LMFDB - Embedded newform 7098.2.a.cp.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.8569169.1
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			1.5
Root			$-1.93682$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.41517 q^{10} -2.07170 q^{11} -1.00000 q^{12} +1.00000 q^{14} -2.41517 q^{15} +1.00000 q^{16} +6.31868 q^{17} -1.00000 q^{18} +1.82515 q^{19} +2.41517 q^{20} +1.00000 q^{21} +2.07170 q^{22} -2.11385 q^{23} +1.00000 q^{24} +0.833070 q^{25} -1.00000 q^{27} -1.00000 q^{28} -4.51844 q^{29} +2.41517 q^{30} -10.2200 q^{31} -1.00000 q^{32} +2.07170 q^{33} -6.31868 q^{34} -2.41517 q^{35} +1.00000 q^{36} +10.3640 q^{37} -1.82515 q^{38} -2.41517 q^{40} -6.82418 q^{41} -1.00000 q^{42} -1.29915 q^{43} -2.07170 q^{44} +2.41517 q^{45} +2.11385 q^{46} -3.78851 q^{47} -1.00000 q^{48} +1.00000 q^{49} -0.833070 q^{50} -6.31868 q^{51} -0.389431 q^{53} +1.00000 q^{54} -5.00352 q^{55} +1.00000 q^{56} -1.82515 q^{57} +4.51844 q^{58} +6.22879 q^{59} -2.41517 q^{60} +5.20571 q^{61} +10.2200 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.07170 q^{66} -9.51616 q^{67} +6.31868 q^{68} +2.11385 q^{69} +2.41517 q^{70} -10.3328 q^{71} -1.00000 q^{72} -8.31831 q^{73} -10.3640 q^{74} -0.833070 q^{75} +1.82515 q^{76} +2.07170 q^{77} +3.45526 q^{79} +2.41517 q^{80} +1.00000 q^{81} +6.82418 q^{82} +13.4106 q^{83} +1.00000 q^{84} +15.2607 q^{85} +1.29915 q^{86} +4.51844 q^{87} +2.07170 q^{88} +5.26268 q^{89} -2.41517 q^{90} -2.11385 q^{92} +10.2200 q^{93} +3.78851 q^{94} +4.40807 q^{95} +1.00000 q^{96} -9.97451 q^{97} -1.00000 q^{98} -2.07170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.41517	1.08010	0.540050	−	0.841633i	$-0.318406\pi$
$5$	2.41517	1.08010	0.540050	+	0.841633i	$0.318406\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.41517	−0.763745
$11$	−2.07170	−0.624642	−0.312321	−	0.949977i	$-0.601106\pi$
$11$	−2.07170	−0.624642	−0.312321	+	0.949977i	$0.601106\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−2.41517	−0.623595
$16$	1.00000	0.250000
$17$	6.31868	1.53251	0.766253	−	0.642539i	$-0.222119\pi$
$17$	6.31868	1.53251	0.766253	+	0.642539i	$0.222119\pi$
$18$	−1.00000	−0.235702
$19$	1.82515	0.418719	0.209360	−	0.977839i	$-0.432862\pi$
$19$	1.82515	0.418719	0.209360	+	0.977839i	$0.432862\pi$
$20$	2.41517	0.540050
$21$	1.00000	0.218218
$22$	2.07170	0.441688
$23$	−2.11385	−0.440767	−0.220384	−	0.975413i	$-0.570731\pi$
$23$	−2.11385	−0.440767	−0.220384	+	0.975413i	$0.570731\pi$
$24$	1.00000	0.204124
$25$	0.833070	0.166614
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−4.51844	−0.839053	−0.419527	−	0.907743i	$-0.637804\pi$
$29$	−4.51844	−0.839053	−0.419527	+	0.907743i	$0.637804\pi$
$30$	2.41517	0.440949
$31$	−10.2200	−1.83556	−0.917779	−	0.397091i	$-0.870020\pi$
$31$	−10.2200	−1.83556	−0.917779	+	0.397091i	$0.870020\pi$
$32$	−1.00000	−0.176777
$33$	2.07170	0.360637
$34$	−6.31868	−1.08364
$35$	−2.41517	−0.408239
$36$	1.00000	0.166667
$37$	10.3640	1.70382	0.851912	−	0.523684i	$-0.175443\pi$
$37$	10.3640	1.70382	0.851912	+	0.523684i	$0.175443\pi$
$38$	−1.82515	−0.296079
$39$	0	0
$40$	−2.41517	−0.381873
$41$	−6.82418	−1.06576	−0.532879	−	0.846191i	$-0.678890\pi$
$41$	−6.82418	−1.06576	−0.532879	+	0.846191i	$0.678890\pi$
$42$	−1.00000	−0.154303
$43$	−1.29915	−0.198118	−0.0990590	−	0.995082i	$-0.531583\pi$
$43$	−1.29915	−0.198118	−0.0990590	+	0.995082i	$0.531583\pi$
$44$	−2.07170	−0.312321
$45$	2.41517	0.360033
$46$	2.11385	0.311670
$47$	−3.78851	−0.552612	−0.276306	−	0.961070i	$-0.589110\pi$
$47$	−3.78851	−0.552612	−0.276306	+	0.961070i	$0.589110\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−0.833070	−0.117814
$51$	−6.31868	−0.884792
$52$	0	0
$53$	−0.389431	−0.0534924	−0.0267462	−	0.999642i	$-0.508515\pi$
$53$	−0.389431	−0.0534924	−0.0267462	+	0.999642i	$0.508515\pi$
$54$	1.00000	0.136083
$55$	−5.00352	−0.674675
$56$	1.00000	0.133631
$57$	−1.82515	−0.241748
$58$	4.51844	0.593300
$59$	6.22879	0.810919	0.405459	−	0.914113i	$-0.367112\pi$
$59$	6.22879	0.810919	0.405459	+	0.914113i	$0.367112\pi$
$60$	−2.41517	−0.311798
$61$	5.20571	0.666523	0.333261	−	0.942835i	$-0.391851\pi$
$61$	5.20571	0.666523	0.333261	+	0.942835i	$0.391851\pi$
$62$	10.2200	1.29794
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.07170	−0.255009
$67$	−9.51616	−1.16258	−0.581292	−	0.813695i	$-0.697453\pi$
$67$	−9.51616	−1.16258	−0.581292	+	0.813695i	$0.697453\pi$
$68$	6.31868	0.766253
$69$	2.11385	0.254477
$70$	2.41517	0.288669
$71$	−10.3328	−1.22628	−0.613138	−	0.789976i	$-0.710093\pi$
$71$	−10.3328	−1.22628	−0.613138	+	0.789976i	$0.710093\pi$
$72$	−1.00000	−0.117851
$73$	−8.31831	−0.973585	−0.486793	−	0.873518i	$-0.661833\pi$
$73$	−8.31831	−0.973585	−0.486793	+	0.873518i	$0.661833\pi$
$74$	−10.3640	−1.20479
$75$	−0.833070	−0.0961946
$76$	1.82515	0.209360
$77$	2.07170	0.236092
$78$	0	0
$79$	3.45526	0.388747	0.194374	−	0.980928i	$-0.437733\pi$
$79$	3.45526	0.388747	0.194374	+	0.980928i	$0.437733\pi$
$80$	2.41517	0.270025
$81$	1.00000	0.111111
$82$	6.82418	0.753605
$83$	13.4106	1.47200	0.736002	−	0.676979i	$-0.236711\pi$
$83$	13.4106	1.47200	0.736002	+	0.676979i	$0.236711\pi$
$84$	1.00000	0.109109
$85$	15.2607	1.65526
$86$	1.29915	0.140091
$87$	4.51844	0.484428
$88$	2.07170	0.220844
$89$	5.26268	0.557843	0.278922	−	0.960314i	$-0.410023\pi$
