# Properties

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

# Learn more

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: $$1$$ Dimension: $$3$$ Coefficient field: 3.3.18257.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - x^{2} - 26x + 8$$ x^3 - x^2 - 26*x + 8 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 1.3 Root $$-4.78415$$ 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)

 $$f(q)$$ $$=$$ $$q+5.78415 q^{2} -9.00000 q^{3} +1.45634 q^{4} +25.0000 q^{5} -52.0573 q^{6} +17.6498 q^{7} -176.669 q^{8} +81.0000 q^{9} +O(q^{10})$$ $$q+5.78415 q^{2} -9.00000 q^{3} +1.45634 q^{4} +25.0000 q^{5} -52.0573 q^{6} +17.6498 q^{7} -176.669 q^{8} +81.0000 q^{9} +144.604 q^{10} +121.000 q^{11} -13.1070 q^{12} +674.396 q^{13} +102.089 q^{14} -225.000 q^{15} -1068.48 q^{16} -2117.62 q^{17} +468.516 q^{18} -2307.79 q^{19} +36.4084 q^{20} -158.848 q^{21} +699.882 q^{22} -3072.47 q^{23} +1590.02 q^{24} +625.000 q^{25} +3900.80 q^{26} -729.000 q^{27} +25.7040 q^{28} -1437.44 q^{29} -1301.43 q^{30} -5157.66 q^{31} -526.846 q^{32} -1089.00 q^{33} -12248.6 q^{34} +441.244 q^{35} +117.963 q^{36} +6928.88 q^{37} -13348.6 q^{38} -6069.56 q^{39} -4416.72 q^{40} +2844.78 q^{41} -918.799 q^{42} -11665.3 q^{43} +176.217 q^{44} +2025.00 q^{45} -17771.6 q^{46} +3451.40 q^{47} +9616.34 q^{48} -16495.5 q^{49} +3615.09 q^{50} +19058.6 q^{51} +982.146 q^{52} -18167.6 q^{53} -4216.64 q^{54} +3025.00 q^{55} -3118.17 q^{56} +20770.1 q^{57} -8314.36 q^{58} -8976.88 q^{59} -327.675 q^{60} -378.820 q^{61} -29832.7 q^{62} +1429.63 q^{63} +31144.1 q^{64} +16859.9 q^{65} -6298.93 q^{66} -12233.7 q^{67} -3083.97 q^{68} +27652.2 q^{69} +2552.22 q^{70} +55867.0 q^{71} -14310.2 q^{72} +19739.6 q^{73} +40077.6 q^{74} -5625.00 q^{75} -3360.92 q^{76} +2135.62 q^{77} -35107.2 q^{78} -13495.8 q^{79} -26712.0 q^{80} +6561.00 q^{81} +16454.6 q^{82} +42078.3 q^{83} -231.336 q^{84} -52940.5 q^{85} -67474.0 q^{86} +12937.0 q^{87} -21376.9 q^{88} -81223.2 q^{89} +11712.9 q^{90} +11902.9 q^{91} -4474.55 q^{92} +46419.0 q^{93} +19963.4 q^{94} -57694.8 q^{95} +4741.62 q^{96} +152101. q^{97} -95412.3 q^{98} +9801.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10})$$ 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9 $$3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 378 q^{12} + 290 q^{13} + 916 q^{14} - 675 q^{15} - 590 q^{16} + 434 q^{17} + 162 q^{18} - 2856 q^{19} - 1050 q^{20} + 612 q^{21} + 242 q^{22} - 640 q^{23} + 216 q^{24} + 1875 q^{25} + 2132 q^{26} - 2187 q^{27} - 580 q^{28} - 4538 q^{29} - 450 q^{30} - 14968 q^{31} - 2496 q^{32} - 3267 q^{33} - 13704 q^{34} - 1700 q^{35} - 3402 q^{36} - 6190 q^{37} - 11668 q^{38} - 2610 q^{39} - 600 q^{40} - 8926 q^{41} - 8244 q^{42} - 33592 q^{43} - 5082 q^{44} + 6075 q^{45} - 35680 q^{46} - 24640 q^{47} + 5310 q^{48} - 14693 q^{49} + 1250 q^{50} - 3906 q^{51} + 18780 q^{52} - 22934 q^{53} - 1458 q^{54} + 9075 q^{55} - 40012 q^{56} + 25704 q^{57} - 32304 q^{58} - 13756 q^{59} + 9450 q^{60} + 24602 q^{61} - 7704 q^{62} - 5508 q^{63} + 35474 q^{64} + 7250 q^{65} - 2178 q^{66} + 16868 q^{67} - 71288 q^{68} + 5760 q^{69} + 22900 q^{70} + 4856 q^{71} - 1944 q^{72} + 1910 q^{73} + 29404 q^{74} - 16875 q^{75} + 6116 q^{76} - 8228 q^{77} - 19188 q^{78} - 36844 q^{79} - 14750 q^{80} + 19683 q^{81} + 84000 q^{82} - 48796 q^{83} + 5220 q^{84} + 10850 q^{85} - 83492 q^{86} + 40842 q^{87} - 2904 q^{88} - 188978 q^{89} + 4050 q^{90} - 93208 q^{91} - 6976 q^{92} + 134712 q^{93} + 70472 q^{94} - 71400 q^{95} + 22464 q^{96} + 247526 q^{97} - 154654 q^{98} + 29403 q^{99}+O(q^{100})$$ 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 378 * q^12 + 290 * q^13 + 916 * q^14 - 675 * q^15 - 590 * q^16 + 434 * q^17 + 162 * q^18 - 2856 * q^19 - 1050 * q^20 + 612 * q^21 + 242 * q^22 - 640 * q^23 + 216 * q^24 + 1875 * q^25 + 2132 * q^26 - 2187 * q^27 - 580 * q^28 - 4538 * q^29 - 450 * q^30 - 14968 * q^31 - 2496 * q^32 - 3267 * q^33 - 13704 * q^34 - 1700 * q^35 - 3402 * q^36 - 6190 * q^37 - 11668 * q^38 - 2610 * q^39 - 600 * q^40 - 8926 * q^41 - 8244 * q^42 - 33592 * q^43 - 5082 * q^44 + 6075 * q^45 - 35680 * q^46 - 24640 * q^47 + 5310 * q^48 - 14693 * q^49 + 1250 * q^50 - 3906 * q^51 + 18780 * q^52 - 22934 * q^53 - 1458 * q^54 + 9075 * q^55 - 40012 * q^56 + 25704 * q^57 - 32304 * q^58 - 13756 * q^59 + 9450 * q^60 + 24602 * q^61 - 7704 * q^62 - 5508 * q^63 + 35474 * q^64 + 7250 * q^65 - 2178 * q^66 + 16868 * q^67 - 71288 * q^68 + 5760 * q^69 + 22900 * q^70 + 4856 * q^71 - 1944 * q^72 + 1910 * q^73 + 29404 * q^74 - 16875 * q^75 + 6116 * q^76 - 8228 * q^77 - 19188 * q^78 - 36844 * q^79 - 14750 * q^80 + 19683 * q^81 + 84000 * q^82 - 48796 * q^83 + 5220 * q^84 + 10850 * q^85 - 83492 * q^86 + 40842 * q^87 - 2904 * q^88 - 188978 * q^89 + 4050 * q^90 - 93208 * q^91 - 6976 * q^92 + 134712 * q^93 + 70472 * q^94 - 71400 * q^95 + 22464 * q^96 + 247526 * q^97 - 154654 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 5.78415 1.02250 0.511251 0.859431i $$-0.329182\pi$$
0.511251 + 0.859431i $$0.329182\pi$$
$$3$$ −9.00000 −0.577350
$$4$$ 1.45634 0.0455105
$$5$$ 25.0000 0.447214
$$6$$ −52.0573 −0.590342
$$7$$ 17.6498 0.136143 0.0680713 0.997680i $$-0.478315\pi$$
0.0680713 + 0.997680i $$0.478315\pi$$
$$8$$ −176.669 −0.975968
$$9$$ 81.0000 0.333333
$$10$$ 144.604 0.457277
$$11$$ 121.000 0.301511
$$12$$ −13.1070 −0.0262755
$$13$$ 674.396 1.10677 0.553384 0.832926i $$-0.313336\pi$$
0.553384 + 0.832926i $$0.313336\pi$$
$$14$$ 102.089 0.139206
$$15$$ −225.000 −0.258199
$$16$$ −1068.48 −1.04344
$$17$$ −2117.62 −1.77716 −0.888579 0.458724i $$-0.848307\pi$$
