# Properties

 Label 1960.2.q.r.361.1 Level $1960$ Weight $2$ Character 1960.361 Analytic conductor $15.651$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1960 = 2^{3} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1960.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.6506787962$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ Defining polynomial: $$x^{4} - x^{3} - 2 x^{2} - 3 x + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 280) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$-1.18614 + 1.26217i$$ of defining polynomial Character $$\chi$$ $$=$$ 1960.361 Dual form 1960.2.q.r.961.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.68614 + 2.92048i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-4.18614 - 7.25061i) q^{9} +O(q^{10})$$ $$q+(-1.68614 + 2.92048i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-4.18614 - 7.25061i) q^{9} +(-0.313859 + 0.543620i) q^{11} +1.37228 q^{13} +3.37228 q^{15} +(2.68614 - 4.65253i) q^{17} +(3.37228 + 5.84096i) q^{19} +(-3.37228 - 5.84096i) q^{23} +(-0.500000 + 0.866025i) q^{25} +18.1168 q^{27} +1.37228 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-1.05842 - 1.83324i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-2.31386 + 4.00772i) q^{39} +4.74456 q^{41} +2.74456 q^{43} +(-4.18614 + 7.25061i) q^{45} +(5.05842 + 8.76144i) q^{47} +(9.05842 + 15.6896i) q^{51} +(0.372281 - 0.644810i) q^{53} +0.627719 q^{55} -22.7446 q^{57} +(4.00000 - 6.92820i) q^{59} +(4.37228 + 7.57301i) q^{61} +(-0.686141 - 1.18843i) q^{65} +(2.00000 - 3.46410i) q^{67} +22.7446 q^{69} +8.00000 q^{71} +(-3.00000 + 5.19615i) q^{73} +(-1.68614 - 2.92048i) q^{75} +(1.05842 + 1.83324i) q^{79} +(-17.9891 + 31.1581i) q^{81} -13.4891 q^{83} -5.37228 q^{85} +(-2.31386 + 4.00772i) q^{87} +(1.62772 + 2.81929i) q^{89} +(-13.4891 - 23.3639i) q^{93} +(3.37228 - 5.84096i) q^{95} -18.8614 q^{97} +5.25544 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - q^{3} - 2q^{5} - 11q^{9} + O(q^{10})$$ $$4q - q^{3} - 2q^{5} - 11q^{9} - 7q^{11} - 6q^{13} + 2q^{15} + 5q^{17} + 2q^{19} - 2q^{23} - 2q^{25} + 38q^{27} - 6q^{29} - 16q^{31} + 13q^{33} + 4q^{37} - 15q^{39} - 4q^{41} - 12q^{43} - 11q^{45} + 3q^{47} + 19q^{51} - 10q^{53} + 14q^{55} - 68q^{57} + 16q^{59} + 6q^{61} + 3q^{65} + 8q^{67} + 68q^{69} + 32q^{71} - 12q^{73} - q^{75} - 13q^{79} - 26q^{81} - 8q^{83} - 10q^{85} - 15q^{87} + 18q^{89} - 8q^{93} + 2q^{95} - 18q^{97} + 44q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$$.

 $$n$$ $$981$$ $$1081$$ $$1177$$ $$1471$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.68614 + 2.92048i −0.973494 + 1.68614i −0.288675 + 0.957427i $$0.593215\pi$$
−0.684819 + 0.728714i $$0.740119\pi$$
$$4$$ 0 0
$$5$$ −0.500000 0.866025i −0.223607 0.387298i
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −4.18614 7.25061i −1.39538 2.41687i
$$10$$ 0 0
$$11$$ −0.313859 + 0.543620i −0.0946322 + 0.163908i −0.909455 0.415802i $$-0.863501\pi$$
0.814823 + 0.579710i $$0.196834\pi$$
$$12$$ 0 0
$$13$$ 1.37228 0.380602 0.190301 0.981726i $$-0.439054\pi$$
0.190301 + 0.981726i $$0.439054\pi$$
$$14$$ 0 0
$$15$$ 3.37228 0.870719
$$16$$ 0 0
$$17$$ 2.68614 4.65253i 0.651485 1.12840i −0.331278 0.943533i $$-0.607480\pi$$
0.982763 0.184872i $$-0.0591869\pi$$
$$18$$ 0 0
$$19$$ 3.37228 + 5.84096i 0.773654 + 1.34001i 0.935548 + 0.353200i $$0.114907\pi$$
−0.161893 + 0.986808i $$0.551760\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.37228 5.84096i −0.703169 1.21792i −0.967348 0.253451i $$-0.918434\pi$$
0.264179 0.964474i $$-0.414899\pi$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 18.1168 3.48659
$$28$$ 0 0
$$29$$ 1.37228 0.254826 0.127413 0.991850i $$-0.459333\pi$$
0.127413 + 0.991850i $$0.459333\pi$$
$$30$$ 0 0
$$31$$ −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i $$0.421802\pi$$
−0.961625 + 0.274367i $$0.911532\pi$$
$$32$$ 0 0
$$33$$ −1.05842 1.83324i −0.184248 0.319126i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i $$-0.114098\pi$$
