# Properties

 Label 825.2.bx.c.499.1 Level $825$ Weight $2$ Character 825.499 Analytic conductor $6.588$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 825.bx (of order $$10$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.58765816676$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$2$$ over $$\Q(\zeta_{10})$$ Coefficient field: $$\Q(\zeta_{20})$$ Defining polynomial: $$x^{8} - x^{6} + x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

## Embedding invariants

 Embedding label 499.1 Root $$0.951057 - 0.309017i$$ of defining polynomial Character $$\chi$$ $$=$$ 825.499 Dual form 825.2.bx.c.124.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.363271 + 0.500000i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.726543 + 0.236068i) q^{7} +(-2.12663 - 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$$ $$q+(-0.363271 + 0.500000i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.726543 + 0.236068i) q^{7} +(-2.12663 - 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.23607 - 0.726543i) q^{11} -1.61803i q^{12} +(-0.726543 + 1.00000i) q^{13} +(0.145898 - 0.449028i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(1.17557 + 1.61803i) q^{17} +(-0.587785 + 0.190983i) q^{18} +(-1.54508 + 4.75528i) q^{19} +0.763932 q^{21} +(-0.812299 + 1.88197i) q^{22} +2.38197i q^{23} +(1.80902 + 1.31433i) q^{24} +(-0.236068 - 0.726543i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.726543 - 1.00000i) q^{28} +(1.80902 + 5.56758i) q^{29} +(-5.66312 - 4.11450i) q^{31} -5.61803i q^{32} +(-3.30220 - 0.309017i) q^{33} -1.23607 q^{34} +(-0.500000 + 1.53884i) q^{36} +(-7.10642 + 2.30902i) q^{37} +(-1.81636 - 2.50000i) q^{38} +(1.00000 - 0.726543i) q^{39} +(0.781153 - 2.40414i) q^{41} +(-0.277515 + 0.381966i) q^{42} -2.09017i q^{43} +(2.73607 + 4.61653i) q^{44} +(-1.19098 - 0.865300i) q^{46} +(-4.84104 - 1.57295i) q^{47} +(1.76336 - 0.572949i) q^{48} +(-5.19098 + 3.77147i) q^{49} +(-0.618034 - 1.90211i) q^{51} +(-1.90211 - 0.618034i) q^{52} +(-4.47777 + 6.16312i) q^{53} +0.618034 q^{54} +1.70820 q^{56} +(2.93893 - 4.04508i) q^{57} +(-3.44095 - 1.11803i) q^{58} +(2.07295 + 6.37988i) q^{59} +(-5.66312 + 4.11450i) q^{61} +(4.11450 - 1.33688i) q^{62} +(-0.726543 - 0.236068i) q^{63} +(-0.190983 - 0.138757i) q^{64} +(1.35410 - 1.53884i) q^{66} +9.38197i q^{67} +(-1.90211 + 2.61803i) q^{68} +(0.736068 - 2.26538i) q^{69} +(6.47214 - 4.70228i) q^{71} +(-1.31433 - 1.80902i) q^{72} +(12.8128 - 4.16312i) q^{73} +(1.42705 - 4.39201i) q^{74} -8.09017 q^{76} +(-2.17963 + 1.29180i) q^{77} +0.763932i q^{78} +(-6.54508 - 4.75528i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.918300 + 1.26393i) q^{82} +(3.35520 + 4.61803i) q^{83} +(0.381966 + 1.17557i) q^{84} +(1.04508 + 0.759299i) q^{86} -5.85410i q^{87} +(-7.38394 - 0.690983i) q^{88} -10.8541 q^{89} +(0.291796 - 0.898056i) q^{91} +(-3.66547 + 1.19098i) q^{92} +(4.11450 + 5.66312i) q^{93} +(2.54508 - 1.84911i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(-6.74315 + 9.28115i) q^{97} -3.96556i q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + O(q^{10})$$ $$8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 28 q^{14} - 12 q^{16} + 10 q^{19} + 24 q^{21} + 10 q^{24} + 16 q^{26} + 10 q^{29} - 14 q^{31} + 8 q^{34} - 4 q^{36} + 8 q^{39} - 34 q^{41} + 4 q^{44} - 14 q^{46} - 46 q^{49} + 4 q^{51} - 4 q^{54} - 40 q^{56} + 30 q^{59} - 14 q^{61} - 6 q^{64} - 16 q^{66} - 12 q^{69} + 16 q^{71} - 2 q^{74} - 20 q^{76} - 30 q^{79} - 2 q^{81} + 12 q^{84} - 14 q^{86} - 60 q^{89} + 56 q^{91} - 2 q^{94} + 4 q^{96} + 2 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$$.

 $$n$$ $$376$$ $$551$$ $$727$$ $$\chi(n)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.363271 + 0.500000i −0.256872 + 0.353553i −0.917903 0.396805i $$-0.870119\pi$$
0.661031 + 0.750358i $$0.270119\pi$$
$$3$$ −0.951057 0.309017i −0.549093 0.178411i
$$4$$ 0.500000 + 1.53884i 0.250000 + 0.769421i
$$5$$ 0 0
$$6$$ 0.500000 0.363271i 0.204124 0.148305i
$$7$$ −0.726543 + 0.236068i −0.274607 + 0.0892253i −0.443083 0.896480i $$-0.646115\pi$$
0.168476 + 0.985706i $$0.446115\pi$$
$$8$$ −2.12663 0.690983i −0.751876 0.244299i
$$9$$ 0.809017 + 0.587785i 0.269672 + 0.195928i
$$10$$ 0 0
$$11$$ 3.23607 0.726543i 0.975711 0.219061i
$$12$$ 1.61803i 0.467086i
$$13$$ −0.726543 + 1.00000i −0.201507 + 0.277350i −0.897796 0.440411i $$-0.854833\pi$$
0.696290 + 0.717761i $$0.254833\pi$$
$$14$$ 0.145898 0.449028i 0.0389929 0.120008i
$$15$$ 0 0
$$16$$ −1.50000 + 1.08981i −0.375000 + 0.272453i
$$17$$ 1.17557 + 1.61803i 0.285118 + 0.392431i 0.927421 0.374020i $$-0.122021\pi$$
−0.642303 + 0.766451i $$0.722021\pi$$
$$18$$ −0.587785 + 0.190983i −0.138542 + 0.0450151i
$$19$$ −1.54508 + 4.75528i −0.354467 + 1.09094i 0.601851 + 0.798608i $$0.294430\pi$$
−0.956318 + 0.292328i $$0.905570\pi$$
$$20$$ 0 0
$$21$$ 0.763932 0.166704
$$22$$ −0.812299 + 1.88197i −0.173183 + 0.401237i
$$23$$ 2.38197i 0.496674i 0.968674 + 0.248337i $$0.0798841\pi$$
−0.968674 + 0.248337i $$0.920116\pi$$
$$24$$ 1.80902 + 1.31433i 0.369264 + 0.268286i
$$25$$ 0 0
$$26$$ −0.236068 0.726543i −0.0462967 0.142487i
$$27$$ −0.587785 0.809017i −0.113119 0.155695i
$$28$$ −0.726543 1.00000i −0.137304 0.188982i
$$29$$ 1.80902 + 5.56758i 0.335926 + 1.03387i 0.966264 + 0.257553i $$0.0829163\pi$$
−0.630338 + 0.776321i $$0.717084\pi$$
$$30$$ 0 0
$$31$$ −5.66312 4.11450i −1.01713 0.738985i −0.0514344 0.998676i $$-0.516379\pi$$