$89$	5.26268	0.557843	0.278922	+	0.960314i	$0.410023\pi$
$90$	−2.41517	−0.254582
$91$	0	0
$92$	−2.11385	−0.220384
$93$	10.2200	1.05976
$94$	3.78851	0.390755
$95$	4.40807	0.452258
$96$	1.00000	0.102062
$97$	−9.97451	−1.01276	−0.506379	−	0.862311i	$-0.669016\pi$
$97$	−9.97451	−1.01276	−0.506379	+	0.862311i	$0.669016\pi$
$98$	−1.00000	−0.101015
$99$	−2.07170	−0.208214
$100$	0.833070	0.0833070
$101$	−12.0877	−1.20277	−0.601385	−	0.798960i	$-0.705384\pi$
$101$	−12.0877	−1.20277	−0.601385	+	0.798960i	$0.705384\pi$
$102$	6.31868	0.625643
$103$	−15.9196	−1.56861	−0.784303	−	0.620377i	$-0.786979\pi$
$103$	−15.9196	−1.56861	−0.784303	+	0.620377i	$0.786979\pi$
$104$	0	0
$105$	2.41517	0.235697
$106$	0.389431	0.0378248
$107$	−4.06207	−0.392695	−0.196348	−	0.980534i	$-0.562908\pi$
$107$	−4.06207	−0.392695	−0.196348	+	0.980534i	$0.562908\pi$
$108$	−1.00000	−0.0962250
$109$	11.7150	1.12210	0.561048	−	0.827784i	$-0.310398\pi$
$109$	11.7150	1.12210	0.561048	+	0.827784i	$0.310398\pi$
$110$	5.00352	0.477067
$111$	−10.3640	−0.983704
$112$	−1.00000	−0.0944911
$113$	4.16614	0.391918	0.195959	−	0.980612i	$-0.437218\pi$
$113$	4.16614	0.391918	0.195959	+	0.980612i	$0.437218\pi$
$114$	1.82515	0.170941
$115$	−5.10531	−0.476073
$116$	−4.51844	−0.419527
$117$	0	0
$118$	−6.22879	−0.573406
$119$	−6.31868	−0.579233
$120$	2.41517	0.220474
$121$	−6.70805	−0.609823
$122$	−5.20571	−0.471303
$123$	6.82418	0.615316
$124$	−10.2200	−0.917779
$125$	−10.0639	−0.900139
$126$	1.00000	0.0890871
$127$	7.33152	0.650567	0.325284	−	0.945616i	$-0.394540\pi$
$127$	7.33152	0.650567	0.325284	+	0.945616i	$0.394540\pi$
$128$	−1.00000	−0.0883883
$129$	1.29915	0.114384
$130$	0	0
$131$	−6.11397	−0.534180	−0.267090	−	0.963672i	$-0.586062\pi$
$131$	−6.11397	−0.534180	−0.267090	+	0.963672i	$0.586062\pi$
$132$	2.07170	0.180319
$133$	−1.82515	−0.158261
$134$	9.51616	0.822071
$135$	−2.41517	−0.207865
$136$	−6.31868	−0.541822
$137$	−4.63132	−0.395680	−0.197840	−	0.980234i	$-0.563393\pi$
$137$	−4.63132	−0.395680	−0.197840	+	0.980234i	$0.563393\pi$
$138$	−2.11385	−0.179943
$139$	8.85600	0.751156	0.375578	−	0.926791i	$-0.377444\pi$
$139$	8.85600	0.751156	0.375578	+	0.926791i	$0.377444\pi$
$140$	−2.41517	−0.204120
$141$	3.78851	0.319050
$142$	10.3328	0.867108
$143$	0	0
$144$	1.00000	0.0833333
$145$	−10.9128	−0.906261
$146$	8.31831	0.688429
$147$	−1.00000	−0.0824786
$148$	10.3640	0.851912
$149$	3.55315	0.291086	0.145543	−	0.989352i	$-0.453507\pi$
$149$	3.55315	0.291086	0.145543	+	0.989352i	$0.453507\pi$
$150$	0.833070	0.0680199
$151$	−16.8113	−1.36809	−0.684043	−	0.729442i	$-0.739780\pi$
$151$	−16.8113	−1.36809	−0.684043	+	0.729442i	$0.739780\pi$
$152$	−1.82515	−0.148040
$153$	6.31868	0.510835
$154$	−2.07170	−0.166943
$155$	−24.6830	−1.98258
$156$	0	0
$157$	9.91804	0.791546	0.395773	−	0.918348i	$-0.370477\pi$
$157$	9.91804	0.791546	0.395773	+	0.918348i	$0.370477\pi$
$158$	−3.45526	−0.274886
$159$	0.389431	0.0308839
$160$	−2.41517	−0.190936
$161$	2.11385	0.166594
$162$	−1.00000	−0.0785674
$163$	5.30092	0.415200	0.207600	−	0.978214i	$-0.433435\pi$
$163$	5.30092	0.415200	0.207600	+	0.978214i	$0.433435\pi$
$164$	−6.82418	−0.532879
$165$	5.00352	0.389524
$166$	−13.4106	−1.04086
$167$	−21.6187	−1.67290	−0.836451	−	0.548042i	$-0.815373\pi$
$167$	−21.6187	−1.67290	−0.836451	+	0.548042i	$0.815373\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	−15.2607	−1.17044
$171$	1.82515	0.139573
$172$	−1.29915	−0.0990590
$173$	21.4699	1.63233	0.816165	−	0.577819i	$-0.196096\pi$
$173$	21.4699	1.63233	0.816165	+	0.577819i	$0.196096\pi$
$174$	−4.51844	−0.342542
$175$	−0.833070	−0.0629741
$176$	−2.07170	−0.156160
$177$	−6.22879	−0.468184
$178$	−5.26268	−0.394455
$179$	3.54821	0.265206	0.132603	−	0.991169i	$-0.457666\pi$
$179$	3.54821	0.265206	0.132603	+	0.991169i	$0.457666\pi$
$180$	2.41517	0.180017
$181$	11.2108	0.833291	0.416646	−	0.909069i	$-0.363206\pi$
$181$	11.2108	0.833291	0.416646	+	0.909069i	$0.363206\pi$
$182$	0	0
$183$	−5.20571	−0.384817
$184$	2.11385	0.155835
$185$	25.0308	1.84030
$186$	−10.2200	−0.749363
$187$	−13.0904	−0.957267
$188$	−3.78851	−0.276306
$189$	1.00000	0.0727393
$190$	−4.40807	−0.319795
$191$	13.7881	0.997670	0.498835	−	0.866697i	$-0.333761\pi$
$191$	13.7881	0.997670	0.498835	+	0.866697i	$0.333761\pi$
$192$	−1.00000	−0.0721688
$193$	−8.69622	−0.625968	−0.312984	−	0.949758i	$-0.601329\pi$
$193$	−8.69622	−0.625968	−0.312984	+	0.949758i	$0.601329\pi$
$194$	9.97451	0.716128
$195$	0	0
$196$	1.00000	0.0714286
$197$	−19.5372	−1.39197	−0.695984	−	0.718058i	$-0.745031\pi$
$197$	−19.5372	−1.39197	−0.695984	+	0.718058i	$0.745031\pi$
$198$	2.07170	0.147229
$199$	−10.3152	−0.731226	−0.365613	−	0.930767i	$-0.619141\pi$
$199$	−10.3152	−0.731226	−0.365613	+	0.930767i	$0.619141\pi$
$200$	−0.833070	−0.0589069
$201$	9.51616	0.671218
$202$	12.0877	0.850486
$203$	4.51844	0.317132
$204$	−6.31868	−0.442396
$205$	−16.4816	−1.15112
$206$	15.9196	1.10917
$207$	−2.11385	−0.146922
$208$	0	0
$209$	−3.78118	−0.261549
$210$	−2.41517	−0.166663
$211$	−4.80635	−0.330883	−0.165442	−	0.986220i	$-0.552905\pi$
$211$	−4.80635	−0.330883	−0.165442	+	0.986220i	$0.552905\pi$
$212$	−0.389431	−0.0267462
$213$	10.3328	0.707991
$214$	4.06207	0.277677
$215$	−3.13767	−0.213987
$216$	1.00000	0.0680414
$217$	10.2200	0.693776
$218$	−11.7150	−0.793441
