LMFDB - Embedded newform 7098.2.a.bo.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.732051 q^{10} +5.19615 q^{11} +1.00000 q^{12} +1.00000 q^{14} -0.732051 q^{15} +1.00000 q^{16} -2.26795 q^{17} -1.00000 q^{18} -0.464102 q^{19} -0.732051 q^{20} -1.00000 q^{21} -5.19615 q^{22} -7.46410 q^{23} -1.00000 q^{24} -4.46410 q^{25} +1.00000 q^{27} -1.00000 q^{28} -3.53590 q^{29} +0.732051 q^{30} +3.26795 q^{31} -1.00000 q^{32} +5.19615 q^{33} +2.26795 q^{34} +0.732051 q^{35} +1.00000 q^{36} +6.73205 q^{37} +0.464102 q^{38} +0.732051 q^{40} +8.46410 q^{41} +1.00000 q^{42} -8.73205 q^{43} +5.19615 q^{44} -0.732051 q^{45} +7.46410 q^{46} +3.92820 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.46410 q^{50} -2.26795 q^{51} -9.92820 q^{53} -1.00000 q^{54} -3.80385 q^{55} +1.00000 q^{56} -0.464102 q^{57} +3.53590 q^{58} -8.92820 q^{59} -0.732051 q^{60} +3.73205 q^{61} -3.26795 q^{62} -1.00000 q^{63} +1.00000 q^{64} -5.19615 q^{66} -10.0000 q^{67} -2.26795 q^{68} -7.46410 q^{69} -0.732051 q^{70} +7.26795 q^{71} -1.00000 q^{72} -1.46410 q^{73} -6.73205 q^{74} -4.46410 q^{75} -0.464102 q^{76} -5.19615 q^{77} +9.00000 q^{79} -0.732051 q^{80} +1.00000 q^{81} -8.46410 q^{82} -9.26795 q^{83} -1.00000 q^{84} +1.66025 q^{85} +8.73205 q^{86} -3.53590 q^{87} -5.19615 q^{88} -16.8564 q^{89} +0.732051 q^{90} -7.46410 q^{92} +3.26795 q^{93} -3.92820 q^{94} +0.339746 q^{95} -1.00000 q^{96} -14.1962 q^{97} -1.00000 q^{98} +5.19615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{12} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + 6 q^{19} + 2 q^{20} - 2 q^{21} - 8 q^{23} - 2 q^{24} - 2 q^{25} + 2 q^{27} - 2 q^{28} - 14 q^{29} - 2 q^{30} + 10 q^{31} - 2 q^{32} + 8 q^{34} - 2 q^{35} + 2 q^{36} + 10 q^{37} - 6 q^{38} - 2 q^{40} + 10 q^{41} + 2 q^{42} - 14 q^{43} + 2 q^{45} + 8 q^{46} - 6 q^{47} + 2 q^{48} + 2 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} - 2 q^{54} - 18 q^{55} + 2 q^{56} + 6 q^{57} + 14 q^{58} - 4 q^{59} + 2 q^{60} + 4 q^{61} - 10 q^{62} - 2 q^{63} + 2 q^{64} - 20 q^{67} - 8 q^{68} - 8 q^{69} + 2 q^{70} + 18 q^{71} - 2 q^{72} + 4 q^{73} - 10 q^{74} - 2 q^{75} + 6 q^{76} + 18 q^{79} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 22 q^{83} - 2 q^{84} - 14 q^{85} + 14 q^{86} - 14 q^{87} - 6 q^{89} - 2 q^{90} - 8 q^{92} + 10 q^{93} + 6 q^{94} + 18 q^{95} - 2 q^{96} - 18 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^12 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + 6 * q^19 + 2 * q^20 - 2 * q^21 - 8 * q^23 - 2 * q^24 - 2 * q^25 + 2 * q^27 - 2 * q^28 - 14 * q^29 - 2 * q^30 + 10 * q^31 - 2 * q^32 + 8 * q^34 - 2 * q^35 + 2 * q^36 + 10 * q^37 - 6 * q^38 - 2 * q^40 + 10 * q^41 + 2 * q^42 - 14 * q^43 + 2 * q^45 + 8 * q^46 - 6 * q^47 + 2 * q^48 + 2 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 - 2 * q^54 - 18 * q^55 + 2 * q^56 + 6 * q^57 + 14 * q^58 - 4 * q^59 + 2 * q^60 + 4 * q^61 - 10 * q^62 - 2 * q^63 + 2 * q^64 - 20 * q^67 - 8 * q^68 - 8 * q^69 + 2 * q^70 + 18 * q^71 - 2 * q^72 + 4 * q^73 - 10 * q^74 - 2 * q^75 + 6 * q^76 + 18 * q^79 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 22 * q^83 - 2 * q^84 - 14 * q^85 + 14 * q^86 - 14 * q^87 - 6 * q^89 - 2 * q^90 - 8 * q^92 + 10 * q^93 + 6 * q^94 + 18 * q^95 - 2 * q^96 - 18 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.732051	−0.327383	−0.163692	−	0.986512i	$-0.552340\pi$
$5$	−0.732051	−0.327383	−0.163692	+	0.986512i	$0.552340\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.732051	0.231495
$11$	5.19615	1.56670	0.783349	−	0.621582i	$-0.213510\pi$
$11$	5.19615	1.56670	0.783349	+	0.621582i	$0.213510\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−0.732051	−0.189015
$16$	1.00000	0.250000
$17$	−2.26795	−0.550058	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	−2.26795	−0.550058	−0.275029	+	0.961436i	$0.588688\pi$
$18$	−1.00000	−0.235702
$19$	−0.464102	−0.106472	−0.0532361	−	0.998582i	$-0.516954\pi$
$19$	−0.464102	−0.106472	−0.0532361	+	0.998582i	$0.516954\pi$
$20$	−0.732051	−0.163692
$21$	−1.00000	−0.218218
$22$	−5.19615	−1.10782
$23$	−7.46410	−1.55637	−0.778186	−	0.628033i	$-0.783860\pi$
$23$	−7.46410	−1.55637	−0.778186	+	0.628033i	$0.783860\pi$
$24$	−1.00000	−0.204124
$25$	−4.46410	−0.892820
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−3.53590	−0.656600	−0.328300	−	0.944574i	$-0.606476\pi$
$29$	−3.53590	−0.656600	−0.328300	+	0.944574i	$0.606476\pi$
$30$	0.732051	0.133654
$31$	3.26795	0.586941	0.293471	−	0.955968i	$-0.405190\pi$
$31$	3.26795	0.586941	0.293471	+	0.955968i	$0.405190\pi$
$32$	−1.00000	−0.176777
$33$	5.19615	0.904534
$34$	2.26795	0.388950
$35$	0.732051	0.123739
$36$	1.00000	0.166667
$37$	6.73205	1.10674	0.553371	−	0.832935i	$-0.313341\pi$
$37$	6.73205	1.10674	0.553371	+	0.832935i	$0.313341\pi$
$38$	0.464102	0.0752872
$39$	0	0
$40$	0.732051	0.115747
$41$	8.46410	1.32187	0.660935	−	0.750443i	$-0.270160\pi$
$41$	8.46410	1.32187	0.660935	+	0.750443i	$0.270160\pi$
$42$	1.00000	0.154303
$43$	−8.73205	−1.33163	−0.665813	−	0.746119i	$-0.731915\pi$
$43$	−8.73205	−1.33163	−0.665813	+	0.746119i	$0.731915\pi$
$44$	5.19615	0.783349
$45$	−0.732051	−0.109128
$46$	7.46410	1.10052
$47$	3.92820	0.572987	0.286494	−	0.958082i	$-0.407510\pi$
$47$	3.92820	0.572987	0.286494	+	0.958082i	$0.407510\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.46410	0.631319
$51$	−2.26795	−0.317576
$52$	0	0
$53$	−9.92820	−1.36374	−0.681872	−	0.731472i	$-0.738834\pi$
$53$	−9.92820	−1.36374	−0.681872	+	0.731472i	$0.738834\pi$
$54$	−1.00000	−0.136083
$55$	−3.80385	−0.512911
$56$	1.00000	0.133631
$57$	−0.464102	−0.0614718
$58$	3.53590	0.464286
$59$	−8.92820	−1.16235	−0.581177	−	0.813778i	$-0.697407\pi$
$59$	−8.92820	−1.16235	−0.581177	+	0.813778i	$0.697407\pi$
$60$	−0.732051	−0.0945074
