# Properties

 Label 169.10.a.a.1.2 Level $169$ Weight $10$ Character 169.1 Self dual yes Analytic conductor $87.041$ Analytic rank $1$ Dimension $4$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,10,Mod(1,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("169.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$10$$ Character orbit: $$[\chi]$$ $$=$$ 169.a (trivial)

## 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: yes Analytic conductor: $$87.0410563117$$ Analytic rank: $$1$$ Dimension: $$4$$ Coefficient field: $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} - 1602x^{2} + 1544x + 342272$$ x^4 - x^3 - 1602*x^2 + 1544*x + 342272 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 13) Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-15.3567$$ of defining polynomial Character $$\chi$$ $$=$$ 169.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-7.35673 q^{2} +42.6243 q^{3} -457.879 q^{4} +1236.25 q^{5} -313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} +O(q^{10})$$ $$q-7.35673 q^{2} +42.6243 q^{3} -457.879 q^{4} +1236.25 q^{5} -313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} -9094.74 q^{10} +27149.8 q^{11} -19516.8 q^{12} +6562.27 q^{14} +52694.2 q^{15} +181943. q^{16} -34643.4 q^{17} +131437. q^{18} -428885. q^{19} -566052. q^{20} -38021.3 q^{21} -199734. q^{22} +2.03704e6 q^{23} +304130. q^{24} -424814. q^{25} -1.60051e6 q^{27} +408432. q^{28} -5.26400e6 q^{29} -387657. q^{30} +4.15910e6 q^{31} -4.99169e6 q^{32} +1.15724e6 q^{33} +254862. q^{34} -1.10275e6 q^{35} +8.18054e6 q^{36} +7.58854e6 q^{37} +3.15519e6 q^{38} +8.82080e6 q^{40} +4.92536e6 q^{41} +279712. q^{42} +1.71882e7 q^{43} -1.24313e7 q^{44} -2.20870e7 q^{45} -1.49859e7 q^{46} +2.95568e7 q^{47} +7.75518e6 q^{48} -3.95579e7 q^{49} +3.12524e6 q^{50} -1.47665e6 q^{51} -2.72331e7 q^{53} +1.17745e7 q^{54} +3.35640e7 q^{55} -6.36461e6 q^{56} -1.82809e7 q^{57} +3.87258e7 q^{58} +1.13602e8 q^{59} -2.41276e7 q^{60} -3.76868e7 q^{61} -3.05973e7 q^{62} +1.59368e7 q^{63} -5.64321e7 q^{64} -8.51352e6 q^{66} -1.90094e8 q^{67} +1.58625e7 q^{68} +8.68273e7 q^{69} +8.11260e6 q^{70} -6.87130e7 q^{71} -1.27477e8 q^{72} -3.61495e8 q^{73} -5.58268e7 q^{74} -1.81074e7 q^{75} +1.96377e8 q^{76} -2.42179e7 q^{77} -1.42229e8 q^{79} +2.24926e8 q^{80} +2.83439e8 q^{81} -3.62346e7 q^{82} +5.80240e7 q^{83} +1.74091e7 q^{84} -4.28279e7 q^{85} -1.26449e8 q^{86} -2.24374e8 q^{87} +1.93718e8 q^{88} +8.59928e8 q^{89} +1.62488e8 q^{90} -9.32716e8 q^{92} +1.77279e8 q^{93} -2.17442e8 q^{94} -5.30208e8 q^{95} -2.12767e8 q^{96} -1.46970e9 q^{97} +2.91017e8 q^{98} -4.85064e8 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10})$$ 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 $$4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 67831 q^{10} + 40140 q^{11} - 155479 q^{12} - 277653 q^{14} - 83307 q^{15} + 726609 q^{16} + 78717 q^{17} - 1691026 q^{18} - 209664 q^{19} - 870843 q^{20} - 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} - 3561573 q^{24} - 2900157 q^{25} - 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} + 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} - 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} - 4636891 q^{37} + 25172466 q^{38} + 22536791 q^{40} - 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} - 66489222 q^{44} + 17423928 q^{45} - 71369332 q^{46} + 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} + 4217748 q^{50} - 19664471 q^{51} - 171019326 q^{53} + 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} + 63389388 q^{59} - 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} - 409056389 q^{70} - 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} + 326897170 q^{76} + 561950454 q^{77} + 115998984 q^{79} + 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} + 79577862 q^{83} - 108899441 q^{84} - 549463469 q^{85} + 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} + 1152240276 q^{89} + 877550038 q^{90} - 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} - 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} - 2132181050 q^{99}+O(q^{100})$$ 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 67831 * q^10 + 40140 * q^11 - 155479 * q^12 - 277653 * q^14 - 83307 * q^15 + 726609 * q^16 + 78717 * q^17 - 1691026 * q^18 - 209664 * q^19 - 870843 * q^20 - 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 - 3561573 * q^24 - 2900157 * q^25 - 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 + 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 - 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 - 4636891 * q^37 + 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 - 66489222 * q^44 + 17423928 * q^45 - 71369332 * q^46 + 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 + 4217748 * q^50 - 19664471 * q^51 - 171019326 * q^53 + 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 + 63389388 * q^59 - 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 - 409056389 * q^70 - 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 + 326897170 * q^76 + 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 + 79577862 * q^83 - 108899441 * q^84 - 549463469 * q^85 + 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 + 1152240276 * q^89 + 877550038 * q^90 - 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 - 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 - 2132181050 * q^99

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −7.35673 −0.325124 −0.162562 0.986698i $$-0.551976\pi$$
−0.162562 + 0.986698i $$0.551976\pi$$
$$3$$ 42.6243 0.303817 0.151908 0.988395i $$-0.451458\pi$$
0.151908 + 0.988395i $$0.451458\pi$$
$$4$$ −457.879 −0.894294
$$5$$ 1236.25 0.884588 0.442294 0.896870i $$-0.354165\pi$$
0.442294 + 0.896870i $$0.354165\pi$$
