LMFDB - Embedded newform 207.8.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,8,Mod(1,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("207.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	207.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:	$64.6637002752$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 466x^{4} + 540x^{3} + 48973x^{2} - 77282x - 1061812 $ x^6 - 2x^5 - 466x^4 + 540x^3 + 48973x^2 - 77282*x - 1061812
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$8.60678$ of defining polynomial
Character	$\chi$	$=$	207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.60678 q^{2} -35.7097 q^{4} -26.4395 q^{5} -248.118 q^{7} -1572.72 q^{8} +O(q^{10})$	\(q+9.60678 q^{2} -35.7097 q^{4} -26.4395 q^{5} -248.118 q^{7} -1572.72 q^{8} -253.998 q^{10} -43.2804 q^{11} -5826.52 q^{13} -2383.62 q^{14} -10538.0 q^{16} -4647.30 q^{17} +45421.2 q^{19} +944.146 q^{20} -415.786 q^{22} +12167.0 q^{23} -77426.0 q^{25} -55974.1 q^{26} +8860.23 q^{28} +257923. q^{29} -140277. q^{31} +100073. q^{32} -44645.6 q^{34} +6560.12 q^{35} +154610. q^{37} +436352. q^{38} +41582.0 q^{40} +633612. q^{41} -542636. q^{43} +1545.53 q^{44} +116886. q^{46} +568868. q^{47} -761980. q^{49} -743814. q^{50} +208063. q^{52} +428507. q^{53} +1144.31 q^{55} +390222. q^{56} +2.47781e6 q^{58} +1.15308e6 q^{59} +2.75009e6 q^{61} -1.34761e6 q^{62} +2.31024e6 q^{64} +154050. q^{65} +2.84531e6 q^{67} +165954. q^{68} +63021.6 q^{70} -259607. q^{71} -1.46832e6 q^{73} +1.48531e6 q^{74} -1.62198e6 q^{76} +10738.7 q^{77} +3.28775e6 q^{79} +278619. q^{80} +6.08697e6 q^{82} +3.90022e6 q^{83} +122872. q^{85} -5.21299e6 q^{86} +68068.1 q^{88} +3.48438e6 q^{89} +1.44567e6 q^{91} -434480. q^{92} +5.46500e6 q^{94} -1.20091e6 q^{95} -1.32707e7 q^{97} -7.32018e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8}+O(q^{10}) $ 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8	\( 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8} - 13042 q^{10} + 14824 q^{11} - 756 q^{13} + 3926 q^{14} - 13022 q^{16} + 69484 q^{17} - 43864 q^{19} - 78886 q^{20} + 98204 q^{22} + 73002 q^{23} + 228018 q^{25} + 311956 q^{26} - 545442 q^{28} + 311100 q^{29} - 245248 q^{31} + 390156 q^{32} + 235834 q^{34} + 1331256 q^{35} - 630044 q^{37} - 80910 q^{38} - 2153982 q^{40} + 969204 q^{41} - 1770208 q^{43} + 1749140 q^{44} + 97336 q^{46} + 1400024 q^{47} + 1985598 q^{49} + 956660 q^{50} + 3217272 q^{52} + 1573516 q^{53} - 431296 q^{55} - 7740702 q^{56} + 5987188 q^{58} + 1410320 q^{59} - 942172 q^{61} - 3334412 q^{62} + 1996866 q^{64} + 420944 q^{65} - 452072 q^{67} + 9258254 q^{68} + 21981136 q^{70} - 122928 q^{71} + 16490716 q^{73} + 600104 q^{74} + 7428658 q^{76} - 7239696 q^{77} + 2458408 q^{79} - 19440230 q^{80} + 20510784 q^{82} + 7566456 q^{83} + 5817744 q^{85} + 669666 q^{86} + 14775668 q^{88} + 20368036 q^{89} + 8815576 q^{91} + 2165726 q^{92} + 16952576 q^{94} - 5143832 q^{95} + 12586972 q^{97} + 39164812 q^{98}+O(q^{100}) \) 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8 - 13042 * q^10 + 14824 * q^11 - 756 * q^13 + 3926 * q^14 - 13022 * q^16 + 69484 * q^17 - 43864 * q^19 - 78886 * q^20 + 98204 * q^22 + 73002 * q^23 + 228018 * q^25 + 311956 * q^26 - 545442 * q^28 + 311100 * q^29 - 245248 * q^31 + 390156 * q^32 + 235834 * q^34 + 1331256 * q^35 - 630044 * q^37 - 80910 * q^38 - 2153982 * q^40 + 969204 * q^41 - 1770208 * q^43 + 1749140 * q^44 + 97336 * q^46 + 1400024 * q^47 + 1985598 * q^49 + 956660 * q^50 + 3217272 * q^52 + 1573516 * q^53 - 431296 * q^55 - 7740702 * q^56 + 5987188 * q^58 + 1410320 * q^59 - 942172 * q^61 - 3334412 * q^62 + 1996866 * q^64 + 420944 * q^65 - 452072 * q^67 + 9258254 * q^68 + 21981136 * q^70 - 122928 * q^71 + 16490716 * q^73 + 600104 * q^74 + 7428658 * q^76 - 7239696 * q^77 + 2458408 * q^79 - 19440230 * q^80 + 20510784 * q^82 + 7566456 * q^83 + 5817744 * q^85 + 669666 * q^86 + 14775668 * q^88 + 20368036 * q^89 + 8815576 * q^91 + 2165726 * q^92 + 16952576 * q^94 - 5143832 * q^95 + 12586972 * q^97 + 39164812 * 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 $

$2$	9.60678	0.849128	0.424564	−	0.905398i	$-0.360427\pi$
$2$	9.60678	0.849128	0.424564	+	0.905398i	$0.360427\pi$
$3$	0	0
$3$	0	0
$4$	−35.7097	−0.278982
$5$	−26.4395	−0.0945927	−0.0472964	−	0.998881i	$-0.515061\pi$
$5$	−26.4395	−0.0945927	−0.0472964	+	0.998881i	$0.515061\pi$
$6$	0	0
$7$	−248.118	−0.273411	−0.136705	−	0.990612i	$-0.543651\pi$
$7$	−248.118	−0.273411	−0.136705	+	0.990612i	$0.543651\pi$
$8$	−1572.72	−1.08602
$9$	0	0
$10$	−253.998	−0.0803213
$11$	−43.2804	−0.00980431	−0.00490215	−	0.999988i	$-0.501560\pi$
$11$	−43.2804	−0.00980431	−0.00490215	+	0.999988i	$0.501560\pi$
$12$	0	0
$13$	−5826.52	−0.735542	−0.367771	−	0.929916i	$-0.619879\pi$
$13$	−5826.52	−0.735542	−0.367771	+	0.929916i	$0.619879\pi$
$14$	−2383.62	−0.232161
$15$	0	0
$16$	−10538.0	−0.643187
$17$	−4647.30	−0.229419	−0.114710	−	0.993399i	$-0.536594\pi$
$17$	−4647.30	−0.229419	−0.114710	+	0.993399i	$0.536594\pi$
$18$	0	0
$19$	45421.2	1.51922	0.759611	−	0.650378i	$-0.225389\pi$
$19$	45421.2	1.51922	0.759611	+	0.650378i	$0.225389\pi$
$20$	944.146	0.0263897
$21$	0	0
$22$	−415.786	−0.00832511
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	−77426.0	−0.991052
$26$	−55974.1	−0.624569
$27$	0	0
$28$	8860.23	0.0762767
$29$	257923.	1.96380	0.981900	−	0.189399i	$-0.0606540\pi$
$29$	257923.	1.96380	0.981900	+	0.189399i	$0.0606540\pi$
$30$	0	0
$31$	−140277.	−0.845709	−0.422855	−	0.906198i	$-0.638972\pi$
$31$	−140277.	−0.845709	−0.422855	+	0.906198i	$0.638972\pi$
$32$	100073.	0.539871
$33$	0	0
$34$	−44645.6	−0.194806
$35$	6560.12	0.0258627
$36$	0	0
