LMFDB - Embedded newform 207.8.a.d.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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 775x^{5} - 474x^{4} + 167184x^{3} - 33920x^{2} - 9348928x + 28965760 $ x^7 - 775x^5 - 474x^4 + 167184x^3 - 33920x^2 - 9348928*x + 28965760
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			$-11.3612$ 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)

$f(q)$	$=$	$q+11.3612 q^{2} +1.07734 q^{4} -392.713 q^{5} -1170.86 q^{7} -1442.00 q^{8} +O(q^{10})$	\(q+11.3612 q^{2} +1.07734 q^{4} -392.713 q^{5} -1170.86 q^{7} -1442.00 q^{8} -4461.70 q^{10} -1763.47 q^{11} -14839.2 q^{13} -13302.4 q^{14} -16520.7 q^{16} +26146.8 q^{17} +42426.4 q^{19} -423.084 q^{20} -20035.2 q^{22} +12167.0 q^{23} +76098.5 q^{25} -168591. q^{26} -1261.41 q^{28} -166035. q^{29} +90693.2 q^{31} -3120.22 q^{32} +297060. q^{34} +459812. q^{35} -38871.7 q^{37} +482016. q^{38} +566291. q^{40} -797288. q^{41} +557159. q^{43} -1899.85 q^{44} +138232. q^{46} +303537. q^{47} +547373. q^{49} +864572. q^{50} -15986.8 q^{52} -1.41335e6 q^{53} +692538. q^{55} +1.68838e6 q^{56} -1.88636e6 q^{58} +724711. q^{59} -2.16696e6 q^{61} +1.03039e6 q^{62} +2.07921e6 q^{64} +5.82753e6 q^{65} +286204. q^{67} +28169.0 q^{68} +5.22403e6 q^{70} -1.87366e6 q^{71} -1.67247e6 q^{73} -441630. q^{74} +45707.6 q^{76} +2.06478e6 q^{77} +5.35515e6 q^{79} +6.48791e6 q^{80} -9.05817e6 q^{82} -9.69011e6 q^{83} -1.02682e7 q^{85} +6.33001e6 q^{86} +2.54292e6 q^{88} +763797. q^{89} +1.73746e7 q^{91} +13108.0 q^{92} +3.44855e6 q^{94} -1.66614e7 q^{95} +1.48153e7 q^{97} +6.21883e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8}+O(q^{10}) $ 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8	\( 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8} - 15310 q^{10} - 9040 q^{11} + 3774 q^{13} - 4536 q^{14} + 52002 q^{16} + 40760 q^{17} + 81598 q^{19} + 88946 q^{20} + 245034 q^{22} + 85169 q^{23} + 321325 q^{25} - 412748 q^{26} + 965948 q^{28} - 154126 q^{29} + 243132 q^{31} - 1278286 q^{32} + 984836 q^{34} + 130296 q^{35} + 582114 q^{37} - 772558 q^{38} - 132618 q^{40} - 113062 q^{41} - 659778 q^{43} - 659390 q^{44} + 591032 q^{47} + 3263235 q^{49} + 702684 q^{50} + 1793280 q^{52} - 207128 q^{53} + 184664 q^{55} - 5390508 q^{56} - 1142916 q^{58} - 447148 q^{59} + 2248970 q^{61} + 5729060 q^{62} + 7212922 q^{64} + 827096 q^{65} + 4467570 q^{67} + 5477620 q^{68} - 12744284 q^{70} + 5154608 q^{71} - 13239250 q^{73} + 2827426 q^{74} - 527434 q^{76} + 18415912 q^{77} + 9594446 q^{79} + 55932394 q^{80} - 20889952 q^{82} + 573720 q^{83} + 7477272 q^{85} + 28416910 q^{86} + 26555702 q^{88} + 3810540 q^{89} + 36092068 q^{91} + 7957218 q^{92} + 33545768 q^{94} - 10497320 q^{95} + 49497978 q^{97} + 1023376 q^{98}+O(q^{100}) \) 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8 - 15310 * q^10 - 9040 * q^11 + 3774 * q^13 - 4536 * q^14 + 52002 * q^16 + 40760 * q^17 + 81598 * q^19 + 88946 * q^20 + 245034 * q^22 + 85169 * q^23 + 321325 * q^25 - 412748 * q^26 + 965948 * q^28 - 154126 * q^29 + 243132 * q^31 - 1278286 * q^32 + 984836 * q^34 + 130296 * q^35 + 582114 * q^37 - 772558 * q^38 - 132618 * q^40 - 113062 * q^41 - 659778 * q^43 - 659390 * q^44 + 591032 * q^47 + 3263235 * q^49 + 702684 * q^50 + 1793280 * q^52 - 207128 * q^53 + 184664 * q^55 - 5390508 * q^56 - 1142916 * q^58 - 447148 * q^59 + 2248970 * q^61 + 5729060 * q^62 + 7212922 * q^64 + 827096 * q^65 + 4467570 * q^67 + 5477620 * q^68 - 12744284 * q^70 + 5154608 * q^71 - 13239250 * q^73 + 2827426 * q^74 - 527434 * q^76 + 18415912 * q^77 + 9594446 * q^79 + 55932394 * q^80 - 20889952 * q^82 + 573720 * q^83 + 7477272 * q^85 + 28416910 * q^86 + 26555702 * q^88 + 3810540 * q^89 + 36092068 * q^91 + 7957218 * q^92 + 33545768 * q^94 - 10497320 * q^95 + 49497978 * q^97 + 1023376 * 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 $

$2$	11.3612	1.00420	0.502100	−	0.864810i	$-0.332561\pi$
$2$	11.3612	1.00420	0.502100	+	0.864810i	$0.332561\pi$
$3$	0	0
$3$	0	0
$4$	1.07734	0.00841670
$5$	−392.713	−1.40501	−0.702506	−	0.711677i	$-0.747936\pi$
$5$	−392.713	−1.40501	−0.702506	+	0.711677i	$0.747936\pi$
$6$	0	0
$7$	−1170.86	−1.29022	−0.645108	−	0.764092i	$-0.723188\pi$
$7$	−1170.86	−1.29022	−0.645108	+	0.764092i	$0.723188\pi$
$8$	−1442.00	−0.995747
$9$	0	0
$10$	−4461.70	−1.41091
$11$	−1763.47	−0.399479	−0.199739	−	0.979849i	$-0.564010\pi$
$11$	−1763.47	−0.399479	−0.199739	+	0.979849i	$0.564010\pi$
$12$	0	0
$13$	−14839.2	−1.87330	−0.936651	−	0.350265i	$-0.886091\pi$
$13$	−14839.2	−1.87330	−0.936651	+	0.350265i	$0.886091\pi$
$14$	−13302.4	−1.29563
$15$	0	0
$16$	−16520.7	−1.00835
$17$	26146.8	1.29077	0.645384	−	0.763859i	$-0.276697\pi$
$17$	26146.8	1.29077	0.645384	+	0.763859i	$0.276697\pi$
$18$	0	0
$19$	42426.4	1.41905	0.709527	−	0.704678i	$-0.248909\pi$
$19$	42426.4	1.41905	0.709527	+	0.704678i	$0.248909\pi$
$20$	−423.084	−0.0118256
$21$	0	0
$22$	−20035.2	−0.401156
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	76098.5	0.974061
$26$	−168591.	−1.88117
$27$	0	0
$28$	−1261.41	−0.0108594
$29$	−166035.	−1.26417	−0.632087	−	0.774898i	$-0.717801\pi$
$29$	−166035.	−1.26417	−0.632087	+	0.774898i	$0.717801\pi$
$30$	0	0
$31$	90693.2	0.546775	0.273388	−	0.961904i	$-0.411856\pi$
$31$	90693.2	0.546775	0.273388	+	0.961904i	$0.411856\pi$
$32$	−3120.22	−0.0168329
$33$	0	0
$34$	297060.	1.29619
$35$	459812.	1.81277
$36$	0	0
$37$	−38871.7	−0.126162	−0.0630808	−	0.998008i	$-0.520093\pi$
$37$	−38871.7	−0.126162	−0.0630808	+	0.998008i	$0.520093\pi$
$38$	482016.	1.42501
$39$	0	0
$40$	566291.	1.39904
$41$	−797288.	−1.80664	−0.903320	−	0.428967i	$-0.858878\pi$
