# Properties

 Label 165.6.a.d.1.3 Level $165$ Weight $6$ Character 165.1 Self dual yes Analytic conductor $26.463$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.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: $$26.4633302691$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.788.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - x^{2} - 7x - 3$$ x^3 - x^2 - 7*x - 3 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$-1.87740$$ of defining polynomial Character $$\chi$$ $$=$$ 165.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+6.55890 q^{2} -9.00000 q^{3} +11.0192 q^{4} +25.0000 q^{5} -59.0301 q^{6} +146.487 q^{7} -137.611 q^{8} +81.0000 q^{9} +O(q^{10})$$ $$q+6.55890 q^{2} -9.00000 q^{3} +11.0192 q^{4} +25.0000 q^{5} -59.0301 q^{6} +146.487 q^{7} -137.611 q^{8} +81.0000 q^{9} +163.973 q^{10} -121.000 q^{11} -99.1731 q^{12} +170.238 q^{13} +960.792 q^{14} -225.000 q^{15} -1255.19 q^{16} +1564.81 q^{17} +531.271 q^{18} +569.786 q^{19} +275.481 q^{20} -1318.38 q^{21} -793.627 q^{22} +3153.25 q^{23} +1238.50 q^{24} +625.000 q^{25} +1116.57 q^{26} -729.000 q^{27} +1614.17 q^{28} +3982.58 q^{29} -1475.75 q^{30} +2990.78 q^{31} -3829.14 q^{32} +1089.00 q^{33} +10263.5 q^{34} +3662.17 q^{35} +892.558 q^{36} +7858.92 q^{37} +3737.17 q^{38} -1532.14 q^{39} -3440.27 q^{40} -5206.60 q^{41} -8647.13 q^{42} +13874.3 q^{43} -1333.33 q^{44} +2025.00 q^{45} +20681.9 q^{46} +6852.01 q^{47} +11296.7 q^{48} +4651.35 q^{49} +4099.32 q^{50} -14083.3 q^{51} +1875.89 q^{52} -3834.15 q^{53} -4781.44 q^{54} -3025.00 q^{55} -20158.2 q^{56} -5128.08 q^{57} +26121.4 q^{58} +9649.38 q^{59} -2479.33 q^{60} -21131.8 q^{61} +19616.2 q^{62} +11865.4 q^{63} +15051.2 q^{64} +4255.95 q^{65} +7142.65 q^{66} -43499.9 q^{67} +17243.0 q^{68} -28379.2 q^{69} +24019.8 q^{70} -52607.2 q^{71} -11146.5 q^{72} -64367.9 q^{73} +51545.9 q^{74} -5625.00 q^{75} +6278.61 q^{76} -17724.9 q^{77} -10049.2 q^{78} +28935.7 q^{79} -31379.8 q^{80} +6561.00 q^{81} -34149.6 q^{82} -4648.64 q^{83} -14527.5 q^{84} +39120.3 q^{85} +91000.1 q^{86} -35843.2 q^{87} +16650.9 q^{88} -103458. q^{89} +13281.8 q^{90} +24937.6 q^{91} +34746.4 q^{92} -26917.0 q^{93} +44941.6 q^{94} +14244.7 q^{95} +34462.2 q^{96} +75809.5 q^{97} +30507.8 q^{98} -9801.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10})$$ 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9 $$3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} - 363 q^{11} + 180 q^{12} - 546 q^{13} - 8 q^{14} - 675 q^{15} - 1360 q^{16} - 314 q^{17} + 162 q^{18} + 1808 q^{19} - 500 q^{20} - 1368 q^{21} - 242 q^{22} + 4288 q^{23} + 216 q^{24} + 1875 q^{25} + 812 q^{26} - 2187 q^{27} + 5888 q^{28} + 5582 q^{29} - 450 q^{30} + 6328 q^{31} - 736 q^{32} + 3267 q^{33} + 11596 q^{34} + 3800 q^{35} - 1620 q^{36} + 16866 q^{37} + 9584 q^{38} + 4914 q^{39} - 600 q^{40} + 23282 q^{41} + 72 q^{42} + 20572 q^{43} + 2420 q^{44} + 6075 q^{45} + 16592 q^{46} + 3432 q^{47} + 12240 q^{48} + 11531 q^{49} + 1250 q^{50} + 2826 q^{51} + 21816 q^{52} + 16138 q^{53} - 1458 q^{54} - 9075 q^{55} + 15648 q^{56} - 16272 q^{57} + 17460 q^{58} + 21972 q^{59} + 4500 q^{60} + 8322 q^{61} + 5056 q^{62} + 12312 q^{63} + 22208 q^{64} - 13650 q^{65} + 2178 q^{66} - 84332 q^{67} + 59832 q^{68} - 38592 q^{69} - 200 q^{70} + 50528 q^{71} - 1944 q^{72} - 53838 q^{73} + 79212 q^{74} - 16875 q^{75} - 52448 q^{76} - 18392 q^{77} - 7308 q^{78} + 6364 q^{79} - 34000 q^{80} + 19683 q^{81} - 68020 q^{82} + 96272 q^{83} - 52992 q^{84} - 7850 q^{85} + 143152 q^{86} - 50238 q^{87} + 2904 q^{88} - 38938 q^{89} + 4050 q^{90} + 104968 q^{91} + 24000 q^{92} - 56952 q^{93} + 49088 q^{94} + 45200 q^{95} + 6624 q^{96} - 103242 q^{97} + 9554 q^{98} - 29403 q^{99}+O(q^{100})$$ 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 - 363 * q^11 + 180 * q^12 - 546 * q^13 - 8 * q^14 - 675 * q^15 - 1360 * q^16 - 314 * q^17 + 162 * q^18 + 1808 * q^19 - 500 * q^20 - 1368 * q^21 - 242 * q^22 + 4288 * q^23 + 216 * q^24 + 1875 * q^25 + 812 * q^26 - 2187 * q^27 + 5888 * q^28 + 5582 * q^29 - 450 * q^30 + 6328 * q^31 - 736 * q^32 + 3267 * q^33 + 11596 * q^34 + 3800 * q^35 - 1620 * q^36 + 16866 * q^37 + 9584 * q^38 + 4914 * q^39 - 600 * q^40 + 23282 * q^41 + 72 * q^42 + 20572 * q^43 + 2420 * q^44 + 6075 * q^45 + 16592 * q^46 + 3432 * q^47 + 12240 * q^48 + 11531 * q^49 + 1250 * q^50 + 2826 * q^51 + 21816 * q^52 + 16138 * q^53 - 1458 * q^54 - 9075 * q^55 + 15648 * q^56 - 16272 * q^57 + 17460 * q^58 + 21972 * q^59 + 4500 * q^60 + 8322 * q^61 + 5056 * q^62 + 12312 * q^63 + 22208 * q^64 - 13650 * q^65 + 2178 * q^66 - 84332 * q^67 + 59832 * q^68 - 38592 * q^69 - 200 * q^70 + 50528 * q^71 - 1944 * q^72 - 53838 * q^73 + 79212 * q^74 - 16875 * q^75 - 52448 * q^76 - 18392 * q^77 - 7308 * q^78 + 6364 * q^79 - 34000 * q^80 + 19683 * q^81 - 68020 * q^82 + 96272 * q^83 - 52992 * q^84 - 7850 * q^85 + 143152 * q^86 - 50238 * q^87 + 2904 * q^88 - 38938 * q^89 + 4050 * q^90 + 104968 * q^91 + 24000 * q^92 - 56952 * q^93 + 49088 * q^94 + 45200 * q^95 + 6624 * q^96 - 103242 * q^97 + 9554 * q^98 - 29403 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 6.55890 1.15946 0.579731 0.814808i $$-0.303158\pi$$
0.579731 + 0.814808i $$0.303158\pi$$
$$3$$ −9.00000 −0.577350
$$4$$ 11.0192 0.344351
$$5$$ 25.0000 0.447214
$$6$$ −59.0301 −0.669415
$$7$$ 146.487 1.12993 0.564967 0.825113i $$-0.308889\pi$$
0.564967 + 0.825113i $$0.308889\pi$$
$$8$$ −137.611 −0.760200
$$9$$ 81.0000 0.333333
$$10$$ 163.973 0.518527
$$11$$ −121.000 −0.301511
$$12$$ −99.1731 −0.198811
$$13$$ 170.238 0.279382 0.139691 0.990195i $$-0.455389\pi$$
0.139691 + 0.990195i $$0.455389\pi$$
