# Properties

 Label 1728.2.bc.a.1009.1 Level $1728$ Weight $2$ Character 1728.1009 Analytic conductor $13.798$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1728 = 2^{6} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1728.bc (of order $$12$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.7981494693$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 144) Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 1009.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1728.1009 Dual form 1728.2.bc.a.721.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 0.267949i) q^{5} +(-2.36603 + 1.36603i) q^{7} +O(q^{10})$$ $$q+(-1.00000 + 0.267949i) q^{5} +(-2.36603 + 1.36603i) q^{7} +(1.13397 - 4.23205i) q^{11} +(0.901924 + 3.36603i) q^{13} +5.73205 q^{17} +(2.36603 - 2.36603i) q^{19} +(-4.09808 - 2.36603i) q^{23} +(-3.40192 + 1.96410i) q^{25} +(-2.36603 - 0.633975i) q^{29} +(0.267949 - 0.464102i) q^{31} +(2.00000 - 2.00000i) q^{35} +(4.73205 + 4.73205i) q^{37} +(2.59808 + 1.50000i) q^{41} +(-2.23205 + 8.33013i) q^{43} +(3.83013 + 6.63397i) q^{47} +(0.232051 - 0.401924i) q^{49} +(7.46410 + 7.46410i) q^{53} +4.53590i q^{55} +(7.33013 - 1.96410i) q^{59} +(11.1962 + 3.00000i) q^{61} +(-1.80385 - 3.12436i) q^{65} +(1.76795 + 6.59808i) q^{67} -2.92820i q^{71} +6.26795i q^{73} +(3.09808 + 11.5622i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-1.36603 - 0.366025i) q^{83} +(-5.73205 + 1.53590i) q^{85} -2.00000i q^{89} +(-6.73205 - 6.73205i) q^{91} +(-1.73205 + 3.00000i) q^{95} +(-5.86603 - 10.1603i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{5} - 6q^{7} + O(q^{10})$$ $$4q - 4q^{5} - 6q^{7} + 8q^{11} + 14q^{13} + 16q^{17} + 6q^{19} - 6q^{23} - 24q^{25} - 6q^{29} + 8q^{31} + 8q^{35} + 12q^{37} - 2q^{43} - 2q^{47} - 6q^{49} + 16q^{53} + 12q^{59} + 24q^{61} - 28q^{65} + 14q^{67} + 2q^{77} + 24q^{79} - 2q^{83} - 16q^{85} - 20q^{91} - 20q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$703$$ $$1217$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −1.00000 + 0.267949i −0.447214 + 0.119831i −0.475395 0.879772i $$-0.657695\pi$$
0.0281817 + 0.999603i $$0.491028\pi$$
$$6$$ 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
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.13397 4.23205i 0.341906 1.27601i −0.554279 0.832331i $$-0.687006\pi$$
0.896185 0.443680i $$-0.146327\pi$$
$$12$$ 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
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 5.73205 1.39023 0.695113 0.718900i $$-0.255354\pi$$
0.695113 + 0.718900i $$0.255354\pi$$
$$18$$ 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
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.09808 2.36603i −0.854508 0.493350i 0.00766135 0.999971i $$-0.497561\pi$$
−0.862169 + 0.506620i $$0.830895\pi$$
$$24$$ 0 0
$$25$$ −3.40192 + 1.96410i −0.680385 + 0.392820i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.36603 0.633975i −0.439360 0.117726i 0.0323566 0.999476i $$-0.489699\pi$$
−0.471717 + 0.881750i $$0.656365\pi$$
$$30$$ 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
$$33$$ 0 0
$$34$$ 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
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2.59808 + 1.50000i 0.405751 + 0.234261i 0.688963 0.724797i $$-0.258066\pi$$
−0.283211 + 0.959058i $$0.591400\pi$$
$$42$$ 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 0
$$46$$ 0 0
$$47$$ 3.83013 + 6.63397i 0.558681 + 0.967665i 0.997607 + 0.0691412i $$0.0220259\pi$$
−0.438925 + 0.898523i $$0.644641\pi$$
$$48$$ 0 0
$$49$$ 0.232051 0.401924i 0.0331501 0.0574177i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 7.46410 + 7.46410i 1.02527 + 1.02527i 0.999672 + 0.0256010i $$0.00814993\pi$$
0.0256010 + 0.999672i $$0.491850\pi$$
$$54$$ 0 0
$$55$$ 4.53590i 0.611620i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 7.33013 1.96410i 0.954301 0.255704i 0.252115 0.967697i $$-0.418874\pi$$