$41$	−797288.	−1.80664	−0.903320	+	0.428967i	$0.858878\pi$
$42$	0	0
$43$	557159.	1.06866	0.534330	−	0.845276i	$-0.320564\pi$
$43$	557159.	1.06866	0.534330	+	0.845276i	$0.320564\pi$
$44$	−1899.85	−0.00336229
$45$	0	0
$46$	138232.	0.209390
$47$	303537.	0.426451	0.213225	−	0.977003i	$-0.431603\pi$
$47$	303537.	0.426451	0.213225	+	0.977003i	$0.431603\pi$
$48$	0	0
$49$	547373.	0.664656
$50$	864572.	0.978151
$51$	0	0
$52$	−15986.8	−0.0157670
$53$	−1.41335e6	−1.30402	−0.652009	−	0.758211i	$-0.726074\pi$
$53$	−1.41335e6	−1.30402	−0.652009	+	0.758211i	$0.726074\pi$
$54$	0	0
$55$	692538.	0.561273
$56$	1.68838e6	1.28473
$57$	0	0
$58$	−1.88636e6	−1.26948
$59$	724711.	0.459391	0.229696	−	0.973263i	$-0.426227\pi$
$59$	724711.	0.459391	0.229696	+	0.973263i	$0.426227\pi$
$60$	0	0
$61$	−2.16696e6	−1.22235	−0.611177	−	0.791494i	$-0.709304\pi$
$61$	−2.16696e6	−1.22235	−0.611177	+	0.791494i	$0.709304\pi$
$62$	1.03039e6	0.549072
$63$	0	0
$64$	2.07921e6	0.991442
$65$	5.82753e6	2.63201
$66$	0	0
$67$	286204.	0.116256	0.0581278	−	0.998309i	$-0.481487\pi$
$67$	286204.	0.116256	0.0581278	+	0.998309i	$0.481487\pi$
$68$	28169.0	0.0108640
$69$	0	0
$70$	5.22403e6	1.82038
$71$	−1.87366e6	−0.621279	−0.310639	−	0.950528i	$-0.600543\pi$
$71$	−1.87366e6	−0.621279	−0.310639	+	0.950528i	$0.600543\pi$
$72$	0	0
$73$	−1.67247e6	−0.503186	−0.251593	−	0.967833i	$-0.580954\pi$
$73$	−1.67247e6	−0.503186	−0.251593	+	0.967833i	$0.580954\pi$
$74$	−441630.	−0.126691
$75$	0	0
$76$	45707.6	0.0119437
$77$	2.06478e6	0.515414
$78$	0	0
$79$	5.35515e6	1.22202	0.611008	−	0.791624i	$-0.290764\pi$
$79$	5.35515e6	1.22202	0.611008	+	0.791624i	$0.290764\pi$
$80$	6.48791e6	1.41674
$81$	0	0
$82$	−9.05817e6	−1.81423
$83$	−9.69011e6	−1.86018	−0.930091	−	0.367330i	$-0.880272\pi$
$83$	−9.69011e6	−1.86018	−0.930091	+	0.367330i	$0.880272\pi$
$84$	0	0
$85$	−1.02682e7	−1.81354
$86$	6.33001e6	1.07315
$87$	0	0
$88$	2.54292e6	0.397780
$89$	763797.	0.114845	0.0574226	−	0.998350i	$-0.481712\pi$
$89$	763797.	0.114845	0.0574226	+	0.998350i	$0.481712\pi$
$90$	0	0
$91$	1.73746e7	2.41696
$92$	13108.0	0.00175500
$93$	0	0
$94$	3.44855e6	0.428242
$95$	−1.66614e7	−1.99379
$96$	0	0
$97$	1.48153e7	1.64819	0.824097	−	0.566449i	$-0.191683\pi$
$97$	1.48153e7	1.64819	0.824097	+	0.566449i	$0.191683\pi$
$98$	6.21883e6	0.667448
$99$	0	0
$100$	81983.7	0.00819837
$101$	−3.67489e6	−0.354911	−0.177455	−	0.984129i	$-0.556787\pi$
$101$	−3.67489e6	−0.354911	−0.177455	+	0.984129i	$0.556787\pi$
$102$	0	0
$103$	−1.01045e6	−0.0911136	−0.0455568	−	0.998962i	$-0.514506\pi$
$103$	−1.01045e6	−0.0911136	−0.0455568	+	0.998962i	$0.514506\pi$
$104$	2.13980e7	1.86533
$105$	0	0
$106$	−1.60574e7	−1.30949
$107$	−7.31751e6	−0.577458	−0.288729	−	0.957411i	$-0.593233\pi$
$107$	−7.31751e6	−0.577458	−0.288729	+	0.957411i	$0.593233\pi$
$108$	0	0
$109$	8.27606e6	0.612112	0.306056	−	0.952014i	$-0.400991\pi$
$109$	8.27606e6	0.612112	0.306056	+	0.952014i	$0.400991\pi$
$110$	7.86807e6	0.563630
$111$	0	0
$112$	1.93435e7	1.30098
$113$	7.73720e6	0.504440	0.252220	−	0.967670i	$-0.418839\pi$
$113$	7.73720e6	0.504440	0.252220	+	0.967670i	$0.418839\pi$
$114$	0	0
$115$	−4.77814e6	−0.292965
$116$	−178876.	−0.0106402
$117$	0	0
$118$	8.23360e6	0.461320
$119$	−3.06143e7	−1.66537
$120$	0	0
$121$	−1.63773e7	−0.840417
$122$	−2.46194e7	−1.22749
$123$	0	0
$124$	97707.2	0.00460204
$125$	795831.	0.0364448
$126$	0	0
$127$	3.87137e7	1.67707	0.838537	−	0.544845i	$-0.183412\pi$
$127$	3.87137e7	1.67707	0.838537	+	0.544845i	$0.183412\pi$
$128$	2.40217e7	1.01244
$129$	0	0
$130$	6.62079e7	2.64307
$131$	1.95939e7	0.761504	0.380752	−	0.924677i	$-0.375665\pi$
$131$	1.95939e7	0.761504	0.380752	+	0.924677i	$0.375665\pi$
$132$	0	0
$133$	−4.96755e7	−1.83089
$134$	3.25162e6	0.116744
$135$	0	0
$136$	−3.77037e7	−1.28528
$137$	−3.83160e7	−1.27309	−0.636544	−	0.771241i	$-0.719636\pi$
$137$	−3.83160e7	−1.27309	−0.636544	+	0.771241i	$0.719636\pi$
$138$	0	0
$139$	1.71827e7	0.542674	0.271337	−	0.962484i	$-0.412534\pi$
$139$	1.71827e7	0.542674	0.271337	+	0.962484i	$0.412534\pi$
$140$	495373.	0.0152575
$141$	0	0
$142$	−2.12871e7	−0.623888
$143$	2.61684e7	0.748344
$144$	0	0
$145$	6.52041e7	1.77618
$146$	−1.90013e7	−0.505299
$147$	0	0
$148$	−41877.9	−0.00106186
$149$	1.49325e7	0.369811	0.184905	−	0.982756i	$-0.440802\pi$
$149$	1.49325e7	0.369811	0.184905	+	0.982756i	$0.440802\pi$
$150$	0	0
$151$	1.92788e7	0.455680	0.227840	−	0.973699i	$-0.426834\pi$
$151$	1.92788e7	0.455680	0.227840	+	0.973699i	$0.426834\pi$
$152$	−6.11788e7	−1.41302
$153$	0	0
$154$	2.34584e7	0.517578
$155$	−3.56164e7	−0.768227
$156$	0	0
$157$	−7.87019e7	−1.62307	−0.811534	−	0.584306i	$-0.801367\pi$
$157$	−7.87019e7	−1.62307	−0.811534	+	0.584306i	$0.801367\pi$
$158$	6.08411e7	1.22715
$159$	0	0
$160$	1.22535e6	0.0236505
$161$	−1.42459e7	−0.269029
$162$	0	0
$163$	8.12119e7	1.46880	0.734401	−	0.678716i	$-0.237463\pi$
$163$	8.12119e7	1.46880	0.734401	+	0.678716i	$0.237463\pi$
$164$	−858948.	−0.0152059
$165$	0	0
$166$	−1.10091e8	−1.86799
$167$	9.86019e6	0.163824	0.0819120	−	0.996640i	$-0.473897\pi$
$167$	9.86019e6	0.163824	0.0819120	+	0.996640i	$0.473897\pi$
$168$	0	0
$169$	1.57452e8	2.50926
$170$	−1.16659e8	−1.82116
$171$	0	0
$172$	600248.	0.00899459
$173$	7.27616e7	1.06842	0.534209	−	0.845353i	$-0.320610\pi$
$173$	7.27616e7	1.06842	0.534209	+	0.845353i	$0.320610\pi$
$174$	0	0
$175$	−8.91008e7	−1.25675
$176$	2.91338e7	0.402813
$177$	0	0
$178$	8.67766e6	0.115327
$179$	−4.97342e6	−0.0648141	−0.0324071	−	0.999475i	$-0.510317\pi$
$179$	−4.97342e6	−0.0648141	−0.0324071	+	0.999475i	$0.510317\pi$
$180$	0	0
$181$	−6.89922e7	−0.864818	−0.432409	−	0.901678i	$-0.642336\pi$