$$14$$ 960.792 1.31012
$$15$$ −225.000 −0.258199
$$16$$ −1255.19 −1.22577
$$17$$ 1564.81 1.31323 0.656614 0.754227i $$-0.271988\pi$$
0.656614 + 0.754227i $$0.271988\pi$$
$$18$$ 531.271 0.386487
$$19$$ 569.786 0.362100 0.181050 0.983474i $$-0.442050\pi$$
0.181050 + 0.983474i $$0.442050\pi$$
$$20$$ 275.481 0.153998
$$21$$ −1318.38 −0.652368
$$22$$ −793.627 −0.349591
$$23$$ 3153.25 1.24291 0.621454 0.783451i $$-0.286542\pi$$
0.621454 + 0.783451i $$0.286542\pi$$
$$24$$ 1238.50 0.438902
$$25$$ 625.000 0.200000
$$26$$ 1116.57 0.323932
$$27$$ −729.000 −0.192450
$$28$$ 1614.17 0.389094
$$29$$ 3982.58 0.879366 0.439683 0.898153i $$-0.355091\pi$$
0.439683 + 0.898153i $$0.355091\pi$$
$$30$$ −1475.75 −0.299372
$$31$$ 2990.78 0.558959 0.279480 0.960152i $$-0.409838\pi$$
0.279480 + 0.960152i $$0.409838\pi$$
$$32$$ −3829.14 −0.661037
$$33$$ 1089.00 0.174078
$$34$$ 10263.5 1.52264
$$35$$ 3662.17 0.505322
$$36$$ 892.558 0.114784
$$37$$ 7858.92 0.943753 0.471877 0.881665i $$-0.343577\pi$$
0.471877 + 0.881665i $$0.343577\pi$$
$$38$$ 3737.17 0.419841
$$39$$ −1532.14 −0.161301
$$40$$ −3440.27 −0.339972
$$41$$ −5206.60 −0.483721 −0.241860 0.970311i $$-0.577758\pi$$
−0.241860 + 0.970311i $$0.577758\pi$$
$$42$$ −8647.13 −0.756395
$$43$$ 13874.3 1.14430 0.572149 0.820149i $$-0.306110\pi$$
0.572149 + 0.820149i $$0.306110\pi$$
$$44$$ −1333.33 −0.103826
$$45$$ 2025.00 0.149071
$$46$$ 20681.9 1.44110
$$47$$ 6852.01 0.452453 0.226226 0.974075i $$-0.427361\pi$$
0.226226 + 0.974075i $$0.427361\pi$$
$$48$$ 11296.7 0.707701
$$49$$ 4651.35 0.276751
$$50$$ 4099.32 0.231892
$$51$$ −14083.3 −0.758192
$$52$$ 1875.89 0.0962054
$$53$$ −3834.15 −0.187490 −0.0937452 0.995596i $$-0.529884\pi$$
−0.0937452 + 0.995596i $$0.529884\pi$$
$$54$$ −4781.44 −0.223138
$$55$$ −3025.00 −0.134840
$$56$$ −20158.2 −0.858976
$$57$$ −5128.08 −0.209058
$$58$$ 26121.4 1.01959
$$59$$ 9649.38 0.360885 0.180443 0.983586i $$-0.442247\pi$$
0.180443 + 0.983586i $$0.442247\pi$$
$$60$$ −2479.33 −0.0889110
$$61$$ −21131.8 −0.727128 −0.363564 0.931569i $$-0.618440\pi$$
−0.363564 + 0.931569i $$0.618440\pi$$
$$62$$ 19616.2 0.648092
$$63$$ 11865.4 0.376645
$$64$$ 15051.2 0.459326
$$65$$ 4255.95 0.124943
$$66$$ 7142.65 0.201836
$$67$$ −43499.9 −1.18386 −0.591931 0.805989i $$-0.701634\pi$$
−0.591931 + 0.805989i $$0.701634\pi$$
$$68$$ 17243.0 0.452211
$$69$$ −28379.2 −0.717593
$$70$$ 24019.8 0.585901
$$71$$ −52607.2 −1.23851 −0.619255 0.785190i $$-0.712565\pi$$
−0.619255 + 0.785190i $$0.712565\pi$$
$$72$$ −11146.5 −0.253400
$$73$$ −64367.9 −1.41372 −0.706858 0.707355i $$-0.749888\pi$$
−0.706858 + 0.707355i $$0.749888\pi$$
$$74$$ 51545.9 1.09425
$$75$$ −5625.00 −0.115470
$$76$$ 6278.61 0.124689
$$77$$ −17724.9 −0.340688
$$78$$ −10049.2 −0.187022
$$79$$ 28935.7 0.521635 0.260817 0.965388i $$-0.416008\pi$$
0.260817 + 0.965388i $$0.416008\pi$$
$$80$$ −31379.8 −0.548183
$$81$$ 6561.00 0.111111
$$82$$ −34149.6 −0.560855
$$83$$ −4648.64 −0.0740681 −0.0370340 0.999314i $$-0.511791\pi$$
−0.0370340 + 0.999314i $$0.511791\pi$$
$$84$$ −14527.5 −0.224643
$$85$$ 39120.3 0.587293
$$86$$ 91000.1 1.32677
$$87$$ −35843.2 −0.507702
$$88$$ 16650.9 0.229209
$$89$$ −103458. −1.38448 −0.692242 0.721666i $$-0.743377\pi$$
−0.692242 + 0.721666i $$0.743377\pi$$
$$90$$ 13281.8 0.172842
$$91$$ 24937.6 0.315683
$$92$$ 34746.4 0.427996
$$93$$ −26917.0 −0.322715
$$94$$ 44941.6 0.524601
$$95$$ 14244.7 0.161936
$$96$$ 34462.2 0.381650
$$97$$ 75809.5 0.818077 0.409039 0.912517i $$-0.365864\pi$$
0.409039 + 0.912517i $$0.365864\pi$$
$$98$$ 30507.8 0.320882
$$99$$ −9801.00 −0.100504
$$100$$ 6887.02 0.0688702
$$101$$ 35023.6 0.341631 0.170816 0.985303i $$-0.445360\pi$$
0.170816 + 0.985303i $$0.445360\pi$$
$$102$$ −92371.1 −0.879095
$$103$$ 16965.7 0.157572 0.0787859 0.996892i $$-0.474896\pi$$
0.0787859 + 0.996892i $$0.474896\pi$$
$$104$$ −23426.6 −0.212386
$$105$$ −32959.5 −0.291748
$$106$$ −25147.8 −0.217388
$$107$$ 12190.4 0.102934 0.0514671 0.998675i $$-0.483610\pi$$
0.0514671 + 0.998675i $$0.483610\pi$$
$$108$$ −8033.02 −0.0662704
$$109$$ 12138.7 0.0978606 0.0489303 0.998802i $$-0.484419\pi$$
0.0489303 + 0.998802i $$0.484419\pi$$
$$110$$ −19840.7 −0.156342
$$111$$ −70730.3 −0.544876
$$112$$ −183869. −1.38504
$$113$$ 204649. 1.50770 0.753848 0.657048i $$-0.228195\pi$$
0.753848 + 0.657048i $$0.228195\pi$$
$$114$$ −33634.6 −0.242395
$$115$$ 78831.2 0.555845
$$116$$ 43885.0 0.302810
$$117$$ 13789.3 0.0931273
$$118$$ 63289.3 0.418433
$$119$$ 229224. 1.48386
$$120$$ 30962.4 0.196283
$$121$$ 14641.0 0.0909091
$$122$$ −138601. −0.843077
$$123$$ 46859.4 0.279276
$$124$$ 32956.1 0.192478
$$125$$ 15625.0 0.0894427
$$126$$ 77824.2 0.436705
$$127$$ −112241. −0.617506 −0.308753 0.951142i $$-0.599912\pi$$
−0.308753 + 0.951142i $$0.599912\pi$$
$$128$$ 221252. 1.19361
$$129$$ −124869. −0.660661
$$130$$ 27914.4 0.144867
$$131$$ −11679.0 −0.0594602 −0.0297301 0.999558i $$-0.509465\pi$$
−0.0297301 + 0.999558i $$0.509465\pi$$
$$132$$ 11999.9 0.0599438
$$133$$ 83466.1 0.409149
$$134$$ −285311. −1.37264
$$135$$ −18225.0 −0.0860663
$$136$$ −215335. −0.998315
$$137$$ −384935. −1.75221 −0.876105 0.482121i $$-0.839867\pi$$
−0.876105 + 0.482121i $$0.839867\pi$$
$$138$$ −186137. −0.832021
$$139$$ −310605. −1.36355 −0.681775 0.731562i $$-0.738792\pi$$
−0.681775 + 0.731562i $$0.738792\pi$$
$$140$$ 40354.3 0.174008
$$141$$ −61668.0 −0.261224
$$142$$ −345046. −1.43600
$$143$$ −20598.8 −0.0842368
$$144$$ −101671. −0.408591
$$145$$ 99564.5 0.393264
$$146$$ −422183. −1.63915
$$147$$ −41862.2 −0.159782
$$148$$ 86599.2 0.324982
$$149$$ 285203. 1.05242 0.526209 0.850355i $$-0.323613\pi$$