−0.888579 + 0.458724i $$0.848307\pi$$
$$18$$ 468.516 0.340834
$$19$$ −2307.79 −1.46660 −0.733302 0.679903i $$-0.762022\pi$$
−0.733302 + 0.679903i $$0.762022\pi$$
$$20$$ 36.4084 0.0203529
$$21$$ −158.848 −0.0786019
$$22$$ 699.882 0.308296
$$23$$ −3072.47 −1.21107 −0.605534 0.795820i $$-0.707040\pi$$
−0.605534 + 0.795820i $$0.707040\pi$$
$$24$$ 1590.02 0.563475
$$25$$ 625.000 0.200000
$$26$$ 3900.80 1.13167
$$27$$ −729.000 −0.192450
$$28$$ 25.7040 0.00619591
$$29$$ −1437.44 −0.317391 −0.158696 0.987328i $$-0.550729\pi$$
−0.158696 + 0.987328i $$0.550729\pi$$
$$30$$ −1301.43 −0.264009
$$31$$ −5157.66 −0.963937 −0.481969 0.876188i $$-0.660078\pi$$
−0.481969 + 0.876188i $$0.660078\pi$$
$$32$$ −526.846 −0.0909513
$$33$$ −1089.00 −0.174078
$$34$$ −12248.6 −1.81715
$$35$$ 441.244 0.0608848
$$36$$ 117.963 0.0151702
$$37$$ 6928.88 0.832067 0.416034 0.909349i $$-0.363420\pi$$
0.416034 + 0.909349i $$0.363420\pi$$
$$38$$ −13348.6 −1.49961
$$39$$ −6069.56 −0.638993
$$40$$ −4416.72 −0.436466
$$41$$ 2844.78 0.264295 0.132147 0.991230i $$-0.457813\pi$$
0.132147 + 0.991230i $$0.457813\pi$$
$$42$$ −918.799 −0.0803706
$$43$$ −11665.3 −0.962113 −0.481057 0.876689i $$-0.659747\pi$$
−0.481057 + 0.876689i $$0.659747\pi$$
$$44$$ 176.217 0.0137219
$$45$$ 2025.00 0.149071
$$46$$ −17771.6 −1.23832
$$47$$ 3451.40 0.227903 0.113952 0.993486i $$-0.463649\pi$$
0.113952 + 0.993486i $$0.463649\pi$$
$$48$$ 9616.34 0.602430
$$49$$ −16495.5 −0.981465
$$50$$ 3615.09 0.204500
$$51$$ 19058.6 1.02604
$$52$$ 982.146 0.0503695
$$53$$ −18167.6 −0.888401 −0.444200 0.895927i $$-0.646512\pi$$
−0.444200 + 0.895927i $$0.646512\pi$$
$$54$$ −4216.64 −0.196781
$$55$$ 3025.00 0.134840
$$56$$ −3118.17 −0.132871
$$57$$ 20770.1 0.846744
$$58$$ −8314.36 −0.324533
$$59$$ −8976.88 −0.335734 −0.167867 0.985810i $$-0.553688\pi$$
−0.167867 + 0.985810i $$0.553688\pi$$
$$60$$ −327.675 −0.0117508
$$61$$ −378.820 −0.0130349 −0.00651746 0.999979i $$-0.502075\pi$$
−0.00651746 + 0.999979i $$0.502075\pi$$
$$62$$ −29832.7 −0.985628
$$63$$ 1429.63 0.0453808
$$64$$ 31144.1 0.950441
$$65$$ 16859.9 0.494962
$$66$$ −6298.93 −0.177995
$$67$$ −12233.7 −0.332945 −0.166473 0.986046i $$-0.553238\pi$$
−0.166473 + 0.986046i $$0.553238\pi$$
$$68$$ −3083.97 −0.0808793
$$69$$ 27652.2 0.699210
$$70$$ 2552.22 0.0622548
$$71$$ 55867.0 1.31525 0.657627 0.753344i $$-0.271560\pi$$
0.657627 + 0.753344i $$0.271560\pi$$
$$72$$ −14310.2 −0.325323
$$73$$ 19739.6 0.433541 0.216771 0.976223i $$-0.430448\pi$$
0.216771 + 0.976223i $$0.430448\pi$$
$$74$$ 40077.6 0.850791
$$75$$ −5625.00 −0.115470
$$76$$ −3360.92 −0.0667459
$$77$$ 2135.62 0.0410485
$$78$$ −35107.2 −0.653371
$$79$$ −13495.8 −0.243293 −0.121647 0.992573i $$-0.538817\pi$$
−0.121647 + 0.992573i $$0.538817\pi$$
$$80$$ −26712.0 −0.466640
$$81$$ 6561.00 0.111111
$$82$$ 16454.6 0.270242
$$83$$ 42078.3 0.670444 0.335222 0.942139i $$-0.391189\pi$$
0.335222 + 0.942139i $$0.391189\pi$$
$$84$$ −231.336 −0.00357721
$$85$$ −52940.5 −0.794769
$$86$$ −67474.0 −0.983763
$$87$$ 12937.0 0.183246
$$88$$ −21376.9 −0.294265
$$89$$ −81223.2 −1.08694 −0.543469 0.839429i $$-0.682890\pi$$
−0.543469 + 0.839429i $$0.682890\pi$$
$$90$$ 11712.9 0.152426
$$91$$ 11902.9 0.150678
$$92$$ −4474.55 −0.0551163
$$93$$ 46419.0 0.556530
$$94$$ 19963.4 0.233031
$$95$$ −57694.8 −0.655885
$$96$$ 4741.62 0.0525108
$$97$$ 152101. 1.64136 0.820680 0.571388i $$-0.193595\pi$$
0.820680 + 0.571388i $$0.193595\pi$$
$$98$$ −95412.3 −1.00355
$$99$$ 9801.00 0.100504
$$100$$ 910.210 0.00910210
$$101$$ 95207.6 0.928684 0.464342 0.885656i $$-0.346291\pi$$
0.464342 + 0.885656i $$0.346291\pi$$
$$102$$ 110238. 1.04913
$$103$$ −150824. −1.40081 −0.700403 0.713748i $$-0.746996\pi$$
−0.700403 + 0.713748i $$0.746996\pi$$
$$104$$ −119145. −1.08017
$$105$$ −3971.20 −0.0351518
$$106$$ −105084. −0.908392
$$107$$ 192242. 1.62327 0.811633 0.584168i $$-0.198579\pi$$
0.811633 + 0.584168i $$0.198579\pi$$
$$108$$ −1061.67 −0.00875850
$$109$$ 96302.8 0.776377 0.388188 0.921580i $$-0.373101\pi$$
0.388188 + 0.921580i $$0.373101\pi$$
$$110$$ 17497.0 0.137874
$$111$$ −62359.9 −0.480394
$$112$$ −18858.5 −0.142056
$$113$$ −210371. −1.54985 −0.774926 0.632052i $$-0.782213\pi$$
−0.774926 + 0.632052i $$0.782213\pi$$
$$114$$ 120138. 0.865798
$$115$$ −76811.8 −0.541606
$$116$$ −2093.39 −0.0144446
$$117$$ 54626.1 0.368923
$$118$$ −51923.6 −0.343289
$$119$$ −37375.5 −0.241947
$$120$$ 39750.5 0.251994
$$121$$ 14641.0 0.0909091
$$122$$ −2191.15 −0.0133282
$$123$$ −25603.0 −0.152591
$$124$$ −7511.29 −0.0438692
$$125$$ 15625.0 0.0894427
$$126$$ 8269.19 0.0464020
$$127$$ −63529.8 −0.349517 −0.174758 0.984611i $$-0.555914\pi$$
−0.174758 + 0.984611i $$0.555914\pi$$
$$128$$ 197001. 1.06278
$$129$$ 104988. 0.555476
$$130$$ 97520.1 0.506099
$$131$$ −88396.0 −0.450043 −0.225022 0.974354i $$-0.572245\pi$$
−0.225022 + 0.974354i $$0.572245\pi$$
$$132$$ −1585.95 −0.00792236
$$133$$ −40732.0 −0.199667
$$134$$ −70761.8 −0.340437
$$135$$ −18225.0 −0.0860663
$$136$$ 374118. 1.73445
$$137$$ −42642.4 −0.194106 −0.0970532 0.995279i $$-0.530942\pi$$
−0.0970532 + 0.995279i $$0.530942\pi$$
$$138$$ 159945. 0.714944
$$139$$ 169503. 0.744114 0.372057 0.928210i $$-0.378653\pi$$
0.372057 + 0.928210i $$0.378653\pi$$
$$140$$ 642.599 0.00277090
$$141$$ −31062.6 −0.131580
$$142$$ 323143. 1.34485
$$143$$ 81601.9 0.333703
$$144$$ −86547.0 −0.347813
$$145$$ −35936.0 −0.141942
$$146$$ 114176. 0.443297
$$147$$ 148459. 0.566649
$$148$$ 10090.8 0.0378678
$$149$$ −72462.8 −0.267393 −0.133696 0.991022i $$-0.542685\pi$$
−0.133696 + 0.991022i $$0.542685\pi$$
$$150$$ −32535.8 −0.118068
