LMFDB - Embedded newform 325.10.a.k.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,10,Mod(1,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.a (trivial)

Newform invariants

comment:select newform

sage:traces = [27,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$167.386646753$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	325.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.55822 q^{2} -263.202 q^{3} -499.339 q^{4} +936.531 q^{6} +8747.23 q^{7} +3598.56 q^{8} +49592.5 q^{9} -74426.3 q^{11} +131427. q^{12} +28561.0 q^{13} -31124.5 q^{14} +242857. q^{16} -107923. q^{17} -176461. q^{18} -1.00971e6 q^{19} -2.30229e6 q^{21} +264825. q^{22} -449477. q^{23} -947151. q^{24} -101626. q^{26} -7.87224e6 q^{27} -4.36783e6 q^{28} -931512. q^{29} +9.30775e6 q^{31} -2.70660e6 q^{32} +1.95892e7 q^{33} +384015. q^{34} -2.47635e7 q^{36} -3.37801e6 q^{37} +3.59277e6 q^{38} -7.51732e6 q^{39} -856311. q^{41} +8.19205e6 q^{42} -1.05883e7 q^{43} +3.71640e7 q^{44} +1.59934e6 q^{46} +1.54223e7 q^{47} -6.39206e7 q^{48} +3.61604e7 q^{49} +2.84057e7 q^{51} -1.42616e7 q^{52} -4.22527e7 q^{53} +2.80111e7 q^{54} +3.14775e7 q^{56} +2.65758e8 q^{57} +3.31452e6 q^{58} +1.10312e8 q^{59} -3.74008e7 q^{61} -3.31190e7 q^{62} +4.33797e8 q^{63} -1.14712e8 q^{64} -6.97026e7 q^{66} +2.02507e7 q^{67} +5.38904e7 q^{68} +1.18303e8 q^{69} +1.96727e8 q^{71} +1.78462e8 q^{72} +2.15616e8 q^{73} +1.20197e7 q^{74} +5.04188e8 q^{76} -6.51024e8 q^{77} +2.67483e7 q^{78} +2.10291e8 q^{79} +1.09586e9 q^{81} +3.04694e6 q^{82} -1.77837e8 q^{83} +1.14962e9 q^{84} +3.76756e7 q^{86} +2.45176e8 q^{87} -2.67828e8 q^{88} +4.06464e8 q^{89} +2.49830e8 q^{91} +2.24441e8 q^{92} -2.44982e9 q^{93} -5.48759e7 q^{94} +7.12384e8 q^{96} -2.02283e8 q^{97} -1.28667e8 q^{98} -3.69098e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 48 q^{2} - 324 q^{3} + 6570 q^{4} - 1786 q^{6} - 3736 q^{7} - 36864 q^{8} + 214173 q^{9} - 66096 q^{11} - 114398 q^{12} + 771147 q^{13} - 359458 q^{14} + 998622 q^{16} - 779040 q^{17} - 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) $ 27 * q - 48 * q^2 - 324 * q^3 + 6570 * q^4 - 1786 * q^6 - 3736 * q^7 - 36864 * q^8 + 214173 * q^9 - 66096 * q^11 - 114398 * q^12 + 771147 * q^13 - 359458 * q^14 + 998622 * q^16 - 779040 * q^17 - 1709648 * q^18 - 761728 * q^19 - 2688628 * q^21 - 6061956 * q^22 - 4311518 * q^23 - 3567212 * q^24 - 1370928 * q^26 - 11899092 * q^27 - 137728 * q^28 + 4433670 * q^29 + 6106898 * q^31 - 32810006 * q^32 + 8840028 * q^33 + 18784070 * q^34 + 97588100 * q^36 - 29239496 * q^37 - 47346226 * q^38 - 9253764 * q^39 - 20531542 * q^41 - 106639738 * q^42 - 47500676 * q^43 + 43383046 * q^44 - 32105710 * q^46 - 134711080 * q^47 - 93484396 * q^48 + 146756645 * q^49 - 68396394 * q^51 + 187645770 * q^52 - 138404222 * q^53 + 1549570 * q^54 - 278046454 * q^56 - 103323872 * q^57 - 45680202 * q^58 - 495705656 * q^59 + 100256494 * q^61 - 380024874 * q^62 - 400619958 * q^63 + 554167194 * q^64 + 78712808 * q^66 - 805369894 * q^67 + 100947682 * q^68 - 659167072 * q^69 - 235437654 * q^71 - 1888149924 * q^72 - 251667626 * q^73 + 1855922170 * q^74 + 463619480 * q^76 - 1309691528 * q^77 - 51009946 * q^78 - 411718216 * q^79 + 1988439299 * q^81 - 2460333322 * q^82 - 2304849010 * q^83 - 476824718 * q^84 + 3316508396 * q^86 - 2481466544 * q^87 - 4501137582 * q^88 - 1619966906 * q^89 - 106703896 * q^91 - 2915597990 * q^92 - 3160578792 * q^93 + 4199181314 * q^94 + 2027406718 * q^96 + 861912866 * q^97 + 3534969754 * q^98 + 2142297632 * 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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−3.55822	−0.157252	−0.0786262	−	0.996904i	$-0.525053\pi$
$2$	−3.55822	−0.157252	−0.0786262	+	0.996904i	$0.525053\pi$
$3$	−263.202	−1.87605	−0.938024	−	0.346570i	$-0.887346\pi$
$3$	−263.202	−1.87605	−0.938024	+	0.346570i	$0.887346\pi$
$4$	−499.339	−0.975272
$5$	0	0
$5$	0	0
$6$	936.531	0.295013
$7$	8747.23	1.37699	0.688493	−	0.725243i	$-0.258273\pi$
$7$	8747.23	1.37699	0.688493	+	0.725243i	$0.258273\pi$
$8$	3598.56	0.310616
$9$	49592.5	2.51956
$10$	0	0
$11$	−74426.3	−1.53271	−0.766354	−	0.642418i	$-0.777931\pi$
$11$	−74426.3	−1.53271	−0.766354	+	0.642418i	$0.777931\pi$
$12$	131427.	1.82966
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−31124.5	−0.216534
$15$	0	0
$16$	242857.	0.926426
$17$	−107923.	−0.313398	−0.156699	−	0.987646i	$-0.550085\pi$
$17$	−107923.	−0.313398	−0.156699	+	0.987646i	$0.550085\pi$
$18$	−176461.	−0.396207
$19$	−1.00971e6	−1.77749	−0.888743	−	0.458407i	$-0.848420\pi$
$19$	−1.00971e6	−1.77749	−0.888743	+	0.458407i	$0.848420\pi$
$20$	0	0
$21$	−2.30229e6	−2.58329
$22$	264825.	0.241022
$23$	−449477.	−0.334913	−0.167456	−	0.985879i	$-0.553555\pi$
$23$	−449477.	−0.334913	−0.167456	+	0.985879i	$0.553555\pi$
$24$	−947151.	−0.582731
$25$	0	0
$26$	−101626.	−0.0436140
$27$	−7.87224e6	−2.85076
$28$	−4.36783e6	−1.34293
$29$	−931512.	−0.244567	−0.122283	−	0.992495i	$-0.539022\pi$
$29$	−931512.	−0.244567	−0.122283	+	0.992495i	$0.539022\pi$
$30$	0	0
$31$	9.30775e6	1.81016	0.905081	−	0.425240i	$-0.139810\pi$
$31$	9.30775e6	1.81016	0.905081	+	0.425240i	$0.139810\pi$
$32$	−2.70660e6	−0.456299
$33$	1.95892e7	2.87543
$34$	384015.	0.0492825
$35$	0	0
$36$	−2.47635e7	−2.45725
$37$	−3.37801e6	−0.296315	−0.148158	−	0.988964i	$-0.547334\pi$
$37$	−3.37801e6	−0.296315	−0.148158	+	0.988964i	$0.547334\pi$
$38$	3.59277e6	0.279514
$39$	−7.51732e6	−0.520322
$40$	0	0
$41$	−856311.	−0.0473265	−0.0236632	−	0.999720i	$-0.507533\pi$
$41$	−856311.	−0.0473265	−0.0236632	+	0.999720i	$0.507533\pi$
$42$	8.19205e6	0.406229
$43$	−1.05883e7	−0.472301	−0.236151	−	0.971716i	$-0.575886\pi$
$43$	−1.05883e7	−0.472301	−0.236151	+	0.971716i	$0.575886\pi$
$44$	3.71640e7	1.49481
$45$	0	0
$46$	1.59934e6	0.0526659
$47$	1.54223e7	0.461009	0.230504	−	0.973071i	$-0.425962\pi$
$47$	1.54223e7	0.461009	0.230504	+	0.973071i	$0.425962\pi$
$48$	−6.39206e7	−1.73802
