# Properties

 Label 336.6.q.e.289.1 Level $336$ Weight $6$ Character 336.289 Analytic conductor $53.889$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 336.q (of order $$3$$, degree $$2$$, not 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: $$53.8889634572$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-83})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} - 20x^{2} - 21x + 441$$ x^4 - x^3 - 20*x^2 - 21*x + 441 Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 289.1 Root $$-3.69493 + 2.71062i$$ of defining polynomial Character $$\chi$$ $$=$$ 336.289 Dual form 336.6.q.e.193.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-4.50000 - 7.79423i) q^{3} +(-19.3645 + 33.5404i) q^{5} +(87.5000 + 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$$ $$q+(-4.50000 - 7.79423i) q^{3} +(-19.3645 + 33.5404i) q^{5} +(87.5000 + 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-288.195 - 499.168i) q^{11} +391.491 q^{13} +348.562 q^{15} +(664.850 + 1151.55i) q^{17} +(471.237 - 816.206i) q^{19} +(351.842 - 1112.46i) q^{21} +(-816.040 + 1413.42i) q^{23} +(812.530 + 1407.34i) q^{25} +729.000 q^{27} -1463.54 q^{29} +(-1956.21 - 3388.25i) q^{31} +(-2593.75 + 4492.51i) q^{33} +(-4902.85 + 1082.38i) q^{35} +(8150.17 - 14116.5i) q^{37} +(-1761.71 - 3051.37i) q^{39} -13103.8 q^{41} -14733.5 q^{43} +(-1568.53 - 2716.77i) q^{45} +(-3407.26 + 5901.55i) q^{47} +(-1494.50 + 16740.4i) q^{49} +(5983.65 - 10364.0i) q^{51} +(1005.67 + 1741.87i) q^{53} +22323.0 q^{55} -8482.26 q^{57} +(25726.6 + 44559.7i) q^{59} +(-20548.9 + 35591.8i) q^{61} +(-10254.1 + 2263.74i) q^{63} +(-7581.04 + 13130.8i) q^{65} +(25289.1 + 43802.0i) q^{67} +14688.7 q^{69} -39970.6 q^{71} +(27843.3 + 48226.0i) q^{73} +(7312.77 - 12666.1i) q^{75} +(22533.2 - 71245.8i) q^{77} +(-31575.7 + 54690.7i) q^{79} +(-3280.50 - 5681.99i) q^{81} -45572.4 q^{83} -51498.1 q^{85} +(6585.95 + 11407.2i) q^{87} +(-7843.34 + 13585.1i) q^{89} +(34255.5 + 37449.9i) q^{91} +(-17605.9 + 30494.3i) q^{93} +(18250.6 + 31610.9i) q^{95} +3128.49 q^{97} +46687.6 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9}+O(q^{10})$$ 4 * q - 18 * q^3 + 33 * q^5 + 350 * q^7 - 162 * q^9 $$4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9} - 1137 q^{11} + 1850 q^{13} - 594 q^{15} + 324 q^{17} + 2311 q^{19} - 1575 q^{21} + 1596 q^{23} - 395 q^{25} + 2916 q^{27} - 4434 q^{29} + 4294 q^{31} - 10233 q^{33} - 15414 q^{35} + 19109 q^{37} - 8325 q^{39} - 25716 q^{41} + 5542 q^{43} + 2673 q^{45} - 23160 q^{47} - 5978 q^{49} + 2916 q^{51} + 31653 q^{53} - 35778 q^{55} - 41598 q^{57} + 41097 q^{59} - 42052 q^{61} - 14175 q^{63} + 23106 q^{65} + 30763 q^{67} - 28728 q^{69} - 204192 q^{71} + 28577 q^{73} - 3555 q^{75} - 96873 q^{77} - 18464 q^{79} - 13122 q^{81} - 122358 q^{83} - 247272 q^{85} + 19953 q^{87} - 29322 q^{89} + 161875 q^{91} + 38646 q^{93} - 61662 q^{95} - 19582 q^{97} + 184194 q^{99}+O(q^{100})$$ 4 * q - 18 * q^3 + 33 * q^5 + 350 * q^7 - 162 * q^9 - 1137 * q^11 + 1850 * q^13 - 594 * q^15 + 324 * q^17 + 2311 * q^19 - 1575 * q^21 + 1596 * q^23 - 395 * q^25 + 2916 * q^27 - 4434 * q^29 + 4294 * q^31 - 10233 * q^33 - 15414 * q^35 + 19109 * q^37 - 8325 * q^39 - 25716 * q^41 + 5542 * q^43 + 2673 * q^45 - 23160 * q^47 - 5978 * q^49 + 2916 * q^51 + 31653 * q^53 - 35778 * q^55 - 41598 * q^57 + 41097 * q^59 - 42052 * q^61 - 14175 * q^63 + 23106 * q^65 + 30763 * q^67 - 28728 * q^69 - 204192 * q^71 + 28577 * q^73 - 3555 * q^75 - 96873 * q^77 - 18464 * q^79 - 13122 * q^81 - 122358 * q^83 - 247272 * q^85 + 19953 * q^87 - 29322 * q^89 + 161875 * q^91 + 38646 * q^93 - 61662 * q^95 - 19582 * q^97 + 184194 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$$.

