856266\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i $$-0.788052\pi$$
0.928166 + 0.372168i $$0.121385\pi$$
$$200$$ 0 0
$$201$$ 5.50000 + 9.52628i 0.387940 + 0.671932i
$$202$$ 0 0
$$203$$ −4.00000 + 20.7846i −0.280745 + 1.45879i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 1.00000 1.73205i 0.0695048 0.120386i
$$208$$ 0 0
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ 0 0
$$213$$ −6.00000 + 10.3923i −0.411113 + 0.712069i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −2.00000 1.73205i −0.135769 0.117579i
$$218$$ 0 0
$$219$$ −1.50000 2.59808i −0.101361 0.175562i
$$220$$ 0 0
$$221$$ 5.00000 8.66025i 0.336336 0.582552i
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ −5.00000 −0.333333
$$226$$ 0 0
$$227$$ 13.0000 22.5167i 0.862840 1.49448i −0.00633544 0.999980i $$-0.502017\pi$$
0.869176 0.494503i $$-0.164650\pi$$
$$228$$ 0 0
$$229$$ −6.50000 11.2583i −0.429532 0.743971i 0.567300 0.823511i $$-0.307988\pi$$
−0.996832 + 0.0795401i $$0.974655\pi$$
$$230$$ 0 0
$$231$$ 5.00000 1.73205i 0.328976 0.113961i
$$232$$ 0 0
$$233$$ 6.00000 + 10.3923i 0.393073 + 0.680823i 0.992853 0.119342i $$-0.0380786\pi$$
−0.599780 + 0.800165i $$0.704745\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 17.0000 1.10427
$$238$$ 0 0
$$239$$ −30.0000 −1.94054 −0.970269 0.242028i $$-0.922188\pi$$
−0.970269 + 0.242028i $$0.922188\pi$$
$$240$$ 0 0
$$241$$ 11.0000 19.0526i 0.708572 1.22728i −0.256814 0.966461i $$-0.582673\pi$$
0.965387 0.260822i $$-0.0839937\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 7.50000 + 12.9904i 0.477214 + 0.826558i
$$248$$ 0 0
$$249$$ 8.00000 13.8564i 0.506979 0.878114i
$$250$$ 0 0
$$251$$ 22.0000 1.38863 0.694314 0.719672i $$-0.255708\pi$$
0.694314 + 0.719672i $$0.255708\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 8.00000 + 13.8564i 0.499026 + 0.864339i 0.999999 0.00112398i $$-0.000357774\pi$$
−0.500973 + 0.865463i $$0.667024\pi$$
$$258$$ 0 0
$$259$$ −12.5000 + 4.33013i −0.776712 + 0.269061i
$$260$$ 0 0
$$261$$ −4.00000 6.92820i −0.247594 0.428845i
$$262$$ 0 0
$$263$$ 4.00000 6.92820i 0.246651 0.427211i −0.715944 0.698158i $$-0.754003\pi$$
0.962594 + 0.270947i $$0.0873367\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.0000 −0.734388
$$268$$ 0 0
$$269$$ 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i $$-0.648441\pi$$
0.998361 0.0572259i $$-0.0182255\pi$$
$$270$$ 0 0
$$271$$ −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i $$-0.328199\pi$$
−0.999870 + 0.0161307i $$0.994865\pi$$
$$272$$ 0 0
$$273$$ 10.0000 + 8.66025i 0.605228 + 0.524142i
$$274$$ 0 0
$$275$$ −5.00000 8.66025i −0.301511 0.522233i
$$276$$ 0 0
$$277$$ −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i $$0.337286\pi$$
−0.999923 + 0.0124177i $$0.996047\pi$$
$$278$$ 0 0
$$279$$ 1.00000 0.0598684
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 15.5000 26.8468i 0.921379 1.59588i 0.124096 0.992270i $$-0.460397\pi$$
0.797283 0.603606i $$-0.206270\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1.00000 + 5.19615i −0.0590281 + 0.306719i
