# Properties

 Label 63.6.e.f.37.4 Level $63$ Weight $6$ Character 63.37 Analytic conductor $10.104$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 63.e (of order $$3$$, degree $$2$$, 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: $$10.1041806482$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} + 187x^{10} + 25399x^{8} + 1518438x^{6} + 66232188x^{4} + 1297462320x^{2} + 18380851776$$ x^12 + 187*x^10 + 25399*x^8 + 1518438*x^6 + 66232188*x^4 + 1297462320*x^2 + 18380851776 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{4}\cdot 3^{5}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 37.4 Root $$2.44476 - 4.23445i$$ of defining polynomial Character $$\chi$$ $$=$$ 63.37 Dual form 63.6.e.f.46.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(2.44476 - 4.23445i) q^{2} +(4.04630 + 7.00840i) q^{4} +(-21.3752 + 37.0229i) q^{5} +(43.2256 - 122.223i) q^{7} +196.034 q^{8} +O(q^{10})$$ $$q+(2.44476 - 4.23445i) q^{2} +(4.04630 + 7.00840i) q^{4} +(-21.3752 + 37.0229i) q^{5} +(43.2256 - 122.223i) q^{7} +196.034 q^{8} +(104.514 + 181.024i) q^{10} +(355.439 + 615.638i) q^{11} +885.624 q^{13} +(-411.872 - 481.843i) q^{14} +(349.773 - 605.825i) q^{16} +(-350.659 - 607.359i) q^{17} +(627.946 - 1087.63i) q^{19} -345.962 q^{20} +3475.85 q^{22} +(-523.092 + 906.022i) q^{23} +(648.701 + 1123.58i) q^{25} +(2165.14 - 3750.13i) q^{26} +(1031.49 - 191.611i) q^{28} -6150.88 q^{29} +(-1147.12 - 1986.87i) q^{31} +(1426.31 + 2470.45i) q^{32} -3429.10 q^{34} +(3601.11 + 4212.89i) q^{35} +(-202.054 + 349.968i) q^{37} +(-3070.35 - 5318.01i) q^{38} +(-4190.26 + 7257.74i) q^{40} +17891.4 q^{41} -14604.8 q^{43} +(-2876.43 + 4982.11i) q^{44} +(2557.67 + 4430.01i) q^{46} +(-10568.6 + 18305.4i) q^{47} +(-13070.1 - 10566.3i) q^{49} +6343.67 q^{50} +(3583.50 + 6206.80i) q^{52} +(53.6064 + 92.8490i) q^{53} -30390.3 q^{55} +(8473.66 - 23959.9i) q^{56} +(-15037.4 + 26045.6i) q^{58} +(-22249.4 - 38537.1i) q^{59} +(11606.2 - 20102.5i) q^{61} -11217.7 q^{62} +36333.5 q^{64} +(-18930.4 + 32788.4i) q^{65} +(3335.66 + 5777.53i) q^{67} +(2837.74 - 4915.11i) q^{68} +(26643.1 - 4949.23i) q^{70} -25110.5 q^{71} +(-4737.49 - 8205.57i) q^{73} +(987.948 + 1711.18i) q^{74} +10163.4 q^{76} +(90609.5 - 16831.6i) q^{77} +(13238.1 - 22929.0i) q^{79} +(14953.0 + 25899.3i) q^{80} +(43740.2 - 75760.2i) q^{82} +7494.03 q^{83} +29981.6 q^{85} +(-35705.3 + 61843.3i) q^{86} +(69678.0 + 120686. i) q^{88} +(16085.6 - 27861.2i) q^{89} +(38281.6 - 108244. i) q^{91} -8466.35 q^{92} +(51675.5 + 89504.7i) q^{94} +(26845.0 + 46496.8i) q^{95} -155070. q^{97} +(-76695.9 + 29512.5i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 182 q^{4} + 142 q^{7}+O(q^{10})$$ 12 * q - 182 * q^4 + 142 * q^7 $$12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100})$$ 12 * q - 182 * q^4 + 142 * q^7 + 686 * q^10 + 308 * q^13 - 1898 * q^16 + 9422 * q^19 - 18292 * q^22 - 7526 * q^25 + 37074 * q^28 + 23422 * q^31 - 55608 * q^34 - 18182 * q^37 + 69258 * q^40 - 87372 * q^43 + 25332 * q^46 + 30354 * q^49 + 34272 * q^52 - 96320 * q^55 - 89782 * q^58 - 16156 * q^61 + 380580 * q^64 + 144650 * q^67 - 187262 * q^70 - 100058 * q^73 - 685440 * q^76 + 101994 * q^79 + 75712 * q^82 + 602352 * q^85 + 752310 * q^88 - 282306 * q^91 - 120456 * q^94 - 866096 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$$.

 $$n$$ $$10$$ $$29$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.44476 4.23445i 0.432177 0.748552i −0.564884 0.825170i $$-0.691079\pi$$
0.997060 + 0.0766186i $$0.0244124\pi$$
$$3$$ 0 0
$$4$$ 4.04630 + 7.00840i 0.126447 + 0.219012i
$$5$$ −21.3752 + 37.0229i −0.382371 + 0.662286i −0.991401 0.130861i $$-0.958226\pi$$
0.609029 + 0.793148i $$0.291559\pi$$
$$6$$ 0 0
$$7$$ 43.2256 122.223i 0.333423 0.942777i
$$8$$ 196.034 1.08294
$$9$$ 0 0
$$10$$ 104.514 + 181.024i 0.330504 + 0.572449i
$$11$$ 355.439 + 615.638i 0.885693 + 1.53407i 0.844917 + 0.534898i $$0.179650\pi$$
0.0407765 + 0.999168i $$0.487017\pi$$
$$12$$ 0 0
$$13$$ 885.624 1.45342 0.726709 0.686945i $$-0.241049\pi$$
0.726709 + 0.686945i $$0.241049\pi$$
$$14$$ −411.872 481.843i −0.561620 0.657031i
$$15$$ 0 0
$$16$$ 349.773 605.825i 0.341576 0.591626i
$$17$$ −350.659 607.359i −0.294281 0.509710i 0.680536 0.732714i $$-0.261747\pi$$
−0.974817 + 0.223005i $$0.928413\pi$$
$$18$$ 0 0
$$19$$ 627.946 1087.63i 0.399060 0.691192i −0.594550 0.804059i $$-0.702670\pi$$
0.993610 + 0.112866i $$0.0360031\pi$$
$$20$$ −345.962 −0.193399
$$21$$ 0 0
$$22$$ 3475.85 1.53110
$$23$$ −523.092 + 906.022i −0.206186 + 0.357124i −0.950510 0.310694i $$-0.899438\pi$$
0.744324 + 0.667818i $$0.232772\pi$$
$$24$$ 0 0
$$25$$ 648.701 + 1123.58i 0.207584 + 0.359547i
$$26$$ 2165.14 3750.13i 0.628134 1.08796i
$$27$$ 0 0
$$28$$ 1031.49 191.611i 0.248640 0.0461875i
$$29$$ −6150.88 −1.35813 −0.679067 0.734077i $$-0.737615\pi$$
−0.679067 + 0.734077i $$0.737615\pi$$