$$151$$ −61316.2 −0.218843 −0.109422 0.993995i $$-0.534900\pi$$
−0.109422 + 0.993995i $$0.534900\pi$$
$$152$$ 407716. 1.43136
$$153$$ −171527. −0.592386
$$154$$ 12352.7 0.0419722
$$155$$ −128942. −0.431086
$$156$$ −8839.32 −0.0290809
$$157$$ 505789. 1.63765 0.818824 0.574045i $$-0.194627\pi$$
0.818824 + 0.574045i $$0.194627\pi$$
$$158$$ −78061.5 −0.248768
$$159$$ 163509. 0.512919
$$160$$ −13171.2 −0.0406747
$$161$$ −54228.4 −0.164878
$$162$$ 37949.8 0.113611
$$163$$ 387702. 1.14295 0.571477 0.820618i $$-0.306371\pi$$
0.571477 + 0.820618i $$0.306371\pi$$
$$164$$ 4142.95 0.0120282
$$165$$ −27225.0 −0.0778499
$$166$$ 243387. 0.685530
$$167$$ −635422. −1.76308 −0.881538 0.472113i $$-0.843491\pi$$
−0.881538 + 0.472113i $$0.843491\pi$$
$$168$$ 28063.5 0.0767129
$$169$$ 83516.8 0.224935
$$170$$ −306216. −0.812653
$$171$$ −186931. −0.488868
$$172$$ −16988.6 −0.0437862
$$173$$ −679820. −1.72695 −0.863473 0.504395i $$-0.831716\pi$$
−0.863473 + 0.504395i $$0.831716\pi$$
$$174$$ 74829.3 0.187369
$$175$$ 11031.1 0.0272285
$$176$$ −129286. −0.314609
$$177$$ 80792.0 0.193836
$$178$$ −469807. −1.11140
$$179$$ −63083.3 −0.147157 −0.0735787 0.997289i $$-0.523442\pi$$
−0.0735787 + 0.997289i $$0.523442\pi$$
$$180$$ 2949.08 0.00678430
$$181$$ 523614. 1.18800 0.593998 0.804466i $$-0.297549\pi$$
0.593998 + 0.804466i $$0.297549\pi$$
$$182$$ 68848.3 0.154069
$$183$$ 3409.38 0.00752571
$$184$$ 542810. 1.18196
$$185$$ 173222. 0.372112
$$186$$ 268494. 0.569053
$$187$$ −256232. −0.535833
$$188$$ 5026.39 0.0103720
$$189$$ −12866.7 −0.0262006
$$190$$ −333715. −0.670644
$$191$$ −684311. −1.35728 −0.678641 0.734470i $$-0.737431\pi$$
−0.678641 + 0.734470i $$0.737431\pi$$
$$192$$ −280297. −0.548738
$$193$$ 527417. 1.01920 0.509601 0.860411i $$-0.329793\pi$$
0.509601 + 0.860411i $$0.329793\pi$$
$$194$$ 879777. 1.67829
$$195$$ −151739. −0.285766
$$196$$ −24023.0 −0.0446669
$$197$$ −467139. −0.857591 −0.428796 0.903402i $$-0.641062\pi$$
−0.428796 + 0.903402i $$0.641062\pi$$
$$198$$ 56690.4 0.102765
$$199$$ −436613. −0.781563 −0.390782 0.920483i $$-0.627795\pi$$
−0.390782 + 0.920483i $$0.627795\pi$$
$$200$$ −110418. −0.195194
$$201$$ 110104. 0.192226
$$202$$ 550694. 0.949581
$$203$$ −25370.5 −0.0432104
$$204$$ 27755.7 0.0466957
$$205$$ 71119.4 0.118196
$$206$$ −872389. −1.43233
$$207$$ −248870. −0.403689
$$208$$ −720580. −1.15484
$$209$$ −279243. −0.442198
$$210$$ −22970.0 −0.0359428
$$211$$ −747312. −1.15557 −0.577785 0.816189i $$-0.696083\pi$$
−0.577785 + 0.816189i $$0.696083\pi$$
$$212$$ −26458.2 −0.0404315
$$213$$ −502803. −0.759362
$$214$$ 1.11196e6 1.65979
$$215$$ −291634. −0.430270
$$216$$ 128792. 0.187825
$$217$$ −91031.6 −0.131233
$$218$$ 557029. 0.793847
$$219$$ −177656. −0.250305
$$220$$ 4405.41 0.00613663
$$221$$ −1.42812e6 −1.96690
$$222$$ −360699. −0.491204
$$223$$ 870654. 1.17242 0.586211 0.810159i $$-0.300619\pi$$
0.586211 + 0.810159i $$0.300619\pi$$
$$224$$ −9298.71 −0.0123823
$$225$$ 50625.0 0.0666667
$$226$$ −1.21682e6 −1.58473
$$227$$ 82323.8 0.106038 0.0530189 0.998594i $$-0.483116\pi$$
0.0530189 + 0.998594i $$0.483116\pi$$
$$228$$ 30248.3 0.0385357
$$229$$ −340134. −0.428609 −0.214305 0.976767i $$-0.568748\pi$$
−0.214305 + 0.976767i $$0.568748\pi$$
$$230$$ −444291. −0.553793
$$231$$ −19220.6 −0.0236994
$$232$$ 253951. 0.309763
$$233$$ −248384. −0.299732 −0.149866 0.988706i $$-0.547884\pi$$
−0.149866 + 0.988706i $$0.547884\pi$$
$$234$$ 315965. 0.377224
$$235$$ 86284.9 0.101921
$$236$$ −13073.4 −0.0152794
$$237$$ 121462. 0.140465
$$238$$ −216185. −0.247391
$$239$$ −1.37978e6 −1.56248 −0.781242 0.624229i $$-0.785413\pi$$
−0.781242 + 0.624229i $$0.785413\pi$$
$$240$$ 240408. 0.269415
$$241$$ −1.53382e6 −1.70110 −0.850552 0.525891i $$-0.823732\pi$$
−0.850552 + 0.525891i $$0.823732\pi$$
$$242$$ 84685.7 0.0929547
$$243$$ −59049.0 −0.0641500
$$244$$ −551.689 −0.000593225 0
$$245$$ −412387. −0.438925
$$246$$ −148091. −0.156024
$$247$$ −1.55637e6 −1.62319
$$248$$ 911199. 0.940772
$$249$$ −378704. −0.387081
$$250$$ 90377.3 0.0914554
$$251$$ 338591. 0.339227 0.169614 0.985511i $$-0.445748\pi$$
0.169614 + 0.985511i $$0.445748\pi$$
$$252$$ 2082.02 0.00206530
$$253$$ −371769. −0.365151
$$254$$ −367466. −0.357382
$$255$$ 476465. 0.458860
$$256$$ 142872. 0.136253
$$257$$ 1.60985e6 1.52038 0.760189 0.649702i $$-0.225106\pi$$
0.760189 + 0.649702i $$0.225106\pi$$
$$258$$ 607266. 0.567976
$$259$$ 122293. 0.113280
$$260$$ 24553.7 0.0225259
$$261$$ −116433. −0.105797
$$262$$ −511295. −0.460170
$$263$$ 458118. 0.408402 0.204201 0.978929i $$-0.434540\pi$$
0.204201 + 0.978929i $$0.434540\pi$$
$$264$$ 192393. 0.169894
$$265$$ −454191. −0.397305
$$266$$ −235600. −0.204160
$$267$$ 731009. 0.627544
$$268$$ −17816.4 −0.0151525
$$269$$ −692380. −0.583397 −0.291698 0.956510i $$-0.594220\pi$$
−0.291698 + 0.956510i $$0.594220\pi$$
$$270$$ −105416. −0.0880030
$$271$$ −486690. −0.402558 −0.201279 0.979534i $$-0.564510\pi$$
−0.201279 + 0.979534i $$0.564510\pi$$
$$272$$ 2.26264e6 1.85436
$$273$$ −107126. −0.0869941
$$274$$ −246650. −0.198474
$$275$$ 75625.0 0.0603023
$$276$$ 40270.9 0.0318214
$$277$$ 2.38271e6 1.86583 0.932915 0.360098i $$-0.117257\pi$$
0.932915 + 0.360098i $$0.117257\pi$$
$$278$$ 980428. 0.760858
$$279$$ −417771. −0.321312
$$280$$ −77954.1 −0.0594216
$$281$$ 1.12154e6 0.847320 0.423660 0.905821i $$-0.360745\pi$$
0.423660 + 0.905821i $$0.360745\pi$$
$$282$$ −179670. −0.134541
$$283$$ 965956. 0.716954 0.358477 0.933539i $$-0.383296\pi$$
0.358477 + 0.933539i $$0.383296\pi$$
$$284$$ 81361.1 0.0598578
$$285$$ 519254. 0.378676
$$286$$ 471997. 0.341212
$$287$$ 50209.6 0.0359817
$$288$$ −42674.5 −0.0303171
