# Properties

 Label 338.8.b.a.337.2 Level $338$ Weight $8$ Character 338.337 Analytic conductor $105.586$ Analytic rank $1$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,8,Mod(337,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("338.337");

S:= CuspForms(chi, 8);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$338 = 2 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 338.b (of order $$2$$, degree $$1$$, 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: $$105.586138614$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 26) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 337.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 338.337 Dual form 338.8.b.a.337.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+8.00000i q^{2} -87.0000 q^{3} -64.0000 q^{4} +321.000i q^{5} -696.000i q^{6} +181.000i q^{7} -512.000i q^{8} +5382.00 q^{9} +O(q^{10})$$ $$q+8.00000i q^{2} -87.0000 q^{3} -64.0000 q^{4} +321.000i q^{5} -696.000i q^{6} +181.000i q^{7} -512.000i q^{8} +5382.00 q^{9} -2568.00 q^{10} -7782.00i q^{11} +5568.00 q^{12} -1448.00 q^{14} -27927.0i q^{15} +4096.00 q^{16} -9069.00 q^{17} +43056.0i q^{18} -37150.0i q^{19} -20544.0i q^{20} -15747.0i q^{21} +62256.0 q^{22} -19008.0 q^{23} +44544.0i q^{24} -24916.0 q^{25} -277965. q^{27} -11584.0i q^{28} +174750. q^{29} +223416. q^{30} +29012.0i q^{31} +32768.0i q^{32} +677034. i q^{33} -72552.0i q^{34} -58101.0 q^{35} -344448. q^{36} -323669. i q^{37} +297200. q^{38} +164352. q^{40} +795312. i q^{41} +125976. q^{42} +314137. q^{43} +498048. i q^{44} +1.72762e6i q^{45} -152064. i q^{46} +447441. i q^{47} -356352. q^{48} +790782. q^{49} -199328. i q^{50} +789003. q^{51} -1.46923e6 q^{53} -2.22372e6i q^{54} +2.49802e6 q^{55} +92672.0 q^{56} +3.23205e6i q^{57} +1.39800e6i q^{58} -1.62777e6i q^{59} +1.78733e6i q^{60} -2.39961e6 q^{61} -232096. q^{62} +974142. i q^{63} -262144. q^{64} -5.41627e6 q^{66} -64066.0i q^{67} +580416. q^{68} +1.65370e6 q^{69} -464808. i q^{70} -322383. i q^{71} -2.75558e6i q^{72} +4.45478e6i q^{73} +2.58935e6 q^{74} +2.16769e6 q^{75} +2.37760e6i q^{76} +1.40854e6 q^{77} +753560. q^{79} +1.31482e6i q^{80} +1.24125e7 q^{81} -6.36250e6 q^{82} -1.21909e6i q^{83} +1.00781e6i q^{84} -2.91115e6i q^{85} +2.51310e6i q^{86} -1.52032e7 q^{87} -3.98438e6 q^{88} -3.39033e6i q^{89} -1.38210e7 q^{90} +1.21651e6 q^{92} -2.52404e6i q^{93} -3.57953e6 q^{94} +1.19252e7 q^{95} -2.85082e6i q^{96} +1.62877e6i q^{97} +6.32626e6i q^{98} -4.18827e7i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 174 q^{3} - 128 q^{4} + 10764 q^{9}+O(q^{10})$$ 2 * q - 174 * q^3 - 128 * q^4 + 10764 * q^9 $$2 q - 174 q^{3} - 128 q^{4} + 10764 q^{9} - 5136 q^{10} + 11136 q^{12} - 2896 q^{14} + 8192 q^{16} - 18138 q^{17} + 124512 q^{22} - 38016 q^{23} - 49832 q^{25} - 555930 q^{27} + 349500 q^{29} + 446832 q^{30} - 116202 q^{35} - 688896 q^{36} + 594400 q^{38} + 328704 q^{40} + 251952 q^{42} + 628274 q^{43} - 712704 q^{48} + 1581564 q^{49} + 1578006 q^{51} - 2938464 q^{53} + 4996044 q^{55} + 185344 q^{56} - 4799216 q^{61} - 464192 q^{62} - 524288 q^{64} - 10832544 q^{66} + 1160832 q^{68} + 3307392 q^{69} + 5178704 q^{74} + 4335384 q^{75} + 2817084 q^{77} + 1507120 q^{79} + 24825042 q^{81} - 12724992 q^{82} - 30406500 q^{87} - 7968768 q^{88} - 27641952 q^{90} + 2433024 q^{92} - 7159056 q^{94} + 23850300 q^{95}+O(q^{100})$$ 2 * q - 174 * q^3 - 128 * q^4 + 10764 * q^9 - 5136 * q^10 + 11136 * q^12 - 2896 * q^14 + 8192 * q^16 - 18138 * q^17 + 124512 * q^22 - 38016 * q^23 - 49832 * q^25 - 555930 * q^27 + 349500 * q^29 + 446832 * q^30 - 116202 * q^35 - 688896 * q^36 + 594400 * q^38 + 328704 * q^40 + 251952 * q^42 + 628274 * q^43 - 712704 * q^48 + 1581564 * q^49 + 1578006 * q^51 - 2938464 * q^53 + 4996044 * q^55 + 185344 * q^56 - 4799216 * q^61 - 464192 * q^62 - 524288 * q^64 - 10832544 * q^66 + 1160832 * q^68 + 3307392 * q^69 + 5178704 * q^74 + 4335384 * q^75 + 2817084 * q^77 + 1507120 * q^79 + 24825042 * q^81 - 12724992 * q^82 - 30406500 * q^87 - 7968768 * q^88 - 27641952 * q^90 + 2433024 * q^92 - 7159056 * q^94 + 23850300 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$$.

 $$n$$ $$171$$ $$\chi(n)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 8.00000i 0.707107i
$$3$$ −87.0000 −1.86035 −0.930175 0.367115i $$-0.880345\pi$$
−0.930175 + 0.367115i $$0.880345\pi$$
$$4$$ −64.0000 −0.500000
$$5$$ 321.000i 1.14844i 0.818699 + 0.574222i $$0.194695\pi$$
−0.818699 + 0.574222i $$0.805305\pi$$
$$6$$ − 696.000i − 1.31547i
$$7$$ 181.000i 0.199451i 0.995015 + 0.0997253i $$0.0317964\pi$$
−0.995015 + 0.0997253i $$0.968204\pi$$
$$8$$ − 512.000i − 0.353553i
$$9$$ 5382.00 2.46091
$$10$$ −2568.00 −0.812073
$$11$$ − 7782.00i − 1.76286i −0.472318 0.881428i $$-0.656583\pi$$
0.472318 0.881428i $$-0.343417\pi$$
$$12$$ 5568.00 0.930175
$$13$$ 0 0
$$14$$ −1448.00 −0.141033
$$15$$ − 27927.0i − 2.13651i
$$16$$ 4096.00 0.250000
$$17$$ −9069.00 −0.447701 −0.223851 0.974623i $$-0.571863\pi$$
−0.223851 + 0.974623i $$0.571863\pi$$
$$18$$ 43056.0i 1.74012i
$$19$$ − 37150.0i − 1.24257i −0.783584 0.621286i $$-0.786611\pi$$
0.783584 0.621286i $$-0.213389\pi$$
$$20$$ − 20544.0i − 0.574222i
$$21$$ − 15747.0i − 0.371048i
$$22$$ 62256.0 1.24653
$$23$$ −19008.0 −0.325753 −0.162877 0.986646i $$-0.552077\pi$$
−0.162877 + 0.986646i $$0.552077\pi$$
$$24$$ 44544.0i 0.657733i
$$25$$ −24916.0 −0.318925
$$26$$ 0 0
$$27$$ −277965. −2.71780
$$28$$ − 11584.0i − 0.0997253i
$$29$$ 174750. 1.33053 0.665264 0.746608i $$-0.268319\pi$$
0.665264 + 0.746608i $$0.268319\pi$$
$$30$$ 223416. 1.51074
$$31$$ 29012.0i 0.174909i 0.996169 + 0.0874544i $$0.0278732\pi$$
−0.996169 + 0.0874544i $$0.972127\pi$$
