# Properties

 Label 13.10.a.a.1.2 Level $13$ Weight $10$ Character 13.1 Self dual yes Analytic conductor $6.695$ 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] = [13,10,Mod(1,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, 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("13.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$13$$ Weight: $$k$$ $$=$$ $$10$$ Character orbit: $$[\chi]$$ $$=$$ 13.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: $$6.69546587013$$ 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: yes Fricke sign: $$+1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$16.5360$$ of defining polynomial Character $$\chi$$ $$=$$ 13.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-24.5360 q^{2} +49.9972 q^{3} +90.0171 q^{4} +1814.98 q^{5} -1226.73 q^{6} -8707.31 q^{7} +10353.8 q^{8} -17183.3 q^{9} +O(q^{10})$$ $$q-24.5360 q^{2} +49.9972 q^{3} +90.0171 q^{4} +1814.98 q^{5} -1226.73 q^{6} -8707.31 q^{7} +10353.8 q^{8} -17183.3 q^{9} -44532.3 q^{10} -82919.7 q^{11} +4500.61 q^{12} -28561.0 q^{13} +213643. q^{14} +90743.8 q^{15} -300130. q^{16} +374907. q^{17} +421610. q^{18} -361501. q^{19} +163379. q^{20} -435341. q^{21} +2.03452e6 q^{22} -2.31340e6 q^{23} +517661. q^{24} +1.34101e6 q^{25} +700774. q^{26} -1.84321e6 q^{27} -783807. q^{28} -649654. q^{29} -2.22649e6 q^{30} +4.32521e6 q^{31} +2.06285e6 q^{32} -4.14575e6 q^{33} -9.19873e6 q^{34} -1.58036e7 q^{35} -1.54679e6 q^{36} +1.21021e7 q^{37} +8.86981e6 q^{38} -1.42797e6 q^{39} +1.87919e7 q^{40} +2.59960e6 q^{41} +1.06816e7 q^{42} +3.08318e6 q^{43} -7.46419e6 q^{44} -3.11872e7 q^{45} +5.67617e7 q^{46} +2.60298e7 q^{47} -1.50057e7 q^{48} +3.54636e7 q^{49} -3.29032e7 q^{50} +1.87443e7 q^{51} -2.57098e6 q^{52} -1.01982e8 q^{53} +4.52251e7 q^{54} -1.50497e8 q^{55} -9.01536e7 q^{56} -1.80741e7 q^{57} +1.59399e7 q^{58} +1.37562e8 q^{59} +8.16850e6 q^{60} -4.29579e7 q^{61} -1.06124e8 q^{62} +1.49620e8 q^{63} +1.03052e8 q^{64} -5.18375e7 q^{65} +1.01720e8 q^{66} +5.54479e7 q^{67} +3.37480e7 q^{68} -1.15664e8 q^{69} +3.87757e8 q^{70} -1.43613e8 q^{71} -1.77912e8 q^{72} +3.37147e7 q^{73} -2.96937e8 q^{74} +6.70469e7 q^{75} -3.25413e7 q^{76} +7.22007e8 q^{77} +3.50367e7 q^{78} -2.66652e8 q^{79} -5.44728e8 q^{80} +2.46063e8 q^{81} -6.37839e7 q^{82} -9.89542e7 q^{83} -3.91882e7 q^{84} +6.80447e8 q^{85} -7.56490e7 q^{86} -3.24809e7 q^{87} -8.58533e8 q^{88} -5.08803e8 q^{89} +7.65211e8 q^{90} +2.48689e8 q^{91} -2.08246e8 q^{92} +2.16249e8 q^{93} -6.38667e8 q^{94} -6.56116e8 q^{95} +1.03137e8 q^{96} -4.53920e8 q^{97} -8.70137e8 q^{98} +1.42483e9 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 33 q^{2} - 163 q^{3} + 1429 q^{4} + 471 q^{5} - 4529 q^{6} - 11241 q^{7} - 45543 q^{8} - 29953 q^{9}+O(q^{10})$$ 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 $$4 q - 33 q^{2} - 163 q^{3} + 1429 q^{4} + 471 q^{5} - 4529 q^{6} - 11241 q^{7} - 45543 q^{8} - 29953 q^{9} - 67831 q^{10} - 40140 q^{11} - 155479 q^{12} - 114244 q^{13} - 277653 q^{14} + 83307 q^{15} + 726609 q^{16} + 78717 q^{17} + 1691026 q^{18} + 209664 q^{19} + 870843 q^{20} + 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} + 3561573 q^{24} - 2900157 q^{25} + 942513 q^{26} - 2077801 q^{27} + 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} - 11366002 q^{31} - 29458959 q^{32} - 14413222 q^{33} + 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} + 4636891 q^{37} + 25172466 q^{38} + 4655443 q^{39} + 22536791 q^{40} + 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} + 66489222 q^{44} - 17423928 q^{45} + 71369332 q^{46} - 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} - 4217748 q^{50} - 19664471 q^{51} - 40813669 q^{52} - 171019326 q^{53} - 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} - 47829030 q^{57} + 79964734 q^{58} - 63389388 q^{59} + 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} - 155695476 q^{63} + 768962465 q^{64} - 13452231 q^{65} - 42396374 q^{66} - 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} + 409056389 q^{70} + 252460989 q^{71} + 562579254 q^{72} + 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} - 326897170 q^{76} + 561950454 q^{77} + 129352769 q^{78} + 115998984 q^{79} - 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} - 79577862 q^{83} + 108899441 q^{84} + 549463469 q^{85} - 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} - 1152240276 q^{89} + 877550038 q^{90} + 321054201 q^{91} - 4213481460 q^{92} + 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} + 3171454029 q^{96} + 1049098084 q^{97} + 420532254 q^{98} + 2132181050 q^{99}+O(q^{100})$$ 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 - 114244 * q^13 - 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 + 942513 * q^26 - 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 + 4655443 * q^39 + 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 - 40813669 * q^52 - 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 - 13452231 * q^65 - 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 + 129352769 * q^78 + 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 + 321054201 * q^91 - 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −24.5360 −1.08435 −0.542175 0.840266i $$-0.682399\pi$$
−0.542175 + 0.840266i $$0.682399\pi$$
$$3$$ 49.9972 0.356369 0.178185 0.983997i $$-0.442978\pi$$
0.178185 + 0.983997i $$0.442978\pi$$
$$4$$ 90.0171 0.175815
$$5$$ 1814.98 1.29869 0.649346 0.760493i $$-0.275043\pi$$
0.649346 + 0.760493i $$0.275043\pi$$
$$6$$ −1226.73 −0.386429
$$7$$ −8707.31 −1.37070 −0.685351 0.728213i $$-0.740351\pi$$
−0.685351 + 0.728213i $$0.740351\pi$$
$$8$$ 10353.8 0.893705
$$9$$ −17183.3 −0.873001
$$10$$ −44532.3 −1.40824
$$11$$ −82919.7 −1.70762 −0.853809 0.520587i $$-0.825713\pi$$
−0.853809 + 0.520587i $$0.825713\pi$$
$$12$$ 4500.61 0.0626550
$$13$$ −28561.0 −0.277350