$37$	154610.	0.501802	0.250901	−	0.968013i	$-0.419273\pi$
$37$	154610.	0.501802	0.250901	+	0.968013i	$0.419273\pi$
$38$	436352.	1.29001
$39$	0	0
$40$	41582.0	0.102730
$41$	633612.	1.43575	0.717876	−	0.696171i	$-0.245114\pi$
$41$	633612.	1.43575	0.717876	+	0.696171i	$0.245114\pi$
$42$	0	0
$43$	−542636.	−1.04080	−0.520402	−	0.853921i	$-0.674218\pi$
$43$	−542636.	−1.04080	−0.520402	+	0.853921i	$0.674218\pi$
$44$	1545.53	0.00273523
$45$	0	0
$46$	116886.	0.177055
$47$	568868.	0.799225	0.399613	−	0.916684i	$-0.369145\pi$
$47$	568868.	0.799225	0.399613	+	0.916684i	$0.369145\pi$
$48$	0	0
$49$	−761980.	−0.925247
$50$	−743814.	−0.841530
$51$	0	0
$52$	208063.	0.205203
$53$	428507.	0.395359	0.197680	−	0.980267i	$-0.436659\pi$
$53$	428507.	0.395359	0.197680	+	0.980267i	$0.436659\pi$
$54$	0	0
$55$	1144.31	0.000927416 0
$56$	390222.	0.296929
$57$	0	0
$58$	2.47781e6	1.66752
$59$	1.15308e6	0.730935	0.365467	−	0.930824i	$-0.380909\pi$
$59$	1.15308e6	0.730935	0.365467	+	0.930824i	$0.380909\pi$
$60$	0	0
$61$	2.75009e6	1.55129	0.775645	−	0.631170i	$-0.217425\pi$
$61$	2.75009e6	1.55129	0.775645	+	0.631170i	$0.217425\pi$
$62$	−1.34761e6	−0.718115
$63$	0	0
$64$	2.31024e6	1.10161
$65$	154050.	0.0695769
$66$	0	0
$67$	2.84531e6	1.15576	0.577880	−	0.816122i	$-0.303880\pi$
$67$	2.84531e6	1.15576	0.577880	+	0.816122i	$0.303880\pi$
$68$	165954.	0.0640038
$69$	0	0
$70$	63021.6	0.0219607
$71$	−259607.	−0.0860820	−0.0430410	−	0.999073i	$-0.513705\pi$
$71$	−259607.	−0.0860820	−0.0430410	+	0.999073i	$0.513705\pi$
$72$	0	0
$73$	−1.46832e6	−0.441765	−0.220882	−	0.975300i	$-0.570894\pi$
$73$	−1.46832e6	−0.441765	−0.220882	+	0.975300i	$0.570894\pi$
$74$	1.48531e6	0.426094
$75$	0	0
$76$	−1.62198e6	−0.423836
$77$	10738.7	0.00268060
$78$	0	0
$79$	3.28775e6	0.750246	0.375123	−	0.926975i	$-0.377600\pi$
$79$	3.28775e6	0.750246	0.375123	+	0.926975i	$0.377600\pi$
$80$	278619.	0.0608408
$81$	0	0
$82$	6.08697e6	1.21914
$83$	3.90022e6	0.748715	0.374357	−	0.927285i	$-0.377863\pi$
$83$	3.90022e6	0.748715	0.374357	+	0.927285i	$0.377863\pi$
$84$	0	0
$85$	122872.	0.0217014
$86$	−5.21299e6	−0.883776
$87$	0	0
$88$	68068.1	0.0106477
$89$	3.48438e6	0.523915	0.261958	−	0.965079i	$-0.415632\pi$
$89$	3.48438e6	0.523915	0.261958	+	0.965079i	$0.415632\pi$
$90$	0	0
$91$	1.44567e6	0.201105
$92$	−434480.	−0.0581718
$93$	0	0
$94$	5.46500e6	0.678644
$95$	−1.20091e6	−0.143707
$96$	0	0
$97$	−1.32707e7	−1.47636	−0.738181	−	0.674602i	$-0.764315\pi$
$97$	−1.32707e7	−1.47636	−0.738181	+	0.674602i	$0.764315\pi$
$98$	−7.32018e6	−0.785653
$99$	0	0
$100$	2.76486e6	0.276486
$101$	−1.25090e7	−1.20809	−0.604044	−	0.796951i	$-0.706445\pi$
$101$	−1.25090e7	−1.20809	−0.604044	+	0.796951i	$0.706445\pi$
$102$	0	0
$103$	4.88961e6	0.440904	0.220452	−	0.975398i	$-0.429247\pi$
$103$	4.88961e6	0.440904	0.220452	+	0.975398i	$0.429247\pi$
$104$	9.16350e6	0.798813
$105$	0	0
$106$	4.11657e6	0.335711
$107$	2.40036e7	1.89423	0.947115	−	0.320894i	$-0.103983\pi$
$107$	2.40036e7	1.89423	0.947115	+	0.320894i	$0.103983\pi$
$108$	0	0
$109$	8.50352e6	0.628936	0.314468	−	0.949268i	$-0.398174\pi$
$109$	8.50352e6	0.628936	0.314468	+	0.949268i	$0.398174\pi$
$110$	10993.2	0.000787495 0
$111$	0	0
$112$	2.61467e6	0.175854
$113$	−1.09729e7	−0.715394	−0.357697	−	0.933838i	$-0.616438\pi$
$113$	−1.09729e7	−0.715394	−0.357697	+	0.933838i	$0.616438\pi$
$114$	0	0
$115$	−321689.	−0.0197239
$116$	−9.21036e6	−0.547865
$117$	0	0
$118$	1.10774e7	0.620657
$119$	1.15308e6	0.0627257
$120$	0	0
$121$	−1.94853e7	−0.999904
$122$	2.64195e7	1.31724
$123$	0	0
$124$	5.00925e6	0.235938
$125$	4.11269e6	0.188339
$126$	0	0
$127$	1.91317e7	0.828784	0.414392	−	0.910099i	$-0.363994\pi$
$127$	1.91317e7	0.828784	0.414392	+	0.910099i	$0.363994\pi$
$128$	9.38465e6	0.395534
$129$	0	0
$130$	1.47993e6	0.0590797
$131$	−2.58491e7	−1.00461	−0.502304	−	0.864691i	$-0.667514\pi$
$131$	−2.58491e7	−1.00461	−0.502304	+	0.864691i	$0.667514\pi$
$132$	0	0
$133$	−1.12698e7	−0.415372
$134$	2.73343e7	0.981387
$135$	0	0
$136$	7.30893e6	0.249154
$137$	1.41054e7	0.468667	0.234333	−	0.972156i	$-0.424709\pi$
$137$	1.41054e7	0.468667	0.234333	+	0.972156i	$0.424709\pi$
$138$	0	0
$139$	4.94081e6	0.156044	0.0780218	−	0.996952i	$-0.475140\pi$
$139$	4.94081e6	0.156044	0.0780218	+	0.996952i	$0.475140\pi$
$140$	−234260.	−0.00721522
$141$	0	0
$142$	−2.49399e6	−0.0730947
$143$	252174.	0.00721148
$144$	0	0
$145$	−6.81935e6	−0.185761
$146$	−1.41059e7	−0.375115
$147$	0	0
$148$	−5.52109e6	−0.139994
$149$	3.14927e7	0.779934	0.389967	−	0.920829i	$-0.372486\pi$
$149$	3.14927e7	0.779934	0.389967	+	0.920829i	$0.372486\pi$
$150$	0	0
$151$	−1.74915e7	−0.413435	−0.206718	−	0.978401i	$-0.566278\pi$
$151$	−1.74915e7	−0.413435	−0.206718	+	0.978401i	$0.566278\pi$
$152$	−7.14350e7	−1.64990
$153$	0	0
$154$	103164.	0.00227618
$155$	3.70885e6	0.0799979
$156$	0	0
$157$	4.58653e7	0.945879	0.472939	−	0.881095i	$-0.343193\pi$
$157$	4.58653e7	0.945879	0.472939	+	0.881095i	$0.343193\pi$
$158$	3.15847e7	0.637055
$159$	0	0
$160$	−2.64587e6	−0.0510679
$161$	−3.01886e6	−0.0570101
$162$	0	0
$163$	−1.29793e7	−0.234744	−0.117372	−	0.993088i	$-0.537447\pi$
$163$	−1.29793e7	−0.234744	−0.117372	+	0.993088i	$0.537447\pi$
$164$	−2.26261e7	−0.400549
$165$	0	0
$166$	3.74686e7	0.635754
$167$	2.71351e7	0.450841	0.225420	−	0.974262i	$-0.427624\pi$
$167$	2.71351e7	0.450841	0.225420	+	0.974262i	$0.427624\pi$
$168$	0	0
$169$	−2.88002e7	−0.458978
$170$	1.18041e6	0.0184273
$171$	0	0
$172$	1.93774e7	0.290366
$173$	6.78041e7	0.995623	0.497811	−	0.867285i	$-0.334137\pi$
$173$	6.78041e7	0.995623	0.497811	+	0.867285i	$0.334137\pi$
$174$	0	0
$175$	1.92108e7	0.270964
$176$	456088.	0.00630600
$177$	0	0
$178$	3.34737e7	0.444871