$219$	8.31831	0.562100
$220$	−5.00352	−0.337337
$221$	0	0
$222$	10.3640	0.695584
$223$	−25.3843	−1.69986	−0.849931	−	0.526895i	$-0.823356\pi$
$223$	−25.3843	−1.69986	−0.849931	+	0.526895i	$0.823356\pi$
$224$	1.00000	0.0668153
$225$	0.833070	0.0555380
$226$	−4.16614	−0.277128
$227$	0.988464	0.0656067	0.0328033	−	0.999462i	$-0.489557\pi$
$227$	0.988464	0.0656067	0.0328033	+	0.999462i	$0.489557\pi$
$228$	−1.82515	−0.120874
$229$	−19.6153	−1.29621	−0.648106	−	0.761550i	$-0.724439\pi$
$229$	−19.6153	−1.29621	−0.648106	+	0.761550i	$0.724439\pi$
$230$	5.10531	0.336634
$231$	−2.07170	−0.136308
$232$	4.51844	0.296650
$233$	−22.3745	−1.46580	−0.732899	−	0.680337i	$-0.761833\pi$
$233$	−22.3745	−1.46580	−0.732899	+	0.680337i	$0.761833\pi$
$234$	0	0
$235$	−9.14993	−0.596875
$236$	6.22879	0.405459
$237$	−3.45526	−0.224443
$238$	6.31868	0.409579
$239$	9.49392	0.614110	0.307055	−	0.951692i	$-0.400656\pi$
$239$	9.49392	0.614110	0.307055	+	0.951692i	$0.400656\pi$
$240$	−2.41517	−0.155899
$241$	−11.1545	−0.718527	−0.359263	−	0.933236i	$-0.616972\pi$
$241$	−11.1545	−0.718527	−0.359263	+	0.933236i	$0.616972\pi$
$242$	6.70805	0.431210
$243$	−1.00000	−0.0641500
$244$	5.20571	0.333261
$245$	2.41517	0.154300
$246$	−6.82418	−0.435094
$247$	0	0
$248$	10.2200	0.648968
$249$	−13.4106	−0.849862
$250$	10.0639	0.636495
$251$	−2.45822	−0.155161	−0.0775807	−	0.996986i	$-0.524720\pi$
$251$	−2.45822	−0.155161	−0.0775807	+	0.996986i	$0.524720\pi$
$252$	−1.00000	−0.0629941
$253$	4.37926	0.275322
$254$	−7.33152	−0.460021
$255$	−15.2607	−0.955663
$256$	1.00000	0.0625000
$257$	−2.11799	−0.132116	−0.0660582	−	0.997816i	$-0.521042\pi$
$257$	−2.11799	−0.132116	−0.0660582	+	0.997816i	$0.521042\pi$
$258$	−1.29915	−0.0808814
$259$	−10.3640	−0.643985
$260$	0	0
$261$	−4.51844	−0.279684
$262$	6.11397	0.377722
$263$	29.3270	1.80838	0.904190	−	0.427131i	$-0.140476\pi$
$263$	29.3270	1.80838	0.904190	+	0.427131i	$0.140476\pi$
$264$	−2.07170	−0.127504
$265$	−0.940543	−0.0577771
$266$	1.82515	0.111907
$267$	−5.26268	−0.322071
$268$	−9.51616	−0.581292
$269$	7.18290	0.437949	0.218975	−	0.975731i	$-0.429729\pi$
$269$	7.18290	0.437949	0.218975	+	0.975731i	$0.429729\pi$
$270$	2.41517	0.146983
$271$	−18.6371	−1.13212	−0.566061	−	0.824364i	$-0.691533\pi$
$271$	−18.6371	−1.13212	−0.566061	+	0.824364i	$0.691533\pi$
$272$	6.31868	0.383126
$273$	0	0
$274$	4.63132	0.279788
$275$	−1.72587	−0.104074
$276$	2.11385	0.127239
$277$	−2.77531	−0.166752	−0.0833760	−	0.996518i	$-0.526570\pi$
$277$	−2.77531	−0.166752	−0.0833760	+	0.996518i	$0.526570\pi$
$278$	−8.85600	−0.531147
$279$	−10.2200	−0.611853
$280$	2.41517	0.144334
$281$	30.6280	1.82711	0.913557	−	0.406710i	$-0.133324\pi$
$281$	30.6280	1.82711	0.913557	+	0.406710i	$0.133324\pi$
$282$	−3.78851	−0.225603
$283$	30.3434	1.80373	0.901864	−	0.432020i	$-0.142199\pi$
$283$	30.3434	1.80373	0.901864	+	0.432020i	$0.142199\pi$
$284$	−10.3328	−0.613138
$285$	−4.40807	−0.261111
$286$	0	0
$287$	6.82418	0.402819
$288$	−1.00000	−0.0589256
$289$	22.9257	1.34857
$290$	10.9128	0.640823
$291$	9.97451	0.584716
$292$	−8.31831	−0.486793
$293$	−13.9756	−0.816465	−0.408233	−	0.912878i	$-0.633855\pi$
$293$	−13.9756	−0.816465	−0.408233	+	0.912878i	$0.633855\pi$
$294$	1.00000	0.0583212
$295$	15.0436	0.875873
$296$	−10.3640	−0.602393
$297$	2.07170	0.120212
$298$	−3.55315	−0.205829
$299$	0	0
$300$	−0.833070	−0.0480973
$301$	1.29915	0.0748816
$302$	16.8113	0.967383
$303$	12.0877	0.694419
$304$	1.82515	0.104680
$305$	12.5727	0.719910
$306$	−6.31868	−0.361215
$307$	−11.3530	−0.647951	−0.323975	−	0.946065i	$-0.605020\pi$
$307$	−11.3530	−0.647951	−0.323975	+	0.946065i	$0.605020\pi$
$308$	2.07170	0.118046
$309$	15.9196	0.905636
$310$	24.6830	1.40190
$311$	22.4586	1.27351	0.636756	−	0.771065i	$-0.280276\pi$
$311$	22.4586	1.27351	0.636756	+	0.771065i	$0.280276\pi$
$312$	0	0
$313$	17.8572	1.00935	0.504676	−	0.863309i	$-0.331612\pi$
$313$	17.8572	1.00935	0.504676	+	0.863309i	$0.331612\pi$
$314$	−9.91804	−0.559708
$315$	−2.41517	−0.136080
$316$	3.45526	0.194374
$317$	20.2626	1.13806	0.569031	−	0.822316i	$-0.307318\pi$
$317$	20.2626	1.13806	0.569031	+	0.822316i	$0.307318\pi$
$318$	−0.389431	−0.0218382
$319$	9.36086	0.524108
$320$	2.41517	0.135012
$321$	4.06207	0.226723
$322$	−2.11385	−0.117800
$323$	11.5326	0.641689
$324$	1.00000	0.0555556
$325$	0	0
$326$	−5.30092	−0.293591
$327$	−11.7150	−0.647842
$328$	6.82418	0.376803
$329$	3.78851	0.208868
$330$	−5.00352	−0.275435
$331$	−28.9234	−1.58978	−0.794888	−	0.606757i	$-0.792470\pi$
$331$	−28.9234	−1.58978	−0.794888	+	0.606757i	$0.792470\pi$
$332$	13.4106	0.736002
$333$	10.3640	0.567942
$334$	21.6187	1.18292
$335$	−22.9832	−1.25571
$336$	1.00000	0.0545545
$337$	−18.1051	−0.986245	−0.493123	−	0.869960i	$-0.664145\pi$
$337$	−18.1051	−0.986245	−0.493123	+	0.869960i	$0.664145\pi$
$338$	0	0
$339$	−4.16614	−0.226274
$340$	15.2607	0.827629
$341$	21.1727	1.14657
$342$	−1.82515	−0.0986930
$343$	−1.00000	−0.0539949
$344$	1.29915	0.0700453
$345$	5.10531	0.274861
$346$	−21.4699	−1.15423
$347$	9.18095	0.492859	0.246430	−	0.969161i	$-0.420743\pi$
$347$	9.18095	0.492859	0.246430	+	0.969161i	$0.420743\pi$
$348$	4.51844	0.242214
$349$	−1.29258	−0.0691903	−0.0345951	−	0.999401i	$-0.511014\pi$
$349$	−1.29258	−0.0691903	−0.0345951	+	0.999401i	$0.511014\pi$
$350$	0.833070	0.0445294
$351$	0	0