$$14$$ 213643. 1.48632
$$15$$ 90743.8 0.462814
$$16$$ −300130. −1.14490
$$17$$ 374907. 1.08869 0.544344 0.838862i $$-0.316779\pi$$
0.544344 + 0.838862i $$0.316779\pi$$
$$18$$ 421610. 0.946638
$$19$$ −361501. −0.636383 −0.318191 0.948026i $$-0.603075\pi$$
−0.318191 + 0.948026i $$0.603075\pi$$
$$20$$ 163379. 0.228329
$$21$$ −435341. −0.488476
$$22$$ 2.03452e6 1.85165
$$23$$ −2.31340e6 −1.72376 −0.861878 0.507116i $$-0.830712\pi$$
−0.861878 + 0.507116i $$0.830712\pi$$
$$24$$ 517661. 0.318489
$$25$$ 1.34101e6 0.686599
$$26$$ 700774. 0.300745
$$27$$ −1.84321e6 −0.667480
$$28$$ −783807. −0.240989
$$29$$ −649654. −0.170565 −0.0852827 0.996357i $$-0.527179\pi$$
−0.0852827 + 0.996357i $$0.527179\pi$$
$$30$$ −2.22649e6 −0.501852
$$31$$ 4.32521e6 0.841162 0.420581 0.907255i $$-0.361826\pi$$
0.420581 + 0.907255i $$0.361826\pi$$
$$32$$ 2.06285e6 0.347771
$$33$$ −4.14575e6 −0.608542
$$34$$ −9.19873e6 −1.18052
$$35$$ −1.58036e7 −1.78012
$$36$$ −1.54679e6 −0.153486
$$37$$ 1.21021e7 1.06158 0.530790 0.847503i $$-0.321895\pi$$
0.530790 + 0.847503i $$0.321895\pi$$
$$38$$ 8.86981e6 0.690062
$$39$$ −1.42797e6 −0.0988391
$$40$$ 1.87919e7 1.16065
$$41$$ 2.59960e6 0.143674 0.0718372 0.997416i $$-0.477114\pi$$
0.0718372 + 0.997416i $$0.477114\pi$$
$$42$$ 1.06816e7 0.529679
$$43$$ 3.08318e6 0.137528 0.0687640 0.997633i $$-0.478094\pi$$
0.0687640 + 0.997633i $$0.478094\pi$$
$$44$$ −7.46419e6 −0.300224
$$45$$ −3.11872e7 −1.13376
$$46$$ 5.67617e7 1.86915
$$47$$ 2.60298e7 0.778090 0.389045 0.921219i $$-0.372805\pi$$
0.389045 + 0.921219i $$0.372805\pi$$
$$48$$ −1.50057e7 −0.408009
$$49$$ 3.54636e7 0.878822
$$50$$ −3.29032e7 −0.744513
$$51$$ 1.87443e7 0.387975
$$52$$ −2.57098e6 −0.0487622
$$53$$ −1.01982e8 −1.77535 −0.887673 0.460475i $$-0.847679\pi$$
−0.887673 + 0.460475i $$0.847679\pi$$
$$54$$ 4.52251e7 0.723782
$$55$$ −1.50497e8 −2.21767
$$56$$ −9.01536e7 −1.22500
$$57$$ −1.80741e7 −0.226787
$$58$$ 1.59399e7 0.184953
$$59$$ 1.37562e8 1.47797 0.738985 0.673722i $$-0.235305\pi$$
0.738985 + 0.673722i $$0.235305\pi$$
$$60$$ 8.16850e6 0.0813695
$$61$$ −4.29579e7 −0.397245 −0.198623 0.980076i $$-0.563647\pi$$
−0.198623 + 0.980076i $$0.563647\pi$$
$$62$$ −1.06124e8 −0.912114
$$63$$ 1.49620e8 1.19662
$$64$$ 1.03052e8 0.767798
$$65$$ −5.18375e7 −0.360192
$$66$$ 1.01720e8 0.659873
$$67$$ 5.54479e7 0.336162 0.168081 0.985773i $$-0.446243\pi$$
0.168081 + 0.985773i $$0.446243\pi$$
$$68$$ 3.37480e7 0.191407
$$69$$ −1.15664e8 −0.614294
$$70$$ 3.87757e8 1.93027
$$71$$ −1.43613e8 −0.670706 −0.335353 0.942093i $$-0.608856\pi$$
−0.335353 + 0.942093i $$0.608856\pi$$
$$72$$ −1.77912e8 −0.780205
$$73$$ 3.37147e7 0.138952 0.0694762 0.997584i $$-0.477867\pi$$
0.0694762 + 0.997584i $$0.477867\pi$$
$$74$$ −2.96937e8 −1.15112
$$75$$ 6.70469e7 0.244683
$$76$$ −3.25413e7 −0.111886
$$77$$ 7.22007e8 2.34063
$$78$$ 3.50367e7 0.107176
$$79$$ −2.66652e8 −0.770236 −0.385118 0.922867i $$-0.625839\pi$$
−0.385118 + 0.922867i $$0.625839\pi$$
$$80$$ −5.44728e8 −1.48688
$$81$$ 2.46063e8 0.635132
$$82$$ −6.37839e7 −0.155793
$$83$$ −9.89542e7 −0.228867 −0.114433 0.993431i $$-0.536505\pi$$
−0.114433 + 0.993431i $$0.536505\pi$$
$$84$$ −3.91882e7 −0.0858812
$$85$$ 6.80447e8 1.41387
$$86$$ −7.56490e7 −0.149128
$$87$$ −3.24809e7 −0.0607843
$$88$$ −8.58533e8 −1.52611
$$89$$ −5.08803e8 −0.859597 −0.429798 0.902925i $$-0.641415\pi$$
−0.429798 + 0.902925i $$0.641415\pi$$
$$90$$ 7.65211e8 1.22939
$$91$$ 2.48689e8 0.380164
$$92$$ −2.08246e8 −0.303062
$$93$$ 2.16249e8 0.299764
$$94$$ −6.38667e8 −0.843722
$$95$$ −6.56116e8 −0.826465
$$96$$ 1.03137e8 0.123935
$$97$$ −4.53920e8 −0.520603 −0.260301 0.965527i $$-0.583822\pi$$
−0.260301 + 0.965527i $$0.583822\pi$$
$$98$$ −8.70137e8 −0.952950
$$99$$ 1.42483e9 1.49075
$$100$$ 1.20714e8 0.120714
$$101$$ 6.44663e8 0.616434 0.308217 0.951316i $$-0.400268\pi$$
0.308217 + 0.951316i $$0.400268\pi$$
$$102$$ −4.59911e8 −0.420700
$$103$$ −1.14825e9 −1.00524 −0.502620 0.864507i $$-0.667631\pi$$
−0.502620 + 0.864507i $$0.667631\pi$$
$$104$$ −2.95715e8 −0.247869
$$105$$ −7.90134e8 −0.634379
$$106$$ 2.50224e9 1.92510
$$107$$ 5.95299e8 0.439044 0.219522 0.975607i $$-0.429550\pi$$
0.219522 + 0.975607i $$0.429550\pi$$
$$108$$ −1.65921e8 −0.117353
$$109$$ 1.00898e9 0.684645 0.342322 0.939583i $$-0.388787\pi$$
0.342322 + 0.939583i $$0.388787\pi$$
$$110$$ 3.69261e9 2.40473
$$111$$ 6.05071e8 0.378315
$$112$$ 2.61332e9 1.56932
$$113$$ −1.59931e9 −0.922739 −0.461370 0.887208i $$-0.652642\pi$$
−0.461370 + 0.887208i $$0.652642\pi$$
$$114$$ 4.43466e8 0.245917
$$115$$ −4.19877e9 −2.23863
$$116$$ −5.84800e7 −0.0299879
$$117$$ 4.90772e8 0.242127
$$118$$ −3.37524e9 −1.60264
$$119$$ −3.26443e9 −1.49226
$$120$$ 9.39542e8 0.413619
$$121$$ 4.51772e9 1.91596
$$122$$ 1.05402e9 0.430753
$$123$$ 1.29973e8 0.0512011
$$124$$ 3.89343e8 0.147889
$$125$$ −1.11097e9 −0.407011
$$126$$ −3.67108e9 −1.29756
$$127$$ −1.58816e9 −0.541723 −0.270861 0.962618i $$-0.587308\pi$$
−0.270861 + 0.962618i $$0.587308\pi$$
$$128$$ −3.58467e9 −1.18033
$$129$$ 1.54151e8 0.0490107
$$130$$ 1.27189e9 0.390574
$$131$$ −3.54703e9 −1.05231 −0.526156 0.850388i $$-0.676367\pi$$
−0.526156 + 0.850388i $$0.676367\pi$$
$$132$$ −3.73189e8 −0.106991
$$133$$ 3.14770e9 0.872291
$$134$$ −1.36047e9 −0.364517
$$135$$ −3.34539e9 −0.866850
$$136$$ 3.88170e9 0.972965
$$137$$ −3.79917e9 −0.921395 −0.460697 0.887557i $$-0.652401\pi$$
−0.460697 + 0.887557i $$0.652401\pi$$
$$138$$ 2.83793e9 0.666109
$$139$$ 3.81526e9 0.866878 0.433439 0.901183i $$-0.357300\pi$$
0.433439 + 0.901183i $$0.357300\pi$$
$$140$$ −1.42259e9 −0.312971
$$141$$ 1.30142e9 0.277287
$$142$$ 3.52370e9 0.727280
$$143$$ 2.36827e9 0.473608
$$144$$ 5.15721e9 0.999502
$$145$$ −1.17911e9 −0.221512
$$146$$ −8.27225e8 −0.150673
$$147$$ 1.77308e9 0.313185
$$148$$ 1.08940e9 0.186641
$$149$$ 1.16149e10 1.93054 0.965269 0.261258i $$-0.0841374\pi$$
0.965269 + 0.261258i $$0.0841374\pi$$
