# Properties

 Label 483.2.h.c.160.8 Level $483$ Weight $2$ Character 483.160 Analytic conductor $3.857$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$483 = 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 483.h (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.85677441763$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 17 x^{10} + 92 x^{8} + 180 x^{6} + 92 x^{4} + 17 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 160.8 Root $$-0.466018i$$ of defining polynomial Character $$\chi$$ $$=$$ 483.160 Dual form 483.2.h.c.160.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.17819 q^{2} +1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} +1.17819i q^{6} +(2.04406 + 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+1.17819 q^{2} +1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} +1.17819i q^{6} +(2.04406 + 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +1.97916 q^{10} +3.72389i q^{11} -0.611859i q^{12} +0.821806i q^{13} +(2.40830 + 1.97916i) q^{14} +1.67982i q^{15} -2.40191 q^{16} +1.97916 q^{17} -1.17819 q^{18} +3.72389 q^{19} -1.02781 q^{20} +(-1.67982 + 2.04406i) q^{21} +4.38746i q^{22} +(4.61186 - 1.31558i) q^{23} -3.07728i q^{24} -2.17819 q^{25} +0.968247i q^{26} -1.00000i q^{27} +(-1.25068 - 1.02781i) q^{28} -5.79005 q^{29} +1.97916i q^{30} -0.566335i q^{31} +3.32464 q^{32} -3.72389 q^{33} +2.33183 q^{34} +(3.43366 + 2.82181i) q^{35} +0.611859 q^{36} +1.25068i q^{37} +4.38746 q^{38} -0.821806 q^{39} -5.16928 q^{40} +5.00000i q^{41} +(-1.97916 + 2.40830i) q^{42} -7.01863i q^{43} -2.27849i q^{44} -1.67982 q^{45} +(5.43366 - 1.55001i) q^{46} -5.14644i q^{47} -2.40191i q^{48} +(1.35639 + 6.86733i) q^{49} -2.56634 q^{50} +1.97916i q^{51} -0.502829i q^{52} -0.0649054i q^{53} -1.17819i q^{54} +6.25547i q^{55} +(-6.29015 - 5.16928i) q^{56} +3.72389i q^{57} -6.82181 q^{58} -11.0455i q^{59} -1.02781i q^{60} +9.36202 q^{61} -0.667253i q^{62} +(-2.04406 - 1.67982i) q^{63} +8.72089 q^{64} +1.38049i q^{65} -4.38746 q^{66} -5.03947i q^{67} -1.21096 q^{68} +(1.31558 + 4.61186i) q^{69} +(4.04552 + 3.32464i) q^{70} -6.40191 q^{71} +3.07728 q^{72} -15.8811i q^{73} +1.47354i q^{74} -2.17819i q^{75} -2.27849 q^{76} +(-6.25547 + 7.61186i) q^{77} -0.968247 q^{78} -17.6032i q^{79} -4.03479 q^{80} +1.00000 q^{81} +5.89097i q^{82} -9.29712 q^{83} +(1.02781 - 1.25068i) q^{84} +3.32464 q^{85} -8.26931i q^{86} -5.79005i q^{87} -11.4594i q^{88} -11.8352 q^{89} -1.97916 q^{90} +(-1.38049 + 1.67982i) q^{91} +(-2.82181 + 0.804951i) q^{92} +0.566335 q^{93} -6.06351i q^{94} +6.25547 q^{95} +3.32464i q^{96} +14.9720 q^{97} +(1.59809 + 8.09105i) q^{98} -3.72389i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + O(q^{10})$$ $$12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} + 20 q^{71} + 24 q^{72} - 52 q^{77} + 52 q^{78} + 12 q^{81} - 44 q^{85} - 44 q^{92} + 40 q^{93} + 52 q^{95} + 116 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$$.

 $$n$$ $$323$$ $$346$$ $$442$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.17819 0.833109 0.416555 0.909111i $$-0.363238\pi$$
0.416555 + 0.909111i $$0.363238\pi$$
$$3$$ 1.00000i 0.577350i
$$4$$ −0.611859 −0.305929
$$5$$ 1.67982 0.751240 0.375620 0.926774i $$-0.377430\pi$$
0.375620 + 0.926774i $$0.377430\pi$$
$$6$$ 1.17819i 0.480996i
$$7$$ 2.04406 + 1.67982i 0.772583 + 0.634913i
$$8$$ −3.07728 −1.08798
$$9$$ −1.00000 −0.333333
$$10$$ 1.97916 0.625865
$$11$$ 3.72389i 1.12279i 0.827547 + 0.561397i $$0.189736\pi$$
−0.827547 + 0.561397i $$0.810264\pi$$
$$12$$ 0.611859i 0.176628i
$$13$$ 0.821806i 0.227928i 0.993485 + 0.113964i $$0.0363548\pi$$
−0.993485 + 0.113964i $$0.963645\pi$$
$$14$$ 2.40830 + 1.97916i 0.643646 + 0.528952i
$$15$$ 1.67982i 0.433728i
$$16$$ −2.40191 −0.600478
$$17$$ 1.97916 0.480016 0.240008 0.970771i $$-0.422850\pi$$
0.240008 + 0.970771i $$0.422850\pi$$
$$18$$ −1.17819 −0.277703
$$19$$ 3.72389 0.854318 0.427159 0.904176i $$-0.359514\pi$$
0.427159 + 0.904176i $$0.359514\pi$$
$$20$$ −1.02781 −0.229826
$$21$$ −1.67982 + 2.04406i −0.366567 + 0.446051i
$$22$$ 4.38746i 0.935410i
$$23$$ 4.61186 1.31558i 0.961639 0.274318i
$$24$$ 3.07728i 0.628146i
$$25$$ −2.17819 −0.435639
$$26$$ 0.968247i 0.189889i
$$27$$ 1.00000i 0.192450i
$$28$$ −1.25068 1.02781i −0.236356 0.194239i
$$29$$ −5.79005 −1.07519 −0.537593 0.843205i $$-0.680666\pi$$
−0.537593 + 0.843205i $$0.680666\pi$$
$$30$$ 1.97916i 0.361343i
$$31$$ 0.566335i 0.101717i −0.998706 0.0508584i $$-0.983804\pi$$
0.998706 0.0508584i $$-0.0161957\pi$$
$$32$$ 3.32464 0.587718
$$33$$ −3.72389 −0.648245
$$34$$ 2.33183 0.399906
$$35$$ 3.43366 + 2.82181i 0.580395 + 0.476972i
$$36$$ 0.611859 0.101976
