# Properties

 Label 260.2.bk.a.197.1 Level $260$ Weight $2$ Character 260.197 Analytic conductor $2.076$ Analytic rank $1$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 260.bk (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.07611045255$$ Analytic rank: $$1$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 197.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 260.197 Dual form 260.2.bk.a.33.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.133975i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-2.13397 - 1.23205i) q^{7} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.133975i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(-2.13397 - 1.23205i) q^{7} +(-2.36603 - 1.36603i) q^{9} +(-1.13397 + 4.23205i) q^{11} +(-2.00000 - 3.00000i) q^{13} +(1.13397 - 0.232051i) q^{15} +(-0.232051 - 0.866025i) q^{17} +(-2.86603 + 0.767949i) q^{19} +(0.901924 + 0.901924i) q^{21} +(-0.0358984 + 0.133975i) q^{23} +(3.00000 - 4.00000i) q^{25} +(2.09808 + 2.09808i) q^{27} +(-1.50000 + 0.866025i) q^{29} +(-5.19615 + 5.19615i) q^{31} +(1.13397 - 1.96410i) q^{33} +(5.50000 + 0.330127i) q^{35} +(1.33013 - 0.767949i) q^{37} +(0.598076 + 1.76795i) q^{39} +(9.33013 + 2.50000i) q^{41} +(-5.96410 + 1.59808i) q^{43} +(6.09808 + 0.366025i) q^{45} -10.9282i q^{47} +(-0.464102 - 0.803848i) q^{49} +0.464102i q^{51} +(2.46410 - 2.46410i) q^{53} +(-1.96410 - 9.59808i) q^{55} +1.53590 q^{57} +(2.33013 + 8.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(3.36603 + 5.83013i) q^{63} +(7.00000 + 4.00000i) q^{65} +(6.13397 + 10.6244i) q^{67} +(0.0358984 - 0.0621778i) q^{69} +(0.598076 + 2.23205i) q^{71} -14.9282 q^{73} +(-2.03590 + 1.59808i) q^{75} +(7.63397 - 7.63397i) q^{77} +0.535898i q^{79} +(3.33013 + 5.76795i) q^{81} -2.92820i q^{83} +(1.33013 + 1.50000i) q^{85} +(0.866025 - 0.232051i) q^{87} +(-14.7942 - 3.96410i) q^{89} +(0.571797 + 8.86603i) q^{91} +(3.29423 - 1.90192i) q^{93} +(4.96410 - 4.40192i) q^{95} +(3.86603 - 6.69615i) q^{97} +(8.46410 - 8.46410i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9}+O(q^{10})$$ 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9 $$4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{15} + 6 q^{17} - 8 q^{19} + 14 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} - 6 q^{29} + 8 q^{33} + 22 q^{35} - 12 q^{37} - 8 q^{39} + 20 q^{41} - 10 q^{43} + 14 q^{45} + 12 q^{49} - 4 q^{53} + 6 q^{55} + 20 q^{57} - 8 q^{59} + 18 q^{61} + 10 q^{63} + 28 q^{65} + 28 q^{67} + 14 q^{69} - 8 q^{71} - 32 q^{73} - 22 q^{75} + 34 q^{77} - 4 q^{81} - 12 q^{85} - 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{95} + 12 q^{97} + 20 q^{99}+O(q^{100})$$ 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9 - 8 * q^11 - 8 * q^13 + 8 * q^15 + 6 * q^17 - 8 * q^19 + 14 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 - 6 * q^29 + 8 * q^33 + 22 * q^35 - 12 * q^37 - 8 * q^39 + 20 * q^41 - 10 * q^43 + 14 * q^45 + 12 * q^49 - 4 * q^53 + 6 * q^55 + 20 * q^57 - 8 * q^59 + 18 * q^61 + 10 * q^63 + 28 * q^65 + 28 * q^67 + 14 * q^69 - 8 * q^71 - 32 * q^73 - 22 * q^75 + 34 * q^77 - 4 * q^81 - 12 * q^85 - 28 * q^89 + 30 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 + 20 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$$.

 $$n$$ $$41$$ $$131$$ $$157$$ $$\chi(n)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$

## 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 0.133975i −0.288675 0.0773503i 0.111576 0.993756i $$-0.464410\pi$$
−0.400251 + 0.916406i $$0.631077\pi$$
$$4$$ 0 0
$$5$$ −2.00000 + 1.00000i −0.894427 + 0.447214i
$$6$$ 0 0
$$7$$ −2.13397 1.23205i −0.806567 0.465671i 0.0391956 0.999232i $$-0.487520\pi$$
−0.845762 + 0.533560i $$0.820854\pi$$
$$8$$ 0 0
$$9$$ −2.36603 1.36603i −0.788675 0.455342i
$$10$$ 0 0
$$11$$ −1.13397 + 4.23205i −0.341906 + 1.27601i 0.554279 + 0.832331i $$0.312994\pi$$
−0.896185 + 0.443680i $$0.853673\pi$$
$$12$$ 0 0
$$13$$ −2.00000 3.00000i −0.554700 0.832050i
$$14$$ 0 0
$$15$$ 1.13397 0.232051i 0.292791 0.0599153i
$$16$$ 0 0
$$17$$ −0.232051 0.866025i −0.0562806 0.210042i 0.932059 0.362306i $$-0.118010\pi$$
−0.988340 + 0.152264i $$0.951344\pi$$
$$18$$ 0 0
$$19$$ −2.86603 + 0.767949i −0.657511 + 0.176180i −0.572123 0.820168i $$-0.693880\pi$$
−0.0853887 + 0.996348i $$0.527213\pi$$
$$20$$ 0 0
$$21$$ 0.901924 + 0.901924i 0.196816 + 0.196816i
$$22$$ 0 0
$$23$$ −0.0358984 + 0.133975i −0.00748533 + 0.0279356i −0.969567 0.244824i $$-0.921270\pi$$
0.962082 + 0.272760i $$0.0879364\pi$$
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 0 0