$$150$$ −1.64507e9 −0.265322
$$151$$ 3.19196e9 0.499645 0.249822 0.968292i $$-0.419628\pi$$
0.249822 + 0.968292i $$0.419628\pi$$
$$152$$ −3.74291e9 −0.568739
$$153$$ −6.44213e9 −0.950425
$$154$$ −1.77152e10 −2.53806
$$155$$ 7.85016e9 1.09241
$$156$$ −1.28542e8 −0.0173774
$$157$$ −5.05861e9 −0.664481 −0.332240 0.943195i $$-0.607805\pi$$
−0.332240 + 0.943195i $$0.607805\pi$$
$$158$$ 6.54260e9 0.835205
$$159$$ −5.09883e9 −0.632679
$$160$$ 3.74403e9 0.451647
$$161$$ 2.01435e10 2.36275
$$162$$ −6.03741e9 −0.688705
$$163$$ −7.83438e9 −0.869282 −0.434641 0.900604i $$-0.643125\pi$$
−0.434641 + 0.900604i $$0.643125\pi$$
$$164$$ 2.34009e8 0.0252601
$$165$$ −7.52444e9 −0.790308
$$166$$ 2.42794e9 0.248172
$$167$$ −1.44048e8 −0.0143312 −0.00716559 0.999974i $$-0.502281\pi$$
−0.00716559 + 0.999974i $$0.502281\pi$$
$$168$$ −4.50743e9 −0.436553
$$169$$ 8.15731e8 0.0769231
$$170$$ −1.66955e10 −1.53313
$$171$$ 6.21178e9 0.555563
$$172$$ 2.77539e8 0.0241794
$$173$$ −1.36123e10 −1.15538 −0.577689 0.816257i $$-0.696045\pi$$
−0.577689 + 0.816257i $$0.696045\pi$$
$$174$$ 7.96952e8 0.0659114
$$175$$ −1.16766e10 −0.941122
$$176$$ 2.48867e10 1.95506
$$177$$ 6.87774e9 0.526703
$$178$$ 1.24840e10 0.932104
$$179$$ 4.98195e8 0.0362711 0.0181355 0.999836i $$-0.494227\pi$$
0.0181355 + 0.999836i $$0.494227\pi$$
$$180$$ −2.80739e9 −0.199331
$$181$$ 2.86758e9 0.198592 0.0992961 0.995058i $$-0.468341\pi$$
0.0992961 + 0.995058i $$0.468341\pi$$
$$182$$ −6.10185e9 −0.412231
$$183$$ −2.14777e9 −0.141566
$$184$$ −2.39525e10 −1.54053
$$185$$ 2.19650e10 1.37866
$$186$$ −5.30588e9 −0.325049
$$187$$ −3.10871e10 −1.85906
$$188$$ 2.34312e9 0.136800
$$189$$ 1.60494e10 0.914916
$$190$$ 1.60985e10 0.896177
$$191$$ −2.83331e10 −1.54044 −0.770218 0.637781i $$-0.779852\pi$$
−0.770218 + 0.637781i $$0.779852\pi$$
$$192$$ 5.15232e9 0.273620
$$193$$ 2.44273e10 1.26726 0.633632 0.773634i $$-0.281563\pi$$
0.633632 + 0.773634i $$0.281563\pi$$
$$194$$ 1.11374e10 0.564516
$$195$$ −2.59173e9 −0.128361
$$196$$ 3.19233e9 0.154510
$$197$$ 1.37323e10 0.649601 0.324800 0.945783i $$-0.394703\pi$$
0.324800 + 0.945783i $$0.394703\pi$$
$$198$$ −3.49597e10 −1.61650
$$199$$ −8.56614e9 −0.387210 −0.193605 0.981080i $$-0.562018\pi$$
−0.193605 + 0.981080i $$0.562018\pi$$
$$200$$ 1.38846e10 0.613617
$$201$$ 2.77224e9 0.119798
$$202$$ −1.58175e10 −0.668430
$$203$$ 5.65673e9 0.233794
$$204$$ 1.68731e9 0.0682117
$$205$$ 4.71821e9 0.186589
$$206$$ 2.81736e10 1.09003
$$207$$ 3.97518e10 1.50484
$$208$$ 8.57200e9 0.317539
$$209$$ 2.99756e10 1.08670
$$210$$ 1.93868e10 0.687889
$$211$$ 2.70272e9 0.0938706 0.0469353 0.998898i $$-0.485055\pi$$
0.0469353 + 0.998898i $$0.485055\pi$$
$$212$$ −9.18015e9 −0.312132
$$213$$ −7.18027e9 −0.239019
$$214$$ −1.46063e10 −0.476078
$$215$$ 5.59590e9 0.178606
$$216$$ −1.90842e10 −0.596530
$$217$$ −3.76610e10 −1.15298
$$218$$ −2.47565e10 −0.742394
$$219$$ 1.68564e9 0.0495184
$$220$$ −1.35473e10 −0.389899
$$221$$ −1.07077e10 −0.301947
$$222$$ −1.48460e10 −0.410225
$$223$$ −3.57969e10 −0.969333 −0.484667 0.874699i $$-0.661059\pi$$
−0.484667 + 0.874699i $$0.661059\pi$$
$$224$$ −1.79619e10 −0.476690
$$225$$ −2.30430e10 −0.599401
$$226$$ 3.92407e10 1.00057
$$227$$ −7.55373e10 −1.88819 −0.944094 0.329675i $$-0.893061\pi$$
−0.944094 + 0.329675i $$0.893061\pi$$
$$228$$ −1.62698e9 −0.0398726
$$229$$ −5.69066e10 −1.36742 −0.683711 0.729753i $$-0.739635\pi$$
−0.683711 + 0.729753i $$0.739635\pi$$
$$230$$ 1.03021e11 2.42745
$$231$$ 3.60984e10 0.834130
$$232$$ −6.72637e9 −0.152435
$$233$$ −4.68000e10 −1.04026 −0.520132 0.854086i $$-0.674117\pi$$
−0.520132 + 0.854086i $$0.674117\pi$$
$$234$$ −1.20416e10 −0.262550
$$235$$ 4.72434e10 1.01050
$$236$$ 1.23830e10 0.259849
$$237$$ −1.33319e10 −0.274488
$$238$$ 8.00961e10 1.61814
$$239$$ −8.79993e9 −0.174457 −0.0872285 0.996188i $$-0.527801\pi$$
−0.0872285 + 0.996188i $$0.527801\pi$$
$$240$$ −2.72349e10 −0.529877
$$241$$ −1.76057e10 −0.336183 −0.168092 0.985771i $$-0.553760\pi$$
−0.168092 + 0.985771i $$0.553760\pi$$
$$242$$ −1.10847e11 −2.07757
$$243$$ 4.85824e10 0.893821
$$244$$ −3.86695e9 −0.0698415
$$245$$ 6.43656e10 1.14132
$$246$$ −3.18902e9 −0.0555200
$$247$$ 1.03248e10 0.176501
$$248$$ 4.47823e10 0.751751
$$249$$ −4.94743e9 −0.0815611
$$250$$ 2.72588e10 0.441343
$$251$$ −1.77113e10 −0.281655 −0.140828 0.990034i $$-0.544976\pi$$
−0.140828 + 0.990034i $$0.544976\pi$$
$$252$$ 1.34684e10 0.210384
$$253$$ 1.91826e11 2.94351
$$254$$ 3.89671e10 0.587417
$$255$$ 3.40204e10 0.503859
$$256$$ 3.51910e10 0.512096
$$257$$ −6.26733e10 −0.896156 −0.448078 0.893994i $$-0.647891\pi$$
−0.448078 + 0.893994i $$0.647891\pi$$
$$258$$ −3.78224e9 −0.0531448
$$259$$ −1.05377e11 −1.45511
$$260$$ −4.66627e9 −0.0633271
$$261$$ 1.11632e10 0.148904
$$262$$ 8.70301e10 1.14107
$$263$$ 4.49501e10 0.579335 0.289667 0.957127i $$-0.406455\pi$$
0.289667 + 0.957127i $$0.406455\pi$$
$$264$$ −4.29243e10 −0.543857
$$265$$ −1.85095e11 −2.30563
$$266$$ −7.72322e10 −0.945869
$$267$$ −2.54388e10 −0.306334
$$268$$ 4.99126e9 0.0591023
$$269$$ −8.65536e10 −1.00786 −0.503930 0.863745i $$-0.668113\pi$$
−0.503930 + 0.863745i $$0.668113\pi$$
$$270$$ 8.20825e10 0.939969
$$271$$ 8.36056e10 0.941615 0.470808 0.882236i $$-0.343963\pi$$
0.470808 + 0.882236i $$0.343963\pi$$
$$272$$ −1.12521e11 −1.24644
$$273$$ 1.24338e10 0.135479
$$274$$ 9.32165e10 0.999114
$$275$$ −1.11196e11 −1.17245
$$276$$ −1.04117e10 −0.108002
$$277$$ 1.73137e11 1.76698 0.883489 0.468452i $$-0.155188\pi$$
0.883489 + 0.468452i $$0.155188\pi$$
$$278$$ −9.36114e10 −0.939999
$$279$$ −7.43213e10 −0.734335
$$280$$ −1.63627e11 −1.59090
$$281$$ 7.57598e10 0.724871 0.362435 0.932009i $$-0.381945\pi$$
0.362435 + 0.932009i $$0.381945\pi$$
$$282$$ −3.19316e10 −0.300676
$$283$$ 1.68901e11 1.56528 0.782642 0.622472i $$-0.213872\pi$$
0.782642 + 0.622472i $$0.213872\pi$$
$$284$$ −1.29277e10 −0.117920