0.526209 + 0.850355i $$0.323613\pi$$
$$150$$ −36893.8 −0.133883
$$151$$ −522357. −1.86434 −0.932170 0.362020i $$-0.882087\pi$$
−0.932170 + 0.362020i $$0.882087\pi$$
$$152$$ −78408.8 −0.275268
$$153$$ 126750. 0.437743
$$154$$ −116256. −0.395015
$$155$$ 74769.5 0.249974
$$156$$ −16883.0 −0.0555442
$$157$$ −2221.66 −0.00719330 −0.00359665 0.999994i $$-0.501145\pi$$
−0.00359665 + 0.999994i $$0.501145\pi$$
$$158$$ 189787. 0.604816
$$159$$ 34507.3 0.108248
$$160$$ −95728.4 −0.295625
$$161$$ 461909. 1.40440
$$162$$ 43033.0 0.128829
$$163$$ 250146. 0.737436 0.368718 0.929541i $$-0.379797\pi$$
0.368718 + 0.929541i $$0.379797\pi$$
$$164$$ −57372.7 −0.166570
$$165$$ 27225.0 0.0778499
$$166$$ −30490.0 −0.0858791
$$167$$ −42083.4 −0.116767 −0.0583834 0.998294i $$-0.518595\pi$$
−0.0583834 + 0.998294i $$0.518595\pi$$
$$168$$ 181423. 0.495930
$$169$$ −342312. −0.921946
$$170$$ 256586. 0.680944
$$171$$ 46152.7 0.120700
$$172$$ 152884. 0.394040
$$173$$ −117206. −0.297737 −0.148869 0.988857i $$-0.547563\pi$$
−0.148869 + 0.988857i $$0.547563\pi$$
$$174$$ −235092. −0.588661
$$175$$ 91554.2 0.225987
$$176$$ 151878. 0.369585
$$177$$ −86844.4 −0.208357
$$178$$ −678569. −1.60526
$$179$$ 582985. 1.35996 0.679978 0.733233i $$-0.261989\pi$$
0.679978 + 0.733233i $$0.261989\pi$$
$$180$$ 22313.9 0.0513328
$$181$$ 235291. 0.533837 0.266919 0.963719i $$-0.413994\pi$$
0.266919 + 0.963719i $$0.413994\pi$$
$$182$$ 163563. 0.366022
$$183$$ 190186. 0.419808
$$184$$ −433921. −0.944858
$$185$$ 196473. 0.422059
$$186$$ −176546. −0.374176
$$187$$ −189342. −0.395953
$$188$$ 75503.8 0.155802
$$189$$ −106789. −0.217456
$$190$$ 93429.4 0.187758
$$191$$ 591788. 1.17377 0.586885 0.809670i $$-0.300354\pi$$
0.586885 + 0.809670i $$0.300354\pi$$
$$192$$ −135461. −0.265192
$$193$$ −540825. −1.04511 −0.522557 0.852605i $$-0.675022\pi$$
−0.522557 + 0.852605i $$0.675022\pi$$
$$194$$ 497227. 0.948529
$$195$$ −38303.5 −0.0721361
$$196$$ 51254.3 0.0952994
$$197$$ 481711. 0.884344 0.442172 0.896930i $$-0.354208\pi$$
0.442172 + 0.896930i $$0.354208\pi$$
$$198$$ −64283.8 −0.116530
$$199$$ −1.01427e6 −1.81560 −0.907801 0.419401i $$-0.862240\pi$$
−0.907801 + 0.419401i $$0.862240\pi$$
$$200$$ −86006.8 −0.152040
$$201$$ 391499. 0.683503
$$202$$ 229717. 0.396108
$$203$$ 583395. 0.993625
$$204$$ −155187. −0.261084
$$205$$ −130165. −0.216326
$$206$$ 111276. 0.182699
$$207$$ 255413. 0.414302
$$208$$ −213681. −0.342459
$$209$$ −68944.2 −0.109177
$$210$$ −216178. −0.338270
$$211$$ 619718. 0.958270 0.479135 0.877741i $$-0.340950\pi$$
0.479135 + 0.877741i $$0.340950\pi$$
$$212$$ −42249.3 −0.0645625
$$213$$ 473465. 0.715054
$$214$$ 79955.8 0.119348
$$215$$ 346857. 0.511746
$$216$$ 100318. 0.146301
$$217$$ 438109. 0.631587
$$218$$ 79616.9 0.113466
$$219$$ 579311. 0.816210
$$220$$ −33333.2 −0.0464323
$$221$$ 266391. 0.366892
$$222$$ −463913. −0.631763
$$223$$ 894252. 1.20420 0.602099 0.798422i $$-0.294331\pi$$
0.602099 + 0.798422i $$0.294331\pi$$
$$224$$ −560918. −0.746928
$$225$$ 50625.0 0.0666667
$$226$$ 1.34227e6 1.74812
$$227$$ 851468. 1.09674 0.548370 0.836236i $$-0.315249\pi$$
0.548370 + 0.836236i $$0.315249\pi$$
$$228$$ −56507.5 −0.0719894
$$229$$ 137840. 0.173695 0.0868475 0.996222i $$-0.472321\pi$$
0.0868475 + 0.996222i $$0.472321\pi$$
$$230$$ 517047. 0.644481
$$231$$ 159524. 0.196696
$$232$$ −548046. −0.668494
$$233$$ −1.31590e6 −1.58793 −0.793965 0.607963i $$-0.791987\pi$$
−0.793965 + 0.607963i $$0.791987\pi$$
$$234$$ 90442.6 0.107977
$$235$$ 171300. 0.202343
$$236$$ 106329. 0.124271
$$237$$ −260422. −0.301166
$$238$$ 1.50346e6 1.72048
$$239$$ 1.11778e6 1.26579 0.632896 0.774237i $$-0.281866\pi$$
0.632896 + 0.774237i $$0.281866\pi$$
$$240$$ 282418. 0.316493
$$241$$ −471581. −0.523015 −0.261507 0.965201i $$-0.584220\pi$$
−0.261507 + 0.965201i $$0.584220\pi$$
$$242$$ 96028.9 0.105406
$$243$$ −59049.0 −0.0641500
$$244$$ −232856. −0.250387
$$245$$ 116284. 0.123767
$$246$$ 307346. 0.323810
$$247$$ 96999.3 0.101164
$$248$$ −411564. −0.424921
$$249$$ 41837.8 0.0427632
$$250$$ 102483. 0.103705
$$251$$ 1.76541e6 1.76873 0.884363 0.466799i $$-0.154593\pi$$
0.884363 + 0.466799i $$0.154593\pi$$
$$252$$ 130748. 0.129698
$$253$$ −381543. −0.374751
$$254$$ −736176. −0.715974
$$255$$ −352083. −0.339074
$$256$$ 969531. 0.924617
$$257$$ −19920.1 −0.0188130 −0.00940652 0.999956i $$-0.502994\pi$$
−0.00940652 + 0.999956i $$0.502994\pi$$
$$258$$ −819001. −0.766011
$$259$$ 1.15123e6 1.06638
$$260$$ 46897.3 0.0430244
$$261$$ 322589. 0.293122
$$262$$ −76601.2 −0.0689418
$$263$$ −2.18348e6 −1.94652 −0.973262 0.229697i $$-0.926227\pi$$
−0.973262 + 0.229697i $$0.926227\pi$$
$$264$$ −149858. −0.132334
$$265$$ −95853.7 −0.0838483
$$266$$ 547446. 0.474392
$$267$$ 931119. 0.799332
$$268$$ −479335. −0.407664
$$269$$ 839300. 0.707190 0.353595 0.935399i $$-0.384959\pi$$
0.353595 + 0.935399i $$0.384959\pi$$
$$270$$ −119536. −0.0997906
$$271$$ 1.42641e6 1.17984 0.589918 0.807463i $$-0.299160\pi$$
0.589918 + 0.807463i $$0.299160\pi$$
$$272$$ −1.96414e6 −1.60972
$$273$$ −224438. −0.182260
$$274$$ −2.52475e6 −2.03162
$$275$$ −75625.0 −0.0603023
$$276$$ −312717. −0.247104
$$277$$ −1.30448e6 −1.02150 −0.510749 0.859730i $$-0.670632\pi$$
−0.510749 + 0.859730i $$0.670632\pi$$
$$278$$ −2.03723e6 −1.58098
$$279$$ 242253. 0.186320
$$280$$ −503954. −0.384146
$$281$$ −580646. −0.438678 −0.219339 0.975649i $$-0.570390\pi$$
−0.219339 + 0.975649i $$0.570390\pi$$
$$282$$ −404475. −0.302879
$$283$$ −601974. −0.446799 −0.223399 0.974727i $$-0.571715\pi$$
−0.223399 + 0.974727i $$0.571715\pi$$
$$284$$ −579691. −0.426482
$$285$$ −128202. −0.0934937
$$286$$ −135106. −0.0976693