$$30$$ 0 0
$$31$$ −1147.12 1986.87i −0.214390 0.371334i 0.738694 0.674041i $$-0.235443\pi$$
−0.953084 + 0.302707i $$0.902110\pi$$
$$32$$ 1426.31 + 2470.45i 0.246229 + 0.426482i
$$33$$ 0 0
$$34$$ −3429.10 −0.508725
$$35$$ 3601.11 + 4212.89i 0.496897 + 0.581312i
$$36$$ 0 0
$$37$$ −202.054 + 349.968i −0.0242641 + 0.0420266i −0.877902 0.478839i $$-0.841058\pi$$
0.853638 + 0.520866i $$0.174391\pi$$
$$38$$ −3070.35 5318.01i −0.344929 0.597434i
$$39$$ 0 0
$$40$$ −4190.26 + 7257.74i −0.414086 + 0.717218i
$$41$$ 17891.4 1.66221 0.831103 0.556119i $$-0.187710\pi$$
0.831103 + 0.556119i $$0.187710\pi$$
$$42$$ 0 0
$$43$$ −14604.8 −1.20455 −0.602275 0.798289i $$-0.705739\pi$$
−0.602275 + 0.798289i $$0.705739\pi$$
$$44$$ −2876.43 + 4982.11i −0.223986 + 0.387956i
$$45$$ 0 0
$$46$$ 2557.67 + 4430.01i 0.178217 + 0.308681i
$$47$$ −10568.6 + 18305.4i −0.697870 + 1.20875i 0.271334 + 0.962485i $$0.412535\pi$$
−0.969204 + 0.246260i $$0.920798\pi$$
$$48$$ 0 0
$$49$$ −13070.1 10566.3i −0.777658 0.628687i
$$50$$ 6343.67 0.358852
$$51$$ 0 0
$$52$$ 3583.50 + 6206.80i 0.183780 + 0.318317i
$$53$$ 53.6064 + 92.8490i 0.00262136 + 0.00454033i 0.867333 0.497728i $$-0.165832\pi$$
−0.864712 + 0.502268i $$0.832499\pi$$
$$54$$ 0 0
$$55$$ −30390.3 −1.35465
$$56$$ 8473.66 23959.9i 0.361078 1.02097i
$$57$$ 0 0
$$58$$ −15037.4 + 26045.6i −0.586953 + 1.01663i
$$59$$ −22249.4 38537.1i −0.832124 1.44128i −0.896351 0.443346i $$-0.853791\pi$$
0.0642267 0.997935i $$-0.479542\pi$$
$$60$$ 0 0
$$61$$ 11606.2 20102.5i 0.399360 0.691712i −0.594287 0.804253i $$-0.702566\pi$$
0.993647 + 0.112541i $$0.0358990\pi$$
$$62$$ −11217.7 −0.370617
$$63$$ 0 0
$$64$$ 36333.5 1.10881
$$65$$ −18930.4 + 32788.4i −0.555746 + 0.962580i
$$66$$ 0 0
$$67$$ 3335.66 + 5777.53i 0.0907809 + 0.157237i 0.907840 0.419317i $$-0.137730\pi$$
−0.817059 + 0.576554i $$0.804397\pi$$
$$68$$ 2837.74 4915.11i 0.0744218 0.128902i
$$69$$ 0 0
$$70$$ 26643.1 4949.23i 0.649890 0.120724i
$$71$$ −25110.5 −0.591166 −0.295583 0.955317i $$-0.595514\pi$$
−0.295583 + 0.955317i $$0.595514\pi$$
$$72$$ 0 0
$$73$$ −4737.49 8205.57i −0.104050 0.180219i 0.809300 0.587396i $$-0.199847\pi$$
−0.913350 + 0.407176i $$0.866513\pi$$
$$74$$ 987.948 + 1711.18i 0.0209727 + 0.0363258i
$$75$$ 0 0
$$76$$ 10163.4 0.201840
$$77$$ 90609.5 16831.6i 1.74159 0.323519i
$$78$$ 0 0
$$79$$ 13238.1 22929.0i 0.238647 0.413349i −0.721679 0.692228i $$-0.756629\pi$$
0.960326 + 0.278879i $$0.0899627\pi$$
$$80$$ 14953.0 + 25899.3i 0.261217 + 0.452442i
$$81$$ 0 0
$$82$$ 43740.2 75760.2i 0.718366 1.24425i
$$83$$ 7494.03 0.119404 0.0597022 0.998216i $$-0.480985\pi$$
0.0597022 + 0.998216i $$0.480985\pi$$
$$84$$ 0 0
$$85$$ 29981.6 0.450098
$$86$$ −35705.3 + 61843.3i −0.520578 + 0.901668i
$$87$$ 0 0
$$88$$ 69678.0 + 120686.i 0.959155 + 1.66131i
$$89$$ 16085.6 27861.2i 0.215260 0.372841i −0.738093 0.674699i $$-0.764273\pi$$
0.953353 + 0.301858i $$0.0976067\pi$$
$$90$$ 0 0
$$91$$ 38281.6 108244.i 0.484603 1.37025i
$$92$$ −8466.35 −0.104286
$$93$$ 0 0
$$94$$ 51675.5 + 89504.7i 0.603206 + 1.04478i
$$95$$ 26845.0 + 46496.8i 0.305178 + 0.528584i
$$96$$ 0 0
$$97$$ −155070. −1.67340 −0.836699 0.547664i $$-0.815517\pi$$
−0.836699 + 0.547664i $$0.815517\pi$$
$$98$$ −76695.9 + 29512.5i −0.806691 + 0.310414i
$$99$$ 0 0
$$100$$ −5249.68 + 9092.71i −0.0524968 + 0.0909271i
$$101$$ −55960.9 96927.1i −0.545860 0.945457i −0.998552 0.0537904i $$-0.982870\pi$$
0.452692 0.891667i $$-0.350464\pi$$
$$102$$ 0 0
$$103$$ 30342.1 52554.1i 0.281808 0.488105i −0.690022 0.723788i $$-0.742399\pi$$
0.971830 + 0.235683i $$0.0757326\pi$$
$$104$$ 173612. 1.57397
$$105$$ 0 0
$$106$$ 524.219 0.00453156
$$107$$ 56266.4 97456.3i 0.475105 0.822906i −0.524488 0.851418i $$-0.675743\pi$$
0.999593 + 0.0285115i $$0.00907672\pi$$
$$108$$ 0 0
$$109$$ 3811.67 + 6602.01i 0.0307291 + 0.0532243i 0.880981 0.473152i $$-0.156884\pi$$
−0.850252 + 0.526376i $$0.823550\pi$$
$$110$$ −74297.0 + 128686.i −0.585450 + 1.01403i
$$111$$ 0 0
$$112$$ −58926.9 68937.6i −0.443883 0.519291i
$$113$$ −41498.7 −0.305730 −0.152865 0.988247i $$-0.548850\pi$$
−0.152865 + 0.988247i $$0.548850\pi$$
$$114$$ 0 0
$$115$$ −22362.4 38732.8i −0.157679 0.273108i
$$116$$ −24888.3 43107.8i −0.171732 0.297448i
$$117$$ 0 0
$$118$$ −217578. −1.43850
$$119$$ −89390.8 + 16605.3i −0.578663 + 0.107493i
$$120$$ 0 0
$$121$$ −172148. + 298170.i −1.06891 + 1.85140i
$$122$$ −56748.6 98291.5i −0.345188 0.597883i
$$123$$ 0 0
$$124$$ 9283.17 16078.9i 0.0542178 0.0939080i
$$125$$ −189060. −1.08224
$$126$$ 0 0
$$127$$ 94796.7 0.521535 0.260768 0.965402i $$-0.416024\pi$$
0.260768 + 0.965402i $$0.416024\pi$$
$$128$$ 43184.6 74797.9i 0.232972 0.403519i
$$129$$ 0 0
$$130$$ 92560.5 + 160319.i 0.480360 + 0.832009i
$$131$$ 105547. 182814.i 0.537365 0.930744i −0.461679 0.887047i $$-0.652753\pi$$
0.999045 0.0436972i $$-0.0139137\pi$$
$$132$$ 0 0
$$133$$ −105791. 123763.i −0.518585 0.606684i
