# Properties

 Label 78.2.k.a.71.2 Level $78$ Weight $2$ Character 78.71 Analytic conductor $0.623$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$78 = 2 \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 78.k (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.622833135766$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$4$$ over $$\Q(\zeta_{12})$$ Coefficient field: 16.0.9349208943630483456.9 Defining polynomial: $$x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \cdots + 25$$ x^16 - 8*x^15 + 48*x^14 - 196*x^13 + 642*x^12 - 1668*x^11 + 3580*x^10 - 6328*x^9 + 9297*x^8 - 11276*x^7 + 11224*x^6 - 9024*x^5 + 5736*x^4 - 2780*x^3 + 972*x^2 - 220*x + 25 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 71.2 Root $$0.500000 - 1.33108i$$ of defining polynomial Character $$\chi$$ $$=$$ 78.71 Dual form 78.2.k.a.11.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.965926 + 0.258819i) q^{2} +(1.73022 + 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.313444 - 0.313444i) q^{5} +(-1.69185 + 0.370982i) q^{6} +(-0.0745867 + 0.278362i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +O(q^{10})$$ $$q+(-0.965926 + 0.258819i) q^{2} +(1.73022 + 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.313444 - 0.313444i) q^{5} +(-1.69185 + 0.370982i) q^{6} +(-0.0745867 + 0.278362i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +(0.383889 + 0.221638i) q^{10} +(-0.150860 - 0.563016i) q^{11} +(1.53819 - 0.796225i) q^{12} +(-1.79144 + 3.12902i) q^{13} -0.288181i q^{14} +(-0.517396 - 0.567261i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.79907 - 4.84812i) q^{17} +(-2.95680 + 0.507306i) q^{18} +(-6.79127 - 1.81971i) q^{19} +(-0.428173 - 0.114729i) q^{20} +(-0.151194 + 0.475695i) q^{21} +(0.291439 + 0.504787i) q^{22} +(-3.32595 + 5.76071i) q^{23} +(-1.27970 + 1.16721i) q^{24} -4.80351i q^{25} +(0.920548 - 3.48606i) q^{26} +(5.14688 + 0.713876i) q^{27} +(0.0745867 + 0.278362i) q^{28} +(3.57681 + 2.06507i) q^{29} +(0.646584 + 0.414020i) q^{30} +(-1.03573 + 1.03573i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.216237 - 0.986144i) q^{33} +(3.95848 + 3.95848i) q^{34} +(0.110630 - 0.0638720i) q^{35} +(2.72474 - 1.25529i) q^{36} +(6.72147 - 1.80101i) q^{37} +7.03084 q^{38} +(-3.34848 + 5.27140i) q^{39} +0.443277 q^{40} +(7.36988 - 1.97475i) q^{41} +(0.0229229 - 0.498618i) q^{42} +(-3.26299 + 1.88389i) q^{43} +(-0.412157 - 0.412157i) q^{44} +(-0.850089 - 1.02264i) q^{45} +(1.72164 - 6.42524i) q^{46} +(-3.71799 + 3.71799i) q^{47} +(0.933998 - 1.45865i) q^{48} +(5.99026 + 3.45848i) q^{49} +(1.24324 + 4.63983i) q^{50} +(-4.45737 - 8.61098i) q^{51} +(0.0130771 + 3.60553i) q^{52} +3.64778i q^{53} +(-5.15627 + 0.642559i) q^{54} +(-0.129188 + 0.223760i) q^{55} +(-0.144091 - 0.249572i) q^{56} +(-11.6057 - 3.68871i) q^{57} +(-3.98942 - 1.06896i) q^{58} +(3.29111 + 0.881850i) q^{59} +(-0.731708 - 0.232564i) q^{60} +(-5.25554 - 9.10286i) q^{61} +(0.732370 - 1.26850i) q^{62} +(-0.299437 + 0.811032i) q^{63} -1.00000i q^{64} +(1.54229 - 0.419256i) q^{65} +(0.464102 + 0.896575i) q^{66} +(2.29144 + 8.55177i) q^{67} +(-4.84812 - 2.79907i) q^{68} +(-6.21286 + 9.70277i) q^{69} +(-0.0903287 + 0.0903287i) q^{70} +(3.98229 - 14.8621i) q^{71} +(-2.30701 + 1.91774i) q^{72} +(3.52053 + 3.52053i) q^{73} +(-6.02630 + 3.47929i) q^{74} +(0.382086 - 8.31114i) q^{75} +(-6.79127 + 1.81971i) q^{76} +0.167974 q^{77} +(1.87005 - 5.95843i) q^{78} +1.10886 q^{79} +(-0.428173 + 0.114729i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-6.60765 + 3.81493i) q^{82} +(8.23032 + 8.23032i) q^{83} +(0.106910 + 0.487560i) q^{84} +(-0.642265 + 2.39697i) q^{85} +(2.66422 - 2.66422i) q^{86} +(6.02442 + 3.85755i) q^{87} +(0.504787 + 0.291439i) q^{88} +(-3.64478 - 13.6025i) q^{89} +(1.08580 + 0.767778i) q^{90} +(-0.737380 - 0.732051i) q^{91} +6.65190i q^{92} +(-1.87442 + 1.70965i) q^{93} +(2.62902 - 4.55359i) q^{94} +(1.55830 + 2.69906i) q^{95} +(-0.524648 + 1.65068i) q^{96} +(2.59245 + 0.694645i) q^{97} +(-6.68126 - 1.79024i) q^{98} +(-0.295697 - 1.72345i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 8 q^{7}+O(q^{10})$$ 16 * q + 8 * q^7 $$16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100})$$ 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$$.

 $$n$$ $$53$$ $$67$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.965926 + 0.258819i −0.683013 + 0.183013i
$$3$$ 1.73022 + 0.0795432i 0.998945 + 0.0459243i
$$4$$ 0.866025 0.500000i 0.433013 0.250000i
$$5$$ −0.313444 0.313444i −0.140176 0.140176i 0.633536 0.773713i $$-0.281603\pi$$
−0.773713 + 0.633536i $$0.781603\pi$$
$$6$$ −1.69185 + 0.370982i −0.690697 + 0.151453i
$$7$$ −0.0745867 + 0.278362i −0.0281911 + 0.105211i −0.978588 0.205830i $$-0.934011\pi$$
0.950397 + 0.311040i $$0.100677\pi$$
$$8$$ −0.707107 + 0.707107i −0.250000 + 0.250000i
$$9$$ 2.98735 + 0.275255i 0.995782 + 0.0917517i
$$10$$ 0.383889 + 0.221638i 0.121396 + 0.0700882i
$$11$$ −0.150860 0.563016i −0.0454859 0.169756i 0.939446 0.342696i $$-0.111340\pi$$
−0.984932 + 0.172940i $$0.944673\pi$$
$$12$$ 1.53819 0.796225i 0.444037 0.229850i
$$13$$ −1.79144 + 3.12902i −0.496856 + 0.867833i
$$14$$ 0.288181i 0.0770196i
$$15$$ −0.517396 0.567261i −0.133591 0.146466i
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ −2.79907 4.84812i −0.678873 1.17584i −0.975321 0.220793i $$-0.929135\pi$$
0.296448 0.955049i $$-0.404198\pi$$
$$18$$ −2.95680 + 0.507306i −0.696923 + 0.119573i
$$19$$ −6.79127 1.81971i −1.55802 0.417471i −0.625986 0.779834i $$-0.715304\pi$$
−0.932037 + 0.362363i $$0.881970\pi$$
$$20$$ −0.428173 0.114729i −0.0957423 0.0256541i
$$21$$ −0.151194 + 0.475695i −0.0329931 + 0.103805i
$$22$$ 0.291439 + 0.504787i 0.0621349 + 0.107621i
$$23$$ −3.32595 + 5.76071i −0.693509 + 1.20119i 0.277172 + 0.960820i $$0.410603\pi$$
−0.970681 + 0.240372i $$0.922731\pi$$
$$24$$ −1.27970 + 1.16721i −0.261217 + 0.238255i
$$25$$ 4.80351i 0.960701i
$$26$$ 0.920548 3.48606i 0.180534 0.683672i
$$27$$ 5.14688 + 0.713876i 0.990518 + 0.137386i
$$28$$ 0.0745867 + 0.278362i 0.0140956 + 0.0526054i
$$29$$ 3.57681 + 2.06507i 0.664198 + 0.383475i 0.793874 0.608082i $$-0.208061\pi$$
−0.129677 + 0.991556i $$0.541394\pi$$
$$30$$ 0.646584 + 0.414020i 0.118050 + 0.0755893i
