# Properties

 Label 1134.2.d.a.1133.4 Level $1134$ Weight $2$ Character 1134.1133 Analytic conductor $9.055$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}\cdot 3^{6}$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1133.4 Root $$-0.0967785 - 1.72934i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.1133 Dual form 1134.2.d.a.1133.12

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{4} -0.366598 q^{5} +(-1.91449 + 1.82612i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{4} -0.366598 q^{5} +(-1.91449 + 1.82612i) q^{7} +1.00000i q^{8} +0.366598i q^{10} -0.669453i q^{11} +1.00156i q^{13} +(1.82612 + 1.91449i) q^{14} +1.00000 q^{16} +4.98906 q^{17} -6.35722i q^{19} +0.366598 q^{20} -0.669453 q^{22} -7.69459i q^{23} -4.86561 q^{25} +1.00156 q^{26} +(1.91449 - 1.82612i) q^{28} -1.82898i q^{29} -6.32588i q^{31} -1.00000i q^{32} -4.98906i q^{34} +(0.701849 - 0.669453i) q^{35} -5.16789 q^{37} -6.35722 q^{38} -0.366598i q^{40} -4.31856 q^{41} -4.49843 q^{43} +0.669453i q^{44} -7.69459 q^{46} +8.32901 q^{47} +(0.330547 - 6.99219i) q^{49} +4.86561i q^{50} -1.00156i q^{52} +0.245420i q^{55} +(-1.82612 - 1.91449i) q^{56} -1.82898 q^{58} +8.72695 q^{59} -4.95771i q^{61} -6.32588 q^{62} -1.00000 q^{64} -0.367172i q^{65} -10.8907 q^{67} -4.98906 q^{68} +(-0.669453 - 0.701849i) q^{70} -5.49843i q^{71} +4.07314i q^{73} +5.16789i q^{74} +6.35722i q^{76} +(1.22250 + 1.28166i) q^{77} +8.35568 q^{79} -0.366598 q^{80} +4.31856i q^{82} +17.0142 q^{83} -1.82898 q^{85} +4.49843i q^{86} +0.669453 q^{88} -10.7113 q^{89} +(-1.82898 - 1.91749i) q^{91} +7.69459i q^{92} -8.32901i q^{94} +2.33055i q^{95} -17.2157i q^{97} +(-6.99219 - 0.330547i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 16 q^{4} - 4 q^{7} + O(q^{10})$$ $$16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ −0.366598 −0.163948 −0.0819738 0.996634i $$-0.526122\pi$$
−0.0819738 + 0.996634i $$0.526122\pi$$
$$6$$ 0 0
$$7$$ −1.91449 + 1.82612i −0.723609 + 0.690210i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 0.366598i 0.115929i
$$11$$ 0.669453i 0.201848i −0.994894 0.100924i $$-0.967820\pi$$
0.994894 0.100924i $$-0.0321799\pi$$
$$12$$ 0 0
$$13$$ 1.00156i 0.277784i 0.990308 + 0.138892i $$0.0443541\pi$$
−0.990308 + 0.138892i $$0.955646\pi$$
$$14$$ 1.82612 + 1.91449i 0.488052 + 0.511669i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.98906 1.21003 0.605013 0.796216i $$-0.293168\pi$$
0.605013 + 0.796216i $$0.293168\pi$$
$$18$$ 0 0
$$19$$ 6.35722i 1.45845i −0.684275 0.729224i $$-0.739881\pi$$
0.684275 0.729224i $$-0.260119\pi$$
$$20$$ 0.366598 0.0819738
$$21$$ 0 0
$$22$$ −0.669453 −0.142728
$$23$$ 7.69459i 1.60443i −0.597034 0.802216i $$-0.703654\pi$$
0.597034 0.802216i $$-0.296346\pi$$
$$24$$ 0 0
$$25$$ −4.86561 −0.973121
$$26$$ 1.00156 0.196423
$$27$$ 0 0
$$28$$ 1.91449 1.82612i 0.361805 0.345105i
$$29$$ 1.82898i 0.339633i −0.985476 0.169817i $$-0.945682\pi$$
0.985476 0.169817i $$-0.0543175\pi$$
$$30$$ 0 0
$$31$$ 6.32588i 1.13616i −0.822973 0.568081i $$-0.807686\pi$$
0.822973 0.568081i $$-0.192314\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 4.98906i 0.855617i
$$35$$ 0.701849 0.669453i 0.118634 0.113158i
$$36$$ 0 0
$$37$$ −5.16789 −0.849595 −0.424798 0.905288i $$-0.639655\pi$$
−0.424798 + 0.905288i $$0.639655\pi$$
$$38$$ −6.35722 −1.03128
$$39$$ 0 0
$$40$$ 0.366598i 0.0579643i
$$41$$ −4.31856 −0.674446 −0.337223 0.941425i $$-0.609488\pi$$
−0.337223 + 0.941425i $$0.609488\pi$$
$$42$$ 0 0
$$43$$ −4.49843 −0.686005 −0.343002 0.939335i $$-0.611444\pi$$
−0.343002 + 0.939335i $$0.611444\pi$$
$$44$$ 0.669453i 0.100924i
$$45$$ 0 0
$$46$$ −7.69459 −1.13450
$$47$$ 8.32901 1.21491 0.607455 0.794354i $$-0.292190\pi$$
0.607455 + 0.794354i $$0.292190\pi$$
$$48$$ 0 0
$$49$$ 0.330547 6.99219i 0.0472209 0.998884i
$$50$$ 4.86561i 0.688101i
$$51$$ 0 0
$$52$$ 1.00156i 0.138892i
