LMFDB - Embedded newform 333.10.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,10,Mod(1,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("333.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	333.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:	$171.506933443$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 5234 x^{12} + 33102 x^{11} + 10421899 x^{10} - 66002244 x^{9} + \cdots + 51\!\cdots\!20 $ x^14 - 6x^13 - 5234x^12 + 33102x^11 + 10421899x^10 - 66002244x^9 - 9839334124x^8 + 60512691564x^7 + 4405897359639x^6 - 25392014044254x^5 - 798948725725074x^4 + 3805427076948774x^3 + 41503424166638973x^2 - 100457651820986424*x + 51865911118483920
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 37)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$27.2642$ of defining polynomial
Character	$\chi$	$=$	333.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-30.2642 q^{2} +403.920 q^{4} -600.015 q^{5} -145.658 q^{7} +3270.94 q^{8} +O(q^{10})$	\(q-30.2642 q^{2} +403.920 q^{4} -600.015 q^{5} -145.658 q^{7} +3270.94 q^{8} +18159.0 q^{10} +66081.7 q^{11} +195642. q^{13} +4408.22 q^{14} -305800. q^{16} +90589.5 q^{17} -912070. q^{19} -242358. q^{20} -1.99991e6 q^{22} -414179. q^{23} -1.59311e6 q^{25} -5.92096e6 q^{26} -58834.3 q^{28} +591572. q^{29} +3.55042e6 q^{31} +7.58005e6 q^{32} -2.74162e6 q^{34} +87397.1 q^{35} +1.87416e6 q^{37} +2.76030e7 q^{38} -1.96261e6 q^{40} -1.38491e7 q^{41} -9.55458e6 q^{43} +2.66918e7 q^{44} +1.25348e7 q^{46} -3.81802e7 q^{47} -4.03324e7 q^{49} +4.82141e7 q^{50} +7.90240e7 q^{52} +4.13773e7 q^{53} -3.96500e7 q^{55} -476439. q^{56} -1.79034e7 q^{58} +9.05072e7 q^{59} -1.58361e8 q^{61} -1.07450e8 q^{62} -7.28347e7 q^{64} -1.17388e8 q^{65} +1.54266e8 q^{67} +3.65910e7 q^{68} -2.64500e6 q^{70} +4.66352e7 q^{71} -1.96666e8 q^{73} -5.67199e7 q^{74} -3.68404e8 q^{76} -9.62534e6 q^{77} +2.94979e8 q^{79} +1.83484e8 q^{80} +4.19132e8 q^{82} -4.20535e8 q^{83} -5.43551e7 q^{85} +2.89161e8 q^{86} +2.16149e8 q^{88} +3.67127e7 q^{89} -2.84969e7 q^{91} -1.67295e8 q^{92} +1.15549e9 q^{94} +5.47256e8 q^{95} +8.10863e8 q^{97} +1.22063e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8}+O(q^{10}) $ 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8	\( 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8} + 129003 q^{10} - 44949 q^{11} + 38913 q^{13} - 16434 q^{14} + 859962 q^{16} - 893196 q^{17} + 1532124 q^{19} - 4974963 q^{20} + 3195323 q^{22} - 5911773 q^{23} + 9978791 q^{25} - 10634475 q^{26} + 9469678 q^{28} - 8764377 q^{29} + 13188927 q^{31} - 23982750 q^{32} + 29914960 q^{34} - 29633556 q^{35} + 26238254 q^{37} - 23342796 q^{38} + 42889049 q^{40} - 22153785 q^{41} + 1779790 q^{43} + 83674089 q^{44} - 23239663 q^{46} - 40080072 q^{47} - 170457752 q^{49} + 89214633 q^{50} - 276889277 q^{52} + 102088122 q^{53} - 206797385 q^{55} + 294922194 q^{56} - 527059089 q^{58} - 56191266 q^{59} - 178507397 q^{61} + 27353505 q^{62} - 242330062 q^{64} + 174258810 q^{65} + 287062499 q^{67} - 308827572 q^{68} - 672888452 q^{70} - 224382678 q^{71} + 271440727 q^{73} - 89959728 q^{74} - 229522980 q^{76} - 671279994 q^{77} + 379128625 q^{79} - 1999017183 q^{80} + 551153781 q^{82} - 1664083206 q^{83} + 1982056546 q^{85} - 520253082 q^{86} + 684092585 q^{88} - 3293434692 q^{89} + 1715813946 q^{91} - 3729310881 q^{92} + 998499458 q^{94} - 878402766 q^{95} + 2385468336 q^{97} + 3234447132 q^{98}+O(q^{100}) \) 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8 + 129003 * q^10 - 44949 * q^11 + 38913 * q^13 - 16434 * q^14 + 859962 * q^16 - 893196 * q^17 + 1532124 * q^19 - 4974963 * q^20 + 3195323 * q^22 - 5911773 * q^23 + 9978791 * q^25 - 10634475 * q^26 + 9469678 * q^28 - 8764377 * q^29 + 13188927 * q^31 - 23982750 * q^32 + 29914960 * q^34 - 29633556 * q^35 + 26238254 * q^37 - 23342796 * q^38 + 42889049 * q^40 - 22153785 * q^41 + 1779790 * q^43 + 83674089 * q^44 - 23239663 * q^46 - 40080072 * q^47 - 170457752 * q^49 + 89214633 * q^50 - 276889277 * q^52 + 102088122 * q^53 - 206797385 * q^55 + 294922194 * q^56 - 527059089 * q^58 - 56191266 * q^59 - 178507397 * q^61 + 27353505 * q^62 - 242330062 * q^64 + 174258810 * q^65 + 287062499 * q^67 - 308827572 * q^68 - 672888452 * q^70 - 224382678 * q^71 + 271440727 * q^73 - 89959728 * q^74 - 229522980 * q^76 - 671279994 * q^77 + 379128625 * q^79 - 1999017183 * q^80 + 551153781 * q^82 - 1664083206 * q^83 + 1982056546 * q^85 - 520253082 * q^86 + 684092585 * q^88 - 3293434692 * q^89 + 1715813946 * q^91 - 3729310881 * q^92 + 998499458 * q^94 - 878402766 * q^95 + 2385468336 * q^97 + 3234447132 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−30.2642	−1.33750	−0.668750	−	0.743487i	$-0.733170\pi$
$2$	−30.2642	−1.33750	−0.668750	+	0.743487i	$0.733170\pi$
$3$	0	0
$3$	0	0
$4$	403.920	0.788907
$5$	−600.015	−0.429336	−0.214668	−	0.976687i	$-0.568867\pi$
$5$	−600.015	−0.429336	−0.214668	+	0.976687i	$0.568867\pi$
$6$	0	0
$7$	−145.658	−0.0229295	−0.0114647	−	0.999934i	$-0.503649\pi$
$7$	−145.658	−0.0229295	−0.0114647	+	0.999934i	$0.503649\pi$
$8$	3270.94	0.282337
$9$	0	0
$10$	18159.0	0.574237
$11$	66081.7	1.36086	0.680431	−	0.732812i	$-0.261792\pi$
$11$	66081.7	1.36086	0.680431	+	0.732812i	$0.261792\pi$
$12$	0	0
$13$	195642.	1.89984	0.949922	−	0.312488i	$-0.101162\pi$
$13$	195642.	1.89984	0.949922	+	0.312488i	$0.101162\pi$
$14$	4408.22	0.0306681
$15$	0	0
$16$	−305800.	−1.16653
$17$	90589.5	0.263062	0.131531	−	0.991312i	$-0.458011\pi$
$17$	90589.5	0.263062	0.131531	+	0.991312i	$0.458011\pi$
$18$	0	0
$19$	−912070.	−1.60560	−0.802799	−	0.596250i	$-0.796657\pi$
$19$	−912070.	−1.60560	−0.802799	+	0.596250i	$0.796657\pi$
$20$	−242358.	−0.338706
$21$	0	0
$22$	−1.99991e6	−1.82015
$23$	−414179.	−0.308612	−0.154306	−	0.988023i	$-0.549314\pi$
$23$	−414179.	−0.308612	−0.154306	+	0.988023i	$0.549314\pi$
