Properties

 Label 950.2.u.g.149.3 Level $950$ Weight $2$ Character 950.149 Analytic conductor $7.586$ Analytic rank $0$ Dimension $36$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.u (of order $$18$$, degree $$6$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$36$$ Relative dimension: $$6$$ over $$\Q(\zeta_{18})$$ Twist minimal: no (minimal twist has level 190) Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

 Embedding label 149.3 Character $$\chi$$ $$=$$ 950.149 Dual form 950.2.u.g.899.3

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.642788 + 0.766044i) q^{2} +(0.811037 + 2.22831i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.22831 - 0.811037i) q^{6} +(-2.73267 + 1.57771i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.00943 + 1.68611i) q^{9} +O(q^{10})$$ $$q+(-0.642788 + 0.766044i) q^{2} +(0.811037 + 2.22831i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.22831 - 0.811037i) q^{6} +(-2.73267 + 1.57771i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.00943 + 1.68611i) q^{9} +(-0.688886 + 1.19319i) q^{11} +(2.05362 - 1.18566i) q^{12} +(-1.47931 + 4.06437i) q^{13} +(0.547933 - 3.10748i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-0.833438 + 0.993253i) q^{17} -2.62313i q^{18} +(-1.08907 - 4.22066i) q^{19} +(-5.73192 - 4.80965i) q^{21} +(-0.471226 - 1.29468i) q^{22} +(2.09271 - 0.369001i) q^{23} +(-0.411774 + 2.33529i) q^{24} +(-2.16260 - 3.74574i) q^{26} +(0.773953 + 0.446842i) q^{27} +(2.02826 + 2.41719i) q^{28} +(0.0998515 - 0.0837854i) q^{29} +(-0.173355 - 0.300259i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-3.21749 - 0.567331i) q^{33} +(-0.225152 - 1.27690i) q^{34} +(2.00943 + 1.68611i) q^{36} -10.3150i q^{37} +(3.93325 + 1.87871i) q^{38} -10.2564 q^{39} +(-10.3451 + 3.76531i) q^{41} +(7.36881 - 1.29932i) q^{42} +(-11.3501 - 2.00132i) q^{43} +(1.29468 + 0.471226i) q^{44} +(-1.06250 + 1.84030i) q^{46} +(-0.0491361 - 0.0585581i) q^{47} +(-1.52425 - 1.81653i) q^{48} +(1.47834 - 2.56055i) q^{49} +(-2.88922 - 1.05159i) q^{51} +(4.25950 + 0.751065i) q^{52} +(-6.12511 + 1.08002i) q^{53} +(-0.839788 + 0.305658i) q^{54} -3.15542 q^{56} +(8.52164 - 5.84988i) q^{57} +0.130347i q^{58} +(6.27104 + 5.26202i) q^{59} +(1.36244 + 7.72680i) q^{61} +(0.341442 + 0.0602055i) q^{62} +(2.83092 - 7.77790i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.50277 - 2.10007i) q^{66} +(0.662508 + 0.789546i) q^{67} +(1.12289 + 0.648300i) q^{68} +(2.51951 + 4.36392i) q^{69} +(2.02349 - 11.4758i) q^{71} +(-2.58328 + 0.455501i) q^{72} +(4.18756 + 11.5052i) q^{73} +(7.90176 + 6.63036i) q^{74} +(-3.96742 + 1.80543i) q^{76} -4.34745i q^{77} +(6.59270 - 7.85688i) q^{78} +(13.1650 - 4.79168i) q^{79} +(-1.73450 + 9.83684i) q^{81} +(3.76531 - 10.3451i) q^{82} +(9.85443 - 5.68946i) q^{83} +(-3.74124 + 6.48003i) q^{84} +(8.82879 - 7.40823i) q^{86} +(0.267683 + 0.154547i) q^{87} +(-1.19319 + 0.688886i) q^{88} +(-17.1195 - 6.23099i) q^{89} +(-2.36992 - 13.4405i) q^{91} +(-0.726790 - 1.99684i) q^{92} +(0.528473 - 0.629809i) q^{93} +0.0764422 q^{94} +2.37131 q^{96} +(-10.4271 + 12.4265i) q^{97} +(1.01124 + 2.77836i) q^{98} +(-0.627577 - 3.55916i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$36q + 36q^{9} + O(q^{10})$$ $$36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{9}\right)$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.642788 + 0.766044i −0.454519 + 0.541675i
$$3$$ 0.811037 + 2.22831i 0.468252 + 1.28651i 0.919140 + 0.393932i $$0.128885\pi$$
−0.450887 + 0.892581i $$0.648892\pi$$
$$4$$ −0.173648 0.984808i −0.0868241 0.492404i
$$5$$ 0 0
$$6$$ −2.22831 0.811037i −0.909702 0.331104i
$$7$$ −2.73267 + 1.57771i −1.03285 + 0.596318i −0.917801 0.397041i $$-0.870037\pi$$
−0.115053 + 0.993359i $$0.536704\pi$$
$$8$$ 0.866025 + 0.500000i 0.306186 + 0.176777i
$$9$$ −2.00943 + 1.68611i −0.669811 + 0.562038i
$$10$$ 0 0
$$11$$ −0.688886 + 1.19319i −0.207707 + 0.359759i −0.950992 0.309216i $$-0.899933\pi$$
0.743285 + 0.668975i $$0.233267\pi$$
$$12$$ 2.05362 1.18566i 0.592828 0.342270i
$$13$$ −1.47931 + 4.06437i −0.410286 + 1.12725i 0.546753 + 0.837294i $$0.315864\pi$$
−0.957039 + 0.289958i $$0.906359\pi$$
$$14$$ 0.547933 3.10748i 0.146441 0.830509i
$$15$$ 0 0
$$16$$ −0.939693 + 0.342020i −0.234923 + 0.0855050i
$$17$$ −0.833438 + 0.993253i −0.202138 + 0.240899i −0.857585 0.514342i $$-0.828036\pi$$
0.655446 + 0.755242i $$0.272480\pi$$
$$18$$ 2.62313i 0.618277i
$$19$$ −1.08907 4.22066i −0.249849 0.968285i
$$20$$ 0 0
$$21$$ −5.73192 4.80965i −1.25081 1.04955i
$$22$$ −0.471226 1.29468i −0.100466 0.276027i
$$23$$ 2.09271 0.369001i 0.436360 0.0769420i 0.0488468 0.998806i $$-0.484445\pi$$
0.387513 + 0.921864i $$0.373334\pi$$
$$24$$ −0.411774 + 2.33529i −0.0840531 + 0.476689i
$$25$$ 0 0
$$26$$ −2.16260 3.74574i −0.424122 0.734600i
$$27$$ 0.773953 + 0.446842i 0.148947 + 0.0859948i
$$28$$ 2.02826 + 2.41719i 0.383306 + 0.456806i
$$29$$ 0.0998515 0.0837854i 0.0185420 0.0155586i −0.633470 0.773768i $$-0.718370\pi$$
0.652012 + 0.758209i $$0.273925\pi$$
$$30$$ 0 0
$$31$$ −0.173355 0.300259i −0.0311355 0.0539282i 0.850038 0.526722i $$-0.176579\pi$$
−0.881173 + 0.472793i $$0.843246\pi$$
$$32$$ 0.342020 0.939693i 0.0604612 0.166116i
$$33$$ −3.21749 0.567331i −0.560094 0.0987596i
$$34$$ −0.225152 1.27690i −0.0386133 0.218987i
$$35$$ 0 0
$$36$$ 2.00943 + 1.68611i 0.334905 + 0.281019i
$$37$$ 10.3150i 1.69578i −0.530174 0.847889i $$-0.677873\pi$$
0.530174 0.847889i $$-0.322127\pi$$
$$38$$ 3.93325 + 1.87871i 0.638057 + 0.304768i