$$31$$ −1.03573 + 1.03573i −0.186022 + 0.186022i −0.793974 0.607952i $$-0.791991\pi$$
0.607952 + 0.793974i $$0.291991\pi$$
$$32$$ −0.258819 + 0.965926i −0.0457532 + 0.170753i
$$33$$ −0.216237 0.986144i −0.0376420 0.171666i
$$34$$ 3.95848 + 3.95848i 0.678873 + 0.678873i
$$35$$ 0.110630 0.0638720i 0.0186998 0.0107963i
$$36$$ 2.72474 1.25529i 0.454124 0.209216i
$$37$$ 6.72147 1.80101i 1.10500 0.296085i 0.340202 0.940352i $$-0.389504\pi$$
0.764800 + 0.644268i $$0.222838\pi$$
$$38$$ 7.03084 1.14055
$$39$$ −3.34848 + 5.27140i −0.536186 + 0.844100i
$$40$$ 0.443277 0.0700882
$$41$$ 7.36988 1.97475i 1.15098 0.308404i 0.367623 0.929975i $$-0.380172\pi$$
0.783358 + 0.621570i $$0.213505\pi$$
$$42$$ 0.0229229 0.498618i 0.00353707 0.0769384i
$$43$$ −3.26299 + 1.88389i −0.497602 + 0.287290i −0.727723 0.685872i $$-0.759421\pi$$
0.230121 + 0.973162i $$0.426088\pi$$
$$44$$ −0.412157 0.412157i −0.0621349 0.0621349i
$$45$$ −0.850089 1.02264i −0.126724 0.152447i
$$46$$ 1.72164 6.42524i 0.253842 0.947350i
$$47$$ −3.71799 + 3.71799i −0.542325 + 0.542325i −0.924210 0.381885i $$-0.875275\pi$$
0.381885 + 0.924210i $$0.375275\pi$$
$$48$$ 0.933998 1.45865i 0.134811 0.210537i
$$49$$ 5.99026 + 3.45848i 0.855751 + 0.494068i
$$50$$ 1.24324 + 4.63983i 0.175821 + 0.656171i
$$51$$ −4.45737 8.61098i −0.624157 1.20578i
$$52$$ 0.0130771 + 3.60553i 0.00181347 + 0.499997i
$$53$$ 3.64778i 0.501062i 0.968109 + 0.250531i $$0.0806052\pi$$
−0.968109 + 0.250531i $$0.919395\pi$$
$$54$$ −5.15627 + 0.642559i −0.701679 + 0.0874413i
$$55$$ −0.129188 + 0.223760i −0.0174197 + 0.0301718i
$$56$$ −0.144091 0.249572i −0.0192549 0.0333505i
$$57$$ −11.6057 3.68871i −1.53721 0.488582i
$$58$$ −3.98942 1.06896i −0.523836 0.140361i
$$59$$ 3.29111 + 0.881850i 0.428466 + 0.114807i 0.466606 0.884465i $$-0.345477\pi$$
−0.0381400 + 0.999272i $$0.512143\pi$$
$$60$$ −0.731708 0.232564i −0.0944632 0.0300239i
$$61$$ −5.25554 9.10286i −0.672903 1.16550i −0.977077 0.212886i $$-0.931714\pi$$
0.304174 0.952616i $$-0.401620\pi$$
$$62$$ 0.732370 1.26850i 0.0930111 0.161100i
$$63$$ −0.299437 + 0.811032i −0.0377255 + 0.102180i
$$64$$ 1.00000i 0.125000i
$$65$$ 1.54229 0.419256i 0.191297 0.0520023i
$$66$$ 0.464102 + 0.896575i 0.0571270 + 0.110361i
$$67$$ 2.29144 + 8.55177i 0.279944 + 1.04476i 0.952455 + 0.304678i $$0.0985488\pi$$
−0.672512 + 0.740087i $$0.734785\pi$$
$$68$$ −4.84812 2.79907i −0.587921 0.339437i
$$69$$ −6.21286 + 9.70277i −0.747941 + 1.16808i
$$70$$ −0.0903287 + 0.0903287i −0.0107963 + 0.0107963i
$$71$$ 3.98229 14.8621i 0.472611 1.76381i −0.157723 0.987483i $$-0.550415\pi$$
0.630334 0.776324i $$-0.282918\pi$$
$$72$$ −2.30701 + 1.91774i −0.271883 + 0.226008i
$$73$$ 3.52053 + 3.52053i 0.412047 + 0.412047i 0.882451 0.470404i $$-0.155892\pi$$
−0.470404 + 0.882451i $$0.655892\pi$$
$$74$$ −6.02630 + 3.47929i −0.700543 + 0.404459i
$$75$$ 0.382086 8.31114i 0.0441195 0.959687i
$$76$$ −6.79127 + 1.81971i −0.779012 + 0.208736i
$$77$$ 0.167974 0.0191424
$$78$$ 1.87005 5.95843i 0.211741 0.674660i
$$79$$ 1.10886 0.124757 0.0623783 0.998053i $$-0.480131\pi$$
0.0623783 + 0.998053i $$0.480131\pi$$
$$80$$ −0.428173 + 0.114729i −0.0478712 + 0.0128270i
$$81$$ 8.84847 + 1.64456i 0.983163 + 0.182729i
$$82$$ −6.60765 + 3.81493i −0.729693 + 0.421288i
$$83$$ 8.23032 + 8.23032i 0.903395 + 0.903395i 0.995728 0.0923332i $$-0.0294325\pi$$
−0.0923332 + 0.995728i $$0.529433\pi$$
$$84$$ 0.106910 + 0.487560i 0.0116648 + 0.0531972i
$$85$$ −0.642265 + 2.39697i −0.0696634 + 0.259987i
$$86$$ 2.66422 2.66422i 0.287290 0.287290i
$$87$$ 6.02442 + 3.85755i 0.645886 + 0.413573i
$$88$$ 0.504787 + 0.291439i 0.0538104 + 0.0310675i
$$89$$ −3.64478 13.6025i −0.386346 1.44186i −0.836034 0.548678i $$-0.815131\pi$$
0.449687 0.893186i $$-0.351535\pi$$
$$90$$ 1.08580 + 0.767778i 0.114454 + 0.0809309i
$$91$$ −0.737380 0.732051i −0.0772985 0.0767398i
$$92$$ 6.65190i 0.693509i
$$93$$ −1.87442 + 1.70965i −0.194369 + 0.177283i
$$94$$ 2.62902 4.55359i 0.271162 0.469667i
$$95$$ 1.55830 + 2.69906i 0.159879 + 0.276918i
$$96$$ −0.524648 + 1.65068i −0.0535466 + 0.168472i
$$97$$ 2.59245 + 0.694645i 0.263223 + 0.0705305i 0.388017 0.921652i $$-0.373160\pi$$
−0.124794 + 0.992183i $$0.539827\pi$$
$$98$$ −6.68126 1.79024i −0.674909 0.180841i
$$99$$ −0.295697 1.72345i −0.0297187 0.173213i
$$100$$ −2.40175 4.15996i −0.240175 0.415996i
$$101$$ −7.12030 + 12.3327i −0.708497 + 1.22715i 0.256918 + 0.966433i $$0.417293\pi$$
−0.965415 + 0.260719i $$0.916040\pi$$
$$102$$ 6.53418 + 7.16392i 0.646980 + 0.709334i
$$103$$ 4.60903i 0.454141i −0.973878 0.227071i $$-0.927085\pi$$
0.973878 0.227071i $$-0.0729148\pi$$
$$104$$ −0.945811 3.47929i −0.0927444 0.341172i
$$105$$ 0.196494 0.101713i 0.0191759 0.00992617i
$$106$$ −0.944116 3.52349i −0.0917007 0.342232i
$$107$$ −11.7017 6.75600i −1.13125 0.653127i −0.187001 0.982360i $$-0.559877\pi$$
−0.944249 + 0.329232i $$0.893210\pi$$
$$108$$ 4.81427 1.95521i 0.463253 0.188140i
$$109$$ 2.06188 2.06188i 0.197492 0.197492i −0.601432 0.798924i $$-0.705403\pi$$
0.798924 + 0.601432i $$0.205403\pi$$
$$110$$ 0.0668726 0.249572i 0.00637606 0.0237958i
$$111$$ 11.7729 2.58151i 1.11743 0.245026i
$$112$$ 0.203775 + 0.203775i 0.0192549 + 0.0192549i
$$113$$ −9.02108 + 5.20832i −0.848632 + 0.489958i −0.860189 0.509975i $$-0.829655\pi$$
0.0115570 + 0.999933i $$0.496321\pi$$
$$114$$ 12.1649 + 0.559256i 1.13935 + 0.0523791i
$$115$$ 2.84816 0.763163i 0.265592 0.0711653i
$$116$$ 4.13015 0.383475
$$117$$ −6.21292 + 8.85435i −0.574385 + 0.818585i
$$118$$ −3.40721 −0.313659
$$119$$ 1.55830 0.417546i 0.142850 0.0382764i
$$120$$ 0.766968 + 0.0352597i 0.0700143 + 0.00321875i
$$121$$ 9.23205 5.33013i 0.839277 0.484557i
$$122$$ 7.43246 + 7.43246i 0.672903 + 0.672903i
$$123$$ 12.9086 2.83054i 1.16393 0.255221i
$$124$$ −0.379103 + 1.41483i −0.0340444 + 0.127055i
$$125$$ −3.07285 + 3.07285i −0.274844 + 0.274844i
$$126$$ 0.0793233 0.860896i 0.00706668 0.0766948i
$$127$$ −0.209104 0.120726i −0.0185550 0.0107127i 0.490694 0.871332i $$-0.336743\pi$$
−0.509249 + 0.860619i $$0.670077\pi$$
$$128$$ 0.258819 + 0.965926i 0.0228766 + 0.0853766i
$$129$$ −5.79555 + 3.00000i −0.510270 + 0.264135i
$$130$$ −1.38122 + 0.804144i −0.121141 + 0.0705281i
$$131$$ 8.09043i 0.706864i −0.935460 0.353432i $$-0.885015\pi$$
0.935460 0.353432i $$-0.114985\pi$$