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0.245420i 0.0330925i
$$56$$ −1.82612 1.91449i −0.244026 0.255835i
$$57$$ 0 0
$$58$$ −1.82898 −0.240157
$$59$$ 8.72695 1.13615 0.568076 0.822976i $$-0.307688\pi$$
0.568076 + 0.822976i $$0.307688\pi$$
$$60$$ 0 0
$$61$$ 4.95771i 0.634770i −0.948297 0.317385i $$-0.897195\pi$$
0.948297 0.317385i $$-0.102805\pi$$
$$62$$ −6.32588 −0.803387
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0.367172i 0.0455420i
$$66$$ 0 0
$$67$$ −10.8907 −1.33052 −0.665258 0.746614i $$-0.731678\pi$$
−0.665258 + 0.746614i $$0.731678\pi$$
$$68$$ −4.98906 −0.605013
$$69$$ 0 0
$$70$$ −0.669453 0.701849i −0.0800150 0.0838869i
$$71$$ 5.49843i 0.652544i −0.945276 0.326272i $$-0.894207\pi$$
0.945276 0.326272i $$-0.105793\pi$$
$$72$$ 0 0
$$73$$ 4.07314i 0.476725i 0.971176 + 0.238363i $$0.0766106\pi$$
−0.971176 + 0.238363i $$0.923389\pi$$
$$74$$ 5.16789i 0.600755i
$$75$$ 0 0
$$76$$ 6.35722i 0.729224i
$$77$$ 1.22250 + 1.28166i 0.139317 + 0.146059i
$$78$$ 0 0
$$79$$ 8.35568 0.940087 0.470044 0.882643i $$-0.344238\pi$$
0.470044 + 0.882643i $$0.344238\pi$$
$$80$$ −0.366598 −0.0409869
$$81$$ 0 0
$$82$$ 4.31856i 0.476905i
$$83$$ 17.0142 1.86756 0.933778 0.357852i $$-0.116491\pi$$
0.933778 + 0.357852i $$0.116491\pi$$
$$84$$ 0 0
$$85$$ −1.82898 −0.198381
$$86$$ 4.49843i 0.485079i
$$87$$ 0 0
$$88$$ 0.669453 0.0713640
$$89$$ −10.7113 −1.13540 −0.567699 0.823236i $$-0.692166\pi$$
−0.567699 + 0.823236i $$0.692166\pi$$
$$90$$ 0 0
$$91$$ −1.82898 1.91749i −0.191729 0.201007i
$$92$$ 7.69459i 0.802216i
$$93$$ 0 0
$$94$$ 8.32901i 0.859071i
$$95$$ 2.33055i 0.239109i
$$96$$ 0 0
$$97$$ 17.2157i 1.74799i −0.485932 0.873997i $$-0.661520\pi$$
0.485932 0.873997i $$-0.338480\pi$$
$$98$$ −6.99219 0.330547i −0.706318 0.0333902i
$$99$$ 0 0
$$100$$ 4.86561 0.486561
$$101$$ −15.7317 −1.56537 −0.782683 0.622421i $$-0.786149\pi$$
−0.782683 + 0.622421i $$0.786149\pi$$
$$102$$ 0 0
$$103$$ 11.4445i 1.12766i 0.825890 + 0.563831i $$0.190673\pi$$
−0.825890 + 0.563831i $$0.809327\pi$$
$$104$$ −1.00156 −0.0982115
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 11.0618i 1.06938i −0.845048 0.534690i $$-0.820428\pi$$
0.845048 0.534690i $$-0.179572\pi$$
$$108$$ 0 0
$$109$$ −10.5633 −1.01178 −0.505891 0.862597i $$-0.668836\pi$$
−0.505891 + 0.862597i $$0.668836\pi$$
$$110$$ 0.245420 0.0233999
$$111$$ 0 0
$$112$$ −1.91449 + 1.82612i −0.180902 + 0.172552i
$$113$$ 4.15953i 0.391295i 0.980674 + 0.195648i $$0.0626809\pi$$
−0.980674 + 0.195648i $$0.937319\pi$$
$$114$$ 0 0
$$115$$ 2.82082i 0.263043i
$$116$$ 1.82898i 0.169817i
$$117$$ 0 0
$$118$$ 8.72695i 0.803381i
$$119$$ −9.55151 + 9.11064i −0.875586 + 0.835171i
$$120$$ 0 0
$$121$$ 10.5518 0.959257
$$122$$ −4.95771 −0.448850
$$123$$ 0 0
$$124$$ 6.32588i 0.568081i
$$125$$ 3.61671 0.323489
$$126$$ 0 0
$$127$$ −1.66945 −0.148140 −0.0740700 0.997253i $$-0.523599\pi$$
−0.0740700 + 0.997253i $$0.523599\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ −0.367172 −0.0322031
$$131$$ 13.5321 1.18231 0.591154 0.806558i $$-0.298672\pi$$
0.591154 + 0.806558i $$0.298672\pi$$
$$132$$ 0 0
$$133$$ 11.6091 + 12.1708i 1.00663 + 1.05535i
$$134$$ 10.8907i 0.940817i
$$135$$ 0 0
$$136$$ 4.98906i 0.427809i
$$137$$ 8.98851i 0.767940i −0.923346 0.383970i $$-0.874557\pi$$
0.923346 0.383970i $$-0.125443\pi$$
$$138$$ 0 0
$$139$$ 9.29922i 0.788750i 0.918950 + 0.394375i $$0.129039\pi$$
−0.918950 + 0.394375i $$0.870961\pi$$
$$140$$ −0.701849 + 0.669453i −0.0593170 + 0.0565791i
$$141$$ 0 0
$$142$$ −5.49843 −0.461418
$$143$$ 0.670501 0.0560701
$$144$$ 0 0
$$145$$ 0.670501i 0.0556821i
$$146$$ 4.07314 0.337096
$$147$$ 0 0
$$148$$ 5.16789 0.424798
$$149$$ 2.83211i 0.232016i −0.993248 0.116008i $$-0.962990\pi$$
0.993248 0.116008i $$-0.0370098\pi$$
$$150$$ 0 0
$$151$$ −16.5518 −1.34697 −0.673484 0.739201i $$-0.735203\pi$$
−0.673484 + 0.739201i $$0.735203\pi$$
$$152$$ 6.35722 0.515639
$$153$$ 0 0
