Properties

 Label 168.2.q.c.121.2 Level $168$ Weight $2$ Character 168.121 Analytic conductor $1.341$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 168.q (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$1.34148675396$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-19})$$ Defining polynomial: $$x^{4} - x^{3} - 4x^{2} - 5x + 25$$ x^4 - x^3 - 4*x^2 - 5*x + 25 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 121.2 Root $$2.13746 - 0.656712i$$ of defining polynomial Character $$\chi$$ $$=$$ 168.121 Dual form 168.2.q.c.25.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{3} +(2.13746 - 3.70219i) q^{5} +(-1.50000 - 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{3} +(2.13746 - 3.70219i) q^{5} +(-1.50000 - 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.13746 + 3.70219i) q^{11} -1.27492 q^{13} +4.27492 q^{15} +(2.00000 + 3.46410i) q^{17} +(-0.637459 + 1.10411i) q^{19} +(1.13746 - 2.38876i) q^{21} +(-2.00000 + 3.46410i) q^{23} +(-6.63746 - 11.4964i) q^{25} -1.00000 q^{27} -2.27492 q^{29} +(0.500000 + 0.866025i) q^{31} +(-2.13746 + 3.70219i) q^{33} +(-11.2749 + 0.894797i) q^{35} +(-2.63746 + 4.56821i) q^{37} +(-0.637459 - 1.10411i) q^{39} +10.5498 q^{41} -7.27492 q^{43} +(2.13746 + 3.70219i) q^{45} +(3.00000 - 5.19615i) q^{47} +(-2.50000 + 6.53835i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-0.862541 - 1.49397i) q^{53} +18.2749 q^{55} -1.27492 q^{57} +(-3.13746 - 5.43424i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(2.63746 - 0.209313i) q^{63} +(-2.72508 + 4.71998i) q^{65} +(-3.63746 - 6.30026i) q^{67} -4.00000 q^{69} +2.00000 q^{71} +(-1.63746 - 2.83616i) q^{73} +(6.63746 - 11.4964i) q^{75} +(4.86254 - 10.2118i) q^{77} +(1.77492 - 3.07425i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.274917 q^{83} +17.0997 q^{85} +(-1.13746 - 1.97014i) q^{87} +(-2.27492 + 3.94027i) q^{89} +(1.91238 + 2.77862i) q^{91} +(-0.500000 + 0.866025i) q^{93} +(2.72508 + 4.71998i) q^{95} +16.2749 q^{97} -4.27492 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{3} + q^{5} - 6 q^{7} - 2 q^{9}+O(q^{10})$$ 4 * q + 2 * q^3 + q^5 - 6 * q^7 - 2 * q^9 $$4 q + 2 q^{3} + q^{5} - 6 q^{7} - 2 q^{9} + q^{11} + 10 q^{13} + 2 q^{15} + 8 q^{17} + 5 q^{19} - 3 q^{21} - 8 q^{23} - 19 q^{25} - 4 q^{27} + 6 q^{29} + 2 q^{31} - q^{33} - 30 q^{35} - 3 q^{37} + 5 q^{39} + 12 q^{41} - 14 q^{43} + q^{45} + 12 q^{47} - 10 q^{49} - 8 q^{51} - 11 q^{53} + 58 q^{55} + 10 q^{57} - 5 q^{59} - 20 q^{61} + 3 q^{63} - 26 q^{65} - 7 q^{67} - 16 q^{69} + 8 q^{71} + q^{73} + 19 q^{75} + 27 q^{77} - 8 q^{79} - 2 q^{81} + 14 q^{83} + 8 q^{85} + 3 q^{87} + 6 q^{89} - 15 q^{91} - 2 q^{93} + 26 q^{95} + 50 q^{97} - 2 q^{99}+O(q^{100})$$ 4 * q + 2 * q^3 + q^5 - 6 * q^7 - 2 * q^9 + q^11 + 10 * q^13 + 2 * q^15 + 8 * q^17 + 5 * q^19 - 3 * q^21 - 8 * q^23 - 19 * q^25 - 4 * q^27 + 6 * q^29 + 2 * q^31 - q^33 - 30 * q^35 - 3 * q^37 + 5 * q^39 + 12 * q^41 - 14 * q^43 + q^45 + 12 * q^47 - 10 * q^49 - 8 * q^51 - 11 * q^53 + 58 * q^55 + 10 * q^57 - 5 * q^59 - 20 * q^61 + 3 * q^63 - 26 * q^65 - 7 * q^67 - 16 * q^69 + 8 * q^71 + q^73 + 19 * q^75 + 27 * q^77 - 8 * q^79 - 2 * q^81 + 14 * q^83 + 8 * q^85 + 3 * q^87 + 6 * q^89 - 15 * q^91 - 2 * q^93 + 26 * q^95 + 50 * q^97 - 2 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$$.

 $$n$$ $$73$$ $$85$$ $$113$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ 2.13746 3.70219i 0.955901 1.65567i 0.223607 0.974679i $$-0.428217\pi$$
0.732294 0.680989i $$-0.238450\pi$$
$$6$$ 0 0
$$7$$ −1.50000 2.17945i −0.566947 0.823754i
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 2.13746 + 3.70219i 0.644468 + 1.11625i 0.984424 + 0.175810i $$0.0562545\pi$$
−0.339956 + 0.940441i $$0.610412\pi$$
$$12$$ 0 0
$$13$$ −1.27492 −0.353598 −0.176799 0.984247i $$-0.556574\pi$$
−0.176799 + 0.984247i $$0.556574\pi$$
$$14$$ 0 0
$$15$$ 4.27492 1.10378
$$16$$ 0 0
$$17$$ 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i $$-0.00546033\pi$$
−0.514782 + 0.857321i $$0.672127\pi$$
$$18$$ 0 0
$$19$$ −0.637459 + 1.10411i −0.146243 + 0.253300i −0.929836 0.367974i $$-0.880051\pi$$
0.783593 + 0.621275i $$0.213385\pi$$
$$20$$ 0 0
$$21$$ 1.13746 2.38876i 0.248214 0.521271i
$$22$$ 0 0
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ 0 0