 $$n$$ $$85$$ $$113$$ $$127$$ $$241$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −4.50000 7.79423i −0.288675 0.500000i
$$4$$ 0 0
$$5$$ −19.3645 + 33.5404i −0.346403 + 0.599988i −0.985608 0.169049i $$-0.945930\pi$$
0.639204 + 0.769037i $$0.279264\pi$$
$$6$$ 0 0
$$7$$ 87.5000 + 95.6596i 0.674937 + 0.737876i
$$8$$ 0 0
$$9$$ −40.5000 + 70.1481i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −288.195 499.168i −0.718133 1.24384i −0.961739 0.273968i $$-0.911664\pi$$
0.243606 0.969874i $$-0.421670\pi$$
$$12$$ 0 0
$$13$$ 391.491 0.642486 0.321243 0.946997i $$-0.395899\pi$$
0.321243 + 0.946997i $$0.395899\pi$$
$$14$$ 0 0
$$15$$ 348.562 0.399992
$$16$$ 0 0
$$17$$ 664.850 + 1151.55i 0.557958 + 0.966412i 0.997667 + 0.0682711i $$0.0217483\pi$$
−0.439709 + 0.898140i $$0.644918\pi$$
$$18$$ 0 0
$$19$$ 471.237 816.206i 0.299471 0.518699i −0.676544 0.736402i $$-0.736523\pi$$
0.976015 + 0.217703i $$0.0698564\pi$$
$$20$$ 0 0
$$21$$ 351.842 1112.46i 0.174100 0.550475i
$$22$$ 0 0
$$23$$ −816.040 + 1413.42i −0.321656 + 0.557124i −0.980830 0.194866i $$-0.937573\pi$$
0.659174 + 0.751991i $$0.270906\pi$$
$$24$$ 0 0
$$25$$ 812.530 + 1407.34i 0.260009 + 0.450350i
$$26$$ 0 0
$$27$$ 729.000 0.192450
$$28$$ 0 0
$$29$$ −1463.54 −0.323155 −0.161577 0.986860i $$-0.551658\pi$$
−0.161577 + 0.986860i $$0.551658\pi$$
$$30$$ 0 0
$$31$$ −1956.21 3388.25i −0.365604 0.633245i 0.623269 0.782008i $$-0.285804\pi$$
−0.988873 + 0.148763i $$0.952471\pi$$
$$32$$ 0 0
$$33$$ −2593.75 + 4492.51i −0.414614 + 0.718133i
$$34$$ 0 0
$$35$$ −4902.85 + 1082.38i −0.676517 + 0.149351i
$$36$$ 0 0
$$37$$ 8150.17 14116.5i 0.978729 1.69521i 0.311691 0.950184i $$-0.399105\pi$$
0.667038 0.745024i $$-0.267562\pi$$
$$38$$ 0 0
$$39$$ −1761.71 3051.37i −0.185470 0.321243i
$$40$$ 0 0
$$41$$ −13103.8 −1.21741 −0.608707 0.793395i $$-0.708312\pi$$
−0.608707 + 0.793395i $$0.708312\pi$$
$$42$$ 0 0
$$43$$ −14733.5 −1.21516 −0.607582 0.794257i $$-0.707860\pi$$
−0.607582 + 0.794257i $$0.707860\pi$$
$$44$$ 0 0
$$45$$ −1568.53 2716.77i −0.115468 0.199996i
$$46$$ 0 0
$$47$$ −3407.26 + 5901.55i −0.224989 + 0.389692i −0.956316 0.292335i $$-0.905568\pi$$
0.731327 + 0.682027i $$0.238901\pi$$
$$48$$ 0 0
$$49$$ −1494.50 + 16740.4i −0.0889213 + 0.996039i
$$50$$ 0 0
$$51$$ 5983.65 10364.0i 0.322137 0.557958i
$$52$$ 0 0
$$53$$ 1005.67 + 1741.87i 0.0491775 + 0.0851779i 0.889566 0.456806i $$-0.151007\pi$$
−0.840389 + 0.541984i $$0.817673\pi$$
$$54$$ 0 0
$$55$$ 22323.0 0.995054
$$56$$ 0 0
$$57$$ −8482.26 −0.345800
$$58$$ 0 0
$$59$$ 25726.6 + 44559.7i 0.962170 + 1.66653i 0.717035 + 0.697037i $$0.245499\pi$$
0.245135 + 0.969489i $$0.421168\pi$$
$$60$$ 0 0
$$61$$ −20548.9 + 35591.8i −0.707073 + 1.22469i 0.258865 + 0.965913i $$0.416651\pi$$
−0.965938 + 0.258773i $$0.916682\pi$$
$$62$$ 0 0
$$63$$ −10254.1 + 2263.74i −0.325496 + 0.0718581i
$$64$$ 0 0
$$65$$ −7581.04 + 13130.8i −0.222559 + 0.385484i
$$66$$ 0 0
$$67$$ 25289.1 + 43802.0i 0.688250 + 1.19208i 0.972404 + 0.233305i $$0.0749542\pi$$
−0.284153 + 0.958779i $$0.591712\pi$$
$$68$$ 0 0
$$69$$ 14688.7 0.371416
$$70$$ 0 0
$$71$$ −39970.6 −0.941012 −0.470506 0.882397i $$-0.655929\pi$$
−0.470506 + 0.882397i $$0.655929\pi$$
$$72$$ 0 0
$$73$$ 27843.3 + 48226.0i 0.611524 + 1.05919i 0.990984 + 0.133983i $$0.0427767\pi$$
−0.379459 + 0.925208i $$0.623890\pi$$
$$74$$ 0 0
$$75$$ 7312.77 12666.1i 0.150117 0.260009i
$$76$$ 0 0
$$77$$ 22533.2 71245.8i 0.433107 1.36941i
$$78$$ 0 0
$$79$$ −31575.7 + 54690.7i −0.569226 + 0.985929i 0.427416 + 0.904055i $$0.359424\pi$$
−0.996643 + 0.0818739i $$0.973910\pi$$
$$80$$ 0 0
$$81$$ −3280.50 5681.99i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −45572.4 −0.726116 −0.363058 0.931766i $$-0.618267\pi$$
−0.363058 + 0.931766i $$0.618267\pi$$
$$84$$ 0 0
$$85$$ −51498.1 −0.773114
$$86$$ 0 0
$$87$$ 6585.95 + 11407.2i 0.0932868 + 0.161577i
$$88$$ 0 0
$$89$$ −7843.34 + 13585.1i −0.104961 + 0.181797i −0.913722 0.406340i $$-0.866805\pi$$
0.808762 + 0.588137i $$0.200138\pi$$
$$90$$ 0 0
$$91$$ 34255.5 + 37449.9i 0.433637 + 0.474075i
$$92$$ 0 0
$$93$$ −17605.9 + 30494.3i −0.211082 + 0.365604i
$$94$$ 0 0
$$95$$ 18250.6 + 31610.9i 0.207476 + 0.359358i
$$96$$ 0 0
$$97$$ 3128.49 0.0337603 0.0168801 0.999858i $$-0.494627\pi$$
0.0168801 + 0.999858i $$0.494627\pi$$
$$98$$ 0 0
$$99$$ 46687.6 0.478755
$$100$$ 0 0
$$101$$ 84505.5 + 146368.i 0.824292 + 1.42772i 0.902459 + 0.430776i $$0.141760\pi$$
−0.0781663 + 0.996940i $$0.524907\pi$$
$$102$$ 0 0
$$103$$ 56410.1 97705.1i 0.523918 0.907453i −0.475694 0.879611i $$-0.657803\pi$$