$$134$$ 32619.5 0.156934
$$135$$ 0 0
$$136$$ −68740.8 119063.i −0.318689 0.551986i
$$137$$ 48096.6 + 83305.7i 0.218934 + 0.379204i 0.954482 0.298268i $$-0.0964088\pi$$
−0.735549 + 0.677472i $$0.763076\pi$$
$$138$$ 0 0
$$139$$ −401994. −1.76475 −0.882375 0.470548i $$-0.844056\pi$$
−0.882375 + 0.470548i $$0.844056\pi$$
$$140$$ −14954.4 + 42284.6i −0.0644835 + 0.182332i
$$141$$ 0 0
$$142$$ −61389.1 + 106329.i −0.255488 + 0.442518i
$$143$$ 314785. + 545224.i 1.28728 + 2.22964i
$$144$$ 0 0
$$145$$ 131476. 227724.i 0.519311 0.899474i
$$146$$ −46328.1 −0.179871
$$147$$ 0 0
$$148$$ −3270.29 −0.0122725
$$149$$ −37650.0 + 65211.8i −0.138931 + 0.240636i −0.927092 0.374833i $$-0.877700\pi$$
0.788161 + 0.615469i $$0.211033\pi$$
$$150$$ 0 0
$$151$$ 245297. + 424867.i 0.875488 + 1.51639i 0.856242 + 0.516574i $$0.172793\pi$$
0.0192454 + 0.999815i $$0.493874\pi$$
$$152$$ 123098. 213213.i 0.432159 0.748522i
$$153$$ 0 0
$$154$$ 150246. 424830.i 0.510505 1.44349i
$$155$$ 98079.6 0.327906
$$156$$ 0 0
$$157$$ 230508. + 399251.i 0.746339 + 1.29270i 0.949567 + 0.313566i $$0.101524\pi$$
−0.203228 + 0.979132i $$0.565143\pi$$
$$158$$ −64727.7 112112.i −0.206276 0.357280i
$$159$$ 0 0
$$160$$ −121951. −0.376604
$$161$$ 88126.1 + 103097.i 0.267941 + 0.313461i
$$162$$ 0 0
$$163$$ 239222. 414344.i 0.705232 1.22150i −0.261376 0.965237i $$-0.584176\pi$$
0.966608 0.256260i $$-0.0824904\pi$$
$$164$$ 72393.9 + 125390.i 0.210181 + 0.364043i
$$165$$ 0 0
$$166$$ 18321.1 31733.1i 0.0516038 0.0893803i
$$167$$ −498852. −1.38414 −0.692070 0.721830i $$-0.743301\pi$$
−0.692070 + 0.721830i $$0.743301\pi$$
$$168$$ 0 0
$$169$$ 413036. 1.11243
$$170$$ 73297.8 126956.i 0.194522 0.336922i
$$171$$ 0 0
$$172$$ −59095.5 102356.i −0.152312 0.263811i
$$173$$ −130322. + 225724.i −0.331056 + 0.573405i −0.982719 0.185103i $$-0.940738\pi$$
0.651663 + 0.758508i $$0.274072\pi$$
$$174$$ 0 0
$$175$$ 165369. 30718.9i 0.408186 0.0758248i
$$176$$ 497292. 1.21012
$$177$$ 0 0
$$178$$ −78651.1 136228.i −0.186061 0.322267i
$$179$$ −266709. 461954.i −0.622164 1.07762i −0.989082 0.147367i $$-0.952920\pi$$
0.366918 0.930253i $$-0.380413\pi$$
$$180$$ 0 0
$$181$$ 185798. 0.421546 0.210773 0.977535i $$-0.432402\pi$$
0.210773 + 0.977535i $$0.432402\pi$$
$$182$$ −364764. 426732.i −0.816269 0.954941i
$$183$$ 0 0
$$184$$ −102544. + 177611.i −0.223287 + 0.386745i
$$185$$ −8637.90 14961.3i −0.0185558 0.0321395i
$$186$$ 0 0
$$187$$ 249275. 431758.i 0.521285 0.902893i
$$188$$ −171055. −0.352974
$$189$$ 0 0
$$190$$ 262518. 0.527564
$$191$$ 354418. 613871.i 0.702964 1.21757i −0.264458 0.964397i $$-0.585193\pi$$
0.967421 0.253171i $$-0.0814736\pi$$
$$192$$ 0 0
$$193$$ 361752. + 626573.i 0.699065 + 1.21082i 0.968791 + 0.247879i $$0.0797337\pi$$
−0.269726 + 0.962937i $$0.586933\pi$$
$$194$$ −379109. + 656637.i −0.723203 + 1.25262i
$$195$$ 0 0
$$196$$ 21167.6 134355.i 0.0393578 0.249812i
$$197$$ −147313. −0.270443 −0.135222 0.990815i $$-0.543175\pi$$
−0.135222 + 0.990815i $$0.543175\pi$$
$$198$$ 0 0
$$199$$ −710.490 1230.60i −0.00127182 0.00220285i 0.865389 0.501101i $$-0.167071\pi$$
−0.866661 + 0.498898i $$0.833738\pi$$
$$200$$ 127167. + 220260.i 0.224802 + 0.389368i
$$201$$ 0 0
$$202$$ −547244. −0.943632
$$203$$ −265875. + 751782.i −0.452833 + 1.28042i
$$204$$ 0 0
$$205$$ −382432. + 662392.i −0.635579 + 1.10086i
$$206$$ −148358. 256964.i −0.243581 0.421895i
$$207$$ 0 0
$$208$$ 309768. 536533.i 0.496452 0.859881i
$$209$$ 892786. 1.41378
$$210$$ 0 0
$$211$$ −30296.2 −0.0468470 −0.0234235 0.999726i $$-0.507457\pi$$
−0.0234235 + 0.999726i $$0.507457\pi$$
$$212$$ −433.815 + 751.389i −0.000662926 + 0.00114822i
$$213$$ 0 0
$$214$$ −275116. 476514.i −0.410659 0.711281i
$$215$$ 312181. 540713.i 0.460585 0.797757i
$$216$$ 0 0
$$217$$ −292427. + 54321.2i −0.421568 + 0.0783106i
$$218$$ 37274.5 0.0531215
$$219$$ 0 0
$$220$$ −122968. 212987.i −0.171292 0.296686i
$$221$$ −310552. 537891.i −0.427714 0.740822i
$$222$$ 0 0
$$223$$ −147864. −0.199114 −0.0995570 0.995032i $$-0.531743\pi$$
−0.0995570 + 0.995032i $$0.531743\pi$$
$$224$$ 363599. 67542.4i 0.484176 0.0899407i
$$225$$ 0 0
$$226$$ −101454. + 175724.i −0.132129 + 0.228855i
$$227$$ 406723. + 704464.i 0.523882 + 0.907391i 0.999614 + 0.0277999i $$0.00885012\pi$$
−0.475731 + 0.879591i $$0.657817\pi$$
$$228$$ 0 0
$$229$$ −641094. + 1.11041e6i −0.807854 + 1.39924i 0.106493 + 0.994313i $$0.466038\pi$$
−0.914347 + 0.404931i $$0.867295\pi$$
$$230$$ −218683. −0.272581
$$231$$ 0 0
$$232$$ −1.20578e6 −1.47078
$$233$$ −617850. + 1.07015e6i −0.745578 + 1.29138i 0.204346 + 0.978899i $$0.434493\pi$$
−0.949924 + 0.312481i $$0.898840\pi$$
$$234$$ 0 0
$$235$$ −451813. 782564.i −0.533691 0.924379i
$$236$$ 180055. 311865.i 0.210439 0.364491i
$$237$$ 0 0
$$238$$ −148225. + 419117.i −0.169621 + 0.479615i
$$239$$ −874240. −0.990001 −0.495001 0.868893i $$-0.664832\pi$$