$$39$$ −10.2564 −1.64234
$$40$$ 0 0
$$41$$ −10.3451 + 3.76531i −1.61563 + 0.588042i −0.982543 0.186037i $$-0.940436\pi$$
−0.633089 + 0.774079i $$0.718213\pi$$
$$42$$ 7.36881 1.29932i 1.13703 0.200490i
$$43$$ −11.3501 2.00132i −1.73087 0.305199i −0.782567 0.622566i $$-0.786090\pi$$
−0.948303 + 0.317367i $$0.897201\pi$$
$$44$$ 1.29468 + 0.471226i 0.195181 + 0.0710400i
$$45$$ 0 0
$$46$$ −1.06250 + 1.84030i −0.156656 + 0.271337i
$$47$$ −0.0491361 0.0585581i −0.00716723 0.00854158i 0.762449 0.647048i $$-0.223997\pi$$
−0.769616 + 0.638507i $$0.779552\pi$$
$$48$$ −1.52425 1.81653i −0.220007 0.262194i
$$49$$ 1.47834 2.56055i 0.211191 0.365793i
$$50$$ 0 0
$$51$$ −2.88922 1.05159i −0.404572 0.147252i
$$52$$ 4.25950 + 0.751065i 0.590686 + 0.104154i
$$53$$ −6.12511 + 1.08002i −0.841348 + 0.148352i −0.577682 0.816262i $$-0.696043\pi$$
−0.263666 + 0.964614i $$0.584932\pi$$
$$54$$ −0.839788 + 0.305658i −0.114281 + 0.0415948i
$$55$$ 0 0
$$56$$ −3.15542 −0.421661
$$57$$ 8.52164 5.84988i 1.12872 0.774835i
$$58$$ 0.130347i 0.0171154i
$$59$$ 6.27104 + 5.26202i 0.816419 + 0.685057i 0.952131 0.305691i $$-0.0988875\pi$$
−0.135711 + 0.990748i $$0.543332\pi$$
$$60$$ 0 0
$$61$$ 1.36244 + 7.72680i 0.174443 + 0.989315i 0.938785 + 0.344504i $$0.111953\pi$$
−0.764342 + 0.644811i $$0.776936\pi$$
$$62$$ 0.341442 + 0.0602055i 0.0433632 + 0.00764611i
$$63$$ 2.83092 7.77790i 0.356663 0.979923i
$$64$$ 0.500000 + 0.866025i 0.0625000 + 0.108253i
$$65$$ 0 0
$$66$$ 2.50277 2.10007i 0.308069 0.258501i
$$67$$ 0.662508 + 0.789546i 0.0809382 + 0.0964584i 0.804994 0.593283i $$-0.202169\pi$$
−0.724056 + 0.689742i $$0.757724\pi$$
$$68$$ 1.12289 + 0.648300i 0.136170 + 0.0786179i
$$69$$ 2.51951 + 4.36392i 0.303313 + 0.525354i
$$70$$ 0 0
$$71$$ 2.02349 11.4758i 0.240144 1.36192i −0.591361 0.806407i $$-0.701409\pi$$
0.831505 0.555517i $$-0.187480\pi$$
$$72$$ −2.58328 + 0.455501i −0.304442 + 0.0536813i
$$73$$ 4.18756 + 11.5052i 0.490117 + 1.34659i 0.900573 + 0.434705i $$0.143147\pi$$
−0.410456 + 0.911881i $$0.634630\pi$$
$$74$$ 7.90176 + 6.63036i 0.918561 + 0.770764i
$$75$$ 0 0
$$76$$ −3.96742 + 1.80543i −0.455094 + 0.207097i
$$77$$ 4.34745i 0.495438i
$$78$$ 6.59270 7.85688i 0.746477 0.889616i
$$79$$ 13.1650 4.79168i 1.48118 0.539106i 0.530070 0.847954i $$-0.322166\pi$$
0.951111 + 0.308848i $$0.0999436\pi$$
$$80$$ 0 0
$$81$$ −1.73450 + 9.83684i −0.192722 + 1.09298i
$$82$$ 3.76531 10.3451i 0.415808 1.14242i
$$83$$ 9.85443 5.68946i 1.08166 0.624499i 0.150319 0.988637i $$-0.451970\pi$$
0.931345 + 0.364138i $$0.118636\pi$$
$$84$$ −3.74124 + 6.48003i −0.408203 + 0.707029i
$$85$$ 0 0
$$86$$ 8.82879 7.40823i 0.952033 0.798850i
$$87$$ 0.267683 + 0.154547i 0.0286986 + 0.0165691i
$$88$$ −1.19319 + 0.688886i −0.127194 + 0.0734355i
$$89$$ −17.1195 6.23099i −1.81466 0.660484i −0.996316 0.0857608i $$-0.972668\pi$$
−0.818348 0.574723i $$-0.805110\pi$$
$$90$$ 0 0
$$91$$ −2.36992 13.4405i −0.248436 1.40895i
$$92$$ −0.726790 1.99684i −0.0757731 0.208185i
$$93$$ 0.528473 0.629809i 0.0548000 0.0653082i
$$94$$ 0.0764422 0.00788441
$$95$$ 0 0
$$96$$ 2.37131 0.242021
$$97$$ −10.4271 + 12.4265i −1.05871 + 1.26172i −0.0948014 + 0.995496i $$0.530222\pi$$
−0.963910 + 0.266227i $$0.914223\pi$$
$$98$$ 1.01124 + 2.77836i 0.102151 + 0.280657i
$$99$$ −0.627577 3.55916i −0.0630738 0.357710i
$$100$$ 0 0
$$101$$ −6.22381 2.26528i −0.619293 0.225404i 0.0132716 0.999912i $$-0.495775\pi$$
−0.632564 + 0.774508i $$0.717998\pi$$
$$102$$ 2.66272 1.53732i 0.263649 0.152218i
$$103$$ 10.7020 + 6.17880i 1.05450 + 0.608815i 0.923906 0.382621i $$-0.124978\pi$$
0.130594 + 0.991436i $$0.458312\pi$$
$$104$$ −3.31330 + 2.78019i −0.324896 + 0.272620i
$$105$$ 0 0
$$106$$ 3.10980 5.38633i 0.302050 0.523167i
$$107$$ −9.48714 + 5.47740i −0.917156 + 0.529521i −0.882727 0.469887i $$-0.844295\pi$$
−0.0344297 + 0.999407i $$0.510961\pi$$
$$108$$ 0.305658 0.839788i 0.0294120 0.0808087i
$$109$$ −1.29211 + 7.32792i −0.123762 + 0.701887i 0.858274 + 0.513192i $$0.171537\pi$$
−0.982036 + 0.188695i $$0.939574\pi$$
$$110$$ 0 0
$$111$$ 22.9850 8.36586i 2.18164 0.794052i
$$112$$ 2.02826 2.41719i 0.191653 0.228403i
$$113$$ 11.6014i 1.09137i −0.837990 0.545686i $$-0.816269\pi$$
0.837990 0.545686i $$-0.183731\pi$$
$$114$$ −0.996338 + 10.2882i −0.0933156 + 0.963577i
$$115$$ 0 0
$$116$$ −0.0998515 0.0837854i −0.00927098 0.00777928i
$$117$$ −3.88041 10.6613i −0.358744 0.985642i
$$118$$ −8.06189 + 1.42153i −0.742157 + 0.130862i
$$119$$ 0.710449 4.02916i 0.0651268 0.369352i
$$120$$ 0 0
$$121$$ 4.55087 + 7.88234i 0.413716 + 0.716577i
$$122$$ −6.79483 3.92300i −0.615175 0.355172i
$$123$$ −16.7805 19.9982i −1.51305 1.80318i
$$124$$ −0.265595 + 0.222861i −0.0238511 + 0.0200135i
$$125$$ 0 0
$$126$$ 4.13853 + 7.16815i 0.368690 + 0.638589i
$$127$$ −5.60862 + 15.4096i −0.497685 + 1.36738i 0.395822 + 0.918327i $$0.370460\pi$$
−0.893507 + 0.449050i $$0.851763\pi$$
$$128$$ −0.984808 0.173648i −0.0870455 0.0153485i
$$129$$ −4.74577 26.9146i −0.417841 2.36970i
$$130$$ 0 0
$$131$$ 8.53118 + 7.15851i 0.745373 + 0.625442i 0.934275 0.356554i $$-0.116048\pi$$
−0.188902 + 0.981996i $$0.560493\pi$$
$$132$$ 3.26713i 0.284367i
$$133$$ 9.63503 + 9.81545i 0.835463 + 0.851107i
$$134$$ −1.03068 −0.0890371
$$135$$ 0 0
$$136$$ −1.21840 + 0.443463i −0.104477 + 0.0380266i
$$137$$ 7.23011 1.27486i 0.617710 0.108919i 0.143968 0.989582i $$-0.454014\pi$$
0.473743 + 0.880663i $$0.342903\pi$$
$$138$$ −4.96247 0.875017i −0.422433 0.0744864i
$$139$$ 11.0992 + 4.03978i 0.941422 + 0.342650i 0.766727 0.641973i $$-0.221884\pi$$
