# Properties

 Label 338.8.b.b.337.1 Level $338$ Weight $8$ Character 338.337 Analytic conductor $105.586$ Analytic rank $0$ 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: $$0$$ 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 337.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 338.337 Dual form 338.8.b.b.337.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-8.00000i q^{2} -39.0000 q^{3} -64.0000 q^{4} +385.000i q^{5} +312.000i q^{6} +293.000i q^{7} +512.000i q^{8} -666.000 q^{9} +O(q^{10})$$ $$q-8.00000i q^{2} -39.0000 q^{3} -64.0000 q^{4} +385.000i q^{5} +312.000i q^{6} +293.000i q^{7} +512.000i q^{8} -666.000 q^{9} +3080.00 q^{10} +5402.00i q^{11} +2496.00 q^{12} +2344.00 q^{14} -15015.0i q^{15} +4096.00 q^{16} +21011.0 q^{17} +5328.00i q^{18} -27326.0i q^{19} -24640.0i q^{20} -11427.0i q^{21} +43216.0 q^{22} +63072.0 q^{23} -19968.0i q^{24} -70100.0 q^{25} +111267. q^{27} -18752.0i q^{28} +122238. q^{29} -120120. q^{30} -208396. i q^{31} -32768.0i q^{32} -210678. i q^{33} -168088. i q^{34} -112805. q^{35} +42624.0 q^{36} +442379. i q^{37} -218608. q^{38} -197120. q^{40} +58000.0i q^{41} -91416.0 q^{42} +202025. q^{43} -345728. i q^{44} -256410. i q^{45} -504576. i q^{46} -588511. i q^{47} -159744. q^{48} +737694. q^{49} +560800. i q^{50} -819429. q^{51} +1.68434e6 q^{53} -890136. i q^{54} -2.07977e6 q^{55} -150016. q^{56} +1.06571e6i q^{57} -977904. i q^{58} +442630. i q^{59} +960960. i q^{60} -1.08361e6 q^{61} -1.66717e6 q^{62} -195138. i q^{63} -262144. q^{64} -1.68542e6 q^{66} +3.44349e6i q^{67} -1.34470e6 q^{68} -2.45981e6 q^{69} +902440. i q^{70} +2.08470e6i q^{71} -340992. i q^{72} -5.93789e6i q^{73} +3.53903e6 q^{74} +2.73390e6 q^{75} +1.74886e6i q^{76} -1.58279e6 q^{77} -6.60926e6 q^{79} +1.57696e6i q^{80} -2.88287e6 q^{81} +464000. q^{82} -142740. i q^{83} +731328. i q^{84} +8.08924e6i q^{85} -1.61620e6i q^{86} -4.76728e6 q^{87} -2.76582e6 q^{88} +6.98529e6i q^{89} -2.05128e6 q^{90} -4.03661e6 q^{92} +8.12744e6i q^{93} -4.70809e6 q^{94} +1.05205e7 q^{95} +1.27795e6i q^{96} -200762. i q^{97} -5.90155e6i q^{98} -3.59773e6i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 78 q^{3} - 128 q^{4} - 1332 q^{9}+O(q^{10})$$ 2 * q - 78 * q^3 - 128 * q^4 - 1332 * q^9 $$2 q - 78 q^{3} - 128 q^{4} - 1332 q^{9} + 6160 q^{10} + 4992 q^{12} + 4688 q^{14} + 8192 q^{16} + 42022 q^{17} + 86432 q^{22} + 126144 q^{23} - 140200 q^{25} + 222534 q^{27} + 244476 q^{29} - 240240 q^{30} - 225610 q^{35} + 85248 q^{36} - 437216 q^{38} - 394240 q^{40} - 182832 q^{42} + 404050 q^{43} - 319488 q^{48} + 1475388 q^{49} - 1638858 q^{51} + 3368672 q^{53} - 4159540 q^{55} - 300032 q^{56} - 2167216 q^{61} - 3334336 q^{62} - 524288 q^{64} - 3370848 q^{66} - 2689408 q^{68} - 4919616 q^{69} + 7078064 q^{74} + 5467800 q^{75} - 3165572 q^{77} - 13218512 q^{79} - 5765742 q^{81} + 928000 q^{82} - 9534564 q^{87} - 5531648 q^{88} - 4102560 q^{90} - 8073216 q^{92} - 9416176 q^{94} + 21041020 q^{95}+O(q^{100})$$ 2 * q - 78 * q^3 - 128 * q^4 - 1332 * q^9 + 6160 * q^10 + 4992 * q^12 + 4688 * q^14 + 8192 * q^16 + 42022 * q^17 + 86432 * q^22 + 126144 * q^23 - 140200 * q^25 + 222534 * q^27 + 244476 * q^29 - 240240 * q^30 - 225610 * q^35 + 85248 * q^36 - 437216 * q^38 - 394240 * q^40 - 182832 * q^42 + 404050 * q^43 - 319488 * q^48 + 1475388 * q^49 - 1638858 * q^51 + 3368672 * q^53 - 4159540 * q^55 - 300032 * q^56 - 2167216 * q^61 - 3334336 * q^62 - 524288 * q^64 - 3370848 * q^66 - 2689408 * q^68 - 4919616 * q^69 + 7078064 * q^74 + 5467800 * q^75 - 3165572 * q^77 - 13218512 * q^79 - 5765742 * q^81 + 928000 * q^82 - 9534564 * q^87 - 5531648 * q^88 - 4102560 * q^90 - 8073216 * q^92 - 9416176 * q^94 + 21041020 * 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
$$3$$ −39.0000 −0.833950 −0.416975 0.908918i $$-0.636910\pi$$
−0.416975 + 0.908918i $$0.636910\pi$$
$$4$$ −64.0000 −0.500000
$$5$$ 385.000i 1.37742i 0.725038 + 0.688709i $$0.241822\pi$$
−0.725038 + 0.688709i $$0.758178\pi$$
$$6$$ 312.000i 0.589692i
$$7$$ 293.000i 0.322868i 0.986884 + 0.161434i $$0.0516118\pi$$
−0.986884 + 0.161434i $$0.948388\pi$$
$$8$$ 512.000i 0.353553i
$$9$$ −666.000 −0.304527
$$10$$ 3080.00 0.973982
$$11$$ 5402.00i 1.22371i 0.790968 + 0.611857i $$0.209577\pi$$
−0.790968 + 0.611857i $$0.790423\pi$$
$$12$$ 2496.00 0.416975
$$13$$ 0 0
$$14$$ 2344.00 0.228302
$$15$$ − 15015.0i − 1.14870i
$$16$$ 4096.00 0.250000
$$17$$ 21011.0 1.03723 0.518616 0.855008i $$-0.326448\pi$$
0.518616 + 0.855008i $$0.326448\pi$$
$$18$$ 5328.00i 0.215333i
$$19$$ − 27326.0i − 0.913984i −0.889471 0.456992i $$-0.848927\pi$$
0.889471 0.456992i $$-0.151073\pi$$
$$20$$ − 24640.0i − 0.688709i
$$21$$ − 11427.0i − 0.269256i
$$22$$ 43216.0 0.865297
$$23$$ 63072.0 1.08091 0.540455 0.841373i $$-0.318252\pi$$
0.540455 + 0.841373i $$0.318252\pi$$
$$24$$ − 19968.0i − 0.294846i
$$25$$ −70100.0 −0.897280
$$26$$ 0 0
$$27$$ 111267. 1.08791
$$28$$ − 18752.0i − 0.161434i
$$29$$ 122238. 0.930708 0.465354 0.885125i $$-0.345927\pi$$
0.465354 + 0.885125i $$0.345927\pi$$
$$30$$ −120120. −0.812252
$$31$$ − 208396.i − 1.25639i −0.778057 0.628194i $$-0.783795\pi$$
0.778057 0.628194i $$-0.216205\pi$$
$$32$$ − 32768.0i − 0.176777i
$$33$$ − 210678.i − 1.02052i
$$34$$ − 168088.i − 0.733433i
$$35$$ −112805. −0.444724
$$36$$ 42624.0 0.152263
$$37$$ 442379.i 1.43578i 0.696156 + 0.717891i $$0.254892\pi$$
−0.696156 + 0.717891i $$0.745108\pi$$
$$38$$ −218608. −0.646284
$$39$$ 0 0
$$40$$ −197120. −0.486991
$$41$$ 58000.0i 0.131427i 0.997839 + 0.0657135i $$0.0209323\pi$$
−0.997839 + 0.0657135i $$0.979068\pi$$
$$42$$ −91416.0 −0.190392