−0.772043 + 0.635571i $$0.780765\pi$$
$$38$$ 0 0
$$39$$ −2.31386 + 4.00772i −0.370514 + 0.641749i
$$40$$ 0 0
$$41$$ 4.74456 0.740976 0.370488 0.928837i $$-0.379190\pi$$
0.370488 + 0.928837i $$0.379190\pi$$
$$42$$ 0 0
$$43$$ 2.74456 0.418542 0.209271 0.977858i $$-0.432891\pi$$
0.209271 + 0.977858i $$0.432891\pi$$
$$44$$ 0 0
$$45$$ −4.18614 + 7.25061i −0.624033 + 1.08086i
$$46$$ 0 0
$$47$$ 5.05842 + 8.76144i 0.737847 + 1.27799i 0.953463 + 0.301510i $$0.0974906\pi$$
−0.215616 + 0.976478i $$0.569176\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 9.05842 + 15.6896i 1.26843 + 2.19699i
$$52$$ 0 0
$$53$$ 0.372281 0.644810i 0.0511368 0.0885715i −0.839324 0.543632i $$-0.817049\pi$$
0.890461 + 0.455060i $$0.150382\pi$$
$$54$$ 0 0
$$55$$ 0.627719 0.0846416
$$56$$ 0 0
$$57$$ −22.7446 −3.01259
$$58$$ 0 0
$$59$$ 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i $$-0.658984\pi$$
0.999709 0.0241347i $$-0.00768307\pi$$
$$60$$ 0 0
$$61$$ 4.37228 + 7.57301i 0.559813 + 0.969625i 0.997512 + 0.0705031i $$0.0224605\pi$$
−0.437698 + 0.899122i $$0.644206\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −0.686141 1.18843i −0.0851053 0.147407i
$$66$$ 0 0
$$67$$ 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i $$-0.754762\pi$$
0.961946 + 0.273241i $$0.0880957\pi$$
$$68$$ 0 0
$$69$$ 22.7446 2.73812
$$70$$ 0 0
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ 0 0
$$73$$ −3.00000 + 5.19615i −0.351123 + 0.608164i −0.986447 0.164083i $$-0.947534\pi$$
0.635323 + 0.772246i $$0.280867\pi$$
$$74$$ 0 0
$$75$$ −1.68614 2.92048i −0.194699 0.337228i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1.05842 + 1.83324i 0.119082 + 0.206256i 0.919404 0.393314i $$-0.128672\pi$$
−0.800322 + 0.599570i $$0.795338\pi$$
$$80$$ 0 0
$$81$$ −17.9891 + 31.1581i −1.99879 + 3.46201i
$$82$$ 0 0
$$83$$ −13.4891 −1.48062 −0.740312 0.672264i $$-0.765322\pi$$
−0.740312 + 0.672264i $$0.765322\pi$$
$$84$$ 0 0
$$85$$ −5.37228 −0.582706
$$86$$ 0 0
$$87$$ −2.31386 + 4.00772i −0.248072 + 0.429673i
$$88$$ 0 0
$$89$$ 1.62772 + 2.81929i 0.172538 + 0.298844i 0.939306 0.343079i $$-0.111470\pi$$
−0.766769 + 0.641924i $$0.778137\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −13.4891 23.3639i −1.39876 2.42272i
$$94$$ 0 0
$$95$$ 3.37228 5.84096i 0.345989 0.599270i
$$96$$ 0 0
$$97$$ −18.8614 −1.91509 −0.957543 0.288291i $$-0.906913\pi$$
−0.957543 + 0.288291i $$0.906913\pi$$
$$98$$ 0 0
$$99$$ 5.25544 0.528191
$$100$$ 0 0
$$101$$ −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i $$-0.929823\pi$$
0.677284 + 0.735721i $$0.263157\pi$$
$$102$$ 0 0
$$103$$ −5.68614 9.84868i −0.560272 0.970420i −0.997472 0.0710555i $$-0.977363\pi$$
0.437200 0.899364i $$-0.355970\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1.37228 + 2.37686i 0.132663 + 0.229780i 0.924702 0.380691i $$-0.124314\pi$$
−0.792039 + 0.610470i $$0.790980\pi$$
$$108$$ 0 0
$$109$$ 2.68614 4.65253i 0.257286 0.445632i −0.708228 0.705984i $$-0.750505\pi$$
0.965514 + 0.260352i $$0.0838386\pi$$
$$110$$ 0 0
$$111$$ −6.74456 −0.640166
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ −3.37228 + 5.84096i −0.314467 + 0.544673i
$$116$$ 0 0
$$117$$ −5.74456 9.94987i −0.531085 0.919866i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.30298 + 9.18504i 0.482090 + 0.835004i
$$122$$ 0 0
$$123$$ −8.00000 + 13.8564i −0.721336 + 1.24939i
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ −4.62772 + 8.01544i −0.407448 + 0.705720i
$$130$$ 0 0
$$131$$ 3.37228 + 5.84096i 0.294638 + 0.510327i 0.974901 0.222641i $$-0.0714677\pi$$
−0.680263 + 0.732968i $$0.738134\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −9.05842 15.6896i −0.779625 1.35035i
$$136$$ 0 0
$$137$$ −1.62772 + 2.81929i −0.139065 + 0.240868i −0.927143 0.374707i $$-0.877743\pi$$
0.788078 + 0.615576i $$0.211076\pi$$
$$138$$ 0 0
$$139$$ −6.74456 −0.572066 −0.286033 0.958220i $$-0.592337\pi$$
−0.286033 + 0.958220i $$0.592337\pi$$