$$288$$ 0 0
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ −7.00000 + 12.1244i −0.410347 + 0.710742i
$$292$$ 0 0
$$293$$ −4.00000 −0.233682 −0.116841 0.993151i $$-0.537277\pi$$
−0.116841 + 0.993151i $$0.537277\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −1.00000 + 1.73205i −0.0580259 + 0.100504i
$$298$$ 0 0
$$299$$ 5.00000 + 8.66025i 0.289157 + 0.500835i
$$300$$ 0 0
$$301$$ 3.50000 18.1865i 0.201737 1.04825i
$$302$$ 0 0
$$303$$ 9.00000 + 15.5885i 0.517036 + 0.895533i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 23.0000 1.31268 0.656340 0.754466i $$-0.272104\pi$$
0.656340 + 0.754466i $$0.272104\pi$$
$$308$$ 0 0
$$309$$ −1.00000 −0.0568880
$$310$$ 0 0
$$311$$ −15.0000 + 25.9808i −0.850572 + 1.47323i 0.0301210 + 0.999546i $$0.490411\pi$$
−0.880693 + 0.473688i $$0.842923\pi$$
$$312$$ 0 0
$$313$$ 8.50000 + 14.7224i 0.480448 + 0.832161i 0.999748 0.0224310i $$-0.00714060\pi$$
−0.519300 + 0.854592i $$0.673807\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −10.0000 17.3205i −0.561656 0.972817i −0.997352 0.0727229i $$-0.976831\pi$$
0.435696 0.900094i $$-0.356502\pi$$
$$318$$ 0 0
$$319$$ 8.00000 13.8564i 0.447914 0.775810i
$$320$$ 0 0
$$321$$ 2.00000 0.111629
$$322$$ 0 0
$$323$$ 6.00000 0.333849
$$324$$ 0 0
$$325$$ 12.5000 21.6506i 0.693375 1.20096i
$$326$$ 0 0
$$327$$ 0.500000 + 0.866025i 0.0276501 + 0.0478913i
$$328$$ 0 0
$$329$$ 20.0000 6.92820i 1.10264 0.381964i
$$330$$ 0 0
$$331$$ −7.50000 12.9904i −0.412237 0.714016i 0.582897 0.812546i $$-0.301919\pi$$
−0.995134 + 0.0985303i $$0.968586\pi$$
$$332$$ 0 0
$$333$$ 2.50000 4.33013i 0.136999 0.237289i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 9.00000 0.490261 0.245131 0.969490i $$-0.421169\pi$$
0.245131 + 0.969490i $$0.421169\pi$$
$$338$$ 0 0
$$339$$ −6.00000 + 10.3923i −0.325875 + 0.564433i
$$340$$ 0 0
$$341$$ 1.00000 + 1.73205i 0.0541530 + 0.0937958i
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i $$0.464631\pi$$
−0.916127 + 0.400887i $$0.868702\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ −5.00000 −0.266880
$$352$$ 0 0
$$353$$ −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i $$0.387192\pi$$
−0.985719 + 0.168397i $$0.946141\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 5.00000 1.73205i 0.264628 0.0916698i
$$358$$ 0 0
$$359$$ 16.0000 + 27.7128i 0.844448 + 1.46263i 0.886100 + 0.463494i $$0.153404\pi$$
−0.0416523 + 0.999132i $$0.513262\pi$$
$$360$$ 0 0
$$361$$ 5.00000 8.66025i 0.263158 0.455803i
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i $$-0.687000\pi$$
0.997960 + 0.0638362i $$0.0203335\pi$$
$$368$$ 0 0
$$369$$ −1.00000 1.73205i −0.0520579 0.0901670i
$$370$$ 0 0
$$371$$ 4.00000 + 3.46410i 0.207670 + 0.179847i
$$372$$ 0 0
$$373$$ 10.5000 + 18.1865i 0.543669 + 0.941663i 0.998689 + 0.0511818i $$0.0162988\pi$$
−0.455020 + 0.890481i $$0.650368\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 40.0000 2.06010
$$378$$ 0 0
$$379$$ −1.00000 −0.0513665 −0.0256833 0.999670i $$-0.508176\pi$$
