LMFDB - Embedded newform 7098.2.a.cr.1.3

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:	$6$
Coefficient field:	6.6.48406561.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 $ x^6 - 3x^5 - 17x^4 + 39x^3 + 111x^2 - 131*x - 281
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			1.3
Root			$2.83411$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.83411 q^{10} -0.198062 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.83411 q^{15} +1.00000 q^{16} +0.445042 q^{17} -1.00000 q^{18} +1.01785 q^{19} -2.83411 q^{20} -1.00000 q^{21} +0.198062 q^{22} -5.03709 q^{23} -1.00000 q^{24} +3.03217 q^{25} +1.00000 q^{27} -1.00000 q^{28} +4.34507 q^{29} +2.83411 q^{30} -2.21481 q^{31} -1.00000 q^{32} -0.198062 q^{33} -0.445042 q^{34} +2.83411 q^{35} +1.00000 q^{36} +7.43142 q^{37} -1.01785 q^{38} +2.83411 q^{40} +0.443500 q^{41} +1.00000 q^{42} +7.64733 q^{43} -0.198062 q^{44} -2.83411 q^{45} +5.03709 q^{46} -3.63873 q^{47} +1.00000 q^{48} +1.00000 q^{49} -3.03217 q^{50} +0.445042 q^{51} +6.50916 q^{53} -1.00000 q^{54} +0.561330 q^{55} +1.00000 q^{56} +1.01785 q^{57} -4.34507 q^{58} -5.45031 q^{59} -2.83411 q^{60} +11.3069 q^{61} +2.21481 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.198062 q^{66} -14.5407 q^{67} +0.445042 q^{68} -5.03709 q^{69} -2.83411 q^{70} -5.80083 q^{71} -1.00000 q^{72} +0.641997 q^{73} -7.43142 q^{74} +3.03217 q^{75} +1.01785 q^{76} +0.198062 q^{77} +1.67721 q^{79} -2.83411 q^{80} +1.00000 q^{81} -0.443500 q^{82} -6.42808 q^{83} -1.00000 q^{84} -1.26130 q^{85} -7.64733 q^{86} +4.34507 q^{87} +0.198062 q^{88} +10.2278 q^{89} +2.83411 q^{90} -5.03709 q^{92} -2.21481 q^{93} +3.63873 q^{94} -2.88471 q^{95} -1.00000 q^{96} +9.69272 q^{97} -1.00000 q^{98} -0.198062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9} + 3 q^{10} - 10 q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 2 q^{17} - 6 q^{18} - 2 q^{19} - 3 q^{20} - 6 q^{21} + 10 q^{22} + 4 q^{23} - 6 q^{24} + 13 q^{25} + 6 q^{27} - 6 q^{28} + 2 q^{29} + 3 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 2 q^{34} + 3 q^{35} + 6 q^{36} - 7 q^{37} + 2 q^{38} + 3 q^{40} - 11 q^{41} + 6 q^{42} - 5 q^{43} - 10 q^{44} - 3 q^{45} - 4 q^{46} - 5 q^{47} + 6 q^{48} + 6 q^{49} - 13 q^{50} + 2 q^{51} - 6 q^{53} - 6 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} - 2 q^{58} - 28 q^{59} - 3 q^{60} + 23 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 10 q^{67} + 2 q^{68} + 4 q^{69} - 3 q^{70} - 21 q^{71} - 6 q^{72} + 7 q^{73} + 7 q^{74} + 13 q^{75} - 2 q^{76} + 10 q^{77} - 14 q^{79} - 3 q^{80} + 6 q^{81} + 11 q^{82} - 17 q^{83} - 6 q^{84} - q^{85} + 5 q^{86} + 2 q^{87} + 10 q^{88} - 17 q^{89} + 3 q^{90} + 4 q^{92} - 9 q^{93} + 5 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{98} - 10 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9 + 3 * q^10 - 10 * q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 2 * q^17 - 6 * q^18 - 2 * q^19 - 3 * q^20 - 6 * q^21 + 10 * q^22 + 4 * q^23 - 6 * q^24 + 13 * q^25 + 6 * q^27 - 6 * q^28 + 2 * q^29 + 3 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 2 * q^34 + 3 * q^35 + 6 * q^36 - 7 * q^37 + 2 * q^38 + 3 * q^40 - 11 * q^41 + 6 * q^42 - 5 * q^43 - 10 * q^44 - 3 * q^45 - 4 * q^46 - 5 * q^47 + 6 * q^48 + 6 * q^49 - 13 * q^50 + 2 * q^51 - 6 * q^53 - 6 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 - 2 * q^58 - 28 * q^59 - 3 * q^60 + 23 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 10 * q^67 + 2 * q^68 + 4 * q^69 - 3 * q^70 - 21 * q^71 - 6 * q^72 + 7 * q^73 + 7 * q^74 + 13 * q^75 - 2 * q^76 + 10 * q^77 - 14 * q^79 - 3 * q^80 + 6 * q^81 + 11 * q^82 - 17 * q^83 - 6 * q^84 - q^85 + 5 * q^86 + 2 * q^87 + 10 * q^88 - 17 * q^89 + 3 * q^90 + 4 * q^92 - 9 * q^93 + 5 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^98 - 10 * 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
$5$	−2.83411	−1.26745	−0.633726	−	0.773558i	$-0.718475\pi$
$5$	−2.83411	−1.26745	−0.633726	+	0.773558i	$0.718475\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.83411	0.896224
$11$	−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
$15$	−2.83411	−0.731764
$16$	1.00000	0.250000
$17$	0.445042	0.107939	0.0539693	−	0.998543i	$-0.482813\pi$
$17$	0.445042	0.107939	0.0539693	+	0.998543i	$0.482813\pi$
$18$	−1.00000	−0.235702
$19$	1.01785	0.233512	0.116756	−	0.993161i	$-0.462751\pi$
$19$	1.01785	0.233512	0.116756	+	0.993161i	$0.462751\pi$
$20$	−2.83411	−0.633726
$21$	−1.00000	−0.218218
$22$	0.198062	0.0422270
$23$	−5.03709	−1.05031	−0.525153	−	0.851008i	$-0.675992\pi$
$23$	−5.03709	−1.05031	−0.525153	+	0.851008i	$0.675992\pi$
$24$	−1.00000	−0.204124
$25$	3.03217	0.606434
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	4.34507	0.806858	0.403429	−	0.915011i	$-0.367818\pi$
$29$	4.34507	0.806858	0.403429	+	0.915011i	$0.367818\pi$
$30$	2.83411	0.517435
$31$	−2.21481	−0.397791	−0.198896	−	0.980021i	$-0.563736\pi$
$31$	−2.21481	−0.397791	−0.198896	+	0.980021i	$0.563736\pi$
$32$	−1.00000	−0.176777
$33$	−0.198062	−0.0344782
$34$	−0.445042	−0.0763241
$35$	2.83411	0.479052
$36$	1.00000	0.166667
$37$	7.43142	1.22172	0.610859	−	0.791740i	$-0.290824\pi$
$37$	7.43142	1.22172	0.610859	+	0.791740i	$0.290824\pi$
$38$	−1.01785	−0.165118
$39$	0	0
$40$	2.83411	0.448112
$41$	0.443500	0.0692631	0.0346315	−	0.999400i	$-0.488974\pi$
$41$	0.443500	0.0692631	0.0346315	+	0.999400i	$0.488974\pi$
$42$	1.00000	0.154303
$43$	7.64733	1.16621	0.583104	−	0.812398i	$-0.301838\pi$
$43$	7.64733	1.16621	0.583104	+	0.812398i	$0.301838\pi$
$44$	−0.198062	−0.0298590
$45$	−2.83411	−0.422484
$46$	5.03709	0.742678
$47$	−3.63873	−0.530763	−0.265381	−	0.964144i	$-0.585498\pi$
$47$	−3.63873	−0.530763	−0.265381	+	0.964144i	$0.585498\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−3.03217	−0.428814
$51$	0.445042	0.0623183
$52$	0	0