$61$	3.73205	0.477840	0.238920	−	0.971039i	$-0.423207\pi$
$61$	3.73205	0.477840	0.238920	+	0.971039i	$0.423207\pi$
$62$	−3.26795	−0.415030
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.19615	−0.639602
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−2.26795	−0.275029
$69$	−7.46410	−0.898572
$70$	−0.732051	−0.0874968
$71$	7.26795	0.862547	0.431273	−	0.902221i	$-0.358064\pi$
$71$	7.26795	0.862547	0.431273	+	0.902221i	$0.358064\pi$
$72$	−1.00000	−0.117851
$73$	−1.46410	−0.171360	−0.0856801	−	0.996323i	$-0.527306\pi$
$73$	−1.46410	−0.171360	−0.0856801	+	0.996323i	$0.527306\pi$
$74$	−6.73205	−0.782585
$75$	−4.46410	−0.515470
$76$	−0.464102	−0.0532361
$77$	−5.19615	−0.592157
$78$	0	0
$79$	9.00000	1.01258	0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000	1.01258	0.506290	+	0.862364i	$0.331017\pi$
$80$	−0.732051	−0.0818458
$81$	1.00000	0.111111
$82$	−8.46410	−0.934704
$83$	−9.26795	−1.01729	−0.508645	−	0.860976i	$-0.669853\pi$
$83$	−9.26795	−1.01729	−0.508645	+	0.860976i	$0.669853\pi$
$84$	−1.00000	−0.109109
$85$	1.66025	0.180080
$86$	8.73205	0.941601
$87$	−3.53590	−0.379088
$88$	−5.19615	−0.553912
$89$	−16.8564	−1.78678	−0.893388	−	0.449286i	$-0.851678\pi$
$89$	−16.8564	−1.78678	−0.893388	+	0.449286i	$0.851678\pi$
$90$	0.732051	0.0771649
$91$	0	0
$92$	−7.46410	−0.778186
$93$	3.26795	0.338871
$94$	−3.92820	−0.405163
$95$	0.339746	0.0348572
$96$	−1.00000	−0.102062
$97$	−14.1962	−1.44140	−0.720700	−	0.693247i	$-0.756180\pi$
$97$	−14.1962	−1.44140	−0.720700	+	0.693247i	$0.756180\pi$
$98$	−1.00000	−0.101015
$99$	5.19615	0.522233
$100$	−4.46410	−0.446410
$101$	4.92820	0.490375	0.245187	−	0.969476i	$-0.421151\pi$
$101$	4.92820	0.490375	0.245187	+	0.969476i	$0.421151\pi$
$102$	2.26795	0.224560
$103$	−16.1962	−1.59585	−0.797927	−	0.602754i	$-0.794070\pi$
$103$	−16.1962	−1.59585	−0.797927	+	0.602754i	$0.794070\pi$
$104$	0	0
$105$	0.732051	0.0714408
$106$	9.92820	0.964312
$107$	−6.07180	−0.586983	−0.293491	−	0.955962i	$-0.594817\pi$
$107$	−6.07180	−0.586983	−0.293491	+	0.955962i	$0.594817\pi$
$108$	1.00000	0.0962250
$109$	−11.2679	−1.07927	−0.539637	−	0.841898i	$-0.681438\pi$
$109$	−11.2679	−1.07927	−0.539637	+	0.841898i	$0.681438\pi$
$110$	3.80385	0.362683
$111$	6.73205	0.638978
$112$	−1.00000	−0.0944911
$113$	7.66025	0.720616	0.360308	−	0.932833i	$-0.382672\pi$
$113$	7.66025	0.720616	0.360308	+	0.932833i	$0.382672\pi$
$114$	0.464102	0.0434671
$115$	5.46410	0.509530
$116$	−3.53590	−0.328300
$117$	0	0
$118$	8.92820	0.821908
$119$	2.26795	0.207903
$120$	0.732051	0.0668268
$121$	16.0000	1.45455
$122$	−3.73205	−0.337884
$123$	8.46410	0.763182
$124$	3.26795	0.293471
$125$	6.92820	0.619677
$126$	1.00000	0.0890871
$127$	14.3923	1.27711	0.638555	−	0.769576i	$-0.279532\pi$
$127$	14.3923	1.27711	0.638555	+	0.769576i	$0.279532\pi$
$128$	−1.00000	−0.0883883
$129$	−8.73205	−0.768814
$130$	0	0
$131$	−14.9282	−1.30428	−0.652142	−	0.758097i	$-0.726129\pi$
$131$	−14.9282	−1.30428	−0.652142	+	0.758097i	$0.726129\pi$
$132$	5.19615	0.452267
$133$	0.464102	0.0402427
$134$	10.0000	0.863868
$135$	−0.732051	−0.0630049
$136$	2.26795	0.194475
$137$	19.4641	1.66293	0.831465	−	0.555577i	$-0.187503\pi$
$137$	19.4641	1.66293	0.831465	+	0.555577i	$0.187503\pi$
$138$	7.46410	0.635387
$139$	17.0526	1.44638	0.723190	−	0.690650i	$-0.242675\pi$
$139$	17.0526	1.44638	0.723190	+	0.690650i	$0.242675\pi$
$140$	0.732051	0.0618696
$141$	3.92820	0.330814
$142$	−7.26795	−0.609913
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.58846	0.214960
$146$	1.46410	0.121170
$147$	1.00000	0.0824786
$148$	6.73205	0.553371
$149$	−8.00000	−0.655386	−0.327693	−	0.944784i	$-0.606271\pi$
$149$	−8.00000	−0.655386	−0.327693	+	0.944784i	$0.606271\pi$
$150$	4.46410	0.364492
$151$	−1.19615	−0.0973415	−0.0486708	−	0.998815i	$-0.515499\pi$
$151$	−1.19615	−0.0973415	−0.0486708	+	0.998815i	$0.515499\pi$
$152$	0.464102	0.0376436
$153$	−2.26795	−0.183353
$154$	5.19615	0.418718
$155$	−2.39230	−0.192155
$156$	0	0
$157$	−11.4641	−0.914935	−0.457467	−	0.889226i	$-0.651243\pi$
$157$	−11.4641	−0.914935	−0.457467	+	0.889226i	$0.651243\pi$
$158$	−9.00000	−0.716002
$159$	−9.92820	−0.787358
$160$	0.732051	0.0578737
$161$	7.46410	0.588254
$162$	−1.00000	−0.0785674
$163$	7.12436	0.558023	0.279011	−	0.960288i	$-0.409993\pi$
$163$	7.12436	0.558023	0.279011	+	0.960288i	$0.409993\pi$
$164$	8.46410	0.660935
$165$	−3.80385	−0.296129
$166$	9.26795	0.719332
$167$	−5.07180	−0.392467	−0.196234	−	0.980557i	$-0.562871\pi$
$167$	−5.07180	−0.392467	−0.196234	+	0.980557i	$0.562871\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−1.66025	−0.127336
$171$	−0.464102	−0.0354907
$172$	−8.73205	−0.665813
$173$	2.19615	0.166970	0.0834852	−	0.996509i	$-0.473395\pi$
$173$	2.19615	0.166970	0.0834852	+	0.996509i	$0.473395\pi$
$174$	3.53590	0.268056
$175$	4.46410	0.337454
$176$	5.19615	0.391675
$177$	−8.92820	−0.671085
$178$	16.8564	1.26344
$179$	−3.46410	−0.258919	−0.129460	−	0.991585i	$-0.541324\pi$
$179$	−3.46410	−0.258919	−0.129460	+	0.991585i	$0.541324\pi$
$180$	−0.732051	−0.0545638
$181$	−14.2679	−1.06053	−0.530264	−	0.847832i	$-0.677907\pi$
$181$	−14.2679	−1.06053	−0.530264	+	0.847832i	$0.677907\pi$
$182$	0	0
$183$	3.73205	0.275881
$184$	7.46410	0.550261
$185$	−4.92820	−0.362329
$186$	−3.26795	−0.239618
$187$	−11.7846	−0.861776
$188$	3.92820	0.286494
$189$	−1.00000	−0.0727393
$190$	−0.339746	−0.0246478
$191$	−8.19615	−0.593053	−0.296526	−	0.955025i	$-0.595828\pi$
$191$	−8.19615	−0.593053	−0.296526	+	0.955025i	$0.595828\pi$
$192$	1.00000	0.0721688
$193$	7.58846	0.546229	0.273115	−	0.961982i	$-0.411946\pi$
$193$	7.58846	0.546229	0.273115	+	0.961982i	$0.411946\pi$
$194$	14.1962	1.01922
$195$	0	0
$196$	1.00000	0.0714286
$197$	−0.267949	−0.0190906	−0.00954529	−	0.999954i	$-0.503038\pi$