$$287$$ −762698. −0.546572
$$288$$ −310160. −0.220346
$$289$$ 1.02878e6 0.724567
$$290$$ 653034. 0.455975
$$291$$ −682286. −0.472317
$$292$$ −709285. −0.486815
$$293$$ −2.40993e6 −1.63996 −0.819982 0.572389i $$-0.806017\pi$$
−0.819982 + 0.572389i $$0.806017\pi$$
$$294$$ −274570. −0.185261
$$295$$ 241234. 0.161393
$$296$$ −1.08147e6 −0.717441
$$297$$ 88209.0 0.0580259
$$298$$ 1.87062e6 1.22024
$$299$$ 536803. 0.347246
$$300$$ −61983.2 −0.0397622
$$301$$ 2.03240e6 1.29298
$$302$$ −3.42609e6 −2.16163
$$303$$ −315213. −0.197241
$$304$$ −715191. −0.443852
$$305$$ −528294. −0.325182
$$306$$ 831340. 0.507546
$$307$$ −1.83380e6 −1.11047 −0.555235 0.831694i $$-0.687371\pi$$
−0.555235 + 0.831694i $$0.687371\pi$$
$$308$$ −195315. −0.117316
$$309$$ −152691. −0.0909742
$$310$$ 490406. 0.289835
$$311$$ 2.27507e6 1.33381 0.666906 0.745142i $$-0.267618\pi$$
0.666906 + 0.745142i $$0.267618\pi$$
$$312$$ 210839. 0.122621
$$313$$ 159585. 0.0920728 0.0460364 0.998940i $$-0.485341\pi$$
0.0460364 + 0.998940i $$0.485341\pi$$
$$314$$ −14571.6 −0.00834035
$$315$$ 296636. 0.168441
$$316$$ 318849. 0.179625
$$317$$ −1.24338e6 −0.694955 −0.347477 0.937688i $$-0.612962\pi$$
−0.347477 + 0.937688i $$0.612962\pi$$
$$318$$ 226330. 0.125509
$$319$$ −481892. −0.265139
$$320$$ 376280. 0.205417
$$321$$ −109714. −0.0594290
$$322$$ 3.02962e6 1.62835
$$323$$ 891609. 0.475519
$$324$$ 72297.2 0.0382612
$$325$$ 106399. 0.0558764
$$326$$ 1.64068e6 0.855029
$$327$$ −109249. −0.0564998
$$328$$ 716485. 0.367724
$$329$$ 1.00373e6 0.511242
$$330$$ 178566. 0.0902640
$$331$$ −958448. −0.480838 −0.240419 0.970669i $$-0.577285\pi$$
−0.240419 + 0.970669i $$0.577285\pi$$
$$332$$ −51224.5 −0.0255054
$$333$$ 636573. 0.314584
$$334$$ −276021. −0.135387
$$335$$ −1.08750e6 −0.529439
$$336$$ 1.65482e6 0.799655
$$337$$ −1.51074e6 −0.724626 −0.362313 0.932056i $$-0.618013\pi$$
−0.362313 + 0.932056i $$0.618013\pi$$
$$338$$ −2.24519e6 −1.06896
$$339$$ −1.84184e6 −0.870469
$$340$$ 431076. 0.202235
$$341$$ −361884. −0.168533
$$342$$ 302711. 0.139947
$$343$$ −1.78064e6 −0.817224
$$344$$ −1.90925e6 −0.869896
$$345$$ −709481. −0.320917
$$346$$ −768741. −0.345215
$$347$$ −1.93847e6 −0.864243 −0.432122 0.901815i $$-0.642235\pi$$
−0.432122 + 0.901815i $$0.642235\pi$$
$$348$$ −394965. −0.174828
$$349$$ −1.62462e6 −0.713985 −0.356992 0.934107i $$-0.616198\pi$$
−0.356992 + 0.934107i $$0.616198\pi$$
$$350$$ 600495. 0.262023
$$351$$ −124103. −0.0537671
$$352$$ 463325. 0.199310
$$353$$ −23347.5 −0.00997249 −0.00498624 0.999988i $$-0.501587\pi$$
−0.00498624 + 0.999988i $$0.501587\pi$$
$$354$$ −569604. −0.241582
$$355$$ −1.31518e6 −0.553878
$$356$$ −1.14002e6 −0.476748
$$357$$ −2.06302e6 −0.856707
$$358$$ 3.82374e6 1.57682
$$359$$ 3.63918e6 1.49028 0.745139 0.666909i $$-0.232383\pi$$
0.745139 + 0.666909i $$0.232383\pi$$
$$360$$ −278662. −0.113324
$$361$$ −2.15144e6 −0.868884
$$362$$ 1.54325e6 0.618964
$$363$$ −131769. −0.0524864
$$364$$ 274793. 0.108706
$$365$$ −1.60920e6 −0.632233
$$366$$ 1.24741e6 0.486751
$$367$$ 2.24713e6 0.870890 0.435445 0.900215i $$-0.356591\pi$$
0.435445 + 0.900215i $$0.356591\pi$$
$$368$$ −3.95793e6 −1.52352
$$369$$ −421735. −0.161240
$$370$$ 1.28865e6 0.489362
$$371$$ −561651. −0.211852
$$372$$ −296605. −0.111127
$$373$$ 3.82745e6 1.42442 0.712208 0.701968i $$-0.247695\pi$$
0.712208 + 0.701968i $$0.247695\pi$$
$$374$$ −1.24188e6 −0.459092
$$375$$ −140625. −0.0516398
$$376$$ −942910. −0.343954
$$377$$ 677986. 0.245679
$$378$$ −700418. −0.252132
$$379$$ −4.26443e6 −1.52498 −0.762489 0.647002i $$-0.776023\pi$$
−0.762489 + 0.647002i $$0.776023\pi$$
$$380$$ 156965. 0.0557628
$$381$$ 1.01017e6 0.356517
$$382$$ 3.88148e6 1.36094
$$383$$ 2.40920e6 0.839221 0.419611 0.907704i $$-0.362167\pi$$
0.419611 + 0.907704i $$0.362167\pi$$
$$384$$ −1.99127e6 −0.689130
$$385$$ −443122. −0.152360
$$386$$ −3.54722e6 −1.21177
$$387$$ 1.12382e6 0.381433
$$388$$ 835362. 0.281706
$$389$$ 3.73204e6 1.25047 0.625233 0.780438i $$-0.285004\pi$$
0.625233 + 0.780438i $$0.285004\pi$$
$$390$$ −251229. −0.0836390
$$391$$ 4.93424e6 1.63222
$$392$$ −640077. −0.210386
$$393$$ 105111. 0.0343293
$$394$$ 3.15950e6 1.02536
$$395$$ 723393. 0.233282
$$396$$ −107999. −0.0346086
$$397$$ −4.89288e6 −1.55808 −0.779038 0.626977i $$-0.784292\pi$$
−0.779038 + 0.626977i $$0.784292\pi$$
$$398$$ −6.65250e6 −2.10512
$$399$$ −751195. −0.236222
$$400$$ −784495. −0.245155
$$401$$ −3.93524e6 −1.22211 −0.611055 0.791588i $$-0.709255\pi$$
−0.611055 + 0.791588i $$0.709255\pi$$
$$402$$ 2.56780e6 0.792495
$$403$$ 509144. 0.156163
$$404$$ 385933. 0.117641
$$405$$ 164025. 0.0496904
$$406$$ 3.82643e6 1.15207
$$407$$ −950929. −0.284552
$$408$$ 1.93802e6 0.576378
$$409$$ 657037. 0.194215 0.0971073 0.995274i $$-0.469041\pi$$
0.0971073 + 0.995274i $$0.469041\pi$$
$$410$$ −853740. −0.250822
$$411$$ 3.46442e6 1.01164
$$412$$ 186949. 0.0542600
$$413$$ 1.41351e6 0.407777
$$414$$ 1.67523e6 0.480368
$$415$$ −116216. −0.0331243
$$416$$ −651864. −0.184682
$$417$$ 2.79544e6 0.787246
$$418$$ −452198. −0.126587
$$419$$ 4.38504e6 1.22022 0.610110 0.792317i $$-0.291125\pi$$
0.610110 + 0.792317i $$0.291125\pi$$
$$420$$ −363188. −0.100464
$$421$$ 2.34058e6 0.643604 0.321802 0.946807i $$-0.395711\pi$$
0.321802 + 0.946807i $$0.395711\pi$$
$$422$$ 4.06467e6 1.11108
$$423$$ 555012. 0.150818
$$424$$ 527620. 0.142530
$$425$$ 978008. 0.262646
$$426$$ 3.10541e6 0.829078
$$427$$ −3.09552e6 −0.821607
$$428$$ 134329. 0.0354455
$$429$$ 185389. 0.0486341
$$430$$ 2.27500e6 0.593350
$$431$$ −2.18215e6 −0.565838 −0.282919 0.959144i $$-0.591303\pi$$
−0.282919 + 0.959144i $$0.591303\pi$$
$$432$$ 915035. 0.235900