$$37$$ 1.25068i 0.205610i 0.994702 + 0.102805i $$0.0327818\pi$$
−0.994702 + 0.102805i $$0.967218\pi$$
$$38$$ 4.38746 0.711740
$$39$$ −0.821806 −0.131594
$$40$$ −5.16928 −0.817335
$$41$$ 5.00000i 0.780869i 0.920631 + 0.390434i $$0.127675\pi$$
−0.920631 + 0.390434i $$0.872325\pi$$
$$42$$ −1.97916 + 2.40830i −0.305391 + 0.371609i
$$43$$ 7.01863i 1.07033i −0.844747 0.535165i $$-0.820249\pi$$
0.844747 0.535165i $$-0.179751\pi$$
$$44$$ 2.27849i 0.343496i
$$45$$ −1.67982 −0.250413
$$46$$ 5.43366 1.55001i 0.801150 0.228537i
$$47$$ 5.14644i 0.750686i −0.926886 0.375343i $$-0.877525\pi$$
0.926886 0.375343i $$-0.122475\pi$$
$$48$$ 2.40191i 0.346686i
$$49$$ 1.35639 + 6.86733i 0.193770 + 0.981047i
$$50$$ −2.56634 −0.362935
$$51$$ 1.97916i 0.277138i
$$52$$ 0.502829i 0.0697299i
$$53$$ 0.0649054i 0.00891544i −0.999990 0.00445772i $$-0.998581\pi$$
0.999990 0.00445772i $$-0.00141894\pi$$
$$54$$ 1.17819i 0.160332i
$$55$$ 6.25547i 0.843487i
$$56$$ −6.29015 5.16928i −0.840556 0.690774i
$$57$$ 3.72389i 0.493241i
$$58$$ −6.82181 −0.895747
$$59$$ 11.0455i 1.43800i −0.695008 0.719002i $$-0.744599\pi$$
0.695008 0.719002i $$-0.255401\pi$$
$$60$$ 1.02781i 0.132690i
$$61$$ 9.36202 1.19868 0.599342 0.800493i $$-0.295429\pi$$
0.599342 + 0.800493i $$0.295429\pi$$
$$62$$ 0.667253i 0.0847412i
$$63$$ −2.04406 1.67982i −0.257528 0.211638i
$$64$$ 8.72089 1.09011
$$65$$ 1.38049i 0.171229i
$$66$$ −4.38746 −0.540059
$$67$$ 5.03947i 0.615669i −0.951440 0.307835i $$-0.900396\pi$$
0.951440 0.307835i $$-0.0996043\pi$$
$$68$$ −1.21096 −0.146851
$$69$$ 1.31558 + 4.61186i 0.158378 + 0.555203i
$$70$$ 4.04552 + 3.32464i 0.483533 + 0.397370i
$$71$$ −6.40191 −0.759767 −0.379884 0.925034i $$-0.624036\pi$$
−0.379884 + 0.925034i $$0.624036\pi$$
$$72$$ 3.07728 0.362661
$$73$$ 15.8811i 1.85874i −0.369147 0.929371i $$-0.620350\pi$$
0.369147 0.929371i $$-0.379650\pi$$
$$74$$ 1.47354i 0.171296i
$$75$$ 2.17819i 0.251516i
$$76$$ −2.27849 −0.261361
$$77$$ −6.25547 + 7.61186i −0.712877 + 0.867452i
$$78$$ −0.968247 −0.109632
$$79$$ 17.6032i 1.98051i −0.139256 0.990256i $$-0.544471\pi$$
0.139256 0.990256i $$-0.455529\pi$$
$$80$$ −4.03479 −0.451103
$$81$$ 1.00000 0.111111
$$82$$ 5.89097i 0.650549i
$$83$$ −9.29712 −1.02049 −0.510246 0.860029i $$-0.670446\pi$$
−0.510246 + 0.860029i $$0.670446\pi$$
$$84$$ 1.02781 1.25068i 0.112144 0.136460i
$$85$$ 3.32464 0.360607
$$86$$ 8.26931i 0.891702i
$$87$$ 5.79005i 0.620759i
$$88$$ 11.4594i 1.22158i
$$89$$ −11.8352 −1.25453 −0.627266 0.778805i $$-0.715826\pi$$
−0.627266 + 0.778805i $$0.715826\pi$$
$$90$$ −1.97916 −0.208622
$$91$$ −1.38049 + 1.67982i −0.144715 + 0.176093i
$$92$$ −2.82181 + 0.804951i −0.294194 + 0.0839219i
$$93$$ 0.566335 0.0587262
$$94$$ 6.06351i 0.625403i
$$95$$ 6.25547 0.641798
$$96$$ 3.32464i 0.339319i
$$97$$ 14.9720 1.52018 0.760089 0.649819i $$-0.225155\pi$$
0.760089 + 0.649819i $$0.225155\pi$$
$$98$$ 1.59809 + 8.09105i 0.161431 + 0.817319i
$$99$$ 3.72389i 0.374265i
$$100$$ 1.33275 0.133275
$$101$$ 12.2692i 1.22084i −0.792080 0.610418i $$-0.791002\pi$$
0.792080 0.610418i $$-0.208998\pi$$
$$102$$ 2.33183i 0.230886i
$$103$$ 8.33421 0.821194 0.410597 0.911817i $$-0.365320\pi$$
0.410597 + 0.911817i $$0.365320\pi$$
$$104$$ 2.52892i 0.247981i
$$105$$ −2.82181 + 3.43366i −0.275380 + 0.335091i
$$106$$ 0.0764712i 0.00742754i
$$107$$ 15.1949i 1.46894i 0.678639 + 0.734472i $$0.262570\pi$$
−0.678639 + 0.734472i $$0.737430\pi$$
$$108$$ 0.611859i 0.0588761i
$$109$$ 7.22491i 0.692021i 0.938231 + 0.346010i $$0.112464\pi$$
−0.938231 + 0.346010i $$0.887536\pi$$
$$110$$ 7.37016i 0.702717i
$$111$$ −1.25068 −0.118709
$$112$$ −4.90966 4.03479i −0.463919 0.381251i
$$113$$ 3.00697i 0.282872i −0.989947 0.141436i $$-0.954828\pi$$
0.989947 0.141436i $$-0.0451720\pi$$
$$114$$ 4.38746i 0.410923i
$$115$$ 7.74711 2.20995i 0.722421 0.206079i
$$116$$ 3.54269 0.328931
$$117$$ 0.821806i 0.0759760i
$$118$$ 13.0138i 1.19801i
$$119$$ 4.04552 + 3.32464i 0.370853 + 0.304769i
$$120$$ 5.16928i 0.471889i
$$121$$ −2.86733 −0.260666
$$122$$ 11.0303 0.998635
$$123$$ −5.00000 −0.450835
$$124$$ 0.346517i 0.0311182i
$$125$$ −12.0581 −1.07851
$$126$$ −2.40830 1.97916i −0.214549 0.176317i
$$127$$ −2.32464 −0.206278 −0.103139 0.994667i $$-0.532889\pi$$
−0.103139 + 0.994667i $$0.532889\pi$$
$$128$$ 3.62563 0.320463
$$129$$ 7.01863 0.617956
$$130$$ 1.62648i 0.142652i
$$131$$ 6.13267i 0.535814i 0.963445 + 0.267907i $$0.0863320\pi$$
−0.963445 + 0.267907i $$0.913668\pi$$
$$132$$ 2.27849 0.198317
$$133$$ 7.61186 + 6.25547i 0.660032 + 0.542418i
$$134$$ 5.93747i 0.512920i
$$135$$ 1.67982i 0.144576i
$$136$$ −6.09042 −0.522249
$$137$$ 17.7611i 1.51744i 0.651419 + 0.758718i $$0.274174\pi$$