$$43$$ 202025. 0.387494 0.193747 0.981051i $$-0.437936\pi$$
0.193747 + 0.981051i $$0.437936\pi$$
$$44$$ − 345728.i − 0.611857i
$$45$$ − 256410.i − 0.419461i
$$46$$ − 504576.i − 0.764318i
$$47$$ − 588511.i − 0.826822i −0.910545 0.413411i $$-0.864337\pi$$
0.910545 0.413411i $$-0.135663\pi$$
$$48$$ −159744. −0.208488
$$49$$ 737694. 0.895757
$$50$$ 560800.i 0.634473i
$$51$$ −819429. −0.864999
$$52$$ 0 0
$$53$$ 1.68434e6 1.55404 0.777022 0.629474i $$-0.216729\pi$$
0.777022 + 0.629474i $$0.216729\pi$$
$$54$$ − 890136.i − 0.769269i
$$55$$ −2.07977e6 −1.68557
$$56$$ −150016. −0.114151
$$57$$ 1.06571e6i 0.762217i
$$58$$ − 977904.i − 0.658110i
$$59$$ 442630.i 0.280581i 0.990110 + 0.140291i $$0.0448037\pi$$
−0.990110 + 0.140291i $$0.955196\pi$$
$$60$$ 960960.i 0.574349i
$$61$$ −1.08361e6 −0.611248 −0.305624 0.952152i $$-0.598865\pi$$
−0.305624 + 0.952152i $$0.598865\pi$$
$$62$$ −1.66717e6 −0.888400
$$63$$ − 195138.i − 0.0983218i
$$64$$ −262144. −0.125000
$$65$$ 0 0
$$66$$ −1.68542e6 −0.721615
$$67$$ 3.44349e6i 1.39874i 0.714761 + 0.699369i $$0.246536\pi$$
−0.714761 + 0.699369i $$0.753464\pi$$
$$68$$ −1.34470e6 −0.518616
$$69$$ −2.45981e6 −0.901425
$$70$$ 902440.i 0.314467i
$$71$$ 2.08470e6i 0.691258i 0.938371 + 0.345629i $$0.112334\pi$$
−0.938371 + 0.345629i $$0.887666\pi$$
$$72$$ − 340992.i − 0.107666i
$$73$$ − 5.93789e6i − 1.78650i −0.449564 0.893248i $$-0.648421\pi$$
0.449564 0.893248i $$-0.351579\pi$$
$$74$$ 3.53903e6 1.01525
$$75$$ 2.73390e6 0.748287
$$76$$ 1.74886e6i 0.456992i
$$77$$ −1.58279e6 −0.395098
$$78$$ 0 0
$$79$$ −6.60926e6 −1.50820 −0.754098 0.656762i $$-0.771926\pi$$
−0.754098 + 0.656762i $$0.771926\pi$$
$$80$$ 1.57696e6i 0.344354i
$$81$$ −2.88287e6 −0.602737
$$82$$ 464000. 0.0929329
$$83$$ − 142740.i − 0.0274014i −0.999906 0.0137007i $$-0.995639\pi$$
0.999906 0.0137007i $$-0.00436120\pi$$
$$84$$ 731328.i 0.134628i
$$85$$ 8.08924e6i 1.42870i
$$86$$ − 1.61620e6i − 0.274000i
$$87$$ −4.76728e6 −0.776164
$$88$$ −2.76582e6 −0.432648
$$89$$ 6.98529e6i 1.05031i 0.851005 + 0.525157i $$0.175993\pi$$
−0.851005 + 0.525157i $$0.824007\pi$$
$$90$$ −2.05128e6 −0.296603
$$91$$ 0 0
$$92$$ −4.03661e6 −0.540455
$$93$$ 8.12744e6i 1.04776i
$$94$$ −4.70809e6 −0.584652
$$95$$ 1.05205e7 1.25894
$$96$$ 1.27795e6i 0.147423i
$$97$$ − 200762.i − 0.0223347i −0.999938 0.0111674i $$-0.996445\pi$$
0.999938 0.0111674i $$-0.00355475\pi$$
$$98$$ − 5.90155e6i − 0.633395i
$$99$$ − 3.59773e6i − 0.372654i
$$100$$ 4.48640e6 0.448640
$$101$$ 5.42144e6 0.523588 0.261794 0.965124i $$-0.415686\pi$$
0.261794 + 0.965124i $$0.415686\pi$$
$$102$$ 6.55543e6i 0.611647i
$$103$$ 1.71897e7 1.55002 0.775011 0.631948i $$-0.217745\pi$$
0.775011 + 0.631948i $$0.217745\pi$$
$$104$$ 0 0
$$105$$ 4.39940e6 0.370877
$$106$$ − 1.34747e7i − 1.09887i
$$107$$ 1.23582e7 0.975242 0.487621 0.873055i $$-0.337865\pi$$
0.487621 + 0.873055i $$0.337865\pi$$
$$108$$ −7.12109e6 −0.543955
$$109$$ 1.70569e7i 1.26156i 0.775964 + 0.630778i $$0.217264\pi$$
−0.775964 + 0.630778i $$0.782736\pi$$
$$110$$ 1.66382e7i 1.19188i
$$111$$ − 1.72528e7i − 1.19737i
$$112$$ 1.20013e6i 0.0807169i
$$113$$ 2.11250e7 1.37728 0.688639 0.725104i $$-0.258208\pi$$
0.688639 + 0.725104i $$0.258208\pi$$
$$114$$ 8.52571e6 0.538969
$$115$$ 2.42827e7i 1.48886i
$$116$$ −7.82323e6 −0.465354
$$117$$ 0 0
$$118$$ 3.54104e6 0.198401
$$119$$ 6.15622e6i 0.334888i
$$120$$ 7.68768e6 0.406126
$$121$$ −9.69443e6 −0.497478
$$122$$ 8.66886e6i 0.432218i
$$123$$ − 2.26200e6i − 0.109604i
$$124$$ 1.33373e7i 0.628194i
$$125$$ 3.08962e6i 0.141488i
$$126$$ −1.56110e6 −0.0695240
$$127$$ 3.24008e7 1.40360 0.701800 0.712374i $$-0.252380\pi$$
0.701800 + 0.712374i $$0.252380\pi$$
$$128$$ 2.09715e6i 0.0883883i
$$129$$ −7.87898e6 −0.323151
$$130$$ 0 0
$$131$$ −2.64669e7 −1.02862 −0.514308 0.857605i $$-0.671951\pi$$
−0.514308 + 0.857605i $$0.671951\pi$$
$$132$$ 1.34834e7i 0.510259i
$$133$$ 8.00652e6 0.295096
$$134$$ 2.75479e7 0.989057
$$135$$ 4.28378e7i 1.49851i
$$136$$ 1.07576e7i 0.366717i
$$137$$ − 5.36201e7i − 1.78158i −0.454413 0.890791i $$-0.650151\pi$$
0.454413 0.890791i $$-0.349849\pi$$
$$138$$ 1.96785e7i 0.637403i
$$139$$ 7.58784e6 0.239644 0.119822 0.992795i $$-0.461768\pi$$
0.119822 + 0.992795i $$0.461768\pi$$
$$140$$ 7.21952e6 0.222362
$$141$$ 2.29519e7i 0.689529i
$$142$$ 1.66776e7 0.488793
$$143$$ 0 0
$$144$$ −2.72794e6 −0.0761317
$$145$$ 4.70616e7i 1.28197i
$$146$$ −4.75031e7 −1.26324
$$147$$ −2.87701e7 −0.747016
$$148$$ − 2.83123e7i − 0.717891i
$$149$$ − 5.70297e7i − 1.41237i −0.708026 0.706187i $$-0.750414\pi$$
0.708026 0.706187i $$-0.249586\pi$$
$$150$$ − 2.18712e7i − 0.529119i
$$151$$ 2.00648e7i 0.474259i 0.971478 + 0.237130i $$0.0762066\pi$$
−0.971478 + 0.237130i $$0.923793\pi$$
$$152$$ 1.39909e7 0.323142
$$153$$ −1.39933e7 −0.315865
$$154$$ 1.26623e7i 0.279376i
$$155$$ 8.02325e7 1.73057
$$156$$ 0 0
$$157$$ −3.15314e7 −0.650272 −0.325136 0.945667i $$-0.605410\pi$$
−0.325136 + 0.945667i $$0.605410\pi$$
$$158$$ 5.28740e7i 1.06646i
$$159$$ −6.56891e7 −1.29600
$$160$$ 1.26157e7 0.243495
$$161$$ 1.84801e7i 0.348991i
$$162$$ 2.30630e7i 0.426199i
$$163$$ 3.13938e7i 0.567789i 0.958855 + 0.283895i $$0.0916266\pi$$
−0.958855 + 0.283895i $$0.908373\pi$$
$$164$$ − 3.71200e6i − 0.0657135i
$$165$$ 8.11110e7 1.40568
$$166$$ −1.14192e6 −0.0193757
$$167$$ − 9.22170e7i − 1.53216i −0.642747 0.766079i $$-0.722205\pi$$
0.642747 0.766079i $$-0.277795\pi$$
$$168$$ 5.85062e6 0.0951962
$$169$$ 0 0
$$170$$ 6.47139e7 1.01024
$$171$$ 1.81991e7i 0.278332i
$$172$$ −1.29296e7 −0.193747
$$173$$ 6.57015e7 0.964748 0.482374 0.875965i $$-0.339775\pi$$
0.482374 + 0.875965i $$0.339775\pi$$