$$25$$ −6.63746 11.4964i −1.32749 2.29928i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −2.27492 −0.422442 −0.211221 0.977438i $$-0.567744\pi$$
−0.211221 + 0.977438i $$0.567744\pi$$
$$30$$ 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
$$33$$ −2.13746 + 3.70219i −0.372084 + 0.644468i
$$34$$ 0 0
$$35$$ −11.2749 + 0.894797i −1.90581 + 0.151248i
$$36$$ 0 0
$$37$$ −2.63746 + 4.56821i −0.433596 + 0.751009i −0.997180 0.0750491i $$-0.976089\pi$$
0.563584 + 0.826059i $$0.309422\pi$$
$$38$$ 0 0
$$39$$ −0.637459 1.10411i −0.102075 0.176799i
$$40$$ 0 0
$$41$$ 10.5498 1.64761 0.823804 0.566875i $$-0.191848\pi$$
0.823804 + 0.566875i $$0.191848\pi$$
$$42$$ 0 0
$$43$$ −7.27492 −1.10941 −0.554707 0.832046i $$-0.687170\pi$$
−0.554707 + 0.832046i $$0.687170\pi$$
$$44$$ 0 0
$$45$$ 2.13746 + 3.70219i 0.318634 + 0.551889i
$$46$$ 0 0
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 0 0
$$49$$ −2.50000 + 6.53835i −0.357143 + 0.934050i
$$50$$ 0 0
$$51$$ −2.00000 + 3.46410i −0.280056 + 0.485071i
$$52$$ 0 0
$$53$$ −0.862541 1.49397i −0.118479 0.205212i 0.800686 0.599084i $$-0.204469\pi$$
−0.919165 + 0.393872i $$0.871135\pi$$
$$54$$ 0 0
$$55$$ 18.2749 2.46419
$$56$$ 0 0
$$57$$ −1.27492 −0.168867
$$58$$ 0 0
$$59$$ −3.13746 5.43424i −0.408462 0.707477i 0.586255 0.810126i $$-0.300602\pi$$
−0.994718 + 0.102649i $$0.967268\pi$$
$$60$$ 0 0
$$61$$ −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i $$0.387809\pi$$
−0.985391 + 0.170305i $$0.945525\pi$$
$$62$$ 0 0
$$63$$ 2.63746 0.209313i 0.332289 0.0263710i
$$64$$ 0 0
$$65$$ −2.72508 + 4.71998i −0.338005 + 0.585442i
$$66$$ 0 0
$$67$$ −3.63746 6.30026i −0.444386 0.769700i 0.553623 0.832767i $$-0.313245\pi$$
−0.998009 + 0.0630678i $$0.979912\pi$$
$$68$$ 0 0
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 0 0
$$73$$ −1.63746 2.83616i −0.191650 0.331948i 0.754147 0.656705i $$-0.228051\pi$$
−0.945797 + 0.324758i $$0.894717\pi$$
$$74$$ 0 0
$$75$$ 6.63746 11.4964i 0.766428 1.32749i
$$76$$ 0 0
$$77$$ 4.86254 10.2118i 0.554138 1.16374i
$$78$$ 0 0
$$79$$ 1.77492 3.07425i 0.199694 0.345880i −0.748735 0.662869i $$-0.769339\pi$$
0.948429 + 0.316989i $$0.102672\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −0.274917 −0.0301761 −0.0150880 0.999886i $$-0.504803\pi$$
−0.0150880 + 0.999886i $$0.504803\pi$$
$$84$$ 0 0
$$85$$ 17.0997 1.85472
$$86$$ 0 0
$$87$$ −1.13746 1.97014i −0.121948 0.211221i
$$88$$ 0 0
$$89$$ −2.27492 + 3.94027i −0.241141 + 0.417668i −0.961040 0.276411i $$-0.910855\pi$$
0.719899 + 0.694079i $$0.244188\pi$$
$$90$$ 0 0
$$91$$ 1.91238 + 2.77862i 0.200471 + 0.291278i
$$92$$ 0 0
$$93$$ −0.500000 + 0.866025i −0.0518476 + 0.0898027i
$$94$$ 0 0
$$95$$ 2.72508 + 4.71998i 0.279588 + 0.484260i
$$96$$ 0 0
$$97$$ 16.2749 1.65247 0.826234 0.563327i $$-0.190479\pi$$
0.826234 + 0.563327i $$0.190479\pi$$
$$98$$ 0 0
$$99$$ −4.27492 −0.429645
$$100$$ 0 0
$$101$$ 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i $$-0.0701767\pi$$
−0.677284 + 0.735721i $$0.736843\pi$$
$$102$$ 0 0
$$103$$ 5.91238 10.2405i 0.582564 1.00903i −0.412611 0.910907i $$-0.635383\pi$$
0.995174 0.0981224i $$-0.0312837\pi$$
$$104$$ 0 0
$$105$$ −6.41238 9.31697i −0.625784 0.909243i
$$106$$ 0 0
$$107$$ −3.41238 + 5.91041i −0.329887 + 0.571381i −0.982489 0.186320i $$-0.940344\pi$$
0.652602 + 0.757701i $$0.273677\pi$$
$$108$$ 0 0
$$109$$ 2.91238 + 5.04438i 0.278955 + 0.483164i 0.971125 0.238570i $$-0.0766786\pi$$
−0.692170 + 0.721734i $$0.743345\pi$$
$$110$$ 0 0
$$111$$ −5.27492 −0.500673
$$112$$ 0 0
$$113$$ 10.5498 0.992445 0.496222 0.868195i $$-0.334720\pi$$
0.496222 + 0.868195i $$0.334720\pi$$
$$114$$ 0 0
$$115$$ 8.54983 + 14.8087i 0.797276 + 1.38092i
$$116$$ 0 0
$$117$$ 0.637459 1.10411i 0.0589331 0.102075i
$$118$$ 0 0
$$119$$ 4.54983 9.55505i 0.417083 0.875910i
$$120$$ 0 0
$$121$$ −3.63746 + 6.30026i −0.330678 + 0.572751i
$$122$$ 0 0
$$123$$ 5.27492 + 9.13642i 0.475623 + 0.823804i
$$124$$ 0 0
$$125$$ −35.3746 −3.16400
$$126$$ 0 0
$$127$$ −21.5498 −1.91224 −0.956119 0.292978i $$-0.905354\pi$$
−0.956119 + 0.292978i $$0.905354\pi$$
$$128$$ 0 0
$$129$$ −3.63746 6.30026i −0.320260 0.554707i
$$130$$ 0 0
$$131$$ 0.137459 0.238085i 0.0120098 0.0208016i −0.859958 0.510365i $$-0.829510\pi$$
0.871968 + 0.489563i $$0.162844\pi$$