$49$	3.61604e7	0.896088
$50$	0	0
$51$	2.84057e7	0.587949
$52$	−1.42616e7	−0.270492
$53$	−4.22527e7	−0.735552	−0.367776	−	0.929915i	$-0.619881\pi$
$53$	−4.22527e7	−0.735552	−0.367776	+	0.929915i	$0.619881\pi$
$54$	2.80111e7	0.448290
$55$	0	0
$56$	3.14775e7	0.427714
$57$	2.65758e8	3.33465
$58$	3.31452e6	0.0384587
$59$	1.10312e8	1.18519	0.592595	−	0.805501i	$-0.298103\pi$
$59$	1.10312e8	1.18519	0.592595	+	0.805501i	$0.298103\pi$
$60$	0	0
$61$	−3.74008e7	−0.345857	−0.172929	−	0.984934i	$-0.555323\pi$
$61$	−3.74008e7	−0.345857	−0.172929	+	0.984934i	$0.555323\pi$
$62$	−3.31190e7	−0.284652
$63$	4.33797e8	3.46939
$64$	−1.14712e8	−0.854672
$65$	0	0
$66$	−6.97026e7	−0.452169
$67$	2.02507e7	0.122773	0.0613866	−	0.998114i	$-0.480448\pi$
$67$	2.02507e7	0.122773	0.0613866	+	0.998114i	$0.480448\pi$
$68$	5.38904e7	0.305648
$69$	1.18303e8	0.628313
$70$	0	0
$71$	1.96727e8	0.918758	0.459379	−	0.888240i	$-0.348072\pi$
$71$	1.96727e8	0.918758	0.459379	+	0.888240i	$0.348072\pi$
$72$	1.78462e8	0.782616
$73$	2.15616e8	0.888646	0.444323	−	0.895867i	$-0.353444\pi$
$73$	2.15616e8	0.888646	0.444323	+	0.895867i	$0.353444\pi$
$74$	1.20197e7	0.0465963
$75$	0	0
$76$	5.04188e8	1.73353
$77$	−6.51024e8	−2.11052
$78$	2.67483e7	0.0818220
$79$	2.10291e8	0.607434	0.303717	−	0.952762i	$-0.401772\pi$
$79$	2.10291e8	0.607434	0.303717	+	0.952762i	$0.401772\pi$
$80$	0	0
$81$	1.09586e9	2.82862
$82$	3.04694e6	0.00744221
$83$	−1.77837e8	−0.411312	−0.205656	−	0.978624i	$-0.565933\pi$
$83$	−1.77837e8	−0.411312	−0.205656	+	0.978624i	$0.565933\pi$
$84$	1.14962e9	2.51941
$85$	0	0
$86$	3.76756e7	0.0742706
$87$	2.45176e8	0.458819
$88$	−2.67828e8	−0.476084
$89$	4.06464e8	0.686701	0.343350	−	0.939207i	$-0.388438\pi$
$89$	4.06464e8	0.686701	0.343350	+	0.939207i	$0.388438\pi$
$90$	0	0
$91$	2.49830e8	0.381907
$92$	2.24441e8	0.326631
$93$	−2.44982e9	−3.39595
$94$	−5.48759e7	−0.0724947
$95$	0	0
$96$	7.12384e8	0.856040
$97$	−2.02283e8	−0.232000	−0.116000	−	0.993249i	$-0.537007\pi$
$97$	−2.02283e8	−0.232000	−0.116000	+	0.993249i	$0.537007\pi$
$98$	−1.28667e8	−0.140912
$99$	−3.69098e9	−3.86175
$100$	0	0
$101$	2.63043e8	0.251525	0.125762	−	0.992060i	$-0.459862\pi$
$101$	2.63043e8	0.251525	0.125762	+	0.992060i	$0.459862\pi$
$102$	−1.01074e8	−0.0924565
$103$	−1.38407e9	−1.21169	−0.605843	−	0.795584i	$-0.707164\pi$
$103$	−1.38407e9	−1.21169	−0.605843	+	0.795584i	$0.707164\pi$
$104$	1.02779e8	0.0861495
$105$	0	0
$106$	1.50344e8	0.115667
$107$	−1.62418e9	−1.19786	−0.598932	−	0.800800i	$-0.704408\pi$
$107$	−1.62418e9	−1.19786	−0.598932	+	0.800800i	$0.704408\pi$
$108$	3.93092e9	2.78027
$109$	2.62866e9	1.78367	0.891836	−	0.452359i	$-0.149418\pi$
$109$	2.62866e9	1.78367	0.891836	+	0.452359i	$0.149418\pi$
$110$	0	0
$111$	8.89101e8	0.555901
$112$	2.12433e9	1.27568
$113$	1.16175e9	0.670286	0.335143	−	0.942167i	$-0.391215\pi$
$113$	1.16175e9	0.670286	0.335143	+	0.942167i	$0.391215\pi$
$114$	−9.45626e8	−0.524382
$115$	0	0
$116$	4.65140e8	0.238519
$117$	1.41641e9	0.698800
$118$	−3.92513e8	−0.186374
$119$	−9.44031e8	−0.431544
$120$	0	0
$121$	3.18133e9	1.34919
$122$	1.33080e8	0.0543869
$123$	2.25383e8	0.0887868
$124$	−4.64773e9	−1.76540
$125$	0	0
$126$	−1.54354e9	−0.545571
$127$	2.39453e9	0.816776	0.408388	−	0.912808i	$-0.366091\pi$
$127$	2.39453e9	0.816776	0.408388	+	0.912808i	$0.366091\pi$
$128$	1.79395e9	0.590699
$129$	2.78687e9	0.886060
$130$	0	0
$131$	−3.42878e9	−1.01723	−0.508614	−	0.860995i	$-0.669842\pi$
$131$	−3.42878e9	−1.01723	−0.508614	+	0.860995i	$0.669842\pi$
$132$	−9.78164e9	−2.80433
$133$	−8.83217e9	−2.44757
$134$	−7.20564e7	−0.0193064
$135$	0	0
$136$	−3.88369e8	−0.0973464
$137$	2.75246e9	0.667541	0.333770	−	0.942654i	$-0.391679\pi$
$137$	2.75246e9	0.667541	0.333770	+	0.942654i	$0.391679\pi$
$138$	−4.20949e8	−0.0988037
$139$	−1.00310e9	−0.227917	−0.113958	−	0.993486i	$-0.536353\pi$
$139$	−1.00310e9	−0.227917	−0.113958	+	0.993486i	$0.536353\pi$
$140$	0	0
$141$	−4.05919e9	−0.864874
$142$	−6.99997e8	−0.144477
$143$	−2.12569e9	−0.425097
$144$	1.20439e10	2.33419
$145$	0	0
$146$	−7.67210e8	−0.139742
$147$	−9.51750e9	−1.68110
$148$	1.68677e9	0.288988
$149$	1.67656e9	0.278665	0.139332	−	0.990246i	$-0.455504\pi$
$149$	1.67656e9	0.278665	0.139332	+	0.990246i	$0.455504\pi$
$150$	0	0
$151$	−4.91436e9	−0.769256	−0.384628	−	0.923072i	$-0.625670\pi$
$151$	−4.91436e9	−0.769256	−0.384628	+	0.923072i	$0.625670\pi$
$152$	−3.63351e9	−0.552116
$153$	−5.35219e9	−0.789623
$154$	2.31648e9	0.331884
$155$	0	0
$156$	3.75369e9	0.507456
$157$	5.01168e9	0.658317	0.329158	−	0.944275i	$-0.393235\pi$
$157$	5.01168e9	0.658317	0.329158	+	0.944275i	$0.393235\pi$
$158$	−7.48262e8	−0.0955205
$159$	1.11210e10	1.37993
$160$	0	0
$161$	−3.93167e9	−0.461170
$162$	−3.89932e9	−0.444807
$163$	7.58951e9	0.842111	0.421056	−	0.907035i	$-0.361660\pi$
$163$	7.58951e9	0.842111	0.421056	+	0.907035i	$0.361660\pi$
$164$	4.27590e8	0.0461562
$165$	0	0
$166$	6.32784e8	0.0646799
$167$	2.19717e9	0.218595	0.109297	−	0.994009i	$-0.465140\pi$
$167$	2.19717e9	0.218595	0.109297	+	0.994009i	$0.465140\pi$
$168$	−8.28494e9	−0.802412
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	−5.00741e10	−4.47848
$172$	5.28716e9	0.460622
$173$	−1.66473e10	−1.41298	−0.706488	−	0.707725i	$-0.749722\pi$
$173$	−1.66473e10	−1.41298	−0.706488	+	0.707725i	$0.749722\pi$
$174$	−8.72390e8	−0.0721504
$175$	0	0
$176$	−1.80750e10	−1.41994
$177$	−2.90343e10	−2.22347
$178$	−1.44629e9	−0.107985
$179$	−1.94126e10	−1.41333	−0.706667	−	0.707547i	$-0.749802\pi$
$179$	−1.94126e10	−1.41333	−0.706667	+	0.707547i	$0.749802\pi$
$180$	0	0
$181$	2.35303e10	1.62957	0.814785	−	0.579763i	$-0.196855\pi$
$181$	2.35303e10	1.62957	0.814785	+	0.579763i	$0.196855\pi$
$182$	−8.88948e8	−0.0600558
$183$	9.84399e9	0.648845
$184$	−1.61747e9	−0.104029
$185$	0	0
$186$	8.71700e9	0.534022
$187$	8.03234e9	0.480347
$188$	−7.70096e9	−0.449609
$189$	−6.88603e10	−3.92546
$190$	0	0