$$27$$ 2.09808 + 2.09808i 0.403775 + 0.403775i
$$28$$ 0 0
$$29$$ −1.50000 + 0.866025i −0.278543 + 0.160817i −0.632764 0.774345i $$-0.718080\pi$$
0.354221 + 0.935162i $$0.384746\pi$$
$$30$$ 0 0
$$31$$ −5.19615 + 5.19615i −0.933257 + 0.933257i −0.997908 0.0646514i $$-0.979406\pi$$
0.0646514 + 0.997908i $$0.479406\pi$$
$$32$$ 0 0
$$33$$ 1.13397 1.96410i 0.197400 0.341906i
$$34$$ 0 0
$$35$$ 5.50000 + 0.330127i 0.929670 + 0.0558017i
$$36$$ 0 0
$$37$$ 1.33013 0.767949i 0.218672 0.126250i −0.386663 0.922221i $$-0.626372\pi$$
0.605335 + 0.795971i $$0.293039\pi$$
$$38$$ 0 0
$$39$$ 0.598076 + 1.76795i 0.0957688 + 0.283098i
$$40$$ 0 0
$$41$$ 9.33013 + 2.50000i 1.45712 + 0.390434i 0.898494 0.438985i $$-0.144662\pi$$
0.558627 + 0.829419i $$0.311329\pi$$
$$42$$ 0 0
$$43$$ −5.96410 + 1.59808i −0.909517 + 0.243704i −0.683099 0.730326i $$-0.739368\pi$$
−0.226418 + 0.974030i $$0.572702\pi$$
$$44$$ 0 0
$$45$$ 6.09808 + 0.366025i 0.909048 + 0.0545638i
$$46$$ 0 0
$$47$$ 10.9282i 1.59404i −0.603951 0.797021i $$-0.706408\pi$$
0.603951 0.797021i $$-0.293592\pi$$
$$48$$ 0 0
$$49$$ −0.464102 0.803848i −0.0663002 0.114835i
$$50$$ 0 0
$$51$$ 0.464102i 0.0649872i
$$52$$ 0 0
$$53$$ 2.46410 2.46410i 0.338470 0.338470i −0.517321 0.855791i $$-0.673071\pi$$
0.855791 + 0.517321i $$0.173071\pi$$
$$54$$ 0 0
$$55$$ −1.96410 9.59808i −0.264839 1.29420i
$$56$$ 0 0
$$57$$ 1.53590 0.203435
$$58$$ 0 0
$$59$$ 2.33013 + 8.69615i 0.303357 + 1.13214i 0.934351 + 0.356355i $$0.115981\pi$$
−0.630994 + 0.775788i $$0.717353\pi$$
$$60$$ 0 0
$$61$$ 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i $$-0.637882\pi$$
0.995914 0.0903080i $$-0.0287851\pi$$
$$62$$ 0 0
$$63$$ 3.36603 + 5.83013i 0.424079 + 0.734527i
$$64$$ 0 0
$$65$$ 7.00000 + 4.00000i 0.868243 + 0.496139i
$$66$$ 0 0
$$67$$ 6.13397 + 10.6244i 0.749384 + 1.29797i 0.948118 + 0.317918i $$0.102984\pi$$
−0.198734 + 0.980053i $$0.563683\pi$$
$$68$$ 0 0
$$69$$ 0.0358984 0.0621778i 0.00432166 0.00748533i
$$70$$ 0 0
$$71$$ 0.598076 + 2.23205i 0.0709786 + 0.264896i 0.992291 0.123927i $$-0.0395487\pi$$
−0.921313 + 0.388822i $$0.872882\pi$$
$$72$$ 0 0
$$73$$ −14.9282 −1.74721 −0.873607 0.486632i $$-0.838225\pi$$
−0.873607 + 0.486632i $$0.838225\pi$$
$$74$$ 0 0
$$75$$ −2.03590 + 1.59808i −0.235085 + 0.184530i
$$76$$ 0 0
$$77$$ 7.63397 7.63397i 0.869972 0.869972i
$$78$$ 0 0
$$79$$ 0.535898i 0.0602933i 0.999545 + 0.0301466i $$0.00959743\pi$$
−0.999545 + 0.0301466i $$0.990403\pi$$
$$80$$ 0 0
$$81$$ 3.33013 + 5.76795i 0.370014 + 0.640883i
$$82$$ 0 0
$$83$$ 2.92820i 0.321412i −0.987002 0.160706i $$-0.948623\pi$$
0.987002 0.160706i $$-0.0513771\pi$$
$$84$$ 0 0
$$85$$ 1.33013 + 1.50000i 0.144273 + 0.162698i
$$86$$ 0 0
$$87$$ 0.866025 0.232051i 0.0928477 0.0248785i
$$88$$ 0 0
$$89$$ −14.7942 3.96410i −1.56819 0.420194i −0.632942 0.774199i $$-0.718153\pi$$
−0.935243 + 0.354005i $$0.884819\pi$$
$$90$$ 0 0
$$91$$ 0.571797 + 8.86603i 0.0599406 + 0.929412i
$$92$$ 0 0
$$93$$ 3.29423 1.90192i 0.341596 0.197220i
$$94$$ 0 0
$$95$$ 4.96410 4.40192i 0.509306 0.451628i
$$96$$ 0 0
$$97$$ 3.86603 6.69615i 0.392535 0.679891i −0.600248 0.799814i $$-0.704931\pi$$
0.992783 + 0.119923i $$0.0382647\pi$$
$$98$$ 0 0
$$99$$ 8.46410 8.46410i 0.850674 0.850674i
$$100$$ 0 0
$$101$$ −14.8923 + 8.59808i −1.48184 + 0.855541i −0.999788 0.0206021i $$-0.993442\pi$$
−0.482052 + 0.876143i $$0.660108\pi$$
$$102$$ 0 0
$$103$$ −11.1962 11.1962i −1.10319 1.10319i −0.994024 0.109166i $$-0.965182\pi$$
−0.109166 0.994024i $$-0.534818\pi$$
$$104$$ 0 0
$$105$$ −2.70577 0.901924i −0.264056 0.0880187i
$$106$$ 0 0
$$107$$ −1.96410 + 7.33013i −0.189877 + 0.708630i 0.803657 + 0.595093i $$0.202885\pi$$
−0.993534 + 0.113537i $$0.963782\pi$$
$$108$$ 0 0
$$109$$ −3.53590 3.53590i −0.338678 0.338678i 0.517192 0.855869i $$-0.326977\pi$$
−0.855869 + 0.517192i $$0.826977\pi$$
$$110$$ 0 0
$$111$$ −0.767949 + 0.205771i −0.0728905 + 0.0195310i
$$112$$ 0 0
$$113$$ 0.767949 + 2.86603i 0.0722426 + 0.269613i 0.992594 0.121480i $$-0.0387639\pi$$
−0.920351 + 0.391093i $$0.872097\pi$$
$$114$$ 0 0
$$115$$ −0.0621778 0.303848i −0.00579811 0.0283339i
$$116$$ 0 0
$$117$$ 0.633975 + 9.83013i 0.0586110 + 0.908796i
$$118$$ 0 0
$$119$$ −0.571797 + 2.13397i −0.0524165 + 0.195621i
$$120$$ 0 0
$$121$$ −7.09808 4.09808i −0.645280 0.372552i
$$122$$ 0 0
$$123$$ −4.33013 2.50000i −0.390434 0.225417i
$$124$$ 0 0
$$125$$ −2.00000 + 11.0000i −0.178885 + 0.983870i
$$126$$ 0 0
$$127$$ −19.8923 5.33013i −1.76516 0.472972i −0.777404 0.629001i $$-0.783464\pi$$
