# Properties

 Label 48.16.c.b.47.3 Level $48$ Weight $16$ Character 48.47 Analytic conductor $68.493$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,16,Mod(47,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("48.47");

S:= CuspForms(chi, 16);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$16$$ Character orbit: $$[\chi]$$ $$=$$ 48.c (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: $$68.4928824480$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 2x^{3} - 32461x^{2} + 32462x + 263623935$$ x^4 - 2*x^3 - 32461*x^2 + 32462*x + 263623935 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{6}\cdot 3^{7}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 47.3 Root $$-126.913 + 1.65831i$$ of defining polynomial Character $$\chi$$ $$=$$ 48.47 Dual form 48.16.c.b.47.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(2293.43 - 3014.81i) q^{3} -76064.4i q^{5} -1.82913e6i q^{7} +(-3.82928e6 - 1.38285e7i) q^{9} +O(q^{10})$$ $$q+(2293.43 - 3014.81i) q^{3} -76064.4i q^{5} -1.82913e6i q^{7} +(-3.82928e6 - 1.38285e7i) q^{9} +7.64125e7 q^{11} +2.54445e8 q^{13} +(-2.29320e8 - 1.74448e8i) q^{15} -7.38677e8i q^{17} -5.32265e8i q^{19} +(-5.51447e9 - 4.19497e9i) q^{21} +1.70562e10 q^{23} +2.47318e10 q^{25} +(-5.04725e10 - 2.01702e10i) q^{27} -1.64361e11i q^{29} +1.19565e11i q^{31} +(1.75247e11 - 2.30369e11i) q^{33} -1.39131e11 q^{35} -1.78908e11 q^{37} +(5.83552e11 - 7.67105e11i) q^{39} +5.29655e11i q^{41} +5.71398e11i q^{43} +(-1.05186e12 + 2.91272e11i) q^{45} -1.37657e12 q^{47} +1.40186e12 q^{49} +(-2.22697e12 - 1.69410e12i) q^{51} +1.30462e13i q^{53} -5.81227e12i q^{55} +(-1.60468e12 - 1.22071e12i) q^{57} -6.31592e11 q^{59} -1.44698e13 q^{61} +(-2.52941e13 + 7.00422e12i) q^{63} -1.93542e13i q^{65} -8.74692e13i q^{67} +(3.91172e13 - 5.14212e13i) q^{69} -8.26841e13 q^{71} +6.67870e13 q^{73} +(5.67206e13 - 7.45617e13i) q^{75} -1.39768e14i q^{77} -1.93474e14i q^{79} +(-1.76564e14 + 1.05906e14i) q^{81} -4.13488e14 q^{83} -5.61870e13 q^{85} +(-4.95518e14 - 3.76951e14i) q^{87} +5.61280e14i q^{89} -4.65412e14i q^{91} +(3.60466e14 + 2.74214e14i) q^{93} -4.04865e13 q^{95} -3.75171e14 q^{97} +(-2.92604e14 - 1.05667e15i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 15317100 q^{9}+O(q^{10})$$ 4 * q - 15317100 * q^9 $$4 q - 15317100 q^{9} + 1017781336 q^{13} - 22057873992 q^{21} + 98927122100 q^{25} + 700986197952 q^{33} - 715633821064 q^{37} - 4207432014720 q^{45} + 5607449975596 q^{49} - 6418720383768 q^{57} - 57879101335528 q^{61} + 156468753896832 q^{69} + 267147849446632 q^{73} - 706257752173596 q^{81} - 224748150612480 q^{85} + 14\!\cdots\!64 q^{93}+ \cdots - 15\!\cdots\!20 q^{97}+O(q^{100})$$ 4 * q - 15317100 * q^9 + 1017781336 * q^13 - 22057873992 * q^21 + 98927122100 * q^25 + 700986197952 * q^33 - 715633821064 * q^37 - 4207432014720 * q^45 + 5607449975596 * q^49 - 6418720383768 * q^57 - 57879101335528 * q^61 + 156468753896832 * q^69 + 267147849446632 * q^73 - 706257752173596 * q^81 - 224748150612480 * q^85 + 1441865040435864 * q^93 - 1500683175752120 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$$.

 $$n$$ $$17$$ $$31$$ $$37$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2293.43 3014.81i 0.605447 0.795886i
$$4$$ 0 0
$$5$$ 76064.4i 0.435418i −0.976014 0.217709i $$-0.930142\pi$$
0.976014 0.217709i $$-0.0698584\pi$$
$$6$$ 0 0
$$7$$ 1.82913e6i 0.839476i −0.907645 0.419738i $$-0.862122\pi$$
0.907645 0.419738i $$-0.137878\pi$$
$$8$$ 0 0
$$9$$ −3.82928e6 1.38285e7i −0.266869 0.963733i
$$10$$ 0 0
$$11$$ 7.64125e7 1.18228 0.591138 0.806570i $$-0.298679\pi$$
0.591138 + 0.806570i $$0.298679\pi$$
$$12$$ 0 0
$$13$$ 2.54445e8 1.12466 0.562328 0.826915i $$-0.309906\pi$$
0.562328 + 0.826915i $$0.309906\pi$$
$$14$$ 0 0
$$15$$ −2.29320e8 1.74448e8i −0.346543 0.263622i
$$16$$ 0 0
$$17$$ 7.38677e8i 0.436604i −0.975881 0.218302i $$-0.929948\pi$$
0.975881 0.218302i $$-0.0700518\pi$$
$$18$$ 0 0
$$19$$ 5.32265e8i 0.136608i −0.997665 0.0683040i $$-0.978241\pi$$
0.997665 0.0683040i $$-0.0217588\pi$$
$$20$$ 0 0