$191$	2.17944e10	1.18493	0.592467	−	0.805595i	$-0.298154\pi$
$191$	2.17944e10	1.18493	0.592467	+	0.805595i	$0.298154\pi$
$192$	3.01925e10	1.60341
$193$	7.49566e9	0.388868	0.194434	−	0.980916i	$-0.437713\pi$
$193$	7.49566e9	0.388868	0.194434	+	0.980916i	$0.437713\pi$
$194$	7.19769e8	0.0364825
$195$	0	0
$196$	−1.80563e10	−0.873929
$197$	3.42067e10	1.61813	0.809064	−	0.587721i	$-0.199975\pi$
$197$	3.42067e10	1.61813	0.809064	+	0.587721i	$0.199975\pi$
$198$	1.31333e10	0.607269
$199$	5.86712e9	0.265208	0.132604	−	0.991169i	$-0.457666\pi$
$199$	5.86712e9	0.265208	0.132604	+	0.991169i	$0.457666\pi$
$200$	0	0
$201$	−5.33003e9	−0.230329
$202$	−9.35965e8	−0.0395529
$203$	−8.14815e9	−0.336765
$204$	−1.41841e10	−0.573410
$205$	0	0
$206$	4.92482e9	0.190541
$207$	−2.22907e10	−0.843832
$208$	6.93624e9	0.256944
$209$	7.51491e10	2.72437
$210$	0	0
$211$	1.22862e10	0.426722	0.213361	−	0.976973i	$-0.431559\pi$
$211$	1.22862e10	0.426722	0.213361	+	0.976973i	$0.431559\pi$
$212$	2.10984e10	0.717363
$213$	−5.17790e10	−1.72364
$214$	5.77919e9	0.188367
$215$	0	0
$216$	−2.83288e10	−0.885494
$217$	8.14170e10	2.49257
$218$	−9.35334e9	−0.280487
$219$	−5.67507e10	−1.66714
$220$	0	0
$221$	−3.08240e9	−0.0869208
$222$	−3.16362e9	−0.0874169
$223$	4.25294e10	1.15164	0.575820	−	0.817576i	$-0.304683\pi$
$223$	4.25294e10	1.15164	0.575820	+	0.817576i	$0.304683\pi$
$224$	−2.36753e10	−0.628317
$225$	0	0
$226$	−4.13376e9	−0.105404
$227$	−7.41525e10	−1.85357	−0.926786	−	0.375590i	$-0.877440\pi$
$227$	−7.41525e10	−1.85357	−0.926786	+	0.375590i	$0.877440\pi$
$228$	−1.32704e11	−3.25219
$229$	2.04402e10	0.491164	0.245582	−	0.969376i	$-0.421021\pi$
$229$	2.04402e10	0.491164	0.245582	+	0.969376i	$0.421021\pi$
$230$	0	0
$231$	1.71351e11	3.95943
$232$	−3.35211e9	−0.0759664
$233$	−2.07650e10	−0.461563	−0.230781	−	0.973006i	$-0.574128\pi$
$233$	−2.07650e10	−0.461563	−0.230781	+	0.973006i	$0.574128\pi$
$234$	−5.03990e9	−0.109888
$235$	0	0
$236$	−5.50830e10	−1.15588
$237$	−5.53491e10	−1.13958
$238$	3.35907e9	0.0678613
$239$	3.32052e10	0.658286	0.329143	−	0.944280i	$-0.393240\pi$
$239$	3.32052e10	0.658286	0.329143	+	0.944280i	$0.393240\pi$
$240$	0	0
$241$	8.15806e10	1.55779	0.778897	−	0.627151i	$-0.215779\pi$
$241$	8.15806e10	1.55779	0.778897	+	0.627151i	$0.215779\pi$
$242$	−1.13199e10	−0.212164
$243$	−1.33485e11	−2.45585
$244$	1.86757e10	0.337305
$245$	0	0
$246$	−8.01962e8	−0.0139619
$247$	−2.88384e10	−0.492986
$248$	3.34946e10	0.562266
$249$	4.68072e10	0.771642
$250$	0	0
$251$	8.31580e10	1.32243	0.661214	−	0.750197i	$-0.270041\pi$
$251$	8.31580e10	1.32243	0.661214	+	0.750197i	$0.270041\pi$
$252$	−2.16612e11	−3.38360
$253$	3.34529e10	0.513324
$254$	−8.52025e9	−0.128440
$255$	0	0
$256$	5.23494e10	0.761783
$257$	−6.69121e10	−0.956766	−0.478383	−	0.878151i	$-0.658777\pi$
$257$	−6.69121e10	−0.956766	−0.478383	+	0.878151i	$0.658777\pi$
$258$	−9.91629e9	−0.139335
$259$	−2.95483e10	−0.408021
$260$	0	0
$261$	−4.61960e10	−0.616200
$262$	1.22003e10	0.159962
$263$	−9.63829e10	−1.24222	−0.621111	−	0.783723i	$-0.713318\pi$
$263$	−9.63829e10	−1.24222	−0.621111	+	0.783723i	$0.713318\pi$
$264$	7.04929e10	0.893157
$265$	0	0
$266$	3.14268e10	0.384887
$267$	−1.06982e11	−1.28828
$268$	−1.01120e10	−0.119737
$269$	−1.09673e11	−1.27706	−0.638532	−	0.769595i	$-0.720458\pi$
$269$	−1.09673e11	−1.27706	−0.638532	+	0.769595i	$0.720458\pi$
$270$	0	0
$271$	−3.45412e10	−0.389023	−0.194511	−	0.980900i	$-0.562312\pi$
$271$	−3.45412e10	−0.389023	−0.194511	+	0.980900i	$0.562312\pi$
$272$	−2.62100e10	−0.290340
$273$	−6.57557e10	−0.716476
$274$	−9.79384e9	−0.104972
$275$	0	0
$276$	−5.90735e10	−0.612776
$277$	1.60561e11	1.63863	0.819316	−	0.573342i	$-0.194353\pi$
$277$	1.60561e11	1.63863	0.819316	+	0.573342i	$0.194353\pi$
$278$	3.56924e9	0.0358405
$279$	4.61594e11	4.56081
$280$	0	0
$281$	−1.25292e11	−1.19879	−0.599397	−	0.800452i	$-0.704593\pi$
$281$	−1.25292e11	−1.19879	−0.599397	+	0.800452i	$0.704593\pi$
$282$	1.44435e10	0.136004
$283$	−6.18119e10	−0.572840	−0.286420	−	0.958104i	$-0.592465\pi$
$283$	−6.18119e10	−0.572840	−0.286420	+	0.958104i	$0.592465\pi$
$284$	−9.82335e10	−0.896039
$285$	0	0
$286$	7.56367e9	0.0668475
$287$	−7.49035e9	−0.0651678
$288$	−1.34227e11	−1.14967
$289$	−1.06940e11	−0.901782
$290$	0	0
$291$	5.32415e10	0.435243
$292$	−1.07666e11	−0.866671
$293$	1.54895e11	1.22782	0.613908	−	0.789378i	$-0.289597\pi$
$293$	1.54895e11	1.22782	0.613908	+	0.789378i	$0.289597\pi$
$294$	3.38653e10	0.264358
$295$	0	0
$296$	−1.21560e10	−0.0920403
$297$	5.85902e11	4.36939
$298$	−5.96558e9	−0.0438207
$299$	−1.28375e10	−0.0928881
$300$	0	0
$301$	−9.26185e10	−0.650352
$302$	1.74864e10	0.120967
$303$	−6.92336e10	−0.471873
$304$	−2.45216e11	−1.64671
$305$	0	0
$306$	1.90443e10	0.124170
$307$	−2.15986e11	−1.38772	−0.693861	−	0.720109i	$-0.744092\pi$
$307$	−2.15986e11	−1.38772	−0.693861	+	0.720109i	$0.744092\pi$
$308$	3.25082e11	2.05833
$309$	3.64290e11	2.27318
$310$	0	0
$311$	−2.65425e10	−0.160886	−0.0804432	−	0.996759i	$-0.525634\pi$
$311$	−2.65425e10	−0.160886	−0.0804432	+	0.996759i	$0.525634\pi$
$312$	−2.70516e10	−0.161621
$313$	−2.86302e11	−1.68606	−0.843032	−	0.537863i	$-0.819232\pi$
$313$	−2.86302e11	−1.68606	−0.843032	+	0.537863i	$0.819232\pi$
$314$	−1.78327e10	−0.103522
$315$	0	0
$316$	−1.05007e11	−0.592413
$317$	1.72511e11	0.959513	0.479756	−	0.877402i	$-0.340725\pi$
$317$	1.72511e11	0.959513	0.479756	+	0.877402i	$0.340725\pi$
$318$	−3.95710e10	−0.216997
$319$	6.93290e10	0.374849
$320$	0	0
$321$	4.27488e11	2.24725
$322$	1.39898e10	0.0725201
$323$	1.08972e11	0.557060
$324$	−5.47207e11	−2.75867
$325$	0	0
$326$	−2.70051e10	−0.132424
$327$	−6.91869e11	−3.34625
$328$	−3.08149e9	−0.0147004
$329$	1.34902e11	0.634802
$330$	0	0
$331$	3.89419e11	1.78316	0.891582	−	0.452860i	$-0.149596\pi$
$331$	3.89419e11	1.78316	0.891582	+	0.452860i	$0.149596\pi$
$332$	8.88012e10	0.401141
$333$	−1.67524e11	−0.746583
$334$	−7.81801e9	−0.0343745
$335$	0	0
$336$	−5.59128e11	−2.39323