0.174695 + 0.984623i $$0.444106\pi$$
$$140$$ 0 0
$$141$$ 0.0906342 0.156983i 0.00763277 0.0132203i
$$142$$ 7.49028 + 8.92657i 0.628570 + 0.749101i
$$143$$ −3.83047 4.56497i −0.320320 0.381742i
$$144$$ 1.31156 2.27169i 0.109297 0.189308i
$$145$$ 0 0
$$146$$ −11.5052 4.18756i −0.952180 0.346565i
$$147$$ 6.90468 + 1.21748i 0.569488 + 0.100416i
$$148$$ −10.1583 + 1.79118i −0.835007 + 0.147234i
$$149$$ 3.30256 1.20203i 0.270556 0.0984745i −0.203179 0.979142i $$-0.565127\pi$$
0.473736 + 0.880667i $$0.342905\pi$$
$$150$$ 0 0
$$151$$ −0.212620 −0.0173028 −0.00865139 0.999963i $$-0.502754\pi$$
−0.00865139 + 0.999963i $$0.502754\pi$$
$$152$$ 1.16717 4.19973i 0.0946700 0.340643i
$$153$$ 3.40114i 0.274966i
$$154$$ 3.33034 + 2.79449i 0.268366 + 0.225186i
$$155$$ 0 0
$$156$$ 1.78101 + 10.1006i 0.142595 + 0.808696i
$$157$$ −7.57072 1.33492i −0.604210 0.106538i −0.136829 0.990595i $$-0.543691\pi$$
−0.467381 + 0.884056i $$0.654802\pi$$
$$158$$ −4.79168 + 13.1650i −0.381205 + 1.04735i
$$159$$ −7.37431 12.7727i −0.584821 1.01294i
$$160$$ 0 0
$$161$$ −5.13651 + 4.31004i −0.404814 + 0.339679i
$$162$$ −6.42054 7.65170i −0.504445 0.601174i
$$163$$ 6.34537 + 3.66350i 0.497008 + 0.286948i 0.727477 0.686132i $$-0.240693\pi$$
−0.230469 + 0.973080i $$0.574026\pi$$
$$164$$ 5.50451 + 9.53409i 0.429830 + 0.744487i
$$165$$ 0 0
$$166$$ −1.97593 + 11.2060i −0.153362 + 0.869758i
$$167$$ −15.6032 + 2.75126i −1.20741 + 0.212899i −0.740899 0.671617i $$-0.765600\pi$$
−0.466511 + 0.884515i $$0.654489\pi$$
$$168$$ −2.55916 7.03124i −0.197444 0.542472i
$$169$$ −4.37215 3.66867i −0.336319 0.282205i
$$170$$ 0 0
$$171$$ 9.30491 + 6.64483i 0.711564 + 0.508143i
$$172$$ 11.5252i 0.878786i
$$173$$ −10.6961 + 12.7471i −0.813211 + 0.969147i −0.999912 0.0132697i $$-0.995776\pi$$
0.186701 + 0.982417i $$0.440220\pi$$
$$174$$ −0.290453 + 0.105716i −0.0220192 + 0.00801432i
$$175$$ 0 0
$$176$$ 0.239248 1.35684i 0.0180340 0.102276i
$$177$$ −6.63936 + 18.2415i −0.499045 + 1.37111i
$$178$$ 15.7774 9.10910i 1.18257 0.682756i
$$179$$ −2.28553 + 3.95866i −0.170829 + 0.295884i −0.938710 0.344708i $$-0.887978\pi$$
0.767881 + 0.640592i $$0.221311\pi$$
$$180$$ 0 0
$$181$$ 1.29338 1.08527i 0.0961360 0.0806677i −0.593453 0.804869i $$-0.702236\pi$$
0.689589 + 0.724201i $$0.257791\pi$$
$$182$$ 11.8194 + 6.82392i 0.876111 + 0.505823i
$$183$$ −16.1127 + 9.30266i −1.19108 + 0.687673i
$$184$$ 1.99684 + 0.726790i 0.147209 + 0.0535796i
$$185$$ 0 0
$$186$$ 0.142766 + 0.809667i 0.0104681 + 0.0593677i
$$187$$ −0.610991 1.67868i −0.0446801 0.122758i
$$188$$ −0.0491361 + 0.0585581i −0.00358362 + 0.00427079i
$$189$$ −2.81995 −0.205121
$$190$$ 0 0
$$191$$ 11.2207 0.811901 0.405951 0.913895i $$-0.366941\pi$$
0.405951 + 0.913895i $$0.366941\pi$$
$$192$$ −1.52425 + 1.81653i −0.110003 + 0.131097i
$$193$$ 7.34927 + 20.1920i 0.529012 + 1.45345i 0.860236 + 0.509897i $$0.170316\pi$$
−0.331223 + 0.943552i $$0.607461\pi$$
$$194$$ −2.81687 15.9752i −0.202239 1.14696i
$$195$$ 0 0
$$196$$ −2.77836 1.01124i −0.198455 0.0722315i
$$197$$ −13.2315 + 7.63921i −0.942705 + 0.544271i −0.890807 0.454381i $$-0.849860\pi$$
−0.0518981 + 0.998652i $$0.516527\pi$$
$$198$$ 3.12988 + 1.80704i 0.222431 + 0.128420i
$$199$$ −0.542940 + 0.455581i −0.0384880 + 0.0322953i −0.661829 0.749655i $$-0.730219\pi$$
0.623341 + 0.781950i $$0.285775\pi$$
$$200$$ 0 0
$$201$$ −1.22203 + 2.11662i −0.0861955 + 0.149295i
$$202$$ 5.73590 3.31162i 0.403576 0.233005i
$$203$$ −0.140673 + 0.386495i −0.00987328 + 0.0271266i
$$204$$ −0.533906 + 3.02793i −0.0373809 + 0.211998i
$$205$$ 0 0
$$206$$ −11.6123 + 4.22655i −0.809071 + 0.294478i
$$207$$ −3.58298 + 4.27002i −0.249034 + 0.296787i
$$208$$ 4.32521i 0.299899i
$$209$$ 5.78627 + 1.60809i 0.400244 + 0.111234i
$$210$$ 0 0
$$211$$ 10.7852 + 9.04988i 0.742486 + 0.623020i 0.933504 0.358567i $$-0.116735\pi$$
−0.191018 + 0.981586i $$0.561179\pi$$
$$212$$ 2.12723 + 5.84451i 0.146099 + 0.401403i
$$213$$ 27.2126 4.79832i 1.86458 0.328776i
$$214$$ 1.90228 10.7884i 0.130037 0.737478i
$$215$$ 0 0
$$216$$ 0.446842 + 0.773953i 0.0304038 + 0.0526608i
$$217$$ 0.947444 + 0.547007i 0.0643167 + 0.0371333i
$$218$$ −4.78296 5.70011i −0.323943 0.386060i
$$219$$ −22.2409 + 18.6623i −1.50290 + 1.26108i
$$220$$ 0 0
$$221$$ −2.80403 4.85673i −0.188620 0.326699i
$$222$$ −8.36586 + 22.9850i −0.561479 + 1.54265i
$$223$$ 11.5389 + 2.03461i 0.772699 + 0.136248i 0.546077 0.837735i $$-0.316121\pi$$
0.226622 + 0.973983i $$0.427232\pi$$
$$224$$ 0.547933 + 3.10748i 0.0366103 + 0.207627i
$$225$$ 0 0
$$226$$ 8.88722 + 7.45727i 0.591169 + 0.496050i
$$227$$ 10.2265i 0.678758i 0.940650 + 0.339379i $$0.110217\pi$$
−0.940650 + 0.339379i $$0.889783\pi$$
$$228$$ −7.24077 7.37636i −0.479532 0.488511i
$$229$$ 5.05689 0.334169 0.167084 0.985943i $$-0.446565\pi$$
0.167084 + 0.985943i $$0.446565\pi$$
$$230$$ 0 0
$$231$$ 9.68744 3.52594i 0.637387 0.231990i
$$232$$ 0.128367 0.0226345i 0.00842768 0.00148603i
$$233$$ −7.14818 1.26042i −0.468293 0.0825727i −0.0654778 0.997854i $$-0.520857\pi$$
−0.402815 + 0.915281i $$0.631968\pi$$
$$234$$ 10.6613 + 3.88041i 0.696954 + 0.253671i
$$235$$ 0 0
$$236$$ 4.09313 7.08951i 0.266440 0.461488i
$$237$$ 21.3546 + 25.4495i 1.38713 + 1.65312i
$$238$$ 2.62985 + 3.13413i 0.170468 + 0.203155i
$$239$$ 7.98657 13.8331i 0.516608 0.894792i −0.483206 0.875507i $$-0.660528\pi$$
0.999814 0.0192850i $$-0.00613899\pi$$
$$240$$ 0 0
$$241$$ −20.8564 7.59111i −1.34348 0.488986i −0.432572 0.901599i $$-0.642394\pi$$
−0.910906 + 0.412613i $$0.864616\pi$$