$$433$$ −3.61080e6 −0.925515 −0.462757 0.886485i $$-0.653140\pi$$
−0.462757 + 0.886485i $$0.653140\pi$$
$$434$$ 2.87352e6 0.732301
$$435$$ −896080. −0.227051
$$436$$ 133760. 0.0336984
$$437$$ 1.79668e6 0.450056
$$438$$ 3.79965e6 0.946364
$$439$$ 6.48191e6 1.60525 0.802624 0.596486i $$-0.203437\pi$$
0.802624 + 0.596486i $$0.203437\pi$$
$$440$$ 416273. 0.102505
$$441$$ 376760. 0.0922503
$$442$$ 1.74723e6 0.425397
$$443$$ −6.81523e6 −1.64995 −0.824976 0.565167i $$-0.808812\pi$$
−0.824976 + 0.565167i $$0.808812\pi$$
$$444$$ −779393. −0.187629
$$445$$ −2.58644e6 −0.619160
$$446$$ 5.86531e6 1.39622
$$447$$ −2.56683e6 −0.607614
$$448$$ 2.20480e6 0.519008
$$449$$ −2.98356e6 −0.698423 −0.349211 0.937044i $$-0.613551\pi$$
−0.349211 + 0.937044i $$0.613551\pi$$
$$450$$ 332045. 0.0772974
$$451$$ 629999. 0.145847
$$452$$ 2.25508e6 0.519177
$$453$$ 4.70122e6 1.07638
$$454$$ 5.58469e6 1.27163
$$455$$ 623440. 0.141178
$$456$$ 705679. 0.158926
$$457$$ −6.11184e6 −1.36893 −0.684466 0.729045i $$-0.739964\pi$$
−0.684466 + 0.729045i $$0.739964\pi$$
$$458$$ 904081. 0.201393
$$459$$ −1.14075e6 −0.252731
$$460$$ 868659. 0.191406
$$461$$ −3.41772e6 −0.749003 −0.374502 0.927226i $$-0.622186\pi$$
−0.374502 + 0.927226i $$0.622186\pi$$
$$462$$ 1.04630e6 0.228062
$$463$$ −4.60011e6 −0.997277 −0.498639 0.866810i $$-0.666166\pi$$
−0.498639 + 0.866810i $$0.666166\pi$$
$$464$$ −4.99890e6 −1.07790
$$465$$ −672925. −0.144323
$$466$$ −8.63083e6 −1.84114
$$467$$ 5.03617e6 1.06858 0.534291 0.845301i $$-0.320579\pi$$
0.534291 + 0.845301i $$0.320579\pi$$
$$468$$ 151947. 0.0320685
$$469$$ −6.37215e6 −1.33769
$$470$$ 1.12354e6 0.234609
$$471$$ 19994.9 0.00415305
$$472$$ −1.32786e6 −0.274345
$$473$$ −1.67879e6 −0.345019
$$474$$ −1.70808e6 −0.349190
$$475$$ 356117. 0.0724199
$$476$$ 2.52587e6 0.510969
$$477$$ −310566. −0.0624968
$$478$$ 7.33142e6 1.46764
$$479$$ −2.82760e6 −0.563091 −0.281545 0.959548i $$-0.590847\pi$$
−0.281545 + 0.959548i $$0.590847\pi$$
$$480$$ 861556. 0.170679
$$481$$ 1.33789e6 0.263668
$$482$$ −3.09306e6 −0.606416
$$483$$ −4.15718e6 −0.810833
$$484$$ 161333. 0.0313046
$$485$$ 1.89524e6 0.365855
$$486$$ −387297. −0.0743795
$$487$$ −5.68931e6 −1.08702 −0.543510 0.839403i $$-0.682905\pi$$
−0.543510 + 0.839403i $$0.682905\pi$$
$$488$$ 2.90796e6 0.552763
$$489$$ −2.25131e6 −0.425759
$$490$$ 762695. 0.143503
$$491$$ 3.23715e6 0.605981 0.302990 0.952994i $$-0.402015\pi$$
0.302990 + 0.952994i $$0.402015\pi$$
$$492$$ 516355. 0.0961690
$$493$$ 6.23199e6 1.15481
$$494$$ 636209. 0.117296
$$495$$ −245025. −0.0449467
$$496$$ −3.75400e6 −0.685157
$$497$$ −7.70626e6 −1.39943
$$498$$ 274410. 0.0495823
$$499$$ −5.08564e6 −0.914312 −0.457156 0.889386i $$-0.651132\pi$$
−0.457156 + 0.889386i $$0.651132\pi$$
$$500$$ 172175. 0.0307997
$$501$$ 378751. 0.0674154
$$502$$ 1.15791e7 2.05077
$$503$$ 9.02252e6 1.59004 0.795019 0.606584i $$-0.207461\pi$$
0.795019 + 0.606584i $$0.207461\pi$$
$$504$$ −1.63281e6 −0.286325
$$505$$ 875591. 0.152782
$$506$$ −2.50251e6 −0.434509
$$507$$ 3.08081e6 0.532286
$$508$$ −1.23681e6 −0.212639
$$509$$ 8.98909e6 1.53788 0.768938 0.639323i $$-0.220785\pi$$
0.768938 + 0.639323i $$0.220785\pi$$
$$510$$ −2.30928e6 −0.393143
$$511$$ −9.42904e6 −1.59741
$$512$$ −720997. −0.121551
$$513$$ −415374. −0.0696861
$$514$$ −130654. −0.0218130
$$515$$ 424143. 0.0704683
$$516$$ −1.37596e6 −0.227499
$$517$$ −829093. −0.136420
$$518$$ 7.55079e6 1.23643
$$519$$ 1.05485e6 0.171899
$$520$$ −585665. −0.0949819
$$521$$ −1.11219e7 −1.79508 −0.897539 0.440936i $$-0.854647\pi$$
−0.897539 + 0.440936i $$0.854647\pi$$
$$522$$ 2.11583e6 0.339863
$$523$$ 3.67510e6 0.587510 0.293755 0.955881i $$-0.405095\pi$$
0.293755 + 0.955881i $$0.405095\pi$$
$$524$$ −128693. −0.0204752
$$525$$ −823988. −0.130474
$$526$$ −1.43212e7 −2.25692
$$527$$ 4.68001e6 0.734040
$$528$$ −1.36690e6 −0.213380
$$529$$ 3.50664e6 0.544818
$$530$$ −628695. −0.0972188
$$531$$ 781600. 0.120295
$$532$$ 919733. 0.140891
$$533$$ −886361. −0.135143
$$534$$ 6.10712e6 0.926795
$$535$$ 304761. 0.0460335
$$536$$ 5.98605e6 0.899971
$$537$$ −5.24687e6 −0.785171
$$538$$ 5.50489e6 0.819960
$$539$$ −562814. −0.0834436
$$540$$ −200825. −0.0296370
$$541$$ −4.31097e6 −0.633260 −0.316630 0.948549i $$-0.602551\pi$$
−0.316630 + 0.948549i $$0.602551\pi$$
$$542$$ 9.35569e6 1.36797
$$543$$ −2.11762e6 −0.308211
$$544$$ −5.99188e6 −0.868092
$$545$$ 303469. 0.0437646
$$546$$ −1.47207e6 −0.211323
$$547$$ −1.80626e6 −0.258114 −0.129057 0.991637i $$-0.541195\pi$$
−0.129057 + 0.991637i $$0.541195\pi$$
$$548$$ −4.24169e6 −0.603375
$$549$$ −1.71167e6 −0.242376
$$550$$ −496017. −0.0699182
$$551$$ 2.26922e6 0.318418
$$552$$ 3.90529e6 0.545514
$$553$$ 4.23870e6 0.589413
$$554$$ −8.55595e6 −1.18439
$$555$$ −1.76826e6 −0.243676
$$556$$ −3.42262e6 −0.469540
$$557$$ 8.42670e6 1.15085 0.575426 0.817854i $$-0.304836\pi$$
0.575426 + 0.817854i $$0.304836\pi$$
$$558$$ 1.58891e6 0.216031
$$559$$ 2.36193e6 0.319696
$$560$$ −4.59672e6 −0.619410
$$561$$ 1.70408e6 0.228604
$$562$$ −3.80840e6 −0.508630
$$563$$ −9.19966e6 −1.22321 −0.611605 0.791163i $$-0.709476\pi$$
−0.611605 + 0.791163i $$0.709476\pi$$
$$564$$ −679534. −0.0899526
$$565$$ 5.11623e6 0.674262
$$566$$ −3.94829e6 −0.518046
$$567$$ 961099. 0.125548
$$568$$ 7.23932e6 0.941515
$$569$$ 5.18644e6 0.671566 0.335783 0.941939i $$-0.390999\pi$$
0.335783 + 0.941939i $$0.390999\pi$$
$$570$$ −840864. −0.108402
$$571$$ −3.29390e6 −0.422786 −0.211393 0.977401i $$-0.567800\pi$$
−0.211393 + 0.977401i $$0.567800\pi$$
$$572$$ −226983. −0.0290070
$$573$$ −5.32609e6 −0.677676
$$574$$ −5.00246e6 −0.633730
$$575$$ 1.97078e6 0.248581
$$576$$ 1.21915e6 0.153109