$$174$$ 3.81383e7i 0.548831i
$$175$$ − 2.05393e7i − 0.289703i
$$176$$ 2.21266e7i 0.305929i
$$177$$ − 1.72626e7i − 0.233991i
$$178$$ 5.58823e7 0.742684
$$179$$ 3.20402e6 0.0417551 0.0208776 0.999782i $$-0.493354\pi$$
0.0208776 + 0.999782i $$0.493354\pi$$
$$180$$ 1.64102e7i 0.209730i
$$181$$ 4.45759e7 0.558760 0.279380 0.960181i $$-0.409871\pi$$
0.279380 + 0.960181i $$0.409871\pi$$
$$182$$ 0 0
$$183$$ 4.22607e7 0.509751
$$184$$ 3.22929e7i 0.382159i
$$185$$ −1.70316e8 −1.97767
$$186$$ 6.50196e7 0.740881
$$187$$ 1.13501e8i 1.26927i
$$188$$ 3.76647e7i 0.413411i
$$189$$ 3.26012e7i 0.351251i
$$190$$ − 8.41641e7i − 0.890203i
$$191$$ 1.86394e8 1.93559 0.967797 0.251733i $$-0.0810004\pi$$
0.967797 + 0.251733i $$0.0810004\pi$$
$$192$$ 1.02236e7 0.104244
$$193$$ 1.52927e8i 1.53120i 0.643314 + 0.765602i $$0.277559\pi$$
−0.643314 + 0.765602i $$0.722441\pi$$
$$194$$ −1.60610e6 −0.0157930
$$195$$ 0 0
$$196$$ −4.72124e7 −0.447878
$$197$$ 9.51837e7i 0.887015i 0.896271 + 0.443507i $$0.146266\pi$$
−0.896271 + 0.443507i $$0.853734\pi$$
$$198$$ −2.87819e7 −0.263506
$$199$$ −1.78585e8 −1.60642 −0.803212 0.595693i $$-0.796878\pi$$
−0.803212 + 0.595693i $$0.796878\pi$$
$$200$$ − 3.58912e7i − 0.317236i
$$201$$ − 1.34296e8i − 1.16648i
$$202$$ − 4.33715e7i − 0.370232i
$$203$$ 3.58157e7i 0.300495i
$$204$$ 5.24435e7 0.432500
$$205$$ −2.23300e7 −0.181030
$$206$$ − 1.37517e8i − 1.09603i
$$207$$ −4.20060e7 −0.329166
$$208$$ 0 0
$$209$$ 1.47615e8 1.11846
$$210$$ − 3.51952e7i − 0.262250i
$$211$$ −1.33235e8 −0.976406 −0.488203 0.872730i $$-0.662348\pi$$
−0.488203 + 0.872730i $$0.662348\pi$$
$$212$$ −1.07798e8 −0.777022
$$213$$ − 8.13035e7i − 0.576475i
$$214$$ − 9.88657e7i − 0.689600i
$$215$$ 7.77796e7i 0.533742i
$$216$$ 5.69687e7i 0.384634i
$$217$$ 6.10600e7 0.405647
$$218$$ 1.36455e8 0.892054
$$219$$ 2.31578e8i 1.48985i
$$220$$ 1.33105e8 0.842783
$$221$$ 0 0
$$222$$ −1.38022e8 −0.846669
$$223$$ 1.19394e8i 0.720969i 0.932765 + 0.360484i $$0.117389\pi$$
−0.932765 + 0.360484i $$0.882611\pi$$
$$224$$ 9.60102e6 0.0570755
$$225$$ 4.66866e7 0.273246
$$226$$ − 1.69000e8i − 0.973883i
$$227$$ 1.13656e7i 0.0644911i 0.999480 + 0.0322456i $$0.0102659\pi$$
−0.999480 + 0.0322456i $$0.989734\pi$$
$$228$$ − 6.82057e7i − 0.381109i
$$229$$ 1.46559e7i 0.0806470i 0.999187 + 0.0403235i $$0.0128389\pi$$
−0.999187 + 0.0403235i $$0.987161\pi$$
$$230$$ 1.94262e8 1.05279
$$231$$ 6.17287e7 0.329492
$$232$$ 6.25859e7i 0.329055i
$$233$$ 2.46924e8 1.27885 0.639423 0.768855i $$-0.279173\pi$$
0.639423 + 0.768855i $$0.279173\pi$$
$$234$$ 0 0
$$235$$ 2.26577e8 1.13888
$$236$$ − 2.83283e7i − 0.140291i
$$237$$ 2.57761e8 1.25776
$$238$$ 4.92498e7 0.236802
$$239$$ − 1.61239e7i − 0.0763971i −0.999270 0.0381985i $$-0.987838\pi$$
0.999270 0.0381985i $$-0.0121619\pi$$
$$240$$ − 6.15014e7i − 0.287175i
$$241$$ − 1.14256e8i − 0.525798i −0.964823 0.262899i $$-0.915321\pi$$
0.964823 0.262899i $$-0.0846787\pi$$
$$242$$ 7.75555e7i 0.351770i
$$243$$ −1.30909e8 −0.585258
$$244$$ 6.93509e7 0.305624
$$245$$ 2.84012e8i 1.23383i
$$246$$ −1.80960e7 −0.0775014
$$247$$ 0 0
$$248$$ 1.06699e8 0.444200
$$249$$ 5.56686e6i 0.0228514i
$$250$$ 2.47170e7 0.100047
$$251$$ −2.22704e8 −0.888935 −0.444467 0.895795i $$-0.646607\pi$$
−0.444467 + 0.895795i $$0.646607\pi$$
$$252$$ 1.24888e7i 0.0491609i
$$253$$ 3.40715e8i 1.32272i
$$254$$ − 2.59207e8i − 0.992494i
$$255$$ − 3.15480e8i − 1.19147i
$$256$$ 1.67772e7 0.0625000
$$257$$ −2.82302e8 −1.03741 −0.518703 0.854955i $$-0.673585\pi$$
−0.518703 + 0.854955i $$0.673585\pi$$
$$258$$ 6.30318e7i 0.228502i
$$259$$ −1.29617e8 −0.463567
$$260$$ 0 0
$$261$$ −8.14105e7 −0.283425
$$262$$ 2.11735e8i 0.727342i
$$263$$ −2.36490e8 −0.801619 −0.400809 0.916162i $$-0.631271\pi$$
−0.400809 + 0.916162i $$0.631271\pi$$
$$264$$ 1.07867e8 0.360807
$$265$$ 6.48469e8i 2.14057i
$$266$$ − 6.40521e7i − 0.208664i
$$267$$ − 2.72426e8i − 0.875910i
$$268$$ − 2.20383e8i − 0.699369i
$$269$$ −4.82172e8 −1.51032 −0.755160 0.655541i $$-0.772441\pi$$
−0.755160 + 0.655541i $$0.772441\pi$$
$$270$$ 3.42702e8 1.05960
$$271$$ − 4.66372e8i − 1.42344i −0.702462 0.711721i $$-0.747916\pi$$
0.702462 0.711721i $$-0.252084\pi$$
$$272$$ 8.60611e7 0.259308
$$273$$ 0 0
$$274$$ −4.28961e8 −1.25977
$$275$$ − 3.78680e8i − 1.09801i
$$276$$ 1.57428e8 0.450712
$$277$$ 1.88709e8 0.533475 0.266738 0.963769i $$-0.414054\pi$$
0.266738 + 0.963769i $$0.414054\pi$$
$$278$$ − 6.07027e7i − 0.169454i
$$279$$ 1.38792e8i 0.382603i
$$280$$ − 5.77562e7i − 0.157234i
$$281$$ 7.15402e8i 1.92344i 0.274040 + 0.961718i $$0.411640\pi$$
−0.274040 + 0.961718i $$0.588360\pi$$
$$282$$ 1.83615e8 0.487570
$$283$$ 4.04602e8 1.06115 0.530573 0.847639i $$-0.321977\pi$$
0.530573 + 0.847639i $$0.321977\pi$$
$$284$$ − 1.33421e8i − 0.345629i
$$285$$ −4.10300e8 −1.04989
$$286$$ 0 0
$$287$$ −1.69940e7 −0.0424335
$$288$$ 2.18235e7i 0.0538332i
$$289$$ 3.11234e7 0.0758482
$$290$$ 3.76493e8 0.906492
$$291$$ 7.82972e6i 0.0186260i
$$292$$ 3.80025e8i 0.893248i
$$293$$ 8.11321e8i 1.88433i 0.335156 + 0.942163i $$0.391211\pi$$
−0.335156 + 0.942163i $$0.608789\pi$$
$$294$$ 2.30161e8i 0.528220i
$$295$$ −1.70413e8 −0.386478
$$296$$ −2.26498e8 −0.507626
$$297$$ 6.01064e8i 1.33129i
$$298$$ −4.56238e8 −0.998699
$$299$$ 0 0
$$300$$ −1.74970e8 −0.374144
$$301$$ 5.91933e7i 0.125109i
$$302$$ 1.60519e8 0.335352
$$303$$ −2.11436e8 −0.436646
$$304$$ − 1.11927e8i − 0.228496i
$$305$$ − 4.17189e8i − 0.841945i
$$306$$ 1.11947e8i 0.223350i
$$307$$ − 4.60958e8i − 0.909237i −0.890686 0.454618i $$-0.849776\pi$$
0.890686 0.454618i $$-0.150224\pi$$
$$308$$ 1.01298e8 0.197549
$$309$$ −6.70398e8 −1.29264
