LMFDB - Embedded newform 7098.2.a.cl.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.24698 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.24698 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.24698 q^{10} -0.198062 q^{11} +1.00000 q^{12} +1.00000 q^{14} -4.24698 q^{15} +1.00000 q^{16} -0.664874 q^{17} +1.00000 q^{18} -2.91185 q^{19} -4.24698 q^{20} +1.00000 q^{21} -0.198062 q^{22} +1.96077 q^{23} +1.00000 q^{24} +13.0368 q^{25} +1.00000 q^{27} +1.00000 q^{28} +4.65279 q^{29} -4.24698 q^{30} -6.67994 q^{31} +1.00000 q^{32} -0.198062 q^{33} -0.664874 q^{34} -4.24698 q^{35} +1.00000 q^{36} +4.96077 q^{37} -2.91185 q^{38} -4.24698 q^{40} -10.0707 q^{41} +1.00000 q^{42} -2.85086 q^{43} -0.198062 q^{44} -4.24698 q^{45} +1.96077 q^{46} -10.6039 q^{47} +1.00000 q^{48} +1.00000 q^{49} +13.0368 q^{50} -0.664874 q^{51} -14.5036 q^{53} +1.00000 q^{54} +0.841166 q^{55} +1.00000 q^{56} -2.91185 q^{57} +4.65279 q^{58} +5.05861 q^{59} -4.24698 q^{60} -0.878002 q^{61} -6.67994 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.198062 q^{66} +6.03684 q^{67} -0.664874 q^{68} +1.96077 q^{69} -4.24698 q^{70} +10.9879 q^{71} +1.00000 q^{72} -4.84117 q^{73} +4.96077 q^{74} +13.0368 q^{75} -2.91185 q^{76} -0.198062 q^{77} +0.423272 q^{79} -4.24698 q^{80} +1.00000 q^{81} -10.0707 q^{82} -11.0881 q^{83} +1.00000 q^{84} +2.82371 q^{85} -2.85086 q^{86} +4.65279 q^{87} -0.198062 q^{88} +15.6407 q^{89} -4.24698 q^{90} +1.96077 q^{92} -6.67994 q^{93} -10.6039 q^{94} +12.3666 q^{95} +1.00000 q^{96} -1.47889 q^{97} +1.00000 q^{98} -0.198062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 8 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 8 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 8 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 8 q^{10} - 5 q^{11} + 3 q^{12} + 3 q^{14} - 8 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} - 5 q^{19} - 8 q^{20} + 3 q^{21} - 5 q^{22} - 7 q^{23} + 3 q^{24} + 11 q^{25} + 3 q^{27} + 3 q^{28} - 4 q^{29} - 8 q^{30} + 4 q^{31} + 3 q^{32} - 5 q^{33} - 3 q^{34} - 8 q^{35} + 3 q^{36} + 2 q^{37} - 5 q^{38} - 8 q^{40} - 18 q^{41} + 3 q^{42} + 5 q^{43} - 5 q^{44} - 8 q^{45} - 7 q^{46} - 23 q^{47} + 3 q^{48} + 3 q^{49} + 11 q^{50} - 3 q^{51} - 12 q^{53} + 3 q^{54} + 11 q^{55} + 3 q^{56} - 5 q^{57} - 4 q^{58} - 16 q^{59} - 8 q^{60} + 17 q^{61} + 4 q^{62} + 3 q^{63} + 3 q^{64} - 5 q^{66} - 10 q^{67} - 3 q^{68} - 7 q^{69} - 8 q^{70} + 14 q^{71} + 3 q^{72} - 23 q^{73} + 2 q^{74} + 11 q^{75} - 5 q^{76} - 5 q^{77} + 4 q^{79} - 8 q^{80} + 3 q^{81} - 18 q^{82} - 37 q^{83} + 3 q^{84} + q^{85} + 5 q^{86} - 4 q^{87} - 5 q^{88} + 10 q^{89} - 8 q^{90} - 7 q^{92} + 4 q^{93} - 23 q^{94} + 11 q^{95} + 3 q^{96} - 20 q^{97} + 3 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 8 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 8 * q^10 - 5 * q^11 + 3 * q^12 + 3 * q^14 - 8 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 - 5 * q^19 - 8 * q^20 + 3 * q^21 - 5 * q^22 - 7 * q^23 + 3 * q^24 + 11 * q^25 + 3 * q^27 + 3 * q^28 - 4 * q^29 - 8 * q^30 + 4 * q^31 + 3 * q^32 - 5 * q^33 - 3 * q^34 - 8 * q^35 + 3 * q^36 + 2 * q^37 - 5 * q^38 - 8 * q^40 - 18 * q^41 + 3 * q^42 + 5 * q^43 - 5 * q^44 - 8 * q^45 - 7 * q^46 - 23 * q^47 + 3 * q^48 + 3 * q^49 + 11 * q^50 - 3 * q^51 - 12 * q^53 + 3 * q^54 + 11 * q^55 + 3 * q^56 - 5 * q^57 - 4 * q^58 - 16 * q^59 - 8 * q^60 + 17 * q^61 + 4 * q^62 + 3 * q^63 + 3 * q^64 - 5 * q^66 - 10 * q^67 - 3 * q^68 - 7 * q^69 - 8 * q^70 + 14 * q^71 + 3 * q^72 - 23 * q^73 + 2 * q^74 + 11 * q^75 - 5 * q^76 - 5 * q^77 + 4 * q^79 - 8 * q^80 + 3 * q^81 - 18 * q^82 - 37 * q^83 + 3 * q^84 + q^85 + 5 * q^86 - 4 * q^87 - 5 * q^88 + 10 * q^89 - 8 * q^90 - 7 * q^92 + 4 * q^93 - 23 * q^94 + 11 * q^95 + 3 * q^96 - 20 * q^97 + 3 * q^98 - 5 * q^99

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−4.24698	−1.89931	−0.949654	−	0.313302i	$-0.898565\pi$
$5$	−4.24698	−1.89931	−0.949654	+	0.313302i	$0.898565\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.24698	−1.34301
$11$	−0.198062	−0.0597180	−0.0298590	−	0.999554i	$-0.509506\pi$
$11$	−0.198062	−0.0597180	−0.0298590	+	0.999554i	$0.509506\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−4.24698	−1.09657
$16$	1.00000	0.250000
$17$	−0.664874	−0.161256	−0.0806279	−	0.996744i	$-0.525693\pi$
$17$	−0.664874	−0.161256	−0.0806279	+	0.996744i	$0.525693\pi$
$18$	1.00000	0.235702
$19$	−2.91185	−0.668025	−0.334013	−	0.942569i	$-0.608403\pi$
$19$	−2.91185	−0.668025	−0.334013	+	0.942569i	$0.608403\pi$
$20$	−4.24698	−0.949654
$21$	1.00000	0.218218
$22$	−0.198062	−0.0422270
$23$	1.96077	0.408849	0.204425	−	0.978882i	$-0.434468\pi$
$23$	1.96077	0.408849	0.204425	+	0.978882i	$0.434468\pi$
$24$	1.00000	0.204124
$25$	13.0368	2.60737
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	4.65279	0.864002	0.432001	−	0.901873i	$-0.357808\pi$
$29$	4.65279	0.864002	0.432001	+	0.901873i	$0.357808\pi$
$30$	−4.24698	−0.775389
$31$	−6.67994	−1.19975	−0.599876	−	0.800093i	$-0.704784\pi$
$31$	−6.67994	−1.19975	−0.599876	+	0.800093i	$0.704784\pi$
$32$	1.00000	0.176777
$33$	−0.198062	−0.0344782
$34$	−0.664874	−0.114025
$35$	−4.24698	−0.717871
$36$	1.00000	0.166667
$37$	4.96077	0.815546	0.407773	−	0.913083i	$-0.366306\pi$
$37$	4.96077	0.815546	0.407773	+	0.913083i	$0.366306\pi$
$38$	−2.91185	−0.472365
$39$	0	0
$40$	−4.24698	−0.671506
$41$	−10.0707	−1.57278	−0.786389	−	0.617732i	$-0.788052\pi$
$41$	−10.0707	−1.57278	−0.786389	+	0.617732i	$0.788052\pi$
$42$	1.00000	0.154303
$43$	−2.85086	−0.434751	−0.217376	−	0.976088i	$-0.569750\pi$
$43$	−2.85086	−0.434751	−0.217376	+	0.976088i	$0.569750\pi$
$44$	−0.198062	−0.0298590
$45$	−4.24698	−0.633102
$46$	1.96077	0.289100
$47$	−10.6039	−1.54673	−0.773367	−	0.633958i	$-0.781429\pi$
$47$	−10.6039	−1.54673	−0.773367	+	0.633958i	$0.781429\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	13.0368	1.84369