$$577$$ −1.02043e7 −1.27598 −0.637989 0.770046i $$-0.720233\pi$$
−0.637989 + 0.770046i $$0.720233\pi$$
$$578$$ 6.74768e6 0.840107
$$579$$ 4.86742e6 0.603396
$$580$$ 1.09712e6 0.135421
$$581$$ −680965. −0.0836921
$$582$$ −4.47505e6 −0.547633
$$583$$ 463932. 0.0565305
$$584$$ 8.85773e6 1.07471
$$585$$ 344732. 0.0416478
$$586$$ −1.58065e7 −1.90148
$$587$$ −1.33951e7 −1.60454 −0.802272 0.596958i $$-0.796376\pi$$
−0.802272 + 0.596958i $$0.796376\pi$$
$$588$$ −461289. −0.0550212
$$589$$ 1.70411e6 0.202399
$$590$$ 1.58223e6 0.187129
$$591$$ −4.33540e6 −0.510576
$$592$$ −9.86445e6 −1.15683
$$593$$ 3.76550e6 0.439730 0.219865 0.975530i $$-0.429438\pi$$
0.219865 + 0.975530i $$0.429438\pi$$
$$594$$ 578554. 0.0672788
$$595$$ 5.73061e6 0.663603
$$596$$ 3.14272e6 0.362401
$$597$$ 9.12843e6 1.04824
$$598$$ 3.52084e6 0.402618
$$599$$ 1.21252e6 0.138077 0.0690384 0.997614i $$-0.478007\pi$$
0.0690384 + 0.997614i $$0.478007\pi$$
$$600$$ 774061. 0.0877803
$$601$$ −7.81714e6 −0.882799 −0.441399 0.897311i $$-0.645518\pi$$
−0.441399 + 0.897311i $$0.645518\pi$$
$$602$$ 1.33303e7 1.49916
$$603$$ −3.52349e6 −0.394620
$$604$$ −5.75597e6 −0.641987
$$605$$ 366025. 0.0406558
$$606$$ −2.06745e6 −0.228693
$$607$$ 5.43853e6 0.599114 0.299557 0.954078i $$-0.403161\pi$$
0.299557 + 0.954078i $$0.403161\pi$$
$$608$$ −2.18179e6 −0.239361
$$609$$ −5.25055e6 −0.573670
$$610$$ −3.46503e6 −0.377036
$$611$$ 1.16647e6 0.126407
$$612$$ 1.39669e6 0.150737
$$613$$ 1.70637e7 1.83409 0.917045 0.398783i $$-0.130567\pi$$
0.917045 + 0.398783i $$0.130567\pi$$
$$614$$ −1.20277e7 −1.28755
$$615$$ 1.17149e6 0.124896
$$616$$ 2.43914e6 0.258991
$$617$$ 7.80667e6 0.825568 0.412784 0.910829i $$-0.364556\pi$$
0.412784 + 0.910829i $$0.364556\pi$$
$$618$$ −1.00149e6 −0.105481
$$619$$ 7.31658e6 0.767506 0.383753 0.923436i $$-0.374631\pi$$
0.383753 + 0.923436i $$0.374631\pi$$
$$620$$ 823902. 0.0860788
$$621$$ −2.29872e6 −0.239198
$$622$$ 1.49220e7 1.54650
$$623$$ −1.51552e7 −1.56438
$$624$$ 1.92313e6 0.197719
$$625$$ 390625. 0.0400000
$$626$$ 1.04670e6 0.106755
$$627$$ 620497. 0.0630335
$$628$$ −24481.0 −0.00247702
$$629$$ 1.22977e7 1.23936
$$630$$ 1.94560e6 0.195300
$$631$$ −1.18729e7 −1.18709 −0.593543 0.804802i $$-0.702271\pi$$
−0.593543 + 0.804802i $$0.702271\pi$$
$$632$$ −3.98187e6 −0.396547
$$633$$ −5.57746e6 −0.553257
$$634$$ −8.15523e6 −0.805773
$$635$$ −2.80602e6 −0.276157
$$636$$ 380244. 0.0372752
$$637$$ 791837. 0.0773192
$$638$$ −3.16068e6 −0.307418
$$639$$ −4.26118e6 −0.412837
$$640$$ 5.53129e6 0.533798
$$641$$ −1.85963e7 −1.78764 −0.893821 0.448424i $$-0.851985\pi$$
−0.893821 + 0.448424i $$0.851985\pi$$
$$642$$ −719603. −0.0689057
$$643$$ −1.18028e7 −1.12579 −0.562894 0.826529i $$-0.690312\pi$$
−0.562894 + 0.826529i $$0.690312\pi$$
$$644$$ 5.08988e6 0.483608
$$645$$ −3.12171e6 −0.295457
$$646$$ 5.84798e6 0.551346
$$647$$ 2.05252e7 1.92764 0.963821 0.266551i $$-0.0858842\pi$$
0.963821 + 0.266551i $$0.0858842\pi$$
$$648$$ −902865. −0.0844666
$$649$$ −1.16757e6 −0.108811
$$650$$ 697859. 0.0647865
$$651$$ −3.94298e6 −0.364647
$$652$$ 2.75642e6 0.253937
$$653$$ −5.78511e6 −0.530919 −0.265460 0.964122i $$-0.585524\pi$$
−0.265460 + 0.964122i $$0.585524\pi$$
$$654$$ −716552. −0.0655094
$$655$$ −291974. −0.0265914
$$656$$ 6.53528e6 0.592932
$$657$$ −5.21380e6 −0.471239
$$658$$ 6.58335e6 0.592765
$$659$$ 1.88598e7 1.69170 0.845852 0.533418i $$-0.179093\pi$$
0.845852 + 0.533418i $$0.179093\pi$$
$$660$$ 299999. 0.0268077
$$661$$ −1.12652e7 −1.00285 −0.501426 0.865201i $$-0.667191\pi$$
−0.501426 + 0.865201i $$0.667191\pi$$
$$662$$ −6.28637e6 −0.557513
$$663$$ −2.39751e6 −0.211825
$$664$$ 639704. 0.0563065
$$665$$ 2.08665e6 0.182977
$$666$$ 4.17522e6 0.364749
$$667$$ 1.25581e7 1.09297
$$668$$ −463727. −0.0402088
$$669$$ −8.04827e6 −0.695244
$$670$$ −7.13279e6 −0.613864
$$671$$ 2.55694e6 0.219237
$$672$$ 5.04826e6 0.431239
$$673$$ 1.51301e7 1.28767 0.643833 0.765166i $$-0.277343\pi$$
0.643833 + 0.765166i $$0.277343\pi$$
$$674$$ −9.90878e6 −0.840176
$$675$$ −455625. −0.0384900
$$676$$ −3.77201e6 −0.317473
$$677$$ −1.12001e7 −0.939187 −0.469593 0.882883i $$-0.655599\pi$$
−0.469593 + 0.882883i $$0.655599\pi$$
$$678$$ −1.20805e7 −1.00928
$$679$$ 1.11051e7 0.924373
$$680$$ −5.38338e6 −0.446460
$$681$$ −7.66321e6 −0.633203
$$682$$ −2.37356e6 −0.195407
$$683$$ 2.12907e7 1.74638 0.873190 0.487379i $$-0.162047\pi$$
0.873190 + 0.487379i $$0.162047\pi$$
$$684$$ 508567. 0.0415631
$$685$$ −9.62338e6 −0.783612
$$686$$ −1.16791e7 −0.947539
$$687$$ −1.24056e6 −0.100283
$$688$$ −1.74149e7 −1.40265
$$689$$ −652717. −0.0523814
$$690$$ −4.65342e6 −0.372091
$$691$$ 1.77648e6 0.141536 0.0707678 0.997493i $$-0.477455\pi$$
0.0707678 + 0.997493i $$0.477455\pi$$
$$692$$ −1.29152e6 −0.102526
$$693$$ −1.43572e6 −0.113563
$$694$$ −1.27143e7 −1.00206
$$695$$ −7.76512e6 −0.609798
$$696$$ 4.93242e6 0.385955
$$697$$ −8.14735e6 −0.635235
$$698$$ −1.06557e7 −0.827838
$$699$$ 1.18431e7 0.916792
$$700$$ 1.00886e6 0.0778188
$$701$$ 94420.1 0.00725720 0.00362860 0.999993i $$-0.498845\pi$$
0.00362860 + 0.999993i $$0.498845\pi$$
$$702$$ −813983. −0.0623408
$$703$$ 4.47791e6 0.341733
$$704$$ −1.82120e6 −0.138492
$$705$$ −1.54170e6 −0.116823
$$706$$ −153134. −0.0115627
$$707$$ 5.13050e6 0.386021
$$708$$ −956958. −0.0717480
$$709$$ −1.46333e7 −1.09327 −0.546633 0.837372i $$-0.684091\pi$$
−0.546633 + 0.837372i $$0.684091\pi$$
$$710$$ −8.62614e6 −0.642201
$$711$$ 2.34379e6 0.173878
$$712$$ 1.42369e7 1.05248
$$713$$ 9.43067e6 0.694734
$$714$$ −1.35311e7 −0.993319
$$715$$ −514970. −0.0376718
$$716$$ 6.42405e6 0.468302
$$717$$ −1.00600e7 −0.730805
$$718$$ 2.38690e7 1.72792