$197$	−0.267949	−0.0190906	−0.00954529	+	0.999954i	$0.503038\pi$
$198$	−5.19615	−0.369274
$199$	24.5885	1.74303	0.871515	−	0.490369i	$-0.163138\pi$
$199$	24.5885	1.74303	0.871515	+	0.490369i	$0.163138\pi$
$200$	4.46410	0.315660
$201$	−10.0000	−0.705346
$202$	−4.92820	−0.346747
$203$	3.53590	0.248171
$204$	−2.26795	−0.158788
$205$	−6.19615	−0.432758
$206$	16.1962	1.12844
$207$	−7.46410	−0.518791
$208$	0	0
$209$	−2.41154	−0.166810
$210$	−0.732051	−0.0505163
$211$	24.9282	1.71613	0.858064	−	0.513543i	$-0.171667\pi$
$211$	24.9282	1.71613	0.858064	+	0.513543i	$0.171667\pi$
$212$	−9.92820	−0.681872
$213$	7.26795	0.497992
$214$	6.07180	0.415059
$215$	6.39230	0.435952
$216$	−1.00000	−0.0680414
$217$	−3.26795	−0.221843
$218$	11.2679	0.763162
$219$	−1.46410	−0.0989348
$220$	−3.80385	−0.256455
$221$	0	0
$222$	−6.73205	−0.451826
$223$	5.46410	0.365903	0.182952	−	0.983122i	$-0.441435\pi$
$223$	5.46410	0.365903	0.182952	+	0.983122i	$0.441435\pi$
$224$	1.00000	0.0668153
$225$	−4.46410	−0.297607
$226$	−7.66025	−0.509553
$227$	−13.3205	−0.884113	−0.442057	−	0.896987i	$-0.645751\pi$
$227$	−13.3205	−0.884113	−0.442057	+	0.896987i	$0.645751\pi$
$228$	−0.464102	−0.0307359
$229$	17.3923	1.14932	0.574658	−	0.818394i	$-0.305135\pi$
$229$	17.3923	1.14932	0.574658	+	0.818394i	$0.305135\pi$
$230$	−5.46410	−0.360292
$231$	−5.19615	−0.341882
$232$	3.53590	0.232143
$233$	−18.5885	−1.21777	−0.608885	−	0.793258i	$-0.708383\pi$
$233$	−18.5885	−1.21777	−0.608885	+	0.793258i	$0.708383\pi$
$234$	0	0
$235$	−2.87564	−0.187586
$236$	−8.92820	−0.581177
$237$	9.00000	0.584613
$238$	−2.26795	−0.147009
$239$	−26.5885	−1.71986	−0.859932	−	0.510408i	$-0.829494\pi$
$239$	−26.5885	−1.71986	−0.859932	+	0.510408i	$0.829494\pi$
$240$	−0.732051	−0.0472537
$241$	−10.9282	−0.703947	−0.351974	−	0.936010i	$-0.614489\pi$
$241$	−10.9282	−0.703947	−0.351974	+	0.936010i	$0.614489\pi$
$242$	−16.0000	−1.02852
$243$	1.00000	0.0641500
$244$	3.73205	0.238920
$245$	−0.732051	−0.0467690
$246$	−8.46410	−0.539651
$247$	0	0
$248$	−3.26795	−0.207515
$249$	−9.26795	−0.587332
$250$	−6.92820	−0.438178
$251$	17.5167	1.10564	0.552821	−	0.833300i	$-0.313551\pi$
$251$	17.5167	1.10564	0.552821	+	0.833300i	$0.313551\pi$
$252$	−1.00000	−0.0629941
$253$	−38.7846	−2.43837
$254$	−14.3923	−0.903054
$255$	1.66025	0.103969
$256$	1.00000	0.0625000
$257$	−25.0526	−1.56274	−0.781368	−	0.624071i	$-0.785478\pi$
$257$	−25.0526	−1.56274	−0.781368	+	0.624071i	$0.785478\pi$
$258$	8.73205	0.543634
$259$	−6.73205	−0.418309
$260$	0	0
$261$	−3.53590	−0.218867
$262$	14.9282	0.922267
$263$	3.12436	0.192656	0.0963280	−	0.995350i	$-0.469290\pi$
$263$	3.12436	0.192656	0.0963280	+	0.995350i	$0.469290\pi$
$264$	−5.19615	−0.319801
$265$	7.26795	0.446467
$266$	−0.464102	−0.0284559
$267$	−16.8564	−1.03160
$268$	−10.0000	−0.610847
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0.732051	0.0445512
$271$	7.66025	0.465327	0.232664	−	0.972557i	$-0.425256\pi$
$271$	7.66025	0.465327	0.232664	+	0.972557i	$0.425256\pi$
$272$	−2.26795	−0.137515
$273$	0	0
$274$	−19.4641	−1.17587
$275$	−23.1962	−1.39878
$276$	−7.46410	−0.449286
$277$	−14.3923	−0.864750	−0.432375	−	0.901694i	$-0.642324\pi$
$277$	−14.3923	−0.864750	−0.432375	+	0.901694i	$0.642324\pi$
$278$	−17.0526	−1.02274
$279$	3.26795	0.195647
$280$	−0.732051	−0.0437484
$281$	12.7321	0.759530	0.379765	−	0.925083i	$-0.376005\pi$
$281$	12.7321	0.759530	0.379765	+	0.925083i	$0.376005\pi$
$282$	−3.92820	−0.233921
$283$	−17.8564	−1.06145	−0.530727	−	0.847543i	$-0.678081\pi$
$283$	−17.8564	−1.06145	−0.530727	+	0.847543i	$0.678081\pi$
$284$	7.26795	0.431273
$285$	0.339746	0.0201248
$286$	0	0
$287$	−8.46410	−0.499620
$288$	−1.00000	−0.0589256
$289$	−11.8564	−0.697436
$290$	−2.58846	−0.151999
$291$	−14.1962	−0.832193
$292$	−1.46410	−0.0856801
$293$	−1.07180	−0.0626150	−0.0313075	−	0.999510i	$-0.509967\pi$
$293$	−1.07180	−0.0626150	−0.0313075	+	0.999510i	$0.509967\pi$
$294$	−1.00000	−0.0583212
$295$	6.53590	0.380535
$296$	−6.73205	−0.391293
$297$	5.19615	0.301511
$298$	8.00000	0.463428
$299$	0	0
$300$	−4.46410	−0.257735
$301$	8.73205	0.503307
$302$	1.19615	0.0688308
$303$	4.92820	0.283118
$304$	−0.464102	−0.0266181
$305$	−2.73205	−0.156437
$306$	2.26795	0.129650
$307$	−5.00000	−0.285365	−0.142683	−	0.989769i	$-0.545573\pi$
$307$	−5.00000	−0.285365	−0.142683	+	0.989769i	$0.545573\pi$
$308$	−5.19615	−0.296078
$309$	−16.1962	−0.921367
$310$	2.39230	0.135874
$311$	−14.8038	−0.839449	−0.419725	−	0.907652i	$-0.637873\pi$
$311$	−14.8038	−0.839449	−0.419725	+	0.907652i	$0.637873\pi$
$312$	0	0
$313$	6.87564	0.388634	0.194317	−	0.980939i	$-0.437751\pi$
$313$	6.87564	0.388634	0.194317	+	0.980939i	$0.437751\pi$
$314$	11.4641	0.646957
$315$	0.732051	0.0412464
$316$	9.00000	0.506290
$317$	−14.7846	−0.830386	−0.415193	−	0.909733i	$-0.636286\pi$
$317$	−14.7846	−0.830386	−0.415193	+	0.909733i	$0.636286\pi$
$318$	9.92820	0.556746
$319$	−18.3731	−1.02869
$320$	−0.732051	−0.0409229
$321$	−6.07180	−0.338895
$322$	−7.46410	−0.415958
$323$	1.05256	0.0585659
$324$	1.00000	0.0555556
$325$	0	0
$326$	−7.12436	−0.394582
$327$	−11.2679	−0.623119
$328$	−8.46410	−0.467352
$329$	−3.92820	−0.216569
$330$	3.80385	0.209395
$331$	6.78461	0.372916	0.186458	−	0.982463i	$-0.440299\pi$
$331$	6.78461	0.372916	0.186458	+	0.982463i	$0.440299\pi$
$332$	−9.26795	−0.508645
$333$	6.73205	0.368914
$334$	5.07180	0.277516
$335$	7.32051	0.399962
$336$	−1.00000	−0.0545545
$337$	11.0000	0.599208	0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000	0.599208	0.299604	+	0.954064i	$0.403145\pi$
$338$	0	0
$339$	7.66025	0.416048
$340$	1.66025	0.0900399
$341$	16.9808	0.919560
$342$	0.464102	0.0250957
$343$	−1.00000	−0.0539949
$344$	8.73205	0.470801
$345$	5.46410	0.294177