$$310$$ − 6.41860e8i − 1.22370i
$$311$$ 2.87718e8 0.542383 0.271192 0.962525i $$-0.412582\pi$$
0.271192 + 0.962525i $$0.412582\pi$$
$$312$$ 0 0
$$313$$ −9.56179e8 −1.76252 −0.881260 0.472632i $$-0.843304\pi$$
−0.881260 + 0.472632i $$0.843304\pi$$
$$314$$ 2.52252e8i 0.459812i
$$315$$ 7.51281e7 0.135430
$$316$$ 4.22992e8 0.754098
$$317$$ 4.92761e8i 0.868818i 0.900716 + 0.434409i $$0.143043\pi$$
−0.900716 + 0.434409i $$0.856957\pi$$
$$318$$ 5.25513e8i 0.916407i
$$319$$ 6.60330e8i 1.13892i
$$320$$ − 1.00925e8i − 0.172177i
$$321$$ −4.81970e8 −0.813303
$$322$$ 1.47841e8 0.246774
$$323$$ − 5.74147e8i − 0.948012i
$$324$$ 1.84504e8 0.301368
$$325$$ 0 0
$$326$$ 2.51150e8 0.401488
$$327$$ − 6.65218e8i − 1.05207i
$$328$$ −2.96960e7 −0.0464665
$$329$$ 1.72434e8 0.266954
$$330$$ − 6.48888e8i − 0.993965i
$$331$$ − 4.83358e8i − 0.732607i −0.930495 0.366304i $$-0.880623\pi$$
0.930495 0.366304i $$-0.119377\pi$$
$$332$$ 9.13536e6i 0.0137007i
$$333$$ − 2.94624e8i − 0.437234i
$$334$$ −7.37736e8 −1.08340
$$335$$ −1.32574e9 −1.92665
$$336$$ − 4.68050e7i − 0.0673139i
$$337$$ −1.30823e9 −1.86200 −0.930998 0.365025i $$-0.881060\pi$$
−0.930998 + 0.365025i $$0.881060\pi$$
$$338$$ 0 0
$$339$$ −8.23874e8 −1.14858
$$340$$ − 5.17711e8i − 0.714350i
$$341$$ 1.12576e9 1.53746
$$342$$ 1.45593e8 0.196811
$$343$$ 4.57442e8i 0.612078i
$$344$$ 1.03437e8i 0.137000i
$$345$$ − 9.47026e8i − 1.24164i
$$346$$ − 5.25612e8i − 0.682180i
$$347$$ −8.94842e8 −1.14972 −0.574861 0.818251i $$-0.694944\pi$$
−0.574861 + 0.818251i $$0.694944\pi$$
$$348$$ 3.05106e8 0.388082
$$349$$ 5.41626e8i 0.682041i 0.940056 + 0.341020i $$0.110772\pi$$
−0.940056 + 0.341020i $$0.889228\pi$$
$$350$$ −1.64314e8 −0.204851
$$351$$ 0 0
$$352$$ 1.77013e8 0.216324
$$353$$ 2.25334e8i 0.272656i 0.990664 + 0.136328i $$0.0435301\pi$$
−0.990664 + 0.136328i $$0.956470\pi$$
$$354$$ −1.38101e8 −0.165457
$$355$$ −8.02611e8 −0.952152
$$356$$ − 4.47058e8i − 0.525157i
$$357$$ − 2.40093e8i − 0.279280i
$$358$$ − 2.56322e7i − 0.0295253i
$$359$$ 4.38763e8i 0.500495i 0.968182 + 0.250247i $$0.0805120\pi$$
−0.968182 + 0.250247i $$0.919488\pi$$
$$360$$ 1.31282e8 0.148302
$$361$$ 1.47161e8 0.164634
$$362$$ − 3.56607e8i − 0.395103i
$$363$$ 3.78083e8 0.414872
$$364$$ 0 0
$$365$$ 2.28609e9 2.46075
$$366$$ − 3.38086e8i − 0.360448i
$$367$$ 8.08568e8 0.853857 0.426929 0.904285i $$-0.359596\pi$$
0.426929 + 0.904285i $$0.359596\pi$$
$$368$$ 2.58343e8 0.270227
$$369$$ − 3.86280e7i − 0.0400230i
$$370$$ 1.36253e9i 1.39843i
$$371$$ 4.93510e8i 0.501750i
$$372$$ − 5.20156e8i − 0.523882i
$$373$$ −1.17884e9 −1.17618 −0.588092 0.808794i $$-0.700121\pi$$
−0.588092 + 0.808794i $$0.700121\pi$$
$$374$$ 9.08011e8 0.897513
$$375$$ − 1.20495e8i − 0.117994i
$$376$$ 3.01318e8 0.292326
$$377$$ 0 0
$$378$$ 2.60810e8 0.248372
$$379$$ − 1.79168e9i − 1.69053i −0.534345 0.845266i $$-0.679442\pi$$
0.534345 0.845266i $$-0.320558\pi$$
$$380$$ −6.73313e8 −0.629469
$$381$$ −1.26363e9 −1.17053
$$382$$ − 1.49115e9i − 1.36867i
$$383$$ − 1.19775e9i − 1.08936i −0.838644 0.544680i $$-0.816651\pi$$
0.838644 0.544680i $$-0.183349\pi$$
$$384$$ − 8.17889e7i − 0.0737115i
$$385$$ − 6.09373e8i − 0.544215i
$$386$$ 1.22341e9 1.08273
$$387$$ −1.34549e8 −0.118002
$$388$$ 1.28488e7i 0.0111674i
$$389$$ 1.43672e8 0.123751 0.0618754 0.998084i $$-0.480292\pi$$
0.0618754 + 0.998084i $$0.480292\pi$$
$$390$$ 0 0
$$391$$ 1.32521e9 1.12115
$$392$$ 3.77699e8i 0.316698i
$$393$$ 1.03221e9 0.857815
$$394$$ 7.61470e8 0.627214
$$395$$ − 2.54456e9i − 2.07742i
$$396$$ 2.30255e8i 0.186327i
$$397$$ 6.17334e8i 0.495169i 0.968866 + 0.247584i $$0.0796367\pi$$
−0.968866 + 0.247584i $$0.920363\pi$$
$$398$$ 1.42868e9i 1.13591i
$$399$$ −3.12254e8 −0.246095
$$400$$ −2.87130e8 −0.224320
$$401$$ − 1.13305e9i − 0.877491i −0.898611 0.438746i $$-0.855423\pi$$
0.898611 0.438746i $$-0.144577\pi$$
$$402$$ −1.07437e9 −0.824825
$$403$$ 0 0
$$404$$ −3.46972e8 −0.261794
$$405$$ − 1.10991e9i − 0.830220i
$$406$$ 2.86526e8 0.212482
$$407$$ −2.38973e9 −1.75699
$$408$$ − 4.19548e8i − 0.305823i
$$409$$ − 1.04283e9i − 0.753670i −0.926280 0.376835i $$-0.877012\pi$$
0.926280 0.376835i $$-0.122988\pi$$
$$410$$ 1.78640e8i 0.128007i
$$411$$ 2.09119e9i 1.48575i
$$412$$ −1.10014e9 −0.775011
$$413$$ −1.29691e8 −0.0905906
$$414$$ 3.36048e8i 0.232755i
$$415$$ 5.49549e7 0.0377431
$$416$$ 0 0
$$417$$ −2.95926e8 −0.199851
$$418$$ − 1.18092e9i − 0.790867i
$$419$$ 7.09302e8 0.471066 0.235533 0.971866i $$-0.424316\pi$$
0.235533 + 0.971866i $$0.424316\pi$$
$$420$$ −2.81561e8 −0.185439
$$421$$ − 1.19877e9i − 0.782974i −0.920184 0.391487i $$-0.871961\pi$$
0.920184 0.391487i $$-0.128039\pi$$
$$422$$ 1.06588e9i 0.690424i
$$423$$ 3.91948e8i 0.251789i
$$424$$ 8.62380e8i 0.549437i
$$425$$ −1.47287e9 −0.930687
$$426$$ −6.50428e8 −0.407629
$$427$$ − 3.17497e8i − 0.197352i
$$428$$ −7.90926e8 −0.487621
$$429$$ 0 0
$$430$$ 6.22237e8 0.377412
$$431$$ 9.54153e8i 0.574047i 0.957924 + 0.287024i $$0.0926658\pi$$
−0.957924 + 0.287024i $$0.907334\pi$$
$$432$$ 4.55750e8 0.271978
$$433$$ 3.81628e8 0.225908 0.112954 0.993600i $$-0.463969\pi$$
0.112954 + 0.993600i $$0.463969\pi$$
$$434$$ − 4.88480e8i − 0.286836i
$$435$$ − 1.83540e9i − 1.06910i
$$436$$ − 1.09164e9i − 0.630778i
$$437$$ − 1.72351e9i − 0.987933i
$$438$$ 1.85262e9 1.05348
$$439$$ −1.11683e8 −0.0630031 −0.0315015 0.999504i $$-0.510029\pi$$
−0.0315015 + 0.999504i $$0.510029\pi$$
$$440$$ − 1.06484e9i − 0.595938i
$$441$$ −4.91304e8 −0.272782
$$442$$ 0 0
$$443$$ 1.45991e9 0.797837 0.398919 0.916986i $$-0.369386\pi$$
0.398919 + 0.916986i $$0.369386\pi$$
$$444$$ 1.10418e9i 0.598685i
$$445$$ −2.68934e9 −1.44672