0.999612 0.0278422i $$-0.00886360\pi$$
$$104$$ 0 0
$$105$$ 30499.1 + 33343.2i 0.269969 + 0.295144i
$$106$$ 0 0
$$107$$ −11154.7 + 19320.6i −0.0941890 + 0.163140i −0.909270 0.416207i $$-0.863359\pi$$
0.815081 + 0.579347i $$0.196692\pi$$
$$108$$ 0 0
$$109$$ 41909.8 + 72589.8i 0.337869 + 0.585207i 0.984032 0.177993i $$-0.0569604\pi$$
−0.646162 + 0.763200i $$0.723627\pi$$
$$110$$ 0 0
$$111$$ −146703. −1.13014
$$112$$ 0 0
$$113$$ −40928.4 −0.301529 −0.150764 0.988570i $$-0.548174\pi$$
−0.150764 + 0.988570i $$0.548174\pi$$
$$114$$ 0 0
$$115$$ −31604.4 54740.5i −0.222845 0.385980i
$$116$$ 0 0
$$117$$ −15855.4 + 27462.3i −0.107081 + 0.185470i
$$118$$ 0 0
$$119$$ −51982.8 + 164360.i −0.336505 + 1.06397i
$$120$$ 0 0
$$121$$ −85587.1 + 148241.i −0.531429 + 0.920462i
$$122$$ 0 0
$$123$$ 58967.2 + 102134.i 0.351437 + 0.608707i
$$124$$ 0 0
$$125$$ −183965. −1.05308
$$126$$ 0 0
$$127$$ −83270.1 −0.458120 −0.229060 0.973412i $$-0.573565\pi$$
−0.229060 + 0.973412i $$0.573565\pi$$
$$128$$ 0 0
$$129$$ 66300.7 + 114836.i 0.350788 + 0.607582i
$$130$$ 0 0
$$131$$ −83437.4 + 144518.i −0.424798 + 0.735772i −0.996402 0.0847580i $$-0.972988\pi$$
0.571603 + 0.820530i $$0.306322\pi$$
$$132$$ 0 0
$$133$$ 119311. 26339.7i 0.584860 0.129117i
$$134$$ 0 0
$$135$$ −14116.7 + 24450.9i −0.0666653 + 0.115468i
$$136$$ 0 0
$$137$$ −19111.9 33102.9i −0.0869969 0.150683i 0.819244 0.573446i $$-0.194394\pi$$
−0.906240 + 0.422763i $$0.861060\pi$$
$$138$$ 0 0
$$139$$ −106263. −0.466492 −0.233246 0.972418i $$-0.574935\pi$$
−0.233246 + 0.972418i $$0.574935\pi$$
$$140$$ 0 0
$$141$$ 61330.7 0.259795
$$142$$ 0 0
$$143$$ −112826. 195420.i −0.461390 0.799151i
$$144$$ 0 0
$$145$$ 28340.8 49087.8i 0.111942 0.193889i
$$146$$ 0 0
$$147$$ 137204. 63683.4i 0.523689 0.243071i
$$148$$ 0 0
$$149$$ −96277.8 + 166758.i −0.355271 + 0.615348i −0.987164 0.159708i $$-0.948945\pi$$
0.631893 + 0.775056i $$0.282278\pi$$
$$150$$ 0 0
$$151$$ 70849.3 + 122715.i 0.252868 + 0.437980i 0.964314 0.264761i $$-0.0852929\pi$$
−0.711447 + 0.702740i $$0.751960\pi$$
$$152$$ 0 0
$$153$$ −107706. −0.371972
$$154$$ 0 0
$$155$$ 151524. 0.506586
$$156$$ 0 0
$$157$$ −282885. 489972.i −0.915928 1.58643i −0.805536 0.592546i $$-0.798123\pi$$
−0.110392 0.993888i $$-0.535211\pi$$
$$158$$ 0 0
$$159$$ 9051.04 15676.9i 0.0283926 0.0491775i
$$160$$ 0 0
$$161$$ −206611. + 45612.4i −0.628186 + 0.138682i
$$162$$ 0 0
$$163$$ −215101. + 372565.i −0.634121 + 1.09833i 0.352579 + 0.935782i $$0.385305\pi$$
−0.986701 + 0.162549i $$0.948029\pi$$
$$164$$ 0 0
$$165$$ −100454. 173991.i −0.287247 0.497527i
$$166$$ 0 0
$$167$$ 240265. 0.666653 0.333327 0.942811i $$-0.391829\pi$$
0.333327 + 0.942811i $$0.391829\pi$$
$$168$$ 0 0
$$169$$ −218028. −0.587212
$$170$$ 0 0
$$171$$ 38170.2 + 66112.7i 0.0998238 + 0.172900i
$$172$$ 0 0
$$173$$ 89650.1 155279.i 0.227738 0.394454i −0.729399 0.684088i $$-0.760200\pi$$
0.957137 + 0.289634i $$0.0935337\pi$$
$$174$$ 0 0
$$175$$ −63529.4 + 200869.i −0.156812 + 0.495812i
$$176$$ 0 0
$$177$$ 231539. 401037.i 0.555509 0.962170i
$$178$$ 0 0
$$179$$ −287780. 498449.i −0.671317 1.16275i −0.977531 0.210792i $$-0.932396\pi$$
0.306214 0.951963i $$-0.400938\pi$$
$$180$$ 0 0
$$181$$ 581006. 1.31821 0.659105 0.752051i $$-0.270935\pi$$
0.659105 + 0.752051i $$0.270935\pi$$
$$182$$ 0 0
$$183$$ 369880. 0.816458
$$184$$ 0 0
$$185$$ 315648. + 546719.i 0.678070 + 1.17445i
$$186$$ 0 0
$$187$$ 383213. 663744.i 0.801376 1.38802i
$$188$$ 0 0
$$189$$ 63787.5 + 69735.8i 0.129892 + 0.142004i
$$190$$ 0 0
$$191$$ −330280. + 572062.i −0.655087 + 1.13464i 0.326785 + 0.945099i $$0.394035\pi$$
−0.981872 + 0.189545i $$0.939299\pi$$
$$192$$ 0 0
$$193$$ 278655. + 482645.i 0.538485 + 0.932684i 0.998986 + 0.0450243i $$0.0143365\pi$$
−0.460501 + 0.887659i $$0.652330\pi$$
$$194$$ 0 0
$$195$$ 136459. 0.256989
$$196$$ 0 0
$$197$$ −761400. −1.39781 −0.698904 0.715216i $$-0.746328\pi$$
−0.698904 + 0.715216i $$0.746328\pi$$
$$198$$ 0 0
$$199$$ −67929.9 117658.i −0.121598 0.210615i 0.798800 0.601597i $$-0.205469\pi$$
−0.920398 + 0.390982i $$0.872135\pi$$
$$200$$ 0 0
$$201$$ 227602. 394218.i 0.397361 0.688250i
$$202$$ 0 0
$$203$$ −128060. 140002.i −0.218109 0.238448i
$$204$$ 0 0
$$205$$ 253750. 439507.i 0.421716 0.730434i
$$206$$ 0 0
$$207$$ −66099.2 114487.i −0.107219 0.185708i
$$208$$ 0 0
$$209$$ −543232. −0.860240
$$210$$ 0 0
$$211$$ 991157. 1.53263 0.766313 0.642467i $$-0.222089\pi$$
0.766313 + 0.642467i $$0.222089\pi$$
$$212$$ 0 0
$$213$$ 179868. + 311540.i 0.271647 + 0.470506i
$$214$$ 0 0