$24$	0	0
$25$	−1.59311e6	−0.815671
$26$	−5.92096e6	−2.54104
$27$	0	0
$28$	−58834.3	−0.0180892
$29$	591572.	0.155316	0.0776580	−	0.996980i	$-0.475256\pi$
$29$	591572.	0.155316	0.0776580	+	0.996980i	$0.475256\pi$
$30$	0	0
$31$	3.55042e6	0.690481	0.345241	−	0.938514i	$-0.387797\pi$
$31$	3.55042e6	0.690481	0.345241	+	0.938514i	$0.387797\pi$
$32$	7.58005e6	1.27790
$33$	0	0
$34$	−2.74162e6	−0.351845
$35$	87397.1	0.00984444
$36$	0	0
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	2.76030e7	2.14749
$39$	0	0
$40$	−1.96261e6	−0.121217
$41$	−1.38491e7	−0.765410	−0.382705	−	0.923871i	$-0.625007\pi$
$41$	−1.38491e7	−0.765410	−0.382705	+	0.923871i	$0.625007\pi$
$42$	0	0
$43$	−9.55458e6	−0.426190	−0.213095	−	0.977031i	$-0.568354\pi$
$43$	−9.55458e6	−0.426190	−0.213095	+	0.977031i	$0.568354\pi$
$44$	2.66918e7	1.07359
$45$	0	0
$46$	1.25348e7	0.412768
$47$	−3.81802e7	−1.14129	−0.570647	−	0.821195i	$-0.693308\pi$
$47$	−3.81802e7	−1.14129	−0.570647	+	0.821195i	$0.693308\pi$
$48$	0	0
$49$	−4.03324e7	−0.999474
$50$	4.82141e7	1.09096
$51$	0	0
$52$	7.90240e7	1.49880
$53$	4.13773e7	0.720311	0.360156	−	0.932892i	$-0.382724\pi$
$53$	4.13773e7	0.720311	0.360156	+	0.932892i	$0.382724\pi$
$54$	0	0
$55$	−3.96500e7	−0.584267
$56$	−476439.	−0.00647383
$57$	0	0
$58$	−1.79034e7	−0.207735
$59$	9.05072e7	0.972409	0.486204	−	0.873845i	$-0.338381\pi$
$59$	9.05072e7	0.972409	0.486204	+	0.873845i	$0.338381\pi$
$60$	0	0
$61$	−1.58361e8	−1.46441	−0.732206	−	0.681083i	$-0.761509\pi$
$61$	−1.58361e8	−1.46441	−0.732206	+	0.681083i	$0.761509\pi$
$62$	−1.07450e8	−0.923519
$63$	0	0
$64$	−7.28347e7	−0.542660
$65$	−1.17388e8	−0.815671
$66$	0	0
$67$	1.54266e8	0.935265	0.467632	−	0.883923i	$-0.345107\pi$
$67$	1.54266e8	0.935265	0.467632	+	0.883923i	$0.345107\pi$
$68$	3.65910e7	0.207531
$69$	0	0
$70$	−2.64500e6	−0.0131669
$71$	4.66352e7	0.217797	0.108898	−	0.994053i	$-0.465268\pi$
$71$	4.66352e7	0.217797	0.108898	+	0.994053i	$0.465268\pi$
$72$	0	0
$73$	−1.96666e8	−0.810543	−0.405272	−	0.914196i	$-0.632823\pi$
$73$	−1.96666e8	−0.810543	−0.405272	+	0.914196i	$0.632823\pi$
$74$	−5.67199e7	−0.219884
$75$	0	0
$76$	−3.68404e8	−1.26667
$77$	−9.62534e6	−0.0312038
$78$	0	0
$79$	2.94979e8	0.852059	0.426030	−	0.904709i	$-0.359912\pi$
$79$	2.94979e8	0.852059	0.426030	+	0.904709i	$0.359912\pi$
$80$	1.83484e8	0.500834
$81$	0	0
$82$	4.19132e8	1.02374
$83$	−4.20535e8	−0.972638	−0.486319	−	0.873781i	$-0.661661\pi$
$83$	−4.20535e8	−0.972638	−0.486319	+	0.873781i	$0.661661\pi$
$84$	0	0
$85$	−5.43551e7	−0.112942
$86$	2.89161e8	0.570030
$87$	0	0
$88$	2.16149e8	0.384222
$89$	3.67127e7	0.0620242	0.0310121	−	0.999519i	$-0.490127\pi$
$89$	3.67127e7	0.0620242	0.0310121	+	0.999519i	$0.490127\pi$
$90$	0	0
$91$	−2.84969e7	−0.0435624
$92$	−1.67295e8	−0.243466
$93$	0	0
$94$	1.15549e9	1.52648
$95$	5.47256e8	0.689341
$96$	0	0
$97$	8.10863e8	0.929982	0.464991	−	0.885315i	$-0.346058\pi$
$97$	8.10863e8	0.929982	0.464991	+	0.885315i	$0.346058\pi$
$98$	1.22063e9	1.33680
$99$	0	0
$100$	−6.43488e8	−0.643488
$101$	−6.23959e8	−0.596637	−0.298318	−	0.954466i	$-0.596426\pi$
$101$	−6.23959e8	−0.596637	−0.298318	+	0.954466i	$0.596426\pi$
$102$	0	0
$103$	−3.04029e6	−0.00266163	−0.00133082	−	0.999999i	$-0.500424\pi$
$103$	−3.04029e6	−0.00266163	−0.00133082	+	0.999999i	$0.500424\pi$
$104$	6.39934e8	0.536396
$105$	0	0
$106$	−1.25225e9	−0.963417
$107$	−2.26313e9	−1.66910	−0.834549	−	0.550933i	$-0.814272\pi$
$107$	−2.26313e9	−1.66910	−0.834549	+	0.550933i	$0.814272\pi$
$108$	0	0
$109$	−2.94736e8	−0.199993	−0.0999963	−	0.994988i	$-0.531883\pi$
$109$	−2.94736e8	−0.199993	−0.0999963	+	0.994988i	$0.531883\pi$
$110$	1.19998e9	0.781457
$111$	0	0
$112$	4.45422e7	0.0267480
$113$	1.99177e9	1.14918	0.574588	−	0.818443i	$-0.305162\pi$
$113$	1.99177e9	1.14918	0.574588	+	0.818443i	$0.305162\pi$
$114$	0	0
$115$	2.48513e8	0.132498
$116$	2.38948e8	0.122530
$117$	0	0
$118$	−2.73913e9	−1.30060
$119$	−1.31951e7	−0.00603186
$120$	0	0
$121$	2.00885e9	0.851947
$122$	4.79266e9	1.95865
$123$	0	0
$124$	1.43409e9	0.544726
$125$	2.12779e9	0.779533
$126$	0	0
$127$	2.52353e9	0.860780	0.430390	−	0.902643i	$-0.358376\pi$
$127$	2.52353e9	0.860780	0.430390	+	0.902643i	$0.358376\pi$
$128$	−1.67671e9	−0.552093
$129$	0	0
$130$	3.55266e9	1.09096
$131$	−4.25243e9	−1.26158	−0.630792	−	0.775952i	$-0.717270\pi$
$131$	−4.25243e9	−1.26158	−0.630792	+	0.775952i	$0.717270\pi$
$132$	0	0
$133$	1.32850e8	0.0368155
$134$	−4.66874e9	−1.25092
$135$	0	0
$136$	2.96313e8	0.0742720
$137$	7.66156e9	1.85812	0.929062	−	0.369925i	$-0.120617\pi$
$137$	7.66156e9	1.85812	0.929062	+	0.369925i	$0.120617\pi$
$138$	0	0
$139$	−2.65515e9	−0.603284	−0.301642	−	0.953421i	$-0.597535\pi$
$139$	−2.65515e9	−0.603284	−0.301642	+	0.953421i	$0.597535\pi$
$140$	3.53015e7	0.00776635
$141$	0	0
$142$	−1.41138e9	−0.291303
$143$	1.29284e10	2.58543
$144$	0	0
$145$	−3.54952e8	−0.0666827
$146$	5.95193e9	1.08410
$147$	0	0
$148$	7.57012e8	0.129696
$149$	−8.29744e9	−1.37913	−0.689566	−	0.724223i	$-0.742199\pi$
$149$	−8.29744e9	−1.37913	−0.689566	+	0.724223i	$0.742199\pi$
$150$	0	0
$151$	4.81034e9	0.752973	0.376486	−	0.926422i	$-0.377132\pi$
$151$	4.81034e9	0.752973	0.376486	+	0.926422i	$0.377132\pi$
$152$	−2.98332e9	−0.453319
$153$	0	0
$154$	2.91303e8	0.0417351
$155$	−2.13030e9	−0.296448
$156$	0	0
$157$	6.25505e9	0.821642	0.410821	−	0.911716i	$-0.365242\pi$
$157$	6.25505e9	0.821642	0.410821	+	0.911716i	$0.365242\pi$
$158$	−8.92731e9	−1.13963
$159$	0	0
$160$	−4.54815e9	−0.548649
$161$	6.03285e7	0.00707630
$162$	0	0
$163$	1.54066e10	1.70948	0.854738	−	0.519060i	$-0.173718\pi$
$163$	1.54066e10	1.70948	0.854738	+	0.519060i	$0.173718\pi$
$164$	−5.59393e9	−0.603837
$165$	0	0
$166$	1.27272e10	1.30090
$167$	−1.42870e9	−0.142141	−0.0710703	−	0.997471i	$-0.522641\pi$
$167$	−1.42870e9	−0.142141	−0.0710703	+	0.997471i	$0.522641\pi$
