# Properties

 Label 930.2.d.i.559.1 Level $930$ Weight $2$ Character 930.559 Analytic conductor $7.426$ Analytic rank $0$ Dimension $6$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(559,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$7.42608738798$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.11669056.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - 2x^{5} + 7x^{4} + 8x^{3} - x^{2} + 54x + 58$$ x^6 - 2*x^5 + 7*x^4 + 8*x^3 - x^2 + 54*x + 58 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 559.1 Root $$-1.23545 - 0.0526623i$$ of defining polynomial Character $$\chi$$ $$=$$ 930.559 Dual form 930.2.d.i.559.4

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.23545 - 0.0526623i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.23545 - 0.0526623i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-0.0526623 + 2.23545i) q^{10} -0.470896 q^{11} -1.00000i q^{12} +6.47090i q^{13} -2.00000 q^{14} +(0.0526623 - 2.23545i) q^{15} +1.00000 q^{16} -7.04712i q^{17} +1.00000i q^{18} +7.04712 q^{19} +(2.23545 + 0.0526623i) q^{20} +2.00000 q^{21} +0.470896i q^{22} +6.94179i q^{23} -1.00000 q^{24} +(4.99445 + 0.235448i) q^{25} +6.47090 q^{26} -1.00000i q^{27} +2.00000i q^{28} +6.94179 q^{29} +(-2.23545 - 0.0526623i) q^{30} -1.00000 q^{31} -1.00000i q^{32} -0.470896i q^{33} -7.04712 q^{34} +(-0.105325 + 4.47090i) q^{35} +1.00000 q^{36} +1.78935i q^{37} -7.04712i q^{38} -6.47090 q^{39} +(0.0526623 - 2.23545i) q^{40} +2.00000 q^{41} -2.00000i q^{42} -0.210649i q^{43} +0.470896 q^{44} +(2.23545 + 0.0526623i) q^{45} +6.94179 q^{46} +7.04712i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(0.235448 - 4.99445i) q^{50} +7.04712 q^{51} -6.47090i q^{52} -3.15244i q^{53} -1.00000 q^{54} +(1.05266 + 0.0247985i) q^{55} +2.00000 q^{56} +7.04712i q^{57} -6.94179i q^{58} +7.15244 q^{59} +(-0.0526623 + 2.23545i) q^{60} +11.2578 q^{61} +1.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(0.340772 - 14.4653i) q^{65} -0.470896 q^{66} +8.26025i q^{67} +7.04712i q^{68} -6.94179 q^{69} +(4.47090 + 0.105325i) q^{70} +0.260246 q^{71} -1.00000i q^{72} +11.8836i q^{73} +1.78935 q^{74} +(-0.235448 + 4.99445i) q^{75} -7.04712 q^{76} +0.941791i q^{77} +6.47090i q^{78} +1.89468 q^{79} +(-2.23545 - 0.0526623i) q^{80} +1.00000 q^{81} -2.00000i q^{82} -11.7783i q^{83} -2.00000 q^{84} +(-0.371118 + 15.7535i) q^{85} -0.210649 q^{86} +6.94179i q^{87} -0.470896i q^{88} -12.0942 q^{89} +(0.0526623 - 2.23545i) q^{90} +12.9418 q^{91} -6.94179i q^{92} -1.00000i q^{93} +7.04712 q^{94} +(-15.7535 - 0.371118i) q^{95} +1.00000 q^{96} +3.52910i q^{97} -3.00000i q^{98} +0.470896 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 6 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10})$$ 6 * q - 6 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^9 $$6 q - 6 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{9} + 16 q^{11} - 12 q^{14} + 6 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} - 6 q^{24} - 8 q^{25} + 20 q^{26} + 4 q^{29} - 4 q^{30} - 6 q^{31} - 4 q^{34} + 6 q^{36} - 20 q^{39} + 12 q^{41} - 16 q^{44} + 4 q^{45} + 4 q^{46} + 18 q^{49} - 8 q^{50} + 4 q^{51} - 6 q^{54} + 6 q^{55} + 12 q^{56} + 4 q^{59} + 28 q^{61} - 6 q^{64} - 8 q^{65} + 16 q^{66} - 4 q^{69} + 8 q^{70} - 16 q^{71} + 12 q^{74} + 8 q^{75} - 4 q^{76} + 12 q^{79} - 4 q^{80} + 6 q^{81} - 12 q^{84} - 22 q^{85} + 4 q^{89} + 40 q^{91} + 4 q^{94} - 28 q^{95} + 6 q^{96} - 16 q^{99}+O(q^{100})$$ 6 * q - 6 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^9 + 16 * q^11 - 12 * q^14 + 6 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 - 6 * q^24 - 8 * q^25 + 20 * q^26 + 4 * q^29 - 4 * q^30 - 6 * q^31 - 4 * q^34 + 6 * q^36 - 20 * q^39 + 12 * q^41 - 16 * q^44 + 4 * q^45 + 4 * q^46 + 18 * q^49 - 8 * q^50 + 4 * q^51 - 6 * q^54 + 6 * q^55 + 12 * q^56 + 4 * q^59 + 28 * q^61 - 6 * q^64 - 8 * q^65 + 16 * q^66 - 4 * q^69 + 8 * q^70 - 16 * q^71 + 12 * q^74 + 8 * q^75 - 4 * q^76 + 12 * q^79 - 4 * q^80 + 6 * q^81 - 12 * q^84 - 22 * q^85 + 4 * q^89 + 40 * q^91 + 4 * q^94 - 28 * q^95 + 6 * q^96 - 16 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$$.