$$32$$ 32768.0i 0.176777i
$$33$$ 677034.i 3.27953i
$$34$$ − 72552.0i − 0.316572i
$$35$$ −58101.0 −0.229058
$$36$$ −344448. −1.23045
$$37$$ − 323669.i − 1.05050i −0.850949 0.525249i $$-0.823972\pi$$
0.850949 0.525249i $$-0.176028\pi$$
$$38$$ 297200. 0.878630
$$39$$ 0 0
$$40$$ 164352. 0.406036
$$41$$ 795312.i 1.80216i 0.433650 + 0.901081i $$0.357225\pi$$
−0.433650 + 0.901081i $$0.642775\pi$$
$$42$$ 125976. 0.262371
$$43$$ 314137. 0.602531 0.301266 0.953540i $$-0.402591\pi$$
0.301266 + 0.953540i $$0.402591\pi$$
$$44$$ 498048.i 0.881428i
$$45$$ 1.72762e6i 2.82621i
$$46$$ − 152064.i − 0.230342i
$$47$$ 447441.i 0.628627i 0.949319 + 0.314314i $$0.101774\pi$$
−0.949319 + 0.314314i $$0.898226\pi$$
$$48$$ −356352. −0.465088
$$49$$ 790782. 0.960219
$$50$$ − 199328.i − 0.225514i
$$51$$ 789003. 0.832881
$$52$$ 0 0
$$53$$ −1.46923e6 −1.35558 −0.677790 0.735256i $$-0.737062\pi$$
−0.677790 + 0.735256i $$0.737062\pi$$
$$54$$ − 2.22372e6i − 1.92177i
$$55$$ 2.49802e6 2.02454
$$56$$ 92672.0 0.0705165
$$57$$ 3.23205e6i 2.31162i
$$58$$ 1.39800e6i 0.940826i
$$59$$ − 1.62777e6i − 1.03184i −0.856638 0.515918i $$-0.827451\pi$$
0.856638 0.515918i $$-0.172549\pi$$
$$60$$ 1.78733e6i 1.06825i
$$61$$ −2.39961e6 −1.35359 −0.676793 0.736173i $$-0.736631\pi$$
−0.676793 + 0.736173i $$0.736631\pi$$
$$62$$ −232096. −0.123679
$$63$$ 974142.i 0.490829i
$$64$$ −262144. −0.125000
$$65$$ 0 0
$$66$$ −5.41627e6 −2.31898
$$67$$ − 64066.0i − 0.0260235i −0.999915 0.0130118i $$-0.995858\pi$$
0.999915 0.0130118i $$-0.00414189\pi$$
$$68$$ 580416. 0.223851
$$69$$ 1.65370e6 0.606016
$$70$$ − 464808.i − 0.161968i
$$71$$ − 322383.i − 0.106898i −0.998571 0.0534488i $$-0.982979\pi$$
0.998571 0.0534488i $$-0.0170214\pi$$
$$72$$ − 2.75558e6i − 0.870061i
$$73$$ 4.45478e6i 1.34028i 0.742233 + 0.670141i $$0.233767\pi$$
−0.742233 + 0.670141i $$0.766233\pi$$
$$74$$ 2.58935e6 0.742814
$$75$$ 2.16769e6 0.593312
$$76$$ 2.37760e6i 0.621286i
$$77$$ 1.40854e6 0.351603
$$78$$ 0 0
$$79$$ 753560. 0.171958 0.0859791 0.996297i $$-0.472598\pi$$
0.0859791 + 0.996297i $$0.472598\pi$$
$$80$$ 1.31482e6i 0.287111i
$$81$$ 1.24125e7 2.59515
$$82$$ −6.36250e6 −1.27432
$$83$$ − 1.21909e6i − 0.234025i −0.993130 0.117013i $$-0.962668\pi$$
0.993130 0.117013i $$-0.0373318\pi$$
$$84$$ 1.00781e6i 0.185524i
$$85$$ − 2.91115e6i − 0.514160i
$$86$$ 2.51310e6i 0.426054i
$$87$$ −1.52032e7 −2.47525
$$88$$ −3.98438e6 −0.623264
$$89$$ − 3.39033e6i − 0.509773i −0.966971 0.254887i $$-0.917962\pi$$
0.966971 0.254887i $$-0.0820381\pi$$
$$90$$ −1.38210e7 −1.99843
$$91$$ 0 0
$$92$$ 1.21651e6 0.162877
$$93$$ − 2.52404e6i − 0.325392i
$$94$$ −3.57953e6 −0.444507
$$95$$ 1.19252e7 1.42702
$$96$$ − 2.85082e6i − 0.328867i
$$97$$ 1.62877e6i 0.181201i 0.995887 + 0.0906003i $$0.0288786\pi$$
−0.995887 + 0.0906003i $$0.971121\pi$$
$$98$$ 6.32626e6i 0.678978i
$$99$$ − 4.18827e7i − 4.33822i
$$100$$ 1.59462e6 0.159462
$$101$$ 1.53503e7 1.48249 0.741244 0.671236i $$-0.234236\pi$$
0.741244 + 0.671236i $$0.234236\pi$$
$$102$$ 6.31202e6i 0.588936i
$$103$$ −6.87643e6 −0.620058 −0.310029 0.950727i $$-0.600339\pi$$
−0.310029 + 0.950727i $$0.600339\pi$$
$$104$$ 0 0
$$105$$ 5.05479e6 0.426128
$$106$$ − 1.17539e7i − 0.958539i
$$107$$ −1.52027e7 −1.19971 −0.599857 0.800107i $$-0.704776\pi$$
−0.599857 + 0.800107i $$0.704776\pi$$
$$108$$ 1.77898e7 1.35890
$$109$$ 6.73260e6i 0.497955i 0.968509 + 0.248978i $$0.0800946\pi$$
−0.968509 + 0.248978i $$0.919905\pi$$
$$110$$ 1.99842e7i 1.43157i
$$111$$ 2.81592e7i 1.95429i
$$112$$ 741376.i 0.0498627i
$$113$$ −1.15292e7 −0.751667 −0.375833 0.926687i $$-0.622644\pi$$
−0.375833 + 0.926687i $$0.622644\pi$$
$$114$$ −2.58564e7 −1.63456
$$115$$ − 6.10157e6i − 0.374110i
$$116$$ −1.11840e7 −0.665264
$$117$$ 0 0
$$118$$ 1.30222e7 0.729619
$$119$$ − 1.64149e6i − 0.0892943i
$$120$$ −1.42986e7 −0.755370
$$121$$ −4.10724e7 −2.10766
$$122$$ − 1.91969e7i − 0.957130i
$$123$$ − 6.91921e7i − 3.35266i
$$124$$ − 1.85677e6i − 0.0874544i
$$125$$ 1.70801e7i 0.782177i
$$126$$ −7.79314e6 −0.347069
$$127$$ −2.06699e7 −0.895418 −0.447709 0.894179i $$-0.647760\pi$$
−0.447709 + 0.894179i $$0.647760\pi$$
$$128$$ − 2.09715e6i − 0.0883883i
$$129$$ −2.73299e7 −1.12092
$$130$$ 0 0
$$131$$ −1.90949e7 −0.742107 −0.371054 0.928611i $$-0.621003\pi$$
−0.371054 + 0.928611i $$0.621003\pi$$
$$132$$ − 4.33302e7i − 1.63977i
$$133$$ 6.72415e6 0.247832
$$134$$ 512528. 0.0184014
$$135$$ − 8.92268e7i − 3.12124i
$$136$$ 4.64333e6i 0.158286i
$$137$$ − 2.96901e7i − 0.986482i −0.869893 0.493241i $$-0.835812\pi$$
0.869893 0.493241i $$-0.164188\pi$$
$$138$$ 1.32296e7i 0.428518i
$$139$$ 1.55652e7 0.491591 0.245795 0.969322i $$-0.420951\pi$$
0.245795 + 0.969322i $$0.420951\pi$$
$$140$$ 3.71846e6 0.114529
$$141$$ − 3.89274e7i − 1.16947i
$$142$$ 2.57906e6 0.0755880
$$143$$ 0 0
$$144$$ 2.20447e7 0.615226
$$145$$ 5.60948e7i 1.52804i
$$146$$ −3.56383e7 −0.947723
$$147$$ −6.87980e7 −1.78635
$$148$$ 2.07148e7i 0.525249i
$$149$$ − 2.49675e6i − 0.0618334i −0.999522 0.0309167i $$-0.990157\pi$$
0.999522 0.0309167i $$-0.00984266\pi$$
$$150$$ 1.73415e7i 0.419535i
$$151$$ − 2.39802e7i − 0.566804i −0.959001 0.283402i $$-0.908537\pi$$
0.959001 0.283402i $$-0.0914630\pi$$
$$152$$ −1.90208e7 −0.439315
$$153$$ −4.88094e7 −1.10175
$$154$$ 1.12683e7i 0.248621i
$$155$$ −9.31285e6 −0.200873
$$156$$ 0 0
$$157$$ 1.70550e7 0.351725 0.175863 0.984415i $$-0.443729\pi$$
0.175863 + 0.984415i $$0.443729\pi$$
$$158$$ 6.02848e6i 0.121593i
$$159$$ 1.27823e8 2.52185
$$160$$ −1.05185e7 −0.203018
$$161$$ − 3.44045e6i − 0.0649717i
$$162$$ 9.93002e7i 1.83505i
$$163$$ 7.34586e7i 1.32857i 0.747477 + 0.664287i $$0.231265\pi$$
−0.747477 + 0.664287i $$0.768735\pi$$
$$164$$ − 5.09000e7i − 0.901081i