$$154$$ 1.28166 1.22250i 0.103279 0.0985122i
$$155$$ 2.31905i 0.186271i
$$156$$ 0 0
$$157$$ 2.83456i 0.226222i −0.993582 0.113111i $$-0.963918\pi$$
0.993582 0.113111i $$-0.0360816\pi$$
$$158$$ 8.35568i 0.664742i
$$159$$ 0 0
$$160$$ 0.366598i 0.0289821i
$$161$$ 14.0513 + 14.7312i 1.10739 + 1.16098i
$$162$$ 0 0
$$163$$ 24.7281 1.93685 0.968426 0.249300i $$-0.0802005\pi$$
0.968426 + 0.249300i $$0.0802005\pi$$
$$164$$ 4.31856 0.337223
$$165$$ 0 0
$$166$$ 17.0142i 1.32056i
$$167$$ −19.3484 −1.49723 −0.748614 0.663006i $$-0.769280\pi$$
−0.748614 + 0.663006i $$0.769280\pi$$
$$168$$ 0 0
$$169$$ 11.9969 0.922836
$$170$$ 1.82898i 0.140276i
$$171$$ 0 0
$$172$$ 4.49843 0.343002
$$173$$ −4.83654 −0.367715 −0.183858 0.982953i $$-0.558859\pi$$
−0.183858 + 0.982953i $$0.558859\pi$$
$$174$$ 0 0
$$175$$ 9.31516 8.88520i 0.704160 0.671658i
$$176$$ 0.669453i 0.0504619i
$$177$$ 0 0
$$178$$ 10.7113i 0.802847i
$$179$$ 3.65796i 0.273409i −0.990612 0.136704i $$-0.956349\pi$$
0.990612 0.136704i $$-0.0436511\pi$$
$$180$$ 0 0
$$181$$ 5.66796i 0.421296i 0.977562 + 0.210648i $$0.0675574\pi$$
−0.977562 + 0.210648i $$0.932443\pi$$
$$182$$ −1.91749 + 1.82898i −0.142134 + 0.135573i
$$183$$ 0 0
$$184$$ 7.69459 0.567252
$$185$$ 1.89454 0.139289
$$186$$ 0 0
$$187$$ 3.33994i 0.244241i
$$188$$ −8.32901 −0.607455
$$189$$ 0 0
$$190$$ 2.33055 0.169076
$$191$$ 27.3777i 1.98098i −0.137587 0.990490i $$-0.543935\pi$$
0.137587 0.990490i $$-0.456065\pi$$
$$192$$ 0 0
$$193$$ −10.0283 −0.721850 −0.360925 0.932595i $$-0.617539\pi$$
−0.360925 + 0.932595i $$0.617539\pi$$
$$194$$ −17.2157 −1.23602
$$195$$ 0 0
$$196$$ −0.330547 + 6.99219i −0.0236105 + 0.499442i
$$197$$ 18.8258i 1.34129i 0.741780 + 0.670643i $$0.233982\pi$$
−0.741780 + 0.670643i $$0.766018\pi$$
$$198$$ 0 0
$$199$$ 5.36406i 0.380248i −0.981760 0.190124i $$-0.939111\pi$$
0.981760 0.190124i $$-0.0608890\pi$$
$$200$$ 4.86561i 0.344050i
$$201$$ 0 0
$$202$$ 15.7317i 1.10688i
$$203$$ 3.33994 + 3.50157i 0.234418 + 0.245762i
$$204$$ 0 0
$$205$$ 1.58318 0.110574
$$206$$ 11.4445 0.797377
$$207$$ 0 0
$$208$$ 1.00156i 0.0694460i
$$209$$ −4.25587 −0.294384
$$210$$ 0 0
$$211$$ 1.65796 0.114139 0.0570694 0.998370i $$-0.481824\pi$$
0.0570694 + 0.998370i $$0.481824\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −11.0618 −0.756166
$$215$$ 1.64912 0.112469
$$216$$ 0 0
$$217$$ 11.5518 + 12.1108i 0.784189 + 0.822137i
$$218$$ 10.5633i 0.715439i
$$219$$ 0 0
$$220$$ 0.245420i 0.0165462i
$$221$$ 4.99687i 0.336126i
$$222$$ 0 0
$$223$$ 17.0372i 1.14090i 0.821334 + 0.570448i $$0.193230\pi$$
−0.821334 + 0.570448i $$0.806770\pi$$
$$224$$ 1.82612 + 1.91449i 0.122013 + 0.127917i
$$225$$ 0 0
$$226$$ 4.15953 0.276688
$$227$$ 5.11024 0.339179 0.169589 0.985515i $$-0.445756\pi$$
0.169589 + 0.985515i $$0.445756\pi$$
$$228$$ 0 0
$$229$$ 15.2669i 1.00887i 0.863451 + 0.504433i $$0.168298\pi$$
−0.863451 + 0.504433i $$0.831702\pi$$
$$230$$ 2.82082 0.185999
$$231$$ 0 0
$$232$$ 1.82898 0.120078
$$233$$ 10.1930i 0.667767i −0.942614 0.333883i $$-0.891641\pi$$
0.942614 0.333883i $$-0.108359\pi$$
$$234$$ 0 0
$$235$$ −3.05340 −0.199182
$$236$$ −8.72695 −0.568076
$$237$$ 0 0
$$238$$ 9.11064 + 9.55151i 0.590555 + 0.619132i
$$239$$ 19.1815i 1.24075i −0.784305 0.620375i $$-0.786980\pi$$
0.784305 0.620375i $$-0.213020\pi$$
$$240$$ 0 0
$$241$$ 20.6853i 1.33245i 0.745749 + 0.666227i $$0.232092\pi$$
−0.745749 + 0.666227i $$0.767908\pi$$
$$242$$ 10.5518i 0.678297i
$$243$$ 0 0
$$244$$ 4.95771i 0.317385i
$$245$$ −0.121178 + 2.56332i −0.00774176 + 0.163765i
$$246$$ 0 0
$$247$$ 6.36717 0.405133
$$248$$ 6.32588 0.401694
$$249$$ 0 0
$$250$$ 3.61671i 0.228741i
$$251$$ 1.81200 0.114373 0.0571864 0.998364i $$-0.481787\pi$$
0.0571864 + 0.998364i $$0.481787\pi$$
$$252$$ 0 0
$$253$$ −5.15117 −0.323851
$$254$$ 1.66945i 0.104751i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 6.45545 0.402680 0.201340 0.979521i $$-0.435470\pi$$