−0.965692 + 0.259691i $$0.916379\pi$$
$$32$$ 5.61803i 0.993137i
$$33$$ −3.30220 0.309017i −0.574839 0.0537930i
$$34$$ −1.23607 −0.211984
$$35$$ 0 0
$$36$$ −0.500000 + 1.53884i −0.0833333 + 0.256474i
$$37$$ −7.10642 + 2.30902i −1.16829 + 0.379600i −0.828004 0.560722i $$-0.810524\pi$$
−0.340285 + 0.940322i $$0.610524\pi$$
$$38$$ −1.81636 2.50000i −0.294652 0.405554i
$$39$$ 1.00000 0.726543i 0.160128 0.116340i
$$40$$ 0 0
$$41$$ 0.781153 2.40414i 0.121996 0.375464i −0.871346 0.490669i $$-0.836752\pi$$
0.993342 + 0.115205i $$0.0367525\pi$$
$$42$$ −0.277515 + 0.381966i −0.0428214 + 0.0589386i
$$43$$ 2.09017i 0.318748i −0.987218 0.159374i $$-0.949052\pi$$
0.987218 0.159374i $$-0.0509476\pi$$
$$44$$ 2.73607 + 4.61653i 0.412478 + 0.695967i
$$45$$ 0 0
$$46$$ −1.19098 0.865300i −0.175601 0.127581i
$$47$$ −4.84104 1.57295i −0.706138 0.229438i −0.0661352 0.997811i $$-0.521067\pi$$
−0.640003 + 0.768372i $$0.721067\pi$$
$$48$$ 1.76336 0.572949i 0.254518 0.0826981i
$$49$$ −5.19098 + 3.77147i −0.741569 + 0.538781i
$$50$$ 0 0
$$51$$ −0.618034 1.90211i −0.0865421 0.266349i
$$52$$ −1.90211 0.618034i −0.263776 0.0857059i
$$53$$ −4.47777 + 6.16312i −0.615069 + 0.846569i −0.996982 0.0776285i $$-0.975265\pi$$
0.381914 + 0.924198i $$0.375265\pi$$
$$54$$ 0.618034 0.0841038
$$55$$ 0 0
$$56$$ 1.70820 0.228268
$$57$$ 2.93893 4.04508i 0.389270 0.535785i
$$58$$ −3.44095 1.11803i −0.451820 0.146805i
$$59$$ 2.07295 + 6.37988i 0.269875 + 0.830590i 0.990530 + 0.137296i $$0.0438412\pi$$
−0.720655 + 0.693294i $$0.756159\pi$$
$$60$$ 0 0
$$61$$ −5.66312 + 4.11450i −0.725088 + 0.526807i −0.888006 0.459832i $$-0.847910\pi$$
0.162918 + 0.986640i $$0.447910\pi$$
$$62$$ 4.11450 1.33688i 0.522542 0.169784i
$$63$$ −0.726543 0.236068i −0.0915358 0.0297418i
$$64$$ −0.190983 0.138757i −0.0238729 0.0173447i
$$65$$ 0 0
$$66$$ 1.35410 1.53884i 0.166678 0.189418i
$$67$$ 9.38197i 1.14619i 0.819489 + 0.573095i $$0.194257\pi$$
−0.819489 + 0.573095i $$0.805743\pi$$
$$68$$ −1.90211 + 2.61803i −0.230665 + 0.317483i
$$69$$ 0.736068 2.26538i 0.0886122 0.272720i
$$70$$ 0 0
$$71$$ 6.47214 4.70228i 0.768101 0.558058i −0.133283 0.991078i $$-0.542552\pi$$
0.901384 + 0.433020i $$0.142552\pi$$
$$72$$ −1.31433 1.80902i −0.154895 0.213195i
$$73$$ 12.8128 4.16312i 1.49962 0.487256i 0.559713 0.828686i $$-0.310911\pi$$
0.939907 + 0.341430i $$0.110911\pi$$
$$74$$ 1.42705 4.39201i 0.165891 0.510561i
$$75$$ 0 0
$$76$$ −8.09017 −0.928006
$$77$$ −2.17963 + 1.29180i −0.248392 + 0.147214i
$$78$$ 0.763932i 0.0864983i
$$79$$ −6.54508 4.75528i −0.736380 0.535011i 0.155196 0.987884i $$-0.450399\pi$$
−0.891575 + 0.452873i $$0.850399\pi$$
$$80$$ 0 0
$$81$$ 0.309017 + 0.951057i 0.0343352 + 0.105673i
$$82$$ 0.918300 + 1.26393i 0.101409 + 0.139578i
$$83$$ 3.35520 + 4.61803i 0.368281 + 0.506895i 0.952433 0.304749i $$-0.0985727\pi$$
−0.584152 + 0.811644i $$0.698573\pi$$
$$84$$ 0.381966 + 1.17557i 0.0416759 + 0.128265i
$$85$$ 0 0
$$86$$ 1.04508 + 0.759299i 0.112694 + 0.0818773i
$$87$$ 5.85410i 0.627626i
$$88$$ −7.38394 0.690983i −0.787130 0.0736590i
$$89$$ −10.8541 −1.15053 −0.575266 0.817966i $$-0.695102\pi$$
−0.575266 + 0.817966i $$0.695102\pi$$
$$90$$ 0 0
$$91$$ 0.291796 0.898056i 0.0305885 0.0941418i
$$92$$ −3.66547 + 1.19098i −0.382152 + 0.124169i
$$93$$ 4.11450 + 5.66312i 0.426653 + 0.587238i
$$94$$ 2.54508 1.84911i 0.262505 0.190721i
$$95$$ 0 0
$$96$$ −1.73607 + 5.34307i −0.177187 + 0.545325i
$$97$$ −6.74315 + 9.28115i −0.684663 + 0.942358i −0.999978 0.00662888i $$-0.997890\pi$$
0.315315 + 0.948987i $$0.397890\pi$$
$$98$$ 3.96556i 0.400582i
$$99$$ 3.04508 + 1.31433i 0.306043 + 0.132095i
$$100$$ 0 0
$$101$$ 0.454915 + 0.330515i 0.0452657 + 0.0328875i 0.610188 0.792257i $$-0.291094\pi$$
−0.564922 + 0.825144i $$0.691094\pi$$
$$102$$ 1.17557 + 0.381966i 0.116399 + 0.0378203i
$$103$$ −2.26538 + 0.736068i −0.223215 + 0.0725269i −0.418489 0.908222i $$-0.637440\pi$$
0.195274 + 0.980749i $$0.437440\pi$$
$$104$$ 2.23607 1.62460i 0.219265 0.159305i
$$105$$ 0 0
$$106$$ −1.45492 4.47777i −0.141314 0.434919i
$$107$$ −2.71441 0.881966i −0.262412 0.0852629i 0.174856 0.984594i $$-0.444054\pi$$
−0.437268 + 0.899331i $$0.644054\pi$$
$$108$$ 0.951057 1.30902i 0.0915155 0.125960i
$$109$$ −4.14590 −0.397105 −0.198553 0.980090i $$-0.563624\pi$$
−0.198553 + 0.980090i $$0.563624\pi$$
$$110$$ 0 0
$$111$$ 7.47214 0.709224
$$112$$ 0.832544 1.14590i 0.0786680 0.108277i
$$113$$ 5.20431 + 1.69098i 0.489580 + 0.159074i 0.543396 0.839477i $$-0.317138\pi$$
−0.0538155 + 0.998551i $$0.517138\pi$$
$$114$$ 0.954915 + 2.93893i 0.0894360 + 0.275256i
$$115$$ 0 0
$$116$$ −7.66312 + 5.56758i −0.711503 + 0.516937i
$$117$$ −1.17557 + 0.381966i −0.108682 + 0.0353128i
$$118$$ −3.94298 1.28115i −0.362981 0.117940i
$$119$$ −1.23607 0.898056i −0.113310 0.0823247i
$$120$$ 0 0
$$121$$ 9.94427 4.70228i 0.904025 0.427480i
$$122$$ 4.32624i 0.391679i
$$123$$ −1.48584 + 2.04508i −0.133974 + 0.184399i
$$124$$ 3.50000 10.7719i 0.314309 0.967344i
$$125$$ 0 0
$$126$$ 0.381966 0.277515i 0.0340282 0.0247230i
$$127$$ 9.37181 + 12.8992i 0.831613 + 1.14462i 0.987621 + 0.156862i $$0.0501377\pi$$
−0.156007 + 0.987756i $$0.549862\pi$$
$$128$$ 10.8249 3.51722i 0.956794 0.310881i
$$129$$ −0.645898 + 1.98787i −0.0568682 + 0.175022i
$$130$$ 0 0
$$131$$ 13.1803 1.15157 0.575786 0.817601i $$-0.304696\pi$$
0.575786 + 0.817601i $$0.304696\pi$$
$$132$$ −1.17557 5.23607i −0.102320 0.455741i