$179$	−2.62722e7	−0.342382	−0.171191	−	0.985238i	$-0.554761\pi$
$179$	−2.62722e7	−0.342382	−0.171191	+	0.985238i	$0.554761\pi$
$180$	0	0
$181$	6.36522e7	0.797882	0.398941	−	0.916977i	$-0.369378\pi$
$181$	6.36522e7	0.797882	0.398941	+	0.916977i	$0.369378\pi$
$182$	1.38882e7	0.170764
$183$	0	0
$184$	−1.91353e7	−0.226451
$185$	−4.08782e6	−0.0474668
$186$	0	0
$187$	201137.	0.00224930
$188$	−2.03141e7	−0.222969
$189$	0	0
$190$	−1.15369e7	−0.122026
$191$	−9.11210e7	−0.946241	−0.473121	−	0.880998i	$-0.656873\pi$
$191$	−9.11210e7	−0.946241	−0.473121	+	0.880998i	$0.656873\pi$
$192$	0	0
$193$	2.57085e7	0.257411	0.128705	−	0.991683i	$-0.458918\pi$
$193$	2.57085e7	0.257411	0.128705	+	0.991683i	$0.458918\pi$
$194$	−1.27489e8	−1.25362
$195$	0	0
$196$	2.72101e7	0.258127
$197$	3.83241e6	0.0357141	0.0178571	−	0.999841i	$-0.494316\pi$
$197$	3.83241e6	0.0357141	0.0178571	+	0.999841i	$0.494316\pi$
$198$	0	0
$199$	−9.79061e7	−0.880692	−0.440346	−	0.897828i	$-0.645144\pi$
$199$	−9.79061e7	−0.880692	−0.440346	+	0.897828i	$0.645144\pi$
$200$	1.21770e8	1.07630
$201$	0	0
$202$	−1.20172e8	−1.02582
$203$	−6.39955e7	−0.536924
$204$	0	0
$205$	−1.67524e7	−0.135812
$206$	4.69735e7	0.374384
$207$	0	0
$208$	6.13997e7	0.473091
$209$	−1.96585e6	−0.0148949
$210$	0	0
$211$	−1.16342e8	−0.852606	−0.426303	−	0.904580i	$-0.640184\pi$
$211$	−1.16342e8	−0.852606	−0.426303	+	0.904580i	$0.640184\pi$
$212$	−1.53018e7	−0.110298
$213$	0	0
$214$	2.30597e8	1.60844
$215$	1.43470e7	0.0984525
$216$	0	0
$217$	3.48053e7	0.231226
$218$	8.16915e7	0.534047
$219$	0	0
$220$	−40863.0	−0.000258732 0
$221$	2.70776e7	0.168747
$222$	0	0
$223$	6.45568e7	0.389829	0.194915	−	0.980820i	$-0.437557\pi$
$223$	6.45568e7	0.389829	0.194915	+	0.980820i	$0.437557\pi$
$224$	−2.48298e7	−0.147607
$225$	0	0
$226$	−1.05414e8	−0.607461
$227$	−7.83882e7	−0.444795	−0.222398	−	0.974956i	$-0.571388\pi$
$227$	−7.83882e7	−0.444795	−0.222398	+	0.974956i	$0.571388\pi$
$228$	0	0
$229$	−2.33792e8	−1.28649	−0.643243	−	0.765662i	$-0.722411\pi$
$229$	−2.33792e8	−1.28649	−0.643243	+	0.765662i	$0.722411\pi$
$230$	−3.09040e6	−0.0167482
$231$	0	0
$232$	−4.05642e8	−2.13272
$233$	−9.61091e7	−0.497758	−0.248879	−	0.968535i	$-0.580062\pi$
$233$	−9.61091e7	−0.497758	−0.248879	+	0.968535i	$0.580062\pi$
$234$	0	0
$235$	−1.50406e7	−0.0756009
$236$	−4.11763e7	−0.203918
$237$	0	0
$238$	1.10774e7	0.0532621
$239$	−1.66830e8	−0.790464	−0.395232	−	0.918581i	$-0.629336\pi$
$239$	−1.66830e8	−0.790464	−0.395232	+	0.918581i	$0.629336\pi$
$240$	0	0
$241$	−2.01583e8	−0.927673	−0.463836	−	0.885921i	$-0.653527\pi$
$241$	−2.01583e8	−0.927673	−0.463836	+	0.885921i	$0.653527\pi$
$242$	−1.87191e8	−0.849046
$243$	0	0
$244$	−9.82050e7	−0.432782
$245$	2.01464e7	0.0875216
$246$	0	0
$247$	−2.64648e8	−1.11745
$248$	2.20617e8	0.918456
$249$	0	0
$250$	3.95097e7	0.159924
$251$	4.35441e8	1.73809	0.869043	−	0.494737i	$-0.164735\pi$
$251$	4.35441e8	1.73809	0.869043	+	0.494737i	$0.164735\pi$
$252$	0	0
$253$	−526593.	−0.00204434
$254$	1.83794e8	0.703743
$255$	0	0
$256$	−2.05554e8	−0.765748
$257$	−1.06639e7	−0.0391876	−0.0195938	−	0.999808i	$-0.506237\pi$
$257$	−1.06639e7	−0.0391876	−0.0195938	+	0.999808i	$0.506237\pi$
$258$	0	0
$259$	−3.83617e7	−0.137198
$260$	−5.50108e6	−0.0194107
$261$	0	0
$262$	−2.48327e8	−0.853040
$263$	−6.21868e7	−0.210791	−0.105396	−	0.994430i	$-0.533611\pi$
$263$	−6.21868e7	−0.210791	−0.105396	+	0.994430i	$0.533611\pi$
$264$	0	0
$265$	−1.13295e7	−0.0373981
$266$	−1.08267e8	−0.352704
$267$	0	0
$268$	−1.01605e8	−0.322436
$269$	−7.45499e7	−0.233515	−0.116757	−	0.993160i	$-0.537250\pi$
$269$	−7.45499e7	−0.233515	−0.116757	+	0.993160i	$0.537250\pi$
$270$	0	0
$271$	5.21697e7	0.159230	0.0796152	−	0.996826i	$-0.474631\pi$
$271$	5.21697e7	0.159230	0.0796152	+	0.996826i	$0.474631\pi$
$272$	4.89732e7	0.147559
$273$	0	0
$274$	1.35508e8	0.397958
$275$	3.35103e6	0.00971658
$276$	0	0
$277$	4.68107e8	1.32332	0.661661	−	0.749803i	$-0.269852\pi$
$277$	4.68107e8	1.32332	0.661661	+	0.749803i	$0.269852\pi$
$278$	4.74653e7	0.132501
$279$	0	0
$280$	−1.03173e7	−0.0280874
$281$	−6.45366e8	−1.73514	−0.867569	−	0.497317i	$-0.834318\pi$
$281$	−6.45366e8	−1.73514	−0.867569	+	0.497317i	$0.834318\pi$
$282$	0	0
$283$	7.35725e7	0.192958	0.0964790	−	0.995335i	$-0.469242\pi$
$283$	7.35725e7	0.192958	0.0964790	+	0.995335i	$0.469242\pi$
$284$	9.27050e6	0.0240153
$285$	0	0
$286$	2.42258e6	0.00612347
$287$	−1.57211e8	−0.392550
$288$	0	0
$289$	−3.88741e8	−0.947367
$290$	−6.55120e7	−0.157735
$291$	0	0
$292$	5.24333e7	0.123244
$293$	−4.75808e8	−1.10508	−0.552541	−	0.833486i	$-0.686342\pi$
$293$	−4.75808e8	−1.10508	−0.552541	+	0.833486i	$0.686342\pi$
$294$	0	0
$295$	−3.04869e7	−0.0691411
$296$	−2.43159e8	−0.544967
$297$	0	0
$298$	3.02544e8	0.662264
$299$	−7.08913e7	−0.153371
$300$	0	0
$301$	1.34638e8	0.284567
$302$	−1.68037e8	−0.351059
$303$	0	0
$304$	−4.78648e8	−0.977144
$305$	−7.27110e7	−0.146741
$306$	0	0
$307$	2.30122e8	0.453914	0.226957	−	0.973905i	$-0.427122\pi$
$307$	2.30122e8	0.453914	0.226957	+	0.973905i	$0.427122\pi$
$308$	−383474.	−0.000747840 0
$309$	0	0
$310$	3.56302e7	0.0679285
$311$	−5.33550e8	−1.00580	−0.502902	−	0.864343i	$-0.667734\pi$
$311$	−5.33550e8	−1.00580	−0.502902	+	0.864343i	$0.667734\pi$
$312$	0	0
$313$	1.00687e9	1.85596	0.927979	−	0.372632i	$-0.121545\pi$
$313$	1.00687e9	1.85596	0.927979	+	0.372632i	$0.121545\pi$
$314$	4.40618e8	0.803172
$315$	0	0
$316$	−1.17405e8	−0.209305
$317$	6.53607e8	1.15242	0.576208	−	0.817303i	$-0.304532\pi$
$317$	6.53607e8	1.15242	0.576208	+	0.817303i	$0.304532\pi$
$318$	0	0
$319$	−1.11630e7	−0.0192537
$320$	−6.10814e7	−0.104204
$321$	0	0
$322$	−2.90015e7	−0.0484089
$323$	−2.11086e8	−0.348539
$324$	0	0