$$289$$ 3.06446e6 2.15829
$$290$$ −207859. −0.145136
$$291$$ −1.36891e6 −0.947640
$$292$$ 28747.4 0.0197307
$$293$$ 2.20819e6 1.50269 0.751343 0.659912i $$-0.229406\pi$$
0.751343 + 0.659912i $$0.229406\pi$$
$$294$$ 858711. 0.579400
$$295$$ −224422. −0.150145
$$296$$ −1.22412e6 −0.812071
$$297$$ −88209.0 −0.0580259
$$298$$ −419135. −0.273410
$$299$$ −2.07206e6 −1.34037
$$300$$ −8191.89 −0.00525510
$$301$$ −205891. −0.130985
$$302$$ −354662. −0.223768
$$303$$ −856868. −0.536176
$$304$$ 2.46584e6 1.53031
$$305$$ −9470.49 −0.00582939
$$306$$ −992139. −0.605716
$$307$$ 805480. 0.487763 0.243881 0.969805i $$-0.421579\pi$$
0.243881 + 0.969805i $$0.421579\pi$$
$$308$$ 3110.18 0.00186814
$$309$$ 1.35742e6 0.808756
$$310$$ −745817. −0.440786
$$311$$ −870766. −0.510505 −0.255253 0.966874i $$-0.582159\pi$$
−0.255253 + 0.966874i $$0.582159\pi$$
$$312$$ 1.07230e6 0.623636
$$313$$ −3.16630e6 −1.82680 −0.913400 0.407063i $$-0.866553\pi$$
−0.913400 + 0.407063i $$0.866553\pi$$
$$314$$ 2.92556e6 1.67450
$$315$$ 35740.8 0.0202949
$$316$$ −19654.4 −0.0110724
$$317$$ 1.72288e6 0.962955 0.481478 0.876458i $$-0.340100\pi$$
0.481478 + 0.876458i $$0.340100\pi$$
$$318$$ 945759. 0.524460
$$319$$ −173930. −0.0956970
$$320$$ 778602. 0.425050
$$321$$ −1.73018e6 −0.937193
$$322$$ −313665. −0.168588
$$323$$ 4.88703e6 2.60639
$$324$$ 9555.02 0.00505672
$$325$$ 421497. 0.221354
$$326$$ 2.24252e6 1.16867
$$327$$ −866725. −0.448241
$$328$$ −502584. −0.257943
$$329$$ 60916.3 0.0310273
$$330$$ −157473. −0.0796017
$$331$$ −3.20493e6 −1.60786 −0.803932 0.594722i $$-0.797262\pi$$
−0.803932 + 0.594722i $$0.797262\pi$$
$$332$$ 61280.1 0.0305122
$$333$$ 561239. 0.277356
$$334$$ −3.67537e6 −1.80275
$$335$$ −305844. −0.148898
$$336$$ 169726. 0.0820163
$$337$$ 2.44638e6 1.17341 0.586703 0.809802i $$-0.300425\pi$$
0.586703 + 0.809802i $$0.300425\pi$$
$$338$$ 483073. 0.229996
$$339$$ 1.89334e6 0.894807
$$340$$ −77099.2 −0.0361703
$$341$$ −624077. −0.290638
$$342$$ −1.08124e6 −0.499869
$$343$$ −587781. −0.269762
$$344$$ 2.06090e6 0.938992
$$345$$ 691306. 0.312696
$$346$$ −3.93218e6 −1.76581
$$347$$ −3.05055e6 −1.36005 −0.680025 0.733189i $$-0.738031\pi$$
−0.680025 + 0.733189i $$0.738031\pi$$
$$348$$ 18840.5 0.00833960
$$349$$ −3.08755e6 −1.35691 −0.678454 0.734643i $$-0.737350\pi$$
−0.678454 + 0.734643i $$0.737350\pi$$
$$350$$ 63805.5 0.0278412
$$351$$ −491635. −0.212998
$$352$$ −63748.4 −0.0274228
$$353$$ 2.98932e6 1.27684 0.638418 0.769690i $$-0.279589\pi$$
0.638418 + 0.769690i $$0.279589\pi$$
$$354$$ 467312. 0.198198
$$355$$ 1.39668e6 0.588200
$$356$$ −118288. −0.0494671
$$357$$ 336380. 0.139688
$$358$$ −364883. −0.150469
$$359$$ −2.29991e6 −0.941836 −0.470918 0.882177i $$-0.656077\pi$$
−0.470918 + 0.882177i $$0.656077\pi$$
$$360$$ −357755. −0.145489
$$361$$ 2.84981e6 1.15093
$$362$$ 3.02866e6 1.21473
$$363$$ −131769. −0.0524864
$$364$$ 17334.7 0.00685743
$$365$$ 493489. 0.193885
$$366$$ 19720.3 0.00769505
$$367$$ 3.58207e6 1.38825 0.694127 0.719852i $$-0.255790\pi$$
0.694127 + 0.719852i $$0.255790\pi$$
$$368$$ 3.28288e6 1.26368
$$369$$ 230427. 0.0880982
$$370$$ 1.00194e6 0.380485
$$371$$ −320655. −0.120949
$$372$$ 67601.6 0.0253279
$$373$$ 511254. 0.190268 0.0951338 0.995464i $$-0.469672\pi$$
0.0951338 + 0.995464i $$0.469672\pi$$
$$374$$ −1.48208e6 −0.547891
$$375$$ −140625. −0.0516398
$$376$$ −609755. −0.222426
$$377$$ −969404. −0.351278
$$378$$ −74422.7 −0.0267902
$$379$$ 2.45209e6 0.876877 0.438438 0.898761i $$-0.355532\pi$$
0.438438 + 0.898761i $$0.355532\pi$$
$$380$$ −84023.0 −0.0298497
$$381$$ 571768. 0.201794
$$382$$ −3.95815e6 −1.38782
$$383$$ −1.46315e6 −0.509674 −0.254837 0.966984i $$-0.582022\pi$$
−0.254837 + 0.966984i $$0.582022\pi$$
$$384$$ −1.77301e6 −0.613596
$$385$$ 53390.5 0.0183575
$$386$$ 3.05065e6 1.04214
$$387$$ −944893. −0.320704
$$388$$ 221511. 0.0746991
$$389$$ −803978. −0.269383 −0.134691 0.990888i $$-0.543004\pi$$
−0.134691 + 0.990888i $$0.543004\pi$$
$$390$$ −877681. −0.292197
$$391$$ 6.50633e6 2.15226
$$392$$ 2.91424e6 0.957878
$$393$$ 795564. 0.259833
$$394$$ −2.70200e6 −0.876889
$$395$$ −337394. −0.108804
$$396$$ 14273.5 0.00457397
$$397$$ −2.87304e6 −0.914883 −0.457441 0.889240i $$-0.651234\pi$$
−0.457441 + 0.889240i $$0.651234\pi$$
$$398$$ −2.52543e6 −0.799150
$$399$$ 366588. 0.115278
$$400$$ −667801. −0.208688
$$401$$ −3.45072e6 −1.07164 −0.535820 0.844332i $$-0.679998\pi$$
−0.535820 + 0.844332i $$0.679998\pi$$
$$402$$ 636856. 0.196551
$$403$$ −3.47831e6 −1.06685
$$404$$ 138654. 0.0422649
$$405$$ 164025. 0.0496904
$$406$$ −146747. −0.0441827
$$407$$ 838394. 0.250878
$$408$$ −3.36706e6 −1.00138
$$409$$ −1.17776e6 −0.348136 −0.174068 0.984734i $$-0.555691\pi$$
−0.174068 + 0.984734i $$0.555691\pi$$
$$410$$ 411365. 0.120856
$$411$$ 383781. 0.112067
$$412$$ −219651. −0.0637513
$$413$$ −158440. −0.0457077
$$414$$ −1.43950e6 −0.412773
$$415$$ 1.05196e6 0.299832
$$416$$ −355303. −0.100662
$$417$$ −1.52552e6 −0.429614
$$418$$ −1.61518e6 −0.452148
$$419$$ −443011. −0.123276 −0.0616381 0.998099i $$-0.519632\pi$$
−0.0616381 + 0.998099i $$0.519632\pi$$
$$420$$ −5783.39 −0.00159978
$$421$$ −3.41894e6 −0.940127 −0.470063 0.882633i $$-0.655769\pi$$
−0.470063 + 0.882633i $$0.655769\pi$$
$$422$$ −4.32256e6 −1.18157
$$423$$ 279563. 0.0759677
$$424$$ 3.20966e6 0.867050
$$425$$ −1.32351e6 −0.355432
$$426$$ −2.90829e6 −0.776450
$$427$$ −6686.08 −0.00177461
$$428$$ 279969. 0.0738756
$$429$$ −734417. −0.192664
$$430$$ −1.68685e6 −0.439952
$$431$$ −4.24640e6 −1.10110 −0.550551 0.834801i $$-0.685583\pi$$
−0.550551 + 0.834801i $$0.685583\pi$$
$$432$$ 778923. 0.200810