$$133$$ 3.81966i 0.331207i
$$134$$ −4.69098 3.40820i −0.405239 0.294424i
$$135$$ 0 0
$$136$$ −1.38197 4.25325i −0.118503 0.364714i
$$137$$ 10.9964 + 15.1353i 0.939486 + 1.29309i 0.956042 + 0.293229i $$0.0947299\pi$$
−0.0165558 + 0.999863i $$0.505270\pi$$
$$138$$ 0.865300 + 1.19098i 0.0736592 + 0.101383i
$$139$$ −6.54508 20.1437i −0.555147 1.70857i −0.695555 0.718473i $$-0.744842\pi$$
0.140408 0.990094i $$-0.455158\pi$$
$$140$$ 0 0
$$141$$ 4.11803 + 2.99193i 0.346801 + 0.251966i
$$142$$ 4.94427i 0.414914i
$$143$$ −1.62460 + 3.76393i −0.135856 + 0.314756i
$$144$$ −1.85410 −0.154508
$$145$$ 0 0
$$146$$ −2.57295 + 7.91872i −0.212939 + 0.655358i
$$147$$ 6.10237 1.98278i 0.503315 0.163537i
$$148$$ −7.10642 9.78115i −0.584144 0.804006i
$$149$$ 16.2812 11.8290i 1.33380 0.969065i 0.334156 0.942518i $$-0.391549\pi$$
0.999648 0.0265477i $$-0.00845140\pi$$
$$150$$ 0 0
$$151$$ −3.32624 + 10.2371i −0.270685 + 0.833084i 0.719643 + 0.694344i $$0.244305\pi$$
−0.990329 + 0.138740i $$0.955695\pi$$
$$152$$ 6.57164 9.04508i 0.533030 0.733653i
$$153$$ 2.00000i 0.161690i
$$154$$ 0.145898 1.55909i 0.0117568 0.125635i
$$155$$ 0 0
$$156$$ 1.61803 + 1.17557i 0.129546 + 0.0941210i
$$157$$ 3.16344 + 1.02786i 0.252470 + 0.0820325i 0.432518 0.901625i $$-0.357625\pi$$
−0.180048 + 0.983658i $$0.557625\pi$$
$$158$$ 4.75528 1.54508i 0.378310 0.122920i
$$159$$ 6.16312 4.47777i 0.488767 0.355110i
$$160$$ 0 0
$$161$$ −0.562306 1.73060i −0.0443159 0.136390i
$$162$$ −0.587785 0.190983i −0.0461808 0.0150050i
$$163$$ 7.97172 10.9721i 0.624394 0.859404i −0.373270 0.927723i $$-0.621763\pi$$
0.997664 + 0.0683187i $$0.0217635\pi$$
$$164$$ 4.09017 0.319389
$$165$$ 0 0
$$166$$ −3.52786 −0.273815
$$167$$ 11.7759 16.2082i 0.911250 1.25423i −0.0554876 0.998459i $$-0.517671\pi$$
0.966738 0.255769i $$-0.0823287\pi$$
$$168$$ −1.62460 0.527864i −0.125340 0.0407256i
$$169$$ 3.54508 + 10.9106i 0.272699 + 0.839281i
$$170$$ 0 0
$$171$$ −4.04508 + 2.93893i −0.309335 + 0.224745i
$$172$$ 3.21644 1.04508i 0.245251 0.0796870i
$$173$$ 3.38795 + 1.10081i 0.257581 + 0.0836933i 0.434961 0.900449i $$-0.356762\pi$$
−0.177380 + 0.984142i $$0.556762\pi$$
$$174$$ 2.92705 + 2.12663i 0.221899 + 0.161219i
$$175$$ 0 0
$$176$$ −4.06231 + 4.61653i −0.306208 + 0.347984i
$$177$$ 6.70820i 0.504219i
$$178$$ 3.94298 5.42705i 0.295539 0.406775i
$$179$$ 6.01722 18.5191i 0.449748 1.38418i −0.427443 0.904042i $$-0.640586\pi$$
0.877192 0.480141i $$-0.159414\pi$$
$$180$$ 0 0
$$181$$ 4.23607 3.07768i 0.314864 0.228762i −0.419117 0.907932i $$-0.637660\pi$$
0.733981 + 0.679170i $$0.237660\pi$$
$$182$$ 0.343027 + 0.472136i 0.0254268 + 0.0349970i
$$183$$ 6.65740 2.16312i 0.492129 0.159902i
$$184$$ 1.64590 5.06555i 0.121337 0.373438i
$$185$$ 0 0
$$186$$ −4.32624 −0.317215
$$187$$ 4.97980 + 4.38197i 0.364159 + 0.320441i
$$188$$ 8.23607i 0.600677i
$$189$$ 0.618034 + 0.449028i 0.0449554 + 0.0326620i
$$190$$ 0 0
$$191$$ 3.21885 + 9.90659i 0.232908 + 0.716816i 0.997392 + 0.0721737i $$0.0229936\pi$$
−0.764484 + 0.644642i $$0.777006\pi$$
$$192$$ 0.138757 + 0.190983i 0.0100139 + 0.0137830i
$$193$$ 12.3637 + 17.0172i 0.889961 + 1.22493i 0.973561 + 0.228427i $$0.0733582\pi$$
−0.0836000 + 0.996499i $$0.526642\pi$$
$$194$$ −2.19098 6.74315i −0.157303 0.484130i
$$195$$ 0 0
$$196$$ −8.39919 6.10237i −0.599942 0.435883i
$$197$$ 14.2361i 1.01428i −0.861864 0.507139i $$-0.830703\pi$$
0.861864 0.507139i $$-0.169297\pi$$
$$198$$ −1.76336 + 1.04508i −0.125316 + 0.0742710i
$$199$$ −19.7984 −1.40347 −0.701735 0.712438i $$-0.747591\pi$$
−0.701735 + 0.712438i $$0.747591\pi$$
$$200$$ 0 0
$$201$$ 2.89919 8.92278i 0.204493 0.629364i
$$202$$ −0.330515 + 0.107391i −0.0232550 + 0.00755600i
$$203$$ −2.62866 3.61803i −0.184495 0.253936i
$$204$$ 2.61803 1.90211i 0.183299 0.133175i
$$205$$ 0 0
$$206$$ 0.454915 1.40008i 0.0316954 0.0975485i
$$207$$ −1.40008 + 1.92705i −0.0973126 + 0.133939i
$$208$$ 2.29180i 0.158907i
$$209$$ −1.54508 + 16.5110i −0.106876 + 1.14209i
$$210$$ 0 0
$$211$$ 3.11803 + 2.26538i 0.214654 + 0.155955i 0.689917 0.723888i $$-0.257647\pi$$
−0.475263 + 0.879844i $$0.657647\pi$$
$$212$$ −11.7229 3.80902i −0.805135 0.261604i
$$213$$ −7.60845 + 2.47214i −0.521323 + 0.169388i
$$214$$ 1.42705 1.03681i 0.0975512 0.0708751i
$$215$$ 0 0
$$216$$ 0.690983 + 2.12663i 0.0470154 + 0.144699i
$$217$$ 5.08580 + 1.65248i 0.345246 + 0.112177i
$$218$$ 1.50609 2.07295i 0.102005 0.140398i
$$219$$ −13.4721 −0.910363
$$220$$ 0 0
$$221$$ −2.47214 −0.166294
$$222$$ −2.71441 + 3.73607i −0.182179 + 0.250748i
$$223$$ 7.64121 + 2.48278i 0.511693 + 0.166259i 0.553472 0.832868i $$-0.313303\pi$$
−0.0417790 + 0.999127i $$0.513303\pi$$
$$224$$ 1.32624 + 4.08174i 0.0886130 + 0.272723i
$$225$$ 0 0
$$226$$ −2.73607 + 1.98787i −0.182001 + 0.132231i
$$227$$ 24.6745 8.01722i 1.63770 0.532122i 0.661679 0.749788i $$-0.269844\pi$$
0.976023 + 0.217666i $$0.0698443\pi$$
$$228$$ 7.69421 + 2.50000i 0.509561 + 0.165567i
$$229$$ 14.6353 + 10.6331i 0.967125 + 0.702657i 0.954795 0.297267i $$-0.0960750\pi$$
0.0123304 + 0.999924i $$0.496075\pi$$
$$230$$ 0 0
$$231$$ 2.47214 0.555029i 0.162655 0.0365182i
$$232$$ 13.0902i 0.859412i
$$233$$ −13.6781 + 18.8262i −0.896080 + 1.23335i 0.0756220 + 0.997137i $$0.475906\pi$$
−0.971702 + 0.236211i $$0.924094\pi$$
$$234$$ 0.236068 0.726543i 0.0154322 0.0474956i
$$235$$ 0 0
$$236$$ −8.78115 + 6.37988i −0.571604 + 0.415295i
$$237$$ 4.75528 + 6.54508i 0.308889 + 0.425149i