$168$	0	0
$169$	2.76714e10	2.60941
$170$	1.64501e9	0.151060
$171$	0	0
$172$	−3.85929e9	−0.336225
$173$	−1.34393e10	−1.14070	−0.570349	−	0.821403i	$-0.693192\pi$
$173$	−1.34393e10	−1.14070	−0.570349	+	0.821403i	$0.693192\pi$
$174$	0	0
$175$	2.32049e8	0.0187029
$176$	−2.02078e10	−1.58749
$177$	0	0
$178$	−1.11108e9	−0.0829574
$179$	1.01581e9	0.0739561	0.0369781	−	0.999316i	$-0.488227\pi$
$179$	1.01581e9	0.0739561	0.0369781	+	0.999316i	$0.488227\pi$
$180$	0	0
$181$	−1.96698e10	−1.36222	−0.681108	−	0.732183i	$-0.738501\pi$
$181$	−1.96698e10	−1.36222	−0.681108	+	0.732183i	$0.738501\pi$
$182$	8.62435e8	0.0582647
$183$	0	0
$184$	−1.35475e9	−0.0871324
$185$	−1.12452e9	−0.0705824
$186$	0	0
$187$	5.98631e9	0.357991
$188$	−1.54218e10	−0.900375
$189$	0	0
$190$	−1.65622e10	−0.921993
$191$	−2.43763e10	−1.32531	−0.662655	−	0.748925i	$-0.730570\pi$
$191$	−2.43763e10	−1.32531	−0.662655	+	0.748925i	$0.730570\pi$
$192$	0	0
$193$	1.03785e10	0.538427	0.269213	−	0.963081i	$-0.413236\pi$
$193$	1.03785e10	0.538427	0.269213	+	0.963081i	$0.413236\pi$
$194$	−2.45401e10	−1.24385
$195$	0	0
$196$	−1.62911e10	−0.788492
$197$	2.89108e10	1.36761	0.683806	−	0.729664i	$-0.260324\pi$
$197$	2.89108e10	1.36761	0.683806	+	0.729664i	$0.260324\pi$
$198$	0	0
$199$	−3.25676e10	−1.47213	−0.736067	−	0.676908i	$-0.763319\pi$
$199$	−3.25676e10	−1.47213	−0.736067	+	0.676908i	$0.763319\pi$
$200$	−5.21095e9	−0.230294
$201$	0	0
$202$	1.88836e10	0.798002
$203$	−8.61672e7	−0.00356131
$204$	0	0
$205$	8.30967e9	0.328618
$206$	9.20119e7	0.00355993
$207$	0	0
$208$	−5.98273e10	−2.21623
$209$	−6.02711e10	−2.18500
$210$	0	0
$211$	6.13266e9	0.212999	0.106500	−	0.994313i	$-0.466036\pi$
$211$	6.13266e9	0.212999	0.106500	+	0.994313i	$0.466036\pi$
$212$	1.67131e10	0.568259
$213$	0	0
$214$	6.84917e10	2.23242
$215$	5.73289e9	0.182979
$216$	0	0
$217$	−5.17147e8	−0.0158324
$218$	8.91994e9	0.267490
$219$	0	0
$220$	−1.60155e10	−0.460933
$221$	1.77231e10	0.499776
$222$	0	0
$223$	−4.44779e10	−1.20441	−0.602203	−	0.798343i	$-0.705710\pi$
$223$	−4.44779e10	−1.20441	−0.602203	+	0.798343i	$0.705710\pi$
$224$	−1.10410e9	−0.0293016
$225$	0	0
$226$	−6.02793e10	−1.53702
$227$	−5.45228e10	−1.36289	−0.681447	−	0.731868i	$-0.738649\pi$
$227$	−5.45228e10	−1.36289	−0.681447	+	0.731868i	$0.738649\pi$
$228$	0	0
$229$	−1.14619e10	−0.275422	−0.137711	−	0.990472i	$-0.543974\pi$
$229$	−1.14619e10	−0.275422	−0.137711	+	0.990472i	$0.543974\pi$
$230$	−7.52105e9	−0.177216
$231$	0	0
$232$	1.93499e9	0.0438514
$233$	−4.18178e10	−0.929521	−0.464761	−	0.885436i	$-0.653860\pi$
$233$	−4.18178e10	−0.929521	−0.464761	+	0.885436i	$0.653860\pi$
$234$	0	0
$235$	2.29087e10	0.489999
$236$	3.65577e10	0.767140
$237$	0	0
$238$	3.99339e8	0.00806762
$239$	−1.09336e10	−0.216756	−0.108378	−	0.994110i	$-0.534566\pi$
$239$	−1.09336e10	−0.216756	−0.108378	+	0.994110i	$0.534566\pi$
$240$	0	0
$241$	−8.20140e10	−1.56607	−0.783035	−	0.621978i	$-0.786329\pi$
$241$	−8.20140e10	−1.56607	−0.783035	+	0.621978i	$0.786329\pi$
$242$	−6.07961e10	−1.13948
$243$	0	0
$244$	−6.39652e10	−1.15529
$245$	2.42000e10	0.429110
$246$	0	0
$247$	−1.78439e11	−3.05038
$248$	1.16132e10	0.194948
$249$	0	0
$250$	−6.43959e10	−1.04263
$251$	−3.67155e10	−0.583872	−0.291936	−	0.956438i	$-0.594299\pi$
$251$	−3.67155e10	−0.583872	−0.291936	+	0.956438i	$0.594299\pi$
$252$	0	0
$253$	−2.73696e10	−0.419978
$254$	−7.63726e10	−1.15129
$255$	0	0
$256$	8.80354e10	1.28108
$257$	8.85674e10	1.26641	0.633206	−	0.773984i	$-0.281739\pi$
$257$	8.85674e10	1.26641	0.633206	+	0.773984i	$0.281739\pi$
$258$	0	0
$259$	−2.72987e8	−0.00376958
$260$	−4.74156e10	−0.643489
$261$	0	0
$262$	1.28696e11	1.68737
$263$	−1.01698e10	−0.131072	−0.0655361	−	0.997850i	$-0.520876\pi$
$263$	−1.01698e10	−0.131072	−0.0655361	+	0.997850i	$0.520876\pi$
$264$	0	0
$265$	−2.48270e10	−0.309256
$266$	−4.02061e9	−0.0492407
$267$	0	0
$268$	6.23113e10	0.737837
$269$	1.18297e11	1.37749	0.688747	−	0.725002i	$-0.258161\pi$
$269$	1.18297e11	1.37749	0.688747	+	0.725002i	$0.258161\pi$
$270$	0	0
$271$	−1.64339e10	−0.185088	−0.0925439	−	0.995709i	$-0.529500\pi$
$271$	−1.64339e10	−0.185088	−0.0925439	+	0.995709i	$0.529500\pi$
$272$	−2.77022e10	−0.306870
$273$	0	0
$274$	−2.31871e11	−2.48524
$275$	−1.05275e11	−1.11002
$276$	0	0
$277$	1.33557e11	1.36304	0.681521	−	0.731799i	$-0.261319\pi$
$277$	1.33557e11	1.36304	0.681521	+	0.731799i	$0.261319\pi$
$278$	8.03558e10	0.806892
$279$	0	0
$280$	2.85871e8	0.00277945
$281$	−2.56040e10	−0.244979	−0.122490	−	0.992470i	$-0.539088\pi$
$281$	−2.56040e10	−0.244979	−0.122490	+	0.992470i	$0.539088\pi$
$282$	0	0
$283$	−1.73577e10	−0.160862	−0.0804309	−	0.996760i	$-0.525630\pi$
$283$	−1.73577e10	−0.160862	−0.0804309	+	0.996760i	$0.525630\pi$
$284$	1.88369e10	0.171821
$285$	0	0
$286$	−3.91267e11	−3.45801
$287$	2.01723e9	0.0175504
$288$	0	0
$289$	−1.10381e11	−0.930799
$290$	1.07423e10	0.0891882
$291$	0	0
$292$	−7.94374e10	−0.639443
$293$	4.35953e10	0.345570	0.172785	−	0.984960i	$-0.444723\pi$
$293$	4.35953e10	0.345570	0.172785	+	0.984960i	$0.444723\pi$
$294$	0	0
$295$	−5.43057e10	−0.417490
$296$	6.13027e9	0.0464159
$297$	0	0
$298$	2.51115e11	1.84459
$299$	−8.10309e10	−0.586314
$300$	0	0
$301$	1.39170e9	0.00977231
$302$	−1.45581e11	−1.00710
$303$	0	0
$304$	2.78910e11	1.87298
$305$	9.50189e10	0.628725
$306$	0	0
$307$	−1.13081e10	−0.0726551	−0.0363276	−	0.999340i	$-0.511566\pi$
$307$	−1.13081e10	−0.0726551	−0.0363276	+	0.999340i	$0.511566\pi$
$308$	−3.88787e9	−0.0246169
$309$	0	0
$310$	6.44719e10	0.396500
$311$	−1.95094e11	−1.18256	−0.591278	−	0.806468i	$-0.701376\pi$
$311$	−1.95094e11	−1.18256	−0.591278	+	0.806468i	$0.701376\pi$
$312$	0	0
$313$	−1.04305e11	−0.614267	−0.307133	−	0.951666i	$-0.599370\pi$
$313$	−1.04305e11	−0.614267	−0.307133	+	0.951666i	$0.599370\pi$
$314$	−1.89304e11	−1.09895
$315$	0	0
$316$	1.19148e11	0.672196