$51$	−0.664874	−0.0931010
$52$	0	0
$53$	−14.5036	−1.99223	−0.996115	−	0.0880662i	$-0.971931\pi$
$53$	−14.5036	−1.99223	−0.996115	+	0.0880662i	$0.971931\pi$
$54$	1.00000	0.136083
$55$	0.841166	0.113423
$56$	1.00000	0.133631
$57$	−2.91185	−0.385684
$58$	4.65279	0.610942
$59$	5.05861	0.658574	0.329287	−	0.944230i	$-0.393192\pi$
$59$	5.05861	0.658574	0.329287	+	0.944230i	$0.393192\pi$
$60$	−4.24698	−0.548283
$61$	−0.878002	−0.112417	−0.0562083	−	0.998419i	$-0.517901\pi$
$61$	−0.878002	−0.112417	−0.0562083	+	0.998419i	$0.517901\pi$
$62$	−6.67994	−0.848353
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.198062	−0.0243798
$67$	6.03684	0.737517	0.368758	−	0.929525i	$-0.379783\pi$
$67$	6.03684	0.737517	0.368758	+	0.929525i	$0.379783\pi$
$68$	−0.664874	−0.0806279
$69$	1.96077	0.236049
$70$	−4.24698	−0.507611
$71$	10.9879	1.30403	0.652013	−	0.758208i	$-0.273925\pi$
$71$	10.9879	1.30403	0.652013	+	0.758208i	$0.273925\pi$
$72$	1.00000	0.117851
$73$	−4.84117	−0.566616	−0.283308	−	0.959029i	$-0.591432\pi$
$73$	−4.84117	−0.566616	−0.283308	+	0.959029i	$0.591432\pi$
$74$	4.96077	0.576678
$75$	13.0368	1.50536
$76$	−2.91185	−0.334013
$77$	−0.198062	−0.0225713
$78$	0	0
$79$	0.423272	0.0476218	0.0238109	−	0.999716i	$-0.492420\pi$
$79$	0.423272	0.0476218	0.0238109	+	0.999716i	$0.492420\pi$
$80$	−4.24698	−0.474827
$81$	1.00000	0.111111
$82$	−10.0707	−1.11212
$83$	−11.0881	−1.21708	−0.608541	−	0.793522i	$-0.708245\pi$
$83$	−11.0881	−1.21708	−0.608541	+	0.793522i	$0.708245\pi$
$84$	1.00000	0.109109
$85$	2.82371	0.306274
$86$	−2.85086	−0.307416
$87$	4.65279	0.498832
$88$	−0.198062	−0.0211135
$89$	15.6407	1.65791	0.828956	−	0.559314i	$-0.188935\pi$
$89$	15.6407	1.65791	0.828956	+	0.559314i	$0.188935\pi$
$90$	−4.24698	−0.447671
$91$	0	0
$92$	1.96077	0.204425
$93$	−6.67994	−0.692677
$94$	−10.6039	−1.09371
$95$	12.3666	1.26878
$96$	1.00000	0.102062
$97$	−1.47889	−0.150159	−0.0750795	−	0.997178i	$-0.523921\pi$
$97$	−1.47889	−0.150159	−0.0750795	+	0.997178i	$0.523921\pi$
$98$	1.00000	0.101015
$99$	−0.198062	−0.0199060
$100$	13.0368	1.30368
$101$	−18.6407	−1.85482	−0.927410	−	0.374046i	$-0.877970\pi$
$101$	−18.6407	−1.85482	−0.927410	+	0.374046i	$0.877970\pi$
$102$	−0.664874	−0.0658324
$103$	12.5700	1.23856	0.619281	−	0.785170i	$-0.287424\pi$
$103$	12.5700	1.23856	0.619281	+	0.785170i	$0.287424\pi$
$104$	0	0
$105$	−4.24698	−0.414463
$106$	−14.5036	−1.40872
$107$	5.98792	0.578874	0.289437	−	0.957197i	$-0.406532\pi$
$107$	5.98792	0.578874	0.289437	+	0.957197i	$0.406532\pi$
$108$	1.00000	0.0962250
$109$	0.850855	0.0814971	0.0407486	−	0.999169i	$-0.487026\pi$
$109$	0.850855	0.0814971	0.0407486	+	0.999169i	$0.487026\pi$
$110$	0.841166	0.0802021
$111$	4.96077	0.470856
$112$	1.00000	0.0944911
$113$	−15.0030	−1.41136	−0.705681	−	0.708530i	$-0.749359\pi$
$113$	−15.0030	−1.41136	−0.705681	+	0.708530i	$0.749359\pi$
$114$	−2.91185	−0.272720
$115$	−8.32736	−0.776530
$116$	4.65279	0.432001
$117$	0	0
$118$	5.05861	0.465682
$119$	−0.664874	−0.0609489
$120$	−4.24698	−0.387694
$121$	−10.9608	−0.996434
$122$	−0.878002	−0.0794906
$123$	−10.0707	−0.908043
$124$	−6.67994	−0.599876
$125$	−34.1323	−3.05288
$126$	1.00000	0.0890871
$127$	−5.11529	−0.453909	−0.226954	−	0.973905i	$-0.572877\pi$
$127$	−5.11529	−0.453909	−0.226954	+	0.973905i	$0.572877\pi$
$128$	1.00000	0.0883883
$129$	−2.85086	−0.251004
$130$	0	0
$131$	−5.97046	−0.521642	−0.260821	−	0.965387i	$-0.583993\pi$
$131$	−5.97046	−0.521642	−0.260821	+	0.965387i	$0.583993\pi$
$132$	−0.198062	−0.0172391
$133$	−2.91185	−0.252490
$134$	6.03684	0.521503
$135$	−4.24698	−0.365522
$136$	−0.664874	−0.0570125
$137$	−13.0271	−1.11298	−0.556492	−	0.830853i	$-0.687853\pi$
$137$	−13.0271	−1.11298	−0.556492	+	0.830853i	$0.687853\pi$
$138$	1.96077	0.166912
$139$	4.36227	0.370003	0.185002	−	0.982738i	$-0.440771\pi$
$139$	4.36227	0.370003	0.185002	+	0.982738i	$0.440771\pi$
$140$	−4.24698	−0.358935
$141$	−10.6039	−0.893007
$142$	10.9879	0.922086
$143$	0	0
$144$	1.00000	0.0833333
$145$	−19.7603	−1.64100
$146$	−4.84117	−0.400658
$147$	1.00000	0.0824786
$148$	4.96077	0.407773
$149$	−3.80194	−0.311467	−0.155733	−	0.987799i	$-0.549774\pi$
$149$	−3.80194	−0.311467	−0.155733	+	0.987799i	$0.549774\pi$
$150$	13.0368	1.06445
$151$	−14.7342	−1.19905	−0.599527	−	0.800354i	$-0.704645\pi$
$151$	−14.7342	−1.19905	−0.599527	+	0.800354i	$0.704645\pi$
$152$	−2.91185	−0.236183
$153$	−0.664874	−0.0537519
$154$	−0.198062	−0.0159603
$155$	28.3696	2.27870
$156$	0	0
$157$	1.15346	0.0920559	0.0460279	−	0.998940i	$-0.485344\pi$
$157$	1.15346	0.0920559	0.0460279	+	0.998940i	$0.485344\pi$
$158$	0.423272	0.0336737
$159$	−14.5036	−1.15021
$160$	−4.24698	−0.335753
$161$	1.96077	0.154530
$162$	1.00000	0.0785674
$163$	−12.0532	−0.944082	−0.472041	−	0.881577i	$-0.656483\pi$
$163$	−12.0532	−0.944082	−0.472041	+	0.881577i	$0.656483\pi$
$164$	−10.0707	−0.786389
$165$	0.841166	0.0654847
$166$	−11.0881	−0.860607
$167$	−17.8291	−1.37966	−0.689828	−	0.723973i	$-0.742314\pi$
$167$	−17.8291	−1.37966	−0.689828	+	0.723973i	$0.742314\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	2.82371	0.216569
$171$	−2.91185	−0.222675
$172$	−2.85086	−0.217376
$173$	16.7332	1.27220	0.636100	−	0.771607i	$-0.280547\pi$
$173$	16.7332	1.27220	0.636100	+	0.771607i	$0.280547\pi$
$174$	4.65279	0.352727
$175$	13.0368	0.985492
$176$	−0.198062	−0.0149295
$177$	5.05861	0.380228
$178$	15.6407	1.17232
$179$	3.67025	0.274327	0.137164	−	0.990548i	$-0.456201\pi$
$179$	3.67025	0.274327	0.137164	+	0.990548i	$0.456201\pi$
$180$	−4.24698	−0.316551
$181$	−14.6189	−1.08662	−0.543309	−	0.839533i	$-0.682829\pi$
$181$	−14.6189	−1.08662	−0.543309	+	0.839533i	$0.682829\pi$
$182$	0	0
$183$	−0.878002	−0.0649038
$184$	1.96077	0.144550
$185$	−21.0683	−1.54897
$186$	−6.67994	−0.489797
$187$	0.131687	0.00962987
$188$	−10.6039	−0.773367
$189$	1.00000	0.0727393
$190$	12.3666	0.897166