 $$n$$ $$187$$ $$311$$ $$871$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 1.00000i 0.577350i
$$4$$ −1.00000 −0.500000
$$5$$ −2.23545 0.0526623i −0.999723 0.0235513i
$$6$$ 1.00000 0.408248
$$7$$ 2.00000i 0.755929i −0.925820 0.377964i $$-0.876624\pi$$
0.925820 0.377964i $$-0.123376\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −1.00000 −0.333333
$$10$$ −0.0526623 + 2.23545i −0.0166533 + 0.706911i
$$11$$ −0.470896 −0.141980 −0.0709902 0.997477i $$-0.522616\pi$$
−0.0709902 + 0.997477i $$0.522616\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 6.47090i 1.79470i 0.441316 + 0.897352i $$0.354512\pi$$
−0.441316 + 0.897352i $$0.645488\pi$$
$$14$$ −2.00000 −0.534522
$$15$$ 0.0526623 2.23545i 0.0135974 0.577190i
$$16$$ 1.00000 0.250000
$$17$$ 7.04712i 1.70918i −0.519306 0.854588i $$-0.673810\pi$$
0.519306 0.854588i $$-0.326190\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 7.04712 1.61672 0.808360 0.588689i $$-0.200356\pi$$
0.808360 + 0.588689i $$0.200356\pi$$
$$20$$ 2.23545 + 0.0526623i 0.499861 + 0.0117757i
$$21$$ 2.00000 0.436436
$$22$$ 0.470896i 0.100395i
$$23$$ 6.94179i 1.44746i 0.690081 + 0.723732i $$0.257575\pi$$
−0.690081 + 0.723732i $$0.742425\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 4.99445 + 0.235448i 0.998891 + 0.0470896i
$$26$$ 6.47090 1.26905
$$27$$ 1.00000i 0.192450i
$$28$$ 2.00000i 0.377964i
$$29$$ 6.94179 1.28906 0.644529 0.764580i $$-0.277053\pi$$
0.644529 + 0.764580i $$0.277053\pi$$
$$30$$ −2.23545 0.0526623i −0.408135 0.00961478i
$$31$$ −1.00000 −0.179605
$$32$$ 1.00000i 0.176777i
$$33$$ 0.470896i 0.0819724i
$$34$$ −7.04712 −1.20857
$$35$$ −0.105325 + 4.47090i −0.0178031 + 0.755719i
$$36$$ 1.00000 0.166667
$$37$$ 1.78935i 0.294167i 0.989124 + 0.147084i $$0.0469887\pi$$
−0.989124 + 0.147084i $$0.953011\pi$$
$$38$$ 7.04712i 1.14319i
$$39$$ −6.47090 −1.03617
$$40$$ 0.0526623 2.23545i 0.00832664 0.353455i
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 2.00000i 0.308607i
$$43$$ 0.210649i 0.0321237i −0.999871 0.0160619i $$-0.994887\pi$$
0.999871 0.0160619i $$-0.00511287\pi$$
$$44$$ 0.470896 0.0709902
$$45$$ 2.23545 + 0.0526623i 0.333241 + 0.00785044i
$$46$$ 6.94179 1.02351
$$47$$ 7.04712i 1.02793i 0.857812 + 0.513964i $$0.171823\pi$$
−0.857812 + 0.513964i $$0.828177\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 3.00000 0.428571
$$50$$ 0.235448 4.99445i 0.0332973 0.706322i
$$51$$ 7.04712 0.986794
$$52$$ 6.47090i 0.897352i
$$53$$ 3.15244i 0.433021i −0.976280 0.216510i $$-0.930532\pi$$
0.976280 0.216510i $$-0.0694676\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 1.05266 + 0.0247985i 0.141941 + 0.00334382i
$$56$$ 2.00000 0.267261
$$57$$ 7.04712i 0.933413i
$$58$$ 6.94179i 0.911502i
$$59$$ 7.15244 0.931168 0.465584 0.885004i $$-0.345844\pi$$
0.465584 + 0.885004i $$0.345844\pi$$
$$60$$ −0.0526623 + 2.23545i −0.00679868 + 0.288595i
$$61$$ 11.2578 1.44141 0.720705 0.693242i $$-0.243818\pi$$
0.720705 + 0.693242i $$0.243818\pi$$
$$62$$ 1.00000i 0.127000i
$$63$$ 2.00000i 0.251976i
$$64$$ −1.00000 −0.125000
$$65$$ 0.340772 14.4653i 0.0422676 1.79421i
$$66$$ −0.470896 −0.0579632
$$67$$ 8.26025i 1.00915i 0.863368 + 0.504575i $$0.168351\pi$$
−0.863368 + 0.504575i $$0.831649\pi$$
$$68$$ 7.04712i 0.854588i
$$69$$ −6.94179 −0.835693
$$70$$ 4.47090 + 0.105325i 0.534374 + 0.0125887i
$$71$$ 0.260246 0.0308855 0.0154428 0.999881i $$-0.495084\pi$$
0.0154428 + 0.999881i $$0.495084\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 11.8836i 1.39087i 0.718590 + 0.695434i $$0.244788\pi$$
−0.718590 + 0.695434i $$0.755212\pi$$
$$74$$ 1.78935 0.208008
$$75$$ −0.235448 + 4.99445i −0.0271872 + 0.576710i
$$76$$ −7.04712 −0.808360
$$77$$ 0.941791i 0.107327i
$$78$$ 6.47090i 0.732685i
$$79$$ 1.89468 0.213168 0.106584 0.994304i $$-0.466009\pi$$
0.106584 + 0.994304i $$0.466009\pi$$
$$80$$ −2.23545 0.0526623i −0.249931 0.00588783i
$$81$$ 1.00000 0.111111
$$82$$ 2.00000i 0.220863i
$$83$$ 11.7783i 1.29283i −0.762985 0.646416i $$-0.776267\pi$$
0.762985 0.646416i $$-0.223733\pi$$
$$84$$ −2.00000 −0.218218
$$85$$ −0.371118 + 15.7535i −0.0402533 + 1.70870i
$$86$$ −0.210649 −0.0227149
$$87$$ 6.94179i 0.744238i
$$88$$ 0.470896i 0.0501976i
$$89$$ −12.0942 −1.28199 −0.640993 0.767547i $$-0.721477\pi$$
−0.640993 + 0.767547i $$0.721477\pi$$
$$90$$ 0.0526623 2.23545i 0.00555110 0.235637i
$$91$$ 12.9418 1.35667
$$92$$ 6.94179i 0.723732i
$$93$$ 1.00000i 0.103695i
$$94$$ 7.04712 0.726854
$$95$$ −15.7535 0.371118i −1.61627 0.0380759i
$$96$$ 1.00000 0.102062
$$97$$ 3.52910i 0.358326i 0.983819 + 0.179163i $$0.0573390\pi$$
−0.983819 + 0.179163i $$0.942661\pi$$
$$98$$ 3.00000i 0.303046i
$$99$$ 0.470896 0.0473268
$$100$$ −4.99445 0.235448i −0.499445 0.0235448i
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 7.04712i 0.697768i
$$103$$ 6.00000i 0.591198i −0.955312 0.295599i $$-0.904481\pi$$
0.955312 0.295599i $$-0.0955191\pi$$
$$104$$ −6.47090 −0.634524
$$105$$ −4.47090 0.105325i −0.436315 0.0102786i
