# Properties

 Label 225.4.h.a.181.6 Level $225$ Weight $4$ Character 225.181 Analytic conductor $13.275$ Analytic rank $0$ Dimension $28$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.h (of order $$5$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.2754297513$$ Analytic rank: $$0$$ Dimension: $$28$$ Relative dimension: $$7$$ over $$\Q(\zeta_{5})$$ Twist minimal: no (minimal twist has level 75) Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

## Embedding invariants

 Embedding label 181.6 Character $$\chi$$ $$=$$ 225.181 Dual form 225.4.h.a.46.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +O(q^{10})$$ $$q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +(-0.895733 - 32.8335i) q^{10} +(1.87505 + 5.77082i) q^{11} +(24.1805 - 74.4201i) q^{13} +(17.1685 + 52.8393i) q^{14} +(-21.2134 + 65.2882i) q^{16} +(31.0670 + 22.5715i) q^{17} +(75.2030 + 54.6382i) q^{19} +(6.64485 - 2.36125i) q^{20} +(-14.4216 + 10.4779i) q^{22} +(25.0398 + 77.0645i) q^{23} +(104.983 + 67.8503i) q^{25} +229.884 q^{26} +(-9.65021 + 7.01128i) q^{28} +(-9.02201 + 6.55487i) q^{29} +(181.125 + 131.595i) q^{31} -28.4793 q^{32} +(-34.8617 + 107.293i) q^{34} +(-202.796 - 59.8295i) q^{35} +(-33.2987 + 102.483i) q^{37} +(-84.3887 + 259.722i) q^{38} +(-147.560 - 191.869i) q^{40} +(108.379 - 333.556i) q^{41} -356.550 q^{43} +(-3.09629 - 2.24959i) q^{44} +(-192.588 + 139.924i) q^{46} +(-236.019 + 171.478i) q^{47} +14.6457 q^{49} +(-94.2687 + 354.921i) q^{50} +(15.2517 + 46.9399i) q^{52} +(554.021 - 402.520i) q^{53} +(-1.85006 - 67.8149i) q^{55} +(331.232 + 240.654i) q^{56} +(-26.5050 - 19.2570i) q^{58} +(69.2082 - 213.001i) q^{59} +(-215.599 - 663.544i) q^{61} +(-203.249 + 625.535i) q^{62} +(143.853 + 442.734i) q^{64} +(-494.737 + 721.537i) q^{65} +(735.443 + 534.330i) q^{67} -24.2211 q^{68} +(-16.9397 - 620.932i) q^{70} +(163.274 - 118.625i) q^{71} +(-90.2156 - 277.655i) q^{73} -316.570 q^{74} -58.6314 q^{76} +(35.4601 + 109.135i) q^{77} +(-573.822 + 416.906i) q^{79} +(434.030 - 633.000i) q^{80} +1030.36 q^{82} +(-897.021 - 651.724i) q^{83} +(-261.736 - 340.329i) q^{85} +(-323.688 - 996.211i) q^{86} +(-40.5940 + 124.935i) q^{88} +(-1.16808 - 3.59497i) q^{89} +(457.291 - 1407.40i) q^{91} +(-41.3483 - 30.0413i) q^{92} +(-693.380 - 503.770i) q^{94} +(-633.576 - 823.824i) q^{95} +(-14.9369 + 10.8523i) q^{97} +(13.2959 + 40.9205i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10})$$ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 $$28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100})$$ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.907834 + 2.79403i 0.320968 + 0.987837i 0.973228 + 0.229842i $$0.0738210\pi$$
−0.652260 + 0.757995i $$0.726179\pi$$
$$3$$ 0 0
$$4$$ −0.510282 + 0.370741i −0.0637852 + 0.0463427i
$$5$$ −10.7234 3.16365i −0.959130 0.282966i
$$6$$ 0 0
$$7$$ 18.9115 1.02113 0.510563 0.859840i $$-0.329437\pi$$
0.510563 + 0.859840i $$0.329437\pi$$
$$8$$ 17.5148 + 12.7253i 0.774053 + 0.562382i
$$9$$ 0 0
$$10$$ −0.895733 32.8335i −0.0283256 1.03829i
$$11$$ 1.87505 + 5.77082i 0.0513955 + 0.158179i 0.973460 0.228857i $$-0.0734989\pi$$
−0.922065 + 0.387036i $$0.873499\pi$$
$$12$$ 0 0
$$13$$ 24.1805 74.4201i 0.515883 1.58772i −0.265787 0.964032i $$-0.585632\pi$$
0.781670 0.623692i $$-0.214368\pi$$
$$14$$ 17.1685 + 52.8393i 0.327749 + 1.00871i
$$15$$ 0 0
$$16$$ −21.2134 + 65.2882i −0.331460 + 1.02013i
$$17$$ 31.0670 + 22.5715i 0.443227 + 0.322023i 0.786916 0.617060i $$-0.211676\pi$$
−0.343689 + 0.939084i $$0.611676\pi$$
$$18$$ 0 0
$$19$$ 75.2030 + 54.6382i 0.908040 + 0.659730i 0.940518 0.339743i $$-0.110340\pi$$
−0.0324785 + 0.999472i $$0.510340\pi$$
$$20$$ 6.64485 2.36125i 0.0742917 0.0263996i
$$21$$ 0 0
$$22$$ −14.4216 + 10.4779i −0.139759 + 0.101541i
$$23$$ 25.0398 + 77.0645i 0.227007 + 0.698655i 0.998082 + 0.0619104i $$0.0197193\pi$$
−0.771075 + 0.636744i $$0.780281\pi$$
$$24$$ 0 0
$$25$$ 104.983 + 67.8503i 0.839861 + 0.542802i
$$26$$ 229.884 1.73399
$$27$$ 0 0
$$28$$ −9.65021 + 7.01128i −0.0651328 + 0.0473217i
$$29$$ −9.02201 + 6.55487i −0.0577705 + 0.0419727i −0.616296 0.787515i $$-0.711367\pi$$
0.558525 + 0.829488i $$0.311367\pi$$
$$30$$ 0 0
$$31$$ 181.125 + 131.595i 1.04939 + 0.762425i 0.972096 0.234583i $$-0.0753725\pi$$
0.0772923 + 0.997008i $$0.475373\pi$$
$$32$$ −28.4793 −0.157327
$$33$$ 0 0
$$34$$ −34.8617 + 107.293i −0.175845 + 0.541196i
$$35$$ −202.796 59.8295i −0.979393 0.288944i
$$36$$ 0 0
$$37$$ −33.2987 + 102.483i −0.147954 + 0.455354i −0.997379 0.0723545i $$-0.976949\pi$$
0.849425 + 0.527709i $$0.176949\pi$$
$$38$$ −84.3887 + 259.722i −0.360254 + 1.10875i
$$39$$ 0 0
$$40$$ −147.560 191.869i −0.583282 0.758428i
$$41$$ 108.379 333.556i 0.412828 1.27056i −0.501350 0.865244i $$-0.667163\pi$$
0.914179 0.405311i $$-0.132837\pi$$
$$42$$ 0 0
$$43$$ −356.550 −1.26450 −0.632249 0.774765i $$-0.717868\pi$$
−0.632249 + 0.774765i $$0.717868\pi$$