−0.0256833 + 0.999670i $$0.508176\pi$$
$$380$$ 0 0
$$381$$ −5.50000 + 9.52628i −0.281774 + 0.488046i
$$382$$ 0 0
$$383$$ −11.0000 19.0526i −0.562074 0.973540i −0.997315 0.0732266i $$-0.976670\pi$$
0.435242 0.900314i $$-0.356663\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 3.50000 + 6.06218i 0.177915 + 0.308158i
$$388$$ 0 0
$$389$$ 12.0000 20.7846i 0.608424 1.05382i −0.383076 0.923717i $$-0.625135\pi$$
0.991500 0.130105i $$-0.0415314\pi$$
$$390$$ 0 0
$$391$$ 4.00000 0.202289
$$392$$ 0 0
$$393$$ −6.00000 −0.302660
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 6.50000 + 11.2583i 0.326226 + 0.565039i 0.981760 0.190126i $$-0.0608897\pi$$
−0.655534 + 0.755166i $$0.727556\pi$$
$$398$$ 0 0
$$399$$ −1.50000 + 7.79423i −0.0750939 + 0.390199i
$$400$$ 0 0
$$401$$ −5.00000 8.66025i −0.249688 0.432472i 0.713751 0.700399i $$-0.246995\pi$$
−0.963439 + 0.267927i $$0.913661\pi$$
$$402$$ 0 0
$$403$$ −2.50000 + 4.33013i −0.124534 + 0.215699i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 10.0000 0.495682
$$408$$ 0 0
$$409$$ 17.5000 30.3109i 0.865319 1.49878i −0.00141047 0.999999i $$-0.500449\pi$$
0.866730 0.498778i $$-0.166218\pi$$
$$410$$ 0 0
$$411$$ 2.00000 + 3.46410i 0.0986527 + 0.170872i
$$412$$ 0 0
$$413$$ 20.0000 + 17.3205i 0.984136 + 0.852286i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0.500000 0.866025i 0.0244851 0.0424094i
$$418$$ 0 0
$$419$$ −18.0000 −0.879358 −0.439679 0.898155i $$-0.644908\pi$$
−0.439679 + 0.898155i $$0.644908\pi$$
$$420$$ 0 0
$$421$$ 9.00000 0.438633 0.219317 0.975654i $$-0.429617\pi$$
0.219317 + 0.975654i $$0.429617\pi$$
$$422$$ 0 0
$$423$$ −4.00000 + 6.92820i −0.194487 + 0.336861i
$$424$$ 0 0
$$425$$ −5.00000 8.66025i −0.242536 0.420084i
$$426$$ 0 0
$$427$$ −5.00000 + 1.73205i −0.241967 + 0.0838198i
$$428$$ 0 0
$$429$$ −5.00000 8.66025i −0.241402 0.418121i
$$430$$ 0 0
$$431$$ 10.0000 17.3205i 0.481683 0.834300i −0.518096 0.855323i $$-0.673359\pi$$
0.999779 + 0.0210230i $$0.00669232\pi$$
$$432$$ 0 0
$$433$$ −17.0000 −0.816968 −0.408484 0.912766i $$-0.633942\pi$$
−0.408484 + 0.912766i $$0.633942\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3.00000 + 5.19615i −0.143509 + 0.248566i
$$438$$ 0 0
$$439$$ −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i $$-0.972552\pi$$
0.423556 0.905870i $$-0.360782\pi$$
$$440$$ 0 0
$$441$$ 1.00000 + 6.92820i 0.0476190 + 0.329914i
$$442$$ 0 0
$$443$$ 3.00000 + 5.19615i 0.142534 + 0.246877i 0.928450 0.371457i $$-0.121142\pi$$
−0.785916 + 0.618333i $$0.787808\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ −24.0000 −1.13263 −0.566315 0.824189i $$-0.691631\pi$$
−0.566315 + 0.824189i $$0.691631\pi$$
$$450$$ 0 0
$$451$$ 2.00000 3.46410i 0.0941763 0.163118i
$$452$$ 0 0
$$453$$ −4.00000 6.92820i −0.187936 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.5000 + 19.9186i 0.537947 + 0.931752i 0.999014 + 0.0443868i $$0.0141334\pi$$
−0.461067 + 0.887365i $$0.652533\pi$$
$$458$$ 0 0
$$459$$ −1.00000 + 1.73205i −0.0466760 + 0.0808452i
$$460$$ 0 0