−0.651419 + 0.758718i $$0.725826\pi$$
$$138$$ 1.55001 + 5.43366i 0.131946 + 0.462544i
$$139$$ 16.3465i 1.38649i 0.720700 + 0.693247i $$0.243820\pi$$
−0.720700 + 0.693247i $$0.756180\pi$$
$$140$$ −2.10092 1.72655i −0.177560 0.145920i
$$141$$ 5.14644 0.433409
$$142$$ −7.54269 −0.632969
$$143$$ −3.06031 −0.255916
$$144$$ 2.40191 0.200159
$$145$$ −9.72626 −0.807722
$$146$$ 18.7110i 1.54853i
$$147$$ −6.86733 + 1.35639i −0.566408 + 0.111873i
$$148$$ 0.765238i 0.0629022i
$$149$$ 18.5661i 1.52099i 0.649342 + 0.760497i $$0.275045\pi$$
−0.649342 + 0.760497i $$0.724955\pi$$
$$150$$ 2.56634i 0.209540i
$$151$$ −1.30099 −0.105873 −0.0529367 0.998598i $$-0.516858\pi$$
−0.0529367 + 0.998598i $$0.516858\pi$$
$$152$$ −11.4594 −0.929482
$$153$$ −1.97916 −0.160005
$$154$$ −7.37016 + 8.96825i −0.593904 + 0.722682i
$$155$$ 0.951343i 0.0764137i
$$156$$ 0.502829 0.0402585
$$157$$ 7.60573 0.607003 0.303502 0.952831i $$-0.401844\pi$$
0.303502 + 0.952831i $$0.401844\pi$$
$$158$$ 20.7400i 1.64998i
$$159$$ 0.0649054 0.00514733
$$160$$ 5.58480 0.441517
$$161$$ 11.6369 + 5.05797i 0.917114 + 0.398624i
$$162$$ 1.17819 0.0925677
$$163$$ −6.68914 −0.523934 −0.261967 0.965077i $$-0.584371\pi$$
−0.261967 + 0.965077i $$0.584371\pi$$
$$164$$ 3.05929i 0.238891i
$$165$$ −6.25547 −0.486988
$$166$$ −10.9538 −0.850181
$$167$$ 2.79816i 0.216528i −0.994122 0.108264i $$-0.965471\pi$$
0.994122 0.108264i $$-0.0345293\pi$$
$$168$$ 5.16928 6.29015i 0.398819 0.485295i
$$169$$ 12.3246 0.948049
$$170$$ 3.91707 0.300425
$$171$$ −3.72389 −0.284773
$$172$$ 4.29441i 0.327446i
$$173$$ 5.88110i 0.447132i −0.974689 0.223566i $$-0.928230\pi$$
0.974689 0.223566i $$-0.0717698\pi$$
$$174$$ 6.82181i 0.517160i
$$175$$ −4.45237 3.65898i −0.336567 0.276593i
$$176$$ 8.94445i 0.674213i
$$177$$ 11.0455 0.830232
$$178$$ −13.9442 −1.04516
$$179$$ −0.100918 −0.00754294 −0.00377147 0.999993i $$-0.501200\pi$$
−0.00377147 + 0.999993i $$0.501200\pi$$
$$180$$ 1.02781 0.0766088
$$181$$ −12.6568 −0.940770 −0.470385 0.882461i $$-0.655885\pi$$
−0.470385 + 0.882461i $$0.655885\pi$$
$$182$$ −1.62648 + 1.97916i −0.120563 + 0.146705i
$$183$$ 9.36202i 0.692061i
$$184$$ −14.1920 + 4.04841i −1.04625 + 0.298453i
$$185$$ 2.10092i 0.154463i
$$186$$ 0.667253 0.0489254
$$187$$ 7.37016i 0.538959i
$$188$$ 3.14889i 0.229657i
$$189$$ 1.67982 2.04406i 0.122189 0.148684i
$$190$$ 7.37016 0.534687
$$191$$ 7.16000i 0.518080i −0.965867 0.259040i $$-0.916594\pi$$
0.965867 0.259040i $$-0.0834061\pi$$
$$192$$ 8.72089i 0.629376i
$$193$$ −6.79005 −0.488759 −0.244379 0.969680i $$-0.578584\pi$$
−0.244379 + 0.969680i $$0.578584\pi$$
$$194$$ 17.6399 1.26647
$$195$$ −1.38049 −0.0988588
$$196$$ −0.829918 4.20184i −0.0592799 0.300131i
$$197$$ −14.4930 −1.03258 −0.516290 0.856414i $$-0.672687\pi$$
−0.516290 + 0.856414i $$0.672687\pi$$
$$198$$ 4.38746i 0.311803i
$$199$$ 11.3412 0.803955 0.401978 0.915650i $$-0.368323\pi$$
0.401978 + 0.915650i $$0.368323\pi$$
$$200$$ 6.70291 0.473967
$$201$$ 5.03947 0.355457
$$202$$ 14.4555i 1.01709i
$$203$$ −11.8352 9.72626i −0.830671 0.682650i
$$204$$ 1.21096i 0.0847845i
$$205$$ 8.39912i 0.586620i
$$206$$ 9.81932 0.684144
$$207$$ −4.61186 + 1.31558i −0.320546 + 0.0914394i
$$208$$ 1.97391i 0.136866i
$$209$$ 13.8673i 0.959223i
$$210$$ −3.32464 + 4.04552i −0.229422 + 0.279168i
$$211$$ 10.6436 0.732736 0.366368 0.930470i $$-0.380601\pi$$
0.366368 + 0.930470i $$0.380601\pi$$
$$212$$ 0.0397129i 0.00272750i
$$213$$ 6.40191i 0.438652i
$$214$$ 17.9025i 1.22379i
$$215$$ 11.7901i 0.804075i
$$216$$ 3.07728i 0.209382i
$$217$$ 0.951343 1.15763i 0.0645814 0.0785847i
$$218$$ 8.51235i 0.576529i
$$219$$ 15.8811 1.07315
$$220$$ 3.82746i 0.258048i
$$221$$ 1.62648i 0.109409i
$$222$$ −1.47354 −0.0988976
$$223$$ 0.877200i 0.0587417i −0.999569 0.0293708i $$-0.990650\pi$$
0.999569 0.0293708i $$-0.00935037\pi$$
$$224$$ 6.79576 + 5.58480i 0.454061 + 0.373150i
$$225$$ 2.17819 0.145213
$$226$$ 3.54280i 0.235663i
$$227$$ −7.95339 −0.527885 −0.263942 0.964538i $$-0.585023\pi$$
−0.263942 + 0.964538i $$0.585023\pi$$
$$228$$ 2.27849i 0.150897i
$$229$$ 12.3293 0.814742 0.407371 0.913263i $$-0.366446\pi$$
0.407371 + 0.913263i $$0.366446\pi$$
$$230$$ 9.12760 2.60375i 0.601856 0.171686i
$$231$$ −7.61186 6.25547i −0.500824 0.411580i
$$232$$ 17.8176 1.16978
$$233$$ −3.38814 −0.221965 −0.110982 0.993822i $$-0.535400\pi$$
−0.110982 + 0.993822i $$0.535400\pi$$
$$234$$ 0.968247i 0.0632963i
$$235$$ 8.64511i 0.563945i
$$236$$ 6.75830i 0.439928i
$$237$$ 17.6032 1.14345
$$238$$ 4.76641 + 3.91707i 0.308961 + 0.253906i
$$239$$ −13.7445 −0.889060 −0.444530 0.895764i $$-0.646629\pi$$
−0.444530 + 0.895764i $$0.646629\pi$$