−0.987752 + 0.156029i $$0.950131\pi$$
$$128$$ 0 0
$$129$$ 3.19615 0.281406
$$130$$ 0 0
$$131$$ 5.85641 0.511677 0.255838 0.966720i $$-0.417649\pi$$
0.255838 + 0.966720i $$0.417649\pi$$
$$132$$ 0 0
$$133$$ 7.06218 + 1.89230i 0.612368 + 0.164084i
$$134$$ 0 0
$$135$$ −6.29423 2.09808i −0.541721 0.180574i
$$136$$ 0 0
$$137$$ −12.4019 7.16025i −1.05957 0.611742i −0.134255 0.990947i $$-0.542864\pi$$
−0.925313 + 0.379205i $$0.876198\pi$$
$$138$$ 0 0
$$139$$ −4.50000 2.59808i −0.381685 0.220366i 0.296866 0.954919i $$-0.404058\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ −1.46410 + 5.46410i −0.123300 + 0.460160i
$$142$$ 0 0
$$143$$ 14.9641 5.06218i 1.25136 0.423321i
$$144$$ 0 0
$$145$$ 2.13397 3.23205i 0.177217 0.268407i
$$146$$ 0 0
$$147$$ 0.124356 + 0.464102i 0.0102567 + 0.0382785i
$$148$$ 0 0
$$149$$ −3.33013 + 0.892305i −0.272815 + 0.0731005i −0.392633 0.919695i $$-0.628436\pi$$
0.119818 + 0.992796i $$0.461769\pi$$
$$150$$ 0 0
$$151$$ −0.267949 0.267949i −0.0218054 0.0218054i 0.696120 0.717925i $$-0.254908\pi$$
−0.717925 + 0.696120i $$0.754908\pi$$
$$152$$ 0 0
$$153$$ −0.633975 + 2.36603i −0.0512538 + 0.191282i
$$154$$ 0 0
$$155$$ 5.19615 15.5885i 0.417365 1.25210i
$$156$$ 0 0
$$157$$ 6.46410 + 6.46410i 0.515891 + 0.515891i 0.916326 0.400434i $$-0.131141\pi$$
−0.400434 + 0.916326i $$0.631141\pi$$
$$158$$ 0 0
$$159$$ −1.56218 + 0.901924i −0.123889 + 0.0715272i
$$160$$ 0 0
$$161$$ 0.241670 0.241670i 0.0190462 0.0190462i
$$162$$ 0 0
$$163$$ −1.59808 + 2.76795i −0.125171 + 0.216803i −0.921800 0.387666i $$-0.873281\pi$$
0.796629 + 0.604469i $$0.206615\pi$$
$$164$$ 0 0
$$165$$ −0.303848 + 5.06218i −0.0236545 + 0.394090i
$$166$$ 0 0
$$167$$ −15.9904 + 9.23205i −1.23737 + 0.714398i −0.968556 0.248794i $$-0.919966\pi$$
−0.268816 + 0.963191i $$0.586632\pi$$
$$168$$ 0 0
$$169$$ −5.00000 + 12.0000i −0.384615 + 0.923077i
$$170$$ 0 0
$$171$$ 7.83013 + 2.09808i 0.598785 + 0.160444i
$$172$$ 0 0
$$173$$ −2.76795 + 0.741670i −0.210443 + 0.0563881i −0.362500 0.931984i $$-0.618077\pi$$
0.152057 + 0.988372i $$0.451410\pi$$
$$174$$ 0 0
$$175$$ −11.3301 + 4.83975i −0.856477 + 0.365850i
$$176$$ 0 0
$$177$$ 4.66025i 0.350286i
$$178$$ 0 0
$$179$$ 6.96410 + 12.0622i 0.520521 + 0.901570i 0.999715 + 0.0238604i $$0.00759573\pi$$
−0.479194 + 0.877709i $$0.659071\pi$$
$$180$$ 0 0
$$181$$ 22.9282i 1.70424i −0.523347 0.852120i $$-0.675317\pi$$
0.523347 0.852120i $$-0.324683\pi$$
$$182$$ 0 0
$$183$$ −3.29423 + 3.29423i −0.243516 + 0.243516i
$$184$$ 0 0
$$185$$ −1.89230 + 2.86603i −0.139125 + 0.210714i
$$186$$ 0 0
$$187$$ 3.92820 0.287259
$$188$$ 0 0
$$189$$ −1.89230 7.06218i −0.137645 0.513698i
$$190$$ 0 0
$$191$$ 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i $$-0.650743\pi$$
0.998749 0.0500060i $$-0.0159241\pi$$
$$192$$ 0 0
$$193$$ 12.7942 + 22.1603i 0.920949 + 1.59513i 0.797950 + 0.602723i $$0.205918\pi$$
0.122998 + 0.992407i $$0.460749\pi$$
$$194$$ 0 0
$$195$$ −2.96410 2.93782i −0.212264 0.210382i
$$196$$ 0 0
$$197$$ 2.13397 + 3.69615i 0.152039 + 0.263340i 0.931977 0.362517i $$-0.118083\pi$$
−0.779938 + 0.625857i $$0.784749\pi$$
$$198$$ 0 0
$$199$$ 9.42820 16.3301i 0.668348 1.15761i −0.310018 0.950731i $$-0.600335\pi$$
0.978366 0.206881i $$-0.0663314\pi$$
$$200$$ 0 0
$$201$$ −1.64359 6.13397i −0.115930 0.432657i
$$202$$ 0 0
$$203$$ 4.26795 0.299551
$$204$$ 0 0
$$205$$ −21.1603 + 4.33013i −1.47790 + 0.302429i
$$206$$ 0 0
$$207$$ 0.267949 0.267949i 0.0186238 0.0186238i
$$208$$ 0 0
$$209$$ 13.0000i 0.899229i
$$210$$ 0 0
$$211$$ −2.96410 5.13397i −0.204057 0.353437i 0.745775 0.666198i $$-0.232080\pi$$
−0.949832 + 0.312761i $$0.898746\pi$$
$$212$$ 0 0
$$213$$ 1.19615i 0.0819590i
$$214$$ 0 0
$$215$$ 10.3301 9.16025i 0.704509 0.624724i
$$216$$ 0 0
$$217$$ 17.4904 4.68653i 1.18732 0.318143i
$$218$$ 0 0
$$219$$ 7.46410 + 2.00000i 0.504377 + 0.135147i
$$220$$ 0 0
$$221$$ −2.13397 + 2.42820i −0.143547 + 0.163339i
$$222$$ 0 0
$$223$$ −1.33013 + 0.767949i −0.0890719 + 0.0514257i −0.543874 0.839167i $$-0.683043\pi$$
0.454802 + 0.890592i $$0.349710\pi$$
$$224$$ 0 0
$$225$$ −12.5622 + 5.36603i −0.837479 + 0.357735i
$$226$$ 0 0
$$227$$ 1.59808 2.76795i 0.106068 0.183715i −0.808106 0.589037i $$-0.799507\pi$$
0.914174 + 0.405322i $$0.132841\pi$$
$$228$$ 0 0
$$229$$ 0.0717968 0.0717968i 0.00474446 0.00474446i −0.704731 0.709475i $$-0.748932\pi$$
0.709475 + 0.704731i $$0.248932\pi$$
$$230$$ 0 0
$$231$$ −4.83975 + 2.79423i −0.318432 + 0.183847i
$$232$$ 0 0
$$233$$ 12.8564 + 12.8564i 0.842251 + 0.842251i 0.989151 0.146900i $$-0.0469296\pi$$