$$461$$ −20.0000 −0.931493 −0.465746 0.884918i $$-0.654214\pi$$
−0.465746 + 0.884918i $$0.654214\pi$$
$$462$$ 0 0
$$463$$ −9.00000 −0.418265 −0.209133 0.977887i $$-0.567064\pi$$
−0.209133 + 0.977887i $$0.567064\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i $$-0.0771121\pi$$
−0.693153 + 0.720791i $$0.743779\pi$$
$$468$$ 0 0
$$469$$ −22.0000 19.0526i −1.01587 0.879765i
$$470$$ 0 0
$$471$$ −3.00000 5.19615i −0.138233 0.239426i
$$472$$ 0 0
$$473$$ −7.00000 + 12.1244i −0.321860 + 0.557478i
$$474$$ 0 0
$$475$$ 15.0000 0.688247
$$476$$ 0 0
$$477$$ −2.00000 −0.0915737
$$478$$ 0 0
$$479$$ 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i $$-0.698436\pi$$
0.995023 + 0.0996406i $$0.0317693\pi$$
$$480$$ 0 0
$$481$$ 12.5000 + 21.6506i 0.569951 + 0.987184i
$$482$$ 0 0
$$483$$ −1.00000 + 5.19615i −0.0455016 + 0.236433i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 10.5000 18.1865i 0.475800 0.824110i −0.523815 0.851832i $$-0.675492\pi$$
0.999616 + 0.0277214i $$0.00882512\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ −32.0000 −1.44414 −0.722070 0.691820i $$-0.756809\pi$$
−0.722070 + 0.691820i $$0.756809\pi$$
$$492$$ 0 0
$$493$$ 8.00000 13.8564i 0.360302 0.624061i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 6.00000 31.1769i 0.269137 1.39848i
$$498$$ 0 0
$$499$$ −20.5000 35.5070i −0.917706 1.58951i −0.802890 0.596127i $$-0.796706\pi$$
−0.114816 0.993387i $$-0.536628\pi$$
$$500$$ 0 0
$$501$$ −10.0000 + 17.3205i −0.446767 + 0.773823i
$$502$$ 0 0
$$503$$ −14.0000 −0.624229 −0.312115 0.950044i $$-0.601037\pi$$
−0.312115 + 0.950044i $$0.601037\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 6.00000 10.3923i 0.266469 0.461538i
$$508$$ 0 0
$$509$$ 2.00000 + 3.46410i 0.0886484 + 0.153544i 0.906940 0.421260i $$-0.138412\pi$$
−0.818292 + 0.574803i $$0.805079\pi$$
$$510$$ 0 0
$$511$$ 6.00000 + 5.19615i 0.265424 + 0.229864i
$$512$$ 0 0
$$513$$ −1.50000 2.59808i −0.0662266 0.114708i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −16.0000 −0.703679
$$518$$ 0 0
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ −16.0000 + 27.7128i −0.700973 + 1.21412i 0.267153 + 0.963654i $$0.413917\pi$$
−0.968125 + 0.250466i $$0.919416\pi$$
$$522$$ 0 0
$$523$$ −5.50000 9.52628i −0.240498 0.416555i 0.720358 0.693602i $$-0.243977\pi$$
−0.960856 + 0.277047i $$0.910644\pi$$
$$524$$ 0 0
$$525$$ 12.5000 4.33013i 0.545545 0.188982i
$$526$$ 0 0
$$527$$ 1.00000 + 1.73205i 0.0435607 + 0.0754493i
$$528$$ 0 0
$$529$$ 9.50000 16.4545i 0.413043 0.715412i
$$530$$ 0 0
$$531$$ −10.0000 −0.433963
$$532$$ 0 0
$$533$$ 10.0000 0.433148
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −6.00000 10.3923i −0.258919 0.448461i
$$538$$ 0 0
$$539$$ −11.0000 + 8.66025i −0.473804 + 0.373024i
$$540$$ 0 0
$$541$$ 13.5000 + 23.3827i 0.580410 + 1.00530i 0.995431 + 0.0954880i $$0.0304412\pi$$
−0.415020 + 0.909812i $$0.636226\pi$$
$$542$$ 0 0
$$543$$ −7.50000 + 12.9904i −0.321856 + 0.557471i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 44.0000 1.88130 0.940652 0.339372i $$-0.110215\pi$$
