LMFDB - Embedded newform 7098.2.a.cs.1.4

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.8569169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 12x^{4} + 11x^{3} + 44x^{2} - 9x - 41 $ x^6 - 2x^5 - 12x^4 + 11x^3 + 44x^2 - 9*x - 41
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.42783$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.635442 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.635442 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.635442 q^{10} +4.10263 q^{11} -1.00000 q^{12} +1.00000 q^{14} -0.635442 q^{15} +1.00000 q^{16} +6.65759 q^{17} +1.00000 q^{18} -0.625344 q^{19} +0.635442 q^{20} -1.00000 q^{21} +4.10263 q^{22} -1.28651 q^{23} -1.00000 q^{24} -4.59621 q^{25} -1.00000 q^{27} +1.00000 q^{28} +3.80437 q^{29} -0.635442 q^{30} +0.351292 q^{31} +1.00000 q^{32} -4.10263 q^{33} +6.65759 q^{34} +0.635442 q^{35} +1.00000 q^{36} -0.0202540 q^{37} -0.625344 q^{38} +0.635442 q^{40} +8.35703 q^{41} -1.00000 q^{42} -0.594019 q^{43} +4.10263 q^{44} +0.635442 q^{45} -1.28651 q^{46} +0.0638654 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.59621 q^{50} -6.65759 q^{51} +14.0522 q^{53} -1.00000 q^{54} +2.60698 q^{55} +1.00000 q^{56} +0.625344 q^{57} +3.80437 q^{58} +2.59962 q^{59} -0.635442 q^{60} -6.33935 q^{61} +0.351292 q^{62} +1.00000 q^{63} +1.00000 q^{64} -4.10263 q^{66} -7.26714 q^{67} +6.65759 q^{68} +1.28651 q^{69} +0.635442 q^{70} -15.6116 q^{71} +1.00000 q^{72} +6.85298 q^{73} -0.0202540 q^{74} +4.59621 q^{75} -0.625344 q^{76} +4.10263 q^{77} -5.37655 q^{79} +0.635442 q^{80} +1.00000 q^{81} +8.35703 q^{82} +10.1345 q^{83} -1.00000 q^{84} +4.23051 q^{85} -0.594019 q^{86} -3.80437 q^{87} +4.10263 q^{88} -12.7069 q^{89} +0.635442 q^{90} -1.28651 q^{92} -0.351292 q^{93} +0.0638654 q^{94} -0.397370 q^{95} -1.00000 q^{96} -13.1644 q^{97} +1.00000 q^{98} +4.10263 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} + 8 q^{19} - 3 q^{20} - 6 q^{21} - 6 q^{22} - 12 q^{23} - 6 q^{24} + 5 q^{25} - 6 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 7 q^{31} + 6 q^{32} + 6 q^{33} + 10 q^{34} - 3 q^{35} + 6 q^{36} + 3 q^{37} + 8 q^{38} - 3 q^{40} + 3 q^{41} - 6 q^{42} - 3 q^{43} - 6 q^{44} - 3 q^{45} - 12 q^{46} + 29 q^{47} - 6 q^{48} + 6 q^{49} + 5 q^{50} - 10 q^{51} - 12 q^{53} - 6 q^{54} + 29 q^{55} + 6 q^{56} - 8 q^{57} + 4 q^{58} + 2 q^{59} + 3 q^{60} + 13 q^{61} + 7 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{66} + 22 q^{67} + 10 q^{68} + 12 q^{69} - 3 q^{70} + q^{71} + 6 q^{72} + 29 q^{73} + 3 q^{74} - 5 q^{75} + 8 q^{76} - 6 q^{77} - 24 q^{79} - 3 q^{80} + 6 q^{81} + 3 q^{82} + 7 q^{83} - 6 q^{84} + 21 q^{85} - 3 q^{86} - 4 q^{87} - 6 q^{88} - 11 q^{89} - 3 q^{90} - 12 q^{92} - 7 q^{93} + 29 q^{94} + 8 q^{95} - 6 q^{96} - 4 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) \) 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 - 6 * q^11 - 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 + 8 * q^19 - 3 * q^20 - 6 * q^21 - 6 * q^22 - 12 * q^23 - 6 * q^24 + 5 * q^25 - 6 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 7 * q^31 + 6 * q^32 + 6 * q^33 + 10 * q^34 - 3 * q^35 + 6 * q^36 + 3 * q^37 + 8 * q^38 - 3 * q^40 + 3 * q^41 - 6 * q^42 - 3 * q^43 - 6 * q^44 - 3 * q^45 - 12 * q^46 + 29 * q^47 - 6 * q^48 + 6 * q^49 + 5 * q^50 - 10 * q^51 - 12 * q^53 - 6 * q^54 + 29 * q^55 + 6 * q^56 - 8 * q^57 + 4 * q^58 + 2 * q^59 + 3 * q^60 + 13 * q^61 + 7 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^66 + 22 * q^67 + 10 * q^68 + 12 * q^69 - 3 * q^70 + q^71 + 6 * q^72 + 29 * q^73 + 3 * q^74 - 5 * q^75 + 8 * q^76 - 6 * q^77 - 24 * q^79 - 3 * q^80 + 6 * q^81 + 3 * q^82 + 7 * q^83 - 6 * q^84 + 21 * q^85 - 3 * q^86 - 4 * q^87 - 6 * q^88 - 11 * q^89 - 3 * q^90 - 12 * q^92 - 7 * q^93 + 29 * q^94 + 8 * q^95 - 6 * q^96 - 4 * q^97 + 6 * q^98 - 6 * 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
$5$	0.635442	0.284178	0.142089	−	0.989854i	$-0.454618\pi$
$5$	0.635442	0.284178	0.142089	+	0.989854i	$0.454618\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.635442	0.200944
$11$	4.10263	1.23699	0.618495	−	0.785789i	$-0.287743\pi$
$11$	4.10263	1.23699	0.618495	+	0.785789i	$0.287743\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−0.635442	−0.164070
$16$	1.00000	0.250000
$17$	6.65759	1.61470	0.807351	−	0.590071i	$-0.200900\pi$
$17$	6.65759	1.61470	0.807351	+	0.590071i	$0.200900\pi$
$18$	1.00000	0.235702
$19$	−0.625344	−0.143464	−0.0717319	−	0.997424i	$-0.522853\pi$
$19$	−0.625344	−0.143464	−0.0717319	+	0.997424i	$0.522853\pi$
$20$	0.635442	0.142089
$21$	−1.00000	−0.218218
$22$	4.10263	0.874684
$23$	−1.28651	−0.268256	−0.134128	−	0.990964i	$-0.542823\pi$
$23$	−1.28651	−0.268256	−0.134128	+	0.990964i	$0.542823\pi$
$24$	−1.00000	−0.204124
$25$	−4.59621	−0.919243
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	3.80437	0.706454	0.353227	−	0.935538i	$-0.385084\pi$
$29$	3.80437	0.706454	0.353227	+	0.935538i	$0.385084\pi$
$30$	−0.635442	−0.116015
$31$	0.351292	0.0630939	0.0315469	−	0.999502i	$-0.489957\pi$
$31$	0.351292	0.0630939	0.0315469	+	0.999502i	$0.489957\pi$
$32$	1.00000	0.176777
$33$	−4.10263	−0.714176
$34$	6.65759	1.14177
$35$	0.635442	0.107409
$36$	1.00000	0.166667
$37$	−0.0202540	−0.00332973	−0.00166487	−	0.999999i	$-0.500530\pi$
$37$	−0.0202540	−0.00332973	−0.00166487	+	0.999999i	$0.500530\pi$
$38$	−0.625344	−0.101444
$39$	0	0
$40$	0.635442	0.100472
$41$	8.35703	1.30515	0.652574	−	0.757725i	$-0.273689\pi$
$41$	8.35703	1.30515	0.652574	+	0.757725i	$0.273689\pi$
$42$	−1.00000	−0.154303
$43$	−0.594019	−0.0905871	−0.0452936	−	0.998974i	$-0.514422\pi$
$43$	−0.594019	−0.0905871	−0.0452936	+	0.998974i	$0.514422\pi$
$44$	4.10263	0.618495
$45$	0.635442	0.0947261
$46$	−1.28651	−0.189686
$47$	0.0638654	0.00931573	0.00465786	−	0.999989i	$-0.498517\pi$
$47$	0.0638654	0.00931573	0.00465786	+	0.999989i	$0.498517\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.59621	−0.650003