−0.495001 + 0.868893i $$0.664832\pi$$
$$240$$ 0 0
$$241$$ 489805. + 848367.i 0.543226 + 0.940895i 0.998716 + 0.0506545i $$0.0161307\pi$$
−0.455490 + 0.890241i $$0.650536\pi$$
$$242$$ 841722. + 1.45791e6i 0.923912 + 1.60026i
$$243$$ 0 0
$$244$$ 187848. 0.201991
$$245$$ 670573. 258036.i 0.713725 0.274641i
$$246$$ 0 0
$$247$$ 556124. 963235.i 0.580002 1.00459i
$$248$$ −224874. 389493.i −0.232172 0.402133i
$$249$$ 0 0
$$250$$ −462205. + 800563.i −0.467719 + 0.810113i
$$251$$ 213005. 0.213406 0.106703 0.994291i $$-0.465971\pi$$
0.106703 + 0.994291i $$0.465971\pi$$
$$252$$ 0 0
$$253$$ −743709. −0.730469
$$254$$ 231755. 401412.i 0.225395 0.390396i
$$255$$ 0 0
$$256$$ 370184. + 641177.i 0.353035 + 0.611474i
$$257$$ 789506. 1.36746e6i 0.745629 1.29147i −0.204272 0.978914i $$-0.565483\pi$$
0.949900 0.312553i $$-0.101184\pi$$
$$258$$ 0 0
$$259$$ 34040.4 + 39823.3i 0.0315315 + 0.0368883i
$$260$$ −306392. −0.281089
$$261$$ 0 0
$$262$$ −516076. 893871.i −0.464473 0.804492i
$$263$$ 144544. + 250357.i 0.128857 + 0.223188i 0.923234 0.384238i $$-0.125536\pi$$
−0.794377 + 0.607425i $$0.792202\pi$$
$$264$$ 0 0
$$265$$ −4583.39 −0.00400933
$$266$$ −782703. + 145395.i −0.678255 + 0.125993i
$$267$$ 0 0
$$268$$ −26994.2 + 46755.2i −0.0229579 + 0.0397643i
$$269$$ −1.02244e6 1.77092e6i −0.861506 1.49217i −0.870475 0.492213i $$-0.836188\pi$$
0.00896851 0.999960i $$-0.497145\pi$$
$$270$$ 0 0
$$271$$ 302981. 524779.i 0.250607 0.434063i −0.713086 0.701076i $$-0.752703\pi$$
0.963693 + 0.267013i $$0.0860366\pi$$
$$272$$ −490604. −0.402077
$$273$$ 0 0
$$274$$ 470338. 0.378472
$$275$$ −461147. + 798731.i −0.367712 + 0.636896i
$$276$$ 0 0
$$277$$ −611375. 1.05893e6i −0.478750 0.829219i 0.520953 0.853585i $$-0.325576\pi$$
−0.999703 + 0.0243664i $$0.992243\pi$$
$$278$$ −982780. + 1.70222e6i −0.762683 + 1.32101i
$$279$$ 0 0
$$280$$ 705939. + 825867.i 0.538111 + 0.629528i
$$281$$ −639205. −0.482919 −0.241460 0.970411i $$-0.577626\pi$$
−0.241460 + 0.970411i $$0.577626\pi$$
$$282$$ 0 0
$$283$$ −236827. 410197.i −0.175779 0.304457i 0.764652 0.644444i $$-0.222911\pi$$
−0.940430 + 0.339986i $$0.889578\pi$$
$$284$$ −101605. 175984.i −0.0747511 0.129473i
$$285$$ 0 0
$$286$$ 3.07830e6 2.22533
$$287$$ 773365. 2.18675e6i 0.554217 1.56709i
$$288$$ 0 0
$$289$$ 464006. 803681.i 0.326797 0.566030i
$$290$$ −642856. 1.11346e6i −0.448868 0.777463i
$$291$$ 0 0
$$292$$ 38338.6 66404.3i 0.0263135 0.0455763i
$$293$$ 829294. 0.564338 0.282169 0.959365i $$-0.408946\pi$$
0.282169 + 0.959365i $$0.408946\pi$$
$$294$$ 0 0
$$295$$ 1.90234e6 1.27272
$$296$$ −39609.4 + 68605.5i −0.0262766 + 0.0455124i
$$297$$ 0 0
$$298$$ 184091. + 318854.i 0.120086 + 0.207994i
$$299$$ −463263. + 802394.i −0.299674 + 0.519051i
$$300$$ 0 0
$$301$$ −631301. + 1.78505e6i −0.401625 + 1.13562i
$$302$$ 2.39877e6 1.51346
$$303$$ 0 0
$$304$$ −439278. 760851.i −0.272618 0.472189i
$$305$$ 496169. + 859390.i 0.305408 + 0.528981i
$$306$$ 0 0
$$307$$ 1.63715e6 0.991385 0.495693 0.868498i $$-0.334914\pi$$
0.495693 + 0.868498i $$0.334914\pi$$
$$308$$ 484596. + 566921.i 0.291074 + 0.340522i
$$309$$ 0 0
$$310$$ 239781. 415313.i 0.141713 0.245455i
$$311$$ 303729. + 526074.i 0.178068 + 0.308422i 0.941219 0.337798i $$-0.109682\pi$$
−0.763151 + 0.646220i $$0.776349\pi$$
$$312$$ 0 0
$$313$$ −789012. + 1.36661e6i −0.455222 + 0.788467i −0.998701 0.0509555i $$-0.983773\pi$$
0.543479 + 0.839423i $$0.317107\pi$$
$$314$$ 2.25414e6 1.29020
$$315$$ 0 0
$$316$$ 214261. 0.120705
$$317$$ −1.09343e6 + 1.89387e6i −0.611142 + 1.05853i 0.379906 + 0.925025i $$0.375956\pi$$
−0.991048 + 0.133505i $$0.957377\pi$$
$$318$$ 0 0
$$319$$ −2.18626e6 3.78672e6i −1.20289 2.08347i
$$320$$ −776635. + 1.34517e6i −0.423977 + 0.734349i
$$321$$ 0 0
$$322$$ 652008. 121117.i 0.350439 0.0650977i
$$323$$ −880779. −0.469743
$$324$$ 0 0
$$325$$ 574505. + 995072.i 0.301707 + 0.522572i
$$326$$ −1.16968e6 2.02595e6i −0.609569 1.05580i
$$327$$ 0 0
$$328$$ 3.50731e6 1.80007
$$329$$ 1.78051e6 + 2.08300e6i 0.906892 + 1.06096i
$$330$$ 0 0
$$331$$ 1.38434e6 2.39775e6i 0.694503 1.20291i −0.275845 0.961202i $$-0.588958\pi$$
0.970348 0.241712i $$-0.0777090\pi$$
$$332$$ 30323.1 + 52521.1i 0.0150983 + 0.0261510i
$$333$$ 0 0
$$334$$ −1.21957e6 + 2.11236e6i −0.598193 + 1.03610i
$$335$$ −285202. −0.138848
$$336$$ 0 0
$$337$$ −2.45187e6 −1.17604 −0.588021 0.808846i $$-0.700093\pi$$
−0.588021 + 0.808846i $$0.700093\pi$$
$$338$$ 1.00977e6 1.74898e6i 0.480765 0.832709i
$$339$$ 0 0
$$340$$ 121315. + 210123.i 0.0569135 + 0.0985771i
$$341$$ 815461. 1.41242e6i 0.379767 0.657776i
$$342$$ 0 0
$$343$$ −1.85642e6 + 1.14074e6i −0.852001 + 0.523540i
$$344$$ −2.86303e6 −1.30446
$$345$$ 0 0
$$346$$ 637210. + 1.10368e6i 0.286149 + 0.495625i
$$347$$ −740499. 1.28258e6i −0.330142 0.571823i 0.652398 0.757877i $$-0.273763\pi$$
−0.982539 + 0.186054i $$0.940430\pi$$
$$348$$ 0 0