$$140$$ 0 0
$$141$$ −34.1168 −2.87316
$$142$$ 0 0
$$143$$ −0.430703 + 0.746000i −0.0360172 + 0.0623837i
$$144$$ 0 0
$$145$$ −0.686141 1.18843i −0.0569809 0.0986938i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 3.74456 + 6.48577i 0.306767 + 0.531335i 0.977653 0.210225i $$-0.0674196\pi$$
−0.670887 + 0.741560i $$0.734086\pi$$
$$150$$ 0 0
$$151$$ 1.05842 1.83324i 0.0861332 0.149187i −0.819740 0.572735i $$-0.805882\pi$$
0.905874 + 0.423548i $$0.139216\pi$$
$$152$$ 0 0
$$153$$ −44.9783 −3.63628
$$154$$ 0 0
$$155$$ 8.00000 0.642575
$$156$$ 0 0
$$157$$ 3.74456 6.48577i 0.298849 0.517621i −0.677024 0.735961i $$-0.736731\pi$$
0.975873 + 0.218340i $$0.0700641\pi$$
$$158$$ 0 0
$$159$$ 1.25544 + 2.17448i 0.0995627 + 0.172448i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 2.62772 + 4.55134i 0.205819 + 0.356489i 0.950393 0.311051i $$-0.100681\pi$$
−0.744574 + 0.667539i $$0.767348\pi$$
$$164$$ 0 0
$$165$$ −1.05842 + 1.83324i −0.0823980 + 0.142718i
$$166$$ 0 0
$$167$$ 11.3723 0.880014 0.440007 0.897994i $$-0.354976\pi$$
0.440007 + 0.897994i $$0.354976\pi$$
$$168$$ 0 0
$$169$$ −11.1168 −0.855142
$$170$$ 0 0
$$171$$ 28.2337 48.9022i 2.15908 3.73964i
$$172$$ 0 0
$$173$$ 2.68614 + 4.65253i 0.204223 + 0.353725i 0.949885 0.312599i $$-0.101200\pi$$
−0.745662 + 0.666325i $$0.767866\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 13.4891 + 23.3639i 1.01390 + 1.75613i
$$178$$ 0 0
$$179$$ −11.4891 + 19.8997i −0.858738 + 1.48738i 0.0143962 + 0.999896i $$0.495417\pi$$
−0.873134 + 0.487481i $$0.837916\pi$$
$$180$$ 0 0
$$181$$ 18.2337 1.35530 0.677650 0.735385i $$-0.262999\pi$$
0.677650 + 0.735385i $$0.262999\pi$$
$$182$$ 0 0
$$183$$ −29.4891 −2.17990
$$184$$ 0 0
$$185$$ 1.00000 1.73205i 0.0735215 0.127343i
$$186$$ 0 0
$$187$$ 1.68614 + 2.92048i 0.123303 + 0.213567i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.4307 + 21.5306i 0.899454 + 1.55790i 0.828193 + 0.560443i $$0.189369\pi$$
0.0712608 + 0.997458i $$0.477298\pi$$
$$192$$ 0 0
$$193$$ 2.37228 4.10891i 0.170761 0.295766i −0.767925 0.640539i $$-0.778711\pi$$
0.938686 + 0.344773i $$0.112044\pi$$
$$194$$ 0 0
$$195$$ 4.62772 0.331398
$$196$$ 0 0
$$197$$ 26.2337 1.86907 0.934536 0.355867i $$-0.115815\pi$$
0.934536 + 0.355867i $$0.115815\pi$$
$$198$$ 0 0
$$199$$ −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i $$0.358603\pi$$
−0.996850 + 0.0793045i $$0.974730\pi$$
$$200$$ 0 0
$$201$$ 6.74456 + 11.6819i 0.475725 + 0.823979i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −2.37228 4.10891i −0.165687 0.286979i
$$206$$ 0 0
$$207$$ −28.2337 + 48.9022i −1.96238 + 3.39894i
$$208$$ 0 0
$$209$$ −4.23369 −0.292850
$$210$$ 0 0
$$211$$ −8.62772 −0.593957 −0.296978 0.954884i $$-0.595979\pi$$
−0.296978 + 0.954884i $$0.595979\pi$$
$$212$$ 0 0
$$213$$ −13.4891 + 23.3639i −0.924260 + 1.60086i
$$214$$ 0 0
$$215$$ −1.37228 2.37686i −0.0935888 0.162101i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −10.1168 17.5229i −0.683633 1.18409i
$$220$$ 0 0
$$221$$ 3.68614 6.38458i 0.247957 0.429474i
$$222$$ 0 0
$$223$$ 11.3723 0.761544 0.380772 0.924669i $$-0.375658\pi$$
0.380772 + 0.924669i $$0.375658\pi$$
$$224$$ 0 0
$$225$$ 8.37228 0.558152
$$226$$ 0 0
$$227$$ −4.43070 + 7.67420i −0.294076 + 0.509355i −0.974770 0.223214i $$-0.928345\pi$$
0.680693 + 0.732568i $$0.261679\pi$$
$$228$$ 0 0
$$229$$ 11.1168 + 19.2549i 0.734622 + 1.27240i 0.954889 + 0.296963i $$0.0959737\pi$$
−0.220267 + 0.975440i $$0.570693\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.37228 + 11.0371i 0.417462 + 0.723065i 0.995683 0.0928145i $$-0.0295863\pi$$
−0.578221 + 0.815880i $$0.696253\pi$$
$$234$$ 0 0
$$235$$ 5.05842 8.76144i 0.329975 0.571534i
$$236$$ 0 0
$$237$$ −7.13859 −0.463701
$$238$$ 0 0
$$239$$ 19.3723 1.25309 0.626544 0.779386i $$-0.284469\pi$$
0.626544 + 0.779386i $$0.284469\pi$$
$$240$$ 0 0
$$241$$ 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i $$-0.517406\pi$$
0.892058 0.451920i $$-0.149261\pi$$
$$242$$ 0 0