$$6$$ −313.575 −0.0987782
$$7$$ −892.010 −0.140420 −0.0702099 0.997532i $$-0.522367\pi$$
−0.0702099 + 0.997532i $$0.522367\pi$$
$$8$$ 7135.13 0.615881
$$9$$ −17866.2 −0.907695
$$10$$ −9094.74 −0.287601
$$11$$ 27149.8 0.559114 0.279557 0.960129i $$-0.409812\pi$$
0.279557 + 0.960129i $$0.409812\pi$$
$$12$$ −19516.8 −0.271702
$$13$$ 0 0
$$14$$ 6562.27 0.0456539
$$15$$ 52694.2 0.268753
$$16$$ 181943. 0.694056
$$17$$ −34643.4 −0.100601 −0.0503003 0.998734i $$-0.516018\pi$$
−0.0503003 + 0.998734i $$0.516018\pi$$
$$18$$ 131437. 0.295114
$$19$$ −428885. −0.755004 −0.377502 0.926009i $$-0.623217\pi$$
−0.377502 + 0.926009i $$0.623217\pi$$
$$20$$ −566052. −0.791081
$$21$$ −38021.3 −0.0426619
$$22$$ −199734. −0.181782
$$23$$ 2.03704e6 1.51783 0.758916 0.651188i $$-0.225729\pi$$
0.758916 + 0.651188i $$0.225729\pi$$
$$24$$ 304130. 0.187115
$$25$$ −424814. −0.217505
$$26$$ 0 0
$$27$$ −1.60051e6 −0.579590
$$28$$ 408432. 0.125577
$$29$$ −5.26400e6 −1.38205 −0.691026 0.722830i $$-0.742841\pi$$
−0.691026 + 0.722830i $$0.742841\pi$$
$$30$$ −387657. −0.0873780
$$31$$ 4.15910e6 0.808856 0.404428 0.914570i $$-0.367471\pi$$
0.404428 + 0.914570i $$0.367471\pi$$
$$32$$ −4.99169e6 −0.841536
$$33$$ 1.15724e6 0.169868
$$34$$ 254862. 0.0327077
$$35$$ −1.10275e6 −0.124214
$$36$$ 8.18054e6 0.811747
$$37$$ 7.58854e6 0.665657 0.332829 0.942987i $$-0.391997\pi$$
0.332829 + 0.942987i $$0.391997\pi$$
$$38$$ 3.15519e6 0.245470
$$39$$ 0 0
$$40$$ 8.82080e6 0.544801
$$41$$ 4.92536e6 0.272214 0.136107 0.990694i $$-0.456541\pi$$
0.136107 + 0.990694i $$0.456541\pi$$
$$42$$ 279712. 0.0138704
$$43$$ 1.71882e7 0.766696 0.383348 0.923604i $$-0.374771\pi$$
0.383348 + 0.923604i $$0.374771\pi$$
$$44$$ −1.24313e7 −0.500012
$$45$$ −2.20870e7 −0.802936
$$46$$ −1.49859e7 −0.493484
$$47$$ 2.95568e7 0.883522 0.441761 0.897133i $$-0.354354\pi$$
0.441761 + 0.897133i $$0.354354\pi$$
$$48$$ 7.75518e6 0.210866
$$49$$ −3.95579e7 −0.980282
$$50$$ 3.12524e6 0.0707161
$$51$$ −1.47665e6 −0.0305642
$$52$$ 0 0
$$53$$ −2.72331e7 −0.474084 −0.237042 0.971499i $$-0.576178\pi$$
−0.237042 + 0.971499i $$0.576178\pi$$
$$54$$ 1.17745e7 0.188439
$$55$$ 3.35640e7 0.494585
$$56$$ −6.36461e6 −0.0864819
$$57$$ −1.82809e7 −0.229383
$$58$$ 3.87258e7 0.449339
$$59$$ 1.13602e8 1.22054 0.610272 0.792192i $$-0.291060\pi$$
0.610272 + 0.792192i $$0.291060\pi$$
$$60$$ −2.41276e7 −0.240344
$$61$$ −3.76868e7 −0.348502 −0.174251 0.984701i $$-0.555750\pi$$
−0.174251 + 0.984701i $$0.555750\pi$$
$$62$$ −3.05973e7 −0.262979
$$63$$ 1.59368e7 0.127458
$$64$$ −5.64321e7 −0.420452
$$65$$ 0 0
$$66$$ −8.51352e6 −0.0552283
$$67$$ −1.90094e8 −1.15247 −0.576237 0.817283i $$-0.695479\pi$$
−0.576237 + 0.817283i $$0.695479\pi$$
$$68$$ 1.58625e7 0.0899666
$$69$$ 8.68273e7 0.461143
$$70$$ 8.11260e6 0.0403849
$$71$$ −6.87130e7 −0.320905 −0.160453 0.987044i $$-0.551295\pi$$
−0.160453 + 0.987044i $$0.551295\pi$$
$$72$$ −1.27477e8 −0.559033
$$73$$ −3.61495e8 −1.48987 −0.744937 0.667135i $$-0.767520\pi$$
−0.744937 + 0.667135i $$0.767520\pi$$
$$74$$ −5.58268e7 −0.216421
$$75$$ −1.81074e7 −0.0660816
$$76$$ 1.96377e8 0.675196
$$77$$ −2.42179e7 −0.0785107
$$78$$ 0 0
$$79$$ −1.42229e8 −0.410834 −0.205417 0.978675i $$-0.565855\pi$$
−0.205417 + 0.978675i $$0.565855\pi$$
$$80$$ 2.24926e8 0.613953
$$81$$ 2.83439e8 0.731606
$$82$$ −3.62346e7 −0.0885035
$$83$$ 5.80240e7 0.134201 0.0671006 0.997746i $$-0.478625\pi$$
0.0671006 + 0.997746i $$0.478625\pi$$
$$84$$ 1.74091e7 0.0381523
$$85$$ −4.28279e7 −0.0889901
$$86$$ −1.26449e8 −0.249272
$$87$$ −2.24374e8 −0.419891
$$88$$ 1.93718e8 0.344348
$$89$$ 8.59928e8 1.45280 0.726402 0.687270i $$-0.241191\pi$$
0.726402 + 0.687270i $$0.241191\pi$$
$$90$$ 1.62488e8 0.261054
$$91$$ 0 0
$$92$$ −9.32716e8 −1.35739
$$93$$ 1.77279e8 0.245744
$$94$$ −2.17442e8 −0.287255
$$95$$ −5.30208e8 −0.667867
$$96$$ −2.12767e8 −0.255673
$$97$$ −1.46970e9 −1.68560 −0.842802 0.538223i $$-0.819096\pi$$
−0.842802 + 0.538223i $$0.819096\pi$$
$$98$$ 2.91017e8 0.318714
$$99$$ −4.85064e8 −0.507505
$$100$$ 1.94513e8 0.194513
$$101$$ −4.15100e8 −0.396923 −0.198462 0.980109i $$-0.563595\pi$$
−0.198462 + 0.980109i $$0.563595\pi$$
$$102$$ 1.08633e7 0.00993716
$$103$$ 1.86377e9 1.63164 0.815821 0.578305i $$-0.196286\pi$$
0.815821 + 0.578305i $$0.196286\pi$$
$$104$$ 0 0
$$105$$ −4.70038e7 −0.0377382
$$106$$ 2.00346e8 0.154136
$$107$$ −7.50777e8 −0.553712 −0.276856 0.960911i $$-0.589293\pi$$
−0.276856 + 0.960911i $$0.589293\pi$$
$$108$$ 7.32838e8 0.518324
$$109$$ −2.07010e9 −1.40467 −0.702333 0.711849i $$-0.747858\pi$$
−0.702333 + 0.711849i $$0.747858\pi$$
$$110$$ −2.46921e8 −0.160802
$$111$$ 3.23456e8 0.202238
$$112$$ −1.62295e8 −0.0974592
$$113$$ −2.10155e9 −1.21251 −0.606257 0.795268i $$-0.707330\pi$$
−0.606257 + 0.795268i $$0.707330\pi$$
$$114$$ 1.34488e8 0.0745780
$$115$$ 2.51829e9 1.34266
$$116$$ 2.41027e9 1.23596
$$117$$ 0 0
$$118$$ −8.35741e8 −0.396828
$$119$$ 3.09023e7 0.0141263
$$120$$ 3.75980e8 0.165520
$$121$$ −1.62083e9 −0.687392
$$122$$ 2.77251e8 0.113306
$$123$$ 2.09940e8 0.0827033
$$124$$ −1.90436e9 −0.723356
$$125$$ −2.93972e9 −1.07699
$$126$$ −1.17243e8 −0.0414398
$$127$$ −4.77696e9 −1.62943 −0.814713 0.579865i $$-0.803105\pi$$
−0.814713 + 0.579865i $$0.803105\pi$$
$$128$$ 2.97090e9 0.978235
$$129$$ 7.32636e8 0.232935
$$130$$ 0 0
$$131$$ −4.62884e9 −1.37326 −0.686628 0.727009i $$-0.740910\pi$$
−0.686628 + 0.727009i $$0.740910\pi$$
$$132$$ −5.29877e8 −0.151912
$$133$$ 3.82569e8 0.106018
$$134$$ 1.39847e9 0.374697
$$135$$ −1.97863e9 −0.512698
$$136$$ −2.47186e8 −0.0619581
$$137$$ −3.85972e9 −0.936080 −0.468040 0.883707i $$-0.655040\pi$$
−0.468040 + 0.883707i $$0.655040\pi$$
$$138$$ −6.38765e8 −0.149929
$$139$$ −8.38068e9 −1.90420 −0.952100 0.305786i $$-0.901081\pi$$