$317$	1.90469e11	1.05940	0.529698	−	0.848186i	$-0.322305\pi$
$317$	1.90469e11	1.05940	0.529698	+	0.848186i	$0.322305\pi$
$318$	0	0
$319$	3.90921e10	0.211364
$320$	4.37019e10	0.232984
$321$	0	0
$322$	−1.82579e9	−0.00946455
$323$	−8.26239e10	−0.422371
$324$	0	0
$325$	−3.11679e11	−1.54965
$326$	−4.66269e11	−2.28642
$327$	0	0
$328$	−4.52995e10	−0.216103
$329$	5.56126e9	0.0261693
$330$	0	0
$331$	2.87995e11	1.31874	0.659369	−	0.751819i	$-0.270823\pi$
$331$	2.87995e11	1.31874	0.659369	+	0.751819i	$0.270823\pi$
$332$	−1.69863e11	−0.767321
$333$	0	0
$334$	4.32385e10	0.190113
$335$	−9.25621e10	−0.401543
$336$	0	0
$337$	−2.87184e11	−1.21290	−0.606450	−	0.795122i	$-0.707407\pi$
$337$	−2.87184e11	−1.21290	−0.606450	+	0.795122i	$0.707407\pi$
$338$	−8.37453e11	−3.49008
$339$	0	0
$340$	−2.19551e10	−0.0891006
$341$	2.34618e11	0.939650
$342$	0	0
$343$	1.17526e10	0.0458468
$344$	−3.12524e10	−0.120329
$345$	0	0
$346$	4.06730e11	1.52568
$347$	4.00865e11	1.48428	0.742139	−	0.670246i	$-0.233811\pi$
$347$	4.00865e11	1.48428	0.742139	+	0.670246i	$0.233811\pi$
$348$	0	0
$349$	−2.02871e11	−0.731990	−0.365995	−	0.930617i	$-0.619271\pi$
$349$	−2.02871e11	−0.731990	−0.365995	+	0.930617i	$0.619271\pi$
$350$	−7.02277e9	−0.0250151
$351$	0	0
$352$	5.00903e11	1.73905
$353$	−2.77118e11	−0.949903	−0.474952	−	0.880012i	$-0.657534\pi$
$353$	−2.77118e11	−0.949903	−0.474952	+	0.880012i	$0.657534\pi$
$354$	0	0
$355$	−2.79818e10	−0.0935080
$356$	1.48290e10	0.0489314
$357$	0	0
$358$	−3.07427e10	−0.0989163
$359$	1.85627e11	0.589815	0.294908	−	0.955526i	$-0.404711\pi$
$359$	1.85627e11	0.589815	0.294908	+	0.955526i	$0.404711\pi$
$360$	0	0
$361$	5.09183e11	1.57794
$362$	5.95290e11	1.82196
$363$	0	0
$364$	−1.15105e10	−0.0343667
$365$	1.18002e11	0.347995
$366$	0	0
$367$	−1.75278e11	−0.504346	−0.252173	−	0.967682i	$-0.581145\pi$
$367$	−1.75278e11	−0.504346	−0.252173	+	0.967682i	$0.581145\pi$
$368$	1.26656e11	0.360006
$369$	0	0
$370$	3.40328e10	0.0944040
$371$	−6.02694e9	−0.0165163
$372$	0	0
$373$	−7.47050e11	−1.99830	−0.999148	−	0.0412732i	$-0.986859\pi$
$373$	−7.47050e11	−1.99830	−0.999148	+	0.0412732i	$0.986859\pi$
$374$	−1.81171e11	−0.478813
$375$	0	0
$376$	−1.24885e11	−0.322229
$377$	1.15736e11	0.295076
$378$	0	0
$379$	4.53099e10	0.112802	0.0564009	−	0.998408i	$-0.482037\pi$
$379$	4.53099e10	0.112802	0.0564009	+	0.998408i	$0.482037\pi$
$380$	2.21048e11	0.543826
$381$	0	0
$382$	7.37728e11	1.77260
$383$	−6.39288e10	−0.151811	−0.0759053	−	0.997115i	$-0.524185\pi$
$383$	−6.39288e10	−0.151811	−0.0759053	+	0.997115i	$0.524185\pi$
$384$	0	0
$385$	5.77535e9	0.0133969
$386$	−3.14097e11	−0.720146
$387$	0	0
$388$	3.27524e11	0.733669
$389$	−9.89182e10	−0.219030	−0.109515	−	0.993985i	$-0.534930\pi$
$389$	−9.89182e10	−0.219030	−0.109515	+	0.993985i	$0.534930\pi$
$390$	0	0
$391$	−3.75202e10	−0.0811839
$392$	−1.31925e11	−0.282188
$393$	0	0
$394$	−8.74963e11	−1.82918
$395$	−1.76992e11	−0.365820
$396$	0	0
$397$	−4.52208e11	−0.913652	−0.456826	−	0.889556i	$-0.651014\pi$
$397$	−4.52208e11	−0.913652	−0.456826	+	0.889556i	$0.651014\pi$
$398$	9.85633e11	1.96898
$399$	0	0
$400$	4.87171e11	0.951507
$401$	1.02424e10	0.0197811	0.00989055	−	0.999951i	$-0.496852\pi$
$401$	1.02424e10	0.0197811	0.00989055	+	0.999951i	$0.496852\pi$
$402$	0	0
$403$	6.94612e11	1.31181
$404$	−2.52030e11	−0.470691
$405$	0	0
$406$	2.60778e9	0.00476326
$407$	1.23848e11	0.223724
$408$	0	0
$409$	−1.46363e11	−0.258628	−0.129314	−	0.991604i	$-0.541278\pi$
$409$	−1.46363e11	−0.258628	−0.129314	+	0.991604i	$0.541278\pi$
$410$	−2.51485e11	−0.439527
$411$	0	0
$412$	−1.22804e9	−0.00209978
$413$	−1.31831e10	−0.0222968
$414$	0	0
$415$	2.52328e11	0.417588
$416$	1.48298e12	2.42781
$417$	0	0
$418$	1.82406e12	2.92244
$419$	−6.64776e10	−0.105369	−0.0526844	−	0.998611i	$-0.516778\pi$
$419$	−6.64776e10	−0.105369	−0.0526844	+	0.998611i	$0.516778\pi$
$420$	0	0
$421$	4.46135e11	0.692144	0.346072	−	0.938208i	$-0.387515\pi$
$421$	4.46135e11	0.692144	0.346072	+	0.938208i	$0.387515\pi$
$422$	−1.85600e11	−0.284887
$423$	0	0
$424$	1.35342e11	0.203370
$425$	−1.44319e11	−0.214572
$426$	0	0
$427$	2.30665e10	0.0335782
$428$	−9.14124e11	−1.31676
$429$	0	0
$430$	−1.73501e11	−0.244734
$431$	−8.08879e11	−1.12911	−0.564554	−	0.825396i	$-0.690952\pi$
$431$	−8.08879e11	−1.12911	−0.564554	+	0.825396i	$0.690952\pi$
$432$	0	0
$433$	−1.06908e12	−1.46155	−0.730775	−	0.682618i	$-0.760841\pi$
$433$	−1.06908e12	−1.46155	−0.730775	+	0.682618i	$0.760841\pi$
$434$	1.56510e10	0.0211758
$435$	0	0
$436$	−1.19050e11	−0.157776
$437$	3.77760e11	0.495506
$438$	0	0
$439$	−3.51205e11	−0.451306	−0.225653	−	0.974208i	$-0.572451\pi$
$439$	−3.51205e11	−0.451306	−0.225653	+	0.974208i	$0.572451\pi$
$440$	−1.29693e11	−0.164960
$441$	0	0
$442$	−5.36376e11	−0.668451
$443$	6.75971e11	0.833895	0.416947	−	0.908931i	$-0.363100\pi$
$443$	6.75971e11	0.833895	0.416947	+	0.908931i	$0.363100\pi$
$444$	0	0
$445$	−2.20282e10	−0.0266292
$446$	1.34609e12	1.61089
$447$	0	0
$448$	1.06090e10	0.0124429
$449$	−6.40975e11	−0.744273	−0.372137	−	0.928178i	$-0.621375\pi$
$449$	−6.40975e11	−0.744273	−0.372137	+	0.928178i	$0.621375\pi$
$450$	0	0
$451$	−9.15172e11	−1.04162
$452$	8.04517e11	0.906593
$453$	0	0
$454$	1.65009e12	1.82287
$455$	1.70986e10	0.0187029
$456$	0	0
$457$	1.27528e12	1.36767	0.683837	−	0.729635i	$-0.260310\pi$
$457$	1.27528e12	1.36767	0.683837	+	0.729635i	$0.260310\pi$
$458$	3.46886e11	0.368377
$459$	0	0
$460$	1.00380e11	0.104529
$461$	3.25176e11	0.335323	0.167662	−	0.985845i	$-0.446378\pi$
$461$	3.25176e11	0.335323	0.167662	+	0.985845i	$0.446378\pi$
$462$	0	0
$463$	2.32530e11	0.235160	0.117580	−	0.993063i	$-0.462486\pi$
$463$	2.32530e11	0.235160	0.117580	+	0.993063i	$0.462486\pi$
$464$	−1.80902e11	−0.181181
$465$	0	0
$466$	1.26558e12	1.24324
$467$	8.50334e11	0.827301	0.413651	−	0.910436i	$-0.364253\pi$
