# Properties

 Label 1764.2.b.n.1567.15 Level $1764$ Weight $2$ Character 1764.1567 Analytic conductor $14.086$ Analytic rank $0$ Dimension $16$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1764.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.0856109166$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 4 x^{14} + 54 x^{12} - 112 x^{11} - 104 x^{10} + 1312 x^{9} - 3159 x^{8} + 2544 x^{7} + 4132 x^{6} - 16824 x^{5} + 27780 x^{4} - 26200 x^{3} + 14608 x^{2} - 4784 x + 782$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{5}\cdot 7^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1567.15 Root $$1.14224 - 0.405613i$$ of defining polynomial Character $$\chi$$ $$=$$ 1764.1567 Dual form 1764.2.b.n.1567.14

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.05050 + 0.946809i) q^{2} +(0.207107 + 1.98925i) q^{4} -1.60804i q^{5} +(-1.66587 + 2.28580i) q^{8} +O(q^{10})$$ $$q+(1.05050 + 0.946809i) q^{2} +(0.207107 + 1.98925i) q^{4} -1.60804i q^{5} +(-1.66587 + 2.28580i) q^{8} +(1.52250 - 1.68925i) q^{10} -2.67798i q^{11} -3.37849i q^{13} +(-3.91421 + 0.823973i) q^{16} -1.60804i q^{17} +4.30629 q^{19} +(3.19879 - 0.333036i) q^{20} +(2.53553 - 2.81322i) q^{22} +6.46521i q^{23} +2.41421 q^{25} +(3.19879 - 3.54911i) q^{26} +4.71179 q^{29} +10.3963 q^{31} +(-4.89203 - 2.84043i) q^{32} +(1.52250 - 1.68925i) q^{34} +0.242641 q^{37} +(4.52377 + 4.07724i) q^{38} +(3.67565 + 2.67878i) q^{40} -11.6464i q^{41} -7.95699i q^{43} +(5.32716 - 0.554628i) q^{44} +(-6.12132 + 6.79172i) q^{46} +9.04753 q^{47} +(2.53613 + 2.28580i) q^{50} +(6.72066 - 0.699709i) q^{52} -2.46148 q^{53} -4.30629 q^{55} +(4.94975 + 4.46117i) q^{58} -9.04753 q^{59} +3.37849i q^{61} +(10.9213 + 9.84332i) q^{62} +(-2.44975 - 7.61569i) q^{64} -5.43275 q^{65} +11.2529i q^{67} +(3.19879 - 0.333036i) q^{68} -8.03394i q^{71} +6.17733i q^{73} +(0.254894 + 0.229734i) q^{74} +(0.891862 + 8.56628i) q^{76} +3.29589i q^{79} +(1.32498 + 6.29420i) q^{80} +(11.0270 - 12.2346i) q^{82} -12.7951 q^{83} -2.58579 q^{85} +(7.53375 - 8.35883i) q^{86} +(6.12132 + 4.46117i) q^{88} -0.275896i q^{89} +(-12.8609 + 1.33899i) q^{92} +(9.50445 + 8.56628i) q^{94} -6.92468i q^{95} +12.9343i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - 8q^{4} + O(q^{10})$$ $$16q - 8q^{4} - 40q^{16} - 16q^{22} + 16q^{25} - 64q^{37} - 64q^{46} + 40q^{64} - 64q^{85} + 64q^{88} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$883$$ $$1081$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.05050 + 0.946809i 0.742817 + 0.669495i
$$3$$ 0 0
$$4$$ 0.207107 + 1.98925i 0.103553 + 0.994624i
$$5$$ 1.60804i 0.719136i −0.933119 0.359568i $$-0.882924\pi$$
0.933119 0.359568i $$-0.117076\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −1.66587 + 2.28580i −0.588974 + 0.808152i
$$9$$ 0 0
$$10$$ 1.52250 1.68925i 0.481458 0.534187i
$$11$$ 2.67798i 0.807441i −0.914882 0.403721i $$-0.867717\pi$$
0.914882 0.403721i $$-0.132283\pi$$
$$12$$ 0 0
$$13$$ 3.37849i 0.937025i −0.883457 0.468513i $$-0.844790\pi$$
0.883457 0.468513i $$-0.155210\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −3.91421 + 0.823973i −0.978553 + 0.205993i
$$17$$ 1.60804i 0.390007i −0.980803 0.195003i $$-0.937528\pi$$
0.980803 0.195003i $$-0.0624717\pi$$
$$18$$ 0 0
$$19$$ 4.30629 0.987931 0.493966 0.869481i $$-0.335547\pi$$
0.493966 + 0.869481i $$0.335547\pi$$
$$20$$ 3.19879 0.333036i 0.715270 0.0744690i
$$21$$ 0 0
$$22$$ 2.53553 2.81322i 0.540578 0.599781i
$$23$$ 6.46521i 1.34809i 0.738690 + 0.674045i $$0.235445\pi$$
−0.738690 + 0.674045i $$0.764555\pi$$
$$24$$ 0 0
$$25$$ 2.41421 0.482843
$$26$$ 3.19879 3.54911i 0.627334 0.696038i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.71179 0.874958 0.437479 0.899229i $$-0.355871\pi$$
0.437479 + 0.899229i $$0.355871\pi$$
$$30$$ 0 0
$$31$$ 10.3963 1.86723 0.933616 0.358275i $$-0.116635\pi$$
0.933616 + 0.358275i $$0.116635\pi$$
$$32$$ −4.89203 2.84043i −0.864797 0.502121i
$$33$$ 0 0
$$34$$ 1.52250 1.68925i 0.261107 0.289703i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.242641 0.0398899 0.0199449 0.999801i $$-0.493651\pi$$
0.0199449 + 0.999801i $$0.493651\pi$$
$$38$$ 4.52377 + 4.07724i 0.733852 + 0.661415i
$$39$$ 0 0
$$40$$ 3.67565 + 2.67878i 0.581171 + 0.423553i
$$41$$ 11.6464i 1.81887i −0.415848 0.909434i $$-0.636515\pi$$
0.415848 0.909434i $$-0.363485\pi$$
$$42$$ 0 0