$$243$$ −33.4891 58.0049i −2.14833 3.72101i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 4.62772 + 8.01544i 0.294455 + 0.510010i
$$248$$ 0 0
$$249$$ 22.7446 39.3947i 1.44138 2.49654i
$$250$$ 0 0
$$251$$ 6.74456 0.425713 0.212857 0.977083i $$-0.431723\pi$$
0.212857 + 0.977083i $$0.431723\pi$$
$$252$$ 0 0
$$253$$ 4.23369 0.266170
$$254$$ 0 0
$$255$$ 9.05842 15.6896i 0.567260 0.982524i
$$256$$ 0 0
$$257$$ −0.255437 0.442430i −0.0159337 0.0275981i 0.857949 0.513736i $$-0.171739\pi$$
−0.873882 + 0.486137i $$0.838405\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −5.74456 9.94987i −0.355580 0.615882i
$$262$$ 0 0
$$263$$ 6.11684 10.5947i 0.377181 0.653296i −0.613470 0.789718i $$-0.710227\pi$$
0.990651 + 0.136422i $$0.0435602\pi$$
$$264$$ 0 0
$$265$$ −0.744563 −0.0457381
$$266$$ 0 0
$$267$$ −10.9783 −0.671858
$$268$$ 0 0
$$269$$ −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i $$-0.891886\pi$$
0.759958 + 0.649972i $$0.225219\pi$$
$$270$$ 0 0
$$271$$ −6.74456 11.6819i −0.409703 0.709626i 0.585153 0.810923i $$-0.301034\pi$$
−0.994856 + 0.101296i $$0.967701\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −0.313859 0.543620i −0.0189264 0.0327815i
$$276$$ 0 0
$$277$$ 10.4891 18.1677i 0.630230 1.09159i −0.357274 0.934000i $$-0.616294\pi$$
0.987504 0.157592i $$-0.0503729\pi$$
$$278$$ 0 0
$$279$$ 66.9783 4.00988
$$280$$ 0 0
$$281$$ −21.6060 −1.28890 −0.644452 0.764645i $$-0.722914\pi$$
−0.644452 + 0.764645i $$0.722914\pi$$
$$282$$ 0 0
$$283$$ −13.0584 + 22.6179i −0.776243 + 1.34449i 0.157851 + 0.987463i $$0.449543\pi$$
−0.934093 + 0.357029i $$0.883790\pi$$
$$284$$ 0 0
$$285$$ 11.3723 + 19.6974i 0.673636 + 1.16677i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −5.93070 10.2723i −0.348865 0.604252i
$$290$$ 0 0
$$291$$ 31.8030 55.0844i 1.86432 3.22910i
$$292$$ 0 0
$$293$$ −7.88316 −0.460539 −0.230269 0.973127i $$-0.573961\pi$$
−0.230269 + 0.973127i $$0.573961\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 0 0
$$297$$ −5.68614 + 9.84868i −0.329943 + 0.571479i
$$298$$ 0 0
$$299$$ −4.62772 8.01544i −0.267628 0.463545i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −10.1168 17.5229i −0.581198 1.00666i
$$304$$ 0 0
$$305$$ 4.37228 7.57301i 0.250356 0.433629i
$$306$$ 0 0
$$307$$ −13.8832 −0.792354 −0.396177 0.918174i $$-0.629663\pi$$
−0.396177 + 0.918174i $$0.629663\pi$$
$$308$$ 0 0
$$309$$ 38.3505 2.18169
$$310$$ 0 0
$$311$$ −0.627719 + 1.08724i −0.0355947 + 0.0616518i −0.883274 0.468857i $$-0.844666\pi$$
0.847679 + 0.530509i $$0.177999\pi$$
$$312$$ 0 0
$$313$$ 10.0584 + 17.4217i 0.568536 + 0.984733i 0.996711 + 0.0810370i $$0.0258232\pi$$
−0.428175 + 0.903696i $$0.640843\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −7.00000 12.1244i −0.393159 0.680972i 0.599705 0.800221i $$-0.295285\pi$$
−0.992864 + 0.119249i $$0.961951\pi$$
$$318$$ 0 0
$$319$$ −0.430703 + 0.746000i −0.0241148 + 0.0417680i
$$320$$ 0 0
$$321$$ −9.25544 −0.516588
$$322$$ 0 0
$$323$$ 36.2337 2.01610
$$324$$ 0 0
$$325$$ −0.686141 + 1.18843i −0.0380602 + 0.0659223i
$$326$$ 0 0
$$327$$ 9.05842 + 15.6896i 0.500932 + 0.867639i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i $$-0.273645\pi$$
−0.982470 + 0.186421i $$0.940311\pi$$
$$332$$ 0 0
$$333$$ 8.37228 14.5012i 0.458798 0.794662i
$$334$$ 0 0
$$335$$ −4.00000 −0.218543
$$336$$ 0 0
$$337$$ 15.4891 0.843746 0.421873 0.906655i $$-0.361373\pi$$
0.421873 + 0.906655i $$0.361373\pi$$
$$338$$ 0 0
$$339$$ −3.37228 + 5.84096i −0.183157 + 0.317238i
$$340$$ 0 0
$$341$$ −2.51087 4.34896i −0.135971 0.235510i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −11.3723 19.6974i −0.612263 1.06047i
$$346$$ 0 0
$$347$$ 6.62772 11.4795i 0.355795 0.616254i −0.631459 0.775409i $$-0.717544\pi$$
0.987254 + 0.159155i $$0.0508769\pi$$
$$348$$ 0 0
$$349$$ 3.48913 0.186769 0.0933843 0.995630i $$-0.470231\pi$$
0.0933843 + 0.995630i $$0.470231\pi$$
$$350$$ 0 0
$$351$$ 24.8614 1.32700
$$352$$ 0 0