$$165$$ −2.17328e8 −3.76636
$$166$$ 9.75274e6 0.165481
$$167$$ − 4.66860e7i − 0.775674i −0.921728 0.387837i $$-0.873222\pi$$
0.921728 0.387837i $$-0.126778\pi$$
$$168$$ −8.06246e6 −0.131185
$$169$$ 0 0
$$170$$ 2.32892e7 0.363566
$$171$$ − 1.99941e8i − 3.05785i
$$172$$ −2.01048e7 −0.301266
$$173$$ 7.80931e7 1.14670 0.573352 0.819309i $$-0.305643\pi$$
0.573352 + 0.819309i $$0.305643\pi$$
$$174$$ − 1.21626e8i − 1.75027i
$$175$$ − 4.50980e6i − 0.0636098i
$$176$$ − 3.18751e7i − 0.440714i
$$177$$ 1.41616e8i 1.91958i
$$178$$ 2.71226e7 0.360464
$$179$$ 5.56163e7 0.724797 0.362399 0.932023i $$-0.381958\pi$$
0.362399 + 0.932023i $$0.381958\pi$$
$$180$$ − 1.10568e8i − 1.41311i
$$181$$ 1.19435e8 1.49711 0.748557 0.663070i $$-0.230747\pi$$
0.748557 + 0.663070i $$0.230747\pi$$
$$182$$ 0 0
$$183$$ 2.08766e8 2.51815
$$184$$ 9.73210e6i 0.115171i
$$185$$ 1.03898e8 1.20644
$$186$$ 2.01924e7 0.230087
$$187$$ 7.05750e7i 0.789233i
$$188$$ − 2.86362e7i − 0.314314i
$$189$$ − 5.03117e7i − 0.542066i
$$190$$ 9.54012e7i 1.00906i
$$191$$ 1.05485e8 1.09540 0.547700 0.836675i $$-0.315504\pi$$
0.547700 + 0.836675i $$0.315504\pi$$
$$192$$ 2.28065e7 0.232544
$$193$$ − 2.12059e7i − 0.212327i −0.994349 0.106164i $$-0.966143\pi$$
0.994349 0.106164i $$-0.0338567\pi$$
$$194$$ −1.30302e7 −0.128128
$$195$$ 0 0
$$196$$ −5.06100e7 −0.480110
$$197$$ − 1.66535e8i − 1.55194i −0.630771 0.775969i $$-0.717261\pi$$
0.630771 0.775969i $$-0.282739\pi$$
$$198$$ 3.35062e8 3.06759
$$199$$ 1.26351e8 1.13656 0.568279 0.822836i $$-0.307609\pi$$
0.568279 + 0.822836i $$0.307609\pi$$
$$200$$ 1.27570e7i 0.112757i
$$201$$ 5.57374e6i 0.0484129i
$$202$$ 1.22802e8i 1.04828i
$$203$$ 3.16298e7i 0.265375i
$$204$$ −5.04962e7 −0.416441
$$205$$ −2.55295e8 −2.06968
$$206$$ − 5.50114e7i − 0.438448i
$$207$$ −1.02301e8 −0.801648
$$208$$ 0 0
$$209$$ −2.89101e8 −2.19047
$$210$$ 4.04383e7i 0.301318i
$$211$$ 1.08571e8 0.795655 0.397828 0.917460i $$-0.369764\pi$$
0.397828 + 0.917460i $$0.369764\pi$$
$$212$$ 9.40308e7 0.677790
$$213$$ 2.80473e7i 0.198867i
$$214$$ − 1.21622e8i − 0.848326i
$$215$$ 1.00838e8i 0.691974i
$$216$$ 1.42318e8i 0.960886i
$$217$$ −5.25117e6 −0.0348857
$$218$$ −5.38608e7 −0.352108
$$219$$ − 3.87566e8i − 2.49340i
$$220$$ −1.59873e8 −1.01227
$$221$$ 0 0
$$222$$ −2.25274e8 −1.38189
$$223$$ − 1.25603e8i − 0.758459i −0.925303 0.379229i $$-0.876189\pi$$
0.925303 0.379229i $$-0.123811\pi$$
$$224$$ −5.93101e6 −0.0352582
$$225$$ −1.34098e8 −0.784844
$$226$$ − 9.22338e7i − 0.531509i
$$227$$ 1.90774e8i 1.08250i 0.840861 + 0.541252i $$0.182049\pi$$
−0.840861 + 0.541252i $$0.817951\pi$$
$$228$$ − 2.06851e8i − 1.15581i
$$229$$ 5.28911e7i 0.291044i 0.989355 + 0.145522i $$0.0464861\pi$$
−0.989355 + 0.145522i $$0.953514\pi$$
$$230$$ 4.88125e7 0.264536
$$231$$ −1.22543e8 −0.654104
$$232$$ − 8.94720e7i − 0.470413i
$$233$$ −1.51254e8 −0.783359 −0.391680 0.920102i $$-0.628106\pi$$
−0.391680 + 0.920102i $$0.628106\pi$$
$$234$$ 0 0
$$235$$ −1.43629e8 −0.721944
$$236$$ 1.04177e8i 0.515918i
$$237$$ −6.55597e7 −0.319903
$$238$$ 1.31319e7 0.0631406
$$239$$ 2.61917e8i 1.24100i 0.784208 + 0.620498i $$0.213070\pi$$
−0.784208 + 0.620498i $$0.786930\pi$$
$$240$$ − 1.14389e8i − 0.534127i
$$241$$ 1.31752e8i 0.606312i 0.952941 + 0.303156i $$0.0980404\pi$$
−0.952941 + 0.303156i $$0.901960\pi$$
$$242$$ − 3.28579e8i − 1.49034i
$$243$$ −4.71980e8 −2.11009
$$244$$ 1.53575e8 0.676793
$$245$$ 2.53841e8i 1.10276i
$$246$$ 5.53537e8 2.37069
$$247$$ 0 0
$$248$$ 1.48541e7 0.0618396
$$249$$ 1.06061e8i 0.435370i
$$250$$ −1.36641e8 −0.553083
$$251$$ −2.47061e8 −0.986159 −0.493080 0.869984i $$-0.664129\pi$$
−0.493080 + 0.869984i $$0.664129\pi$$
$$252$$ − 6.23451e7i − 0.245415i
$$253$$ 1.47920e8i 0.574256i
$$254$$ − 1.65359e8i − 0.633156i
$$255$$ 2.53270e8i 0.956518i
$$256$$ 1.67772e7 0.0625000
$$257$$ −2.27286e8 −0.835231 −0.417616 0.908624i $$-0.637134\pi$$
−0.417616 + 0.908624i $$0.637134\pi$$
$$258$$ − 2.18639e8i − 0.792610i
$$259$$ 5.85841e7 0.209522
$$260$$ 0 0
$$261$$ 9.40504e8 3.27430
$$262$$ − 1.52759e8i − 0.524749i
$$263$$ −4.25872e8 −1.44356 −0.721779 0.692124i $$-0.756675\pi$$
−0.721779 + 0.692124i $$0.756675\pi$$
$$264$$ 3.46641e8 1.15949
$$265$$ − 4.71623e8i − 1.55681i
$$266$$ 5.37932e7i 0.175243i
$$267$$ 2.94959e8i 0.948357i
$$268$$ 4.10022e6i 0.0130118i
$$269$$ −5.14154e8 −1.61050 −0.805250 0.592936i $$-0.797969\pi$$
−0.805250 + 0.592936i $$0.797969\pi$$
$$270$$ 7.13814e8 2.20705
$$271$$ − 4.57096e7i − 0.139513i −0.997564 0.0697565i $$-0.977778\pi$$
0.997564 0.0697565i $$-0.0222222\pi$$
$$272$$ −3.71466e7 −0.111925
$$273$$ 0 0
$$274$$ 2.37521e8 0.697548
$$275$$ 1.93896e8i 0.562218i
$$276$$ −1.05837e8 −0.303008
$$277$$ 2.73964e8 0.774487 0.387244 0.921977i $$-0.373427\pi$$
0.387244 + 0.921977i $$0.373427\pi$$
$$278$$ 1.24522e8i 0.347607i
$$279$$ 1.56143e8i 0.430434i
$$280$$ 2.97477e7i 0.0809842i
$$281$$ − 4.21707e8i − 1.13381i −0.823784 0.566903i $$-0.808141\pi$$
0.823784 0.566903i $$-0.191859\pi$$
$$282$$ 3.11419e8 0.826938
$$283$$ −3.81957e8 −1.00176 −0.500878 0.865518i $$-0.666990\pi$$
−0.500878 + 0.865518i $$0.666990\pi$$
$$284$$ 2.06325e7i 0.0534488i
$$285$$ −1.03749e9 −2.65477
$$286$$ 0 0
$$287$$ −1.43951e8 −0.359443
$$288$$ 1.76357e8i 0.435031i
$$289$$ −3.28092e8 −0.799564
$$290$$ −4.48758e8 −1.08049
$$291$$ − 1.41703e8i − 0.337097i
$$292$$ − 2.85106e8i − 0.670141i
$$293$$ 4.04833e8i 0.940240i 0.882602 + 0.470120i $$0.155789\pi$$
−0.882602 + 0.470120i $$0.844211\pi$$
$$294$$ − 5.50384e8i − 1.26314i
$$295$$ 5.22514e8 1.18501
$$296$$ −1.65719e8 −0.371407
$$297$$ 2.16312e9i 4.79108i
$$298$$ 1.99740e7 0.0437228
$$299$$ 0 0
$$300$$ −1.38732e8 −0.296656
$$301$$ 5.68588e7i 0.120175i
$$302$$ 1.91841e8 0.400791