$346$	−2.19615	−0.118066
$347$	−6.46410	−0.347011	−0.173506	−	0.984833i	$-0.555509\pi$
$347$	−6.46410	−0.347011	−0.173506	+	0.984833i	$0.555509\pi$
$348$	−3.53590	−0.189544
$349$	6.14359	0.328859	0.164430	−	0.986389i	$-0.447422\pi$
$349$	6.14359	0.328859	0.164430	+	0.986389i	$0.447422\pi$
$350$	−4.46410	−0.238616
$351$	0	0
$352$	−5.19615	−0.276956
$353$	−31.3205	−1.66702	−0.833511	−	0.552503i	$-0.813673\pi$
$353$	−31.3205	−1.66702	−0.833511	+	0.552503i	$0.813673\pi$
$354$	8.92820	0.474529
$355$	−5.32051	−0.282383
$356$	−16.8564	−0.893388
$357$	2.26795	0.120033
$358$	3.46410	0.183083
$359$	−34.4449	−1.81793	−0.908965	−	0.416872i	$-0.863126\pi$
$359$	−34.4449	−1.81793	−0.908965	+	0.416872i	$0.863126\pi$
$360$	0.732051	0.0385825
$361$	−18.7846	−0.988664
$362$	14.2679	0.749907
$363$	16.0000	0.839782
$364$	0	0
$365$	1.07180	0.0561004
$366$	−3.73205	−0.195077
$367$	13.3205	0.695325	0.347662	−	0.937620i	$-0.386976\pi$
$367$	13.3205	0.695325	0.347662	+	0.937620i	$0.386976\pi$
$368$	−7.46410	−0.389093
$369$	8.46410	0.440624
$370$	4.92820	0.256205
$371$	9.92820	0.515447
$372$	3.26795	0.169435
$373$	−15.1244	−0.783109	−0.391555	−	0.920155i	$-0.628063\pi$
$373$	−15.1244	−0.783109	−0.391555	+	0.920155i	$0.628063\pi$
$374$	11.7846	0.609368
$375$	6.92820	0.357771
$376$	−3.92820	−0.202582
$377$	0	0
$378$	1.00000	0.0514344
$379$	36.0526	1.85190	0.925948	−	0.377652i	$-0.123268\pi$
$379$	36.0526	1.85190	0.925948	+	0.377652i	$0.123268\pi$
$380$	0.339746	0.0174286
$381$	14.3923	0.737340
$382$	8.19615	0.419352
$383$	31.0000	1.58403	0.792013	−	0.610504i	$-0.209033\pi$
$383$	31.0000	1.58403	0.792013	+	0.610504i	$0.209033\pi$
$384$	−1.00000	−0.0510310
$385$	3.80385	0.193862
$386$	−7.58846	−0.386242
$387$	−8.73205	−0.443875
$388$	−14.1962	−0.720700
$389$	−21.4641	−1.08827	−0.544137	−	0.838997i	$-0.683143\pi$
$389$	−21.4641	−1.08827	−0.544137	+	0.838997i	$0.683143\pi$
$390$	0	0
$391$	16.9282	0.856096
$392$	−1.00000	−0.0505076
$393$	−14.9282	−0.753028
$394$	0.267949	0.0134991
$395$	−6.58846	−0.331501
$396$	5.19615	0.261116
$397$	21.3923	1.07365	0.536825	−	0.843694i	$-0.319624\pi$
$397$	21.3923	1.07365	0.536825	+	0.843694i	$0.319624\pi$
$398$	−24.5885	−1.23251
$399$	0.464102	0.0232341
$400$	−4.46410	−0.223205
$401$	−11.0718	−0.552899	−0.276450	−	0.961028i	$-0.589158\pi$
$401$	−11.0718	−0.552899	−0.276450	+	0.961028i	$0.589158\pi$
$402$	10.0000	0.498755
$403$	0	0
$404$	4.92820	0.245187
$405$	−0.732051	−0.0363759
$406$	−3.53590	−0.175484
$407$	34.9808	1.73393
$408$	2.26795	0.112280
$409$	−16.5885	−0.820246	−0.410123	−	0.912030i	$-0.634514\pi$
$409$	−16.5885	−0.820246	−0.410123	+	0.912030i	$0.634514\pi$
$410$	6.19615	0.306006
$411$	19.4641	0.960093
$412$	−16.1962	−0.797927
$413$	8.92820	0.439328
$414$	7.46410	0.366841
$415$	6.78461	0.333043
$416$	0	0
$417$	17.0526	0.835067
$418$	2.41154	0.117952
$419$	−14.5885	−0.712693	−0.356346	−	0.934354i	$-0.615978\pi$
$419$	−14.5885	−0.712693	−0.356346	+	0.934354i	$0.615978\pi$
$420$	0.732051	0.0357204
$421$	−25.3205	−1.23405	−0.617023	−	0.786945i	$-0.711661\pi$
$421$	−25.3205	−1.23405	−0.617023	+	0.786945i	$0.711661\pi$
$422$	−24.9282	−1.21349
$423$	3.92820	0.190996
$424$	9.92820	0.482156
$425$	10.1244	0.491103
$426$	−7.26795	−0.352133
$427$	−3.73205	−0.180607
$428$	−6.07180	−0.293491
$429$	0	0
$430$	−6.39230	−0.308264
$431$	−13.1244	−0.632178	−0.316089	−	0.948730i	$-0.602370\pi$
$431$	−13.1244	−0.632178	−0.316089	+	0.948730i	$0.602370\pi$
$432$	1.00000	0.0481125
$433$	12.1436	0.583584	0.291792	−	0.956482i	$-0.405749\pi$
$433$	12.1436	0.583584	0.291792	+	0.956482i	$0.405749\pi$
$434$	3.26795	0.156867
$435$	2.58846	0.124107
$436$	−11.2679	−0.539637
$437$	3.46410	0.165710
$438$	1.46410	0.0699575
$439$	23.3205	1.11303	0.556514	−	0.830839i	$-0.312139\pi$
$439$	23.3205	1.11303	0.556514	+	0.830839i	$0.312139\pi$
$440$	3.80385	0.181341
$441$	1.00000	0.0476190
$442$	0	0
$443$	−25.0000	−1.18779	−0.593893	−	0.804544i	$-0.702410\pi$
$443$	−25.0000	−1.18779	−0.593893	+	0.804544i	$0.702410\pi$
$444$	6.73205	0.319489
$445$	12.3397	0.584960
$446$	−5.46410	−0.258733
$447$	−8.00000	−0.378387
$448$	−1.00000	−0.0472456
$449$	−28.9808	−1.36769	−0.683843	−	0.729629i	$-0.739693\pi$
$449$	−28.9808	−1.36769	−0.683843	+	0.729629i	$0.739693\pi$
$450$	4.46410	0.210440
$451$	43.9808	2.07097
$452$	7.66025	0.360308
$453$	−1.19615	−0.0562001
$454$	13.3205	0.625162
$455$	0	0
$456$	0.464102	0.0217335
$457$	29.7128	1.38991	0.694953	−	0.719055i	$-0.255425\pi$
$457$	29.7128	1.38991	0.694953	+	0.719055i	$0.255425\pi$
$458$	−17.3923	−0.812689
$459$	−2.26795	−0.105859
$460$	5.46410	0.254765
$461$	6.92820	0.322679	0.161339	−	0.986899i	$-0.448419\pi$
$461$	6.92820	0.322679	0.161339	+	0.986899i	$0.448419\pi$
$462$	5.19615	0.241747
$463$	15.3397	0.712898	0.356449	−	0.934315i	$-0.383987\pi$
$463$	15.3397	0.712898	0.356449	+	0.934315i	$0.383987\pi$
$464$	−3.53590	−0.164150
$465$	−2.39230	−0.110940
$466$	18.5885	0.861094
$467$	−18.9282	−0.875893	−0.437946	−	0.899001i	$-0.644294\pi$
$467$	−18.9282	−0.875893	−0.437946	+	0.899001i	$0.644294\pi$
$468$	0	0
$469$	10.0000	0.461757
$470$	2.87564	0.132644
$471$	−11.4641	−0.528238
$472$	8.92820	0.410954
$473$	−45.3731	−2.08626
$474$	−9.00000	−0.413384
$475$	2.07180	0.0950606
$476$	2.26795	0.103951
$477$	−9.92820	−0.454581
$478$	26.5885	1.21613
$479$	4.85641	0.221895	0.110947	−	0.993826i	$-0.464611\pi$
$479$	4.85641	0.221895	0.110947	+	0.993826i	$0.464611\pi$
$480$	0.732051	0.0334134
$481$	0	0
$482$	10.9282	0.497766
$483$	7.46410	0.339628
$484$	16.0000	0.727273
$485$	10.3923	0.471890
$486$	−1.00000	−0.0453609
$487$	−29.4449	−1.33427	−0.667137	−	0.744935i	$-0.732480\pi$
$487$	−29.4449	−1.33427	−0.667137	+	0.744935i	$0.732480\pi$
$488$	−3.73205	−0.168942
$489$	7.12436	0.322174