$$132$$ 0 0
$$133$$ 3.36254 0.266857i 0.291569 0.0231395i
$$134$$ 0 0
$$135$$ −2.13746 + 3.70219i −0.183963 + 0.318634i
$$136$$ 0 0
$$137$$ −8.27492 14.3326i −0.706974 1.22451i −0.965974 0.258638i $$-0.916726\pi$$
0.259001 0.965877i $$-0.416607\pi$$
$$138$$ 0 0
$$139$$ 0.725083 0.0615007 0.0307504 0.999527i $$-0.490210\pi$$
0.0307504 + 0.999527i $$0.490210\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 0 0
$$143$$ −2.72508 4.71998i −0.227883 0.394705i
$$144$$ 0 0
$$145$$ −4.86254 + 8.42217i −0.403812 + 0.699423i
$$146$$ 0 0
$$147$$ −6.91238 + 1.10411i −0.570123 + 0.0910655i
$$148$$ 0 0
$$149$$ −0.274917 + 0.476171i −0.0225221 + 0.0390094i −0.877067 0.480368i $$-0.840503\pi$$
0.854545 + 0.519378i $$0.173836\pi$$
$$150$$ 0 0
$$151$$ 7.68729 + 13.3148i 0.625583 + 1.08354i 0.988428 + 0.151692i $$0.0484722\pi$$
−0.362845 + 0.931850i $$0.618194\pi$$
$$152$$ 0 0
$$153$$ −4.00000 −0.323381
$$154$$ 0 0
$$155$$ 4.27492 0.343370
$$156$$ 0 0
$$157$$ −7.27492 12.6005i −0.580602 1.00563i −0.995408 0.0957218i $$-0.969484\pi$$
0.414807 0.909910i $$-0.363849\pi$$
$$158$$ 0 0
$$159$$ 0.862541 1.49397i 0.0684040 0.118479i
$$160$$ 0 0
$$161$$ 10.5498 0.837253i 0.831443 0.0659848i
$$162$$ 0 0
$$163$$ 6.00000 10.3923i 0.469956 0.813988i −0.529454 0.848339i $$-0.677603\pi$$
0.999410 + 0.0343508i $$0.0109363\pi$$
$$164$$ 0 0
$$165$$ 9.13746 + 15.8265i 0.711350 + 1.23209i
$$166$$ 0 0
$$167$$ −6.00000 −0.464294 −0.232147 0.972681i $$-0.574575\pi$$
−0.232147 + 0.972681i $$0.574575\pi$$
$$168$$ 0 0
$$169$$ −11.3746 −0.874968
$$170$$ 0 0
$$171$$ −0.637459 1.10411i −0.0487477 0.0844335i
$$172$$ 0 0
$$173$$ 3.72508 6.45203i 0.283213 0.490539i −0.688961 0.724798i $$-0.741933\pi$$
0.972174 + 0.234259i $$0.0752664\pi$$
$$174$$ 0 0
$$175$$ −15.0997 + 31.7106i −1.14143 + 2.39710i
$$176$$ 0 0
$$177$$ 3.13746 5.43424i 0.235826 0.408462i
$$178$$ 0 0
$$179$$ 0.725083 + 1.25588i 0.0541952 + 0.0938689i 0.891850 0.452331i $$-0.149407\pi$$
−0.837655 + 0.546200i $$0.816074\pi$$
$$180$$ 0 0
$$181$$ 3.82475 0.284292 0.142146 0.989846i $$-0.454600\pi$$
0.142146 + 0.989846i $$0.454600\pi$$
$$182$$ 0 0
$$183$$ −10.0000 −0.739221
$$184$$ 0 0
$$185$$ 11.2749 + 19.5287i 0.828948 + 1.43578i
$$186$$ 0 0
$$187$$ −8.54983 + 14.8087i −0.625226 + 1.08292i
$$188$$ 0 0
$$189$$ 1.50000 + 2.17945i 0.109109 + 0.158532i
$$190$$ 0 0
$$191$$ 5.27492 9.13642i 0.381680 0.661088i −0.609623 0.792692i $$-0.708679\pi$$
0.991302 + 0.131603i $$0.0420124\pi$$
$$192$$ 0 0
$$193$$ −7.77492 13.4666i −0.559651 0.969344i −0.997525 0.0703075i $$-0.977602\pi$$
0.437875 0.899036i $$-0.355731\pi$$
$$194$$ 0 0
$$195$$ −5.45017 −0.390294
$$196$$ 0 0
$$197$$ −16.5498 −1.17913 −0.589563 0.807722i $$-0.700700\pi$$
−0.589563 + 0.807722i $$0.700700\pi$$
$$198$$ 0 0
$$199$$ −12.5498 21.7370i −0.889634 1.54089i −0.840308 0.542109i $$-0.817626\pi$$
−0.0493259 0.998783i $$-0.515707\pi$$
$$200$$ 0 0
$$201$$ 3.63746 6.30026i 0.256567 0.444386i
$$202$$ 0 0
$$203$$ 3.41238 + 4.95807i 0.239502 + 0.347988i
$$204$$ 0 0
$$205$$ 22.5498 39.0575i 1.57495 2.72789i
$$206$$ 0 0
$$207$$ −2.00000 3.46410i −0.139010 0.240772i
$$208$$ 0 0
$$209$$ −5.45017 −0.376996
$$210$$ 0 0
$$211$$ 17.6495 1.21504 0.607521 0.794304i $$-0.292164\pi$$
0.607521 + 0.794304i $$0.292164\pi$$
$$212$$ 0 0
$$213$$ 1.00000 + 1.73205i 0.0685189 + 0.118678i
$$214$$ 0 0
$$215$$ −15.5498 + 26.9331i −1.06049 + 1.83682i
$$216$$ 0 0
$$217$$ 1.13746 2.38876i 0.0772157 0.162160i
$$218$$ 0 0
$$219$$ 1.63746 2.83616i 0.110649 0.191650i
$$220$$ 0 0
$$221$$ −2.54983 4.41644i −0.171520 0.297082i
$$222$$ 0 0
$$223$$ 6.27492 0.420200 0.210100 0.977680i $$-0.432621\pi$$
0.210100 + 0.977680i $$0.432621\pi$$
$$224$$ 0 0
$$225$$ 13.2749 0.884994
$$226$$ 0 0
$$227$$ 1.86254 + 3.22602i 0.123621 + 0.214118i 0.921193 0.389106i $$-0.127216\pi$$
−0.797572 + 0.603224i $$0.793883\pi$$
$$228$$ 0 0
$$229$$ −5.36254 + 9.28819i −0.354367 + 0.613781i −0.987009 0.160663i $$-0.948637\pi$$
0.632643 + 0.774444i $$0.281970\pi$$
$$230$$ 0 0
$$231$$ 11.2749 0.894797i 0.741835 0.0588733i
$$232$$ 0 0
$$233$$ −7.27492 + 12.6005i −0.476596 + 0.825488i −0.999640 0.0268173i $$-0.991463\pi$$
0.523045 + 0.852305i $$0.324796\pi$$
$$234$$ 0 0
$$235$$ −12.8248 22.2131i −0.836595 1.44902i
$$236$$ 0 0