$181$	−6.89922e7	−0.864818	−0.432409	+	0.901678i	$0.642336\pi$
$182$	1.97397e8	2.42711
$183$	0	0
$184$	−1.75448e7	−0.207628
$185$	1.52654e7	0.177259
$186$	0	0
$187$	−4.61092e7	−0.515634
$188$	327012.	0.00358931
$189$	0	0
$190$	−1.89294e8	−2.00216
$191$	1.83352e8	1.90401	0.952004	−	0.306087i	$-0.0990198\pi$
$191$	1.83352e8	1.90401	0.952004	+	0.306087i	$0.0990198\pi$
$192$	0	0
$193$	−9.29213e7	−0.930389	−0.465195	−	0.885208i	$-0.654016\pi$
$193$	−9.29213e7	−0.930389	−0.465195	+	0.885208i	$0.654016\pi$
$194$	1.68319e8	1.65511
$195$	0	0
$196$	589705.	0.00559421
$197$	8.71794e7	0.812423	0.406212	−	0.913779i	$-0.366850\pi$
$197$	8.71794e7	0.812423	0.406212	+	0.913779i	$0.366850\pi$
$198$	0	0
$199$	−1.27549e8	−1.14734	−0.573668	−	0.819088i	$-0.694480\pi$
$199$	−1.27549e8	−1.14734	−0.573668	+	0.819088i	$0.694480\pi$
$200$	−1.09734e8	−0.969919
$201$	0	0
$202$	−4.17512e7	−0.356401
$203$	1.94404e8	1.63106
$204$	0	0
$205$	3.13105e8	2.53835
$206$	−1.14799e7	−0.0914963
$207$	0	0
$208$	2.45154e8	1.88894
$209$	−7.48177e7	−0.566882
$210$	0	0
$211$	1.31901e8	0.966630	0.483315	−	0.875446i	$-0.339433\pi$
$211$	1.31901e8	0.966630	0.483315	+	0.875446i	$0.339433\pi$
$212$	−1.52265e6	−0.0109755
$213$	0	0
$214$	−8.31359e7	−0.579883
$215$	−2.18804e8	−1.50148
$216$	0	0
$217$	−1.06189e8	−0.705458
$218$	9.40261e7	0.614683
$219$	0	0
$220$	746096.	0.00472406
$221$	−3.87997e8	−2.41800
$222$	0	0
$223$	−2.86007e7	−0.172707	−0.0863535	−	0.996265i	$-0.527521\pi$
$223$	−2.86007e7	−0.172707	−0.0863535	+	0.996265i	$0.527521\pi$
$224$	3.65334e6	0.0217181
$225$	0	0
$226$	8.79040e7	0.506558
$227$	−1.68470e8	−0.955942	−0.477971	−	0.878376i	$-0.658628\pi$
$227$	−1.68470e8	−0.955942	−0.477971	+	0.878376i	$0.658628\pi$
$228$	0	0
$229$	−1.94092e8	−1.06803	−0.534015	−	0.845475i	$-0.679317\pi$
$229$	−1.94092e8	−1.06803	−0.534015	+	0.845475i	$0.679317\pi$
$230$	−5.42855e7	−0.294196
$231$	0	0
$232$	2.39422e8	1.25880
$233$	−1.08444e8	−0.561642	−0.280821	−	0.959760i	$-0.590607\pi$
$233$	−1.08444e8	−0.561642	−0.280821	+	0.959760i	$0.590607\pi$
$234$	0	0
$235$	−1.19203e8	−0.599169
$236$	780758.	0.00386656
$237$	0	0
$238$	−3.47816e8	−1.67236
$239$	−4.09522e8	−1.94037	−0.970184	−	0.242369i	$-0.922076\pi$
$239$	−4.09522e8	−1.94037	−0.970184	+	0.242369i	$0.922076\pi$
$240$	0	0
$241$	−1.71366e8	−0.788614	−0.394307	−	0.918979i	$-0.629015\pi$
$241$	−1.71366e8	−0.788614	−0.394307	+	0.918979i	$0.629015\pi$
$242$	−1.86067e8	−0.843946
$243$	0	0
$244$	−2.33455e6	−0.0102882
$245$	−2.14961e8	−0.933851
$246$	0	0
$247$	−6.29573e8	−2.65832
$248$	−1.30779e8	−0.544450
$249$	0	0
$250$	9.04161e6	0.0365979
$251$	−1.27165e8	−0.507586	−0.253793	−	0.967259i	$-0.581678\pi$
$251$	−1.27165e8	−0.507586	−0.253793	+	0.967259i	$0.581678\pi$
$252$	0	0
$253$	−2.14561e7	−0.0832971
$254$	4.39835e8	1.68412
$255$	0	0
$256$	6.77754e6	0.0252483
$257$	1.47963e8	0.543735	0.271867	−	0.962335i	$-0.412359\pi$
$257$	1.47963e8	0.543735	0.271867	+	0.962335i	$0.412359\pi$
$258$	0	0
$259$	4.55134e7	0.162776
$260$	6.27822e6	0.0221528
$261$	0	0
$262$	2.22611e8	0.764702
$263$	−3.15454e8	−1.06928	−0.534639	−	0.845081i	$-0.679552\pi$
$263$	−3.15454e8	−1.06928	−0.534639	+	0.845081i	$0.679552\pi$
$264$	0	0
$265$	5.55040e8	1.83216
$266$	−5.64374e8	−1.83857
$267$	0	0
$268$	308338.	0.000978487 0
$269$	3.49514e8	1.09479	0.547396	−	0.836874i	$-0.315619\pi$
$269$	3.49514e8	1.09479	0.547396	+	0.836874i	$0.315619\pi$
$270$	0	0
$271$	5.74060e8	1.75212	0.876062	−	0.482198i	$-0.160161\pi$
$271$	5.74060e8	1.75212	0.876062	+	0.482198i	$0.160161\pi$
$272$	−4.31965e8	−1.30154
$273$	0	0
$274$	−4.35316e8	−1.27843
$275$	−1.34197e8	−0.389117
$276$	0	0
$277$	−2.81324e7	−0.0795294	−0.0397647	−	0.999209i	$-0.512661\pi$
$277$	−2.81324e7	−0.0795294	−0.0397647	+	0.999209i	$0.512661\pi$
$278$	1.95216e8	0.544953
$279$	0	0
$280$	−6.63048e8	−1.80506
$281$	5.97185e6	0.0160560	0.00802800	−	0.999968i	$-0.497445\pi$
$281$	5.97185e6	0.0160560	0.00802800	+	0.999968i	$0.497445\pi$
$282$	0	0
$283$	−8.59689e7	−0.225470	−0.112735	−	0.993625i	$-0.535961\pi$
$283$	−8.59689e7	−0.225470	−0.112735	+	0.993625i	$0.535961\pi$
$284$	−2.01856e6	−0.00522911
$285$	0	0
$286$	2.97305e8	0.751487
$287$	9.33514e8	2.33096
$288$	0	0
$289$	2.73319e8	0.666081
$290$	7.40798e8	1.78364
$291$	0	0
$292$	−1.80181e6	−0.00423516
$293$	−1.62287e8	−0.376918	−0.188459	−	0.982081i	$-0.560349\pi$
$293$	−1.62287e8	−0.376918	−0.188459	+	0.982081i	$0.560349\pi$
$294$	0	0
$295$	−2.84603e8	−0.645450
$296$	5.60528e7	0.125625
$297$	0	0
$298$	1.69651e8	0.371364
$299$	−1.80548e8	−0.390610
$300$	0	0
$301$	−6.52356e8	−1.37880
$302$	2.19030e8	0.457594
$303$	0	0
$304$	−7.00916e8	−1.43090
$305$	8.50995e8	1.71742
$306$	0	0
$307$	3.30003e8	0.650930	0.325465	−	0.945554i	$-0.394479\pi$
$307$	3.30003e8	0.650930	0.325465	+	0.945554i	$0.394479\pi$
$308$	2.22446e6	0.00433808
$309$	0	0
$310$	−4.04646e8	−0.771453
$311$	−2.46004e8	−0.463746	−0.231873	−	0.972746i	$-0.574485\pi$
$311$	−2.46004e8	−0.463746	−0.231873	+	0.972746i	$0.574485\pi$
$312$	0	0
$313$	6.06687e8	1.11830	0.559152	−	0.829065i	$-0.311127\pi$
$313$	6.06687e8	1.11830	0.559152	+	0.829065i	$0.311127\pi$
$314$	−8.94150e8	−1.62988
$315$	0	0
$316$	5.76931e6	0.0102853
$317$	−4.92260e8	−0.867936	−0.433968	−	0.900928i	$-0.642887\pi$
$317$	−4.92260e8	−0.867936	−0.433968	+	0.900928i	$0.642887\pi$
$318$	0	0
$319$	2.92798e8	0.505010
$320$	−8.16531e8	−1.39299
$321$	0	0
$322$	−1.61850e8	−0.270158
$323$	1.10932e9	1.83167
$324$	0	0
$325$	−1.12924e9	−1.82471
$326$	9.22666e8	1.47497
$327$	0	0
$328$	1.14969e9	1.79896
$329$	−3.55400e8	−0.550214
$330$	0	0