−0.952100 + 0.305786i $$0.901081\pi$$
$$140$$ 5.04924e8 0.111084
$$141$$ 1.25984e9 0.268429
$$142$$ 5.05503e8 0.104334
$$143$$ 0 0
$$144$$ −3.25062e9 −0.629991
$$145$$ −6.50761e9 −1.22255
$$146$$ 2.65942e9 0.484394
$$147$$ −1.68613e9 −0.297826
$$148$$ −3.47463e9 −0.595293
$$149$$ −3.96089e9 −0.658347 −0.329174 0.944269i $$-0.606770\pi$$
−0.329174 + 0.944269i $$0.606770\pi$$
$$150$$ 1.33211e8 0.0214847
$$151$$ −1.11419e10 −1.74407 −0.872036 0.489442i $$-0.837201\pi$$
−0.872036 + 0.489442i $$0.837201\pi$$
$$152$$ −3.06015e9 −0.464993
$$153$$ 6.18946e8 0.0913148
$$154$$ 1.78165e8 0.0255257
$$155$$ 5.14168e9 0.715504
$$156$$ 0 0
$$157$$ −7.39104e9 −0.970861 −0.485430 0.874275i $$-0.661337\pi$$
−0.485430 + 0.874275i $$0.661337\pi$$
$$158$$ 1.04634e9 0.133572
$$159$$ −1.16079e9 −0.144035
$$160$$ −6.17097e9 −0.744412
$$161$$ −1.81706e9 −0.213134
$$162$$ −2.08519e9 −0.237863
$$163$$ 7.32911e8 0.0813218 0.0406609 0.999173i $$-0.487054\pi$$
0.0406609 + 0.999173i $$0.487054\pi$$
$$164$$ −2.25522e9 −0.243440
$$165$$ 1.43064e9 0.150263
$$166$$ −4.26867e8 −0.0436321
$$167$$ 1.23516e10 1.22885 0.614427 0.788974i $$-0.289387\pi$$
0.614427 + 0.788974i $$0.289387\pi$$
$$168$$ −2.71287e8 −0.0262747
$$169$$ 0 0
$$170$$ 3.15073e8 0.0289329
$$171$$ 7.66252e9 0.685314
$$172$$ −7.87012e9 −0.685651
$$173$$ 1.12727e10 0.956794 0.478397 0.878144i $$-0.341218\pi$$
0.478397 + 0.878144i $$0.341218\pi$$
$$174$$ 1.65066e9 0.136517
$$175$$ 3.78938e8 0.0305420
$$176$$ 4.93971e9 0.388056
$$177$$ 4.84222e9 0.370822
$$178$$ −6.32626e9 −0.472342
$$179$$ −3.32764e9 −0.242269 −0.121134 0.992636i $$-0.538653\pi$$
−0.121134 + 0.992636i $$0.538653\pi$$
$$180$$ 1.01132e10 0.718061
$$181$$ 1.56098e10 1.08104 0.540521 0.841330i $$-0.318227\pi$$
0.540521 + 0.841330i $$0.318227\pi$$
$$182$$ 0 0
$$183$$ −1.60637e9 −0.105881
$$184$$ 1.45345e10 0.934805
$$185$$ 9.38133e9 0.588832
$$186$$ −1.30419e9 −0.0798974
$$187$$ −9.40564e8 −0.0562472
$$188$$ −1.35334e10 −0.790129
$$189$$ 1.42767e9 0.0813859
$$190$$ 3.90060e9 0.217140
$$191$$ 2.64757e10 1.43945 0.719725 0.694259i $$-0.244268\pi$$
0.719725 + 0.694259i $$0.244268\pi$$
$$192$$ −2.40538e9 −0.127740
$$193$$ 2.67204e9 0.138623 0.0693114 0.997595i $$-0.477920\pi$$
0.0693114 + 0.997595i $$0.477920\pi$$
$$194$$ 1.08122e10 0.548031
$$195$$ 0 0
$$196$$ 1.81127e10 0.876661
$$197$$ −1.38233e10 −0.653903 −0.326951 0.945041i $$-0.606021\pi$$
−0.326951 + 0.945041i $$0.606021\pi$$
$$198$$ 3.56848e9 0.165002
$$199$$ −1.21811e10 −0.550616 −0.275308 0.961356i $$-0.588780\pi$$
−0.275308 + 0.961356i $$0.588780\pi$$
$$200$$ −3.03110e9 −0.133957
$$201$$ −8.10261e9 −0.350141
$$202$$ 3.05378e9 0.129049
$$203$$ 4.69554e9 0.194068
$$204$$ 6.76128e8 0.0273334
$$205$$ 6.08897e9 0.240797
$$206$$ −1.37112e10 −0.530486
$$207$$ −3.63941e10 −1.37773
$$208$$ 0 0
$$209$$ −1.16441e10 −0.422133
$$210$$ 3.45794e8 0.0122696
$$211$$ −3.16880e9 −0.110058 −0.0550292 0.998485i $$-0.517525\pi$$
−0.0550292 + 0.998485i $$0.517525\pi$$
$$212$$ 1.24695e10 0.423971
$$213$$ −2.92885e9 −0.0974963
$$214$$ 5.52326e9 0.180025
$$215$$ 2.12489e10 0.678210
$$216$$ −1.14198e10 −0.356959
$$217$$ −3.70996e9 −0.113579
$$218$$ 1.52292e10 0.456691
$$219$$ −1.54085e10 −0.452648
$$220$$ −1.53682e10 −0.442305
$$221$$ 0 0
$$222$$ −2.37958e9 −0.0657524
$$223$$ 1.00184e10 0.271285 0.135642 0.990758i $$-0.456690\pi$$
0.135642 + 0.990758i $$0.456690\pi$$
$$224$$ 4.45264e9 0.118168
$$225$$ 7.58980e9 0.197428
$$226$$ 1.54605e10 0.394218
$$227$$ 5.23965e10 1.30974 0.654871 0.755741i $$-0.272723\pi$$
0.654871 + 0.755741i $$0.272723\pi$$
$$228$$ 8.37044e9 0.205136
$$229$$ 2.94853e10 0.708510 0.354255 0.935149i $$-0.384734\pi$$
0.354255 + 0.935149i $$0.384734\pi$$
$$230$$ −1.85263e10 −0.436530
$$231$$ −1.03227e9 −0.0238529
$$232$$ −3.75593e10 −0.851180
$$233$$ −6.67468e10 −1.48364 −0.741820 0.670599i $$-0.766037\pi$$
−0.741820 + 0.670599i $$0.766037\pi$$
$$234$$ 0 0
$$235$$ 3.65396e10 0.781553
$$236$$ −5.20161e10 −1.09152
$$237$$ −6.06241e9 −0.124818
$$238$$ −2.27340e8 −0.00459281
$$239$$ 7.42940e10 1.47286 0.736432 0.676511i $$-0.236509\pi$$
0.736432 + 0.676511i $$0.236509\pi$$
$$240$$ 9.58733e9 0.186529
$$241$$ −9.01496e10 −1.72142 −0.860711 0.509095i $$-0.829980\pi$$
−0.860711 + 0.509095i $$0.829980\pi$$
$$242$$ 1.19240e10 0.223488
$$243$$ 4.35842e10 0.801864
$$244$$ 1.72560e10 0.311663
$$245$$ −4.89034e10 −0.867146
$$246$$ −1.54447e9 −0.0268889
$$247$$ 0 0
$$248$$ 2.96757e10 0.498160
$$249$$ 2.47323e9 0.0407726
$$250$$ 2.16267e10 0.350156
$$251$$ 3.62007e10 0.575685 0.287843 0.957678i $$-0.407062\pi$$
0.287843 + 0.957678i $$0.407062\pi$$
$$252$$ −7.29712e9 −0.113985
$$253$$ 5.53053e10 0.848641
$$254$$ 3.51428e10 0.529766
$$255$$ −1.82551e9 −0.0270367
$$256$$ 7.03715e9 0.102404
$$257$$ −1.97638e10 −0.282600 −0.141300 0.989967i $$-0.545128\pi$$
−0.141300 + 0.989967i $$0.545128\pi$$
$$258$$ −5.38980e9 −0.0757329
$$259$$ −6.76905e9 −0.0934714
$$260$$ 0 0
$$261$$ 9.40474e10 1.25448
$$262$$ 3.40531e10 0.446479
$$263$$ −1.70457e10 −0.219692 −0.109846 0.993949i $$-0.535036\pi$$
−0.109846 + 0.993949i $$0.535036\pi$$
$$264$$ 8.25708e9 0.104619
$$265$$ −3.36669e10 −0.419369
$$266$$ −2.81446e9 −0.0344689
$$267$$ 3.66539e10 0.441386
$$268$$ 8.70398e10 1.03065
$$269$$ 6.56819e10 0.764822 0.382411 0.923992i $$-0.375094\pi$$
0.382411 + 0.923992i $$0.375094\pi$$
$$270$$ 1.45562e10 0.166691
$$271$$ −1.52442e11 −1.71689 −0.858447 0.512902i $$-0.828570\pi$$
−0.858447 + 0.512902i $$0.828570\pi$$
$$272$$ −6.30312e9 −0.0698225
$$273$$ 0 0
$$274$$ 2.83949e10 0.304343
$$275$$ −1.15336e10 −0.121610
$$276$$ −3.97564e10 −0.412397
$$277$$ −1.21612e11 −1.24113 −0.620566 0.784154i $$-0.713097\pi$$
−0.620566 + 0.784154i $$0.713097\pi$$
$$278$$ 6.16544e10 0.619102
$$279$$ −7.43071e10 −0.734195