$$433$$ −1.03407e6 −0.265050 −0.132525 0.991180i $$-0.542309\pi$$
−0.132525 + 0.991180i $$0.542309\pi$$
$$434$$ −526540. −0.134186
$$435$$ 323424. 0.0819500
$$436$$ 140249. 0.0353333
$$437$$ 7.09063e6 1.77616
$$438$$ −1.02759e6 −0.255937
$$439$$ 3.55155e6 0.879542 0.439771 0.898110i $$-0.355060\pi$$
0.439771 + 0.898110i $$0.355060\pi$$
$$440$$ −534424. −0.131599
$$441$$ −1.33613e6 −0.327155
$$442$$ −8.26043e6 −2.01116
$$443$$ 2.35135e6 0.569257 0.284629 0.958638i $$-0.408130\pi$$
0.284629 + 0.958638i $$0.408130\pi$$
$$444$$ −90816.9 −0.0218630
$$445$$ −2.03058e6 −0.486094
$$446$$ 5.03599e6 1.19880
$$447$$ 652165. 0.154379
$$448$$ 549685. 0.129395
$$449$$ 3.01947e6 0.706831 0.353415 0.935467i $$-0.385020\pi$$
0.353415 + 0.935467i $$0.385020\pi$$
$$450$$ 292822. 0.0681668
$$451$$ 344218. 0.0796878
$$452$$ −306371. −0.0705345
$$453$$ 551846. 0.126349
$$454$$ 476173. 0.108424
$$455$$ 297573. 0.0673853
$$456$$ −3.66944e6 −0.826395
$$457$$ 3.80671e6 0.852626 0.426313 0.904576i $$-0.359812\pi$$
0.426313 + 0.904576i $$0.359812\pi$$
$$458$$ −1.96738e6 −0.438254
$$459$$ 1.54375e6 0.342014
$$460$$ −111864. −0.0246487
$$461$$ 7.43481e6 1.62936 0.814680 0.579910i $$-0.196912\pi$$
0.814680 + 0.579910i $$0.196912\pi$$
$$462$$ −111175. −0.0242327
$$463$$ −108747. −0.0235757 −0.0117879 0.999931i $$-0.503752\pi$$
−0.0117879 + 0.999931i $$0.503752\pi$$
$$464$$ 1.53588e6 0.331178
$$465$$ 1.16047e6 0.248888
$$466$$ −1.43669e6 −0.306477
$$467$$ −6.85473e6 −1.45445 −0.727224 0.686400i $$-0.759190\pi$$
−0.727224 + 0.686400i $$0.759190\pi$$
$$468$$ 79553.9 0.0167898
$$469$$ −215923. −0.0453280
$$470$$ 499085. 0.104215
$$471$$ −4.55210e6 −0.945496
$$472$$ 1.58594e6 0.327666
$$473$$ −1.41151e6 −0.290088
$$474$$ 702554. 0.143626
$$475$$ −1.44237e6 −0.293321
$$476$$ −54431.3 −0.0110111
$$477$$ −1.47158e6 −0.296134
$$478$$ −7.98085e6 −1.59764
$$479$$ −9.48659e6 −1.88917 −0.944585 0.328266i $$-0.893536\pi$$
−0.944585 + 0.328266i $$0.893536\pi$$
$$480$$ 118540. 0.0234835
$$481$$ 4.67281e6 0.920905
$$482$$ −8.87182e6 −1.73938
$$483$$ 488056. 0.0951922
$$484$$ 21322.2 0.00413732
$$485$$ 3.80253e6 0.734038
$$486$$ −341548. −0.0655935
$$487$$ 9.79771e6 1.87198 0.935992 0.352021i $$-0.114506\pi$$
0.935992 + 0.352021i $$0.114506\pi$$
$$488$$ 66925.7 0.0127216
$$489$$ −3.48932e6 −0.659885
$$490$$ −2.38531e6 −0.448801
$$491$$ 9.17094e6 1.71676 0.858381 0.513012i $$-0.171470\pi$$
0.858381 + 0.513012i $$0.171470\pi$$
$$492$$ −37286.5 −0.00694447
$$493$$ 3.04395e6 0.564054
$$494$$ −9.00225e6 −1.65972
$$495$$ 245025. 0.0449467
$$496$$ 5.51087e6 1.00581
$$497$$ 986040. 0.179062
$$498$$ −2.19048e6 −0.395791
$$499$$ −1.91031e6 −0.343441 −0.171720 0.985146i $$-0.554933\pi$$
−0.171720 + 0.985146i $$0.554933\pi$$
$$500$$ 22755.2 0.00407058
$$501$$ 5.71880e6 1.01791
$$502$$ 1.95846e6 0.346861
$$503$$ 7.08413e6 1.24844 0.624219 0.781250i $$-0.285417\pi$$
0.624219 + 0.781250i $$0.285417\pi$$
$$504$$ −252571. −0.0442902
$$505$$ 2.38019e6 0.415320
$$506$$ −2.15037e6 −0.373367
$$507$$ −751651. −0.129866
$$508$$ −92520.7 −0.0159067
$$509$$ −7.51321e6 −1.28538 −0.642689 0.766127i $$-0.722181\pi$$
−0.642689 + 0.766127i $$0.722181\pi$$
$$510$$ 2.75594e6 0.469186
$$511$$ 348398. 0.0590234
$$512$$ −5.47764e6 −0.923461
$$513$$ 1.68238e6 0.282248
$$514$$ 9.31158e6 1.55459
$$515$$ −3.77060e6 −0.626459
$$516$$ 152898. 0.0252800
$$517$$ 417619. 0.0687154
$$518$$ 707361. 0.115829
$$519$$ 6.11838e6 0.997053
$$520$$ −2.97862e6 −0.483066
$$521$$ −1.03994e7 −1.67847 −0.839235 0.543770i $$-0.816997\pi$$
−0.839235 + 0.543770i $$0.816997\pi$$
$$522$$ −673463. −0.108178
$$523$$ −9.14037e6 −1.46120 −0.730600 0.682806i $$-0.760759\pi$$
−0.730600 + 0.682806i $$0.760759\pi$$
$$524$$ −128734. −0.0204817
$$525$$ −99279.9 −0.0157204
$$526$$ 2.64982e6 0.417592
$$527$$ 1.09220e7 1.71307
$$528$$ 1.16358e6 0.181639
$$529$$ 3.00374e6 0.466684
$$530$$ −2.62711e6 −0.406245
$$531$$ −727128. −0.111911
$$532$$ −59319.5 −0.00908695
$$533$$ 1.91850e6 0.292513
$$534$$ 4.22826e6 0.641665
$$535$$ 4.80606e6 0.725947
$$536$$ 2.16132e6 0.324944
$$537$$ 567750. 0.0849613
$$538$$ −4.00483e6 −0.596524
$$539$$ −1.99595e6 −0.295923
$$540$$ −26541.7 −0.00391692
$$541$$ 6.47380e6 0.950969 0.475484 0.879724i $$-0.342273\pi$$
0.475484 + 0.879724i $$0.342273\pi$$
$$542$$ −2.81508e6 −0.411617
$$543$$ −4.71253e6 −0.685890
$$544$$ 1.11566e6 0.161635
$$545$$ 2.40757e6 0.347206
$$546$$ −619634. −0.0889516
$$547$$ −226463. −0.0323616 −0.0161808 0.999869i $$-0.505151\pi$$
−0.0161808 + 0.999869i $$0.505151\pi$$
$$548$$ −62101.6 −0.00883388
$$549$$ −30684.4 −0.00434497
$$550$$ 437426. 0.0616592
$$551$$ 3.31731e6 0.465487
$$552$$ −4.88529e6 −0.682406
$$553$$ −238197. −0.0331226
$$554$$ 1.37819e7 1.90781
$$555$$ −1.55900e6 −0.214839
$$556$$ 246853. 0.0338650
$$557$$ −5.45555e6 −0.745076 −0.372538 0.928017i $$-0.621512\pi$$
−0.372538 + 0.928017i $$0.621512\pi$$
$$558$$ −2.41645e6 −0.328543
$$559$$ −7.86706e6 −1.06484
$$560$$ −471461. −0.0635296
$$561$$ 2.30609e6 0.309364
$$562$$ 6.48712e6 0.866386
$$563$$ −1.30266e7 −1.73205 −0.866024 0.500002i $$-0.833333\pi$$
−0.866024 + 0.500002i $$0.833333\pi$$
$$564$$ −45237.5 −0.00598827
$$565$$ −5.25928e6 −0.693115
$$566$$ 5.58723e6 0.733087
$$567$$ 115800. 0.0151269
$$568$$ −9.86997e6 −1.28365
$$569$$ 3.02736e6 0.391998 0.195999 0.980604i $$-0.437205\pi$$
0.195999 + 0.980604i $$0.437205\pi$$
$$570$$ 3.00344e6 0.387197
$$571$$ 9.79560e6 1.25731 0.628653 0.777686i $$-0.283607\pi$$
0.628653 + 0.777686i $$0.283607\pi$$
$$572$$ 118840. 0.0151870
$$573$$ 6.15880e6 0.783627
$$574$$ 290420. 0.0367914
$$575$$ −1.92029e6 −0.242213