$$43$$ 7.95699i 1.21343i −0.794920 0.606715i $$-0.792487\pi$$
0.794920 0.606715i $$-0.207513\pi$$
$$44$$ 5.32716 0.554628i 0.803100 0.0836133i
$$45$$ 0 0
$$46$$ −6.12132 + 6.79172i −0.902539 + 1.00138i
$$47$$ 9.04753 1.31972 0.659859 0.751389i $$-0.270616\pi$$
0.659859 + 0.751389i $$0.270616\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 2.53613 + 2.28580i 0.358664 + 0.323261i
$$51$$ 0 0
$$52$$ 6.72066 0.699709i 0.931988 0.0970321i
$$53$$ −2.46148 −0.338110 −0.169055 0.985607i $$-0.554072\pi$$
−0.169055 + 0.985607i $$0.554072\pi$$
$$54$$ 0 0
$$55$$ −4.30629 −0.580660
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 4.94975 + 4.46117i 0.649934 + 0.585780i
$$59$$ −9.04753 −1.17789 −0.588944 0.808174i $$-0.700456\pi$$
−0.588944 + 0.808174i $$0.700456\pi$$
$$60$$ 0 0
$$61$$ 3.37849i 0.432572i 0.976330 + 0.216286i $$0.0693943\pi$$
−0.976330 + 0.216286i $$0.930606\pi$$
$$62$$ 10.9213 + 9.84332i 1.38701 + 1.25010i
$$63$$ 0 0
$$64$$ −2.44975 7.61569i −0.306218 0.951961i
$$65$$ −5.43275 −0.673849
$$66$$ 0 0
$$67$$ 11.2529i 1.37476i 0.726299 + 0.687379i $$0.241239\pi$$
−0.726299 + 0.687379i $$0.758761\pi$$
$$68$$ 3.19879 0.333036i 0.387910 0.0403865i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.03394i 0.953453i −0.879052 0.476726i $$-0.841823\pi$$
0.879052 0.476726i $$-0.158177\pi$$
$$72$$ 0 0
$$73$$ 6.17733i 0.723002i 0.932372 + 0.361501i $$0.117736\pi$$
−0.932372 + 0.361501i $$0.882264\pi$$
$$74$$ 0.254894 + 0.229734i 0.0296309 + 0.0267061i
$$75$$ 0 0
$$76$$ 0.891862 + 8.56628i 0.102304 + 0.982620i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 3.29589i 0.370817i 0.982662 + 0.185409i $$0.0593608\pi$$
−0.982662 + 0.185409i $$0.940639\pi$$
$$80$$ 1.32498 + 6.29420i 0.148137 + 0.703713i
$$81$$ 0 0
$$82$$ 11.0270 12.2346i 1.21772 1.35109i
$$83$$ −12.7951 −1.40445 −0.702225 0.711955i $$-0.747810\pi$$
−0.702225 + 0.711955i $$0.747810\pi$$
$$84$$ 0 0
$$85$$ −2.58579 −0.280468
$$86$$ 7.53375 8.35883i 0.812385 0.901356i
$$87$$ 0 0
$$88$$ 6.12132 + 4.46117i 0.652535 + 0.475562i
$$89$$ 0.275896i 0.0292449i −0.999893 0.0146224i $$-0.995345\pi$$
0.999893 0.0146224i $$-0.00465463\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −12.8609 + 1.33899i −1.34084 + 0.139599i
$$93$$ 0 0
$$94$$ 9.50445 + 8.56628i 0.980309 + 0.883545i
$$95$$ 6.92468i 0.710457i
$$96$$ 0 0
$$97$$ 12.9343i 1.31328i 0.754204 + 0.656640i $$0.228023\pi$$
−0.754204 + 0.656640i $$0.771977\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0.500000 + 4.80247i 0.0500000 + 0.480247i
$$101$$ 16.1947i 1.61143i −0.592304 0.805714i $$-0.701782\pi$$
0.592304 0.805714i $$-0.298218\pi$$
$$102$$ 0 0
$$103$$ 10.3963 1.02438 0.512189 0.858873i $$-0.328835\pi$$
0.512189 + 0.858873i $$0.328835\pi$$
$$104$$ 7.72255 + 5.62813i 0.757259 + 0.551884i
$$105$$ 0 0
$$106$$ −2.58579 2.33055i −0.251154 0.226363i
$$107$$ 6.46521i 0.625016i 0.949915 + 0.312508i $$0.101169\pi$$
−0.949915 + 0.312508i $$0.898831\pi$$
$$108$$ 0 0
$$109$$ −7.41421 −0.710153 −0.355076 0.934837i $$-0.615545\pi$$
−0.355076 + 0.934837i $$0.615545\pi$$
$$110$$ −4.52377 4.07724i −0.431324 0.388749i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 12.6060 1.18587 0.592937 0.805249i $$-0.297968\pi$$
0.592937 + 0.805249i $$0.297968\pi$$
$$114$$ 0 0
$$115$$ 10.3963 0.969461
$$116$$ 0.975845 + 9.37293i 0.0906049 + 0.870254i
$$117$$ 0 0
$$118$$ −9.50445 8.56628i −0.874955 0.788590i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 3.82843 0.348039
$$122$$ −3.19879 + 3.54911i −0.289604 + 0.321321i
$$123$$ 0 0
$$124$$ 2.15315 + 20.6808i 0.193358 + 1.85719i
$$125$$ 11.9223i 1.06637i
$$126$$ 0 0
$$127$$ 11.2529i 0.998532i −0.866449 0.499266i $$-0.833603\pi$$
0.866449 0.499266i $$-0.166397\pi$$
$$128$$ 4.63714 10.3197i 0.409869 0.912144i
$$129$$ 0 0
$$130$$ −5.70711 5.14377i −0.500546 0.451138i
$$131$$ −12.7951 −1.11792 −0.558958 0.829196i $$-0.688799\pi$$
−0.558958 + 0.829196i $$0.688799\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −10.6543 + 11.8212i −0.920394 + 1.02119i
$$135$$ 0 0
$$136$$ 3.67565 + 2.67878i 0.315184 + 0.229704i
$$137$$ 19.0583 1.62826 0.814132 0.580680i $$-0.197213\pi$$
0.814132 + 0.580680i $$0.197213\pi$$
$$138$$ 0 0
$$139$$ 6.09002 0.516549 0.258274 0.966072i $$-0.416846\pi$$
0.258274 + 0.966072i $$0.416846\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 7.60660 8.43966i 0.638332 0.708241i