$$280$$ −7.86824e9 −0.0765008
$$281$$ 2.03083e11 1.94310 0.971548 0.236842i $$-0.0761124\pi$$
0.971548 + 0.236842i $$0.0761124\pi$$
$$282$$ −9.26829e9 −0.0872728
$$283$$ 3.09567e10 0.286891 0.143445 0.989658i $$-0.454182\pi$$
0.143445 + 0.989658i $$0.454182\pi$$
$$284$$ 3.14622e10 0.286984
$$285$$ −2.25998e10 −0.202909
$$286$$ 0 0
$$287$$ −4.39347e9 −0.0382243
$$288$$ 8.91824e10 0.763858
$$289$$ −1.17388e11 −0.989880
$$290$$ 4.78747e10 0.397480
$$291$$ −6.26449e10 −0.512115
$$292$$ 1.65521e11 1.33238
$$293$$ 7.81733e10 0.619661 0.309831 0.950792i $$-0.399728\pi$$
0.309831 + 0.950792i $$0.399728\pi$$
$$294$$ 1.24044e10 0.0968306
$$295$$ 1.40441e11 1.07968
$$296$$ 5.41452e10 0.409966
$$297$$ −4.34535e10 −0.324057
$$298$$ 2.91392e10 0.214045
$$299$$ 0 0
$$300$$ 8.29099e9 0.0590964
$$301$$ −1.53321e10 −0.107659
$$302$$ 8.19682e10 0.567040
$$303$$ −1.76933e10 −0.120592
$$304$$ −7.80324e10 −0.524015
$$305$$ −4.65902e10 −0.308280
$$306$$ −4.55341e9 −0.0296887
$$307$$ −1.19962e11 −0.770766 −0.385383 0.922757i $$-0.625931\pi$$
−0.385383 + 0.922757i $$0.625931\pi$$
$$308$$ 1.10889e10 0.0702116
$$309$$ 7.94419e10 0.495720
$$310$$ −3.78259e10 −0.232628
$$311$$ 1.16227e11 0.704504 0.352252 0.935905i $$-0.385416\pi$$
0.352252 + 0.935905i $$0.385416\pi$$
$$312$$ 0 0
$$313$$ 9.92344e10 0.584403 0.292202 0.956357i $$-0.405612\pi$$
0.292202 + 0.956357i $$0.405612\pi$$
$$314$$ 5.43738e10 0.315651
$$315$$ 1.97018e10 0.112748
$$316$$ 6.51236e10 0.367406
$$317$$ 2.98194e11 1.65856 0.829281 0.558832i $$-0.188750\pi$$
0.829281 + 0.558832i $$0.188750\pi$$
$$318$$ 8.53963e9 0.0468292
$$319$$ −1.42917e11 −0.772725
$$320$$ −6.97642e10 −0.371927
$$321$$ −3.20014e10 −0.168227
$$322$$ 1.33676e10 0.0692950
$$323$$ 1.48580e10 0.0759539
$$324$$ −1.29781e11 −0.654271
$$325$$ 0 0
$$326$$ −5.39183e9 −0.0264397
$$327$$ −8.82367e10 −0.426761
$$328$$ 3.51431e10 0.167652
$$329$$ −2.63650e10 −0.124064
$$330$$ −1.05248e10 −0.0488542
$$331$$ −6.87707e10 −0.314904 −0.157452 0.987527i $$-0.550328\pi$$
−0.157452 + 0.987527i $$0.550328\pi$$
$$332$$ −2.65680e10 −0.120015
$$333$$ −1.35578e11 −0.604214
$$334$$ −9.08675e10 −0.399530
$$335$$ −2.35003e11 −1.01946
$$336$$ −6.91769e9 −0.0296097
$$337$$ −1.56091e11 −0.659239 −0.329619 0.944114i $$-0.606920\pi$$
−0.329619 + 0.944114i $$0.606920\pi$$
$$338$$ 0 0
$$339$$ −8.95772e10 −0.368382
$$340$$ 1.96100e10 0.0795833
$$341$$ 1.12919e11 0.452243
$$342$$ −5.63711e10 −0.222812
$$343$$ 7.12819e10 0.278071
$$344$$ 1.22640e11 0.472194
$$345$$ 1.07340e11 0.407921
$$346$$ −8.29298e10 −0.311077
$$347$$ −1.65467e11 −0.612673 −0.306337 0.951923i $$-0.599103\pi$$
−0.306337 + 0.951923i $$0.599103\pi$$
$$348$$ 1.02736e11 0.375506
$$349$$ 4.02009e11 1.45051 0.725257 0.688478i $$-0.241721\pi$$
0.725257 + 0.688478i $$0.241721\pi$$
$$350$$ −2.78775e9 −0.00992995
$$351$$ 0 0
$$352$$ −1.35524e11 −0.470514
$$353$$ −2.74001e11 −0.939217 −0.469609 0.882875i $$-0.655605\pi$$
−0.469609 + 0.882875i $$0.655605\pi$$
$$354$$ −3.56229e10 −0.120563
$$355$$ −8.49464e10 −0.283869
$$356$$ −3.93743e11 −1.29923
$$357$$ 1.31719e9 0.00429182
$$358$$ 2.44805e10 0.0787675
$$359$$ −8.26405e10 −0.262584 −0.131292 0.991344i $$-0.541913\pi$$
−0.131292 + 0.991344i $$0.541913\pi$$
$$360$$ −1.57594e11 −0.494513
$$361$$ −1.38746e11 −0.429969
$$362$$ −1.14837e11 −0.351473
$$363$$ −6.90869e10 −0.208841
$$364$$ 0 0
$$365$$ −4.46898e11 −1.31792
$$366$$ 1.18176e10 0.0344244
$$367$$ 4.83059e10 0.138996 0.0694980 0.997582i $$-0.477860\pi$$
0.0694980 + 0.997582i $$0.477860\pi$$
$$368$$ 3.70624e11 1.05346
$$369$$ −8.79974e10 −0.247088
$$370$$ −6.90158e10 −0.191444
$$371$$ 2.42922e10 0.0665708
$$372$$ −8.11721e10 −0.219768
$$373$$ 8.53749e10 0.228371 0.114185 0.993459i $$-0.463574\pi$$
0.114185 + 0.993459i $$0.463574\pi$$
$$374$$ 6.91947e9 0.0182873
$$375$$ −1.25304e11 −0.327207
$$376$$ 2.10892e11 0.544145
$$377$$ 0 0
$$378$$ −1.05030e10 −0.0264605
$$379$$ 2.25085e11 0.560365 0.280182 0.959947i $$-0.409605\pi$$
0.280182 + 0.959947i $$0.409605\pi$$
$$380$$ 2.42771e11 0.597270
$$381$$ −2.03614e11 −0.495047
$$382$$ −1.94774e11 −0.468001
$$383$$ −6.84152e11 −1.62464 −0.812322 0.583210i $$-0.801797\pi$$
−0.812322 + 0.583210i $$0.801797\pi$$
$$384$$ 1.26633e11 0.297204
$$385$$ −2.99394e10 −0.0694495
$$386$$ −1.96574e10 −0.0450696
$$387$$ −3.07088e11 −0.695926
$$388$$ 6.72944e11 1.50743
$$389$$ 7.47317e11 1.65475 0.827374 0.561652i $$-0.189834\pi$$
0.827374 + 0.561652i $$0.189834\pi$$
$$390$$ 0 0
$$391$$ −7.05700e10 −0.152695
$$392$$ −2.82251e11 −0.603738
$$393$$ −1.97301e11 −0.417218
$$394$$ 1.01694e11 0.212600
$$395$$ −1.75830e11 −0.363419
$$396$$ 2.22100e11 0.453859
$$397$$ −1.63235e11 −0.329804 −0.164902 0.986310i $$-0.552731\pi$$
−0.164902 + 0.986310i $$0.552731\pi$$
$$398$$ 8.96133e10 0.179019
$$399$$ 1.63067e10 0.0322099
$$400$$ −7.72918e10 −0.150961
$$401$$ 7.33836e11 1.41726 0.708629 0.705581i $$-0.249314\pi$$
0.708629 + 0.705581i $$0.249314\pi$$
$$402$$ 5.96087e10 0.113839
$$403$$ 0 0
$$404$$ 1.90065e11 0.354966
$$405$$ 3.50401e11 0.647170
$$406$$ −3.45438e10 −0.0630961
$$407$$ 2.06028e11 0.372178
$$408$$ −1.05361e10 −0.0188239
$$409$$ −7.45800e11 −1.31785 −0.658927 0.752207i $$-0.728990\pi$$
−0.658927 + 0.752207i $$0.728990\pi$$
$$410$$ −4.47949e10 −0.0782891
$$411$$ −1.64518e11 −0.284397
$$412$$ −8.53380e11 −1.45917
$$413$$ −1.01334e11 −0.171388
$$414$$ 2.67741e11 0.447934
$$415$$ 7.17321e10 0.118713
$$416$$ 0 0
$$417$$ −3.57221e11 −0.578528
$$418$$ 8.56628e10 0.137246
$$419$$ −5.46254e11 −0.865828 −0.432914 0.901435i $$-0.642515\pi$$
−0.432914 + 0.901435i $$0.642515\pi$$
$$420$$ 2.15220e10 0.0337490
$$421$$ 2.95449e11 0.458366 0.229183 0.973383i $$-0.426394\pi$$
0.229183 + 0.973383i $$0.426394\pi$$
$$422$$ 2.33120e10 0.0357827
$$423$$ −5.28067e11 −0.801969
