# Properties

 Label 35.8.a.a.1.1 Level $35$ Weight $8$ Character 35.1 Self dual yes Analytic conductor $10.933$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,8,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("35.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 35.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: $$10.9334758919$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{11})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - 11$$ x^2 - 11 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-3.31662$$ of defining polynomial Character $$\chi$$ $$=$$ 35.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.36675 q^{2} +24.7995 q^{3} -126.132 q^{4} +125.000 q^{5} +33.8947 q^{6} -343.000 q^{7} -347.335 q^{8} -1571.98 q^{9} +O(q^{10})$$ $$q+1.36675 q^{2} +24.7995 q^{3} -126.132 q^{4} +125.000 q^{5} +33.8947 q^{6} -343.000 q^{7} -347.335 q^{8} -1571.98 q^{9} +170.844 q^{10} -1432.37 q^{11} -3128.01 q^{12} -6136.30 q^{13} -468.795 q^{14} +3099.94 q^{15} +15670.2 q^{16} -15858.5 q^{17} -2148.51 q^{18} -38567.5 q^{19} -15766.5 q^{20} -8506.23 q^{21} -1957.69 q^{22} -63987.4 q^{23} -8613.73 q^{24} +15625.0 q^{25} -8386.79 q^{26} -93220.9 q^{27} +43263.3 q^{28} +94236.6 q^{29} +4236.84 q^{30} +275990. q^{31} +65876.1 q^{32} -35521.9 q^{33} -21674.6 q^{34} -42875.0 q^{35} +198278. q^{36} +156532. q^{37} -52712.1 q^{38} -152177. q^{39} -43416.9 q^{40} -303738. q^{41} -11625.9 q^{42} +636818. q^{43} +180667. q^{44} -196498. q^{45} -87454.9 q^{46} +512021. q^{47} +388612. q^{48} +117649. q^{49} +21355.5 q^{50} -393282. q^{51} +773984. q^{52} -201249. q^{53} -127410. q^{54} -179046. q^{55} +119136. q^{56} -956454. q^{57} +128798. q^{58} -1.81196e6 q^{59} -391001. q^{60} -982021. q^{61} +377210. q^{62} +539191. q^{63} -1.91575e6 q^{64} -767038. q^{65} -48549.6 q^{66} -4.45336e6 q^{67} +2.00026e6 q^{68} -1.58686e6 q^{69} -58599.4 q^{70} +725436. q^{71} +546005. q^{72} +2.17602e6 q^{73} +213940. q^{74} +387492. q^{75} +4.86459e6 q^{76} +491301. q^{77} -207988. q^{78} -5.21525e6 q^{79} +1.95877e6 q^{80} +1.12610e6 q^{81} -415135. q^{82} +6.07921e6 q^{83} +1.07291e6 q^{84} -1.98231e6 q^{85} +870371. q^{86} +2.33702e6 q^{87} +497511. q^{88} -1.06137e7 q^{89} -268564. q^{90} +2.10475e6 q^{91} +8.07086e6 q^{92} +6.84442e6 q^{93} +699805. q^{94} -4.82093e6 q^{95} +1.63369e6 q^{96} +6.64483e6 q^{97} +160797. q^{98} +2.25166e6 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 16 q^{2} - 30 q^{3} - 40 q^{4} + 250 q^{5} - 768 q^{6} - 686 q^{7} - 960 q^{8} - 756 q^{9}+O(q^{10})$$ 2 * q + 16 * q^2 - 30 * q^3 - 40 * q^4 + 250 * q^5 - 768 * q^6 - 686 * q^7 - 960 * q^8 - 756 * q^9 $$2 q + 16 q^{2} - 30 q^{3} - 40 q^{4} + 250 q^{5} - 768 q^{6} - 686 q^{7} - 960 q^{8} - 756 q^{9} + 2000 q^{10} - 7906 q^{11} - 7848 q^{12} - 17818 q^{13} - 5488 q^{14} - 3750 q^{15} - 4320 q^{16} - 2398 q^{17} + 9792 q^{18} - 3612 q^{19} - 5000 q^{20} + 10290 q^{21} - 96688 q^{22} + 13844 q^{23} + 24960 q^{24} + 31250 q^{25} - 179328 q^{26} - 18090 q^{27} + 13720 q^{28} - 126898 q^{29} - 96000 q^{30} + 252768 q^{31} - 148224 q^{32} + 319230 q^{33} + 175296 q^{34} - 85750 q^{35} + 268560 q^{36} - 265860 q^{37} + 458800 q^{38} + 487974 q^{39} - 120000 q^{40} - 111920 q^{41} + 263424 q^{42} + 947572 q^{43} - 376920 q^{44} - 94500 q^{45} + 1051472 q^{46} + 271274 q^{47} + 1484064 q^{48} + 235298 q^{49} + 250000 q^{50} - 1130910 q^{51} - 232184 q^{52} - 1267792 q^{53} + 972000 q^{54} - 988250 q^{55} + 329280 q^{56} - 2871996 q^{57} - 3107120 q^{58} - 1360120 q^{59} - 981000 q^{60} - 1813680 q^{61} + 37392 q^{62} + 259308 q^{63} - 2489984 q^{64} - 2227250 q^{65} + 5142624 q^{66} - 2189312 q^{67} + 3159640 q^{68} - 5851980 q^{69} - 686000 q^{70} - 1494928 q^{71} + 46080 q^{72} + 7169788 q^{73} - 5967024 q^{74} - 468750 q^{75} + 7875376 q^{76} + 2711758 q^{77} + 9159504 q^{78} - 7942974 q^{79} - 540000 q^{80} - 4775598 q^{81} + 2391792 q^{82} - 304712 q^{83} + 2691864 q^{84} - 299750 q^{85} + 5417712 q^{86} + 14455086 q^{87} + 4463680 q^{88} - 17943528 q^{89} + 1224000 q^{90} + 6111574 q^{91} + 14774640 q^{92} + 8116992 q^{93} - 2823104 q^{94} - 451500 q^{95} + 13366272 q^{96} + 4258074 q^{97} + 1882384 q^{98} - 3030732 q^{99}+O(q^{100})$$ 2 * q + 16 * q^2 - 30 * q^3 - 40 * q^4 + 250 * q^5 - 768 * q^6 - 686 * q^7 - 960 * q^8 - 756 * q^9 + 2000 * q^10 - 7906 * q^11 - 7848 * q^12 - 17818 * q^13 - 5488 * q^14 - 3750 * q^15 - 4320 * q^16 - 2398 * q^17 + 9792 * q^18 - 3612 * q^19 - 5000 * q^20 + 10290 * q^21 - 96688 * q^22 + 13844 * q^23 + 24960 * q^24 + 31250 * q^25 - 179328 * q^26 - 18090 * q^27 + 13720 * q^28 - 126898 * q^29 - 96000 * q^30 + 252768 * q^31 - 148224 * q^32 + 319230 * q^33 + 175296 * q^34 - 85750 * q^35 + 268560 * q^36 - 265860 * q^37 + 458800 * q^38 + 487974 * q^39 - 120000 * q^40 - 111920 * q^41 + 263424 * q^42 + 947572 * q^43 - 376920 * q^44 - 94500 * q^45 + 1051472 * q^46 + 271274 * q^47 + 1484064 * q^48 + 235298 * q^49 + 250000 * q^50 - 1130910 * q^51 - 232184 * q^52 - 1267792 * q^53 + 972000 * q^54 - 988250 * q^55 + 329280 * q^56 - 2871996 * q^57 - 3107120 * q^58 - 1360120 * q^59 - 981000 * q^60 - 1813680 * q^61 + 37392 * q^62 + 259308 * q^63 - 2489984 * q^64 - 2227250 * q^65 + 5142624 * q^66 - 2189312 * q^67 + 3159640 * q^68 - 5851980 * q^69 - 686000 * q^70 - 1494928 * q^71 + 46080 * q^72 + 7169788 * q^73 - 5967024 * q^74 - 468750 * q^75 + 7875376 * q^76 + 2711758 * q^77 + 9159504 * q^78 - 7942974 * q^79 - 540000 * q^80 - 4775598 * q^81 + 2391792 * q^82 - 304712 * q^83 + 2691864 * q^84 - 299750 * q^85 + 5417712 * q^86 + 14455086 * q^87 + 4463680 * q^88 - 17943528 * q^89 + 1224000 * q^90 + 6111574 * q^91 + 14774640 * q^92 + 8116992 * q^93 - 2823104 * q^94 - 451500 * q^95 + 13366272 * q^96 + 4258074 * q^97 + 1882384 * q^98 - 3030732 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.36675 0.120805 0.0604024 0.998174i $$-0.480762\pi$$