$$285$$ −3.28040e10 −0.294527
$$286$$ −5.81079e10 −0.513557
$$287$$ −2.26355e10 −0.196935
$$288$$ −3.54466e10 −0.303605
$$289$$ 2.19672e10 0.185240
$$290$$ 2.89306e10 0.240196
$$291$$ −2.26947e10 −0.185527
$$292$$ 3.03490e9 0.0244299
$$293$$ −1.18842e11 −0.942030 −0.471015 0.882125i $$-0.656112\pi$$
−0.471015 + 0.882125i $$0.656112\pi$$
$$294$$ −4.35044e10 −0.339602
$$295$$ 2.49672e11 1.91943
$$296$$ 1.25302e11 0.948740
$$297$$ 1.52839e11 1.13980
$$298$$ −2.84984e11 −2.09338
$$299$$ 6.60730e10 0.478084
$$300$$ 6.03537e9 0.0430188
$$301$$ −2.68462e10 −0.188510
$$302$$ −7.83181e10 −0.541790
$$303$$ 3.22313e10 0.219678
$$304$$ 1.08497e11 0.728597
$$305$$ −7.79675e10 −0.515899
$$306$$ 1.58064e11 1.03059
$$307$$ −1.99530e11 −1.28199 −0.640997 0.767543i $$-0.721479\pi$$
−0.640997 + 0.767543i $$0.721479\pi$$
$$308$$ 6.49930e10 0.411518
$$309$$ −5.74095e10 −0.358237
$$310$$ −1.92612e11 −1.18455
$$311$$ 1.90145e11 1.15256 0.576281 0.817252i $$-0.304503\pi$$
0.576281 + 0.817252i $$0.304503\pi$$
$$312$$ −1.47849e10 −0.0883330
$$313$$ −3.39674e10 −0.200038 −0.100019 0.994986i $$-0.531890\pi$$
−0.100019 + 0.994986i $$0.531890\pi$$
$$314$$ 1.24118e11 0.720530
$$315$$ 2.71557e11 1.55404
$$316$$ −2.40033e10 −0.135419
$$317$$ −8.53565e9 −0.0474756 −0.0237378 0.999718i $$-0.507557\pi$$
−0.0237378 + 0.999718i $$0.507557\pi$$
$$318$$ 1.25105e11 0.686045
$$319$$ 5.38691e10 0.291260
$$320$$ 1.87037e11 0.997133
$$321$$ 2.97633e10 0.156462
$$322$$ −4.94242e11 −2.56205
$$323$$ −1.35529e11 −0.692822
$$324$$ 2.21499e10 0.111665
$$325$$ −3.83007e10 −0.190428
$$326$$ 1.92225e11 0.942606
$$327$$ 5.04464e10 0.243986
$$328$$ 2.69157e10 0.128403
$$329$$ −2.26649e11 −1.06653
$$330$$ 1.84620e11 0.856971
$$331$$ 5.09528e10 0.233315 0.116657 0.993172i $$-0.462782\pi$$
0.116657 + 0.993172i $$0.462782\pi$$
$$332$$ −8.90757e9 −0.0402381
$$333$$ −2.07954e11 −0.926760
$$334$$ 3.53436e9 0.0155400
$$335$$ 1.00637e11 0.436571
$$336$$ 1.30659e11 0.559258
$$337$$ 2.31891e11 0.979375 0.489688 0.871898i $$-0.337111\pi$$
0.489688 + 0.871898i $$0.337111\pi$$
$$338$$ −2.00148e10 −0.0834115
$$339$$ −7.99609e10 −0.328836
$$340$$ 6.12519e10 0.248579
$$341$$ −3.58645e11 −1.43638
$$342$$ −1.52412e11 −0.602425
$$343$$ 4.25786e10 0.166099
$$344$$ 3.19226e10 0.122909
$$345$$ −2.09927e11 −0.797778
$$346$$ 3.33992e11 1.25283
$$347$$ −3.64138e10 −0.134829 −0.0674146 0.997725i $$-0.521475\pi$$
−0.0674146 + 0.997725i $$0.521475\pi$$
$$348$$ −2.92384e9 −0.0106868
$$349$$ 9.86839e10 0.356067 0.178034 0.984024i $$-0.443026\pi$$
0.178034 + 0.984024i $$0.443026\pi$$
$$350$$ 2.86498e11 1.02051
$$351$$ 5.26440e10 0.185126
$$352$$ −1.71051e11 −0.593860
$$353$$ −3.90458e11 −1.33841 −0.669204 0.743078i $$-0.733365\pi$$
−0.669204 + 0.743078i $$0.733365\pi$$
$$354$$ −1.68752e11 −0.571131
$$355$$ −2.60655e11 −0.871040
$$356$$ −4.58010e10 −0.151130
$$357$$ −1.63212e11 −0.531797
$$358$$ −1.22237e10 −0.0393305
$$359$$ −3.86316e11 −1.22749 −0.613744 0.789505i $$-0.710337\pi$$
−0.613744 + 0.789505i $$0.710337\pi$$
$$360$$ −3.22906e11 −1.01325
$$361$$ −1.92005e11 −0.595017
$$362$$ −7.03591e10 −0.215343
$$363$$ 2.25874e11 0.682788
$$364$$ 2.23863e10 0.0668385
$$365$$ 6.11914e10 0.180456
$$366$$ 5.26979e10 0.153507
$$367$$ 1.48155e11 0.426305 0.213152 0.977019i $$-0.431627\pi$$
0.213152 + 0.977019i $$0.431627\pi$$
$$368$$ 6.94320e11 1.97353
$$369$$ −4.46697e10 −0.125428
$$370$$ −5.38934e11 −1.49495
$$371$$ 8.87991e11 2.43347
$$372$$ 1.94661e10 0.0527030
$$373$$ −6.15338e11 −1.64598 −0.822989 0.568057i $$-0.807695\pi$$
−0.822989 + 0.568057i $$0.807695\pi$$
$$374$$ 7.62755e11 2.01587
$$375$$ −5.55453e10 −0.145046
$$376$$ 2.69507e11 0.695383
$$377$$ 1.85548e10 0.0473063
$$378$$ −3.93789e11 −0.992089
$$379$$ 2.48822e10 0.0619459 0.0309729 0.999520i $$-0.490139\pi$$
0.0309729 + 0.999520i $$0.490139\pi$$
$$380$$ −5.90617e10 −0.145305
$$381$$ −7.94035e10 −0.193053
$$382$$ 6.95181e11 1.67037
$$383$$ 4.82478e11 1.14573 0.572866 0.819649i $$-0.305832\pi$$
0.572866 + 0.819649i $$0.305832\pi$$
$$384$$ −1.79224e11 −0.420634
$$385$$ 1.31043e12 3.03976
$$386$$ −5.99349e11 −1.37416
$$387$$ −5.29792e10 −0.120062
$$388$$ −4.08606e10 −0.0915297
$$389$$ 3.80215e11 0.841890 0.420945 0.907086i $$-0.361698\pi$$
0.420945 + 0.907086i $$0.361698\pi$$
$$390$$ 6.35909e10 0.139189
$$391$$ −8.67310e11 −1.87663
$$392$$ 3.67183e11 0.785408
$$393$$ −1.77342e11 −0.375012
$$394$$ −3.36937e11 −0.704394
$$395$$ −4.83968e11 −1.00030
$$396$$ 1.28259e11 0.262096
$$397$$ 7.91759e11 1.59969 0.799845 0.600207i $$-0.204915\pi$$
0.799845 + 0.600207i $$0.204915\pi$$
$$398$$ 2.10179e11 0.419871
$$399$$ 1.57376e11 0.310858
$$400$$ −4.02478e11 −0.786090
$$401$$ −3.06132e11 −0.591234 −0.295617 0.955307i $$-0.595525\pi$$
−0.295617 + 0.955307i $$0.595525\pi$$
$$402$$ −6.80199e10 −0.129903
$$403$$ −1.23532e11 −0.233296
$$404$$ 5.80307e10 0.108378
$$405$$ 4.46598e11 0.824840
$$406$$ −1.38794e11 −0.253515
$$407$$ −1.00350e12 −1.81277
$$408$$ 1.94074e11 0.346735
$$409$$ 9.04916e11 1.59902 0.799509 0.600654i $$-0.205093\pi$$
0.799509 + 0.600654i $$0.205093\pi$$
$$410$$ −1.15766e11 −0.202327
$$411$$ −1.89948e11 −0.328357
$$412$$ −1.03362e11 −0.176736
$$413$$ −1.19780e12 −2.02586
$$414$$ −9.75352e11 −1.63177
$$415$$ −1.79599e11 −0.297227
$$416$$ −5.89172e10 −0.0964544
$$417$$ 1.90753e11 0.308929
$$418$$ −7.35482e11 −1.17836
$$419$$ 3.36210e11 0.532903 0.266451 0.963848i $$-0.414149\pi$$
0.266451 + 0.963848i $$0.414149\pi$$
$$420$$ −7.11256e10 −0.111533
$$421$$ −1.87100e11 −0.290271 −0.145135 0.989412i $$-0.546362\pi$$
−0.145135 + 0.989412i $$0.546362\pi$$
$$422$$ −6.63140e10 −0.101789
$$423$$ −4.47276e11 −0.679273
$$424$$ −1.05590e12 −1.58664
$$425$$ 5.02755e11 0.747491
$$426$$ 1.76175e11 0.259180
$$427$$ 3.74048e11 0.544504
$$428$$ 5.35872e10 0.0771905
$$429$$ 1.18407e11 0.168779
$$430$$ −1.37301e11 −0.193672