$$215$$ 285307. 494167.i 0.420937 0.729084i
$$216$$ 0 0
$$217$$ 152951. 483602.i 0.220496 0.697170i
$$218$$ 0 0
$$219$$ 250590. 434034.i 0.353064 0.611524i
$$220$$ 0 0
$$221$$ 260283. + 450823.i 0.358480 + 0.620906i
$$222$$ 0 0
$$223$$ −543344. −0.731666 −0.365833 0.930681i $$-0.619216\pi$$
−0.365833 + 0.930681i $$0.619216\pi$$
$$224$$ 0 0
$$225$$ −131630. −0.173340
$$226$$ 0 0
$$227$$ 8.16704 + 14.1457i 1.05196e−5 + 1.82205e-5i 0.866031 0.499991i $$-0.166663\pi$$
−0.866020 + 0.500009i $$0.833330\pi$$
$$228$$ 0 0
$$229$$ 38689.5 67012.2i 0.0487534 0.0844433i −0.840619 0.541627i $$-0.817808\pi$$
0.889372 + 0.457184i $$0.151142\pi$$
$$230$$ 0 0
$$231$$ −656705. + 144978.i −0.809731 + 0.178760i
$$232$$ 0 0
$$233$$ 51828.6 89769.9i 0.0625432 0.108328i −0.833058 0.553185i $$-0.813412\pi$$
0.895602 + 0.444857i $$0.146746\pi$$
$$234$$ 0 0
$$235$$ −131960. 228561.i −0.155874 0.269981i
$$236$$ 0 0
$$237$$ 568362. 0.657286
$$238$$ 0 0
$$239$$ −689109. −0.780356 −0.390178 0.920739i $$-0.627587\pi$$
−0.390178 + 0.920739i $$0.627587\pi$$
$$240$$ 0 0
$$241$$ −110148. 190782.i −0.122161 0.211590i 0.798458 0.602050i $$-0.205649\pi$$
−0.920620 + 0.390460i $$0.872316\pi$$
$$242$$ 0 0
$$243$$ −29524.5 + 51137.9i −0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ −532539. 374297.i −0.566809 0.398383i
$$246$$ 0 0
$$247$$ 184485. 319537.i 0.192406 0.333257i
$$248$$ 0 0
$$249$$ 205076. + 355201.i 0.209612 + 0.363058i
$$250$$ 0 0
$$251$$ −1.43641e6 −1.43912 −0.719558 0.694433i $$-0.755655\pi$$
−0.719558 + 0.694433i $$0.755655\pi$$
$$252$$ 0 0
$$253$$ 940714. 0.923966
$$254$$ 0 0
$$255$$ 231741. + 401388.i 0.223179 + 0.386557i
$$256$$ 0 0
$$257$$ 454598. 787388.i 0.429334 0.743628i −0.567480 0.823387i $$-0.692082\pi$$
0.996814 + 0.0797589i $$0.0254151\pi$$
$$258$$ 0 0
$$259$$ 2.06352e6 455553.i 1.91143 0.421977i
$$260$$ 0 0
$$261$$ 59273.5 102665.i 0.0538592 0.0932868i
$$262$$ 0 0
$$263$$ 374528. + 648702.i 0.333884 + 0.578304i 0.983270 0.182155i $$-0.0583073\pi$$
−0.649386 + 0.760459i $$0.724974\pi$$
$$264$$ 0 0
$$265$$ −77897.4 −0.0681410
$$266$$ 0 0
$$267$$ 141180. 0.121198
$$268$$ 0 0
$$269$$ −334972. 580189.i −0.282246 0.488865i 0.689691 0.724104i $$-0.257746\pi$$
−0.971938 + 0.235238i $$0.924413\pi$$
$$270$$ 0 0
$$271$$ 270330. 468225.i 0.223599 0.387285i −0.732299 0.680983i $$-0.761553\pi$$
0.955898 + 0.293698i $$0.0948860\pi$$
$$272$$ 0 0
$$273$$ 137743. 435519.i 0.111857 0.353672i
$$274$$ 0 0
$$275$$ 468334. 811178.i 0.373443 0.646821i
$$276$$ 0 0
$$277$$ 200955. + 348064.i 0.157362 + 0.272558i 0.933916 0.357491i $$-0.116368\pi$$
−0.776555 + 0.630050i $$0.783035\pi$$
$$278$$ 0 0
$$279$$ 316906. 0.243736
$$280$$ 0 0
$$281$$ −429139. −0.324214 −0.162107 0.986773i $$-0.551829\pi$$
−0.162107 + 0.986773i $$0.551829\pi$$
$$282$$ 0 0
$$283$$ −170463. 295251.i −0.126522 0.219142i 0.795805 0.605553i $$-0.207048\pi$$
−0.922327 + 0.386411i $$0.873715\pi$$
$$284$$ 0 0
$$285$$ 164255. 284498.i 0.119786 0.207476i
$$286$$ 0 0
$$287$$ −1.14658e6 1.25351e6i −0.821678 0.898301i
$$288$$ 0 0
$$289$$ −174123. + 301590.i −0.122634 + 0.212409i
$$290$$ 0 0
$$291$$ −14078.2 24384.2i −0.00974575 0.0168801i
$$292$$ 0 0
$$293$$ −388847. −0.264612 −0.132306 0.991209i $$-0.542238\pi$$
−0.132306 + 0.991209i $$0.542238\pi$$
$$294$$ 0 0
$$295$$ −1.99273e6 −1.33319
$$296$$ 0 0
$$297$$ −210094. 363894.i −0.138205 0.239378i
$$298$$ 0 0
$$299$$ −319472. + 553342.i −0.206659 + 0.357945i
$$300$$ 0 0
$$301$$ −1.28918e6 1.40940e6i −0.820158 0.896640i
$$302$$ 0 0
$$303$$ 760549. 1.31731e6i 0.475905 0.824292i
$$304$$ 0 0
$$305$$ −795840. 1.37844e6i −0.489865 0.848471i
$$306$$ 0 0
$$307$$ 2.35747e6 1.42758 0.713789 0.700361i $$-0.246978\pi$$
0.713789 + 0.700361i $$0.246978\pi$$
$$308$$ 0 0
$$309$$ −1.01538e6 −0.604969
$$310$$ 0 0
$$311$$ −718314. 1.24416e6i −0.421127 0.729414i 0.574923 0.818208i $$-0.305032\pi$$
−0.996050 + 0.0887939i $$0.971699\pi$$
$$312$$ 0 0
$$313$$ 411400. 712566.i 0.237358 0.411116i −0.722598 0.691269i $$-0.757052\pi$$
0.959955 + 0.280153i $$0.0903853\pi$$
$$314$$ 0 0
$$315$$ 122639. 387762.i 0.0696388 0.220186i
$$316$$ 0 0
$$317$$ 883467. 1.53021e6i 0.493790 0.855269i −0.506184 0.862425i $$-0.668944\pi$$
0.999974 + 0.00715584i $$0.00227779\pi$$
$$318$$ 0 0
$$319$$ 421786. + 730555.i 0.232068 + 0.401954i
$$320$$ 0 0
$$321$$ 200785. 0.108760
$$322$$ 0 0
$$323$$ 1.25321e6 0.668370
$$324$$ 0 0
$$325$$ 318098. + 550962.i 0.167052 + 0.289343i
$$326$$ 0 0
$$327$$ 377188. 653309.i 0.195069 0.337869i
$$328$$ 0 0
$$329$$ −862675. + 190448.i −0.439397 + 0.0970036i