$337$	−4.19557e11	−1.77197	−0.885985	−	0.463714i	$-0.846517\pi$
$337$	−4.19557e11	−1.77197	−0.885985	+	0.463714i	$0.846517\pi$
$338$	−2.90255e9	−0.0120963
$339$	−3.05776e11	−1.25749
$340$	0	0
$341$	−6.92742e11	−2.77445
$342$	1.78174e11	0.704252
$343$	−3.66791e10	−0.143085
$344$	−3.81028e10	−0.146705
$345$	0	0
$346$	5.92345e10	0.222194
$347$	−7.83183e10	−0.289988	−0.144994	−	0.989433i	$-0.546316\pi$
$347$	−7.83183e10	−0.289988	−0.144994	+	0.989433i	$0.546316\pi$
$348$	−1.22426e11	−0.447473
$349$	−2.44848e11	−0.883450	−0.441725	−	0.897151i	$-0.645633\pi$
$349$	−2.44848e11	−0.883450	−0.441725	+	0.897151i	$0.645633\pi$
$350$	0	0
$351$	−2.24839e11	−0.790660
$352$	2.01443e11	0.699374
$353$	−6.86294e10	−0.235247	−0.117623	−	0.993058i	$-0.537528\pi$
$353$	−6.86294e10	−0.235247	−0.117623	+	0.993058i	$0.537528\pi$
$354$	1.03310e11	0.349647
$355$	0	0
$356$	−2.02964e11	−0.669720
$357$	2.48471e11	0.809597
$358$	6.90742e10	0.222250
$359$	−2.01872e10	−0.0641432	−0.0320716	−	0.999486i	$-0.510210\pi$
$359$	−2.01872e10	−0.0641432	−0.0320716	+	0.999486i	$0.510210\pi$
$360$	0	0
$361$	6.96829e11	2.15945
$362$	−8.37258e10	−0.256254
$363$	−8.37333e11	−2.53115
$364$	−1.24750e11	−0.372463
$365$	0	0
$366$	−3.50270e10	−0.102033
$367$	−3.34629e11	−0.962868	−0.481434	−	0.876482i	$-0.659884\pi$
$367$	−3.34629e11	−0.962868	−0.481434	+	0.876482i	$0.659884\pi$
$368$	−1.09159e11	−0.310272
$369$	−4.24666e10	−0.119242
$370$	0	0
$371$	−3.69594e11	−1.01284
$372$	1.22329e12	3.31197
$373$	−3.35332e11	−0.896985	−0.448493	−	0.893786i	$-0.648039\pi$
$373$	−3.35332e11	−0.896985	−0.448493	+	0.893786i	$0.648039\pi$
$374$	−2.85808e10	−0.0755358
$375$	0	0
$376$	5.54982e10	0.143197
$377$	−2.66049e10	−0.0678306
$378$	2.45020e11	0.617288
$379$	−3.08926e11	−0.769091	−0.384545	−	0.923106i	$-0.625642\pi$
$379$	−3.08926e11	−0.769091	−0.384545	+	0.923106i	$0.625642\pi$
$380$	0	0
$381$	−6.30245e11	−1.53231
$382$	−7.75491e10	−0.186334
$383$	1.34899e11	0.320342	0.160171	−	0.987089i	$-0.448795\pi$
$383$	1.34899e11	0.320342	0.160171	+	0.987089i	$0.448795\pi$
$384$	−4.72172e11	−1.10818
$385$	0	0
$386$	−2.66712e10	−0.0611504
$387$	−5.25101e11	−1.18999
$388$	1.01008e11	0.226263
$389$	3.95179e11	0.875026	0.437513	−	0.899212i	$-0.355859\pi$
$389$	3.95179e11	0.875026	0.437513	+	0.899212i	$0.355859\pi$
$390$	0	0
$391$	4.85091e10	0.104961
$392$	1.30125e11	0.278340
$393$	9.02462e11	1.90837
$394$	−1.21715e11	−0.254455
$395$	0	0
$396$	1.84305e12	3.76625
$397$	4.02134e11	0.812481	0.406241	−	0.913766i	$-0.366839\pi$
$397$	4.02134e11	0.812481	0.406241	+	0.913766i	$0.366839\pi$
$398$	−2.08765e10	−0.0417046
$399$	2.32465e12	4.59176
$400$	0	0
$401$	−4.51492e11	−0.871968	−0.435984	−	0.899954i	$-0.643600\pi$
$401$	−4.51492e11	−0.871968	−0.435984	+	0.899954i	$0.643600\pi$
$402$	1.89654e10	0.0362197
$403$	2.65839e11	0.502048
$404$	−1.31348e11	−0.245305
$405$	0	0
$406$	2.89929e10	0.0529571
$407$	2.51413e11	0.454164
$408$	1.02220e11	0.182627
$409$	−3.71071e11	−0.655695	−0.327848	−	0.944731i	$-0.606323\pi$
$409$	−3.71071e11	−0.655695	−0.327848	+	0.944731i	$0.606323\pi$
$410$	0	0
$411$	−7.24453e11	−1.25234
$412$	6.91120e11	1.18172
$413$	9.64923e11	1.63199
$414$	7.93150e10	0.132695
$415$	0	0
$416$	−7.73033e10	−0.126555
$417$	2.64018e11	0.427583
$418$	−2.67397e11	−0.428413
$419$	−4.49207e11	−0.712006	−0.356003	−	0.934485i	$-0.615861\pi$
$419$	−4.49207e11	−0.712006	−0.356003	+	0.934485i	$0.615861\pi$
$420$	0	0
$421$	2.51498e11	0.390180	0.195090	−	0.980785i	$-0.437500\pi$
$421$	2.51498e11	0.390180	0.195090	+	0.980785i	$0.437500\pi$
$422$	−4.37169e10	−0.0671031
$423$	7.64830e11	1.16154
$424$	−1.52049e11	−0.228474
$425$	0	0
$426$	1.84241e11	0.271046
$427$	−3.27154e11	−0.476241
$428$	8.11017e11	1.16824
$429$	5.59487e11	0.797502
$430$	0	0
$431$	−1.16599e12	−1.62760	−0.813799	−	0.581147i	$-0.802604\pi$
$431$	−1.16599e12	−1.62760	−0.813799	+	0.581147i	$0.802604\pi$
$432$	−1.91183e12	−2.64102
$433$	1.28482e11	0.175649	0.0878247	−	0.996136i	$-0.472008\pi$
$433$	1.28482e11	0.175649	0.0878247	+	0.996136i	$0.472008\pi$
$434$	−2.89700e11	−0.391962
$435$	0	0
$436$	−1.31259e12	−1.73956
$437$	4.53842e11	0.595303
$438$	2.01931e11	0.262162
$439$	−3.01414e11	−0.387322	−0.193661	−	0.981068i	$-0.562036\pi$
$439$	−3.01414e11	−0.387322	−0.193661	+	0.981068i	$0.562036\pi$
$440$	0	0
$441$	1.79328e12	2.25775
$442$	1.09679e10	0.0136685
$443$	−1.16765e12	−1.44044	−0.720222	−	0.693744i	$-0.755960\pi$
$443$	−1.16765e12	−1.44044	−0.720222	+	0.693744i	$0.755960\pi$
$444$	−4.43963e11	−0.542155
$445$	0	0
$446$	−1.51329e11	−0.181098
$447$	−4.41276e11	−0.522789
$448$	−1.00341e12	−1.17687
$449$	1.24861e12	1.44984	0.724919	−	0.688834i	$-0.241877\pi$
$449$	1.24861e12	1.44984	0.724919	+	0.688834i	$0.241877\pi$
$450$	0	0
$451$	6.37321e10	0.0725377
$452$	−5.80108e11	−0.653711
$453$	1.29347e12	1.44316
$454$	2.63851e11	0.291479
$455$	0	0
$456$	9.56349e11	1.03580
$457$	3.93084e11	0.421563	0.210781	−	0.977533i	$-0.432399\pi$
$457$	3.93084e11	0.421563	0.210781	+	0.977533i	$0.432399\pi$
$458$	−7.27308e10	−0.0772367
$459$	8.49599e11	0.893423
$460$	0	0
$461$	1.47557e12	1.52162	0.760810	−	0.648974i	$-0.224802\pi$
$461$	1.47557e12	1.52162	0.760810	+	0.648974i	$0.224802\pi$
$462$	−6.09704e11	−0.622630
$463$	−1.02517e12	−1.03677	−0.518385	−	0.855147i	$-0.673466\pi$
$463$	−1.02517e12	−1.03677	−0.518385	+	0.855147i	$0.673466\pi$
$464$	−2.26224e11	−0.226573
$465$	0	0
$466$	7.38864e10	0.0725819
$467$	1.15145e12	1.12026	0.560128	−	0.828406i	$-0.310752\pi$
$467$	1.15145e12	1.12026	0.560128	+	0.828406i	$0.310752\pi$
$468$	−7.07269e11	−0.681520
$469$	1.77138e11	0.169057
$470$	0	0
$471$	−1.31909e12	−1.23503
$472$	3.96964e11	0.368139
$473$	7.88050e11	0.723900
$474$	1.96944e11	0.179201
$475$	0	0
$476$	4.71392e11	0.420872
$477$	−2.09542e12	−1.85326
$478$	−1.18151e11	−0.103517
$479$	−4.28228e11	−0.371676	−0.185838	−	0.982580i	$-0.559500\pi$
$479$	−4.28228e11	−0.371676	−0.185838	+	0.982580i	$0.559500\pi$
