# Properties

 Label 576.2.bb.c.49.1 Level $576$ Weight $2$ Character 576.49 Analytic conductor $4.599$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 576.bb (of order $$12$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.59938315643$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 144) Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 49.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 576.49 Dual form 576.2.bb.c.529.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 1.50000i) q^{3} +(1.00000 - 0.267949i) q^{5} +(-2.36603 + 1.36603i) q^{7} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 1.50000i) q^{3} +(1.00000 - 0.267949i) q^{5} +(-2.36603 + 1.36603i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(-1.13397 + 4.23205i) q^{11} +(0.901924 + 3.36603i) q^{13} +(-1.26795 - 1.26795i) q^{15} -5.73205 q^{17} +(2.36603 - 2.36603i) q^{19} +(4.09808 + 2.36603i) q^{21} +(4.09808 + 2.36603i) q^{23} +(-3.40192 + 1.96410i) q^{25} +5.19615 q^{27} +(2.36603 + 0.633975i) q^{29} +(0.267949 - 0.464102i) q^{31} +(7.33013 - 1.96410i) q^{33} +(-2.00000 + 2.00000i) q^{35} +(4.73205 + 4.73205i) q^{37} +(4.26795 - 4.26795i) q^{39} +(-2.59808 - 1.50000i) q^{41} +(-2.23205 + 8.33013i) q^{43} +(-0.803848 + 3.00000i) q^{45} +(-3.83013 - 6.63397i) q^{47} +(0.232051 - 0.401924i) q^{49} +(4.96410 + 8.59808i) q^{51} +(-7.46410 - 7.46410i) q^{53} +4.53590i q^{55} +(-5.59808 - 1.50000i) q^{57} +(-7.33013 + 1.96410i) q^{59} +(11.1962 + 3.00000i) q^{61} -8.19615i q^{63} +(1.80385 + 3.12436i) q^{65} +(1.76795 + 6.59808i) q^{67} -8.19615i q^{69} +2.92820i q^{71} +6.26795i q^{73} +(5.89230 + 3.40192i) q^{75} +(-3.09808 - 11.5622i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(1.36603 + 0.366025i) q^{83} +(-5.73205 + 1.53590i) q^{85} +(-1.09808 - 4.09808i) q^{87} +2.00000i q^{89} +(-6.73205 - 6.73205i) q^{91} -0.928203 q^{93} +(1.73205 - 3.00000i) q^{95} +(-5.86603 - 10.1603i) q^{97} +(-9.29423 - 9.29423i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{5} - 6q^{7} - 6q^{9} + O(q^{10})$$ $$4q + 4q^{5} - 6q^{7} - 6q^{9} - 8q^{11} + 14q^{13} - 12q^{15} - 16q^{17} + 6q^{19} + 6q^{21} + 6q^{23} - 24q^{25} + 6q^{29} + 8q^{31} + 12q^{33} - 8q^{35} + 12q^{37} + 24q^{39} - 2q^{43} - 24q^{45} + 2q^{47} - 6q^{49} + 6q^{51} - 16q^{53} - 12q^{57} - 12q^{59} + 24q^{61} + 28q^{65} + 14q^{67} - 18q^{75} - 2q^{77} + 24q^{79} - 18q^{81} + 2q^{83} - 16q^{85} + 6q^{87} - 20q^{91} + 24q^{93} - 20q^{97} - 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$$.

 $$n$$ $$65$$ $$127$$ $$325$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$

## 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
$$3$$ −0.866025 1.50000i −0.500000 0.866025i
$$4$$ 0 0
$$5$$ 1.00000 0.267949i 0.447214 0.119831i −0.0281817 0.999603i $$-0.508972\pi$$
0.475395 + 0.879772i $$0.342305\pi$$
$$6$$ 0 0
$$7$$ −2.36603 + 1.36603i −0.894274 + 0.516309i −0.875338 0.483512i $$-0.839361\pi$$
−0.0189356 + 0.999821i $$0.506028\pi$$
$$8$$ 0 0
$$9$$ −1.50000 + 2.59808i −0.500000 + 0.866025i
$$10$$ 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
$$13$$ 0.901924 + 3.36603i 0.250149 + 0.933567i 0.970725 + 0.240192i $$0.0772105\pi$$
−0.720577 + 0.693375i $$0.756123\pi$$
$$14$$ 0 0
$$15$$ −1.26795 1.26795i −0.327383 0.327383i
$$16$$ 0 0
$$17$$ −5.73205 −1.39023 −0.695113 0.718900i $$-0.744646\pi$$
−0.695113 + 0.718900i $$0.744646\pi$$
$$18$$ 0 0
$$19$$ 2.36603 2.36603i 0.542803 0.542803i −0.381546 0.924350i $$-0.624608\pi$$
0.924350 + 0.381546i $$0.124608\pi$$
$$20$$ 0 0
$$21$$ 4.09808 + 2.36603i 0.894274 + 0.516309i
$$22$$ 0 0
$$23$$ 4.09808 + 2.36603i 0.854508 + 0.493350i 0.862169 0.506620i $$-0.169105\pi$$
−0.00766135 + 0.999971i $$0.502439\pi$$
$$24$$ 0 0
$$25$$ −3.40192 + 1.96410i −0.680385 + 0.392820i
$$26$$ 0 0
$$27$$ 5.19615 1.00000
$$28$$ 0 0
$$29$$ 2.36603 + 0.633975i 0.439360 + 0.117726i 0.471717 0.881750i $$-0.343635\pi$$
−0.0323566 + 0.999476i $$0.510301\pi$$
$$30$$ 0 0
$$31$$ 0.267949 0.464102i 0.0481251 0.0833551i −0.840959 0.541098i $$-0.818009\pi$$
0.889085 + 0.457743i $$0.151342\pi$$
$$32$$ 0 0
$$33$$ 7.33013 1.96410i 1.27601 0.341906i
$$34$$ 0 0
$$35$$ −2.00000 + 2.00000i −0.338062 + 0.338062i
$$36$$ 0 0
$$37$$ 4.73205 + 4.73205i 0.777944 + 0.777944i 0.979481 0.201537i $$-0.0645935\pi$$
−0.201537 + 0.979481i $$0.564594\pi$$
$$38$$ 0 0
$$39$$ 4.26795 4.26795i 0.683419 0.683419i