$$242$$ −8.96347 1.58050i −0.576194 0.101598i
$$243$$ −20.6859 + 3.64748i −1.32700 + 0.233986i
$$244$$ 7.37283 2.68349i 0.471997 0.171793i
$$245$$ 0 0
$$246$$ 26.1058 1.66445
$$247$$ 18.7654 + 1.81729i 1.19401 + 0.115632i
$$248$$ 0.346710i 0.0220161i
$$249$$ 20.6702 + 17.3443i 1.30992 + 1.09915i
$$250$$ 0 0
$$251$$ 3.91622 + 22.2100i 0.247190 + 1.40188i 0.815352 + 0.578966i $$0.196544\pi$$
−0.568162 + 0.822917i $$0.692345\pi$$
$$252$$ −8.15132 1.43730i −0.513485 0.0905412i
$$253$$ −1.00135 + 2.75119i −0.0629544 + 0.172966i
$$254$$ −8.19925 14.2015i −0.514467 0.891083i
$$255$$ 0 0
$$256$$ 0.766044 0.642788i 0.0478778 0.0401742i
$$257$$ −6.88718 8.20783i −0.429611 0.511990i 0.507199 0.861829i $$-0.330681\pi$$
−0.936810 + 0.349839i $$0.886236\pi$$
$$258$$ 23.6683 + 13.6649i 1.47352 + 0.850739i
$$259$$ 16.2741 + 28.1876i 1.01122 + 1.75149i
$$260$$ 0 0
$$261$$ −0.0593732 + 0.336722i −0.00367511 + 0.0208426i
$$262$$ −10.9675 + 1.93386i −0.677573 + 0.119474i
$$263$$ −9.12051 25.0584i −0.562395 1.54517i −0.816115 0.577890i $$-0.803876\pi$$
0.253720 0.967278i $$-0.418346\pi$$
$$264$$ −2.50277 2.10007i −0.154035 0.129250i
$$265$$ 0 0
$$266$$ −13.7123 + 1.07161i −0.840758 + 0.0657049i
$$267$$ 43.2011i 2.64386i
$$268$$ 0.662508 0.789546i 0.0404691 0.0482292i
$$269$$ 1.34180 0.488375i 0.0818110 0.0297768i −0.300790 0.953690i $$-0.597250\pi$$
0.382601 + 0.923913i $$0.375028\pi$$
$$270$$ 0 0
$$271$$ 1.27969 7.25749i 0.0777357 0.440861i −0.920953 0.389673i $$-0.872588\pi$$
0.998689 0.0511882i $$-0.0163008\pi$$
$$272$$ 0.443463 1.21840i 0.0268889 0.0738766i
$$273$$ 28.0275 16.1817i 1.69630 0.979359i
$$274$$ −3.67083 + 6.35806i −0.221763 + 0.384104i
$$275$$ 0 0
$$276$$ 3.86011 3.23902i 0.232351 0.194966i
$$277$$ −2.18698 1.26266i −0.131403 0.0758656i 0.432857 0.901462i $$-0.357505\pi$$
−0.564261 + 0.825597i $$0.690839\pi$$
$$278$$ −10.2291 + 5.90576i −0.613500 + 0.354204i
$$279$$ 0.854616 + 0.311055i 0.0511645 + 0.0186224i
$$280$$ 0 0
$$281$$ 2.99175 + 16.9671i 0.178473 + 1.01217i 0.934058 + 0.357120i $$0.116241\pi$$
−0.755586 + 0.655050i $$0.772648\pi$$
$$282$$ 0.0619974 + 0.170336i 0.00369189 + 0.0101434i
$$283$$ −18.1400 + 21.6184i −1.07831 + 1.28508i −0.122061 + 0.992523i $$0.538950\pi$$
−0.956248 + 0.292556i $$0.905494\pi$$
$$284$$ −11.6528 −0.691467
$$285$$ 0 0
$$286$$ 5.95915 0.352372
$$287$$ 22.3292 26.6109i 1.31805 1.57079i
$$288$$ 0.897162 + 2.46493i 0.0528658 + 0.145248i
$$289$$ 2.66009 + 15.0861i 0.156476 + 0.887418i
$$290$$ 0 0
$$291$$ −36.1469 13.1564i −2.11897 0.771241i
$$292$$ 10.6033 6.12181i 0.620510 0.358252i
$$293$$ 10.9276 + 6.30904i 0.638396 + 0.368578i 0.783996 0.620766i $$-0.213178\pi$$
−0.145601 + 0.989343i $$0.546511\pi$$
$$294$$ −5.37089 + 4.50671i −0.313237 + 0.262837i
$$295$$ 0 0
$$296$$ 5.15751 8.93306i 0.299774 0.519224i
$$297$$ −1.06633 + 0.615647i −0.0618748 + 0.0357234i
$$298$$ −1.20203 + 3.30256i −0.0696320 + 0.191312i
$$299$$ −1.59601 + 9.05140i −0.0922994 + 0.523456i
$$300$$ 0 0
$$301$$ 34.1735 12.4382i 1.96973 0.716923i
$$302$$ 0.136670 0.162877i 0.00786445 0.00937249i
$$303$$ 15.7058i 0.902274i
$$304$$ 2.46694 + 3.59364i 0.141488 + 0.206109i
$$305$$ 0 0
$$306$$ 2.60543 + 2.18621i 0.148942 + 0.124978i
$$307$$ 3.10031 + 8.51802i 0.176944 + 0.486149i 0.996182 0.0873047i $$-0.0278254\pi$$
−0.819238 + 0.573454i $$0.805603\pi$$
$$308$$ −4.28140 + 0.754926i −0.243955 + 0.0430159i
$$309$$ −5.08854 + 28.8586i −0.289477 + 1.64171i
$$310$$ 0 0
$$311$$ 10.8562 + 18.8035i 0.615599 + 1.06625i 0.990279 + 0.139095i $$0.0444192\pi$$
−0.374680 + 0.927154i $$0.622247\pi$$
$$312$$ −8.88232 5.12821i −0.502863 0.290328i
$$313$$ −6.45746 7.69570i −0.364997 0.434987i 0.552022 0.833829i $$-0.313856\pi$$
−0.917019 + 0.398843i $$0.869412\pi$$
$$314$$ 5.88898 4.94144i 0.332334 0.278862i
$$315$$ 0 0
$$316$$ −7.00496 12.1330i −0.394060 0.682532i
$$317$$ 0.721135 1.98130i 0.0405030 0.111281i −0.917792 0.397061i $$-0.870030\pi$$
0.958295 + 0.285780i $$0.0922525\pi$$
$$318$$ 14.5245 + 2.56107i 0.814496 + 0.143618i
$$319$$ 0.0311852 + 0.176860i 0.00174604 + 0.00990226i
$$320$$ 0 0
$$321$$ −19.8997 16.6979i −1.11070 0.931984i
$$322$$ 6.70524i 0.373668i
$$323$$ 5.09985 + 2.43594i 0.283763 + 0.135539i
$$324$$ 9.98859 0.554921
$$325$$ 0 0
$$326$$ −6.88513 + 2.50598i −0.381332 + 0.138794i
$$327$$ −17.3768 + 3.06400i −0.960939 + 0.169439i
$$328$$ −10.8418 1.91170i −0.598636 0.105556i
$$329$$ 0.226661 + 0.0824977i 0.0124962 + 0.00454824i
$$330$$ 0 0
$$331$$ 1.72204 2.98267i 0.0946521 0.163942i −0.814811 0.579726i $$-0.803159\pi$$
0.909463 + 0.415784i $$0.136493\pi$$
$$332$$ −7.31423 8.71676i −0.401420 0.478394i
$$333$$ 17.3923 + 20.7273i 0.953091 + 1.13585i
$$334$$ 7.92194 13.7212i 0.433469 0.750791i
$$335$$ 0 0
$$336$$ 7.03124 + 2.55916i 0.383586 + 0.139614i
$$337$$ 25.4658 + 4.49031i 1.38721 + 0.244603i 0.816877 0.576811i $$-0.195703\pi$$
0.570332 + 0.821414i $$0.306814\pi$$
$$338$$ 5.62072 0.991085i 0.305727 0.0539079i
$$339$$ 25.8516 9.40920i 1.40406 0.511038i
$$340$$ 0 0
$$341$$ 0.477687 0.0258682
$$342$$ −11.0713 + 2.85676i −0.598668 + 0.154476i
$$343$$ 12.7584i 0.688889i
$$344$$ −8.82879 7.40823i −0.476016 0.399425i
$$345$$ 0 0
$$346$$ −2.88954 16.3874i −0.155343 0.880992i
$$347$$ −2.48488 0.438152i −0.133395 0.0235212i 0.106552 0.994307i $$-0.466019\pi$$
−0.239947 + 0.970786i $$0.577130\pi$$
$$348$$ 0.105716 0.290453i 0.00566698 0.0155699i
$$349$$ 1.83973 + 3.18650i 0.0984782 + 0.170569i 0.911055 0.412285i $$-0.135269\pi$$
−0.812577 + 0.582854i $$0.801936\pi$$