$53$	6.50916	0.894102	0.447051	−	0.894508i	$-0.352474\pi$
$53$	6.50916	0.894102	0.447051	+	0.894508i	$0.352474\pi$
$54$	−1.00000	−0.136083
$55$	0.561330	0.0756897
$56$	1.00000	0.133631
$57$	1.01785	0.134818
$58$	−4.34507	−0.570535
$59$	−5.45031	−0.709570	−0.354785	−	0.934948i	$-0.615446\pi$
$59$	−5.45031	−0.709570	−0.354785	+	0.934948i	$0.615446\pi$
$60$	−2.83411	−0.365882
$61$	11.3069	1.44771	0.723853	−	0.689954i	$-0.242369\pi$
$61$	11.3069	1.44771	0.723853	+	0.689954i	$0.242369\pi$
$62$	2.21481	0.281281
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	0.198062	0.0243798
$67$	−14.5407	−1.77643	−0.888217	−	0.459425i	$-0.848056\pi$
$67$	−14.5407	−1.77643	−0.888217	+	0.459425i	$0.848056\pi$
$68$	0.445042	0.0539693
$69$	−5.03709	−0.606394
$70$	−2.83411	−0.338741
$71$	−5.80083	−0.688432	−0.344216	−	0.938890i	$-0.611855\pi$
$71$	−5.80083	−0.688432	−0.344216	+	0.938890i	$0.611855\pi$
$72$	−1.00000	−0.117851
$73$	0.641997	0.0751401	0.0375701	−	0.999294i	$-0.488038\pi$
$73$	0.641997	0.0751401	0.0375701	+	0.999294i	$0.488038\pi$
$74$	−7.43142	−0.863885
$75$	3.03217	0.350125
$76$	1.01785	0.116756
$77$	0.198062	0.0225713
$78$	0	0
$79$	1.67721	0.188701	0.0943505	−	0.995539i	$-0.469923\pi$
$79$	1.67721	0.188701	0.0943505	+	0.995539i	$0.469923\pi$
$80$	−2.83411	−0.316863
$81$	1.00000	0.111111
$82$	−0.443500	−0.0489764
$83$	−6.42808	−0.705573	−0.352787	−	0.935704i	$-0.614766\pi$
$83$	−6.42808	−0.705573	−0.352787	+	0.935704i	$0.614766\pi$
$84$	−1.00000	−0.109109
$85$	−1.26130	−0.136807
$86$	−7.64733	−0.824633
$87$	4.34507	0.465840
$88$	0.198062	0.0211135
$89$	10.2278	1.08415	0.542074	−	0.840330i	$-0.317639\pi$
$89$	10.2278	1.08415	0.542074	+	0.840330i	$0.317639\pi$
$90$	2.83411	0.298741
$91$	0	0
$92$	−5.03709	−0.525153
$93$	−2.21481	−0.229665
$94$	3.63873	0.375306
$95$	−2.88471	−0.295965
$96$	−1.00000	−0.102062
$97$	9.69272	0.984146	0.492073	−	0.870554i	$-0.336239\pi$
$97$	9.69272	0.984146	0.492073	+	0.870554i	$0.336239\pi$
$98$	−1.00000	−0.101015
$99$	−0.198062	−0.0199060
$100$	3.03217	0.303217
$101$	−0.496795	−0.0494329	−0.0247165	−	0.999695i	$-0.507868\pi$
$101$	−0.496795	−0.0494329	−0.0247165	+	0.999695i	$0.507868\pi$
$102$	−0.445042	−0.0440657
$103$	−9.61959	−0.947846	−0.473923	−	0.880566i	$-0.657163\pi$
$103$	−9.61959	−0.947846	−0.473923	+	0.880566i	$0.657163\pi$
$104$	0	0
$105$	2.83411	0.276581
$106$	−6.50916	−0.632226
$107$	−10.8776	−1.05157	−0.525787	−	0.850616i	$-0.676229\pi$
$107$	−10.8776	−1.05157	−0.525787	+	0.850616i	$0.676229\pi$
$108$	1.00000	0.0962250
$109$	−8.51454	−0.815545	−0.407773	−	0.913084i	$-0.633694\pi$
$109$	−8.51454	−0.815545	−0.407773	+	0.913084i	$0.633694\pi$
$110$	−0.561330	−0.0535207
$111$	7.43142	0.705359
$112$	−1.00000	−0.0944911
$113$	−6.97708	−0.656349	−0.328174	−	0.944617i	$-0.606433\pi$
$113$	−6.97708	−0.656349	−0.328174	+	0.944617i	$0.606433\pi$
$114$	−1.01785	−0.0953307
$115$	14.2757	1.33121
$116$	4.34507	0.403429
$117$	0	0
$118$	5.45031	0.501741
$119$	−0.445042	−0.0407969
$120$	2.83411	0.258718
$121$	−10.9608	−0.996434
$122$	−11.3069	−1.02368
$123$	0.443500	0.0399891
$124$	−2.21481	−0.198896
$125$	5.57704	0.498826
$126$	1.00000	0.0890871
$127$	−3.64802	−0.323709	−0.161855	−	0.986815i	$-0.551748\pi$
$127$	−3.64802	−0.323709	−0.161855	+	0.986815i	$0.551748\pi$
$128$	−1.00000	−0.0883883
$129$	7.64733	0.673310
$130$	0	0
$131$	−2.42438	−0.211819	−0.105909	−	0.994376i	$-0.533775\pi$
$131$	−2.42438	−0.211819	−0.105909	+	0.994376i	$0.533775\pi$
$132$	−0.198062	−0.0172391
$133$	−1.01785	−0.0882591
$134$	14.5407	1.25613
$135$	−2.83411	−0.243921
$136$	−0.445042	−0.0381620
$137$	−21.5583	−1.84185	−0.920927	−	0.389735i	$-0.872567\pi$
$137$	−21.5583	−1.84185	−0.920927	+	0.389735i	$0.872567\pi$
$138$	5.03709	0.428785
$139$	−2.63351	−0.223371	−0.111686	−	0.993744i	$-0.535625\pi$
$139$	−2.63351	−0.223371	−0.111686	+	0.993744i	$0.535625\pi$
$140$	2.83411	0.239526
$141$	−3.63873	−0.306436
$142$	5.80083	0.486795
$143$	0	0
$144$	1.00000	0.0833333
$145$	−12.3144	−1.02265
$146$	−0.641997	−0.0531321
$147$	1.00000	0.0824786
$148$	7.43142	0.610859
$149$	−9.09027	−0.744704	−0.372352	−	0.928092i	$-0.621449\pi$
$149$	−9.09027	−0.744704	−0.372352	+	0.928092i	$0.621449\pi$
$150$	−3.03217	−0.247576
$151$	21.2010	1.72531	0.862657	−	0.505790i	$-0.168799\pi$
$151$	21.2010	1.72531	0.862657	+	0.505790i	$0.168799\pi$
$152$	−1.01785	−0.0825588
$153$	0.445042	0.0359795
$154$	−0.198062	−0.0159603
$155$	6.27701	0.504181
$156$	0	0
$157$	9.99173	0.797427	0.398713	−	0.917076i	$-0.369457\pi$
$157$	9.99173	0.797427	0.398713	+	0.917076i	$0.369457\pi$
$158$	−1.67721	−0.133432
$159$	6.50916	0.516210
$160$	2.83411	0.224056
$161$	5.03709	0.396978
$162$	−1.00000	−0.0785674
$163$	−3.18547	−0.249506	−0.124753	−	0.992188i	$-0.539814\pi$
$163$	−3.18547	−0.249506	−0.124753	+	0.992188i	$0.539814\pi$
$164$	0.443500	0.0346315
$165$	0.561330	0.0436995
$166$	6.42808	0.498915
$167$	18.5456	1.43510	0.717550	−	0.696507i	$-0.245263\pi$
$167$	18.5456	1.43510	0.717550	+	0.696507i	$0.245263\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	1.26130	0.0967371
$171$	1.01785	0.0778372
$172$	7.64733	0.583104
$173$	−3.53929	−0.269087	−0.134544	−	0.990908i	$-0.542957\pi$
$173$	−3.53929	−0.269087	−0.134544	+	0.990908i	$0.542957\pi$
$174$	−4.34507	−0.329399
$175$	−3.03217	−0.229211
$176$	−0.198062	−0.0149295
$177$	−5.45031	−0.409670
$178$	−10.2278	−0.766609
$179$	3.24260	0.242363	0.121182	−	0.992630i	$-0.461332\pi$
$179$	3.24260	0.242363	0.121182	+	0.992630i	$0.461332\pi$
$180$	−2.83411	−0.211242
$181$	23.4047	1.73966	0.869829	−	0.493354i	$-0.164229\pi$
$181$	23.4047	1.73966	0.869829	+	0.493354i	$0.164229\pi$
$182$	0	0
$183$	11.3069	0.835833
$184$	5.03709	0.371339
$185$	−21.0614	−1.54847
$186$	2.21481	0.162398
$187$	−0.0881460	−0.00644587
$188$	−3.63873	−0.265381
$189$	−1.00000	−0.0727393
$190$	2.88471	0.209279