$$40$$ 0 0
$$41$$ −2.59808 1.50000i −0.405751 0.234261i 0.283211 0.959058i $$-0.408600\pi$$
−0.688963 + 0.724797i $$0.741934\pi$$
$$42$$ 0 0
$$43$$ −2.23205 + 8.33013i −0.340385 + 1.27033i 0.557528 + 0.830158i $$0.311750\pi$$
−0.897912 + 0.440174i $$0.854917\pi$$
$$44$$ 0 0
$$45$$ −0.803848 + 3.00000i −0.119831 + 0.447214i
$$46$$ 0 0
$$47$$ −3.83013 6.63397i −0.558681 0.967665i −0.997607 0.0691412i $$-0.977974\pi$$
0.438925 0.898523i $$-0.355359\pi$$
$$48$$ 0 0
$$49$$ 0.232051 0.401924i 0.0331501 0.0574177i
$$50$$ 0 0
$$51$$ 4.96410 + 8.59808i 0.695113 + 1.20397i
$$52$$ 0 0
$$53$$ −7.46410 7.46410i −1.02527 1.02527i −0.999672 0.0256010i $$-0.991850\pi$$
−0.0256010 0.999672i $$-0.508150\pi$$
$$54$$ 0 0
$$55$$ 4.53590i 0.611620i
$$56$$ 0 0
$$57$$ −5.59808 1.50000i −0.741483 0.198680i
$$58$$ 0 0
$$59$$ −7.33013 + 1.96410i −0.954301 + 0.255704i −0.702186 0.711993i $$-0.747793\pi$$
−0.252115 + 0.967697i $$0.581126\pi$$
$$60$$ 0 0
$$61$$ 11.1962 + 3.00000i 1.43352 + 0.384111i 0.890260 0.455453i $$-0.150523\pi$$
0.543261 + 0.839564i $$0.317189\pi$$
$$62$$ 0 0
$$63$$ 8.19615i 1.03262i
$$64$$ 0 0
$$65$$ 1.80385 + 3.12436i 0.223740 + 0.387529i
$$66$$ 0 0
$$67$$ 1.76795 + 6.59808i 0.215989 + 0.806083i 0.985816 + 0.167830i $$0.0536760\pi$$
−0.769827 + 0.638253i $$0.779657\pi$$
$$68$$ 0 0
$$69$$ 8.19615i 0.986701i
$$70$$ 0 0
$$71$$ 2.92820i 0.347514i 0.984789 + 0.173757i $$0.0555907\pi$$
−0.984789 + 0.173757i $$0.944409\pi$$
$$72$$ 0 0
$$73$$ 6.26795i 0.733608i 0.930298 + 0.366804i $$0.119548\pi$$
−0.930298 + 0.366804i $$0.880452\pi$$
$$74$$ 0 0
$$75$$ 5.89230 + 3.40192i 0.680385 + 0.392820i
$$76$$ 0 0
$$77$$ −3.09808 11.5622i −0.353059 1.31763i
$$78$$ 0 0
$$79$$ 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i $$0.0692125\pi$$
−0.301401 + 0.953498i $$0.597454\pi$$
$$80$$ 0 0
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ 1.36603 + 0.366025i 0.149941 + 0.0401765i 0.333009 0.942924i $$-0.391936\pi$$
−0.183068 + 0.983100i $$0.558603\pi$$
$$84$$ 0 0
$$85$$ −5.73205 + 1.53590i −0.621728 + 0.166592i
$$86$$ 0 0
$$87$$ −1.09808 4.09808i −0.117726 0.439360i
$$88$$ 0 0
$$89$$ 2.00000i 0.212000i 0.994366 + 0.106000i $$0.0338043\pi$$
−0.994366 + 0.106000i $$0.966196\pi$$
$$90$$ 0 0
$$91$$ −6.73205 6.73205i −0.705711 0.705711i
$$92$$ 0 0
$$93$$ −0.928203 −0.0962502
$$94$$ 0 0
$$95$$ 1.73205 3.00000i 0.177705 0.307794i
$$96$$ 0 0
$$97$$ −5.86603 10.1603i −0.595605 1.03162i −0.993461 0.114170i $$-0.963579\pi$$
0.397857 0.917448i $$-0.369754\pi$$
$$98$$ 0 0
$$99$$ −9.29423 9.29423i −0.934105 0.934105i
$$100$$ 0 0
$$101$$ 0.535898 2.00000i 0.0533239 0.199007i −0.934125 0.356946i $$-0.883818\pi$$
0.987449 + 0.157938i $$0.0504847\pi$$
$$102$$ 0 0
$$103$$ −13.0981 7.56218i −1.29059 0.745124i −0.311833 0.950137i $$-0.600943\pi$$
−0.978759 + 0.205014i $$0.934276\pi$$
$$104$$ 0 0
$$105$$ 4.73205 + 1.26795i 0.461801 + 0.123739i
$$106$$ 0 0
$$107$$ −12.4904 12.4904i −1.20749 1.20749i −0.971837 0.235654i $$-0.924277\pi$$
−0.235654 0.971837i $$-0.575723\pi$$
$$108$$ 0 0
$$109$$ 10.7321 10.7321i 1.02794 1.02794i 0.0283459 0.999598i $$-0.490976\pi$$
0.999598 0.0283459i $$-0.00902398\pi$$
$$110$$ 0 0
$$111$$ 3.00000 11.1962i 0.284747 1.06269i
$$112$$ 0 0
$$113$$ −6.92820 + 12.0000i −0.651751 + 1.12887i 0.330947 + 0.943649i $$0.392632\pi$$
−0.982698 + 0.185216i $$0.940702\pi$$
$$114$$ 0 0
$$115$$ 4.73205 + 1.26795i 0.441266 + 0.118237i
$$116$$ 0 0
$$117$$ −10.0981 2.70577i −0.933567 0.250149i
$$118$$ 0 0
$$119$$ 13.5622 7.83013i 1.24324 0.717787i
$$120$$ 0 0
$$121$$ −7.09808 4.09808i −0.645280 0.372552i
$$122$$ 0 0
$$123$$ 5.19615i 0.468521i
$$124$$ 0 0
$$125$$ −6.53590 + 6.53590i −0.584589 + 0.584589i
$$126$$ 0 0
$$127$$ −4.19615 −0.372348 −0.186174 0.982517i $$-0.559609\pi$$
−0.186174 + 0.982517i $$0.559609\pi$$
$$128$$ 0 0
$$129$$ 14.4282 3.86603i 1.27033 0.340385i
$$130$$ 0 0
$$131$$ −2.09808 7.83013i −0.183310 0.684121i −0.994986 0.100014i $$-0.968111\pi$$
0.811676 0.584108i $$-0.198555\pi$$
$$132$$ 0 0
$$133$$ −2.36603 + 8.83013i −0.205160 + 0.765669i
$$134$$ 0 0
$$135$$ 5.19615 1.39230i 0.447214 0.119831i
$$136$$ 0 0
$$137$$ 8.25833 4.76795i 0.705557 0.407353i −0.103857 0.994592i $$-0.533118\pi$$
0.809414 + 0.587239i $$0.199785\pi$$
$$138$$ 0 0
$$139$$ 11.4282 3.06218i 0.969328 0.259731i 0.260784 0.965397i $$-0.416019\pi$$
0.708544 + 0.705667i $$0.249352\pi$$