$51$	−6.65759	−0.932249
$52$	0	0
$53$	14.0522	1.93021	0.965107	−	0.261857i	$-0.0843349\pi$
$53$	14.0522	1.93021	0.965107	+	0.261857i	$0.0843349\pi$
$54$	−1.00000	−0.136083
$55$	2.60698	0.351526
$56$	1.00000	0.133631
$57$	0.625344	0.0828289
$58$	3.80437	0.499539
$59$	2.59962	0.338442	0.169221	−	0.985578i	$-0.445875\pi$
$59$	2.59962	0.338442	0.169221	+	0.985578i	$0.445875\pi$
$60$	−0.635442	−0.0820352
$61$	−6.33935	−0.811670	−0.405835	−	0.913946i	$-0.633019\pi$
$61$	−6.33935	−0.811670	−0.405835	+	0.913946i	$0.633019\pi$
$62$	0.351292	0.0446141
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.10263	−0.504999
$67$	−7.26714	−0.887823	−0.443911	−	0.896071i	$-0.646409\pi$
$67$	−7.26714	−0.887823	−0.443911	+	0.896071i	$0.646409\pi$
$68$	6.65759	0.807351
$69$	1.28651	0.154878
$70$	0.635442	0.0759499
$71$	−15.6116	−1.85275	−0.926377	−	0.376598i	$-0.877094\pi$
$71$	−15.6116	−1.85275	−0.926377	+	0.376598i	$0.877094\pi$
$72$	1.00000	0.117851
$73$	6.85298	0.802080	0.401040	−	0.916061i	$-0.368649\pi$
$73$	6.85298	0.802080	0.401040	+	0.916061i	$0.368649\pi$
$74$	−0.0202540	−0.00235448
$75$	4.59621	0.530725
$76$	−0.625344	−0.0717319
$77$	4.10263	0.467538
$78$	0	0
$79$	−5.37655	−0.604909	−0.302454	−	0.953164i	$-0.597806\pi$
$79$	−5.37655	−0.604909	−0.302454	+	0.953164i	$0.597806\pi$
$80$	0.635442	0.0710446
$81$	1.00000	0.111111
$82$	8.35703	0.922880
$83$	10.1345	1.11241	0.556205	−	0.831045i	$-0.312257\pi$
$83$	10.1345	1.11241	0.556205	+	0.831045i	$0.312257\pi$
$84$	−1.00000	−0.109109
$85$	4.23051	0.458863
$86$	−0.594019	−0.0640548
$87$	−3.80437	−0.407872
$88$	4.10263	0.437342
$89$	−12.7069	−1.34693	−0.673463	−	0.739221i	$-0.735194\pi$
$89$	−12.7069	−1.34693	−0.673463	+	0.739221i	$0.735194\pi$
$90$	0.635442	0.0669815
$91$	0	0
$92$	−1.28651	−0.134128
$93$	−0.351292	−0.0364273
$94$	0.0638654	0.00658721
$95$	−0.397370	−0.0407693
$96$	−1.00000	−0.102062
$97$	−13.1644	−1.33664	−0.668322	−	0.743873i	$-0.732987\pi$
$97$	−13.1644	−1.33664	−0.668322	+	0.743873i	$0.732987\pi$
$98$	1.00000	0.101015
$99$	4.10263	0.412330
$100$	−4.59621	−0.459621
$101$	13.2011	1.31356	0.656781	−	0.754081i	$-0.271918\pi$
$101$	13.2011	1.31356	0.656781	+	0.754081i	$0.271918\pi$
$102$	−6.65759	−0.659199
$103$	8.87814	0.874789	0.437395	−	0.899270i	$-0.355901\pi$
$103$	8.87814	0.874789	0.437395	+	0.899270i	$0.355901\pi$
$104$	0	0
$105$	−0.635442	−0.0620128
$106$	14.0522	1.36487
$107$	−8.17126	−0.789946	−0.394973	−	0.918693i	$-0.629246\pi$
$107$	−8.17126	−0.789946	−0.394973	+	0.918693i	$0.629246\pi$
$108$	−1.00000	−0.0962250
$109$	11.5772	1.10890	0.554448	−	0.832219i	$-0.312930\pi$
$109$	11.5772	1.10890	0.554448	+	0.832219i	$0.312930\pi$
$110$	2.60698	0.248566
$111$	0.0202540	0.00192242
$112$	1.00000	0.0944911
$113$	−2.98116	−0.280444	−0.140222	−	0.990120i	$-0.544782\pi$
$113$	−2.98116	−0.280444	−0.140222	+	0.990120i	$0.544782\pi$
$114$	0.625344	0.0585688
$115$	−0.817502	−0.0762325
$116$	3.80437	0.353227
$117$	0	0
$118$	2.59962	0.239315
$119$	6.65759	0.610300
$120$	−0.635442	−0.0580077
$121$	5.83158	0.530143
$122$	−6.33935	−0.573938
$123$	−8.35703	−0.753528
$124$	0.351292	0.0315469
$125$	−6.09784	−0.545407
$126$	1.00000	0.0890871
$127$	−11.8250	−1.04930	−0.524648	−	0.851319i	$-0.675803\pi$
$127$	−11.8250	−1.04930	−0.524648	+	0.851319i	$0.675803\pi$
$128$	1.00000	0.0883883
$129$	0.594019	0.0523005
$130$	0	0
$131$	−0.845553	−0.0738763	−0.0369381	−	0.999318i	$-0.511760\pi$
$131$	−0.845553	−0.0738763	−0.0369381	+	0.999318i	$0.511760\pi$
$132$	−4.10263	−0.357088
$133$	−0.625344	−0.0542242
$134$	−7.26714	−0.627785
$135$	−0.635442	−0.0546901
$136$	6.65759	0.570883
$137$	−1.78618	−0.152603	−0.0763017	−	0.997085i	$-0.524311\pi$
$137$	−1.78618	−0.152603	−0.0763017	+	0.997085i	$0.524311\pi$
$138$	1.28651	0.109515
$139$	4.16710	0.353449	0.176724	−	0.984260i	$-0.443450\pi$
$139$	4.16710	0.353449	0.176724	+	0.984260i	$0.443450\pi$
$140$	0.635442	0.0537047
$141$	−0.0638654	−0.00537844
$142$	−15.6116	−1.31009
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.41746	0.200759
$146$	6.85298	0.567156
$147$	−1.00000	−0.0824786
$148$	−0.0202540	−0.00166487
$149$	−6.79403	−0.556589	−0.278294	−	0.960496i	$-0.589769\pi$
$149$	−6.79403	−0.556589	−0.278294	+	0.960496i	$0.589769\pi$
$150$	4.59621	0.375279
$151$	5.43882	0.442605	0.221302	−	0.975205i	$-0.428969\pi$
$151$	5.43882	0.442605	0.221302	+	0.975205i	$0.428969\pi$
$152$	−0.625344	−0.0507221
$153$	6.65759	0.538234
$154$	4.10263	0.330599
$155$	0.223226	0.0179299
$156$	0	0
$157$	−17.8985	−1.42845	−0.714227	−	0.699915i	$-0.753221\pi$
$157$	−17.8985	−1.42845	−0.714227	+	0.699915i	$0.753221\pi$
$158$	−5.37655	−0.427735
$159$	−14.0522	−1.11441
$160$	0.635442	0.0502361
$161$	−1.28651	−0.101391
$162$	1.00000	0.0785674
$163$	6.41932	0.502800	0.251400	−	0.967883i	$-0.419109\pi$
$163$	6.41932	0.502800	0.251400	+	0.967883i	$0.419109\pi$
$164$	8.35703	0.652574
$165$	−2.60698	−0.202953
$166$	10.1345	0.786593
$167$	17.0892	1.32240	0.661199	−	0.750210i	$-0.270048\pi$
$167$	17.0892	1.32240	0.661199	+	0.750210i	$0.270048\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	4.23051	0.324465
$171$	−0.625344	−0.0478213
$172$	−0.594019	−0.0452936
$173$	6.52599	0.496162	0.248081	−	0.968739i	$-0.420200\pi$
$173$	6.52599	0.496162	0.248081	+	0.968739i	$0.420200\pi$
$174$	−3.80437	−0.288409
$175$	−4.59621	−0.347441
$176$	4.10263	0.309247
$177$	−2.59962	−0.195400
$178$	−12.7069	−0.952421
$179$	18.4815	1.38137	0.690685	−	0.723156i	$-0.257309\pi$
$179$	18.4815	1.38137	0.690685	+	0.723156i	$0.257309\pi$
$180$	0.635442	0.0473631
$181$	−13.6239	−1.01266	−0.506329	−	0.862340i	$-0.668998\pi$
$181$	−13.6239	−1.01266	−0.506329	+	0.862340i	$0.668998\pi$
$182$	0	0
$183$	6.33935	0.468618
$184$	−1.28651	−0.0948428
$185$	−0.0128702	−0.000946238 0
$186$	−0.351292	−0.0257580