$$143$$ −9.04753 −0.756593
$$144$$ 0 0
$$145$$ 7.57675i 0.629214i
$$146$$ −5.84875 + 6.48929i −0.484046 + 0.537058i
$$147$$ 0 0
$$148$$ 0.0502525 + 0.482672i 0.00413073 + 0.0396754i
$$149$$ −23.7701 −1.94733 −0.973663 0.227993i $$-0.926784\pi$$
−0.973663 + 0.227993i $$0.926784\pi$$
$$150$$ 0 0
$$151$$ 7.95699i 0.647531i 0.946137 + 0.323765i $$0.104949\pi$$
−0.946137 + 0.323765i $$0.895051\pi$$
$$152$$ −7.17373 + 9.84332i −0.581866 + 0.798398i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 16.7177i 1.34279i
$$156$$ 0 0
$$157$$ 10.9552i 0.874323i −0.899383 0.437162i $$-0.855984\pi$$
0.899383 0.437162i $$-0.144016\pi$$
$$158$$ −3.12058 + 3.46234i −0.248260 + 0.275449i
$$159$$ 0 0
$$160$$ −4.56751 + 7.86657i −0.361094 + 0.621907i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 11.2529i 0.881394i 0.897656 + 0.440697i $$0.145269\pi$$
−0.897656 + 0.440697i $$0.854731\pi$$
$$164$$ 23.1677 2.41206i 1.80909 0.188350i
$$165$$ 0 0
$$166$$ −13.4413 12.1146i −1.04325 0.940272i
$$167$$ −21.8427 −1.69024 −0.845119 0.534579i $$-0.820470\pi$$
−0.845119 + 0.534579i $$0.820470\pi$$
$$168$$ 0 0
$$169$$ 1.58579 0.121984
$$170$$ −2.71637 2.44824i −0.208336 0.187772i
$$171$$ 0 0
$$172$$ 15.8284 1.64795i 1.20691 0.125655i
$$173$$ 11.2563i 0.855798i 0.903827 + 0.427899i $$0.140746\pi$$
−0.903827 + 0.427899i $$0.859254\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.20658 + 10.4822i 0.166328 + 0.790124i
$$177$$ 0 0
$$178$$ 0.261220 0.289829i 0.0195793 0.0217236i
$$179$$ 12.4710i 0.932123i 0.884752 + 0.466062i $$0.154328\pi$$
−0.884752 + 0.466062i $$0.845672\pi$$
$$180$$ 0 0
$$181$$ 14.9134i 1.10850i −0.832349 0.554252i $$-0.813004\pi$$
0.832349 0.554252i $$-0.186996\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −14.7782 10.7702i −1.08946 0.793991i
$$185$$ 0.390175i 0.0286863i
$$186$$ 0 0
$$187$$ −4.30629 −0.314907
$$188$$ 1.87381 + 17.9978i 0.136661 + 1.31262i
$$189$$ 0 0
$$190$$ 6.55635 7.27439i 0.475648 0.527740i
$$191$$ 10.2524i 0.741841i 0.928665 + 0.370921i $$0.120958\pi$$
−0.928665 + 0.370921i $$0.879042\pi$$
$$192$$ 0 0
$$193$$ −7.65685 −0.551152 −0.275576 0.961279i $$-0.588869\pi$$
−0.275576 + 0.961279i $$0.588869\pi$$
$$194$$ −12.2463 + 13.5875i −0.879235 + 0.975527i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 10.1445 0.722769 0.361384 0.932417i $$-0.382304\pi$$
0.361384 + 0.932417i $$0.382304\pi$$
$$198$$ 0 0
$$199$$ −14.7026 −1.04224 −0.521120 0.853483i $$-0.674486\pi$$
−0.521120 + 0.853483i $$0.674486\pi$$
$$200$$ −4.02177 + 5.51841i −0.284382 + 0.390210i
$$201$$ 0 0
$$202$$ 15.3332 17.0125i 1.07884 1.19700i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −18.7279 −1.30801
$$206$$ 10.9213 + 9.84332i 0.760926 + 0.685816i
$$207$$ 0 0
$$208$$ 2.78379 + 13.2241i 0.193021 + 0.916929i
$$209$$ 11.5322i 0.797696i
$$210$$ 0 0
$$211$$ 15.9140i 1.09556i 0.836621 + 0.547782i $$0.184528\pi$$
−0.836621 + 0.547782i $$0.815472\pi$$
$$212$$ −0.509789 4.89649i −0.0350124 0.336292i
$$213$$ 0 0
$$214$$ −6.12132 + 6.79172i −0.418445 + 0.464272i
$$215$$ −12.7951 −0.872622
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −7.78864 7.01984i −0.527513 0.475444i
$$219$$ 0 0
$$220$$ −0.891862 8.56628i −0.0601294 0.577539i
$$221$$ −5.43275 −0.365446
$$222$$ 0 0
$$223$$ 8.61259 0.576741 0.288371 0.957519i $$-0.406886\pi$$
0.288371 + 0.957519i $$0.406886\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 13.2426 + 11.9355i 0.880887 + 0.793937i
$$227$$ 3.74761 0.248738 0.124369 0.992236i $$-0.460309\pi$$
0.124369 + 0.992236i $$0.460309\pi$$
$$228$$ 0 0
$$229$$ 4.19825i 0.277428i 0.990332 + 0.138714i $$0.0442969\pi$$
−0.990332 + 0.138714i $$0.955703\pi$$
$$230$$ 10.9213 + 9.84332i 0.720132 + 0.649049i
$$231$$ 0 0
$$232$$ −7.84924 + 10.7702i −0.515328 + 0.707099i
$$233$$ −3.69222 −0.241885 −0.120943 0.992660i $$-0.538592\pi$$
−0.120943 + 0.992660i $$0.538592\pi$$
$$234$$ 0 0
$$235$$ 14.5488i 0.949058i
$$236$$ −1.87381 17.9978i −0.121974 1.17156i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1.10926i 0.0717518i 0.999356 + 0.0358759i $$0.0114221\pi$$
−0.999356 + 0.0358759i $$0.988578\pi$$
$$240$$ 0 0
$$241$$ 1.39942i 0.0901444i 0.998984 + 0.0450722i $$0.0143518\pi$$
−0.998984 + 0.0450722i $$0.985648\pi$$
$$242$$ 4.02177 + 3.62479i 0.258529 + 0.233010i
$$243$$ 0 0
$$244$$ −6.72066 + 0.699709i −0.430246 + 0.0447943i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 14.5488i 0.925717i