0.201340 + 0.979521i $$0.435470\pi$$
$$258$$ 0 0
$$259$$ 9.89387 9.43720i 0.614775 0.586399i
$$260$$ 0.367172i 0.0227710i
$$261$$ 0 0
$$262$$ 13.5321i 0.836018i
$$263$$ 8.82062i 0.543903i 0.962311 + 0.271951i $$0.0876690\pi$$
−0.962311 + 0.271951i $$0.912331\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 12.1708 11.6091i 0.746242 0.711798i
$$267$$ 0 0
$$268$$ 10.8907 0.665258
$$269$$ −14.2653 −0.869773 −0.434886 0.900485i $$-0.643212\pi$$
−0.434886 + 0.900485i $$0.643212\pi$$
$$270$$ 0 0
$$271$$ 3.05281i 0.185445i 0.995692 + 0.0927226i $$0.0295570\pi$$
−0.995692 + 0.0927226i $$0.970443\pi$$
$$272$$ 4.98906 0.302506
$$273$$ 0 0
$$274$$ −8.98851 −0.543016
$$275$$ 3.25730i 0.196422i
$$276$$ 0 0
$$277$$ 1.26566 0.0760459 0.0380230 0.999277i $$-0.487894\pi$$
0.0380230 + 0.999277i $$0.487894\pi$$
$$278$$ 9.29922 0.557730
$$279$$ 0 0
$$280$$ 0.669453 + 0.701849i 0.0400075 + 0.0419435i
$$281$$ 10.5267i 0.627970i −0.949428 0.313985i $$-0.898336\pi$$
0.949428 0.313985i $$-0.101664\pi$$
$$282$$ 0 0
$$283$$ 19.8718i 1.18125i 0.806945 + 0.590627i $$0.201119\pi$$
−0.806945 + 0.590627i $$0.798881\pi$$
$$284$$ 5.49843i 0.326272i
$$285$$ 0 0
$$286$$ 0.670501i 0.0396475i
$$287$$ 8.26784 7.88623i 0.488035 0.465509i
$$288$$ 0 0
$$289$$ 7.89074 0.464161
$$290$$ 0.670501 0.0393732
$$291$$ 0 0
$$292$$ 4.07314i 0.238363i
$$293$$ 13.4121 0.783544 0.391772 0.920062i $$-0.371862\pi$$
0.391772 + 0.920062i $$0.371862\pi$$
$$294$$ 0 0
$$295$$ −3.19928 −0.186270
$$296$$ 5.16789i 0.300377i
$$297$$ 0 0
$$298$$ −2.83211 −0.164060
$$299$$ 7.70663 0.445686
$$300$$ 0 0
$$301$$ 8.61221 8.21470i 0.496399 0.473487i
$$302$$ 16.5518i 0.952451i
$$303$$ 0 0
$$304$$ 6.35722i 0.364612i
$$305$$ 1.81749i 0.104069i
$$306$$ 0 0
$$307$$ 0.653728i 0.0373102i 0.999826 + 0.0186551i $$0.00593845\pi$$
−0.999826 + 0.0186551i $$0.994062\pi$$
$$308$$ −1.22250 1.28166i −0.0696587 0.0730295i
$$309$$ 0 0
$$310$$ 2.31905 0.131713
$$311$$ 9.24493 0.524232 0.262116 0.965036i $$-0.415580\pi$$
0.262116 + 0.965036i $$0.415580\pi$$
$$312$$ 0 0
$$313$$ 6.16414i 0.348418i −0.984709 0.174209i $$-0.944263\pi$$
0.984709 0.174209i $$-0.0557368\pi$$
$$314$$ −2.83456 −0.159963
$$315$$ 0 0
$$316$$ −8.35568 −0.470044
$$317$$ 20.6548i 1.16009i 0.814584 + 0.580045i $$0.196965\pi$$
−0.814584 + 0.580045i $$0.803035\pi$$
$$318$$ 0 0
$$319$$ −1.22442 −0.0685542
$$320$$ 0.366598 0.0204935
$$321$$ 0 0
$$322$$ 14.7312 14.0513i 0.820938 0.783046i
$$323$$ 31.7166i 1.76476i
$$324$$ 0 0
$$325$$ 4.87322i 0.270318i
$$326$$ 24.7281i 1.36956i
$$327$$ 0 0
$$328$$ 4.31856i 0.238453i
$$329$$ −15.9458 + 15.2098i −0.879121 + 0.838543i
$$330$$ 0 0
$$331$$ 10.7114 0.588750 0.294375 0.955690i $$-0.404889\pi$$
0.294375 + 0.955690i $$0.404889\pi$$
$$332$$ −17.0142 −0.933778
$$333$$ 0 0
$$334$$ 19.3484i 1.05870i
$$335$$ 3.99252 0.218135
$$336$$ 0 0
$$337$$ −7.55183 −0.411375 −0.205687 0.978618i $$-0.565943\pi$$
−0.205687 + 0.978618i $$0.565943\pi$$
$$338$$ 11.9969i 0.652544i
$$339$$ 0 0
$$340$$ 1.82898 0.0991904
$$341$$ −4.23488 −0.229332
$$342$$ 0 0
$$343$$ 12.1358 + 13.9901i 0.655270 + 0.755394i
$$344$$ 4.49843i 0.242539i
$$345$$ 0 0
$$346$$ 4.83654i 0.260014i
$$347$$ 10.9320i 0.586859i −0.955981 0.293430i $$-0.905203\pi$$
0.955981 0.293430i $$-0.0947967\pi$$
$$348$$ 0 0
$$349$$ 1.18429i 0.0633936i 0.999498 + 0.0316968i $$0.0100911\pi$$
−0.999498 + 0.0316968i $$0.989909\pi$$
$$350$$ −8.88520 9.31516i −0.474934 0.497916i
$$351$$ 0 0
$$352$$ −0.669453 −0.0356820
$$353$$ 33.5824 1.78741 0.893706 0.448653i $$-0.148096\pi$$
0.893706 + 0.448653i $$0.148096\pi$$
$$354$$ 0 0
$$355$$ 2.01572i 0.106983i
$$356$$ 10.7113 0.567699
$$357$$ 0 0
$$358$$ −3.65796 −0.193329
$$359$$ 10.1281i 0.534542i 0.963621 + 0.267271i $$0.0861219\pi$$
−0.963621 + 0.267271i $$0.913878\pi$$
$$360$$ 0 0
$$361$$ −21.4143 −1.12707
$$362$$ 5.66796 0.297901
$$363$$ 0 0