$191$	−15.4891	−1.12075	−0.560376	−	0.828239i	$-0.689343\pi$
$191$	−15.4891	−1.12075	−0.560376	+	0.828239i	$0.689343\pi$
$192$	1.00000	0.0721688
$193$	10.7419	0.773217	0.386609	−	0.922244i	$-0.373646\pi$
$193$	10.7419	0.773217	0.386609	+	0.922244i	$0.373646\pi$
$194$	−9.69272	−0.695896
$195$	0	0
$196$	1.00000	0.0714286
$197$	1.63996	0.116843	0.0584213	−	0.998292i	$-0.481393\pi$
$197$	1.63996	0.116843	0.0584213	+	0.998292i	$0.481393\pi$
$198$	0.198062	0.0140757
$199$	−12.4549	−0.882907	−0.441454	−	0.897284i	$-0.645537\pi$
$199$	−12.4549	−0.882907	−0.441454	+	0.897284i	$0.645537\pi$
$200$	−3.03217	−0.214407
$201$	−14.5407	−1.02562
$202$	0.496795	0.0349544
$203$	−4.34507	−0.304964
$204$	0.445042	0.0311592
$205$	−1.25693	−0.0877876
$206$	9.61959	0.670228
$207$	−5.03709	−0.350102
$208$	0	0
$209$	−0.201598	−0.0139448
$210$	−2.83411	−0.195572
$211$	−26.3734	−1.81562	−0.907808	−	0.419385i	$-0.862246\pi$
$211$	−26.3734	−1.81562	−0.907808	+	0.419385i	$0.862246\pi$
$212$	6.50916	0.447051
$213$	−5.80083	−0.397466
$214$	10.8776	0.743575
$215$	−21.6734	−1.47811
$216$	−1.00000	−0.0680414
$217$	2.21481	0.150351
$218$	8.51454	0.576677
$219$	0.641997	0.0433822
$220$	0.561330	0.0378449
$221$	0	0
$222$	−7.43142	−0.498764
$223$	−9.07058	−0.607411	−0.303705	−	0.952766i	$-0.598224\pi$
$223$	−9.07058	−0.607411	−0.303705	+	0.952766i	$0.598224\pi$
$224$	1.00000	0.0668153
$225$	3.03217	0.202145
$226$	6.97708	0.464109
$227$	−20.0785	−1.33266	−0.666328	−	0.745659i	$-0.732135\pi$
$227$	−20.0785	−1.33266	−0.666328	+	0.745659i	$0.732135\pi$
$228$	1.01785	0.0674090
$229$	−2.94223	−0.194428	−0.0972141	−	0.995263i	$-0.530993\pi$
$229$	−2.94223	−0.194428	−0.0972141	+	0.995263i	$0.530993\pi$
$230$	−14.2757	−0.941309
$231$	0.198062	0.0130315
$232$	−4.34507	−0.285268
$233$	−11.8698	−0.777614	−0.388807	−	0.921319i	$-0.627113\pi$
$233$	−11.8698	−0.777614	−0.388807	+	0.921319i	$0.627113\pi$
$234$	0	0
$235$	10.3125	0.672716
$236$	−5.45031	−0.354785
$237$	1.67721	0.108947
$238$	0.445042	0.0288478
$239$	21.0447	1.36127	0.680635	−	0.732622i	$-0.261704\pi$
$239$	21.0447	1.36127	0.680635	+	0.732622i	$0.261704\pi$
$240$	−2.83411	−0.182941
$241$	−17.4505	−1.12408	−0.562042	−	0.827109i	$-0.689984\pi$
$241$	−17.4505	−1.12408	−0.562042	+	0.827109i	$0.689984\pi$
$242$	10.9608	0.704585
$243$	1.00000	0.0641500
$244$	11.3069	0.723853
$245$	−2.83411	−0.181065
$246$	−0.443500	−0.0282765
$247$	0	0
$248$	2.21481	0.140641
$249$	−6.42808	−0.407363
$250$	−5.57704	−0.352723
$251$	−6.73221	−0.424934	−0.212467	−	0.977168i	$-0.568150\pi$
$251$	−6.73221	−0.424934	−0.212467	+	0.977168i	$0.568150\pi$
$252$	−1.00000	−0.0629941
$253$	0.997657	0.0627221
$254$	3.64802	0.228897
$255$	−1.26130	−0.0789855
$256$	1.00000	0.0625000
$257$	−13.6497	−0.851446	−0.425723	−	0.904854i	$-0.639980\pi$
$257$	−13.6497	−0.851446	−0.425723	+	0.904854i	$0.639980\pi$
$258$	−7.64733	−0.476102
$259$	−7.43142	−0.461766
$260$	0	0
$261$	4.34507	0.268953
$262$	2.42438	0.149779
$263$	−5.22545	−0.322215	−0.161108	−	0.986937i	$-0.551507\pi$
$263$	−5.22545	−0.322215	−0.161108	+	0.986937i	$0.551507\pi$
$264$	0.198062	0.0121899
$265$	−18.4477	−1.13323
$266$	1.01785	0.0624086
$267$	10.2278	0.625934
$268$	−14.5407	−0.888217
$269$	−17.4972	−1.06683	−0.533413	−	0.845855i	$-0.679091\pi$
$269$	−17.4972	−1.06683	−0.533413	+	0.845855i	$0.679091\pi$
$270$	2.83411	0.172478
$271$	25.9779	1.57804	0.789021	−	0.614366i	$-0.210588\pi$
$271$	25.9779	1.57804	0.789021	+	0.614366i	$0.210588\pi$
$272$	0.445042	0.0269846
$273$	0	0
$274$	21.5583	1.30239
$275$	−0.600559	−0.0362150
$276$	−5.03709	−0.303197
$277$	−7.25383	−0.435840	−0.217920	−	0.975967i	$-0.569927\pi$
$277$	−7.25383	−0.435840	−0.217920	+	0.975967i	$0.569927\pi$
$278$	2.63351	0.157947
$279$	−2.21481	−0.132597
$280$	−2.83411	−0.169370
$281$	−8.97769	−0.535564	−0.267782	−	0.963480i	$-0.586291\pi$
$281$	−8.97769	−0.535564	−0.267782	+	0.963480i	$0.586291\pi$
$282$	3.63873	0.216683
$283$	−11.4182	−0.678740	−0.339370	−	0.940653i	$-0.610214\pi$
$283$	−11.4182	−0.678740	−0.339370	+	0.940653i	$0.610214\pi$
$284$	−5.80083	−0.344216
$285$	−2.88471	−0.170875
$286$	0	0
$287$	−0.443500	−0.0261790
$288$	−1.00000	−0.0589256
$289$	−16.8019	−0.988349
$290$	12.3144	0.723126
$291$	9.69272	0.568197
$292$	0.641997	0.0375701
$293$	0.481985	0.0281579	0.0140789	−	0.999901i	$-0.495518\pi$
$293$	0.481985	0.0281579	0.0140789	+	0.999901i	$0.495518\pi$
$294$	−1.00000	−0.0583212
$295$	15.4468	0.899345
$296$	−7.43142	−0.431942
$297$	−0.198062	−0.0114927
$298$	9.09027	0.526585
$299$	0	0
$300$	3.03217	0.175062
$301$	−7.64733	−0.440785
$302$	−21.2010	−1.21998
$303$	−0.496795	−0.0285401
$304$	1.01785	0.0583779
$305$	−32.0451	−1.83490
$306$	−0.445042	−0.0254414
$307$	12.1290	0.692239	0.346119	−	0.938190i	$-0.387499\pi$
$307$	12.1290	0.692239	0.346119	+	0.938190i	$0.387499\pi$
$308$	0.198062	0.0112856
$309$	−9.61959	−0.547239
$310$	−6.27701	−0.356510
$311$	−30.0623	−1.70468	−0.852338	−	0.522992i	$-0.824816\pi$
$311$	−30.0623	−1.70468	−0.852338	+	0.522992i	$0.824816\pi$
$312$	0	0
$313$	16.6595	0.941648	0.470824	−	0.882227i	$-0.343957\pi$
$313$	16.6595	0.941648	0.470824	+	0.882227i	$0.343957\pi$
$314$	−9.99173	−0.563866
$315$	2.83411	0.159684
$316$	1.67721	0.0943505
$317$	11.1386	0.625605	0.312803	−	0.949818i	$-0.398732\pi$
$317$	11.1386	0.625605	0.312803	+	0.949818i	$0.398732\pi$
$318$	−6.50916	−0.365016
$319$	−0.860594	−0.0481840
$320$	−2.83411	−0.158431
$321$	−10.8776	−0.607127
$322$	−5.03709	−0.280706
$323$	0.452987	0.0252049
$324$	1.00000	0.0555556
$325$	0	0
$326$	3.18547	0.176427
$327$	−8.51454	−0.470855
$328$	−0.443500	−0.0244882
$329$	3.63873	0.200609
$330$	−0.561330	−0.0309002
$331$	−20.8141	−1.14404	−0.572022	−	0.820238i	$-0.693841\pi$
$331$	−20.8141	−1.14404	−0.572022	+	0.820238i	$0.693841\pi$
$332$	−6.42808	−0.352787
$333$	7.43142	0.407239
$334$	−18.5456	−1.01477