$$44$$ −3.09629 2.24959i −0.0106087 0.00770768i
$$45$$ 0 0
$$46$$ −192.588 + 139.924i −0.617295 + 0.448491i
$$47$$ −236.019 + 171.478i −0.732488 + 0.532184i −0.890350 0.455277i $$-0.849540\pi$$
0.157861 + 0.987461i $$0.449540\pi$$
$$48$$ 0 0
$$49$$ 14.6457 0.0426989
$$50$$ −94.2687 + 354.921i −0.266632 + 1.00387i
$$51$$ 0 0
$$52$$ 15.2517 + 46.9399i 0.0406737 + 0.125181i
$$53$$ 554.021 402.520i 1.43586 1.04322i 0.446975 0.894546i $$-0.352501\pi$$
0.988887 0.148669i $$-0.0474988\pi$$
$$54$$ 0 0
$$55$$ −1.85006 67.8149i −0.00453568 0.166257i
$$56$$ 331.232 + 240.654i 0.790405 + 0.574263i
$$57$$ 0 0
$$58$$ −26.5050 19.2570i −0.0600047 0.0435960i
$$59$$ 69.2082 213.001i 0.152714 0.470006i −0.845208 0.534438i $$-0.820523\pi$$
0.997922 + 0.0644317i $$0.0205235\pi$$
$$60$$ 0 0
$$61$$ −215.599 663.544i −0.452534 1.39276i −0.874006 0.485915i $$-0.838486\pi$$
0.421472 0.906842i $$-0.361514\pi$$
$$62$$ −203.249 + 625.535i −0.416332 + 1.28134i
$$63$$ 0 0
$$64$$ 143.853 + 442.734i 0.280963 + 0.864715i
$$65$$ −494.737 + 721.537i −0.944070 + 1.37686i
$$66$$ 0 0
$$67$$ 735.443 + 534.330i 1.34102 + 0.974311i 0.999406 + 0.0344723i $$0.0109750\pi$$
0.341618 + 0.939839i $$0.389025\pi$$
$$68$$ −24.2211 −0.0431948
$$69$$ 0 0
$$70$$ −16.9397 620.932i −0.0289240 1.06022i
$$71$$ 163.274 118.625i 0.272916 0.198285i −0.442906 0.896568i $$-0.646052\pi$$
0.715822 + 0.698283i $$0.246052\pi$$
$$72$$ 0 0
$$73$$ −90.2156 277.655i −0.144643 0.445165i 0.852322 0.523018i $$-0.175194\pi$$
−0.996965 + 0.0778521i $$0.975194\pi$$
$$74$$ −316.570 −0.497304
$$75$$ 0 0
$$76$$ −58.6314 −0.0884932
$$77$$ 35.4601 + 109.135i 0.0524813 + 0.161521i
$$78$$ 0 0
$$79$$ −573.822 + 416.906i −0.817216 + 0.593742i −0.915914 0.401375i $$-0.868532\pi$$
0.0986978 + 0.995117i $$0.468532\pi$$
$$80$$ 434.030 633.000i 0.606575 0.884644i
$$81$$ 0 0
$$82$$ 1030.36 1.38761
$$83$$ −897.021 651.724i −1.18628 0.861880i −0.193410 0.981118i $$-0.561955\pi$$
−0.992866 + 0.119238i $$0.961955\pi$$
$$84$$ 0 0
$$85$$ −261.736 340.329i −0.333991 0.434281i
$$86$$ −323.688 996.211i −0.405863 1.24912i
$$87$$ 0 0
$$88$$ −40.5940 + 124.935i −0.0491742 + 0.151343i
$$89$$ −1.16808 3.59497i −0.00139119 0.00428165i 0.950359 0.311157i $$-0.100717\pi$$
−0.951750 + 0.306875i $$0.900717\pi$$
$$90$$ 0 0
$$91$$ 457.291 1407.40i 0.526782 1.62127i
$$92$$ −41.3483 30.0413i −0.0468572 0.0340438i
$$93$$ 0 0
$$94$$ −693.380 503.770i −0.760816 0.552765i
$$95$$ −633.576 823.824i −0.684247 0.889711i
$$96$$ 0 0
$$97$$ −14.9369 + 10.8523i −0.0156351 + 0.0113596i −0.595575 0.803299i $$-0.703076\pi$$
0.579940 + 0.814659i $$0.303076\pi$$
$$98$$ 13.2959 + 40.9205i 0.0137050 + 0.0421795i
$$99$$ 0 0
$$100$$ −78.7256 + 4.29863i −0.0787256 + 0.00429863i
$$101$$ 1332.50 1.31276 0.656381 0.754430i $$-0.272087\pi$$
0.656381 + 0.754430i $$0.272087\pi$$
$$102$$ 0 0
$$103$$ −1358.05 + 986.682i −1.29915 + 0.943890i −0.999947 0.0102985i $$-0.996722\pi$$
−0.299206 + 0.954188i $$0.596722\pi$$
$$104$$ 1370.53 995.750i 1.29223 0.938859i
$$105$$ 0 0
$$106$$ 1627.61 + 1182.53i 1.49139 + 1.08356i
$$107$$ −1550.64 −1.40099 −0.700496 0.713657i $$-0.747038\pi$$
−0.700496 + 0.713657i $$0.747038\pi$$
$$108$$ 0 0
$$109$$ 138.127 425.111i 0.121378 0.373562i −0.871846 0.489780i $$-0.837077\pi$$
0.993224 + 0.116218i $$0.0370772\pi$$
$$110$$ 187.797 66.7338i 0.162779 0.0578438i
$$111$$ 0 0
$$112$$ −401.178 + 1234.70i −0.338462 + 1.04168i
$$113$$ 192.146 591.366i 0.159961 0.492310i −0.838668 0.544642i $$-0.816665\pi$$
0.998630 + 0.0523321i $$0.0166654\pi$$
$$114$$ 0 0
$$115$$ −24.7060 905.611i −0.0200334 0.734336i
$$116$$ 2.17360 6.68966i 0.00173978 0.00535448i
$$117$$ 0 0
$$118$$ 657.959 0.513306
$$119$$ 587.525 + 426.862i 0.452591 + 0.328827i
$$120$$ 0 0
$$121$$ 1047.02 760.701i 0.786638 0.571526i
$$122$$ 1658.23 1204.78i 1.23057 0.894060i
$$123$$ 0 0
$$124$$ −141.213 −0.102268
$$125$$ −911.115 1059.71i −0.651941 0.758270i
$$126$$ 0 0
$$127$$ −216.352 665.864i −0.151167 0.465243i 0.846586 0.532252i $$-0.178654\pi$$
−0.997752 + 0.0670095i $$0.978654\pi$$
$$128$$ −1290.74 + 937.776i −0.891298 + 0.647566i
$$129$$ 0 0
$$130$$ −2465.13 727.272i −1.66313 0.490661i
$$131$$ −470.763 342.029i −0.313975 0.228116i 0.419625 0.907697i $$-0.362161\pi$$
−0.733600 + 0.679581i $$0.762161\pi$$
$$132$$ 0 0
$$133$$ 1422.20 + 1033.29i 0.927223 + 0.673667i
$$134$$ −825.273 + 2539.93i −0.532035 + 1.63744i
$$135$$ 0 0
$$136$$ 256.905 + 790.672i 0.161981 + 0.498526i
$$137$$ −186.032 + 572.548i −0.116013 + 0.357051i −0.992157 0.124998i $$-0.960108\pi$$
0.876144 + 0.482050i $$0.160108\pi$$
$$138$$ 0 0
$$139$$ −57.3812 176.601i −0.0350145 0.107763i 0.932022 0.362402i $$-0.118043\pi$$
−0.967036 + 0.254639i $$0.918043\pi$$
$$140$$ 125.664 44.6549i 0.0758612 0.0269573i
$$141$$ 0 0
$$142$$ 479.668 + 348.499i 0.283471 + 0.205953i
$$143$$ 474.805 0.277659
$$144$$ 0 0