$$106$$ −3.15244 −0.306192
$$107$$ 16.7311i 1.61746i −0.588180 0.808730i $$-0.700155\pi$$
0.588180 0.808730i $$-0.299845\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ 11.1524 1.06821 0.534105 0.845418i $$-0.320649\pi$$
0.534105 + 0.845418i $$0.320649\pi$$
$$110$$ 0.0247985 1.05266i 0.00236444 0.100367i
$$111$$ −1.78935 −0.169838
$$112$$ 2.00000i 0.188982i
$$113$$ 16.3049i 1.53383i 0.641746 + 0.766917i $$0.278210\pi$$
−0.641746 + 0.766917i $$0.721790\pi$$
$$114$$ 7.04712 0.660023
$$115$$ 0.365571 15.5180i 0.0340897 1.44706i
$$116$$ −6.94179 −0.644529
$$117$$ 6.47090i 0.598235i
$$118$$ 7.15244i 0.658436i
$$119$$ −14.0942 −1.29202
$$120$$ 2.23545 + 0.0526623i 0.204068 + 0.00480739i
$$121$$ −10.7783 −0.979842
$$122$$ 11.2578i 1.01923i
$$123$$ 2.00000i 0.180334i
$$124$$ 1.00000 0.0898027
$$125$$ −11.1524 0.789351i −0.997505 0.0706017i
$$126$$ 2.00000 0.178174
$$127$$ 0.941791i 0.0835704i −0.999127 0.0417852i $$-0.986695\pi$$
0.999127 0.0417852i $$-0.0133045\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0.210649 0.0185466
$$130$$ −14.4653 0.340772i −1.26870 0.0298877i
$$131$$ −3.15244 −0.275430 −0.137715 0.990472i $$-0.543976\pi$$
−0.137715 + 0.990472i $$0.543976\pi$$
$$132$$ 0.470896i 0.0409862i
$$133$$ 14.0942i 1.22212i
$$134$$ 8.26025 0.713577
$$135$$ −0.0526623 + 2.23545i −0.00453245 + 0.192397i
$$136$$ 7.04712 0.604285
$$137$$ 9.67293i 0.826414i −0.910637 0.413207i $$-0.864409\pi$$
0.910637 0.413207i $$-0.135591\pi$$
$$138$$ 6.94179i 0.590924i
$$139$$ −5.05821 −0.429032 −0.214516 0.976721i $$-0.568817\pi$$
−0.214516 + 0.976721i $$0.568817\pi$$
$$140$$ 0.105325 4.47090i 0.00890156 0.377860i
$$141$$ −7.04712 −0.593474
$$142$$ 0.260246i 0.0218394i
$$143$$ 3.04712i 0.254813i
$$144$$ −1.00000 −0.0833333
$$145$$ −15.5180 0.365571i −1.28870 0.0303590i
$$146$$ 11.8836 0.983492
$$147$$ 3.00000i 0.247436i
$$148$$ 1.78935i 0.147084i
$$149$$ −13.4127 −1.09881 −0.549405 0.835556i $$-0.685146\pi$$
−0.549405 + 0.835556i $$0.685146\pi$$
$$150$$ 4.99445 + 0.235448i 0.407795 + 0.0192242i
$$151$$ 19.5676 1.59239 0.796195 0.605041i $$-0.206843\pi$$
0.796195 + 0.605041i $$0.206843\pi$$
$$152$$ 7.04712i 0.571597i
$$153$$ 7.04712i 0.569726i
$$154$$ 0.941791 0.0758917
$$155$$ 2.23545 + 0.0526623i 0.179555 + 0.00422994i
$$156$$ 6.47090 0.518086
$$157$$ 21.2467i 1.69567i 0.530261 + 0.847835i $$0.322094\pi$$
−0.530261 + 0.847835i $$0.677906\pi$$
$$158$$ 1.89468i 0.150732i
$$159$$ 3.15244 0.250005
$$160$$ −0.0526623 + 2.23545i −0.00416332 + 0.176728i
$$161$$ 13.8836 1.09418
$$162$$ 1.00000i 0.0785674i
$$163$$ 4.26025i 0.333688i −0.985983 0.166844i $$-0.946642\pi$$
0.985983 0.166844i $$-0.0533577\pi$$
$$164$$ −2.00000 −0.156174
$$165$$ −0.0247985 + 1.05266i −0.00193056 + 0.0819497i
$$166$$ −11.7783 −0.914170
$$167$$ 2.00000i 0.154765i −0.997001 0.0773823i $$-0.975344\pi$$
0.997001 0.0773823i $$-0.0246562\pi$$
$$168$$ 2.00000i 0.154303i
$$169$$ −28.8725 −2.22096
$$170$$ 15.7535 + 0.371118i 1.20824 + 0.0284634i
$$171$$ −7.04712 −0.538906
$$172$$ 0.210649i 0.0160619i
$$173$$ 17.9889i 1.36767i 0.729636 + 0.683836i $$0.239689\pi$$
−0.729636 + 0.683836i $$0.760311\pi$$
$$174$$ 6.94179 0.526256
$$175$$ 0.470896 9.98891i 0.0355964 0.755090i
$$176$$ −0.470896 −0.0354951
$$177$$ 7.15244i 0.537610i
$$178$$ 12.0942i 0.906501i
$$179$$ 12.0496 0.900629 0.450315 0.892870i $$-0.351312\pi$$
0.450315 + 0.892870i $$0.351312\pi$$
$$180$$ −2.23545 0.0526623i −0.166620 0.00392522i
$$181$$ −13.6729 −1.01630 −0.508151 0.861268i $$-0.669671\pi$$
−0.508151 + 0.861268i $$0.669671\pi$$
$$182$$ 12.9418i 0.959309i
$$183$$ 11.2578i 0.832198i
$$184$$ −6.94179 −0.511756
$$185$$ 0.0942314 4.00000i 0.00692803 0.294086i
$$186$$ −1.00000 −0.0733236
$$187$$ 3.31846i 0.242669i
$$188$$ 7.04712i 0.513964i
$$189$$ −2.00000 −0.145479
$$190$$ −0.371118 + 15.7535i −0.0269237 + 1.14288i
$$191$$ −14.8254 −1.07273 −0.536363 0.843987i $$-0.680202\pi$$
−0.536363 + 0.843987i $$0.680202\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ 8.04960i 0.579423i −0.957114 0.289711i $$-0.906441\pi$$
0.957114 0.289711i $$-0.0935593\pi$$
$$194$$ 3.52910 0.253375
$$195$$ 14.4653 + 0.340772i 1.03589 + 0.0244032i
$$196$$ −3.00000 −0.214286
$$197$$ 16.3049i 1.16167i −0.814020 0.580837i $$-0.802725\pi$$
0.814020 0.580837i $$-0.197275\pi$$
$$198$$ 0.470896i 0.0334651i
$$199$$ 3.98891 0.282766 0.141383 0.989955i $$-0.454845\pi$$
0.141383 + 0.989955i $$0.454845\pi$$
$$200$$ −0.235448 + 4.99445i −0.0166487 + 0.353161i
$$201$$ −8.26025 −0.582633
$$202$$ 0 0
$$203$$ 13.8836i 0.974436i
$$204$$ −7.04712 −0.493397
$$205$$ −4.47090 0.105325i −0.312261 0.00735619i
$$206$$ −6.00000 −0.418040
$$207$$ 6.94179i 0.482488i
$$208$$ 6.47090i 0.448676i
$$209$$ −3.31846 −0.229542
$$210$$ −0.105325 + 4.47090i −0.00726809 + 0.308521i
$$211$$ 2.11642 0.145700 0.0728501 0.997343i $$-0.476791\pi$$
0.0728501 + 0.997343i $$0.476791\pi$$
$$212$$ 3.15244i 0.216510i