$187$	27.3136	1.99737
$188$	0.0638654	0.00465786
$189$	−1.00000	−0.0727393
$190$	−0.397370	−0.0288282
$191$	−22.5785	−1.63372	−0.816862	−	0.576833i	$-0.804288\pi$
$191$	−22.5785	−1.63372	−0.816862	+	0.576833i	$0.804288\pi$
$192$	−1.00000	−0.0721688
$193$	−21.0445	−1.51481	−0.757407	−	0.652943i	$-0.773534\pi$
$193$	−21.0445	−1.51481	−0.757407	+	0.652943i	$0.773534\pi$
$194$	−13.1644	−0.945149
$195$	0	0
$196$	1.00000	0.0714286
$197$	−0.318174	−0.0226690	−0.0113345	−	0.999936i	$-0.503608\pi$
$197$	−0.318174	−0.0226690	−0.0113345	+	0.999936i	$0.503608\pi$
$198$	4.10263	0.291561
$199$	13.4406	0.952778	0.476389	−	0.879235i	$-0.341945\pi$
$199$	13.4406	0.952778	0.476389	+	0.879235i	$0.341945\pi$
$200$	−4.59621	−0.325001
$201$	7.26714	0.512585
$202$	13.2011	0.928829
$203$	3.80437	0.267015
$204$	−6.65759	−0.466124
$205$	5.31041	0.370895
$206$	8.87814	0.618569
$207$	−1.28651	−0.0894186
$208$	0	0
$209$	−2.56556	−0.177463
$210$	−0.635442	−0.0438497
$211$	9.28125	0.638948	0.319474	−	0.947595i	$-0.396494\pi$
$211$	9.28125	0.638948	0.319474	+	0.947595i	$0.396494\pi$
$212$	14.0522	0.965107
$213$	15.6116	1.06969
$214$	−8.17126	−0.558576
$215$	−0.377465	−0.0257429
$216$	−1.00000	−0.0680414
$217$	0.351292	0.0238473
$218$	11.5772	0.784107
$219$	−6.85298	−0.463081
$220$	2.60698	0.175763
$221$	0	0
$222$	0.0202540	0.00135936
$223$	15.4949	1.03762	0.518808	−	0.854891i	$-0.326376\pi$
$223$	15.4949	1.03762	0.518808	+	0.854891i	$0.326376\pi$
$224$	1.00000	0.0668153
$225$	−4.59621	−0.306414
$226$	−2.98116	−0.198304
$227$	−2.84980	−0.189148	−0.0945740	−	0.995518i	$-0.530149\pi$
$227$	−2.84980	−0.189148	−0.0945740	+	0.995518i	$0.530149\pi$
$228$	0.625344	0.0414144
$229$	12.5456	0.829036	0.414518	−	0.910041i	$-0.363950\pi$
$229$	12.5456	0.829036	0.414518	+	0.910041i	$0.363950\pi$
$230$	−0.817502	−0.0539045
$231$	−4.10263	−0.269933
$232$	3.80437	0.249769
$233$	6.33236	0.414847	0.207423	−	0.978251i	$-0.433492\pi$
$233$	6.33236	0.414847	0.207423	+	0.978251i	$0.433492\pi$
$234$	0	0
$235$	0.0405828	0.00264733
$236$	2.59962	0.169221
$237$	5.37655	0.349244
$238$	6.65759	0.431547
$239$	11.8712	0.767881	0.383940	−	0.923358i	$-0.374567\pi$
$239$	11.8712	0.767881	0.383940	+	0.923358i	$0.374567\pi$
$240$	−0.635442	−0.0410176
$241$	15.4614	0.995953	0.497977	−	0.867190i	$-0.334076\pi$
$241$	15.4614	0.995953	0.497977	+	0.867190i	$0.334076\pi$
$242$	5.83158	0.374868
$243$	−1.00000	−0.0641500
$244$	−6.33935	−0.405835
$245$	0.635442	0.0405969
$246$	−8.35703	−0.532825
$247$	0	0
$248$	0.351292	0.0223071
$249$	−10.1345	−0.642250
$250$	−6.09784	−0.385661
$251$	1.75448	0.110742	0.0553708	−	0.998466i	$-0.482366\pi$
$251$	1.75448	0.110742	0.0553708	+	0.998466i	$0.482366\pi$
$252$	1.00000	0.0629941
$253$	−5.27807	−0.331830
$254$	−11.8250	−0.741964
$255$	−4.23051	−0.264925
$256$	1.00000	0.0625000
$257$	26.5519	1.65626	0.828130	−	0.560537i	$-0.189405\pi$
$257$	26.5519	1.65626	0.828130	+	0.560537i	$0.189405\pi$
$258$	0.594019	0.0369820
$259$	−0.0202540	−0.00125852
$260$	0	0
$261$	3.80437	0.235485
$262$	−0.845553	−0.0522384
$263$	−15.4606	−0.953343	−0.476671	−	0.879082i	$-0.658157\pi$
$263$	−15.4606	−0.953343	−0.476671	+	0.879082i	$0.658157\pi$
$264$	−4.10263	−0.252499
$265$	8.92934	0.548525
$266$	−0.625344	−0.0383423
$267$	12.7069	0.777649
$268$	−7.26714	−0.443911
$269$	−1.87824	−0.114518	−0.0572592	−	0.998359i	$-0.518236\pi$
$269$	−1.87824	−0.114518	−0.0572592	+	0.998359i	$0.518236\pi$
$270$	−0.635442	−0.0386718
$271$	23.3701	1.41963	0.709816	−	0.704387i	$-0.248778\pi$
$271$	23.3701	1.41963	0.709816	+	0.704387i	$0.248778\pi$
$272$	6.65759	0.403676
$273$	0	0
$274$	−1.78618	−0.107907
$275$	−18.8566	−1.13709
$276$	1.28651	0.0774388
$277$	11.1022	0.667066	0.333533	−	0.942738i	$-0.391759\pi$
$277$	11.1022	0.667066	0.333533	+	0.942738i	$0.391759\pi$
$278$	4.16710	0.249926
$279$	0.351292	0.0210313
$280$	0.635442	0.0379749
$281$	18.7670	1.11954	0.559772	−	0.828647i	$-0.310889\pi$
$281$	18.7670	1.11954	0.559772	+	0.828647i	$0.310889\pi$
$282$	−0.0638654	−0.00380313
$283$	−18.4052	−1.09407	−0.547036	−	0.837109i	$-0.684244\pi$
$283$	−18.4052	−1.09407	−0.547036	+	0.837109i	$0.684244\pi$
$284$	−15.6116	−0.926377
$285$	0.397370	0.0235382
$286$	0	0
$287$	8.35703	0.493300
$288$	1.00000	0.0589256
$289$	27.3235	1.60726
$290$	2.41746	0.141958
$291$	13.1644	0.771711
$292$	6.85298	0.401040
$293$	−20.7932	−1.21475	−0.607376	−	0.794415i	$-0.707778\pi$
$293$	−20.7932	−1.21475	−0.607376	+	0.794415i	$0.707778\pi$
$294$	−1.00000	−0.0583212
$295$	1.65191	0.0961779
$296$	−0.0202540	−0.00117724
$297$	−4.10263	−0.238059
$298$	−6.79403	−0.393568
$299$	0	0
$300$	4.59621	0.265363
$301$	−0.594019	−0.0342387
$302$	5.43882	0.312969
$303$	−13.2011	−0.758386
$304$	−0.625344	−0.0358659
$305$	−4.02829	−0.230659
$306$	6.65759	0.380589
$307$	20.1760	1.15150	0.575752	−	0.817624i	$-0.304709\pi$
$307$	20.1760	1.15150	0.575752	+	0.817624i	$0.304709\pi$
$308$	4.10263	0.233769
$309$	−8.87814	−0.505060
$310$	0.223226	0.0126784
$311$	14.9136	0.845671	0.422836	−	0.906206i	$-0.361035\pi$
$311$	14.9136	0.845671	0.422836	+	0.906206i	$0.361035\pi$
$312$	0	0
$313$	2.80693	0.158657	0.0793285	−	0.996849i	$-0.474722\pi$
$313$	2.80693	0.158657	0.0793285	+	0.996849i	$0.474722\pi$
$314$	−17.8985	−1.01007
$315$	0.635442	0.0358031
$316$	−5.37655	−0.302454
$317$	24.9731	1.40263	0.701315	−	0.712851i	$-0.252597\pi$
$317$	24.9731	1.40263	0.701315	+	0.712851i	$0.252597\pi$
$318$	−14.0522	−0.788006
$319$	15.6079	0.873877
$320$	0.635442	0.0355223
$321$	8.17126	0.456075
$322$	−1.28651	−0.0716944
$323$	−4.16328	−0.231651
$324$	1.00000	0.0555556
$325$	0	0
$326$	6.41932	0.355533
$327$	−11.5772	−0.640221
$328$	8.35703	0.461440
$329$	0.0638654	0.00352101
$330$	−2.60698	−0.143510
$331$	8.15503	0.448241	0.224121	−	0.974561i	$-0.428049\pi$
$331$	8.15503	0.448241	0.224121	+	0.974561i	$0.428049\pi$
$332$	10.1345	0.556205