$$431$$ 9.60500e11 1.34076 0.670378 0.742020i $$-0.266132\pi$$
0.670378 + 0.742020i $$0.266132\pi$$
$$432$$ 5.53203e11 0.764200
$$433$$ 1.14812e12 1.56961 0.784806 0.619741i $$-0.212762\pi$$
0.784806 + 0.619741i $$0.212762\pi$$
$$434$$ 9.24051e11 1.25024
$$435$$ −5.89520e10 −0.0789400
$$436$$ 9.08259e10 0.120371
$$437$$ 8.36297e11 1.09697
$$438$$ −4.13590e10 −0.0536953
$$439$$ 5.44277e11 0.699407 0.349703 0.936860i $$-0.386282\pi$$
0.349703 + 0.936860i $$0.386282\pi$$
$$440$$ −1.55822e12 −1.98194
$$441$$ −6.09381e11 −0.767212
$$442$$ 2.62725e11 0.327417
$$443$$ −1.12065e11 −0.138247 −0.0691233 0.997608i $$-0.522020\pi$$
−0.0691233 + 0.997608i $$0.522020\pi$$
$$444$$ 5.44668e10 0.0665133
$$445$$ −9.23466e11 −1.11635
$$446$$ 8.78313e11 1.05110
$$447$$ 5.80714e11 0.687984
$$448$$ −8.97307e11 −1.05242
$$449$$ −1.11883e12 −1.29913 −0.649567 0.760304i $$-0.725050\pi$$
−0.649567 + 0.760304i $$0.725050\pi$$
$$450$$ 5.65384e11 0.649961
$$451$$ −2.15558e11 −0.245341
$$452$$ −1.43965e11 −0.162231
$$453$$ 1.59589e11 0.178058
$$454$$ 1.85339e12 2.04746
$$455$$ 4.51365e11 0.493716
$$456$$ −1.87135e11 −0.202681
$$457$$ −1.38914e12 −1.48978 −0.744890 0.667188i $$-0.767498\pi$$
−0.744890 + 0.667188i $$0.767498\pi$$
$$458$$ 1.39626e12 1.48276
$$459$$ −6.91032e11 −0.726677
$$460$$ −3.77961e11 −0.393583
$$461$$ 1.06041e12 1.09350 0.546752 0.837294i $$-0.315864\pi$$
0.546752 + 0.837294i $$0.315864\pi$$
$$462$$ −8.85711e11 −0.904488
$$463$$ 2.81576e11 0.284762 0.142381 0.989812i $$-0.454524\pi$$
0.142381 + 0.989812i $$0.454524\pi$$
$$464$$ 1.94980e11 0.195281
$$465$$ 3.92486e11 0.389301
$$466$$ 1.14829e12 1.12801
$$467$$ −9.91125e11 −0.964278 −0.482139 0.876095i $$-0.660140\pi$$
−0.482139 + 0.876095i $$0.660140\pi$$
$$468$$ 4.41779e10 0.0425695
$$469$$ −4.82802e11 −0.460778
$$470$$ −1.15917e12 −1.09573
$$471$$ −2.52916e11 −0.236801
$$472$$ 1.42429e12 1.32087
$$473$$ −2.55656e11 −0.234845
$$474$$ 3.27112e11 0.297641
$$475$$ −4.84778e11 −0.436940
$$476$$ −2.93855e11 −0.262362
$$477$$ 1.75239e12 1.54988
$$478$$ 2.15915e11 0.189173
$$479$$ −1.38074e12 −1.19841 −0.599203 0.800597i $$-0.704516\pi$$
−0.599203 + 0.800597i $$0.704516\pi$$
$$480$$ 1.87191e11 0.160953
$$481$$ −3.45648e11 −0.294429
$$482$$ 4.31974e11 0.364541
$$483$$ 1.00712e12 0.842013
$$484$$ 4.06673e11 0.336853
$$485$$ −8.23854e11 −0.676102
$$486$$ −1.19202e12 −0.969215
$$487$$ 9.65212e11 0.777575 0.388788 0.921327i $$-0.372894\pi$$
0.388788 + 0.921327i $$0.372894\pi$$
$$488$$ −4.44777e11 −0.355020
$$489$$ −3.91697e11 −0.309785
$$490$$ −1.57928e12 −1.23759
$$491$$ −1.10735e12 −0.859841 −0.429920 0.902867i $$-0.641458\pi$$
−0.429920 + 0.902867i $$0.641458\pi$$
$$492$$ 1.16998e10 0.00900191
$$493$$ −2.43559e11 −0.185692
$$494$$ −2.53331e11 −0.191389
$$495$$ 2.58604e12 1.93603
$$496$$ −1.29812e12 −0.963050
$$497$$ 1.25049e12 0.919338
$$498$$ 1.21390e11 0.0884407
$$499$$ −2.24583e12 −1.62153 −0.810763 0.585374i $$-0.800948\pi$$
−0.810763 + 0.585374i $$0.800948\pi$$
$$500$$ −1.00006e11 −0.0715586
$$501$$ −7.20198e9 −0.00510719
$$502$$ 4.34564e11 0.305413
$$503$$ 3.98259e11 0.277402 0.138701 0.990334i $$-0.455707\pi$$
0.138701 + 0.990334i $$0.455707\pi$$
$$504$$ 1.54913e12 1.06943
$$505$$ 1.17005e12 0.800557
$$506$$ −4.70666e12 −3.19180
$$507$$ 4.07843e10 0.0274130
$$508$$ −1.42961e11 −0.0952428
$$509$$ 2.66411e12 1.75923 0.879615 0.475687i $$-0.157800\pi$$
0.879615 + 0.475687i $$0.157800\pi$$
$$510$$ −8.34727e11 −0.546360
$$511$$ −2.93564e11 −0.190462
$$512$$ 9.71905e11 0.625042
$$513$$ 6.66323e11 0.424773
$$514$$ 1.53775e12 0.971747
$$515$$ −2.08405e12 −1.30550
$$516$$ 1.38762e10 0.00861681
$$517$$ −2.15838e12 −1.32868
$$518$$ 2.58553e12 1.57785
$$519$$ −6.80577e11 −0.411741
$$520$$ −5.36715e11 −0.321906
$$521$$ −3.11961e12 −1.85494 −0.927472 0.373894i $$-0.878022\pi$$
−0.927472 + 0.373894i $$0.878022\pi$$
$$522$$ −2.73900e11 −0.161464
$$523$$ −2.05566e12 −1.20142 −0.600709 0.799468i $$-0.705115\pi$$
−0.600709 + 0.799468i $$0.705115\pi$$
$$524$$ −3.19294e11 −0.185012
$$525$$ −5.83798e11 −0.335387
$$526$$ −1.10290e12 −0.628202
$$527$$ 1.62155e12 0.915762
$$528$$ 1.24426e12 0.696722
$$529$$ 3.55067e12 1.97133
$$530$$ 4.54150e12 2.50011
$$531$$ −2.36377e12 −1.29027
$$532$$ 2.83347e11 0.153362
$$533$$ −7.42472e10 −0.0398481
$$534$$ 6.24166e11 0.332173
$$535$$ 1.08045e12 0.570183
$$536$$ 5.74096e11 0.300430
$$537$$ 2.49083e10 0.0129259
$$538$$ 2.12368e12 1.09287
$$539$$ −2.94063e12 −1.50069
$$540$$ −3.01142e11 −0.152405
$$541$$ 8.06876e11 0.404966 0.202483 0.979286i $$-0.435099\pi$$
0.202483 + 0.979286i $$0.435099\pi$$
$$542$$ −2.05135e12 −1.02104
$$543$$ 1.43371e11 0.0707721
$$544$$ 7.73378e11 0.378614
$$545$$ 1.83128e12 0.889142
$$546$$ −3.05076e11 −0.146906
$$547$$ 1.93370e12 0.923521 0.461760 0.887005i $$-0.347218\pi$$
0.461760 + 0.887005i $$0.347218\pi$$
$$548$$ −3.41990e11 −0.161995
$$549$$ 7.38157e11 0.346795
$$550$$ 2.72832e12 1.27134
$$551$$ 2.34851e11 0.108545
$$552$$ −1.19756e12 −0.548997
$$553$$ 2.32183e12 1.05576
$$554$$ −4.24810e12 −1.91602
$$555$$ 1.09819e12 0.491314
$$556$$ 3.43439e11 0.152410
$$557$$ 3.06623e12 1.34976 0.674879 0.737928i $$-0.264196\pi$$
0.674879 + 0.737928i $$0.264196\pi$$
$$558$$ 1.82355e12 0.796276
$$559$$ −8.80587e10 −0.0381434
$$560$$ 4.74312e12 2.03806
$$561$$ −1.55427e12 −0.662512
$$562$$ −1.85885e12 −0.786013
$$563$$ −2.59944e12 −1.09042 −0.545208 0.838301i $$-0.683549\pi$$
−0.545208 + 0.838301i $$0.683549\pi$$
$$564$$ 1.17150e11 0.0487512
$$565$$ −2.90270e12 −1.19835
$$566$$ −4.14416e12 −1.69732
$$567$$ −2.14255e12 −0.870576
$$568$$ −1.48694e12 −0.599413
$$569$$ −1.63182e12 −0.652632 −0.326316 0.945261i $$-0.605807\pi$$
−0.326316 + 0.945261i $$0.605807\pi$$
$$570$$ 8.04880e11 0.319370
$$571$$ −1.05673e12 −0.416010 −0.208005 0.978128i $$-0.566697\pi$$
−0.208005 + 0.978128i $$0.566697\pi$$
$$572$$ 2.13185e11 0.0832672