$$719$$ 1.15215e7 0.831161 0.415580 0.909556i $$-0.363578\pi$$
0.415580 + 0.909556i $$0.363578\pi$$
$$720$$ −2.54176e6 −0.182728
$$721$$ 2.48525e6 0.178046
$$722$$ −1.41111e7 −1.00744
$$723$$ 4.24423e6 0.301963
$$724$$ 2.59273e6 0.183827
$$725$$ 2.48911e6 0.175873
$$726$$ −864260. −0.0608559
$$727$$ 1.73993e7 1.22095 0.610473 0.792037i $$-0.290979\pi$$
0.610473 + 0.792037i $$0.290979\pi$$
$$728$$ −3.43168e6 −0.239982
$$729$$ 531441. 0.0370370
$$730$$ −1.05546e7 −0.733050
$$731$$ 2.17107e7 1.50272
$$732$$ 2.09570e6 0.144561
$$733$$ −1.21356e7 −0.834262 −0.417131 0.908846i $$-0.636964\pi$$
−0.417131 + 0.908846i $$0.636964\pi$$
$$734$$ 1.47387e7 1.00976
$$735$$ −1.04655e6 −0.0714568
$$736$$ −1.20742e7 −0.821608
$$737$$ 5.26348e6 0.356948
$$738$$ −2.76612e6 −0.186952
$$739$$ 1.30600e7 0.879692 0.439846 0.898073i $$-0.355033\pi$$
0.439846 + 0.898073i $$0.355033\pi$$
$$740$$ 2.16498e6 0.145337
$$741$$ −872994. −0.0584071
$$742$$ −3.68382e6 −0.245634
$$743$$ −2.36143e6 −0.156929 −0.0784644 0.996917i $$-0.525002\pi$$
−0.0784644 + 0.996917i $$0.525002\pi$$
$$744$$ 3.70407e6 0.245328
$$745$$ 7.13008e6 0.470656
$$746$$ 2.51038e7 1.65156
$$747$$ −376540. −0.0246894
$$748$$ −2.08641e6 −0.136347
$$749$$ 1.78574e6 0.116309
$$750$$ −922346. −0.0598743
$$751$$ 4.12172e6 0.266673 0.133336 0.991071i $$-0.457431\pi$$
0.133336 + 0.991071i $$0.457431\pi$$
$$752$$ −8.60058e6 −0.554604
$$753$$ −1.58887e7 −1.02117
$$754$$ 4.44685e6 0.284855
$$755$$ −1.30589e7 −0.833759
$$756$$ −1.17673e6 −0.0748811
$$757$$ 4.12364e6 0.261542 0.130771 0.991413i $$-0.458255\pi$$
0.130771 + 0.991413i $$0.458255\pi$$
$$758$$ −2.79700e7 −1.76815
$$759$$ 3.43389e6 0.216362
$$760$$ −1.96022e6 −0.123104
$$761$$ −2.08230e7 −1.30341 −0.651706 0.758472i $$-0.725946\pi$$
−0.651706 + 0.758472i $$0.725946\pi$$
$$762$$ 6.62558e6 0.413368
$$763$$ 1.77817e6 0.110576
$$764$$ 6.52105e6 0.404189
$$765$$ 3.16875e6 0.195764
$$766$$ 1.58017e7 0.973045
$$767$$ 1.64269e6 0.100825
$$768$$ −8.72578e6 −0.533828
$$769$$ 1.58156e7 0.964427 0.482213 0.876054i $$-0.339833\pi$$
0.482213 + 0.876054i $$0.339833\pi$$
$$770$$ −2.90640e6 −0.176656
$$771$$ 179281. 0.0108617
$$772$$ −5.95947e6 −0.359886
$$773$$ −2.58350e6 −0.155510 −0.0777552 0.996972i $$-0.524775\pi$$
−0.0777552 + 0.996972i $$0.524775\pi$$
$$774$$ 7.37101e6 0.442257
$$775$$ 1.86924e6 0.111792
$$776$$ −1.04322e7 −0.621902
$$777$$ −1.03610e7 −0.615674
$$778$$ 2.44781e7 1.44987
$$779$$ −2.96665e6 −0.175155
$$780$$ −422076. −0.0248401
$$781$$ 6.36547e6 0.373425
$$782$$ 3.23632e7 1.89250
$$783$$ −2.90330e6 −0.169234
$$784$$ −5.83834e6 −0.339234
$$785$$ −55541.5 −0.00321694
$$786$$ 689411. 0.0398035
$$787$$ −5.64885e6 −0.325105 −0.162552 0.986700i $$-0.551973\pi$$
−0.162552 + 0.986700i $$0.551973\pi$$
$$788$$ 5.30809e6 0.304525
$$789$$ 1.96513e7 1.12383
$$790$$ 4.74467e6 0.270482
$$791$$ 2.99784e7 1.70360
$$792$$ 1.34872e6 0.0764030
$$793$$ −3.59743e6 −0.203146
$$794$$ −3.20920e7 −1.80653
$$795$$ 862683. 0.0484098
$$796$$ −1.11765e7 −0.625204
$$797$$ −3.72876e6 −0.207931 −0.103965 0.994581i $$-0.533153\pi$$
−0.103965 + 0.994581i $$0.533153\pi$$
$$798$$ −4.92702e6 −0.273890
$$799$$ 1.07221e7 0.594173
$$800$$ −2.39321e6 −0.132207
$$801$$ −8.38007e6 −0.461495
$$802$$ −2.58109e7 −1.41699
$$803$$ 7.78852e6 0.426252
$$804$$ 4.31401e6 0.235365
$$805$$ 1.15477e7 0.628068
$$806$$ 3.33943e6 0.181065
$$807$$ −7.55370e6 −0.408296
$$808$$ −4.81963e6 −0.259708
$$809$$ 6.35004e6 0.341119 0.170559 0.985347i $$-0.445443\pi$$
0.170559 + 0.985347i $$0.445443\pi$$
$$810$$ 1.07582e6 0.0576141
$$811$$ 1.34156e7 0.716241 0.358120 0.933675i $$-0.383418\pi$$
0.358120 + 0.933675i $$0.383418\pi$$
$$812$$ 6.42856e6 0.342156
$$813$$ −1.28377e7 −0.681178
$$814$$ −6.23705e6 −0.329928
$$815$$ 6.25365e6 0.329791
$$816$$ 1.76773e7 0.929372
$$817$$ 7.90538e6 0.414350
$$818$$ 4.30945e6 0.225184
$$819$$ 2.01995e6 0.105228
$$820$$ −1.43432e6 −0.0744922
$$821$$ 2.40201e7 1.24370 0.621851 0.783135i $$-0.286381\pi$$
0.621851 + 0.783135i $$0.286381\pi$$
$$822$$ 2.27228e7 1.17296
$$823$$ −1.46523e6 −0.0754058 −0.0377029 0.999289i $$-0.512004\pi$$
−0.0377029 + 0.999289i $$0.512004\pi$$
$$824$$ −2.33466e6 −0.119786
$$825$$ 680625. 0.0348155
$$826$$ 9.27105e6 0.472801
$$827$$ −2.32918e7 −1.18424 −0.592120 0.805850i $$-0.701709\pi$$
−0.592120 + 0.805850i $$0.701709\pi$$
$$828$$ 2.81446e6 0.142665
$$829$$ −2.02821e6 −0.102501 −0.0512503 0.998686i $$-0.516321\pi$$
−0.0512503 + 0.998686i $$0.516321\pi$$
$$830$$ −762250. −0.0384063
$$831$$ 1.17403e7 0.589762
$$832$$ 2.56229e6 0.128327
$$833$$ 7.27850e6 0.363437
$$834$$ 1.83350e7 0.912781
$$835$$ −1.05208e6 −0.0522197
$$836$$ −759712. −0.0375953
$$837$$ −2.18028e6 −0.107572
$$838$$ 2.87610e7 1.41480
$$839$$ −3.07518e7 −1.50822 −0.754111 0.656747i $$-0.771932\pi$$
−0.754111 + 0.656747i $$0.771932\pi$$
$$840$$ 4.53559e6 0.221787
$$841$$ −4.65021e6 −0.226716
$$842$$ 1.53517e7 0.746234
$$843$$ 5.22582e6 0.253271
$$844$$ 6.82881e6 0.329981
$$845$$ −8.55780e6 −0.412307
$$846$$ 3.64027e6 0.174867
$$847$$ 2.14471e6 0.102721
$$848$$ 4.81259e6 0.229821
$$849$$ 5.41777e6 0.257959
$$850$$ 6.41466e6 0.304527
$$851$$ 2.47811e7 1.17300
$$852$$ 5.21722e6 0.246229
$$853$$ −2.05598e7 −0.967491 −0.483745 0.875209i $$-0.660724\pi$$
−0.483745 + 0.875209i $$0.660724\pi$$
$$854$$ −2.03032e7 −0.952621
$$855$$ 1.15382e6 0.0539786
$$856$$ −1.67753e6 −0.0782505
$$857$$ 3.20463e7 1.49048 0.745240 0.666796i $$-0.232335\pi$$
0.745240 + 0.666796i $$0.232335\pi$$
$$858$$ 1.21595e6 0.0563894
$$859$$ 2.34894e6 0.108615 0.0543075 0.998524i $$-0.482705\pi$$
0.0543075 + 0.998524i $$0.482705\pi$$