$333$	−0.0202540	−0.00110991
$334$	17.0892	0.935077
$335$	−4.61785	−0.252300
$336$	−1.00000	−0.0545545
$337$	29.3296	1.59769	0.798843	−	0.601540i	$-0.205446\pi$
$337$	29.3296	1.59769	0.798843	+	0.601540i	$0.205446\pi$
$338$	0	0
$339$	2.98116	0.161914
$340$	4.23051	0.229432
$341$	1.44122	0.0780465
$342$	−0.625344	−0.0338147
$343$	1.00000	0.0539949
$344$	−0.594019	−0.0320274
$345$	0.817502	0.0440129
$346$	6.52599	0.350840
$347$	−21.1061	−1.13303	−0.566516	−	0.824051i	$-0.691709\pi$
$347$	−21.1061	−1.13303	−0.566516	+	0.824051i	$0.691709\pi$
$348$	−3.80437	−0.203936
$349$	23.7028	1.26878	0.634391	−	0.773013i	$-0.281251\pi$
$349$	23.7028	1.26878	0.634391	+	0.773013i	$0.281251\pi$
$350$	−4.59621	−0.245678
$351$	0	0
$352$	4.10263	0.218671
$353$	−27.5037	−1.46388	−0.731938	−	0.681372i	$-0.761384\pi$
$353$	−27.5037	−1.46388	−0.731938	+	0.681372i	$0.761384\pi$
$354$	−2.59962	−0.138168
$355$	−9.92025	−0.526512
$356$	−12.7069	−0.673463
$357$	−6.65759	−0.352357
$358$	18.4815	0.976776
$359$	−6.81905	−0.359896	−0.179948	−	0.983676i	$-0.557593\pi$
$359$	−6.81905	−0.359896	−0.179948	+	0.983676i	$0.557593\pi$
$360$	0.635442	0.0334907
$361$	−18.6089	−0.979418
$362$	−13.6239	−0.716058
$363$	−5.83158	−0.306078
$364$	0	0
$365$	4.35467	0.227934
$366$	6.33935	0.331363
$367$	13.2117	0.689646	0.344823	−	0.938668i	$-0.387939\pi$
$367$	13.2117	0.689646	0.344823	+	0.938668i	$0.387939\pi$
$368$	−1.28651	−0.0670640
$369$	8.35703	0.435050
$370$	−0.0128702	−0.000669091 0
$371$	14.0522	0.729552
$372$	−0.351292	−0.0182136
$373$	−33.4216	−1.73051	−0.865253	−	0.501335i	$-0.832842\pi$
$373$	−33.4216	−1.73051	−0.865253	+	0.501335i	$0.832842\pi$
$374$	27.3136	1.41235
$375$	6.09784	0.314891
$376$	0.0638654	0.00329361
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−28.8115	−1.47995	−0.739974	−	0.672636i	$-0.765162\pi$
$379$	−28.8115	−1.47995	−0.739974	+	0.672636i	$0.765162\pi$
$380$	−0.397370	−0.0203846
$381$	11.8250	0.605811
$382$	−22.5785	−1.15522
$383$	−2.65802	−0.135819	−0.0679093	−	0.997691i	$-0.521633\pi$
$383$	−2.65802	−0.135819	−0.0679093	+	0.997691i	$0.521633\pi$
$384$	−1.00000	−0.0510310
$385$	2.60698	0.132864
$386$	−21.0445	−1.07114
$387$	−0.594019	−0.0301957
$388$	−13.1644	−0.668322
$389$	−9.05857	−0.459288	−0.229644	−	0.973275i	$-0.573756\pi$
$389$	−9.05857	−0.459288	−0.229644	+	0.973275i	$0.573756\pi$
$390$	0	0
$391$	−8.56505	−0.433153
$392$	1.00000	0.0505076
$393$	0.845553	0.0426525
$394$	−0.318174	−0.0160294
$395$	−3.41648	−0.171902
$396$	4.10263	0.206165
$397$	26.1070	1.31027	0.655135	−	0.755511i	$-0.272612\pi$
$397$	26.1070	1.31027	0.655135	+	0.755511i	$0.272612\pi$
$398$	13.4406	0.673716
$399$	0.625344	0.0313064
$400$	−4.59621	−0.229811
$401$	38.1909	1.90716	0.953580	−	0.301139i	$-0.0973668\pi$
$401$	38.1909	1.90716	0.953580	+	0.301139i	$0.0973668\pi$
$402$	7.26714	0.362452
$403$	0	0
$404$	13.2011	0.656781
$405$	0.635442	0.0315754
$406$	3.80437	0.188808
$407$	−0.0830946	−0.00411885
$408$	−6.65759	−0.329600
$409$	−30.7382	−1.51990	−0.759952	−	0.649979i	$-0.774778\pi$
$409$	−30.7382	−1.51990	−0.759952	+	0.649979i	$0.774778\pi$
$410$	5.31041	0.262262
$411$	1.78618	0.0881057
$412$	8.87814	0.437395
$413$	2.59962	0.127919
$414$	−1.28651	−0.0632285
$415$	6.43991	0.316123
$416$	0	0
$417$	−4.16710	−0.204064
$418$	−2.56556	−0.125485
$419$	−4.78334	−0.233682	−0.116841	−	0.993151i	$-0.537277\pi$
$419$	−4.78334	−0.233682	−0.116841	+	0.993151i	$0.537277\pi$
$420$	−0.635442	−0.0310064
$421$	−13.8582	−0.675408	−0.337704	−	0.941252i	$-0.609650\pi$
$421$	−13.8582	−0.675408	−0.337704	+	0.941252i	$0.609650\pi$
$422$	9.28125	0.451804
$423$	0.0638654	0.00310524
$424$	14.0522	0.682433
$425$	−30.5997	−1.48430
$426$	15.6116	0.756384
$427$	−6.33935	−0.306783
$428$	−8.17126	−0.394973
$429$	0	0
$430$	−0.377465	−0.0182030
$431$	−17.3630	−0.836348	−0.418174	−	0.908367i	$-0.637330\pi$
$431$	−17.3630	−0.836348	−0.418174	+	0.908367i	$0.637330\pi$
$432$	−1.00000	−0.0481125
$433$	−1.82159	−0.0875400	−0.0437700	−	0.999042i	$-0.513937\pi$
$433$	−1.82159	−0.0875400	−0.0437700	+	0.999042i	$0.513937\pi$
$434$	0.351292	0.0168626
$435$	−2.41746	−0.115908
$436$	11.5772	0.554448
$437$	0.804511	0.0384850
$438$	−6.85298	−0.327448
$439$	−6.59142	−0.314591	−0.157296	−	0.987552i	$-0.550278\pi$
$439$	−6.59142	−0.314591	−0.157296	+	0.987552i	$0.550278\pi$
$440$	2.60698	0.124283
$441$	1.00000	0.0476190
$442$	0	0
$443$	−9.29816	−0.441769	−0.220884	−	0.975300i	$-0.570894\pi$
$443$	−9.29816	−0.441769	−0.220884	+	0.975300i	$0.570894\pi$
$444$	0.0202540	0.000961211 0
$445$	−8.07449	−0.382767
$446$	15.4949	0.733706
$447$	6.79403	0.321347
$448$	1.00000	0.0472456
$449$	−10.8177	−0.510519	−0.255259	−	0.966873i	$-0.582161\pi$
$449$	−10.8177	−0.510519	−0.255259	+	0.966873i	$0.582161\pi$
$450$	−4.59621	−0.216668
$451$	34.2858	1.61446
$452$	−2.98116	−0.140222
$453$	−5.43882	−0.255538
$454$	−2.84980	−0.133748
$455$	0	0
$456$	0.625344	0.0292844
$457$	35.0327	1.63876	0.819381	−	0.573249i	$-0.194317\pi$
$457$	35.0327	1.63876	0.819381	+	0.573249i	$0.194317\pi$
$458$	12.5456	0.586217
$459$	−6.65759	−0.310750
$460$	−0.817502	−0.0381162
$461$	−1.69987	−0.0791709	−0.0395855	−	0.999216i	$-0.512604\pi$
$461$	−1.69987	−0.0791709	−0.0395855	+	0.999216i	$0.512604\pi$
$462$	−4.10263	−0.190872
$463$	36.4266	1.69289	0.846444	−	0.532477i	$-0.178739\pi$
$463$	36.4266	1.69289	0.846444	+	0.532477i	$0.178739\pi$
$464$	3.80437	0.176614
$465$	−0.223226	−0.0103518
$466$	6.33236	0.293341
$467$	−8.42113	−0.389683	−0.194842	−	0.980835i	$-0.562419\pi$
$467$	−8.42113	−0.389683	−0.194842	+	0.980835i	$0.562419\pi$
$468$	0	0
$469$	−7.26714	−0.335565
$470$	0.0405828	0.00187194
$471$	17.8985	0.824718
$472$	2.59962	0.119657
$473$	−2.43704	−0.112055
$474$	5.37655	0.246953
$475$	2.87422	0.131878
$476$	6.65759	0.305150
$477$	14.0522	0.643404
$478$	11.8712	0.542974
$479$	−8.00631	−0.365818	−0.182909	−	0.983130i	$-0.558551\pi$