$$145$$ 117.484 41.7480i 0.0672863 0.0239102i
$$146$$ 693.875 504.130i 0.393325 0.285768i
$$147$$ 0 0
$$148$$ −21.0029 64.6404i −0.0116651 0.0359014i
$$149$$ −2586.71 −1.42223 −0.711113 0.703078i $$-0.751808\pi$$
−0.711113 + 0.703078i $$0.751808\pi$$
$$150$$ 0 0
$$151$$ −276.537 −0.149035 −0.0745175 0.997220i $$-0.523742\pi$$
−0.0745175 + 0.997220i $$0.523742\pi$$
$$152$$ 621.882 + 1913.96i 0.331850 + 1.02133i
$$153$$ 0 0
$$154$$ −272.734 + 198.153i −0.142711 + 0.103686i
$$155$$ −1525.96 1984.16i −0.790759 1.02821i
$$156$$ 0 0
$$157$$ −3052.85 −1.55187 −0.775937 0.630810i $$-0.782723\pi$$
−0.775937 + 0.630810i $$0.782723\pi$$
$$158$$ −1685.78 1224.79i −0.848821 0.616704i
$$159$$ 0 0
$$160$$ 305.395 + 90.0987i 0.150897 + 0.0445183i
$$161$$ 473.540 + 1457.41i 0.231802 + 0.713415i
$$162$$ 0 0
$$163$$ −248.105 + 763.589i −0.119221 + 0.366926i −0.992804 0.119750i $$-0.961791\pi$$
0.873583 + 0.486676i $$0.161791\pi$$
$$164$$ 68.3593 + 210.388i 0.0325486 + 0.100174i
$$165$$ 0 0
$$166$$ 1006.59 3097.96i 0.470641 1.44848i
$$167$$ 2290.36 + 1664.05i 1.06128 + 0.771064i 0.974325 0.225148i $$-0.0722865\pi$$
0.0869544 + 0.996212i $$0.472287\pi$$
$$168$$ 0 0
$$169$$ −3176.24 2307.67i −1.44572 1.05037i
$$170$$ 713.275 1040.26i 0.321798 0.469319i
$$171$$ 0 0
$$172$$ 181.941 132.188i 0.0806563 0.0586002i
$$173$$ 1273.54 + 3919.54i 0.559683 + 1.72253i 0.683243 + 0.730191i $$0.260569\pi$$
−0.123560 + 0.992337i $$0.539431\pi$$
$$174$$ 0 0
$$175$$ 1985.38 + 1283.15i 0.857604 + 0.554270i
$$176$$ −416.543 −0.178398
$$177$$ 0 0
$$178$$ 8.98403 6.52728i 0.00378304 0.00274854i
$$179$$ −1427.33 + 1037.02i −0.595999 + 0.433019i −0.844457 0.535624i $$-0.820076\pi$$
0.248457 + 0.968643i $$0.420076\pi$$
$$180$$ 0 0
$$181$$ 1207.80 + 877.516i 0.495994 + 0.360361i 0.807485 0.589888i $$-0.200828\pi$$
−0.311491 + 0.950249i $$0.600828\pi$$
$$182$$ 4347.45 1.77063
$$183$$ 0 0
$$184$$ −542.099 + 1668.41i −0.217196 + 0.668460i
$$185$$ 681.297 993.620i 0.270756 0.394878i
$$186$$ 0 0
$$187$$ −72.0039 + 221.605i −0.0281575 + 0.0866598i
$$188$$ 56.8623 175.004i 0.0220591 0.0678909i
$$189$$ 0 0
$$190$$ 1726.60 2518.12i 0.659268 0.961493i
$$191$$ −1130.61 + 3479.65i −0.428313 + 1.31821i 0.471473 + 0.881881i $$0.343723\pi$$
−0.899786 + 0.436332i $$0.856277\pi$$
$$192$$ 0 0
$$193$$ −4695.92 −1.75140 −0.875699 0.482858i $$-0.839599\pi$$
−0.875699 + 0.482858i $$0.839599\pi$$
$$194$$ −43.8817 31.8819i −0.0162398 0.0117989i
$$195$$ 0 0
$$196$$ −7.47344 + 5.42977i −0.00272356 + 0.00197878i
$$197$$ 389.722 283.150i 0.140947 0.102404i −0.515077 0.857144i $$-0.672237\pi$$
0.656024 + 0.754740i $$0.272237\pi$$
$$198$$ 0 0
$$199$$ 494.959 0.176315 0.0881575 0.996107i $$-0.471902\pi$$
0.0881575 + 0.996107i $$0.471902\pi$$
$$200$$ 975.338 + 2524.31i 0.344834 + 0.892480i
$$201$$ 0 0
$$202$$ 1209.69 + 3723.05i 0.421354 + 1.29679i
$$203$$ −170.620 + 123.963i −0.0589910 + 0.0428595i
$$204$$ 0 0
$$205$$ −2217.45 + 3233.99i −0.755480 + 1.10181i
$$206$$ −3989.70 2898.69i −1.34940 0.980394i
$$207$$ 0 0
$$208$$ 4345.80 + 3157.41i 1.44869 + 1.05253i
$$209$$ −174.298 + 536.433i −0.0576862 + 0.177540i
$$210$$ 0 0
$$211$$ 146.406 + 450.590i 0.0477676 + 0.147014i 0.972095 0.234586i $$-0.0753734\pi$$
−0.924328 + 0.381599i $$0.875373\pi$$
$$212$$ −133.476 + 410.797i −0.0432414 + 0.133083i
$$213$$ 0 0
$$214$$ −1407.72 4332.53i −0.449673 1.38395i
$$215$$ 3823.43 + 1128.00i 1.21282 + 0.357810i
$$216$$ 0 0
$$217$$ 3425.35 + 2488.66i 1.07156 + 0.778532i
$$218$$ 1313.17 0.407976
$$219$$ 0 0
$$220$$ 26.0858 + 33.9188i 0.00799412 + 0.0103946i
$$221$$ 2430.99 1766.22i 0.739938 0.537596i
$$222$$ 0 0
$$223$$ 1565.42 + 4817.87i 0.470082 + 1.44676i 0.852477 + 0.522766i $$0.175100\pi$$
−0.382394 + 0.923999i $$0.624900\pi$$
$$224$$ −538.587 −0.160651
$$225$$ 0 0
$$226$$ 1826.73 0.537665
$$227$$ −1635.48 5033.48i −0.478196 1.47174i −0.841599 0.540103i $$-0.818385\pi$$
0.363403 0.931632i $$-0.381615\pi$$
$$228$$ 0 0
$$229$$ −396.216 + 287.868i −0.114335 + 0.0830692i −0.643483 0.765460i $$-0.722511\pi$$
0.529148 + 0.848529i $$0.322511\pi$$
$$230$$ 2507.87 891.173i 0.718974 0.255488i
$$231$$ 0 0
$$232$$ −241.431 −0.0683221
$$233$$ −1763.54 1281.28i −0.495850 0.360256i 0.311579 0.950220i $$-0.399142\pi$$
−0.807430 + 0.589964i $$0.799142\pi$$
$$234$$ 0 0
$$235$$ 3073.43 1092.14i 0.853141 0.303164i
$$236$$ 43.6526 + 134.349i 0.0120404 + 0.0370566i
$$237$$ 0 0
$$238$$ −659.288 + 2029.08i −0.179560 + 0.552629i
$$239$$ −1370.65 4218.41i −0.370961 1.14170i −0.946163 0.323689i $$-0.895077\pi$$
0.575203 0.818011i $$-0.304923\pi$$
$$240$$ 0 0
$$241$$ 742.522 2285.25i 0.198465 0.610812i −0.801454 0.598057i $$-0.795940\pi$$
0.999919 0.0127554i $$-0.00406027\pi$$
$$242$$ 3075.93 + 2234.80i 0.817060 + 0.593629i
$$243$$ 0 0
$$244$$ 356.019 + 258.663i 0.0934091 + 0.0678657i
$$245$$ −157.052 46.3340i −0.0409538 0.0120823i
$$246$$ 0 0
$$247$$ 5884.63 4275.43i 1.51591 1.10137i