$490$	0.732051	0.0330707
$491$	−6.39230	−0.288481	−0.144240	−	0.989543i	$-0.546074\pi$
$491$	−6.39230	−0.288481	−0.144240	+	0.989543i	$0.546074\pi$
$492$	8.46410	0.381591
$493$	8.01924	0.361168
$494$	0	0
$495$	−3.80385	−0.170970
$496$	3.26795	0.146735
$497$	−7.26795	−0.326012
$498$	9.26795	0.415307
$499$	−20.5885	−0.921666	−0.460833	−	0.887487i	$-0.652449\pi$
$499$	−20.5885	−0.921666	−0.460833	+	0.887487i	$0.652449\pi$
$500$	6.92820	0.309839
$501$	−5.07180	−0.226591
$502$	−17.5167	−0.781807
$503$	−30.9282	−1.37902	−0.689510	−	0.724276i	$-0.742174\pi$
$503$	−30.9282	−1.37902	−0.689510	+	0.724276i	$0.742174\pi$
$504$	1.00000	0.0445435
$505$	−3.60770	−0.160540
$506$	38.7846	1.72419
$507$	0	0
$508$	14.3923	0.638555
$509$	29.6603	1.31467	0.657334	−	0.753600i	$-0.271684\pi$
$509$	29.6603	1.31467	0.657334	+	0.753600i	$0.271684\pi$
$510$	−1.66025	−0.0735173
$511$	1.46410	0.0647680
$512$	−1.00000	−0.0441942
$513$	−0.464102	−0.0204906
$514$	25.0526	1.10502
$515$	11.8564	0.522456
$516$	−8.73205	−0.384407
$517$	20.4115	0.897699
$518$	6.73205	0.295789
$519$	2.19615	0.0964004
$520$	0	0
$521$	−21.5885	−0.945807	−0.472904	−	0.881114i	$-0.656794\pi$
$521$	−21.5885	−0.945807	−0.472904	+	0.881114i	$0.656794\pi$
$522$	3.53590	0.154762
$523$	−25.1962	−1.10175	−0.550875	−	0.834587i	$-0.685706\pi$
$523$	−25.1962	−1.10175	−0.550875	+	0.834587i	$0.685706\pi$
$524$	−14.9282	−0.652142
$525$	4.46410	0.194829
$526$	−3.12436	−0.136228
$527$	−7.41154	−0.322852
$528$	5.19615	0.226134
$529$	32.7128	1.42230
$530$	−7.26795	−0.315700
$531$	−8.92820	−0.387451
$532$	0.464102	0.0201214
$533$	0	0
$534$	16.8564	0.729448
$535$	4.44486	0.192168
$536$	10.0000	0.431934
$537$	−3.46410	−0.149487
$538$	4.00000	0.172452
$539$	5.19615	0.223814
$540$	−0.732051	−0.0315025
$541$	8.05256	0.346207	0.173103	−	0.984904i	$-0.444621\pi$
$541$	8.05256	0.346207	0.173103	+	0.984904i	$0.444621\pi$
$542$	−7.66025	−0.329036
$543$	−14.2679	−0.612296
$544$	2.26795	0.0972375
$545$	8.24871	0.353336
$546$	0	0
$547$	−4.19615	−0.179415	−0.0897073	−	0.995968i	$-0.528593\pi$
$547$	−4.19615	−0.179415	−0.0897073	+	0.995968i	$0.528593\pi$
$548$	19.4641	0.831465
$549$	3.73205	0.159280
$550$	23.1962	0.989087
$551$	1.64102	0.0699096
$552$	7.46410	0.317693
$553$	−9.00000	−0.382719
$554$	14.3923	0.611470
$555$	−4.92820	−0.209191
$556$	17.0526	0.723190
$557$	19.7321	0.836074	0.418037	−	0.908430i	$-0.362718\pi$
$557$	19.7321	0.836074	0.418037	+	0.908430i	$0.362718\pi$
$558$	−3.26795	−0.138343
$559$	0	0
$560$	0.732051	0.0309348
$561$	−11.7846	−0.497547
$562$	−12.7321	−0.537069
$563$	−13.6603	−0.575711	−0.287856	−	0.957674i	$-0.592942\pi$
$563$	−13.6603	−0.575711	−0.287856	+	0.957674i	$0.592942\pi$
$564$	3.92820	0.165407
$565$	−5.60770	−0.235918
$566$	17.8564	0.750561
$567$	−1.00000	−0.0419961
$568$	−7.26795	−0.304956
$569$	1.66025	0.0696015	0.0348007	−	0.999394i	$-0.488920\pi$
$569$	1.66025	0.0696015	0.0348007	+	0.999394i	$0.488920\pi$
$570$	−0.339746	−0.0142304
$571$	−39.5167	−1.65372	−0.826860	−	0.562407i	$-0.809875\pi$
$571$	−39.5167	−1.65372	−0.826860	+	0.562407i	$0.809875\pi$
$572$	0	0
$573$	−8.19615	−0.342399
$574$	8.46410	0.353285
$575$	33.3205	1.38956
$576$	1.00000	0.0416667
$577$	28.5885	1.19015	0.595077	−	0.803669i	$-0.297122\pi$
$577$	28.5885	1.19015	0.595077	+	0.803669i	$0.297122\pi$
$578$	11.8564	0.493161
$579$	7.58846	0.315366
$580$	2.58846	0.107480
$581$	9.26795	0.384499
$582$	14.1962	0.588449
$583$	−51.5885	−2.13658
$584$	1.46410	0.0605850
$585$	0	0
$586$	1.07180	0.0442755
$587$	5.12436	0.211505	0.105752	−	0.994392i	$-0.466275\pi$
$587$	5.12436	0.211505	0.105752	+	0.994392i	$0.466275\pi$
$588$	1.00000	0.0412393
$589$	−1.51666	−0.0624929
$590$	−6.53590	−0.269079
$591$	−0.267949	−0.0110220
$592$	6.73205	0.276686
$593$	−37.0000	−1.51941	−0.759704	−	0.650269i	$-0.774656\pi$
$593$	−37.0000	−1.51941	−0.759704	+	0.650269i	$0.774656\pi$
$594$	−5.19615	−0.213201
$595$	−1.66025	−0.0680638
$596$	−8.00000	−0.327693
$597$	24.5885	1.00634
$598$	0	0
$599$	−47.5692	−1.94363	−0.971813	−	0.235754i	$-0.924244\pi$
$599$	−47.5692	−1.94363	−0.971813	+	0.235754i	$0.924244\pi$
$600$	4.46410	0.182246
$601$	−48.3013	−1.97025	−0.985125	−	0.171840i	$-0.945029\pi$
$601$	−48.3013	−1.97025	−0.985125	+	0.171840i	$0.945029\pi$
$602$	−8.73205	−0.355892
$603$	−10.0000	−0.407231
$604$	−1.19615	−0.0486708
$605$	−11.7128	−0.476194
$606$	−4.92820	−0.200195
$607$	−25.6603	−1.04152	−0.520759	−	0.853704i	$-0.674351\pi$
$607$	−25.6603	−1.04152	−0.520759	+	0.853704i	$0.674351\pi$
$608$	0.464102	0.0188218
$609$	3.53590	0.143282
$610$	2.73205	0.110618
$611$	0	0
$612$	−2.26795	−0.0916764
$613$	47.7128	1.92710	0.963551	−	0.267524i	$-0.0862055\pi$
$613$	47.7128	1.92710	0.963551	+	0.267524i	$0.0862055\pi$
$614$	5.00000	0.201784
$615$	−6.19615	−0.249853
$616$	5.19615	0.209359
$617$	13.8038	0.555722	0.277861	−	0.960621i	$-0.410375\pi$
$617$	13.8038	0.555722	0.277861	+	0.960621i	$0.410375\pi$
$618$	16.1962	0.651505
$619$	11.3923	0.457895	0.228948	−	0.973439i	$-0.426472\pi$
$619$	11.3923	0.457895	0.228948	+	0.973439i	$0.426472\pi$
$620$	−2.39230	−0.0960773
$621$	−7.46410	−0.299524
$622$	14.8038	0.593580
$623$	16.8564	0.675338
$624$	0	0
$625$	17.2487	0.689948
$626$	−6.87564	−0.274806
$627$	−2.41154	−0.0963077
$628$	−11.4641	−0.457467
$629$	−15.2679	−0.608773
$630$	−0.732051	−0.0291656
$631$	−1.87564	−0.0746682	−0.0373341	−	0.999303i	$-0.511887\pi$
$631$	−1.87564	−0.0746682	−0.0373341	+	0.999303i	$0.511887\pi$
$632$	−9.00000	−0.358001
$633$	24.9282	0.990807
$634$	14.7846	0.587172
$635$	−10.5359	−0.418104
$636$	−9.92820	−0.393679
$637$	0	0
$638$	18.3731	0.727397
$639$	7.26795	0.287516
$640$	0.732051	0.0289368
$641$	−17.3205	−0.684119	−0.342059	−	0.939678i	$-0.611124\pi$
$641$	−17.3205	−0.684119	−0.342059	+	0.939678i	$0.611124\pi$