$335$	41.2100	2.25154
$336$	−1.00000	−0.0545545
$337$	5.98060	0.325784	0.162892	−	0.986644i	$-0.447918\pi$
$337$	5.98060	0.325784	0.162892	+	0.986644i	$0.447918\pi$
$338$	0	0
$339$	−6.97708	−0.378943
$340$	−1.26130	−0.0684034
$341$	0.438670	0.0237553
$342$	−1.01785	−0.0550392
$343$	−1.00000	−0.0539949
$344$	−7.64733	−0.412317
$345$	14.2757	0.768575
$346$	3.53929	0.190274
$347$	−23.4377	−1.25820	−0.629100	−	0.777324i	$-0.716576\pi$
$347$	−23.4377	−1.25820	−0.629100	+	0.777324i	$0.716576\pi$
$348$	4.34507	0.232920
$349$	0.694217	0.0371606	0.0185803	−	0.999827i	$-0.494085\pi$
$349$	0.694217	0.0371606	0.0185803	+	0.999827i	$0.494085\pi$
$350$	3.03217	0.162076
$351$	0	0
$352$	0.198062	0.0105568
$353$	19.7833	1.05296	0.526480	−	0.850188i	$-0.323512\pi$
$353$	19.7833	1.05296	0.526480	+	0.850188i	$0.323512\pi$
$354$	5.45031	0.289681
$355$	16.4402	0.872554
$356$	10.2278	0.542074
$357$	−0.445042	−0.0235541
$358$	−3.24260	−0.171377
$359$	−30.7362	−1.62219	−0.811097	−	0.584911i	$-0.801129\pi$
$359$	−30.7362	−1.62219	−0.811097	+	0.584911i	$0.801129\pi$
$360$	2.83411	0.149371
$361$	−17.9640	−0.945472
$362$	−23.4047	−1.23012
$363$	−10.9608	−0.575291
$364$	0	0
$365$	−1.81949	−0.0952365
$366$	−11.3069	−0.591023
$367$	−22.0009	−1.14844	−0.574218	−	0.818702i	$-0.694694\pi$
$367$	−22.0009	−1.14844	−0.574218	+	0.818702i	$0.694694\pi$
$368$	−5.03709	−0.262576
$369$	0.443500	0.0230877
$370$	21.0614	1.09493
$371$	−6.50916	−0.337939
$372$	−2.21481	−0.114832
$373$	11.8812	0.615186	0.307593	−	0.951518i	$-0.400476\pi$
$373$	11.8812	0.615186	0.307593	+	0.951518i	$0.400476\pi$
$374$	0.0881460	0.00455792
$375$	5.57704	0.287997
$376$	3.63873	0.187653
$377$	0	0
$378$	1.00000	0.0514344
$379$	2.13559	0.109698	0.0548490	−	0.998495i	$-0.482532\pi$
$379$	2.13559	0.109698	0.0548490	+	0.998495i	$0.482532\pi$
$380$	−2.88471	−0.147982
$381$	−3.64802	−0.186894
$382$	15.4891	0.792491
$383$	−31.0649	−1.58734	−0.793670	−	0.608348i	$-0.791832\pi$
$383$	−31.0649	−1.58734	−0.793670	+	0.608348i	$0.791832\pi$
$384$	−1.00000	−0.0510310
$385$	−0.561330	−0.0286080
$386$	−10.7419	−0.546747
$387$	7.64733	0.388736
$388$	9.69272	0.492073
$389$	32.2971	1.63753	0.818764	−	0.574130i	$-0.194660\pi$
$389$	32.2971	1.63753	0.818764	+	0.574130i	$0.194660\pi$
$390$	0	0
$391$	−2.24171	−0.113368
$392$	−1.00000	−0.0505076
$393$	−2.42438	−0.122294
$394$	−1.63996	−0.0826201
$395$	−4.75340	−0.239169
$396$	−0.198062	−0.00995300
$397$	0.324869	0.0163047	0.00815235	−	0.999967i	$-0.497405\pi$
$397$	0.324869	0.0163047	0.00815235	+	0.999967i	$0.497405\pi$
$398$	12.4549	0.624310
$399$	−1.01785	−0.0509564
$400$	3.03217	0.151609
$401$	−32.5831	−1.62712	−0.813560	−	0.581481i	$-0.802474\pi$
$401$	−32.5831	−1.62712	−0.813560	+	0.581481i	$0.802474\pi$
$402$	14.5407	0.725226
$403$	0	0
$404$	−0.496795	−0.0247165
$405$	−2.83411	−0.140828
$406$	4.34507	0.215642
$407$	−1.47188	−0.0729586
$408$	−0.445042	−0.0220329
$409$	0.898604	0.0444331	0.0222165	−	0.999753i	$-0.492928\pi$
$409$	0.898604	0.0444331	0.0222165	+	0.999753i	$0.492928\pi$
$410$	1.25693	0.0620752
$411$	−21.5583	−1.06339
$412$	−9.61959	−0.473923
$413$	5.45031	0.268192
$414$	5.03709	0.247559
$415$	18.2179	0.894280
$416$	0	0
$417$	−2.63351	−0.128964
$418$	0.201598	0.00986050
$419$	−20.1679	−0.985266	−0.492633	−	0.870237i	$-0.663965\pi$
$419$	−20.1679	−0.985266	−0.492633	+	0.870237i	$0.663965\pi$
$420$	2.83411	0.138290
$421$	3.31432	0.161530	0.0807650	−	0.996733i	$-0.474264\pi$
$421$	3.31432	0.161530	0.0807650	+	0.996733i	$0.474264\pi$
$422$	26.3734	1.28383
$423$	−3.63873	−0.176921
$424$	−6.50916	−0.316113
$425$	1.34944	0.0654576
$426$	5.80083	0.281051
$427$	−11.3069	−0.547181
$428$	−10.8776	−0.525787
$429$	0	0
$430$	21.6734	1.04518
$431$	9.71137	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$431$	9.71137	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$432$	1.00000	0.0481125
$433$	−38.4791	−1.84919	−0.924594	−	0.380955i	$-0.875595\pi$
$433$	−38.4791	−1.84919	−0.924594	+	0.380955i	$0.875595\pi$
$434$	−2.21481	−0.106314
$435$	−12.3144	−0.590430
$436$	−8.51454	−0.407773
$437$	−5.12702	−0.245258
$438$	−0.641997	−0.0306758
$439$	−1.86358	−0.0889437	−0.0444718	−	0.999011i	$-0.514160\pi$
$439$	−1.86358	−0.0889437	−0.0444718	+	0.999011i	$0.514160\pi$
$440$	−0.561330	−0.0267604
$441$	1.00000	0.0476190
$442$	0	0
$443$	−14.9638	−0.710949	−0.355475	−	0.934686i	$-0.615681\pi$
$443$	−14.9638	−0.710949	−0.355475	+	0.934686i	$0.615681\pi$
$444$	7.43142	0.352680
$445$	−28.9868	−1.37411
$446$	9.07058	0.429504
$447$	−9.09027	−0.429955
$448$	−1.00000	−0.0472456
$449$	38.0913	1.79764	0.898821	−	0.438317i	$-0.144425\pi$
$449$	38.0913	1.79764	0.898821	+	0.438317i	$0.144425\pi$
$450$	−3.03217	−0.142938
$451$	−0.0878406	−0.00413625
$452$	−6.97708	−0.328174
$453$	21.2010	0.996110
$454$	20.0785	0.942330
$455$	0	0
$456$	−1.01785	−0.0476654
$457$	−4.68245	−0.219036	−0.109518	−	0.993985i	$-0.534931\pi$
$457$	−4.68245	−0.219036	−0.109518	+	0.993985i	$0.534931\pi$
$458$	2.94223	0.137481
$459$	0.445042	0.0207728
$460$	14.2757	0.665606
$461$	23.2754	1.08405	0.542023	−	0.840364i	$-0.317659\pi$
$461$	23.2754	1.08405	0.542023	+	0.840364i	$0.317659\pi$
$462$	−0.198062	−0.00921469
$463$	−12.3208	−0.572597	−0.286299	−	0.958140i	$-0.592425\pi$
$463$	−12.3208	−0.572597	−0.286299	+	0.958140i	$0.592425\pi$
$464$	4.34507	0.201715
$465$	6.27701	0.291089
$466$	11.8698	0.549856
$467$	−3.26780	−0.151216	−0.0756080	−	0.997138i	$-0.524090\pi$
$467$	−3.26780	−0.151216	−0.0756080	+	0.997138i	$0.524090\pi$
$468$	0	0
$469$	14.5407	0.671429
$470$	−10.3125	−0.475682
$471$	9.99173	0.460395
$472$	5.45031	0.250871
$473$	−1.51465	−0.0696436
$474$	−1.67721	−0.0770369
$475$	3.08631	0.141609
$476$	−0.445042	−0.0203985
$477$	6.50916	0.298034
$478$	−21.0447	−0.962564
$479$	11.2400	0.513568	0.256784	−	0.966469i	$-0.417337\pi$
