# Properties

 Label 672.2.q.c.289.1 Level $672$ Weight $2$ Character 672.289 Analytic conductor $5.366$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## 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 289.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 672.289 Dual form 672.2.q.c.193.1

## $q$-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 $$\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$$.

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

## 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 $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ 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 $$-0.264158\pi$$
−0.976478 + 0.215615i $$0.930824\pi$$
$$12$$ 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 0.961436 0.275029i $$-0.0886875\pi$$
−0.718900 + 0.695113i $$0.755354\pi$$
$$18$$ 0 0
$$19$$ −1.50000 + 2.59808i −0.344124 + 0.596040i −0.985194 0.171442i $$-0.945157\pi$$
0.641071 + 0.767482i $$0.278491\pi$$
$$20$$ 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 $$-0.900196\pi$$
0.742732 + 0.669588i $$0.233529\pi$$
$$24$$ 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 $$-0.138043\pi$$
−0.817625 + 0.575751i $$0.804710\pi$$
$$32$$ 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 −0.584002 0.811752i $$-0.698514\pi$$
0.994999 + 0.0998840i $$0.0318472\pi$$
$$38$$ 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 $$-0.320784\pi$$
0.533745 + 0.845645i $$0.320784\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i $$-0.635032\pi$$
0.995066 0.0992202i $$-0.0316348\pi$$
$$48$$ 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 0.926497 0.376303i $$-0.122805\pi$$
−0.789136 + 0.614218i $$0.789471\pi$$
$$54$$ 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 −0.982894 0.184172i $$-0.941040\pi$$
0.331949 0.943297i $$-0.392294\pi$$
$$60$$ 0 0
$$61$$ 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i $$-0.792466\pi$$
0.922916 + 0.385002i $$0.125799\pi$$
$$62$$ 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 0.977356 + 0.211604i $$0.0678686\pi$$
−0.305424 + 0.952217i $$0.598798\pi$$
$$68$$ 0 0
$$69$$ 2.00000 0.240772
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i $$-0.110493\pi$$
−0.764794 + 0.644275i $$0.777159\pi$$
$$74$$ 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 −0.225018 + 0.974355i $$0.572244\pi$$
−0.731307 + 0.682048i $$0.761089\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −16.0000 −1.75623 −0.878114 0.478451i $$-0.841198\pi$$
−0.878114 + 0.478451i $$0.841198\pi$$
$$84$$ 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 0.350304 + 0.936636i $$0.386078\pi$$
−0.986303 + 0.164946i $$0.947255\pi$$
$$90$$ 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 −0.833143 0.553058i $$-0.813461\pi$$
−0.0623905 0.998052i $$-0.519872\pi$$
$$102$$ 0 0
$$103$$ 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i $$-0.817645\pi$$
0.889607 + 0.456727i $$0.150978\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.00000 + 1.73205i −0.0966736 + 0.167444i −0.910306 0.413936i $$-0.864154\pi$$
0.813632 + 0.581380i $$0.197487\pi$$
$$108$$ 0 0
$$109$$ −0.500000 0.866025i −0.0478913 0.0829502i 0.841086 0.540901i $$-0.181917\pi$$
−0.888977 + 0.457951i $$0.848583\pi$$
$$110$$ 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 $$-0.337710\pi$$
0.488046 + 0.872818i $$0.337710\pi$$
$$128$$ 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 $$-0.748915\pi$$
0.966803 + 0.255524i $$0.0822479\pi$$
$$132$$ 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 0.767853 0.640626i $$-0.221325\pi$$
−0.938725 + 0.344668i $$0.887992\pi$$
$$138$$ 0 0
$$139$$ −1.00000 −0.0848189 −0.0424094 0.999100i $$-0.513503\pi$$
−0.0424094 + 0.999100i $$0.513503\pi$$
$$140$$ 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 −0.999953 0.00974235i $$-0.996899\pi$$