$$140$$ 0 0
$$141$$ −6.63397 + 11.4904i −0.558681 + 0.967665i
$$142$$ 0 0
$$143$$ −15.2679 −1.27677
$$144$$ 0 0
$$145$$ 2.53590 0.210595
$$146$$ 0 0
$$147$$ −0.803848 −0.0663002
$$148$$ 0 0
$$149$$ 7.83013 2.09808i 0.641469 0.171881i 0.0766003 0.997062i $$-0.475593\pi$$
0.564869 + 0.825181i $$0.308927\pi$$
$$150$$ 0 0
$$151$$ −0.633975 + 0.366025i −0.0515921 + 0.0297867i −0.525574 0.850748i $$-0.676149\pi$$
0.473982 + 0.880534i $$0.342816\pi$$
$$152$$ 0 0
$$153$$ 8.59808 14.8923i 0.695113 1.20397i
$$154$$ 0 0
$$155$$ 0.143594 0.535898i 0.0115337 0.0430444i
$$156$$ 0 0
$$157$$ 1.26795 + 4.73205i 0.101193 + 0.377659i 0.997886 0.0649959i $$-0.0207034\pi$$
−0.896692 + 0.442655i $$0.854037\pi$$
$$158$$ 0 0
$$159$$ −4.73205 + 17.6603i −0.375276 + 1.40055i
$$160$$ 0 0
$$161$$ −12.9282 −1.01889
$$162$$ 0 0
$$163$$ 7.00000 7.00000i 0.548282 0.548282i −0.377661 0.925944i $$-0.623272\pi$$
0.925944 + 0.377661i $$0.123272\pi$$
$$164$$ 0 0
$$165$$ 6.80385 3.92820i 0.529679 0.305810i
$$166$$ 0 0
$$167$$ −6.46410 3.73205i −0.500207 0.288795i 0.228592 0.973522i $$-0.426588\pi$$
−0.728799 + 0.684728i $$0.759921\pi$$
$$168$$ 0 0
$$169$$ 0.741670 0.428203i 0.0570515 0.0329387i
$$170$$ 0 0
$$171$$ 2.59808 + 9.69615i 0.198680 + 0.741483i
$$172$$ 0 0
$$173$$ 1.63397 + 0.437822i 0.124229 + 0.0332870i 0.320398 0.947283i $$-0.396183\pi$$
−0.196169 + 0.980570i $$0.562850\pi$$
$$174$$ 0 0
$$175$$ 5.36603 9.29423i 0.405633 0.702578i
$$176$$ 0 0
$$177$$ 9.29423 + 9.29423i 0.698597 + 0.698597i
$$178$$ 0 0
$$179$$ 1.92820 1.92820i 0.144121 0.144121i −0.631365 0.775486i $$-0.717505\pi$$
0.775486 + 0.631365i $$0.217505\pi$$
$$180$$ 0 0
$$181$$ −7.39230 7.39230i −0.549466 0.549466i 0.376821 0.926286i $$-0.377017\pi$$
−0.926286 + 0.376821i $$0.877017\pi$$
$$182$$ 0 0
$$183$$ −5.19615 19.3923i −0.384111 1.43352i
$$184$$ 0 0
$$185$$ 6.00000 + 3.46410i 0.441129 + 0.254686i
$$186$$ 0 0
$$187$$ 6.50000 24.2583i 0.475327 1.77394i
$$188$$ 0 0
$$189$$ −12.2942 + 7.09808i −0.894274 + 0.516309i
$$190$$ 0 0
$$191$$ 12.0263 + 20.8301i 0.870191 + 1.50722i 0.861799 + 0.507250i $$0.169338\pi$$
0.00839227 + 0.999965i $$0.497329\pi$$
$$192$$ 0 0
$$193$$ −10.8660 + 18.8205i −0.782154 + 1.35473i 0.148531 + 0.988908i $$0.452545\pi$$
−0.930685 + 0.365822i $$0.880788\pi$$
$$194$$ 0 0
$$195$$ 3.12436 5.41154i 0.223740 0.387529i
$$196$$ 0 0
$$197$$ 13.6603 + 13.6603i 0.973253 + 0.973253i 0.999651 0.0263987i $$-0.00840394\pi$$
−0.0263987 + 0.999651i $$0.508404\pi$$
$$198$$ 0 0
$$199$$ 25.1244i 1.78102i 0.454965 + 0.890509i $$0.349652\pi$$
−0.454965 + 0.890509i $$0.650348\pi$$
$$200$$ 0 0
$$201$$ 8.36603 8.36603i 0.590094 0.590094i
$$202$$ 0 0
$$203$$ −6.46410 + 1.73205i −0.453691 + 0.121566i
$$204$$ 0 0
$$205$$ −3.00000 0.803848i −0.209529 0.0561432i
$$206$$ 0 0
$$207$$ −12.2942 + 7.09808i −0.854508 + 0.493350i
$$208$$ 0 0
$$209$$ 7.33013 + 12.6962i 0.507035 + 0.878211i
$$210$$ 0 0
$$211$$ 1.09808 + 4.09808i 0.0755947 + 0.282123i 0.993367 0.114983i $$-0.0366812\pi$$
−0.917773 + 0.397106i $$0.870015\pi$$
$$212$$ 0 0
$$213$$ 4.39230 2.53590i 0.300956 0.173757i
$$214$$ 0 0
$$215$$ 8.92820i 0.608898i
$$216$$ 0 0
$$217$$ 1.46410i 0.0993897i
$$218$$ 0 0
$$219$$ 9.40192 5.42820i 0.635323 0.366804i
$$220$$ 0 0
$$221$$ −5.16987 19.2942i −0.347763 1.29787i
$$222$$ 0 0
$$223$$ 8.02628 + 13.9019i 0.537479 + 0.930942i 0.999039 + 0.0438324i $$0.0139568\pi$$
−0.461559 + 0.887109i $$0.652710\pi$$
$$224$$ 0 0
$$225$$ 11.7846i 0.785641i
$$226$$ 0 0
$$227$$ −2.13397 0.571797i −0.141637 0.0379515i 0.187304 0.982302i $$-0.440025\pi$$
−0.328941 + 0.944351i $$0.606692\pi$$
$$228$$ 0 0
$$229$$ 6.83013 1.83013i 0.451347 0.120938i −0.0259823 0.999662i $$-0.508271\pi$$
0.477330 + 0.878724i $$0.341605\pi$$
$$230$$ 0 0
$$231$$ −14.6603 + 14.6603i −0.964574 + 0.964574i
$$232$$ 0 0
$$233$$ 3.19615i 0.209387i 0.994505 + 0.104693i $$0.0333861\pi$$
−0.994505 + 0.104693i $$0.966614\pi$$
$$234$$ 0 0
$$235$$ −5.60770 5.60770i −0.365806 0.365806i
$$236$$ 0 0
$$237$$ 10.3923 18.0000i 0.675053 1.16923i
$$238$$ 0 0
$$239$$ 7.90192 13.6865i 0.511133 0.885308i −0.488784 0.872405i $$-0.662559\pi$$
0.999917 0.0129033i $$-0.00410736\pi$$
$$240$$ 0 0
$$241$$ −11.5981 20.0885i −0.747098 1.29401i −0.949208 0.314649i $$-0.898113\pi$$
0.202110 0.979363i $$-0.435220\pi$$
$$242$$ 0 0
$$243$$ −7.79423 + 13.5000i −0.500000 + 0.866025i
$$244$$ 0 0