$325$	4.51124e8	0.728960
$326$	−1.24689e8	−0.199327
$327$	0	0
$328$	−9.96496e8	−1.55925
$329$	−1.41147e8	−0.218517
$330$	0	0
$331$	1.28659e9	1.95004	0.975020	−	0.222117i	$-0.0712968\pi$
$331$	1.28659e9	1.95004	0.975020	+	0.222117i	$0.0712968\pi$
$332$	−1.39276e8	−0.208878
$333$	0	0
$334$	2.60681e8	0.382821
$335$	−7.52284e7	−0.109326
$336$	0	0
$337$	2.07464e8	0.295283	0.147641	−	0.989041i	$-0.452832\pi$
$337$	2.07464e8	0.295283	0.147641	+	0.989041i	$0.452832\pi$
$338$	−2.76677e8	−0.389731
$339$	0	0
$340$	−4.38773e6	−0.00605430
$341$	6.07125e6	0.00829159
$342$	0	0
$343$	3.93397e8	0.526383
$344$	8.53417e8	1.13033
$345$	0	0
$346$	6.51380e8	0.845411
$347$	1.06759e9	1.37168	0.685841	−	0.727752i	$-0.259435\pi$
$347$	1.06759e9	1.37168	0.685841	+	0.727752i	$0.259435\pi$
$348$	0	0
$349$	−3.53307e8	−0.444901	−0.222451	−	0.974944i	$-0.571406\pi$
$349$	−3.53307e8	−0.444901	−0.222451	+	0.974944i	$0.571406\pi$
$350$	1.84554e8	0.230083
$351$	0	0
$352$	−4.33118e6	−0.00529306
$353$	1.11145e9	1.34487	0.672433	−	0.740158i	$-0.265249\pi$
$353$	1.11145e9	1.34487	0.672433	+	0.740158i	$0.265249\pi$
$354$	0	0
$355$	6.86388e6	0.00814274
$356$	−1.24426e8	−0.146163
$357$	0	0
$358$	−2.52391e8	−0.290726
$359$	1.71519e9	1.95651	0.978257	−	0.207398i	$-0.0664994\pi$
$359$	1.71519e9	1.95651	0.978257	+	0.207398i	$0.0664994\pi$
$360$	0	0
$361$	1.16922e9	1.30804
$362$	6.11493e8	0.677504
$363$	0	0
$364$	−5.16243e7	−0.0561047
$365$	3.88217e7	0.0417878
$366$	0	0
$367$	−1.64037e9	−1.73225	−0.866127	−	0.499823i	$-0.833398\pi$
$367$	−1.64037e9	−1.73225	−0.866127	+	0.499823i	$0.833398\pi$
$368$	−1.28216e8	−0.134114
$369$	0	0
$370$	−3.92708e7	−0.0403054
$371$	−1.06320e8	−0.108096
$372$	0	0
$373$	1.34478e9	1.34175	0.670875	−	0.741571i	$-0.265919\pi$
$373$	1.34478e9	1.34175	0.670875	+	0.741571i	$0.265919\pi$
$374$	1.93228e6	0.00190994
$375$	0	0
$376$	−8.94673e8	−0.867974
$377$	−1.50279e9	−1.44446
$378$	0	0
$379$	1.49615e9	1.41169	0.705843	−	0.708369i	$-0.250569\pi$
$379$	1.49615e9	1.41169	0.705843	+	0.708369i	$0.250569\pi$
$380$	4.28842e7	0.0400918
$381$	0	0
$382$	−8.75380e8	−0.803480
$383$	1.69958e9	1.54577	0.772885	−	0.634546i	$-0.218813\pi$
$383$	1.69958e9	1.54577	0.772885	+	0.634546i	$0.218813\pi$
$384$	0	0
$385$	−283925.	−0.000253566 0
$386$	2.46976e8	0.218575
$387$	0	0
$388$	4.73893e8	0.411879
$389$	−2.52310e8	−0.217325	−0.108663	−	0.994079i	$-0.534657\pi$
$389$	−2.52310e8	−0.217325	−0.108663	+	0.994079i	$0.534657\pi$
$390$	0	0
$391$	−5.65437e7	−0.0478372
$392$	1.19838e9	1.00484
$393$	0	0
$394$	3.68171e7	0.0303259
$395$	−8.69264e7	−0.0709679
$396$	0	0
$397$	2.27253e9	1.82281	0.911407	−	0.411507i	$-0.134997\pi$
$397$	2.27253e9	1.82281	0.911407	+	0.411507i	$0.134997\pi$
$398$	−9.40562e8	−0.747820
$399$	0	0
$400$	8.15913e8	0.637432
$401$	6.27877e8	0.486261	0.243130	−	0.969994i	$-0.421826\pi$
$401$	6.27877e8	0.486261	0.243130	+	0.969994i	$0.421826\pi$
$402$	0	0
$403$	8.17327e8	0.622055
$404$	4.46694e8	0.337035
$405$	0	0
$406$	−6.14791e8	−0.455917
$407$	−6.69160e6	−0.00491982
$408$	0	0
$409$	−2.41268e9	−1.74369	−0.871844	−	0.489783i	$-0.837076\pi$
$409$	−2.41268e9	−1.74369	−0.871844	+	0.489783i	$0.837076\pi$
$410$	−1.60936e8	−0.115322
$411$	0	0
$412$	−1.74607e8	−0.123004
$413$	−2.86101e8	−0.199846
$414$	0	0
$415$	−1.03120e8	−0.0708230
$416$	−5.83075e8	−0.397098
$417$	0	0
$418$	−1.88855e7	−0.0126477
$419$	4.67714e8	0.310621	0.155311	−	0.987866i	$-0.450362\pi$
$419$	4.67714e8	0.310621	0.155311	+	0.987866i	$0.450362\pi$
$420$	0	0
$421$	1.41597e9	0.924839	0.462419	−	0.886661i	$-0.346981\pi$
$421$	1.41597e9	0.924839	0.462419	+	0.886661i	$0.346981\pi$
$422$	−1.11767e9	−0.723971
$423$	0	0
$424$	−6.73923e8	−0.429368
$425$	3.59822e8	0.227366
$426$	0	0
$427$	−6.82348e8	−0.424139
$428$	−8.57160e8	−0.528456
$429$	0	0
$430$	1.37829e8	0.0835988
$431$	−8.23080e8	−0.495190	−0.247595	−	0.968864i	$-0.579640\pi$
$431$	−8.23080e8	−0.495190	−0.247595	+	0.968864i	$0.579640\pi$
$432$	0	0
$433$	2.88474e9	1.70765	0.853825	−	0.520560i	$-0.174277\pi$
$433$	2.88474e9	1.70765	0.853825	+	0.520560i	$0.174277\pi$
$434$	3.34367e8	0.196340
$435$	0	0
$436$	−3.03658e8	−0.175462
$437$	5.52640e8	0.316780
$438$	0	0
$439$	−3.05246e9	−1.72196	−0.860982	−	0.508636i	$-0.830150\pi$
$439$	−3.05246e9	−1.72196	−0.860982	+	0.508636i	$0.830150\pi$
$440$	−1.79969e6	−0.00100719
$441$	0	0
$442$	2.60129e8	0.143288
$443$	2.51773e9	1.37593	0.687964	−	0.725745i	$-0.258505\pi$
$443$	2.51773e9	1.37593	0.687964	+	0.725745i	$0.258505\pi$
$444$	0	0
$445$	−9.21253e7	−0.0495586
$446$	6.20183e8	0.331015
$447$	0	0
$448$	−5.73212e8	−0.301191
$449$	1.61815e9	0.843637	0.421818	−	0.906680i	$-0.361392\pi$
$449$	1.61815e9	0.843637	0.421818	+	0.906680i	$0.361392\pi$
$450$	0	0
$451$	−2.74230e7	−0.0140766
$452$	3.91838e8	0.199582
$453$	0	0
$454$	−7.53058e8	−0.377688
$455$	−3.82227e7	−0.0190231
$456$	0	0
$457$	1.40383e9	0.688032	0.344016	−	0.938964i	$-0.388213\pi$
$457$	1.40383e9	0.688032	0.344016	+	0.938964i	$0.388213\pi$
$458$	−2.24599e9	−1.09239
$459$	0	0
$460$	1.14874e7	0.00550263
$461$	−1.70771e9	−0.811820	−0.405910	−	0.913913i	$-0.633045\pi$
$461$	−1.70771e9	−0.811820	−0.405910	+	0.913913i	$0.633045\pi$
$462$	0	0
$463$	1.92898e9	0.903220	0.451610	−	0.892215i	$-0.350850\pi$
$463$	1.92898e9	0.903220	0.451610	+	0.892215i	$0.350850\pi$
$464$	−2.71799e9	−1.26309
$465$	0	0
$466$	−9.23299e8	−0.422661
$467$	4.29118e8	0.194970	0.0974850	−	0.995237i	$-0.468920\pi$
$467$	4.29118e8	0.194970	0.0974850	+	0.995237i	$0.468920\pi$
$468$	0	0
$469$	−7.05973e8	−0.315997
$470$	−1.44492e8	−0.0641948
$471$	0	0
$472$	−1.81348e9	−0.793809
$473$	2.34855e7	0.0102044
$474$	0	0
$475$	−3.51678e9	−1.50563
$476$	−4.11762e7	−0.0174993