$331$	−6.11729e8	−0.927174	−0.463587	−	0.886051i	$-0.653438\pi$
$331$	−6.11729e8	−0.927174	−0.463587	+	0.886051i	$0.653438\pi$
$332$	−1.04395e7	−0.0156566
$333$	0	0
$334$	1.12024e8	0.164512
$335$	−1.12396e8	−0.163341
$336$	0	0
$337$	3.71805e8	0.529189	0.264595	−	0.964360i	$-0.414762\pi$
$337$	3.71805e8	0.529189	0.264595	+	0.964360i	$0.414762\pi$
$338$	1.78885e9	2.51980
$339$	0	0
$340$	−1.10623e7	−0.0152641
$341$	−1.59935e8	−0.218425
$342$	0	0
$343$	3.23357e8	0.432665
$344$	−8.03421e8	−1.06412
$345$	0	0
$346$	8.26661e8	1.07290
$347$	6.18438e8	0.794590	0.397295	−	0.917691i	$-0.369949\pi$
$347$	6.18438e8	0.794590	0.397295	+	0.917691i	$0.369949\pi$
$348$	0	0
$349$	4.47955e8	0.564086	0.282043	−	0.959402i	$-0.408988\pi$
$349$	4.47955e8	0.564086	0.282043	+	0.959402i	$0.408988\pi$
$350$	−1.01229e9	−1.26203
$351$	0	0
$352$	5.50241e6	0.00672440
$353$	−9.25109e7	−0.111939	−0.0559695	−	0.998432i	$-0.517825\pi$
$353$	−9.25109e7	−0.111939	−0.0559695	+	0.998432i	$0.517825\pi$
$354$	0	0
$355$	7.35811e8	0.872905
$356$	822867.	0.000966617 0
$357$	0	0
$358$	−5.65041e7	−0.0650863
$359$	1.30614e8	0.148990	0.0744952	−	0.997221i	$-0.476265\pi$
$359$	1.30614e8	0.148990	0.0744952	+	0.997221i	$0.476265\pi$
$360$	0	0
$361$	9.06130e8	1.01371
$362$	−7.83835e8	−0.868450
$363$	0	0
$364$	1.87183e7	0.0203428
$365$	6.56801e8	0.706983
$366$	0	0
$367$	1.16358e9	1.22875	0.614377	−	0.789012i	$-0.289407\pi$
$367$	1.16358e9	1.22875	0.614377	+	0.789012i	$0.289407\pi$
$368$	−2.01008e8	−0.210255
$369$	0	0
$370$	1.73434e8	0.178003
$371$	1.65484e9	1.68247
$372$	0	0
$373$	−1.52608e9	−1.52264	−0.761320	−	0.648377i	$-0.775448\pi$
$373$	−1.52608e9	−1.52264	−0.761320	+	0.648377i	$0.775448\pi$
$374$	−5.23856e8	−0.517800
$375$	0	0
$376$	−4.37699e8	−0.424637
$377$	2.46382e9	2.36818
$378$	0	0
$379$	−1.27741e8	−0.120530	−0.0602648	−	0.998182i	$-0.519195\pi$
$379$	−1.27741e8	−0.120530	−0.0602648	+	0.998182i	$0.519195\pi$
$380$	−1.79500e7	−0.0167811
$381$	0	0
$382$	2.08310e9	1.91200
$383$	1.33134e9	1.21086	0.605429	−	0.795899i	$-0.293001\pi$
$383$	1.33134e9	1.21086	0.605429	+	0.795899i	$0.293001\pi$
$384$	0	0
$385$	−8.10865e8	−0.724163
$386$	−1.05570e9	−0.934296
$387$	0	0
$388$	1.59610e7	0.0138723
$389$	−2.18772e8	−0.188438	−0.0942188	−	0.995552i	$-0.530035\pi$
$389$	−2.18772e8	−0.188438	−0.0942188	+	0.995552i	$0.530035\pi$
$390$	0	0
$391$	3.18129e8	0.269144
$392$	−7.89310e8	−0.661830
$393$	0	0
$394$	9.90465e8	0.815835
$395$	−2.10304e9	−1.71695
$396$	0	0
$397$	1.72787e9	1.38594	0.692970	−	0.720967i	$-0.256302\pi$
$397$	1.72787e9	1.38594	0.692970	+	0.720967i	$0.256302\pi$
$398$	−1.44911e9	−1.15215
$399$	0	0
$400$	−1.25720e9	−0.982190
$401$	−6.96045e7	−0.0539054	−0.0269527	−	0.999637i	$-0.508580\pi$
$401$	−6.96045e7	−0.0539054	−0.0269527	+	0.999637i	$0.508580\pi$
$402$	0	0
$403$	−1.34581e9	−1.02428
$404$	−3.95909e6	−0.00298717
$405$	0	0
$406$	2.20867e9	1.63791
$407$	6.85490e7	0.0503989
$408$	0	0
$409$	8.08384e8	0.584233	0.292117	−	0.956383i	$-0.405640\pi$
$409$	8.08384e8	0.584233	0.292117	+	0.956383i	$0.405640\pi$
$410$	3.55726e9	2.54901
$411$	0	0
$412$	−1.08859e6	−0.000766876 0
$413$	−8.48536e8	−0.592714
$414$	0	0
$415$	3.80543e9	2.61358
$416$	4.63014e7	0.0315332
$417$	0	0
$418$	−8.50021e8	−0.569262
$419$	8.78688e8	0.583560	0.291780	−	0.956485i	$-0.405752\pi$
$419$	8.78688e8	0.583560	0.291780	+	0.956485i	$0.405752\pi$
$420$	0	0
$421$	−2.74747e9	−1.79451	−0.897255	−	0.441512i	$-0.854442\pi$
$421$	−2.74747e9	−1.79451	−0.897255	+	0.441512i	$0.854442\pi$
$422$	1.49856e9	0.970690
$423$	0	0
$424$	2.03804e9	1.29847
$425$	1.98974e9	1.25729
$426$	0	0
$427$	2.53721e9	1.57710
$428$	−7.88343e6	−0.00486029
$429$	0	0
$430$	−2.48588e9	−1.50779
$431$	−1.38074e9	−0.830692	−0.415346	−	0.909664i	$-0.636339\pi$
$431$	−1.38074e9	−0.830692	−0.415346	+	0.909664i	$0.636339\pi$
$432$	0	0
$433$	1.29261e9	0.765173	0.382587	−	0.923920i	$-0.375033\pi$
$433$	1.29261e9	0.765173	0.382587	+	0.923920i	$0.375033\pi$
$434$	−1.20644e9	−0.708421
$435$	0	0
$436$	8.91611e6	0.00515196
$437$	5.16202e8	0.295893
$438$	0	0
$439$	2.12976e9	1.20145	0.600723	−	0.799457i	$-0.294880\pi$
$439$	2.12976e9	1.20145	0.600723	+	0.799457i	$0.294880\pi$
$440$	−9.98637e8	−0.558886
$441$	0	0
$442$	−4.40812e9	−2.42815
$443$	2.58813e9	1.41440	0.707200	−	0.707013i	$-0.249958\pi$
$443$	2.58813e9	1.41440	0.707200	+	0.707013i	$0.249958\pi$
$444$	0	0
$445$	−2.99953e8	−0.161359
$446$	−3.24939e8	−0.173432
$447$	0	0
$448$	−2.43446e9	−1.27917
$449$	6.85574e8	0.357431	0.178715	−	0.983901i	$-0.442806\pi$
$449$	6.85574e8	0.357431	0.178715	+	0.983901i	$0.442806\pi$
$450$	0	0
$451$	1.40599e9	0.721714
$452$	8.33557e6	0.00424571
$453$	0	0
$454$	−1.91402e9	−0.959956
$455$	−6.82323e9	−3.39586
$456$	0	0
$457$	1.12411e9	0.550939	0.275470	−	0.961310i	$-0.411167\pi$
$457$	1.12411e9	0.550939	0.275470	+	0.961310i	$0.411167\pi$
$458$	−2.20512e9	−1.07251
$459$	0	0
$460$	−5.14767e6	−0.00246580
$461$	−5.81992e8	−0.276671	−0.138336	−	0.990385i	$-0.544175\pi$
$461$	−5.81992e8	−0.276671	−0.138336	+	0.990385i	$0.544175\pi$
$462$	0	0
$463$	−3.38927e9	−1.58698	−0.793492	−	0.608581i	$-0.791739\pi$
$463$	−3.38927e9	−1.58698	−0.793492	+	0.608581i	$0.791739\pi$
$464$	2.74302e9	1.27472
$465$	0	0
$466$	−1.23206e9	−0.564001
$467$	2.93656e9	1.33423	0.667113	−	0.744957i	$-0.267530\pi$
$467$	2.93656e9	1.33423	0.667113	+	0.744957i	$0.267530\pi$
$468$	0	0
$469$	−3.35105e8	−0.149995
$470$	−1.35429e9	−0.601685
$471$	0	0
$472$	−1.04503e9	−0.457438
$473$	−9.82533e8	−0.426907
$474$	0	0
$475$	3.22859e9	1.38224
$476$	−3.29819e7	−0.0140169
$477$	0	0
$478$	−4.65267e9	−1.94852
$479$	1.16240e9	0.483261	0.241631	−	0.970368i	$-0.422318\pi$