$$349$$ −1.28643e6 −0.565357 −0.282678 0.959215i $$-0.591223\pi$$
−0.282678 + 0.959215i $$0.591223\pi$$
$$350$$ 274209. 775345.i 0.119650 0.338318i
$$351$$ 0 0
$$352$$ −1.01393e6 + 1.75619e6i −0.436167 + 0.755464i
$$353$$ 1.12562e6 + 1.94963e6i 0.480790 + 0.832752i 0.999757 0.0220418i $$-0.00701668\pi$$
−0.518967 + 0.854794i $$0.673683\pi$$
$$354$$ 0 0
$$355$$ 536742. 929664.i 0.226045 0.391521i
$$356$$ 260349. 0.108876
$$357$$ 0 0
$$358$$ −2.60816e6 −1.07554
$$359$$ −362932. + 628617.i −0.148624 + 0.257424i −0.930719 0.365735i $$-0.880818\pi$$
0.782095 + 0.623159i $$0.214151\pi$$
$$360$$ 0 0
$$361$$ 449417. + 778413.i 0.181502 + 0.314371i
$$362$$ 454232. 786753.i 0.182182 0.315549i
$$363$$ 0 0
$$364$$ 913515. 169695.i 0.361378 0.0671298i
$$365$$ 405059. 0.159142
$$366$$ 0 0
$$367$$ −1.71382e6 2.96843e6i −0.664202 1.15043i −0.979501 0.201440i $$-0.935438\pi$$
0.315298 0.948993i $$-0.397895\pi$$
$$368$$ 365927. + 633805.i 0.140856 + 0.243970i
$$369$$ 0 0
$$370$$ −84470.4 −0.0320775
$$371$$ 13665.5 2538.50i 0.00515454 0.000957509i
$$372$$ 0 0
$$373$$ 546522. 946604.i 0.203393 0.352287i −0.746227 0.665692i $$-0.768136\pi$$
0.949619 + 0.313405i $$0.101470\pi$$
$$374$$ −1.21884e6 2.11109e6i −0.450575 0.780418i
$$375$$ 0 0
$$376$$ −2.07181e6 + 3.58847e6i −0.755753 + 1.30900i
$$377$$ −5.44737e6 −1.97394
$$378$$ 0 0
$$379$$ −2.92579e6 −1.04627 −0.523137 0.852249i $$-0.675238\pi$$
−0.523137 + 0.852249i $$0.675238\pi$$
$$380$$ −217245. + 376280.i −0.0771777 + 0.133676i
$$381$$ 0 0
$$382$$ −1.73294e6 3.00153e6i −0.607609 1.05241i
$$383$$ −51966.3 + 90008.2i −0.0181019 + 0.0313534i −0.874934 0.484241i $$-0.839096\pi$$
0.856833 + 0.515595i $$0.172429\pi$$
$$384$$ 0 0
$$385$$ −1.31364e6 + 3.71441e6i −0.451673 + 1.27714i
$$386$$ 3.53759e6 1.20848
$$387$$ 0 0
$$388$$ −627460. 1.08679e6i −0.211596 0.366495i
$$389$$ 86465.6 + 149763.i 0.0289714 + 0.0501799i 0.880148 0.474700i $$-0.157443\pi$$
−0.851176 + 0.524880i $$0.824110\pi$$
$$390$$ 0 0
$$391$$ 733707. 0.242706
$$392$$ −2.56218e6 2.07136e6i −0.842159 0.680832i
$$393$$ 0 0
$$394$$ −360146. + 623791.i −0.116879 + 0.202441i
$$395$$ 565932. + 980224.i 0.182504 + 0.316106i
$$396$$ 0 0
$$397$$ −1.29983e6 + 2.25137e6i −0.413913 + 0.716918i −0.995314 0.0966990i $$-0.969172\pi$$
0.581401 + 0.813617i $$0.302505\pi$$
$$398$$ −6947.91 −0.00219860
$$399$$ 0 0
$$400$$ 907594. 0.283623
$$401$$ 1.72506e6 2.98789e6i 0.535726 0.927904i −0.463402 0.886148i $$-0.653371\pi$$
0.999128 0.0417559i $$-0.0132952\pi$$
$$402$$ 0 0
$$403$$ −1.01592e6 1.75962e6i −0.311598 0.539704i
$$404$$ 452869. 784392.i 0.138045 0.239100i
$$405$$ 0 0
$$406$$ 2.53338e6 + 2.96376e6i 0.762755 + 0.892335i
$$407$$ −287272. −0.0859621
$$408$$ 0 0
$$409$$ 721374. + 1.24946e6i 0.213232 + 0.369329i 0.952724 0.303837i $$-0.0982677\pi$$
−0.739492 + 0.673165i $$0.764934\pi$$
$$410$$ 1.86991e6 + 3.23878e6i 0.549365 + 0.951528i
$$411$$ 0 0
$$412$$ 491093. 0.142535
$$413$$ −5.67187e6 + 1.05361e6i −1.63626 + 0.303952i
$$414$$ 0 0
$$415$$ −160186. + 277451.i −0.0456568 + 0.0790799i
$$416$$ 1.26318e6 + 2.18789e6i 0.357874 + 0.619857i
$$417$$ 0 0
$$418$$ 2.18265e6 3.78046e6i 0.611002 1.05829i
$$419$$ 5.10039e6 1.41928 0.709641 0.704564i $$-0.248857\pi$$
0.709641 + 0.704564i $$0.248857\pi$$
$$420$$ 0 0
$$421$$ 5.08241e6 1.39754 0.698771 0.715346i $$-0.253731\pi$$
0.698771 + 0.715346i $$0.253731\pi$$
$$422$$ −74066.9 + 128288.i −0.0202462 + 0.0350674i
$$423$$ 0 0
$$424$$ 10508.6 + 18201.5i 0.00283878 + 0.00491692i
$$425$$ 454945. 787988.i 0.122176 0.211616i
$$426$$ 0 0
$$427$$ −1.95531e6 2.28749e6i −0.518974 0.607140i
$$428$$ 910683. 0.240302
$$429$$ 0 0
$$430$$ −1.52641e6 2.64383e6i −0.398109 0.689544i
$$431$$ 1.23720e6 + 2.14290e6i 0.320810 + 0.555659i 0.980655 0.195742i $$-0.0627115\pi$$
−0.659845 + 0.751401i $$0.729378\pi$$
$$432$$ 0 0
$$433$$ −331952. −0.0850855 −0.0425428 0.999095i $$-0.513546\pi$$
−0.0425428 + 0.999095i $$0.513546\pi$$
$$434$$ −484892. + 1.37107e6i −0.123572 + 0.349409i
$$435$$ 0 0
$$436$$ −30846.3 + 53427.4i −0.00777119 + 0.0134601i
$$437$$ 656947. + 1.13787e6i 0.164561 + 0.285028i
$$438$$ 0 0
$$439$$ 2.05610e6 3.56127e6i 0.509193 0.881948i −0.490750 0.871300i $$-0.663277\pi$$
0.999943 0.0106480i $$-0.00338942\pi$$
$$440$$ −5.95752e6 −1.46701
$$441$$ 0 0
$$442$$ −3.03690e6 −0.739391
$$443$$ 2.92674e6 5.06927e6i 0.708558 1.22726i −0.256835 0.966455i $$-0.582680\pi$$
0.965392 0.260802i $$-0.0839871\pi$$
$$444$$ 0 0
$$445$$ 687668. + 1.19108e6i 0.164619 + 0.285128i
$$446$$ −361493. + 626124.i −0.0860524 + 0.149047i
$$447$$ 0 0
$$448$$ 1.57053e6 4.44080e6i 0.369702 1.04536i
$$449$$ 3.86497e6 0.904754 0.452377 0.891827i $$-0.350576\pi$$
0.452377 + 0.891827i $$0.350576\pi$$
$$450$$ 0 0
$$451$$ 6.35930e6 + 1.10146e7i 1.47220 + 2.54993i
$$452$$ −167916. 290839.i −0.0386586 0.0669586i
$$453$$ 0 0
$$454$$ 3.97736e6 0.905638