$642$	6.07180	0.239635
$643$	2.32051	0.0915119	0.0457560	−	0.998953i	$-0.485430\pi$
$643$	2.32051	0.0915119	0.0457560	+	0.998953i	$0.485430\pi$
$644$	7.46410	0.294127
$645$	6.39230	0.251697
$646$	−1.05256	−0.0414124
$647$	−23.7321	−0.933003	−0.466502	−	0.884520i	$-0.654486\pi$
$647$	−23.7321	−0.933003	−0.466502	+	0.884520i	$0.654486\pi$
$648$	−1.00000	−0.0392837
$649$	−46.3923	−1.82106
$650$	0	0
$651$	−3.26795	−0.128081
$652$	7.12436	0.279011
$653$	−14.7128	−0.575757	−0.287878	−	0.957667i	$-0.592950\pi$
$653$	−14.7128	−0.575757	−0.287878	+	0.957667i	$0.592950\pi$
$654$	11.2679	0.440612
$655$	10.9282	0.427000
$656$	8.46410	0.330468
$657$	−1.46410	−0.0571200
$658$	3.92820	0.153137
$659$	−13.2487	−0.516097	−0.258048	−	0.966132i	$-0.583079\pi$
$659$	−13.2487	−0.516097	−0.258048	+	0.966132i	$0.583079\pi$
$660$	−3.80385	−0.148065
$661$	22.5359	0.876545	0.438272	−	0.898842i	$-0.355591\pi$
$661$	22.5359	0.876545	0.438272	+	0.898842i	$0.355591\pi$
$662$	−6.78461	−0.263691
$663$	0	0
$664$	9.26795	0.359666
$665$	−0.339746	−0.0131748
$666$	−6.73205	−0.260862
$667$	26.3923	1.02191
$668$	−5.07180	−0.196234
$669$	5.46410	0.211254
$670$	−7.32051	−0.282816
$671$	19.3923	0.748632
$672$	1.00000	0.0385758
$673$	−43.6410	−1.68224	−0.841119	−	0.540850i	$-0.818102\pi$
$673$	−43.6410	−1.68224	−0.841119	+	0.540850i	$0.818102\pi$
$674$	−11.0000	−0.423704
$675$	−4.46410	−0.171823
$676$	0	0
$677$	43.2679	1.66292	0.831461	−	0.555583i	$-0.187505\pi$
$677$	43.2679	1.66292	0.831461	+	0.555583i	$0.187505\pi$
$678$	−7.66025	−0.294190
$679$	14.1962	0.544798
$680$	−1.66025	−0.0636678
$681$	−13.3205	−0.510443
$682$	−16.9808	−0.650227
$683$	17.3205	0.662751	0.331375	−	0.943499i	$-0.392487\pi$
$683$	17.3205	0.662751	0.331375	+	0.943499i	$0.392487\pi$
$684$	−0.464102	−0.0177454
$685$	−14.2487	−0.544415
$686$	1.00000	0.0381802
$687$	17.3923	0.663558
$688$	−8.73205	−0.332906
$689$	0	0
$690$	−5.46410	−0.208015
$691$	−37.0718	−1.41028	−0.705139	−	0.709069i	$-0.749115\pi$
$691$	−37.0718	−1.41028	−0.705139	+	0.709069i	$0.749115\pi$
$692$	2.19615	0.0834852
$693$	−5.19615	−0.197386
$694$	6.46410	0.245374
$695$	−12.4833	−0.473520
$696$	3.53590	0.134028
$697$	−19.1962	−0.727106
$698$	−6.14359	−0.232538
$699$	−18.5885	−0.703080
$700$	4.46410	0.168727
$701$	25.7846	0.973871	0.486936	−	0.873438i	$-0.338115\pi$
$701$	25.7846	0.973871	0.486936	+	0.873438i	$0.338115\pi$
$702$	0	0
$703$	−3.12436	−0.117837
$704$	5.19615	0.195837
$705$	−2.87564	−0.108303
$706$	31.3205	1.17876
$707$	−4.92820	−0.185344
$708$	−8.92820	−0.335542
$709$	−51.3731	−1.92936	−0.964678	−	0.263432i	$-0.915146\pi$
$709$	−51.3731	−1.92936	−0.964678	+	0.263432i	$0.915146\pi$
$710$	5.32051	0.199675
$711$	9.00000	0.337526
$712$	16.8564	0.631721
$713$	−24.3923	−0.913499
$714$	−2.26795	−0.0848759
$715$	0	0
$716$	−3.46410	−0.129460
$717$	−26.5885	−0.992964
$718$	34.4449	1.28547
$719$	39.4449	1.47105	0.735523	−	0.677500i	$-0.236937\pi$
$719$	39.4449	1.47105	0.735523	+	0.677500i	$0.236937\pi$
$720$	−0.732051	−0.0272819
$721$	16.1962	0.603176
$722$	18.7846	0.699091
$723$	−10.9282	−0.406424
$724$	−14.2679	−0.530264
$725$	15.7846	0.586226
$726$	−16.0000	−0.593816
$727$	−3.60770	−0.133802	−0.0669010	−	0.997760i	$-0.521311\pi$
$727$	−3.60770	−0.133802	−0.0669010	+	0.997760i	$0.521311\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.07180	−0.0396690
$731$	19.8038	0.732472
$732$	3.73205	0.137941
$733$	25.7846	0.952376	0.476188	−	0.879343i	$-0.342018\pi$
$733$	25.7846	0.952376	0.476188	+	0.879343i	$0.342018\pi$
$734$	−13.3205	−0.491669
$735$	−0.732051	−0.0270021
$736$	7.46410	0.275130
$737$	−51.9615	−1.91403
$738$	−8.46410	−0.311568
$739$	−39.1769	−1.44115	−0.720573	−	0.693379i	$-0.756121\pi$
$739$	−39.1769	−1.44115	−0.720573	+	0.693379i	$0.756121\pi$
$740$	−4.92820	−0.181164
$741$	0	0
$742$	−9.92820	−0.364476
$743$	−14.0526	−0.515538	−0.257769	−	0.966207i	$-0.582987\pi$
$743$	−14.0526	−0.515538	−0.257769	+	0.966207i	$0.582987\pi$
$744$	−3.26795	−0.119809
$745$	5.85641	0.214562
$746$	15.1244	0.553742
$747$	−9.26795	−0.339097
$748$	−11.7846	−0.430888
$749$	6.07180	0.221859
$750$	−6.92820	−0.252982
$751$	5.14359	0.187692	0.0938462	−	0.995587i	$-0.470084\pi$
$751$	5.14359	0.187692	0.0938462	+	0.995587i	$0.470084\pi$
$752$	3.92820	0.143247
$753$	17.5167	0.638343
$754$	0	0
$755$	0.875644	0.0318680
$756$	−1.00000	−0.0363696
$757$	16.1962	0.588659	0.294330	−	0.955704i	$-0.404904\pi$
$757$	16.1962	0.588659	0.294330	+	0.955704i	$0.404904\pi$
$758$	−36.0526	−1.30949
$759$	−38.7846	−1.40779
$760$	−0.339746	−0.0123239
$761$	18.2487	0.661515	0.330758	−	0.943716i	$-0.392696\pi$
$761$	18.2487	0.661515	0.330758	+	0.943716i	$0.392696\pi$
$762$	−14.3923	−0.521378
$763$	11.2679	0.407927
$764$	−8.19615	−0.296526
$765$	1.66025	0.0600266
$766$	−31.0000	−1.12008
$767$	0	0
$768$	1.00000	0.0360844
$769$	43.2679	1.56028	0.780141	−	0.625604i	$-0.215147\pi$
$769$	43.2679	1.56028	0.780141	+	0.625604i	$0.215147\pi$
$770$	−3.80385	−0.137081
$771$	−25.0526	−0.902246
$772$	7.58846	0.273115
$773$	19.1769	0.689746	0.344873	−	0.938649i	$-0.387922\pi$
$773$	19.1769	0.689746	0.344873	+	0.938649i	$0.387922\pi$
$774$	8.73205	0.313867
$775$	−14.5885	−0.524033
$776$	14.1962	0.509612
$777$	−6.73205	−0.241511
$778$	21.4641	0.769525
$779$	−3.92820	−0.140742
$780$	0	0
$781$	37.7654	1.35135
$782$	−16.9282	−0.605351
$783$	−3.53590	−0.126363
$784$	1.00000	0.0357143
$785$	8.39230	0.299534
$786$	14.9282	0.532471
$787$	−8.85641	−0.315697	−0.157848	−	0.987463i	$-0.550456\pi$
$787$	−8.85641	−0.315697	−0.157848	+	0.987463i	$0.550456\pi$
$788$	−0.267949	−0.00954529
$789$	3.12436	0.111230
$790$	6.58846	0.234407
$791$	−7.66025	−0.272367
$792$	−5.19615	−0.184637
$793$	0	0
$794$	−21.3923	−0.759184
$795$	7.26795	0.257768