$$248$$ −17.3189 + 23.7639i −1.09975 + 1.50901i
$$249$$ 0 0
$$250$$ 11.2882 12.5244i 0.713927 0.792115i
$$251$$ −21.8427 −1.37870 −0.689349 0.724430i $$-0.742103\pi$$
−0.689349 + 0.724430i $$0.742103\pi$$
$$252$$ 0 0
$$253$$ 17.3137 1.08850
$$254$$ 10.6543 11.8212i 0.668512 0.741726i
$$255$$ 0 0
$$256$$ 14.6421 6.45042i 0.915133 0.403151i
$$257$$ 14.3107i 0.892679i 0.894864 + 0.446339i $$0.147273\pi$$
−0.894864 + 0.446339i $$0.852727\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −1.12516 10.8071i −0.0697794 0.670226i
$$261$$ 0 0
$$262$$ −13.4413 12.1146i −0.830407 0.748440i
$$263$$ 2.67798i 0.165131i −0.996586 0.0825656i $$-0.973689\pi$$
0.996586 0.0825656i $$-0.0263114\pi$$
$$264$$ 0 0
$$265$$ 3.95815i 0.243147i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −22.3848 + 2.33055i −1.36737 + 0.142361i
$$269$$ 16.1947i 0.987406i −0.869631 0.493703i $$-0.835643\pi$$
0.869631 0.493703i $$-0.164357\pi$$
$$270$$ 0 0
$$271$$ −16.4863 −1.00147 −0.500737 0.865600i $$-0.666937\pi$$
−0.500737 + 0.865600i $$0.666937\pi$$
$$272$$ 1.32498 + 6.29420i 0.0803388 + 0.381642i
$$273$$ 0 0
$$274$$ 20.0208 + 18.0446i 1.20950 + 1.09011i
$$275$$ 6.46521i 0.389867i
$$276$$ 0 0
$$277$$ 23.7990 1.42994 0.714971 0.699154i $$-0.246440\pi$$
0.714971 + 0.699154i $$0.246440\pi$$
$$278$$ 6.39757 + 5.76608i 0.383701 + 0.345827i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −8.19285 −0.488744 −0.244372 0.969681i $$-0.578582\pi$$
−0.244372 + 0.969681i $$0.578582\pi$$
$$282$$ 0 0
$$283$$ −10.3963 −0.617996 −0.308998 0.951063i $$-0.599994\pi$$
−0.308998 + 0.951063i $$0.599994\pi$$
$$284$$ 15.9815 1.66388i 0.948327 0.0987333i
$$285$$ 0 0
$$286$$ −9.50445 8.56628i −0.562010 0.506535i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 14.4142 0.847895
$$290$$ 7.17373 7.95938i 0.421256 0.467391i
$$291$$ 0 0
$$292$$ −12.2882 + 1.27937i −0.719115 + 0.0748693i
$$293$$ 1.21786i 0.0711483i 0.999367 + 0.0355741i $$0.0113260\pi$$
−0.999367 + 0.0355741i $$0.988674\pi$$
$$294$$ 0 0
$$295$$ 14.5488i 0.847063i
$$296$$ −0.404208 + 0.554628i −0.0234941 + 0.0322371i
$$297$$ 0 0
$$298$$ −24.9706 22.5058i −1.44651 1.30372i
$$299$$ 21.8427 1.26319
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −7.53375 + 8.35883i −0.433518 + 0.480997i
$$303$$ 0 0
$$304$$ −16.8557 + 3.54827i −0.966743 + 0.203507i
$$305$$ 5.43275 0.311078
$$306$$ 0 0
$$307$$ −22.5763 −1.28850 −0.644250 0.764815i $$-0.722830\pi$$
−0.644250 + 0.764815i $$0.722830\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 15.8284 17.5619i 0.898994 0.997451i
$$311$$ −21.8427 −1.23858 −0.619292 0.785161i $$-0.712580\pi$$
−0.619292 + 0.785161i $$0.712580\pi$$
$$312$$ 0 0
$$313$$ 6.17733i 0.349163i 0.984643 + 0.174582i $$0.0558573\pi$$
−0.984643 + 0.174582i $$0.944143\pi$$
$$314$$ 10.3725 11.5085i 0.585355 0.649462i
$$315$$ 0 0
$$316$$ −6.55635 + 0.682602i −0.368823 + 0.0383994i
$$317$$ −10.1445 −0.569774 −0.284887 0.958561i $$-0.591956\pi$$
−0.284887 + 0.958561i $$0.591956\pi$$
$$318$$ 0 0
$$319$$ 12.6181i 0.706477i
$$320$$ −12.2463 + 3.93929i −0.684590 + 0.220213i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 6.92468i 0.385300i
$$324$$ 0 0
$$325$$ 8.15640i 0.452436i
$$326$$ −10.6543 + 11.8212i −0.590089 + 0.654714i
$$327$$ 0 0
$$328$$ 26.6214 + 19.4015i 1.46992 + 1.07127i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 22.5058i 1.23703i −0.785773 0.618514i $$-0.787735\pi$$
0.785773 0.618514i $$-0.212265\pi$$
$$332$$ −2.64996 25.4527i −0.145436 1.39690i
$$333$$ 0 0
$$334$$ −22.9458 20.6808i −1.25554 1.13161i
$$335$$ 18.0951 0.988639
$$336$$ 0 0
$$337$$ −34.3848 −1.87306 −0.936529 0.350590i $$-0.885981\pi$$
−0.936529 + 0.350590i $$0.885981\pi$$
$$338$$ 1.66587 + 1.50144i 0.0906114 + 0.0816674i
$$339$$ 0 0
$$340$$ −0.535534 5.14377i −0.0290434 0.278960i
$$341$$ 27.8411i 1.50768i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 18.1881 + 13.2553i 0.980635 + 0.714679i
$$345$$ 0 0
$$346$$ −10.6575 + 11.8247i −0.572952 + 0.635701i
$$347$$ 14.0397i 0.753690i −0.926276 0.376845i $$-0.877009\pi$$
0.926276 0.376845i $$-0.122991\pi$$
$$348$$ 0 0
$$349$$ 8.15640i 0.436602i −0.975881 0.218301i $$-0.929949\pi$$
0.975881 0.218301i $$-0.0700515\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −7.60660 + 13.1008i −0.405433 + 0.698273i
$$353$$ 1.21786i 0.0648203i −0.999475 0.0324101i $$-0.989682\pi$$