$$240$$ 4.03479i 0.260444i
$$241$$ 19.0883 1.22958 0.614792 0.788689i $$-0.289240\pi$$
0.614792 + 0.788689i $$0.289240\pi$$
$$242$$ −3.37827 −0.217163
$$243$$ 1.00000i 0.0641500i
$$244$$ −5.72824 −0.366713
$$245$$ 2.27849 + 11.5359i 0.145568 + 0.737002i
$$246$$ −5.89097 −0.375595
$$247$$ 3.06031i 0.194723i
$$248$$ 1.74277i 0.110666i
$$249$$ 9.29712i 0.589181i
$$250$$ −14.2068 −0.898516
$$251$$ 7.57758 0.478293 0.239146 0.970984i $$-0.423132\pi$$
0.239146 + 0.970984i $$0.423132\pi$$
$$252$$ 1.25068 + 1.02781i 0.0787853 + 0.0647462i
$$253$$ 4.89908 + 17.1740i 0.308003 + 1.07972i
$$254$$ −2.73887 −0.171852
$$255$$ 3.32464i 0.208197i
$$256$$ −13.1701 −0.823130
$$257$$ 22.1048i 1.37886i 0.724352 + 0.689430i $$0.242139\pi$$
−0.724352 + 0.689430i $$0.757861\pi$$
$$258$$ 8.26931 0.514824
$$259$$ −2.10092 + 2.55646i −0.130545 + 0.158851i
$$260$$ 0.844664i 0.0523838i
$$261$$ 5.79005 0.358395
$$262$$ 7.22548i 0.446391i
$$263$$ 8.67030i 0.534634i −0.963609 0.267317i $$-0.913863\pi$$
0.963609 0.267317i $$-0.0861371\pi$$
$$264$$ 11.4594 0.705279
$$265$$ 0.109030i 0.00669764i
$$266$$ 8.96825 + 7.37016i 0.549878 + 0.451893i
$$267$$ 11.8352i 0.724305i
$$268$$ 3.08344i 0.188351i
$$269$$ 19.6891i 1.20047i −0.799825 0.600234i $$-0.795074\pi$$
0.799825 0.600234i $$-0.204926\pi$$
$$270$$ 1.97916i 0.120448i
$$271$$ 4.65738i 0.282916i 0.989944 + 0.141458i $$0.0451790\pi$$
−0.989944 + 0.141458i $$0.954821\pi$$
$$272$$ −4.75376 −0.288239
$$273$$ −1.67982 1.38049i −0.101668 0.0835510i
$$274$$ 20.9261i 1.26419i
$$275$$ 8.11135i 0.489133i
$$276$$ −0.804951 2.82181i −0.0484524 0.169853i
$$277$$ −23.5011 −1.41204 −0.706021 0.708191i $$-0.749512\pi$$
−0.706021 + 0.708191i $$0.749512\pi$$
$$278$$ 19.2594i 1.15510i
$$279$$ 0.566335i 0.0339056i
$$280$$ −10.5663 8.68348i −0.631459 0.518937i
$$281$$ 1.90269i 0.113505i −0.998388 0.0567524i $$-0.981925\pi$$
0.998388 0.0567524i $$-0.0180746\pi$$
$$282$$ 6.06351 0.361077
$$283$$ −12.3574 −0.734573 −0.367287 0.930108i $$-0.619713\pi$$
−0.367287 + 0.930108i $$0.619713\pi$$
$$284$$ 3.91707 0.232435
$$285$$ 6.25547i 0.370542i
$$286$$ −3.60564 −0.213206
$$287$$ −8.39912 + 10.2203i −0.495784 + 0.603286i
$$288$$ −3.32464 −0.195906
$$289$$ −13.0829 −0.769584
$$290$$ −11.4594 −0.672921
$$291$$ 14.9720i 0.877675i
$$292$$ 9.71699i 0.568644i
$$293$$ 28.4871 1.66423 0.832116 0.554601i $$-0.187129\pi$$
0.832116 + 0.554601i $$0.187129\pi$$
$$294$$ −8.09105 + 1.59809i −0.471879 + 0.0932024i
$$295$$ 18.5545i 1.08029i
$$296$$ 3.84868i 0.223700i
$$297$$ 3.72389 0.216082
$$298$$ 21.8745i 1.26715i
$$299$$ 1.08115 + 3.79005i 0.0625248 + 0.219184i
$$300$$ 1.33275i 0.0769462i
$$301$$ 11.7901 14.3465i 0.679567 0.826920i
$$302$$ −1.53282 −0.0882041
$$303$$ 12.2692 0.704849
$$304$$ −8.94445 −0.512999
$$305$$ 15.7265 0.900499
$$306$$ −2.33183 −0.133302
$$307$$ 24.0357i 1.37179i −0.727702 0.685894i $$-0.759412\pi$$
0.727702 0.685894i $$-0.240588\pi$$
$$308$$ 3.82746 4.65738i 0.218090 0.265379i
$$309$$ 8.33421i 0.474117i
$$310$$ 1.12087i 0.0636610i
$$311$$ 11.7029i 0.663611i 0.943348 + 0.331805i $$0.107658\pi$$
−0.943348 + 0.331805i $$0.892342\pi$$
$$312$$ 2.52892 0.143172
$$313$$ −18.5661 −1.04942 −0.524709 0.851282i $$-0.675826\pi$$
−0.524709 + 0.851282i $$0.675826\pi$$
$$314$$ 8.96103 0.505700
$$315$$ −3.43366 2.82181i −0.193465 0.158991i
$$316$$ 10.7707i 0.605897i
$$317$$ −19.1503 −1.07559 −0.537795 0.843076i $$-0.680743\pi$$
−0.537795 + 0.843076i $$0.680743\pi$$
$$318$$ 0.0764712 0.00428829
$$319$$ 21.5615i 1.20721i
$$320$$ 14.6496 0.818935
$$321$$ −15.1949 −0.848095
$$322$$ 13.7105 + 5.95927i 0.764056 + 0.332097i
$$323$$ 7.37016 0.410087
$$324$$ −0.611859 −0.0339922
$$325$$ 1.79005i 0.0992943i
$$326$$ −7.88110 −0.436494
$$327$$ −7.22491 −0.399538
$$328$$ 15.3864i 0.849571i
$$329$$ 8.64511 10.5197i 0.476620 0.579967i
$$330$$ −7.37016 −0.405714
$$331$$ 16.8811 0.927869 0.463935 0.885869i $$-0.346437\pi$$
0.463935 + 0.885869i $$0.346437\pi$$
$$332$$ 5.68852 0.312198
$$333$$ 1.25068i 0.0685367i
$$334$$ 3.29678i 0.180392i
$$335$$ 8.46542i 0.462515i
$$336$$ 4.03479 4.90966i 0.220116 0.267844i
$$337$$ 32.7447i 1.78372i 0.452313 + 0.891859i $$0.350599\pi$$
−0.452313 + 0.891859i $$0.649401\pi$$
$$338$$ 14.5208 0.789828
$$339$$ 3.00697 0.163316
$$340$$ −2.03421 −0.110320
$$341$$ 2.10897 0.114207
$$342$$ −4.38746 −0.237247
$$343$$ −8.76336 + 16.3157i −0.473177 + 0.880968i
$$344$$ 21.5983i 1.16450i
$$345$$ 2.20995 + 7.74711i 0.118980 + 0.417090i
$$346$$ 6.92908i 0.372509i
$$347$$ 9.01377 0.483885 0.241942 0.970291i $$-0.422216\pi$$
0.241942 + 0.970291i $$0.422216\pi$$
$$348$$ 3.54269i 0.189908i