$$446$$ 9.55154e8 0.509802
$$447$$ 2.22416e9i 1.17785i
$$448$$ − 7.68082e7i − 0.0403585i
$$449$$ 6.34009e8i 0.330547i 0.986248 + 0.165273i $$0.0528507\pi$$
−0.986248 + 0.165273i $$0.947149\pi$$
$$450$$ − 3.73493e8i − 0.193214i
$$451$$ −3.13316e8 −0.160829
$$452$$ −1.35200e9 −0.688639
$$453$$ − 7.82528e8i − 0.395509i
$$454$$ 9.09244e7 0.0456021
$$455$$ 0 0
$$456$$ −5.45646e8 −0.269484
$$457$$ 6.04376e8i 0.296211i 0.988972 + 0.148105i $$0.0473175\pi$$
−0.988972 + 0.148105i $$0.952683\pi$$
$$458$$ 1.17247e8 0.0570261
$$459$$ 2.33783e9 1.12841
$$460$$ − 1.55409e9i − 0.744432i
$$461$$ 2.20565e9i 1.04853i 0.851554 + 0.524267i $$0.175661\pi$$
−0.851554 + 0.524267i $$0.824339\pi$$
$$462$$ − 4.93829e8i − 0.232986i
$$463$$ − 1.04925e9i − 0.491299i −0.969359 0.245650i $$-0.920999\pi$$
0.969359 0.245650i $$-0.0790012\pi$$
$$464$$ 5.00687e8 0.232677
$$465$$ −3.12907e9 −1.44321
$$466$$ − 1.97539e9i − 0.904281i
$$467$$ 2.01461e9 0.915337 0.457668 0.889123i $$-0.348685\pi$$
0.457668 + 0.889123i $$0.348685\pi$$
$$468$$ 0 0
$$469$$ −1.00894e9 −0.451607
$$470$$ − 1.81261e9i − 0.805309i
$$471$$ 1.22973e9 0.542295
$$472$$ −2.26627e8 −0.0992005
$$473$$ 1.09134e9i 0.474183i
$$474$$ − 2.06209e9i − 0.889371i
$$475$$ 1.91555e9i 0.820099i
$$476$$ − 3.93998e8i − 0.167444i
$$477$$ −1.12177e9 −0.473248
$$478$$ −1.28991e8 −0.0540209
$$479$$ − 3.67842e9i − 1.52928i −0.644458 0.764639i $$-0.722917\pi$$
0.644458 0.764639i $$-0.277083\pi$$
$$480$$ −4.92012e8 −0.203063
$$481$$ 0 0
$$482$$ −9.14048e8 −0.371796
$$483$$ − 7.20724e8i − 0.291041i
$$484$$ 6.20444e8 0.248739
$$485$$ 7.72934e7 0.0307642
$$486$$ 1.04727e9i 0.413840i
$$487$$ − 1.91497e8i − 0.0751294i −0.999294 0.0375647i $$-0.988040\pi$$
0.999294 0.0375647i $$-0.0119600\pi$$
$$488$$ − 5.54807e8i − 0.216109i
$$489$$ − 1.22436e9i − 0.473508i
$$490$$ 2.27210e9 0.872450
$$491$$ 3.22321e8 0.122886 0.0614431 0.998111i $$-0.480430\pi$$
0.0614431 + 0.998111i $$0.480430\pi$$
$$492$$ 1.44768e8i 0.0548018i
$$493$$ 2.56834e9 0.965359
$$494$$ 0 0
$$495$$ 1.38513e9 0.513300
$$496$$ − 8.53590e8i − 0.314097i
$$497$$ −6.10819e8 −0.223185
$$498$$ 4.45349e7 0.0161584
$$499$$ 3.86695e9i 1.39321i 0.717455 + 0.696604i $$0.245307\pi$$
−0.717455 + 0.696604i $$0.754693\pi$$
$$500$$ − 1.97736e8i − 0.0707442i
$$501$$ 3.59646e9i 1.27774i
$$502$$ 1.78163e9i 0.628572i
$$503$$ −3.43814e8 −0.120458 −0.0602290 0.998185i $$-0.519183\pi$$
−0.0602290 + 0.998185i $$0.519183\pi$$
$$504$$ 9.99107e7 0.0347620
$$505$$ 2.08725e9i 0.721199i
$$506$$ 2.72572e9 0.935307
$$507$$ 0 0
$$508$$ −2.07365e9 −0.701800
$$509$$ 2.11533e9i 0.710993i 0.934678 + 0.355497i $$0.115688\pi$$
−0.934678 + 0.355497i $$0.884312\pi$$
$$510$$ −2.52384e9 −0.842493
$$511$$ 1.73980e9 0.576802
$$512$$ − 1.34218e8i − 0.0441942i
$$513$$ − 3.04048e9i − 0.994333i
$$514$$ 2.25842e9i 0.733556i
$$515$$ 6.61803e9i 2.13503i
$$516$$ 5.04254e8 0.161576
$$517$$ 3.17914e9 1.01179
$$518$$ 1.03694e9i 0.327792i
$$519$$ −2.56236e9 −0.804552
$$520$$ 0 0
$$521$$ −1.40622e9 −0.435634 −0.217817 0.975990i $$-0.569894\pi$$
−0.217817 + 0.975990i $$0.569894\pi$$
$$522$$ 6.51284e8i 0.200412i
$$523$$ 2.18120e9 0.666712 0.333356 0.942801i $$-0.391819\pi$$
0.333356 + 0.942801i $$0.391819\pi$$
$$524$$ 1.69388e9 0.514308
$$525$$ 8.01033e8i 0.241598i
$$526$$ 1.89192e9i 0.566830i
$$527$$ − 4.37861e9i − 1.30316i
$$528$$ − 8.62937e8i − 0.255129i
$$529$$ 5.73252e8 0.168365
$$530$$ 5.18775e9 1.51361
$$531$$ − 2.94792e8i − 0.0854445i
$$532$$ −5.12417e8 −0.147548
$$533$$ 0 0
$$534$$ −2.17941e9 −0.619362
$$535$$ 4.75791e9i 1.34332i
$$536$$ −1.76306e9 −0.494529
$$537$$ −1.24957e8 −0.0348217
$$538$$ 3.85737e9i 1.06796i
$$539$$ 3.98502e9i 1.09615i
$$540$$ − 2.74162e9i − 0.749254i
$$541$$ − 2.54634e8i − 0.0691395i −0.999402 0.0345698i $$-0.988994\pi$$
0.999402 0.0345698i $$-0.0110061\pi$$
$$542$$ −3.73097e9 −1.00653
$$543$$ −1.73846e9 −0.465978
$$544$$ − 6.88488e8i − 0.183358i
$$545$$ −6.56689e9 −1.73769
$$546$$ 0 0
$$547$$ 2.15158e9 0.562085 0.281043 0.959695i $$-0.409320\pi$$
0.281043 + 0.959695i $$0.409320\pi$$
$$548$$ 3.43169e9i 0.890791i
$$549$$ 7.21683e8 0.186142
$$550$$ −3.02944e9 −0.776414
$$551$$ − 3.34028e9i − 0.850652i
$$552$$ − 1.25942e9i − 0.318702i
$$553$$ − 1.93651e9i − 0.486948i
$$554$$ − 1.50967e9i − 0.377224i
$$555$$ 6.64232e9 1.64928
$$556$$ −4.85622e8 −0.119822
$$557$$ 7.71518e9i 1.89170i 0.324599 + 0.945852i $$0.394771\pi$$
−0.324599 + 0.945852i $$0.605229\pi$$
$$558$$ 1.11033e9 0.270542
$$559$$ 0 0
$$560$$ −4.62049e8 −0.111181
$$561$$ − 4.42656e9i − 1.05851i
$$562$$ 5.72321e9 1.36008
$$563$$ 8.12996e7 0.0192003 0.00960017 0.999954i $$-0.496944\pi$$
0.00960017 + 0.999954i $$0.496944\pi$$
$$564$$ − 1.46892e9i − 0.344764i
$$565$$ 8.13312e9i 1.89709i
$$566$$ − 3.23681e9i − 0.750343i
$$567$$ − 8.44681e8i − 0.194604i
$$568$$ −1.06737e9 −0.244397
$$569$$ 5.08814e9 1.15789 0.578944 0.815367i $$-0.303465\pi$$
0.578944 + 0.815367i $$0.303465\pi$$
$$570$$ 3.28240e9i 0.742385i
$$571$$ 5.61762e9 1.26277 0.631387 0.775468i $$-0.282486\pi$$
0.631387 + 0.775468i $$0.282486\pi$$
$$572$$ 0 0
$$573$$ −7.26935e9 −1.61419
$$574$$ 1.35952e8i 0.0300050i
$$575$$ −4.42135e9 −0.969878
$$576$$ 1.74588e8 0.0380658
$$577$$ 4.12728e9i 0.894435i 0.894425 + 0.447218i $$0.147585\pi$$
−0.894425 + 0.447218i $$0.852415\pi$$
$$578$$ − 2.48988e8i − 0.0536328i
$$579$$ − 5.96415e9i − 1.27695i
$$580$$ − 3.01194e9i − 0.640987i
$$581$$ 4.18228e7 0.00884702
$$582$$ 6.26377e7 0.0131706
$$583$$ 9.09878e9i 1.90171i
$$584$$ 3.04020e9 0.631622
$$585$$ 0 0
$$586$$ 6.49057e9 1.33242
$$587$$ 1.86734e9i 0.381056i 0.981682 + 0.190528i $$0.0610201\pi$$