$$21$$ −5.51447e9 4.19497e9i −0.668127 0.508258i
$$22$$ 0 0
$$23$$ 1.70562e10 1.04454 0.522268 0.852781i $$-0.325086\pi$$
0.522268 + 0.852781i $$0.325086\pi$$
$$24$$ 0 0
$$25$$ 2.47318e10 0.810411
$$26$$ 0 0
$$27$$ −5.04725e10 2.01702e10i −0.928596 0.371092i
$$28$$ 0 0
$$29$$ 1.64361e11i 1.76935i −0.466206 0.884676i $$-0.654380\pi$$
0.466206 0.884676i $$-0.345620\pi$$
$$30$$ 0 0
$$31$$ 1.19565e11i 0.780534i 0.920702 + 0.390267i $$0.127617\pi$$
−0.920702 + 0.390267i $$0.872383\pi$$
$$32$$ 0 0
$$33$$ 1.75247e11 2.30369e11i 0.715805 0.940957i
$$34$$ 0 0
$$35$$ −1.39131e11 −0.365523
$$36$$ 0 0
$$37$$ −1.78908e11 −0.309826 −0.154913 0.987928i $$-0.549510\pi$$
−0.154913 + 0.987928i $$0.549510\pi$$
$$38$$ 0 0
$$39$$ 5.83552e11 7.67105e11i 0.680919 0.895097i
$$40$$ 0 0
$$41$$ 5.29655e11i 0.424731i 0.977190 + 0.212365i $$0.0681167\pi$$
−0.977190 + 0.212365i $$0.931883\pi$$
$$42$$ 0 0
$$43$$ 5.71398e11i 0.320572i 0.987071 + 0.160286i $$0.0512416\pi$$
−0.987071 + 0.160286i $$0.948758\pi$$
$$44$$ 0 0
$$45$$ −1.05186e12 + 2.91272e11i −0.419627 + 0.116200i
$$46$$ 0 0
$$47$$ −1.37657e12 −0.396337 −0.198169 0.980168i $$-0.563499\pi$$
−0.198169 + 0.980168i $$0.563499\pi$$
$$48$$ 0 0
$$49$$ 1.40186e12 0.295281
$$50$$ 0 0
$$51$$ −2.22697e12 1.69410e12i −0.347487 0.264340i
$$52$$ 0 0
$$53$$ 1.30462e13i 1.52551i 0.646685 + 0.762757i $$0.276155\pi$$
−0.646685 + 0.762757i $$0.723845\pi$$
$$54$$ 0 0
$$55$$ 5.81227e12i 0.514785i
$$56$$ 0 0
$$57$$ −1.60468e12 1.22071e12i −0.108724 0.0827089i
$$58$$ 0 0
$$59$$ −6.31592e11 −0.0330405 −0.0165202 0.999864i $$-0.505259\pi$$
−0.0165202 + 0.999864i $$0.505259\pi$$
$$60$$ 0 0
$$61$$ −1.44698e13 −0.589506 −0.294753 0.955574i $$-0.595237\pi$$
−0.294753 + 0.955574i $$0.595237\pi$$
$$62$$ 0 0
$$63$$ −2.52941e13 + 7.00422e12i −0.809030 + 0.224030i
$$64$$ 0 0
$$65$$ 1.93542e13i 0.489695i
$$66$$ 0 0
$$67$$ 8.74692e13i 1.76317i −0.472025 0.881585i $$-0.656477\pi$$
0.472025 0.881585i $$-0.343523\pi$$
$$68$$ 0 0
$$69$$ 3.91172e13 5.14212e13i 0.632411 0.831332i
$$70$$ 0 0
$$71$$ −8.26841e13 −1.07891 −0.539454 0.842015i $$-0.681369\pi$$
−0.539454 + 0.842015i $$0.681369\pi$$
$$72$$ 0 0
$$73$$ 6.67870e13 0.707571 0.353786 0.935327i $$-0.384894\pi$$
0.353786 + 0.935327i $$0.384894\pi$$
$$74$$ 0 0
$$75$$ 5.67206e13 7.45617e13i 0.490661 0.644995i
$$76$$ 0 0
$$77$$ 1.39768e14i 0.992492i
$$78$$ 0 0
$$79$$ 1.93474e14i 1.13349i −0.823892 0.566747i $$-0.808202\pi$$
0.823892 0.566747i $$-0.191798\pi$$
$$80$$ 0 0
$$81$$ −1.76564e14 + 1.05906e14i −0.857562 + 0.514380i
$$82$$ 0 0
$$83$$ −4.13488e14 −1.67254 −0.836271 0.548316i $$-0.815269\pi$$
−0.836271 + 0.548316i $$0.815269\pi$$
$$84$$ 0 0
$$85$$ −5.61870e13 −0.190105
$$86$$ 0 0
$$87$$ −4.95518e14 3.76951e14i −1.40820 1.07125i
$$88$$ 0 0
$$89$$ 5.61280e14i 1.34510i 0.740051 + 0.672550i $$0.234801\pi$$
−0.740051 + 0.672550i $$0.765199\pi$$
$$90$$ 0 0
$$91$$ 4.65412e14i 0.944121i
$$92$$ 0 0
$$93$$ 3.60466e14 + 2.74214e14i 0.621216 + 0.472572i
$$94$$ 0 0
$$95$$ −4.04865e13 −0.0594816
$$96$$ 0 0
$$97$$ −3.75171e14 −0.471456 −0.235728 0.971819i $$-0.575747\pi$$
−0.235728 + 0.971819i $$0.575747\pi$$
$$98$$ 0 0
$$99$$ −2.92604e14 1.05667e15i −0.315513 1.13940i
$$100$$ 0 0
$$101$$ 8.90919e14i 0.826852i −0.910538 0.413426i $$-0.864332\pi$$
0.910538 0.413426i $$-0.135668\pi$$
$$102$$ 0 0
$$103$$ 1.87003e15i 1.49820i −0.662458 0.749099i $$-0.730487\pi$$
0.662458 0.749099i $$-0.269513\pi$$
$$104$$ 0 0
$$105$$ −3.19088e14 + 4.19455e14i −0.221305 + 0.290915i
$$106$$ 0 0
$$107$$ −2.30400e15 −1.38709 −0.693544 0.720414i $$-0.743952\pi$$
−0.693544 + 0.720414i $$0.743952\pi$$
$$108$$ 0 0
$$109$$ 8.68707e14 0.455171 0.227585 0.973758i $$-0.426917\pi$$
0.227585 + 0.973758i $$0.426917\pi$$
$$110$$ 0 0
$$111$$ −4.10314e14 + 5.39375e14i −0.187583 + 0.246586i
$$112$$ 0 0
$$113$$ 1.92630e14i 0.0770259i 0.999258 + 0.0385129i $$0.0122621\pi$$
−0.999258 + 0.0385129i $$0.987738\pi$$
$$114$$ 0 0
$$115$$ 1.29737e15i 0.454810i
$$116$$ 0 0
$$117$$ −9.74341e14 3.51860e15i −0.300135 1.08387i
$$118$$ 0 0
$$119$$ −1.35113e15 −0.366518
$$120$$ 0 0