$479$	−8.00631	−0.365818	−0.182909	+	0.983130i	$0.558551\pi$
$480$	−0.635442	−0.0290038
$481$	0	0
$482$	15.4614	0.704245
$483$	1.28651	0.0585382
$484$	5.83158	0.265072
$485$	−8.36522	−0.379845
$486$	−1.00000	−0.0453609
$487$	6.63415	0.300622	0.150311	−	0.988639i	$-0.451972\pi$
$487$	6.63415	0.300622	0.150311	+	0.988639i	$0.451972\pi$
$488$	−6.33935	−0.286969
$489$	−6.41932	−0.290292
$490$	0.635442	0.0287063
$491$	−33.2667	−1.50131	−0.750653	−	0.660697i	$-0.770261\pi$
$491$	−33.2667	−1.50131	−0.750653	+	0.660697i	$0.770261\pi$
$492$	−8.35703	−0.376764
$493$	25.3280	1.14071
$494$	0	0
$495$	2.60698	0.117175
$496$	0.351292	0.0157735
$497$	−15.6116	−0.700275
$498$	−10.1345	−0.454139
$499$	−29.6521	−1.32741	−0.663704	−	0.747995i	$-0.731017\pi$
$499$	−29.6521	−1.32741	−0.663704	+	0.747995i	$0.731017\pi$
$500$	−6.09784	−0.272704
$501$	−17.0892	−0.763487
$502$	1.75448	0.0783061
$503$	−24.7500	−1.10355	−0.551774	−	0.833993i	$-0.686049\pi$
$503$	−24.7500	−1.10355	−0.551774	+	0.833993i	$0.686049\pi$
$504$	1.00000	0.0445435
$505$	8.38856	0.373286
$506$	−5.27807	−0.234639
$507$	0	0
$508$	−11.8250	−0.524648
$509$	33.6380	1.49098	0.745489	−	0.666518i	$-0.232216\pi$
$509$	33.6380	1.49098	0.745489	+	0.666518i	$0.232216\pi$
$510$	−4.23051	−0.187330
$511$	6.85298	0.303158
$512$	1.00000	0.0441942
$513$	0.625344	0.0276096
$514$	26.5519	1.17115
$515$	5.64154	0.248596
$516$	0.594019	0.0261502
$517$	0.262016	0.0115235
$518$	−0.0202540	−0.000889909 0
$519$	−6.52599	−0.286459
$520$	0	0
$521$	21.4115	0.938053	0.469026	−	0.883184i	$-0.344605\pi$
$521$	21.4115	0.938053	0.469026	+	0.883184i	$0.344605\pi$
$522$	3.80437	0.166513
$523$	−19.5645	−0.855498	−0.427749	−	0.903898i	$-0.640693\pi$
$523$	−19.5645	−0.855498	−0.427749	+	0.903898i	$0.640693\pi$
$524$	−0.845553	−0.0369381
$525$	4.59621	0.200595
$526$	−15.4606	−0.674115
$527$	2.33876	0.101878
$528$	−4.10263	−0.178544
$529$	−21.3449	−0.928039
$530$	8.92934	0.387866
$531$	2.59962	0.112814
$532$	−0.625344	−0.0271121
$533$	0	0
$534$	12.7069	0.549881
$535$	−5.19236	−0.224485
$536$	−7.26714	−0.313893
$537$	−18.4815	−0.797535
$538$	−1.87824	−0.0809767
$539$	4.10263	0.176713
$540$	−0.635442	−0.0273451
$541$	−4.91698	−0.211397	−0.105699	−	0.994398i	$-0.533708\pi$
$541$	−4.91698	−0.211397	−0.105699	+	0.994398i	$0.533708\pi$
$542$	23.3701	1.00383
$543$	13.6239	0.584659
$544$	6.65759	0.285442
$545$	7.35664	0.315124
$546$	0	0
$547$	−21.6535	−0.925837	−0.462918	−	0.886401i	$-0.653198\pi$
$547$	−21.6535	−0.925837	−0.462918	+	0.886401i	$0.653198\pi$
$548$	−1.78618	−0.0763017
$549$	−6.33935	−0.270557
$550$	−18.8566	−0.804047
$551$	−2.37904	−0.101351
$552$	1.28651	0.0547575
$553$	−5.37655	−0.228634
$554$	11.1022	0.471687
$555$	0.0128702	0.000546311 0
$556$	4.16710	0.176724
$557$	−7.06685	−0.299432	−0.149716	−	0.988729i	$-0.547836\pi$
$557$	−7.06685	−0.299432	−0.149716	+	0.988729i	$0.547836\pi$
$558$	0.351292	0.0148714
$559$	0	0
$560$	0.635442	0.0268523
$561$	−27.3136	−1.15318
$562$	18.7670	0.791637
$563$	−21.9519	−0.925161	−0.462580	−	0.886577i	$-0.653076\pi$
$563$	−21.9519	−0.925161	−0.462580	+	0.886577i	$0.653076\pi$
$564$	−0.0638654	−0.00268922
$565$	−1.89435	−0.0796960
$566$	−18.4052	−0.773626
$567$	1.00000	0.0419961
$568$	−15.6116	−0.655047
$569$	−16.4755	−0.690690	−0.345345	−	0.938476i	$-0.612238\pi$
$569$	−16.4755	−0.690690	−0.345345	+	0.938476i	$0.612238\pi$
$570$	0.397370	0.0166440
$571$	−35.5765	−1.48883	−0.744415	−	0.667717i	$-0.767272\pi$
$571$	−35.5765	−1.48883	−0.744415	+	0.667717i	$0.767272\pi$
$572$	0	0
$573$	22.5785	0.943231
$574$	8.35703	0.348816
$575$	5.91307	0.246592
$576$	1.00000	0.0416667
$577$	32.4817	1.35223	0.676115	−	0.736796i	$-0.263662\pi$
$577$	32.4817	1.35223	0.676115	+	0.736796i	$0.263662\pi$
$578$	27.3235	1.13651
$579$	21.0445	0.874578
$580$	2.41746	0.100380
$581$	10.1345	0.420451
$582$	13.1644	0.545682
$583$	57.6508	2.38765
$584$	6.85298	0.283578
$585$	0	0
$586$	−20.7932	−0.858959
$587$	29.8084	1.23032	0.615162	−	0.788401i	$-0.289091\pi$
$587$	29.8084	1.23032	0.615162	+	0.788401i	$0.289091\pi$
$588$	−1.00000	−0.0412393
$589$	−0.219678	−0.00905169
$590$	1.65191	0.0680081
$591$	0.318174	0.0130879
$592$	−0.0202540	−0.000832433 0
$593$	12.4280	0.510355	0.255177	−	0.966894i	$-0.417866\pi$
$593$	12.4280	0.510355	0.255177	+	0.966894i	$0.417866\pi$
$594$	−4.10263	−0.168333
$595$	4.23051	0.173434
$596$	−6.79403	−0.278294
$597$	−13.4406	−0.550087
$598$	0	0
$599$	−4.71849	−0.192792	−0.0963962	−	0.995343i	$-0.530732\pi$
$599$	−4.71849	−0.192792	−0.0963962	+	0.995343i	$0.530732\pi$
$600$	4.59621	0.187640
$601$	−9.76744	−0.398422	−0.199211	−	0.979957i	$-0.563838\pi$
$601$	−9.76744	−0.398422	−0.199211	+	0.979957i	$0.563838\pi$
$602$	−0.594019	−0.0242104
$603$	−7.26714	−0.295941
$604$	5.43882	0.221302
$605$	3.70563	0.150655
$606$	−13.2011	−0.536260
$607$	−3.21761	−0.130599	−0.0652993	−	0.997866i	$-0.520800\pi$
$607$	−3.21761	−0.130599	−0.0652993	+	0.997866i	$0.520800\pi$
$608$	−0.625344	−0.0253611
$609$	−3.80437	−0.154161
$610$	−4.02829	−0.163101
$611$	0	0
$612$	6.65759	0.269117
$613$	16.8648	0.681164	0.340582	−	0.940215i	$-0.389376\pi$
$613$	16.8648	0.681164	0.340582	+	0.940215i	$0.389376\pi$
$614$	20.1760	0.814237
$615$	−5.31041	−0.214136
$616$	4.10263	0.165300
$617$	25.3239	1.01950	0.509751	−	0.860322i	$-0.329738\pi$
$617$	25.3239	1.01950	0.509751	+	0.860322i	$0.329738\pi$
$618$	−8.87814	−0.357131
$619$	−33.5732	−1.34942	−0.674711	−	0.738082i	$-0.735732\pi$
$619$	−33.5732	−1.34942	−0.674711	+	0.738082i	$0.735732\pi$
$620$	0.223226	0.00896496
$621$	1.28651	0.0516259
$622$	14.9136	0.597980
$623$	−12.7069	−0.509090
$624$	0	0
$625$	19.1062	0.764250
$626$	2.80693	0.112187
$627$	2.56556	0.102458
$628$	−17.8985	−0.714227
$629$	−0.134843	−0.00537653
$630$	0.635442	0.0253166
$631$	−13.9266	−0.554411	−0.277205	−	0.960811i	$-0.589408\pi$