0.0604024 + 0.998174i $$0.480762\pi$$
$$3$$ 24.7995 0.530296 0.265148 0.964208i $$-0.414579\pi$$
0.265148 + 0.964208i $$0.414579\pi$$
$$4$$ −126.132 −0.985406
$$5$$ 125.000 0.447214
$$6$$ 33.8947 0.0640623
$$7$$ −343.000 −0.377964
$$8$$ −347.335 −0.239847
$$9$$ −1571.98 −0.718786
$$10$$ 170.844 0.0540256
$$11$$ −1432.37 −0.324474 −0.162237 0.986752i $$-0.551871\pi$$
−0.162237 + 0.986752i $$0.551871\pi$$
$$12$$ −3128.01 −0.522557
$$13$$ −6136.30 −0.774649 −0.387325 0.921943i $$-0.626601\pi$$
−0.387325 + 0.921943i $$0.626601\pi$$
$$14$$ −468.795 −0.0456599
$$15$$ 3099.94 0.237156
$$16$$ 15670.2 0.956432
$$17$$ −15858.5 −0.782871 −0.391436 0.920205i $$-0.628021\pi$$
−0.391436 + 0.920205i $$0.628021\pi$$
$$18$$ −2148.51 −0.0868328
$$19$$ −38567.5 −1.28998 −0.644991 0.764190i $$-0.723139\pi$$
−0.644991 + 0.764190i $$0.723139\pi$$
$$20$$ −15766.5 −0.440687
$$21$$ −8506.23 −0.200433
$$22$$ −1957.69 −0.0391980
$$23$$ −63987.4 −1.09660 −0.548299 0.836282i $$-0.684724\pi$$
−0.548299 + 0.836282i $$0.684724\pi$$
$$24$$ −8613.73 −0.127190
$$25$$ 15625.0 0.200000
$$26$$ −8386.79 −0.0935813
$$27$$ −93220.9 −0.911466
$$28$$ 43263.3 0.372449
$$29$$ 94236.6 0.717508 0.358754 0.933432i $$-0.383202\pi$$
0.358754 + 0.933432i $$0.383202\pi$$
$$30$$ 4236.84 0.0286495
$$31$$ 275990. 1.66390 0.831951 0.554849i $$-0.187224\pi$$
0.831951 + 0.554849i $$0.187224\pi$$
$$32$$ 65876.1 0.355388
$$33$$ −35521.9 −0.172067
$$34$$ −21674.6 −0.0945746
$$35$$ −42875.0 −0.169031
$$36$$ 198278. 0.708296
$$37$$ 156532. 0.508038 0.254019 0.967199i $$-0.418247\pi$$
0.254019 + 0.967199i $$0.418247\pi$$
$$38$$ −52712.1 −0.155836
$$39$$ −152177. −0.410793
$$40$$ −43416.9 −0.107263
$$41$$ −303738. −0.688266 −0.344133 0.938921i $$-0.611827\pi$$
−0.344133 + 0.938921i $$0.611827\pi$$
$$42$$ −11625.9 −0.0242133
$$43$$ 636818. 1.22145 0.610725 0.791843i $$-0.290878\pi$$
0.610725 + 0.791843i $$0.290878\pi$$
$$44$$ 180667. 0.319738
$$45$$ −196498. −0.321451
$$46$$ −87454.9 −0.132474
$$47$$ 512021. 0.719358 0.359679 0.933076i $$-0.382886\pi$$
0.359679 + 0.933076i $$0.382886\pi$$
$$48$$ 388612. 0.507192
$$49$$ 117649. 0.142857
$$50$$ 21355.5 0.0241610
$$51$$ −393282. −0.415154
$$52$$ 773984. 0.763344
$$53$$ −201249. −0.185681 −0.0928406 0.995681i $$-0.529595\pi$$
−0.0928406 + 0.995681i $$0.529595\pi$$
$$54$$ −127410. −0.110109
$$55$$ −179046. −0.145109
$$56$$ 119136. 0.0906535
$$57$$ −956454. −0.684072
$$58$$ 128798. 0.0866784
$$59$$ −1.81196e6 −1.14859 −0.574296 0.818648i $$-0.694724\pi$$
−0.574296 + 0.818648i $$0.694724\pi$$
$$60$$ −391001. −0.233695
$$61$$ −982021. −0.553945 −0.276972 0.960878i $$-0.589331\pi$$
−0.276972 + 0.960878i $$0.589331\pi$$
$$62$$ 377210. 0.201007
$$63$$ 539191. 0.271676
$$64$$ −1.91575e6 −0.913499
$$65$$ −767038. −0.346434
$$66$$ −48549.6 −0.0207865
$$67$$ −4.45336e6 −1.80895 −0.904474 0.426528i $$-0.859736\pi$$
−0.904474 + 0.426528i $$0.859736\pi$$
$$68$$ 2.00026e6 0.771446
$$69$$ −1.58686e6 −0.581522
$$70$$ −58599.4 −0.0204197
$$71$$ 725436. 0.240544 0.120272 0.992741i $$-0.461623\pi$$
0.120272 + 0.992741i $$0.461623\pi$$
$$72$$ 546005. 0.172398
$$73$$ 2.17602e6 0.654685 0.327343 0.944906i $$-0.393847\pi$$
0.327343 + 0.944906i $$0.393847\pi$$
$$74$$ 213940. 0.0613735
$$75$$ 387492. 0.106059
$$76$$ 4.86459e6 1.27116
$$77$$ 491301. 0.122639
$$78$$ −207988. −0.0496258
$$79$$ −5.21525e6 −1.19009 −0.595045 0.803692i $$-0.702866\pi$$
−0.595045 + 0.803692i $$0.702866\pi$$
$$80$$ 1.95877e6 0.427729
$$81$$ 1.12610e6 0.235439
$$82$$ −415135. −0.0831458
$$83$$ 6.07921e6 1.16701 0.583504 0.812110i $$-0.301681\pi$$
0.583504 + 0.812110i $$0.301681\pi$$
$$84$$ 1.07291e6 0.197508
$$85$$ −1.98231e6 −0.350111
$$86$$ 870371. 0.147557
$$87$$ 2.33702e6 0.380492
$$88$$ 497511. 0.0778239
$$89$$ −1.06137e7 −1.59589 −0.797946 0.602729i $$-0.794080\pi$$
−0.797946 + 0.602729i $$0.794080\pi$$
$$90$$ −268564. −0.0388328
$$91$$ 2.10475e6 0.292790
$$92$$ 8.07086e6 1.08059
$$93$$ 6.84442e6 0.882361
$$94$$ 699805. 0.0869019
$$95$$ −4.82093e6 −0.576897
$$96$$ 1.63369e6 0.188461
$$97$$ 6.64483e6 0.739236 0.369618 0.929184i $$-0.379489\pi$$
0.369618 + 0.929184i $$0.379489\pi$$
$$98$$ 160797. 0.0172578
$$99$$ 2.25166e6 0.233227
$$100$$ −1.97081e6 −0.197081
$$101$$ 1.07531e7 1.03851 0.519254 0.854620i $$-0.326210\pi$$
0.519254 + 0.854620i $$0.326210\pi$$
$$102$$ −537519. −0.0501526
$$103$$ −1.05886e7 −0.954788 −0.477394 0.878689i $$-0.658419\pi$$
−0.477394 + 0.878689i $$0.658419\pi$$
$$104$$ 2.13135e6 0.185797
$$105$$ −1.06328e6 −0.0896364
$$106$$ −275057. −0.0224312
$$107$$ −8.37234e6 −0.660699 −0.330349 0.943859i $$-0.607167\pi$$
−0.330349 + 0.943859i $$0.607167\pi$$
$$108$$ 1.17581e7 0.898164
$$109$$ −1.95948e7 −1.44926 −0.724632 0.689136i $$-0.757990\pi$$
−0.724632 + 0.689136i $$0.757990\pi$$
$$110$$ −244711. −0.0175299
$$111$$ 3.88191e6 0.269411
$$112$$ −5.37487e6 −0.361497
$$113$$ 1.36310e7 0.888694 0.444347 0.895855i $$-0.353436\pi$$
0.444347 + 0.895855i $$0.353436\pi$$
$$114$$ −1.30723e6 −0.0826392
$$115$$ −7.99843e6 −0.490413
$$116$$ −1.18863e7 −0.707037
$$117$$ 9.64617e6 0.556807
$$118$$ −2.47649e6 −0.138756
$$119$$ 5.43946e6 0.295898
$$120$$ −1.07672e6 −0.0568810
$$121$$ −1.74355e7 −0.894717
$$122$$ −1.34218e6 −0.0669192
$$123$$ −7.53256e6 −0.364985
$$124$$ −3.48112e7 −1.63962
$$125$$ 1.95312e6 0.0894427
$$126$$ 736939. 0.0328197
$$127$$ 2.23763e7 0.969336 0.484668 0.874698i $$-0.338940\pi$$
0.484668 + 0.874698i $$0.338940\pi$$
$$128$$ −1.10505e7 −0.465743
$$129$$ 1.57928e7 0.647730
$$130$$ −1.04835e6 −0.0418508
$$131$$ −4.53330e6 −0.176183 −0.0880917 0.996112i $$-0.528077\pi$$
−0.0880917 + 0.996112i $$0.528077\pi$$
$$132$$ 4.48045e6 0.169556
$$133$$ 1.32286e7 0.487567
$$134$$ −6.08663e6 −0.218530
$$135$$ −1.16526e7 −0.407620
$$136$$ 5.50821e6 0.187769
$$137$$ −5.07657e7 −1.68674 −0.843371 0.537332i $$-0.819432\pi$$