$$237$$ 3.54983 0.230587
$$238$$ 0 0
$$239$$ 30.5498 1.97610 0.988052 0.154119i $$-0.0492540\pi$$
0.988052 + 0.154119i $$0.0492540\pi$$
$$240$$ 0 0
$$241$$ 6.41238 + 11.1066i 0.413057 + 0.715436i 0.995222 0.0976343i $$-0.0311275\pi$$
−0.582165 + 0.813071i $$0.697794\pi$$
$$242$$ 0 0
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 18.8625 + 23.2309i 1.20508 + 1.48417i
$$246$$ 0 0
$$247$$ 0.812707 1.40765i 0.0517113 0.0895666i
$$248$$ 0 0
$$249$$ −0.137459 0.238085i −0.00871109 0.0150880i
$$250$$ 0 0
$$251$$ 19.3746 1.22291 0.611457 0.791278i $$-0.290584\pi$$
0.611457 + 0.791278i $$0.290584\pi$$
$$252$$ 0 0
$$253$$ −17.0997 −1.07505
$$254$$ 0 0
$$255$$ 8.54983 + 14.8087i 0.535411 + 0.927360i
$$256$$ 0 0
$$257$$ 9.54983 16.5408i 0.595702 1.03179i −0.397745 0.917496i $$-0.630207\pi$$
0.993447 0.114291i $$-0.0364595\pi$$
$$258$$ 0 0
$$259$$ 13.9124 1.10411i 0.864473 0.0686061i
$$260$$ 0 0
$$261$$ 1.13746 1.97014i 0.0704069 0.121948i
$$262$$ 0 0
$$263$$ 12.2749 + 21.2608i 0.756904 + 1.31100i 0.944422 + 0.328735i $$0.106622\pi$$
−0.187518 + 0.982261i $$0.560044\pi$$
$$264$$ 0 0
$$265$$ −7.37459 −0.453017
$$266$$ 0 0
$$267$$ −4.54983 −0.278445
$$268$$ 0 0
$$269$$ −14.1375 24.4868i −0.861976 1.49299i −0.870019 0.493019i $$-0.835893\pi$$
0.00804266 0.999968i $$-0.497440\pi$$
$$270$$ 0 0
$$271$$ 3.13746 5.43424i 0.190587 0.330106i −0.754858 0.655888i $$-0.772294\pi$$
0.945445 + 0.325782i $$0.105628\pi$$
$$272$$ 0 0
$$273$$ −1.45017 + 3.04547i −0.0877680 + 0.184321i
$$274$$ 0 0
$$275$$ 28.3746 49.1462i 1.71105 2.96363i
$$276$$ 0 0
$$277$$ 2.08762 + 3.61587i 0.125433 + 0.217257i 0.921902 0.387423i $$-0.126635\pi$$
−0.796469 + 0.604679i $$0.793301\pi$$
$$278$$ 0 0
$$279$$ −1.00000 −0.0598684
$$280$$ 0 0
$$281$$ −11.4502 −0.683060 −0.341530 0.939871i $$-0.610945\pi$$
−0.341530 + 0.939871i $$0.610945\pi$$
$$282$$ 0 0
$$283$$ −13.4622 23.3172i −0.800245 1.38607i −0.919454 0.393196i $$-0.871369\pi$$
0.119209 0.992869i $$-0.461964\pi$$
$$284$$ 0 0
$$285$$ −2.72508 + 4.71998i −0.161420 + 0.279588i
$$286$$ 0 0
$$287$$ −15.8248 22.9928i −0.934106 1.35722i
$$288$$ 0 0
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ 0 0
$$291$$ 8.13746 + 14.0945i 0.477026 + 0.826234i
$$292$$ 0 0
$$293$$ −5.17525 −0.302341 −0.151171 0.988508i $$-0.548304\pi$$
−0.151171 + 0.988508i $$0.548304\pi$$
$$294$$ 0 0
$$295$$ −26.8248 −1.56180
$$296$$ 0 0
$$297$$ −2.13746 3.70219i −0.124028 0.214823i
$$298$$ 0 0
$$299$$ 2.54983 4.41644i 0.147461 0.255409i
$$300$$ 0 0
$$301$$ 10.9124 + 15.8553i 0.628979 + 0.913885i
$$302$$ 0 0
$$303$$ −3.00000 + 5.19615i −0.172345 + 0.298511i
$$304$$ 0 0
$$305$$ 21.3746 + 37.0219i 1.22391 + 2.11987i
$$306$$ 0 0
$$307$$ −26.3746 −1.50528 −0.752639 0.658434i $$-0.771219\pi$$
−0.752639 + 0.658434i $$0.771219\pi$$
$$308$$ 0 0
$$309$$ 11.8248 0.672687
$$310$$ 0 0
$$311$$ −5.27492 9.13642i −0.299113 0.518079i 0.676820 0.736148i $$-0.263357\pi$$
−0.975933 + 0.218069i $$0.930024\pi$$
$$312$$ 0 0
$$313$$ 2.22508 3.85396i 0.125769 0.217838i −0.796264 0.604949i $$-0.793193\pi$$
0.922033 + 0.387111i $$0.126527\pi$$
$$314$$ 0 0
$$315$$ 4.86254 10.2118i 0.273973 0.575368i
$$316$$ 0 0
$$317$$ 2.58762 4.48190i 0.145335 0.251728i −0.784163 0.620555i $$-0.786907\pi$$
0.929498 + 0.368827i $$0.120241\pi$$
$$318$$ 0 0
$$319$$ −4.86254 8.42217i −0.272250 0.471551i
$$320$$ 0 0
$$321$$ −6.82475 −0.380920
$$322$$ 0 0
$$323$$ −5.09967 −0.283753
$$324$$ 0 0
$$325$$ 8.46221 + 14.6570i 0.469399 + 0.813023i
$$326$$ 0 0
$$327$$ −2.91238 + 5.04438i −0.161055 + 0.278955i
$$328$$ 0 0
$$329$$ −15.8248 + 1.25588i −0.872447 + 0.0692389i
$$330$$ 0 0
$$331$$ −11.9124 + 20.6328i −0.654763 + 1.13408i 0.327190 + 0.944959i $$0.393898\pi$$
−0.981953 + 0.189125i $$0.939435\pi$$
$$332$$ 0 0
$$333$$ −2.63746 4.56821i −0.144532 0.250336i
$$334$$ 0 0
$$335$$ −31.0997 −1.69916
$$336$$ 0 0
$$337$$ 6.09967 0.332270 0.166135 0.986103i $$-0.446871\pi$$
0.166135 + 0.986103i $$0.446871\pi$$
$$338$$ 0 0
$$339$$ 5.27492 + 9.13642i 0.286494 + 0.496222i
$$340$$ 0 0
$$341$$ −2.13746 + 3.70219i −0.115750 + 0.200485i
$$342$$ 0 0
$$343$$ 18.0000 4.35890i 0.971909 0.235358i
$$344$$ 0 0
$$345$$ −8.54983 + 14.8087i −0.460308 + 0.797276i
$$346$$ 0 0
$$347$$ 15.0997 + 26.1534i 0.810593 + 1.40399i 0.912450 + 0.409189i $$0.134188\pi$$