$631$	−13.9266	−0.554411	−0.277205	+	0.960811i	$0.589408\pi$
$632$	−5.37655	−0.213868
$633$	−9.28125	−0.368897
$634$	24.9731	0.991809
$635$	−7.51408	−0.298187
$636$	−14.0522	−0.557205
$637$	0	0
$638$	15.6079	0.617924
$639$	−15.6116	−0.617585
$640$	0.635442	0.0251181
$641$	13.7649	0.543683	0.271841	−	0.962342i	$-0.412367\pi$
$641$	13.7649	0.543683	0.271841	+	0.962342i	$0.412367\pi$
$642$	8.17126	0.322494
$643$	−19.7913	−0.780493	−0.390247	−	0.920710i	$-0.627610\pi$
$643$	−19.7913	−0.780493	−0.390247	+	0.920710i	$0.627610\pi$
$644$	−1.28651	−0.0506956
$645$	0.377465	0.0148627
$646$	−4.16328	−0.163802
$647$	17.5723	0.690837	0.345419	−	0.938449i	$-0.387737\pi$
$647$	17.5723	0.690837	0.345419	+	0.938449i	$0.387737\pi$
$648$	1.00000	0.0392837
$649$	10.6653	0.418649
$650$	0	0
$651$	−0.351292	−0.0137682
$652$	6.41932	0.251400
$653$	−44.3609	−1.73597	−0.867987	−	0.496586i	$-0.834587\pi$
$653$	−44.3609	−1.73597	−0.867987	+	0.496586i	$0.834587\pi$
$654$	−11.5772	−0.452705
$655$	−0.537300	−0.0209940
$656$	8.35703	0.326287
$657$	6.85298	0.267360
$658$	0.0638654	0.00248973
$659$	−45.2044	−1.76091	−0.880457	−	0.474126i	$-0.842764\pi$
$659$	−45.2044	−1.76091	−0.880457	+	0.474126i	$0.842764\pi$
$660$	−2.60698	−0.101477
$661$	49.7052	1.93331	0.966653	−	0.256088i	$-0.0824337\pi$
$661$	49.7052	1.93331	0.966653	+	0.256088i	$0.0824337\pi$
$662$	8.15503	0.316954
$663$	0	0
$664$	10.1345	0.393296
$665$	−0.397370	−0.0154093
$666$	−0.0202540	−0.000784826 0
$667$	−4.89436	−0.189511
$668$	17.0892	0.661199
$669$	−15.4949	−0.599068
$670$	−4.61785	−0.178403
$671$	−26.0080	−1.00403
$672$	−1.00000	−0.0385758
$673$	5.17401	0.199443	0.0997217	−	0.995015i	$-0.468205\pi$
$673$	5.17401	0.199443	0.0997217	+	0.995015i	$0.468205\pi$
$674$	29.3296	1.12973
$675$	4.59621	0.176908
$676$	0	0
$677$	8.30497	0.319186	0.159593	−	0.987183i	$-0.448982\pi$
$677$	8.30497	0.319186	0.159593	+	0.987183i	$0.448982\pi$
$678$	2.98116	0.114491
$679$	−13.1644	−0.505204
$680$	4.23051	0.162233
$681$	2.84980	0.109205
$682$	1.44122	0.0551872
$683$	32.4275	1.24080	0.620402	−	0.784284i	$-0.286969\pi$
$683$	32.4275	1.24080	0.620402	+	0.784284i	$0.286969\pi$
$684$	−0.625344	−0.0239106
$685$	−1.13501	−0.0433666
$686$	1.00000	0.0381802
$687$	−12.5456	−0.478644
$688$	−0.594019	−0.0226468
$689$	0	0
$690$	0.817502	0.0311218
$691$	14.5199	0.552362	0.276181	−	0.961106i	$-0.410931\pi$
$691$	14.5199	0.552362	0.276181	+	0.961106i	$0.410931\pi$
$692$	6.52599	0.248081
$693$	4.10263	0.155846
$694$	−21.1061	−0.801175
$695$	2.64795	0.100442
$696$	−3.80437	−0.144204
$697$	55.6377	2.10743
$698$	23.7028	0.897164
$699$	−6.33236	−0.239512
$700$	−4.59621	−0.173721
$701$	33.2739	1.25674	0.628370	−	0.777915i	$-0.283723\pi$
$701$	33.2739	1.25674	0.628370	+	0.777915i	$0.283723\pi$
$702$	0	0
$703$	0.0126657	0.000477696 0
$704$	4.10263	0.154624
$705$	−0.0405828	−0.00152844
$706$	−27.5037	−1.03512
$707$	13.2011	0.496480
$708$	−2.59962	−0.0976998
$709$	−14.2732	−0.536043	−0.268021	−	0.963413i	$-0.586370\pi$
$709$	−14.2732	−0.536043	−0.268021	+	0.963413i	$0.586370\pi$
$710$	−9.92025	−0.372301
$711$	−5.37655	−0.201636
$712$	−12.7069	−0.476211
$713$	−0.451941	−0.0169253
$714$	−6.65759	−0.249154
$715$	0	0
$716$	18.4815	0.690685
$717$	−11.8712	−0.443336
$718$	−6.81905	−0.254485
$719$	22.9564	0.856130	0.428065	−	0.903748i	$-0.359195\pi$
$719$	22.9564	0.856130	0.428065	+	0.903748i	$0.359195\pi$
$720$	0.635442	0.0236815
$721$	8.87814	0.330639
$722$	−18.6089	−0.692553
$723$	−15.4614	−0.575014
$724$	−13.6239	−0.506329
$725$	−17.4857	−0.649403
$726$	−5.83158	−0.216430
$727$	−48.8472	−1.81164	−0.905822	−	0.423659i	$-0.860745\pi$
$727$	−48.8472	−1.81164	−0.905822	+	0.423659i	$0.860745\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.35467	0.161174
$731$	−3.95474	−0.146271
$732$	6.33935	0.234309
$733$	22.0625	0.814898	0.407449	−	0.913228i	$-0.366418\pi$
$733$	22.0625	0.814898	0.407449	+	0.913228i	$0.366418\pi$
$734$	13.2117	0.487653
$735$	−0.635442	−0.0234386
$736$	−1.28651	−0.0474214
$737$	−29.8144	−1.09823
$738$	8.35703	0.307627
$739$	3.98124	0.146452	0.0732261	−	0.997315i	$-0.476671\pi$
$739$	3.98124	0.146452	0.0732261	+	0.997315i	$0.476671\pi$
$740$	−0.0128702	−0.000473119 0
$741$	0	0
$742$	14.0522	0.515871
$743$	−2.62343	−0.0962442	−0.0481221	−	0.998841i	$-0.515324\pi$
$743$	−2.62343	−0.0962442	−0.0481221	+	0.998841i	$0.515324\pi$
$744$	−0.351292	−0.0128790
$745$	−4.31721	−0.158171
$746$	−33.4216	−1.22365
$747$	10.1345	0.370803
$748$	27.3136	0.998685
$749$	−8.17126	−0.298571
$750$	6.09784	0.222662
$751$	−53.0045	−1.93416	−0.967081	−	0.254467i	$-0.918100\pi$
$751$	−53.0045	−1.93416	−0.967081	+	0.254467i	$0.918100\pi$
$752$	0.0638654	0.00232893
$753$	−1.75448	−0.0639367
$754$	0	0
$755$	3.45605	0.125779
$756$	−1.00000	−0.0363696
$757$	−9.59258	−0.348648	−0.174324	−	0.984688i	$-0.555774\pi$
$757$	−9.59258	−0.348648	−0.174324	+	0.984688i	$0.555774\pi$
$758$	−28.8115	−1.04648
$759$	5.27807	0.191582
$760$	−0.397370	−0.0144141
$761$	−36.8683	−1.33647	−0.668237	−	0.743948i	$-0.732951\pi$
$761$	−36.8683	−1.33647	−0.668237	+	0.743948i	$0.732951\pi$
$762$	11.8250	0.428373
$763$	11.5772	0.419123
$764$	−22.5785	−0.816862
$765$	4.23051	0.152954
$766$	−2.65802	−0.0960383
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−27.7273	−0.999872	−0.499936	−	0.866062i	$-0.666643\pi$
$769$	−27.7273	−0.999872	−0.499936	+	0.866062i	$0.666643\pi$
$770$	2.60698	0.0939492
$771$	−26.5519	−0.956242
$772$	−21.0445	−0.757407
$773$	−4.70617	−0.169269	−0.0846345	−	0.996412i	$-0.526972\pi$
$773$	−4.70617	−0.169269	−0.0846345	+	0.996412i	$0.526972\pi$
$774$	−0.594019	−0.0213516
$775$	−1.61461	−0.0579986
$776$	−13.1644	−0.472575
$777$	0.0202540	0.000726607 0
$778$	−9.05857	−0.324766
$779$	−5.22602	−0.187242
$780$	0	0
$781$	−64.0485	−2.29184
$782$	−8.56505	−0.306286
$783$	−3.80437	−0.135957
$784$	1.00000	0.0357143