−0.843371 + 0.537332i $$0.819432\pi$$
$$138$$ −2.16884e6 −0.0702506
$$139$$ 1.05183e7 0.332195 0.166097 0.986109i $$-0.446883\pi$$
0.166097 + 0.986109i $$0.446883\pi$$
$$140$$ 5.40791e6 0.166564
$$141$$ 1.26979e7 0.381473
$$142$$ 991490. 0.0290589
$$143$$ 8.78942e6 0.251353
$$144$$ −2.46333e7 −0.687470
$$145$$ 1.17796e7 0.320879
$$146$$ 2.97407e6 0.0790891
$$147$$ 2.91764e6 0.0757566
$$148$$ −1.97437e7 −0.500624
$$149$$ 5.43497e7 1.34600 0.673000 0.739642i $$-0.265005\pi$$
0.673000 + 0.739642i $$0.265005\pi$$
$$150$$ 529605. 0.0128125
$$151$$ −2.23258e7 −0.527700 −0.263850 0.964564i $$-0.584992\pi$$
−0.263850 + 0.964564i $$0.584992\pi$$
$$152$$ 1.33958e7 0.309398
$$153$$ 2.49293e7 0.562717
$$154$$ 671486. 0.0148154
$$155$$ 3.44988e7 0.744120
$$156$$ 1.91944e7 0.404798
$$157$$ −4.37788e7 −0.902848 −0.451424 0.892310i $$-0.649084\pi$$
−0.451424 + 0.892310i $$0.649084\pi$$
$$158$$ −7.12794e6 −0.143769
$$159$$ −4.99087e6 −0.0984661
$$160$$ 8.23451e6 0.158934
$$161$$ 2.19477e7 0.414475
$$162$$ 1.53910e6 0.0284422
$$163$$ 4.05451e7 0.733300 0.366650 0.930359i $$-0.380505\pi$$
0.366650 + 0.930359i $$0.380505\pi$$
$$164$$ 3.83111e7 0.678221
$$165$$ −4.44024e6 −0.0769507
$$166$$ 8.30876e6 0.140980
$$167$$ 9.73453e7 1.61736 0.808682 0.588247i $$-0.200182\pi$$
0.808682 + 0.588247i $$0.200182\pi$$
$$168$$ 2.95451e6 0.0480732
$$169$$ −2.50943e7 −0.399919
$$170$$ −2.70932e6 −0.0422951
$$171$$ 6.06275e7 0.927221
$$172$$ −8.03231e7 −1.20362
$$173$$ −5.10607e7 −0.749765 −0.374882 0.927072i $$-0.622317\pi$$
−0.374882 + 0.927072i $$0.622317\pi$$
$$174$$ 3.19412e6 0.0459652
$$175$$ −5.35938e6 −0.0755929
$$176$$ −2.24454e7 −0.310337
$$177$$ −4.49356e7 −0.609094
$$178$$ −1.45063e7 −0.192791
$$179$$ 1.45811e8 1.90023 0.950113 0.311907i $$-0.100968\pi$$
0.950113 + 0.311907i $$0.100968\pi$$
$$180$$ 2.47847e7 0.316760
$$181$$ −6.09656e7 −0.764205 −0.382102 0.924120i $$-0.624800\pi$$
−0.382102 + 0.924120i $$0.624800\pi$$
$$182$$ 2.87667e6 0.0353704
$$183$$ −2.43536e7 −0.293755
$$184$$ 2.22251e7 0.263015
$$185$$ 1.95665e7 0.227202
$$186$$ 9.35462e6 0.106593
$$187$$ 2.27151e7 0.254021
$$188$$ −6.45822e7 −0.708860
$$189$$ 3.19748e7 0.344502
$$190$$ −6.58901e6 −0.0696920
$$191$$ −1.52578e8 −1.58444 −0.792219 0.610237i $$-0.791074\pi$$
−0.792219 + 0.610237i $$0.791074\pi$$
$$192$$ −4.75095e7 −0.484425
$$193$$ −1.39277e8 −1.39453 −0.697267 0.716812i $$-0.745601\pi$$
−0.697267 + 0.716812i $$0.745601\pi$$
$$194$$ 9.08183e6 0.0893033
$$195$$ −1.90221e7 −0.183712
$$196$$ −1.48393e7 −0.140772
$$197$$ 6.52480e7 0.608044 0.304022 0.952665i $$-0.401670\pi$$
0.304022 + 0.952665i $$0.401670\pi$$
$$198$$ 3.07745e6 0.0281750
$$199$$ 1.93503e6 0.0174061 0.00870307 0.999962i $$-0.497230\pi$$
0.00870307 + 0.999962i $$0.497230\pi$$
$$200$$ −5.42711e6 −0.0479693
$$201$$ −1.10441e8 −0.959278
$$202$$ 1.46968e7 0.125457
$$203$$ −3.23232e7 −0.271192
$$204$$ 4.96055e7 0.409095
$$205$$ −3.79673e7 −0.307802
$$206$$ −1.44719e7 −0.115343
$$207$$ 1.00587e8 0.788219
$$208$$ −9.61569e7 −0.740899
$$209$$ 5.52427e7 0.418565
$$210$$ −1.45324e6 −0.0108285
$$211$$ −5.17848e7 −0.379502 −0.189751 0.981832i $$-0.560768\pi$$
−0.189751 + 0.981832i $$0.560768\pi$$
$$212$$ 2.53839e7 0.182971
$$213$$ 1.79904e7 0.127560
$$214$$ −1.14429e7 −0.0798156
$$215$$ 7.96023e7 0.546249
$$216$$ 3.23789e7 0.218612
$$217$$ −9.46647e7 −0.628896
$$218$$ −2.67812e7 −0.175078
$$219$$ 5.39642e7 0.347177
$$220$$ 2.25834e7 0.142991
$$221$$ 9.73124e7 0.606450
$$222$$ 5.30560e6 0.0325461
$$223$$ −1.25065e8 −0.755209 −0.377605 0.925967i $$-0.623252\pi$$
−0.377605 + 0.925967i $$0.623252\pi$$
$$224$$ −2.25955e7 −0.134324
$$225$$ −2.45623e7 −0.143757
$$226$$ 1.86301e7 0.107358
$$227$$ 1.92108e7 0.109007 0.0545036 0.998514i $$-0.482642\pi$$
0.0545036 + 0.998514i $$0.482642\pi$$
$$228$$ 1.20639e8 0.674089
$$229$$ −1.05650e8 −0.581360 −0.290680 0.956820i $$-0.593882\pi$$
−0.290680 + 0.956820i $$0.593882\pi$$
$$230$$ −1.09319e7 −0.0592443
$$231$$ 1.21840e7 0.0650353
$$232$$ −3.27317e7 −0.172092
$$233$$ −2.31646e8 −1.19972 −0.599859 0.800106i $$-0.704776\pi$$
−0.599859 + 0.800106i $$0.704776\pi$$
$$234$$ 1.31839e7 0.0672649
$$235$$ 6.40026e7 0.321707
$$236$$ 2.28546e8 1.13183
$$237$$ −1.29336e8 −0.631101
$$238$$ 7.43438e6 0.0357458
$$239$$ 1.09174e8 0.517281 0.258641 0.965974i $$-0.416725\pi$$
0.258641 + 0.965974i $$0.416725\pi$$
$$240$$ 4.85766e7 0.226823
$$241$$ −8.25277e7 −0.379787 −0.189893 0.981805i $$-0.560814\pi$$
−0.189893 + 0.981805i $$0.560814\pi$$
$$242$$ −2.38300e7 −0.108086
$$243$$ 2.31801e8 1.03632
$$244$$ 1.23864e8 0.545861
$$245$$ 1.47061e7 0.0638877
$$246$$ −1.02951e7 −0.0440919
$$247$$ 2.36662e8 0.999283
$$248$$ −9.58611e7 −0.399081
$$249$$ 1.50761e8 0.618860
$$250$$ 2.66943e6 0.0108051
$$251$$ −2.40987e7 −0.0961912 −0.0480956 0.998843i $$-0.515315\pi$$
−0.0480956 + 0.998843i $$0.515315\pi$$
$$252$$ −6.80092e7 −0.267711
$$253$$ 9.16534e7 0.355817
$$254$$ 3.05828e7 0.117100
$$255$$ −4.91603e7 −0.185662
$$256$$ 2.30112e8 0.857235
$$257$$ 9.75049e7 0.358311 0.179156 0.983821i $$-0.442663\pi$$
0.179156 + 0.983821i $$0.442663\pi$$
$$258$$ 2.15848e7 0.0782489
$$259$$ −5.36904e7 −0.192020
$$260$$ 9.67480e7 0.341378
$$261$$ −1.48139e8 −0.515735
$$262$$ −6.19589e6 −0.0212838
$$263$$ 2.98637e8 1.01228 0.506138 0.862452i $$-0.331073\pi$$
0.506138 + 0.862452i $$0.331073\pi$$
$$264$$ 1.23380e7 0.0412697
$$265$$ −2.51561e7 −0.0830392
$$266$$ 1.80803e7 0.0589005
$$267$$ −2.63216e8 −0.846296
$$268$$ 5.61711e8 1.78255
$$269$$ −3.90722e8 −1.22387 −0.611934 0.790909i $$-0.709608\pi$$
−0.611934 + 0.790909i $$0.709608\pi$$
$$270$$ −1.59262e7 −0.0492424
$$271$$ 2.12098e8 0.647357 0.323678 0.946167i $$-0.395080\pi$$
0.323678 + 0.946167i $$0.395080\pi$$
$$272$$ −2.48505e8 −0.748763
$$273$$ 5.21968e7 0.155265
$$274$$ −6.93841e7 −0.203767
$$275$$ −2.23807e7 −0.0648947
$$276$$ 2.00153e8 0.573035