−0.981682 + 0.190528i $$0.938980\pi$$
$$588$$ 1.84128e9 0.373508
$$589$$ −5.69463e9 −1.14832
$$590$$ 1.36330e9i 0.273281i
$$591$$ − 3.71216e9i − 0.739726i
$$592$$ 1.81198e9i 0.358945i
$$593$$ − 3.31544e9i − 0.652905i −0.945214 0.326453i $$-0.894147\pi$$
0.945214 0.326453i $$-0.105853\pi$$
$$594$$ 4.80851e9 0.941366
$$595$$ −2.37015e9 −0.461281
$$596$$ 3.64990e9i 0.706187i
$$597$$ 6.96483e9 1.33968
$$598$$ 0 0
$$599$$ 1.93367e9 0.367610 0.183805 0.982963i $$-0.441158\pi$$
0.183805 + 0.982963i $$0.441158\pi$$
$$600$$ 1.39976e9i 0.264559i
$$601$$ −5.88820e9 −1.10643 −0.553213 0.833040i $$-0.686598\pi$$
−0.553213 + 0.833040i $$0.686598\pi$$
$$602$$ 4.73547e8 0.0884657
$$603$$ − 2.29336e9i − 0.425953i
$$604$$ − 1.28415e9i − 0.237130i
$$605$$ − 3.73236e9i − 0.685235i
$$606$$ 1.69149e9i 0.308756i
$$607$$ 7.94197e9 1.44135 0.720673 0.693276i $$-0.243833\pi$$
0.720673 + 0.693276i $$0.243833\pi$$
$$608$$ −8.95418e8 −0.161571
$$609$$ − 1.39681e9i − 0.250598i
$$610$$ −3.33751e9 −0.595345
$$611$$ 0 0
$$612$$ 8.95573e8 0.157932
$$613$$ − 2.36146e8i − 0.0414065i −0.999786 0.0207033i $$-0.993409\pi$$
0.999786 0.0207033i $$-0.00659052\pi$$
$$614$$ −3.68766e9 −0.642927
$$615$$ 8.70870e8 0.150970
$$616$$ − 8.10386e8i − 0.139688i
$$617$$ 1.27029e9i 0.217723i 0.994057 + 0.108862i $$0.0347206\pi$$
−0.994057 + 0.108862i $$0.965279\pi$$
$$618$$ 5.36318e9i 0.914035i
$$619$$ − 1.63555e9i − 0.277170i −0.990351 0.138585i $$-0.955745\pi$$
0.990351 0.138585i $$-0.0442554\pi$$
$$620$$ −5.13488e9 −0.865285
$$621$$ 7.01783e9 1.17593
$$622$$ − 2.30175e9i − 0.383523i
$$623$$ −2.04669e9 −0.339112
$$624$$ 0 0
$$625$$ −6.66607e9 −1.09217
$$626$$ 7.64943e9i 1.24629i
$$627$$ −5.75699e9 −0.932736
$$628$$ 2.01801e9 0.325136
$$629$$ 9.29483e9i 1.48924i
$$630$$ − 6.01025e8i − 0.0957636i
$$631$$ − 1.68242e9i − 0.266582i −0.991077 0.133291i $$-0.957445\pi$$
0.991077 0.133291i $$-0.0425546\pi$$
$$632$$ − 3.38394e9i − 0.533228i
$$633$$ 5.19618e9 0.814275
$$634$$ 3.94209e9 0.614347
$$635$$ 1.24743e10i 1.93334i
$$636$$ 4.20410e9 0.647998
$$637$$ 0 0
$$638$$ 5.28264e9 0.805338
$$639$$ − 1.38841e9i − 0.210507i
$$640$$ −8.07404e8 −0.121748
$$641$$ 1.70575e9 0.255807 0.127903 0.991787i $$-0.459175\pi$$
0.127903 + 0.991787i $$0.459175\pi$$
$$642$$ 3.85576e9i 0.575092i
$$643$$ − 1.45635e9i − 0.216036i −0.994149 0.108018i $$-0.965550\pi$$
0.994149 0.108018i $$-0.0344505\pi$$
$$644$$ − 1.18273e9i − 0.174495i
$$645$$ − 3.03341e9i − 0.445114i
$$646$$ −4.59317e9 −0.670346
$$647$$ 3.56464e9 0.517430 0.258715 0.965954i $$-0.416701\pi$$
0.258715 + 0.965954i $$0.416701\pi$$
$$648$$ − 1.47603e9i − 0.213100i
$$649$$ −2.39109e9 −0.343352
$$650$$ 0 0
$$651$$ −2.38134e9 −0.338289
$$652$$ − 2.00920e9i − 0.283895i
$$653$$ −5.86806e9 −0.824705 −0.412352 0.911024i $$-0.635293\pi$$
−0.412352 + 0.911024i $$0.635293\pi$$
$$654$$ −5.32174e9 −0.743929
$$655$$ − 1.01898e10i − 1.41683i
$$656$$ 2.37568e8i 0.0328567i
$$657$$ 3.95463e9i 0.544036i
$$658$$ − 1.37947e9i − 0.188765i
$$659$$ −2.73239e9 −0.371915 −0.185958 0.982558i $$-0.559539\pi$$
−0.185958 + 0.982558i $$0.559539\pi$$
$$660$$ −5.19111e9 −0.702839
$$661$$ − 8.50066e9i − 1.14485i −0.819958 0.572424i $$-0.806003\pi$$
0.819958 0.572424i $$-0.193997\pi$$
$$662$$ −3.86687e9 −0.518032
$$663$$ 0 0
$$664$$ 7.30829e7 0.00968785
$$665$$ 3.08251e9i 0.406470i
$$666$$ −2.35700e9 −0.309171
$$667$$ 7.70980e9 1.00601
$$668$$ 5.90189e9i 0.766079i
$$669$$ − 4.65638e9i − 0.601252i
$$670$$ 1.06059e10i 1.36235i
$$671$$ − 5.85365e9i − 0.747994i
$$672$$ −3.74440e8 −0.0475981
$$673$$ 3.85727e7 0.00487784 0.00243892 0.999997i $$-0.499224\pi$$
0.00243892 + 0.999997i $$0.499224\pi$$
$$674$$ 1.04658e10i 1.31663i
$$675$$ −7.79982e9 −0.976160
$$676$$ 0 0
$$677$$ −7.34428e9 −0.909681 −0.454840 0.890573i $$-0.650304\pi$$
−0.454840 + 0.890573i $$0.650304\pi$$
$$678$$ 6.59100e9i 0.812170i
$$679$$ 5.88233e7 0.00721116
$$680$$ −4.14169e9 −0.505122
$$681$$ − 4.43257e8i − 0.0537824i
$$682$$ − 9.00604e9i − 1.08715i
$$683$$ 7.49577e9i 0.900210i 0.892976 + 0.450105i $$0.148613\pi$$
−0.892976 + 0.450105i $$0.851387\pi$$
$$684$$ − 1.16474e9i − 0.139166i
$$685$$ 2.06438e10 2.45398
$$686$$ 3.65954e9 0.432805
$$687$$ − 5.71580e8i − 0.0672556i
$$688$$ 8.27494e8 0.0968736
$$689$$ 0 0
$$690$$ −7.57621e9 −0.877971
$$691$$ 1.66382e10i 1.91838i 0.282769 + 0.959188i $$0.408747\pi$$
−0.282769 + 0.959188i $$0.591253\pi$$
$$692$$ −4.20490e9 −0.482374
$$693$$ 1.05414e9 0.120318
$$694$$ 7.15873e9i 0.812976i
$$695$$ 2.92132e9i 0.330090i
$$696$$ − 2.44085e9i − 0.274415i
$$697$$ 1.21864e9i 0.136320i
$$698$$ 4.33300e9 0.482275
$$699$$ −9.63005e9 −1.06649
$$700$$ 1.31452e9i 0.144851i
$$701$$ −3.26804e9 −0.358323 −0.179161 0.983820i $$-0.557338\pi$$
−0.179161 + 0.983820i $$0.557338\pi$$
$$702$$ 0 0
$$703$$ 1.20884e10 1.31228
$$704$$ − 1.41610e9i − 0.152964i
$$705$$ −8.83649e9 −0.949769
$$706$$ 1.80267e9 0.192797
$$707$$ 1.58848e9i 0.169050i
$$708$$ 1.10480e9i 0.116995i
$$709$$ − 4.48613e9i − 0.472727i −0.971665 0.236363i $$-0.924044\pi$$
0.971665 0.236363i $$-0.0759555\pi$$
$$710$$ 6.42089e9i 0.673273i
$$711$$ 4.40176e9 0.459286
$$712$$ −3.57647e9 −0.371342
$$713$$ − 1.31440e10i − 1.35804i
$$714$$ −1.92074e9 −0.197481
$$715$$ 0 0
$$716$$ −2.05057e8 −0.0208776
$$717$$ 6.28831e8i 0.0637114i
$$718$$ 3.51011e9 0.353903
$$719$$ −5.42385e9 −0.544198 −0.272099 0.962269i $$-0.587718\pi$$
−0.272099 + 0.962269i $$0.587718\pi$$
$$720$$ − 1.05026e9i − 0.104865i
$$721$$ 5.03658e9i 0.500452i
$$722$$ − 1.17729e9i − 0.116414i
$$723$$ 4.45598e9i 0.438490i
$$724$$ −2.85286e9 −0.279380
$$725$$ −8.56888e9 −0.835105
$$726$$ − 3.02466e9i − 0.293359i