$352$	2.07170	0.110422
$353$	−12.4138	−0.660719	−0.330359	−	0.943855i	$-0.607170\pi$
$353$	−12.4138	−0.660719	−0.330359	+	0.943855i	$0.607170\pi$
$354$	6.22879	0.331056
$355$	−24.9555	−1.32450
$356$	5.26268	0.278922
$357$	6.31868	0.334420
$358$	−3.54821	−0.187529
$359$	30.9571	1.63385	0.816926	−	0.576742i	$-0.195676\pi$
$359$	30.9571	1.63385	0.816926	+	0.576742i	$0.195676\pi$
$360$	−2.41517	−0.127291
$361$	−15.6688	−0.824674
$362$	−11.2108	−0.589226
$363$	6.70805	0.352081
$364$	0	0
$365$	−20.0902	−1.05157
$366$	5.20571	0.272107
$367$	−3.29039	−0.171757	−0.0858786	−	0.996306i	$-0.527370\pi$
$367$	−3.29039	−0.171757	−0.0858786	+	0.996306i	$0.527370\pi$
$368$	−2.11385	−0.110192
$369$	−6.82418	−0.355253
$370$	−25.0308	−1.30129
$371$	0.389431	0.0202182
$372$	10.2200	0.529880
$373$	34.1432	1.76787	0.883934	−	0.467612i	$-0.154886\pi$
$373$	34.1432	1.76787	0.883934	+	0.467612i	$0.154886\pi$
$374$	13.0904	0.676890
$375$	10.0639	0.519696
$376$	3.78851	0.195378
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−2.74720	−0.141114	−0.0705571	−	0.997508i	$-0.522478\pi$
$379$	−2.74720	−0.141114	−0.0705571	+	0.997508i	$0.522478\pi$
$380$	4.40807	0.226129
$381$	−7.33152	−0.375605
$382$	−13.7881	−0.705459
$383$	1.94873	0.0995756	0.0497878	−	0.998760i	$-0.484145\pi$
$383$	1.94873	0.0995756	0.0497878	+	0.998760i	$0.484145\pi$
$384$	1.00000	0.0510310
$385$	5.00352	0.255003
$386$	8.69622	0.442626
$387$	−1.29915	−0.0660394
$388$	−9.97451	−0.506379
$389$	−13.1932	−0.668920	−0.334460	−	0.942410i	$-0.608554\pi$
$389$	−13.1932	−0.668920	−0.334460	+	0.942410i	$0.608554\pi$
$390$	0	0
$391$	−13.3567	−0.675479
$392$	−1.00000	−0.0505076
$393$	6.11397	0.308409
$394$	19.5372	0.984269
$395$	8.34506	0.419885
$396$	−2.07170	−0.104107
$397$	−22.7225	−1.14041	−0.570204	−	0.821503i	$-0.693136\pi$
$397$	−22.7225	−1.14041	−0.570204	+	0.821503i	$0.693136\pi$
$398$	10.3152	0.517055
$399$	1.82515	0.0913720
$400$	0.833070	0.0416535
$401$	1.24388	0.0621165	0.0310583	−	0.999518i	$-0.490112\pi$
$401$	1.24388	0.0621165	0.0310583	+	0.999518i	$0.490112\pi$
$402$	−9.51616	−0.474623
$403$	0	0
$404$	−12.0877	−0.601385
$405$	2.41517	0.120011
$406$	−4.51844	−0.224246
$407$	−21.4710	−1.06428
$408$	6.31868	0.312821
$409$	−33.5856	−1.66070	−0.830350	−	0.557242i	$-0.811860\pi$
$409$	−33.5856	−1.66070	−0.830350	+	0.557242i	$0.811860\pi$
$410$	16.4816	0.813968
$411$	4.63132	0.228446
$412$	−15.9196	−0.784303
$413$	−6.22879	−0.306499
$414$	2.11385	0.103890
$415$	32.3889	1.58991
$416$	0	0
$417$	−8.85600	−0.433680
$418$	3.78118	0.184943
$419$	−15.0147	−0.733514	−0.366757	−	0.930317i	$-0.619532\pi$
$419$	−15.0147	−0.733514	−0.366757	+	0.930317i	$0.619532\pi$
$420$	2.41517	0.117848
$421$	−26.7691	−1.30465	−0.652323	−	0.757941i	$-0.726205\pi$
$421$	−26.7691	−1.30465	−0.652323	+	0.757941i	$0.726205\pi$
$422$	4.80635	0.233970
$423$	−3.78851	−0.184204
$424$	0.389431	0.0189124
$425$	5.26390	0.255337
$426$	−10.3328	−0.500625
$427$	−5.20571	−0.251922
$428$	−4.06207	−0.196348
$429$	0	0
$430$	3.13767	0.151312
$431$	1.14998	0.0553926	0.0276963	−	0.999616i	$-0.491183\pi$
$431$	1.14998	0.0553926	0.0276963	+	0.999616i	$0.491183\pi$
$432$	−1.00000	−0.0481125
$433$	−7.81323	−0.375480	−0.187740	−	0.982219i	$-0.560116\pi$
$433$	−7.81323	−0.375480	−0.187740	+	0.982219i	$0.560116\pi$
$434$	−10.2200	−0.490574
$435$	10.9128	0.523230
$436$	11.7150	0.561048
$437$	−3.85810	−0.184558
$438$	−8.31831	−0.397464
$439$	5.61856	0.268159	0.134080	−	0.990971i	$-0.457192\pi$
$439$	5.61856	0.268159	0.134080	+	0.990971i	$0.457192\pi$
$440$	5.00352	0.238534
$441$	1.00000	0.0476190
$442$	0	0
$443$	−26.7705	−1.27191	−0.635953	−	0.771728i	$-0.719393\pi$
$443$	−26.7705	−1.27191	−0.635953	+	0.771728i	$0.719393\pi$
$444$	−10.3640	−0.491852
$445$	12.7103	0.602526
$446$	25.3843	1.20198
$447$	−3.55315	−0.168058
$448$	−1.00000	−0.0472456
$449$	27.7658	1.31035	0.655174	−	0.755478i	$-0.272595\pi$
$449$	27.7658	1.31035	0.655174	+	0.755478i	$0.272595\pi$
$450$	−0.833070	−0.0392713
$451$	14.1377	0.665717
$452$	4.16614	0.195959
$453$	16.8113	0.789865
$454$	−0.988464	−0.0463909
$455$	0	0
$456$	1.82515	0.0854707
$457$	−20.4219	−0.955298	−0.477649	−	0.878551i	$-0.658511\pi$
$457$	−20.4219	−0.955298	−0.477649	+	0.878551i	$0.658511\pi$
$458$	19.6153	0.916560
$459$	−6.31868	−0.294931
$460$	−5.10531	−0.238036
$461$	3.40664	0.158663	0.0793316	−	0.996848i	$-0.474721\pi$
$461$	3.40664	0.158663	0.0793316	+	0.996848i	$0.474721\pi$
$462$	2.07170	0.0963843
$463$	36.3168	1.68779	0.843893	−	0.536512i	$-0.180258\pi$
$463$	36.3168	1.68779	0.843893	+	0.536512i	$0.180258\pi$
$464$	−4.51844	−0.209763
$465$	24.6830	1.14465
$466$	22.3745	1.03648
$467$	−38.7173	−1.79163	−0.895813	−	0.444432i	$-0.853406\pi$
$467$	−38.7173	−1.79163	−0.895813	+	0.444432i	$0.853406\pi$
$468$	0	0
$469$	9.51616	0.439416
$470$	9.14993	0.422055
$471$	−9.91804	−0.456999
$472$	−6.22879	−0.286703
$473$	2.69145	0.123753
$474$	3.45526	0.158705
$475$	1.52048	0.0697644
$476$	−6.31868	−0.289616
$477$	−0.389431	−0.0178308
$478$	−9.49392	−0.434242
$479$	19.0199	0.869041	0.434520	−	0.900662i	$-0.356918\pi$
$479$	19.0199	0.869041	0.434520	+	0.900662i	$0.356918\pi$
$480$	2.41517	0.110237
$481$	0	0
$482$	11.1545	0.508075
$483$	−2.11385	−0.0961834
$484$	−6.70805	−0.304911
$485$	−24.0902	−1.09388
$486$	1.00000	0.0453609