$$132$$ −0.680339 0.745907i −0.0592159 0.0649229i
$$133$$ 1.01308 1.75470i 0.0878449 0.152152i
$$134$$ −4.42672 7.66730i −0.382410 0.662354i
$$135$$ −1.38950 1.83702i −0.119589 0.158105i
$$136$$ 5.40738 + 1.44890i 0.463679 + 0.124242i
$$137$$ 0.0798882 + 0.0214060i 0.00682531 + 0.00182884i 0.262230 0.965005i $$-0.415542\pi$$
−0.255405 + 0.966834i $$0.582209\pi$$
$$138$$ 3.48990 10.9802i 0.297080 0.934693i
$$139$$ 3.12073 + 5.40526i 0.264697 + 0.458468i 0.967484 0.252932i $$-0.0813949\pi$$
−0.702788 + 0.711400i $$0.748062\pi$$
$$140$$ 0.0638720 0.110630i 0.00539817 0.00934990i
$$141$$ −6.72870 + 6.13721i −0.566658 + 0.516847i
$$142$$ 15.3864i 1.29120i
$$143$$ 2.03194 + 0.536566i 0.169920 + 0.0448699i
$$144$$ 1.73205 2.44949i 0.144338 0.204124i
$$145$$ −0.473846 1.76842i −0.0393507 0.146859i
$$146$$ −4.31175 2.48939i −0.356843 0.206023i
$$147$$ 10.0894 + 6.46042i 0.832158 + 0.532846i
$$148$$ 4.92046 4.92046i 0.404459 0.404459i
$$149$$ −3.76251 + 14.0419i −0.308237 + 1.15036i 0.621886 + 0.783108i $$0.286367\pi$$
−0.930123 + 0.367249i $$0.880300\pi$$
$$150$$ 1.78201 + 8.12683i 0.145501 + 0.663553i
$$151$$ −6.40358 6.40358i −0.521116 0.521116i 0.396793 0.917908i $$-0.370123\pi$$
−0.917908 + 0.396793i $$0.870123\pi$$
$$152$$ 6.08888 3.51542i 0.493874 0.285138i
$$153$$ −7.02730 15.2535i −0.568124 1.23317i
$$154$$ −0.162251 + 0.0434749i −0.0130745 + 0.00350331i
$$155$$ 0.649285 0.0521519
$$156$$ −0.264169 + 6.23941i −0.0211504 + 0.499552i
$$157$$ −10.2127 −0.815065 −0.407532 0.913191i $$-0.633611\pi$$
−0.407532 + 0.913191i $$0.633611\pi$$
$$158$$ −1.07108 + 0.286994i −0.0852103 + 0.0228320i
$$159$$ −0.290157 + 6.31148i −0.0230109 + 0.500533i
$$160$$ 0.383889 0.221638i 0.0303491 0.0175221i
$$161$$ −1.35549 1.35549i −0.106828 0.106828i
$$162$$ −8.97261 + 0.701625i −0.704955 + 0.0551249i
$$163$$ −3.59245 + 13.4072i −0.281382 + 1.05013i 0.670060 + 0.742307i $$0.266268\pi$$
−0.951442 + 0.307827i $$0.900398\pi$$
$$164$$ 5.39512 5.39512i 0.421288 0.421288i
$$165$$ −0.241323 + 0.376879i −0.0187870 + 0.0293400i
$$166$$ −10.0800 5.81971i −0.782363 0.451697i
$$167$$ −3.47123 12.9548i −0.268612 1.00247i −0.960003 0.279991i $$-0.909668\pi$$
0.691391 0.722481i $$-0.256998\pi$$
$$168$$ −0.229457 0.443277i −0.0177030 0.0341996i
$$169$$ −6.58150 11.2109i −0.506269 0.862376i
$$170$$ 2.48152i 0.190324i
$$171$$ −19.7870 7.30545i −1.51315 0.558662i
$$172$$ −1.88389 + 3.26299i −0.143645 + 0.248801i
$$173$$ −0.551099 0.954532i −0.0418993 0.0725717i 0.844315 0.535847i $$-0.180008\pi$$
−0.886215 + 0.463275i $$0.846674\pi$$
$$174$$ −6.81755 2.16687i −0.516837 0.164270i
$$175$$ 1.33711 + 0.358278i 0.101076 + 0.0270833i
$$176$$ −0.563016 0.150860i −0.0424389 0.0113715i
$$177$$ 5.62421 + 1.78758i 0.422741 + 0.134363i
$$178$$ 7.04118 + 12.1957i 0.527759 + 0.914105i
$$179$$ −2.79777 + 4.84589i −0.209115 + 0.362199i −0.951436 0.307846i $$-0.900392\pi$$
0.742321 + 0.670045i $$0.233725\pi$$
$$180$$ −1.24752 0.460590i −0.0929847 0.0343304i
$$181$$ 14.4687i 1.07545i 0.843119 + 0.537727i $$0.180717\pi$$
−0.843119 + 0.537727i $$0.819283\pi$$
$$182$$ 0.901723 + 0.516259i 0.0668402 + 0.0382676i
$$183$$ −8.36919 16.1680i −0.618668 1.19518i
$$184$$ −1.72164 6.42524i −0.126921 0.473675i
$$185$$ −2.67132 1.54229i −0.196399 0.113391i
$$186$$ 1.36806 2.13654i 0.100311 0.156658i
$$187$$ −2.30731 + 2.30731i −0.168727 + 0.168727i
$$188$$ −1.36088 + 5.07887i −0.0992523 + 0.370415i
$$189$$ −0.582605 + 1.37945i −0.0423783 + 0.100340i
$$190$$ −2.20377 2.20377i −0.159879 0.159879i
$$191$$ 5.78136 3.33787i 0.418324 0.241520i −0.276036 0.961147i $$-0.589021\pi$$
0.694360 + 0.719628i $$0.255688\pi$$
$$192$$ 0.0795432 1.73022i 0.00574054 0.124868i
$$193$$ 5.88685 1.57738i 0.423745 0.113542i −0.0406437 0.999174i $$-0.512941\pi$$
0.464388 + 0.885632i $$0.346274\pi$$
$$194$$ −2.68390 −0.192693
$$195$$ 2.70185 0.602728i 0.193484 0.0431623i
$$196$$ 6.91695 0.494068
$$197$$ 14.2844 3.82748i 1.01772 0.272697i 0.288868 0.957369i $$-0.406721\pi$$
0.728851 + 0.684672i $$0.240055\pi$$
$$198$$ 0.731683 + 1.58819i 0.0519984 + 0.112868i
$$199$$ 13.4064 7.74017i 0.950352 0.548686i 0.0571619 0.998365i $$-0.481795\pi$$
0.893190 + 0.449679i $$0.148462\pi$$
$$200$$ 3.39659 + 3.39659i 0.240175 + 0.240175i
$$201$$ 3.28447 + 14.9787i 0.231668 + 1.05652i
$$202$$ 3.68574 13.7554i 0.259328 0.967824i
$$203$$ −0.841620 + 0.841620i −0.0590701 + 0.0590701i
$$204$$ −8.16569 5.22864i −0.571713 0.366078i
$$205$$ −2.92902 1.69107i −0.204572 0.118109i
$$206$$ 1.19291 + 4.45198i 0.0831136 + 0.310184i
$$207$$ −11.5214 + 16.2938i −0.800795 + 1.13249i
$$208$$ 1.81409 + 3.11594i 0.125784 + 0.216052i
$$209$$ 4.09812i 0.283473i
$$210$$ −0.163474 + 0.149104i −0.0112808 + 0.0102891i
$$211$$ −9.40721 + 16.2938i −0.647619 + 1.12171i 0.336071 + 0.941837i $$0.390902\pi$$
−0.983690 + 0.179872i $$0.942432\pi$$
$$212$$ 1.82389 + 3.15907i 0.125265 + 0.216966i
$$213$$ 8.07243 25.3980i 0.553114 1.74024i
$$214$$ 13.0516 + 3.49716i 0.892189 + 0.239061i
$$215$$ 1.61326 + 0.432272i 0.110023 + 0.0294807i
$$216$$ −4.14418 + 3.13461i −0.281976 + 0.213283i
$$217$$ −0.211055 0.365558i −0.0143274 0.0248157i
$$218$$ −1.45797 + 2.52528i −0.0987462 + 0.171033i
$$219$$ 5.81127 + 6.37133i 0.392689 + 0.430535i
$$220$$ 0.258376i 0.0174197i
$$221$$ 20.1842 0.0732075i 1.35774 0.00492447i
$$222$$ −10.7036 + 5.54059i −0.718379 + 0.371860i
$$223$$ −1.86235 6.95039i −0.124712 0.465432i 0.875117 0.483911i $$-0.160784\pi$$
−0.999829 + 0.0184790i $$0.994118\pi$$
$$224$$ −0.249572 0.144091i −0.0166752 0.00962745i
$$225$$ 1.32219 14.3497i 0.0881460 0.956649i
$$226$$ 7.36568 7.36568i 0.489958 0.489958i
$$227$$ −1.38733 + 5.17758i −0.0920803 + 0.343648i −0.996561 0.0828671i $$-0.973592\pi$$
0.904480 + 0.426515i $$0.140259\pi$$
$$228$$ −11.8952 + 2.60831i −0.787776 + 0.172740i
$$229$$ −8.24846 8.24846i −0.545074 0.545074i 0.379938 0.925012i $$-0.375945\pi$$
−0.925012 + 0.379938i $$0.875945\pi$$
$$230$$ −2.55359 + 1.47432i −0.168379 + 0.0972136i
$$231$$ 0.290633 + 0.0133612i 0.0191222 + 0.000879103i
$$232$$ −3.98942 + 1.06896i −0.261918 + 0.0701807i
$$233$$ 9.54763 0.625486 0.312743 0.949838i $$-0.398752\pi$$
0.312743 + 0.949838i $$0.398752\pi$$
$$234$$ 3.70955 10.1607i 0.242501 0.664224i
$$235$$ 2.33077 0.152042