−0.146900 + 0.989151i $$0.546930\pi$$
$$234$$ 0 0
$$235$$ 10.9282 + 21.8564i 0.712877 + 1.42575i
$$236$$ 0 0
$$237$$ 0.0717968 0.267949i 0.00466370 0.0174052i
$$238$$ 0 0
$$239$$ 16.6603 + 16.6603i 1.07766 + 1.07766i 0.996719 + 0.0809436i $$0.0257934\pi$$
0.0809436 + 0.996719i $$0.474207\pi$$
$$240$$ 0 0
$$241$$ 11.3301 3.03590i 0.729838 0.195559i 0.125281 0.992121i $$-0.460017\pi$$
0.604557 + 0.796562i $$0.293350\pi$$
$$242$$ 0 0
$$243$$ −3.19615 11.9282i −0.205033 0.765195i
$$244$$ 0 0
$$245$$ 1.73205 + 1.14359i 0.110657 + 0.0730615i
$$246$$ 0 0
$$247$$ 8.03590 + 7.06218i 0.511312 + 0.449356i
$$248$$ 0 0
$$249$$ −0.392305 + 1.46410i −0.0248613 + 0.0927837i
$$250$$ 0 0
$$251$$ −15.3564 8.86603i −0.969288 0.559619i −0.0702687 0.997528i $$-0.522386\pi$$
−0.899019 + 0.437910i $$0.855719\pi$$
$$252$$ 0 0
$$253$$ −0.526279 0.303848i −0.0330869 0.0191027i
$$254$$ 0 0
$$255$$ −0.464102 0.928203i −0.0290632 0.0581263i
$$256$$ 0 0
$$257$$ 21.6244 + 5.79423i 1.34889 + 0.361434i 0.859725 0.510757i $$-0.170635\pi$$
0.489165 + 0.872191i $$0.337302\pi$$
$$258$$ 0 0
$$259$$ −3.78461 −0.235164
$$260$$ 0 0
$$261$$ 4.73205 0.292907
$$262$$ 0 0
$$263$$ 13.8923 + 3.72243i 0.856636 + 0.229535i 0.660300 0.751002i $$-0.270429\pi$$
0.196336 + 0.980537i $$0.437096\pi$$
$$264$$ 0 0
$$265$$ −2.46410 + 7.39230i −0.151369 + 0.454106i
$$266$$ 0 0
$$267$$ 6.86603 + 3.96410i 0.420194 + 0.242599i
$$268$$ 0 0
$$269$$ 15.8205 + 9.13397i 0.964593 + 0.556908i 0.897584 0.440844i $$-0.145321\pi$$
0.0670097 + 0.997752i $$0.478654\pi$$
$$270$$ 0 0
$$271$$ 4.33013 16.1603i 0.263036 0.981666i −0.700405 0.713746i $$-0.746997\pi$$
0.963441 0.267920i $$-0.0863362\pi$$
$$272$$ 0 0
$$273$$ 0.901924 4.50962i 0.0545869 0.272935i
$$274$$ 0 0
$$275$$ 13.5263 + 17.2321i 0.815665 + 1.03913i
$$276$$ 0 0
$$277$$ −2.76795 10.3301i −0.166310 0.620677i −0.997869 0.0652416i $$-0.979218\pi$$
0.831560 0.555436i $$-0.187448\pi$$
$$278$$ 0 0
$$279$$ 19.3923 5.19615i 1.16099 0.311086i
$$280$$ 0 0
$$281$$ −16.4641 16.4641i −0.982166 0.982166i 0.0176778 0.999844i $$-0.494373\pi$$
−0.999844 + 0.0176778i $$0.994373\pi$$
$$282$$ 0 0
$$283$$ 7.96410 29.7224i 0.473417 1.76682i −0.153937 0.988081i $$-0.549195\pi$$
0.627354 0.778735i $$-0.284138\pi$$
$$284$$ 0 0
$$285$$ −3.07180 + 1.53590i −0.181958 + 0.0909788i
$$286$$ 0 0
$$287$$ −16.8301 16.8301i −0.993451 0.993451i
$$288$$ 0 0
$$289$$ 14.0263 8.09808i 0.825075 0.476357i
$$290$$ 0 0
$$291$$ −2.83013 + 2.83013i −0.165905 + 0.165905i
$$292$$ 0 0
$$293$$ −10.2583 + 17.7679i −0.599298 + 1.03801i 0.393627 + 0.919270i $$0.371220\pi$$
−0.992925 + 0.118744i $$0.962113\pi$$
$$294$$ 0 0
$$295$$ −13.3564 15.0622i −0.777640 0.876954i
$$296$$ 0 0
$$297$$ −11.2583 + 6.50000i −0.653275 + 0.377168i
$$298$$ 0 0
$$299$$ 0.473721 0.160254i 0.0273960 0.00926773i
$$300$$ 0 0
$$301$$ 14.6962 + 3.93782i 0.847072 + 0.226972i
$$302$$ 0 0
$$303$$ 8.59808 2.30385i 0.493947 0.132353i
$$304$$ 0 0
$$305$$ −1.20577 + 20.0885i −0.0690423 + 1.15026i
$$306$$ 0 0
$$307$$ 4.00000i 0.228292i 0.993464 + 0.114146i $$0.0364132\pi$$
−0.993464 + 0.114146i $$0.963587\pi$$
$$308$$ 0 0
$$309$$ 4.09808 + 7.09808i 0.233131 + 0.403795i
$$310$$ 0 0
$$311$$ 3.46410i 0.196431i 0.995165 + 0.0982156i $$0.0313135\pi$$
−0.995165 + 0.0982156i $$0.968687\pi$$
$$312$$ 0 0
$$313$$ −5.53590 + 5.53590i −0.312907 + 0.312907i −0.846035 0.533127i $$-0.821017\pi$$
0.533127 + 0.846035i $$0.321017\pi$$
$$314$$ 0 0
$$315$$ −12.5622 8.29423i −0.707799 0.467327i
$$316$$ 0 0
$$317$$ −18.9282 −1.06311 −0.531557 0.847023i $$-0.678393\pi$$
−0.531557 + 0.847023i $$0.678393\pi$$
$$318$$ 0 0
$$319$$ −1.96410 7.33013i −0.109969 0.410408i
$$320$$ 0 0
$$321$$ 1.96410 3.40192i 0.109625 0.189877i
$$322$$ 0 0
$$323$$ 1.33013 + 2.30385i 0.0740102 + 0.128190i
$$324$$ 0 0
$$325$$ −18.0000 1.00000i −0.998460 0.0554700i
$$326$$ 0 0
$$327$$ 1.29423 + 2.24167i 0.0715710 + 0.123965i
$$328$$ 0 0
$$329$$ −13.4641 + 23.3205i −0.742300 + 1.28570i
$$330$$ 0 0
$$331$$ 4.45448 + 16.6244i 0.244841 + 0.913757i 0.973464 + 0.228842i $$0.0734940\pi$$
−0.728623 + 0.684915i $$0.759839\pi$$
$$332$$ 0 0
$$333$$ −4.19615 −0.229948
$$334$$ 0 0
$$335$$ −22.8923 15.1147i −1.25074 0.825806i
$$336$$ 0 0
$$337$$ −15.9282 + 15.9282i −0.867665 + 0.867665i −0.992213 0.124549i $$-0.960252\pi$$
0.124549 + 0.992213i $$0.460252\pi$$
$$338$$ 0 0
$$339$$ 1.53590i 0.0834185i
$$340$$ 0 0
$$341$$ −16.0981 27.8827i −0.871760 1.50993i
$$342$$ 0 0
$$343$$ 19.5359i 1.05484i
$$344$$ 0 0
$$345$$ −0.00961894 + 0.160254i −0.000517866 + 0.00862779i
$$346$$ 0 0