$479$	11.2400	0.513568	0.256784	+	0.966469i	$0.417337\pi$
$480$	2.83411	0.129359
$481$	0	0
$482$	17.4505	0.794847
$483$	5.03709	0.229195
$484$	−10.9608	−0.498217
$485$	−27.4702	−1.24736
$486$	−1.00000	−0.0453609
$487$	−10.0813	−0.456829	−0.228414	−	0.973564i	$-0.573354\pi$
$487$	−10.0813	−0.456829	−0.228414	+	0.973564i	$0.573354\pi$
$488$	−11.3069	−0.511841
$489$	−3.18547	−0.144052
$490$	2.83411	0.128032
$491$	17.6228	0.795307	0.397654	−	0.917536i	$-0.369825\pi$
$491$	17.6228	0.795307	0.397654	+	0.917536i	$0.369825\pi$
$492$	0.443500	0.0199945
$493$	1.93374	0.0870911
$494$	0	0
$495$	0.561330	0.0252299
$496$	−2.21481	−0.0994479
$497$	5.80083	0.260203
$498$	6.42808	0.288049
$499$	38.6205	1.72889	0.864446	−	0.502726i	$-0.167670\pi$
$499$	38.6205	1.72889	0.864446	+	0.502726i	$0.167670\pi$
$500$	5.57704	0.249413
$501$	18.5456	0.828555
$502$	6.73221	0.300473
$503$	−29.6739	−1.32309	−0.661547	−	0.749904i	$-0.730100\pi$
$503$	−29.6739	−1.32309	−0.661547	+	0.749904i	$0.730100\pi$
$504$	1.00000	0.0445435
$505$	1.40797	0.0626539
$506$	−0.997657	−0.0443513
$507$	0	0
$508$	−3.64802	−0.161855
$509$	−16.8438	−0.746590	−0.373295	−	0.927713i	$-0.621772\pi$
$509$	−16.8438	−0.746590	−0.373295	+	0.927713i	$0.621772\pi$
$510$	1.26130	0.0558512
$511$	−0.641997	−0.0284003
$512$	−1.00000	−0.0441942
$513$	1.01785	0.0449393
$514$	13.6497	0.602063
$515$	27.2630	1.20135
$516$	7.64733	0.336655
$517$	0.720694	0.0316961
$518$	7.43142	0.326518
$519$	−3.53929	−0.155358
$520$	0	0
$521$	−2.68289	−0.117540	−0.0587699	−	0.998272i	$-0.518718\pi$
$521$	−2.68289	−0.117540	−0.0587699	+	0.998272i	$0.518718\pi$
$522$	−4.34507	−0.190178
$523$	12.3515	0.540095	0.270048	−	0.962847i	$-0.412961\pi$
$523$	12.3515	0.540095	0.270048	+	0.962847i	$0.412961\pi$
$524$	−2.42438	−0.105909
$525$	−3.03217	−0.132335
$526$	5.22545	0.227840
$527$	−0.985683	−0.0429370
$528$	−0.198062	−0.00861955
$529$	2.37224	0.103141
$530$	18.4477	0.801316
$531$	−5.45031	−0.236523
$532$	−1.01785	−0.0441295
$533$	0	0
$534$	−10.2278	−0.442602
$535$	30.8282	1.33282
$536$	14.5407	0.628064
$537$	3.24260	0.139929
$538$	17.4972	0.754359
$539$	−0.198062	−0.00853115
$540$	−2.83411	−0.121961
$541$	−40.8196	−1.75497	−0.877487	−	0.479601i	$-0.840782\pi$
$541$	−40.8196	−1.75497	−0.877487	+	0.479601i	$0.840782\pi$
$542$	−25.9779	−1.11584
$543$	23.4047	1.00439
$544$	−0.445042	−0.0190810
$545$	24.1311	1.03366
$546$	0	0
$547$	7.74509	0.331156	0.165578	−	0.986197i	$-0.447051\pi$
$547$	7.74509	0.331156	0.165578	+	0.986197i	$0.447051\pi$
$548$	−21.5583	−0.920927
$549$	11.3069	0.482569
$550$	0.600559	0.0256079
$551$	4.42264	0.188411
$552$	5.03709	0.214393
$553$	−1.67721	−0.0713223
$554$	7.25383	0.308186
$555$	−21.0614	−0.894009
$556$	−2.63351	−0.111686
$557$	−26.9144	−1.14040	−0.570199	−	0.821507i	$-0.693134\pi$
$557$	−26.9144	−1.14040	−0.570199	+	0.821507i	$0.693134\pi$
$558$	2.21481	0.0937603
$559$	0	0
$560$	2.83411	0.119763
$561$	−0.0881460	−0.00372153
$562$	8.97769	0.378701
$563$	31.1150	1.31134	0.655670	−	0.755048i	$-0.272386\pi$
$563$	31.1150	1.31134	0.655670	+	0.755048i	$0.272386\pi$
$564$	−3.63873	−0.153218
$565$	19.7738	0.831890
$566$	11.4182	0.479942
$567$	−1.00000	−0.0419961
$568$	5.80083	0.243397
$569$	−27.4196	−1.14949	−0.574745	−	0.818333i	$-0.694899\pi$
$569$	−27.4196	−1.14949	−0.574745	+	0.818333i	$0.694899\pi$
$570$	2.88471	0.120827
$571$	−8.99728	−0.376524	−0.188262	−	0.982119i	$-0.560285\pi$
$571$	−8.99728	−0.376524	−0.188262	+	0.982119i	$0.560285\pi$
$572$	0	0
$573$	−15.4891	−0.647066
$574$	0.443500	0.0185113
$575$	−15.2733	−0.636941
$576$	1.00000	0.0416667
$577$	−39.9868	−1.66467	−0.832337	−	0.554270i	$-0.812998\pi$
$577$	−39.9868	−1.66467	−0.832337	+	0.554270i	$0.812998\pi$
$578$	16.8019	0.698868
$579$	10.7419	0.446417
$580$	−12.3144	−0.511327
$581$	6.42808	0.266682
$582$	−9.69272	−0.401776
$583$	−1.28922	−0.0533940
$584$	−0.641997	−0.0265660
$585$	0	0
$586$	−0.481985	−0.0199106
$587$	−18.8078	−0.776280	−0.388140	−	0.921600i	$-0.626882\pi$
$587$	−18.8078	−0.776280	−0.388140	+	0.921600i	$0.626882\pi$
$588$	1.00000	0.0412393
$589$	−2.25435	−0.0928889
$590$	−15.4468	−0.635933
$591$	1.63996	0.0674591
$592$	7.43142	0.305429
$593$	−24.5201	−1.00692	−0.503459	−	0.864019i	$-0.667940\pi$
$593$	−24.5201	−1.00692	−0.503459	+	0.864019i	$0.667940\pi$
$594$	0.198062	0.00812659
$595$	1.26130	0.0517081
$596$	−9.09027	−0.372352
$597$	−12.4549	−0.509747
$598$	0	0
$599$	21.7347	0.888056	0.444028	−	0.896013i	$-0.353549\pi$
$599$	21.7347	0.888056	0.444028	+	0.896013i	$0.353549\pi$
$600$	−3.03217	−0.123788
$601$	28.6388	1.16820	0.584100	−	0.811682i	$-0.301448\pi$
$601$	28.6388	1.16820	0.584100	+	0.811682i	$0.301448\pi$
$602$	7.64733	0.311682
$603$	−14.5407	−0.592144
$604$	21.2010	0.862657
$605$	31.0640	1.26293
$606$	0.496795	0.0201809
$607$	−7.42544	−0.301389	−0.150695	−	0.988580i	$-0.548151\pi$
$607$	−7.42544	−0.301389	−0.150695	+	0.988580i	$0.548151\pi$
$608$	−1.01785	−0.0412794
$609$	−4.34507	−0.176071
$610$	32.0451	1.29747
$611$	0	0
$612$	0.445042	0.0179898
$613$	−10.7404	−0.433802	−0.216901	−	0.976194i	$-0.569595\pi$
$613$	−10.7404	−0.433802	−0.216901	+	0.976194i	$0.569595\pi$
$614$	−12.1290	−0.489487
$615$	−1.25693	−0.0506842
$616$	−0.198062	−0.00798016
$617$	−42.1071	−1.69517	−0.847583	−	0.530662i	$-0.821943\pi$
$617$	−42.1071	−1.69517	−0.847583	+	0.530662i	$0.821943\pi$
$618$	9.61959	0.386957
$619$	26.8812	1.08045	0.540224	−	0.841521i	$-0.318339\pi$
$619$	26.8812	1.08045	0.540224	+	0.841521i	$0.318339\pi$
$620$	6.27701	0.252091
$621$	−5.03709	−0.202131
$622$	30.0623	1.20539
$623$	−10.2278	−0.409770
$624$	0	0
$625$	−30.9668	−1.23867
$626$	−16.6595	−0.665846
$627$	−0.201598	−0.00805106
$628$	9.99173	0.398713
$629$	3.30729	0.131870
$630$	−2.83411	−0.112914
$631$	31.2192	1.24282	0.621409	−	0.783487i	$-0.286561\pi$
$631$	31.2192	1.24282	0.621409	+	0.783487i	$0.286561\pi$