$$330$$ 0 0
$$331$$ −1526.14 + 2643.35i −0.000765638 + 0.00132612i −0.866408 0.499337i $$-0.833577\pi$$
0.865642 + 0.500663i $$0.166910\pi$$
$$332$$ 0 0
$$333$$ 660164. + 1.14344e6i 0.326243 + 0.565069i
$$334$$ 0 0
$$335$$ −1.95885e6 −0.953649
$$336$$ 0 0
$$337$$ 2.02939e6 0.973398 0.486699 0.873570i $$-0.338201\pi$$
0.486699 + 0.873570i $$0.338201\pi$$
$$338$$ 0 0
$$339$$ 184178. + 319006.i 0.0870439 + 0.150764i
$$340$$ 0 0
$$341$$ −1.12754e6 + 1.95295e6i −0.525104 + 0.909507i
$$342$$ 0 0
$$343$$ −1.73215e6 + 1.32182e6i −0.794969 + 0.606650i
$$344$$ 0 0
$$345$$ −284440. + 492665.i −0.128660 + 0.222845i
$$346$$ 0 0
$$347$$ 1.89109e6 + 3.27547e6i 0.843119 + 1.46033i 0.887245 + 0.461299i $$0.152617\pi$$
−0.0441252 + 0.999026i $$0.514050\pi$$
$$348$$ 0 0
$$349$$ 291147. 0.127953 0.0639763 0.997951i $$-0.479622\pi$$
0.0639763 + 0.997951i $$0.479622\pi$$
$$350$$ 0 0
$$351$$ 285397. 0.123646
$$352$$ 0 0
$$353$$ −192538. 333486.i −0.0822394 0.142443i 0.821972 0.569528i $$-0.192874\pi$$
−0.904212 + 0.427085i $$0.859541\pi$$
$$354$$ 0 0
$$355$$ 774013. 1.34063e6i 0.325970 0.564596i
$$356$$ 0 0
$$357$$ 1.51498e6 334456.i 0.629126 0.138889i
$$358$$ 0 0
$$359$$ −1.61507e6 + 2.79738e6i −0.661385 + 1.14555i 0.318866 + 0.947800i $$0.396698\pi$$
−0.980252 + 0.197753i $$0.936635\pi$$
$$360$$ 0 0
$$361$$ 793921. + 1.37511e6i 0.320634 + 0.555354i
$$362$$ 0 0
$$363$$ 1.54057e6 0.613641
$$364$$ 0 0
$$365$$ −2.15669e6 −0.847336
$$366$$ 0 0
$$367$$ −239779. 415310.i −0.0929280 0.160956i 0.815814 0.578314i $$-0.196289\pi$$
−0.908742 + 0.417358i $$0.862956\pi$$
$$368$$ 0 0
$$369$$ 530705. 919208.i 0.202902 0.351437i
$$370$$ 0 0
$$371$$ −78630.6 + 248616.i −0.0296590 + 0.0937766i
$$372$$ 0 0
$$373$$ −436333. + 755751.i −0.162385 + 0.281259i −0.935724 0.352734i $$-0.885252\pi$$
0.773339 + 0.633993i $$0.218585\pi$$
$$374$$ 0 0
$$375$$ 827844. + 1.43387e6i 0.303998 + 0.526540i
$$376$$ 0 0
$$377$$ −572965. −0.207622
$$378$$ 0 0
$$379$$ 2.43493e6 0.870742 0.435371 0.900251i $$-0.356617\pi$$
0.435371 + 0.900251i $$0.356617\pi$$
$$380$$ 0 0
$$381$$ 374715. + 649026.i 0.132248 + 0.229060i
$$382$$ 0 0
$$383$$ −1.80584e6 + 3.12781e6i −0.629047 + 1.08954i 0.358696 + 0.933454i $$0.383222\pi$$
−0.987743 + 0.156087i $$0.950112\pi$$
$$384$$ 0 0
$$385$$ 1.95327e6 + 2.13541e6i 0.671598 + 0.734226i
$$386$$ 0 0
$$387$$ 596707. 1.03353e6i 0.202527 0.350788i
$$388$$ 0 0
$$389$$ 87616.2 + 151756.i 0.0293569 + 0.0508477i 0.880331 0.474361i $$-0.157321\pi$$
−0.850974 + 0.525208i $$0.823987\pi$$
$$390$$ 0 0
$$391$$ −2.17018e6 −0.717882
$$392$$ 0 0
$$393$$ 1.50187e6 0.490515
$$394$$ 0 0
$$395$$ −1.22290e6 2.11812e6i −0.394364 0.683058i
$$396$$ 0 0
$$397$$ −942577. + 1.63259e6i −0.300152 + 0.519878i −0.976170 0.217007i $$-0.930371\pi$$
0.676019 + 0.736885i $$0.263704\pi$$
$$398$$ 0 0
$$399$$ −742198. 811409.i −0.233393 0.255157i
$$400$$ 0 0
$$401$$ −669915. + 1.16033e6i −0.208046 + 0.360346i −0.951099 0.308887i $$-0.900044\pi$$
0.743053 + 0.669232i $$0.233377\pi$$
$$402$$ 0 0
$$403$$ −765839. 1.32647e6i −0.234895 0.406851i
$$404$$ 0 0
$$405$$ 254101. 0.0769785
$$406$$ 0 0
$$407$$ −9.39535e6 −2.81143
$$408$$ 0 0
$$409$$ −3.29314e6 5.70388e6i −0.973423 1.68602i −0.685043 0.728503i $$-0.740217\pi$$
−0.288381 0.957516i $$-0.593117\pi$$
$$410$$ 0 0
$$411$$ −172008. + 297926.i −0.0502277 + 0.0869969i
$$412$$ 0 0
$$413$$ −2.01149e6 + 6.35996e6i −0.580286 + 1.83476i
$$414$$ 0 0
$$415$$ 882487. 1.52851e6i 0.251529 0.435661i
$$416$$ 0 0
$$417$$ 478182. + 828236.i 0.134665 + 0.233246i
$$418$$ 0 0
$$419$$ 6.96869e6 1.93917 0.969585 0.244754i $$-0.0787071\pi$$
0.969585 + 0.244754i $$0.0787071\pi$$
$$420$$ 0 0
$$421$$ 3.84041e6 1.05602 0.528010 0.849238i $$-0.322938\pi$$
0.528010 + 0.849238i $$0.322938\pi$$
$$422$$ 0 0
$$423$$ −275988. 478025.i −0.0749962 0.129897i
$$424$$ 0 0
$$425$$ −1.08042e6 + 1.87134e6i −0.290149 + 0.502552i
$$426$$ 0 0
$$427$$ −5.20272e6 + 1.14858e6i −1.38090 + 0.304854i
$$428$$ 0 0
$$429$$ −1.01543e6 + 1.75878e6i −0.266384 + 0.461390i
$$430$$ 0 0
$$431$$ 1.51818e6 + 2.62957e6i 0.393668 + 0.681854i 0.992930 0.118699i $$-0.0378725\pi$$
−0.599262 + 0.800553i $$0.704539\pi$$
$$432$$ 0 0
$$433$$ −941529. −0.241332 −0.120666 0.992693i $$-0.538503\pi$$
−0.120666 + 0.992693i $$0.538503\pi$$
$$434$$ 0 0
$$435$$ −510135. −0.129259
$$436$$ 0 0
$$437$$ 769096. + 1.33211e6i 0.192653 + 0.333686i
$$438$$ 0 0
$$439$$ 670546. 1.16142e6i 0.166061 0.287626i −0.770971 0.636871i $$-0.780229\pi$$
0.937031 + 0.349245i $$0.113562\pi$$
$$440$$ 0 0