$$455$$ 3.18923e6 + 3.73103e6i 0.722200 + 0.844891i
$$456$$ 0 0
$$457$$ 2.69523e6 4.66828e6i 0.603678 1.04560i −0.388581 0.921415i $$-0.627035\pi$$
0.992259 0.124186i $$-0.0396321\pi$$
$$458$$ 3.13464e6 + 5.42936e6i 0.698271 + 1.20944i
$$459$$ 0 0
$$460$$ 180970. 313449.i 0.0398760 0.0690673i
$$461$$ −1.17429e6 −0.257350 −0.128675 0.991687i $$-0.541072\pi$$
−0.128675 + 0.991687i $$0.541072\pi$$
$$462$$ 0 0
$$463$$ 4.03702e6 0.875203 0.437601 0.899169i $$-0.355828\pi$$
0.437601 + 0.899169i $$0.355828\pi$$
$$464$$ −2.15141e6 + 3.72636e6i −0.463905 + 0.803507i
$$465$$ 0 0
$$466$$ 3.02099e6 + 5.23251e6i 0.644443 + 1.11621i
$$467$$ 718550. 1.24456e6i 0.152463 0.264074i −0.779669 0.626191i $$-0.784613\pi$$
0.932132 + 0.362118i $$0.117946\pi$$
$$468$$ 0 0
$$469$$ 850335. 157959.i 0.178508 0.0331597i
$$470$$ −4.41830e6 −0.922594
$$471$$ 0 0
$$472$$ −4.36163e6 7.55456e6i −0.901143 1.56082i
$$473$$ −5.19112e6 8.99129e6i −1.06686 1.84786i
$$474$$ 0 0
$$475$$ 1.62940e6 0.331355
$$476$$ −478078. 559296.i −0.0967123 0.113142i
$$477$$ 0 0
$$478$$ −2.13731e6 + 3.70192e6i −0.427855 + 0.741067i
$$479$$ −1.18608e6 2.05436e6i −0.236198 0.409107i 0.723422 0.690406i $$-0.242568\pi$$
−0.959620 + 0.281299i $$0.909235\pi$$
$$480$$ 0 0
$$481$$ −178944. + 309940.i −0.0352659 + 0.0610823i
$$482$$ 4.78982e6 0.939079
$$483$$ 0 0
$$484$$ −2.78625e6 −0.540639
$$485$$ 3.31466e6 5.74116e6i 0.639859 1.10827i
$$486$$ 0 0
$$487$$ −334534. 579430.i −0.0639172 0.110708i 0.832296 0.554332i $$-0.187026\pi$$
−0.896213 + 0.443624i $$0.853693\pi$$
$$488$$ 2.27520e6 3.94076e6i 0.432484 0.749084i
$$489$$ 0 0
$$490$$ 546751. 3.47034e6i 0.102873 0.652954i
$$491$$ −9.58134e6 −1.79359 −0.896794 0.442448i $$-0.854110\pi$$
−0.896794 + 0.442448i $$0.854110\pi$$
$$492$$ 0 0
$$493$$ 2.15686e6 + 3.73579e6i 0.399673 + 0.692254i
$$494$$ −2.71918e6 4.70976e6i −0.501326 0.868322i
$$495$$ 0 0
$$496$$ −1.60493e6 −0.292921
$$497$$ −1.08541e6 + 3.06909e6i −0.197108 + 0.557338i
$$498$$ 0 0
$$499$$ 1.08902e6 1.88625e6i 0.195788 0.339115i −0.751370 0.659881i $$-0.770607\pi$$
0.947159 + 0.320766i $$0.103940\pi$$
$$500$$ −764991. 1.32500e6i −0.136846 0.237024i
$$501$$ 0 0
$$502$$ 520746. 901959.i 0.0922289 0.159745i
$$503$$ −5.11108e6 −0.900726 −0.450363 0.892846i $$-0.648705\pi$$
−0.450363 + 0.892846i $$0.648705\pi$$
$$504$$ 0 0
$$505$$ 4.78470e6 0.834885
$$506$$ −1.81819e6 + 3.14920e6i −0.315692 + 0.546794i
$$507$$ 0 0
$$508$$ 383576. + 664373.i 0.0659465 + 0.114223i
$$509$$ −3.54335e6 + 6.13725e6i −0.606204 + 1.04998i 0.385656 + 0.922643i $$0.373975\pi$$
−0.991860 + 0.127334i $$0.959358\pi$$
$$510$$ 0 0
$$511$$ −1.20769e6 + 224341.i −0.204599 + 0.0380064i
$$512$$ 6.38385e6 1.07624
$$513$$ 0 0
$$514$$ −3.86031e6 6.68624e6i −0.644487 1.11628i
$$515$$ 1.29714e6 + 2.24671e6i 0.215510 + 0.373275i
$$516$$ 0 0
$$517$$ −1.50260e7 −2.47239
$$518$$ 251850. 46783.8i 0.0412400 0.00766075i
$$519$$ 0 0
$$520$$ −3.71099e6 + 6.42762e6i −0.601841 + 1.04242i
$$521$$ 1.72694e6 + 2.99114e6i 0.278729 + 0.482772i 0.971069 0.238799i $$-0.0767536\pi$$
−0.692340 + 0.721571i $$0.743420\pi$$
$$522$$ 0 0
$$523$$ 278599. 482548.i 0.0445375 0.0771413i −0.842897 0.538074i $$-0.819152\pi$$
0.887435 + 0.460933i $$0.152485\pi$$
$$524$$ 1.70831e6 0.271793
$$525$$ 0 0
$$526$$ 1.41350e6 0.222757
$$527$$ −804494. + 1.39342e6i −0.126182 + 0.218553i
$$528$$ 0 0
$$529$$ 2.67092e6 + 4.62617e6i 0.414975 + 0.718758i
$$530$$ −11205.3 + 19408.1i −0.00173274 + 0.00300119i
$$531$$ 0 0
$$532$$ 439320. 1.24221e6i 0.0672979 0.190290i
$$533$$ 1.58450e7 2.41588
$$534$$ 0 0
$$535$$ 2.40541e6 + 4.16629e6i 0.363333 + 0.629311i
$$536$$ 653901. + 1.13259e6i 0.0983106 + 0.170279i
$$537$$ 0 0
$$538$$ −9.99851e6 −1.48929
$$539$$ 1.85942e6 1.18021e7i 0.275681 1.74980i
$$540$$ 0 0
$$541$$ −2.39364e6 + 4.14591e6i −0.351614 + 0.609013i −0.986532 0.163566i $$-0.947700\pi$$
0.634919 + 0.772579i $$0.281034\pi$$
$$542$$ −1.48143e6 2.56592e6i −0.216613 0.375184i
$$543$$ 0 0
$$544$$ 1.00030e6 1.73257e6i 0.144921 0.251011i
$$545$$ −325901. −0.0469997
$$546$$ 0 0
$$547$$ 2.30360e6 0.329184 0.164592 0.986362i $$-0.447369\pi$$
0.164592 + 0.986362i $$0.447369\pi$$
$$548$$ −389226. + 674159.i −0.0553669 + 0.0958984i
$$549$$ 0 0
$$550$$ 2.25479e6 + 3.90541e6i 0.317833 + 0.550503i
$$551$$ −3.86242e6 + 6.68991e6i −0.541977 + 0.938732i
$$552$$ 0 0
$$553$$ −2.23024e6 2.60912e6i −0.310126 0.362811i
$$554$$ −5.97866e6 −0.827617
$$555$$ 0 0
$$556$$ −1.62659e6 2.81734e6i −0.223147 0.386502i
$$557$$ 6.94253e6 + 1.20248e7i 0.948156 + 1.64225i 0.749305 + 0.662225i $$0.230388\pi$$
0.198851 + 0.980030i $$0.436279\pi$$
$$558$$ 0 0
$$559$$ −1.29344e7 −1.75072
$$560$$ 3.81185e6 708090.i 0.513648 0.0954154i
$$561$$ 0 0
$$562$$ −1.56270e6 + 2.70668e6i −0.208706 + 0.361490i
$$563$$ −1.97962e6 3.42880e6i −0.263215 0.455902i 0.703879 0.710320i $$-0.251450\pi$$
−0.967094 + 0.254417i $$0.918116\pi$$