$477$	0	0
$478$	−1.60270e9	−0.671205
$479$	6.72525e8	0.279598	0.139799	−	0.990180i	$-0.455354\pi$
$479$	6.72525e8	0.279598	0.139799	+	0.990180i	$0.455354\pi$
$480$	0	0
$481$	−9.00840e8	−0.369097
$482$	−1.93657e9	−0.787713
$483$	0	0
$484$	6.95814e8	0.278955
$485$	3.50870e8	0.139653
$486$	0	0
$487$	1.24397e9	0.488044	0.244022	−	0.969770i	$-0.421533\pi$
$487$	1.24397e9	0.488044	0.244022	+	0.969770i	$0.421533\pi$
$488$	−4.32514e9	−1.68473
$489$	0	0
$490$	1.93542e8	0.0743170
$491$	1.47371e9	0.561857	0.280929	−	0.959729i	$-0.409358\pi$
$491$	1.47371e9	0.561857	0.280929	+	0.959729i	$0.409358\pi$
$492$	0	0
$493$	−1.19865e9	−0.450534
$494$	−2.54241e9	−0.948859
$495$	0	0
$496$	1.47824e9	0.543949
$497$	6.44133e7	0.0235358
$498$	0	0
$499$	−9.69631e7	−0.0349345	−0.0174672	−	0.999847i	$-0.505560\pi$
$499$	−9.69631e7	−0.0349345	−0.0174672	+	0.999847i	$0.505560\pi$
$500$	−1.46863e8	−0.0525432
$501$	0	0
$502$	4.18319e9	1.47586
$503$	−1.69034e9	−0.592224	−0.296112	−	0.955153i	$-0.595690\pi$
$503$	−1.69034e9	−0.592224	−0.296112	+	0.955153i	$0.595690\pi$
$504$	0	0
$505$	3.30732e8	0.114276
$506$	−5.05886e6	−0.00173591
$507$	0	0
$508$	−6.83188e8	−0.231216
$509$	−3.47448e9	−1.16782	−0.583912	−	0.811817i	$-0.698479\pi$
$509$	−3.47448e9	−1.16782	−0.583912	+	0.811817i	$0.698479\pi$
$510$	0	0
$511$	3.64318e8	0.120783
$512$	−3.17595e9	−1.04575
$513$	0	0
$514$	−1.02445e8	−0.0332753
$515$	−1.29279e8	−0.0417063
$516$	0	0
$517$	−2.46209e7	−0.00783585
$518$	−3.68532e8	−0.116499
$519$	0	0
$520$	−2.42278e8	−0.0755619
$521$	1.91446e9	0.593080	0.296540	−	0.955020i	$-0.404167\pi$
$521$	1.91446e9	0.593080	0.296540	+	0.955020i	$0.404167\pi$
$522$	0	0
$523$	8.10894e8	0.247861	0.123930	−	0.992291i	$-0.460450\pi$
$523$	8.10894e8	0.247861	0.123930	+	0.992291i	$0.460450\pi$
$524$	9.23065e8	0.280267
$525$	0	0
$526$	−5.97415e8	−0.178989
$527$	6.51911e8	0.194022
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	−1.08840e8	−0.0317558
$531$	0	0
$532$	4.02443e8	0.115881
$533$	−3.69175e9	−1.05606
$534$	0	0
$535$	−6.34642e8	−0.179180
$536$	−4.47488e9	−1.25518
$537$	0	0
$538$	−7.16185e8	−0.198284
$539$	3.29788e7	0.00907140
$540$	0	0
$541$	−3.43691e9	−0.933206	−0.466603	−	0.884467i	$-0.654522\pi$
$541$	−3.43691e9	−0.933206	−0.466603	+	0.884467i	$0.654522\pi$
$542$	5.01183e8	0.135207
$543$	0	0
$544$	−4.65068e8	−0.123857
$545$	−2.24829e8	−0.0594927
$546$	0	0
$547$	−3.08966e9	−0.807150	−0.403575	−	0.914947i	$-0.632233\pi$
$547$	−3.08966e9	−0.807150	−0.403575	+	0.914947i	$0.632233\pi$
$548$	−5.03700e8	−0.130750
$549$	0	0
$550$	3.21926e7	0.00825062
$551$	1.17152e10	2.98345
$552$	0	0
$553$	−8.15751e8	−0.205125
$554$	4.49700e9	1.12367
$555$	0	0
$556$	−1.76435e8	−0.0435334
$557$	−3.94191e9	−0.966525	−0.483262	−	0.875476i	$-0.660548\pi$
$557$	−3.94191e9	−0.966525	−0.483262	+	0.875476i	$0.660548\pi$
$558$	0	0
$559$	3.16168e9	0.765555
$560$	−6.91304e7	−0.0166345
$561$	0	0
$562$	−6.19989e9	−1.47335
$563$	−9.50072e8	−0.224376	−0.112188	−	0.993687i	$-0.535786\pi$
$563$	−9.50072e8	−0.224376	−0.112188	+	0.993687i	$0.535786\pi$
$564$	0	0
$565$	2.90117e8	0.0676711
$566$	7.06795e8	0.163846
$567$	0	0
$568$	4.08290e8	0.0934867
$569$	7.45566e9	1.69665	0.848327	−	0.529473i	$-0.177610\pi$
$569$	7.45566e9	1.69665	0.848327	+	0.529473i	$0.177610\pi$
$570$	0	0
$571$	−6.81054e9	−1.53093	−0.765465	−	0.643478i	$-0.777491\pi$
$571$	−6.81054e9	−1.53093	−0.765465	+	0.643478i	$0.777491\pi$
$572$	−9.00506e6	−0.00201187
$573$	0	0
$574$	−1.51029e9	−0.333325
$575$	−9.42042e8	−0.206649
$576$	0	0
$577$	7.03652e9	1.52490	0.762452	−	0.647045i	$-0.223995\pi$
$577$	7.03652e9	1.52490	0.762452	+	0.647045i	$0.223995\pi$
$578$	−3.73455e9	−0.804435
$579$	0	0
$580$	2.43517e8	0.0518240
$581$	−9.67717e8	−0.204707
$582$	0	0
$583$	−1.85459e7	−0.00387622
$584$	2.30926e9	0.479765
$585$	0	0
$586$	−4.57098e9	−0.938356
$587$	8.51346e9	1.73729	0.868646	−	0.495434i	$-0.164991\pi$
$587$	8.51346e9	1.73729	0.868646	+	0.495434i	$0.164991\pi$
$588$	0	0
$589$	−6.37156e9	−1.28482
$590$	−2.92881e8	−0.0587097
$591$	0	0
$592$	−1.62928e9	−0.322753
$593$	2.68003e9	0.527774	0.263887	−	0.964554i	$-0.414995\pi$
$593$	2.68003e9	0.527774	0.263887	+	0.964554i	$0.414995\pi$
$594$	0	0
$595$	−3.04869e7	−0.00593340
$596$	−1.12460e9	−0.217588
$597$	0	0
$598$	−6.81037e8	−0.130232
$599$	3.25768e9	0.619319	0.309659	−	0.950848i	$-0.399785\pi$
$599$	3.25768e9	0.619319	0.309659	+	0.950848i	$0.399785\pi$
$600$	0	0
$601$	3.28695e9	0.617636	0.308818	−	0.951121i	$-0.400067\pi$
$601$	3.28695e9	0.617636	0.308818	+	0.951121i	$0.400067\pi$
$602$	1.29344e9	0.241634
$603$	0	0
$604$	6.24616e8	0.115341
$605$	5.15181e8	0.0945836
$606$	0	0
$607$	−5.02884e9	−0.912657	−0.456328	−	0.889811i	$-0.650836\pi$
$607$	−5.02884e9	−0.912657	−0.456328	+	0.889811i	$0.650836\pi$
$608$	4.54542e9	0.820184
$609$	0	0
$610$	−6.98519e8	−0.124602
$611$	−3.31452e9	−0.587864
$612$	0	0
$613$	−1.95124e8	−0.0342136	−0.0171068	−	0.999854i	$-0.505446\pi$
$613$	−1.95124e8	−0.0342136	−0.0171068	+	0.999854i	$0.505446\pi$
$614$	2.21073e9	0.385431
$615$	0	0
$616$	−1.68889e7	−0.00291119
$617$	−8.29071e9	−1.42100	−0.710499	−	0.703698i	$-0.751531\pi$
$617$	−8.29071e9	−1.42100	−0.710499	+	0.703698i	$0.751531\pi$
$618$	0	0
$619$	2.68628e9	0.455233	0.227617	−	0.973751i	$-0.426907\pi$
$619$	2.68628e9	0.455233	0.227617	+	0.973751i	$0.426907\pi$
$620$	−1.32442e8	−0.0223180
$621$	0	0
$622$	−5.12570e9	−0.854057
$623$	−8.64540e8	−0.143244
$624$	0	0
$625$	5.94017e9	0.973237
$626$	9.67278e9	1.57595
$627$	0	0
$628$	−1.63784e9	−0.263883
$629$	−7.18521e8	−0.115123
$630$	0	0
$631$	−2.58806e9	−0.410083	−0.205041	−	0.978753i	$-0.565733\pi$
$631$	−2.58806e9	−0.410083	−0.205041	+	0.978753i	$0.565733\pi$