$479$	1.16240e9	0.483261	0.241631	+	0.970368i	$0.422318\pi$
$480$	0	0
$481$	5.76823e8	0.236339
$482$	−1.94692e9	−0.791926
$483$	0	0
$484$	−1.76439e7	−0.00707353
$485$	−5.81814e9	−2.31573
$486$	0	0
$487$	4.38111e9	1.71883	0.859416	−	0.511278i	$-0.170828\pi$
$487$	4.38111e9	1.71883	0.859416	+	0.511278i	$0.170828\pi$
$488$	3.12475e9	1.21716
$489$	0	0
$490$	−2.44221e9	−0.937773
$491$	3.82021e8	0.145647	0.0728235	−	0.997345i	$-0.476799\pi$
$491$	3.82021e8	0.145647	0.0728235	+	0.997345i	$0.476799\pi$
$492$	0	0
$493$	−4.34129e9	−1.63175
$494$	−7.15271e9	−2.66948
$495$	0	0
$496$	−1.49832e9	−0.551339
$497$	2.19380e9	0.801584
$498$	0	0
$499$	−1.92036e9	−0.691881	−0.345940	−	0.938257i	$-0.612440\pi$
$499$	−1.92036e9	−0.691881	−0.345940	+	0.938257i	$0.612440\pi$
$500$	857378.	0.000306745 0
$501$	0	0
$502$	−1.44475e9	−0.509717
$503$	3.49937e9	1.22603	0.613016	−	0.790070i	$-0.289956\pi$
$503$	3.49937e9	1.22603	0.613016	+	0.790070i	$0.289956\pi$
$504$	0	0
$505$	1.44318e9	0.498654
$506$	−2.43768e8	−0.0836469
$507$	0	0
$508$	4.17077e7	0.0141154
$509$	−5.14542e9	−1.72945	−0.864727	−	0.502243i	$-0.832508\pi$
$509$	−5.14542e9	−1.72945	−0.864727	+	0.502243i	$0.832508\pi$
$510$	0	0
$511$	1.95823e9	0.649218
$512$	−2.99778e9	−0.987084
$513$	0	0
$514$	1.68104e9	0.546018
$515$	3.96816e8	0.128016
$516$	0	0
$517$	−5.35278e8	−0.170358
$518$	5.17087e8	0.163459
$519$	0	0
$520$	−8.40328e9	−2.62082
$521$	−1.79927e9	−0.557396	−0.278698	−	0.960379i	$-0.589903\pi$
$521$	−1.79927e9	−0.557396	−0.278698	+	0.960379i	$0.589903\pi$
$522$	0	0
$523$	−4.44596e8	−0.135897	−0.0679484	−	0.997689i	$-0.521645\pi$
$523$	−4.44596e8	−0.135897	−0.0679484	+	0.997689i	$0.521645\pi$
$524$	2.11093e7	0.00640935
$525$	0	0
$526$	−3.58394e9	−1.07377
$527$	2.37134e9	0.705760
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	6.30594e9	1.83986
$531$	0	0
$532$	−5.35172e7	−0.0154100
$533$	1.18311e10	3.38438
$534$	0	0
$535$	2.87368e9	0.811335
$536$	−4.12705e8	−0.115761
$537$	0	0
$538$	3.97091e9	1.09939
$539$	−9.65276e8	−0.265516
$540$	0	0
$541$	4.48022e9	1.21649	0.608246	−	0.793749i	$-0.291874\pi$
$541$	4.48022e9	1.21649	0.608246	+	0.793749i	$0.291874\pi$
$542$	6.52203e9	1.75948
$543$	0	0
$544$	−8.15839e7	−0.0217274
$545$	−3.25012e9	−0.860025
$546$	0	0
$547$	−6.94497e8	−0.181432	−0.0907162	−	0.995877i	$-0.528916\pi$
$547$	−6.94497e8	−0.181432	−0.0907162	+	0.995877i	$0.528916\pi$
$548$	−4.12792e7	−0.0107152
$549$	0	0
$550$	−1.52465e9	−0.390751
$551$	−7.04427e9	−1.79393
$552$	0	0
$553$	−6.27014e9	−1.57667
$554$	−3.19618e8	−0.0798634
$555$	0	0
$556$	1.85115e7	0.00456752
$557$	−6.59351e9	−1.61668	−0.808339	−	0.588717i	$-0.799633\pi$
$557$	−6.59351e9	−1.61668	−0.808339	+	0.588717i	$0.799633\pi$
$558$	0	0
$559$	−8.26777e9	−2.00192
$560$	−7.59644e9	−1.82790
$561$	0	0
$562$	6.78476e7	0.0161234
$563$	4.28123e9	1.01109	0.505544	−	0.862801i	$-0.331292\pi$
$563$	4.28123e9	1.01109	0.505544	+	0.862801i	$0.331292\pi$
$564$	0	0
$565$	−3.03850e9	−0.708744
$566$	−9.76711e8	−0.226417
$567$	0	0
$568$	2.70181e9	0.618637
$569$	4.87363e9	1.10907	0.554536	−	0.832160i	$-0.312896\pi$
$569$	4.87363e9	1.10907	0.554536	+	0.832160i	$0.312896\pi$
$570$	0	0
$571$	−9.55591e8	−0.214806	−0.107403	−	0.994216i	$-0.534253\pi$
$571$	−9.55591e8	−0.214806	−0.107403	+	0.994216i	$0.534253\pi$
$572$	2.81922e7	0.00629858
$573$	0	0
$574$	1.06059e10	2.34074
$575$	9.25891e8	0.203106
$576$	0	0
$577$	4.90266e9	1.06247	0.531235	−	0.847225i	$-0.321728\pi$
$577$	4.90266e9	1.06247	0.531235	+	0.847225i	$0.321728\pi$
$578$	3.10523e9	0.668878
$579$	0	0
$580$	7.02468e7	0.0149496
$581$	1.13458e10	2.40003
$582$	0	0
$583$	2.49240e9	0.520928
$584$	2.41170e9	0.501046
$585$	0	0
$586$	−1.84378e9	−0.378501
$587$	−7.28679e9	−1.48697	−0.743486	−	0.668751i	$-0.766829\pi$
$587$	−7.28679e9	−1.48697	−0.743486	+	0.668751i	$0.766829\pi$
$588$	0	0
$589$	3.84779e9	0.775904
$590$	−3.23344e9	−0.648161
$591$	0	0
$592$	6.42189e8	0.127215
$593$	−2.72582e9	−0.536791	−0.268395	−	0.963309i	$-0.586493\pi$
$593$	−2.72582e9	−0.536791	−0.268395	+	0.963309i	$0.586493\pi$
$594$	0	0
$595$	1.20226e10	2.33986
$596$	1.60873e7	0.00311258
$597$	0	0
$598$	−2.05125e9	−0.392251
$599$	−2.88173e9	−0.547847	−0.273923	−	0.961751i	$-0.588321\pi$
$599$	−2.88173e9	−0.547847	−0.273923	+	0.961751i	$0.588321\pi$
$600$	0	0
$601$	−9.69030e9	−1.82086	−0.910430	−	0.413664i	$-0.864249\pi$
$601$	−9.69030e9	−1.82086	−0.910430	+	0.413664i	$0.864249\pi$
$602$	−7.41156e9	−1.38459
$603$	0	0
$604$	2.07697e7	0.00383532
$605$	6.43160e9	1.18080
$606$	0	0
$607$	3.94372e9	0.715724	0.357862	−	0.933775i	$-0.383506\pi$
$607$	3.94372e9	0.715724	0.357862	+	0.933775i	$0.383506\pi$
$608$	−1.32380e8	−0.0238869
$609$	0	0
$610$	9.66834e9	1.72464
$611$	−4.50423e9	−0.798871
$612$	0	0
$613$	−4.73921e9	−0.830988	−0.415494	−	0.909596i	$-0.636391\pi$
$613$	−4.73921e9	−0.830988	−0.415494	+	0.909596i	$0.636391\pi$
$614$	3.74924e9	0.653663
$615$	0	0
$616$	−2.97740e9	−0.513222
$617$	−6.42115e9	−1.10056	−0.550282	−	0.834979i	$-0.685480\pi$
$617$	−6.42115e9	−1.10056	−0.550282	+	0.834979i	$0.685480\pi$
$618$	0	0
$619$	1.41855e9	0.240396	0.120198	−	0.992750i	$-0.461647\pi$
$619$	1.41855e9	0.240396	0.120198	+	0.992750i	$0.461647\pi$
$620$	−3.83709e7	−0.00646593
$621$	0	0
$622$	−2.79490e9	−0.465694
$623$	−8.94300e8	−0.148175
$624$	0	0
$625$	−6.25773e9	−1.02527
$626$	6.89271e9	1.12300
$627$	0	0
$628$	−8.47885e7	−0.0136609
$629$	−1.01637e9	−0.162845
$630$	0	0
$631$	4.52238e9	0.716579	0.358289	−	0.933611i	$-0.383360\pi$
$631$	4.52238e9	0.716579	0.358289	+	0.933611i	$0.383360\pi$
$632$	−7.72211e9	−1.21682
$633$	0	0
$634$	−5.59268e9	−0.871581