$796$	24.5885	0.871515
$797$	35.3731	1.25298	0.626489	−	0.779430i	$-0.284491\pi$
$797$	35.3731	1.25298	0.626489	+	0.779430i	$0.284491\pi$
$798$	−0.464102	−0.0164290
$799$	−8.90897	−0.315177
$800$	4.46410	0.157830
$801$	−16.8564	−0.595592
$802$	11.0718	0.390959
$803$	−7.60770	−0.268470
$804$	−10.0000	−0.352673
$805$	−5.46410	−0.192584
$806$	0	0
$807$	−4.00000	−0.140807
$808$	−4.92820	−0.173374
$809$	−9.26795	−0.325844	−0.162922	−	0.986639i	$-0.552092\pi$
$809$	−9.26795	−0.325844	−0.162922	+	0.986639i	$0.552092\pi$
$810$	0.732051	0.0257216
$811$	22.1051	0.776216	0.388108	−	0.921614i	$-0.373129\pi$
$811$	22.1051	0.776216	0.388108	+	0.921614i	$0.373129\pi$
$812$	3.53590	0.124086
$813$	7.66025	0.268657
$814$	−34.9808	−1.22608
$815$	−5.21539	−0.182687
$816$	−2.26795	−0.0793941
$817$	4.05256	0.141781
$818$	16.5885	0.580002
$819$	0	0
$820$	−6.19615	−0.216379
$821$	18.8038	0.656259	0.328129	−	0.944633i	$-0.393582\pi$
$821$	18.8038	0.656259	0.328129	+	0.944633i	$0.393582\pi$
$822$	−19.4641	−0.678889
$823$	21.7128	0.756861	0.378431	−	0.925630i	$-0.376464\pi$
$823$	21.7128	0.756861	0.378431	+	0.925630i	$0.376464\pi$
$824$	16.1962	0.564220
$825$	−23.1962	−0.807586
$826$	−8.92820	−0.310652
$827$	−4.39230	−0.152735	−0.0763677	−	0.997080i	$-0.524332\pi$
$827$	−4.39230	−0.152735	−0.0763677	+	0.997080i	$0.524332\pi$
$828$	−7.46410	−0.259395
$829$	1.48334	0.0515185	0.0257593	−	0.999668i	$-0.491800\pi$
$829$	1.48334	0.0515185	0.0257593	+	0.999668i	$0.491800\pi$
$830$	−6.78461	−0.235497
$831$	−14.3923	−0.499264
$832$	0	0
$833$	−2.26795	−0.0785798
$834$	−17.0526	−0.590482
$835$	3.71281	0.128487
$836$	−2.41154	−0.0834049
$837$	3.26795	0.112957
$838$	14.5885	0.503950
$839$	37.3205	1.28845	0.644224	−	0.764837i	$-0.277181\pi$
$839$	37.3205	1.28845	0.644224	+	0.764837i	$0.277181\pi$
$840$	−0.732051	−0.0252582
$841$	−16.4974	−0.568877
$842$	25.3205	0.872602
$843$	12.7321	0.438515
$844$	24.9282	0.858064
$845$	0	0
$846$	−3.92820	−0.135054
$847$	−16.0000	−0.549767
$848$	−9.92820	−0.340936
$849$	−17.8564	−0.612830
$850$	−10.1244	−0.347263
$851$	−50.2487	−1.72250
$852$	7.26795	0.248996
$853$	−25.2487	−0.864499	−0.432250	−	0.901754i	$-0.642280\pi$
$853$	−25.2487	−0.864499	−0.432250	+	0.901754i	$0.642280\pi$
$854$	3.73205	0.127708
$855$	0.339746	0.0116191
$856$	6.07180	0.207530
$857$	19.4641	0.664881	0.332441	−	0.943124i	$-0.392128\pi$
$857$	19.4641	0.664881	0.332441	+	0.943124i	$0.392128\pi$
$858$	0	0
$859$	16.8038	0.573340	0.286670	−	0.958029i	$-0.407452\pi$
$859$	16.8038	0.573340	0.286670	+	0.958029i	$0.407452\pi$
$860$	6.39230	0.217976
$861$	−8.46410	−0.288456
$862$	13.1244	0.447017
$863$	15.8564	0.539758	0.269879	−	0.962894i	$-0.413016\pi$
$863$	15.8564	0.539758	0.269879	+	0.962894i	$0.413016\pi$
$864$	−1.00000	−0.0340207
$865$	−1.60770	−0.0546633
$866$	−12.1436	−0.412656
$867$	−11.8564	−0.402665
$868$	−3.26795	−0.110921
$869$	46.7654	1.58641
$870$	−2.58846	−0.0877569
$871$	0	0
$872$	11.2679	0.381581
$873$	−14.1962	−0.480467
$874$	−3.46410	−0.117175
$875$	−6.92820	−0.234216
$876$	−1.46410	−0.0494674
$877$	−50.5885	−1.70825	−0.854125	−	0.520067i	$-0.825907\pi$
$877$	−50.5885	−1.70825	−0.854125	+	0.520067i	$0.825907\pi$
$878$	−23.3205	−0.787029
$879$	−1.07180	−0.0361508
$880$	−3.80385	−0.128228
$881$	−39.7128	−1.33796	−0.668979	−	0.743281i	$-0.733269\pi$
$881$	−39.7128	−1.33796	−0.668979	+	0.743281i	$0.733269\pi$
$882$	−1.00000	−0.0336718
$883$	25.5167	0.858704	0.429352	−	0.903137i	$-0.358742\pi$
$883$	25.5167	0.858704	0.429352	+	0.903137i	$0.358742\pi$
$884$	0	0
$885$	6.53590	0.219702
$886$	25.0000	0.839891
$887$	−20.6603	−0.693703	−0.346852	−	0.937920i	$-0.612749\pi$
$887$	−20.6603	−0.693703	−0.346852	+	0.937920i	$0.612749\pi$
$888$	−6.73205	−0.225913
$889$	−14.3923	−0.482702
$890$	−12.3397	−0.413629
$891$	5.19615	0.174078
$892$	5.46410	0.182952
$893$	−1.82309	−0.0610072
$894$	8.00000	0.267560
$895$	2.53590	0.0847657
$896$	1.00000	0.0334077
$897$	0	0
$898$	28.9808	0.967101
$899$	−11.5551	−0.385385
$900$	−4.46410	−0.148803
$901$	22.5167	0.750139
$902$	−43.9808	−1.46440
$903$	8.73205	0.290584
$904$	−7.66025	−0.254776
$905$	10.4449	0.347199
$906$	1.19615	0.0397395
$907$	30.3923	1.00916	0.504580	−	0.863365i	$-0.331647\pi$
$907$	30.3923	1.00916	0.504580	+	0.863365i	$0.331647\pi$
$908$	−13.3205	−0.442057
$909$	4.92820	0.163458
$910$	0	0
$911$	39.1244	1.29625	0.648124	−	0.761535i	$-0.275554\pi$
$911$	39.1244	1.29625	0.648124	+	0.761535i	$0.275554\pi$
$912$	−0.464102	−0.0153679
$913$	−48.1577	−1.59379
$914$	−29.7128	−0.982812
$915$	−2.73205	−0.0903188
$916$	17.3923	0.574658
$917$	14.9282	0.492973
$918$	2.26795	0.0748535
$919$	−12.7128	−0.419357	−0.209679	−	0.977770i	$-0.567242\pi$
$919$	−12.7128	−0.419357	−0.209679	+	0.977770i	$0.567242\pi$
$920$	−5.46410	−0.180146
$921$	−5.00000	−0.164756
$922$	−6.92820	−0.228168
$923$	0	0
$924$	−5.19615	−0.170941
$925$	−30.0526	−0.988122
$926$	−15.3397	−0.504095
$927$	−16.1962	−0.531951
$928$	3.53590	0.116072
$929$	3.92820	0.128880	0.0644401	−	0.997922i	$-0.479474\pi$
$929$	3.92820	0.128880	0.0644401	+	0.997922i	$0.479474\pi$
$930$	2.39230	0.0784468
$931$	−0.464102	−0.0152103
$932$	−18.5885	−0.608885
$933$	−14.8038	−0.484656
$934$	18.9282	0.619350
$935$	8.62693	0.282131
$936$	0	0
$937$	43.7128	1.42804	0.714018	−	0.700128i	$-0.246874\pi$
$937$	43.7128	1.42804	0.714018	+	0.700128i	$0.246874\pi$
$938$	−10.0000	−0.326512
$939$	6.87564	0.224378
$940$	−2.87564	−0.0937932
$941$	27.3205	0.890623	0.445312	−	0.895376i	$-0.353093\pi$
$941$	27.3205	0.890623	0.445312	+	0.895376i	$0.353093\pi$
$942$	11.4641	0.373521
$943$	−63.1769	−2.05732
$944$	−8.92820	−0.290588
$945$	0.732051	0.0238136
$946$	45.3731	1.47521
$947$	−42.9090	−1.39435	−0.697177	−	0.716899i	$-0.745561\pi$