0.702186 + 0.711993i $$0.252207\pi$$
$$60$$ 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
$$63$$ 0 0
$$64$$ 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
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 2.92820i 0.347514i −0.984789 0.173757i $$-0.944409\pi$$
0.984789 0.173757i $$-0.0555907\pi$$
$$72$$ 0 0
$$73$$ 6.26795i 0.733608i 0.930298 + 0.366804i $$0.119548\pi$$
−0.930298 + 0.366804i $$0.880452\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 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
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1.36603 0.366025i −0.149941 0.0401765i 0.183068 0.983100i $$-0.441397\pi$$
−0.333009 + 0.942924i $$0.608064\pi$$
$$84$$ 0 0
$$85$$ −5.73205 + 1.53590i −0.621728 + 0.166592i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.00000i 0.212000i −0.994366 0.106000i $$-0.966196\pi$$
0.994366 0.106000i $$-0.0338043\pi$$
$$90$$ 0 0
$$91$$ −6.73205 6.73205i −0.705711 0.705711i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 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
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −0.535898 + 2.00000i −0.0533239 + 0.199007i −0.987449 0.157938i $$-0.949515\pi$$
0.934125 + 0.356946i $$0.116182\pi$$
$$102$$ 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
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 12.4904 + 12.4904i 1.20749 + 1.20749i 0.971837 + 0.235654i $$0.0757231\pi$$
0.235654 + 0.971837i $$0.424277\pi$$
$$108$$ 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
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 6.92820 12.0000i 0.651751 1.12887i −0.330947 0.943649i $$-0.607368\pi$$
0.982698 0.185216i $$-0.0592984\pi$$
$$114$$ 0 0
$$115$$ 4.73205 + 1.26795i 0.441266 + 0.118237i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 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
$$123$$ 0 0
$$124$$ 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
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2.09808 + 7.83013i 0.183310 + 0.684121i 0.994986 + 0.100014i $$0.0318887\pi$$
−0.811676 + 0.584108i $$0.801445\pi$$
$$132$$ 0 0
$$133$$ −2.36603 + 8.83013i −0.205160 + 0.765669i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −8.25833 + 4.76795i −0.705557 + 0.407353i −0.809414 0.587239i $$-0.800215\pi$$
0.103857 + 0.994592i $$0.466882\pi$$
$$138$$ 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
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 15.2679 1.27677
$$144$$ 0 0
$$145$$ 2.53590 0.210595
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −7.83013 + 2.09808i −0.641469 + 0.171881i −0.564869 0.825181i $$-0.691073\pi$$
−0.0766003 + 0.997062i $$0.524407\pi$$
$$150$$ 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
$$153$$ 0 0
$$154$$ 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
$$159$$ 0 0
$$160$$ 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
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.46410 + 3.73205i 0.500207 + 0.288795i 0.728799 0.684728i $$-0.240079\pi$$
−0.228592 + 0.973522i $$0.573412\pi$$
$$168$$ 0 0
$$169$$ 0.741670 0.428203i 0.0570515 0.0329387i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1.63397 0.437822i −0.124229 0.0332870i 0.196169 0.980570i $$-0.437150\pi$$
−0.320398 + 0.947283i $$0.603817\pi$$
$$174$$ 0 0
$$175$$ 5.36603 9.29423i 0.405633 0.702578i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1.92820 + 1.92820i −0.144121 + 0.144121i −0.775486 0.631365i $$-0.782495\pi$$
0.631365 + 0.775486i $$0.282495\pi$$
$$180$$ 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
$$183$$ 0 0
$$184$$ 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
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −12.0263 20.8301i −0.870191 1.50722i −0.861799 0.507250i $$-0.830662\pi$$
−0.00839227 0.999965i $$-0.502671\pi$$
$$192$$ 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