$$350$$ 0 0
$$351$$ −2.96105 + 2.48461i −0.158049 + 0.132619i
$$352$$ 0.885615 + 1.05543i 0.0472034 + 0.0562548i
$$353$$ −2.42172 1.39818i −0.128895 0.0744175i 0.434166 0.900833i $$-0.357043\pi$$
−0.563061 + 0.826415i $$0.690376\pi$$
$$354$$ −9.70609 16.8114i −0.515873 0.893518i
$$355$$ 0 0
$$356$$ −3.16356 + 17.9414i −0.167668 + 0.950893i
$$357$$ 9.55440 1.68470i 0.505672 0.0891637i
$$358$$ −1.56340 4.29540i −0.0826281 0.227019i
$$359$$ −15.4284 12.9460i −0.814280 0.683262i 0.137345 0.990523i $$-0.456143\pi$$
−0.951625 + 0.307261i $$0.900587\pi$$
$$360$$ 0 0
$$361$$ −16.6279 + 9.19314i −0.875151 + 0.483849i
$$362$$ 1.68838i 0.0887395i
$$363$$ −13.8733 + 16.5336i −0.728162 + 0.867789i
$$364$$ −12.8248 + 4.66784i −0.672201 + 0.244661i
$$365$$ 0 0
$$366$$ 3.23078 18.3227i 0.168876 0.957741i
$$367$$ 1.54639 4.24866i 0.0807207 0.221778i −0.892767 0.450520i $$-0.851239\pi$$
0.973487 + 0.228741i $$0.0734610\pi$$
$$368$$ −1.84030 + 1.06250i −0.0959321 + 0.0553864i
$$369$$ 14.4390 25.0091i 0.751666 1.30192i
$$370$$ 0 0
$$371$$ 15.0340 12.6150i 0.780524 0.654938i
$$372$$ −0.712009 0.411079i −0.0369160 0.0213134i
$$373$$ 20.1528 11.6352i 1.04347 0.602449i 0.122657 0.992449i $$-0.460858\pi$$
0.920815 + 0.390000i $$0.127525\pi$$
$$374$$ 1.67868 + 0.610991i 0.0868027 + 0.0315936i
$$375$$ 0 0
$$376$$ −0.0132740 0.0752808i −0.000684556 0.00388231i
$$377$$ 0.192823 + 0.529778i 0.00993091 + 0.0272849i
$$378$$ 1.81263 2.16021i 0.0932315 0.111109i
$$379$$ −9.34667 −0.480106 −0.240053 0.970760i $$-0.577165\pi$$
−0.240053 + 0.970760i $$0.577165\pi$$
$$380$$ 0 0
$$381$$ −38.8860 −1.99219
$$382$$ −7.21252 + 8.59555i −0.369025 + 0.439787i
$$383$$ −11.2306 30.8559i −0.573858 1.57666i −0.798355 0.602187i $$-0.794296\pi$$
0.224497 0.974475i $$-0.427926\pi$$
$$384$$ −0.411774 2.33529i −0.0210133 0.119172i
$$385$$ 0 0
$$386$$ −20.1920 7.34927i −1.02774 0.374068i
$$387$$ 26.1817 15.1160i 1.33089 0.768389i
$$388$$ 14.0484 + 8.11084i 0.713199 + 0.411766i
$$389$$ −8.17650 + 6.86090i −0.414565 + 0.347862i −0.826091 0.563537i $$-0.809440\pi$$
0.411526 + 0.911398i $$0.364996\pi$$
$$390$$ 0 0
$$391$$ −1.37763 + 2.38613i −0.0696698 + 0.120672i
$$392$$ 2.56055 1.47834i 0.129327 0.0746673i
$$393$$ −9.03225 + 24.8159i −0.455617 + 1.25180i
$$394$$ 2.65307 15.0463i 0.133660 0.758022i
$$395$$ 0 0
$$396$$ −3.39612 + 1.23608i −0.170661 + 0.0621156i
$$397$$ 6.46404 7.70354i 0.324421 0.386630i −0.579041 0.815299i $$-0.696573\pi$$
0.903462 + 0.428669i $$0.141017\pi$$
$$398$$ 0.708758i 0.0355268i
$$399$$ −14.0574 + 29.4305i −0.703753 + 1.47337i
$$400$$ 0 0
$$401$$ 9.25312 + 7.76429i 0.462079 + 0.387730i 0.843895 0.536508i $$-0.180257\pi$$
−0.381817 + 0.924238i $$0.624701\pi$$
$$402$$ −0.835919 2.29667i −0.0416918 0.114547i
$$403$$ 1.47681 0.260401i 0.0735651 0.0129715i
$$404$$ −1.15011 + 6.52262i −0.0572203 + 0.324513i
$$405$$ 0 0
$$406$$ −0.205650 0.356196i −0.0102062 0.0176777i
$$407$$ 12.3077 + 7.10587i 0.610071 + 0.352225i
$$408$$ −1.97634 2.35531i −0.0978435 0.116605i
$$409$$ 30.2942 25.4198i 1.49795 1.25693i 0.614040 0.789275i $$-0.289543\pi$$
0.883911 0.467655i $$-0.154901\pi$$
$$410$$ 0 0
$$411$$ 8.70468 + 15.0769i 0.429370 + 0.743691i
$$412$$ 4.22655 11.6123i 0.208227 0.572099i
$$413$$ −25.4386 4.48552i −1.25175 0.220718i
$$414$$ −0.967936 5.48944i −0.0475715 0.269791i
$$415$$ 0 0
$$416$$ 3.31330 + 2.78019i 0.162448 + 0.136310i
$$417$$ 28.0088i 1.37160i
$$418$$ −4.95121 + 3.39887i −0.242172 + 0.166244i
$$419$$ −28.5326 −1.39391 −0.696954 0.717116i $$-0.745462\pi$$
−0.696954 + 0.717116i $$0.745462\pi$$
$$420$$ 0 0
$$421$$ −1.91607 + 0.697393i −0.0933836 + 0.0339888i −0.388289 0.921537i $$-0.626934\pi$$
0.294906 + 0.955526i $$0.404712\pi$$
$$422$$ −13.8652 + 2.44481i −0.674949 + 0.119012i
$$423$$ 0.197471 + 0.0348195i 0.00960138 + 0.00169298i
$$424$$ −5.84451 2.12723i −0.283834 0.103307i
$$425$$ 0 0
$$426$$ −13.8162 + 23.9304i −0.669398 + 1.15943i
$$427$$ −15.9138 18.9653i −0.770121 0.917794i
$$428$$ 7.04161 + 8.39187i 0.340369 + 0.405636i
$$429$$ 7.06551 12.2378i 0.341126 0.590847i
$$430$$ 0 0
$$431$$ −12.7523 4.64147i −0.614258 0.223572i 0.0161074 0.999870i $$-0.494873\pi$$
−0.630365 + 0.776299i $$0.717095\pi$$
$$432$$ −0.880107 0.155187i −0.0423442 0.00746642i
$$433$$ −28.5238 + 5.02952i −1.37077 + 0.241703i −0.810078 0.586323i $$-0.800575\pi$$
−0.560690 + 0.828026i $$0.689464\pi$$
$$434$$ −1.02804 + 0.374175i −0.0493474 + 0.0179610i
$$435$$ 0 0
$$436$$ 7.44096 0.356357
$$437$$ −3.83652 8.43073i −0.183526 0.403297i
$$438$$ 29.0334i 1.38727i
$$439$$ 8.59028 + 7.20810i 0.409992 + 0.344024i 0.824341 0.566094i $$-0.191546\pi$$
−0.414349 + 0.910118i $$0.635991\pi$$
$$440$$ 0 0
$$441$$ 1.34677 + 7.63790i 0.0641318 + 0.363710i
$$442$$ 5.52286 + 0.973830i 0.262696 + 0.0463204i
$$443$$ 2.54804 7.00068i 0.121061 0.332612i −0.864329 0.502927i $$-0.832256\pi$$
0.985390 + 0.170315i $$0.0544785\pi$$
$$444$$ −12.2301 21.1831i −0.580413 1.00530i
$$445$$ 0 0
$$446$$ −8.97564 + 7.53146i −0.425009 + 0.356625i
$$447$$ 5.35700 + 6.38422i 0.253377 + 0.301963i
$$448$$ −2.73267 1.57771i −0.129107 0.0745398i
$$449$$ 2.65192 + 4.59326i 0.125152 + 0.216769i 0.921792 0.387684i $$-0.126725\pi$$
−0.796640 + 0.604453i $$0.793392\pi$$
$$450$$ 0 0
$$451$$ 2.63388 14.9375i 0.124025 0.703378i
$$452$$ −11.4252 + 2.01457i −0.537396 + 0.0947574i
$$453$$ −0.172443 0.473783i −0.00810207 0.0222603i
$$454$$ −7.83397 6.57348i −0.367667 0.308509i
$$455$$ 0 0
$$456$$ 10.3049 0.805323i 0.482571 0.0377127i