$$364$$ 1.82898 + 1.91749i 0.0958646 + 0.100504i
$$365$$ 1.49321i 0.0781580i
$$366$$ 0 0
$$367$$ 18.0021i 0.939701i −0.882746 0.469850i $$-0.844308\pi$$
0.882746 0.469850i $$-0.155692\pi$$
$$368$$ 7.69459i 0.401108i
$$369$$ 0 0
$$370$$ 1.89454i 0.0984923i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 16.4090 0.849627 0.424814 0.905281i $$-0.360340\pi$$
0.424814 + 0.905281i $$0.360340\pi$$
$$374$$ −3.33994 −0.172704
$$375$$ 0 0
$$376$$ 8.32901i 0.429536i
$$377$$ 1.83184 0.0943447
$$378$$ 0 0
$$379$$ −2.91372 −0.149668 −0.0748339 0.997196i $$-0.523843\pi$$
−0.0748339 + 0.997196i $$0.523843\pi$$
$$380$$ 2.33055i 0.119555i
$$381$$ 0 0
$$382$$ −27.3777 −1.40076
$$383$$ −8.57443 −0.438133 −0.219066 0.975710i $$-0.570301\pi$$
−0.219066 + 0.975710i $$0.570301\pi$$
$$384$$ 0 0
$$385$$ −0.448168 0.469855i −0.0228407 0.0239460i
$$386$$ 10.0283i 0.510425i
$$387$$ 0 0
$$388$$ 17.2157i 0.873997i
$$389$$ 35.5539i 1.80266i 0.433137 + 0.901328i $$0.357406\pi$$
−0.433137 + 0.901328i $$0.642594\pi$$
$$390$$ 0 0
$$391$$ 38.3888i 1.94140i
$$392$$ 6.99219 + 0.330547i 0.353159 + 0.0166951i
$$393$$ 0 0
$$394$$ 18.8258 0.948433
$$395$$ −3.06318 −0.154125
$$396$$ 0 0
$$397$$ 3.58034i 0.179692i −0.995956 0.0898460i $$-0.971363\pi$$
0.995956 0.0898460i $$-0.0286375\pi$$
$$398$$ −5.36406 −0.268876
$$399$$ 0 0
$$400$$ −4.86561 −0.243280
$$401$$ 0.190871i 0.00953167i 0.999989 + 0.00476583i $$0.00151702\pi$$
−0.999989 + 0.00476583i $$0.998483\pi$$
$$402$$ 0 0
$$403$$ 6.33577 0.315607
$$404$$ 15.7317 0.782683
$$405$$ 0 0
$$406$$ 3.50157 3.33994i 0.173780 0.165759i
$$407$$ 3.45966i 0.171489i
$$408$$ 0 0
$$409$$ 3.47371i 0.171764i 0.996305 + 0.0858819i $$0.0273708\pi$$
−0.996305 + 0.0858819i $$0.972629\pi$$
$$410$$ 1.58318i 0.0781875i
$$411$$ 0 0
$$412$$ 11.4445i 0.563831i
$$413$$ −16.7077 + 15.9365i −0.822130 + 0.784183i
$$414$$ 0 0
$$415$$ −6.23739 −0.306182
$$416$$ 1.00156 0.0491057
$$417$$ 0 0
$$418$$ 4.25587i 0.208161i
$$419$$ 1.40791 0.0687809 0.0343905 0.999408i $$-0.489051\pi$$
0.0343905 + 0.999408i $$0.489051\pi$$
$$420$$ 0 0
$$421$$ −30.3860 −1.48093 −0.740463 0.672098i $$-0.765393\pi$$
−0.740463 + 0.672098i $$0.765393\pi$$
$$422$$ 1.65796i 0.0807083i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −24.2748 −1.17750
$$426$$ 0 0
$$427$$ 9.05340 + 9.49150i 0.438125 + 0.459326i
$$428$$ 11.0618i 0.534690i
$$429$$ 0 0
$$430$$ 1.64912i 0.0795275i
$$431$$ 27.2747i 1.31378i 0.753988 + 0.656888i $$0.228127\pi$$
−0.753988 + 0.656888i $$0.771873\pi$$
$$432$$ 0 0
$$433$$ 8.15047i 0.391686i 0.980635 + 0.195843i $$0.0627444\pi$$
−0.980635 + 0.195843i $$0.937256\pi$$
$$434$$ 12.1108 11.5518i 0.581338 0.554506i
$$435$$ 0 0
$$436$$ 10.5633 0.505891
$$437$$ −48.9162 −2.33998
$$438$$ 0 0
$$439$$ 12.2404i 0.584203i 0.956387 + 0.292101i $$0.0943545\pi$$
−0.956387 + 0.292101i $$0.905646\pi$$
$$440$$ −0.245420 −0.0117000
$$441$$ 0 0
$$442$$ 4.99687 0.237677
$$443$$ 8.00836i 0.380489i −0.981737 0.190244i $$-0.939072\pi$$
0.981737 0.190244i $$-0.0609280\pi$$
$$444$$ 0 0
$$445$$ 3.92675 0.186146
$$446$$ 17.0372 0.806735
$$447$$ 0 0
$$448$$ 1.91449 1.82612i 0.0904512 0.0862762i
$$449$$ 14.5183i 0.685163i −0.939488 0.342581i $$-0.888699\pi$$
0.939488 0.342581i $$-0.111301\pi$$
$$450$$ 0 0
$$451$$ 2.89108i 0.136135i
$$452$$ 4.15953i 0.195648i
$$453$$ 0 0
$$454$$ 5.11024i 0.239835i
$$455$$ 0.670501 + 0.702947i 0.0314336 + 0.0329547i
$$456$$ 0 0
$$457$$ 9.95501 0.465676 0.232838 0.972516i $$-0.425199\pi$$
0.232838 + 0.972516i $$0.425199\pi$$
$$458$$ 15.2669 0.713375
$$459$$ 0 0
$$460$$ 2.82082i 0.131521i
$$461$$ −32.3270 −1.50562 −0.752810 0.658237i $$-0.771302\pi$$
−0.752810 + 0.658237i $$0.771302\pi$$
$$462$$ 0 0
$$463$$ 9.45032 0.439193 0.219597 0.975591i $$-0.429526\pi$$
0.219597 + 0.975591i $$0.429526\pi$$
$$464$$ 1.82898i 0.0849083i
$$465$$ 0 0
$$466$$ −10.1930 −0.472183
$$467$$ −20.6623 −0.956138 −0.478069 0.878322i $$-0.658663\pi$$