$$727$$ 1.50827e10 1.45582 0.727911 0.685672i $$-0.240492\pi$$
0.727911 + 0.685672i $$0.240492\pi$$
$$728$$ 0 0
$$729$$ 1.14103e10 1.09081
$$730$$ − 1.82887e10i − 1.74001i
$$731$$ 4.24475e9 0.401921
$$732$$ −2.70469e9 −0.254875
$$733$$ − 6.75596e9i − 0.633612i −0.948490 0.316806i $$-0.897390\pi$$
0.948490 0.316806i $$-0.102610\pi$$
$$734$$ − 6.46854e9i − 0.603768i
$$735$$ − 1.10765e10i − 1.02895i
$$736$$ − 2.06674e9i − 0.191080i
$$737$$ −1.86017e10 −1.71166
$$738$$ −3.09024e8 −0.0283006
$$739$$ − 1.08154e10i − 0.985797i −0.870087 0.492899i $$-0.835937\pi$$
0.870087 0.492899i $$-0.164063\pi$$
$$740$$ 1.09002e10 0.988836
$$741$$ 0 0
$$742$$ 3.94808e9 0.354791
$$743$$ − 3.71897e9i − 0.332630i −0.986073 0.166315i $$-0.946813\pi$$
0.986073 0.166315i $$-0.0531869\pi$$
$$744$$ −4.16125e9 −0.370441
$$745$$ 2.19565e10 1.94543
$$746$$ 9.43075e9i 0.831687i
$$747$$ 9.50648e7i 0.00834445i
$$748$$ − 7.26409e9i − 0.634637i
$$749$$ 3.62096e9i 0.314874i
$$750$$ −9.63963e8 −0.0834346
$$751$$ 2.15786e10 1.85902 0.929510 0.368797i $$-0.120230\pi$$
0.929510 + 0.368797i $$0.120230\pi$$
$$752$$ − 2.41054e9i − 0.206706i
$$753$$ 8.68546e9 0.741328
$$754$$ 0 0
$$755$$ −7.72496e9 −0.653253
$$756$$ − 2.08648e9i − 0.175626i
$$757$$ 7.42446e9 0.622056 0.311028 0.950401i $$-0.399327\pi$$
0.311028 + 0.950401i $$0.399327\pi$$
$$758$$ −1.43335e10 −1.19539
$$759$$ − 1.32879e10i − 1.10309i
$$760$$ 5.38650e9i 0.445102i
$$761$$ − 8.57002e9i − 0.704913i −0.935828 0.352457i $$-0.885346\pi$$
0.935828 0.352457i $$-0.114654\pi$$
$$762$$ 1.01091e10i 0.827691i
$$763$$ −4.99766e9 −0.407315
$$764$$ −1.19292e10 −0.967797
$$765$$ − 5.38743e9i − 0.435078i
$$766$$ −9.58202e9 −0.770294
$$767$$ 0 0
$$768$$ −6.54311e8 −0.0521219
$$769$$ 7.81741e9i 0.619899i 0.950753 + 0.309949i $$0.100312\pi$$
−0.950753 + 0.309949i $$0.899688\pi$$
$$770$$ −4.87498e9 −0.384818
$$771$$ 1.10098e10 0.865144
$$772$$ − 9.78732e9i − 0.765602i
$$773$$ 1.30864e10i 1.01904i 0.860457 + 0.509522i $$0.170178\pi$$
−0.860457 + 0.509522i $$0.829822\pi$$
$$774$$ 1.07639e9i 0.0834403i
$$775$$ 1.46086e10i 1.12733i
$$776$$ 1.02790e8 0.00789651
$$777$$ 5.05506e9 0.386592
$$778$$ − 1.14937e9i − 0.0875051i
$$779$$ 1.58491e9 0.120122
$$780$$ 0 0
$$781$$ −1.12616e10 −0.845903
$$782$$ − 1.06016e10i − 0.792775i
$$783$$ 1.36011e10 1.01253
$$784$$ 3.02159e9 0.223939
$$785$$ − 1.21396e10i − 0.895696i
$$786$$ − 8.25767e9i − 0.606567i
$$787$$ − 5.35561e9i − 0.391649i −0.980639 0.195825i $$-0.937262\pi$$
0.980639 0.195825i $$-0.0627383\pi$$
$$788$$ − 6.09176e9i − 0.443507i
$$789$$ 9.22311e9 0.668510
$$790$$ −2.03565e10 −1.46895
$$791$$ 6.18962e9i 0.444679i
$$792$$ 1.84204e9 0.131753
$$793$$ 0 0
$$794$$ 4.93867e9 0.350137
$$795$$ − 2.52903e10i − 1.78513i
$$796$$ 1.14295e10 0.803212
$$797$$ −1.21863e10 −0.852641 −0.426320 0.904572i $$-0.640190\pi$$
−0.426320 + 0.904572i $$0.640190\pi$$
$$798$$ 2.49803e9i 0.174016i
$$799$$ − 1.23652e10i − 0.857606i
$$800$$ 2.29704e9i 0.158618i
$$801$$ − 4.65220e9i − 0.319849i
$$802$$ −9.06438e9 −0.620480
$$803$$ 3.20765e10 2.18616
$$804$$ 8.59494e9i 0.583239i
$$805$$ −7.11484e9 −0.480706
$$806$$ 0 0
$$807$$ 1.88047e10 1.25953
$$808$$ 2.77578e9i 0.185116i
$$809$$ 1.32472e10 0.879636 0.439818 0.898087i $$-0.355043\pi$$
0.439818 + 0.898087i $$0.355043\pi$$
$$810$$ −8.87924e9 −0.587054
$$811$$ 1.45473e10i 0.957658i 0.877908 + 0.478829i $$0.158939\pi$$
−0.877908 + 0.478829i $$0.841061\pi$$
$$812$$ − 2.29221e9i − 0.150248i
$$813$$ 1.81885e10i 1.18708i
$$814$$ 1.91179e10i 1.24238i
$$815$$ −1.20866e10 −0.782083
$$816$$ −3.35638e9 −0.216250
$$817$$ − 5.52054e9i − 0.354164i
$$818$$ −8.34262e9 −0.532925
$$819$$ 0 0
$$820$$ 1.42912e9 0.0905149
$$821$$ 6.51876e9i 0.411115i 0.978645 + 0.205558i $$0.0659008\pi$$
−0.978645 + 0.205558i $$0.934099\pi$$
$$822$$ 1.67295e10 1.05059
$$823$$ 6.77944e9 0.423930 0.211965 0.977277i $$-0.432014\pi$$
0.211965 + 0.977277i $$0.432014\pi$$
$$824$$ 8.80112e9i 0.548015i
$$825$$ 1.47685e10i 0.915690i
$$826$$ 1.03752e9i 0.0640572i
$$827$$ 7.96808e9i 0.489874i 0.969539 + 0.244937i $$0.0787673\pi$$
−0.969539 + 0.244937i $$0.921233\pi$$
$$828$$ 2.68838e9 0.164583
$$829$$ −3.74439e9 −0.228265 −0.114133 0.993466i $$-0.536409\pi$$
−0.114133 + 0.993466i $$0.536409\pi$$
$$830$$ − 4.39639e8i − 0.0266884i
$$831$$ −7.35966e9 −0.444892
$$832$$ 0 0
$$833$$ 1.54997e10 0.929106
$$834$$ 2.36741e9i 0.141316i
$$835$$ 3.55035e10 2.11042
$$836$$ −9.44736e9 −0.559228
$$837$$ − 2.31876e10i − 1.36684i
$$838$$ − 5.67442e9i − 0.333094i
$$839$$ 8.06205e9i 0.471280i 0.971840 + 0.235640i $$0.0757186\pi$$
−0.971840 + 0.235640i $$0.924281\pi$$
$$840$$ 2.25249e9i 0.131125i
$$841$$ −2.30775e9 −0.133783
$$842$$ −9.59013e9 −0.553646
$$843$$ − 2.79007e10i − 1.60405i
$$844$$ 8.52706e9 0.488203
$$845$$ 0 0
$$846$$ 3.13559e9 0.178042
$$847$$ − 2.84047e9i − 0.160619i
$$848$$ 6.89904e9 0.388511
$$849$$ −1.57795e10 −0.884943
$$850$$ 1.17830e10i 0.658095i
$$851$$ 2.79017e10i 1.55195i
$$852$$ 5.20342e9i 0.288238i
$$853$$ 3.31854e9i 0.183074i 0.995802 + 0.0915368i $$0.0291779\pi$$
−0.995802 + 0.0915368i $$0.970822\pi$$
$$854$$ −2.53998e9 −0.139549
$$855$$ −7.00666e9 −0.383380
$$856$$ 6.32740e9i 0.344800i
$$857$$ 1.81939e10 0.987398 0.493699 0.869633i $$-0.335644\pi$$
0.493699 + 0.869633i $$0.335644\pi$$
$$858$$ 0 0
$$859$$ −1.91859e10 −1.03278 −0.516388 0.856355i $$-0.672724\pi$$
−0.516388 + 0.856355i $$0.672724\pi$$
$$860$$ − 4.97790e9i − 0.266871i
$$861$$ 6.62766e8 0.0353874
$$862$$ 7.63322e9 0.405913
$$863$$ − 2.77943e10i − 1.47203i −0.676963 0.736017i $$-0.736704\pi$$
0.676963 0.736017i $$-0.263296\pi$$