$$238$$ 0.898056 0.291796i 0.0582123 0.0189143i
$$239$$ 2.17376 6.69015i 0.140609 0.432750i −0.855811 0.517288i $$-0.826942\pi$$
0.996420 + 0.0845383i $$0.0269415\pi$$
$$240$$ 0 0
$$241$$ −1.61803 −0.104227 −0.0521134 0.998641i $$-0.516596\pi$$
−0.0521134 + 0.998641i $$0.516596\pi$$
$$242$$ −1.26133 + 6.68034i −0.0810812 + 0.429429i
$$243$$ 1.00000i 0.0641500i
$$244$$ −9.16312 6.65740i −0.586609 0.426196i
$$245$$ 0 0
$$246$$ −0.482779 1.48584i −0.0307809 0.0947338i
$$247$$ −3.63271 5.00000i −0.231144 0.318142i
$$248$$ 9.20029 + 12.6631i 0.584219 + 0.804109i
$$249$$ −1.76393 5.42882i −0.111785 0.344038i
$$250$$ 0 0
$$251$$ −6.09017 4.42477i −0.384408 0.279289i 0.378752 0.925498i $$-0.376353\pi$$
−0.763160 + 0.646209i $$0.776353\pi$$
$$252$$ 1.23607i 0.0778650i
$$253$$ 1.73060 + 7.70820i 0.108802 + 0.484611i
$$254$$ −9.85410 −0.618301
$$255$$ 0 0
$$256$$ −2.02786 + 6.24112i −0.126742 + 0.390070i
$$257$$ −10.0453 + 3.26393i −0.626612 + 0.203598i −0.605074 0.796170i $$-0.706856\pi$$
−0.0215381 + 0.999768i $$0.506856\pi$$
$$258$$ −0.759299 1.04508i −0.0472719 0.0650641i
$$259$$ 4.61803 3.35520i 0.286951 0.208482i
$$260$$ 0 0
$$261$$ −1.80902 + 5.56758i −0.111975 + 0.344625i
$$262$$ −4.78804 + 6.59017i −0.295806 + 0.407142i
$$263$$ 27.2148i 1.67814i −0.544027 0.839068i $$-0.683101\pi$$
0.544027 0.839068i $$-0.316899\pi$$
$$264$$ 6.80902 + 2.93893i 0.419066 + 0.180878i
$$265$$ 0 0
$$266$$ 1.90983 + 1.38757i 0.117099 + 0.0850775i
$$267$$ 10.3229 + 3.35410i 0.631749 + 0.205268i
$$268$$ −14.4374 + 4.69098i −0.881902 + 0.286547i
$$269$$ −4.73607 + 3.44095i −0.288763 + 0.209799i −0.722731 0.691130i $$-0.757113\pi$$
0.433967 + 0.900929i $$0.357113\pi$$
$$270$$ 0 0
$$271$$ 6.37132 + 19.6089i 0.387030 + 1.19116i 0.934997 + 0.354656i $$0.115402\pi$$
−0.547966 + 0.836500i $$0.684598\pi$$
$$272$$ −3.52671 1.14590i −0.213838 0.0694803i
$$273$$ −0.555029 + 0.763932i −0.0335919 + 0.0462353i
$$274$$ −11.5623 −0.698504
$$275$$ 0 0
$$276$$ 3.85410 0.231990
$$277$$ 5.08580 7.00000i 0.305576 0.420589i −0.628419 0.777875i $$-0.716298\pi$$
0.933995 + 0.357286i $$0.116298\pi$$
$$278$$ 12.4495 + 4.04508i 0.746671 + 0.242608i
$$279$$ −2.16312 6.65740i −0.129503 0.398568i
$$280$$ 0 0
$$281$$ −8.16312 + 5.93085i −0.486971 + 0.353805i −0.804018 0.594605i $$-0.797309\pi$$
0.317047 + 0.948410i $$0.397309\pi$$
$$282$$ −2.99193 + 0.972136i −0.178167 + 0.0578899i
$$283$$ 12.3965 + 4.02786i 0.736895 + 0.239432i 0.653333 0.757071i $$-0.273370\pi$$
0.0835622 + 0.996503i $$0.473370\pi$$
$$284$$ 10.4721 + 7.60845i 0.621407 + 0.451479i
$$285$$ 0 0
$$286$$ −1.29180 2.17963i −0.0763855 0.128884i
$$287$$ 1.93112i 0.113990i
$$288$$ 3.30220 4.54508i 0.194584 0.267822i
$$289$$ 4.01722 12.3637i 0.236307 0.727279i
$$290$$ 0 0
$$291$$ 9.28115 6.74315i 0.544071 0.395291i
$$292$$ 12.8128 + 17.6353i 0.749810 + 1.03203i
$$293$$ −15.7189 + 5.10739i −0.918310 + 0.298377i −0.729773 0.683689i $$-0.760374\pi$$
−0.188537 + 0.982066i $$0.560374\pi$$
$$294$$ −1.22542 + 3.77147i −0.0714682 + 0.219957i
$$295$$ 0 0
$$296$$ 16.7082 0.971145
$$297$$ −2.48990 2.19098i −0.144479 0.127134i
$$298$$ 12.4377i 0.720496i
$$299$$ −2.38197 1.73060i −0.137753 0.100083i
$$300$$ 0 0
$$301$$ 0.493422 + 1.51860i 0.0284404 + 0.0875305i
$$302$$ −3.91023 5.38197i −0.225008 0.309697i
$$303$$ −0.330515 0.454915i −0.0189876 0.0261342i
$$304$$ −2.86475 8.81678i −0.164304 0.505677i
$$305$$ 0 0
$$306$$ −1.00000 0.726543i −0.0571662 0.0415337i
$$307$$ 12.1246i 0.691988i −0.938237 0.345994i $$-0.887542\pi$$
0.938237 0.345994i $$-0.112458\pi$$
$$308$$ −3.07768 2.70820i −0.175367 0.154314i
$$309$$ 2.38197 0.135505
$$310$$ 0 0
$$311$$ 6.63525 20.4212i 0.376251 1.15798i −0.566380 0.824144i $$-0.691657\pi$$
0.942631 0.333837i $$-0.108343\pi$$
$$312$$ −2.62866 + 0.854102i −0.148818 + 0.0483540i
$$313$$ −0.277515 0.381966i −0.0156860 0.0215900i 0.801102 0.598528i $$-0.204247\pi$$
−0.816788 + 0.576938i $$0.804247\pi$$
$$314$$ −1.66312 + 1.20833i −0.0938552 + 0.0681898i
$$315$$ 0 0
$$316$$ 4.04508 12.4495i 0.227554 0.700339i
$$317$$ −17.8783 + 24.6074i −1.00415 + 1.38209i −0.0813997 + 0.996682i $$0.525939\pi$$
−0.922747 + 0.385407i $$0.874061\pi$$
$$318$$ 4.70820i 0.264023i
$$319$$ 9.89919 + 16.7027i 0.554248 + 0.935174i
$$320$$ 0 0
$$321$$ 2.30902 + 1.67760i 0.128877 + 0.0936344i
$$322$$ 1.06957 + 0.347524i 0.0596048 + 0.0193668i
$$323$$ −9.51057 + 3.09017i −0.529182 + 0.171942i
$$324$$ −1.30902 + 0.951057i −0.0727232 + 0.0528365i
$$325$$ 0 0
$$326$$ 2.59017 + 7.97172i 0.143456 + 0.441513i
$$327$$ 3.94298 + 1.28115i 0.218047 + 0.0708479i
$$328$$ −3.32244 + 4.57295i −0.183451 + 0.252499i
$$329$$ 3.88854 0.214382
$$330$$ 0 0
$$331$$ 21.5967 1.18706 0.593532 0.804810i $$-0.297733\pi$$
0.593532 + 0.804810i $$0.297733\pi$$
$$332$$ −5.42882 + 7.47214i −0.297945 + 0.410087i
$$333$$ −7.10642 2.30902i −0.389430 0.126533i
$$334$$ 3.82624 + 11.7759i 0.209362 + 0.644351i
$$335$$ 0 0
$$336$$ −1.14590 + 0.832544i −0.0625139 + 0.0454190i
$$337$$ −21.0620 + 6.84346i −1.14732 + 0.372787i −0.820133 0.572173i $$-0.806101\pi$$
−0.327187 + 0.944960i $$0.606101\pi$$
$$338$$ −6.74315 2.19098i −0.366779 0.119174i
$$339$$ −4.42705 3.21644i −0.240444 0.174693i
$$340$$ 0 0
$$341$$ −21.3156 9.20029i −1.15430 0.498224i
$$342$$ 3.09017i 0.167097i
$$343$$ 6.02434 8.29180i 0.325284 0.447715i
$$344$$ −1.44427 + 4.44501i −0.0778699 + 0.239659i
$$345$$ 0 0
$$346$$ −1.78115 + 1.29408i −0.0957554 + 0.0695704i