$$277$$ 1.86723e8 0.527861 0.263930 0.964542i $$-0.414981\pi$$
0.263930 + 0.964542i $$0.414981\pi$$
$$278$$ 1.43759e7 0.0401307
$$279$$ −4.33853e8 −1.19599
$$280$$ 1.48920e7 0.0405415
$$281$$ −7.38791e8 −1.98632 −0.993161 0.116756i $$-0.962750\pi$$
−0.993161 + 0.116756i $$0.962750\pi$$
$$282$$ 1.73548e7 0.0460838
$$283$$ −3.11903e8 −0.818026 −0.409013 0.912529i $$-0.634127\pi$$
−0.409013 + 0.912529i $$0.634127\pi$$
$$284$$ −9.15007e7 −0.237034
$$285$$ −1.19557e8 −0.305926
$$286$$ 1.20129e7 0.0303647
$$287$$ 1.04182e8 0.260140
$$288$$ −1.03556e8 −0.255448
$$289$$ −1.58847e8 −0.387113
$$290$$ 1.60997e7 0.0387638
$$291$$ 1.64789e8 0.392014
$$292$$ −2.74466e8 −0.645131
$$293$$ −5.05466e8 −1.17397 −0.586983 0.809599i $$-0.699684\pi$$
−0.586983 + 0.809599i $$0.699684\pi$$
$$294$$ 3.98768e6 0.00915176
$$295$$ −2.26495e8 −0.513666
$$296$$ −5.43690e7 −0.121851
$$297$$ 1.33526e8 0.295747
$$298$$ 7.42825e7 0.162603
$$299$$ 3.92646e8 0.849478
$$300$$ −4.88752e7 −0.104511
$$301$$ −2.18429e8 −0.461665
$$302$$ −3.05137e7 −0.0637487
$$303$$ 2.66672e8 0.550717
$$304$$ −6.04359e8 −1.23378
$$305$$ −1.22753e8 −0.247732
$$306$$ 3.40721e7 0.0679789
$$307$$ 4.67463e8 0.922067 0.461034 0.887383i $$-0.347479\pi$$
0.461034 + 0.887383i $$0.347479\pi$$
$$308$$ −6.19688e7 −0.120850
$$309$$ −2.62591e8 −0.506321
$$310$$ 4.71512e7 0.0898933
$$311$$ 1.16022e7 0.0218714 0.0109357 0.999940i $$-0.496519\pi$$
0.0109357 + 0.999940i $$0.496519\pi$$
$$312$$ 5.28565e7 0.0985274
$$313$$ 8.23197e8 1.51740 0.758698 0.651443i $$-0.225836\pi$$
0.758698 + 0.651443i $$0.225836\pi$$
$$314$$ −5.98346e7 −0.109068
$$315$$ 6.73989e7 0.121497
$$316$$ 6.57810e8 1.17272
$$317$$ 3.89154e8 0.686142 0.343071 0.939309i $$-0.388533\pi$$
0.343071 + 0.939309i $$0.388533\pi$$
$$318$$ −6.82128e6 −0.0118952
$$319$$ −1.34981e8 −0.232812
$$320$$ −2.39468e8 −0.408529
$$321$$ −2.07630e8 −0.350366
$$322$$ 2.99970e7 0.0500706
$$323$$ 6.11621e8 1.00989
$$324$$ −1.42037e8 −0.232003
$$325$$ −9.58797e7 −0.154930
$$326$$ 5.54150e7 0.0885861
$$327$$ −4.85940e8 −0.768539
$$328$$ 1.05499e8 0.165078
$$329$$ −1.75623e8 −0.271892
$$330$$ −6.06870e6 −0.00929602
$$331$$ 1.48582e8 0.225199 0.112600 0.993640i $$-0.464082\pi$$
0.112600 + 0.993640i $$0.464082\pi$$
$$332$$ −7.66783e8 −1.14998
$$333$$ −2.46066e8 −0.365171
$$334$$ 1.33047e8 0.195385
$$335$$ −5.56670e8 −0.808986
$$336$$ −1.33294e8 −0.191701
$$337$$ 1.23379e8 0.175605 0.0878023 0.996138i $$-0.472016\pi$$
0.0878023 + 0.996138i $$0.472016\pi$$
$$338$$ −3.42977e7 −0.0483121
$$339$$ 3.38041e8 0.471271
$$340$$ 2.50033e8 0.345001
$$341$$ −3.95319e8 −0.539892
$$342$$ 8.28626e7 0.112013
$$343$$ −4.03536e7 −0.0539949
$$344$$ −2.21189e8 −0.292961
$$345$$ −1.98357e8 −0.260064
$$346$$ −6.97872e7 −0.0905752
$$347$$ 1.31658e9 1.69159 0.845793 0.533511i $$-0.179128\pi$$
0.845793 + 0.533511i $$0.179128\pi$$
$$348$$ −2.94773e8 −0.374939
$$349$$ 2.64521e8 0.333097 0.166549 0.986033i $$-0.446738\pi$$
0.166549 + 0.986033i $$0.446738\pi$$
$$350$$ −7.32493e6 −0.00913199
$$351$$ 5.72032e8 0.706066
$$352$$ −9.43586e7 −0.115314
$$353$$ 1.30271e9 1.57629 0.788144 0.615490i $$-0.211042\pi$$
0.788144 + 0.615490i $$0.211042\pi$$
$$354$$ −6.14158e7 −0.0735815
$$355$$ 9.06795e7 0.107575
$$356$$ 1.33873e9 1.57260
$$357$$ 1.34896e8 0.156913
$$358$$ 1.99287e8 0.229556
$$359$$ −1.03262e9 −1.17790 −0.588952 0.808168i $$-0.700459\pi$$
−0.588952 + 0.808168i $$0.700459\pi$$
$$360$$ 6.82507e7 0.0770989
$$361$$ 5.93578e8 0.664053
$$362$$ −8.33248e7 −0.0923196
$$363$$ −4.32392e8 −0.474465
$$364$$ −2.65476e8 −0.288517
$$365$$ 2.72002e8 0.292784
$$366$$ −3.32853e7 −0.0354870
$$367$$ 1.13124e9 1.19460 0.597302 0.802017i $$-0.296240\pi$$
0.597302 + 0.802017i $$0.296240\pi$$
$$368$$ −1.00269e9 −1.04882
$$369$$ 4.77472e8 0.494716
$$370$$ 2.67425e7 0.0274470
$$371$$ 6.90284e7 0.0701809
$$372$$ −8.63300e8 −0.869484
$$373$$ 5.38130e8 0.536916 0.268458 0.963291i $$-0.413486\pi$$
0.268458 + 0.963291i $$0.413486\pi$$
$$374$$ 3.10459e7 0.0306870
$$375$$ 4.84365e7 0.0474311
$$376$$ −1.77843e8 −0.172536
$$377$$ −5.78264e8 −0.555817
$$378$$ 4.37015e7 0.0416175
$$379$$ 7.83114e8 0.738904 0.369452 0.929250i $$-0.379545\pi$$
0.369452 + 0.929250i $$0.379545\pi$$
$$380$$ 6.08074e8 0.568478
$$381$$ 5.54920e8 0.514035
$$382$$ −2.08536e8 −0.191408
$$383$$ 8.22468e8 0.748038 0.374019 0.927421i $$-0.377980\pi$$
0.374019 + 0.927421i $$0.377980\pi$$
$$384$$ −2.74047e8 −0.246982
$$385$$ 6.14127e7 0.0548460
$$386$$ −1.90357e8 −0.168466
$$387$$ −1.00107e9 −0.877961
$$388$$ −8.38126e8 −0.728448
$$389$$ −1.07007e9 −0.921696 −0.460848 0.887479i $$-0.652455\pi$$
−0.460848 + 0.887479i $$0.652455\pi$$
$$390$$ −2.59985e7 −0.0221933
$$391$$ 1.01474e9 0.858495
$$392$$ −4.08636e7 −0.0342638
$$393$$ −1.12424e8 −0.0934293
$$394$$ 8.91777e7 0.0734547
$$395$$ −6.51906e8 −0.532225
$$396$$ −2.84006e8 −0.229823
$$397$$ −9.64552e8 −0.773676 −0.386838 0.922148i $$-0.626433\pi$$
−0.386838 + 0.922148i $$0.626433\pi$$
$$398$$ 2.64471e6 0.00210275
$$399$$ 3.28064e8 0.258555
$$400$$ 2.44846e8 0.191286
$$401$$ −1.94810e9 −1.50871 −0.754357 0.656465i $$-0.772051\pi$$
−0.754357 + 0.656465i $$0.772051\pi$$
$$402$$ −1.50945e8 −0.115885
$$403$$ −1.69356e9 −1.28894
$$404$$ −1.35631e9 −1.02335
$$405$$ 1.40762e8 0.105292
$$406$$ −4.41777e7 −0.0327614
$$407$$ −2.24211e8 −0.164845
$$408$$ 1.36601e8 0.0995732
$$409$$ 8.63865e8 0.624330 0.312165 0.950028i $$-0.398946\pi$$
0.312165 + 0.950028i $$0.398946\pi$$
$$410$$ −5.18918e7 −0.0371839
$$411$$ −1.25896e9 −0.894473
$$412$$ 1.33556e9 0.940854
$$413$$ 6.21501e8 0.434127
$$414$$ 1.37478e8 0.0952206
$$415$$ 7.59901e8 0.521902
$$416$$ −4.04236e8 −0.275301
$$417$$ 2.60848e8 0.176162
$$418$$ 7.55030e7 0.0505647
$$419$$ 2.21337e9 1.46996 0.734978 0.678091i $$-0.237192\pi$$
0.734978 + 0.678091i $$0.237192\pi$$
$$420$$ 1.34113e8 0.0883283
$$421$$ −2.89866e9 −1.89326 −0.946631 0.322321i $$-0.895537\pi$$