0.940652 + 0.339372i $$0.110215\pi$$
$$548$$ 0 0
$$549$$ 1.00000 1.73205i 0.0426790 0.0739221i
$$550$$ 0 0
$$551$$ 12.0000 + 20.7846i 0.511217 + 0.885454i
$$552$$ 0 0
$$553$$ −42.5000 + 14.7224i −1.80728 + 0.626061i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −9.00000 + 15.5885i −0.381342 + 0.660504i −0.991254 0.131965i $$-0.957871\pi$$
0.609912 + 0.792469i $$0.291205\pi$$
$$558$$ 0 0
$$559$$ −35.0000 −1.48034
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ 0 0
$$563$$ −10.0000 + 17.3205i −0.421450 + 0.729972i −0.996082 0.0884397i $$-0.971812\pi$$
0.574632 + 0.818412i $$0.305145\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −2.00000 1.73205i −0.0839921 0.0727393i
$$568$$ 0 0
$$569$$ −21.0000 36.3731i −0.880366 1.52484i −0.850935 0.525271i $$-0.823964\pi$$
−0.0294311 0.999567i $$-0.509370\pi$$
$$570$$ 0 0
$$571$$ 11.5000 19.9186i 0.481260 0.833567i −0.518509 0.855072i $$-0.673513\pi$$
0.999769 + 0.0215055i $$0.00684595\pi$$
$$572$$ 0 0
$$573$$ 12.0000 0.501307
$$574$$ 0 0
$$575$$ 10.0000 0.417029
$$576$$ 0 0
$$577$$ −3.50000 + 6.06218i −0.145707 + 0.252372i −0.929636 0.368478i $$-0.879879\pi$$
0.783930 + 0.620850i $$0.213212\pi$$
$$578$$ 0 0
$$579$$ 11.5000 + 19.9186i 0.477924 + 0.827788i
$$580$$ 0 0
$$581$$ −8.00000 + 41.5692i −0.331896 + 1.72458i
$$582$$ 0 0
$$583$$ −2.00000 3.46410i −0.0828315 0.143468i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 24.0000 0.990586 0.495293 0.868726i $$-0.335061\pi$$
0.495293 + 0.868726i $$0.335061\pi$$
$$588$$ 0 0
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ −9.00000 + 15.5885i −0.370211 + 0.641223i
$$592$$ 0 0
$$593$$ −15.0000 25.9808i −0.615976 1.06690i −0.990212 0.139569i $$-0.955428\pi$$
0.374236 0.927333i $$-0.377905\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −2.00000 3.46410i −0.0818546 0.141776i
$$598$$ 0 0
$$599$$ −18.0000 + 31.1769i −0.735460 + 1.27385i 0.219061 + 0.975711i $$0.429701\pi$$
−0.954521 + 0.298143i $$0.903633\pi$$
$$600$$ 0 0
$$601$$ −37.0000 −1.50926 −0.754631 0.656150i $$-0.772184\pi$$
−0.754631 + 0.656150i $$0.772184\pi$$
$$602$$ 0 0
$$603$$ 11.0000 0.447955
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 16.5000 + 28.5788i 0.669714 + 1.15998i 0.977984 + 0.208680i $$0.0669168\pi$$
−0.308270 + 0.951299i $$0.599750\pi$$
$$608$$ 0 0
$$609$$ 16.0000 + 13.8564i 0.648353 + 0.561490i
$$610$$ 0 0
$$611$$ −20.0000 34.6410i −0.809113 1.40143i
$$612$$ 0 0
$$613$$ −13.0000 + 22.5167i −0.525065 + 0.909439i 0.474509 + 0.880251i $$0.342626\pi$$
−0.999574 + 0.0291886i $$0.990708\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −14.0000 −0.563619 −0.281809 0.959470i $$-0.590935\pi$$
−0.281809 + 0.959470i $$0.590935\pi$$
$$618$$ 0 0
$$619$$ 2.50000 4.33013i 0.100483 0.174042i −0.811400 0.584491i $$-0.801294\pi$$
0.911884 + 0.410448i $$0.134628\pi$$
$$620$$ 0 0
$$621$$ −1.00000 1.73205i −0.0401286 0.0695048i
$$622$$ 0 0
$$623$$ 30.0000 10.3923i 1.20192 0.416359i
$$624$$ 0 0
$$625$$ −12.5000 21.6506i −0.500000 0.866025i
$$626$$ 0 0