$$347$$ −10.4282 + 2.79423i −0.559815 + 0.150002i −0.527621 0.849480i $$-0.676916\pi$$
−0.0321938 + 0.999482i $$0.510249\pi$$
$$348$$ 0 0
$$349$$ −7.86603 2.10770i −0.421059 0.112822i 0.0420673 0.999115i $$-0.486606\pi$$
−0.463126 + 0.886292i $$0.653272\pi$$
$$350$$ 0 0
$$351$$ 2.09808 10.4904i 0.111987 0.559935i
$$352$$ 0 0
$$353$$ 9.06218 5.23205i 0.482331 0.278474i −0.239056 0.971006i $$-0.576838\pi$$
0.721387 + 0.692532i $$0.243505\pi$$
$$354$$ 0 0
$$355$$ −3.42820 3.86603i −0.181950 0.205187i
$$356$$ 0 0
$$357$$ 0.571797 0.990381i 0.0302627 0.0524165i
$$358$$ 0 0
$$359$$ 13.1962 13.1962i 0.696466 0.696466i −0.267180 0.963647i $$-0.586092\pi$$
0.963647 + 0.267180i $$0.0860919\pi$$
$$360$$ 0 0
$$361$$ −8.83013 + 5.09808i −0.464744 + 0.268320i
$$362$$ 0 0
$$363$$ 3.00000 + 3.00000i 0.157459 + 0.157459i
$$364$$ 0 0
$$365$$ 29.8564 14.9282i 1.56276 0.781378i
$$366$$ 0 0
$$367$$ −3.96410 + 14.7942i −0.206924 + 0.772252i 0.781930 + 0.623366i $$0.214235\pi$$
−0.988854 + 0.148886i $$0.952431\pi$$
$$368$$ 0 0
$$369$$ −18.6603 18.6603i −0.971414 0.971414i
$$370$$ 0 0
$$371$$ −8.29423 + 2.22243i −0.430615 + 0.115383i
$$372$$ 0 0
$$373$$ 5.30385 + 19.7942i 0.274623 + 1.02491i 0.956094 + 0.293061i $$0.0946739\pi$$
−0.681471 + 0.731845i $$0.738659\pi$$
$$374$$ 0 0
$$375$$ 2.47372 5.23205i 0.127742 0.270182i
$$376$$ 0 0
$$377$$ 5.59808 + 2.76795i 0.288316 + 0.142557i
$$378$$ 0 0
$$379$$ 2.59808 9.69615i 0.133454 0.498058i −0.866545 0.499099i $$-0.833665\pi$$
0.999999 + 0.00104063i $$0.000331242\pi$$
$$380$$ 0 0
$$381$$ 9.23205 + 5.33013i 0.472972 + 0.273071i
$$382$$ 0 0
$$383$$ −22.1147 12.7679i −1.13001 0.652412i −0.186073 0.982536i $$-0.559576\pi$$
−0.943937 + 0.330124i $$0.892909\pi$$
$$384$$ 0 0
$$385$$ −7.63397 + 22.9019i −0.389063 + 1.16719i
$$386$$ 0 0
$$387$$ 16.2942 + 4.36603i 0.828282 + 0.221938i
$$388$$ 0 0
$$389$$ −15.0718 −0.764170 −0.382085 0.924127i $$-0.624794\pi$$
−0.382085 + 0.924127i $$0.624794\pi$$
$$390$$ 0 0
$$391$$ 0.124356 0.00628894
$$392$$ 0 0
$$393$$ −2.92820 0.784610i −0.147708 0.0395783i
$$394$$ 0 0
$$395$$ −0.535898 1.07180i −0.0269640 0.0539279i
$$396$$ 0 0
$$397$$ −9.86603 5.69615i −0.495162 0.285882i 0.231552 0.972823i $$-0.425620\pi$$
−0.726713 + 0.686941i $$0.758953\pi$$
$$398$$ 0 0
$$399$$ −3.27757 1.89230i −0.164084 0.0947337i
$$400$$ 0 0
$$401$$ 2.66987 9.96410i 0.133327 0.497583i −0.866672 0.498878i $$-0.833745\pi$$
0.999999 + 0.00129478i $$0.000412141\pi$$
$$402$$ 0 0
$$403$$ 25.9808 + 5.19615i 1.29419 + 0.258839i
$$404$$ 0 0
$$405$$ −12.4282 8.20577i −0.617562 0.407748i
$$406$$ 0 0
$$407$$ 1.74167 + 6.50000i 0.0863314 + 0.322193i
$$408$$ 0 0
$$409$$ 18.5263 4.96410i 0.916066 0.245459i 0.230163 0.973152i $$-0.426074\pi$$
0.685903 + 0.727693i $$0.259407\pi$$
$$410$$ 0 0
$$411$$ 5.24167 + 5.24167i 0.258553 + 0.258553i
$$412$$ 0 0
$$413$$ 5.74167 21.4282i 0.282529 1.05441i
$$414$$ 0 0
$$415$$ 2.92820 + 5.85641i 0.143740 + 0.287480i
$$416$$ 0 0
$$417$$ 1.90192 + 1.90192i 0.0931376 + 0.0931376i
$$418$$ 0 0
$$419$$ −31.5000 + 18.1865i −1.53888 + 0.888470i −0.539971 + 0.841684i $$0.681565\pi$$
−0.998905 + 0.0467865i $$0.985102\pi$$
$$420$$ 0 0
$$421$$ 6.85641 6.85641i 0.334161 0.334161i −0.520003 0.854164i $$-0.674069\pi$$
0.854164 + 0.520003i $$0.174069\pi$$
$$422$$ 0 0
$$423$$ −14.9282 + 25.8564i −0.725834 + 1.25718i
$$424$$ 0 0
$$425$$ −4.16025 1.66987i −0.201802 0.0810007i
$$426$$ 0 0
$$427$$ −19.2058 + 11.0885i −0.929432 + 0.536608i
$$428$$ 0 0
$$429$$ −8.16025 + 0.526279i −0.393981 + 0.0254090i
$$430$$ 0 0
$$431$$ −23.2583 6.23205i −1.12031 0.300187i −0.349304 0.937010i $$-0.613582\pi$$
−0.771011 + 0.636822i $$0.780249\pi$$
$$432$$ 0 0
$$433$$ 32.5526 8.72243i 1.56438 0.419173i 0.630330 0.776327i $$-0.282919\pi$$
0.934046 + 0.357154i $$0.116253\pi$$
$$434$$ 0 0
$$435$$ −1.50000 + 1.33013i −0.0719195 + 0.0637747i
$$436$$ 0 0
$$437$$ 0.411543i 0.0196868i
$$438$$ 0 0
$$439$$ 0.0358984 + 0.0621778i 0.00171334 + 0.00296759i 0.866881 0.498515i $$-0.166121\pi$$
−0.865167 + 0.501483i $$0.832788\pi$$
$$440$$ 0 0
$$441$$ 2.53590i 0.120757i
$$442$$ 0 0
$$443$$ −15.5885 + 15.5885i −0.740630 + 0.740630i −0.972699 0.232069i $$-0.925450\pi$$
0.232069 + 0.972699i $$0.425450\pi$$
$$444$$ 0 0
$$445$$ 33.5526 6.86603i 1.59054 0.325481i
$$446$$ 0 0
$$447$$ 1.78461 0.0844091
$$448$$ 0 0
$$449$$ −5.20577 19.4282i −0.245676 0.916874i −0.973043 0.230625i $$-0.925923\pi$$
0.727367 0.686249i $$-0.240744\pi$$
$$450$$ 0 0
$$451$$ −21.1603 + 36.6506i −0.996397 + 1.72581i
$$452$$ 0 0