$191$	−24.7928	−1.79395	−0.896973	−	0.442084i	$-0.854239\pi$
$191$	−24.7928	−1.79395	−0.896973	+	0.442084i	$0.854239\pi$
$192$	1.00000	0.0721688
$193$	−18.9487	−1.36396	−0.681978	−	0.731372i	$-0.738880\pi$
$193$	−18.9487	−1.36396	−0.681978	+	0.731372i	$0.738880\pi$
$194$	−1.47889	−0.106178
$195$	0	0
$196$	1.00000	0.0714286
$197$	−4.58642	−0.326769	−0.163384	−	0.986562i	$-0.552241\pi$
$197$	−4.58642	−0.326769	−0.163384	+	0.986562i	$0.552241\pi$
$198$	−0.198062	−0.0140757
$199$	−17.8998	−1.26888	−0.634441	−	0.772972i	$-0.718769\pi$
$199$	−17.8998	−1.26888	−0.634441	+	0.772972i	$0.718769\pi$
$200$	13.0368	0.921843
$201$	6.03684	0.425806
$202$	−18.6407	−1.31156
$203$	4.65279	0.326562
$204$	−0.664874	−0.0465505
$205$	42.7700	2.98719
$206$	12.5700	0.875795
$207$	1.96077	0.136283
$208$	0	0
$209$	0.576728	0.0398931
$210$	−4.24698	−0.293069
$211$	1.95108	0.134318	0.0671590	−	0.997742i	$-0.478607\pi$
$211$	1.95108	0.134318	0.0671590	+	0.997742i	$0.478607\pi$
$212$	−14.5036	−0.996115
$213$	10.9879	0.752880
$214$	5.98792	0.409326
$215$	12.1075	0.825726
$216$	1.00000	0.0680414
$217$	−6.67994	−0.453464
$218$	0.850855	0.0576272
$219$	−4.84117	−0.327136
$220$	0.841166	0.0567114
$221$	0	0
$222$	4.96077	0.332945
$223$	−18.9051	−1.26598	−0.632991	−	0.774159i	$-0.718173\pi$
$223$	−18.9051	−1.26598	−0.632991	+	0.774159i	$0.718173\pi$
$224$	1.00000	0.0668153
$225$	13.0368	0.869122
$226$	−15.0030	−0.997984
$227$	−21.1468	−1.40356	−0.701780	−	0.712394i	$-0.747611\pi$
$227$	−21.1468	−1.40356	−0.701780	+	0.712394i	$0.747611\pi$
$228$	−2.91185	−0.192842
$229$	22.3884	1.47946	0.739732	−	0.672902i	$-0.234952\pi$
$229$	22.3884	1.47946	0.739732	+	0.672902i	$0.234952\pi$
$230$	−8.32736	−0.549090
$231$	−0.198062	−0.0130315
$232$	4.65279	0.305471
$233$	−23.5894	−1.54539	−0.772697	−	0.634776i	$-0.781093\pi$
$233$	−23.5894	−1.54539	−0.772697	+	0.634776i	$0.781093\pi$
$234$	0	0
$235$	45.0344	2.93772
$236$	5.05861	0.329287
$237$	0.423272	0.0274944
$238$	−0.664874	−0.0430974
$239$	−15.9323	−1.03057	−0.515287	−	0.857018i	$-0.672315\pi$
$239$	−15.9323	−1.03057	−0.515287	+	0.857018i	$0.672315\pi$
$240$	−4.24698	−0.274141
$241$	10.3569	0.667146	0.333573	−	0.942724i	$-0.391746\pi$
$241$	10.3569	0.667146	0.333573	+	0.942724i	$0.391746\pi$
$242$	−10.9608	−0.704585
$243$	1.00000	0.0641500
$244$	−0.878002	−0.0562083
$245$	−4.24698	−0.271330
$246$	−10.0707	−0.642084
$247$	0	0
$248$	−6.67994	−0.424177
$249$	−11.0881	−0.702683
$250$	−34.1323	−2.15871
$251$	24.3424	1.53648	0.768240	−	0.640162i	$-0.221133\pi$
$251$	24.3424	1.53648	0.768240	+	0.640162i	$0.221133\pi$
$252$	1.00000	0.0629941
$253$	−0.388355	−0.0244157
$254$	−5.11529	−0.320962
$255$	2.82371	0.176827
$256$	1.00000	0.0625000
$257$	22.6015	1.40984	0.704921	−	0.709286i	$-0.250982\pi$
$257$	22.6015	1.40984	0.704921	+	0.709286i	$0.250982\pi$
$258$	−2.85086	−0.177486
$259$	4.96077	0.308247
$260$	0	0
$261$	4.65279	0.288001
$262$	−5.97046	−0.368856
$263$	−12.3110	−0.759126	−0.379563	−	0.925166i	$-0.623926\pi$
$263$	−12.3110	−0.759126	−0.379563	+	0.925166i	$0.623926\pi$
$264$	−0.198062	−0.0121899
$265$	61.5967	3.78386
$266$	−2.91185	−0.178537
$267$	15.6407	0.957196
$268$	6.03684	0.368758
$269$	5.67563	0.346049	0.173025	−	0.984918i	$-0.444646\pi$
$269$	5.67563	0.346049	0.173025	+	0.984918i	$0.444646\pi$
$270$	−4.24698	−0.258463
$271$	14.4698	0.878978	0.439489	−	0.898248i	$-0.355160\pi$
$271$	14.4698	0.878978	0.439489	+	0.898248i	$0.355160\pi$
$272$	−0.664874	−0.0403139
$273$	0	0
$274$	−13.0271	−0.786999
$275$	−2.58211	−0.155707
$276$	1.96077	0.118025
$277$	27.6383	1.66063	0.830313	−	0.557298i	$-0.188162\pi$
$277$	27.6383	1.66063	0.830313	+	0.557298i	$0.188162\pi$
$278$	4.36227	0.261632
$279$	−6.67994	−0.399918
$280$	−4.24698	−0.253806
$281$	4.25368	0.253754	0.126877	−	0.991918i	$-0.459505\pi$
$281$	4.25368	0.253754	0.126877	+	0.991918i	$0.459505\pi$
$282$	−10.6039	−0.631452
$283$	10.8388	0.644298	0.322149	−	0.946689i	$-0.395595\pi$
$283$	10.8388	0.644298	0.322149	+	0.946689i	$0.395595\pi$
$284$	10.9879	0.652013
$285$	12.3666	0.732533
$286$	0	0
$287$	−10.0707	−0.594454
$288$	1.00000	0.0589256
$289$	−16.5579	−0.973997
$290$	−19.7603	−1.16037
$291$	−1.47889	−0.0866943
$292$	−4.84117	−0.283308
$293$	−15.6160	−0.912294	−0.456147	−	0.889904i	$-0.650771\pi$
$293$	−15.6160	−0.912294	−0.456147	+	0.889904i	$0.650771\pi$
$294$	1.00000	0.0583212
$295$	−21.4838	−1.25083
$296$	4.96077	0.288339
$297$	−0.198062	−0.0114927
$298$	−3.80194	−0.220240
$299$	0	0
$300$	13.0368	0.752682
$301$	−2.85086	−0.164321
$302$	−14.7342	−0.847860
$303$	−18.6407	−1.07088
$304$	−2.91185	−0.167006
$305$	3.72886	0.213514
$306$	−0.664874	−0.0380083
$307$	−11.2838	−0.644001	−0.322001	−	0.946739i	$-0.604355\pi$
$307$	−11.2838	−0.644001	−0.322001	+	0.946739i	$0.604355\pi$
$308$	−0.198062	−0.0112856
$309$	12.5700	0.715084
$310$	28.3696	1.61128
$311$	31.8732	1.80736	0.903682	−	0.428204i	$-0.140853\pi$
$311$	31.8732	1.80736	0.903682	+	0.428204i	$0.140853\pi$
$312$	0	0
$313$	4.55927	0.257705	0.128853	−	0.991664i	$-0.458871\pi$
$313$	4.55927	0.257705	0.128853	+	0.991664i	$0.458871\pi$
$314$	1.15346	0.0650933
$315$	−4.24698	−0.239290
$316$	0.423272	0.0238109
$317$	−22.1239	−1.24260	−0.621301	−	0.783572i	$-0.713396\pi$
$317$	−22.1239	−1.24260	−0.621301	+	0.783572i	$0.713396\pi$
$318$	−14.5036	−0.813324
$319$	−0.921543	−0.0515965
$320$	−4.24698	−0.237413
$321$	5.98792	0.334213
$322$	1.96077	0.109270
$323$	1.93602	0.107723
$324$	1.00000	0.0555556
$325$	0	0
$326$	−12.0532	−0.667567
$327$	0.850855	0.0470524
$328$	−10.0707	−0.556061
$329$	−10.6039	−0.584611
$330$	0.841166	0.0463047
$331$	7.59286	0.417341	0.208671	−	0.977986i	$-0.433086\pi$
$331$	7.59286	0.417341	0.208671	+	0.977986i	$0.433086\pi$
$332$	−11.0881	−0.608541
$333$	4.96077	0.271849
$334$	−17.8291	−0.975564
$335$	−25.6383	−1.40077
$336$	1.00000	0.0545545
$337$	20.7603	1.13089	0.565443	−	0.824787i	$-0.308705\pi$