$487$	−14.2107	−0.643949	−0.321974	−	0.946748i	$-0.604346\pi$
$487$	−14.2107	−0.643949	−0.321974	+	0.946748i	$0.604346\pi$
$488$	−5.20571	−0.235651
$489$	−5.30092	−0.239716
$490$	−2.41517	−0.109106
$491$	−1.36574	−0.0616349	−0.0308175	−	0.999525i	$-0.509811\pi$
$491$	−1.36574	−0.0616349	−0.0308175	+	0.999525i	$0.509811\pi$
$492$	6.82418	0.307658
$493$	−28.5506	−1.28585
$494$	0	0
$495$	−5.00352	−0.224892
$496$	−10.2200	−0.458890
$497$	10.3328	0.463489
$498$	13.4106	0.600943
$499$	−32.6125	−1.45993	−0.729967	−	0.683482i	$-0.760465\pi$
$499$	−32.6125	−1.45993	−0.729967	+	0.683482i	$0.760465\pi$
$500$	−10.0639	−0.450070
$501$	21.6187	0.965850
$502$	2.45822	0.109716
$503$	−38.8385	−1.73172	−0.865862	−	0.500283i	$-0.833229\pi$
$503$	−38.8385	−1.73172	−0.865862	+	0.500283i	$0.833229\pi$
$504$	1.00000	0.0445435
$505$	−29.1939	−1.29911
$506$	−4.37926	−0.194682
$507$	0	0
$508$	7.33152	0.325284
$509$	8.43469	0.373861	0.186931	−	0.982373i	$-0.440146\pi$
$509$	8.43469	0.373861	0.186931	+	0.982373i	$0.440146\pi$
$510$	15.2607	0.675756
$511$	8.31831	0.367981
$512$	−1.00000	−0.0441942
$513$	−1.82515	−0.0805825
$514$	2.11799	0.0934204
$515$	−38.4487	−1.69425
$516$	1.29915	0.0571918
$517$	7.84867	0.345184
$518$	10.3640	0.455366
$519$	−21.4699	−0.942426
$520$	0	0
$521$	33.6352	1.47359	0.736793	−	0.676119i	$-0.236339\pi$
$521$	33.6352	1.47359	0.736793	+	0.676119i	$0.236339\pi$
$522$	4.51844	0.197767
$523$	−22.6010	−0.988273	−0.494137	−	0.869384i	$-0.664516\pi$
$523$	−22.6010	−0.988273	−0.494137	+	0.869384i	$0.664516\pi$
$524$	−6.11397	−0.267090
$525$	0.833070	0.0363581
$526$	−29.3270	−1.27872
$527$	−64.5766	−2.81300
$528$	2.07170	0.0901593
$529$	−18.5317	−0.805724
$530$	0.940543	0.0408546
$531$	6.22879	0.270306
$532$	−1.82515	−0.0791305
$533$	0	0
$534$	5.26268	0.227739
$535$	−9.81061	−0.424150
$536$	9.51616	0.411036
$537$	−3.54821	−0.153117
$538$	−7.18290	−0.309677
$539$	−2.07170	−0.0892345
$540$	−2.41517	−0.103933
$541$	21.4834	0.923642	0.461821	−	0.886973i	$-0.347196\pi$
$541$	21.4834	0.923642	0.461821	+	0.886973i	$0.347196\pi$
$542$	18.6371	0.800531
$543$	−11.2108	−0.481101
$544$	−6.31868	−0.270911
$545$	28.2938	1.21197
$546$	0	0
$547$	−18.5655	−0.793805	−0.396903	−	0.917861i	$-0.629915\pi$
$547$	−18.5655	−0.793805	−0.396903	+	0.917861i	$0.629915\pi$
$548$	−4.63132	−0.197840
$549$	5.20571	0.222174
$550$	1.72587	0.0735914
$551$	−8.24685	−0.351328
$552$	−2.11385	−0.0899713
$553$	−3.45526	−0.146933
$554$	2.77531	0.117912
$555$	−25.0308	−1.06250
$556$	8.85600	0.375578
$557$	−32.5822	−1.38055	−0.690277	−	0.723545i	$-0.742511\pi$
$557$	−32.5822	−1.38055	−0.690277	+	0.723545i	$0.742511\pi$
$558$	10.2200	0.432645
$559$	0	0
$560$	−2.41517	−0.102060
$561$	13.0904	0.552678
$562$	−30.6280	−1.29197
$563$	−14.7832	−0.623037	−0.311519	−	0.950240i	$-0.600838\pi$
$563$	−14.7832	−0.623037	−0.311519	+	0.950240i	$0.600838\pi$
$564$	3.78851	0.159525
$565$	10.0620	0.423310
$566$	−30.3434	−1.27543
$567$	−1.00000	−0.0419961
$568$	10.3328	0.433554
$569$	−11.6587	−0.488760	−0.244380	−	0.969680i	$-0.578584\pi$
$569$	−11.6587	−0.488760	−0.244380	+	0.969680i	$0.578584\pi$
$570$	4.40807	0.184634
$571$	−12.3316	−0.516062	−0.258031	−	0.966137i	$-0.583074\pi$
$571$	−12.3316	−0.516062	−0.258031	+	0.966137i	$0.583074\pi$
$572$	0	0
$573$	−13.7881	−0.576005
$574$	−6.82418	−0.284836
$575$	−1.76098	−0.0734380
$576$	1.00000	0.0416667
$577$	25.6265	1.06685	0.533423	−	0.845848i	$-0.320905\pi$
$577$	25.6265	1.06685	0.533423	+	0.845848i	$0.320905\pi$
$578$	−22.9257	−0.953585
$579$	8.69622	0.361403
$580$	−10.9128	−0.453130
$581$	−13.4106	−0.556365
$582$	−9.97451	−0.413457
$583$	0.806784	0.0334136
$584$	8.31831	0.344214
$585$	0	0
$586$	13.9756	0.577328
$587$	−6.41750	−0.264878	−0.132439	−	0.991191i	$-0.542281\pi$
$587$	−6.41750	−0.264878	−0.132439	+	0.991191i	$0.542281\pi$
$588$	−1.00000	−0.0412393
$589$	−18.6530	−0.768583
$590$	−15.0436	−0.619336
$591$	19.5372	0.803653
$592$	10.3640	0.425956
$593$	−14.3401	−0.588876	−0.294438	−	0.955671i	$-0.595132\pi$
$593$	−14.3401	−0.588876	−0.294438	+	0.955671i	$0.595132\pi$
$594$	−2.07170	−0.0850030
$595$	−15.2607	−0.625629
$596$	3.55315	0.145543
$597$	10.3152	0.422174
$598$	0	0
$599$	−15.9998	−0.653736	−0.326868	−	0.945070i	$-0.605993\pi$
$599$	−15.9998	−0.653736	−0.326868	+	0.945070i	$0.605993\pi$
$600$	0.833070	0.0340099
$601$	−42.4710	−1.73243	−0.866213	−	0.499674i	$-0.833453\pi$
$601$	−42.4710	−1.73243	−0.866213	+	0.499674i	$0.833453\pi$
$602$	−1.29915	−0.0529493
$603$	−9.51616	−0.387528
$604$	−16.8113	−0.684043
$605$	−16.2011	−0.658669
$606$	−12.0877	−0.491028
$607$	−20.0520	−0.813884	−0.406942	−	0.913454i	$-0.633405\pi$
$607$	−20.0520	−0.813884	−0.406942	+	0.913454i	$0.633405\pi$
$608$	−1.82515	−0.0740198
$609$	−4.51844	−0.183096
$610$	−12.5727	−0.509054
$611$	0	0
$612$	6.31868	0.255418
$613$	−45.4256	−1.83472	−0.917362	−	0.398054i	$-0.869686\pi$
$613$	−45.4256	−1.83472	−0.917362	+	0.398054i	$0.869686\pi$
$614$	11.3530	0.458171
$615$	16.4816	0.664602
$616$	−2.07170	−0.0834713
$617$	−8.40051	−0.338192	−0.169096	−	0.985600i	$-0.554085\pi$
$617$	−8.40051	−0.338192	−0.169096	+	0.985600i	$0.554085\pi$
$618$	−15.9196	−0.640381
$619$	19.5691	0.786549	0.393275	−	0.919421i	$-0.371342\pi$
$619$	19.5691	0.786549	0.393275	+	0.919421i	$0.371342\pi$
$620$	−24.6830	−0.991292