$$453$$ 0.0980762 + 0.169873i 0.00460802 + 0.00798133i
$$454$$ 0 0
$$455$$ −10.0096 17.1603i −0.469258 0.804485i
$$456$$ 0 0
$$457$$ −6.79423 11.7679i −0.317821 0.550481i 0.662212 0.749316i $$-0.269618\pi$$
−0.980033 + 0.198835i $$0.936284\pi$$
$$458$$ 0 0
$$459$$ 1.33013 2.30385i 0.0620850 0.107534i
$$460$$ 0 0
$$461$$ 0.813467 + 3.03590i 0.0378869 + 0.141396i 0.982279 0.187427i $$-0.0600148\pi$$
−0.944392 + 0.328823i $$0.893348\pi$$
$$462$$ 0 0
$$463$$ −21.6077 −1.00419 −0.502097 0.864811i $$-0.667438\pi$$
−0.502097 + 0.864811i $$0.667438\pi$$
$$464$$ 0 0
$$465$$ −4.68653 + 7.09808i −0.217333 + 0.329165i
$$466$$ 0 0
$$467$$ 16.6603 16.6603i 0.770945 0.770945i −0.207327 0.978272i $$-0.566476\pi$$
0.978272 + 0.207327i $$0.0664764\pi$$
$$468$$ 0 0
$$469$$ 30.2295i 1.39587i
$$470$$ 0 0
$$471$$ −2.36603 4.09808i −0.109021 0.188829i
$$472$$ 0 0
$$473$$ 27.0526i 1.24388i
$$474$$ 0 0
$$475$$ −5.52628 + 13.7679i −0.253563 + 0.631717i
$$476$$ 0 0
$$477$$ −9.19615 + 2.46410i −0.421063 + 0.112823i
$$478$$ 0 0
$$479$$ −3.13397 0.839746i −0.143195 0.0383690i 0.186510 0.982453i $$-0.440282\pi$$
−0.329705 + 0.944084i $$0.606949\pi$$
$$480$$ 0 0
$$481$$ −4.96410 2.45448i −0.226344 0.111915i
$$482$$ 0 0
$$483$$ −0.153212 + 0.0884573i −0.00697141 + 0.00402495i
$$484$$ 0 0
$$485$$ −1.03590 + 17.2583i −0.0470377 + 0.783660i
$$486$$ 0 0
$$487$$ −0.794229 + 1.37564i −0.0359899 + 0.0623364i −0.883459 0.468508i $$-0.844792\pi$$
0.847469 + 0.530844i $$0.178125\pi$$
$$488$$ 0 0
$$489$$ 1.16987 1.16987i 0.0529035 0.0529035i
$$490$$ 0 0
$$491$$ 5.89230 3.40192i 0.265916 0.153527i −0.361114 0.932522i $$-0.617604\pi$$
0.627030 + 0.778995i $$0.284270\pi$$
$$492$$ 0 0
$$493$$ 1.09808 + 1.09808i 0.0494549 + 0.0494549i
$$494$$ 0 0
$$495$$ −8.46410 + 25.3923i −0.380433 + 1.14130i
$$496$$ 0 0
$$497$$ 1.47372 5.50000i 0.0661054 0.246709i
$$498$$ 0 0
$$499$$ 20.2679 + 20.2679i 0.907318 + 0.907318i 0.996055 0.0887371i $$-0.0282831\pi$$
−0.0887371 + 0.996055i $$0.528283\pi$$
$$500$$ 0 0
$$501$$ 9.23205 2.47372i 0.412458 0.110518i
$$502$$ 0 0
$$503$$ −3.35641 12.5263i −0.149655 0.558519i −0.999504 0.0314933i $$-0.989974\pi$$
0.849849 0.527026i $$-0.176693\pi$$
$$504$$ 0 0
$$505$$ 21.1865 32.0885i 0.942788 1.42792i
$$506$$ 0 0
$$507$$ 4.10770 5.33013i 0.182429 0.236719i
$$508$$ 0 0
$$509$$ −7.45448 + 27.8205i −0.330414 + 1.23312i 0.578342 + 0.815795i $$0.303700\pi$$
−0.908756 + 0.417328i $$0.862967\pi$$
$$510$$ 0 0
$$511$$ 31.8564 + 18.3923i 1.40924 + 0.813628i
$$512$$ 0 0
$$513$$ −7.62436 4.40192i −0.336624 0.194350i
$$514$$ 0 0
$$515$$ 33.5885 + 11.1962i 1.48008 + 0.493361i
$$516$$ 0 0
$$517$$ 46.2487 + 12.3923i 2.03402 + 0.545013i
$$518$$ 0 0
$$519$$ 1.48334 0.0651114
$$520$$ 0 0
$$521$$ −7.85641 −0.344195 −0.172098 0.985080i $$-0.555054\pi$$
−0.172098 + 0.985080i $$0.555054\pi$$
$$522$$ 0 0
$$523$$ 10.9641 + 2.93782i 0.479427 + 0.128462i 0.490436 0.871477i $$-0.336838\pi$$
−0.0110090 + 0.999939i $$0.503504\pi$$
$$524$$ 0 0
$$525$$ 6.31347 0.901924i 0.275542 0.0393632i
$$526$$ 0 0
$$527$$ 5.70577 + 3.29423i 0.248547 + 0.143499i
$$528$$ 0 0
$$529$$ 19.9019 + 11.4904i 0.865301 + 0.499582i
$$530$$ 0 0
$$531$$ 6.36603 23.7583i 0.276262 1.03102i
$$532$$ 0 0
$$533$$ −11.1603 32.9904i −0.483404 1.42897i
$$534$$ 0 0
$$535$$ −3.40192 16.6244i −0.147078 0.718734i
$$536$$ 0 0
$$537$$ −1.86603 6.96410i −0.0805249 0.300523i
$$538$$ 0 0
$$539$$ 3.92820 1.05256i 0.169200 0.0453369i
$$540$$ 0 0
$$541$$ 21.7846 + 21.7846i 0.936594 + 0.936594i 0.998106 0.0615128i $$-0.0195925\pi$$
−0.0615128 + 0.998106i $$0.519592\pi$$
$$542$$ 0 0
$$543$$ −3.07180 + 11.4641i −0.131823 + 0.491972i
$$544$$ 0 0
$$545$$ 10.6077 + 3.53590i 0.454384 + 0.151461i
$$546$$ 0 0
$$547$$ −0.124356 0.124356i −0.00531706 0.00531706i 0.704443 0.709760i $$-0.251197\pi$$
−0.709760 + 0.704443i $$0.751197\pi$$
$$548$$ 0 0
$$549$$ −21.2942 + 12.2942i −0.908816 + 0.524705i
$$550$$ 0 0
$$551$$ 3.63397 3.63397i 0.154813 0.154813i
$$552$$ 0 0
$$553$$ 0.660254 1.14359i 0.0280769 0.0486305i
$$554$$ 0 0
$$555$$ 1.33013 1.17949i 0.0564607 0.0500666i
$$556$$ 0 0
$$557$$ 13.3301 7.69615i 0.564816 0.326096i −0.190260 0.981734i $$-0.560933\pi$$
0.755076 + 0.655637i $$0.227600\pi$$
$$558$$ 0 0
$$559$$ 16.7224 + 14.6962i 0.707284 + 0.621581i
$$560$$ 0 0
$$561$$ −1.96410 0.526279i −0.0829244 0.0222195i
$$562$$ 0 0
$$563$$ −24.8923 + 6.66987i −1.04909 + 0.281102i −0.741874 0.670540i $$-0.766063\pi$$
−0.307212 + 0.951641i $$0.599396\pi$$
$$564$$ 0 0
$$565$$ −4.40192 4.96410i −0.185190 0.208841i
$$566$$ 0 0