$337$	20.7603	1.13089	0.565443	+	0.824787i	$0.308705\pi$
$338$	0	0
$339$	−15.0030	−0.814850
$340$	2.82371	0.153137
$341$	1.32304	0.0716469
$342$	−2.91185	−0.157455
$343$	1.00000	0.0539949
$344$	−2.85086	−0.153708
$345$	−8.32736	−0.448330
$346$	16.7332	0.899581
$347$	−25.5381	−1.37096	−0.685478	−	0.728093i	$-0.740407\pi$
$347$	−25.5381	−1.37096	−0.685478	+	0.728093i	$0.740407\pi$
$348$	4.65279	0.249416
$349$	3.42327	0.183244	0.0916218	−	0.995794i	$-0.470795\pi$
$349$	3.42327	0.183244	0.0916218	+	0.995794i	$0.470795\pi$
$350$	13.0368	0.696848
$351$	0	0
$352$	−0.198062	−0.0105568
$353$	3.18359	0.169445	0.0847226	−	0.996405i	$-0.473000\pi$
$353$	3.18359	0.169445	0.0847226	+	0.996405i	$0.473000\pi$
$354$	5.05861	0.268862
$355$	−46.6655	−2.47675
$356$	15.6407	0.828956
$357$	−0.664874	−0.0351889
$358$	3.67025	0.193979
$359$	22.7429	1.20032	0.600161	−	0.799879i	$-0.295103\pi$
$359$	22.7429	1.20032	0.600161	+	0.799879i	$0.295103\pi$
$360$	−4.24698	−0.223835
$361$	−10.5211	−0.553742
$362$	−14.6189	−0.768354
$363$	−10.9608	−0.575291
$364$	0	0
$365$	20.5603	1.07618
$366$	−0.878002	−0.0458939
$367$	−27.0315	−1.41103	−0.705515	−	0.708695i	$-0.749284\pi$
$367$	−27.0315	−1.41103	−0.705515	+	0.708695i	$0.749284\pi$
$368$	1.96077	0.102212
$369$	−10.0707	−0.524259
$370$	−21.0683	−1.09529
$371$	−14.5036	−0.752992
$372$	−6.67994	−0.346339
$373$	−13.2338	−0.685222	−0.342611	−	0.939477i	$-0.611311\pi$
$373$	−13.2338	−0.685222	−0.342611	+	0.939477i	$0.611311\pi$
$374$	0.131687	0.00680935
$375$	−34.1323	−1.76258
$376$	−10.6039	−0.546853
$377$	0	0
$378$	1.00000	0.0514344
$379$	14.7095	0.755575	0.377788	−	0.925892i	$-0.376685\pi$
$379$	14.7095	0.755575	0.377788	+	0.925892i	$0.376685\pi$
$380$	12.3666	0.634392
$381$	−5.11529	−0.262064
$382$	−24.7928	−1.26851
$383$	15.5754	0.795866	0.397933	−	0.917415i	$-0.369728\pi$
$383$	15.5754	0.795866	0.397933	+	0.917415i	$0.369728\pi$
$384$	1.00000	0.0510310
$385$	0.841166	0.0428698
$386$	−18.9487	−0.964463
$387$	−2.85086	−0.144917
$388$	−1.47889	−0.0750795
$389$	−18.8847	−0.957493	−0.478746	−	0.877953i	$-0.658909\pi$
$389$	−18.8847	−0.957493	−0.478746	+	0.877953i	$0.658909\pi$
$390$	0	0
$391$	−1.30367	−0.0659293
$392$	1.00000	0.0505076
$393$	−5.97046	−0.301170
$394$	−4.58642	−0.231060
$395$	−1.79763	−0.0904484
$396$	−0.198062	−0.00995300
$397$	28.6233	1.43656	0.718280	−	0.695754i	$-0.244930\pi$
$397$	28.6233	1.43656	0.718280	+	0.695754i	$0.244930\pi$
$398$	−17.8998	−0.897235
$399$	−2.91185	−0.145775
$400$	13.0368	0.651842
$401$	22.6601	1.13159	0.565795	−	0.824546i	$-0.308569\pi$
$401$	22.6601	1.13159	0.565795	+	0.824546i	$0.308569\pi$
$402$	6.03684	0.301090
$403$	0	0
$404$	−18.6407	−0.927410
$405$	−4.24698	−0.211034
$406$	4.65279	0.230914
$407$	−0.982542	−0.0487028
$408$	−0.664874	−0.0329162
$409$	11.0325	0.545523	0.272762	−	0.962082i	$-0.412063\pi$
$409$	11.0325	0.545523	0.272762	+	0.962082i	$0.412063\pi$
$410$	42.7700	2.11226
$411$	−13.0271	−0.642582
$412$	12.5700	0.619281
$413$	5.05861	0.248918
$414$	1.96077	0.0963667
$415$	47.0911	2.31161
$416$	0	0
$417$	4.36227	0.213621
$418$	0.576728	0.0282087
$419$	16.0508	0.784135	0.392067	−	0.919937i	$-0.371760\pi$
$419$	16.0508	0.784135	0.392067	+	0.919937i	$0.371760\pi$
$420$	−4.24698	−0.207231
$421$	25.2838	1.23226	0.616129	−	0.787645i	$-0.288700\pi$
$421$	25.2838	1.23226	0.616129	+	0.787645i	$0.288700\pi$
$422$	1.95108	0.0949772
$423$	−10.6039	−0.515578
$424$	−14.5036	−0.704359
$425$	−8.66786	−0.420453
$426$	10.9879	0.532366
$427$	−0.878002	−0.0424895
$428$	5.98792	0.289437
$429$	0	0
$430$	12.1075	0.583877
$431$	−36.0116	−1.73462	−0.867309	−	0.497770i	$-0.834152\pi$
$431$	−36.0116	−1.73462	−0.867309	+	0.497770i	$0.834152\pi$
$432$	1.00000	0.0481125
$433$	27.9299	1.34223	0.671113	−	0.741355i	$-0.265817\pi$
$433$	27.9299	1.34223	0.671113	+	0.741355i	$0.265817\pi$
$434$	−6.67994	−0.320647
$435$	−19.7603	−0.947435
$436$	0.850855	0.0407486
$437$	−5.70948	−0.273121
$438$	−4.84117	−0.231320
$439$	−28.4969	−1.36008	−0.680042	−	0.733173i	$-0.738039\pi$
$439$	−28.4969	−1.36008	−0.680042	+	0.733173i	$0.738039\pi$
$440$	0.841166	0.0401010
$441$	1.00000	0.0476190
$442$	0	0
$443$	33.9366	1.61238	0.806188	−	0.591659i	$-0.201527\pi$
$443$	33.9366	1.61238	0.806188	+	0.591659i	$0.201527\pi$
$444$	4.96077	0.235428
$445$	−66.4258	−3.14888
$446$	−18.9051	−0.895185
$447$	−3.80194	−0.179825
$448$	1.00000	0.0472456
$449$	−3.59312	−0.169570	−0.0847850	−	0.996399i	$-0.527020\pi$
$449$	−3.59312	−0.169570	−0.0847850	+	0.996399i	$0.527020\pi$
$450$	13.0368	0.614562
$451$	1.99462	0.0939231
$452$	−15.0030	−0.705681
$453$	−14.7342	−0.692275
$454$	−21.1468	−0.992466
$455$	0	0
$456$	−2.91185	−0.136360
$457$	16.2591	0.760567	0.380283	−	0.924870i	$-0.375826\pi$
$457$	16.2591	0.760567	0.380283	+	0.924870i	$0.375826\pi$
$458$	22.3884	1.04614
$459$	−0.664874	−0.0310337
$460$	−8.32736	−0.388265
$461$	−33.7372	−1.57130	−0.785649	−	0.618672i	$-0.787671\pi$
$461$	−33.7372	−1.57130	−0.785649	+	0.618672i	$0.787671\pi$
$462$	−0.198062	−0.00921469
$463$	13.6606	0.634860	0.317430	−	0.948282i	$-0.397180\pi$
$463$	13.6606	0.634860	0.317430	+	0.948282i	$0.397180\pi$
$464$	4.65279	0.216000
$465$	28.3696	1.31561
$466$	−23.5894	−1.09276
$467$	1.33081	0.0615827	0.0307914	−	0.999526i	$-0.490197\pi$
$467$	1.33081	0.0615827	0.0307914	+	0.999526i	$0.490197\pi$
$468$	0	0
$469$	6.03684	0.278755
$470$	45.0344	2.07728
$471$	1.15346	0.0531485
$472$	5.05861	0.232841
$473$	0.564647	0.0259625
$474$	0.423272	0.0194415
$475$	−37.9614	−1.74179
$476$	−0.664874	−0.0304745
$477$	−14.5036	−0.664076
$478$	−15.9323	−0.728726
$479$	−39.4416	−1.80213	−0.901066	−	0.433682i	$-0.857214\pi$
$479$	−39.4416	−1.80213	−0.901066	+	0.433682i	$0.857214\pi$
$480$	−4.24698	−0.193847
$481$	0	0
$482$	10.3569	0.471744
$483$	1.96077	0.0892182
$484$	−10.9608	−0.498217
$485$	6.28083	0.285198
$486$	1.00000	0.0453609