$632$	−1.67721	−0.0667159
$633$	−26.3734	−1.04825
$634$	−11.1386	−0.442370
$635$	10.3389	0.410286
$636$	6.50916	0.258105
$637$	0	0
$638$	0.860594	0.0340712
$639$	−5.80083	−0.229477
$640$	2.83411	0.112028
$641$	−35.5823	−1.40542	−0.702709	−	0.711478i	$-0.748026\pi$
$641$	−35.5823	−1.40542	−0.702709	+	0.711478i	$0.748026\pi$
$642$	10.8776	0.429303
$643$	29.8634	1.17770	0.588849	−	0.808243i	$-0.299581\pi$
$643$	29.8634	1.17770	0.588849	+	0.808243i	$0.299581\pi$
$644$	5.03709	0.198489
$645$	−21.6734	−0.853388
$646$	−0.452987	−0.0178226
$647$	33.3922	1.31278	0.656391	−	0.754421i	$-0.272082\pi$
$647$	33.3922	1.31278	0.656391	+	0.754421i	$0.272082\pi$
$648$	−1.00000	−0.0392837
$649$	1.07950	0.0423741
$650$	0	0
$651$	2.21481	0.0868052
$652$	−3.18547	−0.124753
$653$	4.97027	0.194502	0.0972509	−	0.995260i	$-0.468995\pi$
$653$	4.97027	0.194502	0.0972509	+	0.995260i	$0.468995\pi$
$654$	8.51454	0.332945
$655$	6.87095	0.268470
$656$	0.443500	0.0173158
$657$	0.641997	0.0250467
$658$	−3.63873	−0.141852
$659$	30.1774	1.17554	0.587772	−	0.809027i	$-0.300005\pi$
$659$	30.1774	1.17554	0.587772	+	0.809027i	$0.300005\pi$
$660$	0.561330	0.0218497
$661$	26.0514	1.01328	0.506641	−	0.862157i	$-0.330887\pi$
$661$	26.0514	1.01328	0.506641	+	0.862157i	$0.330887\pi$
$662$	20.8141	0.808962
$663$	0	0
$664$	6.42808	0.249458
$665$	2.88471	0.111864
$666$	−7.43142	−0.287962
$667$	−21.8865	−0.847448
$668$	18.5456	0.717550
$669$	−9.07058	−0.350689
$670$	−41.2100	−1.59208
$671$	−2.23948	−0.0864541
$672$	1.00000	0.0385758
$673$	−32.4744	−1.25180	−0.625898	−	0.779905i	$-0.715267\pi$
$673$	−32.4744	−1.25180	−0.625898	+	0.779905i	$0.715267\pi$
$674$	−5.98060	−0.230364
$675$	3.03217	0.116708
$676$	0	0
$677$	24.4172	0.938428	0.469214	−	0.883084i	$-0.344537\pi$
$677$	24.4172	0.938428	0.469214	+	0.883084i	$0.344537\pi$
$678$	6.97708	0.267953
$679$	−9.69272	−0.371972
$680$	1.26130	0.0483685
$681$	−20.0785	−0.769410
$682$	−0.438670	−0.0167975
$683$	−0.310216	−0.0118701	−0.00593505	−	0.999982i	$-0.501889\pi$
$683$	−0.310216	−0.0118701	−0.00593505	+	0.999982i	$0.501889\pi$
$684$	1.01785	0.0389186
$685$	61.0987	2.33446
$686$	1.00000	0.0381802
$687$	−2.94223	−0.112253
$688$	7.64733	0.291552
$689$	0	0
$690$	−14.2757	−0.543465
$691$	−30.0144	−1.14180	−0.570901	−	0.821019i	$-0.693406\pi$
$691$	−30.0144	−1.14180	−0.570901	+	0.821019i	$0.693406\pi$
$692$	−3.53929	−0.134544
$693$	0.198062	0.00752376
$694$	23.4377	0.889682
$695$	7.46365	0.283112
$696$	−4.34507	−0.164699
$697$	0.197376	0.00747615
$698$	−0.694217	−0.0262765
$699$	−11.8698	−0.448956
$700$	−3.03217	−0.114605
$701$	−1.92672	−0.0727712	−0.0363856	−	0.999338i	$-0.511584\pi$
$701$	−1.92672	−0.0727712	−0.0363856	+	0.999338i	$0.511584\pi$
$702$	0	0
$703$	7.56409	0.285285
$704$	−0.198062	−0.00746475
$705$	10.3125	0.388393
$706$	−19.7833	−0.744555
$707$	0.496795	0.0186839
$708$	−5.45031	−0.204835
$709$	−29.3694	−1.10299	−0.551495	−	0.834178i	$-0.685942\pi$
$709$	−29.3694	−1.10299	−0.551495	+	0.834178i	$0.685942\pi$
$710$	−16.4402	−0.616989
$711$	1.67721	0.0629003
$712$	−10.2278	−0.383305
$713$	11.1562	0.417802
$714$	0.445042	0.0166553
$715$	0	0
$716$	3.24260	0.121182
$717$	21.0447	0.785930
$718$	30.7362	1.14706
$719$	−24.8982	−0.928548	−0.464274	−	0.885692i	$-0.653685\pi$
$719$	−24.8982	−0.928548	−0.464274	+	0.885692i	$0.653685\pi$
$720$	−2.83411	−0.105621
$721$	9.61959	0.358252
$722$	17.9640	0.668550
$723$	−17.4505	−0.648990
$724$	23.4047	0.869829
$725$	13.1750	0.489306
$726$	10.9608	0.406792
$727$	26.5085	0.983147	0.491574	−	0.870836i	$-0.336422\pi$
$727$	26.5085	0.983147	0.491574	+	0.870836i	$0.336422\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.81949	0.0673424
$731$	3.40338	0.125879
$732$	11.3069	0.417917
$733$	−14.7617	−0.545235	−0.272618	−	0.962122i	$-0.587889\pi$
$733$	−14.7617	−0.545235	−0.272618	+	0.962122i	$0.587889\pi$
$734$	22.0009	0.812067
$735$	−2.83411	−0.104538
$736$	5.03709	0.185669
$737$	2.87997	0.106085
$738$	−0.443500	−0.0163255
$739$	51.4949	1.89427	0.947135	−	0.320835i	$-0.103964\pi$
$739$	51.4949	1.89427	0.947135	+	0.320835i	$0.103964\pi$
$740$	−21.0614	−0.774234
$741$	0	0
$742$	6.50916	0.238959
$743$	−0.0267377	−0.000980911 0	−0.000490455	−	1.00000i	$-0.500156\pi$
$743$	−0.0267377	−0.000980911 0	−0.000490455		1.00000i	$0.500156\pi$
$744$	2.21481	0.0811988
$745$	25.7628	0.943876
$746$	−11.8812	−0.435002
$747$	−6.42808	−0.235191
$748$	−0.0881460	−0.00322294
$749$	10.8776	0.397458
$750$	−5.57704	−0.203645
$751$	18.8526	0.687941	0.343970	−	0.938980i	$-0.388228\pi$
$751$	18.8526	0.687941	0.343970	+	0.938980i	$0.388228\pi$
$752$	−3.63873	−0.132691
$753$	−6.73221	−0.245335
$754$	0	0
$755$	−60.0860	−2.18675
$756$	−1.00000	−0.0363696
$757$	8.24623	0.299714	0.149857	−	0.988708i	$-0.452119\pi$
$757$	8.24623	0.299714	0.149857	+	0.988708i	$0.452119\pi$
$758$	−2.13559	−0.0775682
$759$	0.997657	0.0362126
$760$	2.88471	0.104639
$761$	0.884412	0.0320599	0.0160300	−	0.999872i	$-0.494897\pi$
$761$	0.884412	0.0320599	0.0160300	+	0.999872i	$0.494897\pi$
$762$	3.64802	0.132154
$763$	8.51454	0.308247
$764$	−15.4891	−0.560376
$765$	−1.26130	−0.0456023
$766$	31.0649	1.12242
$767$	0	0
$768$	1.00000	0.0360844
$769$	26.0436	0.939155	0.469578	−	0.882891i	$-0.344406\pi$
$769$	26.0436	0.939155	0.469578	+	0.882891i	$0.344406\pi$
$770$	0.561330	0.0202289
$771$	−13.6497	−0.491582
$772$	10.7419	0.386609
$773$	−22.3416	−0.803570	−0.401785	−	0.915734i	$-0.631610\pi$
$773$	−22.3416	−0.803570	−0.401785	+	0.915734i	$0.631610\pi$
$774$	−7.64733	−0.274878
$775$	−6.71568	−0.241234
$776$	−9.69272	−0.347948
$777$	−7.43142	−0.266601
$778$	−32.2971	−1.15791
$779$	0.451418	0.0161737
$780$	0	0
$781$	1.14893	0.0411118
$782$	2.24171	0.0801635
$783$	4.34507	0.155280
$784$	1.00000	0.0357143
$785$	−28.3176	−1.01070
$786$	2.42438	0.0864747
$787$	−16.1249	−0.574792	−0.287396	−	0.957812i	$-0.592790\pi$