$$248$$ 1497.79 + 4609.73i 0.383507 + 1.18031i
$$249$$ 0 0
$$250$$ 2133.73 3507.72i 0.539795 0.887392i
$$251$$ 3459.69 0.870014 0.435007 0.900427i $$-0.356746\pi$$
0.435007 + 0.900427i $$0.356746\pi$$
$$252$$ 0 0
$$253$$ −397.775 + 289.000i −0.0988454 + 0.0718154i
$$254$$ 1664.03 1208.99i 0.411065 0.298656i
$$255$$ 0 0
$$256$$ −779.049 566.012i −0.190197 0.138187i
$$257$$ −4772.57 −1.15838 −0.579192 0.815191i $$-0.696632\pi$$
−0.579192 + 0.815191i $$0.696632\pi$$
$$258$$ 0 0
$$259$$ −629.730 + 1938.11i −0.151079 + 0.464974i
$$260$$ −15.0484 551.607i −0.00358947 0.131574i
$$261$$ 0 0
$$262$$ 528.264 1625.83i 0.124566 0.383374i
$$263$$ −1298.07 + 3995.04i −0.304343 + 0.936671i 0.675579 + 0.737288i $$0.263894\pi$$
−0.979922 + 0.199383i $$0.936106\pi$$
$$264$$ 0 0
$$265$$ −7214.43 + 2563.65i −1.67237 + 0.594279i
$$266$$ −1595.92 + 4911.73i −0.367865 + 1.13217i
$$267$$ 0 0
$$268$$ −573.381 −0.130690
$$269$$ −1835.82 1333.80i −0.416105 0.302318i 0.359964 0.932966i $$-0.382789\pi$$
−0.776069 + 0.630648i $$0.782789\pi$$
$$270$$ 0 0
$$271$$ 630.472 458.065i 0.141323 0.102677i −0.514878 0.857264i $$-0.672163\pi$$
0.656200 + 0.754587i $$0.272163\pi$$
$$272$$ −2132.69 + 1549.49i −0.475417 + 0.345411i
$$273$$ 0 0
$$274$$ −1768.60 −0.389945
$$275$$ −194.704 + 733.059i −0.0426949 + 0.160746i
$$276$$ 0 0
$$277$$ −1562.16 4807.84i −0.338849 1.04287i −0.964795 0.263004i $$-0.915287\pi$$
0.625945 0.779867i $$-0.284713\pi$$
$$278$$ 441.336 320.649i 0.0952142 0.0691772i
$$279$$ 0 0
$$280$$ −2790.58 3628.53i −0.595605 0.774451i
$$281$$ −1997.64 1451.37i −0.424089 0.308119i 0.355192 0.934793i $$-0.384416\pi$$
−0.779281 + 0.626675i $$0.784416\pi$$
$$282$$ 0 0
$$283$$ −1534.87 1115.15i −0.322398 0.234236i 0.414800 0.909913i $$-0.363851\pi$$
−0.737198 + 0.675677i $$0.763851\pi$$
$$284$$ −39.3363 + 121.065i −0.00821895 + 0.0252953i
$$285$$ 0 0
$$286$$ 431.044 + 1326.62i 0.0891195 + 0.274282i
$$287$$ 2049.61 6308.06i 0.421550 1.29740i
$$288$$ 0 0
$$289$$ −1062.51 3270.08i −0.216266 0.665597i
$$290$$ 223.301 + 290.353i 0.0452161 + 0.0587935i
$$291$$ 0 0
$$292$$ 148.974 + 108.236i 0.0298562 + 0.0216918i
$$293$$ −1090.95 −0.217522 −0.108761 0.994068i $$-0.534688\pi$$
−0.108761 + 0.994068i $$0.534688\pi$$
$$294$$ 0 0
$$295$$ −1416.01 + 2065.14i −0.279468 + 0.407584i
$$296$$ −1887.34 + 1371.24i −0.370607 + 0.269262i
$$297$$ 0 0
$$298$$ −2348.30 7227.34i −0.456489 1.40493i
$$299$$ 6340.62 1.22638
$$300$$ 0 0
$$301$$ −6742.91 −1.29121
$$302$$ −251.050 772.652i −0.0478354 0.147222i
$$303$$ 0 0
$$304$$ −5162.55 + 3750.81i −0.973988 + 0.707644i
$$305$$ 212.725 + 7797.53i 0.0399364 + 1.46389i
$$306$$ 0 0
$$307$$ 8283.37 1.53992 0.769962 0.638090i $$-0.220275\pi$$
0.769962 + 0.638090i $$0.220275\pi$$
$$308$$ −58.5556 42.5431i −0.0108328 0.00787051i
$$309$$ 0 0
$$310$$ 4158.49 6064.85i 0.761892 1.11116i
$$311$$ 236.303 + 727.265i 0.0430852 + 0.132603i 0.970285 0.241964i $$-0.0777915\pi$$
−0.927200 + 0.374567i $$0.877792\pi$$
$$312$$ 0 0
$$313$$ −1734.95 + 5339.63i −0.313307 + 0.964261i 0.663138 + 0.748497i $$0.269224\pi$$
−0.976446 + 0.215764i $$0.930776\pi$$
$$314$$ −2771.48 8529.75i −0.498102 1.53300i
$$315$$ 0 0
$$316$$ 138.247 425.479i 0.0246107 0.0757439i
$$317$$ −6874.41 4994.55i −1.21800 0.884927i −0.222065 0.975032i $$-0.571280\pi$$
−0.995932 + 0.0901049i $$0.971280\pi$$
$$318$$ 0 0
$$319$$ −54.7438 39.7737i −0.00960835 0.00698087i
$$320$$ −141.935 5202.71i −0.0247951 0.908877i
$$321$$ 0 0
$$322$$ −3642.14 + 2646.17i −0.630337 + 0.457966i
$$323$$ 1103.07 + 3394.89i 0.190020 + 0.584820i
$$324$$ 0 0
$$325$$ 7587.96 6172.15i 1.29509 1.05344i
$$326$$ −2358.72 −0.400729
$$327$$ 0 0
$$328$$ 6142.83 4463.03i 1.03409 0.751309i
$$329$$ −4463.48 + 3242.91i −0.747963 + 0.543427i
$$330$$ 0 0
$$331$$ 2626.81 + 1908.49i 0.436202 + 0.316919i 0.784124 0.620604i $$-0.213113\pi$$
−0.347922 + 0.937523i $$0.613113\pi$$
$$332$$ 699.355 0.115609
$$333$$ 0 0
$$334$$ −2570.12 + 7910.01i −0.421050 + 1.29586i
$$335$$ −6196.01 8056.52i −1.01052 1.31396i
$$336$$ 0 0
$$337$$ −2291.63 + 7052.92i −0.370425 + 1.14005i 0.576089 + 0.817387i $$0.304578\pi$$
−0.946514 + 0.322664i $$0.895422\pi$$
$$338$$ 3564.20 10969.5i 0.573570 1.76527i
$$339$$ 0 0
$$340$$ 259.733 + 76.6273i 0.0414294 + 0.0122226i
$$341$$ −419.793 + 1291.99i −0.0666659 + 0.205176i
$$342$$ 0 0
$$343$$ −6209.68 −0.977525
$$344$$ −6244.91 4537.19i −0.978788 0.711131i
$$345$$ 0 0
$$346$$ −9795.14 + 7116.59i −1.52194 + 1.10575i
$$347$$ 504.270 366.374i 0.0780133 0.0566800i −0.548095 0.836416i $$-0.684647\pi$$
0.626108 + 0.779736i $$0.284647\pi$$
$$348$$ 0 0
$$349$$ 12079.4 1.85271 0.926356 0.376649i $$-0.122924\pi$$
0.926356 + 0.376649i $$0.122924\pi$$
$$350$$ −1782.76 + 6712.09i −0.272265 + 1.02508i
$$351$$ 0 0
$$352$$ −53.4003 164.349i −0.00808592 0.0248859i
$$353$$ 1021.78 742.368i 0.154062 0.111933i −0.508084 0.861308i $$-0.669646\pi$$