$$121$$ 1.66162e15 0.397778
$$122$$ 0 0
$$123$$ 1.59681e15 + 1.21473e15i 0.338037 + 0.257152i
$$124$$ 0 0
$$125$$ 4.20251e15i 0.788286i
$$126$$ 0 0
$$127$$ 1.64302e15i 0.273599i −0.990599 0.136799i $$-0.956318\pi$$
0.990599 0.136799i $$-0.0436816\pi$$
$$128$$ 0 0
$$129$$ 1.72266e15 + 1.31046e15i 0.255138 + 0.194089i
$$130$$ 0 0
$$131$$ 5.77321e15 0.761873 0.380937 0.924601i $$-0.375602\pi$$
0.380937 + 0.924601i $$0.375602\pi$$
$$132$$ 0 0
$$133$$ −9.73580e14 −0.114679
$$134$$ 0 0
$$135$$ −1.53423e15 + 3.83916e15i −0.161580 + 0.404328i
$$136$$ 0 0
$$137$$ 1.98302e16i 1.87035i 0.354185 + 0.935175i $$0.384758\pi$$
−0.354185 + 0.935175i $$0.615242\pi$$
$$138$$ 0 0
$$139$$ 1.91399e16i 1.61930i 0.586912 + 0.809651i $$0.300343\pi$$
−0.586912 + 0.809651i $$0.699657\pi$$
$$140$$ 0 0
$$141$$ −3.15707e15 + 4.15010e15i −0.239961 + 0.315439i
$$142$$ 0 0
$$143$$ 1.94428e16 1.32965
$$144$$ 0 0
$$145$$ −1.25020e16 −0.770408
$$146$$ 0 0
$$147$$ 3.21507e15 4.22635e15i 0.178777 0.235010i
$$148$$ 0 0
$$149$$ 6.29842e15i 0.316472i −0.987401 0.158236i $$-0.949419\pi$$
0.987401 0.158236i $$-0.0505806\pi$$
$$150$$ 0 0
$$151$$ 2.59510e16i 1.17985i 0.807458 + 0.589925i $$0.200843\pi$$
−0.807458 + 0.589925i $$0.799157\pi$$
$$152$$ 0 0
$$153$$ −1.02148e16 + 2.82860e15i −0.420770 + 0.116516i
$$154$$ 0 0
$$155$$ 9.09465e15 0.339859
$$156$$ 0 0
$$157$$ 4.78146e16 1.62298 0.811490 0.584366i $$-0.198657\pi$$
0.811490 + 0.584366i $$0.198657\pi$$
$$158$$ 0 0
$$159$$ 3.93319e16 + 2.99206e16i 1.21413 + 0.923617i
$$160$$ 0 0
$$161$$ 3.11979e16i 0.876863i
$$162$$ 0 0
$$163$$ 5.01923e16i 1.28597i 0.765880 + 0.642984i $$0.222304\pi$$
−0.765880 + 0.642984i $$0.777696\pi$$
$$164$$ 0 0
$$165$$ −1.75229e16 1.33300e16i −0.409710 0.311675i
$$166$$ 0 0
$$167$$ −2.24657e16 −0.479896 −0.239948 0.970786i $$-0.577130\pi$$
−0.239948 + 0.970786i $$0.577130\pi$$
$$168$$ 0 0
$$169$$ 1.35565e16 0.264849
$$170$$ 0 0
$$171$$ −7.36044e15 + 2.03819e15i −0.131654 + 0.0364564i
$$172$$ 0 0
$$173$$ 3.73031e16i 0.611504i −0.952111 0.305752i $$-0.901092\pi$$
0.952111 0.305752i $$-0.0989079\pi$$
$$174$$ 0 0
$$175$$ 4.52375e16i 0.680320i
$$176$$ 0 0
$$177$$ −1.44851e15 + 1.90413e15i −0.0200043 + 0.0262965i
$$178$$ 0 0
$$179$$ 1.37575e17 1.74639 0.873197 0.487367i $$-0.162042\pi$$
0.873197 + 0.487367i $$0.162042\pi$$
$$180$$ 0 0
$$181$$ −6.36349e16 −0.743201 −0.371600 0.928393i $$-0.621191\pi$$
−0.371600 + 0.928393i $$0.621191\pi$$
$$182$$ 0 0
$$183$$ −3.31854e16 + 4.36237e16i −0.356914 + 0.469179i
$$184$$ 0 0
$$185$$ 1.36086e16i 0.134904i
$$186$$ 0 0
$$187$$ 5.64441e16i 0.516187i
$$188$$ 0 0
$$189$$ −3.68938e16 + 9.23206e16i −0.311523 + 0.779534i
$$190$$ 0 0
$$191$$ −1.30203e17 −1.01595 −0.507973 0.861373i $$-0.669605\pi$$
−0.507973 + 0.861373i $$0.669605\pi$$
$$192$$ 0 0
$$193$$ 2.33515e17 1.68513 0.842566 0.538593i $$-0.181044\pi$$
0.842566 + 0.538593i $$0.181044\pi$$
$$194$$ 0 0
$$195$$ −5.83494e16 4.43876e16i −0.389742 0.296484i
$$196$$ 0 0
$$197$$ 2.42634e17i 1.50126i 0.660724 + 0.750629i $$0.270249\pi$$
−0.660724 + 0.750629i $$0.729751\pi$$
$$198$$ 0 0
$$199$$ 1.14963e17i 0.659419i −0.944082 0.329710i $$-0.893049\pi$$
0.944082 0.329710i $$-0.106951\pi$$
$$200$$ 0 0
$$201$$ −2.63703e17 2.00604e17i −1.40328 1.06751i
$$202$$ 0 0
$$203$$ −3.00637e17 −1.48533
$$204$$ 0 0
$$205$$ 4.02879e16 0.184936
$$206$$ 0 0
$$207$$ −6.53129e16 2.35862e17i −0.278754 1.00665i
$$208$$ 0 0
$$209$$ 4.06717e16i 0.161508i
$$210$$ 0 0
$$211$$ 1.14655e17i 0.423913i −0.977279 0.211956i $$-0.932017\pi$$
0.977279 0.211956i $$-0.0679834\pi$$
$$212$$ 0 0
$$213$$ −1.89630e17 + 2.49277e17i −0.653221 + 0.858688i
$$214$$ 0 0
$$215$$ 4.34630e16 0.139583
$$216$$ 0 0
$$217$$ 2.18700e17 0.655239
$$218$$ 0 0
$$219$$ 1.53171e17 2.01350e17i 0.428397 0.563146i
$$220$$ 0 0
$$221$$ 1.87953e17i 0.491029i
$$222$$ 0 0
$$223$$ 4.46157e17i 1.08943i −0.838620 0.544717i $$-0.816637\pi$$
0.838620 0.544717i $$-0.183363\pi$$
$$224$$ 0 0
$$225$$ −9.47048e16 3.42004e17i −0.216273 0.781020i
$$226$$ 0 0
$$227$$ −5.24609e17 −1.12109 −0.560547 0.828123i $$-0.689409\pi$$