$635$	−1.52034e10	−2.35631
$636$	0	0
$637$	−8.12256e9	−1.24510
$638$	3.32654e9	0.507131
$639$	0	0
$640$	−9.43363e9	−1.42249
$641$	8.31176e9	1.24649	0.623247	−	0.782025i	$-0.285813\pi$
$641$	8.31176e9	1.24649	0.623247	+	0.782025i	$0.285813\pi$
$642$	0	0
$643$	6.83021e9	1.01320	0.506601	−	0.862181i	$-0.330902\pi$
$643$	6.83021e9	1.01320	0.506601	+	0.862181i	$0.330902\pi$
$644$	−1.53476e7	−0.00226433
$645$	0	0
$646$	1.26032e10	1.83936
$647$	4.33983e9	0.629952	0.314976	−	0.949100i	$-0.398004\pi$
$647$	4.33983e9	0.629952	0.314976	+	0.949100i	$0.398004\pi$
$648$	0	0
$649$	−1.27801e9	−0.183517
$650$	−1.28295e10	−1.83237
$651$	0	0
$652$	8.74926e7	0.0123625
$653$	−5.82673e9	−0.818896	−0.409448	−	0.912333i	$-0.634279\pi$
$653$	−5.82673e9	−0.818896	−0.409448	+	0.912333i	$0.634279\pi$
$654$	0	0
$655$	−7.69479e9	−1.06992
$656$	1.31718e10	1.82172
$657$	0	0
$658$	−4.03777e9	−0.552524
$659$	−1.11625e9	−0.151937	−0.0759684	−	0.997110i	$-0.524205\pi$
$659$	−1.11625e9	−0.151937	−0.0759684	+	0.997110i	$0.524205\pi$
$660$	0	0
$661$	1.16388e10	1.56748	0.783739	−	0.621090i	$-0.213310\pi$
$661$	1.16388e10	1.56748	0.783739	+	0.621090i	$0.213310\pi$
$662$	−6.94999e9	−0.931068
$663$	0	0
$664$	1.39731e10	1.85227
$665$	1.95082e10	2.57242
$666$	0	0
$667$	−2.02015e9	−0.263598
$668$	1.06228e7	0.00137886
$669$	0	0
$670$	−1.27696e9	−0.164026
$671$	3.82138e9	0.488305
$672$	0	0
$673$	1.09171e10	1.38056	0.690281	−	0.723542i	$-0.257487\pi$
$673$	1.09171e10	1.38056	0.690281	+	0.723542i	$0.257487\pi$
$674$	4.22416e9	0.531412
$675$	0	0
$676$	1.69629e8	0.0211197
$677$	−4.80668e8	−0.0595367	−0.0297683	−	0.999557i	$-0.509477\pi$
$677$	−4.80668e8	−0.0595367	−0.0297683	+	0.999557i	$0.509477\pi$
$678$	0	0
$679$	−1.73466e10	−2.12652
$680$	1.48067e10	1.80583
$681$	0	0
$682$	−1.81705e9	−0.219342
$683$	2.68059e9	0.321927	0.160963	−	0.986960i	$-0.448540\pi$
$683$	2.68059e9	0.321927	0.160963	+	0.986960i	$0.448540\pi$
$684$	0	0
$685$	1.50472e10	1.78870
$686$	3.67372e9	0.434482
$687$	0	0
$688$	−9.20468e9	−1.07758
$689$	2.09729e10	2.44282
$690$	0	0
$691$	1.44729e9	0.166871	0.0834356	−	0.996513i	$-0.473411\pi$
$691$	1.44729e9	0.166871	0.0834356	+	0.996513i	$0.473411\pi$
$692$	7.83888e7	0.00899255
$693$	0	0
$694$	7.02621e9	0.797927
$695$	−6.74786e9	−0.762464
$696$	0	0
$697$	−2.08466e10	−2.33195
$698$	5.08932e9	0.566455
$699$	0	0
$700$	−9.59916e7	−0.0105777
$701$	−1.36631e10	−1.49809	−0.749043	−	0.662522i	$-0.769486\pi$
$701$	−1.36631e10	−1.49809	−0.749043	+	0.662522i	$0.769486\pi$
$702$	0	0
$703$	−1.64919e9	−0.179030
$704$	−3.66662e9	−0.396060
$705$	0	0
$706$	−1.05104e9	−0.112409
$707$	4.30278e9	0.457911
$708$	0	0
$709$	3.34871e8	0.0352870	0.0176435	−	0.999844i	$-0.494384\pi$
$709$	3.34871e8	0.0352870	0.0176435	+	0.999844i	$0.494384\pi$
$710$	8.35971e9	0.876570
$711$	0	0
$712$	−1.10139e9	−0.114357
$713$	1.10346e9	0.114011
$714$	0	0
$715$	−1.02767e10	−1.05143
$716$	−5.35805e6	−0.000545521 0
$717$	0	0
$718$	1.48393e9	0.149616
$719$	−6.19348e9	−0.621418	−0.310709	−	0.950505i	$-0.600566\pi$
$719$	−6.19348e9	−0.621418	−0.310709	+	0.950505i	$0.600566\pi$
$720$	0	0
$721$	1.18309e9	0.117556
$722$	1.02947e10	1.01797
$723$	0	0
$724$	−7.43278e7	−0.00727891
$725$	−1.26350e10	−1.23138
$726$	0	0
$727$	−3.64052e9	−0.351393	−0.175697	−	0.984444i	$-0.556218\pi$
$727$	−3.64052e9	−0.351393	−0.175697	+	0.984444i	$0.556218\pi$
$728$	−2.50541e10	−2.40668
$729$	0	0
$730$	7.46206e9	0.709952
$731$	1.45680e10	1.37939
$732$	0	0
$733$	2.07157e9	0.194283	0.0971415	−	0.995271i	$-0.469030\pi$
$733$	2.07157e9	0.194283	0.0971415	+	0.995271i	$0.469030\pi$
$734$	1.32197e10	1.23391
$735$	0	0
$736$	−3.79637e7	−0.00350991
$737$	−5.04712e8	−0.0464416
$738$	0	0
$739$	−5.37794e9	−0.490185	−0.245093	−	0.969500i	$-0.578818\pi$
$739$	−5.37794e9	−0.490185	−0.245093	+	0.969500i	$0.578818\pi$
$740$	1.64460e7	0.00149193
$741$	0	0
$742$	1.88009e10	1.68953
$743$	−6.20890e9	−0.555333	−0.277667	−	0.960678i	$-0.589561\pi$
$743$	−6.20890e9	−0.555333	−0.277667	+	0.960678i	$0.589561\pi$
$744$	0	0
$745$	−5.86417e9	−0.519589
$746$	−1.73382e10	−1.52903
$747$	0	0
$748$	−4.96751e7	−0.00433994
$749$	8.56779e9	0.745045
$750$	0	0
$751$	−7.13921e9	−0.615050	−0.307525	−	0.951540i	$-0.599501\pi$
$751$	−7.13921e9	−0.615050	−0.307525	+	0.951540i	$0.599501\pi$
$752$	−5.01465e9	−0.430010
$753$	0	0
$754$	2.79920e10	2.37812
$755$	−7.57103e9	−0.640236
$756$	0	0
$757$	−9.00503e9	−0.754483	−0.377242	−	0.926115i	$-0.623127\pi$
$757$	−9.00503e9	−0.754483	−0.377242	+	0.926115i	$0.623127\pi$
$758$	−1.45130e9	−0.121036
$759$	0	0
$760$	2.40257e10	1.98531
$761$	4.51473e9	0.371352	0.185676	−	0.982611i	$-0.440553\pi$
$761$	4.51473e9	0.371352	0.185676	+	0.982611i	$0.440553\pi$
$762$	0	0
$763$	−9.69012e9	−0.789756
$764$	1.97532e8	0.0160254
$765$	0	0
$766$	1.51257e10	1.21594
$767$	−1.07541e10	−0.860578
$768$	0	0
$769$	1.15299e10	0.914285	0.457142	−	0.889394i	$-0.348873\pi$
$769$	1.15299e10	0.914285	0.457142	+	0.889394i	$0.348873\pi$
$770$	−9.21242e9	−0.727204
$771$	0	0
$772$	−1.00108e8	−0.00783080
$773$	1.73559e10	1.35151	0.675754	−	0.737127i	$-0.263818\pi$
$773$	1.73559e10	1.35151	0.675754	+	0.737127i	$0.263818\pi$
$774$	0	0
$775$	6.90162e9	0.532593
$776$	−2.13635e10	−1.64118
$777$	0	0
$778$	−2.48551e9	−0.189229
$779$	−3.38261e10	−2.56372
$780$	0	0
$781$	3.30414e9	0.248188
$782$	3.61433e9	0.270274
$783$	0	0
$784$	−9.04301e9	−0.670204
$785$	3.09073e10	2.28043
$786$	0	0
$787$	−1.78942e9	−0.130858	−0.0654292	−	0.997857i	$-0.520842\pi$
$787$	−1.78942e9	−0.130858	−0.0654292	+	0.997857i	$0.520842\pi$
$788$	9.39216e7	0.00683792
$789$	0	0
$790$	−2.38931e10	−1.72416
$791$	−9.05919e9	−0.650836
$792$	0	0