0.508413 + 0.861113i $$0.330232\pi$$
$$150$$ 0 0
$$151$$ −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i $$-0.272204\pi$$
−0.981617 + 0.190864i $$0.938871\pi$$
$$152$$ 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 0.960550 0.278108i $$-0.0897074\pi$$
−0.721124 + 0.692806i $$0.756374\pi$$
$$158$$ 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 $$-0.883403\pi$$
0.777007 + 0.629492i $$0.216737\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 20.0000 1.54765 0.773823 0.633402i $$-0.218342\pi$$
0.773823 + 0.633402i $$0.218342\pi$$
$$168$$ 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 −0.729155 0.684349i $$-0.760087\pi$$
0.957241 + 0.289292i $$0.0934200\pi$$
$$174$$ 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 $$-0.314694\pi$$
−0.998286 + 0.0585225i $$0.981361\pi$$
$$180$$ 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 $$-0.976283\pi$$
0.563081 + 0.826402i $$0.309616\pi$$
$$192$$ 0 0
$$193$$ −11.5000 19.9186i −0.827788 1.43377i −0.899770 0.436365i $$-0.856266\pi$$
0.0719816 0.997406i $$-0.477068\pi$$
$$194$$ 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 $$-0.211948\pi$$
−0.928166 + 0.372168i $$0.878615\pi$$
$$200$$ 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 $$-0.258301\pi$$
0.688428 + 0.725304i $$0.258301\pi$$
$$212$$ 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 −0.869176 0.494503i $$-0.835350\pi$$
0.00633544 0.999980i $$-0.497983\pi$$
$$228$$ 0 0
$$229$$ −6.50000 + 11.2583i −0.429532 + 0.743971i −0.996832 0.0795401i $$-0.974655\pi$$
0.567300 + 0.823511i $$0.307988\pi$$
$$230$$ 0 0
$$231$$ −5.00000 1.73205i −0.328976 0.113961i
$$232$$ 0 0
$$233$$ 6.00000 10.3923i 0.393073 0.680823i −0.599780 0.800165i $$-0.704745\pi$$
0.992853 + 0.119342i $$0.0380786\pi$$
$$234$$ 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 $$-0.0778125\pi$$
0.970269 + 0.242028i $$0.0778125\pi$$
$$240$$ 0 0
$$241$$ 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i $$0.0839937\pi$$
−0.256814 + 0.966461i $$0.582673\pi$$
$$242$$ 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 $$-0.744292\pi$$
−0.694314 + 0.719672i $$0.744292\pi$$
$$252$$ 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 −0.500973 0.865463i $$-0.667024\pi$$
0.999999 + 0.00112398i $$0.000357774\pi$$
$$258$$ 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 $$-0.245997\pi$$
−0.962594 + 0.270947i $$0.912663\pi$$
$$264$$ 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 0.998361 + 0.0572259i $$0.0182255\pi$$
−0.449622 + 0.893219i $$0.648441\pi$$
$$270$$ 0 0
$$271$$ 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i $$-0.671801\pi$$
0.999870 + 0.0161307i $$0.00513477\pi$$
$$272$$ 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 −0.999923 0.0124177i $$-0.996047\pi$$
0.489207 0.872167i $$-0.337286\pi$$
$$278$$ 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 −0.797283 0.603606i $$-0.793730\pi$$
−0.124096 0.992270i $$-0.539603\pi$$
$$284$$ 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 $$-0.727896\pi$$
−0.656340 + 0.754466i $$0.727896\pi$$
$$308$$ 0 0
$$309$$ −1.00000 −0.0568880
$$310$$ 0 0
$$311$$ 15.0000 + 25.9808i 0.850572 + 1.47323i 0.880693 + 0.473688i $$0.157077\pi$$
−0.0301210 + 0.999546i $$0.509589\pi$$
$$312$$ 0 0
$$313$$ 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i $$-0.673807\pi$$
0.999748 + 0.0224310i $$0.00714060\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −10.0000 + 17.3205i −0.561656 + 0.972817i 0.435696 + 0.900094i $$0.356502\pi$$
−0.997352 + 0.0727229i $$0.976831\pi$$
$$318$$ 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 $$-0.698081\pi$$
0.995134 + 0.0985303i $$0.0314141\pi$$
$$332$$ 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 0.916127 + 0.400887i $$0.131298\pi$$
−0.110885 + 0.993833i $$0.535369\pi$$