−0.478069 + 0.878322i $$0.658663\pi$$
$$468$$ 0 0
$$469$$ 20.8502 19.8878i 0.962773 0.918335i
$$470$$ 3.05340i 0.140843i
$$471$$ 0 0
$$472$$ 8.72695i 0.401691i
$$473$$ 3.01149i 0.138469i
$$474$$ 0 0
$$475$$ 30.9317i 1.41925i
$$476$$ 9.55151 9.11064i 0.437793 0.417586i
$$477$$ 0 0
$$478$$ −19.1815 −0.877343
$$479$$ −10.1608 −0.464261 −0.232131 0.972685i $$-0.574570\pi$$
−0.232131 + 0.972685i $$0.574570\pi$$
$$480$$ 0 0
$$481$$ 5.17597i 0.236004i
$$482$$ 20.6853 0.942188
$$483$$ 0 0
$$484$$ −10.5518 −0.479629
$$485$$ 6.31126i 0.286579i
$$486$$ 0 0
$$487$$ −31.2296 −1.41515 −0.707575 0.706638i $$-0.750211\pi$$
−0.707575 + 0.706638i $$0.750211\pi$$
$$488$$ 4.95771 0.224425
$$489$$ 0 0
$$490$$ 2.56332 + 0.121178i 0.115799 + 0.00547425i
$$491$$ 20.5899i 0.929211i 0.885518 + 0.464605i $$0.153804\pi$$
−0.885518 + 0.464605i $$0.846196\pi$$
$$492$$ 0 0
$$493$$ 9.12490i 0.410965i
$$494$$ 6.36717i 0.286473i
$$495$$ 0 0
$$496$$ 6.32588i 0.284040i
$$497$$ 10.0408 + 10.5267i 0.450392 + 0.472187i
$$498$$ 0 0
$$499$$ −25.1533 −1.12601 −0.563007 0.826452i $$-0.690356\pi$$
−0.563007 + 0.826452i $$0.690356\pi$$
$$500$$ −3.61671 −0.161744
$$501$$ 0 0
$$502$$ 1.81200i 0.0808737i
$$503$$ 31.1553 1.38915 0.694574 0.719421i $$-0.255593\pi$$
0.694574 + 0.719421i $$0.255593\pi$$
$$504$$ 0 0
$$505$$ 5.76722 0.256638
$$506$$ 5.15117i 0.228997i
$$507$$ 0 0
$$508$$ 1.66945 0.0740700
$$509$$ −4.83347 −0.214240 −0.107120 0.994246i $$-0.534163\pi$$
−0.107120 + 0.994246i $$0.534163\pi$$
$$510$$ 0 0
$$511$$ −7.43806 7.79799i −0.329040 0.344963i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 6.45545i 0.284738i
$$515$$ 4.19554i 0.184877i
$$516$$ 0 0
$$517$$ 5.57588i 0.245227i
$$518$$ −9.43720 9.89387i −0.414647 0.434712i
$$519$$ 0 0
$$520$$ 0.367172 0.0161015
$$521$$ −17.5322 −0.768101 −0.384050 0.923312i $$-0.625471\pi$$
−0.384050 + 0.923312i $$0.625471\pi$$
$$522$$ 0 0
$$523$$ 19.1019i 0.835267i −0.908616 0.417633i $$-0.862860\pi$$
0.908616 0.417633i $$-0.137140\pi$$
$$524$$ −13.5321 −0.591154
$$525$$ 0 0
$$526$$ 8.82062 0.384597
$$527$$ 31.5602i 1.37478i
$$528$$ 0 0
$$529$$ −36.2067 −1.57420
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −11.6091 12.1708i −0.503317 0.527673i
$$533$$ 4.32532i 0.187350i
$$534$$ 0 0
$$535$$ 4.05522i 0.175322i
$$536$$ 10.8907i 0.470408i
$$537$$ 0 0
$$538$$ 14.2653i 0.615022i
$$539$$ −4.68095 0.221286i −0.201623 0.00953144i
$$540$$ 0 0
$$541$$ 13.6642 0.587471 0.293735 0.955887i $$-0.405102\pi$$
0.293735 + 0.955887i $$0.405102\pi$$
$$542$$ 3.05281 0.131130
$$543$$ 0 0
$$544$$ 4.98906i 0.213904i
$$545$$ 3.87249 0.165879
$$546$$ 0 0
$$547$$ −9.88761 −0.422764 −0.211382 0.977404i $$-0.567796\pi$$
−0.211382 + 0.977404i $$0.567796\pi$$
$$548$$ 8.98851i 0.383970i
$$549$$ 0 0
$$550$$ 3.25730 0.138892
$$551$$ −11.6272 −0.495337
$$552$$ 0 0
$$553$$ −15.9969 + 15.2585i −0.680256 + 0.648858i
$$554$$ 1.26566i 0.0537726i
$$555$$ 0 0
$$556$$ 9.29922i 0.394375i
$$557$$ 12.5800i 0.533034i 0.963830 + 0.266517i $$0.0858728\pi$$
−0.963830 + 0.266517i $$0.914127\pi$$
$$558$$ 0 0
$$559$$ 4.50547i 0.190561i
$$560$$ 0.701849 0.669453i 0.0296585 0.0282896i
$$561$$ 0 0
$$562$$ −10.5267 −0.444042
$$563$$ 24.3333 1.02553 0.512763 0.858530i $$-0.328622\pi$$
0.512763 + 0.858530i $$0.328622\pi$$
$$564$$ 0 0
$$565$$ 1.52487i 0.0641520i
$$566$$ 19.8718 0.835272
$$567$$ 0 0
$$568$$ 5.49843 0.230709
$$569$$ 9.45406i 0.396335i 0.980168 + 0.198167i $$0.0634990\pi$$
−0.980168 + 0.198167i $$0.936501\pi$$
$$570$$ 0 0
$$571$$ −31.5686 −1.32110 −0.660551 0.750781i $$-0.729677\pi$$
−0.660551 + 0.750781i $$0.729677\pi$$
$$572$$ −0.670501 −0.0280351
$$573$$ 0 0
$$574$$ −7.88623 8.26784i −0.329165 0.345093i
$$575$$ 37.4388i 1.56131i
$$576$$ 0 0
$$577$$ 33.5794i 1.39793i −0.715157 0.698964i $$-0.753645\pi$$
0.715157 0.698964i $$-0.246355\pi$$
$$578$$ 7.89074i 0.328211i
$$579$$ 0 0