−0.560547 + 0.828123i $$0.689409\pi$$
$$228$$ 0 0
$$229$$ 6.48369e17 1.29735 0.648674 0.761067i $$-0.275324\pi$$
0.648674 + 0.761067i $$0.275324\pi$$
$$230$$ 0 0
$$231$$ −4.21374e17 3.20548e17i −0.789911 0.600901i
$$232$$ 0 0
$$233$$ 4.01531e17i 0.705585i −0.935702 0.352793i $$-0.885232\pi$$
0.935702 0.352793i $$-0.114768\pi$$
$$234$$ 0 0
$$235$$ 1.04708e17i 0.172572i
$$236$$ 0 0
$$237$$ −5.83288e17 4.43719e17i −0.902132 0.686271i
$$238$$ 0 0
$$239$$ 1.21318e17 0.176173 0.0880867 0.996113i $$-0.471925\pi$$
0.0880867 + 0.996113i $$0.471925\pi$$
$$240$$ 0 0
$$241$$ 3.65127e17 0.498100 0.249050 0.968491i $$-0.419882\pi$$
0.249050 + 0.968491i $$0.419882\pi$$
$$242$$ 0 0
$$243$$ −8.56502e16 + 7.75197e17i −0.109820 + 0.993951i
$$244$$ 0 0
$$245$$ 1.06632e17i 0.128571i
$$246$$ 0 0
$$247$$ 1.35432e17i 0.153637i
$$248$$ 0 0
$$249$$ −9.48305e17 + 1.24659e18i −1.01263 + 1.33115i
$$250$$ 0 0
$$251$$ 1.39376e18 1.40164 0.700819 0.713339i $$-0.252818\pi$$
0.700819 + 0.713339i $$0.252818\pi$$
$$252$$ 0 0
$$253$$ 1.30331e18 1.23493
$$254$$ 0 0
$$255$$ −1.28861e17 + 1.69393e17i −0.115099 + 0.151302i
$$256$$ 0 0
$$257$$ 1.58617e18i 1.33614i 0.744099 + 0.668070i $$0.232879\pi$$
−0.744099 + 0.668070i $$0.767121\pi$$
$$258$$ 0 0
$$259$$ 3.27246e17i 0.260091i
$$260$$ 0 0
$$261$$ −2.27287e18 + 6.29384e17i −1.70518 + 0.472185i
$$262$$ 0 0
$$263$$ −1.02896e18 −0.729001 −0.364501 0.931203i $$-0.618760\pi$$
−0.364501 + 0.931203i $$0.618760\pi$$
$$264$$ 0 0
$$265$$ 9.92354e17 0.664236
$$266$$ 0 0
$$267$$ 1.69215e18 + 1.28726e18i 1.07055 + 0.814387i
$$268$$ 0 0
$$269$$ 9.01288e17i 0.539165i −0.962977 0.269582i $$-0.913114\pi$$
0.962977 0.269582i $$-0.0868857\pi$$
$$270$$ 0 0
$$271$$ 2.19619e18i 1.24280i 0.783494 + 0.621399i $$0.213435\pi$$
−0.783494 + 0.621399i $$0.786565\pi$$
$$272$$ 0 0
$$273$$ −1.40313e18 1.06739e18i −0.751412 0.571615i
$$274$$ 0 0
$$275$$ 1.88982e18 0.958130
$$276$$ 0 0
$$277$$ 2.49263e18 1.19690 0.598451 0.801159i $$-0.295783\pi$$
0.598451 + 0.801159i $$0.295783\pi$$
$$278$$ 0 0
$$279$$ 1.65341e18 4.57848e17i 0.752226 0.208300i
$$280$$ 0 0
$$281$$ 1.55724e17i 0.0671520i 0.999436 + 0.0335760i $$0.0106896\pi$$
−0.999436 + 0.0335760i $$0.989310\pi$$
$$282$$ 0 0
$$283$$ 2.54289e18i 1.03975i 0.854242 + 0.519875i $$0.174022\pi$$
−0.854242 + 0.519875i $$0.825978\pi$$
$$284$$ 0 0
$$285$$ −9.28528e16 + 1.22059e17i −0.0360129 + 0.0473406i
$$286$$ 0 0
$$287$$ 9.68805e17 0.356551
$$288$$ 0 0
$$289$$ 2.31678e18 0.809377
$$290$$ 0 0
$$291$$ −8.60428e17 + 1.13107e18i −0.285441 + 0.375225i
$$292$$ 0 0
$$293$$ 2.17295e18i 0.684765i −0.939561 0.342383i $$-0.888766\pi$$
0.939561 0.342383i $$-0.111234\pi$$
$$294$$ 0 0
$$295$$ 4.80417e16i 0.0143864i
$$296$$ 0 0
$$297$$ −3.85673e18 1.54125e18i −1.09786 0.438733i
$$298$$ 0 0
$$299$$ 4.33987e18 1.17474
$$300$$ 0 0
$$301$$ 1.04516e18 0.269112
$$302$$ 0 0
$$303$$ −2.68595e18 2.04326e18i −0.658080 0.500615i
$$304$$ 0 0
$$305$$ 1.10064e18i 0.256682i
$$306$$ 0 0
$$307$$ 7.66257e18i 1.70152i 0.525555 + 0.850759i $$0.323858\pi$$
−0.525555 + 0.850759i $$0.676142\pi$$
$$308$$ 0 0
$$309$$ −5.63779e18 4.28878e18i −1.19240 0.907079i
$$310$$ 0 0
$$311$$ −4.84682e18 −0.976685 −0.488342 0.872652i $$-0.662398\pi$$
−0.488342 + 0.872652i $$0.662398\pi$$
$$312$$ 0 0
$$313$$ 8.77812e18 1.68585 0.842926 0.538030i $$-0.180831\pi$$
0.842926 + 0.538030i $$0.180831\pi$$
$$314$$ 0 0
$$315$$ 5.32772e17 + 1.92398e18i 0.0975467 + 0.352267i
$$316$$ 0 0
$$317$$ 6.53956e17i 0.114184i 0.998369 + 0.0570918i $$0.0181828\pi$$
−0.998369 + 0.0570918i $$0.981817\pi$$
$$318$$ 0 0
$$319$$ 1.25592e19i 2.09186i
$$320$$ 0 0
$$321$$ −5.28406e18 + 6.94612e18i −0.839808 + 1.10396i
$$322$$ 0 0
$$323$$ −3.93172e17 −0.0596436
$$324$$ 0 0
$$325$$ 6.29289e18 0.911433
$$326$$ 0 0
$$327$$ 1.99232e18 2.61899e18i 0.275582 0.362264i
$$328$$ 0 0
$$329$$ 2.51792e18i 0.332715i
$$330$$ 0 0
$$331$$ 7.41780e18i 0.936623i −0.883563 0.468312i $$-0.844862\pi$$
0.883563 0.468312i $$-0.155138\pi$$
$$332$$ 0 0
$$333$$ 6.85090e17 + 2.47404e18i 0.0826829 + 0.298590i