$$245$$ 0.124356 0.464102i 0.00794479 0.0296504i
$$246$$ 0 0
$$247$$ 10.0981 + 5.83013i 0.642525 + 0.370962i
$$248$$ 0 0
$$249$$ −0.633975 2.36603i −0.0401765 0.149941i
$$250$$ 0 0
$$251$$ 5.83013 + 5.83013i 0.367994 + 0.367994i 0.866745 0.498751i $$-0.166208\pi$$
−0.498751 + 0.866745i $$0.666208\pi$$
$$252$$ 0 0
$$253$$ −14.6603 + 14.6603i −0.921682 + 0.921682i
$$254$$ 0 0
$$255$$ 7.26795 + 7.26795i 0.455137 + 0.455137i
$$256$$ 0 0
$$257$$ 9.42820 16.3301i 0.588115 1.01865i −0.406364 0.913711i $$-0.633204\pi$$
0.994479 0.104934i $$-0.0334632\pi$$
$$258$$ 0 0
$$259$$ −17.6603 4.73205i −1.09735 0.294035i
$$260$$ 0 0
$$261$$ −5.19615 + 5.19615i −0.321634 + 0.321634i
$$262$$ 0 0
$$263$$ 2.49038 1.43782i 0.153563 0.0886599i −0.421249 0.906945i $$-0.638408\pi$$
0.574813 + 0.818285i $$0.305075\pi$$
$$264$$ 0 0
$$265$$ −9.46410 5.46410i −0.581375 0.335657i
$$266$$ 0 0
$$267$$ 3.00000 1.73205i 0.183597 0.106000i
$$268$$ 0 0
$$269$$ 1.26795 1.26795i 0.0773082 0.0773082i −0.667395 0.744704i $$-0.732591\pi$$
0.744704 + 0.667395i $$0.232591\pi$$
$$270$$ 0 0
$$271$$ 0.392305 0.0238308 0.0119154 0.999929i $$-0.496207\pi$$
0.0119154 + 0.999929i $$0.496207\pi$$
$$272$$ 0 0
$$273$$ −4.26795 + 15.9282i −0.258308 + 0.964019i
$$274$$ 0 0
$$275$$ −4.45448 16.6244i −0.268615 1.00249i
$$276$$ 0 0
$$277$$ −6.75833 + 25.2224i −0.406069 + 1.51547i 0.396007 + 0.918247i $$0.370395\pi$$
−0.802076 + 0.597222i $$0.796271\pi$$
$$278$$ 0 0
$$279$$ 0.803848 + 1.39230i 0.0481251 + 0.0833551i
$$280$$ 0 0
$$281$$ −8.66025 + 5.00000i −0.516627 + 0.298275i −0.735554 0.677466i $$-0.763078\pi$$
0.218926 + 0.975741i $$0.429745\pi$$
$$282$$ 0 0
$$283$$ 19.5622 5.24167i 1.16285 0.311585i 0.374747 0.927127i $$-0.377730\pi$$
0.788104 + 0.615542i $$0.211063\pi$$
$$284$$ 0 0
$$285$$ −6.00000 −0.355409
$$286$$ 0 0
$$287$$ 8.19615 0.483804
$$288$$ 0 0
$$289$$ 15.8564 0.932730
$$290$$ 0 0
$$291$$ −10.1603 + 17.5981i −0.595605 + 1.03162i
$$292$$ 0 0
$$293$$ −5.36603 + 1.43782i −0.313487 + 0.0839985i −0.412132 0.911124i $$-0.635216\pi$$
0.0986454 + 0.995123i $$0.468549\pi$$
$$294$$ 0 0
$$295$$ −6.80385 + 3.92820i −0.396135 + 0.228709i
$$296$$ 0 0
$$297$$ −5.89230 + 21.9904i −0.341906 + 1.27601i
$$298$$ 0 0
$$299$$ −4.26795 + 15.9282i −0.246822 + 0.921152i
$$300$$ 0 0
$$301$$ −6.09808 22.7583i −0.351487 1.31177i
$$302$$ 0 0
$$303$$ −3.46410 + 0.928203i −0.199007 + 0.0533239i
$$304$$ 0 0
$$305$$ 12.0000 0.687118
$$306$$ 0 0
$$307$$ −3.02628 + 3.02628i −0.172719 + 0.172719i −0.788173 0.615454i $$-0.788973\pi$$
0.615454 + 0.788173i $$0.288973\pi$$
$$308$$ 0 0
$$309$$ 26.1962i 1.49025i
$$310$$ 0 0
$$311$$ 19.0981 + 11.0263i 1.08295 + 0.625243i 0.931691 0.363251i $$-0.118333\pi$$
0.151261 + 0.988494i $$0.451667\pi$$
$$312$$ 0 0
$$313$$ 18.6506 10.7679i 1.05420 0.608640i 0.130375 0.991465i $$-0.458382\pi$$
0.923821 + 0.382824i $$0.125049\pi$$
$$314$$ 0 0
$$315$$ −2.19615 8.19615i −0.123739 0.461801i
$$316$$ 0 0
$$317$$ −20.5622 5.50962i −1.15489 0.309451i −0.369965 0.929046i $$-0.620630\pi$$
−0.784922 + 0.619595i $$0.787297\pi$$
$$318$$ 0 0
$$319$$ −5.36603 + 9.29423i −0.300440 + 0.520377i
$$320$$ 0 0
$$321$$ −7.91858 + 29.5526i −0.441972 + 1.64946i
$$322$$ 0 0
$$323$$ −13.5622 + 13.5622i −0.754620 + 0.754620i
$$324$$ 0 0
$$325$$ −9.67949 9.67949i −0.536922 0.536922i
$$326$$ 0 0
$$327$$ −25.3923 6.80385i −1.40420 0.376254i
$$328$$ 0 0
$$329$$ 18.1244 + 10.4641i 0.999228 + 0.576905i
$$330$$ 0 0
$$331$$ −0.0262794 + 0.0980762i −0.00144445 + 0.00539076i −0.966644 0.256123i $$-0.917555\pi$$
0.965200 + 0.261513i $$0.0842216\pi$$
$$332$$ 0 0
$$333$$ −19.3923 + 5.19615i −1.06269 + 0.284747i
$$334$$ 0 0
$$335$$ 3.53590 + 6.12436i 0.193187 + 0.334609i
$$336$$ 0 0
$$337$$ 8.89230 15.4019i 0.484395 0.838996i −0.515445 0.856923i $$-0.672373\pi$$
0.999839 + 0.0179267i $$0.00570654\pi$$
$$338$$ 0 0
$$339$$ 24.0000 1.30350
$$340$$ 0 0
$$341$$ 1.66025 + 1.66025i 0.0899078 + 0.0899078i
$$342$$ 0 0
$$343$$ 17.8564i 0.964155i
$$344$$ 0 0
$$345$$ −2.19615 8.19615i −0.118237 0.441266i
$$346$$ 0 0
$$347$$ 17.6244 4.72243i 0.946125 0.253513i 0.247408 0.968911i $$-0.420421\pi$$
0.698717 + 0.715398i $$0.253755\pi$$
$$348$$ 0 0
$$349$$ 15.9282 + 4.26795i 0.852617 + 0.228458i 0.658556 0.752531i $$-0.271167\pi$$
0.194061 + 0.980989i $$0.437834\pi$$
$$350$$ 0 0
$$351$$ 4.68653 + 17.4904i 0.250149 + 0.933567i
$$352$$ 0 0