$$567$$ 16.4115i 0.689220i
$$568$$ 0 0
$$569$$ 18.8205 + 32.5981i 0.788997 + 1.36658i 0.926582 + 0.376093i $$0.122733\pi$$
−0.137585 + 0.990490i $$0.543934\pi$$
$$570$$ 0 0
$$571$$ 21.6077i 0.904254i 0.891954 + 0.452127i $$0.149335\pi$$
−0.891954 + 0.452127i $$0.850665\pi$$
$$572$$ 0 0
$$573$$ −5.49038 + 5.49038i −0.229364 + 0.229364i
$$574$$ 0 0
$$575$$ 0.428203 + 0.545517i 0.0178573 + 0.0227496i
$$576$$ 0 0
$$577$$ 20.7846 0.865275 0.432637 0.901568i $$-0.357583\pi$$
0.432637 + 0.901568i $$0.357583\pi$$
$$578$$ 0 0
$$579$$ −3.42820 12.7942i −0.142471 0.531710i
$$580$$ 0 0
$$581$$ −3.60770 + 6.24871i −0.149672 + 0.259240i
$$582$$ 0 0
$$583$$ 7.63397 + 13.2224i 0.316167 + 0.547617i
$$584$$ 0 0
$$585$$ −11.0981 19.0263i −0.458849 0.786640i
$$586$$ 0 0
$$587$$ −23.7224 41.0885i −0.979130 1.69590i −0.665573 0.746333i $$-0.731813\pi$$
−0.313556 0.949570i $$-0.601520\pi$$
$$588$$ 0 0
$$589$$ 10.9019 18.8827i 0.449206 0.778048i
$$590$$ 0 0
$$591$$ −0.571797 2.13397i −0.0235206 0.0877800i
$$592$$ 0 0
$$593$$ −30.9282 −1.27007 −0.635035 0.772484i $$-0.719014\pi$$
−0.635035 + 0.772484i $$0.719014\pi$$
$$594$$ 0 0
$$595$$ −0.990381 4.83975i −0.0406017 0.198410i
$$596$$ 0 0
$$597$$ −6.90192 + 6.90192i −0.282477 + 0.282477i
$$598$$ 0 0
$$599$$ 36.2487i 1.48108i 0.672011 + 0.740541i $$0.265431\pi$$
−0.672011 + 0.740541i $$0.734569\pi$$
$$600$$ 0 0
$$601$$ 7.42820 + 12.8660i 0.303003 + 0.524816i 0.976815 0.214087i $$-0.0686775\pi$$
−0.673812 + 0.738903i $$0.735344\pi$$
$$602$$ 0 0
$$603$$ 33.5167i 1.36490i
$$604$$ 0 0
$$605$$ 18.2942 + 1.09808i 0.743766 + 0.0446431i
$$606$$ 0 0
$$607$$ 3.03590 0.813467i 0.123223 0.0330176i −0.196680 0.980468i $$-0.563016\pi$$
0.319904 + 0.947450i $$0.396349\pi$$
$$608$$ 0 0
$$609$$ −2.13397 0.571797i −0.0864730 0.0231704i
$$610$$ 0 0
$$611$$ −32.7846 + 21.8564i −1.32632 + 0.884216i
$$612$$ 0 0
$$613$$ −21.1865 + 12.2321i −0.855716 + 0.494048i −0.862575 0.505929i $$-0.831150\pi$$
0.00685934 + 0.999976i $$0.497817\pi$$
$$614$$ 0 0
$$615$$ 11.1603 + 0.669873i 0.450025 + 0.0270119i
$$616$$ 0 0
$$617$$ 8.79423 15.2321i 0.354042 0.613219i −0.632911 0.774224i $$-0.718140\pi$$
0.986954 + 0.161005i $$0.0514735\pi$$
$$618$$ 0 0
$$619$$ 14.6603 14.6603i 0.589245 0.589245i −0.348182 0.937427i $$-0.613201\pi$$
0.937427 + 0.348182i $$0.113201\pi$$
$$620$$ 0 0
$$621$$ −0.356406 + 0.205771i −0.0143021 + 0.00825732i
$$622$$ 0 0
$$623$$ 26.6865 + 26.6865i 1.06917 + 1.06917i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 0 0
$$627$$ −1.74167 + 6.50000i −0.0695556 + 0.259585i
$$628$$ 0 0
$$629$$ −0.973721 0.973721i −0.0388248 0.0388248i
$$630$$ 0 0
$$631$$ 41.6506 11.1603i 1.65809 0.444283i 0.696225 0.717823i $$-0.254862\pi$$
0.961860 + 0.273541i $$0.0881948\pi$$
$$632$$ 0 0
$$633$$ 0.794229 + 2.96410i 0.0315678 + 0.117812i
$$634$$ 0 0
$$635$$ 45.1147 9.23205i 1.79032 0.366363i
$$636$$ 0 0
$$637$$ −1.48334 + 3.00000i −0.0587721 + 0.118864i
$$638$$ 0 0
$$639$$ 1.63397 6.09808i 0.0646390 0.241236i
$$640$$ 0 0
$$641$$ 5.64359 + 3.25833i 0.222909 + 0.128696i 0.607296 0.794475i $$-0.292254\pi$$
−0.384388 + 0.923172i $$0.625587\pi$$
$$642$$ 0 0
$$643$$ −31.3301 18.0885i −1.23554 0.713339i −0.267360 0.963597i $$-0.586151\pi$$
−0.968179 + 0.250258i $$0.919485\pi$$
$$644$$ 0 0
$$645$$ −6.39230 + 3.19615i −0.251697 + 0.125848i
$$646$$ 0 0
$$647$$ 2.50000 + 0.669873i 0.0982851 + 0.0263354i 0.307626 0.951507i $$-0.400465\pi$$
−0.209341 + 0.977843i $$0.567132\pi$$
$$648$$ 0 0
$$649$$ −39.4449 −1.54835
$$650$$ 0 0
$$651$$ −9.37307 −0.367359
$$652$$ 0 0
$$653$$ 47.9449 + 12.8468i 1.87623 + 0.502734i 0.999774 + 0.0212467i $$0.00676353\pi$$
0.876453 + 0.481487i $$0.159903\pi$$
$$654$$ 0 0
$$655$$ −11.7128 + 5.85641i −0.457657 + 0.228829i
$$656$$ 0 0
$$657$$ 35.3205 + 20.3923i 1.37798 + 0.795580i
$$658$$ 0 0
$$659$$ −35.4282 20.4545i −1.38009 0.796794i −0.387918 0.921694i $$-0.626805\pi$$
−0.992169 + 0.124901i $$0.960139\pi$$
$$660$$ 0 0
$$661$$ −0.794229 + 2.96410i −0.0308919 + 0.115290i −0.979650 0.200713i $$-0.935674\pi$$
0.948758 + 0.316003i $$0.102341\pi$$
$$662$$ 0 0
$$663$$ 1.39230 0.928203i 0.0540726 0.0360484i
$$664$$ 0 0
$$665$$ −16.0167 + 3.27757i −0.621099 + 0.127099i
$$666$$ 0 0
$$667$$ −0.0621778 0.232051i −0.00240754 0.00898504i
$$668$$ 0 0
$$669$$ 0.767949 0.205771i 0.0296906 0.00795558i
$$670$$ 0 0
$$671$$ 27.8827 + 27.8827i 1.07640 + 1.07640i
$$672$$ 0 0
$$673$$ 9.62436 35.9186i 0.370992 1.38456i −0.488122 0.872775i $$-0.662318\pi$$
0.859114 0.511784i $$-0.171015\pi$$
$$674$$ 0 0