$$441$$ −1.11378e6 782823.i −0.272711 0.191676i
$$442$$ 0 0
$$443$$ −386171. + 668867.i −0.0934910 + 0.161931i −0.908978 0.416844i $$-0.863136\pi$$
0.815487 + 0.578776i $$0.196469\pi$$
$$444$$ 0 0
$$445$$ −303765. 526137.i −0.0727174 0.125950i
$$446$$ 0 0
$$447$$ 1.73300e6 0.410232
$$448$$ 0 0
$$449$$ 2.25684e6 0.528304 0.264152 0.964481i $$-0.414908\pi$$
0.264152 + 0.964481i $$0.414908\pi$$
$$450$$ 0 0
$$451$$ 3.77646e6 + 6.54101e6i 0.874265 + 1.51427i
$$452$$ 0 0
$$453$$ 637644. 1.10443e6i 0.145993 0.252868i
$$454$$ 0 0
$$455$$ −1.91942e6 + 423742.i −0.434653 + 0.0959561i
$$456$$ 0 0
$$457$$ −2.14235e6 + 3.71066e6i −0.479844 + 0.831114i −0.999733 0.0231196i $$-0.992640\pi$$
0.519889 + 0.854234i $$0.325973\pi$$
$$458$$ 0 0
$$459$$ 484676. + 839483.i 0.107379 + 0.185986i
$$460$$ 0 0
$$461$$ −3.10462e6 −0.680387 −0.340193 0.940355i $$-0.610493\pi$$
−0.340193 + 0.940355i $$0.610493\pi$$
$$462$$ 0 0
$$463$$ 3.53386e6 0.766121 0.383060 0.923723i $$-0.374870\pi$$
0.383060 + 0.923723i $$0.374870\pi$$
$$464$$ 0 0
$$465$$ −681859. 1.18102e6i −0.146239 0.253293i
$$466$$ 0 0
$$467$$ 1.36230e6 2.35957e6i 0.289054 0.500657i −0.684530 0.728985i $$-0.739993\pi$$
0.973584 + 0.228328i $$0.0733258\pi$$
$$468$$ 0 0
$$469$$ −1.97728e6 + 6.25182e6i −0.415085 + 1.31242i
$$470$$ 0 0
$$471$$ −2.54597e6 + 4.40975e6i −0.528812 + 0.915928i
$$472$$ 0 0
$$473$$ 4.24612e6 + 7.35449e6i 0.872649 + 1.51147i
$$474$$ 0 0
$$475$$ 1.53158e6 0.311461
$$476$$ 0 0
$$477$$ −162919. −0.0327850
$$478$$ 0 0
$$479$$ 489342. + 847566.i 0.0974482 + 0.168785i 0.910628 0.413228i $$-0.135599\pi$$
−0.813180 + 0.582013i $$0.802265\pi$$
$$480$$ 0 0
$$481$$ 3.19072e6 5.52649e6i 0.628819 1.08915i
$$482$$ 0 0
$$483$$ 1.28526e6 + 1.40512e6i 0.250682 + 0.274059i
$$484$$ 0 0
$$485$$ −60581.8 + 104931.i −0.0116947 + 0.0202558i
$$486$$ 0 0
$$487$$ 1.96372e6 + 3.40126e6i 0.375195 + 0.649857i 0.990356 0.138544i $$-0.0442423\pi$$
−0.615161 + 0.788401i $$0.710909\pi$$
$$488$$ 0 0
$$489$$ 3.87181e6 0.732220
$$490$$ 0 0
$$491$$ −2.63241e6 −0.492777 −0.246388 0.969171i $$-0.579244\pi$$
−0.246388 + 0.969171i $$0.579244\pi$$
$$492$$ 0 0
$$493$$ −973037. 1.68535e6i −0.180307 0.312301i
$$494$$ 0 0
$$495$$ −904083. + 1.56592e6i −0.165842 + 0.287247i
$$496$$ 0 0
$$497$$ −3.49743e6 3.82357e6i −0.635123 0.694350i
$$498$$ 0 0
$$499$$ 1.06272e6 1.84069e6i 0.191059 0.330924i −0.754542 0.656251i $$-0.772141\pi$$
0.945601 + 0.325327i $$0.105474\pi$$
$$500$$ 0 0
$$501$$ −1.08119e6 1.87268e6i −0.192446 0.333327i
$$502$$ 0 0
$$503$$ −2.60929e6 −0.459835 −0.229917 0.973210i $$-0.573846\pi$$
−0.229917 + 0.973210i $$0.573846\pi$$
$$504$$ 0 0
$$505$$ −6.54564e6 −1.14215
$$506$$ 0 0
$$507$$ 981124. + 1.69936e6i 0.169513 + 0.293606i
$$508$$ 0 0
$$509$$ 5.00911e6 8.67603e6i 0.856970 1.48432i −0.0178348 0.999841i $$-0.505677\pi$$
0.874805 0.484475i $$-0.160989\pi$$
$$510$$ 0 0
$$511$$ −2.17699e6 + 6.88326e6i −0.368811 + 1.16612i
$$512$$ 0 0
$$513$$ 343532. 595014.i 0.0576333 0.0998238i
$$514$$ 0 0
$$515$$ 2.18471e6 + 3.78403e6i 0.362974 + 0.628689i
$$516$$ 0 0
$$517$$ 3.92782e6 0.646287
$$518$$ 0 0
$$519$$ −1.61370e6 −0.262969
$$520$$ 0 0
$$521$$ 2.08970e6 + 3.61947e6i 0.337280 + 0.584186i 0.983920 0.178609i $$-0.0571598\pi$$
−0.646640 + 0.762795i $$0.723826\pi$$
$$522$$ 0 0
$$523$$ 1.80263e6 3.12224e6i 0.288172 0.499128i −0.685202 0.728353i $$-0.740286\pi$$
0.973373 + 0.229225i $$0.0736193\pi$$
$$524$$ 0 0
$$525$$ 1.85150e6 408746.i 0.293174 0.0647225i
$$526$$ 0 0
$$527$$ 2.60117e6 4.50536e6i 0.407983 0.706648i
$$528$$ 0 0
$$529$$ 1.88633e6 + 3.26722e6i 0.293075 + 0.507621i
$$530$$ 0 0
$$531$$ −4.16770e6 −0.641446
$$532$$ 0 0
$$533$$ −5.13003e6 −0.782172
$$534$$ 0 0
$$535$$ −432013. 748268.i −0.0652547 0.113025i
$$536$$ 0 0
$$537$$ −2.59002e6 + 4.48604e6i −0.387585 + 0.671317i
$$538$$ 0 0
$$539$$ 8.78699e6 4.07850e6i 1.30277 0.604684i
$$540$$ 0 0
$$541$$ 3.34083e6 5.78648e6i 0.490751 0.850005i −0.509193 0.860653i $$-0.670056\pi$$
0.999943 + 0.0106475i $$0.00338926\pi$$
$$542$$ 0 0
$$543$$ −2.61453e6 4.52850e6i −0.380534 0.659105i
$$544$$ 0 0
$$545$$ −3.24625e6 −0.468156
$$546$$ 0 0
$$547$$ −8.69076e6 −1.24191 −0.620954 0.783847i $$-0.713255\pi$$
−0.620954 + 0.783847i $$0.713255\pi$$
$$548$$ 0 0
$$549$$ −1.66446e6 2.88293e6i −0.235691 0.408229i
$$550$$ 0 0
$$551$$ −689676. + 1.19455e6i −0.0967756 + 0.167620i
$$552$$ 0 0
$$553$$ −7.99456e6 + 1.76492e6i −1.11168 + 0.245421i
$$554$$ 0 0
$$555$$ 2.84084e6 4.92047e6i 0.391484 0.678070i
$$556$$ 0 0
$$557$$ −3.12371e6 5.41042e6i −0.426612 0.738913i 0.569958 0.821674i $$-0.306960\pi$$