$$353$$ 7.16025 + 12.4019i 0.381102 + 0.660088i 0.991220 0.132223i $$-0.0422114\pi$$
−0.610118 + 0.792310i $$0.708878\pi$$
$$354$$ 0 0
$$355$$ 0.784610 + 2.92820i 0.0416428 + 0.155413i
$$356$$ 0 0
$$357$$ −23.4904 13.5622i −1.24324 0.717787i
$$358$$ 0 0
$$359$$ 11.2679i 0.594700i 0.954769 + 0.297350i $$0.0961028\pi$$
−0.954769 + 0.297350i $$0.903897\pi$$
$$360$$ 0 0
$$361$$ 7.80385i 0.410729i
$$362$$ 0 0
$$363$$ 14.1962i 0.745105i
$$364$$ 0 0
$$365$$ 1.67949 + 6.26795i 0.0879086 + 0.328079i
$$366$$ 0 0
$$367$$ −14.1244 24.4641i −0.737285 1.27702i −0.953713 0.300717i $$-0.902774\pi$$
0.216428 0.976299i $$-0.430559\pi$$
$$368$$ 0 0
$$369$$ 7.79423 4.50000i 0.405751 0.234261i
$$370$$ 0 0
$$371$$ 27.8564 + 7.46410i 1.44623 + 0.387517i
$$372$$ 0 0
$$373$$ 27.4904 7.36603i 1.42340 0.381398i 0.536710 0.843767i $$-0.319667\pi$$
0.886688 + 0.462368i $$0.153000\pi$$
$$374$$ 0 0
$$375$$ 15.4641 + 4.14359i 0.798563 + 0.213974i
$$376$$ 0 0
$$377$$ 8.53590i 0.439621i
$$378$$ 0 0
$$379$$ −3.75833 3.75833i −0.193052 0.193052i 0.603961 0.797014i $$-0.293588\pi$$
−0.797014 + 0.603961i $$0.793588\pi$$
$$380$$ 0 0
$$381$$ 3.63397 + 6.29423i 0.186174 + 0.322463i
$$382$$ 0 0
$$383$$ 6.73205 11.6603i 0.343992 0.595811i −0.641178 0.767392i $$-0.721554\pi$$
0.985170 + 0.171581i $$0.0548874\pi$$
$$384$$ 0 0
$$385$$ −6.19615 10.7321i −0.315785 0.546956i
$$386$$ 0 0
$$387$$ −18.2942 18.2942i −0.929948 0.929948i
$$388$$ 0 0
$$389$$ −5.29423 + 19.7583i −0.268428 + 1.00179i 0.691691 + 0.722194i $$0.256866\pi$$
−0.960119 + 0.279593i $$0.909800\pi$$
$$390$$ 0 0
$$391$$ −23.4904 13.5622i −1.18796 0.685869i
$$392$$ 0 0
$$393$$ −9.92820 + 9.92820i −0.500812 + 0.500812i
$$394$$ 0 0
$$395$$ 8.78461 + 8.78461i 0.442002 + 0.442002i
$$396$$ 0 0
$$397$$ −9.26795 + 9.26795i −0.465145 + 0.465145i −0.900337 0.435192i $$-0.856680\pi$$
0.435192 + 0.900337i $$0.356680\pi$$
$$398$$ 0 0
$$399$$ 15.2942 4.09808i 0.765669 0.205160i
$$400$$ 0 0
$$401$$ −1.79423 + 3.10770i −0.0895995 + 0.155191i −0.907342 0.420393i $$-0.861892\pi$$
0.817742 + 0.575584i $$0.195225\pi$$
$$402$$ 0 0
$$403$$ 1.80385 + 0.483340i 0.0898560 + 0.0240769i
$$404$$ 0 0
$$405$$ −6.58846 6.58846i −0.327383 0.327383i
$$406$$ 0 0
$$407$$ −25.3923 + 14.6603i −1.25865 + 0.726682i
$$408$$ 0 0
$$409$$ 27.8660 + 16.0885i 1.37789 + 0.795523i 0.991905 0.126984i $$-0.0405295\pi$$
0.385981 + 0.922507i $$0.373863\pi$$
$$410$$ 0 0
$$411$$ −14.3038 8.25833i −0.705557 0.407353i
$$412$$ 0 0
$$413$$ 14.6603 14.6603i 0.721384 0.721384i
$$414$$ 0 0
$$415$$ 1.46410 0.0718699
$$416$$ 0 0
$$417$$ −14.4904 14.4904i −0.709597 0.709597i
$$418$$ 0 0
$$419$$ −1.77757 6.63397i −0.0868399 0.324091i 0.908816 0.417196i $$-0.136987\pi$$
−0.995656 + 0.0931055i $$0.970321\pi$$
$$420$$ 0 0
$$421$$ 8.19615 30.5885i 0.399456 1.49079i −0.414600 0.910004i $$-0.636078\pi$$
0.814056 0.580786i $$-0.197255\pi$$
$$422$$ 0 0
$$423$$ 22.9808 1.11736
$$424$$ 0 0
$$425$$ 19.5000 11.2583i 0.945889 0.546109i
$$426$$ 0 0
$$427$$ −30.5885 + 8.19615i −1.48028 + 0.396640i
$$428$$ 0 0
$$429$$ 13.2224 + 22.9019i 0.638385 + 1.10572i
$$430$$ 0 0
$$431$$ 16.1962 0.780141 0.390071 0.920785i $$-0.372451\pi$$
0.390071 + 0.920785i $$0.372451\pi$$
$$432$$ 0 0
$$433$$ −5.73205 −0.275465 −0.137732 0.990469i $$-0.543981\pi$$
−0.137732 + 0.990469i $$0.543981\pi$$
$$434$$ 0 0
$$435$$ −2.19615 3.80385i −0.105297 0.182381i
$$436$$ 0 0
$$437$$ 15.2942 4.09808i 0.731622 0.196038i
$$438$$ 0 0
$$439$$ 22.8564 13.1962i 1.09088 0.629818i 0.157067 0.987588i $$-0.449796\pi$$
0.933810 + 0.357770i $$0.116463\pi$$
$$440$$ 0 0
$$441$$ 0.696152 + 1.20577i 0.0331501 + 0.0574177i
$$442$$ 0 0
$$443$$ 4.62436 17.2583i 0.219710 0.819968i −0.764745 0.644332i $$-0.777135\pi$$
0.984455 0.175636i $$-0.0561980\pi$$
$$444$$ 0 0
$$445$$ 0.535898 + 2.00000i 0.0254040 + 0.0948091i
$$446$$ 0 0
$$447$$ −9.92820 9.92820i −0.469588 0.469588i
$$448$$ 0 0
$$449$$ −3.33975 −0.157612 −0.0788062 0.996890i $$-0.525111\pi$$
−0.0788062 + 0.996890i $$0.525111\pi$$
$$450$$ 0 0
$$451$$ 9.29423 9.29423i 0.437648 0.437648i
$$452$$ 0 0
$$453$$ 1.09808 + 0.633975i 0.0515921 + 0.0297867i
$$454$$ 0 0
$$455$$ −8.53590 4.92820i −0.400169 0.231038i
$$456$$ 0 0
$$457$$ 2.25833 1.30385i 0.105640 0.0609914i −0.446249 0.894909i $$-0.647240\pi$$
0.551889 + 0.833917i $$0.313907\pi$$
$$458$$ 0 0
$$459$$ −29.7846 −1.39023
$$460$$ 0 0