−0.101857 + 0.994799i $$0.532478\pi$$
$$348$$ 0 0
$$349$$ −6.00000 −0.321173 −0.160586 0.987022i $$-0.551338\pi$$
−0.160586 + 0.987022i $$0.551338\pi$$
$$350$$ 0 0
$$351$$ 1.27492 0.0680500
$$352$$ 0 0
$$353$$ 2.72508 + 4.71998i 0.145042 + 0.251219i 0.929388 0.369103i $$-0.120335\pi$$
−0.784347 + 0.620322i $$0.787002\pi$$
$$354$$ 0 0
$$355$$ 4.27492 7.40437i 0.226889 0.392983i
$$356$$ 0 0
$$357$$ 10.5498 0.837253i 0.558356 0.0443122i
$$358$$ 0 0
$$359$$ −12.8248 + 22.2131i −0.676865 + 1.17236i 0.299056 + 0.954236i $$0.403328\pi$$
−0.975920 + 0.218128i $$0.930005\pi$$
$$360$$ 0 0
$$361$$ 8.68729 + 15.0468i 0.457226 + 0.791939i
$$362$$ 0 0
$$363$$ −7.27492 −0.381834
$$364$$ 0 0
$$365$$ −14.0000 −0.732793
$$366$$ 0 0
$$367$$ 4.04983 + 7.01452i 0.211400 + 0.366155i 0.952153 0.305622i $$-0.0988645\pi$$
−0.740753 + 0.671777i $$0.765531\pi$$
$$368$$ 0 0
$$369$$ −5.27492 + 9.13642i −0.274601 + 0.475623i
$$370$$ 0 0
$$371$$ −1.96221 + 4.12081i −0.101873 + 0.213942i
$$372$$ 0 0
$$373$$ −0.637459 + 1.10411i −0.0330064 + 0.0571687i −0.882057 0.471143i $$-0.843841\pi$$
0.849050 + 0.528312i $$0.177175\pi$$
$$374$$ 0 0
$$375$$ −17.6873 30.6353i −0.913368 1.58200i
$$376$$ 0 0
$$377$$ 2.90033 0.149375
$$378$$ 0 0
$$379$$ 35.8248 1.84019 0.920097 0.391691i $$-0.128110\pi$$
0.920097 + 0.391691i $$0.128110\pi$$
$$380$$ 0 0
$$381$$ −10.7749 18.6627i −0.552016 0.956119i
$$382$$ 0 0
$$383$$ 2.27492 3.94027i 0.116243 0.201339i −0.802033 0.597280i $$-0.796248\pi$$
0.918276 + 0.395941i $$0.129582\pi$$
$$384$$ 0 0
$$385$$ −27.4124 39.8293i −1.39706 2.02989i
$$386$$ 0 0
$$387$$ 3.63746 6.30026i 0.184902 0.320260i
$$388$$ 0 0
$$389$$ 1.00000 + 1.73205i 0.0507020 + 0.0878185i 0.890263 0.455448i $$-0.150521\pi$$
−0.839561 + 0.543266i $$0.817187\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ 0.274917 0.0138677
$$394$$ 0 0
$$395$$ −7.58762 13.1422i −0.381775 0.661253i
$$396$$ 0 0
$$397$$ −17.1873 + 29.7693i −0.862606 + 1.49408i 0.00679974 + 0.999977i $$0.497836\pi$$
−0.869405 + 0.494100i $$0.835498\pi$$
$$398$$ 0 0
$$399$$ 1.91238 + 2.77862i 0.0957385 + 0.139105i
$$400$$ 0 0
$$401$$ −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i $$0.371202\pi$$
−0.992932 + 0.118686i $$0.962132\pi$$
$$402$$ 0 0
$$403$$ −0.637459 1.10411i −0.0317541 0.0549997i
$$404$$ 0 0
$$405$$ −4.27492 −0.212422
$$406$$ 0 0
$$407$$ −22.5498 −1.11775
$$408$$ 0 0
$$409$$ −12.7749 22.1268i −0.631679 1.09410i −0.987208 0.159435i $$-0.949033\pi$$
0.355529 0.934665i $$-0.384301\pi$$
$$410$$ 0 0
$$411$$ 8.27492 14.3326i 0.408172 0.706974i
$$412$$ 0 0
$$413$$ −7.13746 + 14.9893i −0.351211 + 0.737575i
$$414$$ 0 0
$$415$$ −0.587624 + 1.01779i −0.0288453 + 0.0499616i
$$416$$ 0 0
$$417$$ 0.362541 + 0.627940i 0.0177537 + 0.0307504i
$$418$$ 0 0
$$419$$ 13.4502 0.657084 0.328542 0.944489i $$-0.393443\pi$$
0.328542 + 0.944489i $$0.393443\pi$$
$$420$$ 0 0
$$421$$ −13.8248 −0.673777 −0.336889 0.941545i $$-0.609375\pi$$
−0.336889 + 0.941545i $$0.609375\pi$$
$$422$$ 0 0
$$423$$ 3.00000 + 5.19615i 0.145865 + 0.252646i
$$424$$ 0 0
$$425$$ 26.5498 45.9857i 1.28786 2.23063i
$$426$$ 0 0
$$427$$ 26.3746 2.09313i 1.27636 0.101294i
$$428$$ 0 0
$$429$$ 2.72508 4.71998i 0.131568 0.227883i
$$430$$ 0 0
$$431$$ −13.8248 23.9452i −0.665915 1.15340i −0.979036 0.203685i $$-0.934708\pi$$
0.313122 0.949713i $$-0.398625\pi$$
$$432$$ 0 0
$$433$$ 25.8248 1.24106 0.620529 0.784183i $$-0.286918\pi$$
0.620529 + 0.784183i $$0.286918\pi$$
$$434$$ 0 0
$$435$$ −9.72508 −0.466282
$$436$$ 0 0
$$437$$ −2.54983 4.41644i −0.121975 0.211267i
$$438$$ 0 0
$$439$$ −4.86254 + 8.42217i −0.232076 + 0.401968i −0.958419 0.285365i $$-0.907885\pi$$
0.726343 + 0.687333i $$0.241219\pi$$
$$440$$ 0 0
$$441$$ −4.41238 5.43424i −0.210113 0.258773i
$$442$$ 0 0
$$443$$ −15.6873 + 27.1712i −0.745326 + 1.29094i 0.204717 + 0.978821i $$0.434373\pi$$
−0.950042 + 0.312121i $$0.898961\pi$$
$$444$$ 0 0
$$445$$ 9.72508 + 16.8443i 0.461013 + 0.798498i
$$446$$ 0 0
$$447$$ −0.549834 −0.0260063
$$448$$ 0 0
$$449$$ 5.45017 0.257209 0.128605 0.991696i $$-0.458950\pi$$
0.128605 + 0.991696i $$0.458950\pi$$
$$450$$ 0 0
$$451$$ 22.5498 + 39.0575i 1.06183 + 1.83914i
$$452$$ 0 0
$$453$$ −7.68729 + 13.3148i −0.361181 + 0.625583i
$$454$$ 0 0