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −13.6603 13.6603i −0.973253 0.973253i 0.0263987 0.999651i $$-0.491596\pi$$
−0.999651 + 0.0263987i $$0.991596\pi$$
$$198$$ 0 0
$$199$$ 25.1244i 1.78102i 0.454965 + 0.890509i $$0.349652\pi$$
−0.454965 + 0.890509i $$0.650348\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 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
$$207$$ 0 0
$$208$$ 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
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 8.92820i 0.608898i
$$216$$ 0 0
$$217$$ 1.46410i 0.0993897i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 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
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2.13397 + 0.571797i 0.141637 + 0.0379515i 0.328941 0.944351i $$-0.393308\pi$$
−0.187304 + 0.982302i $$0.559975\pi$$
$$228$$ 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
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3.19615i 0.209387i −0.994505 0.104693i $$-0.966614\pi$$
0.994505 0.104693i $$-0.0333861\pi$$
$$234$$ 0 0
$$235$$ −5.60770 5.60770i −0.365806 0.365806i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −7.90192 + 13.6865i −0.511133 + 0.885308i 0.488784 + 0.872405i $$0.337441\pi$$
−0.999917 + 0.0129033i $$0.995893\pi$$
$$240$$ 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
$$243$$ 0 0
$$244$$ 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 0
$$250$$ 0 0
$$251$$ −5.83013 5.83013i −0.367994 0.367994i 0.498751 0.866745i $$-0.333792\pi$$
−0.866745 + 0.498751i $$0.833792\pi$$
$$252$$ 0 0
$$253$$ −14.6603 + 14.6603i −0.921682 + 0.921682i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −9.42820 + 16.3301i −0.588115 + 1.01865i 0.406364 + 0.913711i $$0.366796\pi$$
−0.994479 + 0.104934i $$0.966537\pi$$
$$258$$ 0 0
$$259$$ −17.6603 4.73205i −1.09735 0.294035i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −2.49038 + 1.43782i −0.153563 + 0.0886599i −0.574813 0.818285i $$-0.694925\pi$$
0.421249 + 0.906945i $$0.361592\pi$$
$$264$$ 0 0
$$265$$ −9.46410 5.46410i −0.581375 0.335657i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.26795 + 1.26795i −0.0773082 + 0.0773082i −0.744704 0.667395i $$-0.767409\pi$$
0.667395 + 0.744704i $$0.267409\pi$$
$$270$$ 0 0
$$271$$ 0.392305 0.0238308 0.0119154 0.999929i $$-0.496207\pi$$
0.0119154 + 0.999929i $$0.496207\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 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 0
$$280$$ 0 0
$$281$$ 8.66025 5.00000i 0.516627 0.298275i −0.218926 0.975741i $$-0.570255\pi$$
0.735554 + 0.677466i $$0.236922\pi$$
$$282$$ 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
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −8.19615 −0.483804
$$288$$ 0 0
$$289$$ 15.8564 0.932730
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 5.36603 1.43782i 0.313487 0.0839985i −0.0986454 0.995123i $$-0.531451\pi$$
0.412132 + 0.911124i $$0.364784\pi$$
$$294$$ 0 0
$$295$$ −6.80385 + 3.92820i −0.396135 + 0.228709i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 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
$$303$$ 0 0
$$304$$ 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
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −19.0981 11.0263i −1.08295 0.625243i −0.151261 0.988494i $$-0.548333\pi$$
−0.931691 + 0.363251i $$0.881667\pi$$
$$312$$ 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
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 20.5622 + 5.50962i 1.15489 + 0.309451i 0.784922 0.619595i $$-0.212703\pi$$
0.369965 + 0.929046i $$0.379370\pi$$
$$318$$ 0 0
$$319$$ −5.36603 + 9.29423i −0.300440 + 0.520377i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 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
$$327$$ 0 0
$$328$$ 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
$$333$$ 0 0