$$353$$ 13.4307 23.2627i 0.714844 1.23815i −0.248175 0.968715i $$-0.579831\pi$$
0.963020 0.269431i $$-0.0868357\pi$$
$$354$$ 0 0
$$355$$ −4.00000 6.92820i −0.212298 0.367711i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$360$$ 0 0
$$361$$ −13.2446 + 22.9403i −0.697082 + 1.20738i
$$362$$ 0 0
$$363$$ −35.7663 −1.87724
$$364$$ 0 0
$$365$$ 6.00000 0.314054
$$366$$ 0 0
$$367$$ −4.43070 + 7.67420i −0.231281 + 0.400590i −0.958185 0.286148i $$-0.907625\pi$$
0.726904 + 0.686739i $$0.240958\pi$$
$$368$$ 0 0
$$369$$ −19.8614 34.4010i −1.03394 1.79084i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 9.62772 + 16.6757i 0.498504 + 0.863435i 0.999999 0.00172614i $$-0.000549447\pi$$
−0.501494 + 0.865161i $$0.667216\pi$$
$$374$$ 0 0
$$375$$ −1.68614 + 2.92048i −0.0870719 + 0.150813i
$$376$$ 0 0
$$377$$ 1.88316 0.0969875
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 0 0
$$381$$ −13.4891 + 23.3639i −0.691069 + 1.19697i
$$382$$ 0 0
$$383$$ 2.74456 + 4.75372i 0.140241 + 0.242904i 0.927587 0.373607i $$-0.121879\pi$$
−0.787347 + 0.616511i $$0.788546\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −11.4891 19.8997i −0.584025 1.01156i
$$388$$ 0 0
$$389$$ 5.43070 9.40625i 0.275348 0.476916i −0.694875 0.719130i $$-0.744540\pi$$
0.970223 + 0.242214i $$0.0778737\pi$$
$$390$$ 0 0
$$391$$ −36.2337 −1.83242
$$392$$ 0 0
$$393$$ −22.7446 −1.14731
$$394$$ 0 0
$$395$$ 1.05842 1.83324i 0.0532550 0.0922403i
$$396$$ 0 0
$$397$$ 18.6861 + 32.3653i 0.937831 + 1.62437i 0.769507 + 0.638638i $$0.220502\pi$$
0.168323 + 0.985732i $$0.446165\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −0.802985 1.39081i −0.0400991 0.0694537i 0.845279 0.534325i $$-0.179434\pi$$
−0.885378 + 0.464871i $$0.846101\pi$$
$$402$$ 0 0
$$403$$ −5.48913 + 9.50744i −0.273433 + 0.473600i
$$404$$ 0 0
$$405$$ 35.9783 1.78777
$$406$$ 0 0
$$407$$ −1.25544 −0.0622297
$$408$$ 0 0
$$409$$ −5.74456 + 9.94987i −0.284050 + 0.491990i −0.972378 0.233410i $$-0.925012\pi$$
0.688328 + 0.725399i $$0.258345\pi$$
$$410$$ 0 0
$$411$$ −5.48913 9.50744i −0.270759 0.468968i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 6.74456 + 11.6819i 0.331078 + 0.573443i
$$416$$ 0 0
$$417$$ 11.3723 19.6974i 0.556903 0.964584i
$$418$$ 0 0
$$419$$ 37.4891 1.83146 0.915732 0.401790i $$-0.131612\pi$$
0.915732 + 0.401790i $$0.131612\pi$$
$$420$$ 0 0
$$421$$ 21.6060 1.05301 0.526505 0.850172i $$-0.323502\pi$$
0.526505 + 0.850172i $$0.323502\pi$$
$$422$$ 0 0
$$423$$ 42.3505 73.3533i 2.05915 3.56656i
$$424$$ 0 0
$$425$$ 2.68614 + 4.65253i 0.130297 + 0.225681i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −1.45245 2.51572i −0.0701251 0.121460i
$$430$$ 0 0
$$431$$ −6.31386 + 10.9359i −0.304128 + 0.526765i −0.977067 0.212933i $$-0.931698\pi$$
0.672939 + 0.739698i $$0.265032\pi$$
$$432$$ 0 0
$$433$$ 16.9783 0.815923 0.407961 0.912999i $$-0.366240\pi$$
0.407961 + 0.912999i $$0.366240\pi$$
$$434$$ 0 0
$$435$$ 4.62772 0.221882
$$436$$ 0 0
$$437$$ 22.7446 39.3947i 1.08802 1.88451i
$$438$$ 0 0
$$439$$ 14.1168 + 24.4511i 0.673760 + 1.16699i 0.976830 + 0.214018i $$0.0686553\pi$$
−0.303069 + 0.952968i $$0.598011\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 2.62772 + 4.55134i 0.124847 + 0.216241i 0.921673 0.387968i $$-0.126823\pi$$
−0.796826 + 0.604208i $$0.793489\pi$$
$$444$$ 0 0
$$445$$ 1.62772 2.81929i 0.0771613 0.133647i
$$446$$ 0 0
$$447$$ −25.2554 −1.19454
$$448$$ 0 0
$$449$$ −0.116844 −0.00551421 −0.00275710 0.999996i $$-0.500878\pi$$
−0.00275710 + 0.999996i $$0.500878\pi$$
$$450$$ 0 0
$$451$$ −1.48913 + 2.57924i −0.0701202 + 0.121452i
$$452$$ 0 0
$$453$$ 3.56930 + 6.18220i 0.167700 + 0.290465i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −8.37228 14.5012i −0.391639 0.678338i 0.601027 0.799229i $$-0.294758\pi$$
−0.992666 + 0.120890i $$0.961425\pi$$
$$458$$ 0 0
$$459$$ 48.6644 84.2892i 2.27146 3.93428i
$$460$$ 0 0
$$461$$ 12.7446 0.593573 0.296787 0.954944i $$-0.404085\pi$$
0.296787 + 0.954944i $$0.404085\pi$$
$$462$$ 0 0