$$455$$ 14.3746 1.14079i 0.673891 0.0534812i
$$456$$ 0 0
$$457$$ 4.32475 7.49069i 0.202303 0.350400i −0.746967 0.664861i $$-0.768491\pi$$
0.949270 + 0.314462i $$0.101824\pi$$
$$458$$ 0 0
$$459$$ −2.00000 3.46410i −0.0933520 0.161690i
$$460$$ 0 0
$$461$$ 41.6495 1.93981 0.969905 0.243482i $$-0.0782897\pi$$
0.969905 + 0.243482i $$0.0782897\pi$$
$$462$$ 0 0
$$463$$ 35.8248 1.66492 0.832459 0.554087i $$-0.186933\pi$$
0.832459 + 0.554087i $$0.186933\pi$$
$$464$$ 0 0
$$465$$ 2.13746 + 3.70219i 0.0991223 + 0.171685i
$$466$$ 0 0
$$467$$ −12.7251 + 22.0405i −0.588847 + 1.01991i 0.405537 + 0.914079i $$0.367084\pi$$
−0.994384 + 0.105834i $$0.966249\pi$$
$$468$$ 0 0
$$469$$ −8.27492 + 17.3781i −0.382100 + 0.802444i
$$470$$ 0 0
$$471$$ 7.27492 12.6005i 0.335210 0.580602i
$$472$$ 0 0
$$473$$ −15.5498 26.9331i −0.714982 1.23839i
$$474$$ 0 0
$$475$$ 16.9244 0.776546
$$476$$ 0 0
$$477$$ 1.72508 0.0789861
$$478$$ 0 0
$$479$$ 10.2749 + 17.7967i 0.469473 + 0.813151i 0.999391 0.0348979i $$-0.0111106\pi$$
−0.529918 + 0.848049i $$0.677777\pi$$
$$480$$ 0 0
$$481$$ 3.36254 5.82409i 0.153319 0.265556i
$$482$$ 0 0
$$483$$ 6.00000 + 8.71780i 0.273009 + 0.396674i
$$484$$ 0 0
$$485$$ 34.7870 60.2528i 1.57959 2.73594i
$$486$$ 0 0
$$487$$ −0.500000 0.866025i −0.0226572 0.0392434i 0.854475 0.519493i $$-0.173879\pi$$
−0.877132 + 0.480250i $$0.840546\pi$$
$$488$$ 0 0
$$489$$ 12.0000 0.542659
$$490$$ 0 0
$$491$$ −15.9244 −0.718659 −0.359330 0.933211i $$-0.616995\pi$$
−0.359330 + 0.933211i $$0.616995\pi$$
$$492$$ 0 0
$$493$$ −4.54983 7.88054i −0.204914 0.354922i
$$494$$ 0 0
$$495$$ −9.13746 + 15.8265i −0.410698 + 0.711350i
$$496$$ 0 0
$$497$$ −3.00000 4.35890i −0.134568 0.195523i
$$498$$ 0 0
$$499$$ −12.3625 + 21.4125i −0.553423 + 0.958557i 0.444601 + 0.895729i $$0.353345\pi$$
−0.998024 + 0.0628286i $$0.979988\pi$$
$$500$$ 0 0
$$501$$ −3.00000 5.19615i −0.134030 0.232147i
$$502$$ 0 0
$$503$$ 7.64950 0.341074 0.170537 0.985351i $$-0.445450\pi$$
0.170537 + 0.985351i $$0.445450\pi$$
$$504$$ 0 0
$$505$$ 25.6495 1.14139
$$506$$ 0 0
$$507$$ −5.68729 9.85068i −0.252582 0.437484i
$$508$$ 0 0
$$509$$ 1.86254 3.22602i 0.0825557 0.142991i −0.821791 0.569789i $$-0.807025\pi$$
0.904347 + 0.426798i $$0.140358\pi$$
$$510$$ 0 0
$$511$$ −3.72508 + 7.82300i −0.164788 + 0.346069i
$$512$$ 0 0
$$513$$ 0.637459 1.10411i 0.0281445 0.0487477i
$$514$$ 0 0
$$515$$ −25.2749 43.7774i −1.11375 1.92906i
$$516$$ 0 0
$$517$$ 25.6495 1.12806
$$518$$ 0 0
$$519$$ 7.45017 0.327026
$$520$$ 0 0
$$521$$ −0.274917 0.476171i −0.0120443 0.0208614i 0.859940 0.510394i $$-0.170501\pi$$
−0.871985 + 0.489533i $$0.837167\pi$$
$$522$$ 0 0
$$523$$ 12.6375 21.8887i 0.552597 0.957127i −0.445489 0.895288i $$-0.646970\pi$$
0.998086 0.0618393i $$-0.0196966\pi$$
$$524$$ 0 0
$$525$$ −35.0120 + 2.77862i −1.52805 + 0.121269i
$$526$$ 0 0
$$527$$ −2.00000 + 3.46410i −0.0871214 + 0.150899i
$$528$$ 0 0
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ 0 0
$$531$$ 6.27492 0.272308
$$532$$ 0 0
$$533$$ −13.4502 −0.582591
$$534$$ 0 0
$$535$$ 14.5876 + 25.2665i 0.630678 + 1.09237i
$$536$$ 0 0
$$537$$ −0.725083 + 1.25588i −0.0312896 + 0.0541952i
$$538$$ 0 0
$$539$$ −29.5498 + 4.71998i −1.27280 + 0.203304i
$$540$$ 0 0
$$541$$ 0.362541 0.627940i 0.0155869 0.0269973i −0.858127 0.513438i $$-0.828372\pi$$
0.873714 + 0.486441i $$0.161705\pi$$
$$542$$ 0 0
$$543$$ 1.91238 + 3.31233i 0.0820679 + 0.142146i
$$544$$ 0 0
$$545$$ 24.9003 1.06661
$$546$$ 0 0
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ 0 0
$$549$$ −5.00000 8.66025i −0.213395 0.369611i
$$550$$ 0 0
$$551$$ 1.45017 2.51176i 0.0617791 0.107005i
$$552$$ 0 0
$$553$$ −9.36254 + 0.743028i −0.398136 + 0.0315968i
$$554$$ 0 0
$$555$$ −11.2749 + 19.5287i −0.478594 + 0.828948i
$$556$$ 0 0
$$557$$ 3.58762 + 6.21395i 0.152013 + 0.263293i 0.931967 0.362543i $$-0.118091\pi$$
−0.779955 + 0.625836i $$0.784758\pi$$
$$558$$ 0 0
$$559$$ 9.27492 0.392287
$$560$$ 0 0
$$561$$ −17.0997 −0.721949
$$562$$ 0 0
$$563$$ −3.86254 6.69012i −0.162787 0.281955i 0.773080 0.634308i $$-0.218715\pi$$
−0.935867 + 0.352353i $$0.885382\pi$$
$$564$$ 0 0
$$565$$ 22.5498 39.0575i 0.948679 1.64316i
$$566$$ 0 0
$$567$$ −1.13746 + 2.38876i −0.0477688 + 0.100319i
$$568$$ 0 0
$$569$$ −13.2749 + 22.9928i −0.556513 + 0.963910i 0.441271 + 0.897374i $$0.354528\pi$$