$$236$$ 3.29111 0.881850i 0.214233 0.0574036i
$$237$$ 1.91858 + 0.0882024i 0.124625 + 0.00572936i
$$238$$ −1.39714 + 0.806638i −0.0905630 + 0.0522865i
$$239$$ 20.6375 + 20.6375i 1.33493 + 1.33493i 0.900895 + 0.434036i $$0.142911\pi$$
0.434036 + 0.900895i $$0.357089\pi$$
$$240$$ −0.749960 + 0.164448i −0.0484097 + 0.0106151i
$$241$$ −2.88685 + 10.7739i −0.185958 + 0.694006i 0.808465 + 0.588544i $$0.200299\pi$$
−0.994423 + 0.105462i $$0.966368\pi$$
$$242$$ −7.53794 + 7.53794i −0.484557 + 0.484557i
$$243$$ 15.1790 + 3.54930i 0.973734 + 0.227688i
$$244$$ −9.10286 5.25554i −0.582751 0.336451i
$$245$$ −0.793572 2.96165i −0.0506994 0.189213i
$$246$$ −11.7362 + 6.07508i −0.748270 + 0.387333i
$$247$$ 17.8601 17.9901i 1.13641 1.14468i
$$248$$ 1.46474i 0.0930111i
$$249$$ 13.5856 + 14.8950i 0.860954 + 0.943930i
$$250$$ 2.17283 3.76346i 0.137422 0.238022i
$$251$$ −2.23476 3.87071i −0.141057 0.244317i 0.786838 0.617159i $$-0.211717\pi$$
−0.927895 + 0.372842i $$0.878383\pi$$
$$252$$ 0.146196 + 0.852093i 0.00920948 + 0.0536768i
$$253$$ 3.74513 + 1.00350i 0.235454 + 0.0630898i
$$254$$ 0.233226 + 0.0624926i 0.0146339 + 0.00392114i
$$255$$ −1.30192 + 4.09620i −0.0815297 + 0.256514i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 5.97416 10.3475i 0.372658 0.645462i −0.617316 0.786715i $$-0.711780\pi$$
0.989973 + 0.141254i $$0.0451133\pi$$
$$258$$ 4.82162 4.39778i 0.300181 0.273794i
$$259$$ 2.00533i 0.124605i
$$260$$ 1.12603 1.13423i 0.0698336 0.0703420i
$$261$$ 10.1168 + 7.15363i 0.626211 + 0.442798i
$$262$$ 2.09396 + 7.81476i 0.129365 + 0.482797i
$$263$$ 2.38262 + 1.37560i 0.146918 + 0.0848234i 0.571657 0.820493i $$-0.306301\pi$$
−0.424739 + 0.905316i $$0.639634\pi$$
$$264$$ 0.850212 + 0.544406i 0.0523269 + 0.0335059i
$$265$$ 1.14338 1.14338i 0.0702371 0.0702371i
$$266$$ −0.524407 + 1.95711i −0.0321535 + 0.119998i
$$267$$ −5.22430 23.8253i −0.319722 1.45809i
$$268$$ 6.26033 + 6.26033i 0.382410 + 0.382410i
$$269$$ −5.40423 + 3.12013i −0.329502 + 0.190238i −0.655620 0.755091i $$-0.727593\pi$$
0.326118 + 0.945329i $$0.394259\pi$$
$$270$$ 1.81761 + 1.41480i 0.110616 + 0.0861017i
$$271$$ −21.6057 + 5.78922i −1.31245 + 0.351670i −0.846144 0.532954i $$-0.821082\pi$$
−0.466306 + 0.884624i $$0.654415\pi$$
$$272$$ −5.59813 −0.339437
$$273$$ −1.21760 1.32527i −0.0736927 0.0802087i
$$274$$ −0.0827063 −0.00499647
$$275$$ −2.70445 + 0.724656i −0.163085 + 0.0436984i
$$276$$ −0.529114 + 11.5093i −0.0318489 + 0.692777i
$$277$$ −4.84833 + 2.79919i −0.291308 + 0.168187i −0.638532 0.769596i $$-0.720458\pi$$
0.347224 + 0.937782i $$0.387125\pi$$
$$278$$ −4.41337 4.41337i −0.264697 0.264697i
$$279$$ −3.37917 + 2.80899i −0.202305 + 0.168170i
$$280$$ −0.0330626 + 0.123391i −0.00197587 + 0.00737404i
$$281$$ 8.82870 8.82870i 0.526676 0.526676i −0.392903 0.919580i $$-0.628529\pi$$
0.919580 + 0.392903i $$0.128529\pi$$
$$282$$ 4.91099 7.66961i 0.292445 0.456719i
$$283$$ −5.93983 3.42936i −0.353086 0.203854i 0.312958 0.949767i $$-0.398680\pi$$
−0.666044 + 0.745913i $$0.732014\pi$$
$$284$$ −3.98229 14.8621i −0.236305 0.881904i
$$285$$ 2.48152 + 4.79393i 0.146993 + 0.283968i
$$286$$ −2.10158 + 0.00762236i −0.124269 + 0.000450720i
$$287$$ 2.19878i 0.129790i
$$288$$ −1.03906 + 2.81431i −0.0612271 + 0.165835i
$$289$$ −7.16953 + 12.4180i −0.421737 + 0.730470i
$$290$$ 0.915400 + 1.58552i 0.0537541 + 0.0931049i
$$291$$ 4.43026 + 1.40810i 0.259707 + 0.0825445i
$$292$$ 4.80913 + 1.28860i 0.281433 + 0.0754098i
$$293$$ −26.4232 7.08007i −1.54366 0.413622i −0.616213 0.787579i $$-0.711334\pi$$
−0.927446 + 0.373957i $$0.878001\pi$$
$$294$$ −11.4177 3.62896i −0.665892 0.211645i
$$295$$ −0.755168 1.30799i −0.0439676 0.0761541i
$$296$$ −3.47929 + 6.02630i −0.202229 + 0.350272i
$$297$$ −0.374533 3.00547i −0.0217326 0.174395i
$$298$$ 14.5372i 0.842119i
$$299$$ −12.0671 20.7269i −0.697861 1.19867i
$$300$$ −3.82467 7.38870i −0.220818 0.426587i
$$301$$ −0.281026 1.04880i −0.0161981 0.0604521i
$$302$$ 7.84275 + 4.52801i 0.451300 + 0.260558i
$$303$$ −13.3007 + 20.7720i −0.764105 + 1.19332i
$$304$$ −4.97155 + 4.97155i −0.285138 + 0.285138i
$$305$$ −1.20592 + 4.50056i −0.0690508 + 0.257701i
$$306$$ 10.7357 + 12.9149i 0.613722 + 0.738297i
$$307$$ −15.4869 15.4869i −0.883883 0.883883i 0.110044 0.993927i $$-0.464901\pi$$
−0.993927 + 0.110044i $$0.964901\pi$$
$$308$$ 0.145470 0.0839871i 0.00828892 0.00478561i
$$309$$ 0.366617 7.97465i 0.0208561 0.453662i
$$310$$ −0.627161 + 0.168047i −0.0356204 + 0.00954445i
$$311$$ −31.8012 −1.80328 −0.901642 0.432484i $$-0.857637\pi$$
−0.901642 + 0.432484i $$0.857637\pi$$
$$312$$ −1.35971 6.09518i −0.0769784 0.345071i
$$313$$ −23.7424 −1.34200 −0.670999 0.741458i $$-0.734135\pi$$
−0.670999 + 0.741458i $$0.734135\pi$$
$$314$$ 9.86474 2.64325i 0.556700 0.149167i
$$315$$ 0.348070 0.160356i 0.0196115 0.00903506i
$$316$$ 0.960301 0.554430i 0.0540212 0.0311891i
$$317$$ −16.8936 16.8936i −0.948841 0.948841i 0.0499128 0.998754i $$-0.484106\pi$$
−0.998754 + 0.0499128i $$0.984106\pi$$
$$318$$ −1.35326 6.17152i −0.0758872 0.346082i
$$319$$ 0.623073 2.32534i 0.0348854 0.130194i
$$320$$ −0.313444 + 0.313444i −0.0175221 + 0.0175221i
$$321$$ −19.7092 12.6202i −1.10006 0.704390i
$$322$$ 1.66013 + 0.958476i 0.0925154 + 0.0534138i
$$323$$ 10.1870 + 38.0184i 0.566820 + 2.11540i
$$324$$ 8.48528 3.00000i 0.471405 0.166667i
$$325$$ 15.0303 + 8.60519i 0.833728 + 0.477330i
$$326$$ 13.8802i 0.768751i
$$327$$ 3.73152 3.40351i 0.206354 0.188214i
$$328$$ −3.81493 + 6.60765i −0.210644 + 0.364846i
$$329$$ −0.757633 1.31226i −0.0417697 0.0723472i
$$330$$ 0.135556 0.426496i 0.00746213 0.0234778i
$$331$$ 15.9259 + 4.26733i 0.875367 + 0.234554i 0.668407 0.743795i $$-0.266976\pi$$
0.206960 + 0.978349i $$0.433643\pi$$
$$332$$ 11.2428 + 3.01251i 0.617030 + 0.165333i
$$333$$ 20.5751 3.53013i 1.12751 0.193450i
$$334$$ 6.70590 + 11.6150i 0.366930 + 0.635542i
$$335$$ 1.96226 3.39874i 0.107210 0.185693i
$$336$$ 0.336367 + 0.368785i 0.0183503 + 0.0201189i
$$337$$ 3.24846i 0.176955i 0.996078 + 0.0884775i $$0.0282001\pi$$
−0.996078 + 0.0884775i $$0.971800\pi$$
$$338$$ 9.25883 + 9.12547i 0.503614 + 0.496360i
$$339$$ −16.0228 + 8.29400i −0.870238 + 0.450468i
$$340$$ 0.642265 + 2.39697i 0.0348317 + 0.129994i
$$341$$ 0.739381 + 0.426882i 0.0400397 + 0.0231169i