$$457$$ 14.9890i 0.701154i −0.936534 0.350577i $$-0.885986\pi$$
0.936534 0.350577i $$-0.114014\pi$$
$$458$$ −3.25051 + 3.87381i −0.151886 + 0.181011i
$$459$$ −1.08887 + 0.396316i −0.0508241 + 0.0184984i
$$460$$ 0 0
$$461$$ −1.19157 + 6.75771i −0.0554968 + 0.314738i −0.999901 0.0140479i $$-0.995528\pi$$
0.944405 + 0.328786i $$0.106639\pi$$
$$462$$ −3.52594 + 9.68744i −0.164042 + 0.450701i
$$463$$ 17.8738 10.3194i 0.830665 0.479585i −0.0234152 0.999726i $$-0.507454\pi$$
0.854080 + 0.520141i $$0.174121\pi$$
$$464$$ −0.0651735 + 0.112884i −0.00302560 + 0.00524050i
$$465$$ 0 0
$$466$$ 5.56030 4.66564i 0.257576 0.216132i
$$467$$ −10.4226 6.01750i −0.482301 0.278457i 0.239074 0.971001i $$-0.423156\pi$$
−0.721375 + 0.692545i $$0.756490\pi$$
$$468$$ −9.82555 + 5.67279i −0.454186 + 0.262225i
$$469$$ −3.05609 1.11233i −0.141117 0.0513625i
$$470$$ 0 0
$$471$$ −3.16552 17.9526i −0.145859 0.827210i
$$472$$ 2.79986 + 7.69256i 0.128874 + 0.354079i
$$473$$ 10.2069 12.1641i 0.469312 0.559304i
$$474$$ −33.2219 −1.52593
$$475$$ 0 0
$$476$$ −4.09132 −0.187525
$$477$$ 10.4869 12.4979i 0.480164 0.572238i
$$478$$ 5.46314 + 15.0098i 0.249878 + 0.686534i
$$479$$ −3.95553 22.4329i −0.180733 1.02499i −0.931316 0.364211i $$-0.881339\pi$$
0.750583 0.660776i $$-0.229773\pi$$
$$480$$ 0 0
$$481$$ 41.9240 + 15.2591i 1.91157 + 0.695754i
$$482$$ 19.2214 11.0975i 0.875509 0.505475i
$$483$$ −13.7700 7.95011i −0.626556 0.361743i
$$484$$ 6.97234 5.85049i 0.316925 0.265931i
$$485$$ 0 0
$$486$$ 10.5025 18.1909i 0.476403 0.825155i
$$487$$ −5.58510 + 3.22456i −0.253085 + 0.146119i −0.621176 0.783671i $$-0.713345\pi$$
0.368091 + 0.929790i $$0.380011\pi$$
$$488$$ −2.68349 + 7.37283i −0.121476 + 0.333752i
$$489$$ −3.01707 + 17.1107i −0.136437 + 0.773771i
$$490$$ 0 0
$$491$$ 22.8944 8.33289i 1.03321 0.376058i 0.230908 0.972975i $$-0.425830\pi$$
0.802303 + 0.596917i $$0.203608\pi$$
$$492$$ −16.7805 + 19.9982i −0.756524 + 0.901590i
$$493$$ 0.169008i 0.00761173i
$$494$$ −13.4543 + 13.2070i −0.605336 + 0.594209i
$$495$$ 0 0
$$496$$ 0.265595 + 0.222861i 0.0119256 + 0.0100067i
$$497$$ 12.5759 + 34.5520i 0.564106 + 1.54987i
$$498$$ −26.5730 + 4.68554i −1.19077 + 0.209964i
$$499$$ −0.282127 + 1.60002i −0.0126298 + 0.0716269i −0.990471 0.137720i $$-0.956023\pi$$
0.977841 + 0.209347i $$0.0671337\pi$$
$$500$$ 0 0
$$501$$ −18.7854 32.5373i −0.839270 1.45366i
$$502$$ −19.5311 11.2763i −0.871717 0.503286i
$$503$$ 22.6234 + 26.9615i 1.00873 + 1.20215i 0.979264 + 0.202588i $$0.0649353\pi$$
0.0294632 + 0.999566i $$0.490620\pi$$
$$504$$ 6.34060 5.32040i 0.282433 0.236989i
$$505$$ 0 0
$$506$$ −1.46388 2.53551i −0.0650772 0.112717i
$$507$$ 4.62894 12.7179i 0.205578 0.564822i
$$508$$ 16.1494 + 2.84757i 0.716513 + 0.126341i
$$509$$ 4.20711 + 23.8597i 0.186477 + 1.05756i 0.924043 + 0.382288i $$0.124864\pi$$
−0.737567 + 0.675274i $$0.764025\pi$$
$$510$$ 0 0
$$511$$ −29.5952 24.8333i −1.30921 1.09856i
$$512$$ 1.00000i 0.0441942i
$$513$$ 1.04308 3.75323i 0.0460532 0.165709i
$$514$$ 10.7146 0.472599
$$515$$ 0 0
$$516$$ −25.6816 + 9.34733i −1.13057 + 0.411493i
$$517$$ 0.103720 0.0182886i 0.00456159 0.000804332i
$$518$$ −32.0537 5.65193i −1.40836 0.248332i
$$519$$ −37.0795 13.4958i −1.62761 0.592401i
$$520$$ 0 0
$$521$$ 3.95859 6.85648i 0.173429 0.300388i −0.766187 0.642617i $$-0.777849\pi$$
0.939616 + 0.342229i $$0.111182\pi$$
$$522$$ −0.219780 0.261923i −0.00961950 0.0114641i
$$523$$ −1.57943 1.88229i −0.0690637 0.0823069i 0.730406 0.683013i $$-0.239331\pi$$
−0.799470 + 0.600706i $$0.794886\pi$$
$$524$$ 5.56833 9.64464i 0.243254 0.421328i
$$525$$ 0 0
$$526$$ 25.0584 + 9.12051i 1.09260 + 0.397673i
$$527$$ 0.442714 + 0.0780624i 0.0192849 + 0.00340045i
$$528$$ 3.21749 0.567331i 0.140023 0.0246899i
$$529$$ −17.3697 + 6.32204i −0.755203 + 0.274871i
$$530$$ 0 0
$$531$$ −21.4736 −0.931874
$$532$$ 7.99322 11.1931i 0.346550 0.485282i
$$533$$ 47.6163i 2.06249i
$$534$$ 33.0939 + 27.7691i 1.43211 + 1.20169i
$$535$$ 0 0
$$536$$ 0.178976 + 1.01502i 0.00773057 + 0.0438422i
$$537$$ −10.6748 1.88225i −0.460650 0.0812250i
$$538$$ −0.488375 + 1.34180i −0.0210554 + 0.0578491i
$$539$$ 2.03681 + 3.52786i 0.0877316 + 0.151956i
$$540$$ 0 0
$$541$$ 17.2132 14.4436i 0.740054 0.620979i −0.192798 0.981238i $$-0.561756\pi$$
0.932852 + 0.360260i $$0.117312\pi$$
$$542$$ 4.73699 + 5.64532i 0.203471 + 0.242487i
$$543$$ 3.46730 + 2.00184i 0.148796 + 0.0859074i
$$544$$ 0.648300 + 1.12289i 0.0277956 + 0.0481434i
$$545$$ 0 0
$$546$$ −5.61983 + 31.8717i −0.240507 + 1.36398i
$$547$$ −26.3908 + 4.65342i −1.12839 + 0.198966i −0.706522 0.707691i $$-0.749737\pi$$
−0.421869 + 0.906657i $$0.638626\pi$$
$$548$$ −2.51099 6.89889i −0.107264 0.294706i
$$549$$ −15.7660 13.2292i −0.672876 0.564610i
$$550$$ 0 0
$$551$$ −0.462374 0.330191i −0.0196978 0.0140666i
$$552$$ 5.03902i 0.214475i
$$553$$ −28.4158 + 33.8647i −1.20836 + 1.44007i
$$554$$ 2.37302 0.863707i 0.100820 0.0366954i
$$555$$ 0 0
$$556$$ 2.05105 11.6321i 0.0869839 0.493310i
$$557$$ 13.3749 36.7473i 0.566714 1.55704i −0.242887 0.970055i $$-0.578094\pi$$
0.809601 0.586980i $$-0.199683\pi$$
$$558$$ −0.787619 + 0.454732i −0.0333426 + 0.0192503i
$$559$$ 24.9244 43.1703i 1.05419 1.82591i
$$560$$ 0 0
$$561$$ 3.24508 2.72295i 0.137008 0.114963i
$$562$$ −14.9206 8.61440i −0.629387 0.363377i
$$563$$ 7.46645 4.31076i 0.314673 0.181677i −0.334343 0.942452i $$-0.608514\pi$$
0.649016 + 0.760775i $$0.275181\pi$$
$$564$$ −0.170336 0.0619974i −0.00717246 0.00261056i
$$565$$ 0 0
$$566$$ −4.90049 27.7920i −0.205983 1.16819i