$$213$$ 0.260246i 0.0178318i
$$214$$ −16.7311 −1.14372
$$215$$ −0.0110933 + 0.470896i −0.000756556 + 0.0321148i
$$216$$ 1.00000 0.0680414
$$217$$ 2.00000i 0.135769i
$$218$$ 11.1524i 0.755339i
$$219$$ −11.8836 −0.803018
$$220$$ −1.05266 0.0247985i −0.0709705 0.00167191i
$$221$$ 45.6011 3.06747
$$222$$ 1.78935i 0.120093i
$$223$$ 2.58731i 0.173259i −0.996241 0.0866297i $$-0.972390\pi$$
0.996241 0.0866297i $$-0.0276097\pi$$
$$224$$ −2.00000 −0.133631
$$225$$ −4.99445 0.235448i −0.332964 0.0156965i
$$226$$ 16.3049 1.08458
$$227$$ 4.94179i 0.327998i −0.986460 0.163999i $$-0.947561\pi$$
0.986460 0.163999i $$-0.0524394\pi$$
$$228$$ 7.04712i 0.466707i
$$229$$ 11.6791 0.771774 0.385887 0.922546i $$-0.373895\pi$$
0.385887 + 0.922546i $$0.373895\pi$$
$$230$$ −15.5180 0.365571i −1.02323 0.0241050i
$$231$$ −0.941791 −0.0619653
$$232$$ 6.94179i 0.455751i
$$233$$ 13.7894i 0.903370i 0.892177 + 0.451685i $$0.149177\pi$$
−0.892177 + 0.451685i $$0.850823\pi$$
$$234$$ −6.47090 −0.423016
$$235$$ 0.371118 15.7535i 0.0242090 1.02764i
$$236$$ −7.15244 −0.465584
$$237$$ 1.89468i 0.123072i
$$238$$ 14.0942i 0.913593i
$$239$$ 12.7311 0.823509 0.411755 0.911295i $$-0.364916\pi$$
0.411755 + 0.911295i $$0.364916\pi$$
$$240$$ 0.0526623 2.23545i 0.00339934 0.144298i
$$241$$ −3.15244 −0.203067 −0.101533 0.994832i $$-0.532375\pi$$
−0.101533 + 0.994832i $$0.532375\pi$$
$$242$$ 10.7783i 0.692853i
$$243$$ 1.00000i 0.0641500i
$$244$$ −11.2578 −0.720705
$$245$$ −6.70634 0.157987i −0.428453 0.0100934i
$$246$$ 2.00000 0.127515
$$247$$ 45.6011i 2.90153i
$$248$$ 1.00000i 0.0635001i
$$249$$ 11.7783 0.746417
$$250$$ −0.789351 + 11.1524i −0.0499229 + 0.705342i
$$251$$ 3.05821 0.193032 0.0965162 0.995331i $$-0.469230\pi$$
0.0965162 + 0.995331i $$0.469230\pi$$
$$252$$ 2.00000i 0.125988i
$$253$$ 3.26886i 0.205511i
$$254$$ −0.941791 −0.0590932
$$255$$ −15.7535 0.371118i −0.986520 0.0232403i
$$256$$ 1.00000 0.0625000
$$257$$ 16.0942i 1.00393i 0.864888 + 0.501965i $$0.167389\pi$$
−0.864888 + 0.501965i $$0.832611\pi$$
$$258$$ 0.210649i 0.0131145i
$$259$$ 3.57870 0.222370
$$260$$ −0.340772 + 14.4653i −0.0211338 + 0.897103i
$$261$$ −6.94179 −0.429686
$$262$$ 3.15244i 0.194758i
$$263$$ 0.0942314i 0.00581056i −0.999996 0.00290528i $$-0.999075\pi$$
0.999996 0.00290528i $$-0.000924780\pi$$
$$264$$ 0.470896 0.0289816
$$265$$ −0.166015 + 7.04712i −0.0101982 + 0.432901i
$$266$$ −14.0942 −0.864173
$$267$$ 12.0942i 0.740155i
$$268$$ 8.26025i 0.504575i
$$269$$ 23.8836 1.45621 0.728104 0.685467i $$-0.240402\pi$$
0.728104 + 0.685467i $$0.240402\pi$$
$$270$$ 2.23545 + 0.0526623i 0.136045 + 0.00320493i
$$271$$ 24.4102 1.48281 0.741407 0.671055i $$-0.234159\pi$$
0.741407 + 0.671055i $$0.234159\pi$$
$$272$$ 7.04712i 0.427294i
$$273$$ 12.9418i 0.783273i
$$274$$ −9.67293 −0.584363
$$275$$ −2.35187 0.110871i −0.141823 0.00668579i
$$276$$ 6.94179 0.417847
$$277$$ 7.41269i 0.445385i −0.974889 0.222693i $$-0.928515\pi$$
0.974889 0.222693i $$-0.0714846\pi$$
$$278$$ 5.05821i 0.303371i
$$279$$ 1.00000 0.0598684
$$280$$ −4.47090 0.105325i −0.267187 0.00629435i
$$281$$ −11.8836 −0.708915 −0.354458 0.935072i $$-0.615334\pi$$
−0.354458 + 0.935072i $$0.615334\pi$$
$$282$$ 7.04712i 0.419650i
$$283$$ 22.9864i 1.36640i −0.730231 0.683201i $$-0.760587\pi$$
0.730231 0.683201i $$-0.239413\pi$$
$$284$$ −0.260246 −0.0154428
$$285$$ 0.371118 15.7535i 0.0219831 0.933154i
$$286$$ −3.04712 −0.180180
$$287$$ 4.00000i 0.236113i
$$288$$ 1.00000i 0.0589256i
$$289$$ −32.6618 −1.92128
$$290$$ −0.365571 + 15.5180i −0.0214671 + 0.911249i
$$291$$ −3.52910 −0.206880
$$292$$ 11.8836i 0.695434i
$$293$$ 14.4213i 0.842501i 0.906944 + 0.421251i $$0.138409\pi$$
−0.906944 + 0.421251i $$0.861591\pi$$
$$294$$ 3.00000 0.174964
$$295$$ −15.9889 0.376664i −0.930910 0.0219302i
$$296$$ −1.78935 −0.104004
$$297$$ 0.470896i 0.0273241i
$$298$$ 13.4127i 0.776976i
$$299$$ −44.9196 −2.59777
$$300$$ 0.235448 4.99445i 0.0135936 0.288355i
$$301$$ −0.421299 −0.0242832
$$302$$ 19.5676i 1.12599i
$$303$$ 0 0
$$304$$ 7.04712 0.404180
$$305$$ −25.1661 0.592860i −1.44101 0.0339471i
$$306$$ 7.04712 0.402857
$$307$$ 24.9418i 1.42350i 0.702431 + 0.711752i $$0.252098\pi$$
−0.702431 + 0.711752i $$0.747902\pi$$
$$308$$ 0.941791i 0.0536635i
$$309$$ 6.00000 0.341328
$$310$$ 0.0526623 2.23545i 0.00299102 0.126965i
$$311$$ −24.4487 −1.38636 −0.693180 0.720765i $$-0.743791\pi$$
−0.693180 + 0.720765i $$0.743791\pi$$
$$312$$ 6.47090i 0.366342i
$$313$$ 14.1885i 0.801979i 0.916083 + 0.400990i $$0.131334\pi$$
−0.916083 + 0.400990i $$0.868666\pi$$
$$314$$ 21.2467 1.19902
$$315$$ 0.105325 4.47090i 0.00593437 0.251906i
$$316$$ −1.89468 −0.106584
$$317$$ 21.9889i 1.23502i 0.786563 + 0.617510i $$0.211859\pi$$
−0.786563 + 0.617510i $$0.788141\pi$$
$$318$$ 3.15244i 0.176780i
$$319$$ −3.26886 −0.183021
$$320$$ 2.23545 + 0.0526623i 0.124965 + 0.00294391i
$$321$$ 16.7311 0.933841
$$322$$ 13.8836i 0.773702i
$$323$$ 49.6618i 2.76326i
$$324$$ −1.00000 −0.0555556