$$864$$ − 3.64600e9i − 0.192317i
$$865$$ 2.52951e10i 1.32886i
$$866$$ − 3.05302e9i − 0.159741i
$$867$$ −1.21381e9 −0.0632536
$$868$$ −3.90784e9 −0.202823
$$869$$ − 3.57032e10i − 1.84560i
$$870$$ −1.46832e10 −0.755969
$$871$$ 0 0
$$872$$ −8.73311e9 −0.446027
$$873$$ 1.33707e8i 0.00680152i
$$874$$ −1.37880e10 −0.698574
$$875$$ −9.05260e8 −0.0456820
$$876$$ − 1.48210e10i − 0.744925i
$$877$$ − 3.40401e10i − 1.70409i −0.523471 0.852043i $$-0.675363\pi$$
0.523471 0.852043i $$-0.324637\pi$$
$$878$$ 8.93465e8i 0.0445499i
$$879$$ − 3.16415e10i − 1.57143i
$$880$$ −8.51874e9 −0.421392
$$881$$ −3.24476e10 −1.59870 −0.799350 0.600866i $$-0.794823\pi$$
−0.799350 + 0.600866i $$0.794823\pi$$
$$882$$ 3.93043e9i 0.192886i
$$883$$ −1.15866e10 −0.566362 −0.283181 0.959066i $$-0.591390\pi$$
−0.283181 + 0.959066i $$0.591390\pi$$
$$884$$ 0 0
$$885$$ 6.64609e9 0.322303
$$886$$ − 1.16793e10i − 0.564156i
$$887$$ −2.86160e10 −1.37682 −0.688408 0.725323i $$-0.741690\pi$$
−0.688408 + 0.725323i $$0.741690\pi$$
$$888$$ 8.83342e9 0.423335
$$889$$ 9.49344e9i 0.453177i
$$890$$ 2.15147e10i 1.02299i
$$891$$ − 1.55733e10i − 0.737578i
$$892$$ − 7.64123e9i − 0.360484i
$$893$$ −1.60817e10 −0.755702
$$894$$ 1.77933e10 0.832865
$$895$$ 1.23355e9i 0.0575142i
$$896$$ −6.14466e8 −0.0285377
$$897$$ 0 0
$$898$$ 5.07207e9 0.233732
$$899$$ − 2.54739e10i − 1.16933i
$$900$$ −2.98794e9 −0.136623
$$901$$ 3.53896e10 1.61190
$$902$$ 2.50653e9i 0.113723i
$$903$$ − 2.30854e9i − 0.104335i
$$904$$ 1.08160e10i 0.486942i
$$905$$ 1.71617e10i 0.769646i
$$906$$ −6.26022e9 −0.279667
$$907$$ −2.28278e10 −1.01587 −0.507936 0.861395i $$-0.669591\pi$$
−0.507936 + 0.861395i $$0.669591\pi$$
$$908$$ − 7.27395e8i − 0.0322456i
$$909$$ −3.61068e9 −0.159446
$$910$$ 0 0
$$911$$ −1.76175e10 −0.772024 −0.386012 0.922494i $$-0.626148\pi$$
−0.386012 + 0.922494i $$0.626148\pi$$
$$912$$ 4.36516e9i 0.190554i
$$913$$ 7.71081e8 0.0335315
$$914$$ 4.83501e9 0.209453
$$915$$ 1.62704e10i 0.702140i
$$916$$ − 9.37978e8i − 0.0403235i
$$917$$ − 7.75480e9i − 0.332107i
$$918$$ − 1.87026e10i − 0.797910i
$$919$$ −4.93202e9 −0.209614 −0.104807 0.994493i $$-0.533423\pi$$
−0.104807 + 0.994493i $$0.533423\pi$$
$$920$$ −1.24328e10 −0.526393
$$921$$ 1.79774e10i 0.758258i
$$922$$ 1.76452e10 0.741425
$$923$$ 0 0
$$924$$ −3.95063e9 −0.164746
$$925$$ − 3.10108e10i − 1.28830i
$$926$$ −8.39401e9 −0.347401
$$927$$ −1.14483e10 −0.472023
$$928$$ − 4.00549e9i − 0.164527i
$$929$$ − 2.68352e10i − 1.09812i −0.835783 0.549061i $$-0.814986\pi$$
0.835783 0.549061i $$-0.185014\pi$$
$$930$$ 2.50325e10i 1.02050i
$$931$$ − 2.01582e10i − 0.818707i
$$932$$ −1.58032e10 −0.639423
$$933$$ −1.12210e10 −0.452321
$$934$$ − 1.61168e10i − 0.647241i
$$935$$ −4.36980e10 −1.74832
$$936$$ 0 0
$$937$$ −2.08650e10 −0.828570 −0.414285 0.910147i $$-0.635968\pi$$
−0.414285 + 0.910147i $$0.635968\pi$$
$$938$$ 8.07153e9i 0.319335i
$$939$$ 3.72910e10 1.46985
$$940$$ −1.45009e10 −0.569440
$$941$$ − 3.07099e10i − 1.20147i −0.799447 0.600737i $$-0.794874\pi$$
0.799447 0.600737i $$-0.205126\pi$$
$$942$$ − 9.83781e9i − 0.383460i
$$943$$ 3.65818e9i 0.142061i
$$944$$ 1.81301e9i 0.0701453i
$$945$$ −1.25515e10 −0.483820
$$946$$ 8.73071e9 0.335298
$$947$$ 1.03377e9i 0.0395548i 0.999804 + 0.0197774i $$0.00629575\pi$$
−0.999804 + 0.0197774i $$0.993704\pi$$
$$948$$ −1.64967e10 −0.628880
$$949$$ 0 0
$$950$$ 1.53244e10 0.579898
$$951$$ − 1.92177e10i − 0.724552i
$$952$$ −3.15199e9 −0.118401
$$953$$ 1.78629e9 0.0668540 0.0334270 0.999441i $$-0.489358\pi$$
0.0334270 + 0.999441i $$0.489358\pi$$
$$954$$ 8.97414e9i 0.334637i
$$955$$ 7.17615e10i 2.66612i
$$956$$ 1.03193e9i 0.0381985i
$$957$$ − 2.57529e10i − 0.949803i
$$958$$ −2.94273e10 −1.08136
$$959$$ 1.57107e10 0.575215
$$960$$ 3.93609e9i 0.143587i
$$961$$ −1.59163e10 −0.578508
$$962$$ 0 0
$$963$$ −8.23057e9 −0.296987
$$964$$ 7.31238e9i 0.262899i
$$965$$ −5.88768e10 −2.10911
$$966$$ −5.76579e9 −0.205797
$$967$$ − 1.53418e10i − 0.545613i −0.962069 0.272806i $$-0.912048\pi$$
0.962069 0.272806i $$-0.0879518\pi$$
$$968$$ − 4.96355e9i − 0.175885i
$$969$$ 2.23917e10i 0.790595i
$$970$$ − 6.18347e8i − 0.0217536i
$$971$$ −5.22182e8 −0.0183043 −0.00915217 0.999958i $$-0.502913\pi$$
−0.00915217 + 0.999958i $$0.502913\pi$$
$$972$$ 8.37817e9 0.292629
$$973$$ 2.22324e9i 0.0773733i
$$974$$ −1.53197e9 −0.0531245
$$975$$ 0 0
$$976$$ −4.43846e9 −0.152812
$$977$$ 5.68857e10i 1.95152i 0.218851 + 0.975758i $$0.429769\pi$$
−0.218851 + 0.975758i $$0.570231\pi$$
$$978$$ −9.79486e9 −0.334821
$$979$$ −3.77345e10 −1.28528
$$980$$ − 1.81768e10i − 0.616916i
$$981$$ − 1.13599e10i − 0.384177i
$$982$$ − 2.57857e9i − 0.0868936i
$$983$$ 1.15736e10i 0.388624i 0.980940 + 0.194312i $$0.0622474\pi$$
−0.980940 + 0.194312i $$0.937753\pi$$
$$984$$ 1.15814e9 0.0387507
$$985$$ −3.66457e10 −1.22179
$$986$$ − 2.05467e10i − 0.682612i
$$987$$ −6.72492e9 −0.222626
$$988$$ 0 0
$$989$$ 1.27421e10 0.418846
$$990$$ − 1.10810e10i − 0.362958i
$$991$$ 1.38509e10 0.452086 0.226043 0.974117i $$-0.427421\pi$$
0.226043 + 0.974117i $$0.427421\pi$$
$$992$$ −6.82872e9 −0.222100
$$993$$ 1.88510e10i 0.610958i
$$994$$ 4.88655e9i 0.157816i
$$995$$ − 6.87554e10i − 2.21272i
$$996$$ − 3.56279e8i − 0.0114257i
$$997$$ 5.45316e9 0.174267 0.0871334 0.996197i $$-0.472229\pi$$
0.0871334 + 0.996197i $$0.472229\pi$$
$$998$$ 3.09356e10 0.985147
$$999$$ 4.92222e10i 1.56200i
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.b.337.1 2
13.5 odd 4 26.8.a.a.1.1 1
13.8 odd 4 338.8.a.c.1.1 1
13.12 even 2 inner 338.8.b.b.337.2 2
39.5 even 4 234.8.a.d.1.1 1
52.31 even 4 208.8.a.c.1.1 1

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