$$334$$ 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
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.66025 1.66025i −0.0899078 0.0899078i
$$342$$ 0 0
$$343$$ 17.8564i 0.964155i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −17.6244 + 4.72243i −0.946125 + 0.253513i −0.698717 0.715398i $$-0.746245\pi$$
−0.247408 + 0.968911i $$0.579579\pi$$
$$348$$ 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
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −7.16025 12.4019i −0.381102 0.660088i 0.610118 0.792310i $$-0.291122\pi$$
−0.991220 + 0.132223i $$0.957789\pi$$
$$354$$ 0 0
$$355$$ 0.784610 + 2.92820i 0.0416428 + 0.155413i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 11.2679i 0.594700i −0.954769 0.297350i $$-0.903897\pi$$
0.954769 0.297350i $$-0.0961028\pi$$
$$360$$ 0 0
$$361$$ 7.80385i 0.410729i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 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
$$369$$ 0 0
$$370$$ 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
$$375$$ 0 0
$$376$$ 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
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −6.73205 + 11.6603i −0.343992 + 0.595811i −0.985170 0.171581i $$-0.945113\pi$$
0.641178 + 0.767392i $$0.278446\pi$$
$$384$$ 0 0
$$385$$ −6.19615 10.7321i −0.315785 0.546956i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 5.29423 19.7583i 0.268428 1.00179i −0.691691 0.722194i $$-0.743134\pi$$
0.960119 0.279593i $$-0.0901996\pi$$
$$390$$ 0 0
$$391$$ −23.4904 13.5622i −1.18796 0.685869i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 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
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1.79423 3.10770i 0.0895995 0.155191i −0.817742 0.575584i $$-0.804775\pi$$
0.907342 + 0.420393i $$0.138108\pi$$
$$402$$ 0 0
$$403$$ 1.80385 + 0.483340i 0.0898560 + 0.0240769i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 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
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −14.6603 + 14.6603i −0.721384 + 0.721384i
$$414$$ 0 0
$$415$$ 1.46410 0.0718699
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1.77757 + 6.63397i 0.0868399 + 0.324091i 0.995656 0.0931055i $$-0.0296794\pi$$
−0.908816 + 0.417196i $$0.863013\pi$$
$$420$$ 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
$$423$$ 0 0
$$424$$ 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
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −16.1962 −0.780141 −0.390071 0.920785i $$-0.627549\pi$$
−0.390071 + 0.920785i $$0.627549\pi$$
$$432$$ 0 0
$$433$$ −5.73205 −0.275465 −0.137732 0.990469i $$-0.543981\pi$$
−0.137732 + 0.990469i $$0.543981\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 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 0
$$442$$ 0 0
$$443$$ −4.62436 + 17.2583i −0.219710 + 0.819968i 0.764745 + 0.644332i $$0.222865\pi$$
−0.984455 + 0.175636i $$0.943802\pi$$
$$444$$ 0 0
$$445$$ 0.535898 + 2.00000i 0.0254040 + 0.0948091i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 3.33975 0.157612 0.0788062 0.996890i $$-0.474889\pi$$
0.0788062 + 0.996890i $$0.474889\pi$$
$$450$$ 0 0
$$451$$ 9.29423 9.29423i 0.437648 0.437648i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 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
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −35.6865 9.56218i −1.66209 0.445355i −0.699127 0.714997i $$-0.746428\pi$$
−0.962961 + 0.269642i $$0.913094\pi$$
$$462$$ 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 0
$$466$$ 0 0
$$467$$ 2.63397 2.63397i 0.121886 0.121886i −0.643533 0.765419i $$-0.722532\pi$$
0.765419 + 0.643533i $$0.222532\pi$$
$$468$$ 0 0
$$469$$ −13.1962 13.1962i −0.609342 0.609342i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 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
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 4.16987 + 7.22243i 0.190526 + 0.330001i 0.945425 0.325840i $$-0.105647\pi$$