$480$	0	0
$481$	−9.64795e10	−0.0821830
$482$	−2.90282e11	−0.244967
$483$	1.03483e12	0.865177
$484$	−1.58856e12	−1.31583
$485$	0	0
$486$	4.74967e11	0.386189
$487$	1.44075e12	1.16067	0.580335	−	0.814378i	$-0.302922\pi$
$487$	1.44075e12	1.16067	0.580335	+	0.814378i	$0.302922\pi$
$488$	−1.34589e11	−0.107429
$489$	−1.99758e12	−1.57984
$490$	0	0
$491$	−1.72894e11	−0.134250	−0.0671249	−	0.997745i	$-0.521383\pi$
$491$	−1.72894e11	−0.134250	−0.0671249	+	0.997745i	$0.521383\pi$
$492$	−1.12543e11	−0.0865912
$493$	1.00532e11	0.0766466
$494$	1.02613e11	0.0775232
$495$	0	0
$496$	2.26045e12	1.67698
$497$	1.72082e12	1.26512
$498$	−1.66550e11	−0.121343
$499$	6.18199e11	0.446350	0.223175	−	0.974778i	$-0.428358\pi$
$499$	6.18199e11	0.446350	0.223175	+	0.974778i	$0.428358\pi$
$500$	0	0
$501$	−5.78300e11	−0.410094
$502$	−2.95894e11	−0.207955
$503$	1.01848e12	0.709410	0.354705	−	0.934978i	$-0.384581\pi$
$503$	1.01848e12	0.709410	0.354705	+	0.934978i	$0.384581\pi$
$504$	1.56104e12	1.07765
$505$	0	0
$506$	−1.19033e11	−0.0807214
$507$	−2.14702e11	−0.144311
$508$	−1.19568e12	−0.796578
$509$	−6.26512e11	−0.413713	−0.206856	−	0.978371i	$-0.566323\pi$
$509$	−6.26512e11	−0.413713	−0.206856	+	0.978371i	$0.566323\pi$
$510$	0	0
$511$	1.88605e12	1.22365
$512$	−1.10477e12	−0.710491
$513$	7.94869e12	5.06719
$514$	2.38088e11	0.150454
$515$	0	0
$516$	−1.39159e12	−0.864149
$517$	−1.14783e12	−0.706592
$518$	1.05139e11	0.0641624
$519$	4.38160e12	2.65081
$520$	0	0
$521$	−2.06660e11	−0.122881	−0.0614406	−	0.998111i	$-0.519569\pi$
$521$	−2.06660e11	−0.122881	−0.0614406	+	0.998111i	$0.519569\pi$
$522$	1.64375e11	0.0968990
$523$	−1.01877e12	−0.595416	−0.297708	−	0.954657i	$-0.596222\pi$
$523$	−1.01877e12	−0.595416	−0.297708	+	0.954657i	$0.596222\pi$
$524$	1.71212e12	0.992074
$525$	0	0
$526$	3.42951e11	0.195343
$527$	−1.00452e12	−0.567300
$528$	4.75737e12	2.66388
$529$	−1.59912e12	−0.887833
$530$	0	0
$531$	5.47064e12	2.98616
$532$	4.41025e12	2.38705
$533$	−2.44571e10	−0.0131260
$534$	3.80667e11	0.202586
$535$	0	0
$536$	7.28735e10	0.0381354
$537$	5.10943e12	2.65148
$538$	3.90239e11	0.200822
$539$	−2.69128e12	−1.37344
$540$	0	0
$541$	−2.19901e12	−1.10367	−0.551834	−	0.833954i	$-0.686072\pi$
$541$	−2.19901e12	−1.10367	−0.551834	+	0.833954i	$0.686072\pi$
$542$	1.22905e11	0.0611748
$543$	−6.19322e12	−3.05715
$544$	2.92106e11	0.143003
$545$	0	0
$546$	2.33973e11	0.112668
$547$	−3.37601e12	−1.61236	−0.806178	−	0.591673i	$-0.798468\pi$
$547$	−3.37601e12	−1.61236	−0.806178	+	0.591673i	$0.798468\pi$
$548$	−1.37441e12	−0.651034
$549$	−1.85480e12	−0.871408
$550$	0	0
$551$	9.40558e11	0.434714
$552$	4.25722e11	0.195164
$553$	1.83947e12	0.836428
$554$	−5.71311e11	−0.257679
$555$	0	0
$556$	5.00886e11	0.222281
$557$	1.19171e12	0.524593	0.262296	−	0.964987i	$-0.415520\pi$
$557$	1.19171e12	0.524593	0.262296	+	0.964987i	$0.415520\pi$
$558$	−1.64245e12	−0.717198
$559$	−3.02413e11	−0.130993
$560$	0	0
$561$	−2.11413e12	−0.901154
$562$	4.45816e11	0.188513
$563$	2.92427e12	1.22667	0.613337	−	0.789821i	$-0.289827\pi$
$563$	2.92427e12	1.22667	0.613337	+	0.789821i	$0.289827\pi$
$564$	2.02691e12	0.843488
$565$	0	0
$566$	2.19940e11	0.0900805
$567$	9.58577e12	3.89496
$568$	7.07935e11	0.285381
$569$	−2.23751e12	−0.894870	−0.447435	−	0.894317i	$-0.647662\pi$
$569$	−2.23751e12	−0.894870	−0.447435	+	0.894317i	$0.647662\pi$
$570$	0	0
$571$	−6.04695e11	−0.238053	−0.119026	−	0.992891i	$-0.537977\pi$
$571$	−6.04695e11	−0.238053	−0.119026	+	0.992891i	$0.537977\pi$
$572$	1.06144e12	0.414585
$573$	−5.73633e12	−2.22299
$574$	2.66523e10	0.0102478
$575$	0	0
$576$	−5.68886e12	−2.15340
$577$	−2.69590e12	−1.01254	−0.506270	−	0.862375i	$-0.668976\pi$
$577$	−2.69590e12	−1.01254	−0.506270	+	0.862375i	$0.668976\pi$
$578$	3.80517e11	0.141807
$579$	−1.97288e12	−0.729535
$580$	0	0
$581$	−1.55558e12	−0.566371
$582$	−1.89445e11	−0.0684430
$583$	3.14471e12	1.12739
$584$	7.75909e11	0.276028
$585$	0	0
$586$	−5.51150e11	−0.193077
$587$	−4.59660e11	−0.159796	−0.0798980	−	0.996803i	$-0.525459\pi$
$587$	−4.59660e11	−0.159796	−0.0798980	+	0.996803i	$0.525459\pi$
$588$	4.75246e12	1.63953
$589$	−9.39814e12	−3.21753
$590$	0	0
$591$	−9.00328e12	−3.03569
$592$	−8.20375e11	−0.274514
$593$	−1.64019e12	−0.544689	−0.272344	−	0.962200i	$-0.587799\pi$
$593$	−1.64019e12	−0.544689	−0.272344	+	0.962200i	$0.587799\pi$
$594$	−2.08477e12	−0.687098
$595$	0	0
$596$	−8.37174e11	−0.271774
$597$	−1.54424e12	−0.497542
$598$	4.56786e10	0.0146069
$599$	−5.20878e11	−0.165316	−0.0826581	−	0.996578i	$-0.526341\pi$
$599$	−5.20878e11	−0.165316	−0.0826581	+	0.996578i	$0.526341\pi$
$600$	0	0
$601$	2.82531e12	0.883346	0.441673	−	0.897176i	$-0.354385\pi$
$601$	2.82531e12	0.883346	0.441673	+	0.897176i	$0.354385\pi$
$602$	3.29557e11	0.102269
$603$	1.00428e12	0.309334
$604$	2.45393e12	0.750233
$605$	0	0
$606$	2.46348e11	0.0742031
$607$	1.67746e12	0.501538	0.250769	−	0.968047i	$-0.419316\pi$
$607$	1.67746e12	0.501538	0.250769	+	0.968047i	$0.419316\pi$
$608$	2.73289e12	0.811065
$609$	2.14461e12	0.631787
$610$	0	0
$611$	4.40477e11	0.127861
$612$	2.67256e12	0.770097
$613$	−1.32865e12	−0.380049	−0.190025	−	0.981779i	$-0.560857\pi$
$613$	−1.32865e12	−0.380049	−0.190025	+	0.981779i	$0.560857\pi$
$614$	7.68525e11	0.218223
$615$	0	0
$616$	−2.34275e12	−0.655561
$617$	−4.57147e12	−1.26991	−0.634954	−	0.772550i	$-0.718981\pi$
$617$	−4.57147e12	−1.26991	−0.634954	+	0.772550i	$0.718981\pi$
$618$	−1.29622e12	−0.357464
$619$	4.54328e12	1.24383	0.621916	−	0.783084i	$-0.286355\pi$
$619$	4.54328e12	1.24383	0.621916	+	0.783084i	$0.286355\pi$
$620$	0	0
$621$	3.53839e12	0.954758
$622$	9.44438e10	0.0252998
$623$	3.55544e12	0.945577
$624$	−1.82564e12	−0.482040
$625$	0	0
$626$	1.01872e12	0.265138
$627$	−1.97794e13	−5.11104
$628$	−2.50253e12	−0.642038
$629$	3.64567e11	0.0928644
$630$	0	0
$631$	1.79363e12	0.450402	0.225201	−	0.974312i	$-0.427696\pi$