$$461$$ 35.6865 + 9.56218i 1.66209 + 0.445355i 0.962961 0.269642i $$-0.0869055\pi$$
0.699127 + 0.714997i $$0.253572\pi$$
$$462$$ 0 0
$$463$$ −1.19615 + 2.07180i −0.0555899 + 0.0962846i −0.892481 0.451085i $$-0.851037\pi$$
0.836891 + 0.547369i $$0.184371\pi$$
$$464$$ 0 0
$$465$$ −0.928203 + 0.248711i −0.0430444 + 0.0115337i
$$466$$ 0 0
$$467$$ −2.63397 + 2.63397i −0.121886 + 0.121886i −0.765419 0.643533i $$-0.777468\pi$$
0.643533 + 0.765419i $$0.277468\pi$$
$$468$$ 0 0
$$469$$ −13.1962 13.1962i −0.609342 0.609342i
$$470$$ 0 0
$$471$$ 6.00000 6.00000i 0.276465 0.276465i
$$472$$ 0 0
$$473$$ −32.7224 18.8923i −1.50458 0.868669i
$$474$$ 0 0
$$475$$ −3.40192 + 12.6962i −0.156091 + 0.582539i
$$476$$ 0 0
$$477$$ 30.5885 8.19615i 1.40055 0.375276i
$$478$$ 0 0
$$479$$ −4.16987 7.22243i −0.190526 0.330001i 0.754898 0.655842i $$-0.227686\pi$$
−0.945425 + 0.325840i $$0.894353\pi$$
$$480$$ 0 0
$$481$$ −11.6603 + 20.1962i −0.531662 + 0.920865i
$$482$$ 0 0
$$483$$ 11.1962 + 19.3923i 0.509443 + 0.882380i
$$484$$ 0 0
$$485$$ −8.58846 8.58846i −0.389982 0.389982i
$$486$$ 0 0
$$487$$ 5.80385i 0.262997i 0.991316 + 0.131499i $$0.0419789\pi$$
−0.991316 + 0.131499i $$0.958021\pi$$
$$488$$ 0 0
$$489$$ −16.5622 4.43782i −0.748968 0.200685i
$$490$$ 0 0
$$491$$ 13.8923 3.72243i 0.626951 0.167991i 0.0686652 0.997640i $$-0.478126\pi$$
0.558286 + 0.829649i $$0.311459\pi$$
$$492$$ 0 0
$$493$$ −13.5622 3.63397i −0.610810 0.163666i
$$494$$ 0 0
$$495$$ −11.7846 6.80385i −0.529679 0.305810i
$$496$$ 0 0
$$497$$ −4.00000 6.92820i −0.179425 0.310772i
$$498$$ 0 0
$$499$$ 2.33013 + 8.69615i 0.104311 + 0.389293i 0.998266 0.0588630i $$-0.0187475\pi$$
−0.893955 + 0.448156i $$0.852081\pi$$
$$500$$ 0 0
$$501$$ 12.9282i 0.577590i
$$502$$ 0 0
$$503$$ 27.7128i 1.23565i −0.786314 0.617827i $$-0.788013\pi$$
0.786314 0.617827i $$-0.211987\pi$$
$$504$$ 0 0
$$505$$ 2.14359i 0.0953887i
$$506$$ 0 0
$$507$$ −1.28461 0.741670i −0.0570515 0.0329387i
$$508$$ 0 0
$$509$$ 3.07180 + 11.4641i 0.136155 + 0.508137i 0.999990 + 0.00436335i $$0.00138890\pi$$
−0.863835 + 0.503774i $$0.831944\pi$$
$$510$$ 0 0
$$511$$ −8.56218 14.8301i −0.378768 0.656046i
$$512$$ 0 0
$$513$$ 12.2942 12.2942i 0.542803 0.542803i
$$514$$ 0 0
$$515$$ −15.1244 4.05256i −0.666459 0.178577i
$$516$$ 0 0
$$517$$ 32.4186 8.68653i 1.42577 0.382033i
$$518$$ 0 0
$$519$$ −0.758330 2.83013i −0.0332870 0.124229i
$$520$$ 0 0
$$521$$ 13.0000i 0.569540i −0.958596 0.284770i $$-0.908083\pi$$
0.958596 0.284770i $$-0.0919173\pi$$
$$522$$ 0 0
$$523$$ 7.53590 + 7.53590i 0.329522 + 0.329522i 0.852405 0.522883i $$-0.175143\pi$$
−0.522883 + 0.852405i $$0.675143\pi$$
$$524$$ 0 0
$$525$$ −18.5885 −0.811267
$$526$$ 0 0
$$527$$ −1.53590 + 2.66025i −0.0669048 + 0.115882i
$$528$$ 0 0
$$529$$ −0.303848 0.526279i −0.0132108 0.0228817i
$$530$$ 0 0
$$531$$ 5.89230 21.9904i 0.255704 0.954301i
$$532$$ 0 0
$$533$$ 2.70577 10.0981i 0.117200 0.437396i
$$534$$ 0 0
$$535$$ −15.8372 9.14359i −0.684701 0.395312i
$$536$$ 0 0
$$537$$ −4.56218 1.22243i −0.196873 0.0527518i
$$538$$ 0 0
$$539$$ 1.43782 + 1.43782i 0.0619314 + 0.0619314i
$$540$$ 0 0
$$541$$ 2.19615 2.19615i 0.0944200 0.0944200i −0.658319 0.752739i $$-0.728732\pi$$
0.752739 + 0.658319i $$0.228732\pi$$
$$542$$ 0 0
$$543$$ −4.68653 + 17.4904i −0.201118 + 0.750584i
$$544$$ 0 0
$$545$$ 7.85641 13.6077i 0.336531 0.582890i
$$546$$ 0 0
$$547$$ −32.6244 8.74167i −1.39492 0.373767i −0.518400 0.855138i $$-0.673472\pi$$
−0.876517 + 0.481371i $$0.840139\pi$$
$$548$$ 0 0
$$549$$ −24.5885 + 24.5885i −1.04941 + 1.04941i
$$550$$ 0 0
$$551$$ 7.09808 4.09808i 0.302388 0.174584i
$$552$$ 0 0
$$553$$ −28.3923 16.3923i −1.20736 0.697072i
$$554$$ 0 0
$$555$$ 12.0000i 0.509372i
$$556$$ 0 0
$$557$$ −14.8038 + 14.8038i −0.627259 + 0.627259i −0.947378 0.320118i $$-0.896277\pi$$
0.320118 + 0.947378i $$0.396277\pi$$
$$558$$ 0 0
$$559$$ −30.0526 −1.27109
$$560$$ 0 0
$$561$$ −42.0167 + 11.2583i −1.77394 + 0.475327i
$$562$$ 0 0
$$563$$ 7.23205 + 26.9904i 0.304795 + 1.13751i 0.933122 + 0.359560i $$0.117073\pi$$
−0.628327 + 0.777949i $$0.716260\pi$$
$$564$$ 0 0
$$565$$ −3.71281 + 13.8564i −0.156199 + 0.582943i
$$566$$ 0 0
$$567$$ 21.2942 + 12.2942i 0.894274 + 0.516309i
$$568$$ 0 0
$$569$$ −18.4019 + 10.6244i −0.771449 + 0.445396i −0.833391 0.552684i $$-0.813604\pi$$
0.0619424 + 0.998080i $$0.480270\pi$$
$$570$$ 0 0
$$571$$ 3.33013 0.892305i 0.139361 0.0373418i −0.188464 0.982080i $$-0.560351\pi$$