$$303$$ −1.33547e9 −2.75795
$$304$$ − 1.52166e8i − 0.310643i
$$305$$ − 7.70274e8i − 1.55452i
$$306$$ − 3.90475e8i − 0.779055i
$$307$$ 4.75520e7i 0.0937960i 0.998900 + 0.0468980i $$0.0149336\pi$$
−0.998900 + 0.0468980i $$0.985066\pi$$
$$308$$ −9.01467e7 −0.175801
$$309$$ 5.98249e8 1.15353
$$310$$ − 7.45028e7i − 0.142039i
$$311$$ 3.02841e8 0.570892 0.285446 0.958395i $$-0.407858\pi$$
0.285446 + 0.958395i $$0.407858\pi$$
$$312$$ 0 0
$$313$$ −6.31685e8 −1.16438 −0.582191 0.813052i $$-0.697804\pi$$
−0.582191 + 0.813052i $$0.697804\pi$$
$$314$$ 1.36440e8i 0.248707i
$$315$$ −3.12700e8 −0.563690
$$316$$ −4.82278e7 −0.0859791
$$317$$ 7.93332e8i 1.39877i 0.714743 + 0.699387i $$0.246544\pi$$
−0.714743 + 0.699387i $$0.753456\pi$$
$$318$$ 1.02259e9i 1.78322i
$$319$$ − 1.35990e9i − 2.34553i
$$320$$ − 8.41482e7i − 0.143556i
$$321$$ 1.32264e9 2.23189
$$322$$ 2.75236e7 0.0459420
$$323$$ 3.36913e8i 0.556300i
$$324$$ −7.94401e8 −1.29757
$$325$$ 0 0
$$326$$ −5.87669e8 −0.939444
$$327$$ − 5.85737e8i − 0.926372i
$$328$$ 4.07200e8 0.637161
$$329$$ −8.09868e7 −0.125380
$$330$$ − 1.73862e9i − 2.66322i
$$331$$ − 1.21628e9i − 1.84346i −0.387829 0.921731i $$-0.626775\pi$$
0.387829 0.921731i $$-0.373225\pi$$
$$332$$ 7.80219e7i 0.117013i
$$333$$ − 1.74199e9i − 2.58518i
$$334$$ 3.73488e8 0.548484
$$335$$ 2.05652e7 0.0298866
$$336$$ − 6.44997e7i − 0.0927620i
$$337$$ 1.51221e8 0.215232 0.107616 0.994193i $$-0.465678\pi$$
0.107616 + 0.994193i $$0.465678\pi$$
$$338$$ 0 0
$$339$$ 1.00304e9 1.39836
$$340$$ 1.86314e8i 0.257080i
$$341$$ 2.25771e8 0.308339
$$342$$ 1.59953e9 2.16223
$$343$$ 2.92193e8i 0.390967i
$$344$$ − 1.60838e8i − 0.213027i
$$345$$ 5.30836e8i 0.695975i
$$346$$ 6.24745e8i 0.810842i
$$347$$ −5.97234e8 −0.767347 −0.383673 0.923469i $$-0.625341\pi$$
−0.383673 + 0.923469i $$0.625341\pi$$
$$348$$ 9.73008e8 1.23762
$$349$$ − 1.19600e8i − 0.150606i −0.997161 0.0753029i $$-0.976008\pi$$
0.997161 0.0753029i $$-0.0239924\pi$$
$$350$$ 3.60784e7 0.0449789
$$351$$ 0 0
$$352$$ 2.55001e8 0.311632
$$353$$ − 4.66414e8i − 0.564366i −0.959361 0.282183i $$-0.908942\pi$$
0.959361 0.282183i $$-0.0910585\pi$$
$$354$$ −1.13293e9 −1.35735
$$355$$ 1.03485e8 0.122766
$$356$$ 2.16981e8i 0.254887i
$$357$$ 1.42810e8i 0.166119i
$$358$$ 4.44931e8i 0.512509i
$$359$$ 7.70102e8i 0.878451i 0.898377 + 0.439225i $$0.144747\pi$$
−0.898377 + 0.439225i $$0.855253\pi$$
$$360$$ 8.84542e8 0.999217
$$361$$ −4.86251e8 −0.543983
$$362$$ 9.55477e8i 1.05862i
$$363$$ 3.57329e9 3.92099
$$364$$ 0 0
$$365$$ −1.42999e9 −1.53924
$$366$$ 1.67013e9i 1.78060i
$$367$$ −8.55319e8 −0.903227 −0.451613 0.892214i $$-0.649151\pi$$
−0.451613 + 0.892214i $$0.649151\pi$$
$$368$$ −7.78568e7 −0.0814384
$$369$$ 4.28037e9i 4.43495i
$$370$$ 8.31182e8i 0.853081i
$$371$$ − 2.65931e8i − 0.270371i
$$372$$ 1.61539e8i 0.162696i
$$373$$ −5.29609e8 −0.528414 −0.264207 0.964466i $$-0.585110\pi$$
−0.264207 + 0.964466i $$0.585110\pi$$
$$374$$ −5.64600e8 −0.558072
$$375$$ − 1.48597e9i − 1.45512i
$$376$$ 2.29090e8 0.222253
$$377$$ 0 0
$$378$$ 4.02493e8 0.383299
$$379$$ 1.98358e9i 1.87159i 0.352540 + 0.935797i $$0.385318\pi$$
−0.352540 + 0.935797i $$0.614682\pi$$
$$380$$ −7.63210e8 −0.713512
$$381$$ 1.79828e9 1.66579
$$382$$ 8.43877e8i 0.774564i
$$383$$ 8.98756e8i 0.817422i 0.912664 + 0.408711i $$0.134022\pi$$
−0.912664 + 0.408711i $$0.865978\pi$$
$$384$$ 1.82452e8i 0.164433i
$$385$$ 4.52142e8i 0.403796i
$$386$$ 1.69647e8 0.150138
$$387$$ 1.69069e9 1.48277
$$388$$ − 1.04242e8i − 0.0906003i
$$389$$ −1.82475e9 −1.57174 −0.785868 0.618395i $$-0.787783\pi$$
−0.785868 + 0.618395i $$0.787783\pi$$
$$390$$ 0 0
$$391$$ 1.72384e8 0.145840
$$392$$ − 4.04880e8i − 0.339489i
$$393$$ 1.66125e9 1.38058
$$394$$ 1.33228e9 1.09739
$$395$$ 2.41893e8i 0.197485i
$$396$$ 2.68049e9i 2.16911i
$$397$$ − 4.93083e8i − 0.395506i −0.980252 0.197753i $$-0.936636\pi$$
0.980252 0.197753i $$-0.0633645\pi$$
$$398$$ 1.01081e9i 0.803668i
$$399$$ −5.85001e8 −0.461054
$$400$$ −1.02056e8 −0.0797312
$$401$$ 5.68280e8i 0.440105i 0.975488 + 0.220053i $$0.0706229\pi$$
−0.975488 + 0.220053i $$0.929377\pi$$
$$402$$ −4.45899e7 −0.0342331
$$403$$ 0 0
$$404$$ −9.82417e8 −0.741244
$$405$$ 3.98442e9i 2.98039i
$$406$$ −2.53038e8 −0.187648
$$407$$ −2.51879e9 −1.85188
$$408$$ − 4.03970e8i − 0.294468i
$$409$$ − 1.28472e9i − 0.928489i −0.885707 0.464245i $$-0.846326\pi$$
0.885707 0.464245i $$-0.153674\pi$$
$$410$$ − 2.04236e9i − 1.46349i
$$411$$ 2.58304e9i 1.83520i
$$412$$ 4.40091e8 0.310029
$$413$$ 2.94626e8 0.205801
$$414$$ − 8.18408e8i − 0.566851i
$$415$$ 3.91329e8 0.268765
$$416$$ 0 0
$$417$$ −1.35418e9 −0.914532
$$418$$ − 2.31281e9i − 1.54890i
$$419$$ 2.74847e8 0.182533 0.0912667 0.995826i $$-0.470908\pi$$
0.0912667 + 0.995826i $$0.470908\pi$$
$$420$$ −3.23506e8 −0.213064
$$421$$ 7.51368e8i 0.490756i 0.969428 + 0.245378i $$0.0789120\pi$$
−0.969428 + 0.245378i $$0.921088\pi$$
$$422$$ 8.68568e8i 0.562613i
$$423$$ 2.40813e9i 1.54699i
$$424$$ 7.52247e8i 0.479270i
$$425$$ 2.25963e8 0.142783
$$426$$ −2.24379e8 −0.140620
$$427$$ − 4.34329e8i − 0.269974i
$$428$$ 9.72974e8 0.599857
$$429$$ 0 0
$$430$$ −8.06704e8 −0.489299
$$431$$ − 1.30756e8i − 0.0786668i −0.999226 0.0393334i $$-0.987477\pi$$
0.999226 0.0393334i $$-0.0125234\pi$$
$$432$$ −1.13854e9 −0.679449
$$433$$ −1.66736e9 −0.987010 −0.493505 0.869743i $$-0.664284\pi$$
−0.493505 + 0.869743i $$0.664284\pi$$
$$434$$ − 4.20094e7i − 0.0246679i
$$435$$ − 4.88024e9i − 2.84269i
$$436$$ − 4.30887e8i − 0.248978i
$$437$$ 7.06147e8i 0.404772i
$$438$$ 3.10053e9 1.76310
$$439$$ −2.31478e9 −1.30582 −0.652910 0.757436i $$-0.726452\pi$$
−0.652910 + 0.757436i $$0.726452\pi$$
$$440$$ − 1.27899e9i − 0.715784i
$$441$$ 4.25599e9 2.36301