$$348$$ 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 −0.985719 0.168397i $$-0.946141\pi$$
0.347024 0.937856i $$-0.387192\pi$$
$$354$$ 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 0.0416523 + 0.999132i $$0.486738\pi$$
−0.886100 + 0.463494i $$0.846596\pi$$
$$360$$ 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 $$-0.313000\pi$$
−0.997960 + 0.0638362i $$0.979666\pi$$
$$368$$ 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 −0.455020 0.890481i $$-0.650368\pi$$
0.998689 0.0511818i $$-0.0162988\pi$$
$$374$$ 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 $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ 0 0
$$381$$ −5.50000 9.52628i −0.281774 0.488046i
$$382$$ 0 0
$$383$$ 11.0000 19.0526i 0.562074 0.973540i −0.435242 0.900314i $$-0.643337\pi$$
0.997315 0.0732266i $$-0.0233296\pi$$
$$384$$ 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 0.991500 + 0.130105i $$0.0415314\pi$$
−0.383076 + 0.923717i $$0.625135\pi$$
$$390$$ 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 −0.655534 0.755166i $$-0.727556\pi$$
0.981760 + 0.190126i $$0.0608897\pi$$
$$398$$ 0 0
$$399$$ 1.50000 + 7.79423i 0.0750939 + 0.390199i
$$400$$ 0 0
$$401$$ −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i $$-0.913661\pi$$
0.713751 + 0.700399i $$0.246995\pi$$
$$402$$ 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 0.866730 + 0.498778i $$0.166218\pi$$
−0.00141047 + 0.999999i $$0.500449\pi$$
$$410$$ 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 $$-0.355092\pi$$
0.439679 + 0.898155i $$0.355092\pi$$
$$420$$ 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 $$-0.326641\pi$$
−0.999779 + 0.0210230i $$0.993308\pi$$
$$432$$ 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 −0.423556 0.905870i $$-0.639218\pi$$
0.996284 0.0861252i $$-0.0274485\pi$$
$$440$$ 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 $$-0.878858\pi$$
0.785916 + 0.618333i $$0.212192\pi$$
$$444$$ 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 −0.461067 0.887365i $$-0.652533\pi$$
0.999014 0.0443868i $$-0.0141334\pi$$
$$458$$ 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 $$-0.432936\pi$$
0.209133 + 0.977887i $$0.432936\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i $$-0.922888\pi$$
0.693153 + 0.720791i $$0.256221\pi$$
$$468$$ 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 $$-0.301564\pi$$
−0.995023 + 0.0996406i $$0.968231\pi$$
$$480$$ 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 $$-0.324508\pi$$
−0.999616 + 0.0277214i $$0.991175\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ 32.0000 1.44414 0.722070 0.691820i $$-0.243191\pi$$
0.722070 + 0.691820i $$0.243191\pi$$
$$492$$ 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 0.114816 0.993387i $$-0.463372\pi$$
0.802890 0.596127i $$-0.203294\pi$$
$$500$$ 0 0
$$501$$ −10.0000 17.3205i −0.446767 0.773823i
$$502$$ 0 0
$$503$$ 14.0000 0.624229 0.312115 0.950044i $$-0.398963\pi$$
0.312115 + 0.950044i $$0.398963\pi$$
$$504$$ 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 −0.818292 0.574803i $$-0.805079\pi$$
0.906940 + 0.421260i $$0.138412\pi$$
$$510$$ 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 −0.968125 0.250466i $$-0.919416\pi$$
0.267153 0.963654i $$-0.413917\pi$$
$$522$$ 0 0
$$523$$ 5.50000 9.52628i 0.240498 0.416555i −0.720358 0.693602i $$-0.756023\pi$$
0.960856 + 0.277047i $$0.0893559\pi$$
$$524$$ 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 −0.415020 0.909812i $$-0.636226\pi$$
0.995431 0.0954880i $$-0.0304412\pi$$
$$542$$ 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 $$-0.889785\pi$$
−0.940652 + 0.339372i $$0.889785\pi$$
$$548$$ 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 0.609912 0.792469i $$-0.291205\pi$$
−0.991254 + 0.131965i $$0.957871\pi$$
$$558$$ 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 $$-0.0281881\pi$$
−0.574632 + 0.818412i $$0.694855\pi$$