$785$	−11.3734	−0.405935
$786$	0.845553	0.0301599
$787$	7.84512	0.279648	0.139824	−	0.990176i	$-0.455346\pi$
$787$	7.84512	0.279648	0.139824	+	0.990176i	$0.455346\pi$
$788$	−0.318174	−0.0113345
$789$	15.4606	0.550413
$790$	−3.41648	−0.121553
$791$	−2.98116	−0.105998
$792$	4.10263	0.145781
$793$	0	0
$794$	26.1070	0.926501
$795$	−8.92934	−0.316691
$796$	13.4406	0.476389
$797$	−6.84643	−0.242513	−0.121256	−	0.992621i	$-0.538692\pi$
$797$	−6.84643	−0.242513	−0.121256	+	0.992621i	$0.538692\pi$
$798$	0.625344	0.0221369
$799$	0.425190	0.0150421
$800$	−4.59621	−0.162501
$801$	−12.7069	−0.448976
$802$	38.1909	1.34857
$803$	28.1152	0.992165
$804$	7.26714	0.256292
$805$	−0.817502	−0.0288132
$806$	0	0
$807$	1.87824	0.0661172
$808$	13.2011	0.464414
$809$	−41.7545	−1.46801	−0.734005	−	0.679145i	$-0.762351\pi$
$809$	−41.7545	−1.46801	−0.734005	+	0.679145i	$0.762351\pi$
$810$	0.635442	0.0223272
$811$	−24.8505	−0.872618	−0.436309	−	0.899797i	$-0.643715\pi$
$811$	−24.8505	−0.872618	−0.436309	+	0.899797i	$0.643715\pi$
$812$	3.80437	0.133507
$813$	−23.3701	−0.819625
$814$	−0.0830946	−0.00291246
$815$	4.07911	0.142885
$816$	−6.65759	−0.233062
$817$	0.371467	0.0129960
$818$	−30.7382	−1.07473
$819$	0	0
$820$	5.31041	0.185448
$821$	−23.6207	−0.824367	−0.412184	−	0.911101i	$-0.635234\pi$
$821$	−23.6207	−0.824367	−0.412184	+	0.911101i	$0.635234\pi$
$822$	1.78618	0.0623001
$823$	43.3592	1.51141	0.755703	−	0.654915i	$-0.227295\pi$
$823$	43.3592	1.51141	0.755703	+	0.654915i	$0.227295\pi$
$824$	8.87814	0.309285
$825$	18.8566	0.656501
$826$	2.59962	0.0904525
$827$	−20.7836	−0.722715	−0.361358	−	0.932427i	$-0.617687\pi$
$827$	−20.7836	−0.722715	−0.361358	+	0.932427i	$0.617687\pi$
$828$	−1.28651	−0.0447093
$829$	41.9471	1.45688	0.728442	−	0.685107i	$-0.240245\pi$
$829$	41.9471	1.45688	0.728442	+	0.685107i	$0.240245\pi$
$830$	6.43991	0.223533
$831$	−11.1022	−0.385131
$832$	0	0
$833$	6.65759	0.230672
$834$	−4.16710	−0.144295
$835$	10.8592	0.375797
$836$	−2.56556	−0.0887316
$837$	−0.351292	−0.0121424
$838$	−4.78334	−0.165238
$839$	−51.6829	−1.78429	−0.892146	−	0.451747i	$-0.850801\pi$
$839$	−51.6829	−1.78429	−0.892146	+	0.451747i	$0.850801\pi$
$840$	−0.635442	−0.0219248
$841$	−14.5267	−0.500922
$842$	−13.8582	−0.477585
$843$	−18.7670	−0.646369
$844$	9.28125	0.319474
$845$	0	0
$846$	0.0638654	0.00219574
$847$	5.83158	0.200375
$848$	14.0522	0.482553
$849$	18.4052	0.631663
$850$	−30.5997	−1.04956
$851$	0.0260569	0.000893220 0
$852$	15.6116	0.534844
$853$	−33.8533	−1.15912	−0.579558	−	0.814931i	$-0.696775\pi$
$853$	−33.8533	−1.15912	−0.579558	+	0.814931i	$0.696775\pi$
$854$	−6.33935	−0.216928
$855$	−0.397370	−0.0135898
$856$	−8.17126	−0.279288
$857$	52.6326	1.79790	0.898948	−	0.438055i	$-0.144332\pi$
$857$	52.6326	1.79790	0.898948	+	0.438055i	$0.144332\pi$
$858$	0	0
$859$	−41.6285	−1.42035	−0.710174	−	0.704026i	$-0.751384\pi$
$859$	−41.6285	−1.42035	−0.710174	+	0.704026i	$0.751384\pi$
$860$	−0.377465	−0.0128714
$861$	−8.35703	−0.284807
$862$	−17.3630	−0.591387
$863$	−6.77082	−0.230481	−0.115241	−	0.993338i	$-0.536764\pi$
$863$	−6.77082	−0.230481	−0.115241	+	0.993338i	$0.536764\pi$
$864$	−1.00000	−0.0340207
$865$	4.14689	0.140999
$866$	−1.82159	−0.0619001
$867$	−27.3235	−0.927954
$868$	0.351292	0.0119236
$869$	−22.0580	−0.748266
$870$	−2.41746	−0.0819595
$871$	0	0
$872$	11.5772	0.392054
$873$	−13.1644	−0.445548
$874$	0.804511	0.0272130
$875$	−6.09784	−0.206145
$876$	−6.85298	−0.231541
$877$	35.9208	1.21296	0.606480	−	0.795098i	$-0.292581\pi$
$877$	35.9208	1.21296	0.606480	+	0.795098i	$0.292581\pi$
$878$	−6.59142	−0.222450
$879$	20.7932	0.701337
$880$	2.60698	0.0878814
$881$	−10.6552	−0.358983	−0.179492	−	0.983760i	$-0.557445\pi$
$881$	−10.6552	−0.358983	−0.179492	+	0.983760i	$0.557445\pi$
$882$	1.00000	0.0336718
$883$	−13.8698	−0.466755	−0.233377	−	0.972386i	$-0.574978\pi$
$883$	−13.8698	−0.466755	−0.233377	+	0.972386i	$0.574978\pi$
$884$	0	0
$885$	−1.65191	−0.0555283
$886$	−9.29816	−0.312378
$887$	19.8623	0.666912	0.333456	−	0.942766i	$-0.391785\pi$
$887$	19.8623	0.666912	0.333456	+	0.942766i	$0.391785\pi$
$888$	0.0202540	0.000679679 0
$889$	−11.8250	−0.396597
$890$	−8.07449	−0.270657
$891$	4.10263	0.137443
$892$	15.4949	0.518808
$893$	−0.0399379	−0.00133647
$894$	6.79403	0.227226
$895$	11.7439	0.392555
$896$	1.00000	0.0334077
$897$	0	0
$898$	−10.8177	−0.360991
$899$	1.33645	0.0445730
$900$	−4.59621	−0.153207
$901$	93.5535	3.11672
$902$	34.2858	1.14159
$903$	0.594019	0.0197677
$904$	−2.98116	−0.0991518
$905$	−8.65722	−0.287776
$906$	−5.43882	−0.180693
$907$	−15.6899	−0.520973	−0.260487	−	0.965477i	$-0.583883\pi$
$907$	−15.6899	−0.520973	−0.260487	+	0.965477i	$0.583883\pi$
$908$	−2.84980	−0.0945740
$909$	13.2011	0.437854
$910$	0	0
$911$	32.0975	1.06344	0.531719	−	0.846921i	$-0.321546\pi$
$911$	32.0975	1.06344	0.531719	+	0.846921i	$0.321546\pi$
$912$	0.625344	0.0207072
$913$	41.5783	1.37604
$914$	35.0327	1.15878
$915$	4.02829	0.133171
$916$	12.5456	0.414518
$917$	−0.845553	−0.0279226
$918$	−6.65759	−0.219733
$919$	39.4668	1.30189	0.650944	−	0.759126i	$-0.274373\pi$
$919$	39.4668	1.30189	0.650944	+	0.759126i	$0.274373\pi$
$920$	−0.817502	−0.0269523
$921$	−20.1760	−0.664822
$922$	−1.69987	−0.0559823
$923$	0	0
$924$	−4.10263	−0.134967
$925$	0.0930916	0.00306083
$926$	36.4266	1.19705
$927$	8.87814	0.291596
$928$	3.80437	0.124885
$929$	−38.0118	−1.24713	−0.623564	−	0.781772i	$-0.714316\pi$
$929$	−38.0118	−1.24713	−0.623564	+	0.781772i	$0.714316\pi$
$930$	−0.223226	−0.00731986
$931$	−0.625344	−0.0204948
$932$	6.33236	0.207423
$933$	−14.9136	−0.488249
$934$	−8.42113	−0.275548
$935$	17.3562	0.567609
$936$	0	0
$937$	−50.3831	−1.64594	−0.822972	−	0.568082i	$-0.807686\pi$
$937$	−50.3831	−1.64594	−0.822972	+	0.568082i	$0.807686\pi$
$938$	−7.26714	−0.237281
$939$	−2.80693	−0.0916007
$940$	0.0405828	0.00132366
$941$	−2.87802	−0.0938209	−0.0469105	−	0.998899i	$-0.514938\pi$