$$334$$ 0 0
$$335$$ −6.65330e18 −0.767716
$$336$$ 0 0
$$337$$ −7.56506e18 −0.834811 −0.417405 0.908720i $$-0.637060\pi$$
−0.417405 + 0.908720i $$0.637060\pi$$
$$338$$ 0 0
$$339$$ 5.80744e17 + 4.41784e17i 0.0613038 + 0.0466350i
$$340$$ 0 0
$$341$$ 9.13626e18i 0.922807i
$$342$$ 0 0
$$343$$ 1.12481e19i 1.08736i
$$344$$ 0 0
$$345$$ −3.91133e18 2.97543e18i −0.361977 0.275363i
$$346$$ 0 0
$$347$$ −5.19618e18 −0.460483 −0.230241 0.973134i $$-0.573952\pi$$
−0.230241 + 0.973134i $$0.573952\pi$$
$$348$$ 0 0
$$349$$ −3.25826e18 −0.276563 −0.138282 0.990393i $$-0.544158\pi$$
−0.138282 + 0.990393i $$0.544158\pi$$
$$350$$ 0 0
$$351$$ −1.28425e19 5.13221e18i −1.04435 0.417350i
$$352$$ 0 0
$$353$$ 1.05498e19i 0.822121i −0.911608 0.411060i $$-0.865159\pi$$
0.911608 0.411060i $$-0.134841\pi$$
$$354$$ 0 0
$$355$$ 6.28932e18i 0.469776i
$$356$$ 0 0
$$357$$ −3.09873e18 + 4.07341e18i −0.221907 + 0.291707i
$$358$$ 0 0
$$359$$ −2.60617e19 −1.78976 −0.894880 0.446308i $$-0.852739\pi$$
−0.894880 + 0.446308i $$0.852739\pi$$
$$360$$ 0 0
$$361$$ 1.48978e19 0.981338
$$362$$ 0 0
$$363$$ 3.81080e18 5.00946e18i 0.240833 0.316586i
$$364$$ 0 0
$$365$$ 5.08011e18i 0.308089i
$$366$$ 0 0
$$367$$ 3.03458e19i 1.76646i −0.468942 0.883229i $$-0.655365\pi$$
0.468942 0.883229i $$-0.344635\pi$$
$$368$$ 0 0
$$369$$ 7.32434e18 2.02819e18i 0.409327 0.113347i
$$370$$ 0 0
$$371$$ 2.38632e19 1.28063
$$372$$ 0 0
$$373$$ 9.93056e18 0.511868 0.255934 0.966694i $$-0.417617\pi$$
0.255934 + 0.966694i $$0.417617\pi$$
$$374$$ 0 0
$$375$$ −1.26698e19 9.63816e18i −0.627386 0.477265i
$$376$$ 0 0
$$377$$ 4.18209e19i 1.98991i
$$378$$ 0 0
$$379$$ 4.08110e19i 1.86631i 0.359480 + 0.933153i $$0.382954\pi$$
−0.359480 + 0.933153i $$0.617046\pi$$
$$380$$ 0 0
$$381$$ −4.95339e18 3.76814e18i −0.217753 0.165650i
$$382$$ 0 0
$$383$$ 2.12130e19 0.896626 0.448313 0.893877i $$-0.352025\pi$$
0.448313 + 0.893877i $$0.352025\pi$$
$$384$$ 0 0
$$385$$ −1.06314e19 −0.432149
$$386$$ 0 0
$$387$$ 7.90158e18 2.18804e18i 0.308945 0.0855505i
$$388$$ 0 0
$$389$$ 3.25171e19i 1.22318i 0.791176 + 0.611588i $$0.209469\pi$$
−0.791176 + 0.611588i $$0.790531\pi$$
$$390$$ 0 0
$$391$$ 1.25990e19i 0.456049i
$$392$$ 0 0
$$393$$ 1.32404e19 1.74051e19i 0.461273 0.606364i
$$394$$ 0 0
$$395$$ −1.47165e19 −0.493544
$$396$$ 0 0
$$397$$ −3.17360e19 −1.02476 −0.512382 0.858758i $$-0.671237\pi$$
−0.512382 + 0.858758i $$0.671237\pi$$
$$398$$ 0 0
$$399$$ −2.23284e18 + 2.93516e18i −0.0694321 + 0.0912715i
$$400$$ 0 0
$$401$$ 5.30666e19i 1.58942i 0.606989 + 0.794710i $$0.292377\pi$$
−0.606989 + 0.794710i $$0.707623\pi$$
$$402$$ 0 0
$$403$$ 3.04228e19i 0.877831i
$$404$$ 0 0
$$405$$ 8.05571e18 + 1.34303e19i 0.223971 + 0.373398i
$$406$$ 0 0
$$407$$ −1.36708e19 −0.366300
$$408$$ 0 0
$$409$$ −2.32775e19 −0.601189 −0.300595 0.953752i $$-0.597185\pi$$
−0.300595 + 0.953752i $$0.597185\pi$$
$$410$$ 0 0
$$411$$ 5.97844e19 + 4.54792e19i 1.48859 + 1.13240i
$$412$$ 0 0
$$413$$ 1.15526e18i 0.0277367i
$$414$$ 0 0
$$415$$ 3.14517e19i 0.728255i
$$416$$ 0 0
$$417$$ 5.77031e19 + 4.38959e19i 1.28878 + 0.980401i
$$418$$ 0 0
$$419$$ 6.13766e19 1.32251 0.661253 0.750163i $$-0.270025\pi$$
0.661253 + 0.750163i $$0.270025\pi$$
$$420$$ 0 0
$$421$$ −3.49520e19 −0.726703 −0.363351 0.931652i $$-0.618368\pi$$
−0.363351 + 0.931652i $$0.618368\pi$$
$$422$$ 0 0
$$423$$ 5.27127e18 + 1.90359e19i 0.105770 + 0.381963i
$$424$$ 0 0
$$425$$ 1.82688e19i 0.353829i
$$426$$ 0 0
$$427$$ 2.64670e19i 0.494876i
$$428$$ 0 0
$$429$$ 4.45907e19 5.86164e19i 0.805034 1.05825i
$$430$$ 0 0
$$431$$ 6.15689e17 0.0107345 0.00536725 0.999986i $$-0.498292\pi$$
0.00536725 + 0.999986i $$0.498292\pi$$
$$432$$ 0 0
$$433$$ −6.85272e19 −1.15399 −0.576997 0.816746i $$-0.695776\pi$$
−0.576997 + 0.816746i $$0.695776\pi$$
$$434$$ 0 0
$$435$$ −2.86725e19 + 3.76913e19i −0.466441 + 0.613157i
$$436$$ 0 0
$$437$$ 9.07843e18i 0.142692i
$$438$$ 0 0
$$439$$ 7.27308e18i 0.110467i −0.998473 0.0552337i $$-0.982410\pi$$
0.998473 0.0552337i $$-0.0175904\pi$$
$$440$$ 0 0
$$441$$ −5.36812e18 1.93857e19i −0.0788011 0.284572i
$$442$$ 0 0