−0.754898 + 0.655842i $$0.772314\pi$$
$$480$$ 0 0
$$481$$ −11.6603 + 20.1962i −0.531662 + 0.920865i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 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
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −13.8923 + 3.72243i −0.626951 + 0.167991i −0.558286 0.829649i $$-0.688541\pi$$
−0.0686652 + 0.997640i $$0.521874\pi$$
$$492$$ 0 0
$$493$$ −13.5622 3.63397i −0.610810 0.163666i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 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
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 27.7128i 1.23565i 0.786314 + 0.617827i $$0.211987\pi$$
−0.786314 + 0.617827i $$0.788013\pi$$
$$504$$ 0 0
$$505$$ 2.14359i 0.0953887i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −3.07180 11.4641i −0.136155 0.508137i −0.999990 0.00436335i $$-0.998611\pi$$
0.863835 0.503774i $$-0.168056\pi$$
$$510$$ 0 0
$$511$$ −8.56218 14.8301i −0.378768 0.656046i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 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 0
$$520$$ 0 0
$$521$$ 13.0000i 0.569540i 0.958596 + 0.284770i $$0.0919173\pi$$
−0.958596 + 0.284770i $$0.908083\pi$$
$$522$$ 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
$$525$$ 0 0
$$526$$ 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
$$531$$ 0 0
$$532$$ 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
$$537$$ 0 0
$$538$$ 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
$$543$$ 0 0
$$544$$ 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
$$549$$ 0 0
$$550$$ 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
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 14.8038 14.8038i 0.627259 0.627259i −0.320118 0.947378i $$-0.603723\pi$$
0.947378 + 0.320118i $$0.103723\pi$$
$$558$$ 0 0
$$559$$ −30.0526 −1.27109
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −7.23205 26.9904i −0.304795 1.13751i −0.933122 0.359560i $$-0.882927\pi$$
0.628327 0.777949i $$-0.283740\pi$$
$$564$$ 0 0
$$565$$ −3.71281 + 13.8564i −0.156199 + 0.582943i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.4019 10.6244i 0.771449 0.445396i −0.0619424 0.998080i $$-0.519730\pi$$
0.833391 + 0.552684i $$0.186396\pi$$
$$570$$ 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
$$573$$ 0 0
$$574$$ 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
$$579$$ 0 0
$$580$$ 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
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7.23205 26.9904i 0.298499 1.11401i −0.639900 0.768458i $$-0.721024\pi$$
0.938399 0.345554i $$-0.112309\pi$$
$$588$$ 0 0
$$589$$ −0.464102 1.73205i −0.0191230 0.0713679i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −17.4641 −0.717165 −0.358582 0.933498i $$-0.616740\pi$$
−0.358582 + 0.933498i $$0.616740\pi$$
$$594$$ 0 0
$$595$$ 11.4641 11.4641i 0.469982 0.469982i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 11.3205 + 6.53590i 0.462543 + 0.267050i 0.713113 0.701049i $$-0.247285\pi$$
−0.250570 + 0.968099i $$0.580618\pi$$
$$600$$ 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
$$603$$ 0 0
$$604$$ 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
$$609$$ 0 0
$$610$$ 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
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 35.0885 + 20.2583i 1.41261 + 0.815570i 0.995633 0.0933485i $$-0.0297571\pi$$
0.416975 + 0.908918i $$0.363090\pi$$
$$618$$ 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
$$621$$ 0 0
$$622$$ 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
$$627$$ 0 0
$$628$$ 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
$$633$$ 0 0
$$634$$ 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
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 19.7942 + 34.2846i 0.781825 + 1.35416i 0.930878 + 0.365331i $$0.119044\pi$$