$$573$$ −1.41658e12 −0.548964
$$574$$ 5.55386e11 0.213546
$$575$$ −3.10230e12 −1.18353
$$576$$ −1.77077e12 −0.670289
$$577$$ −8.51110e11 −0.319665 −0.159832 0.987144i $$-0.551095\pi$$
−0.159832 + 0.987144i $$0.551095\pi$$
$$578$$ −5.38987e11 −0.200865
$$579$$ 1.22130e12 0.451614
$$580$$ −1.06140e11 −0.0389450
$$581$$ 8.61624e11 0.313708
$$582$$ 5.56839e11 0.201176
$$583$$ 8.45633e12 3.03161
$$584$$ 3.49075e11 0.124183
$$585$$ 8.90739e11 0.314448
$$586$$ 2.91591e12 1.02149
$$587$$ 6.19927e11 0.215511 0.107755 0.994177i $$-0.465634\pi$$
0.107755 + 0.994177i $$0.465634\pi$$
$$588$$ 1.59608e11 0.0550626
$$589$$ −1.56357e12 −0.535301
$$590$$ −6.12597e12 −2.08133
$$591$$ 6.86579e11 0.231498
$$592$$ −3.63220e12 −1.21541
$$593$$ −3.79034e12 −1.25873 −0.629364 0.777110i $$-0.716685\pi$$
−0.629364 + 0.777110i $$0.716685\pi$$
$$594$$ −3.75005e12 −1.23594
$$595$$ −5.92486e12 −1.93799
$$596$$ 1.04554e12 0.339417
$$597$$ −4.28283e11 −0.137990
$$598$$ −1.62117e12 −0.518410
$$599$$ 2.62045e12 0.831679 0.415839 0.909438i $$-0.363488\pi$$
0.415839 + 0.909438i $$0.363488\pi$$
$$600$$ 6.94190e11 0.218674
$$601$$ 1.11042e12 0.347178 0.173589 0.984818i $$-0.444464\pi$$
0.173589 + 0.984818i $$0.444464\pi$$
$$602$$ 6.58700e11 0.204411
$$603$$ −9.52777e11 −0.293470
$$604$$ 2.87331e11 0.0878449
$$605$$ 8.19956e12 2.48824
$$606$$ −7.90829e11 −0.238208
$$607$$ 4.57077e12 1.36660 0.683298 0.730140i $$-0.260545\pi$$
0.683298 + 0.730140i $$0.260545\pi$$
$$608$$ −7.45724e11 −0.221316
$$609$$ 2.82821e11 0.0833171
$$610$$ 1.91301e12 0.559415
$$611$$ −7.43436e11 −0.215803
$$612$$ −5.79902e11 −0.167099
$$613$$ −5.61998e12 −1.60754 −0.803772 0.594938i $$-0.797177\pi$$
−0.803772 + 0.594938i $$0.797177\pi$$
$$614$$ 4.89568e12 1.39013
$$615$$ 2.35898e11 0.0664945
$$616$$ 7.47551e12 2.09184
$$617$$ 2.17420e12 0.603970 0.301985 0.953313i $$-0.402351\pi$$
0.301985 + 0.953313i $$0.402351\pi$$
$$618$$ 1.40860e12 0.388454
$$619$$ 5.91455e12 1.61925 0.809625 0.586947i $$-0.199670\pi$$
0.809625 + 0.586947i $$0.199670\pi$$
$$620$$ 7.06649e11 0.192062
$$621$$ 4.26409e12 1.15057
$$622$$ −4.66542e12 −1.24978
$$623$$ 4.43031e12 1.17825
$$624$$ 4.28576e11 0.113161
$$625$$ −4.63555e12 −1.21518
$$626$$ 8.33426e11 0.216912
$$627$$ 1.49869e12 0.387266
$$628$$ −4.55361e11 −0.116826
$$629$$ 4.53716e12 1.15573
$$630$$ −6.66293e12 −1.68513
$$631$$ −5.05658e12 −1.26977 −0.634884 0.772607i $$-0.718952\pi$$
−0.634884 + 0.772607i $$0.718952\pi$$
$$632$$ −2.76086e12 −0.688364
$$633$$ 1.35128e11 0.0334526
$$634$$ 2.09431e11 0.0514801
$$635$$ −2.88247e12 −0.703530
$$636$$ −4.58982e11 −0.111234
$$637$$ −1.01288e12 −0.243741
$$638$$ −1.32173e12 −0.315828
$$639$$ 2.46775e12 0.585527
$$640$$ −6.50609e12 −1.53289
$$641$$ 1.51370e12 0.354142 0.177071 0.984198i $$-0.443338\pi$$
0.177071 + 0.984198i $$0.443338\pi$$
$$642$$ −7.30274e11 −0.169660
$$643$$ 3.90178e12 0.900146 0.450073 0.892992i $$-0.351398\pi$$
0.450073 + 0.892992i $$0.351398\pi$$
$$644$$ 1.81326e12 0.415407
$$645$$ 2.79779e11 0.0636498
$$646$$ 3.32535e12 0.751261
$$647$$ 7.88115e12 1.76815 0.884077 0.467341i $$-0.154788\pi$$
0.884077 + 0.467341i $$0.154788\pi$$
$$648$$ 2.54768e12 0.567620
$$649$$ −1.14066e13 −2.52381
$$650$$ 9.39747e11 0.206491
$$651$$ −1.88294e12 −0.410887
$$652$$ −7.05229e11 −0.152833
$$653$$ −5.10697e12 −1.09914 −0.549571 0.835447i $$-0.685209\pi$$
−0.549571 + 0.835447i $$0.685209\pi$$
$$654$$ −1.23776e12 −0.264567
$$655$$ −6.43778e12 −1.36663
$$656$$ −7.80217e11 −0.164493
$$657$$ −5.79329e11 −0.121306
$$658$$ 5.56107e12 1.15649
$$659$$ −5.45308e11 −0.112631 −0.0563154 0.998413i $$-0.517935\pi$$
−0.0563154 + 0.998413i $$0.517935\pi$$
$$660$$ −6.77329e11 −0.138948
$$661$$ −3.05503e12 −0.622456 −0.311228 0.950335i $$-0.600740\pi$$
−0.311228 + 0.950335i $$0.600740\pi$$
$$662$$ −1.25018e12 −0.252995
$$663$$ −5.35356e11 −0.107605
$$664$$ −1.02455e12 −0.204539
$$665$$ 5.71301e12 1.13284
$$666$$ 5.10236e12 1.00493
$$667$$ 1.50291e12 0.294013
$$668$$ −1.29668e10 −0.00251963
$$669$$ −1.78974e12 −0.345441
$$670$$ −2.46923e12 −0.473395
$$671$$ 3.56205e12 0.678343
$$672$$ −8.98046e11 −0.169878
$$673$$ −1.57419e12 −0.295795 −0.147897 0.989003i $$-0.547251\pi$$
−0.147897 + 0.989003i $$0.547251\pi$$
$$674$$ −5.68968e12 −1.06199
$$675$$ −2.47177e12 −0.458291
$$676$$ 7.34298e10 0.0135242
$$677$$ −2.62249e11 −0.0479805 −0.0239903 0.999712i $$-0.507637\pi$$
−0.0239903 + 0.999712i $$0.507637\pi$$
$$678$$ 1.96192e12 0.356573
$$679$$ 3.95242e12 0.713591
$$680$$ 7.04520e12 1.26358
$$681$$ −3.77666e12 −0.672892
$$682$$ 8.79973e12 1.55754
$$683$$ −3.64995e12 −0.641791 −0.320896 0.947115i $$-0.603984\pi$$
−0.320896 + 0.947115i $$0.603984\pi$$
$$684$$ 5.59166e11 0.0976762
$$685$$ −6.89539e12 −1.19661
$$686$$ −1.04471e12 −0.180110
$$687$$ −2.84517e12 −0.487307
$$688$$ −9.25354e11 −0.157456
$$689$$ 2.91271e12 0.492392
$$690$$ 5.15077e12 0.865070
$$691$$ −1.69603e12 −0.282998 −0.141499 0.989938i $$-0.545192\pi$$
−0.141499 + 0.989938i $$0.545192\pi$$
$$692$$ −1.22534e12 −0.203132
$$693$$ −1.24065e13 −2.04337
$$694$$ 8.93451e11 0.146202
$$695$$ 6.92461e12 1.12581
$$696$$ −3.36300e11 −0.0543232
$$697$$ 9.74608e11 0.156416
$$698$$ −2.42131e12 −0.386101
$$699$$ −2.33987e12 −0.370718
$$700$$ −1.05110e12 −0.165463
$$701$$ 1.15906e13 1.81291 0.906454 0.422304i $$-0.138778\pi$$
0.906454 + 0.422304i $$0.138778\pi$$
$$702$$ −1.29167e12 −0.200741
$$703$$ −4.37492e12 −0.675571
$$704$$ −8.54505e12 −1.31111
$$705$$ 2.36204e12 0.360111
$$706$$ 9.58030e12 1.45130
$$707$$ −5.61328e12 −0.844946
$$708$$ 6.19114e11 0.0926022
$$709$$ −6.98541e12 −1.03821 −0.519104 0.854711i $$-0.673734\pi$$
−0.519104 + 0.854711i $$0.673734\pi$$
$$710$$ 6.39544e12 0.944512
$$711$$ 4.58196e12 0.672417
$$712$$ −5.26804e12 −0.768226
$$713$$ −1.00059e13 −1.44996
$$714$$ 4.00459e12 0.576654
$$715$$ 4.29835e12 0.615070
$$716$$ 4.48461e10 0.00637699
$$717$$ −4.39972e11 −0.0621711