0.662146 + 0.749375i $$0.269646\pi$$
$$354$$ 0 0
$$355$$ −2126.14 + 755.525i −0.317870 + 0.112955i
$$356$$ 1.92886 + 1.40140i 0.000287160 + 0.000208634i
$$357$$ 0 0
$$358$$ −4193.24 3046.56i −0.619049 0.449765i
$$359$$ 48.5654 149.469i 0.00713979 0.0219740i −0.947423 0.319983i $$-0.896323\pi$$
0.954563 + 0.298009i $$0.0963227\pi$$
$$360$$ 0 0
$$361$$ 550.615 + 1694.62i 0.0802763 + 0.247065i
$$362$$ −1355.32 + 4171.26i −0.196780 + 0.605625i
$$363$$ 0 0
$$364$$ 288.433 + 887.706i 0.0415330 + 0.127825i
$$365$$ 89.0131 + 3262.82i 0.0127648 + 0.467901i
$$366$$ 0 0
$$367$$ −5574.94 4050.43i −0.792941 0.576106i 0.115894 0.993262i $$-0.463027\pi$$
−0.908835 + 0.417156i $$0.863027\pi$$
$$368$$ −5562.58 −0.787961
$$369$$ 0 0
$$370$$ 3394.71 + 1001.52i 0.476979 + 0.140720i
$$371$$ 10477.4 7612.27i 1.46620 1.06525i
$$372$$ 0 0
$$373$$ −1192.38 3669.78i −0.165521 0.509421i 0.833553 0.552439i $$-0.186303\pi$$
−0.999074 + 0.0430178i $$0.986303\pi$$
$$374$$ −684.538 −0.0946434
$$375$$ 0 0
$$376$$ −6315.93 −0.866275
$$377$$ 269.657 + 829.919i 0.0368383 + 0.113377i
$$378$$ 0 0
$$379$$ 4056.09 2946.92i 0.549730 0.399402i −0.277956 0.960594i $$-0.589657\pi$$
0.827686 + 0.561192i $$0.189657\pi$$
$$380$$ 628.728 + 185.489i 0.0848764 + 0.0250405i
$$381$$ 0 0
$$382$$ −10748.6 −1.43965
$$383$$ 11340.8 + 8239.61i 1.51303 + 1.09928i 0.964811 + 0.262944i $$0.0846936\pi$$
0.548218 + 0.836335i $$0.315306\pi$$
$$384$$ 0 0
$$385$$ −34.9875 1282.48i −0.00463150 0.169770i
$$386$$ −4263.12 13120.5i −0.562142 1.73010i
$$387$$ 0 0
$$388$$ 3.59863 11.0754i 0.000470857 0.00144915i
$$389$$ 29.9938 + 92.3116i 0.00390938 + 0.0120318i 0.952992 0.302995i $$-0.0979865\pi$$
−0.949083 + 0.315027i $$0.897987\pi$$
$$390$$ 0 0
$$391$$ −961.552 + 2959.35i −0.124368 + 0.382764i
$$392$$ 256.517 + 186.370i 0.0330512 + 0.0240131i
$$393$$ 0 0
$$394$$ 1144.93 + 831.841i 0.146398 + 0.106364i
$$395$$ 7472.27 2655.28i 0.951825 0.338232i
$$396$$ 0 0
$$397$$ 4234.34 3076.43i 0.535303 0.388921i −0.287034 0.957920i $$-0.592669\pi$$
0.822338 + 0.569000i $$0.192669\pi$$
$$398$$ 449.340 + 1382.93i 0.0565915 + 0.174171i
$$399$$ 0 0
$$400$$ −6656.86 + 5414.79i −0.832108 + 0.676849i
$$401$$ 10349.0 1.28879 0.644396 0.764692i $$-0.277109\pi$$
0.644396 + 0.764692i $$0.277109\pi$$
$$402$$ 0 0
$$403$$ 14173.0 10297.3i 1.75188 1.27282i
$$404$$ −679.951 + 494.014i −0.0837348 + 0.0608369i
$$405$$ 0 0
$$406$$ −501.249 364.179i −0.0612724 0.0445170i
$$407$$ −653.848 −0.0796316
$$408$$ 0 0
$$409$$ −3148.95 + 9691.47i −0.380698 + 1.17167i 0.558855 + 0.829265i $$0.311241\pi$$
−0.939553 + 0.342403i $$0.888759\pi$$
$$410$$ −11048.9 3259.69i −1.33090 0.392645i
$$411$$ 0 0
$$412$$ 327.185 1006.97i 0.0391244 0.120412i
$$413$$ 1308.83 4028.17i 0.155940 0.479935i
$$414$$ 0 0
$$415$$ 7557.29 + 9826.56i 0.893910 + 1.16233i
$$416$$ −688.645 + 2119.43i −0.0811625 + 0.249793i
$$417$$ 0 0
$$418$$ −1657.04 −0.193896
$$419$$ 8398.42 + 6101.81i 0.979212 + 0.711439i 0.957532 0.288326i $$-0.0930986\pi$$
0.0216796 + 0.999765i $$0.493099\pi$$
$$420$$ 0 0
$$421$$ 7922.06 5755.72i 0.917097 0.666310i −0.0257029 0.999670i $$-0.508182\pi$$
0.942800 + 0.333360i $$0.108182\pi$$
$$422$$ −1126.05 + 818.122i −0.129894 + 0.0943733i
$$423$$ 0 0
$$424$$ 14825.8 1.69812
$$425$$ 1730.01 + 4477.52i 0.197454 + 0.511040i
$$426$$ 0 0
$$427$$ −4077.30 12548.6i −0.462094 1.42218i
$$428$$ 791.264 574.887i 0.0893625 0.0649257i
$$429$$ 0 0
$$430$$ 319.374 + 11706.8i 0.0358176 + 1.31291i
$$431$$ 3207.40 + 2330.31i 0.358457 + 0.260434i 0.752408 0.658697i $$-0.228892\pi$$
−0.393951 + 0.919131i $$0.628892\pi$$
$$432$$ 0 0
$$433$$ −3610.83 2623.42i −0.400752 0.291163i 0.369095 0.929391i $$-0.379668\pi$$
−0.769847 + 0.638228i $$0.779668\pi$$
$$434$$ −3843.74 + 11829.8i −0.425128 + 1.30841i
$$435$$ 0 0
$$436$$ 87.1225 + 268.136i 0.00956975 + 0.0294527i
$$437$$ −2327.60 + 7163.61i −0.254792 + 0.784169i
$$438$$ 0 0
$$439$$ −5124.83 15772.6i −0.557164 1.71477i −0.690160 0.723657i $$-0.742460\pi$$
0.132997 0.991116i $$-0.457540\pi$$
$$440$$ 830.558 1211.31i 0.0899893 0.131243i
$$441$$ 0 0
$$442$$ 7141.80 + 5188.82i 0.768554 + 0.558387i
$$443$$ −5664.63 −0.607528 −0.303764 0.952747i $$-0.598243\pi$$
−0.303764 + 0.952747i $$0.598243\pi$$
$$444$$ 0 0
$$445$$ 1.15251 + 42.2457i 0.000122773 + 0.00450032i
$$446$$ −12040.1 + 8747.66i −1.27829 + 0.928730i
$$447$$ 0 0
$$448$$ 2720.48 + 8372.77i 0.286899 + 0.882983i
$$449$$ 14047.7 1.47651 0.738253 0.674524i $$-0.235651\pi$$
0.738253 + 0.674524i $$0.235651\pi$$
$$450$$ 0 0
$$451$$ 2128.11 0.222193
$$452$$ 121.195 + 373.000i 0.0126118 + 0.0388151i
$$453$$ 0 0
$$454$$ 12578.9 9139.13i 1.30035 0.944759i
$$455$$ −9356.23 + 13645.4i −0.964015 + 1.40594i
$$456$$ 0 0
$$457$$ −11501.1 −1.17724 −0.588622 0.808409i $$-0.700329\pi$$
−0.588622 + 0.808409i $$0.700329\pi$$
$$458$$ −1164.01 845.702i −0.118757 0.0862817i
$$459$$ 0 0