0.999475 0.0324101i $$-0.0103183\pi$$
$$354$$ 0 0
$$355$$ −12.9189 −0.685663
$$356$$ 0.548825 0.0571399i 0.0290877 0.00302841i
$$357$$ 0 0
$$358$$ −11.8076 + 13.1008i −0.624052 + 0.692397i
$$359$$ 6.46521i 0.341221i −0.985339 0.170610i $$-0.945426\pi$$
0.985339 0.170610i $$-0.0545740\pi$$
$$360$$ 0 0
$$361$$ −0.455844 −0.0239918
$$362$$ 14.1201 15.6665i 0.742137 0.823415i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 9.93338 0.519937
$$366$$ 0 0
$$367$$ −18.2701 −0.953689 −0.476844 0.878988i $$-0.658220\pi$$
−0.476844 + 0.878988i $$0.658220\pi$$
$$368$$ −5.32716 25.3062i −0.277698 1.31918i
$$369$$ 0 0
$$370$$ 0.369422 0.409880i 0.0192053 0.0213086i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 2.82843 0.146450 0.0732252 0.997315i $$-0.476671\pi$$
0.0732252 + 0.997315i $$0.476671\pi$$
$$374$$ −4.52377 4.07724i −0.233918 0.210829i
$$375$$ 0 0
$$376$$ −15.0720 + 20.6808i −0.777280 + 1.06653i
$$377$$ 15.9188i 0.819858i
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 13.7749 1.43415i 0.706638 0.0735703i
$$381$$ 0 0
$$382$$ −9.70711 + 10.7702i −0.496659 + 0.551052i
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −8.04354 7.24958i −0.409405 0.368994i
$$387$$ 0 0
$$388$$ −25.7296 + 2.67878i −1.30622 + 0.135995i
$$389$$ −0.211161 −0.0107063 −0.00535315 0.999986i $$-0.501704\pi$$
−0.00535315 + 0.999986i $$0.501704\pi$$
$$390$$ 0 0
$$391$$ 10.3963 0.525764
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 10.6569 + 9.60494i 0.536885 + 0.483890i
$$395$$ 5.29992 0.266668
$$396$$ 0 0
$$397$$ 7.33664i 0.368216i −0.982906 0.184108i $$-0.941060\pi$$
0.982906 0.184108i $$-0.0589395\pi$$
$$398$$ −15.4451 13.9206i −0.774193 0.697774i
$$399$$ 0 0
$$400$$ −9.44975 + 1.98925i −0.472487 + 0.0994624i
$$401$$ 29.9238 1.49432 0.747162 0.664642i $$-0.231416\pi$$
0.747162 + 0.664642i $$0.231416\pi$$
$$402$$ 0 0
$$403$$ 35.1239i 1.74964i
$$404$$ 32.2152 3.35402i 1.60277 0.166869i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0.649787i 0.0322087i
$$408$$ 0 0
$$409$$ 33.2053i 1.64189i 0.571004 + 0.820947i $$0.306554\pi$$
−0.571004 + 0.820947i $$0.693446\pi$$
$$410$$ −19.6737 17.7318i −0.971615 0.875709i
$$411$$ 0 0
$$412$$ 2.15315 + 20.6808i 0.106078 + 1.01887i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 20.5751i 1.00999i
$$416$$ −9.59636 + 16.5277i −0.470500 + 0.810337i
$$417$$ 0 0
$$418$$ 10.9188 12.1146i 0.534054 0.592542i
$$419$$ 34.6378 1.69217 0.846084 0.533049i $$-0.178954\pi$$
0.846084 + 0.533049i $$0.178954\pi$$
$$420$$ 0 0
$$421$$ 16.0000 0.779792 0.389896 0.920859i $$-0.372511\pi$$
0.389896 + 0.920859i $$0.372511\pi$$
$$422$$ −15.0675 + 16.7177i −0.733474 + 0.813803i
$$423$$ 0 0
$$424$$ 4.10051 5.62644i 0.199138 0.273244i
$$425$$ 3.88215i 0.188312i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −12.8609 + 1.33899i −0.621656 + 0.0647225i
$$429$$ 0 0
$$430$$ −13.4413 12.1146i −0.648198 0.584216i
$$431$$ 2.67798i 0.128994i 0.997918 + 0.0644969i $$0.0205442\pi$$
−0.997918 + 0.0644969i $$0.979456\pi$$
$$432$$ 0 0
$$433$$ 25.6285i 1.23163i 0.787891 + 0.615814i $$0.211173\pi$$
−0.787891 + 0.615814i $$0.788827\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.53553 14.7487i −0.0735387 0.706335i
$$437$$ 27.8411i 1.33182i
$$438$$ 0 0
$$439$$ −14.7026 −0.701717 −0.350858 0.936429i $$-0.614110\pi$$
−0.350858 + 0.936429i $$0.614110\pi$$
$$440$$ 7.17373 9.84332i 0.341994 0.469262i
$$441$$ 0 0
$$442$$ −5.70711 5.14377i −0.271459 0.244664i
$$443$$ 33.8948i 1.61039i 0.593010 + 0.805195i $$0.297939\pi$$
−0.593010 + 0.805195i $$0.702061\pi$$
$$444$$ 0 0
$$445$$ −0.443651 −0.0210311
$$446$$ 9.04753 + 8.15447i 0.428413 + 0.386125i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 8.70264 0.410703 0.205351 0.978688i $$-0.434166\pi$$
0.205351 + 0.978688i $$0.434166\pi$$
$$450$$ 0 0
$$451$$ −31.1889 −1.46863
$$452$$ 2.61079 + 25.0765i 0.122801 + 1.17950i
$$453$$ 0 0
$$454$$ 3.93687 + 3.54827i 0.184767 + 0.166529i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 32.4853 1.51960 0.759799 0.650158i $$-0.225297\pi$$
0.759799 + 0.650158i $$0.225297\pi$$
$$458$$ −3.97494 + 4.41027i −0.185737 + 0.206078i
$$459$$ 0 0
$$460$$ 2.15315 + 20.6808i 0.100391 + 0.964249i
$$461$$ 29.4491i 1.37158i 0.727798 + 0.685792i $$0.240544\pi$$
−0.727798 + 0.685792i $$0.759456\pi$$
$$462$$ 0 0