$$443$$ 8.96453e19 1.27204 0.636018 0.771674i $$-0.280580\pi$$
0.636018 + 0.771674i $$0.280580\pi$$
$$444$$ 0 0
$$445$$ 4.26935e19 0.585681
$$446$$ 0 0
$$447$$ −1.89886e19 1.44450e19i −0.251875 0.191607i
$$448$$ 0 0
$$449$$ 2.97759e19i 0.381959i 0.981594 + 0.190980i $$0.0611665\pi$$
−0.981594 + 0.190980i $$0.938834\pi$$
$$450$$ 0 0
$$451$$ 4.04722e19i 0.502149i
$$452$$ 0 0
$$453$$ 7.82374e19 + 5.95168e19i 0.939026 + 0.714336i
$$454$$ 0 0
$$455$$ −3.54013e19 −0.411087
$$456$$ 0 0
$$457$$ −5.35657e19 −0.601887 −0.300944 0.953642i $$-0.597302\pi$$
−0.300944 + 0.953642i $$0.597302\pi$$
$$458$$ 0 0
$$459$$ −1.48992e19 + 3.72829e19i −0.162020 + 0.405429i
$$460$$ 0 0
$$461$$ 1.88829e20i 1.98752i −0.111527 0.993761i $$-0.535574\pi$$
0.111527 0.993761i $$-0.464426\pi$$
$$462$$ 0 0
$$463$$ 2.55431e19i 0.260265i −0.991497 0.130133i $$-0.958460\pi$$
0.991497 0.130133i $$-0.0415403\pi$$
$$464$$ 0 0
$$465$$ 2.08579e19 2.74187e19i 0.205766 0.270489i
$$466$$ 0 0
$$467$$ 5.46072e19 0.521642 0.260821 0.965387i $$-0.416007\pi$$
0.260821 + 0.965387i $$0.416007\pi$$
$$468$$ 0 0
$$469$$ −1.59992e20 −1.48014
$$470$$ 0 0
$$471$$ 1.09659e20 1.44152e20i 0.982628 1.29171i
$$472$$ 0 0
$$473$$ 4.36619e19i 0.379004i
$$474$$ 0 0
$$475$$ 1.31639e19i 0.110709i
$$476$$ 0 0
$$477$$ 1.80410e20 4.99576e19i 1.47019 0.407112i
$$478$$ 0 0
$$479$$ −1.65419e20 −1.30638 −0.653188 0.757196i $$-0.726569\pi$$
−0.653188 + 0.757196i $$0.726569\pi$$
$$480$$ 0 0
$$481$$ −4.55224e19 −0.348447
$$482$$ 0 0
$$483$$ −9.40559e19 7.15502e19i −0.697883 0.530894i
$$484$$ 0 0
$$485$$ 2.85372e19i 0.205280i
$$486$$ 0 0
$$487$$ 5.27556e19i 0.367960i −0.982930 0.183980i $$-0.941102\pi$$
0.982930 0.183980i $$-0.0588982\pi$$
$$488$$ 0 0
$$489$$ 1.51320e20 + 1.15112e20i 1.02348 + 0.778585i
$$490$$ 0 0
$$491$$ −2.76893e20 −1.81636 −0.908178 0.418584i $$-0.862526\pi$$
−0.908178 + 0.418584i $$0.862526\pi$$
$$492$$ 0 0
$$493$$ −1.21410e20 −0.772506
$$494$$ 0 0
$$495$$ −8.03751e19 + 2.22568e19i −0.496115 + 0.137380i
$$496$$ 0 0
$$497$$ 1.51240e20i 0.905717i
$$498$$ 0 0
$$499$$ 1.21401e20i 0.705453i −0.935726 0.352727i $$-0.885255\pi$$
0.935726 0.352727i $$-0.114745\pi$$
$$500$$ 0 0
$$501$$ −5.15235e19 + 6.77299e19i −0.290551 + 0.381942i
$$502$$ 0 0
$$503$$ 1.34169e20 0.734330 0.367165 0.930156i $$-0.380328\pi$$
0.367165 + 0.930156i $$0.380328\pi$$
$$504$$ 0 0
$$505$$ −6.77672e19 −0.360026
$$506$$ 0 0
$$507$$ 3.10909e19 4.08704e19i 0.160352 0.210790i
$$508$$ 0 0
$$509$$ 1.59029e20i 0.796328i 0.917314 + 0.398164i $$0.130353\pi$$
−0.917314 + 0.398164i $$0.869647\pi$$
$$510$$ 0 0
$$511$$ 1.22162e20i 0.593989i
$$512$$ 0 0
$$513$$ −1.07359e19 + 2.68648e19i −0.0506941 + 0.126854i
$$514$$ 0 0
$$515$$ −1.42243e20 −0.652343
$$516$$ 0 0
$$517$$ −1.05187e20 −0.468580
$$518$$ 0 0
$$519$$ −1.12462e20 8.55521e19i −0.486688 0.370233i
$$520$$ 0 0
$$521$$ 2.22638e20i 0.936087i −0.883706 0.468043i $$-0.844959\pi$$
0.883706 0.468043i $$-0.155041\pi$$
$$522$$ 0 0
$$523$$ 4.79645e20i 1.95955i −0.200093 0.979777i $$-0.564124\pi$$
0.200093 0.979777i $$-0.435876\pi$$
$$524$$ 0 0
$$525$$ −1.36383e20 1.03749e20i −0.541457 0.411898i
$$526$$ 0 0
$$527$$ 8.83200e19 0.340784
$$528$$ 0 0
$$529$$ 2.42788e19 0.0910563
$$530$$ 0 0
$$531$$ 2.41854e18 + 8.73398e18i 0.00881747 + 0.0318422i
$$532$$ 0 0
$$533$$ 1.34768e20i 0.477676i
$$534$$ 0 0
$$535$$ 1.75252e20i 0.603963i
$$536$$ 0 0
$$537$$ 3.15519e20 4.14763e20i 1.05735 1.38993i
$$538$$ 0 0
$$539$$ 1.07120e20 0.349103
$$540$$ 0 0
$$541$$ 4.62548e20 1.46615 0.733074 0.680149i $$-0.238085\pi$$
0.733074 + 0.680149i $$0.238085\pi$$
$$542$$ 0 0
$$543$$ −1.45942e20 + 1.91847e20i −0.449968 + 0.591503i
$$544$$ 0 0
$$545$$ 6.60777e19i 0.198190i
$$546$$ 0 0
$$547$$ 1.52374e20i 0.444638i 0.974974 + 0.222319i $$0.0713626\pi$$
−0.974974 + 0.222319i $$0.928637\pi$$
$$548$$ 0 0
$$549$$ 5.54087e19 + 2.00095e20i 0.157321 + 0.568126i
$$550$$ 0 0
$$551$$ −8.74838e19 −0.241708
$$552$$ 0 0
$$553$$ −3.53888e20 −0.951541
$$554$$ 0 0
$$555$$ 4.10273e19 + 3.12103e19i 0.107368 + 0.0816771i
$$556$$ 0 0