$632$	−5.17072e9	−0.814782
$633$	0	0
$634$	6.27906e9	0.978548
$635$	−5.05833e8	−0.0783969
$636$	0	0
$637$	4.43969e9	0.680558
$638$	−1.07241e8	−0.0163489
$639$	0	0
$640$	−2.48125e8	−0.0374146
$641$	−1.80731e9	−0.271037	−0.135519	−	0.990775i	$-0.543270\pi$
$641$	−1.80731e9	−0.271037	−0.135519	+	0.990775i	$0.543270\pi$
$642$	0	0
$643$	2.43229e9	0.360808	0.180404	−	0.983593i	$-0.442259\pi$
$643$	2.43229e9	0.360808	0.180404	+	0.983593i	$0.442259\pi$
$644$	1.07802e8	0.0159048
$645$	0	0
$646$	−2.02786e9	−0.295954
$647$	−9.57829e9	−1.39035	−0.695173	−	0.718842i	$-0.744672\pi$
$647$	−9.57829e9	−1.39035	−0.695173	+	0.718842i	$0.744672\pi$
$648$	0	0
$649$	−4.99059e7	−0.00716631
$650$	4.33385e9	0.618981
$651$	0	0
$652$	4.63486e8	0.0654892
$653$	8.03962e8	0.112990	0.0564949	−	0.998403i	$-0.482008\pi$
$653$	8.03962e8	0.112990	0.0564949	+	0.998403i	$0.482008\pi$
$654$	0	0
$655$	6.83437e8	0.0950286
$656$	−6.67698e9	−0.923457
$657$	0	0
$658$	−1.35597e9	−0.185549
$659$	−7.10914e9	−0.967650	−0.483825	−	0.875165i	$-0.660753\pi$
$659$	−7.10914e9	−0.967650	−0.483825	+	0.875165i	$0.660753\pi$
$660$	0	0
$661$	4.44762e9	0.598994	0.299497	−	0.954097i	$-0.403181\pi$
$661$	4.44762e9	0.598994	0.299497	+	0.954097i	$0.403181\pi$
$662$	1.23600e10	1.65583
$663$	0	0
$664$	−6.13398e9	−0.813118
$665$	2.97969e8	0.0392911
$666$	0	0
$667$	3.13815e9	0.409481
$668$	−9.68985e8	−0.125776
$669$	0	0
$670$	−7.22703e8	−0.0928321
$671$	−1.19025e8	−0.0152093
$672$	0	0
$673$	1.48070e10	1.87246	0.936232	−	0.351383i	$-0.114289\pi$
$673$	1.48070e10	1.87246	0.936232	+	0.351383i	$0.114289\pi$
$674$	1.99306e9	0.250733
$675$	0	0
$676$	1.02845e9	0.128047
$677$	4.06381e9	0.503353	0.251677	−	0.967811i	$-0.419018\pi$
$677$	4.06381e9	0.503353	0.251677	+	0.967811i	$0.419018\pi$
$678$	0	0
$679$	3.29271e9	0.403653
$680$	−1.93244e8	−0.0235681
$681$	0	0
$682$	5.83252e7	0.00704062
$683$	−1.30395e10	−1.56599	−0.782993	−	0.622030i	$-0.786308\pi$
$683$	−1.30395e10	−1.56599	−0.782993	+	0.622030i	$0.786308\pi$
$684$	0	0
$685$	−3.72940e8	−0.0443325
$686$	3.77928e9	0.446967
$687$	0	0
$688$	5.71829e9	0.669432
$689$	−2.49670e9	−0.290803
$690$	0	0
$691$	−9.14083e8	−0.105393	−0.0526966	−	0.998611i	$-0.516782\pi$
$691$	−9.14083e8	−0.105393	−0.0526966	+	0.998611i	$0.516782\pi$
$692$	−2.42126e9	−0.277761
$693$	0	0
$694$	1.02562e10	1.16473
$695$	−1.30632e8	−0.0147606
$696$	0	0
$697$	−2.94459e9	−0.329389
$698$	−3.39415e9	−0.377778
$699$	0	0
$700$	−6.86012e8	−0.0755942
$701$	9.88966e9	1.08435	0.542173	−	0.840267i	$-0.317602\pi$
$701$	9.88966e9	1.08435	0.542173	+	0.840267i	$0.317602\pi$
$702$	0	0
$703$	7.02259e9	0.762349
$704$	−9.99880e7	−0.0108005
$705$	0	0
$706$	1.06775e10	1.14196
$707$	3.10372e9	0.330305
$708$	0	0
$709$	8.39063e9	0.884164	0.442082	−	0.896975i	$-0.354240\pi$
$709$	8.39063e9	0.884164	0.442082	+	0.896975i	$0.354240\pi$
$710$	6.59398e7	0.00691422
$711$	0	0
$712$	−5.47997e9	−0.568982
$713$	−1.70675e9	−0.176343
$714$	0	0
$715$	−6.66735e6	−0.000682154 0
$716$	9.38171e8	0.0955183
$717$	0	0
$718$	1.64775e10	1.66133
$719$	1.04368e9	0.104717	0.0523584	−	0.998628i	$-0.483326\pi$
$719$	1.04368e9	0.104717	0.0523584	+	0.998628i	$0.483326\pi$
$720$	0	0
$721$	−1.21320e9	−0.120548
$722$	1.12324e10	1.11069
$723$	0	0
$724$	−2.27300e9	−0.222595
$725$	−1.99699e10	−1.94623
$726$	0	0
$727$	−1.07363e10	−1.03629	−0.518146	−	0.855292i	$-0.673378\pi$
$727$	−1.07363e10	−1.03629	−0.518146	+	0.855292i	$0.673378\pi$
$728$	−2.27363e9	−0.218404
$729$	0	0
$730$	3.72951e8	0.0354831
$731$	2.52179e9	0.238781
$732$	0	0
$733$	5.31520e9	0.498490	0.249245	−	0.968441i	$-0.419818\pi$
$733$	5.31520e9	0.498490	0.249245	+	0.968441i	$0.419818\pi$
$734$	−1.57587e10	−1.47091
$735$	0	0
$736$	1.21758e9	0.112571
$737$	−1.23146e8	−0.0113314
$738$	0	0
$739$	1.20671e9	0.109989	0.0549944	−	0.998487i	$-0.482486\pi$
$739$	1.20671e9	0.109989	0.0549944	+	0.998487i	$0.482486\pi$
$740$	1.45975e8	0.0132424
$741$	0	0
$742$	−1.02140e9	−0.0917869
$743$	−1.74038e10	−1.55662	−0.778312	−	0.627878i	$-0.783924\pi$
$743$	−1.74038e10	−1.55662	−0.778312	+	0.627878i	$0.783924\pi$
$744$	0	0
$745$	−8.32651e8	−0.0737761
$746$	1.29190e10	1.13932
$747$	0	0
$748$	−7.18255e6	−0.000627513 0
$749$	−5.95573e9	−0.517903
$750$	0	0
$751$	−1.83469e10	−1.58061	−0.790303	−	0.612716i	$-0.790077\pi$
$751$	−1.83469e10	−1.58061	−0.790303	+	0.612716i	$0.790077\pi$
$752$	−5.99472e9	−0.514051
$753$	0	0
$754$	−1.44370e10	−1.22653
$755$	4.62466e8	0.0391080
$756$	0	0
$757$	8.47193e9	0.709818	0.354909	−	0.934901i	$-0.384512\pi$
$757$	8.47193e9	0.709818	0.354909	+	0.934901i	$0.384512\pi$
$758$	1.43732e10	1.19870
$759$	0	0
$760$	1.88870e9	0.156069
$761$	1.10923e10	0.912381	0.456190	−	0.889882i	$-0.349214\pi$
$761$	1.10923e10	0.912381	0.456190	+	0.889882i	$0.349214\pi$
$762$	0	0
$763$	−2.10988e9	−0.171958
$764$	3.25391e9	0.263984
$765$	0	0
$766$	1.63275e10	1.31256
$767$	−6.71846e9	−0.537633
$768$	0	0
$769$	−2.14651e10	−1.70213	−0.851063	−	0.525064i	$-0.824041\pi$
$769$	−2.14651e10	−1.70213	−0.851063	+	0.525064i	$0.824041\pi$
$770$	−2.72760e6	−0.000215310 0
$771$	0	0
$772$	−9.18044e8	−0.0718129
$773$	−7.45126e9	−0.580232	−0.290116	−	0.956992i	$-0.593694\pi$
$773$	−7.45126e9	−0.580232	−0.290116	+	0.956992i	$0.593694\pi$
$774$	0	0
$775$	1.08611e10	0.838142
$776$	2.08712e10	1.60336
$777$	0	0
$778$	−2.42389e9	−0.184537
$779$	2.87794e10	2.18123
$780$	0	0
$781$	1.12359e7	0.000843975 0
$782$	−5.43204e8	−0.0406199
$783$	0	0
$784$	8.02973e9	0.595107
$785$	−1.21265e9	−0.0894733
$786$	0	0
$787$	4.24118e8	0.0310153	0.0155076	−	0.999880i	$-0.495064\pi$
$787$	4.24118e8	0.0310153	0.0155076	+	0.999880i	$0.495064\pi$
$788$	−1.36854e8	−0.00996360
$789$	0	0