$$424$$ −1.94312e11 −0.291980
$$425$$ 1.47170e10 0.0218811
$$426$$ 2.15467e10 0.0316984
$$427$$ 3.36170e10 0.0489365
$$428$$ 3.43765e11 0.495182
$$429$$ 0 0
$$430$$ −1.56323e11 −0.220502
$$431$$ 5.49479e11 0.767014 0.383507 0.923538i $$-0.374716\pi$$
0.383507 + 0.923538i $$0.374716\pi$$
$$432$$ −2.91201e11 −0.402268
$$433$$ −7.54093e11 −1.03093 −0.515465 0.856910i $$-0.672381\pi$$
−0.515465 + 0.856910i $$0.672381\pi$$
$$434$$ 2.72931e10 0.0369275
$$435$$ −2.77382e11 −0.371430
$$436$$ 9.47856e11 1.25618
$$437$$ −8.73654e11 −1.14597
$$438$$ 1.13356e11 0.147167
$$439$$ 9.98220e10 0.128273 0.0641366 0.997941i $$-0.479571\pi$$
0.0641366 + 0.997941i $$0.479571\pi$$
$$440$$ 2.39483e11 0.304606
$$441$$ 7.06749e11 0.889798
$$442$$ 0 0
$$443$$ −1.08040e12 −1.33281 −0.666404 0.745591i $$-0.732168\pi$$
−0.666404 + 0.745591i $$0.732168\pi$$
$$444$$ −1.48104e11 −0.180860
$$445$$ 1.06309e12 1.28513
$$446$$ −7.37024e10 −0.0882013
$$447$$ −1.68830e11 −0.200017
$$448$$ 5.03380e10 0.0590398
$$449$$ −1.02947e12 −1.19538 −0.597688 0.801729i $$-0.703914\pi$$
−0.597688 + 0.801729i $$0.703914\pi$$
$$450$$ −5.58361e10 −0.0641887
$$451$$ 1.33723e11 0.152199
$$452$$ 9.62256e11 1.08435
$$453$$ −4.74917e11 −0.529878
$$454$$ −3.85466e11 −0.425829
$$455$$ 0 0
$$456$$ −1.30437e11 −0.141273
$$457$$ −1.06106e12 −1.13793 −0.568966 0.822361i $$-0.692657\pi$$
−0.568966 + 0.822361i $$0.692657\pi$$
$$458$$ −2.16915e11 −0.230354
$$459$$ 5.54471e10 0.0583071
$$460$$ −1.15307e12 −1.20073
$$461$$ 7.20760e11 0.743253 0.371626 0.928382i $$-0.378800\pi$$
0.371626 + 0.928382i $$0.378800\pi$$
$$462$$ 7.59414e9 0.00775514
$$463$$ −1.41179e11 −0.142776 −0.0713880 0.997449i $$-0.522743\pi$$
−0.0713880 + 0.997449i $$0.522743\pi$$
$$464$$ −9.57745e11 −0.959222
$$465$$ 2.19161e11 0.217382
$$466$$ 4.91038e11 0.482368
$$467$$ −5.23104e11 −0.508935 −0.254467 0.967081i $$-0.581900\pi$$
−0.254467 + 0.967081i $$0.581900\pi$$
$$468$$ 0 0
$$469$$ 1.69565e11 0.161830
$$470$$ −2.68812e11 −0.254102
$$471$$ −3.15038e11 −0.294964
$$472$$ 8.10568e11 0.751710
$$473$$ 4.66658e11 0.428670
$$474$$ 4.45995e10 0.0405814
$$475$$ 1.82196e11 0.164217
$$476$$ −1.41495e10 −0.0126331
$$477$$ 4.86551e11 0.430324
$$478$$ −5.46560e11 −0.478864
$$479$$ −1.22387e12 −1.06224 −0.531122 0.847295i $$-0.678230\pi$$
−0.531122 + 0.847295i $$0.678230\pi$$
$$480$$ −2.63033e11 −0.226165
$$481$$ 0 0
$$482$$ 6.63206e11 0.559676
$$483$$ −7.74508e10 −0.0647536
$$484$$ 7.42145e11 0.614730
$$485$$ −1.81691e12 −1.49107
$$486$$ −3.20637e11 −0.260706
$$487$$ 3.77344e11 0.303988 0.151994 0.988381i $$-0.451431\pi$$
0.151994 + 0.988381i $$0.451431\pi$$
$$488$$ −2.68900e11 −0.214636
$$489$$ 3.12398e10 0.0247069
$$490$$ 3.59769e11 0.281930
$$491$$ −2.35736e12 −1.83046 −0.915229 0.402934i $$-0.867990\pi$$
−0.915229 + 0.402934i $$0.867990\pi$$
$$492$$ −9.61271e10 −0.0739610
$$493$$ 1.82363e11 0.139035
$$494$$ 0 0
$$495$$ −5.99659e11 −0.448933
$$496$$ 7.56717e11 0.561392
$$497$$ 6.12927e10 0.0450614
$$498$$ −1.81949e10 −0.0132562
$$499$$ 2.64345e12 1.90862 0.954309 0.298822i $$-0.0965938\pi$$
0.954309 + 0.298822i $$0.0965938\pi$$
$$500$$ 1.34604e12 0.963145
$$501$$ 5.26480e11 0.373346
$$502$$ −2.66319e11 −0.187169
$$503$$ 1.53328e11 0.106799 0.0533994 0.998573i $$-0.482994\pi$$
0.0533994 + 0.998573i $$0.482994\pi$$
$$504$$ 1.13711e11 0.0784993
$$505$$ −5.13167e11 −0.351113
$$506$$ −4.06866e11 −0.275914
$$507$$ 0 0
$$508$$ 2.18727e12 1.45719
$$509$$ 6.36840e11 0.420533 0.210267 0.977644i $$-0.432567\pi$$
0.210267 + 0.977644i $$0.432567\pi$$
$$510$$ 1.34298e10 0.00879029
$$511$$ 3.22457e11 0.209208
$$512$$ −1.57287e12 −1.01153
$$513$$ 6.86433e11 0.437593
$$514$$ 1.45397e11 0.0918801
$$515$$ 2.30408e12 1.44333
$$516$$ −3.35458e11 −0.208312
$$517$$ 8.02463e11 0.493989
$$518$$ 4.97981e10 0.0303899
$$519$$ 4.80489e11 0.290690
$$520$$ 0 0
$$521$$ 1.84033e12 1.09427 0.547137 0.837043i $$-0.315718\pi$$
0.547137 + 0.837043i $$0.315718\pi$$
$$522$$ −6.91881e11 −0.407863
$$523$$ −1.13176e10 −0.00661447 −0.00330724 0.999995i $$-0.501053\pi$$
−0.00330724 + 0.999995i $$0.501053\pi$$
$$524$$ 2.11945e12 1.22809
$$525$$ 1.61520e10 0.00927917
$$526$$ 1.25401e11 0.0714272
$$527$$ −1.44085e11 −0.0813715
$$528$$ 2.10552e11 0.117898
$$529$$ 2.34837e12 1.30382
$$530$$ 2.47678e11 0.136347
$$531$$ −2.02964e12 −1.10788
$$532$$ −1.75170e11 −0.0948108
$$533$$ 0 0
$$534$$ −2.69652e11 −0.143506
$$535$$ −9.28148e11 −0.489807
$$536$$ −1.35634e12 −0.709787
$$537$$ −1.41838e11 −0.0736053
$$538$$ −4.83203e11 −0.248662
$$539$$ −1.07399e12 −0.548089
$$540$$ 9.05970e11 0.458503
$$541$$ 2.25189e12 1.13021 0.565107 0.825018i $$-0.308835\pi$$
0.565107 + 0.825018i $$0.308835\pi$$
$$542$$ 1.12148e12 0.558204
$$543$$ 6.65356e11 0.328439
$$544$$ 1.72929e11 0.0846591
$$545$$ −2.55916e12 −1.24255
$$546$$ 0 0
$$547$$ 1.92777e11 0.0920686 0.0460343 0.998940i $$-0.485342\pi$$
0.0460343 + 0.998940i $$0.485342\pi$$
$$548$$ 1.76728e12 0.837131
$$549$$ 6.73318e11 0.316333
$$550$$ 8.48498e10 0.0395384
$$551$$ 2.25765e12 1.04346
$$552$$ 6.19524e11 0.284009
$$553$$ 1.26870e11 0.0576892
$$554$$ 8.94667e11 0.403522
$$555$$ 3.99873e11 0.178897
$$556$$ 3.83733e12 1.70292
$$557$$ −3.00574e12 −1.32313 −0.661566 0.749887i $$-0.730108\pi$$
−0.661566 + 0.749887i $$0.730108\pi$$
$$558$$ 5.46657e11 0.238705
$$559$$ 0 0
$$560$$ −2.00636e11 −0.0862112
$$561$$ −4.00909e10 −0.0170888
$$562$$ −1.49402e12 −0.631748
$$563$$ −1.64962e11 −0.0691984 −0.0345992 0.999401i $$-0.511015\pi$$
−0.0345992 + 0.999401i $$0.511015\pi$$
$$564$$ −5.76854e11 −0.240054
$$565$$ −2.59804e12 −1.07258
$$566$$ −2.27740e11 −0.0932751
$$567$$ −2.52831e11 −0.102732
$$568$$ −4.90277e11 −0.197639
$$569$$ −2.35127e11 −0.0940368 −0.0470184 0.998894i $$-0.514972\pi$$
−0.0470184 + 0.998894i $$0.514972\pi$$