$467$	8.50334e11	0.827301	0.413651	+	0.910436i	$0.364253\pi$
$468$	0	0
$469$	−2.24701e10	−0.0214451
$470$	−6.93313e11	−0.655373
$471$	0	0
$472$	2.96043e11	0.274547
$473$	−6.31383e11	−0.579986
$474$	0	0
$475$	1.45302e12	1.30964
$476$	−5.32977e9	−0.00475858
$477$	0	0
$478$	3.30896e11	0.289912
$479$	3.41895e11	0.296745	0.148372	−	0.988932i	$-0.452597\pi$
$479$	3.41895e11	0.296745	0.148372	+	0.988932i	$0.452597\pi$
$480$	0	0
$481$	3.66665e11	0.312332
$482$	2.48208e12	2.09462
$483$	0	0
$484$	8.11414e11	0.672107
$485$	−4.86530e11	−0.399275
$486$	0	0
$487$	−2.09280e12	−1.68596	−0.842981	−	0.537943i	$-0.819201\pi$
$487$	−2.09280e12	−1.68596	−0.842981	+	0.537943i	$0.819201\pi$
$488$	−5.17989e11	−0.413458
$489$	0	0
$490$	−7.32394e11	−0.573935
$491$	2.22502e12	1.72769	0.863847	−	0.503755i	$-0.168048\pi$
$491$	2.22502e12	1.72769	0.863847	+	0.503755i	$0.168048\pi$
$492$	0	0
$493$	5.35902e10	0.0408577
$494$	5.40032e12	4.07989
$495$	0	0
$496$	−1.08572e12	−0.805469
$497$	−6.79280e9	−0.00499396
$498$	0	0
$499$	−1.23529e12	−0.891900	−0.445950	−	0.895058i	$-0.647134\pi$
$499$	−1.23529e12	−0.891900	−0.445950	+	0.895058i	$0.647134\pi$
$500$	8.59459e11	0.614979
$501$	0	0
$502$	1.11116e12	0.780929
$503$	1.12859e12	0.786103	0.393051	−	0.919516i	$-0.371419\pi$
$503$	1.12859e12	0.786103	0.393051	+	0.919516i	$0.371419\pi$
$504$	0	0
$505$	3.74385e11	0.256157
$506$	8.28319e11	0.561721
$507$	0	0
$508$	1.01931e12	0.679075
$509$	−2.94301e12	−1.94340	−0.971698	−	0.236227i	$-0.924089\pi$
$509$	−2.94301e12	−1.94340	−0.971698	+	0.236227i	$0.924089\pi$
$510$	0	0
$511$	2.86460e10	0.0185853
$512$	−1.80585e12	−1.16136
$513$	0	0
$514$	−2.68042e12	−1.69383
$515$	1.82422e9	0.00114273
$516$	0	0
$517$	−2.52301e12	−1.55315
$518$	8.26172e9	0.00504181
$519$	0	0
$520$	−3.83970e11	−0.230294
$521$	−5.75677e11	−0.342302	−0.171151	−	0.985245i	$-0.554749\pi$
$521$	−5.75677e11	−0.342302	−0.171151	+	0.985245i	$0.554749\pi$
$522$	0	0
$523$	−1.79678e12	−1.05011	−0.525057	−	0.851067i	$-0.675956\pi$
$523$	−1.79678e12	−1.05011	−0.525057	+	0.851067i	$0.675956\pi$
$524$	−1.71764e12	−0.995273
$525$	0	0
$526$	3.07780e11	0.175309
$527$	3.21631e11	0.181639
$528$	0	0
$529$	−1.62961e12	−0.904759
$530$	7.51368e11	0.413629
$531$	0	0
$532$	5.36610e10	0.0290440
$533$	−2.70947e12	−1.45416
$534$	0	0
$535$	1.35791e12	0.716604
$536$	5.04596e11	0.264060
$537$	0	0
$538$	−3.58017e12	−1.84240
$539$	−2.66523e12	−1.36015
$540$	0	0
$541$	−5.51533e11	−0.276811	−0.138406	−	0.990376i	$-0.544198\pi$
$541$	−5.51533e11	−0.276811	−0.138406	+	0.990376i	$0.544198\pi$
$542$	4.97357e11	0.247555
$543$	0	0
$544$	6.86673e11	0.336167
$545$	1.76846e11	0.0858640
$546$	0	0
$547$	−1.19064e12	−0.568639	−0.284320	−	0.958730i	$-0.591768\pi$
$547$	−1.19064e12	−0.568639	−0.284320	+	0.958730i	$0.591768\pi$
$548$	3.09466e12	1.46589
$549$	0	0
$550$	3.18607e12	1.48465
$551$	−5.39554e11	−0.249375
$552$	0	0
$553$	−4.29662e10	−0.0195373
$554$	−4.04201e12	−1.82307
$555$	0	0
$556$	−1.07247e12	−0.475935
$557$	2.96543e12	1.30539	0.652695	−	0.757621i	$-0.273639\pi$
$557$	2.96543e12	1.30539	0.652695	+	0.757621i	$0.273639\pi$
$558$	0	0
$559$	−1.86928e12	−0.809695
$560$	−2.67260e10	−0.0114839
$561$	0	0
$562$	7.74883e11	0.327660
$563$	−8.35493e11	−0.350473	−0.175237	−	0.984526i	$-0.556069\pi$
$563$	−8.35493e11	−0.350473	−0.175237	+	0.984526i	$0.556069\pi$
$564$	0	0
$565$	−1.19509e12	−0.493382
$566$	5.25316e11	0.215153
$567$	0	0
$568$	1.52541e11	0.0614920
$569$	−1.84629e12	−0.738405	−0.369203	−	0.929349i	$-0.620369\pi$
$569$	−1.84629e12	−0.738405	−0.369203	+	0.929349i	$0.620369\pi$
$570$	0	0
$571$	1.20489e12	0.474335	0.237167	−	0.971469i	$-0.423781\pi$
$571$	1.20489e12	0.474335	0.237167	+	0.971469i	$0.423781\pi$
$572$	5.22204e12	2.03966
$573$	0	0
$574$	−6.10499e10	−0.0234737
$575$	6.59831e11	0.251725
$576$	0	0
$577$	−6.55037e11	−0.246022	−0.123011	−	0.992405i	$-0.539255\pi$
$577$	−6.55037e11	−0.246022	−0.123011	+	0.992405i	$0.539255\pi$
$578$	3.34060e12	1.24494
$579$	0	0
$580$	−1.43372e11	−0.0526065
$581$	6.12544e10	0.0223020
$582$	0	0
$583$	2.73428e12	0.980245
$584$	−6.43282e11	−0.228846
$585$	0	0
$586$	−1.31938e12	−0.462200
$587$	9.24536e11	0.321405	0.160702	−	0.987003i	$-0.448624\pi$
$587$	9.24536e11	0.321405	0.160702	+	0.987003i	$0.448624\pi$
$588$	0	0
$589$	−3.23823e12	−1.10864
$590$	1.64352e12	0.558393
$591$	0	0
$592$	−5.73118e11	−0.191777
$593$	−1.47452e12	−0.489670	−0.244835	−	0.969565i	$-0.578734\pi$
$593$	−1.47452e12	−0.489670	−0.244835	+	0.969565i	$0.578734\pi$
$594$	0	0
$595$	7.91726e9	0.00258969
$596$	−3.35151e12	−1.08801
$597$	0	0
$598$	2.45233e12	0.784195
$599$	8.35093e11	0.265042	0.132521	−	0.991180i	$-0.457693\pi$
$599$	8.35093e11	0.265042	0.132521	+	0.991180i	$0.457693\pi$
$600$	0	0
$601$	2.80777e12	0.877861	0.438931	−	0.898521i	$-0.355357\pi$
$601$	2.80777e12	0.877861	0.438931	+	0.898521i	$0.355357\pi$
$602$	−4.21187e10	−0.0130705
$603$	0	0
$604$	1.94299e12	0.594026
$605$	−1.20534e12	−0.365771
$606$	0	0
$607$	−1.65202e11	−0.0493932	−0.0246966	−	0.999695i	$-0.507862\pi$
$607$	−1.65202e11	−0.0493932	−0.0246966	+	0.999695i	$0.507862\pi$
$608$	−6.91353e12	−2.05180
$609$	0	0
$610$	−2.87567e12	−0.840920
$611$	−7.46966e12	−2.16828
$612$	0	0
$613$	−3.34796e12	−0.957652	−0.478826	−	0.877910i	$-0.658937\pi$
$613$	−3.34796e12	−0.957652	−0.478826	+	0.877910i	$0.658937\pi$
$614$	3.42230e11	0.0971762
$615$	0	0
$616$	−3.14839e10	−0.00880999
$617$	1.04652e12	0.290712	0.145356	−	0.989379i	$-0.453567\pi$
$617$	1.04652e12	0.290712	0.145356	+	0.989379i	$0.453567\pi$
$618$	0	0
$619$	6.98655e12	1.91274	0.956368	−	0.292166i	$-0.0943760\pi$
$619$	6.98655e12	1.91274	0.956368	+	0.292166i	$0.0943760\pi$
$620$	−8.60474e11	−0.233870
$621$	0	0
$622$	5.90435e12	1.58167
$623$	−5.34750e9	−0.00142218
$624$	0	0
$625$	1.83483e12	0.480989
$626$	3.15671e12	0.821582
$627$	0	0
$628$	2.52654e12	0.648199