$$442$$ 0 0
$$443$$ −6.90047e8 −0.377108 −0.188554 0.982063i $$-0.560380\pi$$
−0.188554 + 0.982063i $$0.560380\pi$$
$$444$$ − 1.80219e9i − 0.977147i
$$445$$ 1.08830e9 0.585446
$$446$$ 1.00482e9 0.536311
$$447$$ 2.17217e8i 0.115032i
$$448$$ − 4.74481e7i − 0.0249313i
$$449$$ − 2.63806e9i − 1.37538i −0.726004 0.687690i $$-0.758625\pi$$
0.726004 0.687690i $$-0.241375\pi$$
$$450$$ − 1.07278e9i − 0.554968i
$$451$$ 6.18912e9 3.17695
$$452$$ 7.37870e8 0.375833
$$453$$ 2.08627e9i 1.05445i
$$454$$ −1.52619e9 −0.765445
$$455$$ 0 0
$$456$$ 1.65481e9 0.817280
$$457$$ − 6.16222e8i − 0.302016i −0.988533 0.151008i $$-0.951748\pi$$
0.988533 0.151008i $$-0.0482520\pi$$
$$458$$ −4.23129e8 −0.205799
$$459$$ 2.52086e9 1.21676
$$460$$ 3.90500e8i 0.187055i
$$461$$ 1.23621e9i 0.587679i 0.955855 + 0.293839i $$0.0949330\pi$$
−0.955855 + 0.293839i $$0.905067\pi$$
$$462$$ − 9.80345e8i − 0.462522i
$$463$$ − 6.78469e7i − 0.0317685i −0.999874 0.0158843i $$-0.994944\pi$$
0.999874 0.0158843i $$-0.00505633\pi$$
$$464$$ 7.15776e8 0.332632
$$465$$ 8.10218e8 0.373694
$$466$$ − 1.21003e9i − 0.553919i
$$467$$ 1.17502e9 0.533869 0.266934 0.963715i $$-0.413989\pi$$
0.266934 + 0.963715i $$0.413989\pi$$
$$468$$ 0 0
$$469$$ 1.15959e7 0.00519040
$$470$$ − 1.14903e9i − 0.510491i
$$471$$ −1.48379e9 −0.654332
$$472$$ −8.33418e8 −0.364809
$$473$$ − 2.44461e9i − 1.06218i
$$474$$ − 5.24478e8i − 0.226205i
$$475$$ 9.25629e8i 0.396287i
$$476$$ 1.05055e8i 0.0446471i
$$477$$ −7.90741e9 −3.33595
$$478$$ −2.09533e9 −0.877517
$$479$$ − 3.96154e8i − 0.164699i −0.996604 0.0823494i $$-0.973758\pi$$
0.996604 0.0823494i $$-0.0262423\pi$$
$$480$$ 9.15112e8 0.377685
$$481$$ 0 0
$$482$$ −1.05401e9 −0.428728
$$483$$ 2.99319e8i 0.120870i
$$484$$ 2.62863e9 1.05383
$$485$$ −5.22836e8 −0.208099
$$486$$ − 3.77584e9i − 1.49206i
$$487$$ − 3.03665e9i − 1.19136i −0.803222 0.595680i $$-0.796883\pi$$
0.803222 0.595680i $$-0.203117\pi$$
$$488$$ 1.22860e9i 0.478565i
$$489$$ − 6.39090e9i − 2.47162i
$$490$$ −2.03073e9 −0.779768
$$491$$ 2.91974e9 1.11316 0.556582 0.830793i $$-0.312113\pi$$
0.556582 + 0.830793i $$0.312113\pi$$
$$492$$ 4.42830e9i 1.67633i
$$493$$ −1.58481e9 −0.595679
$$494$$ 0 0
$$495$$ 1.34444e10 4.98221
$$496$$ 1.18833e8i 0.0437272i
$$497$$ 5.83513e7 0.0213208
$$498$$ −8.48488e8 −0.307853
$$499$$ − 1.62343e9i − 0.584898i −0.956281 0.292449i $$-0.905530\pi$$
0.956281 0.292449i $$-0.0944702\pi$$
$$500$$ − 1.09313e9i − 0.391089i
$$501$$ 4.06168e9i 1.44303i
$$502$$ − 1.97649e9i − 0.697320i
$$503$$ 4.75888e9 1.66731 0.833655 0.552285i $$-0.186244\pi$$
0.833655 + 0.552285i $$0.186244\pi$$
$$504$$ 4.98761e8 0.173534
$$505$$ 4.92744e9i 1.70256i
$$506$$ −1.18336e9 −0.406061
$$507$$ 0 0
$$508$$ 1.32288e9 0.447709
$$509$$ − 9.19375e8i − 0.309016i −0.987992 0.154508i $$-0.950621\pi$$
0.987992 0.154508i $$-0.0493792\pi$$
$$510$$ −2.02616e9 −0.676360
$$511$$ −8.06316e8 −0.267320
$$512$$ 1.34218e8i 0.0441942i
$$513$$ 1.03264e10i 3.37706i
$$514$$ − 1.81829e9i − 0.590598i
$$515$$ − 2.20733e9i − 0.712103i
$$516$$ 1.74911e9 0.560460
$$517$$ 3.48199e9 1.10818
$$518$$ 4.68673e8i 0.148155i
$$519$$ −6.79410e9 −2.13327
$$520$$ 0 0
$$521$$ −1.46089e9 −0.452569 −0.226284 0.974061i $$-0.572658\pi$$
−0.226284 + 0.974061i $$0.572658\pi$$
$$522$$ 7.52404e9i 2.31528i
$$523$$ 2.12856e9 0.650624 0.325312 0.945607i $$-0.394531\pi$$
0.325312 + 0.945607i $$0.394531\pi$$
$$524$$ 1.22207e9 0.371054
$$525$$ 3.92352e8i 0.118336i
$$526$$ − 3.40698e9i − 1.02075i
$$527$$ − 2.63110e8i − 0.0783069i
$$528$$ 2.77313e9i 0.819883i
$$529$$ −3.04352e9 −0.893885
$$530$$ 3.77299e9 1.10083
$$531$$ − 8.76066e9i − 2.53925i
$$532$$ −4.30346e8 −0.123916
$$533$$ 0 0
$$534$$ −2.35967e9 −0.670590
$$535$$ − 4.88007e9i − 1.37781i
$$536$$ −3.28018e7 −0.00920070
$$537$$ −4.83862e9 −1.34838
$$538$$ − 4.11323e9i − 1.13879i
$$539$$ − 6.15387e9i − 1.69273i
$$540$$ 5.71051e9i 1.56062i
$$541$$ 1.72479e7i 0.00468324i 0.999997 + 0.00234162i $$0.000745361\pi$$
−0.999997 + 0.00234162i $$0.999255\pi$$
$$542$$ 3.65677e8 0.0986507
$$543$$ −1.03908e10 −2.78516
$$544$$ − 2.97173e8i − 0.0791431i
$$545$$ −2.16117e9 −0.571874
$$546$$ 0 0
$$547$$ 7.51154e8 0.196234 0.0981168 0.995175i $$-0.468718\pi$$
0.0981168 + 0.995175i $$0.468718\pi$$
$$548$$ 1.90016e9i 0.493241i
$$549$$ −1.29147e10 −3.33105
$$550$$ −1.55117e9 −0.397549
$$551$$ − 6.49196e9i − 1.65328i
$$552$$ − 8.46692e8i − 0.214259i
$$553$$ 1.36394e8i 0.0342972i
$$554$$ 2.19171e9i 0.547645i
$$555$$ −9.03910e9 −2.24440
$$556$$ −9.96175e8 −0.245795
$$557$$ − 3.00701e9i − 0.737295i −0.929569 0.368647i $$-0.879821\pi$$
0.929569 0.368647i $$-0.120179\pi$$
$$558$$ −1.24914e9 −0.304363
$$559$$ 0 0
$$560$$ −2.37982e8 −0.0572645
$$561$$ − 6.14002e9i − 1.46825i
$$562$$ 3.37366e9 0.801722
$$563$$ −2.82880e9 −0.668070 −0.334035 0.942561i $$-0.608410\pi$$
−0.334035 + 0.942561i $$0.608410\pi$$
$$564$$ 2.49135e9i 0.584734i
$$565$$ − 3.70088e9i − 0.863248i
$$566$$ − 3.05566e9i − 0.708349i
$$567$$ 2.24667e9i 0.517604i
$$568$$ −1.65060e8 −0.0377940
$$569$$ −7.67290e9 −1.74609 −0.873045 0.487639i $$-0.837858\pi$$
−0.873045 + 0.487639i $$0.837858\pi$$
$$570$$ − 8.29990e9i − 1.87720i
$$571$$ 3.09363e9 0.695411 0.347706 0.937604i $$-0.386961\pi$$
0.347706 + 0.937604i $$0.386961\pi$$
$$572$$ 0 0
$$573$$ −9.17717e9 −2.03783
$$574$$ − 1.15161e9i − 0.254164i
$$575$$ 4.73603e8 0.103891
$$576$$ −1.41086e9 −0.307613
$$577$$ 3.71815e9i 0.805770i 0.915251 + 0.402885i $$0.131993\pi$$
−0.915251 + 0.402885i $$0.868007\pi$$
$$578$$ − 2.62474e9i − 0.565377i
$$579$$ 1.84491e9i 0.395003i
$$580$$ − 3.59006e9i − 0.764019i
$$581$$ 2.20656e8 0.0466765
$$582$$ 1.13363e9 0.238363
$$583$$ 1.14336e10i 2.38969i
$$584$$ 2.28085e9 0.473862
$$585$$ 0 0