$$342$$ 21.0035 + 1.93527i 1.13574 + 0.104648i
$$343$$ −2.83592 + 2.83592i −0.153125 + 0.153125i
$$344$$ 0.975173 3.63939i 0.0525778 0.196223i
$$345$$ 4.98866 1.09389i 0.268580 0.0588930i
$$346$$ 0.779372 + 0.779372i 0.0418993 + 0.0418993i
$$347$$ 7.11715 4.10909i 0.382069 0.220587i −0.296649 0.954986i $$-0.595869\pi$$
0.678718 + 0.734399i $$0.262536\pi$$
$$348$$ 7.14608 + 0.328525i 0.383070 + 0.0176108i
$$349$$ 7.73980 2.07387i 0.414302 0.111012i −0.0456462 0.998958i $$-0.514535\pi$$
0.459948 + 0.887946i $$0.347868\pi$$
$$350$$ −1.38428 −0.0739928
$$351$$ −11.4541 + 14.8258i −0.611372 + 0.791343i
$$352$$ 0.582877 0.0310675
$$353$$ −2.70035 + 0.723557i −0.143725 + 0.0385111i −0.329964 0.943993i $$-0.607037\pi$$
0.186239 + 0.982504i $$0.440370\pi$$
$$354$$ −5.89523 0.271020i −0.313328 0.0144046i
$$355$$ −5.90666 + 3.41021i −0.313493 + 0.180995i
$$356$$ −9.95774 9.95774i −0.527759 0.527759i
$$357$$ 2.72943 0.598496i 0.144457 0.0316758i
$$358$$ 1.44823 5.40488i 0.0765416 0.285657i
$$359$$ −11.6531 + 11.6531i −0.615028 + 0.615028i −0.944252 0.329224i $$-0.893213\pi$$
0.329224 + 0.944252i $$0.393213\pi$$
$$360$$ 1.32422 + 0.122014i 0.0697926 + 0.00643072i
$$361$$ 26.3555 + 15.2163i 1.38713 + 0.800860i
$$362$$ −3.74479 13.9757i −0.196822 0.734548i
$$363$$ 16.3975 8.48796i 0.860645 0.445503i
$$364$$ −1.00462 0.265284i −0.0526562 0.0139047i
$$365$$ 2.20698i 0.115519i
$$366$$ 12.2686 + 13.4510i 0.641290 + 0.703096i
$$367$$ 18.5929 32.2039i 0.970544 1.68103i 0.276626 0.960978i $$-0.410784\pi$$
0.693918 0.720054i $$-0.255883\pi$$
$$368$$ 3.32595 + 5.76071i 0.173377 + 0.300298i
$$369$$ 22.5599 3.87067i 1.17442 0.201499i
$$370$$ 2.97947 + 0.798347i 0.154895 + 0.0415041i
$$371$$ −1.01540 0.272076i −0.0527171 0.0141255i
$$372$$ −0.768472 + 2.41782i −0.0398434 + 0.125358i
$$373$$ 3.94412 + 6.83141i 0.204219 + 0.353717i 0.949883 0.312604i $$-0.101201\pi$$
−0.745665 + 0.666321i $$0.767868\pi$$
$$374$$ 1.63151 2.82586i 0.0843635 0.146122i
$$375$$ −5.56114 + 5.07229i −0.287176 + 0.261932i
$$376$$ 5.25803i 0.271162i
$$377$$ −12.8693 + 7.49246i −0.662802 + 0.385881i
$$378$$ 0.205726 1.48323i 0.0105814 0.0762893i
$$379$$ 0.481911 + 1.79852i 0.0247541 + 0.0923837i 0.977198 0.212331i $$-0.0681055\pi$$
−0.952444 + 0.304715i $$0.901439\pi$$
$$380$$ 2.69906 + 1.55830i 0.138459 + 0.0799393i
$$381$$ −0.352194 0.225517i −0.0180435 0.0115536i
$$382$$ −4.72046 + 4.72046i −0.241520 + 0.241520i
$$383$$ −0.745523 + 2.78233i −0.0380945 + 0.142170i −0.982354 0.187032i $$-0.940113\pi$$
0.944259 + 0.329202i $$0.106780\pi$$
$$384$$ 0.370982 + 1.69185i 0.0189316 + 0.0863371i
$$385$$ −0.0526505 0.0526505i −0.00268332 0.00268332i
$$386$$ −5.27801 + 3.04726i −0.268643 + 0.155101i
$$387$$ −10.2662 + 4.72967i −0.521862 + 0.240423i
$$388$$ 2.59245 0.694645i 0.131612 0.0352653i
$$389$$ 23.4187 1.18738 0.593688 0.804695i $$-0.297671\pi$$
0.593688 + 0.804695i $$0.297671\pi$$
$$390$$ −2.45379 + 1.28148i −0.124253 + 0.0648903i
$$391$$ 37.2382 1.88322
$$392$$ −6.68126 + 1.79024i −0.337455 + 0.0904207i
$$393$$ 0.643539 13.9983i 0.0324623 0.706119i
$$394$$ −12.8070 + 7.39413i −0.645208 + 0.372511i
$$395$$ −0.347566 0.347566i −0.0174879 0.0174879i
$$396$$ −1.11781 1.34470i −0.0561719 0.0675738i
$$397$$ 4.76427 17.7805i 0.239112 0.892378i −0.737140 0.675740i $$-0.763824\pi$$
0.976252 0.216638i $$-0.0695092\pi$$
$$398$$ −10.9463 + 10.9463i −0.548686 + 0.548686i
$$399$$ 1.89242 2.95544i 0.0947397 0.147957i
$$400$$ −4.15996 2.40175i −0.207998 0.120088i
$$401$$ 1.75607 + 6.55376i 0.0876942 + 0.327279i 0.995811 0.0914383i $$-0.0291464\pi$$
−0.908117 + 0.418717i $$0.862480\pi$$
$$402$$ −7.04933 13.6183i −0.351589 0.679217i
$$403$$ −1.38537 5.09625i −0.0690100 0.253862i
$$404$$ 14.2406i 0.708497i
$$405$$ −2.25802 3.28898i −0.112202 0.163431i
$$406$$ 0.595115 1.03077i 0.0295351 0.0511562i
$$407$$ −2.02800 3.51260i −0.100524 0.174113i
$$408$$ 9.24072 + 2.93705i 0.457484 + 0.145405i
$$409$$ −28.2895 7.58014i −1.39882 0.374814i −0.520902 0.853617i $$-0.674404\pi$$
−0.877923 + 0.478803i $$0.841071\pi$$
$$410$$ 3.26690 + 0.875362i 0.161340 + 0.0432311i
$$411$$ 0.136522 + 0.0433917i 0.00673412 + 0.00214035i
$$412$$ −2.30452 3.99154i −0.113535 0.196649i
$$413$$ −0.490946 + 0.850344i −0.0241579 + 0.0418427i
$$414$$ 6.91171 18.7205i 0.339692 0.920064i
$$415$$ 5.15949i 0.253269i
$$416$$ −2.55874 2.54025i −0.125453 0.124546i
$$417$$ 4.96960 + 9.60053i 0.243362 + 0.470140i
$$418$$ −1.06067 3.95848i −0.0518791 0.193615i
$$419$$ −8.00397 4.62109i −0.391020 0.225755i 0.291582 0.956546i $$-0.405818\pi$$
−0.682602 + 0.730791i $$0.739152\pi$$
$$420$$ 0.119313 0.186333i 0.00582186 0.00909213i
$$421$$ −18.4490 + 18.4490i −0.899149 + 0.899149i −0.995361 0.0962115i $$-0.969327\pi$$
0.0962115 + 0.995361i $$0.469327\pi$$
$$422$$ 4.86953 18.1733i 0.237045 0.884664i
$$423$$ −12.1303 + 10.0835i −0.589796 + 0.490278i
$$424$$ −2.57937 2.57937i −0.125265 0.125265i
$$425$$ −23.2880 + 13.4453i −1.12963 + 0.652194i
$$426$$ −1.22388 + 26.6219i −0.0592973 + 1.28983i
$$427$$ 2.92588 0.783987i 0.141593 0.0379398i
$$428$$ −13.5120 −0.653127
$$429$$ 3.47304 + 1.09001i 0.167680 + 0.0526260i
$$430$$ −1.67017 −0.0805427
$$431$$ −21.6015 + 5.78811i −1.04051 + 0.278803i −0.738324 0.674446i $$-0.764383\pi$$
−0.302184 + 0.953249i $$0.597716\pi$$
$$432$$ 3.19168 4.10039i 0.153560 0.197280i
$$433$$ 3.41910 1.97402i 0.164311 0.0948652i −0.415589 0.909552i $$-0.636425\pi$$
0.579901 + 0.814687i $$0.303091\pi$$
$$434$$ 0.298477 + 0.298477i 0.0143274 + 0.0143274i
$$435$$ −0.679193 3.09745i −0.0325648 0.148511i
$$436$$ 0.754701 2.81658i 0.0361436 0.134890i
$$437$$ 33.0703 33.0703i 1.58197 1.58197i
$$438$$ −7.26228 4.65017i −0.347005 0.222194i
$$439$$ 15.8569 + 9.15500i 0.756810 + 0.436944i 0.828149 0.560508i $$-0.189394\pi$$
−0.0713394 + 0.997452i $$0.522727\pi$$
$$440$$ −0.0668726 0.249572i −0.00318803 0.0118979i
$$441$$ 16.9430 + 11.9805i 0.806810 + 0.570501i
$$442$$ −19.4775 + 5.29477i −0.926450 + 0.251847i
$$443$$ 5.86371i 0.278593i −0.990251 0.139297i $$-0.955516\pi$$
0.990251 0.139297i $$-0.0444841\pi$$
$$444$$ 8.90488 8.12210i 0.422607 0.385458i
$$445$$ −3.12119 + 5.40607i −0.147959 + 0.256272i
$$446$$ 3.59778 + 6.23155i 0.170360 + 0.295072i
$$447$$ −7.62693 + 23.9963i −0.360741 + 1.13499i