$$325$$ −1.52356 + 32.3186i −0.0845118 + 1.79271i
$$326$$ −4.26025 −0.235953
$$327$$ 11.1524i 0.616731i
$$328$$ 2.00000i 0.110432i
$$329$$ 14.0942 0.777040
$$330$$ 1.05266 + 0.0247985i 0.0579472 + 0.00136511i
$$331$$ −15.3631 −0.844432 −0.422216 0.906495i $$-0.638748\pi$$
−0.422216 + 0.906495i $$0.638748\pi$$
$$332$$ 11.7783i 0.646416i
$$333$$ 1.78935i 0.0980558i
$$334$$ −2.00000 −0.109435
$$335$$ 0.435004 18.4653i 0.0237668 1.00887i
$$336$$ 2.00000 0.109109
$$337$$ 13.9778i 0.761420i −0.924694 0.380710i $$-0.875680\pi$$
0.924694 0.380710i $$-0.124320\pi$$
$$338$$ 28.8725i 1.57046i
$$339$$ −16.3049 −0.885560
$$340$$ 0.371118 15.7535i 0.0201267 0.854351i
$$341$$ 0.470896 0.0255004
$$342$$ 7.04712i 0.381064i
$$343$$ 20.0000i 1.07990i
$$344$$ 0.210649 0.0113574
$$345$$ 15.5180 + 0.365571i 0.835462 + 0.0196817i
$$346$$ 17.9889 0.967090
$$347$$ 17.6618i 0.948137i −0.880488 0.474069i $$-0.842785\pi$$
0.880488 0.474069i $$-0.157215\pi$$
$$348$$ 6.94179i 0.372119i
$$349$$ 7.67293 0.410723 0.205361 0.978686i $$-0.434163\pi$$
0.205361 + 0.978686i $$0.434163\pi$$
$$350$$ −9.98891 0.470896i −0.533930 0.0251704i
$$351$$ 6.47090 0.345391
$$352$$ 0.470896i 0.0250988i
$$353$$ 11.0471i 0.587979i 0.955809 + 0.293989i $$0.0949830\pi$$
−0.955809 + 0.293989i $$0.905017\pi$$
$$354$$ 7.15244 0.380148
$$355$$ −0.581767 0.0137052i −0.0308770 0.000727395i
$$356$$ 12.0942 0.640993
$$357$$ 14.0942i 0.745946i
$$358$$ 12.0496i 0.636841i
$$359$$ 35.9282 1.89622 0.948109 0.317944i $$-0.102993\pi$$
0.948109 + 0.317944i $$0.102993\pi$$
$$360$$ −0.0526623 + 2.23545i −0.00277555 + 0.117818i
$$361$$ 30.6618 1.61378
$$362$$ 13.6729i 0.718633i
$$363$$ 10.7783i 0.565712i
$$364$$ −12.9418 −0.678334
$$365$$ 0.625817 26.5651i 0.0327568 1.39048i
$$366$$ 11.2578 0.588453
$$367$$ 19.2963i 1.00726i −0.863920 0.503629i $$-0.831998\pi$$
0.863920 0.503629i $$-0.168002\pi$$
$$368$$ 6.94179i 0.361866i
$$369$$ −2.00000 −0.104116
$$370$$ −4.00000 0.0942314i −0.207950 0.00489886i
$$371$$ −6.30488 −0.327333
$$372$$ 1.00000i 0.0518476i
$$373$$ 24.0942i 1.24755i −0.781603 0.623776i $$-0.785598\pi$$
0.781603 0.623776i $$-0.214402\pi$$
$$374$$ 3.31846 0.171593
$$375$$ 0.789351 11.1524i 0.0407619 0.575910i
$$376$$ −7.04712 −0.363427
$$377$$ 44.9196i 2.31348i
$$378$$ 2.00000i 0.102869i
$$379$$ −25.1413 −1.29142 −0.645712 0.763581i $$-0.723439\pi$$
−0.645712 + 0.763581i $$0.723439\pi$$
$$380$$ 15.7535 + 0.371118i 0.808135 + 0.0190379i
$$381$$ 0.941791 0.0482494
$$382$$ 14.8254i 0.758532i
$$383$$ 22.9196i 1.17114i 0.810623 + 0.585569i $$0.199129\pi$$
−0.810623 + 0.585569i $$0.800871\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0.0495969 2.10532i 0.00252769 0.107297i
$$386$$ −8.04960 −0.409714
$$387$$ 0.210649i 0.0107079i
$$388$$ 3.52910i 0.179163i
$$389$$ 21.0360 1.06657 0.533284 0.845936i $$-0.320958\pi$$
0.533284 + 0.845936i $$0.320958\pi$$
$$390$$ 0.340772 14.4653i 0.0172557 0.732481i
$$391$$ 48.9196 2.47397
$$392$$ 3.00000i 0.151523i
$$393$$ 3.15244i 0.159020i
$$394$$ −16.3049 −0.821428
$$395$$ −4.23545 0.0997780i −0.213109 0.00502038i
$$396$$ −0.470896 −0.0236634
$$397$$ 38.4983i 1.93217i 0.258216 + 0.966087i $$0.416865\pi$$
−0.258216 + 0.966087i $$0.583135\pi$$
$$398$$ 3.98891i 0.199946i
$$399$$ 14.0942 0.705594
$$400$$ 4.99445 + 0.235448i 0.249723 + 0.0117724i
$$401$$ −12.3545 −0.616953 −0.308477 0.951232i $$-0.599819\pi$$
−0.308477 + 0.951232i $$0.599819\pi$$
$$402$$ 8.26025i 0.411984i
$$403$$ 6.47090i 0.322338i
$$404$$ 0 0
$$405$$ −2.23545 0.0526623i −0.111080 0.00261681i
$$406$$ −13.8836 −0.689031
$$407$$ 0.842597i 0.0417660i
$$408$$ 7.04712i 0.348884i
$$409$$ 32.6147 1.61269 0.806347 0.591443i $$-0.201441\pi$$
0.806347 + 0.591443i $$0.201441\pi$$
$$410$$ −0.105325 + 4.47090i −0.00520161 + 0.220802i
$$411$$ 9.67293 0.477131
$$412$$ 6.00000i 0.295599i
$$413$$ 14.3049i 0.703897i
$$414$$ −6.94179 −0.341170
$$415$$ −0.620270 + 26.3297i −0.0304479 + 1.29247i
$$416$$ 6.47090 0.317262
$$417$$ 5.05821i 0.247702i
$$418$$ 3.31846i 0.162311i
$$419$$ −10.9418 −0.534541 −0.267271 0.963621i $$-0.586122\pi$$
−0.267271 + 0.963621i $$0.586122\pi$$
$$420$$ 4.47090 + 0.105325i 0.218157 + 0.00513932i
$$421$$ −22.4213 −1.09275 −0.546374 0.837542i $$-0.683992\pi$$
−0.546374 + 0.837542i $$0.683992\pi$$
$$422$$ 2.11642i 0.103026i
$$423$$ 7.04712i 0.342642i
$$424$$ 3.15244 0.153096
$$425$$ 1.65923 35.1965i 0.0804844 1.70728i
$$426$$ 0.260246 0.0126090
$$427$$ 22.5155i 1.08960i
$$428$$ 16.7311i 0.808730i
$$429$$ 3.04712 0.147116
$$430$$ 0.470896 + 0.0110933i 0.0227086 + 0.000534966i
$$431$$ 33.1303 1.59583 0.797914 0.602771i $$-0.205937\pi$$
0.797914 + 0.602771i $$0.205937\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 9.78935i 0.470446i −0.971941 0.235223i $$-0.924418\pi$$
0.971941 0.235223i $$-0.0755821\pi$$
$$434$$ 2.00000 0.0960031
$$435$$ 0.365571 15.5180i 0.0175278 0.744032i
$$436$$ −11.1524 −0.534105
$$437$$ 48.9196i 2.34014i
$$438$$ 11.8836i 0.567820i