$$570$$ 1.66260e11 0.0659707
$$571$$ −2.71697e12 −1.06960 −0.534801 0.844978i $$-0.679613\pi$$
−0.534801 + 0.844978i $$0.679613\pi$$
$$572$$ 0 0
$$573$$ 1.12851e12 0.437329
$$574$$ 3.23216e10 0.0124276
$$575$$ −8.65362e11 −0.330136
$$576$$ 1.00823e12 0.381643
$$577$$ 3.01507e12 1.13242 0.566209 0.824262i $$-0.308410\pi$$
0.566209 + 0.824262i $$0.308410\pi$$
$$578$$ 8.63589e11 0.321834
$$579$$ 1.13894e11 0.0421159
$$580$$ 2.97969e12 1.09332
$$581$$ −5.17580e10 −0.0188445
$$582$$ 4.60862e11 0.166501
$$583$$ −7.39374e11 −0.265067
$$584$$ −2.57931e12 −0.917585
$$585$$ 0 0
$$586$$ −5.75100e11 −0.201467
$$587$$ 9.84708e11 0.342323 0.171161 0.985243i $$-0.445248\pi$$
0.171161 + 0.985243i $$0.445248\pi$$
$$588$$ 7.72042e11 0.266344
$$589$$ −1.78377e12 −0.610690
$$590$$ −1.03318e12 −0.351030
$$591$$ −5.89208e11 −0.198667
$$592$$ 1.38068e12 0.462003
$$593$$ −1.01065e12 −0.335625 −0.167812 0.985819i $$-0.553670\pi$$
−0.167812 + 0.985819i $$0.553670\pi$$
$$594$$ 3.19676e11 0.105359
$$595$$ 3.82029e10 0.0124960
$$596$$ 1.81361e12 0.588756
$$597$$ −5.19213e11 −0.167286
$$598$$ 0 0
$$599$$ 5.47507e12 1.73768 0.868839 0.495095i $$-0.164867\pi$$
0.868839 + 0.495095i $$0.164867\pi$$
$$600$$ −1.29199e11 −0.0406984
$$601$$ 9.94557e11 0.310953 0.155476 0.987840i $$-0.450309\pi$$
0.155476 + 0.987840i $$0.450309\pi$$
$$602$$ 1.12794e11 0.0350027
$$603$$ 3.39624e12 1.04609
$$604$$ 5.10165e12 1.55971
$$605$$ −2.00375e12 −0.608058
$$606$$ 1.30165e11 0.0392074
$$607$$ 4.57629e12 1.36825 0.684124 0.729366i $$-0.260185\pi$$
0.684124 + 0.729366i $$0.260185\pi$$
$$608$$ 2.14086e12 0.635363
$$609$$ 2.00144e11 0.0589610
$$610$$ 3.42752e11 0.100229
$$611$$ 0 0
$$612$$ −2.83402e11 −0.0816623
$$613$$ −2.27107e12 −0.649617 −0.324809 0.945780i $$-0.605300\pi$$
−0.324809 + 0.945780i $$0.605300\pi$$
$$614$$ 8.82531e11 0.250595
$$615$$ 2.59538e11 0.0731583
$$616$$ −1.72798e11 −0.0483532
$$617$$ −3.53862e12 −0.982994 −0.491497 0.870879i $$-0.663550\pi$$
−0.491497 + 0.870879i $$0.663550\pi$$
$$618$$ −5.84432e11 −0.161171
$$619$$ −1.97957e12 −0.541956 −0.270978 0.962586i $$-0.587347\pi$$
−0.270978 + 0.962586i $$0.587347\pi$$
$$620$$ −2.35426e12 −0.639871
$$621$$ −3.26029e12 −0.879720
$$622$$ −8.55047e11 −0.229052
$$623$$ −7.67065e11 −0.204003
$$624$$ 0 0
$$625$$ −2.80452e12 −0.735187
$$626$$ −7.30040e11 −0.190004
$$627$$ −4.96324e11 −0.128251
$$628$$ 3.38420e12 0.868235
$$629$$ −2.62893e11 −0.0669656
$$630$$ −1.44941e11 −0.0366572
$$631$$ −3.71649e11 −0.0933256 −0.0466628 0.998911i $$-0.514859\pi$$
−0.0466628 + 0.998911i $$0.514859\pi$$
$$632$$ −1.01482e12 −0.253025
$$633$$ −1.35068e11 −0.0334376
$$634$$ −2.19373e12 −0.539239
$$635$$ −5.90551e12 −1.44137
$$636$$ 5.31502e11 0.128809
$$637$$ 0 0
$$638$$ 1.05140e12 0.251232
$$639$$ 1.22764e12 0.291284
$$640$$ 3.67277e12 0.865335
$$641$$ 1.07772e12 0.252143 0.126071 0.992021i $$-0.459763\pi$$
0.126071 + 0.992021i $$0.459763\pi$$
$$642$$ 2.35425e11 0.0546947
$$643$$ 6.69209e12 1.54388 0.771938 0.635698i $$-0.219288\pi$$
0.771938 + 0.635698i $$0.219288\pi$$
$$644$$ 8.31992e11 0.190604
$$645$$ 9.05721e11 0.206051
$$646$$ −1.09307e11 −0.0246945
$$647$$ 1.58975e12 0.356664 0.178332 0.983970i $$-0.442930\pi$$
0.178332 + 0.983970i $$0.442930\pi$$
$$648$$ 2.02238e12 0.450583
$$649$$ 3.08429e12 0.682423
$$650$$ 0 0
$$651$$ −1.58134e11 −0.0345073
$$652$$ −3.35584e11 −0.0727256
$$653$$ −1.96565e12 −0.423055 −0.211527 0.977372i $$-0.567844\pi$$
−0.211527 + 0.977372i $$0.567844\pi$$
$$654$$ 6.49133e11 0.138750
$$655$$ −5.72240e12 −1.21476
$$656$$ 8.96134e11 0.188932
$$657$$ 6.45853e12 1.35235
$$658$$ 1.93960e11 0.0403362
$$659$$ 1.09426e11 0.0226014 0.0113007 0.999936i $$-0.496403\pi$$
0.0113007 + 0.999936i $$0.496403\pi$$
$$660$$ −6.55060e11 −0.134380
$$661$$ 2.69590e12 0.549285 0.274643 0.961546i $$-0.411440\pi$$
0.274643 + 0.961546i $$0.411440\pi$$
$$662$$ 5.05927e11 0.102383
$$663$$ 0 0
$$664$$ 4.14009e11 0.0826520
$$665$$ 4.72951e11 0.0937818
$$666$$ 9.97411e11 0.196445
$$667$$ −1.07230e13 −2.09772
$$668$$ −5.65555e12 −1.09896
$$669$$ 4.27026e11 0.0824208
$$670$$ 1.72885e12 0.331452
$$671$$ −1.02319e12 −0.194852
$$672$$ 1.89790e11 0.0359015
$$673$$ −6.37187e12 −1.19729 −0.598644 0.801015i $$-0.704294\pi$$
−0.598644 + 0.801015i $$0.704294\pi$$
$$674$$ 1.14832e12 0.214335
$$675$$ 6.79918e11 0.126064
$$676$$ 0 0
$$677$$ −6.61270e12 −1.20985 −0.604923 0.796284i $$-0.706796\pi$$
−0.604923 + 0.796284i $$0.706796\pi$$
$$678$$ 6.58995e11 0.119770
$$679$$ 1.31099e12 0.236692
$$680$$ −3.05583e11 −0.0548073
$$681$$ 2.23336e12 0.397921
$$682$$ −8.30713e11 −0.147035
$$683$$ −3.52480e12 −0.619785 −0.309893 0.950772i $$-0.600293\pi$$
−0.309893 + 0.950772i $$0.600293\pi$$
$$684$$ −3.50851e12 −0.612872
$$685$$ −4.77157e12 −0.828045
$$686$$ −5.24401e11 −0.0904076
$$687$$ 1.25679e12 0.215257
$$688$$ 3.12727e12 0.532130
$$689$$ 0 0
$$690$$ −7.89672e11 −0.132625
$$691$$ −1.21020e12 −0.201932 −0.100966 0.994890i $$-0.532193\pi$$
−0.100966 + 0.994890i $$0.532193\pi$$
$$692$$ −5.16151e12 −0.855656
$$693$$ 4.32681e11 0.0712638
$$694$$ 1.21730e12 0.199195
$$695$$ −1.03606e13 −1.68443
$$696$$ −1.60094e12 −0.258603
$$697$$ −1.70632e11 −0.0273849
$$698$$ −2.95747e12 −0.471597
$$699$$ −2.84503e12 −0.450755
$$700$$ −1.73508e11 −0.0273135
$$701$$ 3.34752e12 0.523591 0.261796 0.965123i $$-0.415685\pi$$
0.261796 + 0.965123i $$0.415685\pi$$
$$702$$ 0 0
$$703$$ −3.25461e12 −0.502574
$$704$$ −1.53212e12 −0.235081
$$705$$ 1.55748e12 0.237449
$$706$$ 2.01575e12 0.305362
$$707$$ 3.70273e11 0.0557359
$$708$$ −2.21715e12 −0.331624
$$709$$ −1.09345e13 −1.62514 −0.812568 0.582866i $$-0.801931\pi$$
−0.812568 + 0.582866i $$0.801931\pi$$
$$710$$ 6.24928e11 0.0922926
$$711$$ 2.54109e12 0.372912
$$712$$ 6.13570e12 0.894755
$$713$$ 8.47224e12 1.22771