0.327825 + 0.944738i $$0.393684\pi$$
$$572$$ 0 0
$$573$$ 20.8301 36.0788i 0.870191 1.50722i
$$574$$ 0 0
$$575$$ −18.5885 −0.775192
$$576$$ 0 0
$$577$$ −5.78461 −0.240816 −0.120408 0.992724i $$-0.538420\pi$$
−0.120408 + 0.992724i $$0.538420\pi$$
$$578$$ 0 0
$$579$$ 37.6410 1.56431
$$580$$ 0 0
$$581$$ −3.73205 + 1.00000i −0.154832 + 0.0414870i
$$582$$ 0 0
$$583$$ 40.0526 23.1244i 1.65881 0.957713i
$$584$$ 0 0
$$585$$ −10.8231 −0.447480
$$586$$ 0 0
$$587$$ −7.23205 + 26.9904i −0.298499 + 1.11401i 0.639900 + 0.768458i $$0.278976\pi$$
−0.938399 + 0.345554i $$0.887691\pi$$
$$588$$ 0 0
$$589$$ −0.464102 1.73205i −0.0191230 0.0713679i
$$590$$ 0 0
$$591$$ 8.66025 32.3205i 0.356235 1.32949i
$$592$$ 0 0
$$593$$ 17.4641 0.717165 0.358582 0.933498i $$-0.383260\pi$$
0.358582 + 0.933498i $$0.383260\pi$$
$$594$$ 0 0
$$595$$ 11.4641 11.4641i 0.469982 0.469982i
$$596$$ 0 0
$$597$$ 37.6865 21.7583i 1.54241 0.890509i
$$598$$ 0 0
$$599$$ −11.3205 6.53590i −0.462543 0.267050i 0.250570 0.968099i $$-0.419382\pi$$
−0.713113 + 0.701049i $$0.752715\pi$$
$$600$$ 0 0
$$601$$ −20.5526 + 11.8660i −0.838356 + 0.484025i −0.856705 0.515806i $$-0.827492\pi$$
0.0183488 + 0.999832i $$0.494159\pi$$
$$602$$ 0 0
$$603$$ −19.7942 5.30385i −0.806083 0.215989i
$$604$$ 0 0
$$605$$ −8.19615 2.19615i −0.333221 0.0892863i
$$606$$ 0 0
$$607$$ 8.58846 14.8756i 0.348595 0.603784i −0.637405 0.770529i $$-0.719992\pi$$
0.986000 + 0.166745i $$0.0533256\pi$$
$$608$$ 0 0
$$609$$ 8.19615 + 8.19615i 0.332125 + 0.332125i
$$610$$ 0 0
$$611$$ 18.8756 18.8756i 0.763627 0.763627i
$$612$$ 0 0
$$613$$ −15.6603 15.6603i −0.632512 0.632512i 0.316186 0.948697i $$-0.397598\pi$$
−0.948697 + 0.316186i $$0.897598\pi$$
$$614$$ 0 0
$$615$$ 1.39230 + 5.19615i 0.0561432 + 0.209529i
$$616$$ 0 0
$$617$$ −35.0885 20.2583i −1.41261 0.815570i −0.416975 0.908918i $$-0.636910\pi$$
−0.995633 + 0.0933485i $$0.970243\pi$$
$$618$$ 0 0
$$619$$ −4.17949 + 15.5981i −0.167988 + 0.626940i 0.829652 + 0.558281i $$0.188539\pi$$
−0.997640 + 0.0686590i $$0.978128\pi$$
$$620$$ 0 0
$$621$$ 21.2942 + 12.2942i 0.854508 + 0.493350i
$$622$$ 0 0
$$623$$ −2.73205 4.73205i −0.109457 0.189586i
$$624$$ 0 0
$$625$$ 5.03590 8.72243i 0.201436 0.348897i
$$626$$ 0 0
$$627$$ 12.6962 21.9904i 0.507035 0.878211i
$$628$$ 0 0
$$629$$ −27.1244 27.1244i −1.08152 1.08152i
$$630$$ 0 0
$$631$$ 17.6077i 0.700951i 0.936572 + 0.350476i $$0.113980\pi$$
−0.936572 + 0.350476i $$0.886020\pi$$
$$632$$ 0 0
$$633$$ 5.19615 5.19615i 0.206529 0.206529i
$$634$$ 0 0
$$635$$ −4.19615 + 1.12436i −0.166519 + 0.0446187i
$$636$$ 0 0
$$637$$ 1.56218 + 0.418584i 0.0618957 + 0.0165849i
$$638$$ 0 0
$$639$$ −7.60770 4.39230i −0.300956 0.173757i
$$640$$ 0 0
$$641$$ −19.7942 34.2846i −0.781825 1.35416i −0.930878 0.365331i $$-0.880956\pi$$
0.149053 0.988829i $$-0.452378\pi$$
$$642$$ 0 0
$$643$$ 2.34936 + 8.76795i 0.0926499 + 0.345774i 0.996653 0.0817525i $$-0.0260517\pi$$
−0.904003 + 0.427527i $$0.859385\pi$$
$$644$$ 0 0
$$645$$ 13.3923 7.73205i 0.527321 0.304449i
$$646$$ 0 0
$$647$$ 16.7321i 0.657805i 0.944364 + 0.328902i $$0.106679\pi$$
−0.944364 + 0.328902i $$0.893321\pi$$
$$648$$ 0 0
$$649$$ 33.2487i 1.30513i
$$650$$ 0 0
$$651$$ 2.19615 1.26795i 0.0860740 0.0496948i
$$652$$ 0 0
$$653$$ 7.36603 + 27.4904i 0.288255 + 1.07578i 0.946428 + 0.322915i $$0.104663\pi$$
−0.658173 + 0.752867i $$0.728671\pi$$
$$654$$ 0 0
$$655$$ −4.19615 7.26795i −0.163957 0.283982i
$$656$$ 0 0
$$657$$ −16.2846 9.40192i −0.635323 0.366804i
$$658$$ 0 0
$$659$$ 15.0263 + 4.02628i 0.585341 + 0.156842i 0.539323 0.842099i $$-0.318680\pi$$
0.0460178 + 0.998941i $$0.485347\pi$$
$$660$$ 0 0
$$661$$ −8.19615 + 2.19615i −0.318793 + 0.0854204i −0.414667 0.909973i $$-0.636102\pi$$
0.0958740 + 0.995393i $$0.469435\pi$$
$$662$$ 0 0
$$663$$ −24.4641 + 24.4641i −0.950107 + 0.950107i
$$664$$ 0 0
$$665$$ 9.46410i 0.367002i
$$666$$ 0 0
$$667$$ 8.19615 + 8.19615i 0.317356 + 0.317356i
$$668$$ 0 0
$$669$$ 13.9019 24.0788i 0.537479 0.930942i
$$670$$ 0 0
$$671$$ −25.3923 + 43.9808i −0.980259 + 1.69786i
$$672$$ 0 0
$$673$$ 19.1962 + 33.2487i 0.739957 + 1.28164i 0.952514 + 0.304495i $$0.0984877\pi$$
−0.212557 + 0.977149i $$0.568179\pi$$
$$674$$ 0 0
$$675$$ −17.6769 + 10.2058i −0.680385 + 0.392820i
$$676$$ 0 0
$$677$$ 1.26795 4.73205i 0.0487312 0.181867i −0.937270 0.348603i $$-0.886656\pi$$
0.986002 + 0.166736i $$0.0533227\pi$$