$621$	2.11385	0.0848257
$622$	−22.4586	−0.900509
$623$	−5.26268	−0.210845
$624$	0	0
$625$	−28.4713	−1.13885
$626$	−17.8572	−0.713719
$627$	3.78118	0.151006
$628$	9.91804	0.395773
$629$	65.4866	2.61112
$630$	2.41517	0.0962229
$631$	17.4476	0.694578	0.347289	−	0.937758i	$-0.387102\pi$
$631$	17.4476	0.694578	0.347289	+	0.937758i	$0.387102\pi$
$632$	−3.45526	−0.137443
$633$	4.80635	0.191035
$634$	−20.2626	−0.804731
$635$	17.7069	0.702677
$636$	0.389431	0.0154419
$637$	0	0
$638$	−9.36086	−0.370600
$639$	−10.3328	−0.408759
$640$	−2.41517	−0.0954682
$641$	−26.1301	−1.03208	−0.516038	−	0.856566i	$-0.672594\pi$
$641$	−26.1301	−1.03208	−0.516038	+	0.856566i	$0.672594\pi$
$642$	−4.06207	−0.160317
$643$	−7.34552	−0.289679	−0.144840	−	0.989455i	$-0.546267\pi$
$643$	−7.34552	−0.289679	−0.144840	+	0.989455i	$0.546267\pi$
$644$	2.11385	0.0832972
$645$	3.13767	0.123546
$646$	−11.5326	−0.453743
$647$	37.8703	1.48883	0.744417	−	0.667715i	$-0.232727\pi$
$647$	37.8703	1.48883	0.744417	+	0.667715i	$0.232727\pi$
$648$	−1.00000	−0.0392837
$649$	−12.9042	−0.506534
$650$	0	0
$651$	−10.2200	−0.400552
$652$	5.30092	0.207600
$653$	−7.51225	−0.293977	−0.146988	−	0.989138i	$-0.546958\pi$
$653$	−7.51225	−0.293977	−0.146988	+	0.989138i	$0.546958\pi$
$654$	11.7150	0.458093
$655$	−14.7663	−0.576967
$656$	−6.82418	−0.266440
$657$	−8.31831	−0.324528
$658$	−3.78851	−0.147692
$659$	−2.89639	−0.112827	−0.0564137	−	0.998407i	$-0.517967\pi$
$659$	−2.89639	−0.112827	−0.0564137	+	0.998407i	$0.517967\pi$
$660$	5.00352	0.194762
$661$	17.2747	0.671906	0.335953	−	0.941879i	$-0.390942\pi$
$661$	17.2747	0.671906	0.335953	+	0.941879i	$0.390942\pi$
$662$	28.9234	1.12414
$663$	0	0
$664$	−13.4106	−0.520432
$665$	−4.40807	−0.170938
$666$	−10.3640	−0.401595
$667$	9.55129	0.369827
$668$	−21.6187	−0.836451
$669$	25.3843	0.981415
$670$	22.9832	0.887918
$671$	−10.7847	−0.416338
$672$	−1.00000	−0.0385758
$673$	−24.1740	−0.931841	−0.465920	−	0.884827i	$-0.654277\pi$
$673$	−24.1740	−0.931841	−0.465920	+	0.884827i	$0.654277\pi$
$674$	18.1051	0.697381
$675$	−0.833070	−0.0320649
$676$	0	0
$677$	−0.587936	−0.0225962	−0.0112981	−	0.999936i	$-0.503596\pi$
$677$	−0.587936	−0.0225962	−0.0112981	+	0.999936i	$0.503596\pi$
$678$	4.16614	0.160000
$679$	9.97451	0.382787
$680$	−15.2607	−0.585222
$681$	−0.988464	−0.0378780
$682$	−21.1727	−0.810745
$683$	−37.5367	−1.43630	−0.718151	−	0.695887i	$-0.755011\pi$
$683$	−37.5367	−1.43630	−0.718151	+	0.695887i	$0.755011\pi$
$684$	1.82515	0.0697865
$685$	−11.1854	−0.427374
$686$	1.00000	0.0381802
$687$	19.6153	0.748368
$688$	−1.29915	−0.0495295
$689$	0	0
$690$	−5.10531	−0.194356
$691$	−4.21124	−0.160203	−0.0801015	−	0.996787i	$-0.525524\pi$
$691$	−4.21124	−0.160203	−0.0801015	+	0.996787i	$0.525524\pi$
$692$	21.4699	0.816165
$693$	2.07170	0.0786975
$694$	−9.18095	−0.348504
$695$	21.3888	0.811323
$696$	−4.51844	−0.171271
$697$	−43.1198	−1.63328
$698$	1.29258	0.0489249
$699$	22.3745	0.846279
$700$	−0.833070	−0.0314871
$701$	33.7614	1.27515	0.637576	−	0.770388i	$-0.279937\pi$
$701$	33.7614	1.27515	0.637576	+	0.770388i	$0.279937\pi$
$702$	0	0
$703$	18.9158	0.713424
$704$	−2.07170	−0.0780802
$705$	9.14993	0.344606
$706$	12.4138	0.467199
$707$	12.0877	0.454604
$708$	−6.22879	−0.234092
$709$	−50.7805	−1.90710	−0.953551	−	0.301231i	$-0.902602\pi$
$709$	−50.7805	−1.90710	−0.953551	+	0.301231i	$0.902602\pi$
$710$	24.9555	0.936563
$711$	3.45526	0.129582
$712$	−5.26268	−0.197227
$713$	21.6034	0.809054
$714$	−6.31868	−0.236471
$715$	0	0
$716$	3.54821	0.132603
$717$	−9.49392	−0.354557
$718$	−30.9571	−1.15531
$719$	32.5653	1.21448	0.607241	−	0.794518i	$-0.292276\pi$
$719$	32.5653	1.21448	0.607241	+	0.794518i	$0.292276\pi$
$720$	2.41517	0.0900083
$721$	15.9196	0.592878
$722$	15.6688	0.583133
$723$	11.1545	0.414842
$724$	11.2108	0.416646
$725$	−3.76418	−0.139798
$726$	−6.70805	−0.248959
$727$	−2.25932	−0.0837934	−0.0418967	−	0.999122i	$-0.513340\pi$
$727$	−2.25932	−0.0837934	−0.0418967	+	0.999122i	$0.513340\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	20.0902	0.743571
$731$	−8.20890	−0.303617
$732$	−5.20571	−0.192408
$733$	5.80249	0.214320	0.107160	−	0.994242i	$-0.465824\pi$
$733$	5.80249	0.214320	0.107160	+	0.994242i	$0.465824\pi$
$734$	3.29039	0.121451
$735$	−2.41517	−0.0890851
$736$	2.11385	0.0779174
$737$	19.7147	0.726198
$738$	6.82418	0.251202
$739$	1.46884	0.0540320	0.0270160	−	0.999635i	$-0.491399\pi$
$739$	1.46884	0.0540320	0.0270160	+	0.999635i	$0.491399\pi$
$740$	25.0308	0.920150
$741$	0	0
$742$	−0.389431	−0.0142964
$743$	18.4387	0.676449	0.338224	−	0.941066i	$-0.390174\pi$
$743$	18.4387	0.676449	0.338224	+	0.941066i	$0.390174\pi$
$744$	−10.2200	−0.374682
$745$	8.58149	0.314401
$746$	−34.1432	−1.25007
$747$	13.4106	0.490668
$748$	−13.0904	−0.478633
$749$	4.06207	0.148425
$750$	−10.0639	−0.367480
$751$	−0.338066	−0.0123362	−0.00616810	−	0.999981i	$-0.501963\pi$
$751$	−0.338066	−0.0123362	−0.00616810	+	0.999981i	$0.501963\pi$
$752$	−3.78851	−0.138153
$753$	2.45822	0.0895825
$754$	0	0
$755$	−40.6023	−1.47767
$756$	1.00000	0.0363696
$757$	21.9978	0.799523	0.399761	−	0.916619i	$-0.369093\pi$
$757$	21.9978	0.799523	0.399761	+	0.916619i	$0.369093\pi$
$758$	2.74720	0.0997828
$759$	−4.37926	−0.158957
$760$	−4.40807	−0.159897
$761$	−2.81245	−0.101951	−0.0509757	−	0.998700i	$-0.516233\pi$