−0.996569 + 0.0827611i $$0.973626\pi$$
$$558$$ 0 0
$$559$$ −5.76803e6 −0.780725
$$560$$ 0 0
$$561$$ −6.89783e6 −0.925349
$$562$$ 0 0
$$563$$ −5.95223e6 1.03096e7i −0.791423 1.37078i −0.925086 0.379758i $$-0.876007\pi$$
0.133663 0.991027i $$-0.457326\pi$$
$$564$$ 0 0
$$565$$ 792560. 1.37275e6i 0.104451 0.180914i
$$566$$ 0 0
$$567$$ 256493. 810986.i 0.0335057 0.105939i
$$568$$ 0 0
$$569$$ −10707.2 + 18545.4i −0.00138642 + 0.00240135i −0.866718 0.498799i $$-0.833775\pi$$
0.865331 + 0.501200i $$0.167108\pi$$
$$570$$ 0 0
$$571$$ 3.55823e6 + 6.16304e6i 0.456714 + 0.791051i 0.998785 0.0492811i $$-0.0156930\pi$$
−0.542071 + 0.840333i $$0.682360\pi$$
$$572$$ 0 0
$$573$$ 5.94504e6 0.756429
$$574$$ 0 0
$$575$$ −2.65223e6 −0.334534
$$576$$ 0 0
$$577$$ 5.33259e6 + 9.23632e6i 0.666805 + 1.15494i 0.978793 + 0.204854i $$0.0656719\pi$$
−0.311988 + 0.950086i $$0.600995\pi$$
$$578$$ 0 0
$$579$$ 2.50790e6 4.34380e6i 0.310895 0.538485i
$$580$$ 0 0
$$581$$ −3.98758e6 4.35943e6i −0.490083 0.535784i
$$582$$ 0 0
$$583$$ 579659. 1.00400e6i 0.0706319 0.122338i
$$584$$ 0 0
$$585$$ −614065. 1.06359e6i −0.0741864 0.128495i
$$586$$ 0 0
$$587$$ 1.30101e7 1.55843 0.779213 0.626759i $$-0.215619\pi$$
0.779213 + 0.626759i $$0.215619\pi$$
$$588$$ 0 0
$$589$$ −3.68735e6 −0.437952
$$590$$ 0 0
$$591$$ 3.42630e6 + 5.93453e6i 0.403512 + 0.698904i
$$592$$ 0 0
$$593$$ −2.13043e6 + 3.69002e6i −0.248789 + 0.430915i −0.963190 0.268821i $$-0.913366\pi$$
0.714401 + 0.699736i $$0.246699\pi$$
$$594$$ 0 0
$$595$$ −4.50608e6 4.92628e6i −0.521803 0.570462i
$$596$$ 0 0
$$597$$ −611369. + 1.05892e6i −0.0702049 + 0.121598i
$$598$$ 0 0
$$599$$ −6.89790e6 1.19475e7i −0.785507 1.36054i −0.928696 0.370842i $$-0.879069\pi$$
0.143189 0.989695i $$-0.454264\pi$$
$$600$$ 0 0
$$601$$ 4.99695e6 0.564311 0.282155 0.959369i $$-0.408951\pi$$
0.282155 + 0.959369i $$0.408951\pi$$
$$602$$ 0 0
$$603$$ −4.09683e6 −0.458833
$$604$$ 0 0
$$605$$ −3.31471e6 5.74125e6i −0.368177 0.637702i
$$606$$ 0 0
$$607$$ −1.52473e6 + 2.64091e6i −0.167966 + 0.290926i −0.937705 0.347434i $$-0.887053\pi$$
0.769739 + 0.638359i $$0.220387\pi$$
$$608$$ 0 0
$$609$$ −514937. + 1.62814e6i −0.0562614 + 0.177889i
$$610$$ 0 0
$$611$$ −1.33391e6 + 2.31040e6i −0.144552 + 0.250372i
$$612$$ 0 0
$$613$$ 3.51813e6 + 6.09357e6i 0.378147 + 0.654969i 0.990793 0.135388i $$-0.0432282\pi$$
−0.612646 + 0.790357i $$0.709895\pi$$
$$614$$ 0 0
$$615$$ −4.56749e6 −0.486956
$$616$$ 0 0
$$617$$ 1.00066e7 1.05822 0.529108 0.848554i $$-0.322527\pi$$
0.529108 + 0.848554i $$0.322527\pi$$
$$618$$ 0 0
$$619$$ −3.27533e6 5.67304e6i −0.343581 0.595099i 0.641514 0.767111i $$-0.278307\pi$$
−0.985095 + 0.172012i $$0.944973\pi$$
$$620$$ 0 0
$$621$$ −594893. + 1.03038e6i −0.0619027 + 0.107219i
$$622$$ 0 0
$$623$$ −1.98583e6 + 438403.i −0.204985 + 0.0452536i
$$624$$ 0 0
$$625$$ 1.02325e6 1.77232e6i 0.104781 0.181485i
$$626$$ 0 0
$$627$$ 2.44455e6 + 4.23408e6i 0.248330 + 0.430120i
$$628$$ 0 0
$$629$$ 2.16746e7 2.18436
$$630$$ 0 0
$$631$$ −2.22672e6 −0.222635 −0.111317 0.993785i $$-0.535507\pi$$
−0.111317 + 0.993785i $$0.535507\pi$$
$$632$$ 0 0
$$633$$ −4.46021e6 7.72531e6i −0.442431 0.766313i
$$634$$ 0 0
$$635$$ 1.61249e6 2.79291e6i 0.158694 0.274867i
$$636$$ 0 0
$$637$$ −585084. + 6.55373e6i −0.0571307 + 0.639941i
$$638$$ 0 0
$$639$$ 1.61881e6 2.80386e6i 0.156835 0.271647i
$$640$$ 0 0
$$641$$ 7.96698e6 + 1.37992e7i 0.765859 + 1.32651i 0.939791 + 0.341749i $$0.111019\pi$$
−0.173932 + 0.984758i $$0.555647\pi$$
$$642$$ 0 0
$$643$$ 1.49933e7 1.43011 0.715056 0.699067i $$-0.246401\pi$$
0.715056 + 0.699067i $$0.246401\pi$$
$$644$$ 0 0
$$645$$ −5.13553e6 −0.486056
$$646$$ 0 0
$$647$$ 6.49027e6 + 1.12415e7i 0.609540 + 1.05575i 0.991316 + 0.131500i $$0.0419792\pi$$
−0.381776 + 0.924255i $$0.624687\pi$$
$$648$$ 0 0
$$649$$ 1.48285e7 2.56838e7i 1.38193 2.39357i
$$650$$ 0 0
$$651$$ −4.45758e6 + 984079.i −0.412237 + 0.0910075i
$$652$$ 0 0
$$653$$ 8.27460e6 1.43320e7i 0.759389 1.31530i −0.183774 0.982969i $$-0.558831\pi$$
0.943163 0.332332i $$-0.107835\pi$$
$$654$$ 0 0
$$655$$ −3.23145e6 5.59704e6i −0.294303 0.509748i
$$656$$ 0 0
$$657$$ −4.51062e6 −0.407683
$$658$$ 0 0
$$659$$ −5.86879e6 −0.526423 −0.263212 0.964738i $$-0.584782\pi$$
−0.263212 + 0.964738i $$0.584782\pi$$
$$660$$ 0 0
$$661$$ −3.63843e6 6.30195e6i −0.323900 0.561011i 0.657389 0.753551i $$-0.271661\pi$$
−0.981289 + 0.192540i $$0.938327\pi$$
$$662$$ 0 0
$$663$$ 2.34255e6 4.05741e6i 0.206969 0.358480i
$$664$$ 0 0
$$665$$ −1.42696e6 + 4.51179e6i −0.125129 + 0.395635i