−0.997784 + 0.0665355i $$0.978805\pi$$
$$570$$ 0 0
$$571$$ −0.362541 0.627940i −0.0151719 0.0262785i 0.858340 0.513082i $$-0.171496\pi$$
−0.873512 + 0.486803i $$0.838163\pi$$
$$572$$ 0 0
$$573$$ 10.5498 0.440726
$$574$$ 0 0
$$575$$ 53.0997 2.21441
$$576$$ 0 0
$$577$$ 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i $$0.00754370\pi$$
−0.479337 + 0.877631i $$0.659123\pi$$
$$578$$ 0 0
$$579$$ 7.77492 13.4666i 0.323115 0.559651i
$$580$$ 0 0
$$581$$ 0.412376 + 0.599168i 0.0171082 + 0.0248577i
$$582$$ 0 0
$$583$$ 3.68729 6.38658i 0.152712 0.264505i
$$584$$ 0 0
$$585$$ −2.72508 4.71998i −0.112668 0.195147i
$$586$$ 0 0
$$587$$ 1.72508 0.0712018 0.0356009 0.999366i $$-0.488665\pi$$
0.0356009 + 0.999366i $$0.488665\pi$$
$$588$$ 0 0
$$589$$ −1.27492 −0.0525320
$$590$$ 0 0
$$591$$ −8.27492 14.3326i −0.340385 0.589563i
$$592$$ 0 0
$$593$$ −7.27492 + 12.6005i −0.298745 + 0.517442i −0.975849 0.218446i $$-0.929901\pi$$
0.677104 + 0.735887i $$0.263235\pi$$
$$594$$ 0 0
$$595$$ −25.6495 37.2679i −1.05153 1.52783i
$$596$$ 0 0
$$597$$ 12.5498 21.7370i 0.513631 0.889634i
$$598$$ 0 0
$$599$$ −3.72508 6.45203i −0.152203 0.263623i 0.779834 0.625986i $$-0.215303\pi$$
−0.932037 + 0.362363i $$0.881970\pi$$
$$600$$ 0 0
$$601$$ −26.0997 −1.06463 −0.532314 0.846547i $$-0.678677\pi$$
−0.532314 + 0.846547i $$0.678677\pi$$
$$602$$ 0 0
$$603$$ 7.27492 0.296258
$$604$$ 0 0
$$605$$ 15.5498 + 26.9331i 0.632191 + 1.09499i
$$606$$ 0 0
$$607$$ 3.50000 6.06218i 0.142061 0.246056i −0.786212 0.617957i $$-0.787961\pi$$
0.928272 + 0.371901i $$0.121294\pi$$
$$608$$ 0 0
$$609$$ −2.58762 + 5.43424i −0.104856 + 0.220206i
$$610$$ 0 0
$$611$$ −3.82475 + 6.62466i −0.154733 + 0.268005i
$$612$$ 0 0
$$613$$ −3.27492 5.67232i −0.132273 0.229103i 0.792280 0.610158i $$-0.208894\pi$$
−0.924552 + 0.381055i $$0.875561\pi$$
$$614$$ 0 0
$$615$$ 45.0997 1.81859
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 0 0
$$619$$ −3.08762 5.34792i −0.124102 0.214951i 0.797280 0.603610i $$-0.206272\pi$$
−0.921382 + 0.388659i $$0.872938\pi$$
$$620$$ 0 0
$$621$$ 2.00000 3.46410i 0.0802572 0.139010i
$$622$$ 0 0
$$623$$ 12.0000 0.952341i 0.480770 0.0381547i
$$624$$ 0 0
$$625$$ −42.4244 + 73.4813i −1.69698 + 2.93925i
$$626$$ 0 0
$$627$$ −2.72508 4.71998i −0.108829 0.188498i
$$628$$ 0 0
$$629$$ −21.0997 −0.841299
$$630$$ 0 0
$$631$$ −2.82475 −0.112452 −0.0562258 0.998418i $$-0.517907\pi$$
−0.0562258 + 0.998418i $$0.517907\pi$$
$$632$$ 0 0
$$633$$ 8.82475 + 15.2849i 0.350752 + 0.607521i
$$634$$ 0 0
$$635$$ −46.0619 + 79.7815i −1.82791 + 3.16603i
$$636$$ 0 0
$$637$$ 3.18729 8.33585i 0.126285 0.330279i
$$638$$ 0 0
$$639$$ −1.00000 + 1.73205i −0.0395594 + 0.0685189i
$$640$$ 0 0
$$641$$ −20.8248 36.0695i −0.822528 1.42466i −0.903794 0.427968i $$-0.859230\pi$$
0.0812655 0.996692i $$-0.474104\pi$$
$$642$$ 0 0
$$643$$ −32.3746 −1.27673 −0.638365 0.769734i $$-0.720389\pi$$
−0.638365 + 0.769734i $$0.720389\pi$$
$$644$$ 0 0
$$645$$ −31.0997 −1.22455
$$646$$ 0 0
$$647$$ 17.0000 + 29.4449i 0.668339 + 1.15760i 0.978368 + 0.206870i $$0.0663277\pi$$
−0.310029 + 0.950727i $$0.600339\pi$$
$$648$$ 0 0
$$649$$ 13.4124 23.2309i 0.526482 0.911893i
$$650$$ 0 0
$$651$$ 2.63746 0.209313i 0.103370 0.00820364i
$$652$$ 0 0
$$653$$ −22.9622 + 39.7717i −0.898581 + 1.55639i −0.0692713 + 0.997598i $$0.522067\pi$$
−0.829309 + 0.558790i $$0.811266\pi$$
$$654$$ 0 0
$$655$$ −0.587624 1.01779i −0.0229604 0.0397685i
$$656$$ 0 0
$$657$$ 3.27492 0.127767
$$658$$ 0 0
$$659$$ 18.1993 0.708946 0.354473 0.935066i $$-0.384660\pi$$
0.354473 + 0.935066i $$0.384660\pi$$
$$660$$ 0 0
$$661$$ −14.9124 25.8290i −0.580024 1.00463i −0.995476 0.0950161i $$-0.969710\pi$$
0.415452 0.909615i $$-0.363624\pi$$
$$662$$ 0 0
$$663$$ 2.54983 4.41644i 0.0990274 0.171520i
$$664$$ 0 0
$$665$$ 6.19934 13.0192i 0.240400 0.504861i
$$666$$ 0 0
$$667$$ 4.54983 7.88054i 0.176170 0.305136i
$$668$$ 0 0
$$669$$ 3.13746 + 5.43424i 0.121301 + 0.210100i
$$670$$ 0 0
$$671$$ −42.7492 −1.65031
$$672$$ 0 0
$$673$$ 26.4502 1.01958 0.509789 0.860299i $$-0.329723\pi$$
0.509789 + 0.860299i $$0.329723\pi$$
$$674$$ 0 0
$$675$$ 6.63746 + 11.4964i 0.255476 + 0.442497i
$$676$$ 0 0
$$677$$ 2.86254 4.95807i 0.110016 0.190554i −0.805760 0.592242i $$-0.798243\pi$$