$$463$$ −29.4891 −1.37048 −0.685238 0.728319i $$-0.740302\pi$$
−0.685238 + 0.728319i $$0.740302\pi$$
$$464$$ 0 0
$$465$$ −13.4891 + 23.3639i −0.625543 + 1.08347i
$$466$$ 0 0
$$467$$ −15.8030 27.3716i −0.731275 1.26661i −0.956339 0.292261i $$-0.905592\pi$$
0.225064 0.974344i $$-0.427741\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 12.6277 + 21.8719i 0.581855 + 1.00780i
$$472$$ 0 0
$$473$$ −0.861407 + 1.49200i −0.0396075 + 0.0686022i
$$474$$ 0 0
$$475$$ −6.74456 −0.309462
$$476$$ 0 0
$$477$$ −6.23369 −0.285421
$$478$$ 0 0
$$479$$ −6.11684 + 10.5947i −0.279486 + 0.484083i −0.971257 0.238033i $$-0.923497\pi$$
0.691771 + 0.722117i $$0.256831\pi$$
$$480$$ 0 0
$$481$$ 1.37228 + 2.37686i 0.0625706 + 0.108376i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 9.43070 + 16.3345i 0.428226 + 0.741709i
$$486$$ 0 0
$$487$$ 2.11684 3.66648i 0.0959234 0.166144i −0.814070 0.580766i $$-0.802753\pi$$
0.909994 + 0.414622i $$0.136086\pi$$
$$488$$ 0 0
$$489$$ −17.7228 −0.801453
$$490$$ 0 0
$$491$$ 17.8832 0.807056 0.403528 0.914967i $$-0.367784\pi$$
0.403528 + 0.914967i $$0.367784\pi$$
$$492$$ 0 0
$$493$$ 3.68614 6.38458i 0.166015 0.287547i
$$494$$ 0 0
$$495$$ −2.62772 4.55134i −0.118107 0.204568i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1.56930 2.71810i −0.0702514 0.121679i 0.828760 0.559604i $$-0.189047\pi$$
−0.899011 + 0.437925i $$0.855713\pi$$
$$500$$ 0 0
$$501$$ −19.1753 + 33.2125i −0.856688 + 1.48383i
$$502$$ 0 0
$$503$$ 12.6277 0.563042 0.281521 0.959555i $$-0.409161\pi$$
0.281521 + 0.959555i $$0.409161\pi$$
$$504$$ 0 0
$$505$$ 6.00000 0.266996
$$506$$ 0 0
$$507$$ 18.7446 32.4665i 0.832475 1.44189i
$$508$$ 0 0
$$509$$ 2.48913 + 4.31129i 0.110329 + 0.191095i 0.915903 0.401400i $$-0.131476\pi$$
−0.805574 + 0.592495i $$0.798143\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 61.0951 + 105.820i 2.69741 + 4.67206i
$$514$$ 0 0
$$515$$ −5.68614 + 9.84868i −0.250561 + 0.433985i
$$516$$ 0 0
$$517$$ −6.35053 −0.279296
$$518$$ 0 0
$$519$$ −18.1168 −0.795241
$$520$$ 0 0
$$521$$ −15.0000 + 25.9808i −0.657162 + 1.13824i 0.324185 + 0.945994i $$0.394910\pi$$
−0.981347 + 0.192244i $$0.938423\pi$$
$$522$$ 0 0
$$523$$ 16.2337 + 28.1176i 0.709850 + 1.22950i 0.964913 + 0.262571i $$0.0845704\pi$$
−0.255063 + 0.966924i $$0.582096\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 21.4891 + 37.2203i 0.936081 + 1.62134i
$$528$$ 0 0
$$529$$ −11.2446 + 19.4762i −0.488894 + 0.846789i
$$530$$ 0 0
$$531$$ −66.9783 −2.90661
$$532$$ 0 0
$$533$$ 6.51087 0.282017
$$534$$ 0 0
$$535$$ 1.37228 2.37686i 0.0593289 0.102761i
$$536$$ 0 0
$$537$$ −38.7446 67.1076i −1.67195 2.89590i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −10.1753 17.6241i −0.437469 0.757718i 0.560025 0.828476i $$-0.310792\pi$$
−0.997494 + 0.0707576i $$0.977458\pi$$
$$542$$ 0 0
$$543$$ −30.7446 + 53.2511i −1.31938 + 2.28523i
$$544$$ 0 0
$$545$$ −5.37228 −0.230123
$$546$$ 0 0
$$547$$ 14.9783 0.640424 0.320212 0.947346i $$-0.396246\pi$$
0.320212 + 0.947346i $$0.396246\pi$$
$$548$$ 0 0
$$549$$ 36.6060 63.4034i 1.56230 2.70599i
$$550$$ 0 0
$$551$$ 4.62772 + 8.01544i 0.197147 + 0.341469i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 3.37228 + 5.84096i 0.143145 + 0.247935i
$$556$$ 0 0
$$557$$ 19.1168 33.1113i 0.810007 1.40297i −0.102852 0.994697i $$-0.532797\pi$$
0.912859 0.408276i $$-0.133870\pi$$
$$558$$ 0 0
$$559$$ 3.76631 0.159298
$$560$$ 0 0
$$561$$ −11.3723 −0.480138
$$562$$ 0 0
$$563$$ −2.74456 + 4.75372i −0.115670 + 0.200345i −0.918047 0.396471i $$-0.870235\pi$$
0.802378 + 0.596817i $$0.203568\pi$$
$$564$$ 0 0
$$565$$ −1.00000 1.73205i −0.0420703 0.0728679i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −10.4891 18.1677i −0.439727 0.761630i 0.557941 0.829880i $$-0.311591\pi$$
−0.997668 + 0.0682510i $$0.978258\pi$$
$$570$$ 0 0
$$571$$ 10.0000 17.3205i 0.418487 0.724841i −0.577301 0.816532i $$-0.695894\pi$$
0.995788 + 0.0916910i $$0.0292272\pi$$
$$572$$ 0 0
$$573$$ −83.8397 −3.50245