$$347$$ 3.42071 + 4.70820i 0.183633 + 0.252750i 0.890902 0.454195i $$-0.150073\pi$$
−0.707269 + 0.706945i $$0.750073\pi$$
$$348$$ 9.00854 2.92705i 0.482908 0.156906i
$$349$$ −8.57953 + 26.4051i −0.459252 + 1.41343i 0.406819 + 0.913509i $$0.366638\pi$$
−0.866070 + 0.499922i $$0.833362\pi$$
$$350$$ 0 0
$$351$$ 1.23607 0.0659764
$$352$$ −4.08174 18.1803i −0.217558 0.969015i
$$353$$ 35.8328i 1.90719i −0.301095 0.953594i $$-0.597352\pi$$
0.301095 0.953594i $$-0.402648\pi$$
$$354$$ 3.35410 + 2.43690i 0.178269 + 0.129520i
$$355$$ 0 0
$$356$$ −5.42705 16.7027i −0.287633 0.885244i
$$357$$ 0.898056 + 1.23607i 0.0475302 + 0.0654197i
$$358$$ 7.07367 + 9.73607i 0.373855 + 0.514567i
$$359$$ −5.16312 15.8904i −0.272499 0.838666i −0.989870 0.141975i $$-0.954655\pi$$
0.717371 0.696691i $$-0.245345\pi$$
$$360$$ 0 0
$$361$$ −4.85410 3.52671i −0.255479 0.185616i
$$362$$ 3.23607i 0.170084i
$$363$$ −10.9106 + 1.39919i −0.572661 + 0.0734383i
$$364$$ 1.52786 0.0800818
$$365$$ 0 0
$$366$$ −1.33688 + 4.11450i −0.0698799 + 0.215068i
$$367$$ −17.2375 + 5.60081i −0.899792 + 0.292360i −0.722151 0.691735i $$-0.756846\pi$$
−0.177641 + 0.984095i $$0.556846\pi$$
$$368$$ −2.59590 3.57295i −0.135321 0.186253i
$$369$$ 2.04508 1.48584i 0.106463 0.0773498i
$$370$$ 0 0
$$371$$ 1.79837 5.53483i 0.0933669 0.287354i
$$372$$ −6.65740 + 9.16312i −0.345170 + 0.475086i
$$373$$ 9.74265i 0.504455i 0.967668 + 0.252228i $$0.0811631\pi$$
−0.967668 + 0.252228i $$0.918837\pi$$
$$374$$ −4.00000 + 0.898056i −0.206835 + 0.0464374i
$$375$$ 0 0
$$376$$ 9.20820 + 6.69015i 0.474877 + 0.345018i
$$377$$ −6.88191 2.23607i −0.354436 0.115163i
$$378$$ −0.449028 + 0.145898i −0.0230955 + 0.00750419i
$$379$$ −4.04508 + 2.93893i −0.207782 + 0.150963i −0.686810 0.726837i $$-0.740989\pi$$
0.479028 + 0.877800i $$0.340989\pi$$
$$380$$ 0 0
$$381$$ −4.92705 15.1639i −0.252420 0.776870i
$$382$$ −6.12261 1.98936i −0.313260 0.101784i
$$383$$ −18.4333 + 25.3713i −0.941900 + 1.29641i 0.0131328 + 0.999914i $$0.495820\pi$$
−0.955033 + 0.296500i $$0.904180\pi$$
$$384$$ −11.3820 −0.580834
$$385$$ 0 0
$$386$$ −13.0000 −0.661683
$$387$$ 1.22857 1.69098i 0.0624518 0.0859575i
$$388$$ −17.6538 5.73607i −0.896236 0.291205i
$$389$$ 12.0344 + 37.0382i 0.610170 + 1.87791i 0.456316 + 0.889818i $$0.349169\pi$$
0.153855 + 0.988093i $$0.450831\pi$$
$$390$$ 0 0
$$391$$ −3.85410 + 2.80017i −0.194910 + 0.141611i
$$392$$ 13.6453 4.43363i 0.689192 0.223932i
$$393$$ −12.5352 4.07295i −0.632320 0.205453i
$$394$$ 7.11803 + 5.17155i 0.358601 + 0.260539i
$$395$$ 0 0
$$396$$ −0.500000 + 5.34307i −0.0251259 + 0.268499i
$$397$$ 36.2705i 1.82036i −0.414208 0.910182i $$-0.635941\pi$$
0.414208 0.910182i $$-0.364059\pi$$
$$398$$ 7.19218 9.89919i 0.360511 0.496201i
$$399$$ −1.18034 + 3.63271i −0.0590909 + 0.181863i
$$400$$ 0 0
$$401$$ −3.95492 + 2.87341i −0.197499 + 0.143491i −0.682140 0.731222i $$-0.738950\pi$$
0.484641 + 0.874713i $$0.338950\pi$$
$$402$$ 3.40820 + 4.69098i 0.169985 + 0.233965i
$$403$$ 8.22899 2.67376i 0.409915 0.133190i
$$404$$ −0.281153 + 0.865300i −0.0139879 + 0.0430503i
$$405$$ 0 0
$$406$$ 2.76393 0.137172
$$407$$ −21.3193 + 12.6353i −1.05676 + 0.626306i
$$408$$ 4.47214i 0.221404i
$$409$$ 29.3713 + 21.3395i 1.45232 + 1.05517i 0.985283 + 0.170933i $$0.0546781\pi$$
0.467036 + 0.884238i $$0.345322\pi$$
$$410$$ 0 0
$$411$$ −5.78115 17.7926i −0.285163 0.877642i
$$412$$ −2.26538 3.11803i −0.111607 0.153615i
$$413$$ −3.01217 4.14590i −0.148219 0.204006i
$$414$$ −0.454915 1.40008i −0.0223579 0.0688104i
$$415$$ 0 0
$$416$$ 5.61803 + 4.08174i 0.275447 + 0.200124i
$$417$$ 21.1803i 1.03721i
$$418$$ −7.69421 6.77051i −0.376336 0.331156i
$$419$$ −24.5967 −1.20163 −0.600815 0.799388i $$-0.705157\pi$$
−0.600815 + 0.799388i $$0.705157\pi$$
$$420$$ 0 0
$$421$$ 0.881966 2.71441i 0.0429844 0.132292i −0.927261 0.374415i $$-0.877844\pi$$
0.970246 + 0.242123i $$0.0778436\pi$$
$$422$$ −2.26538 + 0.736068i −0.110277 + 0.0358312i
$$423$$ −2.99193 4.11803i −0.145472 0.200226i
$$424$$ 13.7812 10.0126i 0.669272 0.486255i
$$425$$ 0 0
$$426$$ 1.52786 4.70228i 0.0740253 0.227826i
$$427$$ 3.14320 4.32624i 0.152110 0.209361i
$$428$$ 4.61803i 0.223221i
$$429$$ 2.70820 3.07768i 0.130753 0.148592i
$$430$$ 0 0
$$431$$ −16.0902 11.6902i −0.775036 0.563097i 0.128449 0.991716i $$-0.459000\pi$$
−0.903485 + 0.428619i $$0.859000\pi$$
$$432$$ 1.76336 + 0.572949i 0.0848395 + 0.0275660i
$$433$$ −26.6623 + 8.66312i −1.28131 + 0.416323i −0.869041 0.494739i $$-0.835264\pi$$
−0.412269 + 0.911062i $$0.635264\pi$$
$$434$$ −2.67376 + 1.94260i −0.128345 + 0.0932479i
$$435$$ 0 0
$$436$$ −2.07295 6.37988i −0.0992763 0.305541i
$$437$$ −11.3269 3.68034i −0.541840 0.176055i
$$438$$ 4.89404 6.73607i 0.233846 0.321862i
$$439$$ −9.67376 −0.461703 −0.230852 0.972989i $$-0.574151\pi$$
−0.230852 + 0.972989i $$0.574151\pi$$
$$440$$ 0 0
$$441$$ −6.41641 −0.305543
$$442$$ 0.898056 1.23607i 0.0427162 0.0587938i
$$443$$ 24.0337 + 7.80902i 1.14187 + 0.371018i 0.818077 0.575109i $$-0.195040\pi$$
0.323798 + 0.946126i $$0.395040\pi$$
$$444$$ 3.73607 + 11.4984i 0.177306 + 0.545692i
$$445$$ 0 0
$$446$$ −4.01722 + 2.91868i −0.190221 + 0.138204i
$$447$$ −19.1396 + 6.21885i −0.905274 + 0.294141i
$$448$$ 0.171513 + 0.0557281i 0.00810325 + 0.00263290i
$$449$$ −0.590170 0.428784i −0.0278518 0.0202355i 0.573772 0.819015i $$-0.305479\pi$$
−0.601624 + 0.798779i $$0.705479\pi$$
$$450$$ 0 0
$$451$$ 0.781153 8.34751i 0.0367831 0.393069i