−0.149053 + 0.988829i $$0.547622\pi$$
$$642$$ 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
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 16.7321i 0.657805i −0.944364 0.328902i $$-0.893321\pi$$
0.944364 0.328902i $$-0.106679\pi$$
$$648$$ 0 0
$$649$$ 33.2487i 1.30513i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −7.36603 27.4904i −0.288255 1.07578i −0.946428 0.322915i $$-0.895337\pi$$
0.658173 0.752867i $$-0.271329\pi$$
$$654$$ 0 0
$$655$$ −4.19615 7.26795i −0.163957 0.283982i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −15.0263 4.02628i −0.585341 0.156842i −0.0460178 0.998941i $$-0.514653\pi$$
−0.539323 + 0.842099i $$0.681320\pi$$
$$660$$ 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
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 9.46410i 0.367002i
$$666$$ 0 0
$$667$$ 8.19615 + 8.19615i 0.317356 + 0.317356i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 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
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1.26795 + 4.73205i −0.0487312 + 0.181867i −0.986002 0.166736i $$-0.946677\pi$$
0.937270 + 0.348603i $$0.113344\pi$$
$$678$$ 0 0
$$679$$ 27.7583 + 16.0263i 1.06527 + 0.615032i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −20.2942 20.2942i −0.776537 0.776537i 0.202703 0.979240i $$-0.435027\pi$$
−0.979240 + 0.202703i $$0.935027\pi$$
$$684$$ 0 0
$$685$$ 6.98076 6.98076i 0.266721 0.266721i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 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
$$693$$ 0 0
$$694$$ 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
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 6.66025 6.66025i 0.251554 0.251554i −0.570053 0.821608i $$-0.693077\pi$$
0.821608 + 0.570053i $$0.193077\pi$$
$$702$$ 0 0
$$703$$ 22.3923 0.844542
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 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
$$711$$ 0 0
$$712$$ 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
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 4.39230 0.163805 0.0819027 0.996640i $$-0.473900\pi$$
0.0819027 + 0.996640i $$0.473900\pi$$
$$720$$ 0 0
$$721$$ 41.3205 1.53886
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 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
$$729$$ 0 0
$$730$$ 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 0
$$736$$ 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
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.7583 + 14.2942i 0.908295 + 0.524404i 0.879882 0.475192i $$-0.157621\pi$$
0.0284129 + 0.999596i $$0.490955\pi$$
$$744$$ 0 0
$$745$$ 7.26795 4.19615i 0.266277 0.153735i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 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
$$753$$ 0 0
$$754$$ 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
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −45.3731 26.1962i −1.64477 0.949610i −0.979104 0.203363i $$-0.934813\pi$$
−0.665669 0.746247i $$-0.731854\pi$$
$$762$$ 0 0
$$763$$ −10.7321 + 40.0526i −0.388526 + 1.45000i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 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
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −35.5885 35.5885i −1.28003 1.28003i −0.940650 0.339378i $$-0.889784\pi$$
−0.339378 0.940650i $$-0.610216\pi$$
$$774$$ 0 0
$$775$$ 2.10512i 0.0756181i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 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
$$783$$ 0 0
$$784$$ 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
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 37.8564i 1.34602i
$$792$$ 0 0
$$793$$ 40.3923i 1.43437i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −8.17691 30.5167i −0.289641 1.08096i −0.945381 0.325968i $$-0.894310\pi$$
0.655740 0.754987i $$-0.272357\pi$$
$$798$$ 0 0
$$799$$ 21.9545 + 38.0263i 0.776694 + 1.34527i
$$800$$ 0 0