$631$	1.79363e12	0.450402	0.225201	+	0.974312i	$0.427696\pi$
$632$	7.56746e11	0.188679
$633$	−3.23375e12	−0.800552
$634$	−6.13833e11	−0.150886
$635$	0	0
$636$	−5.55315e12	−1.34581
$637$	1.03278e12	0.248530
$638$	−2.46688e11	−0.0589460
$639$	9.75617e12	2.31487
$640$	0	0
$641$	−2.69122e10	−0.00629633	−0.00314816	−	0.999995i	$-0.501002\pi$
$641$	−2.69122e10	−0.00629633	−0.00314816	+	0.999995i	$0.501002\pi$
$642$	−1.52110e12	−0.353386
$643$	−4.08182e12	−0.941683	−0.470841	−	0.882218i	$-0.656050\pi$
$643$	−4.08182e12	−0.941683	−0.470841	+	0.882218i	$0.656050\pi$
$644$	1.96324e12	0.449766
$645$	0	0
$646$	−3.87744e11	−0.0875990
$647$	−5.34464e12	−1.19908	−0.599541	−	0.800344i	$-0.704650\pi$
$647$	−5.34464e12	−1.19908	−0.599541	+	0.800344i	$0.704650\pi$
$648$	3.94354e12	0.878614
$649$	−8.21010e12	−1.81655
$650$	0	0
$651$	−2.14292e13	−4.67617
$652$	−3.78974e12	−0.821287
$653$	5.76044e12	1.23979	0.619893	−	0.784687i	$-0.287176\pi$
$653$	5.76044e12	1.23979	0.619893	+	0.784687i	$0.287176\pi$
$654$	2.46182e12	0.526207
$655$	0	0
$656$	−2.07961e11	−0.0438445
$657$	1.06929e13	2.23900
$658$	−4.80012e11	−0.0998242
$659$	−3.13175e12	−0.646849	−0.323424	−	0.946254i	$-0.604834\pi$
$659$	−3.13175e12	−0.646849	−0.323424	+	0.946254i	$0.604834\pi$
$660$	0	0
$661$	4.20558e12	0.856878	0.428439	−	0.903571i	$-0.359064\pi$
$661$	4.20558e12	0.856878	0.428439	+	0.903571i	$0.359064\pi$
$662$	−1.38564e12	−0.280407
$663$	8.11295e11	0.163068
$664$	−6.39960e11	−0.127760
$665$	0	0
$666$	5.96087e11	0.117402
$667$	4.18693e11	0.0819085
$668$	−1.09713e12	−0.213189
$669$	−1.11938e13	−2.16053
$670$	0	0
$671$	2.78361e12	0.530098
$672$	6.23139e12	1.17875
$673$	−2.12765e12	−0.399791	−0.199896	−	0.979817i	$-0.564060\pi$
$673$	−2.12765e12	−0.399791	−0.199896	+	0.979817i	$0.564060\pi$
$674$	1.49288e12	0.278647
$675$	0	0
$676$	−4.07326e11	−0.0750209
$677$	−1.28416e12	−0.234947	−0.117473	−	0.993076i	$-0.537480\pi$
$677$	−1.28416e12	−0.234947	−0.117473	+	0.993076i	$0.537480\pi$
$678$	1.08802e12	0.197743
$679$	−1.76942e12	−0.319460
$680$	0	0
$681$	1.95171e13	3.47739
$682$	2.46493e12	0.436289
$683$	5.56147e12	0.977905	0.488953	−	0.872310i	$-0.337379\pi$
$683$	5.56147e12	0.977905	0.488953	+	0.872310i	$0.337379\pi$
$684$	2.50039e13	4.36773
$685$	0	0
$686$	1.30512e11	0.0225005
$687$	−5.37992e12	−0.921447
$688$	−2.57145e12	−0.437552
$689$	−1.20678e12	−0.204005
$690$	0	0
$691$	3.68773e12	0.615329	0.307665	−	0.951495i	$-0.400453\pi$
$691$	3.68773e12	0.615329	0.307665	+	0.951495i	$0.400453\pi$
$692$	8.31262e12	1.37804
$693$	−3.22859e13	−5.31757
$694$	2.78673e11	0.0456014
$695$	0	0
$696$	8.82282e11	0.142517
$697$	9.24160e10	0.0148320
$698$	8.71222e11	0.138925
$699$	5.46540e12	0.865914
$700$	0	0
$701$	−5.20245e12	−0.813724	−0.406862	−	0.913490i	$-0.633377\pi$
$701$	−5.20245e12	−0.813724	−0.406862	+	0.913490i	$0.633377\pi$
$702$	8.00026e11	0.124333
$703$	3.41082e12	0.526696
$704$	8.53760e12	1.30996
$705$	0	0
$706$	2.44198e11	0.0369932
$707$	2.30090e12	0.346346
$708$	1.44980e13	2.16849
$709$	−4.86534e12	−0.723111	−0.361556	−	0.932351i	$-0.617754\pi$
$709$	−4.86534e12	−0.723111	−0.361556	+	0.932351i	$0.617754\pi$
$710$	0	0
$711$	1.04289e13	1.53047
$712$	1.46269e12	0.213300
$713$	−4.18362e12	−0.606246
$714$	−8.84114e11	−0.127311
$715$	0	0
$716$	9.69346e12	1.37838
$717$	−8.73967e12	−1.23498
$718$	7.18304e10	0.0100867
$719$	−1.37103e12	−0.191323	−0.0956615	−	0.995414i	$-0.530497\pi$
$719$	−1.37103e12	−0.191323	−0.0956615	+	0.995414i	$0.530497\pi$
$720$	0	0
$721$	−1.21068e13	−1.66847
$722$	−2.47947e12	−0.339579
$723$	−2.14722e13	−2.92250
$724$	−1.17496e13	−1.58927
$725$	0	0
$726$	2.97941e12	0.398030
$727$	4.71537e12	0.626053	0.313027	−	0.949744i	$-0.398657\pi$
$727$	4.71537e12	0.626053	0.313027	+	0.949744i	$0.398657\pi$
$728$	8.99028e11	0.118627
$729$	1.35636e13	1.77869
$730$	0	0
$731$	1.14273e12	0.148018
$732$	−4.91549e12	−0.632800
$733$	−3.53043e12	−0.451710	−0.225855	−	0.974161i	$-0.572518\pi$
$733$	−3.53043e12	−0.451710	−0.225855	+	0.974161i	$0.572518\pi$
$734$	1.19068e12	0.151413
$735$	0	0
$736$	1.21655e12	0.152820
$737$	−1.50719e12	−0.188176
$738$	1.51105e11	0.0187511
$739$	4.47202e12	0.551574	0.275787	−	0.961219i	$-0.411061\pi$
$739$	4.47202e12	0.551574	0.275787	+	0.961219i	$0.411061\pi$
$740$	0	0
$741$	7.59032e12	0.924865
$742$	1.31510e12	0.159272
$743$	6.83692e12	0.823021	0.411510	−	0.911405i	$-0.365001\pi$
$743$	6.83692e12	0.823021	0.411510	+	0.911405i	$0.365001\pi$
$744$	−8.81584e12	−1.05484
$745$	0	0
$746$	1.19318e12	0.141053
$747$	−8.81940e12	−1.03633
$748$	−4.01086e12	−0.468469
$749$	−1.42071e13	−1.64944
$750$	0	0
$751$	−1.11725e13	−1.28165	−0.640825	−	0.767687i	$-0.721407\pi$
$751$	−1.11725e13	−1.28165	−0.640825	+	0.767687i	$0.721407\pi$
$752$	3.74542e12	0.427091
$753$	−2.18874e13	−2.48094
$754$	9.46660e10	0.0106665
$755$	0	0
$756$	3.43846e13	3.82839
$757$	−4.83288e12	−0.534903	−0.267451	−	0.963571i	$-0.586181\pi$
$757$	−4.83288e12	−0.534903	−0.267451	+	0.963571i	$0.586181\pi$
$758$	1.09923e12	0.120941
$759$	−8.80488e12	−0.963020
$760$	0	0
$761$	1.21260e12	0.131065	0.0655327	−	0.997850i	$-0.479125\pi$
$761$	1.21260e12	0.131065	0.0655327	+	0.997850i	$0.479125\pi$
$762$	2.24255e12	0.240960
$763$	2.29935e13	2.45609
$764$	−1.08828e13	−1.15563
$765$	0	0
$766$	−4.80000e11	−0.0503746
$767$	3.15062e12	0.328713
$768$	−1.37785e13	−1.42914
$769$	−8.88598e11	−0.0916298	−0.0458149	−	0.998950i	$-0.514588\pi$
$769$	−8.88598e11	−0.0916298	−0.0458149	+	0.998950i	$0.514588\pi$
$770$	0	0
$771$	1.76114e13	1.79494
$772$	−3.74288e12	−0.379252
$773$	1.29728e13	1.30685	0.653427	−	0.756990i	$-0.273331\pi$
$773$	1.29728e13	1.30685	0.653427	+	0.756990i	$0.273331\pi$
$774$	1.86842e12	0.187129
$775$	0	0
$776$	−7.27930e11	−0.0720629
$777$	7.77717e12	0.765468
$778$	−1.40613e12	−0.137600
$779$	8.64627e11	0.0841221
$780$	0	0
$781$	−1.46417e13	−1.40819
$782$	−1.72606e11	−0.0165054
$783$	7.33308e12	0.697202
$784$	8.78181e12	0.830160
$785$	0	0