$629$	1.69779e11	0.0432471
$630$	0	0
$631$	−3.98579e12	−1.00088	−0.500440	−	0.865771i	$-0.666828\pi$
$631$	−3.98579e12	−1.00088	−0.500440	+	0.865771i	$0.666828\pi$
$632$	9.64860e11	0.240568
$633$	0	0
$634$	−5.76440e12	−1.41694
$635$	−1.51416e12	−0.369564
$636$	0	0
$637$	−7.89072e12	−1.89884
$638$	−1.18309e12	−0.282699
$639$	0	0
$640$	1.00605e12	0.237033
$641$	1.85369e11	0.0433686	0.0216843	−	0.999765i	$-0.493097\pi$
$641$	1.85369e11	0.0433686	0.0216843	+	0.999765i	$0.493097\pi$
$642$	0	0
$643$	6.07454e12	1.40141	0.700703	−	0.713453i	$-0.252870\pi$
$643$	6.07454e12	1.40141	0.700703	+	0.713453i	$0.252870\pi$
$644$	2.43679e10	0.00558254
$645$	0	0
$646$	2.50055e12	0.564922
$647$	−8.64572e12	−1.93969	−0.969845	−	0.243724i	$-0.921631\pi$
$647$	−8.64572e12	−1.93969	−0.969845	+	0.243724i	$0.921631\pi$
$648$	0	0
$649$	5.98087e12	1.32332
$650$	9.43271e12	2.07265
$651$	0	0
$652$	6.22305e12	1.34862
$653$	3.03713e11	0.0653663	0.0326831	−	0.999466i	$-0.489595\pi$
$653$	3.03713e11	0.0653663	0.0326831	+	0.999466i	$0.489595\pi$
$654$	0	0
$655$	2.55152e12	0.541644
$656$	4.23505e12	0.892876
$657$	0	0
$658$	−1.68307e11	−0.0350014
$659$	5.32280e12	1.09940	0.549700	−	0.835362i	$-0.314742\pi$
$659$	5.32280e12	1.09940	0.549700	+	0.835362i	$0.314742\pi$
$660$	0	0
$661$	2.57132e12	0.523901	0.261950	−	0.965081i	$-0.415634\pi$
$661$	2.57132e12	0.523901	0.261950	+	0.965081i	$0.415634\pi$
$662$	−8.71592e12	−1.76381
$663$	0	0
$664$	−1.37555e12	−0.274611
$665$	−7.97122e10	−0.0158062
$666$	0	0
$667$	−2.45016e11	−0.0479323
$668$	−5.77083e11	−0.112136
$669$	0	0
$670$	2.80132e12	0.537063
$671$	−1.04648e13	−1.99286
$672$	0	0
$673$	4.35627e12	0.818554	0.409277	−	0.912410i	$-0.365781\pi$
$673$	4.35627e12	0.818554	0.409277	+	0.912410i	$0.365781\pi$
$674$	8.69138e12	1.62225
$675$	0	0
$676$	1.11771e13	2.05858
$677$	6.14723e12	1.12468	0.562342	−	0.826905i	$-0.309901\pi$
$677$	6.14723e12	1.12468	0.562342	+	0.826905i	$0.309901\pi$
$678$	0	0
$679$	−1.18109e11	−0.0213240
$680$	−1.77792e11	−0.0318876
$681$	0	0
$682$	−7.10051e12	−1.25678
$683$	2.51421e12	0.442088	0.221044	−	0.975264i	$-0.429054\pi$
$683$	2.51421e12	0.442088	0.221044	+	0.975264i	$0.429054\pi$
$684$	0	0
$685$	−4.59705e12	−0.797759
$686$	−3.55682e11	−0.0613202
$687$	0	0
$688$	2.92179e12	0.497165
$689$	8.09514e12	1.36848
$690$	0	0
$691$	2.14470e12	0.357862	0.178931	−	0.983862i	$-0.442736\pi$
$691$	2.14470e12	0.357862	0.178931	+	0.983862i	$0.442736\pi$
$692$	−5.42842e12	−0.899904
$693$	0	0
$694$	−1.21318e13	−1.98522
$695$	1.59313e12	0.259011
$696$	0	0
$697$	−1.25458e12	−0.201350
$698$	6.13972e12	0.979036
$699$	0	0
$700$	9.37293e10	0.0147548
$701$	−7.67507e12	−1.20047	−0.600235	−	0.799824i	$-0.704926\pi$
$701$	−7.67507e12	−1.20047	−0.600235	+	0.799824i	$0.704926\pi$
$702$	0	0
$703$	−1.70937e12	−0.263959
$704$	−4.81304e12	−0.738486
$705$	0	0
$706$	8.38676e12	1.27050
$707$	9.08847e10	0.0136805
$708$	0	0
$709$	3.12348e12	0.464227	0.232114	−	0.972689i	$-0.425436\pi$
$709$	3.12348e12	0.464227	0.232114	+	0.972689i	$0.425436\pi$
$710$	8.46847e11	0.125067
$711$	0	0
$712$	1.20085e11	0.0175117
$713$	−1.47051e12	−0.213091
$714$	0	0
$715$	−7.75723e12	−1.11002
$716$	4.10307e11	0.0583445
$717$	0	0
$718$	−5.61785e12	−0.788878
$719$	5.15721e12	0.719673	0.359836	−	0.933015i	$-0.382832\pi$
$719$	5.15721e12	0.719673	0.359836	+	0.933015i	$0.382832\pi$
$720$	0	0
$721$	4.42843e8	6.10297e−5 0
$722$	−1.54100e13	−2.11050
$723$	0	0
$724$	−7.94502e12	−1.07466
$725$	−9.42437e11	−0.126687
$726$	0	0
$727$	−7.14105e12	−0.948107	−0.474053	−	0.880496i	$-0.657210\pi$
$727$	−7.14105e12	−0.948107	−0.474053	+	0.880496i	$0.657210\pi$
$728$	−9.32116e10	−0.0122993
$729$	0	0
$730$	−3.57125e12	−0.465444
$731$	−8.65544e11	−0.112114
$732$	0	0
$733$	3.16277e12	0.404669	0.202335	−	0.979316i	$-0.435147\pi$
$733$	3.16277e12	0.404669	0.202335	+	0.979316i	$0.435147\pi$
$734$	5.30463e12	0.674564
$735$	0	0
$736$	−3.13949e12	−0.394375
$737$	1.01942e13	1.27277
$738$	0	0
$739$	−1.79699e12	−0.221639	−0.110819	−	0.993841i	$-0.535348\pi$
$739$	−1.79699e12	−0.221639	−0.110819	+	0.993841i	$0.535348\pi$
$740$	−4.54219e11	−0.0556829
$741$	0	0
$742$	1.82400e11	0.0220906
$743$	−9.21252e12	−1.10899	−0.554496	−	0.832186i	$-0.687089\pi$
$743$	−9.21252e12	−1.10899	−0.554496	+	0.832186i	$0.687089\pi$
$744$	0	0
$745$	4.97859e12	0.592111
$746$	2.26088e13	2.67272
$747$	0	0
$748$	2.41799e12	0.282422
$749$	3.29643e11	0.0382715
$750$	0	0
$751$	5.67356e12	0.650843	0.325421	−	0.945569i	$-0.394494\pi$
$751$	5.67356e12	0.650843	0.325421	+	0.945569i	$0.394494\pi$
$752$	1.16755e13	1.33136
$753$	0	0
$754$	−3.50267e12	−0.394664
$755$	−2.88628e12	−0.323278
$756$	0	0
$757$	5.41977e12	0.599859	0.299929	−	0.953961i	$-0.403037\pi$
$757$	5.41977e12	0.599859	0.299929	+	0.953961i	$0.403037\pi$
$758$	−1.37127e12	−0.150873
$759$	0	0
$760$	1.79004e12	0.194626
$761$	−2.15873e12	−0.233328	−0.116664	−	0.993171i	$-0.537220\pi$
$761$	−2.15873e12	−0.233328	−0.116664	+	0.993171i	$0.537220\pi$
$762$	0	0
$763$	4.29307e10	0.00458572
$764$	−9.84608e12	−1.04555
$765$	0	0
$766$	1.93475e12	0.203047
$767$	1.77070e13	1.84742
$768$	0	0
$769$	−4.28032e12	−0.441375	−0.220688	−	0.975345i	$-0.570830\pi$
$769$	−4.28032e12	−0.441375	−0.220688	+	0.975345i	$0.570830\pi$
$770$	−1.74786e11	−0.0179184
$771$	0	0
$772$	4.19209e12	0.424769
$773$	−1.20590e13	−1.21480	−0.607400	−	0.794396i	$-0.707788\pi$
$773$	−1.20590e13	−1.21480	−0.607400	+	0.794396i	$0.707788\pi$
$774$	0	0
$775$	−5.65620e12	−0.563205
$776$	2.65228e12	0.262568
$777$	0	0
$778$	2.99368e12	0.292952
$779$	1.26313e13	1.22894
$780$	0	0
$781$	3.08174e12	0.296391
$782$	1.13552e12	0.108584
$783$	0	0
$784$	1.23336e13	1.16592
$785$	−3.75313e12	−0.352760
$786$	0	0
$787$	−8.78555e12	−0.816362	−0.408181	−	0.912901i	$-0.633837\pi$
$787$	−8.78555e12	−0.816362	−0.408181	+	0.912901i	$0.633837\pi$