$$448$$ 0.278362 + 0.0745867i 0.0131513 + 0.00352389i
$$449$$ 27.5332 + 7.37750i 1.29937 + 0.348166i 0.841213 0.540704i $$-0.181842\pi$$
0.458160 + 0.888870i $$0.348509\pi$$
$$450$$ 2.43685 + 14.2030i 0.114874 + 0.669535i
$$451$$ −2.22364 3.85145i −0.104707 0.181358i
$$452$$ −5.20832 + 9.02108i −0.244979 + 0.424316i
$$453$$ −10.5703 11.5890i −0.496634 0.544498i
$$454$$ 5.36023i 0.251568i
$$455$$ 0.00167052 + 0.460585i 7.83154e−5 + 0.0215925i
$$456$$ 10.8148 5.59813i 0.506447 0.262156i
$$457$$ −4.96154 18.5167i −0.232091 0.866175i −0.979439 0.201742i $$-0.935340\pi$$
0.747348 0.664433i $$-0.231327\pi$$
$$458$$ 10.1023 + 5.83254i 0.472048 + 0.272537i
$$459$$ −10.9455 26.9509i −0.510892 1.25796i
$$460$$ 2.08500 2.08500i 0.0972136 0.0972136i
$$461$$ 7.67398 28.6397i 0.357413 1.33388i −0.520007 0.854162i $$-0.674071\pi$$
0.877421 0.479722i $$-0.159262\pi$$
$$462$$ −0.284188 + 0.0623154i −0.0132216 + 0.00289917i
$$463$$ 18.2554 + 18.2554i 0.848400 + 0.848400i 0.989934 0.141533i $$-0.0452032\pi$$
−0.141533 + 0.989934i $$0.545203\pi$$
$$464$$ 3.57681 2.06507i 0.166049 0.0958687i
$$465$$ 1.12341 + 0.0516463i 0.0520968 + 0.00239504i
$$466$$ −9.22231 + 2.47111i −0.427215 + 0.114472i
$$467$$ 32.4456 1.50140 0.750701 0.660642i $$-0.229716\pi$$
0.750701 + 0.660642i $$0.229716\pi$$
$$468$$ −0.953374 + 10.7746i −0.0440697 + 0.498054i
$$469$$ −2.55139 −0.117812
$$470$$ −2.25135 + 0.603246i −0.103847 + 0.0278257i
$$471$$ −17.6703 0.812354i −0.814205 0.0374313i
$$472$$ −2.95073 + 1.70360i −0.135818 + 0.0784147i
$$473$$ 1.55291 + 1.55291i 0.0714031 + 0.0714031i
$$474$$ −1.87603 + 0.411367i −0.0861690 + 0.0188947i
$$475$$ −8.74101 + 32.6219i −0.401065 + 1.49680i
$$476$$ 1.14076 1.14076i 0.0522865 0.0522865i
$$477$$ −1.00407 + 10.8972i −0.0459733 + 0.498948i
$$478$$ −25.2757 14.5929i −1.15608 0.667466i
$$479$$ 2.14571 + 8.00792i 0.0980402 + 0.365891i 0.997463 0.0711890i $$-0.0226793\pi$$
−0.899423 + 0.437080i $$0.856013\pi$$
$$480$$ 0.681844 0.352948i 0.0311218 0.0161098i
$$481$$ −6.40570 + 24.2580i −0.292075 + 1.10607i
$$482$$ 11.1539i 0.508048i
$$483$$ −2.23748 2.45312i −0.101809 0.111621i
$$484$$ 5.33013 9.23205i 0.242279 0.419639i
$$485$$ −0.594856 1.03032i −0.0270110 0.0467845i
$$486$$ −15.5804 + 0.500258i −0.706743 + 0.0226921i
$$487$$ −31.0359 8.31604i −1.40637 0.376836i −0.525742 0.850644i $$-0.676212\pi$$
−0.880628 + 0.473808i $$0.842879\pi$$
$$488$$ 10.1529 + 2.72047i 0.459601 + 0.123150i
$$489$$ −7.28219 + 22.9117i −0.329312 + 1.03610i
$$490$$ 1.53306 + 2.65534i 0.0692567 + 0.119956i
$$491$$ 13.2100 22.8803i 0.596157 1.03257i −0.397226 0.917721i $$-0.630027\pi$$
0.993383 0.114853i $$-0.0366397\pi$$
$$492$$ 9.76391 8.90562i 0.440191 0.401496i
$$493$$ 23.1211i 1.04132i
$$494$$ −12.5953 + 21.9996i −0.566690 + 0.989809i
$$495$$ −0.447520 + 0.632890i −0.0201145 + 0.0284463i
$$496$$ 0.379103 + 1.41483i 0.0170222 + 0.0635277i
$$497$$ 3.84001 + 2.21703i 0.172248 + 0.0994475i
$$498$$ −16.9778 10.8712i −0.760794 0.487150i
$$499$$ −9.27427 + 9.27427i −0.415173 + 0.415173i −0.883536 0.468363i $$-0.844844\pi$$
0.468363 + 0.883536i $$0.344844\pi$$
$$500$$ −1.12474 + 4.19759i −0.0503000 + 0.187722i
$$501$$ −4.97553 22.6908i −0.222290 1.01375i
$$502$$ 3.16043 + 3.16043i 0.141057 + 0.141057i
$$503$$ 26.4513 15.2717i 1.17941 0.680931i 0.223529 0.974697i $$-0.428242\pi$$
0.955877 + 0.293767i $$0.0949089\pi$$
$$504$$ −0.361752 0.785220i −0.0161137 0.0349765i
$$505$$ 6.09744 1.63380i 0.271332 0.0727033i
$$506$$ −3.87724 −0.172364
$$507$$ −10.4957 19.9208i −0.466131 0.884716i
$$508$$ −0.241453 −0.0107127
$$509$$ −23.0380 + 6.17302i −1.02114 + 0.273614i −0.730278 0.683150i $$-0.760610\pi$$
−0.290865 + 0.956764i $$0.593943\pi$$
$$510$$ 0.197388 4.29359i 0.00874050 0.190123i
$$511$$ −1.24256 + 0.717395i −0.0549678 + 0.0317357i
$$512$$ 0.707107 + 0.707107i 0.0312500 + 0.0312500i
$$513$$ −33.6548 14.2140i −1.48590 0.627562i
$$514$$ −3.09245 + 11.5412i −0.136402 + 0.509060i
$$515$$ −1.44467 + 1.44467i −0.0636599 + 0.0636599i
$$516$$ −3.51910 + 5.49585i −0.154920 + 0.241941i
$$517$$ 2.65418 + 1.53239i 0.116731 + 0.0673946i
$$518$$ −0.519017 1.93700i −0.0228043 0.0851069i
$$519$$ −0.877598 1.69539i −0.0385223 0.0744193i
$$520$$ −0.794103 + 1.38702i −0.0348237 + 0.0608249i
$$521$$ 42.5422i 1.86381i 0.362704 + 0.931904i $$0.381854\pi$$
−0.362704 + 0.931904i $$0.618146\pi$$
$$522$$ −11.6235 4.29146i −0.508748 0.187832i
$$523$$ 17.0400 29.5141i 0.745107 1.29056i −0.205037 0.978754i $$-0.565732\pi$$
0.950145 0.311809i $$-0.100935\pi$$
$$524$$ −4.04522 7.00652i −0.176716 0.306081i
$$525$$ 2.28500 + 0.726259i 0.0997257 + 0.0316965i
$$526$$ −2.65746 0.712065i −0.115871 0.0310475i
$$527$$ 7.92040 + 2.12227i 0.345018 + 0.0924473i
$$528$$ −0.962144 0.305805i −0.0418719 0.0133085i
$$529$$ −10.6239 18.4011i −0.461908 0.800048i
$$530$$ −0.808489 + 1.40034i −0.0351185 + 0.0608271i
$$531$$ 9.58895 + 3.54029i 0.416125 + 0.153635i
$$532$$ 2.02615i 0.0878449i
$$533$$ −7.02365 + 26.5981i −0.304228 + 1.15209i
$$534$$ 11.2127 + 21.6613i 0.485222 + 0.937378i
$$535$$ 1.55021 + 5.78547i 0.0670215 + 0.250128i
$$536$$ −7.66730 4.42672i −0.331177 0.191205i
$$537$$ −5.22623 + 8.16192i −0.225529 + 0.352213i
$$538$$ 4.41254 4.41254i 0.190238 0.190238i
$$539$$ 1.04349 3.89436i 0.0449463 0.167742i
$$540$$ −2.12185 0.896156i −0.0913100 0.0385644i
$$541$$ 18.5013 + 18.5013i 0.795434 + 0.795434i 0.982372 0.186938i $$-0.0598564\pi$$
−0.186938 + 0.982372i $$0.559856\pi$$
$$542$$ 19.3711 11.1839i 0.832060 0.480390i
$$543$$ −1.15089 + 25.0342i −0.0493895 + 1.07432i
$$544$$ 5.40738 1.44890i 0.231839 0.0621212i
$$545$$ −1.29257 −0.0553676
$$546$$ 1.51912 + 0.964969i 0.0650123 + 0.0412969i
$$547$$ 39.5058 1.68915 0.844573 0.535440i $$-0.179854\pi$$
0.844573 + 0.535440i $$0.179854\pi$$
$$548$$ 0.0798882 0.0214060i 0.00341265 0.000914418i
$$549$$ −13.1945 28.6400i −0.563128 1.22233i
$$550$$ 2.42475 1.39993i 0.103391 0.0596931i
$$551$$ −20.5332 20.5332i −0.874746 0.874746i
$$552$$ −2.46773 11.2540i −0.105034 0.479004i
$$553$$ −0.0827063 + 0.308664i −0.00351703 + 0.0131257i
$$554$$ 3.95865 3.95865i 0.168187 0.168187i
$$555$$ −4.49930 2.88099i −0.190985 0.122291i
$$556$$ 5.40526 + 3.12073i 0.229234 + 0.132348i