$$718$$ 9.47866e12 1.33103
$$719$$ −3.43730e12 −0.479665 −0.239832 0.970814i $$-0.577092\pi$$
−0.239832 + 0.970814i $$0.577092\pi$$
$$720$$ 9.36022e12 1.29804
$$721$$ 9.99820e12 1.37788
$$722$$ 4.71103e12 0.645206
$$723$$ −8.80236e11 −0.119805
$$724$$ 2.58131e11 0.0349154
$$725$$ −8.71194e11 −0.117110
$$726$$ −5.54205e12 −0.740381
$$727$$ 1.25723e12 0.166920 0.0834601 0.996511i $$-0.473403\pi$$
0.0834601 + 0.996511i $$0.473403\pi$$
$$728$$ 2.57488e12 0.339755
$$729$$ −2.41427e12 −0.316601
$$730$$ −1.50139e12 −0.195678
$$731$$ 1.15591e12 0.149725
$$732$$ −1.93337e11 −0.0248894
$$733$$ −1.51950e12 −0.194416 −0.0972079 0.995264i $$-0.530991\pi$$
−0.0972079 + 0.995264i $$0.530991\pi$$
$$734$$ −3.63515e12 −0.462264
$$735$$ 3.21810e12 0.406731
$$736$$ −4.77221e12 −0.599473
$$737$$ −4.59772e12 −0.574036
$$738$$ 1.09602e12 0.136008
$$739$$ 1.19661e13 1.47589 0.737944 0.674862i $$-0.235797\pi$$
0.737944 + 0.674862i $$0.235797\pi$$
$$740$$ 1.97723e12 0.242390
$$741$$ 5.16213e11 0.0628995
$$742$$ −2.17878e13 −2.63873
$$743$$ 1.52097e12 0.183093 0.0915465 0.995801i $$-0.470819\pi$$
0.0915465 + 0.995801i $$0.470819\pi$$
$$744$$ 2.23899e12 0.267901
$$745$$ 2.10808e13 2.50717
$$746$$ 1.50980e13 1.78482
$$747$$ 1.70036e12 0.199801
$$748$$ −2.79838e12 −0.326850
$$749$$ −5.18346e12 −0.601799
$$750$$ 1.36286e12 0.157281
$$751$$ −8.06595e12 −0.925286 −0.462643 0.886545i $$-0.653099\pi$$
−0.462643 + 0.886545i $$0.653099\pi$$
$$752$$ −7.81230e12 −0.890838
$$753$$ −8.85513e11 −0.100373
$$754$$ −4.55260e11 −0.0512966
$$755$$ 5.79333e12 0.648884
$$756$$ 1.44472e12 0.160856
$$757$$ 8.72882e12 0.966104 0.483052 0.875592i $$-0.339528\pi$$
0.483052 + 0.875592i $$0.339528\pi$$
$$758$$ −6.10511e11 −0.0671710
$$759$$ 9.59079e12 1.04898
$$760$$ −6.79329e12 −0.738616
$$761$$ 7.63407e11 0.0825135 0.0412568 0.999149i $$-0.486864\pi$$
0.0412568 + 0.999149i $$0.486864\pi$$
$$762$$ 1.94825e12 0.209337
$$763$$ −8.78554e12 −0.938443
$$764$$ −2.55046e12 −0.270831
$$765$$ −1.16923e13 −1.23431
$$766$$ −1.18381e13 −1.24237
$$767$$ −3.92892e12 −0.409915
$$768$$ 1.75945e12 0.182495
$$769$$ −5.30538e12 −0.547076 −0.273538 0.961861i $$-0.588194\pi$$
−0.273538 + 0.961861i $$0.588194\pi$$
$$770$$ −3.21527e13 −3.29616
$$771$$ −3.13349e12 −0.319363
$$772$$ 2.19887e12 0.222804
$$773$$ −1.53974e12 −0.155110 −0.0775550 0.996988i $$-0.524711\pi$$
−0.0775550 + 0.996988i $$0.524711\pi$$
$$774$$ 1.29990e12 0.130189
$$775$$ 5.80017e12 0.577541
$$776$$ −4.69979e12 −0.465266
$$777$$ −5.26854e12 −0.518556
$$778$$ −9.32896e12 −0.912904
$$779$$ −9.39759e11 −0.0914319
$$780$$ −2.33300e11 −0.0225678
$$781$$ 1.19084e13 1.14531
$$782$$ 2.12803e13 2.03492
$$783$$ 1.19745e12 0.113849
$$784$$ −1.06437e13 −1.00617
$$785$$ −9.18125e12 −0.862955
$$786$$ 4.35127e12 0.406644
$$787$$ −2.94759e12 −0.273893 −0.136946 0.990578i $$-0.543729\pi$$
−0.136946 + 0.990578i $$0.543729\pi$$
$$788$$ 1.23615e12 0.114209
$$789$$ 2.24738e12 0.206457
$$790$$ 1.18747e13 1.08467
$$791$$ 1.39257e13 1.26480
$$792$$ 1.47524e13 1.33229
$$793$$ 1.22692e12 0.110176
$$794$$ −1.94266e13 −1.73462
$$795$$ −9.25425e12 −0.821654
$$796$$ −7.71099e11 −0.0680772
$$797$$ −1.83481e13 −1.61075 −0.805376 0.592764i $$-0.798037\pi$$
−0.805376 + 0.592764i $$0.798037\pi$$
$$798$$ −3.86139e12 −0.337079
$$799$$ 9.75873e12 0.847096
$$800$$ 2.76632e12 0.238779
$$801$$ 8.74291e12 0.750429
$$802$$ 7.51127e12 0.641104
$$803$$ −2.79561e12 −0.237278
$$804$$ 2.49549e11 0.0210622
$$805$$ 3.65600e13 3.06849
$$806$$ 3.03099e12 0.252975
$$807$$ −4.32744e12 −0.359170
$$808$$ 6.67470e12 0.550910
$$809$$ −9.70701e12 −0.796741 −0.398371 0.917225i $$-0.630424\pi$$
−0.398371 + 0.917225i $$0.630424\pi$$
$$810$$ −1.09578e13 −0.894415
$$811$$ 6.14421e12 0.498738 0.249369 0.968409i $$-0.419777\pi$$
0.249369 + 0.968409i $$0.419777\pi$$
$$812$$ 5.09203e11 0.0411045
$$813$$ 4.18005e12 0.335563
$$814$$ 2.46220e13 1.96568
$$815$$ −1.42192e13 −1.12893
$$816$$ −5.62572e12 −0.444194
$$817$$ −1.11457e12 −0.0875205
$$818$$ −2.22030e13 −1.73389
$$819$$ −4.27330e12 −0.331884
$$820$$ 4.24720e11 0.0328050
$$821$$ 1.41092e13 1.08383 0.541913 0.840434i $$-0.317700\pi$$
0.541913 + 0.840434i $$0.317700\pi$$
$$822$$ 4.66057e12 0.356054
$$823$$ 7.99374e12 0.607366 0.303683 0.952773i $$-0.401784\pi$$
0.303683 + 0.952773i $$0.401784\pi$$
$$824$$ −1.18888e13 −0.898389
$$825$$ −5.55951e12 −0.417824
$$826$$ 2.93892e13 2.19674
$$827$$ −4.82994e12 −0.359060 −0.179530 0.983752i $$-0.557458\pi$$
−0.179530 + 0.983752i $$0.557458\pi$$
$$828$$ 3.57834e12 0.264573
$$829$$ 1.41648e13 1.04163 0.520816 0.853669i $$-0.325628\pi$$
0.520816 + 0.853669i $$0.325628\pi$$
$$830$$ 4.40666e12 0.322298
$$831$$ 8.65637e12 0.629697
$$832$$ −2.94327e12 −0.212949
$$833$$ 1.32956e13 0.956762
$$834$$ −4.68031e12 −0.334987
$$835$$ −2.61443e11 −0.0186118
$$836$$ 2.69831e12 0.191058
$$837$$ −7.97228e12 −0.561459
$$838$$ −8.24927e12 −0.577853
$$839$$ 1.79477e13 1.25049 0.625246 0.780428i $$-0.284999\pi$$
0.625246 + 0.780428i $$0.284999\pi$$
$$840$$ −8.18088e12 −0.566948
$$841$$ −1.40851e13 −0.970907
$$842$$ 4.59068e12 0.314755
$$843$$ 3.78778e12 0.258322
$$844$$ 2.43291e11 0.0165038
$$845$$ 1.48053e12 0.0998993
$$846$$ 1.09744e13 0.736570
$$847$$ −3.93372e13 −2.62620
$$848$$ 3.06079e13 2.03260
$$849$$ 8.44458e12 0.557819
$$850$$ −1.23356e13 −0.810542
$$851$$ −2.79970e13 −1.82990
$$852$$ −6.46347e11 −0.0420231
$$853$$ −8.65463e12 −0.559729 −0.279865 0.960039i $$-0.590290\pi$$
−0.279865 + 0.960039i $$0.590290\pi$$
$$854$$ −9.17764e12 −0.590433
$$855$$ 1.12742e13 0.721505
$$856$$ 6.16360e12 0.392376
$$857$$ −1.17199e13 −0.742185 −0.371092 0.928596i $$-0.621017\pi$$
−0.371092 + 0.928596i $$0.621017\pi$$
$$858$$ −2.90524e12 −0.183016
$$859$$ −2.70022e13 −1.69211 −0.846057 0.533092i $$-0.821030\pi$$
−0.846057 + 0.533092i $$0.821030\pi$$
$$860$$ 5.03727e11 0.0314016
$$861$$ −1.13171e12 −0.0701815