$$564$$ 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 −0.0294311 + 0.999567i $$0.509370\pi$$
−0.850935 + 0.525271i $$0.823964\pi$$
$$570$$ 0 0
$$571$$ −11.5000 19.9186i −0.481260 0.833567i 0.518509 0.855072i $$-0.326487\pi$$
−0.999769 + 0.0215055i $$0.993154\pi$$
$$572$$ 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 0.783930 0.620850i $$-0.213212\pi$$
−0.929636 + 0.368478i $$0.879879\pi$$
$$578$$ 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 $$-0.664939\pi$$
−0.495293 + 0.868726i $$0.664939\pi$$
$$588$$ 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 0.374236 + 0.927333i $$0.377905\pi$$
−0.990212 + 0.139569i $$0.955428\pi$$
$$594$$ 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 0.954521 + 0.298143i $$0.0963673\pi$$
−0.219061 + 0.975711i $$0.570299\pi$$
$$600$$ 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 0.308270 + 0.951299i $$0.400250\pi$$
−0.977984 + 0.208680i $$0.933083\pi$$
$$608$$ 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 −0.999574 0.0291886i $$-0.990708\pi$$
0.474509 0.880251i $$-0.342626\pi$$
$$614$$ 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 $$-0.198706\pi$$
−0.911884 + 0.410448i $$0.865372\pi$$
$$620$$ 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 $$-0.525370\pi$$
−0.0796187 + 0.996825i $$0.525370\pi$$
$$632$$ 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 −0.999878 0.0156233i $$-0.995027\pi$$
0.486409 0.873731i $$-0.338307\pi$$
$$642$$ 0 0
$$643$$ 11.0000 0.433798 0.216899 0.976194i $$-0.430406\pi$$
0.216899 + 0.976194i $$0.430406\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i $$-0.0515470\pi$$
−0.633090 + 0.774078i $$0.718214\pi$$
$$648$$ 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 −0.695934 0.718106i $$-0.745009\pi$$
0.969865 + 0.243643i $$0.0783426\pi$$
$$654$$ 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 $$-0.804941\pi$$
−0.818044 + 0.575156i $$0.804941\pi$$
$$660$$ 0 0
$$661$$ −1.50000 2.59808i −0.0583432 0.101053i 0.835379 0.549675i $$-0.185248\pi$$
−0.893722 + 0.448622i $$0.851915\pi$$
$$662$$ 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 −0.727386 0.686229i $$-0.759265\pi$$
0.957984 + 0.286820i $$0.0925982\pi$$
$$678$$ 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 0.996154 + 0.0876211i $$0.0279265\pi$$
−0.422195 + 0.906505i $$0.638740\pi$$
$$684$$ 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 $$-0.863652\pi$$
0.814548 + 0.580097i $$0.196985\pi$$
$$692$$ 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 −0.582115 0.813107i $$-0.697775\pi$$
0.995228 + 0.0975728i $$0.0311079\pi$$
$$710$$ 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 $$-0.797646\pi$$
0.916529 + 0.399969i $$0.130979\pi$$
$$720$$ 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 $$-0.422501\pi$$
0.241072 + 0.970507i $$0.422501\pi$$
$$728$$ 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 −0.635515 0.772088i $$-0.719212\pi$$
0.986406 + 0.164328i $$0.0525456\pi$$
$$734$$ 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 $$-0.0654407\pi$$
−0.666264 + 0.745716i $$0.732107\pi$$
$$740$$ 0 0
$$741$$ 15.0000 0.551039
$$742$$ 0 0
$$743$$ −14.0000 −0.513610 −0.256805 0.966463i $$-0.582670\pi$$
−0.256805 + 0.966463i $$0.582670\pi$$
$$744$$ 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 $$-0.997295\pi$$
0.507342 + 0.861745i $$0.330628\pi$$
$$752$$ 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 0.454935 + 0.890525i $$0.349663\pi$$
−0.998684 + 0.0512772i $$0.983671\pi$$
$$762$$ 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 0.657542 0.753418i $$-0.271596\pi$$
−0.981250 + 0.192740i $$0.938263\pi$$
$$774$$ 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 0.963755 + 0.266788i $$0.0859624\pi$$
−0.250832 + 0.968031i $$0.580704\pi$$
$$788$$ 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