$$627$$ 3.00000 5.19615i 0.119808 0.207514i
$$628$$ 0 0
$$629$$ 10.0000 0.398726
$$630$$ 0 0
$$631$$ 4.00000 0.159237 0.0796187 0.996825i $$-0.474630\pi$$
0.0796187 + 0.996825i $$0.474630\pi$$
$$632$$ 0 0
$$633$$ −10.0000 + 17.3205i −0.397464 + 0.688428i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −32.5000 12.9904i −1.28770 0.514698i
$$638$$ 0 0
$$639$$ 6.00000 + 10.3923i 0.237356 + 0.411113i
$$640$$ 0 0
$$641$$ −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i $$0.338307\pi$$
−0.999878 + 0.0156233i $$0.995027\pi$$
$$642$$ 0 0
$$643$$ −11.0000 −0.433798 −0.216899 0.976194i $$-0.569594\pi$$
−0.216899 + 0.976194i $$0.569594\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i $$-0.948453\pi$$
0.633090 + 0.774078i $$0.281786\pi$$
$$648$$ 0 0
$$649$$ −10.0000 17.3205i −0.392534 0.679889i
$$650$$ 0 0
$$651$$ −2.50000 + 0.866025i −0.0979827 + 0.0339422i
$$652$$ 0 0
$$653$$ 7.00000 + 12.1244i 0.273931 + 0.474463i 0.969865 0.243643i $$-0.0783426\pi$$
−0.695934 + 0.718106i $$0.745009\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −3.00000 −0.117041
$$658$$ 0 0
$$659$$ 42.0000 1.63609 0.818044 0.575156i $$-0.195059\pi$$
0.818044 + 0.575156i $$0.195059\pi$$
$$660$$ 0 0
$$661$$ −1.50000 + 2.59808i −0.0583432 + 0.101053i −0.893722 0.448622i $$-0.851915\pi$$
0.835379 + 0.549675i $$0.185248\pi$$
$$662$$ 0 0
$$663$$ −5.00000 8.66025i −0.194184 0.336336i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 8.00000 + 13.8564i 0.309761 + 0.536522i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ −21.0000 −0.809491 −0.404745 0.914429i $$-0.632640\pi$$
−0.404745 + 0.914429i $$0.632640\pi$$
$$674$$ 0 0
$$675$$ −2.50000 + 4.33013i −0.0962250 + 0.166667i
$$676$$ 0 0
$$677$$ 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i $$-0.0925982\pi$$
−0.727386 + 0.686229i $$0.759265\pi$$
$$678$$ 0 0
$$679$$ 7.00000 36.3731i 0.268635 1.39587i
$$680$$ 0 0
$$681$$ −13.0000 22.5167i −0.498161 0.862840i
$$682$$ 0 0
$$683$$ −15.0000 + 25.9808i −0.573959 + 0.994126i 0.422195 + 0.906505i $$0.361260\pi$$
−0.996154 + 0.0876211i $$0.972074\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −13.0000 −0.495981
$$688$$ 0 0
$$689$$ 5.00000 8.66025i 0.190485 0.329929i
$$690$$ 0 0
$$691$$ 2.50000 + 4.33013i 0.0951045 + 0.164726i 0.909652 0.415371i $$-0.136348\pi$$
−0.814548 + 0.580097i $$0.803015\pi$$
$$692$$ 0 0
$$693$$ 1.00000 5.19615i 0.0379869 0.197386i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 2.00000 3.46410i 0.0757554 0.131212i
$$698$$ 0 0
$$699$$ 12.0000 0.453882
$$700$$ 0 0
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 0 0
$$703$$ −7.50000 + 12.9904i −0.282868 + 0.489942i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −36.0000 31.1769i −1.35392 1.17253i
$$708$$ 0 0
$$709$$ 11.0000 + 19.0526i 0.413114 + 0.715534i 0.995228 0.0975728i $$-0.0311079\pi$$
−0.582115 + 0.813107i $$0.697775\pi$$
$$710$$ 0 0
$$711$$ 8.50000 14.7224i 0.318775 0.552134i
$$712$$ 0 0
$$713$$ −2.00000 −0.0749006