−0.946631 + 0.322321i $$0.895537\pi$$
$$422$$ −7.07769e7 −0.0458456
$$423$$ −8.04889e8 −0.517065
$$424$$ 6.99008e7 0.0445350
$$425$$ −2.47789e8 −0.156574
$$426$$ 2.45884e7 0.0154098
$$427$$ 3.36833e8 0.209371
$$428$$ 1.05602e9 0.651057
$$429$$ 2.17973e8 0.133292
$$430$$ 1.08796e8 0.0659895
$$431$$ −2.42056e9 −1.45628 −0.728142 0.685426i $$-0.759616\pi$$
−0.728142 + 0.685426i $$0.759616\pi$$
$$432$$ −1.46079e9 −0.871754
$$433$$ −2.26686e9 −1.34189 −0.670946 0.741506i $$-0.734112\pi$$
−0.670946 + 0.741506i $$0.734112\pi$$
$$434$$ −1.29383e8 −0.0759737
$$435$$ 2.92128e8 0.170161
$$436$$ 2.47153e9 1.42811
$$437$$ 2.46783e9 1.41459
$$438$$ 7.37555e7 0.0419407
$$439$$ 1.98911e9 1.12210 0.561052 0.827780i $$-0.310397\pi$$
0.561052 + 0.827780i $$0.310397\pi$$
$$440$$ 6.21888e7 0.0348039
$$441$$ −1.84942e8 −0.102684
$$442$$ 1.33002e8 0.0732621
$$443$$ −8.78038e8 −0.479844 −0.239922 0.970792i $$-0.577122\pi$$
−0.239922 + 0.970792i $$0.577122\pi$$
$$444$$ −4.89633e8 −0.265479
$$445$$ −1.32672e9 −0.713705
$$446$$ −1.70932e8 −0.0912329
$$447$$ 1.34785e9 0.713779
$$448$$ 6.57101e8 0.345270
$$449$$ 1.53113e8 0.0798270 0.0399135 0.999203i $$-0.487292\pi$$
0.0399135 + 0.999203i $$0.487292\pi$$
$$450$$ −3.35705e7 −0.0173666
$$451$$ 4.35064e8 0.223324
$$452$$ −1.71930e9 −0.875724
$$453$$ −5.53668e8 −0.279837
$$454$$ 2.62564e7 0.0131686
$$455$$ 2.63094e8 0.130940
$$456$$ 3.32210e8 0.164072
$$457$$ −2.39624e9 −1.17442 −0.587210 0.809435i $$-0.699774\pi$$
−0.587210 + 0.809435i $$0.699774\pi$$
$$458$$ −1.44397e8 −0.0702311
$$459$$ 1.47834e9 0.713560
$$460$$ 1.00886e9 0.483256
$$461$$ 1.61913e9 0.769713 0.384856 0.922977i $$-0.374251\pi$$
0.384856 + 0.922977i $$0.374251\pi$$
$$462$$ 1.66525e7 0.00785657
$$463$$ 1.16133e9 0.543778 0.271889 0.962329i $$-0.412352\pi$$
0.271889 + 0.962329i $$0.412352\pi$$
$$464$$ 1.47670e9 0.686247
$$465$$ 8.55553e8 0.394604
$$466$$ −3.16602e8 −0.144932
$$467$$ 2.83969e9 1.29021 0.645107 0.764092i $$-0.276813\pi$$
0.645107 + 0.764092i $$0.276813\pi$$
$$468$$ −1.21669e9 −0.548681
$$469$$ 1.52750e9 0.683718
$$470$$ 8.74756e7 0.0388637
$$471$$ −1.08569e9 −0.478777
$$472$$ 6.29356e8 0.275486
$$473$$ −9.12156e8 −0.396328
$$474$$ −1.76769e8 −0.0762400
$$475$$ −6.02617e8 −0.257996
$$476$$ −6.86090e8 −0.291579
$$477$$ 3.16360e8 0.133465
$$478$$ 1.49214e8 0.0624901
$$479$$ 2.38771e9 0.992676 0.496338 0.868129i $$-0.334678\pi$$
0.496338 + 0.868129i $$0.334678\pi$$
$$480$$ 2.04212e8 0.0842823
$$481$$ −9.60526e8 −0.393551
$$482$$ −1.12795e8 −0.0458801
$$483$$ 5.44292e8 0.219794
$$484$$ 2.19917e9 0.881660
$$485$$ 8.30604e8 0.330596
$$486$$ 3.16814e8 0.125192
$$487$$ −2.20508e9 −0.865113 −0.432556 0.901607i $$-0.642388\pi$$
−0.432556 + 0.901607i $$0.642388\pi$$
$$488$$ 3.41090e8 0.132862
$$489$$ 1.00550e9 0.388866
$$490$$ 2.00996e7 0.00771794
$$491$$ 4.28064e8 0.163201 0.0816006 0.996665i $$-0.473997\pi$$
0.0816006 + 0.996665i $$0.473997\pi$$
$$492$$ 9.50097e8 0.359658
$$493$$ −1.49445e9 −0.561716
$$494$$ 3.23457e8 0.120718
$$495$$ 2.81457e8 0.104302
$$496$$ 4.32482e9 1.59141
$$497$$ −2.48824e8 −0.0909171
$$498$$ 2.06053e8 0.0747613
$$499$$ −2.95178e9 −1.06349 −0.531743 0.846906i $$-0.678463\pi$$
−0.531743 + 0.846906i $$0.678463\pi$$
$$500$$ −2.46352e8 −0.0881374
$$501$$ 2.41412e9 0.857681
$$502$$ −3.29369e7 −0.0116204
$$503$$ −5.22380e9 −1.83020 −0.915099 0.403229i $$-0.867888\pi$$
−0.915099 + 0.403229i $$0.867888\pi$$
$$504$$ −1.87280e8 −0.0651605
$$505$$ 1.34414e9 0.464435
$$506$$ 1.25267e8 0.0429844
$$507$$ −6.22326e8 −0.212075
$$508$$ −2.82236e9 −0.955190
$$509$$ −2.80532e9 −0.942911 −0.471455 0.881890i $$-0.656271\pi$$
−0.471455 + 0.881890i $$0.656271\pi$$
$$510$$ −6.71899e7 −0.0224289
$$511$$ −7.46374e8 −0.247448
$$512$$ 1.72897e9 0.569301
$$513$$ 3.59530e9 1.17577
$$514$$ 1.33265e8 0.0432857
$$515$$ −1.32357e9 −0.426994
$$516$$ −1.99197e9 −0.638277
$$517$$ −7.33401e8 −0.233413
$$518$$ −7.33814e7 −0.0231970
$$519$$ −1.26628e9 −0.397597
$$520$$ 2.66419e8 0.0830909
$$521$$ 1.40563e8 0.0435450 0.0217725 0.999763i $$-0.493069\pi$$
0.0217725 + 0.999763i $$0.493069\pi$$
$$522$$ −2.02468e8 −0.0623032
$$523$$ −1.81127e9 −0.553638 −0.276819 0.960922i $$-0.589280\pi$$
−0.276819 + 0.960922i $$0.589280\pi$$
$$524$$ 5.71794e8 0.173612
$$525$$ −1.32910e8 −0.0400866
$$526$$ 4.08163e8 0.122288
$$527$$ −4.37679e9 −1.30262
$$528$$ −5.56635e8 −0.164570
$$529$$ 6.89567e8 0.202526
$$530$$ −3.43821e7 −0.0100315
$$531$$ 2.84837e9 0.825592
$$532$$ −1.66855e9 −0.480452
$$533$$ 1.86383e9 0.533164
$$534$$ −3.59750e8 −0.102237
$$535$$ −1.04654e9 −0.295474
$$536$$ 1.54681e9 0.433870
$$537$$ 3.61604e9 1.00768
$$538$$ −5.34019e8 −0.147849
$$539$$ −1.68516e8 −0.0463534
$$540$$ 1.46977e9 0.401671
$$541$$ −7.11633e9 −1.93226 −0.966130 0.258058i $$-0.916918\pi$$
−0.966130 + 0.258058i $$0.916918\pi$$
$$542$$ 2.89885e8 0.0782038
$$543$$ −1.51192e9 −0.405255
$$544$$ −1.04469e9 −0.278223
$$545$$ −2.44935e9 −0.648130
$$546$$ 7.13400e7 0.0187568
$$547$$ −6.02390e9 −1.57370 −0.786850 0.617144i $$-0.788290\pi$$
−0.786850 + 0.617144i $$0.788290\pi$$
$$548$$ 6.40318e9 1.66213
$$549$$ 1.54372e9 0.398168
$$550$$ −3.05888e7 −0.00783959
$$551$$ −3.63447e9 −0.925572
$$552$$ 5.51171e8 0.139476
$$553$$ 1.78883e9 0.449812
$$554$$ 2.55204e8 0.0637681
$$555$$ 4.85239e8 0.120484
$$556$$ −1.32669e9 −0.327347
$$557$$ 3.55726e9 0.872214 0.436107 0.899895i $$-0.356357\pi$$
0.436107 + 0.899895i $$0.356357\pi$$
$$558$$ −5.92968e8 −0.144481
$$559$$ −3.90771e9 −0.946195
$$560$$ −6.71859e8 −0.161666
$$561$$ 5.63324e8 0.134706
$$562$$ −1.00974e9 −0.239957
$$563$$ 2.51240e9 0.593347 0.296673 0.954979i $$-0.404123\pi$$
0.296673 + 0.954979i $$0.404123\pi$$
$$564$$ −1.60161e9 −0.375906
$$565$$ 1.70387e9 0.397436
$$566$$ −4.26293e8 −0.0988214
$$567$$ −3.86252e8 −0.0889877
$$568$$ −2.51969e8 −0.0576937
$$569$$ 3.02191e9 0.687683 0.343841 0.939028i $$-0.388272\pi$$
0.343841 + 0.939028i $$0.388272\pi$$