$$439$$ 22.6147 1.07934 0.539671 0.841876i $$-0.318549\pi$$
0.539671 + 0.841876i $$0.318549\pi$$
$$440$$ −0.0247985 + 1.05266i −0.00118222 + 0.0501837i
$$441$$ −3.00000 −0.142857
$$442$$ 45.6011i 2.16903i
$$443$$ 0.210649i 0.0100083i 0.999987 + 0.00500413i $$0.00159287\pi$$
−0.999987 + 0.00500413i $$0.998407\pi$$
$$444$$ 1.78935 0.0849188
$$445$$ 27.0360 + 0.636910i 1.28163 + 0.0301924i
$$446$$ −2.58731 −0.122513
$$447$$ 13.4127i 0.634398i
$$448$$ 2.00000i 0.0944911i
$$449$$ 27.4127 1.29368 0.646842 0.762624i $$-0.276089\pi$$
0.646842 + 0.762624i $$0.276089\pi$$
$$450$$ −0.235448 + 4.99445i −0.0110991 + 0.235441i
$$451$$ −0.941791 −0.0443472
$$452$$ 16.3049i 0.766917i
$$453$$ 19.5676i 0.919366i
$$454$$ −4.94179 −0.231930
$$455$$ −28.9307 0.681545i −1.35629 0.0319513i
$$456$$ −7.04712 −0.330011
$$457$$ 26.9196i 1.25925i −0.776901 0.629623i $$-0.783209\pi$$
0.776901 0.629623i $$-0.216791\pi$$
$$458$$ 11.6791i 0.545727i
$$459$$ −7.04712 −0.328931
$$460$$ −0.365571 + 15.5180i −0.0170448 + 0.723531i
$$461$$ 29.0360 1.35234 0.676171 0.736745i $$-0.263638\pi$$
0.676171 + 0.736745i $$0.263638\pi$$
$$462$$ 0.941791i 0.0438161i
$$463$$ 16.8922i 0.785047i −0.919742 0.392523i $$-0.871602\pi$$
0.919742 0.392523i $$-0.128398\pi$$
$$464$$ 6.94179 0.322265
$$465$$ −0.0526623 + 2.23545i −0.00244216 + 0.103666i
$$466$$ 13.7894 0.638779
$$467$$ 7.76716i 0.359421i −0.983719 0.179711i $$-0.942484\pi$$
0.983719 0.179711i $$-0.0575162\pi$$
$$468$$ 6.47090i 0.299117i
$$469$$ 16.5205 0.762845
$$470$$ −15.7535 0.371118i −0.726653 0.0171184i
$$471$$ −21.2467 −0.978995
$$472$$ 7.15244i 0.329218i
$$473$$ 0.0991938i 0.00456094i
$$474$$ 1.89468 0.0870253
$$475$$ 35.1965 + 1.65923i 1.61493 + 0.0761306i
$$476$$ 14.0942 0.646008
$$477$$ 3.15244i 0.144340i
$$478$$ 12.7311i 0.582309i
$$479$$ −32.4487 −1.48262 −0.741310 0.671163i $$-0.765795\pi$$
−0.741310 + 0.671163i $$0.765795\pi$$
$$480$$ −2.23545 0.0526623i −0.102034 0.00240370i
$$481$$ −11.5787 −0.527943
$$482$$ 3.15244i 0.143590i
$$483$$ 13.8836i 0.631725i
$$484$$ 10.7783 0.489921
$$485$$ 0.185851 7.88913i 0.00843905 0.358227i
$$486$$ 1.00000 0.0453609
$$487$$ 35.4847i 1.60797i −0.594652 0.803983i $$-0.702710\pi$$
0.594652 0.803983i $$-0.297290\pi$$
$$488$$ 11.2578i 0.509615i
$$489$$ 4.26025 0.192655
$$490$$ −0.157987 + 6.70634i −0.00713712 + 0.302962i
$$491$$ 25.9828 1.17259 0.586293 0.810099i $$-0.300587\pi$$
0.586293 + 0.810099i $$0.300587\pi$$
$$492$$ 2.00000i 0.0901670i
$$493$$ 48.9196i 2.20323i
$$494$$ 45.6011 2.05169
$$495$$ −1.05266 0.0247985i −0.0473137 0.00111461i
$$496$$ −1.00000 −0.0449013
$$497$$ 0.520492i 0.0233473i
$$498$$ 11.7783i 0.527796i
$$499$$ −7.90577 −0.353911 −0.176955 0.984219i $$-0.556625\pi$$
−0.176955 + 0.984219i $$0.556625\pi$$
$$500$$ 11.1524 + 0.789351i 0.498752 + 0.0353008i
$$501$$ 2.00000 0.0893534
$$502$$ 3.05821i 0.136495i
$$503$$ 9.14135i 0.407593i 0.979013 + 0.203796i $$0.0653280\pi$$
−0.979013 + 0.203796i $$0.934672\pi$$
$$504$$ −2.00000 −0.0890871
$$505$$ 0 0
$$506$$ −3.26886 −0.145318
$$507$$ 28.8725i 1.28227i
$$508$$ 0.941791i 0.0417852i
$$509$$ −28.5155 −1.26393 −0.631964 0.774997i $$-0.717751\pi$$
−0.631964 + 0.774997i $$0.717751\pi$$
$$510$$ −0.371118 + 15.7535i −0.0164334 + 0.697575i
$$511$$ 23.7672 1.05140
$$512$$ 1.00000i 0.0441942i
$$513$$ 7.04712i 0.311138i
$$514$$ 16.0942 0.709886
$$515$$ −0.315974 + 13.4127i −0.0139235 + 0.591034i
$$516$$ −0.210649 −0.00927332
$$517$$ 3.31846i 0.145945i
$$518$$ 3.57870i 0.157239i
$$519$$ −17.9889 −0.789625
$$520$$ 14.4653 + 0.340772i 0.634348 + 0.0149439i
$$521$$ 23.3631 1.02356 0.511778 0.859118i $$-0.328987\pi$$
0.511778 + 0.859118i $$0.328987\pi$$
$$522$$ 6.94179i 0.303834i
$$523$$ 42.0942i 1.84065i −0.391152 0.920326i $$-0.627923\pi$$
0.391152 0.920326i $$-0.372077\pi$$
$$524$$ 3.15244 0.137715
$$525$$ 9.98891 + 0.470896i 0.435952 + 0.0205516i
$$526$$ −0.0942314 −0.00410868
$$527$$ 7.04712i 0.306977i
$$528$$ 0.470896i 0.0204931i
$$529$$ −25.1885 −1.09515
$$530$$ 7.04712 + 0.166015i 0.306107 + 0.00721122i
$$531$$ −7.15244 −0.310389
$$532$$ 14.0942i 0.611062i
$$533$$ 12.9418i 0.560571i
$$534$$ −12.0942 −0.523369
$$535$$ −0.881101 + 37.4016i −0.0380933 + 1.61701i
$$536$$ −8.26025 −0.356788
$$537$$ 12.0496i 0.519978i
$$538$$ 23.8836i 1.02969i
$$539$$ −1.41269 −0.0608487
$$540$$ 0.0526623 2.23545i 0.00226623 0.0961984i
$$541$$ −44.5925 −1.91718 −0.958591 0.284785i $$-0.908078\pi$$
−0.958591 + 0.284785i $$0.908078\pi$$
$$542$$ 24.4102i 1.04851i
$$543$$ 13.6729i 0.586762i
$$544$$ −7.04712 −0.302143
$$545$$ −24.9307 0.587313i −1.06791 0.0251577i
$$546$$ 12.9418 0.553858
$$547$$ 4.52049i 0.193282i −0.995319 0.0966411i $$-0.969190\pi$$
0.995319 0.0966411i $$-0.0308099\pi$$
$$548$$ 9.67293i 0.413207i
$$549$$ −11.2578 −0.480470
$$550$$ −0.110871 + 2.35187i −0.00472757 + 0.100284i
$$551$$ 48.9196 2.08405
$$552$$ 6.94179i 0.295462i
$$553$$ 3.78935i 0.161140i
$$554$$ −7.41269 −0.314935