$790$	−8.35083e8	−0.0602608
$791$	2.72257e9	0.195597
$792$	0	0
$793$	−1.60235e10	−1.14104
$794$	2.18317e10	1.54780
$795$	0	0
$796$	3.49620e9	0.245697
$797$	−1.53803e10	−1.07612	−0.538061	−	0.842906i	$-0.680843\pi$
$797$	−1.53803e10	−1.07612	−0.538061	+	0.842906i	$0.680843\pi$
$798$	0	0
$799$	−2.64370e9	−0.183358
$800$	−7.74821e9	−0.535041
$801$	0	0
$802$	6.03188e9	0.412898
$803$	6.35496e7	0.00433120
$804$	0	0
$805$	7.98170e7	0.00539274
$806$	7.85189e9	0.528204
$807$	0	0
$808$	1.96732e10	1.31201
$809$	−2.48681e10	−1.65129	−0.825643	−	0.564193i	$-0.809187\pi$
$809$	−2.48681e10	−1.65129	−0.825643	+	0.564193i	$0.809187\pi$
$810$	0	0
$811$	−1.83550e10	−1.20832	−0.604160	−	0.796863i	$-0.706491\pi$
$811$	−1.83550e10	−1.20832	−0.604160	+	0.796863i	$0.706491\pi$
$812$	2.28526e9	0.149792
$813$	0	0
$814$	−6.42848e7	−0.00417756
$815$	3.43165e8	0.0222050
$816$	0	0
$817$	−2.46472e10	−1.58121
$818$	−2.31781e10	−1.48061
$819$	0	0
$820$	5.98222e8	0.0378890
$821$	2.24866e10	1.41815	0.709077	−	0.705131i	$-0.249112\pi$
$821$	2.24866e10	1.41815	0.709077	+	0.705131i	$0.249112\pi$
$822$	0	0
$823$	−4.63172e9	−0.289630	−0.144815	−	0.989459i	$-0.546259\pi$
$823$	−4.63172e9	−0.289630	−0.144815	+	0.989459i	$0.546259\pi$
$824$	−7.69001e9	−0.478830
$825$	0	0
$826$	−2.74851e9	−0.169694
$827$	1.05014e10	0.645623	0.322811	−	0.946463i	$-0.395372\pi$
$827$	1.05014e10	0.645623	0.322811	+	0.946463i	$0.395372\pi$
$828$	0	0
$829$	1.35535e9	0.0826248	0.0413124	−	0.999146i	$-0.486846\pi$
$829$	1.35535e9	0.0826248	0.0413124	+	0.999146i	$0.486846\pi$
$830$	−9.90650e8	−0.0601377
$831$	0	0
$832$	−1.34606e10	−0.810278
$833$	3.54115e9	0.212269
$834$	0	0
$835$	−7.17437e8	−0.0426463
$836$	7.01999e7	0.00415541
$837$	0	0
$838$	4.49323e9	0.263757
$839$	1.87560e10	1.09641	0.548205	−	0.836344i	$-0.315311\pi$
$839$	1.87560e10	1.09641	0.548205	+	0.836344i	$0.315311\pi$
$840$	0	0
$841$	4.92745e10	2.85651
$842$	1.36029e10	0.785306
$843$	0	0
$844$	4.15454e9	0.237862
$845$	7.61462e8	0.0434160
$846$	0	0
$847$	4.83466e9	0.273385
$848$	−4.51559e9	−0.254290
$849$	0	0
$850$	3.45673e9	0.193063
$851$	1.88114e9	0.104633
$852$	0	0
$853$	1.73392e10	0.956550	0.478275	−	0.878210i	$-0.341262\pi$
$853$	1.73392e10	0.956550	0.478275	+	0.878210i	$0.341262\pi$
$854$	−6.55517e9	−0.360149
$855$	0	0
$856$	−3.77510e10	−2.05717
$857$	1.88348e10	1.02218	0.511090	−	0.859527i	$-0.329242\pi$
$857$	1.88348e10	1.02218	0.511090	+	0.859527i	$0.329242\pi$
$858$	0	0
$859$	1.62746e10	0.876063	0.438032	−	0.898960i	$-0.355676\pi$
$859$	1.62746e10	0.876063	0.438032	+	0.898960i	$0.355676\pi$
$860$	−5.12327e8	−0.0274665
$861$	0	0
$862$	−7.90715e9	−0.420479
$863$	1.82813e10	0.968209	0.484104	−	0.875010i	$-0.339146\pi$
$863$	1.82813e10	0.968209	0.484104	+	0.875010i	$0.339146\pi$
$864$	0	0
$865$	−1.79271e9	−0.0941787
$866$	2.77131e10	1.45001
$867$	0	0
$868$	−1.24289e9	−0.0645079
$869$	−1.42295e8	−0.00735565
$870$	0	0
$871$	−1.65782e10	−0.850109
$872$	−1.33737e10	−0.683036
$873$	0	0
$874$	5.30909e9	0.268986
$875$	−1.02043e9	−0.0514939
$876$	0	0
$877$	9.58880e9	0.480027	0.240014	−	0.970770i	$-0.422848\pi$
$877$	9.58880e9	0.480027	0.240014	+	0.970770i	$0.422848\pi$
$878$	−2.93243e10	−1.46217
$879$	0	0
$880$	−1.20587e7	−0.000596502 0
$881$	−2.73565e10	−1.34786	−0.673930	−	0.738795i	$-0.735395\pi$
$881$	−2.73565e10	−1.34786	−0.673930	+	0.738795i	$0.735395\pi$
$882$	0	0
$883$	−2.36005e10	−1.15361	−0.576804	−	0.816882i	$-0.695701\pi$
$883$	−2.36005e10	−1.15361	−0.576804	+	0.816882i	$0.695701\pi$
$884$	−9.66933e8	−0.0470775
$885$	0	0
$886$	2.41873e10	1.16834
$887$	−2.62009e10	−1.26062	−0.630309	−	0.776344i	$-0.717072\pi$
$887$	−2.62009e10	−1.26062	−0.630309	+	0.776344i	$0.717072\pi$
$888$	0	0
$889$	−4.74693e9	−0.226598
$890$	−8.85028e8	−0.0420816
$891$	0	0
$892$	−2.30530e9	−0.108755
$893$	2.58387e10	1.21420
$894$	0	0
$895$	6.94622e8	0.0323868
$896$	−2.32850e9	−0.108143
$897$	0	0
$898$	1.55452e10	0.716355
$899$	−3.61807e10	−1.66080
$900$	0	0
$901$	−1.99140e9	−0.0907030
$902$	−2.63447e8	−0.0119528
$903$	0	0
$904$	1.72573e10	0.776932
$905$	−1.68293e9	−0.0754738
$906$	0	0
$907$	−4.16192e10	−1.85212	−0.926058	−	0.377382i	$-0.876825\pi$
$907$	−4.16192e10	−1.85212	−0.926058	+	0.377382i	$0.876825\pi$
$908$	2.79922e9	0.124090
$909$	0	0
$910$	−3.67197e8	−0.0161530
$911$	−2.08260e10	−0.912622	−0.456311	−	0.889820i	$-0.650830\pi$
$911$	−2.08260e10	−0.912622	−0.456311	+	0.889820i	$0.650830\pi$
$912$	0	0
$913$	−1.68803e8	−0.00734063
$914$	1.34863e10	0.584227
$915$	0	0
$916$	8.34863e9	0.358906
$917$	6.41364e9	0.274671
$918$	0	0
$919$	1.11315e10	0.473096	0.236548	−	0.971620i	$-0.423984\pi$
$919$	1.11315e10	0.473096	0.236548	+	0.971620i	$0.423984\pi$
$920$	5.05928e8	0.0214206
$921$	0	0
$922$	−1.64056e10	−0.689339
$923$	1.51261e9	0.0633170
$924$	0	0
$925$	−1.19709e10	−0.497312
$926$	1.85313e10	0.766950
$927$	0	0
$928$	2.58110e10	1.06020
$929$	2.38295e10	0.975122	0.487561	−	0.873089i	$-0.337887\pi$
$929$	2.38295e10	0.975122	0.487561	+	0.873089i	$0.337887\pi$
$930$	0	0
$931$	−3.46101e10	−1.40565
$932$	3.43203e9	0.138866
$933$	0	0
$934$	4.12244e9	0.165554
$935$	−5.31796e6	−0.000212767 0
$936$	0	0
$937$	−4.63387e10	−1.84016	−0.920079	−	0.391733i	$-0.871876\pi$
$937$	−4.63387e10	−1.84016	−0.920079	+	0.391733i	$0.871876\pi$
$938$	−6.78213e9	−0.268322
$939$	0	0
$940$	5.37094e8	0.0210913
$941$	2.57971e9	0.100927	0.0504634	−	0.998726i	$-0.483930\pi$
$941$	2.57971e9	0.100927	0.0504634	+	0.998726i	$0.483930\pi$
$942$	0	0
$943$	7.70915e9	0.299375
$944$	−1.21512e10	−0.470128
$945$	0	0
$946$	2.25620e8	0.00866481
$947$	−1.31682e10	−0.503849	−0.251924	−	0.967747i	$-0.581063\pi$
$947$	−1.31682e10	−0.503849	−0.251924	+	0.967747i	$0.581063\pi$