$$570$$ −1.63404e8 −0.0369574
$$571$$ 4.13151e9 0.928716 0.464358 0.885648i $$-0.346285\pi$$
0.464358 + 0.885648i $$0.346285\pi$$
$$572$$ −1.10863e9 −0.247685
$$573$$ −3.78386e9 −0.840221
$$574$$ 1.42391e8 0.0314262
$$575$$ −9.99804e8 −0.219320
$$576$$ 3.01152e9 0.656610
$$577$$ −3.66048e9 −0.793274 −0.396637 0.917976i $$-0.629823\pi$$
−0.396637 + 0.917976i $$0.629823\pi$$
$$578$$ −2.17105e8 −0.0467651
$$579$$ −3.45400e9 −0.739516
$$580$$ −1.48578e9 −0.316196
$$581$$ −2.08517e9 −0.441088
$$582$$ 2.25225e8 0.0473572
$$583$$ 2.88262e8 0.0602487
$$584$$ −7.55807e8 −0.157024
$$585$$ 1.20577e9 0.249012
$$586$$ −6.90846e8 −0.141821
$$587$$ 8.93156e9 1.82261 0.911305 0.411731i $$-0.135076\pi$$
0.911305 + 0.411731i $$0.135076\pi$$
$$588$$ −3.68007e8 −0.0746510
$$589$$ −1.06442e10 −2.14640
$$590$$ −3.09562e8 −0.0620534
$$591$$ 1.61812e9 0.322444
$$592$$ 2.45288e9 0.485904
$$593$$ 8.00218e9 1.57586 0.787929 0.615766i $$-0.211153\pi$$
0.787929 + 0.615766i $$0.211153\pi$$
$$594$$ 1.82497e8 0.0357276
$$595$$ 6.79932e8 0.132329
$$596$$ −6.85524e9 −1.32636
$$597$$ 4.79879e7 0.00923041
$$598$$ 5.36649e8 0.102621
$$599$$ 6.37081e9 1.21116 0.605579 0.795785i $$-0.292941\pi$$
0.605579 + 0.795785i $$0.292941\pi$$
$$600$$ −1.34590e8 −0.0254379
$$601$$ 7.97677e9 1.49888 0.749439 0.662073i $$-0.230323\pi$$
0.749439 + 0.662073i $$0.230323\pi$$
$$602$$ −2.98537e8 −0.0557713
$$603$$ 7.00062e9 1.30025
$$604$$ 2.81599e9 0.519999
$$605$$ −2.17944e9 −0.400130
$$606$$ 3.64474e8 0.0665293
$$607$$ 5.42119e9 0.983863 0.491931 0.870634i $$-0.336291\pi$$
0.491931 + 0.870634i $$0.336291\pi$$
$$608$$ −2.54067e9 −0.458444
$$609$$ −8.01598e8 −0.143812
$$610$$ −1.67772e8 −0.0299272
$$611$$ −3.14191e9 −0.557250
$$612$$ −3.14438e9 −0.554505
$$613$$ 8.21824e9 1.44101 0.720505 0.693450i $$-0.243910\pi$$
0.720505 + 0.693450i $$0.243910\pi$$
$$614$$ 6.38905e8 0.111390
$$615$$ −9.41570e8 −0.163226
$$616$$ −1.70646e8 −0.0294147
$$617$$ 8.15621e9 1.39795 0.698973 0.715148i $$-0.253641\pi$$
0.698973 + 0.715148i $$0.253641\pi$$
$$618$$ −3.58897e8 −0.0611660
$$619$$ −6.46052e9 −1.09484 −0.547420 0.836858i $$-0.684390\pi$$
−0.547420 + 0.836858i $$0.684390\pi$$
$$620$$ −4.35140e9 −0.733260
$$621$$ 5.96497e9 0.999511
$$622$$ 1.58573e7 0.00264218
$$623$$ 3.64051e9 0.603191
$$624$$ −2.38464e9 −0.392896
$$625$$ 2.44141e8 0.0400000
$$626$$ 1.12511e9 0.183309
$$627$$ 1.36999e9 0.221963
$$628$$ 5.52190e9 0.889672
$$629$$ −2.48236e9 −0.397729
$$630$$ 9.21174e7 0.0146774
$$631$$ −8.82660e9 −1.39859 −0.699295 0.714833i $$-0.746503\pi$$
−0.699295 + 0.714833i $$0.746503\pi$$
$$632$$ 1.81144e9 0.285439
$$633$$ −1.28424e9 −0.201248
$$634$$ 5.31876e8 0.0828893
$$635$$ 2.79703e9 0.433500
$$636$$ 6.29509e8 0.0970291
$$637$$ −7.21930e8 −0.110664
$$638$$ −1.84486e8 −0.0281249
$$639$$ −1.14037e9 −0.172900
$$640$$ −1.38131e9 −0.208287
$$641$$ 8.54151e9 1.28095 0.640474 0.767980i $$-0.278738\pi$$
0.640474 + 0.767980i $$0.278738\pi$$
$$642$$ −2.83778e8 −0.0423259
$$643$$ −1.20342e10 −1.78517 −0.892585 0.450878i $$-0.851111\pi$$
−0.892585 + 0.450878i $$0.851111\pi$$
$$644$$ −2.76831e9 −0.408426
$$645$$ 1.97410e9 0.289674
$$646$$ 8.35934e8 0.122000
$$647$$ 1.89174e8 0.0274598 0.0137299 0.999906i $$-0.495630\pi$$
0.0137299 + 0.999906i $$0.495630\pi$$
$$648$$ −3.91133e8 −0.0564693
$$649$$ 2.59539e9 0.372688
$$650$$ −1.31044e8 −0.0187163
$$651$$ −2.34764e9 −0.333501
$$652$$ −5.11403e9 −0.722598
$$653$$ 8.70977e9 1.22408 0.612041 0.790826i $$-0.290349\pi$$
0.612041 + 0.790826i $$0.290349\pi$$
$$654$$ −6.64159e8 −0.0928432
$$655$$ −5.66662e8 −0.0787916
$$656$$ −4.75963e9 −0.658279
$$657$$ −3.42067e9 −0.470579
$$658$$ −2.40033e8 −0.0328458
$$659$$ −7.48288e8 −0.101852 −0.0509260 0.998702i $$-0.516217\pi$$
−0.0509260 + 0.998702i $$0.516217\pi$$
$$660$$ 5.60057e8 0.0758277
$$661$$ 8.45586e9 1.13881 0.569407 0.822056i $$-0.307173\pi$$
0.569407 + 0.822056i $$0.307173\pi$$
$$662$$ 2.03074e8 0.0272052
$$663$$ 2.41330e9 0.321598
$$664$$ −2.11152e9 −0.279903
$$665$$ 1.65358e9 0.218047
$$666$$ −3.36310e8 −0.0441144
$$667$$ −6.02996e9 −0.786817
$$668$$ −1.22784e10 −1.59376
$$669$$ −3.10154e9 −0.400485
$$670$$ −7.60829e8 −0.0977294
$$671$$ 1.40661e9 0.179740
$$672$$ −5.60357e8 −0.0712316
$$673$$ 4.78543e9 0.605157 0.302578 0.953124i $$-0.402153\pi$$
0.302578 + 0.953124i $$0.402153\pi$$
$$674$$ 1.68628e8 0.0212139
$$675$$ −1.45658e9 −0.182293
$$676$$ 3.16520e9 0.394083
$$677$$ −1.29662e10 −1.60603 −0.803015 0.595958i $$-0.796772\pi$$
−0.803015 + 0.595958i $$0.796772\pi$$
$$678$$ 4.62018e8 0.0569318
$$679$$ −2.27918e9 −0.279405
$$680$$ 6.88526e8 0.0839729
$$681$$ 4.76419e8 0.0578061
$$682$$ −5.40302e8 −0.0652216
$$683$$ −9.15988e9 −1.10006 −0.550031 0.835144i $$-0.685384\pi$$
−0.550031 + 0.835144i $$0.685384\pi$$
$$684$$ −7.64706e9 −0.913689
$$685$$ −6.34572e9 −0.754334
$$686$$ −5.51533e7 −0.00652285
$$687$$ −2.62007e9 −0.308293
$$688$$ 9.97905e9 1.16823
$$689$$ 1.23492e9 0.143838
$$690$$ −2.71105e8 −0.0314170
$$691$$ 1.05298e10 1.21407 0.607037 0.794673i $$-0.292358\pi$$
0.607037 + 0.794673i $$0.292358\pi$$
$$692$$ 6.44038e9 0.738823
$$693$$ −7.72318e8 −0.0881515
$$694$$ 1.79944e9 0.204352
$$695$$ 1.31478e9 0.148562
$$696$$ −8.11729e8 −0.0912596
$$697$$ 4.81683e9 0.538824
$$698$$ 3.61534e8 0.0402398
$$699$$ −5.74470e9 −0.636205
$$700$$ 6.75989e8 0.0744897
$$701$$ 1.27411e9 0.139699 0.0698497 0.997558i $$-0.477748\pi$$
0.0698497 + 0.997558i $$0.477748\pi$$
$$702$$ 7.81825e8 0.0852962
$$703$$ −6.03703e9 −0.655360
$$704$$ 2.74405e9 0.296406
$$705$$ 1.58723e9 0.170600
$$706$$ 1.78048e9 0.190423
$$707$$ −3.68832e9 −0.392519
$$708$$ 5.66782e9 0.600205
$$709$$ −7.17795e9 −0.756378 −0.378189 0.925728i $$-0.623453\pi$$
−0.378189 + 0.925728i $$0.623453\pi$$
$$710$$ 1.23936e8 0.0129955
$$711$$ 8.19829e9 0.855421
$$712$$ 3.68653e9 0.382769
$$713$$ −1.76599e10 −1.82463
$$714$$ 1.84369e8 0.0189559