$$666$$ 0 0
$$667$$ 1.19431e6 2.06861e6i 0.103945 0.180038i
$$668$$ 0 0
$$669$$ 2.44505e6 + 4.23495e6i 0.211214 + 0.365833i
$$670$$ 0 0
$$671$$ 2.36884e7 2.03109
$$672$$ 0 0
$$673$$ −1.82417e7 −1.55248 −0.776241 0.630437i $$-0.782876\pi$$
−0.776241 + 0.630437i $$0.782876\pi$$
$$674$$ 0 0
$$675$$ 592334. + 1.02595e6i 0.0500388 + 0.0866698i
$$676$$ 0 0
$$677$$ 3.88203e6 6.72387e6i 0.325527 0.563829i −0.656092 0.754681i $$-0.727792\pi$$
0.981619 + 0.190852i $$0.0611250\pi$$
$$678$$ 0 0
$$679$$ 273743. + 299270.i 0.0227860 + 0.0249109i
$$680$$ 0 0
$$681$$ 73.5034 127.312i 6.07351e−6 1.05196e-5i
$$682$$ 0 0
$$683$$ 4.28162e6 + 7.41598e6i 0.351201 + 0.608299i 0.986460 0.164001i $$-0.0524399\pi$$
−0.635259 + 0.772299i $$0.719107\pi$$
$$684$$ 0 0
$$685$$ 1.48038e6 0.120544
$$686$$ 0 0
$$687$$ −696411. −0.0562955
$$688$$ 0 0
$$689$$ 393712. + 681928.i 0.0315959 + 0.0547256i
$$690$$ 0 0
$$691$$ 8.22547e6 1.42469e7i 0.655338 1.13508i −0.326471 0.945207i $$-0.605860\pi$$
0.981809 0.189872i $$-0.0608071\pi$$
$$692$$ 0 0
$$693$$ 4.08516e6 + 4.46611e6i 0.323129 + 0.353262i
$$694$$ 0 0
$$695$$ 2.05773e6 3.56409e6i 0.161594 0.279890i
$$696$$ 0 0
$$697$$ −8.71208e6 1.50898e7i −0.679266 1.17652i
$$698$$ 0 0
$$699$$ −932916. −0.0722187
$$700$$ 0 0
$$701$$ −1.66928e7 −1.28302 −0.641512 0.767113i $$-0.721693\pi$$
−0.641512 + 0.767113i $$0.721693\pi$$
$$702$$ 0 0
$$703$$ −7.68132e6 1.33044e7i −0.586202 1.01533i
$$704$$ 0 0
$$705$$ −1.18764e6 + 2.05705e6i −0.0899937 + 0.155874i
$$706$$ 0 0
$$707$$ −6.60725e6 + 2.08909e7i −0.497132 + 1.57184i
$$708$$ 0 0
$$709$$ −2.80890e6 + 4.86515e6i −0.209855 + 0.363480i −0.951669 0.307126i $$-0.900633\pi$$
0.741813 + 0.670606i $$0.233966\pi$$
$$710$$ 0 0
$$711$$ −2.55763e6 4.42994e6i −0.189742 0.328643i
$$712$$ 0 0
$$713$$ 6.38537e6 0.470395
$$714$$ 0 0
$$715$$ 8.73927e6 0.639308
$$716$$ 0 0
$$717$$ 3.10099e6 + 5.37107e6i 0.225269 + 0.390178i
$$718$$ 0 0
$$719$$ 5.18592e6 8.98227e6i 0.374113 0.647983i −0.616081 0.787683i $$-0.711280\pi$$
0.990194 + 0.139700i $$0.0446138\pi$$
$$720$$ 0 0
$$721$$ 1.42823e7 3.15303e6i 1.02320 0.225887i
$$722$$ 0 0
$$723$$ −991332. + 1.71704e6i −0.0705299 + 0.122161i
$$724$$ 0 0
$$725$$ −1.18917e6 2.05971e6i −0.0840233 0.145533i
$$726$$ 0 0
$$727$$ −1.15369e7 −0.809565 −0.404783 0.914413i $$-0.632653\pi$$
−0.404783 + 0.914413i $$0.632653\pi$$
$$728$$ 0 0
$$729$$ 531441. 0.0370370
$$730$$ 0 0
$$731$$ −9.79557e6 1.69664e7i −0.678010 1.17435i
$$732$$ 0 0
$$733$$ −7.47349e6 + 1.29445e7i −0.513764 + 0.889865i 0.486109 + 0.873898i $$0.338416\pi$$
−0.999873 + 0.0159667i $$0.994917\pi$$
$$734$$ 0 0
$$735$$ −520925. + 5.83507e6i −0.0355678 + 0.398408i
$$736$$ 0 0
$$737$$ 1.45764e7 2.52470e7i 0.988510 1.71215i
$$738$$ 0 0
$$739$$ 4.50682e6 + 7.80604e6i 0.303570 + 0.525799i 0.976942 0.213505i $$-0.0684880\pi$$
−0.673372 + 0.739304i $$0.735155\pi$$
$$740$$ 0 0
$$741$$ −3.32073e6 −0.222171
$$742$$ 0 0
$$743$$ 2.10239e7 1.39714 0.698571 0.715541i $$-0.253820\pi$$
0.698571 + 0.715541i $$0.253820\pi$$
$$744$$ 0 0
$$745$$ −3.72875e6 6.45838e6i −0.246134 0.426317i
$$746$$ 0 0
$$747$$ 1.84568e6 3.19681e6i 0.121019 0.209612i
$$748$$ 0 0
$$749$$ −2.82424e6 + 623493.i −0.183949 + 0.0406094i
$$750$$ 0 0
$$751$$ 2.02110e6 3.50064e6i 0.130764 0.226489i −0.793207 0.608952i $$-0.791590\pi$$
0.923971 + 0.382462i $$0.124924\pi$$
$$752$$ 0 0
$$753$$ 6.46387e6 + 1.11957e7i 0.415437 + 0.719558i
$$754$$ 0 0
$$755$$ −5.48786e6 −0.350377
$$756$$ 0 0
$$757$$ −1.82059e7 −1.15471 −0.577353 0.816495i $$-0.695914\pi$$
−0.577353 + 0.816495i $$0.695914\pi$$
$$758$$ 0 0
$$759$$ −4.23321e6 7.33214e6i −0.266726 0.461983i
$$760$$ 0 0
$$761$$ 9.45999e6 1.63852e7i 0.592146 1.02563i −0.401797 0.915729i $$-0.631614\pi$$
0.993943 0.109898i $$-0.0350526\pi$$
$$762$$ 0 0
$$763$$ −3.27681e6 + 1.03607e7i −0.203770 + 0.644283i
$$764$$ 0 0
$$765$$ 2.08567e6 3.61249e6i 0.128852 0.223179i
$$766$$ 0 0
$$767$$ 1.00717e7 + 1.74447e7i 0.618180 + 1.07072i
$$768$$ 0 0
$$769$$ −1.12831e7 −0.688037 −0.344019 0.938963i $$-0.611788\pi$$
−0.344019 + 0.938963i $$0.611788\pi$$
$$770$$ 0 0
$$771$$ −8.18277e6 −0.495752
$$772$$ 0 0
$$773$$ 1.84282e6 + 3.19186e6i 0.110926 + 0.192130i 0.916144 0.400849i $$-0.131285\pi$$
−0.805218 + 0.592979i $$0.797952\pi$$
$$774$$ 0 0
$$775$$ 3.17896e6 5.50611e6i 0.190121 0.329299i
$$776$$ 0 0
$$777$$ −1.28365e7 1.40335e7i −0.762772 0.833902i
$$778$$ 0 0
$$779$$ −6.17501e6 + 1.06954e7i −0.364581 + 0.631472i
$$780$$ 0 0
$$781$$ 1.15193e7 + 1.99521e7i 0.675771 + 1.17047i