$787$	−16.1249	−0.574792	−0.287396	+	0.957812i	$0.592790\pi$
$788$	1.63996	0.0584213
$789$	−5.22545	−0.186031
$790$	4.75340	0.169118
$791$	6.97708	0.248077
$792$	0.198062	0.00703784
$793$	0	0
$794$	−0.324869	−0.0115292
$795$	−18.4477	−0.654272
$796$	−12.4549	−0.441454
$797$	−31.8969	−1.12985	−0.564923	−	0.825143i	$-0.691094\pi$
$797$	−31.8969	−1.12985	−0.564923	+	0.825143i	$0.691094\pi$
$798$	1.01785	0.0360316
$799$	−1.61939	−0.0572897
$800$	−3.03217	−0.107203
$801$	10.2278	0.361383
$802$	32.5831	1.15055
$803$	−0.127155	−0.00448722
$804$	−14.5407	−0.512812
$805$	−14.2757	−0.503151
$806$	0	0
$807$	−17.4972	−0.615932
$808$	0.496795	0.0174772
$809$	18.0337	0.634032	0.317016	−	0.948420i	$-0.397319\pi$
$809$	18.0337	0.634032	0.317016	+	0.948420i	$0.397319\pi$
$810$	2.83411	0.0995804
$811$	−45.5552	−1.59966	−0.799830	−	0.600227i	$-0.795077\pi$
$811$	−45.5552	−1.59966	−0.799830	+	0.600227i	$0.795077\pi$
$812$	−4.34507	−0.152482
$813$	25.9779	0.911083
$814$	1.47188	0.0515895
$815$	9.02798	0.316236
$816$	0.445042	0.0155796
$817$	7.78387	0.272323
$818$	−0.898604	−0.0314189
$819$	0	0
$820$	−1.25693	−0.0438938
$821$	−0.104162	−0.00363529	−0.00181764	−	0.999998i	$-0.500579\pi$
$821$	−0.104162	−0.00363529	−0.00181764	+	0.999998i	$0.500579\pi$
$822$	21.5583	0.751934
$823$	−20.2077	−0.704397	−0.352198	−	0.935925i	$-0.614566\pi$
$823$	−20.2077	−0.704397	−0.352198	+	0.935925i	$0.614566\pi$
$824$	9.61959	0.335114
$825$	−0.600559	−0.0209088
$826$	−5.45031	−0.189640
$827$	27.7803	0.966015	0.483008	−	0.875616i	$-0.339544\pi$
$827$	27.7803	0.966015	0.483008	+	0.875616i	$0.339544\pi$
$828$	−5.03709	−0.175051
$829$	−50.2962	−1.74686	−0.873430	−	0.486950i	$-0.838109\pi$
$829$	−50.2962	−1.74686	−0.873430	+	0.486950i	$0.838109\pi$
$830$	−18.2179	−0.632351
$831$	−7.25383	−0.251633
$832$	0	0
$833$	0.445042	0.0154198
$834$	2.63351	0.0911910
$835$	−52.5602	−1.81892
$836$	−0.201598	−0.00697242
$837$	−2.21481	−0.0765550
$838$	20.1679	0.696688
$839$	7.00881	0.241971	0.120986	−	0.992654i	$-0.461395\pi$
$839$	7.00881	0.241971	0.120986	+	0.992654i	$0.461395\pi$
$840$	−2.83411	−0.0977860
$841$	−10.1204	−0.348980
$842$	−3.31432	−0.114219
$843$	−8.97769	−0.309208
$844$	−26.3734	−0.907808
$845$	0	0
$846$	3.63873	0.125102
$847$	10.9608	0.376617
$848$	6.50916	0.223526
$849$	−11.4182	−0.391871
$850$	−1.34944	−0.0462855
$851$	−37.4327	−1.28318
$852$	−5.80083	−0.198733
$853$	−50.7948	−1.73918	−0.869591	−	0.493773i	$-0.835617\pi$
$853$	−50.7948	−1.73918	−0.869591	+	0.493773i	$0.835617\pi$
$854$	11.3069	0.386916
$855$	−2.88471	−0.0986549
$856$	10.8776	0.371788
$857$	33.5289	1.14533	0.572663	−	0.819791i	$-0.305910\pi$
$857$	33.5289	1.14533	0.572663	+	0.819791i	$0.305910\pi$
$858$	0	0
$859$	16.3516	0.557909	0.278954	−	0.960304i	$-0.410012\pi$
$859$	16.3516	0.557909	0.278954	+	0.960304i	$0.410012\pi$
$860$	−21.6734	−0.739056
$861$	−0.443500	−0.0151144
$862$	−9.71137	−0.330771
$863$	3.70831	0.126232	0.0631162	−	0.998006i	$-0.479896\pi$
$863$	3.70831	0.126232	0.0631162	+	0.998006i	$0.479896\pi$
$864$	−1.00000	−0.0340207
$865$	10.0307	0.341055
$866$	38.4791	1.30757
$867$	−16.8019	−0.570624
$868$	2.21481	0.0751755
$869$	−0.332192	−0.0112689
$870$	12.3144	0.417497
$871$	0	0
$872$	8.51454	0.288339
$873$	9.69272	0.328049
$874$	5.12702	0.173424
$875$	−5.57704	−0.188538
$876$	0.641997	0.0216911
$877$	54.7168	1.84766	0.923828	−	0.382809i	$-0.125043\pi$
$877$	54.7168	1.84766	0.923828	+	0.382809i	$0.125043\pi$
$878$	1.86358	0.0628927
$879$	0.481985	0.0162570
$880$	0.561330	0.0189224
$881$	57.8325	1.94843	0.974213	−	0.225632i	$-0.0724446\pi$
$881$	57.8325	1.94843	0.974213	+	0.225632i	$0.0724446\pi$
$882$	−1.00000	−0.0336718
$883$	2.25108	0.0757549	0.0378774	−	0.999282i	$-0.487940\pi$
$883$	2.25108	0.0757549	0.0378774	+	0.999282i	$0.487940\pi$
$884$	0	0
$885$	15.4468	0.519237
$886$	14.9638	0.502717
$887$	36.8882	1.23859	0.619293	−	0.785160i	$-0.287419\pi$
$887$	36.8882	1.23859	0.619293	+	0.785160i	$0.287419\pi$
$888$	−7.43142	−0.249382
$889$	3.64802	0.122351
$890$	28.9868	0.971640
$891$	−0.198062	−0.00663534
$892$	−9.07058	−0.303705
$893$	−3.70369	−0.123939
$894$	9.09027	0.304024
$895$	−9.18989	−0.307184
$896$	1.00000	0.0334077
$897$	0	0
$898$	−38.0913	−1.27112
$899$	−9.62349	−0.320961
$900$	3.03217	0.101072
$901$	2.89685	0.0965081
$902$	0.0878406	0.00292477
$903$	−7.64733	−0.254487
$904$	6.97708	0.232054
$905$	−66.3314	−2.20493
$906$	−21.2010	−0.704356
$907$	−17.3337	−0.575556	−0.287778	−	0.957697i	$-0.592917\pi$
$907$	−17.3337	−0.575556	−0.287778	+	0.957697i	$0.592917\pi$
$908$	−20.0785	−0.666328
$909$	−0.496795	−0.0164776
$910$	0	0
$911$	−21.0683	−0.698023	−0.349011	−	0.937118i	$-0.613483\pi$
$911$	−21.0683	−0.698023	−0.349011	+	0.937118i	$0.613483\pi$
$912$	1.01785	0.0337045
$913$	1.27316	0.0421354
$914$	4.68245	0.154882
$915$	−32.0451	−1.05938
$916$	−2.94223	−0.0972141
$917$	2.42438	0.0800600
$918$	−0.445042	−0.0146886
$919$	3.15373	0.104032	0.0520159	−	0.998646i	$-0.483435\pi$
$919$	3.15373	0.104032	0.0520159	+	0.998646i	$0.483435\pi$
$920$	−14.2757	−0.470654
$921$	12.1290	0.399664
$922$	−23.2754	−0.766536
$923$	0	0
$924$	0.198062	0.00651577
$925$	22.5333	0.740891
$926$	12.3208	0.404887
$927$	−9.61959	−0.315949
$928$	−4.34507	−0.142634
$929$	0.341011	0.0111882	0.00559411	−	0.999984i	$-0.498219\pi$
$929$	0.341011	0.0111882	0.00559411	+	0.999984i	$0.498219\pi$
$930$	−6.27701	−0.205831
$931$	1.01785	0.0333588
$932$	−11.8698	−0.388807
$933$	−30.0623	−0.984195
$934$	3.26780	0.106926
$935$	0.249815	0.00816983
$936$	0	0
$937$	−25.3681	−0.828740	−0.414370	−	0.910109i	$-0.635998\pi$
$937$	−25.3681	−0.828740	−0.414370	+	0.910109i	$0.635998\pi$
$938$	−14.5407	−0.474772
$939$	16.6595	0.543661
$940$	10.3125	0.336358
$941$	48.2127	1.57169	0.785845	−	0.618424i	$-0.212229\pi$
$941$	48.2127	1.57169	0.785845	+	0.618424i	$0.212229\pi$