$$715$$ 1.09868e9 0.112409
$$716$$ −1.83914e10 −1.87249
$$717$$ 2.70746e9 0.274312
$$718$$ −1.41133e9 −0.142296
$$719$$ 1.18502e10 1.18898 0.594488 0.804104i $$-0.297355\pi$$
0.594488 + 0.804104i $$0.297355\pi$$
$$720$$ −3.07916e9 −0.307446
$$721$$ 3.63188e9 0.360876
$$722$$ 8.11273e8 0.0802208
$$723$$ −2.04665e9 −0.201400
$$724$$ 7.68971e9 0.753052
$$725$$ 1.47245e9 0.143502
$$726$$ −5.90971e8 −0.0573176
$$727$$ −4.67874e9 −0.451605 −0.225802 0.974173i $$-0.572500\pi$$
−0.225802 + 0.974173i $$0.572500\pi$$
$$728$$ −7.31054e8 −0.0702246
$$729$$ 3.28577e9 0.314116
$$730$$ 3.71759e8 0.0353697
$$731$$ −1.00990e10 −0.956238
$$732$$ 3.07177e9 0.289468
$$733$$ 1.28552e9 0.120563 0.0602817 0.998181i $$-0.480800\pi$$
0.0602817 + 0.998181i $$0.480800\pi$$
$$734$$ 1.54612e9 0.144314
$$735$$ 3.64705e8 0.0338794
$$736$$ −4.21524e9 −0.389718
$$737$$ 6.37884e9 0.586956
$$738$$ 6.52585e8 0.0597641
$$739$$ −5.26720e9 −0.480091 −0.240046 0.970762i $$-0.577162\pi$$
−0.240046 + 0.970762i $$0.577162\pi$$
$$740$$ −2.46796e9 −0.223886
$$741$$ 5.86909e9 0.529916
$$742$$ 9.43446e7 0.00847819
$$743$$ 4.15012e9 0.371193 0.185596 0.982626i $$-0.440578\pi$$
0.185596 + 0.982626i $$0.440578\pi$$
$$744$$ −2.37731e9 −0.211631
$$745$$ 6.79371e9 0.601950
$$746$$ 7.35489e8 0.0648620
$$747$$ −9.55643e9 −0.838829
$$748$$ −2.86511e9 −0.250314
$$749$$ 2.87171e9 0.249721
$$750$$ 6.62006e7 0.00572991
$$751$$ −6.37970e9 −0.549618 −0.274809 0.961499i $$-0.588615\pi$$
−0.274809 + 0.961499i $$0.588615\pi$$
$$752$$ 8.02346e9 0.688017
$$753$$ −5.97635e8 −0.0510098
$$754$$ −7.90343e8 −0.0671453
$$755$$ −2.79072e9 −0.235995
$$756$$ −4.03304e9 −0.339474
$$757$$ −1.19658e10 −1.00255 −0.501274 0.865289i $$-0.667135\pi$$
−0.501274 + 0.865289i $$0.667135\pi$$
$$758$$ 1.07032e9 0.0892631
$$759$$ 2.27296e9 0.188688
$$760$$ 1.67448e9 0.138367
$$761$$ −2.00959e10 −1.65296 −0.826479 0.562967i $$-0.809660\pi$$
−0.826479 + 0.562967i $$0.809660\pi$$
$$762$$ 7.58437e8 0.0620979
$$763$$ 6.72100e9 0.547770
$$764$$ 1.92450e10 1.56131
$$765$$ 3.11616e9 0.251655
$$766$$ 1.12411e9 0.0903665
$$767$$ 1.11187e10 0.889756
$$768$$ 5.70667e9 0.454588
$$769$$ 2.46683e10 1.95613 0.978064 0.208304i $$-0.0667944\pi$$
0.978064 + 0.208304i $$0.0667944\pi$$
$$770$$ 8.39358e7 0.00662567
$$771$$ 2.41807e9 0.190011
$$772$$ 1.75673e10 1.37418
$$773$$ 8.88824e9 0.692130 0.346065 0.938211i $$-0.387518\pi$$
0.346065 + 0.938211i $$0.387518\pi$$
$$774$$ −1.36821e9 −0.106062
$$775$$ 4.31235e9 0.332781
$$776$$ −2.30798e9 −0.177303
$$777$$ −1.33149e9 −0.101828
$$778$$ −1.46252e9 −0.111345
$$779$$ 1.17144e10 0.887850
$$780$$ 2.39930e9 0.181031
$$781$$ −1.03909e9 −0.0780502
$$782$$ 1.38690e9 0.103710
$$783$$ −8.78483e9 −0.653984
$$784$$ 1.84358e9 0.136633
$$785$$ −5.47235e9 −0.403766
$$786$$ −1.53655e8 −0.0112867
$$787$$ −4.65006e9 −0.340053 −0.170027 0.985439i $$-0.554385\pi$$
−0.170027 + 0.985439i $$0.554385\pi$$
$$788$$ −8.22986e9 −0.599171
$$789$$ 7.40606e9 0.536806
$$790$$ −8.90993e8 −0.0642953
$$791$$ −4.67542e9 −0.335895
$$792$$ −7.82079e8 −0.0559387
$$793$$ 6.02598e9 0.429113
$$794$$ −1.31830e9 −0.0934638
$$795$$ −6.23859e8 −0.0440354
$$796$$ −2.44070e8 −0.0171521
$$797$$ 1.42890e10 0.999762 0.499881 0.866094i $$-0.333377\pi$$
0.499881 + 0.866094i $$0.333377\pi$$
$$798$$ 4.48381e8 0.0312347
$$799$$ −8.11987e9 −0.563165
$$800$$ 1.02931e9 0.0710776
$$801$$ 1.66846e10 1.14711
$$802$$ −2.66257e9 −0.182260
$$803$$ −3.11685e9 −0.212428
$$804$$ 1.39302e10 0.945279
$$805$$ 2.74346e9 0.185359
$$806$$ −2.31467e9 −0.155710
$$807$$ −9.68971e9 −0.649013
$$808$$ −3.73494e9 −0.249083
$$809$$ −4.92320e9 −0.326909 −0.163455 0.986551i $$-0.552264\pi$$
−0.163455 + 0.986551i $$0.552264\pi$$
$$810$$ 1.92387e8 0.0127197
$$811$$ 2.35801e10 1.55229 0.776145 0.630555i $$-0.217173\pi$$
0.776145 + 0.630555i $$0.217173\pi$$
$$812$$ 4.07698e9 0.267235
$$813$$ 5.25992e9 0.343291
$$814$$ −3.06440e8 −0.0199141
$$815$$ 5.06813e9 0.327942
$$816$$ −6.16280e9 −0.397066
$$817$$ −2.45605e10 −1.57565
$$818$$ 1.18069e9 0.0754221
$$819$$ −3.30864e9 −0.210453
$$820$$ 4.78889e9 0.303310
$$821$$ −2.86630e10 −1.80768 −0.903838 0.427875i $$-0.859262\pi$$
−0.903838 + 0.427875i $$0.859262\pi$$
$$822$$ −1.72069e9 −0.108057
$$823$$ −2.76897e10 −1.73148 −0.865742 0.500490i $$-0.833153\pi$$
−0.865742 + 0.500490i $$0.833153\pi$$
$$824$$ 3.67778e9 0.229003
$$825$$ −5.55030e8 −0.0344134
$$826$$ 8.49437e8 0.0524447
$$827$$ −1.27176e10 −0.781873 −0.390936 0.920418i $$-0.627849\pi$$
−0.390936 + 0.920418i $$0.627849\pi$$
$$828$$ −1.26873e10 −0.776716
$$829$$ −1.50770e10 −0.919127 −0.459563 0.888145i $$-0.651994\pi$$
−0.459563 + 0.888145i $$0.651994\pi$$
$$830$$ 1.03860e9 0.0630483
$$831$$ 4.63064e9 0.279923
$$832$$ 1.17556e10 0.707641
$$833$$ −1.86573e9 −0.111839
$$834$$ 3.56514e8 0.0212812
$$835$$ 1.21682e10 0.723307
$$836$$ −6.96787e9 −0.412457
$$837$$ −2.57281e10 −1.51659
$$838$$ 3.02512e9 0.177578
$$839$$ 4.59511e9 0.268614 0.134307 0.990940i $$-0.457119\pi$$
0.134307 + 0.990940i $$0.457119\pi$$
$$840$$ 3.69314e8 0.0214990
$$841$$ −8.36934e9 −0.485182
$$842$$ −3.96175e9 −0.228715
$$843$$ −1.83216e10 −1.05334
$$844$$ 6.53172e9 0.373963
$$845$$ −3.13679e9 −0.178849
$$846$$ −1.10008e9 −0.0624639
$$847$$ 5.98038e9 0.338171
$$848$$ −3.15361e9 −0.177591
$$849$$ −7.73504e9 −0.433796
$$850$$ −3.38665e8 −0.0189149
$$851$$ −1.00161e10 −0.557114
$$852$$ −2.26917e9 −0.125698
$$853$$ −1.13971e9 −0.0628740 −0.0314370 0.999506i $$-0.510008\pi$$
−0.0314370 + 0.999506i $$0.510008\pi$$
$$854$$ 4.60367e8 0.0252931
$$855$$ 7.57844e9 0.414666
$$856$$ 2.90801e9 0.158466
$$857$$ 7.79419e9 0.422998 0.211499 0.977378i $$-0.432166\pi$$
0.211499 + 0.977378i $$0.432166\pi$$
$$858$$ 2.97915e8 0.0161023
$$859$$ 1.27280e10 0.685147 0.342573 0.939491i $$-0.388701\pi$$
0.342573 + 0.939491i $$0.388701\pi$$
$$860$$ −1.00404e10 −0.538277
$$861$$ 2.58367e9 0.137951