$$349$$ 23.6337i 1.26509i 0.774526 + 0.632543i $$0.217989\pi$$
−0.774526 + 0.632543i $$0.782011\pi$$
$$350$$ −5.24575 4.31099i −0.280397 0.230432i
$$351$$ 0.821806 0.0438648
$$352$$ 12.3806i 0.659886i
$$353$$ 20.0357i 1.06639i 0.845992 + 0.533195i $$0.179009\pi$$
−0.845992 + 0.533195i $$0.820991\pi$$
$$354$$ 13.0138 0.691674
$$355$$ −10.7541 −0.570767
$$356$$ 7.24149 0.383798
$$357$$ −3.32464 + 4.04552i −0.175958 + 0.214112i
$$358$$ −0.118901 −0.00628409
$$359$$ 1.67982i 0.0886577i 0.999017 + 0.0443288i $$0.0141149\pi$$
−0.999017 + 0.0443288i $$0.985885\pi$$
$$360$$ 5.16928 0.272445
$$361$$ −5.13267 −0.270141
$$362$$ −14.9121 −0.783764
$$363$$ 2.86733i 0.150496i
$$364$$ 0.844664 1.02781i 0.0442724 0.0538721i
$$365$$ 26.6774i 1.39636i
$$366$$ 11.0303i 0.576562i
$$367$$ 5.53352 0.288847 0.144424 0.989516i $$-0.453867\pi$$
0.144424 + 0.989516i $$0.453867\pi$$
$$368$$ −11.0773 + 3.15991i −0.577443 + 0.164722i
$$369$$ 5.00000i 0.260290i
$$370$$ 2.47529i 0.128684i
$$371$$ 0.109030 0.132671i 0.00566053 0.00688792i
$$372$$ −0.346517 −0.0179661
$$373$$ 11.1998i 0.579904i −0.957041 0.289952i $$-0.906361\pi$$
0.957041 0.289952i $$-0.0936393\pi$$
$$374$$ 8.68348i 0.449012i
$$375$$ 12.0581i 0.622677i
$$376$$ 15.8370i 0.816732i
$$377$$ 4.75830i 0.245065i
$$378$$ 1.97916 2.40830i 0.101797 0.123870i
$$379$$ 6.71929i 0.345147i −0.984997 0.172573i $$-0.944792\pi$$
0.984997 0.172573i $$-0.0552082\pi$$
$$380$$ −3.82746 −0.196345
$$381$$ 2.32464i 0.119095i
$$382$$ 8.43587i 0.431617i
$$383$$ 25.9655 1.32678 0.663389 0.748275i $$-0.269118\pi$$
0.663389 + 0.748275i $$0.269118\pi$$
$$384$$ 3.62563i 0.185020i
$$385$$ −10.5081 + 12.7866i −0.535542 + 0.651664i
$$386$$ −8.00000 −0.407189
$$387$$ 7.01863i 0.356777i
$$388$$ −9.16076 −0.465067
$$389$$ 9.29712i 0.471383i 0.971828 + 0.235691i $$0.0757354\pi$$
−0.971828 + 0.235691i $$0.924265\pi$$
$$390$$ −1.62648 −0.0823602
$$391$$ 9.12760 2.60375i 0.461602 0.131677i
$$392$$ −4.17398 21.1327i −0.210818 1.06736i
$$393$$ −6.13267 −0.309352
$$394$$ −17.0755 −0.860252
$$395$$ 29.5702i 1.48784i
$$396$$ 2.27849i 0.114499i
$$397$$ 3.02188i 0.151664i −0.997121 0.0758320i $$-0.975839\pi$$
0.997121 0.0758320i $$-0.0241613\pi$$
$$398$$ 13.3621 0.669782
$$399$$ −6.25547 + 7.61186i −0.313165 + 0.381070i
$$400$$ 5.23183 0.261591
$$401$$ 33.8540i 1.69059i −0.534300 0.845295i $$-0.679425\pi$$
0.534300 0.845295i $$-0.320575\pi$$
$$402$$ 5.93747 0.296134
$$403$$ 0.465418 0.0231841
$$404$$ 7.50704i 0.373489i
$$405$$ 1.67982 0.0834711
$$406$$ −13.9442 11.4594i −0.692039 0.568722i
$$407$$ −4.65738 −0.230858
$$408$$ 6.09042i 0.301520i
$$409$$ 18.8592i 0.932528i −0.884646 0.466264i $$-0.845600\pi$$
0.884646 0.466264i $$-0.154400\pi$$
$$410$$ 9.89579i 0.488718i
$$411$$ −17.7611 −0.876092
$$412$$ −5.09936 −0.251227
$$413$$ 18.5545 22.5777i 0.913009 1.11098i
$$414$$ −5.43366 + 1.55001i −0.267050 + 0.0761790i
$$415$$ −15.6175 −0.766634
$$416$$ 2.73220i 0.133957i
$$417$$ −16.3465 −0.800492
$$418$$ 16.3384i 0.799138i
$$419$$ −25.9490 −1.26769 −0.633845 0.773460i $$-0.718524\pi$$
−0.633845 + 0.773460i $$0.718524\pi$$
$$420$$ 1.72655 2.10092i 0.0842468 0.102514i
$$421$$ 1.15763i 0.0564192i −0.999602 0.0282096i $$-0.991019\pi$$
0.999602 0.0282096i $$-0.00898059\pi$$
$$422$$ 12.5402 0.610449
$$423$$ 5.14644i 0.250229i
$$424$$ 0.199732i 0.00969984i
$$425$$ −4.31099 −0.209114
$$426$$ 7.54269i 0.365445i
$$427$$ 19.1366 + 15.7265i 0.926084 + 0.761061i
$$428$$ 9.29712i 0.449393i
$$429$$ 3.06031i 0.147753i
$$430$$ 13.8910i 0.669882i
$$431$$ 37.6962i 1.81576i −0.419230 0.907880i $$-0.637700\pi$$
0.419230 0.907880i $$-0.362300\pi$$
$$432$$ 2.40191i 0.115562i
$$433$$ −39.9213 −1.91850 −0.959248 0.282566i $$-0.908814\pi$$
−0.959248 + 0.282566i $$0.908814\pi$$
$$434$$ 1.12087 1.36391i 0.0538033 0.0654696i
$$435$$ 9.72626i 0.466339i
$$436$$ 4.42062i 0.211709i
$$437$$ 17.1740 4.89908i 0.821546 0.234355i
$$438$$ 18.7110 0.894047
$$439$$ 16.3483i 0.780261i −0.920760 0.390130i $$-0.872430\pi$$
0.920760 0.390130i $$-0.127570\pi$$
$$440$$ 19.2498i 0.917699i
$$441$$ −1.35639 6.86733i −0.0645899 0.327016i
$$442$$ 1.91631i 0.0911497i
$$443$$ 12.1821 0.578789 0.289394 0.957210i $$-0.406546\pi$$
0.289394 + 0.957210i $$0.406546\pi$$
$$444$$ 0.765238 0.0363166
$$445$$ −19.8811 −0.942455
$$446$$ 1.03351i 0.0489382i
$$447$$ −18.5661 −0.878146
$$448$$ 17.8260 + 14.6496i 0.842202 + 0.692126i
$$449$$ 6.70291 0.316330 0.158165 0.987413i $$-0.449442\pi$$
0.158165 + 0.987413i $$0.449442\pi$$
$$450$$ 2.56634 0.120978
$$451$$ −18.6194 −0.876755
$$452$$ 1.83984i 0.0865389i
$$453$$ 1.30099i 0.0611260i
$$454$$ −9.37064 −0.439786
$$455$$ −2.31898 + 2.82181i −0.108715 + 0.132288i