$$678$$ 0 0
$$679$$ 27.7583 + 16.0263i 1.06527 + 0.615032i
$$680$$ 0 0
$$681$$ 0.990381 + 3.69615i 0.0379515 + 0.141637i
$$682$$ 0 0
$$683$$ 20.2942 + 20.2942i 0.776537 + 0.776537i 0.979240 0.202703i $$-0.0649726\pi$$
−0.202703 + 0.979240i $$0.564973\pi$$
$$684$$ 0 0
$$685$$ 6.98076 6.98076i 0.266721 0.266721i
$$686$$ 0 0
$$687$$ −8.66025 8.66025i −0.330409 0.330409i
$$688$$ 0 0
$$689$$ 18.3923 31.8564i 0.700691 1.21363i
$$690$$ 0 0
$$691$$ −9.29423 2.49038i −0.353569 0.0947386i 0.0776628 0.996980i $$-0.475254\pi$$
−0.431232 + 0.902241i $$0.641921\pi$$
$$692$$ 0 0
$$693$$ 34.6865 + 9.29423i 1.31763 + 0.353059i
$$694$$ 0 0
$$695$$ 10.6077 6.12436i 0.402373 0.232310i
$$696$$ 0 0
$$697$$ 14.8923 + 8.59808i 0.564086 + 0.325675i
$$698$$ 0 0
$$699$$ 4.79423 2.76795i 0.181334 0.104693i
$$700$$ 0 0
$$701$$ −6.66025 + 6.66025i −0.251554 + 0.251554i −0.821608 0.570053i $$-0.806923\pi$$
0.570053 + 0.821608i $$0.306923\pi$$
$$702$$ 0 0
$$703$$ 22.3923 0.844542
$$704$$ 0 0
$$705$$ −3.55514 + 13.2679i −0.133894 + 0.499700i
$$706$$ 0 0
$$707$$ 1.46410 + 5.46410i 0.0550632 + 0.205499i
$$708$$ 0 0
$$709$$ −9.80385 + 36.5885i −0.368191 + 1.37411i 0.494852 + 0.868978i $$0.335222\pi$$
−0.863043 + 0.505131i $$0.831444\pi$$
$$710$$ 0 0
$$711$$ −36.0000 −1.35011
$$712$$ 0 0
$$713$$ 2.19615 1.26795i 0.0822466 0.0474851i
$$714$$ 0 0
$$715$$ −15.2679 + 4.09103i −0.570989 + 0.152996i
$$716$$ 0 0
$$717$$ −27.3731 −1.02227
$$718$$ 0 0
$$719$$ −4.39230 −0.163805 −0.0819027 0.996640i $$-0.526100\pi$$
−0.0819027 + 0.996640i $$0.526100\pi$$
$$720$$ 0 0
$$721$$ 41.3205 1.53886
$$722$$ 0 0
$$723$$ −20.0885 + 34.7942i −0.747098 + 1.29401i
$$724$$ 0 0
$$725$$ −9.29423 + 2.49038i −0.345179 + 0.0924904i
$$726$$ 0 0
$$727$$ 28.8109 16.6340i 1.06854 0.616920i 0.140755 0.990044i $$-0.455047\pi$$
0.927781 + 0.373124i $$0.121714\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 12.7942 47.7487i 0.473212 1.76605i
$$732$$ 0 0
$$733$$ 2.95448 + 11.0263i 0.109126 + 0.407265i 0.998781 0.0493698i $$-0.0157213\pi$$
−0.889654 + 0.456635i $$0.849055\pi$$
$$734$$ 0 0
$$735$$ −0.803848 + 0.215390i −0.0296504 + 0.00794479i
$$736$$ 0 0
$$737$$ −29.9282 −1.10242
$$738$$ 0 0
$$739$$ 8.22243 8.22243i 0.302467 0.302467i −0.539511 0.841978i $$-0.681391\pi$$
0.841978 + 0.539511i $$0.181391\pi$$
$$740$$ 0 0
$$741$$ 20.1962i 0.741924i
$$742$$ 0 0
$$743$$ −24.7583 14.2942i −0.908295 0.524404i −0.0284129 0.999596i $$-0.509045\pi$$
−0.879882 + 0.475192i $$0.842379\pi$$
$$744$$ 0 0
$$745$$ 7.26795 4.19615i 0.266277 0.153735i
$$746$$ 0 0
$$747$$ −3.00000 + 3.00000i −0.109764 + 0.109764i
$$748$$ 0 0
$$749$$ 46.6147 + 12.4904i 1.70327 + 0.456389i
$$750$$ 0 0
$$751$$ 8.85641 15.3397i 0.323175 0.559755i −0.657966 0.753047i $$-0.728583\pi$$
0.981141 + 0.193292i $$0.0619165\pi$$
$$752$$ 0 0
$$753$$ 3.69615 13.7942i 0.134695 0.502690i
$$754$$ 0 0
$$755$$ −0.535898 + 0.535898i −0.0195033 + 0.0195033i
$$756$$ 0 0
$$757$$ −19.9282 19.9282i −0.724303 0.724303i 0.245176 0.969479i $$-0.421154\pi$$
−0.969479 + 0.245176i $$0.921154\pi$$
$$758$$ 0 0
$$759$$ 34.6865 + 9.29423i 1.25904 + 0.337359i
$$760$$ 0 0
$$761$$ 45.3731 + 26.1962i 1.64477 + 0.949610i 0.979104 + 0.203363i $$0.0651870\pi$$
0.665669 + 0.746247i $$0.268146\pi$$
$$762$$ 0 0
$$763$$ −10.7321 + 40.0526i −0.388526 + 1.45000i
$$764$$ 0 0
$$765$$ 4.60770 17.1962i 0.166592 0.621728i
$$766$$ 0 0
$$767$$ −13.2224 22.9019i −0.477434 0.826941i
$$768$$ 0 0
$$769$$ −14.1244 + 24.4641i −0.509337 + 0.882198i 0.490604 + 0.871383i $$0.336776\pi$$
−0.999942 + 0.0108155i $$0.996557\pi$$
$$770$$ 0 0
$$771$$ −32.6603 −1.17623
$$772$$ 0 0
$$773$$ 35.5885 + 35.5885i 1.28003 + 1.28003i 0.940650 + 0.339378i $$0.110216\pi$$
0.339378 + 0.940650i $$0.389784\pi$$
$$774$$ 0 0
$$775$$ 2.10512i 0.0756181i
$$776$$ 0 0
$$777$$ 8.19615 + 30.5885i 0.294035 + 1.09735i
$$778$$ 0 0
$$779$$ −9.69615 + 2.59808i −0.347401 + 0.0930857i
$$780$$ 0 0
$$781$$ −12.3923 3.32051i −0.443432 0.118817i
$$782$$ 0 0
$$783$$ 12.2942 + 3.29423i 0.439360 + 0.117726i
$$784$$ 0 0
$$785$$ 2.53590 + 4.39230i 0.0905101 + 0.156768i
$$786$$ 0 0
$$787$$ 10.8109 + 40.3468i 0.385367 + 1.43821i 0.837588 + 0.546302i $$0.183965\pi$$
−0.452222 + 0.891906i $$0.649368\pi$$
$$788$$ 0 0
$$789$$ −4.31347 2.49038i −0.153563 0.0886599i
$$790$$ 0 0
$$791$$ 37.8564i 1.34602i
$$792$$ 0 0
$$793$$ 40.3923i 1.43437i
$$794$$