$$574$$ 0 0
$$575$$ 6.74456 0.281268
$$576$$ 0 0
$$577$$ 8.80298 15.2472i 0.366473 0.634750i −0.622538 0.782589i $$-0.713899\pi$$
0.989011 + 0.147839i $$0.0472319\pi$$
$$578$$ 0 0
$$579$$ 8.00000 + 13.8564i 0.332469 + 0.575853i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0.233688 + 0.404759i 0.00967837 + 0.0167634i
$$584$$ 0 0
$$585$$ −5.74456 + 9.94987i −0.237508 + 0.411377i
$$586$$ 0 0
$$587$$ −10.9783 −0.453121 −0.226560 0.973997i $$-0.572748\pi$$
−0.226560 + 0.973997i $$0.572748\pi$$
$$588$$ 0 0
$$589$$ −53.9565 −2.22324
$$590$$ 0 0
$$591$$ −44.2337 + 76.6150i −1.81953 + 3.15152i
$$592$$ 0 0
$$593$$ −12.6861 21.9730i −0.520957 0.902325i −0.999703 0.0243710i $$-0.992242\pi$$
0.478746 0.877954i $$-0.341092\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −26.9783 46.7277i −1.10415 1.91244i
$$598$$ 0 0
$$599$$ −3.80298 + 6.58696i −0.155386 + 0.269136i −0.933199 0.359359i $$-0.882995\pi$$
0.777814 + 0.628495i $$0.216329\pi$$
$$600$$ 0 0
$$601$$ −39.4891 −1.61080 −0.805398 0.592735i $$-0.798048\pi$$
−0.805398 + 0.592735i $$0.798048\pi$$
$$602$$ 0 0
$$603$$ −33.4891 −1.36378
$$604$$ 0 0
$$605$$ 5.30298 9.18504i 0.215597 0.373425i
$$606$$ 0 0
$$607$$ −7.80298 13.5152i −0.316713 0.548564i 0.663087 0.748542i $$-0.269246\pi$$
−0.979800 + 0.199979i $$0.935913\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 6.94158 + 12.0232i 0.280826 + 0.486405i
$$612$$ 0 0
$$613$$ 15.7446 27.2704i 0.635917 1.10144i −0.350403 0.936599i $$-0.613955\pi$$
0.986320 0.164841i $$-0.0527112\pi$$
$$614$$ 0 0
$$615$$ 16.0000 0.645182
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 0 0
$$619$$ −0.627719 + 1.08724i −0.0252301 + 0.0436999i −0.878365 0.477991i $$-0.841365\pi$$
0.853135 + 0.521691i $$0.174699\pi$$
$$620$$ 0 0
$$621$$ −61.0951 105.820i −2.45166 4.24640i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 0 0
$$627$$ 7.13859 12.3644i 0.285088 0.493787i
$$628$$ 0 0
$$629$$ 10.7446 0.428414
$$630$$ 0 0
$$631$$ −3.37228 −0.134248 −0.0671242 0.997745i $$-0.521382\pi$$
−0.0671242 + 0.997745i $$0.521382\pi$$
$$632$$ 0 0
$$633$$ 14.5475 25.1971i 0.578213 1.00149i
$$634$$ 0 0
$$635$$ −4.00000 6.92820i −0.158735 0.274937i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −33.4891 58.0049i −1.32481 2.29464i
$$640$$ 0 0
$$641$$ −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i $$-0.845909\pi$$
0.845601 + 0.533816i $$0.179242\pi$$
$$642$$ 0 0
$$643$$ −12.6277 −0.497989 −0.248994 0.968505i $$-0.580100\pi$$
−0.248994 + 0.968505i $$0.580100\pi$$
$$644$$ 0 0
$$645$$ 9.25544 0.364432
$$646$$ 0 0
$$647$$ −8.00000 + 13.8564i −0.314512 + 0.544752i −0.979334 0.202251i $$-0.935174\pi$$
0.664821 + 0.747002i $$0.268508\pi$$
$$648$$ 0 0
$$649$$ 2.51087 + 4.34896i 0.0985605 + 0.170712i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i $$-0.204122\pi$$
−0.918736 + 0.394872i $$0.870789\pi$$
$$654$$ 0 0
$$655$$ 3.37228 5.84096i 0.131766 0.228225i
$$656$$ 0 0
$$657$$ 50.2337 1.95980
$$658$$ 0 0
$$659$$ 6.11684 0.238278 0.119139 0.992878i $$-0.461987\pi$$
0.119139 + 0.992878i $$0.461987\pi$$
$$660$$ 0 0
$$661$$ 1.62772 2.81929i 0.0633109 0.109658i −0.832633 0.553826i $$-0.813167\pi$$
0.895943 + 0.444168i $$0.146501\pi$$
$$662$$ 0 0
$$663$$ 12.4307 + 21.5306i 0.482769 + 0.836180i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −4.62772 8.01544i −0.179186 0.310359i
$$668$$ 0 0
$$669$$ −19.1753 + 33.2125i −0.741359 + 1.28407i
$$670$$ 0 0
$$671$$ −5.48913 −0.211905
$$672$$ 0 0
$$673$$ −31.7228 −1.22282 −0.611412 0.791312i $$-0.709398\pi$$
−0.611412 + 0.791312i $$0.709398\pi$$
$$674$$ 0 0
$$675$$ −9.05842 + 15.6896i −0.348659 + 0.603895i
$$676$$ 0 0
$$677$$ −18.1753 31.4805i −0.698532 1.20989i −0.968975 0.247157i $$-0.920504\pi$$
0.270443 0.962736i $$-0.412830\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −14.9416 25.8796i −0.572563 0.991707i
$$682$$ 0 0
$$683$$ −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i $$0.408507\pi$$