$$456$$ 11.4594i 0.536637i
$$457$$ 27.3828i 1.28091i −0.767995 0.640456i $$-0.778745\pi$$
0.767995 0.640456i $$-0.221255\pi$$
$$458$$ 14.5263 0.678769
$$459$$ 1.97916i 0.0923792i
$$460$$ −4.74013 + 1.35218i −0.221010 + 0.0630455i
$$461$$ 34.2357i 1.59452i 0.603638 + 0.797258i $$0.293717\pi$$
−0.603638 + 0.797258i $$0.706283\pi$$
$$462$$ −8.96825 7.37016i −0.417241 0.342891i
$$463$$ 22.8892 1.06375 0.531876 0.846822i $$-0.321487\pi$$
0.531876 + 0.846822i $$0.321487\pi$$
$$464$$ 13.9072 0.645625
$$465$$ 0.951343 0.0441175
$$466$$ −3.99189 −0.184921
$$467$$ 6.19709 0.286767 0.143384 0.989667i $$-0.454202\pi$$
0.143384 + 0.989667i $$0.454202\pi$$
$$468$$ 0.502829i 0.0232433i
$$469$$ 8.46542 10.3010i 0.390897 0.475656i
$$470$$ 10.1856i 0.469828i
$$471$$ 7.60573i 0.350454i
$$472$$ 33.9901i 1.56452i
$$473$$ 26.1366 1.20176
$$474$$ 20.7400 0.952618
$$475$$ −8.11135 −0.372174
$$476$$ −2.47529 2.03421i −0.113455 0.0932377i
$$477$$ 0.0649054i 0.00297181i
$$478$$ −16.1937 −0.740684
$$479$$ −34.1418 −1.55998 −0.779989 0.625793i $$-0.784775\pi$$
−0.779989 + 0.625793i $$0.784775\pi$$
$$480$$ 5.58480i 0.254910i
$$481$$ −1.02781 −0.0468643
$$482$$ 22.4897 1.02438
$$483$$ −5.05797 + 11.6369i −0.230146 + 0.529496i
$$484$$ 1.75440 0.0797455
$$485$$ 25.1503 1.14202
$$486$$ 1.17819i 0.0534440i
$$487$$ 27.6793 1.25427 0.627134 0.778912i $$-0.284228\pi$$
0.627134 + 0.778912i $$0.284228\pi$$
$$488$$ −28.8095 −1.30415
$$489$$ 6.68914i 0.302493i
$$490$$ 2.68451 + 13.5915i 0.121274 + 0.614003i
$$491$$ 5.62563 0.253881 0.126941 0.991910i $$-0.459484\pi$$
0.126941 + 0.991910i $$0.459484\pi$$
$$492$$ 3.05929 0.137924
$$493$$ −11.4594 −0.516107
$$494$$ 3.60564i 0.162225i
$$495$$ 6.25547i 0.281162i
$$496$$ 1.36029i 0.0610787i
$$497$$ −13.0859 10.7541i −0.586983 0.482386i
$$498$$ 10.9538i 0.490852i
$$499$$ −16.2555 −0.727695 −0.363847 0.931459i $$-0.618537\pi$$
−0.363847 + 0.931459i $$0.618537\pi$$
$$500$$ 7.37785 0.329948
$$501$$ 2.79816 0.125013
$$502$$ 8.92786 0.398470
$$503$$ −16.5754 −0.739059 −0.369530 0.929219i $$-0.620481\pi$$
−0.369530 + 0.929219i $$0.620481\pi$$
$$504$$ 6.29015 + 5.16928i 0.280185 + 0.230258i
$$505$$ 20.6102i 0.917140i
$$506$$ 5.77207 + 20.2343i 0.256600 + 0.899527i
$$507$$ 12.3246i 0.547356i
$$508$$ 1.42235 0.0631065
$$509$$ 24.3067i 1.07737i −0.842506 0.538687i $$-0.818921\pi$$
0.842506 0.538687i $$-0.181079\pi$$
$$510$$ 3.91707i 0.173451i
$$511$$ 26.6774 32.4620i 1.18014 1.43603i
$$512$$ −22.7682 −1.00622
$$513$$ 3.72389i 0.164414i
$$514$$ 26.0438i 1.14874i
$$515$$ 14.0000 0.616914
$$516$$ −4.29441 −0.189051
$$517$$ 19.1648 0.842865
$$518$$ −2.47529 + 3.01201i −0.108758 + 0.132340i
$$519$$ 5.88110 0.258152
$$520$$ 4.24815i 0.186293i
$$521$$ −15.1783 −0.664973 −0.332487 0.943108i $$-0.607888\pi$$
−0.332487 + 0.943108i $$0.607888\pi$$
$$522$$ 6.82181 0.298582
$$523$$ −21.4569 −0.938244 −0.469122 0.883133i $$-0.655430\pi$$
−0.469122 + 0.883133i $$0.655430\pi$$
$$524$$ 3.75233i 0.163921i
$$525$$ 3.65898 4.45237i 0.159691 0.194317i
$$526$$ 10.2153i 0.445408i
$$527$$ 1.12087i 0.0488257i
$$528$$ 8.94445 0.389257
$$529$$ 19.5385 12.1346i 0.849499 0.527590i
$$530$$ 0.128458i 0.00557986i
$$531$$ 11.0455i 0.479335i
$$532$$ −4.65738 3.82746i −0.201923 0.165942i
$$533$$ −4.10903 −0.177982
$$534$$ 13.9442i 0.603425i
$$535$$ 25.5247i 1.10353i
$$536$$ 15.5078i 0.669837i
$$537$$ 0.100918i 0.00435492i
$$538$$ 23.1976i 1.00012i
$$539$$ −25.5732 + 5.05104i −1.10151 + 0.217563i
$$540$$ 1.02781i 0.0442301i
$$541$$ −35.3920 −1.52162 −0.760811 0.648973i $$-0.775199\pi$$
−0.760811 + 0.648973i $$0.775199\pi$$
$$542$$ 5.48730i 0.235700i
$$543$$ 12.6568i 0.543154i
$$544$$ 6.57998 0.282114
$$545$$ 12.1366i 0.519874i
$$546$$ −1.97916 1.62648i −0.0847001 0.0696071i
$$547$$ −13.4792 −0.576328 −0.288164 0.957581i $$-0.593045\pi$$
−0.288164 + 0.957581i $$0.593045\pi$$
$$548$$ 10.8673i 0.464228i
$$549$$ −9.36202 −0.399561
$$550$$ 9.55674i 0.407501i
$$551$$ −21.5615 −0.918551
$$552$$ −4.04841 14.1920i −0.172312 0.604050i
$$553$$ 29.5702 35.9820i 1.25745 1.53011i
$$554$$ −27.6888 −1.17639
$$555$$ −2.10092 −0.0891790
$$556$$ 10.0018i 0.424169i
$$557$$ 46.4826i 1.96953i 0.173883 + 0.984766i $$0.444369\pi$$
−0.173883 + 0.984766i $$0.555631\pi$$
$$558$$ 0.667253i 0.0282471i
$$559$$ 5.76795 0.243958
$$560$$ −8.24736 6.77773i −0.348515 0.286411i
$$561$$ −7.37016 −0.311168
$$562$$ 2.24173i 0.0945618i
$$563$$ 4.98613 0.210140 0.105070 0.994465i $$-0.466493\pi$$
0.105070 + 0.994465i $$0.466493\pi$$
$$564$$ −3.14889 −0.132592
$$565$$ 5.05118i 0.212505i
$$566$$ −14.5595 −0.611979
$$567$$ 2.04406 + 1.67982i 0.0858426 + 0.0705459i
$$568$$ 19.7005 0.826613