$$463$$ 38.4198i 1.78552i 0.450535 + 0.892759i $$0.351233\pi$$
−0.450535 + 0.892759i $$0.648767\pi$$
$$464$$ −18.4430 + 3.88239i −0.856193 + 0.180236i
$$465$$ 0 0
$$466$$ −3.87868 3.49582i −0.179676 0.161941i
$$467$$ 9.04753 0.418670 0.209335 0.977844i $$-0.432870\pi$$
0.209335 + 0.977844i $$0.432870\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 13.7749 15.2835i 0.635389 0.704976i
$$471$$ 0 0
$$472$$ 15.0720 20.6808i 0.693746 0.951913i
$$473$$ −21.3087 −0.979773
$$474$$ 0 0
$$475$$ 10.3963 0.477015
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −1.05025 + 1.16527i −0.0480374 + 0.0532984i
$$479$$ 34.6378 1.58264 0.791321 0.611401i $$-0.209394\pi$$
0.791321 + 0.611401i $$0.209394\pi$$
$$480$$ 0 0
$$481$$ 0.819760i 0.0373778i
$$482$$ −1.32498 + 1.47009i −0.0603512 + 0.0669608i
$$483$$ 0 0
$$484$$ 0.792893 + 7.61569i 0.0360406 + 0.346168i
$$485$$ 20.7989 0.944428
$$486$$ 0 0
$$487$$ 14.5488i 0.659268i −0.944109 0.329634i $$-0.893075\pi$$
0.944109 0.329634i $$-0.106925\pi$$
$$488$$ −7.72255 5.62813i −0.349584 0.254774i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 32.3261i 1.45886i 0.684058 + 0.729428i $$0.260213\pi$$
−0.684058 + 0.729428i $$0.739787\pi$$
$$492$$ 0 0
$$493$$ 7.57675i 0.341239i
$$494$$ 13.7749 15.2835i 0.619762 0.687638i
$$495$$ 0 0
$$496$$ −40.6934 + 8.56628i −1.82719 + 0.384637i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 19.2099i 0.859952i −0.902840 0.429976i $$-0.858522\pi$$
0.902840 0.429976i $$-0.141478\pi$$
$$500$$ 23.7165 2.46920i 1.06063 0.110426i
$$501$$ 0 0
$$502$$ −22.9458 20.6808i −1.02412 0.923031i
$$503$$ −5.29992 −0.236312 −0.118156 0.992995i $$-0.537698\pi$$
−0.118156 + 0.992995i $$0.537698\pi$$
$$504$$ 0 0
$$505$$ −26.0416 −1.15884
$$506$$ 18.1881 + 16.3928i 0.808559 + 0.728747i
$$507$$ 0 0
$$508$$ 22.3848 2.33055i 0.993164 0.103401i
$$509$$ 1.21786i 0.0539808i −0.999636 0.0269904i $$-0.991408\pi$$
0.999636 0.0269904i $$-0.00859236\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 21.4889 + 7.08713i 0.949684 + 0.313210i
$$513$$ 0 0
$$514$$ −13.5495 + 15.0334i −0.597644 + 0.663097i
$$515$$ 16.7177i 0.736668i
$$516$$ 0 0
$$517$$ 24.2291i 1.06559i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 9.05025 12.4182i 0.396880 0.544572i
$$521$$ 15.6429i 0.685327i 0.939458 + 0.342663i $$0.111329\pi$$
−0.939458 + 0.342663i $$0.888671\pi$$
$$522$$ 0 0
$$523$$ 14.7026 0.642900 0.321450 0.946927i $$-0.395830\pi$$
0.321450 + 0.946927i $$0.395830\pi$$
$$524$$ −2.64996 25.4527i −0.115764 1.11191i
$$525$$ 0 0
$$526$$ 2.53553 2.81322i 0.110555 0.122662i
$$527$$ 16.7177i 0.728233i
$$528$$ 0 0
$$529$$ −18.7990 −0.817347
$$530$$ −3.74761 + 4.15804i −0.162786 + 0.180614i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −39.3474 −1.70433
$$534$$ 0 0
$$535$$ 10.3963 0.449472
$$536$$ −25.7218 18.7459i −1.11101 0.809698i
$$537$$ 0 0
$$538$$ 15.3332 17.0125i 0.661063 0.733462i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −33.1127 −1.42363 −0.711813 0.702369i $$-0.752126\pi$$
−0.711813 + 0.702369i $$0.752126\pi$$
$$542$$ −17.3189 15.6094i −0.743911 0.670481i
$$543$$ 0 0
$$544$$ −4.56751 + 7.86657i −0.195831 + 0.337277i
$$545$$ 11.9223i 0.510697i
$$546$$ 0 0
$$547$$ 3.29589i 0.140922i −0.997515 0.0704611i $$-0.977553\pi$$
0.997515 0.0704611i $$-0.0224471\pi$$
$$548$$ 3.94711 + 37.9118i 0.168612 + 1.61951i
$$549$$ 0 0
$$550$$ 6.12132 6.79172i 0.261014 0.289600i
$$551$$ 20.2904 0.864399
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 25.0009 + 22.5331i 1.06219 + 0.957339i
$$555$$ 0 0
$$556$$ 1.26128 + 12.1146i 0.0534904 + 0.513772i
$$557$$ −31.4532 −1.33271 −0.666357 0.745633i $$-0.732147\pi$$
−0.666357 + 0.745633i $$0.732147\pi$$
$$558$$ 0 0
$$559$$ −26.8826 −1.13701
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −8.60660 7.75706i −0.363048 0.327212i
$$563$$ −3.74761 −0.157943 −0.0789715 0.996877i $$-0.525164\pi$$
−0.0789715 + 0.996877i $$0.525164\pi$$
$$564$$ 0 0
$$565$$ 20.2710i 0.852806i
$$566$$ −10.9213 9.84332i −0.459058 0.413745i
$$567$$ 0 0
$$568$$ 18.3640 + 13.3835i 0.770535 + 0.561559i
$$569$$ −12.0962 −0.507100 −0.253550 0.967322i $$-0.581598\pi$$
−0.253550 + 0.967322i $$0.581598\pi$$
$$570$$ 0 0
$$571$$ 30.4628i 1.27483i 0.770522 + 0.637413i $$0.219996\pi$$
−0.770522 + 0.637413i $$0.780004\pi$$
$$572$$ −1.87381 17.9978i −0.0783477 0.752525i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 15.6084i 0.650916i