$793$	3.21559e10	2.28984
$794$	1.96307e10	1.39176
$795$	0	0
$796$	−1.37413e8	−0.00965678
$797$	1.34591e9	0.0941700	0.0470850	−	0.998891i	$-0.485007\pi$
$797$	1.34591e9	0.0941700	0.0470850	+	0.998891i	$0.485007\pi$
$798$	0	0
$799$	7.93653e9	0.550449
$800$	−2.37444e8	−0.0163963
$801$	0	0
$802$	−7.90792e8	−0.0541317
$803$	2.94935e9	0.201012
$804$	0	0
$805$	5.59454e9	0.377989
$806$	−1.52901e10	−1.02858
$807$	0	0
$808$	5.29917e9	0.353401
$809$	−8.51154e9	−0.565182	−0.282591	−	0.959240i	$-0.591194\pi$
$809$	−8.51154e9	−0.565182	−0.282591	+	0.959240i	$0.591194\pi$
$810$	0	0
$811$	9.09661e9	0.598834	0.299417	−	0.954122i	$-0.403208\pi$
$811$	9.09661e9	0.598834	0.299417	+	0.954122i	$0.403208\pi$
$812$	2.09439e8	0.0137281
$813$	0	0
$814$	7.78801e8	0.0506105
$815$	−3.18930e10	−2.06368
$816$	0	0
$817$	2.36383e10	1.51649
$818$	9.18423e9	0.586687
$819$	0	0
$820$	3.37320e8	0.0213645
$821$	2.41553e10	1.52339	0.761695	−	0.647935i	$-0.224367\pi$
$821$	2.41553e10	1.52339	0.761695	+	0.647935i	$0.224367\pi$
$822$	0	0
$823$	−2.48269e10	−1.55247	−0.776233	−	0.630446i	$-0.782872\pi$
$823$	−2.48269e10	−1.55247	−0.776233	+	0.630446i	$0.782872\pi$
$824$	1.45706e9	0.0907262
$825$	0	0
$826$	−9.64040e9	−0.595203
$827$	1.17861e9	0.0724602	0.0362301	−	0.999343i	$-0.488465\pi$
$827$	1.17861e9	0.0724602	0.0362301	+	0.999343i	$0.488465\pi$
$828$	0	0
$829$	−2.31094e10	−1.40879	−0.704396	−	0.709807i	$-0.748782\pi$
$829$	−2.31094e10	−1.40879	−0.704396	+	0.709807i	$0.748782\pi$
$830$	4.32343e10	2.62455
$831$	0	0
$832$	−3.08537e10	−1.85727
$833$	1.43121e10	0.857917
$834$	0	0
$835$	−3.87223e9	−0.230175
$836$	−8.06039e7	−0.00477127
$837$	0	0
$838$	9.98297e9	0.586011
$839$	6.66669e9	0.389712	0.194856	−	0.980832i	$-0.437576\pi$
$839$	6.66669e9	0.389712	0.194856	+	0.980832i	$0.437576\pi$
$840$	0	0
$841$	1.03178e10	0.598135
$842$	−3.12146e10	−1.80205
$843$	0	0
$844$	1.42102e8	0.00813583
$845$	−6.18335e10	−3.52554
$846$	0	0
$847$	1.91756e10	1.08432
$848$	2.33496e10	1.31490
$849$	0	0
$850$	2.26058e10	1.26257
$851$	−4.72952e8	−0.0263065
$852$	0	0
$853$	−2.12290e10	−1.17114	−0.585570	−	0.810622i	$-0.699129\pi$
$853$	−2.12290e10	−1.17114	−0.585570	+	0.810622i	$0.699129\pi$
$854$	2.88258e10	1.58372
$855$	0	0
$856$	1.05518e10	0.575002
$857$	3.89583e9	0.211430	0.105715	−	0.994396i	$-0.466287\pi$
$857$	3.89583e9	0.211430	0.105715	+	0.994396i	$0.466287\pi$
$858$	0	0
$859$	3.53189e9	0.190122	0.0950608	−	0.995471i	$-0.469695\pi$
$859$	3.53189e9	0.190122	0.0950608	+	0.995471i	$0.469695\pi$
$860$	−2.35725e8	−0.0126375
$861$	0	0
$862$	−1.56868e10	−0.834181
$863$	−1.47909e10	−0.783349	−0.391675	−	0.920104i	$-0.628104\pi$
$863$	−1.47909e10	−0.783349	−0.391675	+	0.920104i	$0.628104\pi$
$864$	0	0
$865$	−2.85744e10	−1.50114
$866$	1.46856e10	0.768387
$867$	0	0
$868$	−1.14402e8	−0.00593763
$869$	−9.44365e9	−0.488170
$870$	0	0
$871$	−4.24702e9	−0.217782
$872$	−1.19340e10	−0.609509
$873$	0	0
$874$	5.86469e9	0.297136
$875$	−9.31808e8	−0.0470217
$876$	0	0
$877$	2.99364e10	1.49865	0.749326	−	0.662201i	$-0.230378\pi$
$877$	2.99364e10	1.49865	0.749326	+	0.662201i	$0.230378\pi$
$878$	2.41966e10	1.20649
$879$	0	0
$880$	−1.14412e10	−0.565957
$881$	8.65058e9	0.426216	0.213108	−	0.977029i	$-0.431641\pi$
$881$	8.65058e9	0.426216	0.213108	+	0.977029i	$0.431641\pi$
$882$	0	0
$883$	6.35296e9	0.310537	0.155269	−	0.987872i	$-0.450376\pi$
$883$	6.35296e9	0.310537	0.155269	+	0.987872i	$0.450376\pi$
$884$	−4.18004e8	−0.0203515
$885$	0	0
$886$	2.94043e10	1.42034
$887$	2.63325e10	1.26695	0.633475	−	0.773763i	$-0.281628\pi$
$887$	2.63325e10	1.26695	0.633475	+	0.773763i	$0.281628\pi$
$888$	0	0
$889$	−4.53284e10	−2.16379
$890$	−3.40783e9	−0.162037
$891$	0	0
$892$	−3.08126e7	−0.00145362
$893$	1.28780e10	0.605157
$894$	0	0
$895$	1.95313e9	0.0910647
$896$	−2.81261e10	−1.30626
$897$	0	0
$898$	7.78895e9	0.358932
$899$	−1.50583e10	−0.691219
$900$	0	0
$901$	−3.69546e10	−1.68318
$902$	1.59738e10	0.724745
$903$	0	0
$904$	−1.11570e10	−0.502294
$905$	2.70941e10	1.21508
$906$	0	0
$907$	1.26762e9	0.0564110	0.0282055	−	0.999602i	$-0.491021\pi$
$907$	1.26762e9	0.0564110	0.0282055	+	0.999602i	$0.491021\pi$
$908$	−1.81499e8	−0.00804587
$909$	0	0
$910$	−7.75202e10	−3.41012
$911$	2.38159e10	1.04364	0.521821	−	0.853055i	$-0.325253\pi$
$911$	2.38159e10	1.04364	0.521821	+	0.853055i	$0.325253\pi$
$912$	0	0
$913$	1.70882e10	0.743103
$914$	1.27713e10	0.553253
$915$	0	0
$916$	−2.09102e8	−0.00898928
$917$	−2.29418e10	−0.982504
$918$	0	0
$919$	1.46627e10	0.623176	0.311588	−	0.950217i	$-0.399139\pi$
$919$	1.46627e10	0.623176	0.311588	+	0.950217i	$0.399139\pi$
$920$	6.89006e9	0.291720
$921$	0	0
$922$	−6.61214e9	−0.277833
$923$	2.78035e10	1.16384
$924$	0	0
$925$	−2.95808e9	−0.122889
$926$	−3.85062e10	−1.59365
$927$	0	0
$928$	5.18066e8	0.0212798
$929$	−3.68901e10	−1.50958	−0.754788	−	0.655968i	$-0.772260\pi$
$929$	−3.68901e10	−1.50958	−0.754788	+	0.655968i	$0.772260\pi$
$930$	0	0
$931$	2.32231e10	0.943183
$932$	−1.16831e8	−0.00472717
$933$	0	0
$934$	3.33629e10	1.33983
$935$	1.81077e10	0.724473
$936$	0	0
$937$	2.46605e10	0.979294	0.489647	−	0.871921i	$-0.337126\pi$
$937$	2.46605e10	0.979294	0.489647	+	0.871921i	$0.337126\pi$
$938$	−3.80720e9	−0.150625
$939$	0	0
$940$	−1.28422e8	−0.00504302
$941$	−2.85433e10	−1.11671	−0.558355	−	0.829602i	$-0.688567\pi$
$941$	−2.85433e10	−1.11671	−0.558355	+	0.829602i	$0.688567\pi$
$942$	0	0
$943$	−9.70060e9	−0.376711
$944$	−1.19728e10	−0.463225
$945$	0	0
$946$	−1.11628e10	−0.428700
$947$	−4.45286e10	−1.70378	−0.851891	−	0.523719i	$-0.824544\pi$
$947$	−4.45286e10	−1.70378	−0.851891	+	0.523719i	$0.824544\pi$
$948$	0	0
$949$	2.48181e10	0.942619