$761$	−2.81245	−0.101951	−0.0509757	+	0.998700i	$0.516233\pi$
$762$	7.33152	0.265593
$763$	−11.7150	−0.424112
$764$	13.7881	0.498835
$765$	15.2607	0.551753
$766$	−1.94873	−0.0704106
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	2.44610	0.0882087	0.0441043	−	0.999027i	$-0.485957\pi$
$769$	2.44610	0.0882087	0.0441043	+	0.999027i	$0.485957\pi$
$770$	−5.00352	−0.180314
$771$	2.11799	0.0762774
$772$	−8.69622	−0.312984
$773$	31.3028	1.12588	0.562941	−	0.826497i	$-0.309670\pi$
$773$	31.3028	1.12588	0.562941	+	0.826497i	$0.309670\pi$
$774$	1.29915	0.0466969
$775$	−8.51393	−0.305830
$776$	9.97451	0.358064
$777$	10.3640	0.371805
$778$	13.1932	0.472998
$779$	−12.4552	−0.446253
$780$	0	0
$781$	21.4065	0.765983
$782$	13.3567	0.477635
$783$	4.51844	0.161476
$784$	1.00000	0.0357143
$785$	23.9538	0.854948
$786$	−6.11397	−0.218078
$787$	51.5345	1.83701	0.918503	−	0.395414i	$-0.129399\pi$
$787$	51.5345	1.83701	0.918503	+	0.395414i	$0.129399\pi$
$788$	−19.5372	−0.695984
$789$	−29.3270	−1.04407
$790$	−8.34506	−0.296904
$791$	−4.16614	−0.148131
$792$	2.07170	0.0736147
$793$	0	0
$794$	22.7225	0.806391
$795$	0.940543	0.0333576
$796$	−10.3152	−0.365613
$797$	−36.0275	−1.27616	−0.638080	−	0.769970i	$-0.720271\pi$
$797$	−36.0275	−1.27616	−0.638080	+	0.769970i	$0.720271\pi$
$798$	−1.82515	−0.0646098
$799$	−23.9384	−0.846880
$800$	−0.833070	−0.0294535
$801$	5.26268	0.185948
$802$	−1.24388	−0.0439230
$803$	17.2331	0.608142
$804$	9.51616	0.335609
$805$	5.10531	0.179939
$806$	0	0
$807$	−7.18290	−0.252850
$808$	12.0877	0.425243
$809$	35.5857	1.25113	0.625564	−	0.780173i	$-0.284869\pi$
$809$	35.5857	1.25113	0.625564	+	0.780173i	$0.284869\pi$
$810$	−2.41517	−0.0848606
$811$	−52.3677	−1.83888	−0.919439	−	0.393233i	$-0.871356\pi$
$811$	−52.3677	−1.83888	−0.919439	+	0.393233i	$0.871356\pi$
$812$	4.51844	0.158566
$813$	18.6371	0.653631
$814$	21.4710	0.752560
$815$	12.8026	0.448457
$816$	−6.31868	−0.221198
$817$	−2.37114	−0.0829558
$818$	33.5856	1.17429
$819$	0	0
$820$	−16.4816	−0.575562
$821$	−35.1450	−1.22657	−0.613284	−	0.789862i	$-0.710152\pi$
$821$	−35.1450	−1.22657	−0.613284	+	0.789862i	$0.710152\pi$
$822$	−4.63132	−0.161536
$823$	−44.5204	−1.55188	−0.775942	−	0.630804i	$-0.782725\pi$
$823$	−44.5204	−1.55188	−0.775942	+	0.630804i	$0.782725\pi$
$824$	15.9196	0.554586
$825$	1.72587	0.0600872
$826$	6.22879	0.216727
$827$	−40.0686	−1.39332	−0.696661	−	0.717401i	$-0.745332\pi$
$827$	−40.0686	−1.39332	−0.696661	+	0.717401i	$0.745332\pi$
$828$	−2.11385	−0.0734612
$829$	−25.0689	−0.870680	−0.435340	−	0.900266i	$-0.643372\pi$
$829$	−25.0689	−0.870680	−0.435340	+	0.900266i	$0.643372\pi$
$830$	−32.3889	−1.12424
$831$	2.77531	0.0962744
$832$	0	0
$833$	6.31868	0.218929
$834$	8.85600	0.306658
$835$	−52.2128	−1.80690
$836$	−3.78118	−0.130775
$837$	10.2200	0.353253
$838$	15.0147	0.518673
$839$	−1.70570	−0.0588873	−0.0294436	−	0.999566i	$-0.509374\pi$
$839$	−1.70570	−0.0588873	−0.0294436	+	0.999566i	$0.509374\pi$
$840$	−2.41517	−0.0833314
$841$	−8.58369	−0.295989
$842$	26.7691	0.922524
$843$	−30.6280	−1.05489
$844$	−4.80635	−0.165442
$845$	0	0
$846$	3.78851	0.130252
$847$	6.70805	0.230491
$848$	−0.389431	−0.0133731
$849$	−30.3434	−1.04138
$850$	−5.26390	−0.180550
$851$	−21.9078	−0.750991
$852$	10.3328	0.353995
$853$	−21.3368	−0.730559	−0.365280	−	0.930898i	$-0.619027\pi$
$853$	−21.3368	−0.730559	−0.365280	+	0.930898i	$0.619027\pi$
$854$	5.20571	0.178136
$855$	4.40807	0.150753
$856$	4.06207	0.138839
$857$	−46.0871	−1.57431	−0.787153	−	0.616758i	$-0.788446\pi$
$857$	−46.0871	−1.57431	−0.787153	+	0.616758i	$0.788446\pi$
$858$	0	0
$859$	5.25235	0.179208	0.0896040	−	0.995977i	$-0.471440\pi$
$859$	5.25235	0.179208	0.0896040	+	0.995977i	$0.471440\pi$
$860$	−3.13767	−0.106994
$861$	−6.82418	−0.232568
$862$	−1.14998	−0.0391685
$863$	−26.8267	−0.913190	−0.456595	−	0.889675i	$-0.650931\pi$
$863$	−26.8267	−0.913190	−0.456595	+	0.889675i	$0.650931\pi$
$864$	1.00000	0.0340207
$865$	51.8537	1.76308
$866$	7.81323	0.265504
$867$	−22.9257	−0.778599
$868$	10.2200	0.346888
$869$	−7.15827	−0.242828
$870$	−10.9128	−0.369979
$871$	0	0
$872$	−11.7150	−0.396720
$873$	−9.97451	−0.337586
$874$	3.85810	0.130502
$875$	10.0639	0.340221
$876$	8.31831	0.281050
$877$	5.07515	0.171376	0.0856878	−	0.996322i	$-0.472691\pi$
$877$	5.07515	0.171376	0.0856878	+	0.996322i	$0.472691\pi$
$878$	−5.61856	−0.189617
$879$	13.9756	0.471386
$880$	−5.00352	−0.168669
$881$	0.983129	0.0331225	0.0165612	−	0.999863i	$-0.494728\pi$
$881$	0.983129	0.0331225	0.0165612	+	0.999863i	$0.494728\pi$
$882$	−1.00000	−0.0336718
$883$	−16.1277	−0.542739	−0.271370	−	0.962475i	$-0.587477\pi$
$883$	−16.1277	−0.542739	−0.271370	+	0.962475i	$0.587477\pi$
$884$	0	0
$885$	−15.0436	−0.505685
$886$	26.7705	0.899374
$887$	−46.7758	−1.57058	−0.785289	−	0.619129i	$-0.787486\pi$
$887$	−46.7758	−1.57058	−0.785289	+	0.619129i	$0.787486\pi$
$888$	10.3640	0.347792
$889$	−7.33152	−0.245891
$890$	−12.7103	−0.426050
$891$	−2.07170	−0.0694046
$892$	−25.3843	−0.849931
$893$	−6.91462	−0.231389
$894$	3.55315	0.118835
$895$	8.56956	0.286449
$896$	1.00000	0.0334077
$897$	0	0
$898$	−27.7658	−0.926556
$899$	46.1783	1.54013
$900$	0.833070	0.0277690
$901$	−2.46069	−0.0819774
$902$	−14.1377	−0.470733
$903$	−1.29915	−0.0432329
$904$	−4.16614	−0.138564
$905$	27.0760	0.900037