$$460$$ 348.354 + 452.957i 0.0353089 + 0.0459114i
$$461$$ −497.651 1531.61i −0.0502775 0.154738i 0.922766 0.385362i $$-0.125923\pi$$
−0.973043 + 0.230624i $$0.925923\pi$$
$$462$$ 0 0
$$463$$ 606.515 1866.66i 0.0608793 0.187367i −0.915991 0.401198i $$-0.868594\pi$$
0.976871 + 0.213830i $$0.0685940\pi$$
$$464$$ −236.568 728.082i −0.0236690 0.0728456i
$$465$$ 0 0
$$466$$ 1978.94 6090.56i 0.196723 0.605450i
$$467$$ 1274.21 + 925.764i 0.126260 + 0.0917329i 0.649123 0.760684i $$-0.275136\pi$$
−0.522863 + 0.852417i $$0.675136\pi$$
$$468$$ 0 0
$$469$$ 13908.3 + 10105.0i 1.36935 + 0.994895i
$$470$$ 5841.64 + 7595.75i 0.573308 + 0.745459i
$$471$$ 0 0
$$472$$ 3922.66 2849.98i 0.382532 0.277926i
$$473$$ −668.551 2057.59i −0.0649895 0.200017i
$$474$$ 0 0
$$475$$ 4187.79 + 10838.6i 0.404524 + 1.04697i
$$476$$ −458.059 −0.0441073
$$477$$ 0 0
$$478$$ 10542.0 7659.24i 1.00875 0.732898i
$$479$$ 7933.01 5763.67i 0.756719 0.549789i −0.141183 0.989983i $$-0.545091\pi$$
0.897902 + 0.440195i $$0.145091\pi$$
$$480$$ 0 0
$$481$$ 6821.61 + 4956.19i 0.646650 + 0.469819i
$$482$$ 7059.13 0.667084
$$483$$ 0 0
$$484$$ −252.249 + 776.344i −0.0236898 + 0.0729098i
$$485$$ 194.507 69.1181i 0.0182105 0.00647112i
$$486$$ 0 0
$$487$$ −2414.05 + 7429.69i −0.224623 + 0.691317i 0.773707 + 0.633543i $$0.218400\pi$$
−0.998330 + 0.0577737i $$0.981600\pi$$
$$488$$ 4667.60 14365.4i 0.432976 1.33256i
$$489$$ 0 0
$$490$$ −13.1186 480.870i −0.00120947 0.0443337i
$$491$$ −1550.87 + 4773.07i −0.142545 + 0.438708i −0.996687 0.0813313i $$-0.974083\pi$$
0.854142 + 0.520040i $$0.174083\pi$$
$$492$$ 0 0
$$493$$ −428.241 −0.0391217
$$494$$ 17287.9 + 12560.4i 1.57454 + 1.14397i
$$495$$ 0 0
$$496$$ −12433.9 + 9033.76i −1.12560 + 0.817798i
$$497$$ 3087.76 2243.39i 0.278682 0.202474i
$$498$$ 0 0
$$499$$ −16251.9 −1.45798 −0.728991 0.684523i $$-0.760011\pi$$
−0.728991 + 0.684523i $$0.760011\pi$$
$$500$$ 857.805 + 202.965i 0.0767244 + 0.0181537i
$$501$$ 0 0
$$502$$ 3140.82 + 9666.45i 0.279246 + 0.859432i
$$503$$ 89.3910 64.9464i 0.00792395 0.00575709i −0.583816 0.811886i $$-0.698441\pi$$
0.591740 + 0.806129i $$0.298441\pi$$
$$504$$ 0 0
$$505$$ −14289.0 4215.58i −1.25911 0.371467i
$$506$$ −1168.59 849.029i −0.102668 0.0745927i
$$507$$ 0 0
$$508$$ 357.264 + 259.567i 0.0312028 + 0.0226702i
$$509$$ −4592.45 + 14134.1i −0.399915 + 1.23081i 0.525152 + 0.851008i $$0.324008\pi$$
−0.925067 + 0.379804i $$0.875992\pi$$
$$510$$ 0 0
$$511$$ −1706.11 5250.88i −0.147699 0.454570i
$$512$$ −3069.94 + 9448.29i −0.264987 + 0.815546i
$$513$$ 0 0
$$514$$ −4332.70 13334.7i −0.371804 1.14429i
$$515$$ 17684.4 6284.18i 1.51315 0.537697i
$$516$$ 0 0
$$517$$ −1432.12 1040.50i −0.121827 0.0885124i
$$518$$ −5986.82 −0.507810
$$519$$ 0 0
$$520$$ −17847.0 + 6341.93i −1.50508 + 0.534831i
$$521$$ −6248.48 + 4539.79i −0.525433 + 0.381750i −0.818647 0.574297i $$-0.805275\pi$$
0.293213 + 0.956047i $$0.405275\pi$$
$$522$$ 0 0
$$523$$ −1432.62 4409.15i −0.119778 0.368640i 0.873135 0.487478i $$-0.162083\pi$$
−0.992914 + 0.118838i $$0.962083\pi$$
$$524$$ 367.026 0.0305985
$$525$$ 0 0
$$526$$ −12340.7 −1.02296
$$527$$ 2656.72 + 8176.54i 0.219599 + 0.675855i
$$528$$ 0 0
$$529$$ 4531.36 3292.23i 0.372431 0.270587i
$$530$$ −13712.4 17829.9i −1.12383 1.46129i
$$531$$ 0 0
$$532$$ −1108.81 −0.0903627
$$533$$ −22202.6 16131.2i −1.80432 1.31092i
$$534$$ 0 0
$$535$$ 16628.1 + 4905.69i 1.34373 + 0.396433i
$$536$$ 6081.65 + 18717.4i 0.490088 + 1.50834i
$$537$$ 0 0
$$538$$ 2060.06 6340.21i 0.165085 0.508078i
$$539$$ 27.4615 + 84.5179i 0.00219453 + 0.00675407i
$$540$$ 0 0
$$541$$ −2574.24 + 7922.70i −0.204575 + 0.629618i 0.795155 + 0.606406i $$0.207389\pi$$
−0.999731 + 0.0232123i $$0.992611\pi$$
$$542$$ 1852.21 + 1345.71i 0.146788 + 0.106648i
$$543$$ 0 0
$$544$$ −884.768 642.821i −0.0697318 0.0506631i
$$545$$ −2826.09 + 4121.65i −0.222122 + 0.323948i
$$546$$ 0 0
$$547$$ −11703.1 + 8502.77i −0.914783 + 0.664629i −0.942220 0.334995i $$-0.891265\pi$$
0.0274369 + 0.999624i $$0.491265\pi$$
$$548$$ −117.338 361.130i −0.00914680 0.0281510i
$$549$$ 0 0
$$550$$ −2224.94 + 121.488i −0.172494 + 0.00941867i
$$551$$ −1036.63 −0.0801486
$$552$$ 0 0
$$553$$ −10851.9 + 7884.33i −0.834481 + 0.606286i
$$554$$ 12015.1 8729.45i 0.921427 0.669456i
$$555$$ 0 0
$$556$$ 94.7539 + 68.8428i 0.00722745 + 0.00525105i
$$557$$ −21991.8 −1.67293 −0.836467 0.548017i $$-0.815383\pi$$
−0.836467 + 0.548017i $$0.815383\pi$$
$$558$$ 0 0
$$559$$ −8621.58 + 26534.5i −0.652333 + 2.00767i
$$560$$ 8208.16 11971.0i 0.619389 0.903333i
$$561$$ 0 0
$$562$$ 2241.64 6899.05i 0.168252 0.517827i
$$563$$ 3935.09 12111.0i 0.294573 0.906602i −0.688792 0.724959i $$-0.741859\pi$$
0.983365 0.181643i $$-0.0581414\pi$$
$$564$$ 0 0
$$565$$ −3931.34 + 5733.57i −0.292731 + 0.426926i
$$566$$ 1722.35 5300.84i 0.127907 0.393659i
$$567$$ 0 0
$$568$$ 4369.25 0.322763
$$569$$ −3083.27 2240.13i −0.227166 0.165046i 0.468381 0.883527i $$-0.344838\pi$$