$$586$$ −3.23866e9 −0.664850
$$587$$ − 2.74853e9i − 0.560876i −0.959872 0.280438i $$-0.909520\pi$$
0.959872 0.280438i $$-0.0904796\pi$$
$$588$$ 4.40307e9 0.893173
$$589$$ 1.07780e9 0.217337
$$590$$ 4.18011e9i 0.837927i
$$591$$ 1.44886e10i 2.88715i
$$592$$ − 1.32575e9i − 0.262624i
$$593$$ 9.11262e9i 1.79453i 0.441488 + 0.897267i $$0.354451\pi$$
−0.441488 + 0.897267i $$0.645549\pi$$
$$594$$ −1.73050e10 −3.38781
$$595$$ 5.26918e8 0.102550
$$596$$ 1.59792e8i 0.0309167i
$$597$$ −1.09925e10 −2.11440
$$598$$ 0 0
$$599$$ −5.52493e9 −1.05035 −0.525174 0.850995i $$-0.676000\pi$$
−0.525174 + 0.850995i $$0.676000\pi$$
$$600$$ − 1.10986e9i − 0.209767i
$$601$$ −1.78219e9 −0.334883 −0.167441 0.985882i $$-0.553551\pi$$
−0.167441 + 0.985882i $$0.553551\pi$$
$$602$$ −4.54870e8 −0.0849767
$$603$$ − 3.44803e8i − 0.0640414i
$$604$$ 1.53473e9i 0.283402i
$$605$$ − 1.31842e10i − 2.42053i
$$606$$ − 1.06838e10i − 1.95016i
$$607$$ 9.53705e9 1.73083 0.865414 0.501058i $$-0.167056\pi$$
0.865414 + 0.501058i $$0.167056\pi$$
$$608$$ 1.21733e9 0.219658
$$609$$ − 2.75179e9i − 0.493690i
$$610$$ 6.16219e9 1.09921
$$611$$ 0 0
$$612$$ 3.12380e9 0.550875
$$613$$ − 1.18627e9i − 0.208004i −0.994577 0.104002i $$-0.966835\pi$$
0.994577 0.104002i $$-0.0331648\pi$$
$$614$$ −3.80416e8 −0.0663238
$$615$$ 2.22107e10 3.85034
$$616$$ − 7.21174e8i − 0.124310i
$$617$$ 1.32256e9i 0.226682i 0.993556 + 0.113341i $$0.0361552\pi$$
−0.993556 + 0.113341i $$0.963845\pi$$
$$618$$ 4.78599e9i 0.815666i
$$619$$ 3.59450e9i 0.609147i 0.952489 + 0.304573i $$0.0985138\pi$$
−0.952489 + 0.304573i $$0.901486\pi$$
$$620$$ 5.96023e8 0.100437
$$621$$ 5.28356e9 0.885332
$$622$$ 2.42273e9i 0.403681i
$$623$$ 6.13650e8 0.101675
$$624$$ 0 0
$$625$$ −7.42927e9 −1.21721
$$626$$ − 5.05348e9i − 0.823343i
$$627$$ 2.51518e10 4.07505
$$628$$ −1.09152e9 −0.175863
$$629$$ 2.93535e9i 0.470309i
$$630$$ − 2.50160e9i − 0.398589i
$$631$$ − 7.49102e6i − 0.00118697i −1.00000 0.000593483i $$-0.999811\pi$$
1.00000 0.000593483i $$-0.000188911\pi$$
$$632$$ − 3.85823e8i − 0.0607964i
$$633$$ −9.44567e9 −1.48020
$$634$$ −6.34666e9 −0.989083
$$635$$ − 6.63505e9i − 1.02834i
$$636$$ −8.18068e9 −1.26093
$$637$$ 0 0
$$638$$ 1.08792e10 1.65854
$$639$$ − 1.73507e9i − 0.263065i
$$640$$ 6.73186e8 0.101509
$$641$$ −4.06396e9 −0.609462 −0.304731 0.952438i $$-0.598567\pi$$
−0.304731 + 0.952438i $$0.598567\pi$$
$$642$$ 1.05811e10i 1.57818i
$$643$$ 1.56544e6i 0 0.000232219i 1.00000 0.000116109i $$3.69588e-5\pi$$
−1.00000 0.000116109i $$0.999963\pi$$
$$644$$ 2.20189e8i 0.0324859i
$$645$$ − 8.77290e9i − 1.28731i
$$646$$ −2.69531e9 −0.393364
$$647$$ −1.31025e10 −1.90191 −0.950956 0.309325i $$-0.899897\pi$$
−0.950956 + 0.309325i $$0.899897\pi$$
$$648$$ − 6.35521e9i − 0.917524i
$$649$$ −1.26673e10 −1.81898
$$650$$ 0 0
$$651$$ 4.56852e8 0.0648996
$$652$$ − 4.70135e9i − 0.664287i
$$653$$ 7.63326e9 1.07279 0.536394 0.843968i $$-0.319786\pi$$
0.536394 + 0.843968i $$0.319786\pi$$
$$654$$ 4.68589e9 0.655044
$$655$$ − 6.12945e9i − 0.852269i
$$656$$ 3.25760e9i 0.450541i
$$657$$ 2.39756e10i 3.29831i
$$658$$ − 6.47895e8i − 0.0886571i
$$659$$ −9.25900e9 −1.26027 −0.630137 0.776484i $$-0.717001\pi$$
−0.630137 + 0.776484i $$0.717001\pi$$
$$660$$ 1.39090e10 1.88318
$$661$$ − 4.79962e9i − 0.646401i −0.946330 0.323201i $$-0.895241\pi$$
0.946330 0.323201i $$-0.104759\pi$$
$$662$$ 9.73021e9 1.30352
$$663$$ 0 0
$$664$$ −6.24175e8 −0.0827405
$$665$$ 2.15845e9i 0.284621i
$$666$$ 1.39359e10 1.82799
$$667$$ −3.32165e9 −0.433424
$$668$$ 2.98791e9i 0.387837i
$$669$$ 1.09274e10i 1.41100i
$$670$$ 1.64521e8i 0.0211330i
$$671$$ 1.86737e10i 2.38618i
$$672$$ 5.15998e8 0.0655927
$$673$$ 1.08997e10 1.37836 0.689182 0.724589i $$-0.257970\pi$$
0.689182 + 0.724589i $$0.257970\pi$$
$$674$$ 1.20977e9i 0.152192i
$$675$$ 6.92578e9 0.866773
$$676$$ 0 0
$$677$$ 3.44099e9 0.426210 0.213105 0.977029i $$-0.431642\pi$$
0.213105 + 0.977029i $$0.431642\pi$$
$$678$$ 8.02434e9i 0.988793i
$$679$$ −2.94808e8 −0.0361406
$$680$$ −1.49051e9 −0.181783
$$681$$ − 1.65974e10i − 2.01384i
$$682$$ 1.80617e9i 0.218029i
$$683$$ − 5.53553e9i − 0.664794i −0.943140 0.332397i $$-0.892143\pi$$
0.943140 0.332397i $$-0.107857\pi$$
$$684$$ 1.27962e10i 1.52892i
$$685$$ 9.53051e9 1.13292
$$686$$ −2.33754e9 −0.276455
$$687$$ − 4.60153e9i − 0.541444i
$$688$$ 1.28671e9 0.150633
$$689$$ 0 0
$$690$$ −4.24669e9 −0.492129
$$691$$ 4.21595e8i 0.0486097i 0.999705 + 0.0243048i $$0.00773723\pi$$
−0.999705 + 0.0243048i $$0.992263\pi$$
$$692$$ −4.99796e9 −0.573352
$$693$$ 7.58077e9 0.865261
$$694$$ − 4.77788e9i − 0.542596i
$$695$$ 4.99644e9i 0.564565i
$$696$$ 7.78406e9i 0.875133i
$$697$$ − 7.21268e9i − 0.806830i
$$698$$ 9.56799e8 0.106494
$$699$$ 1.31591e10 1.45732
$$700$$ 2.88627e8i 0.0318049i
$$701$$ 5.14995e9 0.564663 0.282332 0.959317i $$-0.408892\pi$$
0.282332 + 0.959317i $$0.408892\pi$$
$$702$$ 0 0
$$703$$ −1.20243e10 −1.30532
$$704$$ 2.04000e9i 0.220357i
$$705$$ 1.24957e10 1.34307
$$706$$ 3.73132e9 0.399067
$$707$$ 2.77840e9i 0.295683i
$$708$$ − 9.06342e9i − 0.959789i
$$709$$ − 1.05683e10i − 1.11363i −0.830635 0.556817i $$-0.812022\pi$$
0.830635 0.556817i $$-0.187978\pi$$
$$710$$ 8.27880e8i 0.0868086i
$$711$$ 4.05566e9 0.423173
$$712$$ −1.73585e9 −0.180232
$$713$$ − 5.51460e8i − 0.0569772i
$$714$$ −1.14248e9 −0.117464
$$715$$ 0 0
$$716$$ −3.55944e9 −0.362399
$$717$$ − 2.27868e10i − 2.30869i
$$718$$ −6.16081e9 −0.621159
$$719$$ −1.53690e10 −1.54204 −0.771020 0.636811i $$-0.780253\pi$$
−0.771020 + 0.636811i $$0.780253\pi$$
$$720$$ 7.07634e9i 0.706553i
$$721$$ − 1.24463e9i − 0.123671i
$$722$$ − 3.89001e9i − 0.384654i
$$723$$ − 1.14624e10i − 1.12795i
$$724$$ −7.64381e9 −0.748557
$$725$$ −4.35407e9 −0.424339