$$564$$ 0 0
$$565$$ 887042. 1.53640e6i 0.116902 0.202481i
$$566$$ −2.31595e6 −0.303870
$$567$$ 0 0
$$568$$ −4.92250e6 −0.640199
$$569$$ −4.75540e6 + 8.23659e6i −0.615752 + 1.06651i 0.374500 + 0.927227i $$0.377815\pi$$
−0.990252 + 0.139287i $$0.955519\pi$$
$$570$$ 0 0
$$571$$ 4.53978e6 + 7.86313e6i 0.582699 + 1.00926i 0.995158 + 0.0982881i $$0.0313367\pi$$
−0.412459 + 0.910976i $$0.635330\pi$$
$$572$$ −2.54743e6 + 4.41228e6i −0.325546 + 0.563862i
$$573$$ 0 0
$$574$$ −7.36897e6 8.62085e6i −0.933528 1.09212i
$$575$$ −1.35732e6 −0.171204
$$576$$ 0 0
$$577$$ 1.79193e6 + 3.10371e6i 0.224069 + 0.388099i 0.956040 0.293237i $$-0.0947326\pi$$
−0.731971 + 0.681336i $$0.761399\pi$$
$$578$$ −2.26876e6 3.92962e6i −0.282468 0.489250i
$$579$$ 0 0
$$580$$ 2.12797e6 0.262661
$$581$$ 323934. 915945.i 0.0398121 0.112572i
$$582$$ 0 0
$$583$$ −38107.6 + 66004.3i −0.00464344 + 0.00804268i
$$584$$ −928706. 1.60857e6i −0.112680 0.195167i
$$585$$ 0 0
$$586$$ 2.02742e6 3.51160e6i 0.243894 0.422436i
$$587$$ 6.14848e6 0.736499 0.368250 0.929727i $$-0.379957\pi$$
0.368250 + 0.929727i $$0.379957\pi$$
$$588$$ 0 0
$$589$$ −2.88131e6 −0.342218
$$590$$ 4.65077e6 8.05536e6i 0.550040 0.952698i
$$591$$ 0 0
$$592$$ 141346. + 244819.i 0.0165760 + 0.0287105i
$$593$$ 6.64979e6 1.15178e7i 0.776554 1.34503i −0.157363 0.987541i $$-0.550299\pi$$
0.933917 0.357490i $$-0.116367\pi$$
$$594$$ 0 0
$$595$$ 1.29597e6 3.66445e6i 0.150073 0.424343i
$$596$$ −609373. −0.0702697
$$597$$ 0 0
$$598$$ 2.26513e6 + 3.92332e6i 0.259024 + 0.448643i
$$599$$ 2.30732e6 + 3.99639e6i 0.262748 + 0.455094i 0.966971 0.254885i $$-0.0820377\pi$$
−0.704223 + 0.709979i $$0.748704\pi$$
$$600$$ 0 0
$$601$$ 8.17563e6 0.923284 0.461642 0.887066i $$-0.347260\pi$$
0.461642 + 0.887066i $$0.347260\pi$$
$$602$$ 6.01532e6 + 7.03723e6i 0.676500 + 0.791426i
$$603$$ 0 0
$$604$$ −1.98509e6 + 3.43828e6i −0.221405 + 0.383485i
$$605$$ −7.35941e6 1.27469e7i −0.817437 1.41584i
$$606$$ 0 0
$$607$$ 2.18494e6 3.78443e6i 0.240696 0.416897i −0.720217 0.693749i $$-0.755958\pi$$
0.960913 + 0.276852i $$0.0892911\pi$$
$$608$$ 3.58259e6 0.393041
$$609$$ 0 0
$$610$$ 4.85205e6 0.527960
$$611$$ −9.35983e6 + 1.62117e7i −1.01430 + 1.75681i
$$612$$ 0 0
$$613$$ −2.72460e6 4.71914e6i −0.292854 0.507238i 0.681629 0.731698i $$-0.261272\pi$$
−0.974483 + 0.224460i $$0.927938\pi$$
$$614$$ 4.00244e6 6.93243e6i 0.428453 0.742103i
$$615$$ 0 0
$$616$$ 1.77625e7 3.29957e6i 1.88605 0.350352i
$$617$$ −1.32758e7 −1.40394 −0.701969 0.712208i $$-0.747695\pi$$
−0.701969 + 0.712208i $$0.747695\pi$$
$$618$$ 0 0
$$619$$ 2.23142e6 + 3.86494e6i 0.234075 + 0.405430i 0.959004 0.283394i $$-0.0914605\pi$$
−0.724928 + 0.688824i $$0.758127\pi$$
$$620$$ 396859. + 687381.i 0.0414627 + 0.0718155i
$$621$$ 0 0
$$622$$ 2.97018e6 0.307827
$$623$$ −2.70997e6 3.17036e6i −0.279734 0.327256i
$$624$$ 0 0
$$625$$ 2.01399e6 3.48834e6i 0.206233 0.357206i
$$626$$ 3.85789e6 + 6.68206e6i 0.393472 + 0.681514i
$$627$$ 0 0
$$628$$ −1.86541e6 + 3.23098e6i −0.188744 + 0.326915i
$$629$$ 283408. 0.0285618
$$630$$ 0 0
$$631$$ 8.00421e6 0.800286 0.400143 0.916453i $$-0.368960\pi$$
0.400143 + 0.916453i $$0.368960\pi$$
$$632$$ 2.59510e6 4.49485e6i 0.258441 0.447634i
$$633$$ 0 0
$$634$$ 5.34634e6 + 9.26014e6i 0.528243 + 0.914943i
$$635$$ −2.02630e6 + 3.50965e6i −0.199420 + 0.345406i
$$636$$ 0 0
$$637$$ −1.15752e7 9.35780e6i −1.13026 0.913746i
$$638$$ −2.13796e7 −2.07944
$$639$$ 0 0
$$640$$ 1.84616e6 + 3.19764e6i 0.178164 + 0.308588i
$$641$$ −1.94455e6 3.36806e6i −0.186928 0.323768i 0.757297 0.653071i $$-0.226520\pi$$
−0.944224 + 0.329303i $$0.893186\pi$$
$$642$$ 0 0
$$643$$ −1.77478e7 −1.69285 −0.846423 0.532511i $$-0.821249\pi$$
−0.846423 + 0.532511i $$0.821249\pi$$
$$644$$ −365962. + 1.03479e6i −0.0347714 + 0.0983186i
$$645$$ 0 0
$$646$$ −2.15329e6 + 3.72961e6i −0.203012 + 0.351627i
$$647$$ −4.36138e6 7.55413e6i −0.409603 0.709453i 0.585242 0.810858i $$-0.300999\pi$$
−0.994845 + 0.101405i $$0.967666\pi$$
$$648$$ 0 0
$$649$$ 1.58166e7 2.73952e7i 1.47401 2.55307i
$$650$$ 5.61811e6 0.521563
$$651$$ 0 0
$$652$$ 3.87185e6 0.356697
$$653$$ 714958. 1.23834e6i 0.0656141 0.113647i −0.831352 0.555746i $$-0.812433\pi$$
0.896966 + 0.442099i $$0.145766\pi$$
$$654$$ 0 0
$$655$$ 4.51220e6 + 7.81536e6i 0.410946 + 0.711780i
$$656$$ 6.25793e6 1.08391e7i 0.567769 0.983404i
$$657$$ 0 0
$$658$$ 1.31733e7 2.44707e6i 1.18612 0.220334i
$$659$$ 9.20182e6 0.825392 0.412696 0.910869i $$-0.364587\pi$$
0.412696 + 0.910869i $$0.364587\pi$$
$$660$$ 0 0
$$661$$ −717566. 1.24286e6i −0.0638790 0.110642i 0.832317 0.554300i $$-0.187014\pi$$
−0.896196 + 0.443658i $$0.853681\pi$$
$$662$$ −6.76878e6 1.17239e7i −0.600296 1.03974i
$$663$$ 0 0
$$664$$ 1.46908e6 0.129308
$$665$$ 6.84339e6 1.27123e6i 0.600091 0.111473i
$$666$$ 0 0
$$667$$ 3.21748e6 5.57283e6i 0.280028 0.485022i
$$668$$ −2.01850e6 3.49615e6i −0.175020 0.303144i