$$576$$ 0 0
$$577$$ 18.8715i 0.785632i −0.919617 0.392816i $$-0.871501\pi$$
0.919617 0.392816i $$-0.128499\pi$$
$$578$$ 15.1422 + 13.6475i 0.629831 + 0.567661i
$$579$$ 0 0
$$580$$ 15.0720 1.56920i 0.625832 0.0651573i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 6.59179i 0.273004i
$$584$$ −14.1201 10.2906i −0.584295 0.425829i
$$585$$ 0 0
$$586$$ −1.15308 + 1.27937i −0.0476334 + 0.0528501i
$$587$$ 34.6378 1.42966 0.714828 0.699300i $$-0.246505\pi$$
0.714828 + 0.699300i $$0.246505\pi$$
$$588$$ 0 0
$$589$$ 44.7696 1.84470
$$590$$ −13.7749 + 15.2835i −0.567104 + 0.629212i
$$591$$ 0 0
$$592$$ −0.949747 + 0.199929i −0.0390344 + 0.00821705i
$$593$$ 18.4688i 0.758421i −0.925310 0.379211i $$-0.876196\pi$$
0.925310 0.379211i $$-0.123804\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −4.92296 47.2847i −0.201652 1.93686i
$$597$$ 0 0
$$598$$ 22.9458 + 20.6808i 0.938322 + 0.845702i
$$599$$ 16.5273i 0.675289i 0.941274 + 0.337644i $$0.109630\pi$$
−0.941274 + 0.337644i $$0.890370\pi$$
$$600$$ 0 0
$$601$$ 16.8925i 0.689058i 0.938776 + 0.344529i $$0.111961\pi$$
−0.938776 + 0.344529i $$0.888039\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −15.8284 + 1.64795i −0.644050 + 0.0670540i
$$605$$ 6.15626i 0.250287i
$$606$$ 0 0
$$607$$ −2.52257 −0.102388 −0.0511939 0.998689i $$-0.516303\pi$$
−0.0511939 + 0.998689i $$0.516303\pi$$
$$608$$ −21.0665 12.2317i −0.854360 0.496061i
$$609$$ 0 0
$$610$$ 5.70711 + 5.14377i 0.231074 + 0.208265i
$$611$$ 30.5670i 1.23661i
$$612$$ 0 0
$$613$$ 22.0416 0.890253 0.445127 0.895468i $$-0.353159\pi$$
0.445127 + 0.895468i $$0.353159\pi$$
$$614$$ −23.7165 21.3755i −0.957119 0.862644i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −16.5969 −0.668165 −0.334082 0.942544i $$-0.608426\pi$$
−0.334082 + 0.942544i $$0.608426\pi$$
$$618$$ 0 0
$$619$$ 6.09002 0.244778 0.122389 0.992482i $$-0.460944\pi$$
0.122389 + 0.992482i $$0.460944\pi$$
$$620$$ 33.2556 3.46234i 1.33558 0.139051i
$$621$$ 0 0
$$622$$ −22.9458 20.6808i −0.920041 0.829226i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −7.10051 −0.284020
$$626$$ −5.84875 + 6.48929i −0.233763 + 0.259364i
$$627$$ 0 0
$$628$$ 21.7927 2.26890i 0.869623 0.0905391i
$$629$$ 0.390175i 0.0155573i
$$630$$ 0 0
$$631$$ 45.0115i 1.79188i −0.444174 0.895941i $$-0.646503\pi$$
0.444174 0.895941i $$-0.353497\pi$$
$$632$$ −7.53375 5.49053i −0.299676 0.218402i
$$633$$ 0 0
$$634$$ −10.6569 9.60494i −0.423238 0.381461i
$$635$$ −18.0951 −0.718081
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 11.9469 13.2553i 0.472983 0.524783i
$$639$$ 0 0
$$640$$ −16.5945 7.45669i −0.655956 0.294752i
$$641$$ 28.9043 1.14165 0.570825 0.821072i $$-0.306624\pi$$
0.570825 + 0.821072i $$0.306624\pi$$
$$642$$ 0 0
$$643$$ 45.8915 1.80979 0.904893 0.425640i $$-0.139951\pi$$
0.904893 + 0.425640i $$0.139951\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 6.55635 7.27439i 0.257956 0.286207i
$$647$$ 27.1426 1.06709 0.533543 0.845773i $$-0.320860\pi$$
0.533543 + 0.845773i $$0.320860\pi$$
$$648$$ 0 0
$$649$$ 24.2291i 0.951076i
$$650$$ 7.72255 8.56831i 0.302903 0.336077i
$$651$$ 0 0
$$652$$ −22.3848 + 2.33055i −0.876655 + 0.0912713i
$$653$$ 37.3083 1.45999 0.729993 0.683455i $$-0.239523\pi$$
0.729993 + 0.683455i $$0.239523\pi$$
$$654$$ 0 0
$$655$$ 20.5751i 0.803935i
$$656$$ 9.59636 + 45.5867i 0.374675 + 1.77986i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 31.6763i 1.23393i 0.786990 + 0.616966i $$0.211639\pi$$
−0.786990 + 0.616966i $$0.788361\pi$$
$$660$$ 0 0
$$661$$ 43.5809i 1.69510i −0.530717 0.847549i $$-0.678077\pi$$
0.530717 0.847549i $$-0.321923\pi$$
$$662$$ 21.3087 23.6423i 0.828184 0.918886i
$$663$$ 0 0
$$664$$ 21.3151 29.2471i 0.827185 1.13501i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 30.4628i 1.17952i
$$668$$ −4.52377 43.4505i −0.175030 1.68115i
$$669$$ 0 0
$$670$$ 19.0089 + 17.1326i 0.734378 + 0.661889i
$$671$$ 9.04753 0.349276
$$672$$ 0 0
$$673$$ −16.1005 −0.620629 −0.310314 0.950634i $$-0.600434\pi$$
−0.310314 + 0.950634i $$0.600434\pi$$
$$674$$ −36.1213 32.5558i −1.39134 1.25400i
$$675$$ 0 0
$$676$$ 0.328427 + 3.15452i 0.0126318 + 0.121328i
$$677$$ 31.8849i 1.22543i 0.790302 + 0.612717i $$0.209924\pi$$
−0.790302 + 0.612717i $$0.790076\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 4.30759 5.91059i 0.165188 0.226661i
$$681$$ 0 0
$$682$$ 26.3602 29.2471i 1.00938 1.11993i