$$452$$ 8.85410i 0.416462i
$$453$$ 6.32688 8.70820i 0.297263 0.409147i
$$454$$ −4.95492 + 15.2497i −0.232546 + 0.715702i
$$455$$ 0 0
$$456$$ −9.04508 + 6.57164i −0.423575 + 0.307745i
$$457$$ 0.865300 + 1.19098i 0.0404770 + 0.0557118i 0.828776 0.559581i $$-0.189038\pi$$
−0.788299 + 0.615293i $$0.789038\pi$$
$$458$$ −10.6331 + 3.45492i −0.496854 + 0.161438i
$$459$$ 0.618034 1.90211i 0.0288474 0.0887830i
$$460$$ 0 0
$$461$$ 25.9443 1.20835 0.604173 0.796853i $$-0.293504\pi$$
0.604173 + 0.796853i $$0.293504\pi$$
$$462$$ −0.620541 + 1.43769i −0.0288702 + 0.0668876i
$$463$$ 33.2705i 1.54621i −0.634277 0.773106i $$-0.718702\pi$$
0.634277 0.773106i $$-0.281298\pi$$
$$464$$ −8.78115 6.37988i −0.407655 0.296179i
$$465$$ 0 0
$$466$$ −4.44427 13.6781i −0.205877 0.633624i
$$467$$ 2.87341 + 3.95492i 0.132966 + 0.183012i 0.870308 0.492507i $$-0.163920\pi$$
−0.737342 + 0.675519i $$0.763920\pi$$
$$468$$ −1.17557 1.61803i −0.0543408 0.0747936i
$$469$$ −2.21478 6.81640i −0.102269 0.314752i
$$470$$ 0 0
$$471$$ −2.69098 1.95511i −0.123994 0.0900869i
$$472$$ 15.0000i 0.690431i
$$473$$ −1.51860 6.76393i −0.0698252 0.311006i
$$474$$ −5.00000 −0.229658
$$475$$ 0 0
$$476$$ 0.763932 2.35114i 0.0350148 0.107764i
$$477$$ −7.24518 + 2.35410i −0.331734 + 0.107787i
$$478$$ 2.55541 + 3.51722i 0.116882 + 0.160874i
$$479$$ 27.0344 19.6417i 1.23524 0.897451i 0.237964 0.971274i $$-0.423520\pi$$
0.997271 + 0.0738231i $$0.0235200\pi$$
$$480$$ 0 0
$$481$$ 2.85410 8.78402i 0.130136 0.400517i
$$482$$ 0.587785 0.809017i 0.0267729 0.0368497i
$$483$$ 1.81966i 0.0827974i
$$484$$ 12.2082 + 12.9515i 0.554918 + 0.588705i
$$485$$ 0 0
$$486$$ 0.500000 + 0.363271i 0.0226805 + 0.0164783i
$$487$$ 13.4863 + 4.38197i 0.611123 + 0.198566i 0.598195 0.801351i $$-0.295885\pi$$
0.0129278 + 0.999916i $$0.495885\pi$$
$$488$$ 14.8864 4.83688i 0.673875 0.218955i
$$489$$ −10.9721 + 7.97172i −0.496177 + 0.360494i
$$490$$ 0 0
$$491$$ 9.82624 + 30.2421i 0.443452 + 1.36480i 0.884173 + 0.467160i $$0.154723\pi$$
−0.440721 + 0.897644i $$0.645277\pi$$
$$492$$ −3.88998 1.26393i −0.175374 0.0569825i
$$493$$ −6.88191 + 9.47214i −0.309946 + 0.426604i
$$494$$ 3.81966 0.171855
$$495$$ 0 0
$$496$$ 12.9787 0.582761
$$497$$ −3.59222 + 4.94427i −0.161133 + 0.221781i
$$498$$ 3.35520 + 1.09017i 0.150350 + 0.0488517i
$$499$$ 3.45492 + 10.6331i 0.154663 + 0.476005i 0.998127 0.0611822i $$-0.0194871\pi$$
−0.843463 + 0.537187i $$0.819487\pi$$
$$500$$ 0 0
$$501$$ −16.2082 + 11.7759i −0.724129 + 0.526111i
$$502$$ 4.42477 1.43769i 0.197487 0.0641674i
$$503$$ −20.8172 6.76393i −0.928195 0.301589i −0.194371 0.980928i $$-0.562266\pi$$
−0.733824 + 0.679339i $$0.762266\pi$$
$$504$$ 1.38197 + 1.00406i 0.0615577 + 0.0447243i
$$505$$ 0 0
$$506$$ −4.48278 1.93487i −0.199284 0.0860154i
$$507$$ 11.4721i 0.509495i
$$508$$ −15.1639 + 20.8713i −0.672789 + 0.926015i
$$509$$ −0.163119 + 0.502029i −0.00723012 + 0.0222520i −0.954606 0.297870i $$-0.903724\pi$$
0.947376 + 0.320122i $$0.103724\pi$$
$$510$$ 0 0
$$511$$ −8.32624 + 6.04937i −0.368331 + 0.267608i
$$512$$ 10.9964 + 15.1353i 0.485977 + 0.668890i
$$513$$ 4.75528 1.54508i 0.209951 0.0682172i
$$514$$ 2.01722 6.20837i 0.0889758 0.273839i
$$515$$ 0 0
$$516$$ −3.38197 −0.148883
$$517$$ −16.8087 1.57295i −0.739248 0.0691782i
$$518$$ 3.52786i 0.155005i
$$519$$ −2.88197 2.09387i −0.126504 0.0919107i
$$520$$ 0 0
$$521$$ −4.74671 14.6089i −0.207957 0.640026i −0.999579 0.0290150i $$-0.990763\pi$$
0.791622 0.611011i $$-0.209237\pi$$
$$522$$ −2.12663 2.92705i −0.0930799 0.128114i
$$523$$ −4.84104 6.66312i −0.211684 0.291358i 0.689951 0.723856i $$-0.257632\pi$$
−0.901635 + 0.432498i $$0.857632\pi$$
$$524$$ 6.59017 + 20.2825i 0.287893 + 0.886043i
$$525$$ 0 0
$$526$$ 13.6074 + 9.88635i 0.593310 + 0.431065i
$$527$$ 14.0000i 0.609850i
$$528$$ 5.29007 3.13525i 0.230221 0.136444i
$$529$$ 17.3262 0.753315
$$530$$ 0 0
$$531$$ −2.07295 + 6.37988i −0.0899583 + 0.276863i
$$532$$ 5.87785 1.90983i 0.254837 0.0828016i
$$533$$ 1.83660 + 2.52786i 0.0795520 + 0.109494i
$$534$$ −5.42705 + 3.94298i −0.234851 + 0.170630i
$$535$$ 0 0
$$536$$ 6.48278 19.9519i 0.280013 0.861793i
$$537$$ −11.4454 + 15.7533i −0.493907 + 0.679805i
$$538$$ 3.61803i 0.155985i
$$539$$ −14.0582 + 15.9762i −0.605531 + 0.688144i
$$540$$ 0 0
$$541$$ −0.500000 0.363271i −0.0214967 0.0156183i 0.576985 0.816755i $$-0.304229\pi$$
−0.598482 + 0.801136i $$0.704229\pi$$
$$542$$ −12.1190 3.93769i −0.520555 0.169138i
$$543$$ −4.97980 + 1.61803i −0.213704 + 0.0694365i
$$544$$ 9.09017 6.60440i 0.389738 0.283161i
$$545$$ 0 0
$$546$$ −0.180340 0.555029i −0.00771783 0.0237531i
$$547$$ 24.1194 + 7.83688i 1.03127 + 0.335081i 0.775293 0.631601i $$-0.217602\pi$$
0.255979 + 0.966682i $$0.417602\pi$$
$$548$$ −17.7926 + 24.4894i −0.760060 + 1.04613i
$$549$$ −7.00000 −0.298753
$$550$$ 0 0
$$551$$ −29.2705 −1.24697
$$552$$ −3.13068 + 4.30902i −0.133251 + 0.183404i
$$553$$ 5.87785 + 1.90983i 0.249952 + 0.0812142i
$$554$$ 1.65248 + 5.08580i 0.0702070 + 0.216075i
$$555$$ 0 0
$$556$$ 27.7254 20.1437i 1.17582 0.854283i
$$557$$ 29.8585 9.70163i 1.26515 0.411071i 0.401821 0.915718i $$-0.368377\pi$$
0.863326 + 0.504647i $$0.168377\pi$$
$$558$$ 4.11450 + 1.33688i 0.174181 + 0.0565947i
$$559$$ 2.09017 + 1.51860i 0.0884048 + 0.0642298i
$$560$$ 0 0
$$561$$ −3.38197 5.70634i −0.142787 0.240922i
$$562$$ 6.23607i 0.263053i
$$563$$ 21.3520 29.3885i 0.899881 1.23858i −0.0706255 0.997503i $$-0.522500\pi$$