$$557$$ 5.19363e20i 1.32299i −0.749949 0.661495i $$-0.769922\pi$$
0.749949 0.661495i $$-0.230078\pi$$
$$558$$ 0 0
$$559$$ 1.45389e20i 0.360532i
$$560$$ 0 0
$$561$$ −1.70168e20 1.29451e20i −0.410826 0.312523i
$$562$$ 0 0
$$563$$ −1.10226e20 −0.259102 −0.129551 0.991573i $$-0.541354\pi$$
−0.129551 + 0.991573i $$0.541354\pi$$
$$564$$ 0 0
$$565$$ 1.46523e19 0.0335385
$$566$$ 0 0
$$567$$ 1.93716e20 + 3.22958e20i 0.431810 + 0.719903i
$$568$$ 0 0
$$569$$ 1.11868e20i 0.242864i −0.992600 0.121432i $$-0.961251\pi$$
0.992600 0.121432i $$-0.0387486\pi$$
$$570$$ 0 0
$$571$$ 2.44274e20i 0.516543i 0.966072 + 0.258271i $$0.0831529\pi$$
−0.966072 + 0.258271i $$0.916847\pi$$
$$572$$ 0 0
$$573$$ −2.98611e20 + 3.92537e20i −0.615101 + 0.808577i
$$574$$ 0 0
$$575$$ 4.21830e20 0.846504
$$576$$ 0 0
$$577$$ 2.24168e20 0.438284 0.219142 0.975693i $$-0.429674\pi$$
0.219142 + 0.975693i $$0.429674\pi$$
$$578$$ 0 0
$$579$$ 5.35549e20 7.04002e20i 1.02026 1.34117i
$$580$$ 0 0
$$581$$ 7.56321e20i 1.40406i
$$582$$ 0 0
$$583$$ 9.96895e20i 1.80358i
$$584$$ 0 0
$$585$$ −2.67640e20 + 7.41127e19i −0.471935 + 0.130684i
$$586$$ 0 0
$$587$$ 1.36189e19 0.0234075 0.0117038 0.999932i $$-0.496274\pi$$
0.0117038 + 0.999932i $$0.496274\pi$$
$$588$$ 0 0
$$589$$ 6.36404e19 0.106627
$$590$$ 0 0
$$591$$ 7.31497e20 + 5.56464e20i 1.19483 + 0.908932i
$$592$$ 0 0
$$593$$ 5.06250e20i 0.806222i 0.915151 + 0.403111i $$0.132071\pi$$
−0.915151 + 0.403111i $$0.867929\pi$$
$$594$$ 0 0
$$595$$ 1.02773e20i 0.159589i
$$596$$ 0 0
$$597$$ −3.46593e20 2.63661e20i −0.524823 0.399243i
$$598$$ 0 0
$$599$$ 1.02091e21 1.50760 0.753802 0.657102i $$-0.228218\pi$$
0.753802 + 0.657102i $$0.228218\pi$$
$$600$$ 0 0
$$601$$ 1.06150e21 1.52884 0.764421 0.644717i $$-0.223025\pi$$
0.764421 + 0.644717i $$0.223025\pi$$
$$602$$ 0 0
$$603$$ −1.20957e21 + 3.34944e20i −1.69922 + 0.470535i
$$604$$ 0 0
$$605$$ 1.26390e20i 0.173200i
$$606$$ 0 0
$$607$$ 4.51118e20i 0.603080i 0.953453 + 0.301540i $$0.0975007\pi$$
−0.953453 + 0.301540i $$0.902499\pi$$
$$608$$ 0 0
$$609$$ −6.89490e20 + 9.06364e20i −0.899287 + 1.18215i
$$610$$ 0 0
$$611$$ −3.50262e20 −0.445743
$$612$$ 0 0
$$613$$ 4.84225e20 0.601304 0.300652 0.953734i $$-0.402796\pi$$
0.300652 + 0.953734i $$0.402796\pi$$
$$614$$ 0 0
$$615$$ 9.23974e19 1.21460e20i 0.111969 0.147188i
$$616$$ 0 0
$$617$$ 1.04009e21i 1.23008i −0.788497 0.615038i $$-0.789141\pi$$
0.788497 0.615038i $$-0.210859\pi$$
$$618$$ 0 0
$$619$$ 5.15454e19i 0.0594990i −0.999557 0.0297495i $$-0.990529\pi$$
0.999557 0.0297495i $$-0.00947096\pi$$
$$620$$ 0 0
$$621$$ −8.60870e20 3.44026e20i −0.969953 0.387619i
$$622$$ 0 0
$$623$$ 1.02665e21 1.12918
$$624$$ 0 0
$$625$$ 4.35092e20 0.467177
$$626$$ 0 0
$$627$$ −1.22618e20 9.32777e19i −0.128542 0.0977848i
$$628$$ 0 0
$$629$$ 1.32156e20i 0.135271i
$$630$$ 0 0
$$631$$ 2.22096e20i 0.221984i −0.993821 0.110992i $$-0.964597\pi$$
0.993821 0.110992i $$-0.0354028\pi$$
$$632$$ 0 0
$$633$$ −3.45665e20 2.62954e20i −0.337386 0.256656i
$$634$$ 0 0
$$635$$ −1.24975e20 −0.119130
$$636$$ 0 0
$$637$$ 3.56697e20 0.332089
$$638$$ 0 0
$$639$$ 3.16620e20 + 1.14340e21i 0.287927 + 1.03978i
$$640$$ 0 0
$$641$$ 5.19914e19i 0.0461845i −0.999733 0.0230922i $$-0.992649\pi$$
0.999733 0.0230922i $$-0.00735114\pi$$
$$642$$ 0 0
$$643$$ 6.41865e20i 0.557008i −0.960435 0.278504i $$-0.910161\pi$$
0.960435 0.278504i $$-0.0898385\pi$$
$$644$$ 0 0
$$645$$ 9.96794e19 1.31033e20i 0.0845099 0.111092i
$$646$$ 0 0
$$647$$ −1.59499e21 −1.32122 −0.660611 0.750729i $$-0.729703\pi$$
−0.660611 + 0.750729i $$0.729703\pi$$
$$648$$ 0 0
$$649$$ −4.82615e19 −0.0390630
$$650$$ 0 0
$$651$$ 5.01572e20 6.59338e20i 0.396712 0.521496i
$$652$$ 0 0
$$653$$ 3.61572e17i 0.000279477i 1.00000 0.000139739i $$4.44802e-5\pi$$
−1.00000 0.000139739i $$0.999956\pi$$
$$654$$ 0 0
$$655$$ 4.39136e20i 0.331733i
$$656$$ 0 0
$$657$$ −2.55746e20 9.23564e20i −0.188829 0.681910i
$$658$$ 0 0
$$659$$ −9.68333e20 −0.698851 −0.349425 0.936964i $$-0.613623\pi$$
−0.349425 + 0.936964i $$0.613623\pi$$
$$660$$ 0 0
$$661$$ 1.92498e21 1.35805 0.679025 0.734115i $$-0.262403\pi$$