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −15.0000 + 25.9808i −0.560185 + 0.970269i
$$718$$ 0 0
$$719$$ −3.00000 5.19615i −0.111881 0.193784i 0.804648 0.593753i $$-0.202354\pi$$
−0.916529 + 0.399969i $$0.869021\pi$$
$$720$$ 0 0
$$721$$ 2.50000 0.866025i 0.0931049 0.0322525i
$$722$$ 0 0
$$723$$ −11.0000 19.0526i −0.409094 0.708572i
$$724$$ 0 0
$$725$$ 20.0000 34.6410i 0.742781 1.28654i
$$726$$ 0 0
$$727$$ −13.0000 −0.482143 −0.241072 0.970507i $$-0.577499\pi$$
−0.241072 + 0.970507i $$0.577499\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −7.00000 + 12.1244i −0.258904 + 0.448435i
$$732$$ 0 0
$$733$$ 9.50000 + 16.4545i 0.350891 + 0.607760i 0.986406 0.164328i $$-0.0525456\pi$$
−0.635515 + 0.772088i $$0.719212\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 11.0000 + 19.0526i 0.405190 + 0.701810i
$$738$$ 0 0
$$739$$ −8.50000 + 14.7224i −0.312678 + 0.541573i −0.978941 0.204143i $$-0.934559\pi$$
0.666264 + 0.745716i $$0.267893\pi$$
$$740$$ 0 0
$$741$$ 15.0000 0.551039
$$742$$ 0 0
$$743$$ 14.0000 0.513610 0.256805 0.966463i $$-0.417330\pi$$
0.256805 + 0.966463i $$0.417330\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −8.00000 13.8564i −0.292705 0.506979i
$$748$$ 0 0
$$749$$ −5.00000 + 1.73205i −0.182696 + 0.0632878i
$$750$$ 0 0
$$751$$ 13.5000 + 23.3827i 0.492622 + 0.853246i 0.999964 0.00849853i $$-0.00270520\pi$$
−0.507342 + 0.861745i $$0.669372\pi$$
$$752$$ 0 0
$$753$$ 11.0000 19.0526i 0.400862 0.694314i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 22.0000 0.799604 0.399802 0.916602i $$-0.369079\pi$$
0.399802 + 0.916602i $$0.369079\pi$$
$$758$$ 0 0
$$759$$ 2.00000 3.46410i 0.0725954 0.125739i
$$760$$ 0 0
$$761$$ −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i $$-0.983671\pi$$
0.454935 0.890525i $$-0.349663\pi$$
$$762$$ 0 0
$$763$$ −2.00000 1.73205i −0.0724049 0.0627044i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 25.0000 43.3013i 0.902698 1.56352i
$$768$$ 0 0
$$769$$ −9.00000 −0.324548 −0.162274 0.986746i $$-0.551883\pi$$
−0.162274 + 0.986746i $$0.551883\pi$$
$$770$$ 0 0
$$771$$ 16.0000 0.576226
$$772$$ 0 0
$$773$$ −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i $$-0.938263\pi$$
0.657542 + 0.753418i $$0.271596\pi$$
$$774$$ 0 0
$$775$$ 2.50000 + 4.33013i 0.0898027 + 0.155543i
$$776$$ 0 0
$$777$$ −2.50000 + 12.9904i −0.0896870 + 0.466027i
$$778$$ 0 0
$$779$$ 3.00000 + 5.19615i 0.107486 + 0.186171i
$$780$$ 0 0
$$781$$ −12.0000 + 20.7846i −0.429394 + 0.743732i
$$782$$ 0 0
$$783$$ −8.00000 −0.285897
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −20.0000 + 34.6410i −0.712923 + 1.23482i 0.250832 + 0.968031i $$0.419296\pi$$
−0.963755 + 0.266788i $$0.914038\pi$$
$$788$$ 0 0
$$789$$ −4.00000 6.92820i −0.142404 0.246651i
$$790$$ 0 0
$$791$$ 6.00000 31.1769i 0.213335 1.10852i
$$792$$ 0 0
$$793$$ 5.00000 + 8.66025i 0.177555 + 0.307535i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −34.0000 −1.20434 −0.602171 0.798367i $$-0.705697\pi$$
−0.602171 + 0.798367i $$0.705697\pi$$
$$798$$ 0 0
$$799$$ −16.0000 −0.566039
$$800$$