$$569$$ 7.34611i 0.307965i −0.988074 0.153982i $$-0.950790\pi$$
0.988074 0.153982i $$-0.0492099\pi$$
$$570$$ 7.37016i 0.308702i
$$571$$ 25.2039i 1.05475i −0.849633 0.527375i $$-0.823176\pi$$
0.849633 0.527375i $$-0.176824\pi$$
$$572$$ 1.87248 0.0782923
$$573$$ 7.16000 0.299113
$$574$$ −9.89579 + 12.0415i −0.413042 + 0.502603i
$$575$$ −10.0455 + 2.86560i −0.418927 + 0.119504i
$$576$$ −8.72089 −0.363370
$$577$$ 5.84545i 0.243349i 0.992570 + 0.121675i $$0.0388264\pi$$
−0.992570 + 0.121675i $$0.961174\pi$$
$$578$$ −15.4142 −0.641148
$$579$$ 6.79005i 0.282185i
$$580$$ 5.95110 0.247106
$$581$$ −19.0039 15.6175i −0.788415 0.647924i
$$582$$ 17.6399i 0.731199i
$$583$$ 0.241700 0.0100102
$$584$$ 48.8705i 2.02228i
$$585$$ 1.38049i 0.0570762i
$$586$$ 33.5633 1.38649
$$587$$ 14.0318i 0.579152i −0.957155 0.289576i $$-0.906486\pi$$
0.957155 0.289576i $$-0.0935144\pi$$
$$588$$ 4.20184 0.829918i 0.173281 0.0342252i
$$589$$ 2.10897i 0.0868985i
$$590$$ 21.8608i 0.899996i
$$591$$ 14.4930i 0.596161i
$$592$$ 3.00402i 0.123464i
$$593$$ 1.70712i 0.0701029i −0.999386 0.0350515i $$-0.988840\pi$$
0.999386 0.0350515i $$-0.0111595\pi$$
$$594$$ 4.38746 0.180020
$$595$$ 6.79576 + 5.58480i 0.278599 + 0.228954i
$$596$$ 11.3598i 0.465317i
$$597$$ 11.3412i 0.464164i
$$598$$ 1.27381 + 4.46542i 0.0520899 + 0.182605i
$$599$$ 2.97636 0.121611 0.0608054 0.998150i $$-0.480633\pi$$
0.0608054 + 0.998150i $$0.480633\pi$$
$$600$$ 6.70291i 0.273645i
$$601$$ 10.7502i 0.438509i 0.975668 + 0.219255i $$0.0703625\pi$$
−0.975668 + 0.219255i $$0.929637\pi$$
$$602$$ 13.8910 16.9030i 0.566154 0.688914i
$$603$$ 5.03947i 0.205223i
$$604$$ 0.796024 0.0323898
$$605$$ −4.81661 −0.195823
$$606$$ 14.4555 0.587216
$$607$$ 26.4019i 1.07162i −0.844338 0.535810i $$-0.820006\pi$$
0.844338 0.535810i $$-0.179994\pi$$
$$608$$ 12.3806 0.502098
$$609$$ 9.72626 11.8352i 0.394128 0.479588i
$$610$$ 18.5289 0.750214
$$611$$ 4.22938 0.171102
$$612$$ 1.21096 0.0489504
$$613$$ 36.7167i 1.48297i 0.670968 + 0.741486i $$0.265879\pi$$
−0.670968 + 0.741486i $$0.734121\pi$$
$$614$$ 28.3187i 1.14285i
$$615$$ −8.39912 −0.338685
$$616$$ 19.2498 23.4238i 0.775597 0.943772i
$$617$$ 0.688767i 0.0277287i −0.999904 0.0138644i $$-0.995587\pi$$
0.999904 0.0138644i $$-0.00441330\pi$$
$$618$$ 9.81932i 0.394991i
$$619$$ 9.51998 0.382640 0.191320 0.981528i $$-0.438723\pi$$
0.191320 + 0.981528i $$0.438723\pi$$
$$620$$ 0.582088i 0.0233772i
$$621$$ −1.31558 4.61186i −0.0527925 0.185068i
$$622$$ 13.7883i 0.552860i
$$623$$ −24.1920 19.8811i −0.969231 0.796519i
$$624$$ 1.97391 0.0790194
$$625$$ −9.36450 −0.374580
$$626$$ −21.8745 −0.874279
$$627$$ −13.8673 −0.553808
$$628$$ −4.65363 −0.185700
$$629$$ 2.47529i 0.0986962i
$$630$$ −4.04552 3.32464i −0.161178 0.132457i
$$631$$ 23.8032i 0.947592i −0.880635 0.473796i $$-0.842883\pi$$
0.880635 0.473796i $$-0.157117\pi$$
$$632$$ 54.1699i 2.15476i
$$633$$ 10.6436i 0.423046i
$$634$$ −22.5628 −0.896084
$$635$$ −3.90498 −0.154964
$$636$$ −0.0397129 −0.00157472
$$637$$ −5.64361 + 1.11469i −0.223608 + 0.0441655i
$$638$$ 25.4036i 1.00574i
$$639$$ 6.40191 0.253256
$$640$$ 6.09042 0.240745
$$641$$ 14.4383i 0.570277i −0.958486 0.285138i $$-0.907960\pi$$
0.958486 0.285138i $$-0.0920395\pi$$
$$642$$ −17.9025 −0.706556
$$643$$ −3.08846 −0.121797 −0.0608985 0.998144i $$-0.519397\pi$$
−0.0608985 + 0.998144i $$0.519397\pi$$
$$644$$ −7.12012 3.09476i −0.280572 0.121951i
$$645$$ 11.7901 0.464233
$$646$$ 8.68348 0.341647
$$647$$ 49.1503i 1.93230i 0.257982 + 0.966150i $$0.416942\pi$$
−0.257982 + 0.966150i $$0.583058\pi$$
$$648$$ −3.07728 −0.120887
$$649$$ 41.1323 1.61458
$$650$$ 2.10903i 0.0827229i
$$651$$ 1.15763 + 0.951343i 0.0453709 + 0.0372861i
$$652$$ 4.09281 0.160287
$$653$$ −21.3684 −0.836210 −0.418105 0.908399i $$-0.637306\pi$$
−0.418105 + 0.908399i $$0.637306\pi$$
$$654$$ −8.51235 −0.332859
$$655$$ 10.3018i 0.402525i
$$656$$ 12.0096i 0.468894i
$$657$$ 15.8811i 0.619581i
$$658$$ 10.1856 12.3942i 0.397077 0.483176i
$$659$$ 19.0601i 0.742478i 0.928537 + 0.371239i $$0.121067\pi$$
−0.928537 + 0.371239i $$0.878933\pi$$
$$660$$ 3.82746 0.148984
$$661$$ −26.3500 −1.02489 −0.512447 0.858719i $$-0.671261\pi$$
−0.512447 + 0.858719i $$0.671261\pi$$
$$662$$ 19.8892 0.773016
$$663$$ −1.62648 −0.0631674
$$664$$ 28.6098 1.11028
$$665$$ 12.7866 + 10.5081i 0.495842 + 0.407486i
$$666$$ 1.47354i 0.0570986i
$$667$$ −26.7029 + 7.61730i −1.03394 + 0.294943i
$$668$$ 1.71208i 0.0662424i
$$669$$ 0.877200 0.0339145
$$670$$ 9.97391i 0.385326i
$$671$$ 34.8631i 1.34588i
$$672$$ −5.58480 + 6.79576i −0.215438 + 0.262152i
$$673$$ −31.4474 −1.21221 −0.606105 0.795385i $$-0.707269\pi$$
−0.606105 + 0.795385i $$0.707269\pi$$