$788$	1.16777e13	1.07892
$789$	0	0
$790$	5.35652e12	0.489284
$791$	−2.90118e11	−0.0263500
$792$	0	0
$793$	−3.09821e13	−2.78215
$794$	1.36857e13	1.22201
$795$	0	0
$796$	−1.31547e13	−1.16138
$797$	−5.07818e12	−0.445806	−0.222903	−	0.974841i	$-0.571553\pi$
$797$	−5.07818e12	−0.445806	−0.222903	+	0.974841i	$0.571553\pi$
$798$	0	0
$799$	−3.45872e12	−0.300231
$800$	−1.20758e13	−1.04235
$801$	0	0
$802$	−3.09977e11	−0.0264572
$803$	−1.29960e13	−1.10304
$804$	0	0
$805$	−3.61980e10	−0.00303811
$806$	−2.10219e13	−1.75454
$807$	0	0
$808$	−2.04093e12	−0.168452
$809$	−1.90437e13	−1.56308	−0.781542	−	0.623852i	$-0.785567\pi$
$809$	−1.90437e13	−1.56308	−0.781542	+	0.623852i	$0.785567\pi$
$810$	0	0
$811$	4.93947e12	0.400947	0.200473	−	0.979699i	$-0.435752\pi$
$811$	4.93947e12	0.400947	0.200473	+	0.979699i	$0.435752\pi$
$812$	−3.48047e10	−0.00280954
$813$	0	0
$814$	−3.74815e12	−0.299232
$815$	−9.24420e12	−0.733939
$816$	0	0
$817$	8.71444e12	0.684290
$818$	4.42956e12	0.345916
$819$	0	0
$820$	3.35644e12	0.259249
$821$	−6.16249e11	−0.0473382	−0.0236691	−	0.999720i	$-0.507535\pi$
$821$	−6.16249e11	−0.0473382	−0.0236691	+	0.999720i	$0.507535\pi$
$822$	0	0
$823$	−1.09076e13	−0.828763	−0.414382	−	0.910103i	$-0.636002\pi$
$823$	−1.09076e13	−0.828763	−0.414382	+	0.910103i	$0.636002\pi$
$824$	−9.94461e9	−0.000751476 0
$825$	0	0
$826$	3.98976e11	0.0298220
$827$	−1.53397e13	−1.14036	−0.570180	−	0.821520i	$-0.693126\pi$
$827$	−1.53397e13	−1.14036	−0.570180	+	0.821520i	$0.693126\pi$
$828$	0	0
$829$	1.86138e13	1.36880	0.684398	−	0.729109i	$-0.260065\pi$
$829$	1.86138e13	1.36880	0.684398	+	0.729109i	$0.260065\pi$
$830$	−7.63649e12	−0.558524
$831$	0	0
$832$	−1.42495e13	−1.03097
$833$	−3.65369e12	−0.262923
$834$	0	0
$835$	8.57244e11	0.0610260
$836$	−2.43447e13	−1.72376
$837$	0	0
$838$	2.01189e12	0.140931
$839$	−1.61742e12	−0.112692	−0.0563462	−	0.998411i	$-0.517945\pi$
$839$	−1.61742e12	−0.112692	−0.0563462	+	0.998411i	$0.517945\pi$
$840$	0	0
$841$	−1.41572e13	−0.975877
$842$	−1.35019e13	−0.925743
$843$	0	0
$844$	2.47711e12	0.168037
$845$	−1.66033e13	−1.12031
$846$	0	0
$847$	−2.92605e11	−0.0195347
$848$	−1.26531e13	−0.840267
$849$	0	0
$850$	4.36769e12	0.286990
$851$	−7.76237e11	−0.0507354
$852$	0	0
$853$	−1.32159e13	−0.854722	−0.427361	−	0.904081i	$-0.640557\pi$
$853$	−1.32159e13	−0.854722	−0.427361	+	0.904081i	$0.640557\pi$
$854$	−6.98090e11	−0.0449108
$855$	0	0
$856$	−7.40255e12	−0.471248
$857$	−1.80486e13	−1.14296	−0.571478	−	0.820617i	$-0.693630\pi$
$857$	−1.80486e13	−1.14296	−0.571478	+	0.820617i	$0.693630\pi$
$858$	0	0
$859$	4.76460e12	0.298578	0.149289	−	0.988794i	$-0.452302\pi$
$859$	4.76460e12	0.298578	0.149289	+	0.988794i	$0.452302\pi$
$860$	2.31563e12	0.144353
$861$	0	0
$862$	2.44800e13	1.51018
$863$	−2.58565e13	−1.58680	−0.793399	−	0.608702i	$-0.791690\pi$
$863$	−2.58565e13	−1.58680	−0.793399	+	0.608702i	$0.791690\pi$
$864$	0	0
$865$	8.06380e12	0.489742
$866$	3.23548e13	1.95482
$867$	0	0
$868$	−2.08886e11	−0.0124903
$869$	1.94928e13	1.15954
$870$	0	0
$871$	3.01810e13	1.77686
$872$	−9.64063e11	−0.0564653
$873$	0	0
$874$	−1.14326e13	−0.662740
$875$	−3.09930e11	−0.0178743
$876$	0	0
$877$	4.98151e12	0.284356	0.142178	−	0.989841i	$-0.454589\pi$
$877$	4.98151e12	0.284356	0.142178	+	0.989841i	$0.454589\pi$
$878$	1.06289e13	0.603621
$879$	0	0
$880$	1.21250e13	0.681567
$881$	−1.02559e12	−0.0573567	−0.0286783	−	0.999589i	$-0.509130\pi$
$881$	−1.02559e12	−0.0573567	−0.0286783	+	0.999589i	$0.509130\pi$
$882$	0	0
$883$	−2.77027e13	−1.53355	−0.766776	−	0.641915i	$-0.778140\pi$
$883$	−2.77027e13	−1.53355	−0.766776	+	0.641915i	$0.778140\pi$
$884$	7.15874e12	0.394277
$885$	0	0
$886$	−2.04577e13	−1.11533
$887$	−2.56421e13	−1.39090	−0.695452	−	0.718572i	$-0.744796\pi$
$887$	−2.56421e13	−1.39090	−0.695452	+	0.718572i	$0.744796\pi$
$888$	0	0
$889$	−3.67573e11	−0.0197372
$890$	6.66665e11	0.0356166
$891$	0	0
$892$	−1.79656e13	−0.950164
$893$	3.48230e13	1.83246
$894$	0	0
$895$	−6.09502e11	−0.0317520
$896$	2.44226e11	0.0126592
$897$	0	0
$898$	1.93986e13	0.995466
$899$	2.10033e12	0.107243
$900$	0	0
$901$	3.74835e12	0.189486
$902$	2.76969e13	1.39316
$903$	0	0
$904$	6.51496e12	0.324455
$905$	1.18022e13	0.584848
$906$	0	0
$907$	−2.92105e13	−1.43320	−0.716599	−	0.697485i	$-0.754302\pi$
$907$	−2.92105e13	−1.43320	−0.716599	+	0.697485i	$0.754302\pi$
$908$	−2.20229e13	−1.07520
$909$	0	0
$910$	−5.17474e11	−0.0250151
$911$	2.51001e13	1.20738	0.603688	−	0.797221i	$-0.293697\pi$
$911$	2.51001e13	1.20738	0.603688	+	0.797221i	$0.293697\pi$
$912$	0	0
$913$	−2.77897e13	−1.32363
$914$	−3.85953e13	−1.82927
$915$	0	0
$916$	−4.62971e12	−0.217282
$917$	6.19401e11	0.0289274
$918$	0	0
$919$	2.38576e13	1.10333	0.551667	−	0.834065i	$-0.313992\pi$
$919$	2.38576e13	1.10333	0.551667	+	0.834065i	$0.313992\pi$
$920$	8.12872e11	0.0374091
$921$	0	0
$922$	−9.84117e12	−0.448495
$923$	9.12382e12	0.413780
$924$	0	0
$925$	−2.98574e12	−0.134095
$926$	−7.03732e12	−0.314527
$927$	0	0
$928$	4.48414e12	0.198479
$929$	2.47859e13	1.09178	0.545888	−	0.837858i	$-0.316192\pi$
$929$	2.47859e13	1.09178	0.545888	+	0.837858i	$0.316192\pi$
$930$	0	0
$931$	3.67859e13	1.60475
$932$	−1.68911e13	−0.733306
$933$	0	0
$934$	−2.57347e13	−1.10652
$935$	−3.59188e12	−0.153698
$936$	0	0
$937$	2.19643e13	0.930870	0.465435	−	0.885082i	$-0.345898\pi$
$937$	2.19643e13	0.930870	0.465435	+	0.885082i	$0.345898\pi$
$938$	6.80041e11	0.0286828
$939$	0	0
$940$	9.25329e12	0.386563
$941$	−1.69142e13	−0.703231	−0.351616	−	0.936144i	$-0.614368\pi$
$941$	−1.69142e13	−0.703231	−0.351616	+	0.936144i	$0.614368\pi$
$942$	0	0
$943$	5.73600e12	0.236214
$944$	−2.76771e13	−1.13435
$945$	0	0
$946$	1.91083e13	0.775732
$947$	3.75974e13	1.51909	0.759544	−	0.650455i	$-0.225422\pi$
$947$	3.75974e13	1.51909	0.759544	+	0.650455i	$0.225422\pi$
$948$	0	0
$949$	−3.84762e13	−1.53991