$948$	0	0
$949$	8.55521e9	0.324937
$950$	−3.37850e10	−1.27847
$951$	0	0
$952$	−1.81348e9	−0.0681213
$953$	−2.13562e10	−0.799278	−0.399639	−	0.916673i	$-0.630865\pi$
$953$	−2.13562e10	−0.799278	−0.399639	+	0.916673i	$0.630865\pi$
$954$	0	0
$955$	2.40919e9	0.0895075
$956$	5.95745e9	0.220525
$957$	0	0
$958$	6.46080e9	0.237414
$959$	−3.49981e9	−0.128139
$960$	0	0
$961$	−7.83494e9	−0.284776
$962$	−8.65418e9	−0.313410
$963$	0	0
$964$	7.19848e9	0.258804
$965$	−6.79720e8	−0.0243492
$966$	0	0
$967$	2.11847e10	0.753409	0.376704	−	0.926334i	$-0.377057\pi$
$967$	2.11847e10	0.753409	0.376704	+	0.926334i	$0.377057\pi$
$968$	3.06450e10	1.08591
$969$	0	0
$970$	3.37074e9	0.118583
$971$	−2.17880e10	−0.763748	−0.381874	−	0.924214i	$-0.624721\pi$
$971$	−2.17880e10	−0.763748	−0.381874	+	0.924214i	$0.624721\pi$
$972$	0	0
$973$	−1.22590e9	−0.0426640
$974$	1.19506e10	0.414411
$975$	0	0
$976$	−2.89804e10	−0.997769
$977$	1.65903e10	0.569146	0.284573	−	0.958654i	$-0.408148\pi$
$977$	1.65903e10	0.569146	0.284573	+	0.958654i	$0.408148\pi$
$978$	0	0
$979$	−1.50806e8	−0.00513663
$980$	−7.19420e8	−0.0244170
$981$	0	0
$982$	1.41576e10	0.477089
$983$	−3.36549e9	−0.113008	−0.0565042	−	0.998402i	$-0.517995\pi$
$983$	−3.36549e9	−0.113008	−0.0565042	+	0.998402i	$0.517995\pi$
$984$	0	0
$985$	−1.01327e8	−0.00337830
$986$	−1.15151e10	−0.382561
$987$	0	0
$988$	9.45049e9	0.311749
$989$	−6.60225e9	−0.217023
$990$	0	0
$991$	−3.59823e10	−1.17444	−0.587220	−	0.809427i	$-0.699778\pi$
$991$	−3.59823e10	−1.17444	−0.587220	+	0.809427i	$0.699778\pi$
$992$	−1.40379e10	−0.456574
$993$	0	0
$994$	6.18805e8	0.0199849
$995$	2.58858e9	0.0833070
$996$	0	0
$997$	3.76524e10	1.20326	0.601630	−	0.798775i	$-0.294518\pi$
$997$	3.76524e10	1.20326	0.601630	+	0.798775i	$0.294518\pi$
$998$	−9.31503e8	−0.0296638
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.c.1.5		6
3.2	odd	2		69.8.a.b.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.b.1.2	✓	6	3.2	odd	2
207.8.a.c.1.5		6	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	207.a (trivial)

\(f(q)\)	\(=\)	\(q+9.60678 q^{2} -35.7097 q^{4} -26.4395 q^{5} -248.118 q^{7} -1572.72 q^{8} +O(q^{10})\)	\(q+9.60678 q^{2} -35.7097 q^{4} -26.4395 q^{5} -248.118 q^{7} -1572.72 q^{8} -253.998 q^{10} -43.2804 q^{11} -5826.52 q^{13} -2383.62 q^{14} -10538.0 q^{16} -4647.30 q^{17} +45421.2 q^{19} +944.146 q^{20} -415.786 q^{22} +12167.0 q^{23} -77426.0 q^{25} -55974.1 q^{26} +8860.23 q^{28} +257923. q^{29} -140277. q^{31} +100073. q^{32} -44645.6 q^{34} +6560.12 q^{35} +154610. q^{37} +436352. q^{38} +41582.0 q^{40} +633612. q^{41} -542636. q^{43} +1545.53 q^{44} +116886. q^{46} +568868. q^{47} -761980. q^{49} -743814. q^{50} +208063. q^{52} +428507. q^{53} +1144.31 q^{55} +390222. q^{56} +2.47781e6 q^{58} +1.15308e6 q^{59} +2.75009e6 q^{61} -1.34761e6 q^{62} +2.31024e6 q^{64} +154050. q^{65} +2.84531e6 q^{67} +165954. q^{68} +63021.6 q^{70} -259607. q^{71} -1.46832e6 q^{73} +1.48531e6 q^{74} -1.62198e6 q^{76} +10738.7 q^{77} +3.28775e6 q^{79} +278619. q^{80} +6.08697e6 q^{82} +3.90022e6 q^{83} +122872. q^{85} -5.21299e6 q^{86} +68068.1 q^{88} +3.48438e6 q^{89} +1.44567e6 q^{91} -434480. q^{92} +5.46500e6 q^{94} -1.20091e6 q^{95} -1.32707e7 q^{97} -7.32018e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8}+O(q^{10}) \) 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8	\( 6 q + 8 q^{2} + 178 q^{4} + 372 q^{5} - 1104 q^{7} + 1956 q^{8} - 13042 q^{10} + 14824 q^{11} - 756 q^{13} + 3926 q^{14} - 13022 q^{16} + 69484 q^{17} - 43864 q^{19} - 78886 q^{20} + 98204 q^{22} + 73002 q^{23} + 228018 q^{25} + 311956 q^{26} - 545442 q^{28} + 311100 q^{29} - 245248 q^{31} + 390156 q^{32} + 235834 q^{34} + 1331256 q^{35} - 630044 q^{37} - 80910 q^{38} - 2153982 q^{40} + 969204 q^{41} - 1770208 q^{43} + 1749140 q^{44} + 97336 q^{46} + 1400024 q^{47} + 1985598 q^{49} + 956660 q^{50} + 3217272 q^{52} + 1573516 q^{53} - 431296 q^{55} - 7740702 q^{56} + 5987188 q^{58} + 1410320 q^{59} - 942172 q^{61} - 3334412 q^{62} + 1996866 q^{64} + 420944 q^{65} - 452072 q^{67} + 9258254 q^{68} + 21981136 q^{70} - 122928 q^{71} + 16490716 q^{73} + 600104 q^{74} + 7428658 q^{76} - 7239696 q^{77} + 2458408 q^{79} - 19440230 q^{80} + 20510784 q^{82} + 7566456 q^{83} + 5817744 q^{85} + 669666 q^{86} + 14775668 q^{88} + 20368036 q^{89} + 8815576 q^{91} + 2165726 q^{92} + 16952576 q^{94} - 5143832 q^{95} + 12586972 q^{97} + 39164812 q^{98}+O(q^{100}) \) 6 * q + 8 * q^2 + 178 * q^4 + 372 * q^5 - 1104 * q^7 + 1956 * q^8 - 13042 * q^10 + 14824 * q^11 - 756 * q^13 + 3926 * q^14 - 13022 * q^16 + 69484 * q^17 - 43864 * q^19 - 78886 * q^20 + 98204 * q^22 + 73002 * q^23 + 228018 * q^25 + 311956 * q^26 - 545442 * q^28 + 311100 * q^29 - 245248 * q^31 + 390156 * q^32 + 235834 * q^34 + 1331256 * q^35 - 630044 * q^37 - 80910 * q^38 - 2153982 * q^40 + 969204 * q^41 - 1770208 * q^43 + 1749140 * q^44 + 97336 * q^46 + 1400024 * q^47 + 1985598 * q^49 + 956660 * q^50 + 3217272 * q^52 + 1573516 * q^53 - 431296 * q^55 - 7740702 * q^56 + 5987188 * q^58 + 1410320 * q^59 - 942172 * q^61 - 3334412 * q^62 + 1996866 * q^64 + 420944 * q^65 - 452072 * q^67 + 9258254 * q^68 + 21981136 * q^70 - 122928 * q^71 + 16490716 * q^73 + 600104 * q^74 + 7428658 * q^76 - 7239696 * q^77 + 2458408 * q^79 - 19440230 * q^80 + 20510784 * q^82 + 7566456 * q^83 + 5817744 * q^85 + 669666 * q^86 + 14775668 * q^88 + 20368036 * q^89 + 8815576 * q^91 + 2165726 * q^92 + 16952576 * q^94 - 5143832 * q^95 + 12586972 * q^97 + 39164812 * q^98

Introduction

L-functions

Modular forms

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Database

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