0.970506 0.241077i $$-0.0775005\pi$$
$$564$$ −2.54508 + 7.83297i −0.107167 + 0.329827i
$$565$$ 0 0
$$566$$ −6.51722 + 4.73504i −0.273939 + 0.199028i
$$567$$ −0.449028 0.618034i −0.0188574 0.0259550i
$$568$$ −17.0130 + 5.52786i −0.713850 + 0.231944i
$$569$$ 0.753289 2.31838i 0.0315795 0.0971917i −0.934024 0.357209i $$-0.883728\pi$$
0.965604 + 0.260017i $$0.0837283\pi$$
$$570$$ 0 0
$$571$$ 0.0901699 0.00377349 0.00188675 0.999998i $$-0.499399\pi$$
0.00188675 + 0.999998i $$0.499399\pi$$
$$572$$ −6.60440 0.618034i −0.276144 0.0258413i
$$573$$ 10.4164i 0.435152i
$$574$$ −0.965558 0.701519i −0.0403016 0.0292808i
$$575$$ 0 0
$$576$$ −0.0729490 0.224514i −0.00303954 0.00935475i
$$577$$ −27.0459 37.2254i −1.12593 1.54971i −0.795571 0.605861i $$-0.792829\pi$$
−0.330363 0.943854i $$-0.607171\pi$$
$$578$$ 4.72253 + 6.50000i 0.196431 + 0.270364i
$$579$$ −6.50000 20.0049i −0.270131 0.831377i
$$580$$ 0 0
$$581$$ −3.52786 2.56314i −0.146360 0.106337i
$$582$$ 7.09017i 0.293897i
$$583$$ −10.0126 + 23.1976i −0.414679 + 0.960745i
$$584$$ −30.1246 −1.24657
$$585$$ 0 0
$$586$$ 3.15654 9.71483i 0.130396 0.401316i
$$587$$ −18.4333 + 5.98936i −0.760826 + 0.247207i −0.663633 0.748058i $$-0.730986\pi$$
−0.0971926 + 0.995266i $$0.530986\pi$$
$$588$$ 6.10237 + 8.39919i 0.251657 + 0.346377i
$$589$$ 28.3156 20.5725i 1.16672 0.847674i
$$590$$ 0 0
$$591$$ −4.39919 + 13.5393i −0.180958 + 0.556933i
$$592$$ 8.14324 11.2082i 0.334685 0.460654i
$$593$$ 38.8885i 1.59696i 0.602021 + 0.798481i $$0.294362\pi$$
−0.602021 + 0.798481i $$0.705638\pi$$
$$594$$ 2.00000 0.449028i 0.0820610 0.0184238i
$$595$$ 0 0
$$596$$ 26.3435 + 19.1396i 1.07907 + 0.783990i
$$597$$ 18.8294 + 6.11803i 0.770635 + 0.250394i
$$598$$ 1.73060 0.562306i 0.0707695 0.0229944i
$$599$$ −17.9894 + 13.0700i −0.735025 + 0.534027i −0.891149 0.453710i $$-0.850100\pi$$
0.156124 + 0.987737i $$0.450100\pi$$
$$600$$ 0 0
$$601$$ 10.6180 + 32.6789i 0.433119 + 1.33300i 0.895002 + 0.446062i $$0.147174\pi$$
−0.461884 + 0.886941i $$0.652826\pi$$
$$602$$ −0.938545 0.304952i −0.0382522 0.0124289i
$$603$$ −5.51458 + 7.59017i −0.224571 + 0.309096i
$$604$$ −17.4164 −0.708664
$$605$$ 0 0
$$606$$ 0.347524 0.0141172
$$607$$ 19.3969 26.6976i 0.787296 1.08362i −0.207143 0.978311i $$-0.566417\pi$$
0.994439 0.105310i $$-0.0335835\pi$$
$$608$$ 26.7153 + 8.68034i 1.08345 + 0.352034i
$$609$$ 1.38197 + 4.25325i 0.0560001 + 0.172351i
$$610$$ 0 0
$$611$$ 5.09017 3.69822i 0.205926 0.149614i
$$612$$ −3.07768 + 1.00000i −0.124408 + 0.0404226i
$$613$$ 7.83297 + 2.54508i 0.316371 + 0.102795i 0.462898 0.886412i $$-0.346810\pi$$
−0.146527 + 0.989207i $$0.546810\pi$$
$$614$$ 6.06231 + 4.40452i 0.244655 + 0.177752i
$$615$$ 0 0
$$616$$ 5.52786 1.24108i 0.222724 0.0500047i
$$617$$ 38.2492i 1.53986i 0.638131 + 0.769928i $$0.279708\pi$$
−0.638131 + 0.769928i $$0.720292\pi$$
$$618$$ −0.865300 + 1.19098i −0.0348075 + 0.0479084i
$$619$$ −2.19756 + 6.76340i −0.0883274 + 0.271844i −0.985457 0.169923i $$-0.945648\pi$$
0.897130 + 0.441767i $$0.145648\pi$$
$$620$$ 0 0
$$621$$ 1.92705 1.40008i 0.0773299 0.0561835i
$$622$$ 7.80021 + 10.7361i 0.312760 + 0.430477i
$$623$$ 7.88597 2.56231i 0.315945 0.102657i
$$624$$ −0.708204 + 2.17963i −0.0283508 + 0.0872549i
$$625$$ 0 0
$$626$$ 0.291796 0.0116625
$$627$$ 6.57164 15.2254i 0.262446 0.608045i
$$628$$ 5.38197i 0.214764i
$$629$$ −12.0902 8.78402i −0.482067 0.350242i
$$630$$ 0 0
$$631$$ 11.9377 + 36.7404i 0.475232 + 1.46261i 0.845644 + 0.533747i $$0.179216\pi$$
−0.370412 + 0.928867i $$0.620784\pi$$
$$632$$ 10.6331 + 14.6353i 0.422963 + 0.582159i
$$633$$ −2.26538 3.11803i −0.0900409 0.123931i
$$634$$ −5.80902 17.8783i −0.230706 0.710039i
$$635$$ 0 0
$$636$$ 9.97214 + 7.24518i 0.395421 + 0.287290i
$$637$$ 7.93112i 0.314242i
$$638$$ −11.9475 1.11803i −0.473005 0.0442634i
$$639$$ 8.00000 0.316475
$$640$$ 0 0
$$641$$ −0.0729490 + 0.224514i −0.00288131 + 0.00886777i −0.952487 0.304580i $$-0.901484\pi$$
0.949606 + 0.313448i $$0.101484\pi$$
$$642$$ −1.67760 + 0.545085i −0.0662096 + 0.0215128i
$$643$$ 17.2375 + 23.7254i 0.679782 + 0.935639i 0.999931 0.0117276i $$-0.00373311\pi$$
−0.320149 + 0.947367i $$0.603733\pi$$
$$644$$ 2.38197 1.73060i 0.0938626 0.0681952i
$$645$$ 0 0
$$646$$ 1.90983 5.87785i 0.0751413 0.231261i
$$647$$ 10.3431 14.2361i 0.406630 0.559678i −0.555763 0.831341i $$-0.687574\pi$$
0.962392 + 0.271663i $$0.0875737\pi$$
$$648$$ 2.23607i 0.0878410i
$$649$$ 11.3435 + 19.1396i 0.445270 + 0.751297i
$$650$$ 0 0
$$651$$ −4.32624 3.14320i −0.169559 0.123192i
$$652$$ 20.8702 + 6.78115i 0.817342 + 0.265570i
$$653$$ −22.2906 + 7.24265i −0.872297 + 0.283427i −0.710755 0.703439i $$-0.751647\pi$$
−0.161542 + 0.986866i $$0.551647\pi$$
$$654$$ −2.07295 + 1.50609i −0.0810587 + 0.0588926i
$$655$$ 0 0
$$656$$ 1.44834 + 4.45752i 0.0565481 + 0.174037i
$$657$$ 12.8128 + 4.16312i 0.499873 + 0.162419i
$$658$$ −1.41260 + 1.94427i −0.0550687 + 0.0757956i
$$659$$ −12.9656 −0.505066 −0.252533 0.967588i $$-0.581264\pi$$
−0.252533 + 0.967588i $$0.581264\pi$$
$$660$$ 0 0
$$661$$ 3.90983 0.152075 0.0760374 0.997105i $$-0.475773\pi$$
0.0760374 + 0.997105i $$0.475773\pi$$
$$662$$ −7.84548 + 10.7984i −0.304923 + 0.419691i
$$663$$ 2.35114 + 0.763932i 0.0913108 + 0.0296687i
$$664$$ −3.94427 12.1392i −0.153067 0.471093i
$$665$$ 0 0
$$666$$ 3.73607 2.71441i 0.144770 0.105181i
$$667$$ −13.2618 + 4.30902i −0.513499 + 0.166846i
$$668$$ 30.8298 + 10.0172i 1.19284 + 0.387578i