−0.972242 + 0.233977i $$0.924826\pi$$
$$684$$ 0 0
$$685$$ 3.25544 0.124384
$$686$$ 0 0
$$687$$ −74.9783 −2.86060
$$688$$ 0 0
$$689$$ 0.510875 0.884861i 0.0194628 0.0337105i
$$690$$ 0 0
$$691$$ 6.74456 + 11.6819i 0.256575 + 0.444401i 0.965322 0.261061i $$-0.0840725\pi$$
−0.708747 + 0.705463i $$0.750739\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 3.37228 + 5.84096i 0.127918 + 0.221560i
$$696$$ 0 0
$$697$$ 12.7446 22.0742i 0.482735 0.836121i
$$698$$ 0 0
$$699$$ −42.9783 −1.62559
$$700$$ 0 0
$$701$$ 30.8614 1.16562 0.582810 0.812609i $$-0.301953\pi$$
0.582810 + 0.812609i $$0.301953\pi$$
$$702$$ 0 0
$$703$$ −6.74456 + 11.6819i −0.254376 + 0.440592i
$$704$$ 0 0
$$705$$ 17.0584 + 29.5461i 0.642457 + 1.11277i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 16.8030 + 29.1036i 0.631049 + 1.09301i 0.987338 + 0.158633i $$0.0507088\pi$$
−0.356288 + 0.934376i $$0.615958\pi$$
$$710$$ 0 0
$$711$$ 8.86141 15.3484i 0.332329 0.575610i
$$712$$ 0 0
$$713$$ 53.9565 2.02069
$$714$$ 0 0
$$715$$ 0.861407 0.0322148
$$716$$ 0 0
$$717$$ −32.6644 + 56.5764i −1.21987 + 2.11288i
$$718$$ 0 0
$$719$$ 7.37228 + 12.7692i 0.274940 + 0.476210i 0.970120 0.242626i $$-0.0780088\pi$$
−0.695180 + 0.718836i $$0.744675\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 43.8397 + 75.9325i 1.63041 + 2.82396i
$$724$$ 0 0
$$725$$ −0.686141 + 1.18843i −0.0254826 + 0.0441372i
$$726$$ 0 0
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ 0 0
$$729$$ 117.935 4.36795
$$730$$ 0 0
$$731$$ 7.37228 12.7692i 0.272674 0.472285i
$$732$$ 0 0
$$733$$ −19.4307 33.6550i −0.717689 1.24307i −0.961913 0.273356i $$-0.911866\pi$$
0.244224 0.969719i $$-0.421467\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 1.25544 + 2.17448i 0.0462446 + 0.0800980i
$$738$$ 0 0
$$739$$ −9.80298 + 16.9793i −0.360609 + 0.624592i −0.988061 0.154062i $$-0.950764\pi$$
0.627453 + 0.778655i $$0.284098\pi$$
$$740$$ 0 0
$$741$$ −31.2119 −1.14660
$$742$$ 0 0
$$743$$ −29.4891 −1.08185 −0.540926 0.841070i $$-0.681926\pi$$
−0.540926 + 0.841070i $$0.681926\pi$$
$$744$$ 0 0
$$745$$ 3.74456 6.48577i 0.137190 0.237620i
$$746$$ 0 0
$$747$$ 56.4674 + 97.8044i 2.06603 + 3.57847i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −24.4307 42.3152i −0.891489 1.54410i −0.838091 0.545531i $$-0.816328\pi$$
−0.0533984 0.998573i $$-0.517005\pi$$
$$752$$ 0 0
$$753$$ −11.3723 + 19.6974i −0.414429 + 0.717812i
$$754$$ 0 0
$$755$$ −2.11684 −0.0770398
$$756$$ 0 0
$$757$$ −38.2337 −1.38963 −0.694814 0.719190i $$-0.744513\pi$$
−0.694814 + 0.719190i $$0.744513\pi$$
$$758$$ 0 0
$$759$$ −7.13859 + 12.3644i −0.259115 + 0.448800i
$$760$$ 0 0
$$761$$ −20.4891 35.4882i −0.742730 1.28645i −0.951248 0.308428i $$-0.900197\pi$$
0.208518 0.978019i $$-0.433136\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 22.4891 + 38.9523i 0.813096 + 1.40832i
$$766$$ 0 0
$$767$$ 5.48913 9.50744i 0.198201 0.343294i
$$768$$ 0 0
$$769$$ 19.4891 0.702796 0.351398 0.936226i $$-0.385706\pi$$
0.351398 + 0.936226i $$0.385706\pi$$
$$770$$ 0 0
$$771$$ 1.72281 0.0620456
$$772$$ 0 0
$$773$$ −0.686141 + 1.18843i −0.0246788 + 0.0427449i −0.878101 0.478475i $$-0.841190\pi$$
0.853422 + 0.521220i $$0.174523\pi$$
$$774$$ 0 0
$$775$$ −4.00000 6.92820i −0.143684 0.248868i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 16.0000 + 27.7128i 0.573259 + 0.992915i
$$780$$ 0 0
$$781$$ −2.51087 + 4.34896i −0.0898462 + 0.155618i
$$782$$ 0 0
$$783$$ 24.8614 0.888474
$$784$$ 0 0
$$785$$ −7.48913 −0.267298
$$786$$ 0 0
$$787$$ −6.94158 + 12.0232i −0.247441 + 0.428580i −0.962815 0.270162i $$-0.912923\pi$$
0.715374 + 0.698741i $$0.246256\pi$$
$$788$$ 0 0
$$789$$ 20.6277 + 35.7283i 0.734366 + 1.27196i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 6.00000 + 10.3923i 0.213066 + 0.369042i
$$794$$ 0 0
$$795$$ 1.25544 2.17448i 0.0445258 0.0771209i
$$796$$ 0 0
$$797$$ −21.3723 −0.757045 −0.378523 0.925592i $$-0.623568\pi$$
−0.378523 + 0.925592i $$0.623568\pi$$
$$798$$ 0 0
$$799$$