$$557$$ 4.08768 + 15.2554i 0.173201 + 0.646394i 0.996851 + 0.0792958i $$0.0252672\pi$$
−0.823650 + 0.567098i $$0.808066\pi$$
$$558$$ 2.53700 3.58786i 0.107400 0.151886i
$$559$$ −0.0492717 13.5848i −0.00208397 0.574577i
$$560$$ 0.127744i 0.00539817i
$$561$$ −4.17568 + 3.80862i −0.176298 + 0.160800i
$$562$$ −6.24284 + 10.8129i −0.263338 + 0.456115i
$$563$$ 10.6906 + 18.5166i 0.450555 + 0.780383i 0.998421 0.0561827i $$-0.0178929\pi$$
−0.547866 + 0.836566i $$0.684560\pi$$
$$564$$ −2.75862 + 8.67933i −0.116159 + 0.365466i
$$565$$ 4.46012 + 1.19509i 0.187639 + 0.0502777i
$$566$$ 6.62502 + 1.77517i 0.278470 + 0.0746159i
$$567$$ −1.11776 + 2.34041i −0.0469416 + 0.0982880i
$$568$$ 7.69319 + 13.3250i 0.322799 + 0.559105i
$$569$$ 14.5203 25.1500i 0.608725 1.05434i −0.382726 0.923862i $$-0.625015\pi$$
0.991451 0.130480i $$-0.0416519\pi$$
$$570$$ −3.63773 3.98832i −0.152368 0.167052i
$$571$$ 9.91137i 0.414778i −0.978259 0.207389i $$-0.933503\pi$$
0.978259 0.207389i $$-0.0664966\pi$$
$$572$$ 2.02800 0.551292i 0.0847948 0.0230507i
$$573$$ 10.2685 5.31539i 0.428974 0.222054i
$$574$$ −0.569086 2.12386i −0.0237532 0.0886481i
$$575$$ 27.6716 + 15.9762i 1.15399 + 0.666254i
$$576$$ 0.275255 2.98735i 0.0114690 0.124473i
$$577$$ −4.91283 + 4.91283i −0.204524 + 0.204524i −0.801935 0.597411i $$-0.796196\pi$$
0.597411 + 0.801935i $$0.296196\pi$$
$$578$$ 3.71122 13.8505i 0.154366 0.576104i
$$579$$ 10.3110 2.26095i 0.428512 0.0939621i
$$580$$ −1.29457 1.29457i −0.0537541 0.0537541i
$$581$$ −2.90488 + 1.67713i −0.120515 + 0.0695791i
$$582$$ −4.64375 0.213486i −0.192490 0.00884929i
$$583$$ 2.05376 0.550304i 0.0850581 0.0227913i
$$584$$ −4.97878 −0.206023
$$585$$ 4.72275 0.827940i 0.195262 0.0342311i
$$586$$ 27.3553 1.13004
$$587$$ −23.2001 + 6.21644i −0.957569 + 0.256580i −0.703571 0.710625i $$-0.748412\pi$$
−0.253998 + 0.967205i $$0.581746\pi$$
$$588$$ 11.9679 + 0.550197i 0.493547 + 0.0226897i
$$589$$ 8.91863 5.14917i 0.367486 0.212168i
$$590$$ 1.06797 + 1.06797i 0.0439676 + 0.0439676i
$$591$$ 25.0196 5.48618i 1.02917 0.225671i
$$592$$ 1.80101 6.72147i 0.0740211 0.276251i
$$593$$ −22.0744 + 22.0744i −0.906489 + 0.906489i −0.995987 0.0894984i $$-0.971474\pi$$
0.0894984 + 0.995987i $$0.471474\pi$$
$$594$$ 1.13964 + 2.80613i 0.0467602 + 0.115137i
$$595$$ −0.619319 0.357564i −0.0253896 0.0146587i
$$596$$ 3.76251 + 14.0419i 0.154119 + 0.575178i
$$597$$ 23.8117 12.3258i 0.974548 0.504463i
$$598$$ 17.0205 + 16.8975i 0.696019 + 0.690989i
$$599$$ 35.2538i 1.44043i −0.693750 0.720216i $$-0.744043\pi$$
0.693750 0.720216i $$-0.255957\pi$$
$$600$$ 5.60669 + 6.14704i 0.228892 + 0.250952i
$$601$$ −10.0883 + 17.4735i −0.411512 + 0.712759i −0.995055 0.0993227i $$-0.968332\pi$$
0.583544 + 0.812082i $$0.301666\pi$$
$$602$$ 0.542901 + 0.940332i 0.0221270 + 0.0383251i
$$603$$ 4.49140 + 26.1778i 0.182904 + 1.06604i
$$604$$ −8.74745 2.34387i −0.355929 0.0953708i
$$605$$ −4.56443 1.22304i −0.185570 0.0497234i
$$606$$ 7.47130 23.5067i 0.303501 0.954894i
$$607$$ 2.42837 + 4.20607i 0.0985647 + 0.170719i 0.911091 0.412206i $$-0.135242\pi$$
−0.812526 + 0.582925i $$0.801908\pi$$
$$608$$ 3.51542 6.08888i 0.142569 0.246937i
$$609$$ −1.52314 + 1.38925i −0.0617206 + 0.0562951i
$$610$$ 4.65932i 0.188650i
$$611$$ −4.97311 18.2942i −0.201190 0.740105i
$$612$$ −13.7126 9.69625i −0.554297 0.391948i
$$613$$ −0.235455 0.878731i −0.00950994 0.0354916i 0.961008 0.276521i $$-0.0891816\pi$$
−0.970518 + 0.241030i $$0.922515\pi$$
$$614$$ 18.9675 + 10.9509i 0.765465 + 0.441941i
$$615$$ −4.93334 3.15891i −0.198932 0.127380i
$$616$$ −0.118776 + 0.118776i −0.00478561 + 0.00478561i
$$617$$ −11.6445 + 43.4580i −0.468792 + 1.74956i 0.175210 + 0.984531i $$0.443940\pi$$
−0.644002 + 0.765024i $$0.722727\pi$$
$$618$$ 1.70987 + 7.79781i 0.0687809 + 0.313674i
$$619$$ 11.7433 + 11.7433i 0.472003 + 0.472003i 0.902562 0.430559i $$-0.141684\pi$$
−0.430559 + 0.902562i $$0.641684\pi$$
$$620$$ 0.562298 0.324643i 0.0225824 0.0130380i
$$621$$ −21.2307 + 27.2754i −0.851959 + 1.09452i
$$622$$ 30.7176 8.23077i 1.23167 0.330024i
$$623$$ 4.05827 0.162591
$$624$$ 2.89093 + 5.53557i 0.115730 + 0.221600i
$$625$$ −22.0912 −0.883648
$$626$$ 22.9334 6.14498i 0.916602 0.245603i
$$627$$ −0.325977 + 7.09066i −0.0130183 + 0.283174i
$$628$$ −8.84449 + 5.10637i −0.352933 + 0.203766i
$$629$$ −27.5454 27.5454i −1.09831 1.09831i
$$630$$ −0.294706 + 0.244980i −0.0117414 + 0.00976022i
$$631$$ 9.44656 35.2551i 0.376062 1.40348i −0.475725 0.879594i $$-0.657814\pi$$
0.851787 0.523888i $$-0.175519\pi$$
$$632$$ −0.784083 + 0.784083i −0.0311891 + 0.0311891i
$$633$$ −17.5726 + 27.4436i −0.698449 + 1.09078i
$$634$$ 20.6904 + 11.9456i 0.821720 + 0.474420i
$$635$$ 0.0277015 + 0.103384i 0.00109930 + 0.00410265i
$$636$$ 2.90446 + 5.61098i 0.115169 + 0.222490i
$$637$$ −21.5528 + 12.5480i −0.853953 + 0.497168i
$$638$$ 2.40737i 0.0953087i
$$639$$ 15.9873 43.3021i 0.632450 1.71300i
$$640$$ 0.221638 0.383889i 0.00876103 0.0151745i
$$641$$ 0.424453 + 0.735175i 0.0167649 + 0.0290377i 0.874286 0.485411i $$-0.161330\pi$$
−0.857521 + 0.514449i $$0.827997\pi$$
$$642$$ 22.3040 + 7.08904i 0.880269 + 0.279782i
$$643$$ −16.6824 4.47005i −0.657891 0.176281i −0.0855970 0.996330i $$-0.527280\pi$$
−0.572294 + 0.820048i $$0.693946\pi$$
$$644$$ −1.85163 0.496144i −0.0729646 0.0195508i
$$645$$ 2.75692 + 0.876250i 0.108553 + 0.0345023i
$$646$$ −19.6798 34.0864i −0.774290 1.34111i
$$647$$ −7.87623 + 13.6420i −0.309646 + 0.536323i −0.978285 0.207264i $$-0.933544\pi$$
0.668639 + 0.743588i $$0.266877\pi$$
$$648$$ −7.41970 + 5.09393i −0.291473 + 0.200108i
$$649$$ 1.98598i 0.0779567i
$$650$$ −16.7453 4.42186i −0.656804 0.173439i
$$651$$ −0.336095 0.649285i −0.0131726 0.0254475i
$$652$$ 3.59245 + 13.4072i 0.140691 + 0.525067i
$$653$$ −21.3400 12.3207i −0.835099 0.482145i 0.0204964 0.999790i $$-0.493475\pi$$
−0.855595 + 0.517645i $$0.826809\pi$$
$$654$$ −2.72348 + 4.25332i −0.106497 + 0.166318i
$$655$$ −2.53590 + 2.53590i −0.0990857 + 0.0990857i
$$656$$ 1.97475 7.36988i 0.0771011 0.287745i
$$657$$ 9.54799 + 11.4861i 0.372503 + 0.448115i
$$658$$ 1.07145 + 1.07145i 0.0417697 + 0.0417697i
$$659$$ 15.3411 8.85721i 0.597606 0.345028i −0.170493 0.985359i $$-0.554536\pi$$
0.768099 + 0.640331i $$0.221203\pi$$
$$660$$ −0.0205521 + 0.447048i −0.000799988 + 0.0174013i