$950$	3.66807e10	1.38805
$951$	0	0
$952$	4.41457e10	1.65829
$953$	−1.29354e10	−0.484122	−0.242061	−	0.970261i	$-0.577823\pi$
$953$	−1.29354e10	−0.484122	−0.242061	+	0.970261i	$0.577823\pi$
$954$	0	0
$955$	−7.20047e10	−2.67515
$956$	−4.41193e8	−0.0163315
$957$	0	0
$958$	1.32063e10	0.485291
$959$	4.48627e10	1.64256
$960$	0	0
$961$	−1.92873e10	−0.701037
$962$	6.55342e9	0.237331
$963$	0	0
$964$	−1.84619e8	−0.00663752
$965$	3.64914e10	1.30721
$966$	0	0
$967$	−1.49195e10	−0.530595	−0.265297	−	0.964167i	$-0.585470\pi$
$967$	−1.49195e10	−0.530595	−0.265297	+	0.964167i	$0.585470\pi$
$968$	2.36161e10	0.836843
$969$	0	0
$970$	−6.61012e10	−2.32546
$971$	−1.64648e10	−0.577150	−0.288575	−	0.957457i	$-0.593181\pi$
$971$	−1.64648e10	−0.577150	−0.288575	+	0.957457i	$0.593181\pi$
$972$	0	0
$973$	−2.01185e10	−0.700167
$974$	4.97748e10	1.72605
$975$	0	0
$976$	3.57998e10	1.23256
$977$	−1.10912e10	−0.380494	−0.190247	−	0.981736i	$-0.560929\pi$
$977$	−1.10912e10	−0.380494	−0.190247	+	0.981736i	$0.560929\pi$
$978$	0	0
$979$	−1.34693e9	−0.0458782
$980$	−2.31585e8	−0.00785994
$981$	0	0
$982$	4.34022e9	0.146259
$983$	1.69926e10	0.570588	0.285294	−	0.958440i	$-0.407909\pi$
$983$	1.69926e10	0.570588	0.285294	+	0.958440i	$0.407909\pi$
$984$	0	0
$985$	−3.42365e10	−1.14146
$986$	−4.93224e10	−1.63861
$987$	0	0
$988$	−6.78262e8	−0.0223742
$989$	6.77895e9	0.222831
$990$	0	0
$991$	−2.43624e10	−0.795176	−0.397588	−	0.917564i	$-0.630153\pi$
$991$	−2.43624e10	−0.795176	−0.397588	+	0.917564i	$0.630153\pi$
$992$	−2.82983e8	−0.00920384
$993$	0	0
$994$	2.49242e10	0.804950
$995$	5.00901e10	1.61202
$996$	0	0
$997$	2.37159e10	0.757890	0.378945	−	0.925419i	$-0.376287\pi$
$997$	2.37159e10	0.757890	0.378945	+	0.925419i	$0.376287\pi$
$998$	−2.18177e10	−0.694786
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.8.a.d.1.5		7
3.2	odd	2		69.8.a.c.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.a.c.1.3	✓	7	3.2	odd	2
207.8.a.d.1.5		7	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)

\(f(q)\)	\(=\)	\(q+11.3612 q^{2} +1.07734 q^{4} -392.713 q^{5} -1170.86 q^{7} -1442.00 q^{8} +O(q^{10})\)	\(q+11.3612 q^{2} +1.07734 q^{4} -392.713 q^{5} -1170.86 q^{7} -1442.00 q^{8} -4461.70 q^{10} -1763.47 q^{11} -14839.2 q^{13} -13302.4 q^{14} -16520.7 q^{16} +26146.8 q^{17} +42426.4 q^{19} -423.084 q^{20} -20035.2 q^{22} +12167.0 q^{23} +76098.5 q^{25} -168591. q^{26} -1261.41 q^{28} -166035. q^{29} +90693.2 q^{31} -3120.22 q^{32} +297060. q^{34} +459812. q^{35} -38871.7 q^{37} +482016. q^{38} +566291. q^{40} -797288. q^{41} +557159. q^{43} -1899.85 q^{44} +138232. q^{46} +303537. q^{47} +547373. q^{49} +864572. q^{50} -15986.8 q^{52} -1.41335e6 q^{53} +692538. q^{55} +1.68838e6 q^{56} -1.88636e6 q^{58} +724711. q^{59} -2.16696e6 q^{61} +1.03039e6 q^{62} +2.07921e6 q^{64} +5.82753e6 q^{65} +286204. q^{67} +28169.0 q^{68} +5.22403e6 q^{70} -1.87366e6 q^{71} -1.67247e6 q^{73} -441630. q^{74} +45707.6 q^{76} +2.06478e6 q^{77} +5.35515e6 q^{79} +6.48791e6 q^{80} -9.05817e6 q^{82} -9.69011e6 q^{83} -1.02682e7 q^{85} +6.33001e6 q^{86} +2.54292e6 q^{88} +763797. q^{89} +1.73746e7 q^{91} +13108.0 q^{92} +3.44855e6 q^{94} -1.66614e7 q^{95} +1.48153e7 q^{97} +6.21883e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8}+O(q^{10}) \) 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8	\( 7 q + 654 q^{4} + 516 q^{5} + 1018 q^{7} - 1422 q^{8} - 15310 q^{10} - 9040 q^{11} + 3774 q^{13} - 4536 q^{14} + 52002 q^{16} + 40760 q^{17} + 81598 q^{19} + 88946 q^{20} + 245034 q^{22} + 85169 q^{23} + 321325 q^{25} - 412748 q^{26} + 965948 q^{28} - 154126 q^{29} + 243132 q^{31} - 1278286 q^{32} + 984836 q^{34} + 130296 q^{35} + 582114 q^{37} - 772558 q^{38} - 132618 q^{40} - 113062 q^{41} - 659778 q^{43} - 659390 q^{44} + 591032 q^{47} + 3263235 q^{49} + 702684 q^{50} + 1793280 q^{52} - 207128 q^{53} + 184664 q^{55} - 5390508 q^{56} - 1142916 q^{58} - 447148 q^{59} + 2248970 q^{61} + 5729060 q^{62} + 7212922 q^{64} + 827096 q^{65} + 4467570 q^{67} + 5477620 q^{68} - 12744284 q^{70} + 5154608 q^{71} - 13239250 q^{73} + 2827426 q^{74} - 527434 q^{76} + 18415912 q^{77} + 9594446 q^{79} + 55932394 q^{80} - 20889952 q^{82} + 573720 q^{83} + 7477272 q^{85} + 28416910 q^{86} + 26555702 q^{88} + 3810540 q^{89} + 36092068 q^{91} + 7957218 q^{92} + 33545768 q^{94} - 10497320 q^{95} + 49497978 q^{97} + 1023376 q^{98}+O(q^{100}) \) 7 * q + 654 * q^4 + 516 * q^5 + 1018 * q^7 - 1422 * q^8 - 15310 * q^10 - 9040 * q^11 + 3774 * q^13 - 4536 * q^14 + 52002 * q^16 + 40760 * q^17 + 81598 * q^19 + 88946 * q^20 + 245034 * q^22 + 85169 * q^23 + 321325 * q^25 - 412748 * q^26 + 965948 * q^28 - 154126 * q^29 + 243132 * q^31 - 1278286 * q^32 + 984836 * q^34 + 130296 * q^35 + 582114 * q^37 - 772558 * q^38 - 132618 * q^40 - 113062 * q^41 - 659778 * q^43 - 659390 * q^44 + 591032 * q^47 + 3263235 * q^49 + 702684 * q^50 + 1793280 * q^52 - 207128 * q^53 + 184664 * q^55 - 5390508 * q^56 - 1142916 * q^58 - 447148 * q^59 + 2248970 * q^61 + 5729060 * q^62 + 7212922 * q^64 + 827096 * q^65 + 4467570 * q^67 + 5477620 * q^68 - 12744284 * q^70 + 5154608 * q^71 - 13239250 * q^73 + 2827426 * q^74 - 527434 * q^76 + 18415912 * q^77 + 9594446 * q^79 + 55932394 * q^80 - 20889952 * q^82 + 573720 * q^83 + 7477272 * q^85 + 28416910 * q^86 + 26555702 * q^88 + 3810540 * q^89 + 36092068 * q^91 + 7957218 * q^92 + 33545768 * q^94 - 10497320 * q^95 + 49497978 * q^97 + 1023376 * q^98

Introduction

L-functions

Modular forms

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Groups

Database

Properties

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