$$675$$ 14.6865 2.09808i 0.565285 0.0807550i
$$676$$ 0 0
$$677$$ −28.1769 28.1769i −1.08293 1.08293i −0.996235 0.0866916i $$-0.972371\pi$$
−0.0866916 0.996235i $$-0.527629\pi$$
$$678$$ 0 0
$$679$$ −16.5000 + 9.52628i −0.633212 + 0.365585i
$$680$$ 0 0
$$681$$ −1.16987 + 1.16987i −0.0448296 + 0.0448296i
$$682$$ 0 0
$$683$$ 7.33013 12.6962i 0.280480 0.485805i −0.691023 0.722832i $$-0.742840\pi$$
0.971503 + 0.237028i $$0.0761732\pi$$
$$684$$ 0 0
$$685$$ 31.9641 + 1.91858i 1.22129 + 0.0733053i
$$686$$ 0 0
$$687$$ −0.0455173 + 0.0262794i −0.00173659 + 0.00100262i
$$688$$ 0 0
$$689$$ −12.3205 2.46410i −0.469374 0.0938748i
$$690$$ 0 0
$$691$$ −37.6506 10.0885i −1.43230 0.383783i −0.542468 0.840076i $$-0.682510\pi$$
−0.889829 + 0.456293i $$0.849177\pi$$
$$692$$ 0 0
$$693$$ −28.4904 + 7.63397i −1.08226 + 0.289991i
$$694$$ 0 0
$$695$$ 11.5981 + 0.696152i 0.439940 + 0.0264066i
$$696$$ 0 0
$$697$$ 8.66025i 0.328031i
$$698$$ 0 0
$$699$$ −4.70577 8.15064i −0.177989 0.308285i
$$700$$ 0 0
$$701$$ 21.0718i 0.795871i 0.917413 + 0.397935i $$0.130273\pi$$
−0.917413 + 0.397935i $$0.869727\pi$$
$$702$$ 0 0
$$703$$ −3.22243 + 3.22243i −0.121536 + 0.121536i
$$704$$ 0 0
$$705$$ −2.53590 12.3923i −0.0955075 0.466721i
$$706$$ 0 0
$$707$$ 42.3731 1.59360
$$708$$ 0 0
$$709$$ −4.27757 15.9641i −0.160647 0.599544i −0.998555 0.0537328i $$-0.982888\pi$$
0.837908 0.545812i $$-0.183779\pi$$
$$710$$ 0 0
$$711$$ 0.732051 1.26795i 0.0274541 0.0475518i
$$712$$ 0 0
$$713$$ −0.509619 0.882686i −0.0190854 0.0330568i
$$714$$ 0 0
$$715$$ −24.8660 + 25.0885i −0.929937 + 0.938255i
$$716$$ 0 0
$$717$$ −6.09808 10.5622i −0.227737 0.394452i
$$718$$ 0 0
$$719$$ −20.9641 + 36.3109i −0.781829 + 1.35417i 0.149046 + 0.988830i $$0.452380\pi$$
−0.930875 + 0.365337i $$0.880954\pi$$
$$720$$ 0 0
$$721$$ 10.0981 + 37.6865i 0.376072 + 1.40352i
$$722$$ 0 0
$$723$$ −6.07180 −0.225813
$$724$$ 0 0
$$725$$ −1.03590 + 8.59808i −0.0384723 + 0.319325i
$$726$$ 0 0
$$727$$ −33.5885 + 33.5885i −1.24573 + 1.24573i −0.288138 + 0.957589i $$0.593036\pi$$
−0.957589 + 0.288138i $$0.906964\pi$$
$$728$$ 0 0
$$729$$ 13.5885i 0.503276i
$$730$$ 0 0
$$731$$ 2.76795 + 4.79423i 0.102376 + 0.177321i
$$732$$ 0 0
$$733$$ 26.7846i 0.989312i −0.869089 0.494656i $$-0.835294\pi$$
0.869089 0.494656i $$-0.164706\pi$$
$$734$$ 0 0
$$735$$ −0.712813 0.803848i −0.0262925 0.0296504i
$$736$$ 0 0
$$737$$ −51.9186 + 13.9115i −1.91245 + 0.512438i
$$738$$ 0 0
$$739$$ −37.9186 10.1603i −1.39486 0.373751i −0.518362 0.855161i $$-0.673458\pi$$
−0.876495 + 0.481410i $$0.840125\pi$$
$$740$$ 0 0
$$741$$ −3.07180 4.60770i −0.112845 0.169268i
$$742$$ 0 0
$$743$$ −19.3301 + 11.1603i −0.709154 + 0.409430i −0.810748 0.585396i $$-0.800939\pi$$
0.101594 + 0.994826i $$0.467606\pi$$
$$744$$ 0 0
$$745$$ 5.76795 5.11474i 0.211321 0.187389i
$$746$$ 0 0
$$747$$ −4.00000 + 6.92820i −0.146352 + 0.253490i
$$748$$ 0 0
$$749$$ 13.2224 13.2224i 0.483137 0.483137i
$$750$$ 0 0
$$751$$ 17.6436 10.1865i 0.643824 0.371712i −0.142262 0.989829i $$-0.545438\pi$$
0.786086 + 0.618117i $$0.212104\pi$$
$$752$$ 0 0
$$753$$ 6.49038 + 6.49038i 0.236523 + 0.236523i
$$754$$ 0 0
$$755$$ 0.803848 + 0.267949i 0.0292550 + 0.00975167i
$$756$$ 0 0
$$757$$ −4.83975 + 18.0622i −0.175904 + 0.656481i 0.820492 + 0.571657i $$0.193699\pi$$
−0.996396 + 0.0848236i $$0.972967\pi$$
$$758$$ 0 0
$$759$$ 0.222432 + 0.222432i 0.00807377 + 0.00807377i
$$760$$ 0 0
$$761$$ −0.669873 + 0.179492i −0.0242829 + 0.00650658i −0.270940 0.962596i $$-0.587335\pi$$
0.246657 + 0.969103i $$0.420668\pi$$
$$762$$ 0 0
$$763$$ 3.18911 + 11.9019i 0.115454 + 0.430879i
$$764$$ 0 0
$$765$$ −1.09808 5.36603i −0.0397010 0.194009i
$$766$$ 0 0
$$767$$ 21.4282 24.3827i 0.773728 0.880408i
$$768$$ 0 0
$$769$$ 5.47372 20.4282i 0.197387 0.736660i −0.794248 0.607593i $$-0.792135\pi$$
0.991636 0.129067i $$-0.0411982\pi$$
$$770$$ 0 0
$$771$$ −10.0359 5.79423i −0.361434 0.208674i
$$772$$ 0 0
$$773$$ 17.0429 + 9.83975i 0.612992 + 0.353911i 0.774136 0.633020i $$-0.218185\pi$$
−0.161144 + 0.986931i $$0.551518\pi$$
$$774$$ 0 0
$$775$$ 5.19615 + 36.3731i 0.186651 + 1.30656i
$$776$$ 0 0
$$777$$ 1.89230 + 0.507042i 0.0678861 + 0.0181900i
$$778$$ 0 0
$$779$$ −28.6603 −1.02686
$$780$$ 0 0
$$781$$ −10.1244 −0.362278
$$782$$ 0 0
$$783$$ −4.96410 1.33013i −0.177403 0.0475349i
$$784$$ 0 0
$$785$$ −19.3923 6.46410i −0.692141 0.230714i
$$786$$ 0 0
$$787$$ −37.4545 21.6244i −1.33511 0.770825i −0.349031 0.937111i $$-0.613489\pi$$
−0.986078 + 0.166286i $$0.946822\pi$$
$$788$$ 0 0
$$789$$ −6.44744 3.72243i −0.229535 0.132522i
$$790$$ 0