$786$	−3.21116e12	−0.300096
$787$	−1.45875e13	−1.35549	−0.677743	−	0.735299i	$-0.737042\pi$
$787$	−1.45875e13	−1.35549	−0.677743	+	0.735299i	$0.737042\pi$
$788$	−1.70807e13	−1.57811
$789$	2.53682e13	2.33047
$790$	0	0
$791$	1.01621e13	0.922974
$792$	−1.32822e13	−1.19952
$793$	−1.06821e12	−0.0959236
$794$	−1.43088e12	−0.127765
$795$	0	0
$796$	−2.92968e12	−0.258649
$797$	3.89178e12	0.341653	0.170827	−	0.985301i	$-0.445356\pi$
$797$	3.89178e12	0.341653	0.170827	+	0.985301i	$0.445356\pi$
$798$	−8.27161e12	−0.722066
$799$	−1.66443e12	−0.144479
$800$	0	0
$801$	2.01576e13	1.73018
$802$	1.60651e12	0.137119
$803$	−1.60475e13	−1.36204
$804$	2.66149e12	0.224633
$805$	0	0
$806$	−9.45912e11	−0.0789484
$807$	2.88661e13	2.39584
$808$	9.46578e11	0.0781277
$809$	−9.37803e12	−0.769739	−0.384869	−	0.922971i	$-0.625753\pi$
$809$	−9.37803e12	−0.769739	−0.384869	+	0.922971i	$0.625753\pi$
$810$	0	0
$811$	−3.71605e12	−0.301639	−0.150820	−	0.988561i	$-0.548191\pi$
$811$	−3.71605e12	−0.301639	−0.150820	+	0.988561i	$0.548191\pi$
$812$	4.06869e12	0.328437
$813$	9.09131e12	0.729826
$814$	−8.94583e11	−0.0714185
$815$	0	0
$816$	6.89853e12	0.544692
$817$	1.06911e13	0.839509
$818$	1.32035e12	0.103110
$819$	1.23897e13	0.962237
$820$	0	0
$821$	1.34163e12	0.103059	0.0515297	−	0.998671i	$-0.483590\pi$
$821$	1.34163e12	0.103059	0.0515297	+	0.998671i	$0.483590\pi$
$822$	2.57776e12	0.196933
$823$	−1.75595e13	−1.33417	−0.667086	−	0.744980i	$-0.732459\pi$
$823$	−1.75595e13	−1.33417	−0.667086	+	0.744980i	$0.732459\pi$
$824$	−4.98066e12	−0.376370
$825$	0	0
$826$	−3.43340e12	−0.256634
$827$	−1.53041e13	−1.13771	−0.568856	−	0.822437i	$-0.692614\pi$
$827$	−1.53041e13	−1.13771	−0.568856	+	0.822437i	$0.692614\pi$
$828$	1.11306e13	0.822966
$829$	−3.79518e12	−0.279086	−0.139543	−	0.990216i	$-0.544563\pi$
$829$	−3.79518e12	−0.279086	−0.139543	+	0.990216i	$0.544563\pi$
$830$	0	0
$831$	−4.22601e13	−3.07415
$832$	−3.27629e12	−0.237043
$833$	−3.90255e12	−0.280832
$834$	−9.39432e11	−0.0672385
$835$	0	0
$836$	−3.75249e13	−2.65700
$837$	−7.32729e13	−5.16034
$838$	1.59838e12	0.111965
$839$	−2.03599e13	−1.41856	−0.709279	−	0.704928i	$-0.750979\pi$
$839$	−2.03599e13	−1.41856	−0.709279	+	0.704928i	$0.750979\pi$
$840$	0	0
$841$	−1.36394e13	−0.940187
$842$	−8.94884e11	−0.0613568
$843$	3.29771e13	2.24900
$844$	−6.13496e12	−0.416170
$845$	0	0
$846$	−2.72143e12	−0.182655
$847$	2.78278e13	1.85782
$848$	−1.02614e13	−0.681434
$849$	1.62690e13	1.07467
$850$	0	0
$851$	1.51834e12	0.0992397
$852$	2.58553e13	1.68101
$853$	1.62725e13	1.05240	0.526202	−	0.850359i	$-0.323616\pi$
$853$	1.62725e13	1.05240	0.526202	+	0.850359i	$0.323616\pi$
$854$	1.16408e12	0.0748900
$855$	0	0
$856$	−5.84472e12	−0.372076
$857$	2.82976e13	1.79199	0.895995	−	0.444063i	$-0.146463\pi$
$857$	2.82976e13	1.79199	0.895995	+	0.444063i	$0.146463\pi$
$858$	−1.99077e12	−0.125409
$859$	9.52876e12	0.597128	0.298564	−	0.954390i	$-0.403492\pi$
$859$	9.52876e12	0.597128	0.298564	+	0.954390i	$0.403492\pi$
$860$	0	0
$861$	1.97148e12	0.122258
$862$	4.14885e12	0.255944
$863$	−2.74609e13	−1.68526	−0.842628	−	0.538496i	$-0.818993\pi$
$863$	−2.74609e13	−1.68526	−0.842628	+	0.538496i	$0.818993\pi$
$864$	2.13070e13	1.30080
$865$	0	0
$866$	−4.57167e11	−0.0276213
$867$	2.81470e13	1.69179
$868$	−4.06547e13	−2.43093
$869$	−1.56512e13	−0.931019
$870$	0	0
$871$	5.78381e11	0.0340512
$872$	9.45940e12	0.554038
$873$	−1.00317e13	−0.584537
$874$	−1.61487e12	−0.0936128
$875$	0	0
$876$	2.83379e13	1.62592
$877$	−2.65120e13	−1.51337	−0.756684	−	0.653780i	$-0.773182\pi$
$877$	−2.65120e13	−1.51337	−0.756684	+	0.653780i	$0.773182\pi$
$878$	1.07250e12	0.0609074
$879$	−4.07687e13	−2.30344
$880$	0	0
$881$	−2.54720e13	−1.42453	−0.712266	−	0.701910i	$-0.752331\pi$
$881$	−2.54720e13	−1.42453	−0.712266	+	0.701910i	$0.752331\pi$
$882$	−6.38089e12	−0.355036
$883$	1.99724e13	1.10563	0.552813	−	0.833306i	$-0.313555\pi$
$883$	1.99724e13	1.10563	0.552813	+	0.833306i	$0.313555\pi$
$884$	1.53916e12	0.0847714
$885$	0	0
$886$	4.15476e12	0.226513
$887$	−1.07964e13	−0.585627	−0.292814	−	0.956170i	$-0.594592\pi$
$887$	−1.07964e13	−0.585627	−0.292814	+	0.956170i	$0.594592\pi$
$888$	3.19949e12	0.172672
$889$	2.09455e13	1.12469
$890$	0	0
$891$	−8.15611e13	−4.33544
$892$	−2.12366e13	−1.12316
$893$	−1.55721e13	−0.819436
$894$	1.57016e12	0.0822098
$895$	0	0
$896$	1.56921e13	0.813383
$897$	3.37886e12	0.174263
$898$	−4.44284e12	−0.227991
$899$	−8.67028e12	−0.442705
$900$	0	0
$901$	4.56006e12	0.230520
$902$	−2.26773e11	−0.0114067
$903$	2.43774e13	1.22009
$904$	4.18064e12	0.208202
$905$	0	0
$906$	−4.60245e12	−0.226941
$907$	−2.76658e13	−1.35741	−0.678705	−	0.734411i	$-0.737459\pi$
$907$	−2.76658e13	−1.35741	−0.678705	+	0.734411i	$0.737459\pi$
$908$	3.70272e13	1.80774
$909$	1.30450e13	0.633731
$910$	0	0
$911$	1.89840e13	0.913179	0.456590	−	0.889677i	$-0.349071\pi$
$911$	1.89840e13	0.913179	0.456590	+	0.889677i	$0.349071\pi$
$912$	6.45413e13	3.08931
$913$	1.32358e13	0.630422
$914$	−1.39868e12	−0.0662918
$915$	0	0
$916$	−1.02066e13	−0.479018
$917$	−2.99923e13	−1.40071
$918$	−3.02306e12	−0.140493
$919$	3.63901e13	1.68292	0.841460	−	0.540319i	$-0.181696\pi$
$919$	3.63901e13	1.68292	0.841460	+	0.540319i	$0.181696\pi$
$920$	0	0
$921$	5.68480e13	2.60343
$922$	−5.25041e12	−0.239279
$923$	5.61872e12	0.254818
$924$	−8.55623e13	−3.86152
$925$	0	0
$926$	3.64778e12	0.163035
$927$	−6.86394e13	−3.05291
$928$	2.52123e12	0.111596
$929$	−2.01262e13	−0.886525	−0.443263	−	0.896392i	$-0.646179\pi$
$929$	−2.01262e13	−0.886525	−0.443263	+	0.896392i	$0.646179\pi$
$930$	0	0
$931$	−3.65115e13	−1.59278
$932$	1.03688e13	0.450149
$933$	6.98604e12	0.301831
$934$	−4.09709e12	−0.176163
$935$	0	0
$936$	5.09704e12	0.217059
$937$	2.56608e12	0.108753	0.0543765	−	0.998521i	$-0.482683\pi$
$937$	2.56608e12	0.108753	0.0543765	+	0.998521i	$0.482683\pi$
$938$	−6.30294e11	−0.0265846
$939$	7.53552e13	3.16314
$940$	0	0