$$567$$ −10.7799 29.6174i −0.452711 1.24381i
$$568$$ 7.49028 8.92657i 0.314285 0.374550i
$$569$$ −23.0260 −0.965300 −0.482650 0.875813i $$-0.660326\pi$$
−0.482650 + 0.875813i $$0.660326\pi$$
$$570$$ 0 0
$$571$$ −29.9673 −1.25409 −0.627047 0.778981i $$-0.715737\pi$$
−0.627047 + 0.778981i $$0.715737\pi$$
$$572$$ −3.83047 + 4.56497i −0.160160 + 0.190871i
$$573$$ 9.10040 + 25.0031i 0.380175 + 1.04452i
$$574$$ 6.03220 + 34.2103i 0.251779 + 1.42791i
$$575$$ 0 0
$$576$$ −2.46493 0.897162i −0.102706 0.0373818i
$$577$$ −3.93622 + 2.27258i −0.163867 + 0.0946087i −0.579691 0.814837i $$-0.696827\pi$$
0.415824 + 0.909445i $$0.363493\pi$$
$$578$$ −13.2665 7.65941i −0.551813 0.318590i
$$579$$ −39.0333 + 32.7529i −1.62217 + 1.36116i
$$580$$ 0 0
$$581$$ −17.9526 + 31.0949i −0.744800 + 1.29003i
$$582$$ 33.3131 19.2334i 1.38087 0.797248i
$$583$$ 2.93083 8.05240i 0.121383 0.333496i
$$584$$ −2.12608 + 12.0576i −0.0879779 + 0.498947i
$$585$$ 0 0
$$586$$ −11.8571 + 4.31563i −0.489813 + 0.178277i
$$587$$ 11.8709 14.1471i 0.489963 0.583915i −0.463245 0.886230i $$-0.653315\pi$$
0.953208 + 0.302315i $$0.0977595\pi$$
$$588$$ 7.01120i 0.289137i
$$589$$ −1.07850 + 1.05867i −0.0444387 + 0.0436219i
$$590$$ 0 0
$$591$$ −27.7537 23.2881i −1.14164 0.957946i
$$592$$ 3.52794 + 9.69294i 0.144998 + 0.398377i
$$593$$ 15.7488 2.77694i 0.646726 0.114035i 0.159343 0.987223i $$-0.449062\pi$$
0.487384 + 0.873188i $$0.337951\pi$$
$$594$$ 0.213812 1.21259i 0.00877280 0.0497530i
$$595$$ 0 0
$$596$$ −1.75726 3.04366i −0.0719800 0.124673i
$$597$$ −1.45552 0.840343i −0.0595704 0.0343930i
$$598$$ −5.90788 7.04074i −0.241591 0.287917i
$$599$$ −3.02967 + 2.54220i −0.123789 + 0.103871i −0.702581 0.711604i $$-0.747969\pi$$
0.578792 + 0.815476i $$0.303524\pi$$
$$600$$ 0 0
$$601$$ 1.10855 + 1.92006i 0.0452186 + 0.0783209i 0.887749 0.460328i $$-0.152268\pi$$
−0.842530 + 0.538649i $$0.818935\pi$$
$$602$$ −12.4382 + 34.1735i −0.506941 + 1.39281i
$$603$$ −2.66253 0.469476i −0.108427 0.0191185i
$$604$$ 0.0369211 + 0.209390i 0.00150230 + 0.00851996i
$$605$$ 0 0
$$606$$ 12.0313 + 10.0955i 0.488739 + 0.410101i
$$607$$ 17.4964i 0.710155i −0.934837 0.355078i $$-0.884454\pi$$
0.934837 0.355078i $$-0.115546\pi$$
$$608$$ −4.33860 0.420163i −0.175954 0.0170399i
$$609$$ −0.975319 −0.0395219
$$610$$ 0 0
$$611$$ 0.310689 0.113082i 0.0125691 0.00457479i
$$612$$ −3.34947 + 0.590603i −0.135394 + 0.0238737i
$$613$$ 8.98922 + 1.58504i 0.363071 + 0.0640193i 0.352208 0.935922i $$-0.385431\pi$$
0.0108633 + 0.999941i $$0.496542\pi$$
$$614$$ −8.51802 3.10031i −0.343759 0.125118i
$$615$$ 0 0
$$616$$ 2.17372 3.76500i 0.0875818 0.151696i
$$617$$ −1.00026 1.19206i −0.0402689 0.0479906i 0.745534 0.666467i $$-0.232194\pi$$
−0.785803 + 0.618477i $$0.787750\pi$$
$$618$$ −18.8361 22.4480i −0.757699 0.902990i
$$619$$ 16.2140 28.0835i 0.651695 1.12877i −0.331016 0.943625i $$-0.607391\pi$$
0.982711 0.185144i $$-0.0592753\pi$$
$$620$$ 0 0
$$621$$ 1.78454 + 0.649520i 0.0716112 + 0.0260644i
$$622$$ −21.3826 3.77032i −0.857362 0.151176i
$$623$$ 56.6127 9.98235i 2.26814 0.399934i
$$624$$ 9.63789 3.50790i 0.385824 0.140429i
$$625$$ 0 0
$$626$$ 10.0460 0.401520
$$627$$ 1.10955 + 14.1978i 0.0443112 + 0.567005i
$$628$$ 7.68751i 0.306765i
$$629$$ 10.2454 + 8.59692i 0.408511 + 0.342782i
$$630$$ 0 0
$$631$$ −1.67744 9.51323i −0.0667778 0.378716i −0.999820 0.0189499i $$-0.993968\pi$$
0.933043 0.359766i $$-0.117143\pi$$
$$632$$ 13.7971 + 2.43280i 0.548819 + 0.0967715i
$$633$$ −11.4187 + 31.3726i −0.453852 + 1.24695i
$$634$$ 1.05423 + 1.82598i 0.0418688 + 0.0725189i
$$635$$ 0 0
$$636$$ −11.2981 + 9.48023i −0.447999 + 0.375915i
$$637$$ 8.22011 + 9.79635i 0.325693 + 0.388145i
$$638$$ −0.155528 0.0897942i −0.00615741 0.00355498i
$$639$$ 15.2834 + 26.4716i 0.604602 + 1.04720i
$$640$$ 0 0
$$641$$ 7.05763 40.0258i 0.278759 1.58092i −0.448001 0.894033i $$-0.647864\pi$$
0.726761 0.686891i $$-0.241025\pi$$
$$642$$ 25.5826 4.51091i 1.00967 0.178031i
$$643$$ 14.3882 + 39.5312i 0.567414 + 1.55896i 0.808526 + 0.588460i $$0.200266\pi$$
−0.241112 + 0.970497i $$0.577512\pi$$
$$644$$ 5.13651 + 4.31004i 0.202407 + 0.169840i
$$645$$ 0 0
$$646$$ −5.14416 + 2.34092i −0.202394 + 0.0921022i
$$647$$ 18.0072i 0.707936i −0.935258 0.353968i $$-0.884832\pi$$
0.935258 0.353968i $$-0.115168\pi$$
$$648$$ −6.42054 + 7.65170i −0.252223 + 0.300587i
$$649$$ −10.5986 + 3.85757i −0.416031 + 0.151423i
$$650$$ 0 0
$$651$$ −0.450487 + 2.55484i −0.0176560 + 0.100132i
$$652$$ 2.50598 6.88513i 0.0981419 0.269643i
$$653$$ 34.1968 19.7435i 1.33822 0.772624i 0.351680 0.936120i $$-0.385610\pi$$
0.986544 + 0.163496i $$0.0522772\pi$$
$$654$$ 8.82243 15.2809i 0.344984 0.597530i
$$655$$ 0 0
$$656$$ 8.43340 7.07646i 0.329269 0.276289i
$$657$$ −27.8138 16.0583i −1.08512 0.626493i
$$658$$ −0.208891 + 0.120604i −0.00814344 + 0.00470162i
$$659$$ 33.6395 + 12.2438i 1.31041 + 0.476949i 0.900372 0.435120i $$-0.143294\pi$$
0.410035 + 0.912070i $$0.365516\pi$$
$$660$$ 0 0
$$661$$ 2.36241 + 13.3979i 0.0918871 + 0.521118i 0.995657 + 0.0930988i $$0.0296772\pi$$
−0.903770 + 0.428019i $$0.859212\pi$$
$$662$$ 1.17795 + 3.23639i 0.0457822 + 0.125786i
$$663$$ 8.54809 10.1872i 0.331980 0.395639i
$$664$$ 11.3789 0.441588
$$665$$ 0 0
$$666$$ −27.0576 −1.04846
$$667$$ 0.178043 0.212184i 0.00689386 0.00821578i
$$668$$ 5.41893 + 14.8884i 0.209665 + 0.576049i
$$669$$ 4.82470 + 27.3623i 0.186534 + 1.05789i
$$670$$ 0 0
$$671$$ −10.1581 3.69724i −0.392148 0.142730i
$$672$$ −6.48003 + 3.74124i −0.249972 + 0.144322i