$$683$$ 16.5273i 0.632401i 0.948692 + 0.316201i $$0.102407\pi$$
−0.948692 + 0.316201i $$0.897593\pi$$
$$684$$ 0 0
$$685$$ 30.6465i 1.17094i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 6.55635 + 31.1454i 0.249958 + 1.18741i
$$689$$ 8.31609i 0.316818i
$$690$$ 0 0
$$691$$ −12.1800 −0.463350 −0.231675 0.972793i $$-0.574421\pi$$
−0.231675 + 0.972793i $$0.574421\pi$$
$$692$$ −22.3915 + 2.33125i −0.851197 + 0.0886208i
$$693$$ 0 0
$$694$$ 13.2929 14.7487i 0.504591 0.559853i
$$695$$ 9.79298i 0.371469i
$$696$$ 0 0
$$697$$ −18.7279 −0.709371
$$698$$ 7.72255 8.56831i 0.292303 0.324315i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −19.0583 −0.719824 −0.359912 0.932986i $$-0.617193\pi$$
−0.359912 + 0.932986i $$0.617193\pi$$
$$702$$ 0 0
$$703$$ 1.04488 0.0394085
$$704$$ −20.3947 + 6.56037i −0.768653 + 0.247253i
$$705$$ 0 0
$$706$$ 1.15308 1.27937i 0.0433968 0.0481496i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −31.4142 −1.17979 −0.589893 0.807482i $$-0.700830\pi$$
−0.589893 + 0.807482i $$0.700830\pi$$
$$710$$ −13.5713 12.2317i −0.509322 0.459048i
$$711$$ 0 0
$$712$$ 0.630642 + 0.459607i 0.0236343 + 0.0172245i
$$713$$ 67.2144i 2.51720i
$$714$$ 0 0
$$715$$ 14.5488i 0.544093i
$$716$$ −24.8078 + 2.58282i −0.927112 + 0.0965245i
$$717$$ 0 0
$$718$$ 6.12132 6.79172i 0.228446 0.253465i
$$719$$ −43.6854 −1.62919 −0.814594 0.580031i $$-0.803040\pi$$
−0.814594 + 0.580031i $$0.803040\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −0.478865 0.431597i −0.0178215 0.0160624i
$$723$$ 0 0
$$724$$ 29.6664 3.08866i 1.10254 0.114789i
$$725$$ 11.3753 0.422467
$$726$$ 0 0
$$727$$ 1.78372 0.0661547 0.0330773 0.999453i $$-0.489469\pi$$
0.0330773 + 0.999453i $$0.489469\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 10.4350 + 9.40501i 0.386218 + 0.348095i
$$731$$ −12.7951 −0.473246
$$732$$ 0 0
$$733$$ 23.3099i 0.860971i 0.902598 + 0.430485i $$0.141658\pi$$
−0.902598 + 0.430485i $$0.858342\pi$$
$$734$$ −19.1927 17.2982i −0.708416 0.638490i
$$735$$ 0 0
$$736$$ 18.3640 31.6280i 0.676905 1.16582i
$$737$$ 30.1350 1.11004
$$738$$ 0 0
$$739$$ 31.8280i 1.17081i 0.810741 + 0.585405i $$0.199065\pi$$
−0.810741 + 0.585405i $$0.800935\pi$$
$$740$$ 0.776156 0.0808080i 0.0285321 0.00297056i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 17.8269i 0.654006i −0.945023 0.327003i $$-0.893961\pi$$
0.945023 0.327003i $$-0.106039\pi$$
$$744$$ 0 0
$$745$$ 38.2233i 1.40039i
$$746$$ 2.97127 + 2.67798i 0.108786 + 0.0980478i
$$747$$ 0 0
$$748$$ −0.891862 8.56628i −0.0326097 0.313214i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 36.4891i 1.33150i −0.746173 0.665752i $$-0.768111\pi$$
0.746173 0.665752i $$-0.231889\pi$$
$$752$$ −35.4140 + 7.45493i −1.29141 + 0.271853i
$$753$$ 0 0
$$754$$ 15.0720 16.7227i 0.548891 0.609004i
$$755$$ 12.7951 0.465663
$$756$$ 0 0
$$757$$ 11.8995 0.432494 0.216247 0.976339i $$-0.430618\pi$$
0.216247 + 0.976339i $$0.430618\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 15.8284 + 11.5356i 0.574157 + 0.418441i
$$761$$ 8.26875i 0.299742i −0.988706 0.149871i $$-0.952114\pi$$
0.988706 0.149871i $$-0.0478858\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −20.3947 + 2.12335i −0.737853 + 0.0768202i
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 30.5670i 1.10371i
$$768$$ 0 0
$$769$$ 43.5809i 1.57157i 0.618502 + 0.785783i $$0.287740\pi$$
−0.618502 + 0.785783i $$0.712260\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −1.58579 15.2314i −0.0570737 0.548189i
$$773$$ 41.7617i 1.50206i 0.660267 + 0.751031i $$0.270443\pi$$
−0.660267 + 0.751031i $$0.729557\pi$$
$$774$$ 0 0
$$775$$ 25.0989 0.901580
$$776$$ −29.5652 21.5469i −1.06133 0.773489i
$$777$$ 0 0
$$778$$ −0.221825 0.199929i −0.00795283 0.00716782i
$$779$$ 50.1530i 1.79692i
$$780$$ 0 0
$$781$$ −21.5147 −0.769857
$$782$$ 10.9213 + 9.84332i 0.390546 + 0.351996i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −17.6164 −0.628758
$$786$$ 0 0
$$787$$ 44.1078 1.57227 0.786137 0.618053i $$-0.212078\pi$$
0.786137 + 0.618053i $$0.212078\pi$$
$$788$$ 2.10100 + 20.1800i 0.0748451 + 0.718883i
$$789$$ 0 0
$$790$$ 5.56758 + 5.01801i 0.198085 + 0.178533i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 11.4142 0.405331
$$794$$ 6.94640 7.70715i 0.246518 0.273517i
$$795$$ 0 0
$$796$$ −3.04501 29.2471i −0.107927 1.03664i
$$797$$ 28.5072i 1.00978i 0.863185 +