$487$	14.7549	0.668610	0.334305	−	0.942465i	$-0.391498\pi$
$487$	14.7549	0.668610	0.334305	+	0.942465i	$0.391498\pi$
$488$	−0.878002	−0.0397453
$489$	−12.0532	−0.545066
$490$	−4.24698	−0.191859
$491$	−20.5187	−0.925997	−0.462998	−	0.886359i	$-0.653226\pi$
$491$	−20.5187	−0.925997	−0.462998	+	0.886359i	$0.653226\pi$
$492$	−10.0707	−0.454022
$493$	−3.09352	−0.139325
$494$	0	0
$495$	0.841166	0.0378076
$496$	−6.67994	−0.299938
$497$	10.9879	0.492876
$498$	−11.0881	−0.496872
$499$	43.8678	1.96379	0.981897	−	0.189415i	$-0.0606592\pi$
$499$	43.8678	1.96379	0.981897	+	0.189415i	$0.0606592\pi$
$500$	−34.1323	−1.52644
$501$	−17.8291	−0.796545
$502$	24.3424	1.08646
$503$	8.50498	0.379218	0.189609	−	0.981860i	$-0.439278\pi$
$503$	8.50498	0.379218	0.189609	+	0.981860i	$0.439278\pi$
$504$	1.00000	0.0445435
$505$	79.1667	3.52287
$506$	−0.388355	−0.0172645
$507$	0	0
$508$	−5.11529	−0.226954
$509$	−35.7512	−1.58464	−0.792322	−	0.610103i	$-0.791128\pi$
$509$	−35.7512	−1.58464	−0.792322	+	0.610103i	$0.791128\pi$
$510$	2.82371	0.125036
$511$	−4.84117	−0.214161
$512$	1.00000	0.0441942
$513$	−2.91185	−0.128561
$514$	22.6015	0.996909
$515$	−53.3846	−2.35241
$516$	−2.85086	−0.125502
$517$	2.10023	0.0923679
$518$	4.96077	0.217964
$519$	16.7332	0.734505
$520$	0	0
$521$	15.5157	0.679756	0.339878	−	0.940469i	$-0.389614\pi$
$521$	15.5157	0.679756	0.339878	+	0.940469i	$0.389614\pi$
$522$	4.65279	0.203647
$523$	44.6413	1.95203	0.976014	−	0.217708i	$-0.0698581\pi$
$523$	44.6413	1.95203	0.976014	+	0.217708i	$0.0698581\pi$
$524$	−5.97046	−0.260821
$525$	13.0368	0.568974
$526$	−12.3110	−0.536783
$527$	4.44132	0.193467
$528$	−0.198062	−0.00861955
$529$	−19.1554	−0.832842
$530$	61.5967	2.67559
$531$	5.05861	0.219525
$532$	−2.91185	−0.126245
$533$	0	0
$534$	15.6407	0.676840
$535$	−25.4306	−1.09946
$536$	6.03684	0.260752
$537$	3.67025	0.158383
$538$	5.67563	0.244694
$539$	−0.198062	−0.00853115
$540$	−4.24698	−0.182761
$541$	24.7530	1.06422	0.532108	−	0.846677i	$-0.321400\pi$
$541$	24.7530	1.06422	0.532108	+	0.846677i	$0.321400\pi$
$542$	14.4698	0.621531
$543$	−14.6189	−0.627359
$544$	−0.664874	−0.0285063
$545$	−3.61356	−0.154788
$546$	0	0
$547$	0.242668	0.0103757	0.00518786	−	0.999987i	$-0.498349\pi$
$547$	0.242668	0.0103757	0.00518786	+	0.999987i	$0.498349\pi$
$548$	−13.0271	−0.556492
$549$	−0.878002	−0.0374722
$550$	−2.58211	−0.110101
$551$	−13.5483	−0.577175
$552$	1.96077	0.0834560
$553$	0.423272	0.0179993
$554$	27.6383	1.17424
$555$	−21.0683	−0.894299
$556$	4.36227	0.185002
$557$	46.9197	1.98805	0.994027	−	0.109138i	$-0.0348090\pi$
$557$	46.9197	1.98805	0.994027	+	0.109138i	$0.0348090\pi$
$558$	−6.67994	−0.282784
$559$	0	0
$560$	−4.24698	−0.179468
$561$	0.131687	0.00555981
$562$	4.25368	0.179431
$563$	0.718578	0.0302844	0.0151422	−	0.999885i	$-0.495180\pi$
$563$	0.718578	0.0302844	0.0151422	+	0.999885i	$0.495180\pi$
$564$	−10.6039	−0.446504
$565$	63.7174	2.68061
$566$	10.8388	0.455588
$567$	1.00000	0.0419961
$568$	10.9879	0.461043
$569$	−0.486189	−0.0203821	−0.0101911	−	0.999948i	$-0.503244\pi$
$569$	−0.486189	−0.0203821	−0.0101911	+	0.999948i	$0.503244\pi$
$570$	12.3666	0.517979
$571$	−27.3260	−1.14356	−0.571779	−	0.820407i	$-0.693747\pi$
$571$	−27.3260	−1.14356	−0.571779	+	0.820407i	$0.693747\pi$
$572$	0	0
$573$	−24.7928	−1.03574
$574$	−10.0707	−0.420342
$575$	25.5623	1.06602
$576$	1.00000	0.0416667
$577$	36.6276	1.52483	0.762413	−	0.647091i	$-0.224015\pi$
$577$	36.6276	1.52483	0.762413	+	0.647091i	$0.224015\pi$
$578$	−16.5579	−0.688720
$579$	−18.9487	−0.787481
$580$	−19.7603	−0.820502
$581$	−11.0881	−0.460014
$582$	−1.47889	−0.0613021
$583$	2.87263	0.118972
$584$	−4.84117	−0.200329
$585$	0	0
$586$	−15.6160	−0.645089
$587$	−8.96077	−0.369851	−0.184925	−	0.982753i	$-0.559204\pi$
$587$	−8.96077	−0.369851	−0.184925	+	0.982753i	$0.559204\pi$
$588$	1.00000	0.0412393
$589$	19.4510	0.801465
$590$	−21.4838	−0.884474
$591$	−4.58642	−0.188660
$592$	4.96077	0.203886
$593$	−15.2489	−0.626197	−0.313099	−	0.949721i	$-0.601367\pi$
$593$	−15.2489	−0.626197	−0.313099	+	0.949721i	$0.601367\pi$
$594$	−0.198062	−0.00812659
$595$	2.82371	0.115761
$596$	−3.80194	−0.155733
$597$	−17.8998	−0.732589
$598$	0	0
$599$	9.64204	0.393963	0.196982	−	0.980407i	$-0.436886\pi$
$599$	9.64204	0.393963	0.196982	+	0.980407i	$0.436886\pi$
$600$	13.0368	0.532227
$601$	−8.21446	−0.335075	−0.167537	−	0.985866i	$-0.553581\pi$
$601$	−8.21446	−0.335075	−0.167537	+	0.985866i	$0.553581\pi$
$602$	−2.85086	−0.116192
$603$	6.03684	0.245839
$604$	−14.7342	−0.599527
$605$	46.5502	1.89253
$606$	−18.6407	−0.757227
$607$	28.5448	1.15860	0.579299	−	0.815115i	$-0.303326\pi$
$607$	28.5448	1.15860	0.579299	+	0.815115i	$0.303326\pi$
$608$	−2.91185	−0.118091
$609$	4.65279	0.188541
$610$	3.72886	0.150977
$611$	0	0
$612$	−0.664874	−0.0268760
$613$	3.14244	0.126922	0.0634610	−	0.997984i	$-0.479786\pi$
$613$	3.14244	0.126922	0.0634610	+	0.997984i	$0.479786\pi$
$614$	−11.2838	−0.455378
$615$	42.7700	1.72465
$616$	−0.198062	−0.00798016
$617$	19.3690	0.779766	0.389883	−	0.920864i	$-0.372516\pi$
$617$	19.3690	0.779766	0.389883	+	0.920864i	$0.372516\pi$
$618$	12.5700	0.505641
$619$	−14.9004	−0.598896	−0.299448	−	0.954113i	$-0.596803\pi$
$619$	−14.9004	−0.598896	−0.299448	+	0.954113i	$0.596803\pi$
$620$	28.3696	1.13935
$621$	1.96077	0.0786830
$622$	31.8732	1.27800
$623$	15.6407	0.626632
$624$	0	0
$625$	79.7749	3.19100
$626$	4.55927	0.182225
$627$	0.576728	0.0230323
$628$	1.15346	0.0460279
$629$	−3.29829	−0.131511
$630$	−4.24698	−0.169204
$631$	−0.809707	−0.0322339	−0.0161170	−	0.999870i	$-0.505130\pi$
$631$	−0.809707	−0.0322339	−0.0161170	+	0.999870i	$0.505130\pi$
$632$	0.423272	0.0168368
$633$	1.95108	0.0775486
$634$	−22.1239	−0.878653
$635$	21.7245	0.862112
$636$	−14.5036	−0.575107
$637$	0	0
$638$	−0.921543	−0.0364842
$639$	10.9879	0.434675
$640$	−4.24698	−0.167877
$641$	30.4868	1.20416	0.602078	−	0.798437i	$-0.294340\pi$