$906$	−16.8113	−0.558519
$907$	−46.1824	−1.53346	−0.766731	−	0.641969i	$-0.778118\pi$
$907$	−46.1824	−1.53346	−0.766731	+	0.641969i	$0.778118\pi$
$908$	0.988464	0.0328033
$909$	−12.0877	−0.400923
$910$	0	0
$911$	−0.389067	−0.0128904	−0.00644519	−	0.999979i	$-0.502052\pi$
$911$	−0.389067	−0.0128904	−0.00644519	+	0.999979i	$0.502052\pi$
$912$	−1.82515	−0.0604369
$913$	−27.7828	−0.919475
$914$	20.4219	0.675497
$915$	−12.5727	−0.415640
$916$	−19.6153	−0.648106
$917$	6.11397	0.201901
$918$	6.31868	0.208548
$919$	35.3421	1.16583	0.582914	−	0.812534i	$-0.301913\pi$
$919$	35.3421	1.16583	0.582914	+	0.812534i	$0.301913\pi$
$920$	5.10531	0.168317
$921$	11.3530	0.374095
$922$	−3.40664	−0.112192
$923$	0	0
$924$	−2.07170	−0.0681540
$925$	8.63390	0.283881
$926$	−36.3168	−1.19344
$927$	−15.9196	−0.522869
$928$	4.51844	0.148325
$929$	32.2799	1.05907	0.529534	−	0.848289i	$-0.322367\pi$
$929$	32.2799	1.05907	0.529534	+	0.848289i	$0.322367\pi$
$930$	−24.6830	−0.809387
$931$	1.82515	0.0598170
$932$	−22.3745	−0.732899
$933$	−22.4586	−0.735263
$934$	38.7173	1.26687
$935$	−31.6157	−1.03394
$936$	0	0
$937$	0.828583	0.0270686	0.0135343	−	0.999908i	$-0.495692\pi$
$937$	0.828583	0.0270686	0.0135343	+	0.999908i	$0.495692\pi$
$938$	−9.51616	−0.310714
$939$	−17.8572	−0.582749
$940$	−9.14993	−0.298438
$941$	35.1405	1.14555	0.572774	−	0.819713i	$-0.305867\pi$
$941$	35.1405	1.14555	0.572774	+	0.819713i	$0.305867\pi$
$942$	9.91804	0.323147
$943$	14.4253	0.469752
$944$	6.22879	0.202730
$945$	2.41517	0.0785656
$946$	−2.69145	−0.0875064
$947$	47.3657	1.53918	0.769589	−	0.638540i	$-0.220461\pi$
$947$	47.3657	1.53918	0.769589	+	0.638540i	$0.220461\pi$
$948$	−3.45526	−0.112222
$949$	0	0
$950$	−1.52048	−0.0493309
$951$	−20.2626	−0.657060
$952$	6.31868	0.204790
$953$	−21.9841	−0.712136	−0.356068	−	0.934460i	$-0.615883\pi$
$953$	−21.9841	−0.712136	−0.356068	+	0.934460i	$0.615883\pi$
$954$	0.389431	0.0126083
$955$	33.3006	1.07758
$956$	9.49392	0.307055
$957$	−9.36086	−0.302594
$958$	−19.0199	−0.614505
$959$	4.63132	0.149553
$960$	−2.41517	−0.0779494
$961$	73.4475	2.36927
$962$	0	0
$963$	−4.06207	−0.130898
$964$	−11.1545	−0.359263
$965$	−21.0029	−0.676107
$966$	2.11385	0.0680119
$967$	−28.3710	−0.912350	−0.456175	−	0.889890i	$-0.650781\pi$
$967$	−28.3710	−0.912350	−0.456175	+	0.889890i	$0.650781\pi$
$968$	6.70805	0.215605
$969$	−11.5326	−0.370480
$970$	24.0902	0.773489
$971$	48.0597	1.54231	0.771154	−	0.636648i	$-0.219680\pi$
$971$	48.0597	1.54231	0.771154	+	0.636648i	$0.219680\pi$
$972$	−1.00000	−0.0320750
$973$	−8.85600	−0.283910
$974$	14.2107	0.455341
$975$	0	0
$976$	5.20571	0.166631
$977$	59.8368	1.91435	0.957174	−	0.289512i	$-0.0934932\pi$
$977$	59.8368	1.91435	0.957174	+	0.289512i	$0.0934932\pi$
$978$	5.30092	0.169505
$979$	−10.9027	−0.348452
$980$	2.41517	0.0771499
$981$	11.7150	0.374032
$982$	1.36574	0.0435825
$983$	45.1363	1.43963	0.719813	−	0.694168i	$-0.244228\pi$
$983$	45.1363	1.43963	0.719813	+	0.694168i	$0.244228\pi$
$984$	−6.82418	−0.217547
$985$	−47.1857	−1.50346
$986$	28.5506	0.909236
$987$	−3.78851	−0.120590
$988$	0	0
$989$	2.74620	0.0873240
$990$	5.00352	0.159022
$991$	16.5393	0.525388	0.262694	−	0.964879i	$-0.415389\pi$
$991$	16.5393	0.525388	0.262694	+	0.964879i	$0.415389\pi$
$992$	10.2200	0.324484
$993$	28.9234	0.917857
$994$	−10.3328	−0.327736
$995$	−24.9131	−0.789797
$996$	−13.4106	−0.424931
$997$	57.6965	1.82727	0.913634	−	0.406539i	$-0.133264\pi$
$997$	57.6965	1.82727	0.913634	+	0.406539i	$0.133264\pi$
$998$	32.6125	1.03233
$999$	−10.3640	−0.327901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cp.1.5	✓	6
13.12	even	2		7098.2.a.cs.1.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cp.1.5	✓	6	1.1	even	1	trivial
7098.2.a.cs.1.2	yes	6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.41517 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.41517 q^{10} -2.07170 q^{11} -1.00000 q^{12} +1.00000 q^{14} -2.41517 q^{15} +1.00000 q^{16} +6.31868 q^{17} -1.00000 q^{18} +1.82515 q^{19} +2.41517 q^{20} +1.00000 q^{21} +2.07170 q^{22} -2.11385 q^{23} +1.00000 q^{24} +0.833070 q^{25} -1.00000 q^{27} -1.00000 q^{28} -4.51844 q^{29} +2.41517 q^{30} -10.2200 q^{31} -1.00000 q^{32} +2.07170 q^{33} -6.31868 q^{34} -2.41517 q^{35} +1.00000 q^{36} +10.3640 q^{37} -1.82515 q^{38} -2.41517 q^{40} -6.82418 q^{41} -1.00000 q^{42} -1.29915 q^{43} -2.07170 q^{44} +2.41517 q^{45} +2.11385 q^{46} -3.78851 q^{47} -1.00000 q^{48} +1.00000 q^{49} -0.833070 q^{50} -6.31868 q^{51} -0.389431 q^{53} +1.00000 q^{54} -5.00352 q^{55} +1.00000 q^{56} -1.82515 q^{57} +4.51844 q^{58} +6.22879 q^{59} -2.41517 q^{60} +5.20571 q^{61} +10.2200 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.07170 q^{66} -9.51616 q^{67} +6.31868 q^{68} +2.11385 q^{69} +2.41517 q^{70} -10.3328 q^{71} -1.00000 q^{72} -8.31831 q^{73} -10.3640 q^{74} -0.833070 q^{75} +1.82515 q^{76} +2.07170 q^{77} +3.45526 q^{79} +2.41517 q^{80} +1.00000 q^{81} +6.82418 q^{82} +13.4106 q^{83} +1.00000 q^{84} +15.2607 q^{85} +1.29915 q^{86} +4.51844 q^{87} +2.07170 q^{88} +5.26268 q^{89} -2.41517 q^{90} -2.11385 q^{92} +10.2200 q^{93} +3.78851 q^{94} +4.40807 q^{95} +1.00000 q^{96} -9.97451 q^{97} -1.00000 q^{98} -2.07170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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