0.679025 + 0.734115i $$0.262403\pi$$
$$662$$ 0 0
$$663$$ −5.66643e20 4.31057e20i −0.390803 0.297292i
$$664$$ 0 0
$$665$$ 7.40548e19i 0.0499334i
$$666$$ 0 0
$$667$$ 2.80338e21i 1.84815i
$$668$$ 0 0
$$669$$ −1.34508e21 1.02323e21i −0.867065 0.659594i
$$670$$ 0 0
$$671$$ −1.10567e21 −0.696959
$$672$$ 0 0
$$673$$ 5.09103e20 0.313829 0.156914 0.987612i $$-0.449845\pi$$
0.156914 + 0.987612i $$0.449845\pi$$
$$674$$ 0 0
$$675$$ −1.24828e21 4.98844e20i −0.752545 0.300737i
$$676$$ 0 0
$$677$$ 1.96477e21i 1.15850i −0.815148 0.579252i $$-0.803345\pi$$
0.815148 0.579252i $$-0.196655\pi$$
$$678$$ 0 0
$$679$$ 6.86234e20i 0.395776i
$$680$$ 0 0
$$681$$ −1.20315e21 + 1.58160e21i −0.678762 + 0.892262i
$$682$$ 0 0
$$683$$ −2.40991e20 −0.132998 −0.0664991 0.997786i $$-0.521183\pi$$
−0.0664991 + 0.997786i $$0.521183\pi$$
$$684$$ 0 0
$$685$$ 1.50837e21 0.814385
$$686$$ 0 0
$$687$$ 1.48699e21 1.95471e21i 0.785474 1.03254i
$$688$$ 0 0
$$689$$ 3.31955e21i 1.71568i
$$690$$ 0 0
$$691$$ 9.40696e20i 0.475734i −0.971298 0.237867i $$-0.923552\pi$$
0.971298 0.237867i $$-0.0764482\pi$$
$$692$$ 0 0
$$693$$ −1.93278e21 + 5.35210e20i −0.956498 + 0.264865i
$$694$$ 0 0
$$695$$ 1.45586e21 0.705073
$$696$$ 0 0
$$697$$ 3.91244e20 0.185439
$$698$$ 0 0
$$699$$ −1.21054e21 9.20883e20i −0.561565 0.427194i
$$700$$ 0 0
$$701$$ 2.13672e21i 0.970201i 0.874458 + 0.485101i $$0.161217\pi$$
−0.874458 + 0.485101i $$0.838783\pi$$
$$702$$ 0 0
$$703$$ 9.52268e19i 0.0423247i
$$704$$ 0 0
$$705$$ 3.15675e20 + 2.40141e20i 0.137348 + 0.104483i
$$706$$ 0 0
$$707$$ −1.62960e21 −0.694122
$$708$$ 0 0
$$709$$ −5.05315e20 −0.210724 −0.105362 0.994434i $$-0.533600\pi$$
−0.105362 + 0.994434i $$0.533600\pi$$
$$710$$ 0 0
$$711$$ −2.67546e21 + 7.40865e20i −1.09239 + 0.302494i
$$712$$ 0 0
$$713$$ 2.03933e21i 0.815296i
$$714$$ 0 0
$$715$$ 1.47891e21i 0.578955i
$$716$$ 0 0
$$717$$ 2.78234e20 3.65750e20i 0.106664 0.140214i
$$718$$ 0 0
$$719$$ −1.96314e21 −0.737030 −0.368515 0.929622i $$-0.620134\pi$$
−0.368515 + 0.929622i $$0.620134\pi$$
$$720$$ 0 0
$$721$$ −3.42052e21 −1.25770
$$722$$ 0 0
$$723$$ 8.37393e20 1.10079e21i 0.301573 0.396430i
$$724$$ 0 0
$$725$$ 4.06494e21i 1.43390i
$$726$$ 0 0
$$727$$ 1.15913e21i 0.400519i 0.979743 + 0.200259i $$0.0641785\pi$$
−0.979743 + 0.200259i $$0.935822\pi$$
$$728$$ 0 0
$$729$$ 2.14064e21 + 2.03608e21i 0.724582 + 0.689189i
$$730$$ 0 0
$$731$$ 4.22078e20 0.139963
$$732$$ 0 0
$$733$$ 2.01215e21 0.653703 0.326852 0.945076i $$-0.394012\pi$$
0.326852 + 0.945076i $$0.394012\pi$$
$$734$$ 0 0
$$735$$ −3.21475e20 2.44553e20i −0.102327 0.0778426i
$$736$$ 0 0
$$737$$ 6.68374e21i 2.08455i
$$738$$ 0 0
$$739$$ 3.78711e21i 1.15738i 0.815549 + 0.578688i $$0.196435\pi$$
−0.815549 + 0.578688i $$0.803565\pi$$
$$740$$ 0 0
$$741$$ −4.08303e20 3.10605e20i −0.122277 0.0930190i
$$742$$ 0 0
$$743$$ 3.73122e21 1.09505 0.547525 0.836789i $$-0.315570\pi$$
0.547525 + 0.836789i $$0.315570\pi$$
$$744$$ 0 0
$$745$$ −4.79086e20 −0.137798
$$746$$ 0 0
$$747$$ 1.58336e21 + 5.71792e21i 0.446349 + 1.61188i
$$748$$ 0 0
$$749$$ 4.21430e21i 1.16443i
$$750$$ 0 0
$$751$$ 1.59970e21i 0.433251i −0.976255 0.216626i $$-0.930495\pi$$
0.976255 0.216626i $$-0.0695051\pi$$
$$752$$ 0 0
$$753$$ 3.19650e21 4.20193e21i 0.848617 1.11554i
$$754$$ 0 0
$$755$$ 1.97395e21 0.513728
$$756$$ 0 0
$$757$$ 1.89582e21 0.483702 0.241851 0.970313i $$-0.422245\pi$$
0.241851 + 0.970313i $$0.422245\pi$$
$$758$$ 0 0
$$759$$ 2.98904e21 3.92922e21i 0.747685 0.982864i
$$760$$ 0 0
$$761$$ 2.60427e21i 0.638706i −0.947636 0.319353i $$-0.896534\pi$$
0.947636 0.319353i $$-0.103466\pi$$
$$762$$ 0 0
$$763$$ 1.58897e21i 0.382105i
$$764$$ 0 0
$$765$$ 2.15156e20 + 7.76983e20i 0.0507332 + 0.183211i
$$766$$ 0 0
$$767$$ −1.60706e20 −0.0371592
$$768$$ 0 0
$$769$$ −1.38301e21 −0.313601 −0.156801 0.987630i $$-0.550118\pi$$
−0.156801 + 0.987630i $$0.550118\pi$$
$$770$$ 0 0
$$771$$ 4.78201e21 + 3.63777e21i 1.06341 + 0.808961i
$$772$$ 0 0
$$773$$ 2.47373e21i 0.539519i 0.962928 + 0.269760i $$0.0869442\pi$$
−0.962928 + 0.269760i $$0.913056\pi$$
$$774$$ 0 0