$941$	−2.94879e13	−1.22600	−0.613000	−	0.790083i	$-0.710038\pi$
$941$	−2.94879e13	−1.22600	−0.613000	+	0.790083i	$0.710038\pi$
$942$	4.69359e12	0.194212
$943$	3.84892e11	0.0158502
$944$	2.67900e13	1.09799
$945$	0	0
$946$	−2.80405e12	−0.113835
$947$	−5.93754e12	−0.239901	−0.119950	−	0.992780i	$-0.538274\pi$
$947$	−5.93754e12	−0.239901	−0.119950	+	0.992780i	$0.538274\pi$
$948$	2.76380e13	1.11140
$949$	6.15822e12	0.246466
$950$	0	0
$951$	−4.54054e13	−1.80009
$952$	−3.39716e12	−0.134045
$953$	−3.16358e13	−1.24240	−0.621199	−	0.783653i	$-0.713354\pi$
$953$	−3.16358e13	−1.24240	−0.621199	+	0.783653i	$0.713354\pi$
$954$	7.45594e12	0.291430
$955$	0	0
$956$	−1.65806e13	−0.642008
$957$	−1.82476e13	−0.703236
$958$	1.52373e12	0.0584470
$959$	2.40764e13	0.919194
$960$	0	0
$961$	6.01947e13	2.27668
$962$	3.43295e11	0.0129235
$963$	−8.05471e13	−3.01809
$964$	−4.07364e13	−1.51927
$965$	0	0
$966$	−3.68214e12	−0.136051
$967$	2.71105e13	0.997053	0.498526	−	0.866875i	$-0.333875\pi$
$967$	2.71105e13	0.997053	0.498526	+	0.866875i	$0.333875\pi$
$968$	1.14482e13	0.419082
$969$	−2.86816e13	−1.04507
$970$	0	0
$971$	−3.10338e13	−1.12034	−0.560168	−	0.828379i	$-0.689264\pi$
$971$	−3.10338e13	−1.12034	−0.560168	+	0.828379i	$0.689264\pi$
$972$	6.66540e13	2.39513
$973$	−8.77432e12	−0.313838
$974$	−5.12651e12	−0.182518
$975$	0	0
$976$	−9.08306e12	−0.320411
$977$	−4.89033e13	−1.71717	−0.858584	−	0.512672i	$-0.828656\pi$
$977$	−4.89033e13	−1.71717	−0.858584	+	0.512672i	$0.828656\pi$
$978$	7.10781e12	0.248434
$979$	−3.02516e13	−1.05251
$980$	0	0
$981$	1.30362e14	4.49406
$982$	6.15195e11	0.0211111
$983$	−7.20011e12	−0.245951	−0.122975	−	0.992410i	$-0.539244\pi$
$983$	−7.20011e12	−0.245951	−0.122975	+	0.992410i	$0.539244\pi$
$984$	8.11055e11	0.0275786
$985$	0	0
$986$	−3.57715e11	−0.0120529
$987$	−3.55066e13	−1.19092
$988$	1.44001e13	0.480795
$989$	4.75920e12	0.158180
$990$	0	0
$991$	−1.28220e13	−0.422303	−0.211151	−	0.977453i	$-0.567721\pi$
$991$	−1.28220e13	−0.422303	−0.211151	+	0.977453i	$0.567721\pi$
$992$	−2.51924e13	−0.825975
$993$	−1.02496e14	−3.34530
$994$	−6.12304e12	−0.198943
$995$	0	0
$996$	−2.33727e13	−0.752561
$997$	2.00149e13	0.641541	0.320771	−	0.947157i	$-0.396058\pi$
$997$	2.00149e13	0.641541	0.320771	+	0.947157i	$0.396058\pi$
$998$	−2.19969e12	−0.0701897
$999$	2.65925e13	0.844725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.k.1.14		27
5.2	odd	4		65.10.b.a.14.27	✓	54
5.3	odd	4		65.10.b.a.14.28	yes	54
5.4	even	2		325.10.a.l.1.14		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.10.b.a.14.27	✓	54	5.2	odd	4
65.10.b.a.14.28	yes	54	5.3	odd	4
325.10.a.k.1.14		27	1.1	even	1	trivial
325.10.a.l.1.14		27	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-3.55822 q^{2} -263.202 q^{3} -499.339 q^{4} +936.531 q^{6} +8747.23 q^{7} +3598.56 q^{8} +49592.5 q^{9} -74426.3 q^{11} +131427. q^{12} +28561.0 q^{13} -31124.5 q^{14} +242857. q^{16} -107923. q^{17} -176461. q^{18} -1.00971e6 q^{19} -2.30229e6 q^{21} +264825. q^{22} -449477. q^{23} -947151. q^{24} -101626. q^{26} -7.87224e6 q^{27} -4.36783e6 q^{28} -931512. q^{29} +9.30775e6 q^{31} -2.70660e6 q^{32} +1.95892e7 q^{33} +384015. q^{34} -2.47635e7 q^{36} -3.37801e6 q^{37} +3.59277e6 q^{38} -7.51732e6 q^{39} -856311. q^{41} +8.19205e6 q^{42} -1.05883e7 q^{43} +3.71640e7 q^{44} +1.59934e6 q^{46} +1.54223e7 q^{47} -6.39206e7 q^{48} +3.61604e7 q^{49} +2.84057e7 q^{51} -1.42616e7 q^{52} -4.22527e7 q^{53} +2.80111e7 q^{54} +3.14775e7 q^{56} +2.65758e8 q^{57} +3.31452e6 q^{58} +1.10312e8 q^{59} -3.74008e7 q^{61} -3.31190e7 q^{62} +4.33797e8 q^{63} -1.14712e8 q^{64} -6.97026e7 q^{66} +2.02507e7 q^{67} +5.38904e7 q^{68} +1.18303e8 q^{69} +1.96727e8 q^{71} +1.78462e8 q^{72} +2.15616e8 q^{73} +1.20197e7 q^{74} +5.04188e8 q^{76} -6.51024e8 q^{77} +2.67483e7 q^{78} +2.10291e8 q^{79} +1.09586e9 q^{81} +3.04694e6 q^{82} -1.77837e8 q^{83} +1.14962e9 q^{84} +3.76756e7 q^{86} +2.45176e8 q^{87} -2.67828e8 q^{88} +4.06464e8 q^{89} +2.49830e8 q^{91} +2.24441e8 q^{92} -2.44982e9 q^{93} -5.48759e7 q^{94} +7.12384e8 q^{96} -2.02283e8 q^{97} -1.28667e8 q^{98} -3.69098e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 48 q^{2} - 324 q^{3} + 6570 q^{4} - 1786 q^{6} - 3736 q^{7} - 36864 q^{8} + 214173 q^{9} - 66096 q^{11} - 114398 q^{12} + 771147 q^{13} - 359458 q^{14} + 998622 q^{16} - 779040 q^{17} - 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) \) 27 * q - 48 * q^2 - 324 * q^3 + 6570 * q^4 - 1786 * q^6 - 3736 * q^7 - 36864 * q^8 + 214173 * q^9 - 66096 * q^11 - 114398 * q^12 + 771147 * q^13 - 359458 * q^14 + 998622 * q^16 - 779040 * q^17 - 1709648 * q^18 - 761728 * q^19 - 2688628 * q^21 - 6061956 * q^22 - 4311518 * q^23 - 3567212 * q^24 - 1370928 * q^26 - 11899092 * q^27 - 137728 * q^28 + 4433670 * q^29 + 6106898 * q^31 - 32810006 * q^32 + 8840028 * q^33 + 18784070 * q^34 + 97588100 * q^36 - 29239496 * q^37 - 47346226 * q^38 - 9253764 * q^39 - 20531542 * q^41 - 106639738 * q^42 - 47500676 * q^43 + 43383046 * q^44 - 32105710 * q^46 - 134711080 * q^47 - 93484396 * q^48 + 146756645 * q^49 - 68396394 * q^51 + 187645770 * q^52 - 138404222 * q^53 + 1549570 * q^54 - 278046454 * q^56 - 103323872 * q^57 - 45680202 * q^58 - 495705656 * q^59 + 100256494 * q^61 - 380024874 * q^62 - 400619958 * q^63 + 554167194 * q^64 + 78712808 * q^66 - 805369894 * q^67 + 100947682 * q^68 - 659167072 * q^69 - 235437654 * q^71 - 1888149924 * q^72 - 251667626 * q^73 + 1855922170 * q^74 + 463619480 * q^76 - 1309691528 * q^77 - 51009946 * q^78 - 411718216 * q^79 + 1988439299 * q^81 - 2460333322 * q^82 - 2304849010 * q^83 - 476824718 * q^84 + 3316508396 * q^86 - 2481466544 * q^87 - 4501137582 * q^88 - 1619966906 * q^89 - 106703896 * q^91 - 2915597990 * q^92 - 3160578792 * q^93 + 4199181314 * q^94 + 2027406718 * q^96 + 861912866 * q^97 + 3534969754 * q^98 + 2142297632 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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