$$714$$ −9.69020e9 −0.00139537
$$715$$ 0 0
$$716$$ 1.52365e12 0.216660
$$717$$ 3.16673e12 0.447481
$$718$$ 6.07964e11 0.0853724
$$719$$ 4.73071e12 0.660156 0.330078 0.943954i $$-0.392925\pi$$
0.330078 + 0.943954i $$0.392925\pi$$
$$720$$ −4.01857e12 −0.557283
$$721$$ −1.66250e12 −0.229115
$$722$$ 1.02071e12 0.139793
$$723$$ −3.84256e12 −0.522997
$$724$$ −7.14738e12 −0.966770
$$725$$ 2.23622e12 0.300603
$$726$$ 5.08254e11 0.0678994
$$727$$ 1.40402e13 1.86410 0.932049 0.362333i $$-0.118020\pi$$
0.932049 + 0.362333i $$0.118020\pi$$
$$728$$ 0 0
$$729$$ −3.72119e12 −0.487987
$$730$$ 3.28770e12 0.428489
$$731$$ −5.95459e11 −0.0771301
$$732$$ 7.35524e11 0.0946884
$$733$$ 1.78493e12 0.228377 0.114188 0.993459i $$-0.463573\pi$$
0.114188 + 0.993459i $$0.463573\pi$$
$$734$$ −3.55373e11 −0.0451910
$$735$$ −2.08448e12 −0.263453
$$736$$ −1.01683e13 −1.27731
$$737$$ −5.16101e12 −0.644364
$$738$$ 6.47373e11 0.0803342
$$739$$ 1.24956e13 1.54119 0.770595 0.637325i $$-0.219959\pi$$
0.770595 + 0.637325i $$0.219959\pi$$
$$740$$ −4.29551e12 −0.526589
$$741$$ 0 0
$$742$$ −1.78711e11 −0.0216438
$$743$$ −4.21591e12 −0.507506 −0.253753 0.967269i $$-0.581665\pi$$
−0.253753 + 0.967269i $$0.581665\pi$$
$$744$$ 1.26491e12 0.151349
$$745$$ −4.89665e12 −0.582366
$$746$$ −6.28080e11 −0.0742489
$$747$$ −1.03667e12 −0.121814
$$748$$ 4.30664e11 0.0503016
$$749$$ 6.69701e11 0.0777522
$$750$$ 9.21825e11 0.106383
$$751$$ 9.94988e12 1.14140 0.570701 0.821158i $$-0.306672\pi$$
0.570701 + 0.821158i $$0.306672\pi$$
$$752$$ 5.37765e12 0.613214
$$753$$ 1.54303e12 0.174903
$$754$$ 0 0
$$755$$ −1.37742e13 −1.54278
$$756$$ −6.53699e11 −0.0727829
$$757$$ −1.61992e13 −1.79293 −0.896465 0.443115i $$-0.853873\pi$$
−0.896465 + 0.443115i $$0.853873\pi$$
$$758$$ −1.65589e12 −0.182188
$$759$$ 2.35735e12 0.257831
$$760$$ −3.78310e12 −0.411327
$$761$$ −4.79250e12 −0.518001 −0.259001 0.965877i $$-0.583393\pi$$
−0.259001 + 0.965877i $$0.583393\pi$$
$$762$$ 1.49794e12 0.160952
$$763$$ 1.84655e12 0.197243
$$764$$ −1.21226e13 −1.28729
$$765$$ 7.65171e11 0.0807759
$$766$$ 5.03312e12 0.528211
$$767$$ 0 0
$$768$$ 2.99954e11 0.0311121
$$769$$ 8.41625e11 0.0867861 0.0433930 0.999058i $$-0.486183\pi$$
0.0433930 + 0.999058i $$0.486183\pi$$
$$770$$ 2.20256e11 0.0225797
$$771$$ −8.42419e11 −0.0858585
$$772$$ −1.22347e12 −0.123970
$$773$$ −3.90333e12 −0.393213 −0.196607 0.980482i $$-0.562992\pi$$
−0.196607 + 0.980482i $$0.562992\pi$$
$$774$$ 2.25916e12 0.226263
$$775$$ −1.76684e12 −0.175930
$$776$$ −1.04865e13 −1.03813
$$777$$ −2.88526e11 −0.0283982
$$778$$ −5.49781e12 −0.537999
$$779$$ −2.11241e12 −0.205523
$$780$$ 0 0
$$781$$ −1.86555e12 −0.179422
$$782$$ 5.19164e11 0.0496449
$$783$$ 8.42507e12 0.801024
$$784$$ −7.19727e12 −0.680371
$$785$$ −9.13716e12 −0.858812
$$786$$ 1.45149e12 0.135648
$$787$$ 1.42677e13 1.32577 0.662884 0.748723i $$-0.269332\pi$$
0.662884 + 0.748723i $$0.269332\pi$$
$$788$$ 6.32939e12 0.584782
$$789$$ −7.26562e11 −0.0667461
$$790$$ 1.29354e12 0.118156
$$791$$ 1.87460e12 0.170261
$$792$$ −3.46099e12 −0.312563
$$793$$ 0 0
$$794$$ 1.20087e12 0.107227
$$795$$ −1.43503e12 −0.127411
$$796$$ 5.57748e12 0.492413
$$797$$ 1.77300e13 1.55649 0.778245 0.627960i $$-0.216110\pi$$
0.778245 + 0.627960i $$0.216110\pi$$
$$798$$ −1.19964e11 −0.0104722
$$799$$ −1.02395e12 −0.0888829
$$800$$ 2.12054e12 0.183038
$$801$$ −1.53636e13 −1.31870
$$802$$ −5.39863e12 −0.460785
$$803$$ −9.81453e12 −0.833009
$$804$$ 3.71001e12 0.313129
$$805$$ −2.24634e12 −0.188535
$$806$$ 0 0
$$807$$ 2.79964e12 0.232366
$$808$$ −2.96179e12 −0.244458
$$809$$ 6.57374e12 0.539565 0.269783 0.962921i $$-0.413048\pi$$
0.269783 + 0.962921i $$0.413048\pi$$
$$810$$ −2.57781e12 −0.210411
$$811$$ −1.30848e13 −1.06212 −0.531060 0.847334i $$-0.678206\pi$$
−0.531060 + 0.847334i $$0.678206\pi$$
$$812$$ −2.14999e12 −0.173553
$$813$$ −6.49774e12 −0.521621
$$814$$ −1.51569e12 −0.121004
$$815$$ 9.06060e11 0.0719363
$$816$$ −2.68666e11 −0.0212132
$$817$$ −7.37177e12 −0.578858
$$818$$ 5.48665e12 0.428467
$$819$$ 0 0
$$820$$ −2.78801e12 −0.215344
$$821$$ −4.25638e12 −0.326961 −0.163480 0.986547i $$-0.552272\pi$$
−0.163480 + 0.986547i $$0.552272\pi$$
$$822$$ 1.21031e12 0.0924644
$$823$$ −4.41691e12 −0.335598 −0.167799 0.985821i $$-0.553666\pi$$
−0.167799 + 0.985821i $$0.553666\pi$$
$$824$$ 1.32982e13 1.00490
$$825$$ −4.91613e11 −0.0369471
$$826$$ 7.45489e11 0.0557226
$$827$$ 1.65971e13 1.23384 0.616919 0.787026i $$-0.288380\pi$$
0.616919 + 0.787026i $$0.288380\pi$$
$$828$$ 1.66641e13 1.23210
$$829$$ −1.79742e13 −1.32176 −0.660882 0.750490i $$-0.729817\pi$$
−0.660882 + 0.750490i $$0.729817\pi$$
$$830$$ −5.27714e11 −0.0385964
$$831$$ −5.18363e12 −0.377077
$$832$$ 0 0
$$833$$ 1.37042e12 0.0986171
$$834$$ 2.62798e12 0.188094
$$835$$ 1.52697e13 1.08703
$$836$$ 5.33161e12 0.377511
$$837$$ −6.65667e12 −0.468805
$$838$$ 4.01864e12 0.281502
$$839$$ −3.10688e12 −0.216469 −0.108234 0.994125i $$-0.534520\pi$$
−0.108234 + 0.994125i $$0.534520\pi$$
$$840$$ −3.35378e11 −0.0232422
$$841$$ 1.32025e13 0.910070
$$842$$ −2.17354e12 −0.149026
$$843$$ 8.65626e12 0.590345
$$844$$ 1.45092e12 0.0984246
$$845$$ 0 0
$$846$$ 3.88485e12 0.260740
$$847$$ 1.44580e12 0.0965234
$$848$$ −4.95486e12 −0.329041
$$849$$ 1.31951e12 0.0871622
$$850$$ −1.08269e11 −0.00711409
$$851$$ 1.54581e13 1.01036
$$852$$ 1.34106e12 0.0871904
$$853$$ −1.20700e13 −0.780613 −0.390306 0.920685i $$-0.627631\pi$$
−0.390306 + 0.920685i $$0.627631\pi$$
$$854$$ −2.47311e11 −0.0159105
$$855$$ 9.47279e12 0.606220
$$856$$ −5.35690e12 −0.341021
$$857$$ −6.31368e12 −0.399824 −0.199912 0.979814i $$-0.564066\pi$$
−0.199912 + 0.979814i $$0.564066\pi$$
$$858$$ 0 0
$$859$$ 1.86663e13 1.16974 0.584870 0.811127i $$-0.301146\pi$$
0.584870 + 0.811127i $$0.301146\pi$$