$947$	−42.9090	−1.39435	−0.697177	+	0.716899i	$0.745561\pi$
$948$	9.00000	0.292306
$949$	0	0
$950$	−2.07180	−0.0672180
$951$	−14.7846	−0.479424
$952$	−2.26795	−0.0735047
$953$	−0.339746	−0.0110055	−0.00550273	−	0.999985i	$-0.501752\pi$
$953$	−0.339746	−0.0110055	−0.00550273	+	0.999985i	$0.501752\pi$
$954$	9.92820	0.321437
$955$	6.00000	0.194155
$956$	−26.5885	−0.859932
$957$	−18.3731	−0.593917
$958$	−4.85641	−0.156903
$959$	−19.4641	−0.628529
$960$	−0.732051	−0.0236268
$961$	−20.3205	−0.655500
$962$	0	0
$963$	−6.07180	−0.195661
$964$	−10.9282	−0.351974
$965$	−5.55514	−0.178826
$966$	−7.46410	−0.240154
$967$	12.7846	0.411125	0.205563	−	0.978644i	$-0.434098\pi$
$967$	12.7846	0.411125	0.205563	+	0.978644i	$0.434098\pi$
$968$	−16.0000	−0.514259
$969$	1.05256	0.0338131
$970$	−10.3923	−0.333677
$971$	38.1051	1.22285	0.611426	−	0.791302i	$-0.290596\pi$
$971$	38.1051	1.22285	0.611426	+	0.791302i	$0.290596\pi$
$972$	1.00000	0.0320750
$973$	−17.0526	−0.546680
$974$	29.4449	0.943474
$975$	0	0
$976$	3.73205	0.119460
$977$	40.3923	1.29226	0.646132	−	0.763226i	$-0.276385\pi$
$977$	40.3923	1.29226	0.646132	+	0.763226i	$0.276385\pi$
$978$	−7.12436	−0.227812
$979$	−87.5885	−2.79934
$980$	−0.732051	−0.0233845
$981$	−11.2679	−0.359758
$982$	6.39230	0.203987
$983$	18.0000	0.574111	0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000	0.574111	0.287055	+	0.957914i	$0.407324\pi$
$984$	−8.46410	−0.269826
$985$	0.196152	0.00624994
$986$	−8.01924	−0.255385
$987$	−3.92820	−0.125036
$988$	0	0
$989$	65.1769	2.07251
$990$	3.80385	0.120894
$991$	37.2487	1.18324	0.591622	−	0.806215i	$-0.298488\pi$
$991$	37.2487	1.18324	0.591622	+	0.806215i	$0.298488\pi$
$992$	−3.26795	−0.103757
$993$	6.78461	0.215303
$994$	7.26795	0.230525
$995$	−18.0000	−0.570638
$996$	−9.26795	−0.293666
$997$	56.9090	1.80233	0.901163	−	0.433481i	$-0.142715\pi$
$997$	56.9090	1.80233	0.901163	+	0.433481i	$0.142715\pi$
$998$	20.5885	0.651716
$999$	6.73205	0.212993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bo.1.1		2
13.6	odd	12		546.2.s.b.127.2	yes	4
13.11	odd	12		546.2.s.b.43.2	✓	4
13.12	even	2		7098.2.a.by.1.2		2
39.11	even	12		1638.2.bj.a.1135.1		4
39.32	even	12		1638.2.bj.a.127.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.b.43.2	✓	4	13.11	odd	12
546.2.s.b.127.2	yes	4	13.6	odd	12
1638.2.bj.a.127.1		4	39.32	even	12
1638.2.bj.a.1135.1		4	39.11	even	12
7098.2.a.bo.1.1		2	1.1	even	1	trivial
7098.2.a.by.1.2		2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.732051 q^{10} +5.19615 q^{11} +1.00000 q^{12} +1.00000 q^{14} -0.732051 q^{15} +1.00000 q^{16} -2.26795 q^{17} -1.00000 q^{18} -0.464102 q^{19} -0.732051 q^{20} -1.00000 q^{21} -5.19615 q^{22} -7.46410 q^{23} -1.00000 q^{24} -4.46410 q^{25} +1.00000 q^{27} -1.00000 q^{28} -3.53590 q^{29} +0.732051 q^{30} +3.26795 q^{31} -1.00000 q^{32} +5.19615 q^{33} +2.26795 q^{34} +0.732051 q^{35} +1.00000 q^{36} +6.73205 q^{37} +0.464102 q^{38} +0.732051 q^{40} +8.46410 q^{41} +1.00000 q^{42} -8.73205 q^{43} +5.19615 q^{44} -0.732051 q^{45} +7.46410 q^{46} +3.92820 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.46410 q^{50} -2.26795 q^{51} -9.92820 q^{53} -1.00000 q^{54} -3.80385 q^{55} +1.00000 q^{56} -0.464102 q^{57} +3.53590 q^{58} -8.92820 q^{59} -0.732051 q^{60} +3.73205 q^{61} -3.26795 q^{62} -1.00000 q^{63} +1.00000 q^{64} -5.19615 q^{66} -10.0000 q^{67} -2.26795 q^{68} -7.46410 q^{69} -0.732051 q^{70} +7.26795 q^{71} -1.00000 q^{72} -1.46410 q^{73} -6.73205 q^{74} -4.46410 q^{75} -0.464102 q^{76} -5.19615 q^{77} +9.00000 q^{79} -0.732051 q^{80} +1.00000 q^{81} -8.46410 q^{82} -9.26795 q^{83} -1.00000 q^{84} +1.66025 q^{85} +8.73205 q^{86} -3.53590 q^{87} -5.19615 q^{88} -16.8564 q^{89} +0.732051 q^{90} -7.46410 q^{92} +3.26795 q^{93} -3.92820 q^{94} +0.339746 q^{95} -1.00000 q^{96} -14.1962 q^{97} -1.00000 q^{98} +5.19615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{12} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + 6 q^{19} + 2 q^{20} - 2 q^{21} - 8 q^{23} - 2 q^{24} - 2 q^{25} + 2 q^{27} - 2 q^{28} - 14 q^{29} - 2 q^{30} + 10 q^{31} - 2 q^{32} + 8 q^{34} - 2 q^{35} + 2 q^{36} + 10 q^{37} - 6 q^{38} - 2 q^{40} + 10 q^{41} + 2 q^{42} - 14 q^{43} + 2 q^{45} + 8 q^{46} - 6 q^{47} + 2 q^{48} + 2 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} - 2 q^{54} - 18 q^{55} + 2 q^{56} + 6 q^{57} + 14 q^{58} - 4 q^{59} + 2 q^{60} + 4 q^{61} - 10 q^{62} - 2 q^{63} + 2 q^{64} - 20 q^{67} - 8 q^{68} - 8 q^{69} + 2 q^{70} + 18 q^{71} - 2 q^{72} + 4 q^{73} - 10 q^{74} - 2 q^{75} + 6 q^{76} + 18 q^{79} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 22 q^{83} - 2 q^{84} - 14 q^{85} + 14 q^{86} - 14 q^{87} - 6 q^{89} - 2 q^{90} - 8 q^{92} + 10 q^{93} + 6 q^{94} + 18 q^{95} - 2 q^{96} - 18 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^12 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + 6 * q^19 + 2 * q^20 - 2 * q^21 - 8 * q^23 - 2 * q^24 - 2 * q^25 + 2 * q^27 - 2 * q^28 - 14 * q^29 - 2 * q^30 + 10 * q^31 - 2 * q^32 + 8 * q^34 - 2 * q^35 + 2 * q^36 + 10 * q^37 - 6 * q^38 - 2 * q^40 + 10 * q^41 + 2 * q^42 - 14 * q^43 + 2 * q^45 + 8 * q^46 - 6 * q^47 + 2 * q^48 + 2 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 - 2 * q^54 - 18 * q^55 + 2 * q^56 + 6 * q^57 + 14 * q^58 - 4 * q^59 + 2 * q^60 + 4 * q^61 - 10 * q^62 - 2 * q^63 + 2 * q^64 - 20 * q^67 - 8 * q^68 - 8 * q^69 + 2 * q^70 + 18 * q^71 - 2 * q^72 + 4 * q^73 - 10 * q^74 - 2 * q^75 + 6 * q^76 + 18 * q^79 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 22 * q^83 - 2 * q^84 - 14 * q^85 + 14 * q^86 - 14 * q^87 - 6 * q^89 - 2 * q^90 - 8 * q^92 + 10 * q^93 + 6 * q^94 + 18 * q^95 - 2 * q^96 - 18 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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