$641$	30.4868	1.20416	0.602078	+	0.798437i	$0.294340\pi$
$642$	5.98792	0.236324
$643$	−1.37004	−0.0540292	−0.0270146	−	0.999635i	$-0.508600\pi$
$643$	−1.37004	−0.0540292	−0.0270146	+	0.999635i	$0.508600\pi$
$644$	1.96077	0.0772652
$645$	12.1075	0.476733
$646$	1.93602	0.0761716
$647$	−41.9995	−1.65117	−0.825586	−	0.564276i	$-0.809155\pi$
$647$	−41.9995	−1.65117	−0.825586	+	0.564276i	$0.809155\pi$
$648$	1.00000	0.0392837
$649$	−1.00192	−0.0393288
$650$	0	0
$651$	−6.67994	−0.261807
$652$	−12.0532	−0.472041
$653$	14.8226	0.580055	0.290027	−	0.957018i	$-0.406336\pi$
$653$	14.8226	0.580055	0.290027	+	0.957018i	$0.406336\pi$
$654$	0.850855	0.0332711
$655$	25.3564	0.990757
$656$	−10.0707	−0.393194
$657$	−4.84117	−0.188872
$658$	−10.6039	−0.413382
$659$	21.5120	0.837989	0.418994	−	0.907989i	$-0.362383\pi$
$659$	21.5120	0.837989	0.418994	+	0.907989i	$0.362383\pi$
$660$	0.841166	0.0327424
$661$	12.5224	0.487066	0.243533	−	0.969893i	$-0.421694\pi$
$661$	12.5224	0.487066	0.243533	+	0.969893i	$0.421694\pi$
$662$	7.59286	0.295105
$663$	0	0
$664$	−11.0881	−0.430304
$665$	12.3666	0.479556
$666$	4.96077	0.192226
$667$	9.12306	0.353246
$668$	−17.8291	−0.689828
$669$	−18.9051	−0.730915
$670$	−25.6383	−0.990495
$671$	0.173899	0.00671330
$672$	1.00000	0.0385758
$673$	−35.4040	−1.36472	−0.682362	−	0.731014i	$-0.739047\pi$
$673$	−35.4040	−1.36472	−0.682362	+	0.731014i	$0.739047\pi$
$674$	20.7603	0.799658
$675$	13.0368	0.501788
$676$	0	0
$677$	0.301274	0.0115789	0.00578945	−	0.999983i	$-0.498157\pi$
$677$	0.301274	0.0115789	0.00578945	+	0.999983i	$0.498157\pi$
$678$	−15.0030	−0.576186
$679$	−1.47889	−0.0567547
$680$	2.82371	0.108284
$681$	−21.1468	−0.810345
$682$	1.32304	0.0506620
$683$	29.3293	1.12225	0.561127	−	0.827730i	$-0.310368\pi$
$683$	29.3293	1.12225	0.561127	+	0.827730i	$0.310368\pi$
$684$	−2.91185	−0.111338
$685$	55.3260	2.11390
$686$	1.00000	0.0381802
$687$	22.3884	0.854169
$688$	−2.85086	−0.108688
$689$	0	0
$690$	−8.32736	−0.317017
$691$	−0.896789	−0.0341154	−0.0170577	−	0.999855i	$-0.505430\pi$
$691$	−0.896789	−0.0341154	−0.0170577	+	0.999855i	$0.505430\pi$
$692$	16.7332	0.636100
$693$	−0.198062	−0.00752376
$694$	−25.5381	−0.969413
$695$	−18.5265	−0.702750
$696$	4.65279	0.176364
$697$	6.69574	0.253619
$698$	3.42327	0.129573
$699$	−23.5894	−0.892233
$700$	13.0368	0.492746
$701$	−4.67994	−0.176759	−0.0883794	−	0.996087i	$-0.528169\pi$
$701$	−4.67994	−0.176759	−0.0883794	+	0.996087i	$0.528169\pi$
$702$	0	0
$703$	−14.4450	−0.544805
$704$	−0.198062	−0.00746475
$705$	45.0344	1.69610
$706$	3.18359	0.119816
$707$	−18.6407	−0.701056
$708$	5.05861	0.190114
$709$	−38.2180	−1.43531	−0.717654	−	0.696400i	$-0.754784\pi$
$709$	−38.2180	−1.43531	−0.717654	+	0.696400i	$0.754784\pi$
$710$	−46.6655	−1.75132
$711$	0.423272	0.0158739
$712$	15.6407	0.586160
$713$	−13.0978	−0.490518
$714$	−0.664874	−0.0248823
$715$	0	0
$716$	3.67025	0.137164
$717$	−15.9323	−0.595003
$718$	22.7429	0.848756
$719$	−1.42088	−0.0529898	−0.0264949	−	0.999649i	$-0.508435\pi$
$719$	−1.42088	−0.0529898	−0.0264949	+	0.999649i	$0.508435\pi$
$720$	−4.24698	−0.158276
$721$	12.5700	0.468132
$722$	−10.5211	−0.391555
$723$	10.3569	0.385177
$724$	−14.6189	−0.543309
$725$	60.6577	2.25277
$726$	−10.9608	−0.406792
$727$	−30.8079	−1.14260	−0.571301	−	0.820741i	$-0.693561\pi$
$727$	−30.8079	−1.14260	−0.571301	+	0.820741i	$0.693561\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	20.5603	0.760972
$731$	1.89546	0.0701061
$732$	−0.878002	−0.0324519
$733$	−18.3502	−0.677780	−0.338890	−	0.940826i	$-0.610051\pi$
$733$	−18.3502	−0.677780	−0.338890	+	0.940826i	$0.610051\pi$
$734$	−27.0315	−0.997749
$735$	−4.24698	−0.156652
$736$	1.96077	0.0722750
$737$	−1.19567	−0.0440430
$738$	−10.0707	−0.370707
$739$	−5.93794	−0.218431	−0.109215	−	0.994018i	$-0.534834\pi$
$739$	−5.93794	−0.218431	−0.109215	+	0.994018i	$0.534834\pi$
$740$	−21.0683	−0.774486
$741$	0	0
$742$	−14.5036	−0.532446
$743$	1.76377	0.0647066	0.0323533	−	0.999476i	$-0.489700\pi$
$743$	1.76377	0.0647066	0.0323533	+	0.999476i	$0.489700\pi$
$744$	−6.67994	−0.244898
$745$	16.1468	0.591571
$746$	−13.2338	−0.484525
$747$	−11.0881	−0.405694
$748$	0.131687	0.00481494
$749$	5.98792	0.218794
$750$	−34.1323	−1.24633
$751$	12.2440	0.446790	0.223395	−	0.974728i	$-0.428286\pi$
$751$	12.2440	0.446790	0.223395	+	0.974728i	$0.428286\pi$
$752$	−10.6039	−0.386684
$753$	24.3424	0.887087
$754$	0	0
$755$	62.5760	2.27737
$756$	1.00000	0.0363696
$757$	19.9912	0.726591	0.363296	−	0.931674i	$-0.381651\pi$
$757$	19.9912	0.726591	0.363296	+	0.931674i	$0.381651\pi$
$758$	14.7095	0.534272
$759$	−0.388355	−0.0140964
$760$	12.3666	0.448583
$761$	−1.78448	−0.0646873	−0.0323437	−	0.999477i	$-0.510297\pi$
$761$	−1.78448	−0.0646873	−0.0323437	+	0.999477i	$0.510297\pi$
$762$	−5.11529	−0.185308
$763$	0.850855	0.0308030
$764$	−24.7928	−0.896973
$765$	2.82371	0.102091
$766$	15.5754	0.562762
$767$	0	0
$768$	1.00000	0.0360844
$769$	3.72050	0.134165	0.0670823	−	0.997747i	$-0.478631\pi$
$769$	3.72050	0.134165	0.0670823	+	0.997747i	$0.478631\pi$
$770$	0.841166	0.0303135
$771$	22.6015	0.813973
$772$	−18.9487	−0.681978
$773$	7.26444	0.261284	0.130642	−	0.991430i	$-0.458296\pi$
$773$	7.26444	0.261284	0.130642	+	0.991430i	$0.458296\pi$
$774$	−2.85086	−0.102472
$775$	−87.0853	−3.12820
$776$	−1.47889	−0.0530892
$777$	4.96077	0.177967
$778$	−18.8847	−0.677050
$779$	29.3244	1.05065
$780$	0	0
$781$	−2.17629	−0.0778739
$782$	−1.30367	−0.0466190
$783$	4.65279	0.166277
$784$	1.00000	0.0357143
$785$	−4.89871	−0.174842
$786$	−5.97046	−0.212959
$787$	−15.9748	−0.569439	−0.284720	−	0.958611i	$-0.591900\pi$
$787$	−15.9748	−0.569439	−0.284720	+	0.958611i	$0.591900\pi$
$788$	−4.58642	−0.163384
$789$	−12.3110	−0.438282
$790$	−1.79763	−0.0639567
$791$	−15.0030	−0.533445
$792$	−0.198062	−0.00703784
$793$	0	0
$794$	28.6233	1.01580
$795$	61.5967	2.18461
$796$	−17.8998	−0.634441