$$673$$ 36.5649 + 21.1108i 1.40947 + 0.813760i 0.995337 0.0964549i $$-0.0307504\pi$$
0.414136 + 0.910215i $$0.364084\pi$$
$$674$$ −19.8089 + 16.6216i −0.763009 + 0.640241i
$$675$$ 0 0
$$676$$ −2.85372 + 4.94278i −0.109758 + 0.190107i
$$677$$ 37.8202 21.8355i 1.45355 0.839207i 0.454869 0.890558i $$-0.349686\pi$$
0.998681 + 0.0513514i $$0.0163528\pi$$
$$678$$ −9.40920 + 25.8516i −0.361358 + 0.992824i
$$679$$ 8.88840 50.4086i 0.341105 1.93450i
$$680$$ 0 0
$$681$$ −22.7878 + 8.29409i −0.873231 + 0.317830i
$$682$$ −0.307051 + 0.365929i −0.0117576 + 0.0140122i
$$683$$ 9.22100i 0.352832i 0.984316 + 0.176416i $$0.0564504\pi$$
−0.984316 + 0.176416i $$0.943550\pi$$
$$684$$ 4.92810 10.3174i 0.188431 0.394496i
$$685$$ 0 0
$$686$$ 9.77350 + 8.20094i 0.373154 + 0.313113i
$$687$$ 4.10133 + 11.2683i 0.156475 + 0.429913i
$$688$$ 11.3501 2.00132i 0.432717 0.0762998i
$$689$$ 4.67132 26.4924i 0.177963 1.00928i
$$690$$ 0 0
$$691$$ 20.0044 + 34.6487i 0.761004 + 1.31810i 0.942334 + 0.334675i $$0.108626\pi$$
−0.181330 + 0.983422i $$0.558040\pi$$
$$692$$ 14.4108 + 8.32010i 0.547818 + 0.316283i
$$693$$ 7.33029 + 8.73590i 0.278455 + 0.331849i
$$694$$ 1.93290 1.62189i 0.0733717 0.0615662i
$$695$$ 0 0
$$696$$ 0.154547 + 0.267683i 0.00585808 + 0.0101465i
$$697$$ 4.88209 13.4134i 0.184922 0.508070i
$$698$$ −3.62355 0.638930i −0.137153 0.0241839i
$$699$$ −2.98884 16.9506i −0.113048 0.641130i
$$700$$ 0 0
$$701$$ −1.37655 1.15507i −0.0519917 0.0436262i 0.616422 0.787416i $$-0.288582\pi$$
−0.668413 + 0.743790i $$0.733026\pi$$
$$702$$ 3.86537i 0.145889i
$$703$$ −43.5361 + 11.2337i −1.64200 + 0.423688i
$$704$$ −1.37777 −0.0519267
$$705$$ 0 0
$$706$$ 2.62772 0.956410i 0.0988954 0.0359950i
$$707$$ 20.5816 3.62909i 0.774051 0.136486i
$$708$$ 19.1173 + 3.37089i 0.718471 + 0.126686i
$$709$$ 31.8904 + 11.6072i 1.19767 + 0.435916i 0.862410 0.506210i $$-0.168954\pi$$
0.335259 + 0.942126i $$0.391176\pi$$
$$710$$ 0 0
$$711$$ −18.3749 + 31.8263i −0.689113 + 1.19358i
$$712$$ −11.7104 13.9559i −0.438867 0.523021i
$$713$$ −0.473577 0.564387i −0.0177356 0.0211365i
$$714$$ −4.85090 + 8.40200i −0.181540 + 0.314437i
$$715$$ 0 0
$$716$$ 4.29540 + 1.56340i 0.160527 + 0.0584269i
$$717$$ 37.3019 + 6.57733i 1.39306 + 0.245635i
$$718$$ 19.8344 3.49734i 0.740212 0.130519i
$$719$$ −4.77790 + 1.73901i −0.178186 + 0.0648542i −0.429572 0.903033i $$-0.641336\pi$$
0.251387 + 0.967887i $$0.419113\pi$$
$$720$$ 0 0
$$721$$ −38.9934 −1.45219
$$722$$ 3.64584 18.6469i 0.135684 0.693967i
$$723$$ 52.6311i 1.95737i
$$724$$ −1.29338 1.08527i −0.0480680 0.0403338i
$$725$$ 0 0
$$726$$ −3.74786 21.2552i −0.139096 0.788854i
$$727$$ 21.2529 + 3.74747i 0.788228 + 0.138986i 0.553250 0.833015i $$-0.313387\pi$$
0.234977 + 0.972001i $$0.424498\pi$$
$$728$$ 4.66784 12.8248i 0.173002 0.475318i
$$729$$ −9.92186 17.1852i −0.367476 0.636487i
$$730$$ 0 0
$$731$$ 11.4474 9.60551i 0.423397 0.355273i
$$732$$ 11.9593 + 14.2525i 0.442027 + 0.526788i
$$733$$ −8.20601 4.73774i −0.303096 0.174993i 0.340737 0.940159i $$-0.389323\pi$$
−0.643833 + 0.765166i $$0.722657\pi$$
$$734$$ 2.26066 + 3.91559i 0.0834426 + 0.144527i
$$735$$ 0 0
$$736$$ 0.369001 2.09271i 0.0136015 0.0771382i
$$737$$ −1.39847 + 0.246588i −0.0515132 + 0.00908317i
$$738$$ 9.87687 + 27.1365i 0.363573 + 0.998908i
$$739$$ 6.02954 + 5.05938i 0.221800 + 0.186112i 0.746916 0.664918i $$-0.231534\pi$$
−0.525116 + 0.851031i $$0.675978\pi$$
$$740$$ 0 0
$$741$$ 11.1699 + 43.2888i 0.410337 + 1.59026i
$$742$$ 19.6254i 0.720473i
$$743$$ −31.1013 + 37.0651i −1.14100 + 1.35979i −0.217553 + 0.976049i $$0.569807\pi$$
−0.923442 + 0.383737i $$0.874637\pi$$
$$744$$ 0.772575 0.281194i 0.0283240 0.0103091i
$$745$$ 0 0
$$746$$ −4.04087 + 22.9169i −0.147947 + 0.839048i
$$747$$ −10.2087 + 28.0483i −0.373518 + 1.02623i
$$748$$ −1.54708 + 0.893209i −0.0565670 + 0.0326590i
$$749$$ 17.2835 29.9359i 0.631525 1.09383i
$$750$$ 0 0
$$751$$ −9.30243 + 7.80567i −0.339451 + 0.284833i −0.796537 0.604589i $$-0.793337\pi$$
0.457087 + 0.889422i $$0.348893\pi$$
$$752$$ 0.0662008 + 0.0382211i 0.00241410 + 0.00139378i
$$753$$ −46.3145 + 26.7397i −1.68779 + 0.974447i
$$754$$ −0.529778 0.192823i −0.0192934 0.00702221i
$$755$$ 0 0
$$756$$ 0.489679 + 2.77711i 0.0178095 + 0.101002i
$$757$$ 11.9596 + 32.8586i 0.434677 + 1.19427i 0.942910 + 0.333046i $$0.108077\pi$$
−0.508233 + 0.861220i $$0.669701\pi$$
$$758$$ 6.00792 7.15997i 0.218218 0.260062i
$$759$$ −6.94262 −0.252001
$$760$$ 0 0
$$761$$ 46.9073 1.70039 0.850194 0.526470i $$-0.176485\pi$$
0.850194 + 0.526470i $$0.176485\pi$$
$$762$$ 24.9954 29.7884i 0.905489 1.07912i
$$763$$ −8.03041 22.0634i −0.290720 0.798748i
$$764$$ −1.94845 11.0502i −0.0704926 0.399783i
$$765$$ 0 0
$$766$$ 30.8559 + 11.2306i 1.11487 + 0.405779i
$$767$$ −30.6636 + 17.7036i −1.10720 + 0.639241i
$$768$$ 2.05362 + 1.18566i 0.0741035 + 0.0427837i
$$769$$ −1.06182 + 0.890969i −0.0382900 + 0.0321292i −0.661732 0.749741i $$-0.730178\pi$$
0.623442 + 0.781870i $$0.285734\pi$$
$$770$$ 0 0
$$771$$ 12.7038 22.0036i 0.457516 0.792440i
$$772$$ 18.6090 10.7439i 0.669753 0.386682i
$$773$$ 2.20242 6.05111i 0.0792157 0.217643i −0.893762 0.448541i $$-0.851944\pi$$
0.972978 + 0.230897i $$0.0741662\pi$$
$$774$$ −5.24973 + 29.7727i −0.188698 + 1.07016i
$$775$$ 0 0
$$776$$ −15.2434 + 5.54814i −0.547206 + 0.199167i
$$777$$ −49.6116 + 59.1248i −1.77981 + 2.12109i
$$778$$ 10.6737i 0.382670i
$$779$$ 27.1585 + 39.5624i 0.973056 + 1.41747i
$$780$$ 0 0
$$781$$ 12.2988 + 10.3199i 0.440085 + 0.369275i
$$782$$ −0.942355 2.58910i −0.0336985 0.0925860i