$$576$$ 2.52267e6 0.316814
$$577$$ 56282.7 0.00703778 0.00351889 0.999994i $$-0.498880\pi$$
0.00351889 + 0.999994i $$0.498880\pi$$
$$578$$ 1.77253e7 2.20686
$$579$$ −4.74675e6 −0.588437
$$580$$ −52334.9 −0.00645983
$$581$$ 742671. 0.0912759
$$582$$ −7.91799e6 −0.968963
$$583$$ −2.19829e6 −0.267863
$$584$$ −3.48737e6 −0.423122
$$585$$ 1.36565e6 0.164987
$$586$$ 1.27725e7 1.53650
$$587$$ −7.92842e6 −0.949711 −0.474855 0.880064i $$-0.657500\pi$$
−0.474855 + 0.880064i $$0.657500\pi$$
$$588$$ 216207. 0.0257885
$$589$$ 1.19028e7 1.41371
$$590$$ −1.29809e6 −0.153523
$$591$$ 4.20425e6 0.495130
$$592$$ −7.40338e6 −0.868212
$$593$$ −5.11910e6 −0.597801 −0.298900 0.954284i $$-0.596620\pi$$
−0.298900 + 0.954284i $$0.596620\pi$$
$$594$$ −510214. −0.0593316
$$595$$ −934388. −0.108202
$$596$$ −105530. −0.0121692
$$597$$ 3.92952e6 0.451236
$$598$$ −1.19851e7 −1.37053
$$599$$ −1.00831e7 −1.14822 −0.574110 0.818778i $$-0.694652\pi$$
−0.574110 + 0.818778i $$0.694652\pi$$
$$600$$ 993763. 0.112695
$$601$$ 1.32233e7 1.49332 0.746659 0.665207i $$-0.231657\pi$$
0.746659 + 0.665207i $$0.231657\pi$$
$$602$$ −1.19090e6 −0.133932
$$603$$ −990934. −0.110982
$$604$$ −89296.9 −0.00995965
$$605$$ 366025. 0.0406558
$$606$$ −4.95625e6 −0.548241
$$607$$ 937160. 0.103239 0.0516193 0.998667i $$-0.483562\pi$$
0.0516193 + 0.998667i $$0.483562\pi$$
$$608$$ 1.21585e6 0.133390
$$609$$ 228334. 0.0249475
$$610$$ −54778.7 −0.00596056
$$611$$ 2.32761e6 0.252236
$$612$$ −249801. −0.0269598
$$613$$ 3.05919e6 0.328818 0.164409 0.986392i $$-0.447428\pi$$
0.164409 + 0.986392i $$0.447428\pi$$
$$614$$ 4.65901e6 0.498738
$$615$$ −640074. −0.0682406
$$616$$ −377298. −0.0400620
$$617$$ 8.74474e6 0.924771 0.462385 0.886679i $$-0.346994\pi$$
0.462385 + 0.886679i $$0.346994\pi$$
$$618$$ 7.85150e6 0.826954
$$619$$ −4.14486e6 −0.434793 −0.217397 0.976083i $$-0.569757\pi$$
−0.217397 + 0.976083i $$0.569757\pi$$
$$620$$ −187782. −0.0196189
$$621$$ 2.23983e6 0.233070
$$622$$ −5.03664e6 −0.521993
$$623$$ −1.43357e6 −0.147979
$$624$$ 6.48522e6 0.666750
$$625$$ 390625. 0.0400000
$$626$$ −1.83143e7 −1.86791
$$627$$ 2.51319e6 0.255303
$$628$$ 736598. 0.0745301
$$629$$ −1.46727e7 −1.47872
$$630$$ 206730. 0.0207516
$$631$$ −4.44508e6 −0.444433 −0.222216 0.974997i $$-0.571329\pi$$
−0.222216 + 0.974997i $$0.571329\pi$$
$$632$$ 2.38429e6 0.237446
$$633$$ 6.72581e6 0.667168
$$634$$ 9.96537e6 0.984624
$$635$$ −1.58825e6 −0.156309
$$636$$ 238124. 0.0233432
$$637$$ −1.11245e7 −1.08625
$$638$$ −1.00604e6 −0.0978504
$$639$$ 4.52523e6 0.438418
$$640$$ 4.92502e6 0.475289
$$641$$ 1.08278e7 1.04086 0.520432 0.853903i $$-0.325771\pi$$
0.520432 + 0.853903i $$0.325771\pi$$
$$642$$ −1.00076e7 −0.958282
$$643$$ −1.23064e7 −1.17383 −0.586915 0.809649i $$-0.699658\pi$$
−0.586915 + 0.809649i $$0.699658\pi$$
$$644$$ −78974.7 −0.00750367
$$645$$ 2.62470e6 0.248417
$$646$$ 2.82673e7 2.66504
$$647$$ −1.26477e7 −1.18782 −0.593912 0.804530i $$-0.702417\pi$$
−0.593912 + 0.804530i $$0.702417\pi$$
$$648$$ −1.15913e6 −0.108441
$$649$$ −1.08620e6 −0.101228
$$650$$ 2.43800e6 0.226334
$$651$$ 819284. 0.0757673
$$652$$ 564624. 0.0520164
$$653$$ −578855. −0.0531235 −0.0265618 0.999647i $$-0.508456\pi$$
−0.0265618 + 0.999647i $$0.508456\pi$$
$$654$$ −5.01326e6 −0.458328
$$655$$ −2.20990e6 −0.201265
$$656$$ −3.03959e6 −0.275775
$$657$$ 1.59890e6 0.144514
$$658$$ 352349. 0.0317255
$$659$$ 1.71481e7 1.53816 0.769081 0.639151i $$-0.220714\pi$$
0.769081 + 0.639151i $$0.220714\pi$$
$$660$$ −39648.7 −0.00354299
$$661$$ 6.99329e6 0.622555 0.311278 0.950319i $$-0.399243\pi$$
0.311278 + 0.950319i $$0.399243\pi$$
$$662$$ −1.85378e7 −1.64404
$$663$$ 1.28530e7 1.13559
$$664$$ −7.43392e6 −0.654332
$$665$$ −1.01830e6 −0.0892939
$$666$$ 3.24629e6 0.283597
$$667$$ 4.41649e6 0.384382
$$668$$ −925387. −0.0802384
$$669$$ −7.83589e6 −0.676898
$$670$$ −1.76904e6 −0.152248
$$671$$ −45837.2 −0.00393017
$$672$$ 83688.4 0.00714895
$$673$$ 1.98109e7 1.68604 0.843018 0.537885i $$-0.180777\pi$$
0.843018 + 0.537885i $$0.180777\pi$$
$$674$$ 1.41502e7 1.19981
$$675$$ −455625. −0.0384900
$$676$$ 121628. 0.0102369
$$677$$ −2.85012e6 −0.238996 −0.119498 0.992834i $$-0.538129\pi$$
−0.119498 + 0.992834i $$0.538129\pi$$
$$678$$ 1.09514e7 0.914942
$$679$$ 2.68455e6 0.223459
$$680$$ 9.35295e6 0.775669
$$681$$ −740914. −0.0612210
$$682$$ −3.60975e6 −0.297178
$$683$$ 4.58865e6 0.376386 0.188193 0.982132i $$-0.439737\pi$$
0.188193 + 0.982132i $$0.439737\pi$$
$$684$$ −272235. −0.0222486
$$685$$ −1.06606e6 −0.0868070
$$686$$ −3.39981e6 −0.275832
$$687$$ 3.06121e6 0.247458
$$688$$ 1.24642e7 1.00391
$$689$$ −1.22522e7 −0.983254
$$690$$ 3.99862e6 0.319733
$$691$$ −2.65609e6 −0.211616 −0.105808 0.994387i $$-0.533743\pi$$
−0.105808 + 0.994387i $$0.533743\pi$$
$$692$$ −990046. −0.0785942
$$693$$ 172985. 0.0136828
$$694$$ −1.76448e7 −1.39065
$$695$$ 4.23757e6 0.332778
$$696$$ −2.28556e6 −0.178842
$$697$$ −6.02416e6 −0.469693
$$698$$ −1.78588e7 −1.38744
$$699$$ 2.23546e6 0.173051
$$700$$ 16065.0 0.00123918
$$701$$ −7.90907e6 −0.607898 −0.303949 0.952688i $$-0.598305\pi$$
−0.303949 + 0.952688i $$0.598305\pi$$
$$702$$ −2.84369e6 −0.217790
$$703$$ −1.59904e7 −1.22031
$$704$$ 3.76843e6 0.286569
$$705$$ −776564. −0.0588443
$$706$$ 1.72906e7 1.30557
$$707$$ 1.68039e6 0.126433
$$708$$ 117660. 0.00882158
$$709$$ −2.38057e7 −1.77855 −0.889273 0.457378i $$-0.848789\pi$$
−0.889273 + 0.457378i $$0.848789\pi$$
$$710$$ 8.07857e6 0.601435
$$711$$ −1.09316e6 −0.0810978
$$712$$ 1.43496e7 1.06082
$$713$$ 1.58468e7 1.16739
$$714$$ 1.94567e6 0.142831
$$715$$ 2.04005e6 0.149237
$$716$$ −91870.5 −0.00669720
$$717$$ 1.24180e7 0.902100