$$555$$ 4.00000 + 0.0942314i 0.169791 + 0.00399990i
$$556$$ 5.05821 0.214516
$$557$$ 20.5155i 0.869271i −0.900606 0.434635i $$-0.856877\pi$$
0.900606 0.434635i $$-0.143123\pi$$
$$558$$ 1.00000i 0.0423334i
$$559$$ 1.36309 0.0576525
$$560$$ −0.105325 + 4.47090i −0.00445078 + 0.188930i
$$561$$ −3.31846 −0.140105
$$562$$ 11.8836i 0.501279i
$$563$$ 34.6147i 1.45884i −0.684068 0.729418i $$-0.739791\pi$$
0.684068 0.729418i $$-0.260209\pi$$
$$564$$ 7.04712 0.296737
$$565$$ 0.858653 36.4487i 0.0361238 1.53341i
$$566$$ −22.9864 −0.966192
$$567$$ 2.00000i 0.0839921i
$$568$$ 0.260246i 0.0109197i
$$569$$ −7.25163 −0.304004 −0.152002 0.988380i $$-0.548572\pi$$
−0.152002 + 0.988380i $$0.548572\pi$$
$$570$$ −15.7535 0.371118i −0.659840 0.0155444i
$$571$$ −0.0942314 −0.00394346 −0.00197173 0.999998i $$-0.500628\pi$$
−0.00197173 + 0.999998i $$0.500628\pi$$
$$572$$ 3.04712i 0.127406i
$$573$$ 14.8254i 0.619339i
$$574$$ −4.00000 −0.166957
$$575$$ −1.63443 + 34.6705i −0.0681604 + 1.44586i
$$576$$ 1.00000 0.0416667
$$577$$ 9.41269i 0.391855i 0.980618 + 0.195928i $$0.0627718\pi$$
−0.980618 + 0.195928i $$0.937228\pi$$
$$578$$ 32.6618i 1.35855i
$$579$$ 8.04960 0.334530
$$580$$ 15.5180 + 0.365571i 0.644350 + 0.0151795i
$$581$$ −23.5565 −0.977289
$$582$$ 3.52910i 0.146286i
$$583$$ 1.48447i 0.0614805i
$$584$$ −11.8836 −0.491746
$$585$$ −0.340772 + 14.4653i −0.0140892 + 0.598069i
$$586$$ 14.4213 0.595738
$$587$$ 42.2938i 1.74565i 0.488032 + 0.872826i $$0.337715\pi$$
−0.488032 + 0.872826i $$0.662285\pi$$
$$588$$ 3.00000i 0.123718i
$$589$$ −7.04712 −0.290371
$$590$$ −0.376664 + 15.9889i −0.0155070 + 0.658253i
$$591$$ 16.3049 0.670693
$$592$$ 1.78935i 0.0735419i
$$593$$ 5.88854i 0.241814i 0.992664 + 0.120907i $$0.0385802\pi$$
−0.992664 + 0.120907i $$0.961420\pi$$
$$594$$ 0.470896 0.0193211
$$595$$ 31.5069 + 0.742235i 1.29166 + 0.0304287i
$$596$$ 13.4127 0.549405
$$597$$ 3.98891i 0.163255i
$$598$$ 44.9196i 1.83690i
$$599$$ 0.780739 0.0319001 0.0159501 0.999873i $$-0.494923\pi$$
0.0159501 + 0.999873i $$0.494923\pi$$
$$600$$ −4.99445 0.235448i −0.203898 0.00961211i
$$601$$ −25.5787 −1.04338 −0.521688 0.853136i $$-0.674698\pi$$
−0.521688 + 0.853136i $$0.674698\pi$$
$$602$$ 0.421299i 0.0171708i
$$603$$ 8.26025i 0.336383i
$$604$$ −19.5676 −0.796195
$$605$$ 24.0942 + 0.567608i 0.979570 + 0.0230766i
$$606$$ 0 0
$$607$$ 7.46228i 0.302885i 0.988466 + 0.151442i $$0.0483918\pi$$
−0.988466 + 0.151442i $$0.951608\pi$$
$$608$$ 7.04712i 0.285798i
$$609$$ 13.8836 0.562591
$$610$$ −0.592860 + 25.1661i −0.0240042 + 1.01895i
$$611$$ −45.6011 −1.84483
$$612$$ 7.04712i 0.284863i
$$613$$ 4.68651i 0.189286i 0.995511 + 0.0946431i $$0.0301710\pi$$
−0.995511 + 0.0946431i $$0.969829\pi$$
$$614$$ 24.9418 1.00657
$$615$$ 0.105325 4.47090i 0.00424710 0.180284i
$$616$$ −0.941791 −0.0379458
$$617$$ 7.69512i 0.309794i 0.987931 + 0.154897i $$0.0495045\pi$$
−0.987931 + 0.154897i $$0.950495\pi$$
$$618$$ 6.00000i 0.241355i
$$619$$ −33.7894 −1.35811 −0.679054 0.734088i $$-0.737610\pi$$
−0.679054 + 0.734088i $$0.737610\pi$$
$$620$$ −2.23545 0.0526623i −0.0897777 0.00211497i
$$621$$ 6.94179 0.278564
$$622$$ 24.4487i 0.980304i
$$623$$ 24.1885i 0.969090i
$$624$$ −6.47090 −0.259043
$$625$$ 24.8891 + 2.35187i 0.995565 + 0.0940746i
$$626$$ 14.1885 0.567085
$$627$$ 3.31846i 0.132526i
$$628$$ 21.2467i 0.847835i
$$629$$ 12.6098 0.502784
$$630$$ −4.47090 0.105325i −0.178125 0.00419623i
$$631$$ −34.3049 −1.36566 −0.682828 0.730579i $$-0.739250\pi$$
−0.682828 + 0.730579i $$0.739250\pi$$
$$632$$ 1.89468i 0.0753661i
$$633$$ 2.11642i 0.0841201i
$$634$$ 21.9889 0.873291
$$635$$ −0.0495969 + 2.10532i −0.00196819 + 0.0835473i
$$636$$ −3.15244 −0.125002
$$637$$ 19.4127i 0.769159i
$$638$$ 3.26886i 0.129415i
$$639$$ −0.260246 −0.0102952
$$640$$ 0.0526623 2.23545i 0.00208166 0.0883638i
$$641$$ 3.83399 0.151433 0.0757167 0.997129i $$-0.475876\pi$$
0.0757167 + 0.997129i $$0.475876\pi$$
$$642$$ 16.7311i 0.660325i
$$643$$ 12.9640i 0.511249i −0.966776 0.255625i $$-0.917719\pi$$
0.966776 0.255625i $$-0.0822811\pi$$
$$644$$ −13.8836 −0.547090
$$645$$ −0.470896 0.0110933i −0.0185415 0.000436798i
$$646$$ −49.6618 −1.95392
$$647$$ 29.3459i 1.15371i 0.816848 + 0.576853i $$0.195719\pi$$
−0.816848 + 0.576853i $$0.804281\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ −3.36805 −0.132208
$$650$$ 32.3186 + 1.52356i 1.26764 + 0.0597589i
$$651$$ −2.00000 −0.0783862
$$652$$ 4.26025i 0.166844i
$$653$$ 4.52662i 0.177140i 0.996070 + 0.0885702i $$0.0282298\pi$$
−0.996070 + 0.0885702i $$0.971770\pi$$
$$654$$ 11.1524 0.436095
$$655$$ 7.04712 + 0.166015i 0.275354 + 0.00648674i
$$656$$ 2.00000 0.0780869
$$657$$ 11.8836i 0.463623i
$$658$$ 14.0942i 0.549450i
$$659$$ 15.8836 0.618737 0.309368 0.950942i $$-0.399882\pi$$
0.309368 + 0.950942i $$0.399882\pi$$
$$660$$ 0.0247985 1.05266i 0.000965278 0.0409748i
$$661$$ 12.8254 0.498849 0.249425 0.968394i $$-0.419759\pi$$
0.249425 + 0.968394i $$0.419759\pi$$
$$662$$ 15.3631i 0.597103i