−0.695546 + 0.718481i $$0.744838\pi$$
$$570$$ 0 0
$$571$$ 16776.5 12188.9i 1.22955 0.893324i 0.232698 0.972549i $$-0.425245\pi$$
0.996857 + 0.0792254i $$0.0252447\pi$$
$$572$$ −242.284 + 176.030i −0.0177105 + 0.0128674i
$$573$$ 0 0
$$574$$ 19485.6 1.41692
$$575$$ −2600.11 + 9789.39i −0.188577 + 0.709992i
$$576$$ 0 0
$$577$$ −8200.30 25237.9i −0.591652 1.82092i −0.570733 0.821136i $$-0.693341\pi$$
−0.0209185 0.999781i $$-0.506659\pi$$
$$578$$ 8172.10 5937.38i 0.588088 0.427271i
$$579$$ 0 0
$$580$$ −44.4722 + 64.8594i −0.00318381 + 0.00464335i
$$581$$ −16964.0 12325.1i −1.21134 0.880088i
$$582$$ 0 0
$$583$$ 3361.69 + 2442.41i 0.238812 + 0.173507i
$$584$$ 1953.12 6011.09i 0.138392 0.425926i
$$585$$ 0 0
$$586$$ −990.402 3048.14i −0.0698177 0.214877i
$$587$$ 6201.38 19085.9i 0.436045 1.34201i −0.455968 0.889996i $$-0.650707\pi$$
0.892012 0.452011i $$-0.149293\pi$$
$$588$$ 0 0
$$589$$ 6431.04 + 19792.7i 0.449892 + 1.38462i
$$590$$ −7055.56 2081.56i −0.492327 0.145248i
$$591$$ 0 0
$$592$$ −5984.55 4348.03i −0.415479 0.301863i
$$593$$ −5902.00 −0.408712 −0.204356 0.978897i $$-0.565510\pi$$
−0.204356 + 0.978897i $$0.565510\pi$$
$$594$$ 0 0
$$595$$ −4949.82 6436.14i −0.341047 0.443455i
$$596$$ 1319.95 959.001i 0.0907170 0.0659097i
$$597$$ 0 0
$$598$$ 5756.23 + 17715.9i 0.393628 + 1.21146i
$$599$$ 1759.46 0.120016 0.0600079 0.998198i $$-0.480887\pi$$
0.0600079 + 0.998198i $$0.480887\pi$$
$$600$$ 0 0
$$601$$ 22974.1 1.55929 0.779646 0.626220i $$-0.215399\pi$$
0.779646 + 0.626220i $$0.215399\pi$$
$$602$$ −6121.44 18839.9i −0.414437 1.27551i
$$603$$ 0 0
$$604$$ 141.112 102.524i 0.00950623 0.00690668i
$$605$$ −13634.2 + 4844.91i −0.916210 + 0.325576i
$$606$$ 0 0
$$607$$ −18961.8 −1.26794 −0.633968 0.773359i $$-0.718575\pi$$
−0.633968 + 0.773359i $$0.718575\pi$$
$$608$$ −2141.73 1556.06i −0.142860 0.103794i
$$609$$ 0 0
$$610$$ −21593.4 + 7673.22i −1.43326 + 0.509311i
$$611$$ 7054.33 + 21711.0i 0.467083 + 1.43753i
$$612$$ 0 0
$$613$$ 6808.93 20955.7i 0.448630 1.38074i −0.429824 0.902913i $$-0.641424\pi$$
0.878454 0.477827i $$-0.158576\pi$$
$$614$$ 7519.92 + 23143.9i 0.494266 + 1.52119i
$$615$$ 0 0
$$616$$ −767.694 + 2362.72i −0.0502131 + 0.154540i
$$617$$ 5152.77 + 3743.71i 0.336212 + 0.244272i 0.743062 0.669223i $$-0.233373\pi$$
−0.406850 + 0.913495i $$0.633373\pi$$
$$618$$ 0 0
$$619$$ −6709.39 4874.66i −0.435659 0.316525i 0.348249 0.937402i $$-0.386777\pi$$
−0.783908 + 0.620877i $$0.786777\pi$$
$$620$$ 1514.28 + 446.748i 0.0980886 + 0.0289384i
$$621$$ 0 0
$$622$$ −1817.47 + 1320.47i −0.117161 + 0.0851224i
$$623$$ −22.0901 67.9865i −0.00142058 0.00437210i
$$624$$ 0 0
$$625$$ 6417.68 + 14246.2i 0.410732 + 0.911756i
$$626$$ −16494.1 −1.05309
$$627$$ 0 0
$$628$$ 1557.82 1131.82i 0.0989867 0.0719180i
$$629$$ −3347.69 + 2432.24i −0.212212 + 0.154181i
$$630$$ 0 0
$$631$$ −18624.6 13531.5i −1.17501 0.853696i −0.183411 0.983036i $$-0.558714\pi$$
−0.991600 + 0.129340i $$0.958714\pi$$
$$632$$ −15355.6 −0.966478
$$633$$ 0 0
$$634$$ 7714.08 23741.5i 0.483226 1.48722i
$$635$$ 213.468 + 7824.78i 0.0133405 + 0.489003i
$$636$$ 0 0
$$637$$ 354.141 1089.94i 0.0220276 0.0677940i
$$638$$ 61.4304 189.063i 0.00381200 0.0117321i
$$639$$ 0 0
$$640$$ 16807.9 5972.69i 1.03811 0.368893i
$$641$$ 7178.47 22093.1i 0.442329 1.36135i −0.443058 0.896493i $$-0.646106\pi$$
0.885387 0.464855i $$-0.153894\pi$$
$$642$$ 0 0
$$643$$ 17439.0 1.06956 0.534780 0.844991i $$-0.320395\pi$$
0.534780 + 0.844991i $$0.320395\pi$$
$$644$$ −781.960 568.127i −0.0478471 0.0347630i
$$645$$ 0 0
$$646$$ −8484.02 + 6164.00i −0.516717 + 0.375417i
$$647$$ 13233.9 9614.98i 0.804139 0.584241i −0.107987 0.994152i $$-0.534440\pi$$
0.912125 + 0.409911i $$0.134440\pi$$
$$648$$ 0 0
$$649$$ 1358.96 0.0821939
$$650$$ 24133.8 + 15597.7i 1.45631 + 0.941216i
$$651$$ 0 0
$$652$$ −156.490 481.628i −0.00939975 0.0289295i
$$653$$ 13116.1 9529.41i 0.786023 0.571079i −0.120758 0.992682i $$-0.538532\pi$$
0.906781 + 0.421603i $$0.138532\pi$$
$$654$$ 0 0
$$655$$ 3966.11 + 5157.04i 0.236594 + 0.307637i
$$656$$ 19478.2 + 14151.8i 1.15929 + 0.842276i
$$657$$ 0 0
$$658$$ −13112.9 9527.06i −0.776889 0.564443i
$$659$$ −3337.93 + 10273.1i −0.197310 + 0.607258i 0.802632 + 0.596475i $$0.203433\pi$$
−0.999942 + 0.0107834i $$0.996567\pi$$
$$660$$ 0 0
$$661$$ 4696.20 + 14453.4i 0.276341 + 0.850489i 0.988862 + 0.148838i $$0.0475534\pi$$
−0.712521 + 0.701651i $$0.752447\pi$$
$$662$$ −2947.66 + 9071.98i −0.173058 + 0.532617i
$$663$$ 0 0
$$664$$ −7417.80 22829.6i −0.433534 1.33428i
$$665$$ −11981.9 15579.8i −0.698703 0.908507i
$$666$$ 0 0
$$667$$ −731.057 531.144i −0.0424387 0.0308336i
$$668$$ −1785.66 −0.103427
$$669$$ 0 0
$$670$$ 16885.2 24625.8i 0.973630 1.41997i
$$671$$ 3424.94 2488.36i 0.197047 0.143163i
$$672$$ 0 0
$$673$$ 2910.35 + 8957.12i 0.166695 + 0.513034i 0.999157 0.0410478i $$-0.0130696\pi$$