$$580$$ 0.670501i 0.0278410i
$$581$$ −32.5736 + 31.0701i −1.35138 + 1.28901i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −4.07314 −0.168548
$$585$$ 0 0
$$586$$ 13.4121i 0.554049i
$$587$$ −19.3171 −0.797302 −0.398651 0.917103i $$-0.630521\pi$$
−0.398651 + 0.917103i $$0.630521\pi$$
$$588$$ 0 0
$$589$$ −40.2150 −1.65703
$$590$$ 3.19928i 0.131712i
$$591$$ 0 0
$$592$$ −5.16789 −0.212399
$$593$$ −0.733196 −0.0301088 −0.0150544 0.999887i $$-0.504792\pi$$
−0.0150544 + 0.999887i $$0.504792\pi$$
$$594$$ 0 0
$$595$$ 3.50157 3.33994i 0.143550 0.136924i
$$596$$ 2.83211i 0.116008i
$$597$$ 0 0
$$598$$ 7.70663i 0.315147i
$$599$$ 30.7783i 1.25757i 0.777580 + 0.628785i $$0.216447\pi$$
−0.777580 + 0.628785i $$0.783553\pi$$
$$600$$ 0 0
$$601$$ 0.908670i 0.0370654i −0.999828 0.0185327i $$-0.994101\pi$$
0.999828 0.0185327i $$-0.00589948\pi$$
$$602$$ −8.21470 8.61221i −0.334806 0.351007i
$$603$$ 0 0
$$604$$ 16.5518 0.673484
$$605$$ −3.86828 −0.157268
$$606$$ 0 0
$$607$$ 44.7773i 1.81746i −0.417389 0.908728i $$-0.637055\pi$$
0.417389 0.908728i $$-0.362945\pi$$
$$608$$ −6.35722 −0.257820
$$609$$ 0 0
$$610$$ 1.81749 0.0735880
$$611$$ 8.34204i 0.337483i
$$612$$ 0 0
$$613$$ 18.1480 0.732992 0.366496 0.930420i $$-0.380557\pi$$
0.366496 + 0.930420i $$0.380557\pi$$
$$614$$ 0.653728 0.0263823
$$615$$ 0 0
$$616$$ −1.28166 + 1.22250i −0.0516396 + 0.0492561i
$$617$$ 22.7930i 0.917610i −0.888537 0.458805i $$-0.848278\pi$$
0.888537 0.458805i $$-0.151722\pi$$
$$618$$ 0 0
$$619$$ 44.3668i 1.78325i −0.452772 0.891626i $$-0.649565\pi$$
0.452772 0.891626i $$-0.350435\pi$$
$$620$$ 2.31905i 0.0931355i
$$621$$ 0 0
$$622$$ 9.24493i 0.370688i
$$623$$ 20.5067 19.5602i 0.821584 0.783663i
$$624$$ 0 0
$$625$$ 23.0021 0.920086
$$626$$ −6.16414 −0.246368
$$627$$ 0 0
$$628$$ 2.83456i 0.113111i
$$629$$ −25.7829 −1.02803
$$630$$ 0 0
$$631$$ −32.5707 −1.29662 −0.648310 0.761377i $$-0.724524\pi$$
−0.648310 + 0.761377i $$0.724524\pi$$
$$632$$ 8.35568i 0.332371i
$$633$$ 0 0
$$634$$ 20.6548 0.820308
$$635$$ 0.612018 0.0242872
$$636$$ 0 0
$$637$$ 7.00313 + 0.331064i 0.277474 + 0.0131172i
$$638$$ 1.22442i 0.0484751i
$$639$$ 0 0
$$640$$ 0.366598i 0.0144911i
$$641$$ 11.8091i 0.466433i 0.972425 + 0.233216i $$0.0749250\pi$$
−0.972425 + 0.233216i $$0.925075\pi$$
$$642$$ 0 0
$$643$$ 29.2964i 1.15534i −0.816272 0.577668i $$-0.803963\pi$$
0.816272 0.577668i $$-0.196037\pi$$
$$644$$ −14.0513 14.7312i −0.553697 0.580491i
$$645$$ 0 0
$$646$$ −31.7166 −1.24787
$$647$$ 28.1683 1.10741 0.553705 0.832713i $$-0.313214\pi$$
0.553705 + 0.832713i $$0.313214\pi$$
$$648$$ 0 0
$$649$$ 5.84229i 0.229330i
$$650$$ −4.87322 −0.191143
$$651$$ 0 0
$$652$$ −24.7281 −0.968426
$$653$$ 45.0974i 1.76480i 0.470502 + 0.882399i $$0.344073\pi$$
−0.470502 + 0.882399i $$0.655927\pi$$
$$654$$ 0 0
$$655$$ −4.96086 −0.193837
$$656$$ −4.31856 −0.168611
$$657$$ 0 0
$$658$$ 15.2098 + 15.9458i 0.592939 + 0.621632i
$$659$$ 31.8045i 1.23893i −0.785026 0.619463i $$-0.787350\pi$$
0.785026 0.619463i $$-0.212650\pi$$
$$660$$ 0 0
$$661$$ 19.7724i 0.769056i −0.923113 0.384528i $$-0.874364\pi$$
0.923113 0.384528i $$-0.125636\pi$$
$$662$$ 10.7114i 0.416309i
$$663$$ 0 0
$$664$$ 17.0142i 0.660281i
$$665$$ −4.25587 4.46181i −0.165035 0.173022i
$$666$$ 0 0
$$667$$ −14.0733 −0.544918
$$668$$ 19.3484 0.748614
$$669$$ 0 0
$$670$$ 3.99252i 0.154245i
$$671$$ −3.31896 −0.128127
$$672$$ 0 0
$$673$$ 1.89074 0.0728826 0.0364413 0.999336i $$-0.488398\pi$$
0.0364413 + 0.999336i $$0.488398\pi$$
$$674$$ 7.55183i 0.290886i
$$675$$ 0 0
$$676$$ −11.9969 −0.461418
$$677$$ 21.1322 0.812175 0.406088 0.913834i $$-0.366893\pi$$
0.406088 + 0.913834i $$0.366893\pi$$
$$678$$ 0 0
$$679$$ 31.4381 + 32.9594i 1.20648 + 1.26486i
$$680$$ 1.82898i 0.0701382i
$$681$$ 0 0
$$682$$ 4.23488i 0.162162i
$$683$$ 8.71972i 0.333651i 0.985986 + 0.166825i $$0.0533516\pi$$
−0.985986 + 0.166825i $$0.946648\pi$$
$$684$$ 0 0