$$718$$ −1.33030e7 −0.963029
$$719$$ −2.00866e7 −1.44905 −0.724527 0.689246i $$-0.757942\pi$$
−0.724527 + 0.689246i $$0.757942\pi$$
$$720$$ −2.16368e6 −0.155547
$$721$$ −2.66201e6 −0.190709
$$722$$ 1.64837e7 1.17683
$$723$$ 1.38043e7 0.982133
$$724$$ 762558. 0.0540663
$$725$$ −898400. −0.0634782
$$726$$ −762171. −0.0536674
$$727$$ −1.00897e7 −0.708012 −0.354006 0.935243i $$-0.615181\pi$$
−0.354006 + 0.935243i $$0.615181\pi$$
$$728$$ −2.10288e6 −0.147057
$$729$$ 531441. 0.0370370
$$730$$ 2.85441e6 0.198248
$$731$$ 2.47028e7 1.70983
$$732$$ 4965.20 0.000342499 0
$$733$$ −1.48230e7 −1.01901 −0.509504 0.860468i $$-0.670171\pi$$
−0.509504 + 0.860468i $$0.670171\pi$$
$$734$$ 2.07192e7 1.41949
$$735$$ 3.71148e6 0.253413
$$736$$ 1.61872e6 0.110148
$$737$$ −1.48028e6 −0.100387
$$738$$ 1.33282e6 0.0900806
$$739$$ −1.85393e7 −1.24877 −0.624383 0.781118i $$-0.714650\pi$$
−0.624383 + 0.781118i $$0.714650\pi$$
$$740$$ 252269. 0.0169350
$$741$$ 1.40073e7 0.937149
$$742$$ −1.85471e6 −0.123671
$$743$$ −8.68829e6 −0.577381 −0.288690 0.957423i $$-0.593220\pi$$
−0.288690 + 0.957423i $$0.593220\pi$$
$$744$$ −8.20079e6 −0.543155
$$745$$ −1.81157e6 −0.119582
$$746$$ 2.95717e6 0.194549
$$747$$ 3.40834e6 0.223481
$$748$$ −373160. −0.0243860
$$749$$ 3.39303e6 0.220995
$$750$$ −813395. −0.0528018
$$751$$ −1.37377e7 −0.888821 −0.444411 0.895823i $$-0.646587\pi$$
−0.444411 + 0.895823i $$0.646587\pi$$
$$752$$ −3.68776e6 −0.237803
$$753$$ −3.04732e6 −0.195853
$$754$$ −5.60717e6 −0.359183
$$755$$ −1.53291e6 −0.0978696
$$756$$ −18738.2 −0.00119240
$$757$$ 5.59097e6 0.354607 0.177304 0.984156i $$-0.443263\pi$$
0.177304 + 0.984156i $$0.443263\pi$$
$$758$$ 1.41832e7 0.896608
$$759$$ 3.34592e6 0.210820
$$760$$ 1.01929e7 0.640123
$$761$$ −2.44147e7 −1.52823 −0.764117 0.645078i $$-0.776825\pi$$
−0.764117 + 0.645078i $$0.776825\pi$$
$$762$$ 3.30719e6 0.206334
$$763$$ 1.69972e6 0.105698
$$764$$ −996586. −0.0617706
$$765$$ −4.28818e6 −0.264923
$$766$$ −8.46309e6 −0.521143
$$767$$ −6.05397e6 −0.371580
$$768$$ −1.28584e6 −0.0786657
$$769$$ 1.99742e7 1.21802 0.609008 0.793164i $$-0.291568\pi$$
0.609008 + 0.793164i $$0.291568\pi$$
$$770$$ 308819. 0.0187705
$$771$$ −1.44886e7 −0.877790
$$772$$ 768096. 0.0463844
$$773$$ −2.64430e7 −1.59170 −0.795852 0.605492i $$-0.792976\pi$$
−0.795852 + 0.605492i $$0.792976\pi$$
$$774$$ −5.46540e6 −0.327921
$$775$$ −3.22354e6 −0.192787
$$776$$ −2.68716e7 −1.60191
$$777$$ −1.10064e6 −0.0654021
$$778$$ −4.65032e6 −0.275445
$$779$$ −6.56515e6 −0.387616
$$780$$ −220983. −0.0130054
$$781$$ 6.75991e6 0.396564
$$782$$ 3.76336e7 2.20069
$$783$$ 1.04789e6 0.0610819
$$784$$ 1.76251e7 1.02410
$$785$$ 1.26447e7 0.732378
$$786$$ 4.60166e6 0.265679
$$787$$ −2.87892e6 −0.165689 −0.0828443 0.996562i $$-0.526400\pi$$
−0.0828443 + 0.996562i $$0.526400\pi$$
$$788$$ −680310. −0.0390294
$$789$$ −4.12306e6 −0.235791
$$790$$ −1.95154e6 −0.111252
$$791$$ −3.71300e6 −0.211001
$$792$$ −1.73153e6 −0.0980884
$$793$$ −255474. −0.0144266
$$794$$ −1.66181e7 −0.935469
$$795$$ 4.08772e6 0.229384
$$796$$ −635855. −0.0355693
$$797$$ −2.55634e7 −1.42552 −0.712759 0.701409i $$-0.752554\pi$$
−0.712759 + 0.701409i $$0.752554\pi$$
$$798$$ 2.12040e6 0.117872
$$799$$ −7.30875e6 −0.405020
$$800$$ −329279. −0.0181903
$$801$$ −6.57908e6 −0.362313
$$802$$ −1.99595e7 −1.09575
$$803$$ 2.38849e6 0.130718
$$804$$ 160348. 0.00874829
$$805$$ −1.35571e6 −0.0737356
$$806$$ −2.01190e7 −1.09086
$$807$$ 6.23142e6 0.336824
$$808$$ −1.68202e7 −0.906365
$$809$$ −2.32458e6 −0.124874 −0.0624371 0.998049i $$-0.519887\pi$$
−0.0624371 + 0.998049i $$0.519887\pi$$
$$810$$ 948744. 0.0508085
$$811$$ 1.44240e7 0.770076 0.385038 0.922901i $$-0.374188\pi$$
0.385038 + 0.922901i $$0.374188\pi$$
$$812$$ −36947.9 −0.00196653
$$813$$ 4.38021e6 0.232417
$$814$$ 4.84939e6 0.256523
$$815$$ 9.69255e6 0.511145
$$816$$ −2.03638e7 −1.07061
$$817$$ 2.69212e7 1.41104
$$818$$ −6.81233e6 −0.355969
$$819$$ 964137. 0.0502260
$$820$$ 103574. 0.00537916
$$821$$ 9.95289e6 0.515337 0.257668 0.966233i $$-0.417046\pi$$
0.257668 + 0.966233i $$0.417046\pi$$
$$822$$ 2.21985e6 0.114589
$$823$$ 2.46452e7 1.26833 0.634165 0.773198i $$-0.281344\pi$$
0.634165 + 0.773198i $$0.281344\pi$$
$$824$$ 2.66460e7 1.36714
$$825$$ −680625. −0.0348155
$$826$$ −916439. −0.0467362
$$827$$ −2.09014e7 −1.06270 −0.531351 0.847152i $$-0.678315\pi$$
−0.531351 + 0.847152i $$0.678315\pi$$
$$828$$ −362438. −0.0183721
$$829$$ −8.31387e6 −0.420162 −0.210081 0.977684i $$-0.567373\pi$$
−0.210081 + 0.977684i $$0.567373\pi$$
$$830$$ 6.08467e6 0.306579
$$831$$ −2.14444e7 −1.07724
$$832$$ 2.10034e7 1.05192
$$833$$ 3.49312e7 1.74422
$$834$$ −8.82385e6 −0.439282
$$835$$ −1.58855e7 −0.788472
$$836$$ −406671. −0.0201246
$$837$$ 3.75994e6 0.185510
$$838$$ −2.56244e6 −0.126050
$$839$$ −4.03176e7 −1.97738 −0.988690 0.149977i $$-0.952080\pi$$
−0.988690 + 0.149977i $$0.952080\pi$$
$$840$$ 701587. 0.0343071
$$841$$ −1.84449e7 −0.899263
$$842$$ −1.97757e7 −0.961282
$$843$$ −1.00938e7 −0.489200
$$844$$ −1.08834e6 −0.0525905
$$845$$ 2.08792e6 0.100594
$$846$$ 1.61703e6 0.0776771
$$847$$ 258410. 0.0123766
$$848$$ 1.94118e7 0.926992
$$849$$ −8.69361e6 −0.413934
$$850$$ −7.65539e6 −0.363430
$$851$$ −2.12888e7 −1.00769
$$852$$ −732250. −0.0345589
$$853$$ −2.11646e7 −0.995951 −0.497976 0.867191i $$-0.665923\pi$$
−0.497976 + 0.867191i $$0.665923\pi$$
$$854$$ −38673.3 −0.00181454
$$855$$ −4.67328e6 −0.218628
$$856$$ −3.39633e7 −1.58425
$$857$$ −1.03622e7 −0.481946 −0.240973 0.970532i $$-0.577467\pi$$
−0.240973 + 0.970532i $$0.577467\pi$$
$$858$$ −4.24797e6 −0.196999
$$859$$ −1.77409e7 −0.820336 −0.410168 0.912010i $$-0.634530\pi$$