$$669$$ −6.50000 4.72253i −0.251305 0.182583i
$$670$$ 0 0
$$671$$ −15.3369 + 17.4293i −0.592074 + 0.672850i
$$672$$ 4.29180i 0.165560i
$$673$$ 16.0494 22.0902i 0.618661 0.851513i −0.378594 0.925563i $$-0.623592\pi$$
0.997255 + 0.0740494i $$0.0235923\pi$$
$$674$$ 4.22949 13.0170i 0.162914 0.501397i
$$675$$ 0 0
$$676$$ −15.0172 + 10.9106i −0.577585 + 0.419640i
$$677$$ −7.02067 9.66312i −0.269826 0.371384i 0.652505 0.757785i $$-0.273718\pi$$
−0.922331 + 0.386401i $$0.873718\pi$$
$$678$$ 3.21644 1.04508i 0.123527 0.0401362i
$$679$$ 2.70820 8.33499i 0.103931 0.319868i
$$680$$ 0 0
$$681$$ −25.9443 −0.994187
$$682$$ 12.3435 7.31559i 0.472657 0.280129i
$$683$$ 2.29180i 0.0876931i −0.999038 0.0438466i $$-0.986039\pi$$
0.999038 0.0438466i $$-0.0139613\pi$$
$$684$$ −6.54508 4.75528i −0.250258 0.181823i
$$685$$ 0 0
$$686$$ 1.95743 + 6.02434i 0.0747349 + 0.230010i
$$687$$ −10.6331 14.6353i −0.405679 0.558370i
$$688$$ 2.27790 + 3.13525i 0.0868440 + 0.119530i
$$689$$ −2.90983 8.95554i −0.110856 0.341179i
$$690$$ 0 0
$$691$$ −26.9443 19.5762i −1.02501 0.744712i −0.0577049 0.998334i $$-0.518378\pi$$
−0.967304 + 0.253621i $$0.918378\pi$$
$$692$$ 5.76393i 0.219112i
$$693$$ −2.52265 0.236068i −0.0958277 0.00896748i
$$694$$ −3.59675 −0.136531
$$695$$ 0 0
$$696$$ −4.04508 + 12.4495i −0.153329 + 0.471897i
$$697$$ 4.80828 1.56231i 0.182127 0.0591766i
$$698$$ −10.0858 13.8820i −0.381755 0.525440i
$$699$$ 18.8262 13.6781i 0.712074 0.517352i
$$700$$ 0 0
$$701$$ 4.19756 12.9188i 0.158540 0.487935i −0.839963 0.542644i $$-0.817423\pi$$
0.998502 + 0.0547093i $$0.0174232\pi$$
$$702$$ −0.449028 + 0.618034i −0.0169475 + 0.0233262i
$$703$$ 37.3607i 1.40908i
$$704$$ −0.718847 0.310271i −0.0270926 0.0116938i
$$705$$ 0 0
$$706$$ 17.9164 + 13.0170i 0.674293 + 0.489902i
$$707$$ −0.408539 0.132742i −0.0153647 0.00499229i
$$708$$ 10.3229 3.35410i 0.387957 0.126055i
$$709$$ 33.3156 24.2052i 1.25119 0.909045i 0.252903 0.967492i $$-0.418615\pi$$
0.998291 + 0.0584464i $$0.0186147\pi$$
$$710$$ 0 0
$$711$$ −2.50000 7.69421i −0.0937573 0.288555i
$$712$$ 23.0826 + 7.50000i 0.865058 + 0.281074i
$$713$$ 9.80059 13.4894i 0.367035 0.505180i
$$714$$ −0.944272 −0.0353385
$$715$$ 0 0
$$716$$ 31.5066 1.17746
$$717$$ −4.13474 + 5.69098i −0.154415 + 0.212534i
$$718$$ 9.82084 + 3.19098i 0.366510 + 0.119086i
$$719$$ −11.7705 36.2259i −0.438966 1.35100i −0.888967 0.457970i $$-0.848577\pi$$
0.450001 0.893028i $$-0.351423\pi$$
$$720$$ 0 0
$$721$$ 1.47214 1.06957i 0.0548252 0.0398328i
$$722$$ 3.52671 1.14590i 0.131251 0.0426459i
$$723$$ 1.53884 + 0.500000i 0.0572301 + 0.0185952i
$$724$$ 6.85410 + 4.97980i 0.254731 + 0.185073i
$$725$$ 0 0
$$726$$ 3.26393 5.96361i 0.121136 0.221330i
$$727$$ 37.3262i 1.38435i −0.721728 0.692177i $$-0.756652\pi$$
0.721728 0.692177i $$-0.243348\pi$$
$$728$$ −1.24108 + 1.70820i −0.0459976 + 0.0633102i
$$729$$ −0.309017 + 0.951057i −0.0114451 + 0.0352243i
$$730$$ 0 0
$$731$$ 3.38197 2.45714i 0.125087 0.0908807i
$$732$$ 6.65740 + 9.16312i 0.246064 + 0.338679i
$$733$$ −1.76336 + 0.572949i −0.0651310 + 0.0211624i −0.341401 0.939918i $$-0.610902\pi$$
0.276270 + 0.961080i $$0.410902\pi$$
$$734$$ 3.46149 10.6534i 0.127766 0.393223i
$$735$$ 0 0
$$736$$ 13.3820 0.493266
$$737$$ 6.81640 + 30.3607i 0.251085 + 1.11835i
$$738$$ 1.56231i 0.0575093i
$$739$$ −16.1803 11.7557i −0.595203 0.432441i 0.248970 0.968511i $$-0.419908\pi$$
−0.844173 + 0.536071i $$0.819908\pi$$
$$740$$ 0 0
$$741$$ 1.90983 + 5.87785i 0.0701594 + 0.215928i
$$742$$ 2.11412 + 2.90983i 0.0776116 + 0.106823i
$$743$$ −0.204270 0.281153i −0.00749392 0.0103145i 0.805254 0.592931i $$-0.202029\pi$$
−0.812748 + 0.582616i $$0.802029\pi$$
$$744$$ −4.83688 14.8864i −0.177329 0.545762i
$$745$$ 0 0
$$746$$ −4.87132 3.53922i −0.178352 0.129580i
$$747$$ 5.70820i 0.208852i
$$748$$ −4.25325 + 9.85410i −0.155514 + 0.360302i
$$749$$ 2.18034 0.0796679
$$750$$ 0 0
$$751$$ −14.1803 + 43.6426i −0.517448 + 1.59254i 0.261335 + 0.965248i $$0.415837\pi$$
−0.778783 + 0.627293i $$0.784163\pi$$
$$752$$ 8.97578 2.91641i 0.327313 0.106350i
$$753$$ 4.42477 + 6.09017i 0.161247 + 0.221938i
$$754$$ 3.61803 2.62866i 0.131761 0.0957300i
$$755$$ 0 0
$$756$$ −0.381966 + 1.17557i −0.0138920 + 0.0427551i
$$757$$ 14.2128 19.5623i 0.516575 0.711004i −0.468436 0.883497i $$-0.655182\pi$$
0.985011 + 0.172493i $$0.0551823\pi$$
$$758$$ 3.09017i 0.112240i
$$759$$ 0.736068 7.86572i 0.0267176 0.285508i
$$760$$ 0 0
$$761$$ −31.5795 22.9439i −1.14476 0.831715i −0.156982 0.987601i $$-0.550176\pi$$
−0.987775 + 0.155887i $$0.950176\pi$$
$$762$$ 9.37181 + 3.04508i 0.339505 + 0.110312i
$$763$$ 3.01217 0.978714i 0.109048 0.0354318i
$$764$$ −13.6353 + 9.90659i −0.493306 + 0.358408i
$$765$$ 0 0
$$766$$ −5.98936 18.4333i −0.216404 0.666024i
$$767$$ −7.88597 2.56231i −0.284746 0.0925195i
$$768$$ 3.85723 5.30902i 0.139186 0.191573i
$$769$$ −12.7639 −0.460279 −0.230140 0.973158i $$-0.573918\pi$$
−0.230140 + 0.973158i $$0.573918\pi$$
$$770$$ 0 0
$$771$$ 10.5623 0.380392
$$772$$ −20.0049 + 27.5344i −0.719994 + 0.990986i
$$773$$ −9.99235 3.24671i −0.359400 0.116776i 0.123751 0.992313i $$-0.460508\pi$$
−0.483151 + 0.875537i $$0.660508\pi$$
$$774$$ 0.399187 + 1.22857i 0.0143485 + 0.0441601i
$$775$$ 0 0
$$776$$ 20.7533 15.0781i 0.745000 0.541274i
$$777$$ −5.42882 + 1.76393i −0.194758 + 0.0632807i
$$778$$ −22.8909 7.43769i −0.820677 0.266654i
$$779$$ 10.2254 + 7.42921i 0.366364 + 0.266179i
$$780$$ 0 0