$$726$$ 2.85864e10i 2.77256i
$$727$$ −4.88599e9 −0.471609 −0.235804 0.971801i $$-0.575772\pi$$
−0.235804 + 0.971801i $$0.575772\pi$$
$$728$$ 0 0
$$729$$ 1.39161e10 1.33036
$$730$$ − 1.14399e10i − 1.08841i
$$731$$ −2.84891e9 −0.269754
$$732$$ −1.33610e10 −1.25907
$$733$$ 3.59889e9i 0.337524i 0.985657 + 0.168762i $$0.0539769\pi$$
−0.985657 + 0.168762i $$0.946023\pi$$
$$734$$ − 6.84255e9i − 0.638678i
$$735$$ − 2.20842e10i − 2.05152i
$$736$$ − 6.22854e8i − 0.0575856i
$$737$$ −4.98562e8 −0.0458757
$$738$$ −3.42430e10 −3.13598
$$739$$ − 2.78886e9i − 0.254198i −0.991890 0.127099i $$-0.959433\pi$$
0.991890 0.127099i $$-0.0405666\pi$$
$$740$$ −6.64946e9 −0.603219
$$741$$ 0 0
$$742$$ 2.12745e9 0.191181
$$743$$ − 3.08130e9i − 0.275597i −0.990460 0.137798i $$-0.955997\pi$$
0.990460 0.137798i $$-0.0440026\pi$$
$$744$$ −1.29231e9 −0.115043
$$745$$ 8.01457e8 0.0710122
$$746$$ − 4.23687e9i − 0.373645i
$$747$$ − 6.56115e9i − 0.575915i
$$748$$ − 4.51680e9i − 0.394616i
$$749$$ − 2.75169e9i − 0.239284i
$$750$$ 1.18877e10 1.02893
$$751$$ 6.41281e8 0.0552470 0.0276235 0.999618i $$-0.491206\pi$$
0.0276235 + 0.999618i $$0.491206\pi$$
$$752$$ 1.83272e9i 0.157157i
$$753$$ 2.14943e10 1.83460
$$754$$ 0 0
$$755$$ 7.69763e9 0.650943
$$756$$ 3.21995e9i 0.271033i
$$757$$ −1.60219e10 −1.34239 −0.671195 0.741280i $$-0.734219\pi$$
−0.671195 + 0.741280i $$0.734219\pi$$
$$758$$ −1.58686e10 −1.32342
$$759$$ − 1.28691e10i − 1.06832i
$$760$$ − 6.10568e9i − 0.504529i
$$761$$ 5.73623e9i 0.471824i 0.971774 + 0.235912i $$0.0758077\pi$$
−0.971774 + 0.235912i $$0.924192\pi$$
$$762$$ 1.43863e10i 1.17789i
$$763$$ −1.21860e9 −0.0993175
$$764$$ −6.75102e9 −0.547700
$$765$$ − 1.56678e10i − 1.26530i
$$766$$ −7.19005e9 −0.578005
$$767$$ 0 0
$$768$$ −1.45962e9 −0.116272
$$769$$ 2.45874e10i 1.94971i 0.222832 + 0.974857i $$0.428470\pi$$
−0.222832 + 0.974857i $$0.571530\pi$$
$$770$$ −3.61714e9 −0.285527
$$771$$ 1.97739e10 1.55382
$$772$$ 1.35718e9i 0.106164i
$$773$$ − 1.31517e10i − 1.02413i −0.858947 0.512065i $$-0.828881\pi$$
0.858947 0.512065i $$-0.171119\pi$$
$$774$$ 1.35255e10i 1.04848i
$$775$$ − 7.22863e8i − 0.0557828i
$$776$$ 8.33932e8 0.0640641
$$777$$ −5.09682e9 −0.389785
$$778$$ − 1.45980e10i − 1.11138i
$$779$$ 2.95458e10 2.23932
$$780$$ 0 0
$$781$$ −2.50878e9 −0.188445
$$782$$ 1.37907e9i 0.103125i
$$783$$ −4.85744e10 −3.61611
$$784$$ 3.23904e9 0.240055
$$785$$ 5.47466e9i 0.403937i
$$786$$ 1.32900e10i 0.976218i
$$787$$ 7.38863e9i 0.540322i 0.962815 + 0.270161i $$0.0870769\pi$$
−0.962815 + 0.270161i $$0.912923\pi$$
$$788$$ 1.06583e10i 0.775969i
$$789$$ 3.70509e10 2.68552
$$790$$ −1.93514e9 −0.139643
$$791$$ − 2.08679e9i − 0.149920i
$$792$$ −2.14440e10 −1.53379
$$793$$ 0 0
$$794$$ 3.94467e9 0.279665
$$795$$ 4.10312e10i 2.89621i
$$796$$ −8.08645e9 −0.568279
$$797$$ 5.22399e9 0.365509 0.182754 0.983159i $$-0.441499\pi$$
0.182754 + 0.983159i $$0.441499\pi$$
$$798$$ − 4.68001e9i − 0.326014i
$$799$$ − 4.05784e9i − 0.281437i
$$800$$ − 8.16447e8i − 0.0563785i
$$801$$ − 1.82468e10i − 1.25450i
$$802$$ −4.54624e9 −0.311202
$$803$$ 3.46671e10 2.36273
$$804$$ − 3.56719e8i − 0.0242064i
$$805$$ 1.10438e9 0.0746164
$$806$$ 0 0
$$807$$ 4.47314e10 2.99609
$$808$$ − 7.85934e9i − 0.524139i
$$809$$ −7.92102e9 −0.525970 −0.262985 0.964800i $$-0.584707\pi$$
−0.262985 + 0.964800i $$0.584707\pi$$
$$810$$ −3.18754e10 −2.10745
$$811$$ − 8.16607e9i − 0.537576i −0.963199 0.268788i $$-0.913377\pi$$
0.963199 0.268788i $$-0.0866232\pi$$
$$812$$ − 2.02430e9i − 0.132687i
$$813$$ 3.97674e9i 0.259543i
$$814$$ − 2.01503e10i − 1.30947i
$$815$$ −2.35802e10 −1.52579
$$816$$ 3.23176e9 0.208220
$$817$$ − 1.16702e10i − 0.748688i
$$818$$ 1.02778e10 0.656541
$$819$$ 0 0
$$820$$ 1.63389e10 1.03484
$$821$$ 2.63749e10i 1.66338i 0.555244 + 0.831688i $$0.312625\pi$$
−0.555244 + 0.831688i $$0.687375\pi$$
$$822$$ −2.06643e10 −1.29768
$$823$$ −2.04085e10 −1.27618 −0.638090 0.769962i $$-0.720275\pi$$
−0.638090 + 0.769962i $$0.720275\pi$$
$$824$$ 3.52073e9i 0.219224i
$$825$$ − 1.68690e10i − 1.04592i
$$826$$ 2.35701e9i 0.145523i
$$827$$ 2.55307e10i 1.56962i 0.619738 + 0.784809i $$0.287239\pi$$
−0.619738 + 0.784809i $$0.712761\pi$$
$$828$$ 6.54727e9 0.400824
$$829$$ −8.48208e9 −0.517085 −0.258542 0.966000i $$-0.583242\pi$$
−0.258542 + 0.966000i $$0.583242\pi$$
$$830$$ 3.13063e9i 0.190046i
$$831$$ −2.38349e10 −1.44082
$$832$$ 0 0
$$833$$ −7.17160e9 −0.429891
$$834$$ − 1.08334e10i − 0.646672i
$$835$$ 1.49862e10 0.890819
$$836$$ 1.85025e10 1.09524
$$837$$ − 8.06432e9i − 0.475367i
$$838$$ 2.19878e9i 0.129071i
$$839$$ 2.29323e10i 1.34055i 0.742115 + 0.670273i $$0.233823\pi$$
−0.742115 + 0.670273i $$0.766177\pi$$
$$840$$ − 2.58805e9i − 0.150659i
$$841$$ 1.32877e10 0.770306
$$842$$ −6.01094e9 −0.347017
$$843$$ 3.66885e10i 2.10928i
$$844$$ −6.94854e9 −0.397828
$$845$$ 0 0
$$846$$ −1.92650e10 −1.09389
$$847$$ − 7.43410e9i − 0.420374i
$$848$$ −6.01797e9 −0.338895
$$849$$ 3.32303e10 1.86362
$$850$$ 1.80771e9i 0.100963i
$$851$$ 6.15230e9i 0.342203i
$$852$$ − 1.79503e9i − 0.0994335i
$$853$$ − 2.47175e10i − 1.36358i −0.731546 0.681792i $$-0.761201\pi$$
0.731546 0.681792i $$-0.238799\pi$$
$$854$$ 3.47463e9 0.190900
$$855$$ 6.41812e10 3.51177
$$856$$ 7.78379e9i 0.424163i
$$857$$ −1.19081e10 −0.646265 −0.323133 0.946354i $$-0.604736\pi$$
−0.323133 + 0.946354i $$0.604736\pi$$
$$858$$ 0 0
$$859$$ −4.94214e9 −0.266035 −0.133018 0.991114i $$-0.542467\pi$$
−0.133018 + 0.991114i $$0.542467\pi$$
$$860$$ − 6.45363e9i − 0.345987i
$$861$$ 1.25238e10 0.668689
$$862$$ 1.04605e9 0.0556259
$$863$$ − 2.05387e10i − 1.08776i −0.839162 0.543881i $$-0.816954\pi$$
0.839162 0.543881i $$-0.183046\pi$$
$$864$$ − 9.10836e9i − 0.480443i