−0.410168 + 0.912010i $$0.634530\pi$$
$$860$$ −424716. −0.0195818
$$861$$ −451886. −0.0207741
$$862$$ −2.45618e7 −1.12588
$$863$$ −2.62577e6 −0.120014 −0.0600068 0.998198i $$-0.519112\pi$$
−0.0600068 + 0.998198i $$0.519112\pi$$
$$864$$ 384071. 0.0175036
$$865$$ −1.69955e7 −0.772314
$$866$$ −5.98118e6 −0.271014
$$867$$ −2.75802e7 −1.24609
$$868$$ −132572. −0.00597247
$$869$$ −1.63299e6 −0.0733557
$$870$$ 1.87073e6 0.0837941
$$871$$ −8.25039e6 −0.368493
$$872$$ −1.70137e7 −0.757718
$$873$$ 1.23202e7 0.547120
$$874$$ 4.10132e7 1.81612
$$875$$ 275778. 0.0121770
$$876$$ −258727. −0.0113915
$$877$$ 7.30171e6 0.320572 0.160286 0.987071i $$-0.448758\pi$$
0.160286 + 0.987071i $$0.448758\pi$$
$$878$$ 2.05427e7 0.899334
$$879$$ −1.98737e7 −0.867576
$$880$$ −3.23216e6 −0.140697
$$881$$ 6.08524e6 0.264142 0.132071 0.991240i $$-0.457837\pi$$
0.132071 + 0.991240i $$0.457837\pi$$
$$882$$ −7.72840e6 −0.334517
$$883$$ 1.66311e7 0.717828 0.358914 0.933371i $$-0.383147\pi$$
0.358914 + 0.933371i $$0.383147\pi$$
$$884$$ −2.07981e6 −0.0895146
$$885$$ 2.01980e6 0.0866862
$$886$$ 1.36006e7 0.582067
$$887$$ −1.47741e7 −0.630511 −0.315256 0.949007i $$-0.602090\pi$$
−0.315256 + 0.949007i $$0.602090\pi$$
$$888$$ 1.10171e7 0.468849
$$889$$ −1.12129e6 −0.0475841
$$890$$ −1.17452e7 −0.497032
$$891$$ 793881. 0.0335013
$$892$$ 1.26796e6 0.0533574
$$893$$ −7.96511e6 −0.334244
$$894$$ 3.77222e6 0.157853
$$895$$ −1.57708e6 −0.0658108
$$896$$ 3.47702e6 0.144689
$$897$$ 1.86486e7 0.773863
$$898$$ 1.74651e7 0.722736
$$899$$ 7.41383e6 0.305945
$$900$$ 73727.0 0.00303403
$$901$$ 3.84722e7 1.57883
$$902$$ 1.99101e6 0.0814810
$$903$$ 1.85301e6 0.0756240
$$904$$ 3.71661e7 1.51261
$$905$$ 1.30904e7 0.531288
$$906$$ 3.19196e6 0.129192
$$907$$ −9.23123e6 −0.372599 −0.186299 0.982493i $$-0.559649\pi$$
−0.186299 + 0.982493i $$0.559649\pi$$
$$908$$ 119891. 0.00482583
$$909$$ 7.71181e6 0.309561
$$910$$ 1.72121e6 0.0689016
$$911$$ −1.55931e7 −0.622495 −0.311247 0.950329i $$-0.600747\pi$$
−0.311247 + 0.950329i $$0.600747\pi$$
$$912$$ −2.21925e7 −0.883526
$$913$$ 5.09147e6 0.202146
$$914$$ 2.20185e7 0.871812
$$915$$ 85234.5 0.00336560
$$916$$ −495349. −0.0195062
$$917$$ −1.56017e6 −0.0612700
$$918$$ 8.92925e6 0.349710
$$919$$ −4.21091e6 −0.164470 −0.0822351 0.996613i $$-0.526206\pi$$
−0.0822351 + 0.996613i $$0.526206\pi$$
$$920$$ 1.35703e7 0.528590
$$921$$ −7.24932e6 −0.281610
$$922$$ 4.30040e7 1.66602
$$923$$ 3.76765e7 1.45568
$$924$$ −27991.6 −0.00107857
$$925$$ 4.33055e6 0.166413
$$926$$ −629009. −0.0241062
$$927$$ −1.22168e7 −0.466935
$$928$$ 757310. 0.0288671
$$929$$ 4.10363e7 1.56002 0.780008 0.625770i $$-0.215215\pi$$
0.780008 + 0.625770i $$0.215215\pi$$
$$930$$ 6.71235e6 0.254488
$$931$$ 3.80682e7 1.43942
$$932$$ −361730. −0.0136410
$$933$$ 7.83689e6 0.294740
$$934$$ −3.96488e7 −1.48718
$$935$$ −6.40581e6 −0.239632
$$936$$ −9.65073e6 −0.360056
$$937$$ 2.41565e7 0.898844 0.449422 0.893320i $$-0.351630\pi$$
0.449422 + 0.893320i $$0.351630\pi$$
$$938$$ −1.24893e6 −0.0463479
$$939$$ 2.84967e7 1.05470
$$940$$ 125660. 0.00463849
$$941$$ 3.13080e7 1.15261 0.576304 0.817236i $$-0.304495\pi$$
0.576304 + 0.817236i $$0.304495\pi$$
$$942$$ −2.63300e7 −0.966772
$$943$$ −8.74049e6 −0.320079
$$944$$ 9.59164e6 0.350318
$$945$$ −321667. −0.0117173
$$946$$ −8.16436e6 −0.296616
$$947$$ 5699.21 0.000206509 0 0.000103255 1.00000i $$-0.499967\pi$$
0.000103255 1.00000i $$0.499967\pi$$
$$948$$ 176889. 0.00639265
$$949$$ 1.33123e7 0.479829
$$950$$ −8.34288e6 −0.299921
$$951$$ −1.55059e7 −0.555963
$$952$$ 6.60310e6 0.236132
$$953$$ −4.24159e7 −1.51285 −0.756427 0.654078i $$-0.773057\pi$$
−0.756427 + 0.654078i $$0.773057\pi$$
$$954$$ −8.51183e6 −0.302797
$$955$$ −1.71078e7 −0.606995
$$956$$ −2.00942e6 −0.0711094
$$957$$ 1.56537e6 0.0552507
$$958$$ −5.48718e7 −1.93168
$$959$$ −752628. −0.0264261
$$960$$ −7.00741e6 −0.245403
$$961$$ −2.02765e6 −0.0708247
$$962$$ 2.70282e7 0.941628
$$963$$ 1.55716e7 0.541089
$$964$$ −2.23375e6 −0.0774180
$$965$$ 1.31854e7 0.455801
$$966$$ 2.82298e6 0.0973342
$$967$$ 1.43147e7 0.492284 0.246142 0.969234i $$-0.420837\pi$$
0.246142 + 0.969234i $$0.420837\pi$$
$$968$$ −2.58661e6 −0.0887243
$$969$$ −4.39833e7 −1.50480
$$970$$ 2.19944e7 0.750556
$$971$$ −1.06931e7 −0.363960 −0.181980 0.983302i $$-0.558251\pi$$
−0.181980 + 0.983302i $$0.558251\pi$$
$$972$$ −85995.1 −0.00291950
$$973$$ 2.99168e6 0.101306
$$974$$ 5.66714e7 1.91411
$$975$$ −3.79348e6 −0.127799
$$976$$ 404762. 0.0136011
$$977$$ 5.44429e7 1.82476 0.912378 0.409349i $$-0.134244\pi$$
0.912378 + 0.409349i $$0.134244\pi$$
$$978$$ −2.01827e7 −0.674734
$$979$$ −9.82800e6 −0.327724
$$980$$ −600574. −0.0199757
$$981$$ 7.80052e6 0.258792
$$982$$ 5.30461e7 1.75539
$$983$$ 4.16457e7 1.37463 0.687316 0.726359i $$-0.258789\pi$$
0.687316 + 0.726359i $$0.258789\pi$$
$$984$$ 4.52325e6 0.148923
$$985$$ −1.16785e7 −0.383526
$$986$$ 1.76067e7 0.576746
$$987$$ −548247. −0.0179136
$$988$$ −2.26659e6 −0.0738722
$$989$$ 3.58414e7 1.16518
$$990$$ 1.41726e6 0.0459581
$$991$$ −9.62055e6 −0.311183 −0.155591 0.987821i $$-0.549728\pi$$
−0.155591 + 0.987821i $$0.549728\pi$$
$$992$$ 2.71730e6 0.0876714
$$993$$ 2.88444e7 0.928300
$$994$$ 5.70340e6 0.183091
$$995$$ −1.09153e7 −0.349526
$$996$$ −551520. −0.0176162
$$997$$ 3.05865e7 0.974523 0.487262 0.873256i $$-0.337996\pi$$
0.487262 + 0.873256i $$0.337996\pi$$
$$998$$ −1.10495e7 −0.351169
$$999$$ −5.05115e6 −0.160131
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.c.1.3 3
3.2 odd 2 495.6.a.b.1.1 3
5.4 even 2 825.6.a.g.1.1 3

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