$950$	−4.39746e13	−1.75164
$951$	0	0
$952$	−4.31604e10	−0.00170302
$953$	−2.47537e13	−0.972126	−0.486063	−	0.873924i	$-0.661567\pi$
$953$	−2.47537e13	−0.972126	−0.486063	+	0.873924i	$0.661567\pi$
$954$	0	0
$955$	1.46261e13	0.569003
$956$	−4.41630e12	−0.171001
$957$	0	0
$958$	−1.03472e13	−0.396896
$959$	−1.11597e12	−0.0426058
$960$	0	0
$961$	−1.38342e13	−0.523236
$962$	−1.10968e13	−0.417745
$963$	0	0
$964$	−3.31271e13	−1.23548
$965$	−6.22726e12	−0.231166
$966$	0	0
$967$	2.81613e13	1.03570	0.517849	−	0.855472i	$-0.326733\pi$
$967$	2.81613e13	1.03570	0.517849	+	0.855472i	$0.326733\pi$
$968$	6.57081e12	0.240536
$969$	0	0
$970$	1.47244e13	0.534030
$971$	−2.69137e13	−0.971599	−0.485800	−	0.874070i	$-0.661472\pi$
$971$	−2.69137e13	−0.971599	−0.485800	+	0.874070i	$0.661472\pi$
$972$	0	0
$973$	3.86744e11	0.0138330
$974$	6.33369e13	2.25497
$975$	0	0
$976$	4.84267e13	1.70829
$977$	2.48025e13	0.870905	0.435452	−	0.900212i	$-0.356588\pi$
$977$	2.48025e13	0.870905	0.435452	+	0.900212i	$0.356588\pi$
$978$	0	0
$979$	2.42604e12	0.0844064
$980$	9.77489e12	0.338528
$981$	0	0
$982$	−6.73383e13	−2.31079
$983$	−8.03233e12	−0.274379	−0.137190	−	0.990545i	$-0.543807\pi$
$983$	−8.03233e12	−0.274379	−0.137190	+	0.990545i	$0.543807\pi$
$984$	0	0
$985$	−1.73469e13	−0.587165
$986$	−1.62186e12	−0.0546472
$987$	0	0
$988$	−7.20753e13	−2.40647
$989$	3.95730e12	0.131527
$990$	0	0
$991$	−5.11207e13	−1.68370	−0.841850	−	0.539711i	$-0.818534\pi$
$991$	−5.11207e13	−1.68370	−0.841850	+	0.539711i	$0.818534\pi$
$992$	2.69124e13	0.882367
$993$	0	0
$994$	2.05579e11	0.00667942
$995$	1.95411e13	0.632040
$996$	0	0
$997$	−2.04571e13	−0.655717	−0.327859	−	0.944727i	$-0.606327\pi$
$997$	−2.04571e13	−0.655717	−0.327859	+	0.944727i	$0.606327\pi$
$998$	3.73850e13	1.19292
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.10.a.d.1.4		14
3.2	odd	2		37.10.a.b.1.11	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.11	✓	14	3.2	odd	2
333.10.a.d.1.4		14	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	333.a (trivial)

\(f(q)\)	\(=\)	\(q-30.2642 q^{2} +403.920 q^{4} -600.015 q^{5} -145.658 q^{7} +3270.94 q^{8} +O(q^{10})\)	\(q-30.2642 q^{2} +403.920 q^{4} -600.015 q^{5} -145.658 q^{7} +3270.94 q^{8} +18159.0 q^{10} +66081.7 q^{11} +195642. q^{13} +4408.22 q^{14} -305800. q^{16} +90589.5 q^{17} -912070. q^{19} -242358. q^{20} -1.99991e6 q^{22} -414179. q^{23} -1.59311e6 q^{25} -5.92096e6 q^{26} -58834.3 q^{28} +591572. q^{29} +3.55042e6 q^{31} +7.58005e6 q^{32} -2.74162e6 q^{34} +87397.1 q^{35} +1.87416e6 q^{37} +2.76030e7 q^{38} -1.96261e6 q^{40} -1.38491e7 q^{41} -9.55458e6 q^{43} +2.66918e7 q^{44} +1.25348e7 q^{46} -3.81802e7 q^{47} -4.03324e7 q^{49} +4.82141e7 q^{50} +7.90240e7 q^{52} +4.13773e7 q^{53} -3.96500e7 q^{55} -476439. q^{56} -1.79034e7 q^{58} +9.05072e7 q^{59} -1.58361e8 q^{61} -1.07450e8 q^{62} -7.28347e7 q^{64} -1.17388e8 q^{65} +1.54266e8 q^{67} +3.65910e7 q^{68} -2.64500e6 q^{70} +4.66352e7 q^{71} -1.96666e8 q^{73} -5.67199e7 q^{74} -3.68404e8 q^{76} -9.62534e6 q^{77} +2.94979e8 q^{79} +1.83484e8 q^{80} +4.19132e8 q^{82} -4.20535e8 q^{83} -5.43551e7 q^{85} +2.89161e8 q^{86} +2.16149e8 q^{88} +3.67127e7 q^{89} -2.84969e7 q^{91} -1.67295e8 q^{92} +1.15549e9 q^{94} +5.47256e8 q^{95} +8.10863e8 q^{97} +1.22063e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8}+O(q^{10}) \) 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8	\( 14 q - 48 q^{2} + 3498 q^{4} - 2841 q^{5} + 6632 q^{7} - 41046 q^{8} + 129003 q^{10} - 44949 q^{11} + 38913 q^{13} - 16434 q^{14} + 859962 q^{16} - 893196 q^{17} + 1532124 q^{19} - 4974963 q^{20} + 3195323 q^{22} - 5911773 q^{23} + 9978791 q^{25} - 10634475 q^{26} + 9469678 q^{28} - 8764377 q^{29} + 13188927 q^{31} - 23982750 q^{32} + 29914960 q^{34} - 29633556 q^{35} + 26238254 q^{37} - 23342796 q^{38} + 42889049 q^{40} - 22153785 q^{41} + 1779790 q^{43} + 83674089 q^{44} - 23239663 q^{46} - 40080072 q^{47} - 170457752 q^{49} + 89214633 q^{50} - 276889277 q^{52} + 102088122 q^{53} - 206797385 q^{55} + 294922194 q^{56} - 527059089 q^{58} - 56191266 q^{59} - 178507397 q^{61} + 27353505 q^{62} - 242330062 q^{64} + 174258810 q^{65} + 287062499 q^{67} - 308827572 q^{68} - 672888452 q^{70} - 224382678 q^{71} + 271440727 q^{73} - 89959728 q^{74} - 229522980 q^{76} - 671279994 q^{77} + 379128625 q^{79} - 1999017183 q^{80} + 551153781 q^{82} - 1664083206 q^{83} + 1982056546 q^{85} - 520253082 q^{86} + 684092585 q^{88} - 3293434692 q^{89} + 1715813946 q^{91} - 3729310881 q^{92} + 998499458 q^{94} - 878402766 q^{95} + 2385468336 q^{97} + 3234447132 q^{98}+O(q^{100}) \) 14 * q - 48 * q^2 + 3498 * q^4 - 2841 * q^5 + 6632 * q^7 - 41046 * q^8 + 129003 * q^10 - 44949 * q^11 + 38913 * q^13 - 16434 * q^14 + 859962 * q^16 - 893196 * q^17 + 1532124 * q^19 - 4974963 * q^20 + 3195323 * q^22 - 5911773 * q^23 + 9978791 * q^25 - 10634475 * q^26 + 9469678 * q^28 - 8764377 * q^29 + 13188927 * q^31 - 23982750 * q^32 + 29914960 * q^34 - 29633556 * q^35 + 26238254 * q^37 - 23342796 * q^38 + 42889049 * q^40 - 22153785 * q^41 + 1779790 * q^43 + 83674089 * q^44 - 23239663 * q^46 - 40080072 * q^47 - 170457752 * q^49 + 89214633 * q^50 - 276889277 * q^52 + 102088122 * q^53 - 206797385 * q^55 + 294922194 * q^56 - 527059089 * q^58 - 56191266 * q^59 - 178507397 * q^61 + 27353505 * q^62 - 242330062 * q^64 + 174258810 * q^65 + 287062499 * q^67 - 308827572 * q^68 - 672888452 * q^70 - 224382678 * q^71 + 271440727 * q^73 - 89959728 * q^74 - 229522980 * q^76 - 671279994 * q^77 + 379128625 * q^79 - 1999017183 * q^80 + 551153781 * q^82 - 1664083206 * q^83 + 1982056546 * q^85 - 520253082 * q^86 + 684092585 * q^88 - 3293434692 * q^89 + 1715813946 * q^91 - 3729310881 * q^92 + 998499458 * q^94 - 878402766 * q^95 + 2385468336 * q^97 + 3234447132 * q^98

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