$$685$$ 3.29517i 0.125902i
$$686$$ 13.9901 12.1358i 0.534145 0.463346i
$$687$$ 0 0
$$688$$ −4.49843 −0.171501
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 18.1370i 0.689964i −0.938609 0.344982i $$-0.887885\pi$$
0.938609 0.344982i $$-0.112115\pi$$
$$692$$ 4.83654 0.183858
$$693$$ 0 0
$$694$$ −10.9320 −0.414972
$$695$$ 3.40908i 0.129314i
$$696$$ 0 0
$$697$$ −21.5456 −0.816097
$$698$$ 1.18429 0.0448260
$$699$$ 0 0
$$700$$ −9.31516 + 8.88520i −0.352080 + 0.335829i
$$701$$ 35.6167i 1.34523i −0.739995 0.672613i $$-0.765172\pi$$
0.739995 0.672613i $$-0.234828\pi$$
$$702$$ 0 0
$$703$$ 32.8534i 1.23909i
$$704$$ 0.669453i 0.0252310i
$$705$$ 0 0
$$706$$ 33.5824i 1.26389i
$$707$$ 30.1182 28.7281i 1.13271 1.08043i
$$708$$ 0 0
$$709$$ −3.60770 −0.135490 −0.0677449 0.997703i $$-0.521580\pi$$
−0.0677449 + 0.997703i $$0.521580\pi$$
$$710$$ 2.01572 0.0756485
$$711$$ 0 0
$$712$$ 10.7113i 0.401424i
$$713$$ −48.6750 −1.82289
$$714$$ 0 0
$$715$$ −0.245804 −0.00919256
$$716$$ 3.65796i 0.136704i
$$717$$ 0 0
$$718$$ 10.1281 0.377978
$$719$$ 25.7829 0.961540 0.480770 0.876847i $$-0.340357\pi$$
0.480770 + 0.876847i $$0.340357\pi$$
$$720$$ 0 0
$$721$$ −20.8991 21.9104i −0.778323 0.815987i
$$722$$ 21.4143i 0.796958i
$$723$$ 0 0
$$724$$ 5.66796i 0.210648i
$$725$$ 8.89910i 0.330504i
$$726$$ 0 0
$$727$$ 1.52909i 0.0567107i 0.999598 + 0.0283554i $$0.00902700\pi$$
−0.999598 + 0.0283554i $$0.990973\pi$$
$$728$$ 1.91749 1.82898i 0.0710668 0.0677865i
$$729$$ 0 0
$$730$$ −1.49321 −0.0552660
$$731$$ −22.4430 −0.830083
$$732$$ 0 0
$$733$$ 20.7739i 0.767303i 0.923478 + 0.383651i $$0.125334\pi$$
−0.923478 + 0.383651i $$0.874666\pi$$
$$734$$ −18.0021 −0.664469
$$735$$ 0 0
$$736$$ −7.69459 −0.283626
$$737$$ 7.29084i 0.268562i
$$738$$ 0 0
$$739$$ −11.8709 −0.436678 −0.218339 0.975873i $$-0.570064\pi$$
−0.218339 + 0.975873i $$0.570064\pi$$
$$740$$ −1.89454 −0.0696446
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 43.4059i 1.59241i −0.605028 0.796204i $$-0.706838\pi$$
0.605028 0.796204i $$-0.293162\pi$$
$$744$$ 0 0
$$745$$ 1.03825i 0.0380384i
$$746$$ 16.4090i 0.600777i
$$747$$ 0 0
$$748$$ 3.33994i 0.122120i
$$749$$ 20.2001 + 21.1776i 0.738097 + 0.773814i
$$750$$ 0 0
$$751$$ 2.31383 0.0844327 0.0422164 0.999108i $$-0.486558\pi$$
0.0422164 + 0.999108i $$0.486558\pi$$
$$752$$ 8.32901 0.303728
$$753$$ 0 0
$$754$$ 1.83184i 0.0667118i
$$755$$ 6.06787 0.220832
$$756$$ 0 0
$$757$$ −15.0946 −0.548624 −0.274312 0.961641i $$-0.588450\pi$$
−0.274312 + 0.961641i $$0.588450\pi$$
$$758$$ 2.91372i 0.105831i
$$759$$ 0 0
$$760$$ −2.33055 −0.0845378
$$761$$ 23.3379 0.845998 0.422999 0.906130i $$-0.360977\pi$$
0.422999 + 0.906130i $$0.360977\pi$$
$$762$$ 0 0
$$763$$ 20.2234 19.2899i 0.732136 0.698342i
$$764$$ 27.3777i 0.990490i
$$765$$ 0 0
$$766$$ 8.57443i 0.309807i
$$767$$ 8.74061i 0.315605i
$$768$$ 0 0
$$769$$ 18.2750i 0.659012i 0.944153 + 0.329506i $$0.106882\pi$$
−0.944153 + 0.329506i $$0.893118\pi$$
$$770$$ −0.469855 + 0.448168i −0.0169324 + 0.0161508i
$$771$$ 0 0
$$772$$ 10.0283 0.360925
$$773$$ 0.438507 0.0157720 0.00788600 0.999969i $$-0.497490\pi$$
0.00788600 + 0.999969i $$0.497490\pi$$
$$774$$ 0 0
$$775$$ 30.7792i 1.10562i
$$776$$ 17.2157 0.618009
$$777$$ 0 0
$$778$$ 35.5539 1.27467
$$779$$ 27.4541i 0.983644i
$$780$$ 0 0
$$781$$ −3.68095 −0.131715
$$782$$ −38.3888 −1.37278
$$783$$ 0 0
$$784$$ 0.330547 6.99219i 0.0118052 0.249721i
$$785$$ 1.03914i 0.0370886i
$$786$$ 0 0
$$787$$ 38.2572i 1.36372i 0.731481 + 0.681861i $$0.238829\pi$$
−0.731481 + 0.681861i $$0.761171\pi$$
$$788$$ 18.8258i 0.670643i
$$789$$ 0 0
$$790$$ 3.06318i 0.108983i
$$791$$ −7.59581 7.96337i −0.270076 0.283145i
$$792$$ 0 0
$$793$$ 4.96547 0.176329
$$794$$ −3.58034 −0.127061
$$795$$ 0 0
$$796$$ 5.36406i 0.190124i
$$797$$ 35.3225 1.25119 0.625594 0.780149i $$-0.284857\pi$$
0.625594 + 0.780149i $$0.284857\pi$$
$$798$$ 0 0
$$799$$ 41.5539 1.47007