$$860$$ 3.82210e6 0.176220
$$861$$ 6.86428e6 0.315564
$$862$$ −1.43125e7 −0.656068
$$863$$ −1.44887e7 −0.662219 −0.331110 0.943592i $$-0.607423\pi$$
−0.331110 + 0.943592i $$0.607423\pi$$
$$864$$ 2.79144e6 0.127217
$$865$$ −2.93014e6 −0.133152
$$866$$ −2.36829e7 −1.07310
$$867$$ −9.25903e6 −0.418329
$$868$$ 4.82763e6 0.217488
$$869$$ −3.50122e6 −0.157279
$$870$$ −5.87731e6 −0.263257
$$871$$ −7.40533e6 −0.330749
$$872$$ −1.67042e6 −0.0743936
$$873$$ 6.14057e6 0.272692
$$874$$ 1.17842e7 0.521823
$$875$$ 2.28885e6 0.101064
$$876$$ 6.38356e6 0.281063
$$877$$ −3.17684e7 −1.39475 −0.697376 0.716705i $$-0.745649\pi$$
−0.697376 + 0.716705i $$0.745649\pi$$
$$878$$ 4.25143e7 1.86122
$$879$$ 2.16893e7 0.946834
$$880$$ 3.79696e6 0.165283
$$881$$ 1.06777e7 0.463486 0.231743 0.972777i $$-0.425557\pi$$
0.231743 + 0.972777i $$0.425557\pi$$
$$882$$ 2.47113e6 0.106961
$$883$$ 1.77890e7 0.767804 0.383902 0.923374i $$-0.374580\pi$$
0.383902 + 0.923374i $$0.374580\pi$$
$$884$$ 2.93542e6 0.126340
$$885$$ −2.17111e6 −0.0931802
$$886$$ −4.47005e7 −1.91306
$$887$$ 3.13731e7 1.33890 0.669450 0.742857i $$-0.266530\pi$$
0.669450 + 0.742857i $$0.266530\pi$$
$$888$$ 9.73326e6 0.414215
$$889$$ −1.64418e7 −0.697741
$$890$$ −1.69642e7 −0.717892
$$891$$ −793881. −0.0335013
$$892$$ 9.85397e6 0.414667
$$893$$ 3.90418e6 0.163833
$$894$$ −1.68356e7 −0.704505
$$895$$ 1.45746e7 0.608191
$$896$$ 3.24104e7 1.34870
$$897$$ −4.83123e6 −0.200482
$$898$$ −1.95689e7 −0.809795
$$899$$ 1.19110e7 0.491529
$$900$$ 557849. 0.0229567
$$901$$ −5.99972e6 −0.246218
$$902$$ 4.13210e6 0.169104
$$903$$ −1.82916e7 −0.746504
$$904$$ −2.81620e7 −1.14615
$$905$$ 5.88228e6 0.238739
$$906$$ 3.08348e7 1.24802
$$907$$ −8.46355e6 −0.341613 −0.170807 0.985305i $$-0.554637\pi$$
−0.170807 + 0.985305i $$0.554637\pi$$
$$908$$ 9.38252e6 0.377663
$$909$$ 2.83691e6 0.113877
$$910$$ 4.08908e6 0.163690
$$911$$ −2.18411e7 −0.871923 −0.435961 0.899965i $$-0.643592\pi$$
−0.435961 + 0.899965i $$0.643592\pi$$
$$912$$ 6.43672e6 0.256258
$$913$$ 562486. 0.0223324
$$914$$ −4.00870e7 −1.58722
$$915$$ 4.75464e6 0.187744
$$916$$ 1.51889e6 0.0598120
$$917$$ −1.71081e6 −0.0671861
$$918$$ −7.48206e6 −0.293032
$$919$$ 4.18752e7 1.63557 0.817784 0.575525i $$-0.195202\pi$$
0.817784 + 0.575525i $$0.195202\pi$$
$$920$$ −1.08480e7 −0.422553
$$921$$ 1.65042e7 0.641130
$$922$$ −2.24165e7 −0.868440
$$923$$ −8.95575e6 −0.346017
$$924$$ 1.75783e6 0.0677325
$$925$$ 4.91183e6 0.188751
$$926$$ −3.01717e7 −1.15630
$$927$$ 1.37422e6 0.0525240
$$928$$ −1.52498e7 −0.581293
$$929$$ 8.03740e6 0.305546 0.152773 0.988261i $$-0.451180\pi$$
0.152773 + 0.988261i $$0.451180\pi$$
$$930$$ −4.41365e6 −0.167337
$$931$$ 2.65028e6 0.100211
$$932$$ −1.45002e7 −0.546805
$$933$$ −2.04757e7 −0.770077
$$934$$ 3.30317e7 1.23898
$$935$$ −4.73356e6 −0.177076
$$936$$ −1.89755e6 −0.0707953
$$937$$ −1.78192e6 −0.0663038 −0.0331519 0.999450i $$-0.510555\pi$$
−0.0331519 + 0.999450i $$0.510555\pi$$
$$938$$ −4.17943e7 −1.55099
$$939$$ −1.43627e6 −0.0531583
$$940$$ 1.88760e6 0.0696770
$$941$$ 2.97245e7 1.09431 0.547154 0.837032i $$-0.315711\pi$$
0.547154 + 0.837032i $$0.315711\pi$$
$$942$$ 131145. 0.00481531
$$943$$ −1.64177e7 −0.601220
$$944$$ −1.21118e7 −0.442364
$$945$$ −2.66972e6 −0.0972492
$$946$$ −1.10110e7 −0.400036
$$947$$ 931083. 0.0337375 0.0168688 0.999858i $$-0.494630\pi$$
0.0168688 + 0.999858i $$0.494630\pi$$
$$948$$ −2.86965e6 −0.103707
$$949$$ −1.09579e7 −0.394967
$$950$$ 2.33573e6 0.0839681
$$951$$ 1.11904e7 0.401232
$$952$$ −3.15437e7 −1.12803
$$953$$ −2.74983e7 −0.980784 −0.490392 0.871502i $$-0.663146\pi$$
−0.490392 + 0.871502i $$0.663146\pi$$
$$954$$ −2.03697e6 −0.0724626
$$955$$ 1.47947e7 0.524926
$$956$$ 1.23171e7 0.435876
$$957$$ 4.33703e6 0.153078
$$958$$ −1.85459e7 −0.652882
$$959$$ −5.63879e7 −1.97988
$$960$$ −3.38652e6 −0.118598
$$961$$ −1.96844e7 −0.687565
$$962$$ 8.77507e6 0.305712
$$963$$ 987424. 0.0343114
$$964$$ −5.19646e6 −0.180101
$$965$$ −1.35206e7 −0.467389
$$966$$ −2.72666e7 −0.940129
$$967$$ 4.33623e6 0.149123 0.0745617 0.997216i $$-0.476244\pi$$
0.0745617 + 0.997216i $$0.476244\pi$$
$$968$$ −2.01476e6 −0.0691091
$$969$$ −8.02448e6 −0.274541
$$970$$ 1.24307e7 0.424195
$$971$$ −5.44123e7 −1.85204 −0.926018 0.377480i $$-0.876791\pi$$
−0.926018 + 0.377480i $$0.876791\pi$$
$$972$$ −650675. −0.0220901
$$973$$ −4.54995e7 −1.54072
$$974$$ −3.73157e7 −1.26036
$$975$$ −957589. −0.0322602
$$976$$ 2.65244e7 0.891294
$$977$$ −3.16213e7 −1.05985 −0.529924 0.848045i $$-0.677780\pi$$
−0.529924 + 0.848045i $$0.677780\pi$$
$$978$$ −1.47662e7 −0.493651
$$979$$ 1.25184e7 0.417438
$$980$$ 1.28136e6 0.0426192
$$981$$ 983239. 0.0326202
$$982$$ 2.12321e7 0.702611
$$983$$ 1.31368e7 0.433617 0.216808 0.976214i $$-0.430435\pi$$
0.216808 + 0.976214i $$0.430435\pi$$
$$984$$ −6.44836e6 −0.212306
$$985$$ 1.20428e7 0.395491
$$986$$ 4.08750e7 1.33895
$$987$$ −9.03355e6 −0.295165
$$988$$ 1.06886e6 0.0348359
$$989$$ 4.37491e7 1.42226
$$990$$ −1.60710e6 −0.0521139
$$991$$ −3.53335e7 −1.14288 −0.571442 0.820643i $$-0.693616\pi$$
−0.571442 + 0.820643i $$0.693616\pi$$
$$992$$ −1.14521e7 −0.369493
$$993$$ 8.62603e6 0.277612
$$994$$ −5.05446e7 −1.62259
$$995$$ −2.53567e7 −0.811962
$$996$$ 461020. 0.0147256
$$997$$ 3.72145e7 1.18570 0.592850 0.805313i $$-0.298003\pi$$
0.592850 + 0.805313i $$0.298003\pi$$
$$998$$ −3.33563e7 −1.06011
$$999$$ −5.72915e6 −0.181625
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 165.6.a.d.1.3 3
3.2 odd 2 495.6.a.c.1.1 3
5.4 even 2 825.6.a.h.1.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.a.d.1.3 3 1.1 even 1 trivial
495.6.a.c.1.1 3 3.2 odd 2
825.6.a.h.1.1 3 5.4 even 2