$$860$$ −9.72943e12 −0.606519
$$861$$ −1.87269e11 −0.0116132
$$862$$ −4.04237e12 −0.249375
$$863$$ 1.78712e13 1.09675 0.548373 0.836234i $$-0.315247\pi$$
0.548373 + 0.836234i $$0.315247\pi$$
$$864$$ 7.98924e12 0.487746
$$865$$ 1.39358e13 0.846368
$$866$$ 5.54766e12 0.335181
$$867$$ −5.00357e12 −0.300742
$$868$$ 1.69871e12 0.101573
$$869$$ −3.86149e12 −0.229703
$$870$$ 2.04063e12 0.120761
$$871$$ 0 0
$$872$$ −1.47705e13 −0.865107
$$873$$ 2.62579e13 1.53002
$$874$$ 6.42723e12 0.372583
$$875$$ 2.62226e12 0.151231
$$876$$ 7.05521e12 0.404801
$$877$$ 3.76100e12 0.214687 0.107343 0.994222i $$-0.465766\pi$$
0.107343 + 0.994222i $$0.465766\pi$$
$$878$$ −7.34363e11 −0.0417047
$$879$$ 3.33208e12 0.188263
$$880$$ 6.10671e12 0.343270
$$881$$ 2.05824e13 1.15108 0.575539 0.817775i $$-0.304792\pi$$
0.575539 + 0.817775i $$0.304792\pi$$
$$882$$ −5.19936e12 −0.289295
$$883$$ −3.01536e13 −1.66923 −0.834616 0.550833i $$-0.814310\pi$$
−0.834616 + 0.550833i $$0.814310\pi$$
$$884$$ 0 0
$$885$$ 5.98619e12 0.328024
$$886$$ 7.94821e12 0.433329
$$887$$ −3.34317e13 −1.81343 −0.906717 0.421739i $$-0.861420\pi$$
−0.906717 + 0.421739i $$0.861420\pi$$
$$888$$ 2.30790e12 0.124554
$$889$$ 4.26109e12 0.228804
$$890$$ −7.82083e12 −0.417828
$$891$$ 7.69533e12 0.409051
$$892$$ −4.58720e12 −0.242608
$$893$$ −1.26765e13 −0.667063
$$894$$ 1.24204e12 0.0650304
$$895$$ −4.11379e12 −0.214308
$$896$$ −2.65007e12 −0.137364
$$897$$ 0 0
$$898$$ 7.57351e12 0.388646
$$899$$ −2.18935e13 −1.11788
$$900$$ −3.47521e12 −0.176559
$$901$$ 9.43448e11 0.0476932
$$902$$ −9.83762e11 −0.0494835
$$903$$ −6.53519e11 −0.0327087
$$904$$ −1.49948e13 −0.746765
$$905$$ 1.92976e13 0.956277
$$906$$ 3.49384e12 0.172276
$$907$$ 2.03004e13 0.996030 0.498015 0.867169i $$-0.334063\pi$$
0.498015 + 0.867169i $$0.334063\pi$$
$$908$$ −2.39912e13 −1.17129
$$909$$ 7.41625e12 0.360285
$$910$$ 0 0
$$911$$ 1.74407e13 0.838940 0.419470 0.907769i $$-0.362216\pi$$
0.419470 + 0.907769i $$0.362216\pi$$
$$912$$ −3.32608e12 −0.159205
$$913$$ 1.57534e12 0.0750337
$$914$$ 7.80592e12 0.369970
$$915$$ −1.98588e12 −0.0936607
$$916$$ −1.35007e13 −0.633617
$$917$$ 4.12897e12 0.192832
$$918$$ −4.07909e11 −0.0189571
$$919$$ 1.69619e13 0.784430 0.392215 0.919874i $$-0.371709\pi$$
0.392215 + 0.919874i $$0.371709\pi$$
$$920$$ 1.79683e13 0.826917
$$921$$ −5.11332e12 −0.234172
$$922$$ −5.30243e12 −0.241650
$$923$$ 0 0
$$924$$ 4.72655e11 0.0213315
$$925$$ −3.22372e12 −0.144784
$$926$$ 1.03861e12 0.0464200
$$927$$ −3.32984e13 −1.48103
$$928$$ 2.62762e13 1.16305
$$929$$ −4.90922e12 −0.216243 −0.108121 0.994138i $$-0.534484\pi$$
−0.108121 + 0.994138i $$0.534484\pi$$
$$930$$ −1.61230e12 −0.0706763
$$931$$ 1.69658e13 0.740117
$$932$$ 3.05619e13 1.32681
$$933$$ 4.95408e12 0.214040
$$934$$ 3.84833e12 0.165467
$$935$$ −1.16277e12 −0.0497556
$$936$$ 0 0
$$937$$ 1.13139e13 0.479497 0.239749 0.970835i $$-0.422935\pi$$
0.239749 + 0.970835i $$0.422935\pi$$
$$938$$ −1.24745e12 −0.0526149
$$939$$ 4.22980e12 0.177552
$$940$$ −1.67307e13 −0.698938
$$941$$ −7.23052e11 −0.0300619 −0.0150310 0.999887i $$-0.504785\pi$$
−0.0150310 + 0.999887i $$0.504785\pi$$
$$942$$ 2.31765e12 0.0958999
$$943$$ 1.00332e13 0.413176
$$944$$ 2.06691e13 0.847126
$$945$$ 1.76495e12 0.0719930
$$946$$ −3.43307e12 −0.139371
$$947$$ −4.04364e13 −1.63380 −0.816898 0.576782i $$-0.804308\pi$$
−0.816898 + 0.576782i $$0.804308\pi$$
$$948$$ 2.77585e12 0.111624
$$949$$ 0 0
$$950$$ −1.34037e12 −0.0533910
$$951$$ 1.27103e13 0.503899
$$952$$ 2.20492e11 0.00870014
$$953$$ 4.03093e13 1.58302 0.791511 0.611155i $$-0.209295\pi$$
0.791511 + 0.611155i $$0.209295\pi$$
$$954$$ −3.57942e12 −0.139909
$$955$$ 3.27305e13 1.27332
$$956$$ −3.40176e13 −1.31717
$$957$$ −6.09172e12 −0.234767
$$958$$ 9.00366e12 0.345362
$$959$$ 3.44291e12 0.131444
$$960$$ −2.97365e12 −0.112998
$$961$$ −9.14153e12 −0.345751
$$962$$ 0 0
$$963$$ 1.34135e13 0.502602
$$964$$ 4.12776e13 1.53946
$$965$$ 3.30330e12 0.122624
$$966$$ 5.69784e11 0.0210530
$$967$$ −1.74415e13 −0.641451 −0.320726 0.947172i $$-0.603927\pi$$
−0.320726 + 0.947172i $$0.603927\pi$$
$$968$$ −1.15649e13 −0.423352
$$969$$ 6.33314e11 0.0230761
$$970$$ 1.33665e13 0.484782
$$971$$ −5.09597e13 −1.83967 −0.919836 0.392303i $$-0.871678\pi$$
−0.919836 + 0.392303i $$0.871678\pi$$
$$972$$ −1.99563e13 −0.717102
$$973$$ 7.47565e12 0.267388
$$974$$ −2.77601e12 −0.0988340
$$975$$ 0 0
$$976$$ −6.85683e12 −0.241880
$$977$$ −3.19652e13 −1.12241 −0.561205 0.827677i $$-0.689662\pi$$
−0.561205 + 0.827677i $$0.689662\pi$$
$$978$$ −2.29823e11 −0.00803283
$$979$$ 2.33469e13 0.812283
$$980$$ 2.23918e13 0.775483
$$981$$ 3.69848e13 1.27501
$$982$$ 1.73425e13 0.595127
$$983$$ 5.12376e13 1.75024 0.875121 0.483904i $$-0.160782\pi$$
0.875121 + 0.483904i $$0.160782\pi$$
$$984$$ 1.49795e12 0.0509354
$$985$$ −1.70890e13 −0.578434
$$986$$ −1.34159e12 −0.0452038
$$987$$ −1.12379e12 −0.0376927
$$988$$ 0 0
$$989$$ 3.50131e13 1.16372
$$990$$ 4.41153e12 0.145959
$$991$$ −1.90444e13 −0.627243 −0.313622 0.949548i $$-0.601542\pi$$
−0.313622 + 0.949548i $$0.601542\pi$$
$$992$$ −2.07609e13 −0.680682
$$993$$ −2.93130e12 −0.0956730
$$994$$ −4.50914e11 −0.0146506
$$995$$ −1.50589e13 −0.487068
$$996$$ −1.13244e12 −0.0364627
$$997$$ 4.27709e13 1.37095 0.685473 0.728098i $$-0.259595\pi$$
0.685473 + 0.728098i $$0.259595\pi$$
$$998$$ −1.94471e13 −0.620538
$$999$$ −1.21455e13 −0.385808
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 169.10.a.a.1.2 4
13.12 even 2 13.10.a.a.1.3 4
39.38 odd 2 117.10.a.c.1.2 4
52.51 odd 2 208.10.a.g.1.2 4
65.64 even 2 325.10.a.a.1.2 4

By twisted newform
Twist Min Dim Char Parity Ord Type
13.10.a.a.1.3 4 13.12 even 2
117.10.a.c.1.2 4 39.38 odd 2
169.10.a.a.1.2 4 1.1 even 1 trivial
208.10.a.g.1.2 4 52.51 odd 2
325.10.a.a.1.2 4 65.64 even 2