$941$	−2.87802	−0.0938209	−0.0469105	+	0.998899i	$0.514938\pi$
$942$	17.8985	0.583164
$943$	−10.7514	−0.350114
$944$	2.59962	0.0846105
$945$	−0.635442	−0.0206709
$946$	−2.43704	−0.0792351
$947$	43.4007	1.41033	0.705167	−	0.709041i	$-0.250872\pi$
$947$	43.4007	1.41033	0.705167	+	0.709041i	$0.250872\pi$
$948$	5.37655	0.174622
$949$	0	0
$950$	2.87422	0.0932519
$951$	−24.9731	−0.809809
$952$	6.65759	0.215774
$953$	−34.8499	−1.12890	−0.564450	−	0.825467i	$-0.690912\pi$
$953$	−34.8499	−1.12890	−0.564450	+	0.825467i	$0.690912\pi$
$954$	14.0522	0.454956
$955$	−14.3473	−0.464269
$956$	11.8712	0.383940
$957$	−15.6079	−0.504533
$958$	−8.00631	−0.258672
$959$	−1.78618	−0.0576787
$960$	−0.635442	−0.0205088
$961$	−30.8766	−0.996019
$962$	0	0
$963$	−8.17126	−0.263315
$964$	15.4614	0.497977
$965$	−13.3725	−0.430477
$966$	1.28651	0.0413928
$967$	1.53090	0.0492304	0.0246152	−	0.999697i	$-0.492164\pi$
$967$	1.53090	0.0492304	0.0246152	+	0.999697i	$0.492164\pi$
$968$	5.83158	0.187434
$969$	4.16328	0.133744
$970$	−8.36522	−0.268591
$971$	30.4810	0.978181	0.489090	−	0.872233i	$-0.337329\pi$
$971$	30.4810	0.978181	0.489090	+	0.872233i	$0.337329\pi$
$972$	−1.00000	−0.0320750
$973$	4.16710	0.133591
$974$	6.63415	0.212572
$975$	0	0
$976$	−6.33935	−0.202918
$977$	10.2083	0.326594	0.163297	−	0.986577i	$-0.447787\pi$
$977$	10.2083	0.326594	0.163297	+	0.986577i	$0.447787\pi$
$978$	−6.41932	−0.205267
$979$	−52.1316	−1.66613
$980$	0.635442	0.0202985
$981$	11.5772	0.369632
$982$	−33.2667	−1.06158
$983$	−13.3174	−0.424760	−0.212380	−	0.977187i	$-0.568121\pi$
$983$	−13.3174	−0.424760	−0.212380	+	0.977187i	$0.568121\pi$
$984$	−8.35703	−0.266412
$985$	−0.202181	−0.00644203
$986$	25.3280	0.806606
$987$	−0.0638654	−0.00203286
$988$	0	0
$989$	0.764212	0.0243005
$990$	2.60698	0.0828554
$991$	56.7034	1.80124	0.900621	−	0.434604i	$-0.143112\pi$
$991$	56.7034	1.80124	0.900621	+	0.434604i	$0.143112\pi$
$992$	0.351292	0.0111535
$993$	−8.15503	−0.258792
$994$	−15.6116	−0.495169
$995$	8.54072	0.270759
$996$	−10.1345	−0.321125
$997$	0.197764	0.00626323	0.00313162	−	0.999995i	$-0.499003\pi$
$997$	0.197764	0.00626323	0.00313162	+	0.999995i	$0.499003\pi$
$998$	−29.6521	−0.938620
$999$	0.0202540	0.000640808 0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.635442 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.635442 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.635442 q^{10} +4.10263 q^{11} -1.00000 q^{12} +1.00000 q^{14} -0.635442 q^{15} +1.00000 q^{16} +6.65759 q^{17} +1.00000 q^{18} -0.625344 q^{19} +0.635442 q^{20} -1.00000 q^{21} +4.10263 q^{22} -1.28651 q^{23} -1.00000 q^{24} -4.59621 q^{25} -1.00000 q^{27} +1.00000 q^{28} +3.80437 q^{29} -0.635442 q^{30} +0.351292 q^{31} +1.00000 q^{32} -4.10263 q^{33} +6.65759 q^{34} +0.635442 q^{35} +1.00000 q^{36} -0.0202540 q^{37} -0.625344 q^{38} +0.635442 q^{40} +8.35703 q^{41} -1.00000 q^{42} -0.594019 q^{43} +4.10263 q^{44} +0.635442 q^{45} -1.28651 q^{46} +0.0638654 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.59621 q^{50} -6.65759 q^{51} +14.0522 q^{53} -1.00000 q^{54} +2.60698 q^{55} +1.00000 q^{56} +0.625344 q^{57} +3.80437 q^{58} +2.59962 q^{59} -0.635442 q^{60} -6.33935 q^{61} +0.351292 q^{62} +1.00000 q^{63} +1.00000 q^{64} -4.10263 q^{66} -7.26714 q^{67} +6.65759 q^{68} +1.28651 q^{69} +0.635442 q^{70} -15.6116 q^{71} +1.00000 q^{72} +6.85298 q^{73} -0.0202540 q^{74} +4.59621 q^{75} -0.625344 q^{76} +4.10263 q^{77} -5.37655 q^{79} +0.635442 q^{80} +1.00000 q^{81} +8.35703 q^{82} +10.1345 q^{83} -1.00000 q^{84} +4.23051 q^{85} -0.594019 q^{86} -3.80437 q^{87} +4.10263 q^{88} -12.7069 q^{89} +0.635442 q^{90} -1.28651 q^{92} -0.351292 q^{93} +0.0638654 q^{94} -0.397370 q^{95} -1.00000 q^{96} -13.1644 q^{97} +1.00000 q^{98} +4.10263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} + 8 q^{19} - 3 q^{20} - 6 q^{21} - 6 q^{22} - 12 q^{23} - 6 q^{24} + 5 q^{25} - 6 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 7 q^{31} + 6 q^{32} + 6 q^{33} + 10 q^{34} - 3 q^{35} + 6 q^{36} + 3 q^{37} + 8 q^{38} - 3 q^{40} + 3 q^{41} - 6 q^{42} - 3 q^{43} - 6 q^{44} - 3 q^{45} - 12 q^{46} + 29 q^{47} - 6 q^{48} + 6 q^{49} + 5 q^{50} - 10 q^{51} - 12 q^{53} - 6 q^{54} + 29 q^{55} + 6 q^{56} - 8 q^{57} + 4 q^{58} + 2 q^{59} + 3 q^{60} + 13 q^{61} + 7 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{66} + 22 q^{67} + 10 q^{68} + 12 q^{69} - 3 q^{70} + q^{71} + 6 q^{72} + 29 q^{73} + 3 q^{74} - 5 q^{75} + 8 q^{76} - 6 q^{77} - 24 q^{79} - 3 q^{80} + 6 q^{81} + 3 q^{82} + 7 q^{83} - 6 q^{84} + 21 q^{85} - 3 q^{86} - 4 q^{87} - 6 q^{88} - 11 q^{89} - 3 q^{90} - 12 q^{92} - 7 q^{93} + 29 q^{94} + 8 q^{95} - 6 q^{96} - 4 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) \) 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 - 6 * q^11 - 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 + 8 * q^19 - 3 * q^20 - 6 * q^21 - 6 * q^22 - 12 * q^23 - 6 * q^24 + 5 * q^25 - 6 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 7 * q^31 + 6 * q^32 + 6 * q^33 + 10 * q^34 - 3 * q^35 + 6 * q^36 + 3 * q^37 + 8 * q^38 - 3 * q^40 + 3 * q^41 - 6 * q^42 - 3 * q^43 - 6 * q^44 - 3 * q^45 - 12 * q^46 + 29 * q^47 - 6 * q^48 + 6 * q^49 + 5 * q^50 - 10 * q^51 - 12 * q^53 - 6 * q^54 + 29 * q^55 + 6 * q^56 - 8 * q^57 + 4 * q^58 + 2 * q^59 + 3 * q^60 + 13 * q^61 + 7 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^66 + 22 * q^67 + 10 * q^68 + 12 * q^69 - 3 * q^70 + q^71 + 6 * q^72 + 29 * q^73 + 3 * q^74 - 5 * q^75 + 8 * q^76 - 6 * q^77 - 24 * q^79 - 3 * q^80 + 6 * q^81 + 3 * q^82 + 7 * q^83 - 6 * q^84 + 21 * q^85 - 3 * q^86 - 4 * q^87 - 6 * q^88 - 11 * q^89 - 3 * q^90 - 12 * q^92 - 7 * q^93 + 29 * q^94 + 8 * q^95 - 6 * q^96 - 4 * q^97 + 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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