−0.832462 + 0.554081i $$0.813070\pi$$
$$674$$ −21786.5 −1.24508
$$675$$ 0 0
$$676$$ 2476.33 0.140892
$$677$$ 4739.48 + 14586.6i 0.269059 + 0.828079i 0.990730 + 0.135843i $$0.0433743\pi$$
−0.721671 + 0.692236i $$0.756626\pi$$
$$678$$ 0 0
$$679$$ −282.479 + 205.233i −0.0159655 + 0.0115996i
$$680$$ −253.480 9291.45i −0.0142949 0.523986i
$$681$$ 0 0
$$682$$ −3990.95 −0.224079
$$683$$ 5893.00 + 4281.51i 0.330145 + 0.239865i 0.740492 0.672065i $$-0.234592\pi$$
−0.410347 + 0.911929i $$0.634592\pi$$
$$684$$ 0 0
$$685$$ 3806.24 5551.12i 0.212305 0.309631i
$$686$$ −5637.36 17350.0i −0.313754 0.965636i
$$687$$ 0 0
$$688$$ 7563.65 23278.5i 0.419130 1.28995i
$$689$$ −16559.0 50963.5i −0.915601 2.81793i
$$690$$ 0 0
$$691$$ 4164.62 12817.4i 0.229276 0.705639i −0.768553 0.639786i $$-0.779023\pi$$
0.997829 0.0658530i $$-0.0209768\pi$$
$$692$$ −2103.00 1527.92i −0.115526 0.0839346i
$$693$$ 0 0
$$694$$ 1481.45 + 1076.34i 0.0810304 + 0.0588720i
$$695$$ 56.6163 + 2075.30i 0.00309004 + 0.113267i
$$696$$ 0 0
$$697$$ 10895.9 7916.33i 0.592125 0.430204i
$$698$$ 10966.1 + 33750.2i 0.594661 + 1.83018i
$$699$$ 0 0
$$700$$ −1488.82 + 81.2937i −0.0803888 + 0.00438945i
$$701$$ −16099.1 −0.867413 −0.433706 0.901054i $$-0.642794\pi$$
−0.433706 + 0.901054i $$0.642794\pi$$
$$702$$ 0 0
$$703$$ −8103.65 + 5887.65i −0.434758 + 0.315870i
$$704$$ −2285.21 + 1660.30i −0.122339 + 0.0888848i
$$705$$ 0 0
$$706$$ 3001.81 + 2180.94i 0.160020 + 0.116262i
$$707$$ 25199.6 1.34050
$$708$$ 0 0
$$709$$ 1824.52 5615.31i 0.0966452 0.297443i −0.891034 0.453937i $$-0.850019\pi$$
0.987679 + 0.156494i $$0.0500191\pi$$
$$710$$ −4041.14 5254.60i −0.213607 0.277749i
$$711$$ 0 0
$$712$$ 25.2883 77.8294i 0.00133107 0.00409660i
$$713$$ −5605.98 + 17253.4i −0.294454 + 0.906236i
$$714$$ 0 0
$$715$$ −5091.52 1502.12i −0.266311 0.0785679i
$$716$$ 343.876 1058.34i 0.0179487 0.0552404i
$$717$$ 0 0
$$718$$ 461.710 0.0239984
$$719$$ −3639.38 2644.16i −0.188770 0.137150i 0.489386 0.872067i $$-0.337221\pi$$
−0.678156 + 0.734918i $$0.737221\pi$$
$$720$$ 0 0
$$721$$ −25682.8 + 18659.7i −1.32660 + 0.963831i
$$722$$ −4234.94 + 3076.86i −0.218294 + 0.158600i
$$723$$ 0 0
$$724$$ −941.649 −0.0483372
$$725$$ −1391.90 + 76.0017i −0.0713021 + 0.00389329i
$$726$$ 0 0
$$727$$ −1876.26 5774.55i −0.0957177 0.294589i 0.891722 0.452583i $$-0.149497\pi$$
−0.987440 + 0.157994i $$0.949497\pi$$
$$728$$ 25918.8 18831.1i 1.31953 0.958693i
$$729$$ 0 0
$$730$$ −9035.59 + 3210.80i −0.458113 + 0.162791i
$$731$$ −11077.0 8047.88i −0.560460 0.407198i
$$732$$ 0 0
$$733$$ −21042.7 15288.4i −1.06034 0.770382i −0.0861888 0.996279i $$-0.527469\pi$$
−0.974151 + 0.225897i $$0.927469\pi$$
$$734$$ 6255.89 19253.6i 0.314590 0.968208i
$$735$$ 0 0
$$736$$ −713.115 2194.74i −0.0357144 0.109918i
$$737$$ −1704.53 + 5246.01i −0.0851930 + 0.262197i
$$738$$ 0 0
$$739$$ 9514.09 + 29281.4i 0.473588 + 1.45755i 0.847853 + 0.530232i $$0.177895\pi$$
−0.374265 + 0.927322i $$0.622105\pi$$
$$740$$ 20.7230 + 759.611i 0.00102945 + 0.0377350i
$$741$$ 0 0
$$742$$ 30780.6 + 22363.4i 1.52290 + 1.10645i
$$743$$ −29872.6 −1.47499 −0.737496 0.675352i $$-0.763992\pi$$
−0.737496 + 0.675352i $$0.763992\pi$$
$$744$$ 0 0
$$745$$ 27738.3 + 8183.46i 1.36410 + 0.402441i
$$746$$ 9170.98 6663.11i 0.450098 0.327016i
$$747$$ 0 0
$$748$$ −45.4160 139.776i −0.00222002 0.00683251i
$$749$$ −29325.0 −1.43059
$$750$$ 0 0
$$751$$ −22462.4 −1.09143 −0.545716 0.837970i $$-0.683742\pi$$
−0.545716 + 0.837970i $$0.683742\pi$$
$$752$$ −6188.72 19046.9i −0.300106 0.923630i
$$753$$ 0 0
$$754$$ −2074.01 + 1506.86i −0.100174 + 0.0727805i
$$755$$ 2965.42 + 874.869i 0.142944 + 0.0421718i
$$756$$ 0 0
$$757$$ 22613.9 1.08575 0.542876 0.839813i $$-0.317335\pi$$
0.542876 + 0.839813i $$0.317335\pi$$
$$758$$ 11916.0 + 8657.51i 0.570990 + 0.414848i
$$759$$ 0 0
$$760$$ −613.592 22491.5i −0.0292860 1.07349i
$$761$$ −5096.57 15685.6i −0.242773 0.747179i −0.995995 0.0894121i $$-0.971501\pi$$
0.753222 0.657767i $$-0.228499\pi$$
$$762$$ 0 0
$$763$$ 2612.19 8039.49i 0.123942 0.381454i
$$764$$ −713.122 2194.76i −0.0337694 0.103932i
$$765$$ 0 0
$$766$$ −12726.1 + 39166.8i −0.600276 + 1.84746i
$$767$$ −14178.0 10301.0i −0.667457 0.484936i
$$768$$ 0 0
$$769$$ −1931.73 1403.49i −0.0905853 0.0658140i 0.541571 0.840655i $$-0.317830\pi$$
−0.632156 + 0.774841i $$0.717830\pi$$
$$770$$ 3551.53 1262.04i 0.166218 0.0590658i
$$771$$ 0 0
$$772$$ 2396.24 1740.97i 0.111713 0.0811644i
$$773$$ 11956.5 + 36798.2i 0.556332 + 1.71221i 0.692400 + 0.721514i $$0.256553\pi$$
−0.136068 + 0.990699i $$0.543447\pi$$
$$774$$ 0 0
$$775$$ 10086.2 + 26104.6i 0.467494 + 1.20994i
$$776$$ −399.714 −0.0184909
$$777$$ 0 0
$$778$$ −230.691 + 167.607i −0.0106307 + 0.00772366i
$$779$$ 26375.4 19162.8i 1.21309 0.881360i
$$780$$ 0 0
$$781$$ 990.713 + 719.795i 0.0453912 + 0.0329786i
$$782$$ −9141.43 −0.418027
$$783$$ 0 0
$$784$$ −310.686 + 956.193i −0.0141530 + 0.0435583i