0.915777 + 0.401688i $$0.131576\pi$$
$$678$$ 0 0
$$679$$ −24.4124 35.4704i −0.936861 1.36123i
$$680$$ 0 0
$$681$$ −1.86254 + 3.22602i −0.0713727 + 0.123621i
$$682$$ 0 0
$$683$$ −17.4124 30.1591i −0.666266 1.15401i −0.978940 0.204146i $$-0.934558\pi$$
0.312674 0.949860i $$-0.398775\pi$$
$$684$$ 0 0
$$685$$ −70.7492 −2.70319
$$686$$ 0 0
$$687$$ −10.7251 −0.409187
$$688$$ 0 0
$$689$$ 1.09967 + 1.90468i 0.0418940 + 0.0725626i
$$690$$ 0 0
$$691$$ −5.91238 + 10.2405i −0.224917 + 0.389568i −0.956295 0.292405i $$-0.905545\pi$$
0.731377 + 0.681973i $$0.238878\pi$$
$$692$$ 0 0
$$693$$ 6.41238 + 9.31697i 0.243586 + 0.353922i
$$694$$ 0 0
$$695$$ 1.54983 2.68439i 0.0587886 0.101825i
$$696$$ 0 0
$$697$$ 21.0997 + 36.5457i 0.799207 + 1.38427i
$$698$$ 0 0
$$699$$ −14.5498 −0.550325
$$700$$ 0 0
$$701$$ 39.9244 1.50792 0.753962 0.656918i $$-0.228140\pi$$
0.753962 + 0.656918i $$0.228140\pi$$
$$702$$ 0 0
$$703$$ −3.36254 5.82409i −0.126821 0.219660i
$$704$$ 0 0
$$705$$ 12.8248 22.2131i 0.483008 0.836595i
$$706$$ 0 0
$$707$$ 6.82475 14.3326i 0.256671 0.539032i
$$708$$ 0 0
$$709$$ −16.0997 + 27.8854i −0.604636 + 1.04726i 0.387473 + 0.921881i $$0.373348\pi$$
−0.992109 + 0.125379i $$0.959985\pi$$
$$710$$ 0 0
$$711$$ 1.77492 + 3.07425i 0.0665646 + 0.115293i
$$712$$ 0 0
$$713$$ −4.00000 −0.149801
$$714$$ 0 0
$$715$$ −23.2990 −0.871333
$$716$$ 0 0
$$717$$ 15.2749 + 26.4569i 0.570452 + 0.988052i
$$718$$ 0 0
$$719$$ 16.0997 27.8854i 0.600416 1.03995i −0.392342 0.919820i $$-0.628335\pi$$
0.992758 0.120132i $$-0.0383318\pi$$
$$720$$ 0 0
$$721$$ −31.1873 + 2.47508i −1.16148 + 0.0921767i
$$722$$ 0 0
$$723$$ −6.41238 + 11.1066i −0.238479 + 0.413057i
$$724$$ 0 0
$$725$$ 15.0997 + 26.1534i 0.560788 + 0.971313i
$$726$$ 0 0
$$727$$ 16.4502 0.610103 0.305051 0.952336i $$-0.401326\pi$$
0.305051 + 0.952336i $$0.401326\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −14.5498 25.2011i −0.538145 0.932095i
$$732$$ 0 0
$$733$$ 23.4622 40.6377i 0.866597 1.50099i 0.00114334 0.999999i $$-0.499636\pi$$
0.865453 0.500990i $$-0.167031\pi$$
$$734$$ 0 0
$$735$$ −10.6873 + 27.9509i −0.394207 + 1.03098i
$$736$$ 0 0
$$737$$ 15.5498 26.9331i 0.572786 0.992094i
$$738$$ 0 0
$$739$$ 18.1873 + 31.5013i 0.669030 + 1.15879i 0.978176 + 0.207780i $$0.0666237\pi$$
−0.309145 + 0.951015i $$0.600043\pi$$
$$740$$ 0 0
$$741$$ 1.62541 0.0597111
$$742$$ 0 0
$$743$$ 16.1993 0.594296 0.297148 0.954831i $$-0.403965\pi$$
0.297148 + 0.954831i $$0.403965\pi$$
$$744$$ 0 0
$$745$$ 1.17525 + 2.03559i 0.0430578 + 0.0745782i
$$746$$ 0 0
$$747$$ 0.137459 0.238085i 0.00502935 0.00871109i
$$748$$ 0 0
$$749$$ 18.0000 1.42851i 0.657706 0.0521967i
$$750$$ 0 0
$$751$$ 12.7749 22.1268i 0.466163 0.807419i −0.533090 0.846059i $$-0.678969\pi$$
0.999253 + 0.0386400i $$0.0123026\pi$$
$$752$$ 0 0
$$753$$ 9.68729 + 16.7789i 0.353025 + 0.611457i
$$754$$ 0 0
$$755$$ 65.7251 2.39198
$$756$$ 0 0
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ 0 0
$$759$$ −8.54983 14.8087i −0.310339 0.537523i
$$760$$ 0 0
$$761$$ −2.54983 + 4.41644i −0.0924314 + 0.160096i −0.908534 0.417812i $$-0.862797\pi$$
0.816102 + 0.577907i $$0.196131\pi$$
$$762$$ 0 0
$$763$$ 6.62541 13.9140i 0.239856 0.503719i
$$764$$ 0 0
$$765$$ −8.54983 + 14.8087i −0.309120 + 0.535411i
$$766$$ 0 0
$$767$$ 4.00000 + 6.92820i 0.144432 + 0.250163i
$$768$$ 0 0
$$769$$ 12.6495 0.456153 0.228076 0.973643i $$-0.426756\pi$$
0.228076 + 0.973643i $$0.426756\pi$$
$$770$$ 0 0
$$771$$ 19.0997 0.687858
$$772$$ 0 0
$$773$$ 13.5498 + 23.4690i 0.487354 + 0.844121i 0.999894 0.0145417i $$-0.00462892\pi$$
−0.512541 + 0.858663i $$0.671296\pi$$
$$774$$ 0 0
$$775$$ 6.63746 11.4964i 0.238425 0.412963i
$$776$$ 0 0
$$777$$ 7.91238 + 11.4964i 0.283855 + 0.412432i
$$778$$ 0 0
$$779$$ −6.72508 + 11.6482i −0.240951 + 0.417340i
$$780$$ 0 0
$$781$$ 4.27492 + 7.40437i 0.152969 + 0.264949i
$$782$$ 0 0
$$783$$ 2.27492 0.0812989
$$784$$ 0 0
$$785$$ −62.1993 −2.21999
$$786$$ 0 0
$$787$$ 6.27492 + 10.8685i 0.223677 + 0.387419i 0.955922 0.293622i $$-0.0948607\pi$$
−0.732245 + 0.681041i $$0.761527\pi$$
$$788$$ 0 0
$$789$$ −12.2749 + 21.2608i −0.436999 + 0.756904i
$$790$$ 0 0
$$791$$ −15.8248 22.9928i −0.562663 0.817531i
$$792$$ 0 0
$$793$$ 6.37459 11.0411i 0.226368 0.392081i
$$794$$ 0 0
$$795$$