$$862$$ −2.35669e13 −1.45385
$$863$$ 2.11111e13 1.29557 0.647786 0.761823i $$-0.275695\pi$$
0.647786 + 0.761823i $$0.275695\pi$$
$$864$$ −3.80228e12 −0.232130
$$865$$ −2.47060e13 −1.50048
$$866$$ −2.81704e13 −1.70201
$$867$$ 1.09830e12 0.0660137
$$868$$ −3.39013e12 −0.202711
$$869$$ 2.21107e13 1.31527
$$870$$ 1.44645e12 0.0855986
$$871$$ −1.58365e12 −0.0932346
$$872$$ 1.04468e13 0.611870
$$873$$ 7.79984e12 0.454487
$$874$$ −2.05194e13 −1.18950
$$875$$ 9.67354e12 0.557891
$$876$$ 1.51737e11 0.00870606
$$877$$ −1.48840e13 −0.849614 −0.424807 0.905284i $$-0.639658\pi$$
−0.424807 + 0.905284i $$0.639658\pi$$
$$878$$ −1.33544e13 −0.758402
$$879$$ −5.94176e12 −0.335711
$$880$$ 4.51687e13 2.53902
$$881$$ 8.21496e11 0.0459424 0.0229712 0.999736i $$-0.492687\pi$$
0.0229712 + 0.999736i $$0.492687\pi$$
$$882$$ 1.49518e13 0.831926
$$883$$ −5.06069e12 −0.280147 −0.140074 0.990141i $$-0.544734\pi$$
−0.140074 + 0.990141i $$0.544734\pi$$
$$884$$ −9.63878e11 −0.0530868
$$885$$ 1.24829e13 0.684025
$$886$$ 2.74964e12 0.149908
$$887$$ −4.00796e12 −0.217404 −0.108702 0.994074i $$-0.534669\pi$$
−0.108702 + 0.994074i $$0.534669\pi$$
$$888$$ 6.26478e12 0.338102
$$889$$ 1.38286e13 0.742540
$$890$$ 2.26582e13 1.21051
$$891$$ −2.04035e13 −1.08456
$$892$$ −3.22233e12 −0.170423
$$893$$ −9.40979e12 −0.495163
$$894$$ −1.42484e13 −0.746016
$$895$$ 9.04211e11 0.0471049
$$896$$ 3.12129e13 1.61788
$$897$$ 3.30347e12 0.170374
$$898$$ 2.74516e13 1.40872
$$899$$ −2.80989e12 −0.143473
$$900$$ −2.07427e12 −0.105384
$$901$$ −3.82338e13 −1.93280
$$902$$ 5.28894e12 0.266035
$$903$$ −1.34224e12 −0.0671791
$$904$$ −1.65589e13 −0.824657
$$905$$ 5.20459e12 0.257910
$$906$$ −3.91569e12 −0.193077
$$907$$ 4.52189e12 0.221864 0.110932 0.993828i $$-0.464616\pi$$
0.110932 + 0.993828i $$0.464616\pi$$
$$908$$ −6.79966e12 −0.331971
$$909$$ −1.10774e13 −0.538147
$$910$$ −1.10747e13 −0.535361
$$911$$ −5.68437e12 −0.273432 −0.136716 0.990610i $$-0.543655\pi$$
−0.136716 + 0.990610i $$0.543655\pi$$
$$912$$ 5.42456e12 0.259650
$$913$$ 8.20525e12 0.390817
$$914$$ 3.40839e13 1.61544
$$915$$ −3.89816e12 −0.183850
$$916$$ −5.12257e12 −0.240413
$$917$$ 3.08851e13 1.44241
$$918$$ 1.69552e13 0.787972
$$919$$ 3.28047e13 1.51711 0.758555 0.651609i $$-0.225906\pi$$
0.758555 + 0.651609i $$0.225906\pi$$
$$920$$ −4.34731e13 −2.00067
$$921$$ −9.97597e12 −0.456864
$$922$$ −2.60183e13 −1.18574
$$923$$ 4.10174e12 0.186020
$$924$$ 3.24947e12 0.146652
$$925$$ 1.62291e13 0.728880
$$926$$ −6.90877e12 −0.308782
$$927$$ 1.97308e13 0.877576
$$928$$ −1.34014e12 −0.0593177
$$929$$ 1.82868e13 0.805504 0.402752 0.915309i $$-0.368054\pi$$
0.402752 + 0.915309i $$0.368054\pi$$
$$930$$ −9.63005e12 −0.422139
$$931$$ −1.28201e13 −0.559267
$$932$$ −4.21280e12 −0.182894
$$933$$ 9.50675e12 0.410738
$$934$$ 2.43183e13 1.04562
$$935$$ −5.64224e13 −2.41435
$$936$$ 5.08134e12 0.216390
$$937$$ 2.71335e13 1.14995 0.574974 0.818171i $$-0.305012\pi$$
0.574974 + 0.818171i $$0.305012\pi$$
$$938$$ 1.18461e13 0.499644
$$939$$ −1.69828e12 −0.0712875
$$940$$ 4.25271e12 0.177660
$$941$$ −9.48833e12 −0.394490 −0.197245 0.980354i $$-0.563200\pi$$
−0.197245 + 0.980354i $$0.563200\pi$$
$$942$$ 6.20556e12 0.256775
$$943$$ −6.01392e12 −0.247660
$$944$$ −4.12866e13 −1.69213
$$945$$ 2.91293e13 1.18819
$$946$$ 6.27279e12 0.254654
$$947$$ 1.99262e13 0.805100 0.402550 0.915398i $$-0.368124\pi$$
0.402550 + 0.915398i $$0.368124\pi$$
$$948$$ −1.20010e12 −0.0482591
$$949$$ −9.62925e11 −0.0385385
$$950$$ 1.18945e13 0.473796
$$951$$ −4.26759e11 −0.0169188
$$952$$ −3.37992e13 −1.33364
$$953$$ 2.48922e13 0.977565 0.488782 0.872406i $$-0.337441\pi$$
0.488782 + 0.872406i $$0.337441\pi$$
$$954$$ −4.29967e13 −1.68061
$$955$$ −5.14238e13 −2.00055
$$956$$ −7.92144e11 −0.0306721
$$957$$ 2.69330e12 0.103796
$$958$$ 3.38780e13 1.29949
$$959$$ 3.30805e13 1.26296
$$960$$ 9.35134e12 0.355347
$$961$$ −7.73217e12 −0.292446
$$962$$ 8.48083e12 0.319264
$$963$$ −1.02292e13 −0.383286
$$964$$ −1.58481e12 −0.0591060
$$965$$ 4.43349e13 1.64579
$$966$$ −2.47107e13 −0.913037
$$967$$ −4.20642e13 −1.54701 −0.773505 0.633790i $$-0.781499\pi$$
−0.773505 + 0.633790i $$0.781499\pi$$
$$968$$ 4.67756e13 1.71230
$$969$$ −6.77609e12 −0.246900
$$970$$ 2.02141e13 0.733132
$$971$$ −1.34740e12 −0.0486418 −0.0243209 0.999704i $$-0.507742\pi$$
−0.0243209 + 0.999704i $$0.507742\pi$$
$$972$$ 4.37325e12 0.157147
$$973$$ −3.32207e13 −1.18823
$$974$$ −2.36825e13 −0.843164
$$975$$ −1.91493e12 −0.0678628
$$976$$ 1.28929e13 0.454807
$$977$$ −2.05822e13 −0.722714 −0.361357 0.932428i $$-0.617686\pi$$
−0.361357 + 0.932428i $$0.617686\pi$$
$$978$$ 9.61070e12 0.335916
$$979$$ 4.21898e13 1.46786
$$980$$ 5.79401e12 0.200661
$$981$$ −1.73377e13 −0.597695
$$982$$ 2.71700e13 0.932368
$$983$$ −5.72322e13 −1.95501 −0.977506 0.210906i $$-0.932359\pi$$
−0.977506 + 0.210906i $$0.932359\pi$$
$$984$$ 1.34571e12 0.0457587
$$985$$ 2.49239e13 0.843631
$$986$$ 5.97598e12 0.201355
$$987$$ −1.13318e13 −0.380078
$$988$$ 9.29412e11 0.0310315
$$989$$ −7.13263e12 −0.237065
$$990$$ −6.34511e13 −2.09933
$$991$$ 1.46766e13 0.483386 0.241693 0.970353i $$-0.422297\pi$$
0.241693 + 0.970353i $$0.422297\pi$$
$$992$$ 8.92228e12 0.292532
$$993$$ 2.54750e12 0.0831462
$$994$$ −3.06820e13 −0.996884
$$995$$ −1.55473e13 −0.502866
$$996$$ −4.45354e11 −0.0143396
$$997$$ −5.31286e13 −1.70294 −0.851471 0.524402i $$-0.824289\pi$$
−0.851471 + 0.524402i $$0.824289\pi$$
$$998$$ 5.51037e13 1.75830
$$999$$ −2.23067e13 −0.708583
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 13.10.a.a.1.2 4
3.2 odd 2 117.10.a.c.1.3 4
4.3 odd 2 208.10.a.g.1.1 4
5.4 even 2 325.10.a.a.1.3 4
13.12 even 2 169.10.a.a.1.3 4

By twisted newform
Twist Min Dim Char Parity Ord Type
13.10.a.a.1.2 4 1.1 even 1 trivial
117.10.a.c.1.3 4 3.2 odd 2
169.10.a.a.1.3 4 13.12 even 2
208.10.a.g.1.1 4 4.3 odd 2
325.10.a.a.1.3 4 5.4 even 2