$942$	−9.99173	−0.325548
$943$	−2.23395	−0.0727474
$944$	−5.45031	−0.177392
$945$	2.83411	0.0921936
$946$	1.51465	0.0492455
$947$	−46.3365	−1.50573	−0.752867	−	0.658173i	$-0.771329\pi$
$947$	−46.3365	−1.50573	−0.752867	+	0.658173i	$0.771329\pi$
$948$	1.67721	0.0544733
$949$	0	0
$950$	−3.08631	−0.100133
$951$	11.1386	0.361193
$952$	0.445042	0.0144239
$953$	−2.30904	−0.0747971	−0.0373986	−	0.999300i	$-0.511907\pi$
$953$	−2.30904	−0.0747971	−0.0373986	+	0.999300i	$0.511907\pi$
$954$	−6.50916	−0.210742
$955$	43.8978	1.42050
$956$	21.0447	0.680635
$957$	−0.860594	−0.0278190
$958$	−11.2400	−0.363148
$959$	21.5583	0.696155
$960$	−2.83411	−0.0914705
$961$	−26.0946	−0.841762
$962$	0	0
$963$	−10.8776	−0.350525
$964$	−17.4505	−0.562042
$965$	−30.4437	−0.980016
$966$	−5.03709	−0.162066
$967$	50.8169	1.63416	0.817081	−	0.576523i	$-0.195591\pi$
$967$	50.8169	1.63416	0.817081	+	0.576523i	$0.195591\pi$
$968$	10.9608	0.352293
$969$	0.452987	0.0145521
$970$	27.4702	0.882015
$971$	32.9502	1.05742	0.528711	−	0.848802i	$-0.322676\pi$
$971$	32.9502	1.05742	0.528711	+	0.848802i	$0.322676\pi$
$972$	1.00000	0.0320750
$973$	2.63351	0.0844264
$974$	10.0813	0.323027
$975$	0	0
$976$	11.3069	0.361926
$977$	−4.75978	−0.152279	−0.0761394	−	0.997097i	$-0.524259\pi$
$977$	−4.75978	−0.152279	−0.0761394	+	0.997097i	$0.524259\pi$
$978$	3.18547	0.101860
$979$	−2.02575	−0.0647432
$980$	−2.83411	−0.0905323
$981$	−8.51454	−0.271848
$982$	−17.6228	−0.562367
$983$	27.2726	0.869861	0.434931	−	0.900464i	$-0.356773\pi$
$983$	27.2726	0.869861	0.434931	+	0.900464i	$0.356773\pi$
$984$	−0.443500	−0.0141383
$985$	−4.64783	−0.148092
$986$	−1.93374	−0.0615827
$987$	3.63873	0.115822
$988$	0	0
$989$	−38.5203	−1.22487
$990$	−0.561330	−0.0178402
$991$	−32.9413	−1.04642	−0.523208	−	0.852205i	$-0.675265\pi$
$991$	−32.9413	−1.04642	−0.523208	+	0.852205i	$0.675265\pi$
$992$	2.21481	0.0703203
$993$	−20.8141	−0.660515
$994$	−5.80083	−0.183991
$995$	35.2987	1.11904
$996$	−6.42808	−0.203681
$997$	−25.7062	−0.814122	−0.407061	−	0.913401i	$-0.633446\pi$
$997$	−25.7062	−0.814122	−0.407061	+	0.913401i	$0.633446\pi$
$998$	−38.6205	−1.22251
$999$	7.43142	0.235120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cr.1.3	✓	6
13.12	even	2		7098.2.a.ct.1.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cr.1.3	✓	6	1.1	even	1	trivial
7098.2.a.ct.1.4	yes	6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.83411 q^{10} -0.198062 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.83411 q^{15} +1.00000 q^{16} +0.445042 q^{17} -1.00000 q^{18} +1.01785 q^{19} -2.83411 q^{20} -1.00000 q^{21} +0.198062 q^{22} -5.03709 q^{23} -1.00000 q^{24} +3.03217 q^{25} +1.00000 q^{27} -1.00000 q^{28} +4.34507 q^{29} +2.83411 q^{30} -2.21481 q^{31} -1.00000 q^{32} -0.198062 q^{33} -0.445042 q^{34} +2.83411 q^{35} +1.00000 q^{36} +7.43142 q^{37} -1.01785 q^{38} +2.83411 q^{40} +0.443500 q^{41} +1.00000 q^{42} +7.64733 q^{43} -0.198062 q^{44} -2.83411 q^{45} +5.03709 q^{46} -3.63873 q^{47} +1.00000 q^{48} +1.00000 q^{49} -3.03217 q^{50} +0.445042 q^{51} +6.50916 q^{53} -1.00000 q^{54} +0.561330 q^{55} +1.00000 q^{56} +1.01785 q^{57} -4.34507 q^{58} -5.45031 q^{59} -2.83411 q^{60} +11.3069 q^{61} +2.21481 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.198062 q^{66} -14.5407 q^{67} +0.445042 q^{68} -5.03709 q^{69} -2.83411 q^{70} -5.80083 q^{71} -1.00000 q^{72} +0.641997 q^{73} -7.43142 q^{74} +3.03217 q^{75} +1.01785 q^{76} +0.198062 q^{77} +1.67721 q^{79} -2.83411 q^{80} +1.00000 q^{81} -0.443500 q^{82} -6.42808 q^{83} -1.00000 q^{84} -1.26130 q^{85} -7.64733 q^{86} +4.34507 q^{87} +0.198062 q^{88} +10.2278 q^{89} +2.83411 q^{90} -5.03709 q^{92} -2.21481 q^{93} +3.63873 q^{94} -2.88471 q^{95} -1.00000 q^{96} +9.69272 q^{97} -1.00000 q^{98} -0.198062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9} + 3 q^{10} - 10 q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 2 q^{17} - 6 q^{18} - 2 q^{19} - 3 q^{20} - 6 q^{21} + 10 q^{22} + 4 q^{23} - 6 q^{24} + 13 q^{25} + 6 q^{27} - 6 q^{28} + 2 q^{29} + 3 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 2 q^{34} + 3 q^{35} + 6 q^{36} - 7 q^{37} + 2 q^{38} + 3 q^{40} - 11 q^{41} + 6 q^{42} - 5 q^{43} - 10 q^{44} - 3 q^{45} - 4 q^{46} - 5 q^{47} + 6 q^{48} + 6 q^{49} - 13 q^{50} + 2 q^{51} - 6 q^{53} - 6 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} - 2 q^{58} - 28 q^{59} - 3 q^{60} + 23 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 10 q^{67} + 2 q^{68} + 4 q^{69} - 3 q^{70} - 21 q^{71} - 6 q^{72} + 7 q^{73} + 7 q^{74} + 13 q^{75} - 2 q^{76} + 10 q^{77} - 14 q^{79} - 3 q^{80} + 6 q^{81} + 11 q^{82} - 17 q^{83} - 6 q^{84} - q^{85} + 5 q^{86} + 2 q^{87} + 10 q^{88} - 17 q^{89} + 3 q^{90} + 4 q^{92} - 9 q^{93} + 5 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9 + 3 * q^10 - 10 * q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 2 * q^17 - 6 * q^18 - 2 * q^19 - 3 * q^20 - 6 * q^21 + 10 * q^22 + 4 * q^23 - 6 * q^24 + 13 * q^25 + 6 * q^27 - 6 * q^28 + 2 * q^29 + 3 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 2 * q^34 + 3 * q^35 + 6 * q^36 - 7 * q^37 + 2 * q^38 + 3 * q^40 - 11 * q^41 + 6 * q^42 - 5 * q^43 - 10 * q^44 - 3 * q^45 - 4 * q^46 - 5 * q^47 + 6 * q^48 + 6 * q^49 - 13 * q^50 + 2 * q^51 - 6 * q^53 - 6 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 - 2 * q^58 - 28 * q^59 - 3 * q^60 + 23 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 10 * q^67 + 2 * q^68 + 4 * q^69 - 3 * q^70 - 21 * q^71 - 6 * q^72 + 7 * q^73 + 7 * q^74 + 13 * q^75 - 2 * q^76 + 10 * q^77 - 14 * q^79 - 3 * q^80 + 6 * q^81 + 11 * q^82 - 17 * q^83 - 6 * q^84 - q^85 + 5 * q^86 + 2 * q^87 + 10 * q^88 - 17 * q^89 + 3 * q^90 + 4 * q^92 - 9 * q^93 + 5 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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