$$669$$ 0 0
$$670$$ −697249. + 1.20767e6i −0.0600069 + 0.103935i
$$671$$ 1.65012e7 1.41484
$$672$$ 0 0
$$673$$ 2.10985e7 1.79562 0.897808 0.440388i $$-0.145159\pi$$
0.897808 + 0.440388i $$0.145159\pi$$
$$674$$ −5.99423e6 + 1.03823e7i −0.508258 + 0.880328i
$$675$$ 0 0
$$676$$ 1.67127e6 + 2.89472e6i 0.140663 + 0.243635i
$$677$$ −1.16835e7 + 2.02364e7i −0.979720 + 1.69692i −0.316333 + 0.948648i $$0.602452\pi$$
−0.663387 + 0.748276i $$0.730882\pi$$
$$678$$ 0 0
$$679$$ −6.70300e6 + 1.89532e7i −0.557949 + 1.57764i
$$680$$ 5.87740e6 0.487431
$$681$$ 0 0
$$682$$ −3.98721e6 6.90606e6i −0.328253 0.568551i
$$683$$ 6.67445e6 + 1.15605e7i 0.547474 + 0.948253i 0.998447 + 0.0557153i $$0.0177439\pi$$
−0.450972 + 0.892538i $$0.648923\pi$$
$$684$$ 0 0
$$685$$ −4.11229e6 −0.334856
$$686$$ 291894. + 1.06497e7i 0.0236818 + 0.864029i
$$687$$ 0 0
$$688$$ −5.10838e6 + 8.84797e6i −0.411445 + 0.712644i
$$689$$ 47475.1 + 82229.2i 0.00380993 + 0.00659900i
$$690$$ 0 0
$$691$$ −6.57343e6 + 1.13855e7i −0.523717 + 0.907105i 0.475901 + 0.879499i $$0.342122\pi$$
−0.999619 + 0.0276066i $$0.991211\pi$$
$$692$$ −2.10928e6 −0.167444
$$693$$ 0 0
$$694$$ −7.24137e6 −0.570718
$$695$$ 8.59271e6 1.48830e7i 0.674789 1.16877i
$$696$$ 0 0
$$697$$ −6.27377e6 1.08665e7i −0.489155 0.847242i
$$698$$ −3.14501e6 + 5.44732e6i −0.244334 + 0.423199i
$$699$$ 0 0
$$700$$ 884421. + 1.03467e6i 0.0682204 + 0.0798100i
$$701$$ 7.87304e6 0.605128 0.302564 0.953129i $$-0.402157\pi$$
0.302564 + 0.953129i $$0.402157\pi$$
$$702$$ 0 0
$$703$$ 253758. + 439522.i 0.0193657 + 0.0335423i
$$704$$ 1.29143e7 + 2.23683e7i 0.982065 + 1.70099i
$$705$$ 0 0
$$706$$ 1.10075e7 0.831144
$$707$$ −1.42657e7 + 2.65000e6i −1.07336 + 0.199387i
$$708$$ 0 0
$$709$$ 7.47288e6 1.29434e7i 0.558306 0.967014i −0.439332 0.898325i $$-0.644785\pi$$
0.997638 0.0686895i $$-0.0218818\pi$$
$$710$$ −2.62441e6 4.54561e6i −0.195383 0.338413i
$$711$$ 0 0
$$712$$ 3.15333e6 5.46172e6i 0.233114 0.403766i
$$713$$ 2.40019e6 0.176816
$$714$$ 0 0
$$715$$ −2.69144e7 −1.96888
$$716$$ 2.15837e6 3.73840e6i 0.157341 0.272523i
$$717$$ 0 0
$$718$$ 1.77456e6 + 3.07363e6i 0.128464 + 0.222506i
$$719$$ 177912. 308153.i 0.0128347 0.0222303i −0.859537 0.511074i $$-0.829248\pi$$
0.872371 + 0.488844i $$0.162581\pi$$
$$720$$ 0 0
$$721$$ −5.11178e6 5.98020e6i −0.366214 0.428428i
$$722$$ 4.39487e6 0.313764
$$723$$ 0 0
$$724$$ 751795. + 1.30215e6i 0.0533032 + 0.0923238i
$$725$$ −3.99009e6 6.91103e6i −0.281927 0.488312i
$$726$$ 0 0
$$727$$ −1.16451e7 −0.817160 −0.408580 0.912722i $$-0.633976\pi$$
−0.408580 + 0.912722i $$0.633976\pi$$
$$728$$ 7.50447e6 2.12194e7i 0.524797 1.48390i
$$729$$ 0 0
$$730$$ 990272. 1.71520e6i 0.0687776 0.119126i
$$731$$ 5.12130e6 + 8.87036e6i 0.354476 + 0.613971i
$$732$$ 0 0
$$733$$ −7.84459e6 + 1.35872e7i −0.539275 + 0.934052i 0.459668 + 0.888091i $$0.347968\pi$$
−0.998943 + 0.0459613i $$0.985365\pi$$
$$734$$ −1.67595e7 −1.14821
$$735$$ 0 0
$$736$$ −2.98437e6 −0.203076
$$737$$ −2.37125e6 + 4.10712e6i −0.160808 + 0.278528i
$$738$$ 0 0
$$739$$ −7.48534e6 1.29650e7i −0.504197 0.873295i −0.999988 0.00485312i $$-0.998455\pi$$
0.495791 0.868442i $$-0.334878\pi$$
$$740$$ 69903.1 121076.i 0.00469264 0.00812789i
$$741$$ 0 0
$$742$$ 22659.6 64071.8i 0.00151093 0.00427225i
$$743$$ 1.51503e7 1.00682 0.503408 0.864049i $$-0.332079\pi$$
0.503408 + 0.864049i $$0.332079\pi$$
$$744$$ 0 0
$$745$$ −1.60955e6 2.78783e6i −0.106247 0.184025i
$$746$$ −2.67223e6 4.62844e6i −0.175803 0.304500i
$$747$$ 0 0
$$748$$ 4.03457e6 0.263660
$$749$$ −9.47929e6 1.10897e7i −0.617406 0.722294i
$$750$$ 0 0
$$751$$ −1.06857e7 + 1.85082e7i −0.691359 + 1.19747i 0.280034 + 0.959990i $$0.409654\pi$$
−0.971393 + 0.237478i $$0.923679\pi$$
$$752$$ 7.39325e6 + 1.28055e7i 0.476750 + 0.825756i
$$753$$ 0 0
$$754$$ −1.33175e7 + 2.30666e7i −0.853089 + 1.47759i
$$755$$ −2.09731e7 −1.33905
$$756$$ 0 0
$$757$$ −1.74578e7 −1.10726 −0.553632 0.832762i $$-0.686758\pi$$
−0.553632 + 0.832762i $$0.686758\pi$$
$$758$$ −7.15286e6 + 1.23891e7i −0.452175 + 0.783190i
$$759$$ 0 0
$$760$$ 5.26251e6 + 9.11494e6i 0.330491 + 0.572426i
$$761$$ 6.12587e6 1.06103e7i 0.383448 0.664151i −0.608105 0.793857i $$-0.708070\pi$$
0.991553 + 0.129706i $$0.0414033\pi$$
$$762$$ 0 0
$$763$$ 971682. 180500.i 0.0604245 0.0112245i
$$764$$ 5.73633e6 0.355550
$$765$$ 0 0
$$766$$ 254090. + 440097.i 0.0156465 + 0.0271004i
$$767$$ −1.97046e7 3.41293e7i −1.20942 2.09479i
$$768$$ 0 0
$$769$$ 7.26941e6 0.443285 0.221643 0.975128i $$-0.428858\pi$$
0.221643 + 0.975128i $$0.428858\pi$$
$$770$$ 1.25169e7 + 1.46434e7i 0.760801 + 0.890050i
$$771$$ 0 0
$$772$$ −2.92751e6 + 5.07060e6i −0.176789 + 0.306208i
$$773$$ 1.01072e6 + 1.75062e6i 0.0608389 + 0.105376i 0.894841 0.446386i $$-0.147289\pi$$
−0.834002 + 0.551762i $$0.813956\pi$$
$$774$$ 0 0
$$775$$ 1.48827e6 2.57777e6i 0.0890080 0.154166i
$$776$$ −3.03990e7 −1.81219