$$661$$ −9.15665 + 2.45352i −0.356153 + 0.0954308i −0.432459 0.901654i $$-0.642354\pi$$
0.0763064 + 0.997084i $$0.475687\pi$$
$$662$$ −16.4877 −0.640813
$$663$$ 34.9290 + 1.47885i 1.35653 + 0.0574339i
$$664$$ −11.6394 −0.451697
$$665$$ −0.867544 + 0.232458i −0.0336419 + 0.00901432i
$$666$$ −18.9603 + 8.73506i −0.734698 + 0.338477i
$$667$$ −23.7926 + 13.7367i −0.921253 + 0.531886i
$$668$$ −9.48357 9.48357i −0.366930 0.366930i
$$669$$ −2.66943 12.1739i −0.103206 0.470669i
$$670$$ −1.01574 + 3.79080i −0.0392415 + 0.146451i
$$671$$ −4.33221 + 4.33221i −0.167243 + 0.167243i
$$672$$ −0.420354 0.269161i −0.0162155 0.0103831i
$$673$$ −0.150089 0.0866536i −0.00578549 0.00334025i 0.497104 0.867691i $$-0.334397\pi$$
−0.502890 + 0.864350i $$0.667730\pi$$
$$674$$ −0.840764 3.13777i −0.0323850 0.120862i
$$675$$ 3.42911 24.7231i 0.131986 0.951591i
$$676$$ −11.3052 6.41816i −0.434815 0.246852i
$$677$$ 2.12205i 0.0815568i 0.999168 + 0.0407784i $$0.0129838\pi$$
−0.999168 + 0.0407784i $$0.987016\pi$$
$$678$$ 13.3302 12.1584i 0.511942 0.466940i
$$679$$ −0.386725 + 0.669827i −0.0148411 + 0.0257056i
$$680$$ −1.24076 2.14906i −0.0475810 0.0824127i
$$681$$ −2.81223 + 8.84802i −0.107765 + 0.339057i
$$682$$ −0.824672 0.220970i −0.0315783 0.00846139i
$$683$$ −30.9953 8.30516i −1.18600 0.317788i −0.388697 0.921365i $$-0.627075\pi$$
−0.797305 + 0.603577i $$0.793742\pi$$
$$684$$ −20.7888 + 3.56679i −0.794878 + 0.136379i
$$685$$ −0.0183309 0.0317500i −0.000700388 0.00121311i
$$686$$ 2.00530 3.47328i 0.0765627 0.132611i
$$687$$ −13.6156 14.9278i −0.519466 0.569531i
$$688$$ 3.76778i 0.143645i
$$689$$ −11.4140 6.53478i −0.434838 0.248955i
$$690$$ −4.53556 + 2.34778i −0.172666 + 0.0893783i
$$691$$ 7.89090 + 29.4492i 0.300184 + 1.12030i 0.937012 + 0.349296i $$0.113579\pi$$
−0.636829 + 0.771005i $$0.719754\pi$$
$$692$$ −0.954532 0.551099i −0.0362858 0.0209496i
$$693$$ 0.501797 + 0.0462358i 0.0190617 + 0.00175635i
$$694$$ −5.81113 + 5.81113i −0.220587 + 0.220587i
$$695$$ 0.716073 2.67242i 0.0271622 0.101371i
$$696$$ −6.98761 + 1.53221i −0.264865 + 0.0580783i
$$697$$ −30.2026 30.2026i −1.14401 1.14401i
$$698$$ −6.93931 + 4.00641i −0.262657 + 0.151645i
$$699$$ 16.5195 + 0.759450i 0.624826 + 0.0287250i
$$700$$ 1.33711 0.358278i 0.0505381 0.0135416i
$$701$$ −1.23549 −0.0466638 −0.0233319 0.999728i $$-0.507427\pi$$
−0.0233319 + 0.999728i $$0.507427\pi$$
$$702$$ 7.22656 17.2852i 0.272749 0.652386i
$$703$$ −48.9246 −1.84523
$$704$$ −0.563016 + 0.150860i −0.0212195 + 0.00568574i
$$705$$ 4.03274 + 0.185397i 0.151882 + 0.00698244i
$$706$$ 2.42107 1.39781i 0.0911182 0.0526071i
$$707$$ −2.90188 2.90188i −0.109136 0.109136i
$$708$$ 5.76450 1.26401i 0.216643 0.0475045i
$$709$$ 4.09728 15.2913i 0.153877 0.574276i −0.845322 0.534257i $$-0.820592\pi$$
0.999199 0.0400188i $$-0.0127418\pi$$
$$710$$ 4.82277 4.82277i 0.180995 0.180995i
$$711$$ 3.31255 + 0.305220i 0.124230 + 0.0114466i
$$712$$ 12.1957 + 7.04118i 0.457053 + 0.263879i
$$713$$ −2.52175 9.41131i −0.0944404 0.352456i
$$714$$ −2.48152 + 1.28453i −0.0928686 + 0.0480723i
$$715$$ −0.468717 0.805084i −0.0175290 0.0301084i
$$716$$ 5.59555i 0.209115i
$$717$$ 34.0660 + 37.3491i 1.27222 + 1.39483i
$$718$$ 8.24000 14.2721i 0.307514 0.532630i
$$719$$ 1.55033 + 2.68525i 0.0578176 + 0.100143i 0.893486 0.449092i $$-0.148252\pi$$
−0.835668 + 0.549235i $$0.814919\pi$$
$$720$$ −1.31068 + 0.224877i −0.0488461 + 0.00838067i
$$721$$ 1.28298 + 0.343773i 0.0477806 + 0.0128028i
$$722$$ −29.3957 7.87656i −1.09400 0.293135i
$$723$$ −5.85188 + 18.4116i −0.217634 + 0.684734i
$$724$$ 7.23437 + 12.5303i 0.268863 + 0.465685i
$$725$$ 9.91959 17.1812i 0.368404 0.638095i
$$726$$ −13.6419 + 12.4427i −0.506299 + 0.461793i
$$727$$ 20.0877i 0.745011i 0.928030 + 0.372506i $$0.121501\pi$$
−0.928030 + 0.372506i $$0.878499\pi$$
$$728$$ 1.03904 0.00376858i 0.0385096 0.000139673i
$$729$$ 25.9808 + 7.34847i 0.962250 + 0.272166i
$$730$$ 0.571208 + 2.13178i 0.0211414 + 0.0789006i
$$731$$ 18.2667 + 10.5463i 0.675617 + 0.390067i
$$732$$ −15.3319 9.81733i −0.566685 0.362859i
$$733$$ 35.4832 35.4832i 1.31060 1.31060i 0.389628 0.920972i $$-0.372604\pi$$
0.920972 0.389628i $$-0.127396\pi$$
$$734$$ −9.62442 + 35.9188i −0.355244 + 1.32579i
$$735$$ −1.13748 5.18744i −0.0419565 0.191342i
$$736$$ −4.70360 4.70360i −0.173377 0.173377i
$$737$$ 4.46910 2.58023i 0.164621 0.0950442i
$$738$$ −20.7894 + 9.57772i −0.765269 + 0.352561i
$$739$$ −22.4899 + 6.02615i −0.827305 + 0.221676i −0.647538 0.762034i $$-0.724201\pi$$
−0.179767 + 0.983709i $$0.557534\pi$$
$$740$$ −3.08458 −0.113391
$$741$$ 32.3329 29.7062i 1.18778 1.09129i
$$742$$ 1.05122 0.0385916
$$743$$ 25.8872 6.93645i 0.949709 0.254474i 0.249470 0.968382i $$-0.419743\pi$$
0.700239 + 0.713909i $$0.253077\pi$$
$$744$$ 0.116510 2.53433i 0.00427147 0.0929129i
$$745$$ 5.58069 3.22201i 0.204461 0.118045i
$$746$$ −5.57782 5.57782i −0.204219 0.204219i
$$747$$ 22.3214 + 26.8522i 0.816696 + 0.982472i
$$748$$ −0.844533 + 3.15184i −0.0308792 + 0.115243i
$$749$$ 2.75341 2.75341i 0.100607 0.100607i
$$750$$ 4.05885 6.33879i 0.148208 0.231460i
$$751$$ −15.4295 8.90822i −0.563030 0.325065i 0.191331 0.981526i $$-0.438720\pi$$
−0.754361 + 0.656460i $$0.772053\pi$$
$$752$$ 1.36088 + 5.07887i 0.0496262 + 0.185207i
$$753$$ −3.55874 6.87496i −0.129688 0.250537i
$$754$$ 10.4916 10.5680i 0.382081 0.384863i
$$755$$ 4.01433i 0.146096i
$$756$$ 0.185173 + 1.48594i 0.00673469 + 0.0540431i
$$757$$ −12.3906 + 21.4612i −0.450345 + 0.780020i −0.998407 0.0564171i $$-0.982032\pi$$
0.548062 + 0.836438i $$0.315366\pi$$
$$758$$ −0.930981 1.61251i −0.0338148 0.0585689i
$$759$$ 6.40009 + 2.03419i 0.232308 + 0.0738363i
$$760$$ −3.01041 0.806638i −0.109199 0.0292598i
$$761$$ 14.6883 + 3.93572i 0.532451 + 0.142670i 0.515020 0.857178i $$-0.327785\pi$$
0.0174313 + 0.999848i $$0.494451\pi$$
$$762$$ 0.398562 + 0.126678i 0.0144384 + 0.00458905i
$$763$$ 0.420159 + 0.727738i 0.0152108 + 0.0263459i
$$764$$ 3.33787 5.78136i 0.120760 0.209162i
$$765$$ −2.57845 + 6.98378i −0.0932239 + 0.252499i
$$766$$ 2.88048i 0.104076i
$$767$$ −8.65515 + 8.71816i −0.312519 + 0.314794i
$$768$$ −0.796225 1.53819i −0.0287313 0.0555046i
$$769$$ 4.74330 + 17.7022i 0.171048 + 0.638359i 0.997191 + 0.0748992i $$0.0238635\pi$$
−0.826143 + 0.563460i $$0.809470\pi$$