$$865$$ 2.50679e10i 1.31693i
$$866$$ − 1.33389e10i − 0.697921i
$$867$$ 2.85440e10 1.48747
$$868$$ 3.36075e8 0.0174428
$$869$$ − 5.86420e9i − 0.303138i
$$870$$ 3.90419e10 2.01008
$$871$$ 0 0
$$872$$ 3.44709e9 0.176054
$$873$$ 8.76606e9i 0.445918i
$$874$$ −5.64918e9 −0.286217
$$875$$ −3.09150e9 −0.156006
$$876$$ 2.48042e10i 1.24670i
$$877$$ − 1.42584e10i − 0.713791i −0.934144 0.356895i $$-0.883835\pi$$
0.934144 0.356895i $$-0.116165\pi$$
$$878$$ − 1.85182e10i − 0.923354i
$$879$$ − 3.52204e10i − 1.74918i
$$880$$ 1.02319e10 0.506136
$$881$$ −1.78398e10 −0.878971 −0.439486 0.898250i $$-0.644839\pi$$
−0.439486 + 0.898250i $$0.644839\pi$$
$$882$$ 3.40479e10i 1.67090i
$$883$$ −3.79954e10 −1.85724 −0.928622 0.371028i $$-0.879005\pi$$
−0.928622 + 0.371028i $$0.879005\pi$$
$$884$$ 0 0
$$885$$ −4.54587e10 −2.20453
$$886$$ − 5.52038e9i − 0.266656i
$$887$$ 8.45195e7 0.00406653 0.00203327 0.999998i $$-0.499353\pi$$
0.00203327 + 0.999998i $$0.499353\pi$$
$$888$$ 1.44175e10 0.690947
$$889$$ − 3.74126e9i − 0.178592i
$$890$$ 8.70637e9i 0.413973i
$$891$$ − 9.65942e10i − 4.57488i
$$892$$ 8.03857e9i 0.379229i
$$893$$ 1.66224e10 0.781114
$$894$$ −1.73774e9 −0.0813398
$$895$$ 1.78528e10i 0.832390i
$$896$$ 3.79585e8 0.0176291
$$897$$ 0 0
$$898$$ 2.11045e10 0.972541
$$899$$ 5.06985e9i 0.232721i
$$900$$ 8.58227e9 0.392422
$$901$$ 1.33245e10 0.606894
$$902$$ 4.95129e10i 2.24645i
$$903$$ − 4.94672e9i − 0.223568i
$$904$$ 5.90296e9i 0.265754i
$$905$$ 3.83385e10i 1.71935i
$$906$$ −1.66902e10 −0.745611
$$907$$ −1.82024e10 −0.810033 −0.405017 0.914309i $$-0.632734\pi$$
−0.405017 + 0.914309i $$0.632734\pi$$
$$908$$ − 1.22096e10i − 0.541252i
$$909$$ 8.26151e10 3.64826
$$910$$ 0 0
$$911$$ −3.66963e10 −1.60808 −0.804040 0.594575i $$-0.797320\pi$$
−0.804040 + 0.594575i $$0.797320\pi$$
$$912$$ 1.32385e10i 0.577905i
$$913$$ −9.48697e9 −0.412553
$$914$$ 4.92978e9 0.213558
$$915$$ 6.70139e10i 2.89195i
$$916$$ − 3.38503e9i − 0.145522i
$$917$$ − 3.45617e9i − 0.148014i
$$918$$ 2.01669e10i 0.860380i
$$919$$ 1.33474e10 0.567275 0.283638 0.958932i $$-0.408459\pi$$
0.283638 + 0.958932i $$0.408459\pi$$
$$920$$ −3.12400e9 −0.132268
$$921$$ − 4.13702e9i − 0.174493i
$$922$$ −9.88970e9 −0.415552
$$923$$ 0 0
$$924$$ 7.84276e9 0.327052
$$925$$ 8.06454e9i 0.335030i
$$926$$ 5.42775e8 0.0224637
$$927$$ −3.70089e10 −1.52591
$$928$$ 5.72621e9i 0.235206i
$$929$$ 2.71771e10i 1.11211i 0.831146 + 0.556055i $$0.187686\pi$$
−0.831146 + 0.556055i $$0.812314\pi$$
$$930$$ 6.48174e9i 0.264242i
$$931$$ − 2.93776e10i − 1.19314i
$$932$$ 9.68025e9 0.391680
$$933$$ −2.63472e10 −1.06206
$$934$$ 9.40012e9i 0.377502i
$$935$$ −2.26546e10 −0.906390
$$936$$ 0 0
$$937$$ 4.04333e10 1.60565 0.802825 0.596214i $$-0.203329\pi$$
0.802825 + 0.596214i $$0.203329\pi$$
$$938$$ 9.27676e7i 0.00367017i
$$939$$ 5.49566e10 2.16616
$$940$$ 9.19223e9 0.360972
$$941$$ − 8.49843e9i − 0.332487i −0.986085 0.166244i $$-0.946836\pi$$
0.986085 0.166244i $$-0.0531638\pi$$
$$942$$ − 1.18703e10i − 0.462683i
$$943$$ − 1.51173e10i − 0.587061i
$$944$$ − 6.66735e9i − 0.257959i
$$945$$ 1.61500e10 0.622533
$$946$$ 1.95569e10 0.751072
$$947$$ 4.40082e9i 0.168387i 0.996449 + 0.0841935i $$0.0268314\pi$$
−0.996449 + 0.0841935i $$0.973169\pi$$
$$948$$ 4.19582e9 0.159951
$$949$$ 0 0
$$950$$ −7.40504e9 −0.280217
$$951$$ − 6.90199e10i − 2.60221i
$$952$$ −8.40442e8 −0.0315703
$$953$$ 1.73133e10 0.647970 0.323985 0.946062i $$-0.394977\pi$$
0.323985 + 0.946062i $$0.394977\pi$$
$$954$$ − 6.32593e10i − 2.35887i
$$955$$ 3.38606e10i 1.25801i
$$956$$ − 1.67627e10i − 0.620498i
$$957$$ 1.18312e11i 4.36351i
$$958$$ 3.16924e9 0.116460
$$959$$ 5.37390e9 0.196754
$$960$$ 7.32090e9i 0.267064i
$$961$$ 2.66709e10 0.969407
$$962$$ 0 0
$$963$$ −8.18210e10 −2.95238
$$964$$ − 8.43211e9i − 0.303156i
$$965$$ 6.80708e9 0.243846
$$966$$ −2.39455e9 −0.0854681
$$967$$ 1.40918e10i 0.501158i 0.968096 + 0.250579i $$0.0806210\pi$$
−0.968096 + 0.250579i $$0.919379\pi$$
$$968$$ 2.10290e10i 0.745171i
$$969$$ − 2.93115e10i − 1.03491i
$$970$$ − 4.18269e9i − 0.147148i
$$971$$ −7.27843e9 −0.255135 −0.127568 0.991830i $$-0.540717\pi$$
−0.127568 + 0.991830i $$0.540717\pi$$
$$972$$ 3.02067e10 1.05505
$$973$$ 2.81731e9i 0.0980481i
$$974$$ 2.42932e10 0.842419
$$975$$ 0 0
$$976$$ −9.82879e9 −0.338397
$$977$$ 2.43791e10i 0.836348i 0.908367 + 0.418174i $$0.137330\pi$$
−0.908367 + 0.418174i $$0.862670\pi$$
$$978$$ 5.11272e10 1.74770
$$979$$ −2.63835e10 −0.898657
$$980$$ − 1.62458e10i − 0.551379i
$$981$$ 3.62349e10i 1.22542i
$$982$$ 2.33579e10i 0.787126i
$$983$$ − 4.06556e10i − 1.36516i −0.730811 0.682579i $$-0.760858\pi$$
0.730811 0.682579i $$-0.239142\pi$$
$$984$$ −3.54264e10 −1.18534
$$985$$ 5.34578e10 1.78231
$$986$$ − 1.26785e10i − 0.421209i
$$987$$ 7.04585e9 0.233251
$$988$$ 0 0
$$989$$ −5.97112e9 −0.196277
$$990$$ 1.07555e11i 3.52295i
$$991$$ −4.86636e10 −1.58835 −0.794175 0.607689i $$-0.792097\pi$$
−0.794175 + 0.607689i $$0.792097\pi$$
$$992$$ −9.50665e8 −0.0309198
$$993$$ 1.05816e11i 3.42949i
$$994$$ 4.66811e8i 0.0150761i
$$995$$ 4.05586e10i 1.30527i
$$996$$ − 6.78790e9i − 0.217685i
$$997$$ −1.76682e10 −0.564622 −0.282311 0.959323i $$-0.591101\pi$$
−0.282311 + 0.959323i $$0.591101\pi$$
$$998$$ 1.29874e10 0.413586
$$999$$ 8.99687e10i 2.85504i
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 338.8.b.a.337.2 2
13.5 odd 4 26.8.a.b.1.1 1
13.8 odd 4 338.8.a.a.1.1 1
13.12 even 2 inner 338.8.b.a.337.1 2
39.5 even 4 234.8.a.a.1.1 1
52.31 even 4 208.8.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
26.8.a.b.1.1 1 13.5 odd 4
208.8.a.e.1.1 1 52.31 even 4
234.8.a.a.1.1 1 39.5 even 4
338.8.a.a.1.1 1 13.8 odd 4
338.8.b.a.337.1 2 13.12 even 2 inner
338.8.b.a.337.2 2 1.1 even 1 trivial