$797$	−30.3588	−1.07536	−0.537682	−	0.843148i	$-0.680700\pi$
$797$	−30.3588	−1.07536	−0.537682	+	0.843148i	$0.680700\pi$
$798$	−2.91185	−0.103079
$799$	7.05025	0.249420
$800$	13.0368	0.460922
$801$	15.6407	0.552637
$802$	22.6601	0.800156
$803$	0.958852	0.0338372
$804$	6.03684	0.212903
$805$	−8.32736	−0.293501
$806$	0	0
$807$	5.67563	0.199792
$808$	−18.6407	−0.655778
$809$	−16.8595	−0.592748	−0.296374	−	0.955072i	$-0.595777\pi$
$809$	−16.8595	−0.592748	−0.296374	+	0.955072i	$0.595777\pi$
$810$	−4.24698	−0.149224
$811$	−25.1612	−0.883530	−0.441765	−	0.897131i	$-0.645648\pi$
$811$	−25.1612	−0.883530	−0.441765	+	0.897131i	$0.645648\pi$
$812$	4.65279	0.163281
$813$	14.4698	0.507478
$814$	−0.982542	−0.0344381
$815$	51.1898	1.79310
$816$	−0.664874	−0.0232753
$817$	8.30127	0.290425
$818$	11.0325	0.385743
$819$	0	0
$820$	42.7700	1.49359
$821$	−24.8394	−0.866900	−0.433450	−	0.901178i	$-0.642704\pi$
$821$	−24.8394	−0.866900	−0.433450	+	0.901178i	$0.642704\pi$
$822$	−13.0271	−0.454374
$823$	−17.4252	−0.607404	−0.303702	−	0.952767i	$-0.598223\pi$
$823$	−17.4252	−0.607404	−0.303702	+	0.952767i	$0.598223\pi$
$824$	12.5700	0.437898
$825$	−2.58211	−0.0898974
$826$	5.05861	0.176011
$827$	42.9517	1.49358	0.746788	−	0.665062i	$-0.231595\pi$
$827$	42.9517	1.49358	0.746788	+	0.665062i	$0.231595\pi$
$828$	1.96077	0.0681415
$829$	−37.5230	−1.30323	−0.651614	−	0.758550i	$-0.725908\pi$
$829$	−37.5230	−1.30323	−0.651614	+	0.758550i	$0.725908\pi$
$830$	47.0911	1.63456
$831$	27.6383	0.958763
$832$	0	0
$833$	−0.664874	−0.0230365
$834$	4.36227	0.151053
$835$	75.7198	2.62039
$836$	0.576728	0.0199466
$837$	−6.67994	−0.230892
$838$	16.0508	0.554467
$839$	−1.56406	−0.0539972	−0.0269986	−	0.999635i	$-0.508595\pi$
$839$	−1.56406	−0.0539972	−0.0269986	+	0.999635i	$0.508595\pi$
$840$	−4.24698	−0.146535
$841$	−7.35152	−0.253501
$842$	25.2838	0.871338
$843$	4.25368	0.146505
$844$	1.95108	0.0671590
$845$	0	0
$846$	−10.6039	−0.364569
$847$	−10.9608	−0.376617
$848$	−14.5036	−0.498057
$849$	10.8388	0.371986
$850$	−8.66786	−0.297305
$851$	9.72694	0.333435
$852$	10.9879	0.376440
$853$	16.9256	0.579521	0.289761	−	0.957099i	$-0.406424\pi$
$853$	16.9256	0.579521	0.289761	+	0.957099i	$0.406424\pi$
$854$	−0.878002	−0.0300446
$855$	12.3666	0.422928
$856$	5.98792	0.204663
$857$	−10.5362	−0.359909	−0.179954	−	0.983675i	$-0.557595\pi$
$857$	−10.5362	−0.359909	−0.179954	+	0.983675i	$0.557595\pi$
$858$	0	0
$859$	41.4607	1.41462	0.707310	−	0.706903i	$-0.249908\pi$
$859$	41.4607	1.41462	0.707310	+	0.706903i	$0.249908\pi$
$860$	12.1075	0.412863
$861$	−10.0707	−0.343208
$862$	−36.0116	−1.22656
$863$	−5.30798	−0.180686	−0.0903428	−	0.995911i	$-0.528796\pi$
$863$	−5.30798	−0.180686	−0.0903428	+	0.995911i	$0.528796\pi$
$864$	1.00000	0.0340207
$865$	−71.0654	−2.41630
$866$	27.9299	0.949097
$867$	−16.5579	−0.562337
$868$	−6.67994	−0.226732
$869$	−0.0838341	−0.00284388
$870$	−19.7603	−0.669937
$871$	0	0
$872$	0.850855	0.0288136
$873$	−1.47889	−0.0500530
$874$	−5.70948	−0.193126
$875$	−34.1323	−1.15388
$876$	−4.84117	−0.163568
$877$	−29.0549	−0.981114	−0.490557	−	0.871409i	$-0.663207\pi$
$877$	−29.0549	−0.981114	−0.490557	+	0.871409i	$0.663207\pi$
$878$	−28.4969	−0.961725
$879$	−15.6160	−0.526713
$880$	0.841166	0.0283557
$881$	−16.5013	−0.555941	−0.277971	−	0.960590i	$-0.589662\pi$
$881$	−16.5013	−0.555941	−0.277971	+	0.960590i	$0.589662\pi$
$882$	1.00000	0.0336718
$883$	18.6189	0.626577	0.313289	−	0.949658i	$-0.398569\pi$
$883$	18.6189	0.626577	0.313289	+	0.949658i	$0.398569\pi$
$884$	0	0
$885$	−21.4838	−0.722170
$886$	33.9366	1.14012
$887$	47.2161	1.58536	0.792681	−	0.609637i	$-0.208685\pi$
$887$	47.2161	1.58536	0.792681	+	0.609637i	$0.208685\pi$
$888$	4.96077	0.166473
$889$	−5.11529	−0.171561
$890$	−66.4258	−2.22660
$891$	−0.198062	−0.00663534
$892$	−18.9051	−0.632991
$893$	30.8769	1.03326
$894$	−3.80194	−0.127156
$895$	−15.5875	−0.521032
$896$	1.00000	0.0334077
$897$	0	0
$898$	−3.59312	−0.119904
$899$	−31.0804	−1.03659
$900$	13.0368	0.434561
$901$	9.64310	0.321258
$902$	1.99462	0.0664137
$903$	−2.85086	−0.0948705
$904$	−15.0030	−0.498992
$905$	62.0863	2.06382
$906$	−14.7342	−0.489512
$907$	−42.1997	−1.40122	−0.700609	−	0.713545i	$-0.747088\pi$
$907$	−42.1997	−1.40122	−0.700609	+	0.713545i	$0.747088\pi$
$908$	−21.1468	−0.701780
$909$	−18.6407	−0.618273
$910$	0	0
$911$	−30.3967	−1.00709	−0.503544	−	0.863970i	$-0.667971\pi$
$911$	−30.3967	−1.00709	−0.503544	+	0.863970i	$0.667971\pi$
$912$	−2.91185	−0.0964211
$913$	2.19614	0.0726817
$914$	16.2591	0.537802
$915$	3.72886	0.123272
$916$	22.3884	0.739732
$917$	−5.97046	−0.197162
$918$	−0.664874	−0.0219441
$919$	41.8944	1.38197	0.690984	−	0.722870i	$-0.257177\pi$
$919$	41.8944	1.38197	0.690984	+	0.722870i	$0.257177\pi$
$920$	−8.32736	−0.274545
$921$	−11.2838	−0.371814
$922$	−33.7372	−1.11108
$923$	0	0
$924$	−0.198062	−0.00651577
$925$	64.6728	2.12643
$926$	13.6606	0.448914
$927$	12.5700	0.412854
$928$	4.65279	0.152735
$929$	21.6093	0.708977	0.354488	−	0.935060i	$-0.384655\pi$
$929$	21.6093	0.708977	0.354488	+	0.935060i	$0.384655\pi$
$930$	28.3696	0.930275
$931$	−2.91185	−0.0954322
$932$	−23.5894	−0.772697
$933$	31.8732	1.04348
$934$	1.33081	0.0435456
$935$	−0.559270	−0.0182901
$936$	0	0
$937$	−0.396125	−0.0129408	−0.00647041	−	0.999979i	$-0.502060\pi$
$937$	−0.396125	−0.0129408	−0.00647041	+	0.999979i	$0.502060\pi$
$938$	6.03684	0.197110
$939$	4.55927	0.148786
$940$	45.0344	1.46886
$941$	39.7875	1.29703	0.648517	−	0.761200i	$-0.275389\pi$
$941$	39.7875	1.29703	0.648517	+	0.761200i	$0.275389\pi$
$942$	1.15346	0.0375817
$943$	−19.7463	−0.643029
$944$	5.05861	0.164644
$945$	−4.24698	−0.138154
$946$	0.564647	0.0183583
$947$	−15.4461	−0.501931	−0.250966	−	0.967996i	$-0.580748\pi$
$947$	−15.4461	−0.501931	−0.250966	+	0.967996i	$0.580748\pi$
$948$	0.423272	0.0137472
$949$	0	0
$950$	−37.9614	−1.23163
$951$	−22.1239	−0.717417
$952$	−0.664874	−0.0215487