$$663$$ 45.6011i 1.77100i
$$664$$ 11.7783 0.457085
$$665$$ −0.742235 + 31.5069i −0.0287826 + 1.22179i
$$666$$ −1.78935 −0.0693359
$$667$$ 48.1885i 1.86586i
$$668$$ 2.00000i 0.0773823i
$$669$$ 2.58731 0.100031
$$670$$ −18.4653 0.435004i −0.713379 0.0168057i
$$671$$ −5.30123 −0.204652
$$672$$ 2.00000i 0.0771517i
$$673$$ 27.9828i 1.07866i −0.842096 0.539328i $$-0.818678\pi$$
0.842096 0.539328i $$-0.181322\pi$$
$$674$$ −13.9778 −0.538405
$$675$$ 0.235448 4.99445i 0.00906239 0.192237i
$$676$$ 28.8725 1.11048
$$677$$ 27.6729i 1.06356i −0.846883 0.531779i $$-0.821524\pi$$
0.846883 0.531779i $$-0.178476\pi$$
$$678$$ 16.3049i 0.626185i
$$679$$ 7.05821 0.270869
$$680$$ −15.7535 0.371118i −0.604118 0.0142317i
$$681$$ 4.94179 0.189370
$$682$$ 0.470896i 0.0180315i
$$683$$ 8.18846i 0.313323i 0.987652 + 0.156661i $$0.0500731\pi$$
−0.987652 + 0.156661i $$0.949927\pi$$
$$684$$ 7.04712 0.269453
$$685$$ −0.509399 + 21.6233i −0.0194631 + 0.826185i
$$686$$ −20.0000 −0.763604
$$687$$ 11.6791i 0.445584i
$$688$$ 0.210649i 0.00803093i
$$689$$ 20.3991 0.777144
$$690$$ 0.365571 15.5180i 0.0139170 0.590761i
$$691$$ 22.4152 0.852713 0.426357 0.904555i $$-0.359797\pi$$
0.426357 + 0.904555i $$0.359797\pi$$
$$692$$ 17.9889i 0.683836i
$$693$$ 0.941791i 0.0357757i
$$694$$ −17.6618 −0.670434
$$695$$ 11.3074 + 0.266377i 0.428913 + 0.0101043i
$$696$$ −6.94179 −0.263128
$$697$$ 14.0942i 0.533857i
$$698$$ 7.67293i 0.290425i
$$699$$ −13.7894 −0.521561
$$700$$ −0.470896 + 9.98891i −0.0177982 + 0.377545i
$$701$$ −20.4709 −0.773175 −0.386588 0.922253i $$-0.626346\pi$$
−0.386588 + 0.922253i $$0.626346\pi$$
$$702$$ 6.47090i 0.244228i
$$703$$ 12.6098i 0.475586i
$$704$$ 0.470896 0.0177475
$$705$$ 15.7535 + 0.371118i 0.593310 + 0.0139771i
$$706$$ 11.0471 0.415764
$$707$$ 0 0
$$708$$ 7.15244i 0.268805i
$$709$$ 48.7200 1.82972 0.914860 0.403771i $$-0.132301\pi$$
0.914860 + 0.403771i $$0.132301\pi$$
$$710$$ −0.0137052 + 0.581767i −0.000514346 + 0.0218333i
$$711$$ −1.89468 −0.0710559
$$712$$ 12.0942i 0.453250i
$$713$$ 6.94179i 0.259972i
$$714$$ −14.0942 −0.527463
$$715$$ −0.160468 + 6.81167i −0.00600117 + 0.254742i
$$716$$ −12.0496 −0.450315
$$717$$ 12.7311i 0.475453i
$$718$$ 35.9282i 1.34083i
$$719$$ −50.8032 −1.89464 −0.947320 0.320290i $$-0.896220\pi$$
−0.947320 + 0.320290i $$0.896220\pi$$
$$720$$ 2.23545 + 0.0526623i 0.0833102 + 0.00196261i
$$721$$ −12.0000 −0.446903
$$722$$ 30.6618i 1.14112i
$$723$$ 3.15244i 0.117241i
$$724$$ 13.6729 0.508151
$$725$$ 34.6705 + 1.63443i 1.28763 + 0.0607012i
$$726$$ −10.7783 −0.400019
$$727$$ 33.1352i 1.22892i −0.788949 0.614459i $$-0.789375\pi$$
0.788949 0.614459i $$-0.210625\pi$$
$$728$$ 12.9418i 0.479655i
$$729$$ −1.00000 −0.0370370
$$730$$ −26.5651 0.625817i −0.983219 0.0231625i
$$731$$ −1.48447 −0.0549051
$$732$$ 11.2578i 0.416099i
$$733$$ 2.96398i 0.109477i 0.998501 + 0.0547385i $$0.0174325\pi$$
−0.998501 + 0.0547385i $$0.982567\pi$$
$$734$$ −19.2963 −0.712238
$$735$$ 0.157987 6.70634i 0.00582744 0.247367i
$$736$$ 6.94179 0.255878
$$737$$ 3.88971i 0.143279i
$$738$$ 2.00000i 0.0736210i
$$739$$ 6.52049 0.239860 0.119930 0.992782i $$-0.461733\pi$$
0.119930 + 0.992782i $$0.461733\pi$$
$$740$$ −0.0942314 + 4.00000i −0.00346401 + 0.147043i
$$741$$ −45.6011 −1.67520
$$742$$ 6.30488i 0.231459i
$$743$$ 20.0942i 0.737186i −0.929591 0.368593i $$-0.879840\pi$$
0.929591 0.368593i $$-0.120160\pi$$
$$744$$ 1.00000 0.0366618
$$745$$ 29.9834 + 0.706343i 1.09851 + 0.0258784i
$$746$$ −24.0942 −0.882152
$$747$$ 11.7783i 0.430944i
$$748$$ 3.31846i 0.121335i
$$749$$ −33.4623 −1.22269
$$750$$ −11.1524 0.789351i −0.407230 0.0288230i
$$751$$ −46.0942 −1.68200 −0.841001 0.541033i $$-0.818033\pi$$
−0.841001 + 0.541033i $$0.818033\pi$$
$$752$$ 7.04712i 0.256982i
$$753$$ 3.05821i 0.111447i
$$754$$ 44.9196 1.63588
$$755$$ −43.7424 1.03048i −1.59195 0.0375029i
$$756$$ 2.00000 0.0727393
$$757$$ 28.2827i 1.02795i 0.857805 + 0.513976i $$0.171828\pi$$
−0.857805 + 0.513976i $$0.828172\pi$$
$$758$$ 25.1413i 0.913175i
$$759$$ 3.26886 0.118652
$$760$$ 0.371118 15.7535i 0.0134618 0.571438i
$$761$$ −41.0634 −1.48855 −0.744274 0.667874i $$-0.767204\pi$$
−0.744274 + 0.667874i $$0.767204\pi$$
$$762$$ 0.941791i 0.0341175i
$$763$$ 22.3049i 0.807491i
$$764$$ 14.8254 0.536363
$$765$$ 0.371118 15.7535i 0.0134178 0.569568i
$$766$$ 22.9196 0.828119
$$767$$ 46.2827i 1.67117i
$$768$$ 1.00000i 0.0360844i
$$769$$ 32.4933 1.17174 0.585870 0.810405i $$-0.300753\pi$$
0.585870 + 0.810405i $$0.300753\pi$$
$$770$$ −2.10532 0.0495969i −0.0758706 0.00178735i
$$771$$ −16.0942 −0.579620
$$772$$ 8.04960i 0.289711i
$$773$$ 50.3991i 1.81273i 0.422495 + 0.906365i $$0.361154\pi$$
−0.422495 + 0.906365i $$0.638846\pi$$
$$774$$ 0.210649 0.00757163
$$775$$ −4.99445 0.235448i −0.179406 0.00845753i
$$776$$ −3.52910 −0.126687
$$777$$ 3.57870i 0.128385i
$$778$$ 21.0360i 0.754178i
$$779$$ 14.0942 0.504978
$$780$$ −14.4653 0.340772i −0.517943 0.0122016i
$$781$$ −0.122549