$$862$$ −3.30831e9 −0.175926
$$863$$ 2.53204e9 0.134101 0.0670507 0.997750i $$-0.478641\pi$$
0.0670507 + 0.997750i $$0.478641\pi$$
$$864$$ −6.14103e9 −0.323924
$$865$$ −6.38258e9 −0.335305
$$866$$ −3.09823e9 −0.162107
$$867$$ −3.93933e9 −0.205284
$$868$$ 1.19402e10 0.619718
$$869$$ 7.47014e9 0.386153
$$870$$ 3.99265e8 0.0205563
$$871$$ 2.73272e10 1.40130
$$872$$ 6.80595e9 0.347601
$$873$$ −1.04456e10 −0.531352
$$874$$ 3.37291e9 0.170889
$$875$$ −6.69922e8 −0.0338062
$$876$$ −6.80661e9 −0.342110
$$877$$ 5.00988e9 0.250800 0.125400 0.992106i $$-0.459979\pi$$
0.125400 + 0.992106i $$0.459979\pi$$
$$878$$ 2.71862e9 0.135556
$$879$$ −1.25353e10 −0.622550
$$880$$ −2.80568e9 −0.138787
$$881$$ 9.46900e9 0.466539 0.233270 0.972412i $$-0.425058\pi$$
0.233270 + 0.972412i $$0.425058\pi$$
$$882$$ −2.52770e8 −0.0124047
$$883$$ 1.11146e10 0.543289 0.271644 0.962398i $$-0.412433\pi$$
0.271644 + 0.962398i $$0.412433\pi$$
$$884$$ −1.22742e10 −0.597600
$$885$$ −5.61696e9 −0.272395
$$886$$ −1.20006e9 −0.0579675
$$887$$ −7.27986e9 −0.350260 −0.175130 0.984545i $$-0.556035\pi$$
−0.175130 + 0.984545i $$0.556035\pi$$
$$888$$ −1.34832e9 −0.0646173
$$889$$ −7.67506e9 −0.366375
$$890$$ −1.81329e9 −0.0862190
$$891$$ −1.61298e9 −0.0763938
$$892$$ 1.57746e10 0.744188
$$893$$ −1.97473e10 −0.927959
$$894$$ 1.84217e9 0.0862280
$$895$$ 1.82264e10 0.849807
$$896$$ 3.79032e9 0.176034
$$897$$ 9.73743e9 0.450475
$$898$$ 2.09267e8 0.00964348
$$899$$ 2.60084e10 1.19386
$$900$$ 3.09809e9 0.141659
$$901$$ 3.19150e9 0.145365
$$902$$ 5.94624e8 0.0269786
$$903$$ −5.41692e9 −0.244819
$$904$$ −4.73451e9 −0.213150
$$905$$ −7.62070e9 −0.341763
$$906$$ −7.56726e8 −0.0338057
$$907$$ −1.39503e10 −0.620809 −0.310405 0.950605i $$-0.600465\pi$$
−0.310405 + 0.950605i $$0.600465\pi$$
$$908$$ −2.42310e9 −0.107416
$$909$$ −1.69038e10 −0.746465
$$910$$ 3.59584e8 0.0158181
$$911$$ 2.98148e8 0.0130653 0.00653263 0.999979i $$-0.497921\pi$$
0.00653263 + 0.999979i $$0.497921\pi$$
$$912$$ −1.49878e10 −0.654268
$$913$$ −8.70765e9 −0.378663
$$914$$ −3.27506e9 −0.141876
$$915$$ −3.04420e9 −0.131371
$$916$$ 1.33259e10 0.572876
$$917$$ 1.55492e9 0.0665910
$$918$$ 2.02053e9 0.0862015
$$919$$ 2.67202e10 1.13563 0.567814 0.823157i $$-0.307789\pi$$
0.567814 + 0.823157i $$0.307789\pi$$
$$920$$ 2.77813e9 0.117624
$$921$$ 1.15928e10 0.488969
$$922$$ 2.21295e9 0.0929850
$$923$$ −4.45149e9 −0.186337
$$924$$ −1.53680e9 −0.0640861
$$925$$ 2.44581e9 0.101608
$$926$$ 1.58725e9 0.0656910
$$927$$ 1.66451e10 0.686288
$$928$$ 6.20794e9 0.254994
$$929$$ −3.66336e10 −1.49908 −0.749540 0.661959i $$-0.769725\pi$$
−0.749540 + 0.661959i $$0.769725\pi$$
$$930$$ 1.16933e9 0.0476701
$$931$$ −4.53742e9 −0.184283
$$932$$ 2.92180e10 1.18221
$$933$$ 2.87728e8 0.0115983
$$934$$ 3.88115e9 0.155864
$$935$$ 2.83939e9 0.113602
$$936$$ −3.35045e9 −0.133548
$$937$$ 1.28088e10 0.508649 0.254325 0.967119i $$-0.418147\pi$$
0.254325 + 0.967119i $$0.418147\pi$$
$$938$$ 2.08772e9 0.0825965
$$939$$ 2.04149e10 0.804669
$$940$$ −8.07278e9 −0.317012
$$941$$ −1.20663e10 −0.472073 −0.236037 0.971744i $$-0.575849\pi$$
−0.236037 + 0.971744i $$0.575849\pi$$
$$942$$ −1.48387e9 −0.0578386
$$943$$ 1.94354e10 0.754751
$$944$$ −2.83937e10 −1.09855
$$945$$ 3.99685e9 0.154066
$$946$$ −1.24669e9 −0.0478784
$$947$$ 8.36023e9 0.319885 0.159942 0.987126i $$-0.448869\pi$$
0.159942 + 0.987126i $$0.448869\pi$$
$$948$$ 1.63133e10 0.621890
$$949$$ −1.33527e10 −0.507151
$$950$$ −8.23627e8 −0.0311672
$$951$$ 9.65082e9 0.363859
$$952$$ −1.88931e9 −0.0709700
$$953$$ 4.49530e10 1.68242 0.841209 0.540710i $$-0.181844\pi$$
0.841209 + 0.540710i $$0.181844\pi$$
$$954$$ 4.32386e8 0.0161232
$$955$$ −1.90722e10 −0.708582
$$956$$ −1.37703e10 −0.509732
$$957$$ −3.34747e9 −0.123459
$$958$$ 3.26341e9 0.119920
$$959$$ 1.74126e10 0.637528
$$960$$ −5.93869e9 −0.216641
$$961$$ 4.86580e10 1.76857
$$962$$ −1.31280e9 −0.0475429
$$963$$ 1.31612e10 0.474901
$$964$$ 1.04094e10 0.374244
$$965$$ −1.74096e10 −0.623654
$$966$$ 7.43911e8 0.0265522
$$967$$ 1.34247e8 0.00477432 0.00238716 0.999997i $$-0.499240\pi$$
0.00238716 + 0.999997i $$0.499240\pi$$
$$968$$ 6.05596e9 0.214595
$$969$$ 1.51679e10 0.535541
$$970$$ 1.13523e9 0.0399376
$$971$$ −3.00377e10 −1.05293 −0.526465 0.850197i $$-0.676483\pi$$
−0.526465 + 0.850197i $$0.676483\pi$$
$$972$$ −2.92375e10 −1.02119
$$973$$ −3.60777e9 −0.125558
$$974$$ −3.01379e9 −0.104510
$$975$$ −2.37777e9 −0.0821587
$$976$$ −1.53884e10 −0.529810
$$977$$ 4.52860e10 1.55358 0.776789 0.629761i $$-0.216847\pi$$
0.776789 + 0.629761i $$0.216847\pi$$
$$978$$ 1.37426e9 0.0469769
$$979$$ 1.52028e10 0.517825
$$980$$ −1.85491e9 −0.0629553
$$981$$ 3.08027e10 1.04171
$$982$$ 5.85057e8 0.0197155
$$983$$ 4.61443e10 1.54946 0.774731 0.632290i $$-0.217885\pi$$
0.774731 + 0.632290i $$0.217885\pi$$
$$984$$ 2.61632e9 0.0875404
$$985$$ 8.15600e9 0.271926
$$986$$ −2.04254e9 −0.0678580
$$987$$ −4.35537e9 −0.144183
$$988$$ −2.98506e10 −0.984700
$$989$$ −4.07484e10 −1.33944
$$990$$ 3.84682e8 0.0126002
$$991$$ −1.05400e10 −0.344018 −0.172009 0.985095i $$-0.555026\pi$$
−0.172009 + 0.985095i $$0.555026\pi$$
$$992$$ 1.81812e10 0.591331
$$993$$ 3.68475e9 0.119422
$$994$$ −3.40081e8 −0.0109832
$$995$$ 2.41879e8 0.00778427
$$996$$ −1.90158e10 −0.609828
$$997$$ −5.00734e10 −1.60020 −0.800099 0.599868i $$-0.795220\pi$$
−0.800099 + 0.599868i $$0.795220\pi$$
$$998$$ −4.03435e9 −0.128474
$$999$$ −1.45920e10 −0.463059
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 35.8.a.a.1.1 2
3.2 odd 2 315.8.a.c.1.2 2
4.3 odd 2 560.8.a.i.1.1 2
5.2 odd 4 175.8.b.c.99.3 4
5.3 odd 4 175.8.b.c.99.2 4
5.4 even 2 175.8.a.b.1.2 2
7.6 odd 2 245.8.a.b.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
35.8.a.a.1.1 2 1.1 even 1 trivial
175.8.a.b.1.2 2 5.4 even 2
175.8.b.c.99.2 4 5.3 odd 4
175.8.b.c.99.3 4 5.2 odd 4
245.8.a.b.1.1 2 7.6 odd 2
315.8.a.c.1.2 2 3.2 odd 2
560.8.a.i.1.1 2 4.3 odd 2