$953$	−9.19998	−0.298017	−0.149008	−	0.988836i	$-0.547608\pi$
$953$	−9.19998	−0.298017	−0.149008	+	0.988836i	$0.547608\pi$
$954$	−14.5036	−0.469573
$955$	105.295	3.40726
$956$	−15.9323	−0.515287
$957$	−0.921543	−0.0297892
$958$	−39.4416	−1.27430
$959$	−13.0271	−0.420669
$960$	−4.24698	−0.137071
$961$	13.6216	0.439406
$962$	0	0
$963$	5.98792	0.192958
$964$	10.3569	0.333573
$965$	80.4747	2.59057
$966$	1.96077	0.0630868
$967$	−24.3521	−0.783111	−0.391556	−	0.920154i	$-0.628063\pi$
$967$	−24.3521	−0.783111	−0.391556	+	0.920154i	$0.628063\pi$
$968$	−10.9608	−0.352293
$969$	1.93602	0.0621938
$970$	6.28083	0.201665
$971$	27.1795	0.872233	0.436116	−	0.899890i	$-0.356354\pi$
$971$	27.1795	0.872233	0.436116	+	0.899890i	$0.356354\pi$
$972$	1.00000	0.0320750
$973$	4.36227	0.139848
$974$	14.7549	0.472779
$975$	0	0
$976$	−0.878002	−0.0281042
$977$	−34.5532	−1.10545	−0.552727	−	0.833363i	$-0.686413\pi$
$977$	−34.5532	−1.10545	−0.552727	+	0.833363i	$0.686413\pi$
$978$	−12.0532	−0.385420
$979$	−3.09783	−0.0990072
$980$	−4.24698	−0.135665
$981$	0.850855	0.0271657
$982$	−20.5187	−0.654778
$983$	7.51094	0.239562	0.119781	−	0.992800i	$-0.461781\pi$
$983$	7.51094	0.239562	0.119781	+	0.992800i	$0.461781\pi$
$984$	−10.0707	−0.321042
$985$	19.4784	0.620634
$986$	−3.09352	−0.0985178
$987$	−10.6039	−0.337525
$988$	0	0
$989$	−5.58987	−0.177748
$990$	0.841166	0.0267340
$991$	4.78853	0.152113	0.0760563	−	0.997104i	$-0.475767\pi$
$991$	4.78853	0.152113	0.0760563	+	0.997104i	$0.475767\pi$
$992$	−6.67994	−0.212088
$993$	7.59286	0.240952
$994$	10.9879	0.348516
$995$	76.0200	2.41000
$996$	−11.0881	−0.351341
$997$	−41.3274	−1.30885	−0.654425	−	0.756127i	$-0.727089\pi$
$997$	−41.3274	−1.30885	−0.654425	+	0.756127i	$0.727089\pi$
$998$	43.8678	1.38861
$999$	4.96077	0.156952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cl.1.1	yes	3
13.12	even	2		7098.2.a.cg.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cg.1.3	✓	3	13.12	even	2
7098.2.a.cl.1.1	yes	3	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:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.24698 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.24698 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.24698 q^{10} -0.198062 q^{11} +1.00000 q^{12} +1.00000 q^{14} -4.24698 q^{15} +1.00000 q^{16} -0.664874 q^{17} +1.00000 q^{18} -2.91185 q^{19} -4.24698 q^{20} +1.00000 q^{21} -0.198062 q^{22} +1.96077 q^{23} +1.00000 q^{24} +13.0368 q^{25} +1.00000 q^{27} +1.00000 q^{28} +4.65279 q^{29} -4.24698 q^{30} -6.67994 q^{31} +1.00000 q^{32} -0.198062 q^{33} -0.664874 q^{34} -4.24698 q^{35} +1.00000 q^{36} +4.96077 q^{37} -2.91185 q^{38} -4.24698 q^{40} -10.0707 q^{41} +1.00000 q^{42} -2.85086 q^{43} -0.198062 q^{44} -4.24698 q^{45} +1.96077 q^{46} -10.6039 q^{47} +1.00000 q^{48} +1.00000 q^{49} +13.0368 q^{50} -0.664874 q^{51} -14.5036 q^{53} +1.00000 q^{54} +0.841166 q^{55} +1.00000 q^{56} -2.91185 q^{57} +4.65279 q^{58} +5.05861 q^{59} -4.24698 q^{60} -0.878002 q^{61} -6.67994 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.198062 q^{66} +6.03684 q^{67} -0.664874 q^{68} +1.96077 q^{69} -4.24698 q^{70} +10.9879 q^{71} +1.00000 q^{72} -4.84117 q^{73} +4.96077 q^{74} +13.0368 q^{75} -2.91185 q^{76} -0.198062 q^{77} +0.423272 q^{79} -4.24698 q^{80} +1.00000 q^{81} -10.0707 q^{82} -11.0881 q^{83} +1.00000 q^{84} +2.82371 q^{85} -2.85086 q^{86} +4.65279 q^{87} -0.198062 q^{88} +15.6407 q^{89} -4.24698 q^{90} +1.96077 q^{92} -6.67994 q^{93} -10.6039 q^{94} +12.3666 q^{95} +1.00000 q^{96} -1.47889 q^{97} +1.00000 q^{98} -0.198062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 8 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 8 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 8 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 8 q^{10} - 5 q^{11} + 3 q^{12} + 3 q^{14} - 8 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} - 5 q^{19} - 8 q^{20} + 3 q^{21} - 5 q^{22} - 7 q^{23} + 3 q^{24} + 11 q^{25} + 3 q^{27} + 3 q^{28} - 4 q^{29} - 8 q^{30} + 4 q^{31} + 3 q^{32} - 5 q^{33} - 3 q^{34} - 8 q^{35} + 3 q^{36} + 2 q^{37} - 5 q^{38} - 8 q^{40} - 18 q^{41} + 3 q^{42} + 5 q^{43} - 5 q^{44} - 8 q^{45} - 7 q^{46} - 23 q^{47} + 3 q^{48} + 3 q^{49} + 11 q^{50} - 3 q^{51} - 12 q^{53} + 3 q^{54} + 11 q^{55} + 3 q^{56} - 5 q^{57} - 4 q^{58} - 16 q^{59} - 8 q^{60} + 17 q^{61} + 4 q^{62} + 3 q^{63} + 3 q^{64} - 5 q^{66} - 10 q^{67} - 3 q^{68} - 7 q^{69} - 8 q^{70} + 14 q^{71} + 3 q^{72} - 23 q^{73} + 2 q^{74} + 11 q^{75} - 5 q^{76} - 5 q^{77} + 4 q^{79} - 8 q^{80} + 3 q^{81} - 18 q^{82} - 37 q^{83} + 3 q^{84} + q^{85} + 5 q^{86} - 4 q^{87} - 5 q^{88} + 10 q^{89} - 8 q^{90} - 7 q^{92} + 4 q^{93} - 23 q^{94} + 11 q^{95} + 3 q^{96} - 20 q^{97} + 3 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 8 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 8 * q^10 - 5 * q^11 + 3 * q^12 + 3 * q^14 - 8 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 - 5 * q^19 - 8 * q^20 + 3 * q^21 - 5 * q^22 - 7 * q^23 + 3 * q^24 + 11 * q^25 + 3 * q^27 + 3 * q^28 - 4 * q^29 - 8 * q^30 + 4 * q^31 + 3 * q^32 - 5 * q^33 - 3 * q^34 - 8 * q^35 + 3 * q^36 + 2 * q^37 - 5 * q^38 - 8 * q^40 - 18 * q^41 + 3 * q^42 + 5 * q^43 - 5 * q^44 - 8 * q^45 - 7 * q^46 - 23 * q^47 + 3 * q^48 + 3 * q^49 + 11 * q^50 - 3 * q^51 - 12 * q^53 + 3 * q^54 + 11 * q^55 + 3 * q^56 - 5 * q^57 - 4 * q^58 - 16 * q^59 - 8 * q^60 + 17 * q^61 + 4 * q^62 + 3 * q^63 + 3 * q^64 - 5 * q^66 - 10 * q^67 - 3 * q^68 - 7 * q^69 - 8 * q^70 + 14 * q^71 + 3 * q^72 - 23 * q^73 + 2 * q^74 + 11 * q^75 - 5 * q^76 - 5 * q^77 + 4 * q^79 - 8 * q^80 + 3 * q^81 - 18 * q^82 - 37 * q^83 + 3 * q^84 + q^85 + 5 * q^86 - 4 * q^87 - 5 * q^88 + 10 * q^89 - 8 * q^90 - 7 * q^92 + 4 * q^93 - 23 * q^94 + 11 * q^95 + 3 * q^96 - 20 * q^97 + 3 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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