$$674$$ 38.5796i 1.48603i
$$675$$ 2.17819i 0.0838387i
$$676$$ −7.54094 −0.290036
$$677$$ 22.9586 0.882369 0.441185 0.897416i $$-0.354558\pi$$
0.441185 + 0.897416i $$0.354558\pi$$
$$678$$ 3.54280 0.136060
$$679$$ 30.6037 + 25.1503i 1.17446 + 0.965181i
$$680$$ −10.2308 −0.392334
$$681$$ 7.95339i 0.304775i
$$682$$ 2.48477 0.0951469
$$683$$ −26.0829 −0.998036 −0.499018 0.866592i $$-0.666306\pi$$
−0.499018 + 0.866592i $$0.666306\pi$$
$$684$$ 2.27849 0.0871203
$$685$$ 29.8356i 1.13996i
$$686$$ −10.3249 + 19.2231i −0.394208 + 0.733942i
$$687$$ 12.3293i 0.470392i
$$688$$ 16.8581i 0.642710i
$$689$$ 0.0533396 0.00203208
$$690$$ 2.60375 + 9.12760i 0.0991229 + 0.347482i
$$691$$ 22.9404i 0.872694i −0.899779 0.436347i $$-0.856272\pi$$
0.899779 0.436347i $$-0.143728\pi$$
$$692$$ 3.59840i 0.136791i
$$693$$ 6.25547 7.61186i 0.237626 0.289151i
$$694$$ 10.6200 0.403129
$$695$$ 27.4593i 1.04159i
$$696$$ 17.8176i 0.675374i
$$697$$ 9.89579i 0.374830i
$$698$$ 27.8451i 1.05395i
$$699$$ 3.38814i 0.128151i
$$700$$ 2.72422 + 2.23878i 0.102966 + 0.0846179i
$$701$$ 42.0469i 1.58809i 0.607860 + 0.794044i $$0.292028\pi$$
−0.607860 + 0.794044i $$0.707972\pi$$
$$702$$ 0.968247 0.0365441
$$703$$ 4.65738i 0.175656i
$$704$$ 32.4756i 1.22397i
$$705$$ 8.64511 0.325594
$$706$$ 23.6059i 0.888419i
$$707$$ 20.6102 25.0791i 0.775125 0.943197i
$$708$$ −6.75830 −0.253992
$$709$$ 25.1440i 0.944303i 0.881517 + 0.472152i $$0.156522\pi$$
−0.881517 + 0.472152i $$0.843478\pi$$
$$710$$ −12.6704 −0.475511
$$711$$ 17.6032i 0.660171i
$$712$$ 36.4203 1.36491
$$713$$ −0.745061 2.61186i −0.0279028 0.0978149i
$$714$$ −3.91707 + 4.76641i −0.146592 + 0.178378i
$$715$$ −5.14078 −0.192254
$$716$$ 0.0617473 0.00230761
$$717$$ 13.7445i 0.513299i
$$718$$ 1.97916i 0.0738615i
$$719$$ 40.4831i 1.50976i −0.655860 0.754882i $$-0.727694\pi$$
0.655860 0.754882i $$-0.272306\pi$$
$$720$$ 4.03479 0.150368
$$721$$ 17.0357 + 14.0000i 0.634441 + 0.521387i
$$722$$ −6.04728 −0.225057
$$723$$ 19.0883i 0.709901i
$$724$$ 7.74415 0.287809
$$725$$ 12.6119 0.468393
$$726$$ 3.37827i 0.125379i
$$727$$ 46.9536 1.74141 0.870706 0.491805i $$-0.163663\pi$$
0.870706 + 0.491805i $$0.163663\pi$$
$$728$$ 4.24815 5.16928i 0.157447 0.191586i
$$729$$ −1.00000 −0.0370370
$$730$$ 31.4312i 1.16332i
$$731$$ 13.8910i 0.513776i
$$732$$ 5.72824i 0.211722i
$$733$$ 30.7288 1.13499 0.567497 0.823375i $$-0.307912\pi$$
0.567497 + 0.823375i $$0.307912\pi$$
$$734$$ 6.51956 0.240641
$$735$$ −11.5359 + 2.27849i −0.425508 + 0.0840435i
$$736$$ 15.3327 4.37383i 0.565173 0.161222i
$$737$$ 18.7664 0.691270
$$738$$ 5.89097i 0.216850i
$$739$$ 45.8338 1.68602 0.843012 0.537895i $$-0.180780\pi$$
0.843012 + 0.537895i $$0.180780\pi$$
$$740$$ 1.28546i 0.0472546i
$$741$$ −3.06031 −0.112423
$$742$$ 0.128458 0.156312i 0.00471584 0.00573839i
$$743$$ 23.6056i 0.866004i 0.901393 + 0.433002i $$0.142546\pi$$
−0.901393 + 0.433002i $$0.857454\pi$$
$$744$$ −1.74277 −0.0638931
$$745$$ 31.1878i 1.14263i
$$746$$ 13.1955i 0.483123i
$$747$$ 9.29712 0.340164
$$748$$ 4.50950i 0.164883i
$$749$$ −25.5247 + 31.0593i −0.932653 + 1.13488i
$$750$$ 14.2068i 0.518758i
$$751$$ 1.36391i 0.0497697i 0.999690 + 0.0248848i $$0.00792191\pi$$
−0.999690 + 0.0248848i $$0.992078\pi$$
$$752$$ 12.3613i 0.450770i
$$753$$ 7.57758i 0.276142i
$$754$$ 5.60620i 0.204166i
$$755$$ −2.18544 −0.0795363
$$756$$ −1.02781 + 1.25068i −0.0373812 + 0.0454867i
$$757$$ 49.5797i 1.80201i 0.433814 + 0.901003i $$0.357168\pi$$
−0.433814 + 0.901003i $$0.642832\pi$$
$$758$$ 7.91663i 0.287545i
$$759$$ −17.1740 + 4.89908i −0.623378 + 0.177825i
$$760$$ −19.2498 −0.698264
$$761$$ 31.9227i 1.15720i −0.815612 0.578599i $$-0.803600\pi$$
0.815612 0.578599i $$-0.196400\pi$$
$$762$$ 2.73887i 0.0992188i
$$763$$ −12.1366 + 14.7682i −0.439373 + 0.534644i
$$764$$ 4.38091i 0.158496i
$$765$$ −3.32464 −0.120202
$$766$$ 30.5924 1.10535
$$767$$ 9.07728 0.327761
$$768$$ 13.1701i 0.475234i
$$769$$ −18.7009 −0.674372 −0.337186 0.941438i $$-0.609475\pi$$
−0.337186 + 0.941438i $$0.609475\pi$$
$$770$$ −12.3806 + 15.0651i −0.446165 + 0.542907i
$$771$$ −22.1048 −0.796086
$$772$$ 4.15455 0.149526
$$773$$ −6.40633 −0.230420 −0.115210 0.993341i $$-0.536754\pi$$
−0.115210 + 0.993341i $$0.536754\pi$$
$$774$$ 8.26931i 0.297234i
$$775$$ 1.23359i 0.0443118i
$$776$$ −46.0730 −1.65393
$$777$$ −2.55646 2.10092i −0.0917127 0.0753700i
$$778$$ 10.9538i 0.392713i
$$779$$ 18.6194i 0.667110i
$$780$$ 0.844664 0.0302438
$$781$$ 23.8400i 0.853062i
$$782$$ 10.7541 3.06772i 0.384565 0.109701i
$$783$$ 5.79005i 0.206920i
$$784$$ −3.25792 16.4947i −0.116354 0.589097i
$$785$$ 12.7763 0.456005
$$786$$ −7.22548 −0.257724
$$787$$ 46.2085