LMFDB - Embedded newform 7098.2.a.cj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.24698 q^{10} -0.692021 q^{11} -1.00000 q^{12} -1.00000 q^{14} -2.24698 q^{15} +1.00000 q^{16} -2.44504 q^{17} +1.00000 q^{18} -3.40581 q^{19} +2.24698 q^{20} +1.00000 q^{21} -0.692021 q^{22} -0.753020 q^{23} -1.00000 q^{24} +0.0489173 q^{25} -1.00000 q^{27} -1.00000 q^{28} -3.66487 q^{29} -2.24698 q^{30} +4.40581 q^{31} +1.00000 q^{32} +0.692021 q^{33} -2.44504 q^{34} -2.24698 q^{35} +1.00000 q^{36} -6.96077 q^{37} -3.40581 q^{38} +2.24698 q^{40} -5.63102 q^{41} +1.00000 q^{42} -1.64310 q^{43} -0.692021 q^{44} +2.24698 q^{45} -0.753020 q^{46} -2.10992 q^{47} -1.00000 q^{48} +1.00000 q^{49} +0.0489173 q^{50} +2.44504 q^{51} -1.69202 q^{53} -1.00000 q^{54} -1.55496 q^{55} -1.00000 q^{56} +3.40581 q^{57} -3.66487 q^{58} -4.96077 q^{59} -2.24698 q^{60} -5.09783 q^{61} +4.40581 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.692021 q^{66} -7.84117 q^{67} -2.44504 q^{68} +0.753020 q^{69} -2.24698 q^{70} +8.76809 q^{71} +1.00000 q^{72} -11.2131 q^{73} -6.96077 q^{74} -0.0489173 q^{75} -3.40581 q^{76} +0.692021 q^{77} +1.97285 q^{79} +2.24698 q^{80} +1.00000 q^{81} -5.63102 q^{82} +9.22952 q^{83} +1.00000 q^{84} -5.49396 q^{85} -1.64310 q^{86} +3.66487 q^{87} -0.692021 q^{88} +3.44504 q^{89} +2.24698 q^{90} -0.753020 q^{92} -4.40581 q^{93} -2.10992 q^{94} -7.65279 q^{95} -1.00000 q^{96} -4.46681 q^{97} +1.00000 q^{98} -0.692021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} + 3 q^{21} + 3 q^{22} - 7 q^{23} - 3 q^{24} - 9 q^{25} - 3 q^{27} - 3 q^{28} - 12 q^{29} - 2 q^{30} + 3 q^{32} - 3 q^{33} - 7 q^{34} - 2 q^{35} + 3 q^{36} - 8 q^{37} + 3 q^{38} + 2 q^{40} - 2 q^{41} + 3 q^{42} - 9 q^{43} + 3 q^{44} + 2 q^{45} - 7 q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} - 9 q^{50} + 7 q^{51} - 3 q^{54} - 5 q^{55} - 3 q^{56} - 3 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{63} + 3 q^{64} - 3 q^{66} - 32 q^{67} - 7 q^{68} + 7 q^{69} - 2 q^{70} + 6 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} + 9 q^{75} + 3 q^{76} - 3 q^{77} + 12 q^{79} + 2 q^{80} + 3 q^{81} - 2 q^{82} + 7 q^{83} + 3 q^{84} - 7 q^{85} - 9 q^{86} + 12 q^{87} + 3 q^{88} + 10 q^{89} + 2 q^{90} - 7 q^{92} - 7 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 + 3 * q^21 + 3 * q^22 - 7 * q^23 - 3 * q^24 - 9 * q^25 - 3 * q^27 - 3 * q^28 - 12 * q^29 - 2 * q^30 + 3 * q^32 - 3 * q^33 - 7 * q^34 - 2 * q^35 + 3 * q^36 - 8 * q^37 + 3 * q^38 + 2 * q^40 - 2 * q^41 + 3 * q^42 - 9 * q^43 + 3 * q^44 + 2 * q^45 - 7 * q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 - 9 * q^50 + 7 * q^51 - 3 * q^54 - 5 * q^55 - 3 * q^56 - 3 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^63 + 3 * q^64 - 3 * q^66 - 32 * q^67 - 7 * q^68 + 7 * q^69 - 2 * q^70 + 6 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 + 9 * q^75 + 3 * q^76 - 3 * q^77 + 12 * q^79 + 2 * q^80 + 3 * q^81 - 2 * q^82 + 7 * q^83 + 3 * q^84 - 7 * q^85 - 9 * q^86 + 12 * q^87 + 3 * q^88 + 10 * q^89 + 2 * q^90 - 7 * q^92 - 7 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 3 * q^98 + 3 * 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
$5$	2.24698	1.00488	0.502440	−	0.864612i	$-0.332436\pi$
$5$	2.24698	1.00488	0.502440	+	0.864612i	$0.332436\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.24698	0.710557
$11$	−0.692021	−0.208652	−0.104326	−	0.994543i	$-0.533269\pi$
$11$	−0.692021	−0.208652	−0.104326	+	0.994543i	$0.533269\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−2.24698	−0.580168
$16$	1.00000	0.250000
$17$	−2.44504	−0.593010	−0.296505	−	0.955031i	$-0.595821\pi$
$17$	−2.44504	−0.593010	−0.296505	+	0.955031i	$0.595821\pi$
$18$	1.00000	0.235702
$19$	−3.40581	−0.781347	−0.390674	−	0.920529i	$-0.627758\pi$
$19$	−3.40581	−0.781347	−0.390674	+	0.920529i	$0.627758\pi$
$20$	2.24698	0.502440
$21$	1.00000	0.218218
$22$	−0.692021	−0.147539
$23$	−0.753020	−0.157016	−0.0785078	−	0.996913i	$-0.525016\pi$
$23$	−0.753020	−0.157016	−0.0785078	+	0.996913i	$0.525016\pi$
$24$	−1.00000	−0.204124
$25$	0.0489173	0.00978347
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−3.66487	−0.680550	−0.340275	−	0.940326i	$-0.610520\pi$
$29$	−3.66487	−0.680550	−0.340275	+	0.940326i	$0.610520\pi$
$30$	−2.24698	−0.410240
$31$	4.40581	0.791307	0.395654	−	0.918400i	$-0.370518\pi$
$31$	4.40581	0.791307	0.395654	+	0.918400i	$0.370518\pi$
$32$	1.00000	0.176777
$33$	0.692021	0.120465
$34$	−2.44504	−0.419321
$35$	−2.24698	−0.379809
$36$	1.00000	0.166667
$37$	−6.96077	−1.14434	−0.572172	−	0.820134i	$-0.693899\pi$
$37$	−6.96077	−1.14434	−0.572172	+	0.820134i	$0.693899\pi$
$38$	−3.40581	−0.552496
$39$	0	0
$40$	2.24698	0.355279
$41$	−5.63102	−0.879418	−0.439709	−	0.898140i	$-0.644918\pi$
$41$	−5.63102	−0.879418	−0.439709	+	0.898140i	$0.644918\pi$
$42$	1.00000	0.154303
$43$	−1.64310	−0.250571	−0.125286	−	0.992121i	$-0.539985\pi$
$43$	−1.64310	−0.250571	−0.125286	+	0.992121i	$0.539985\pi$
$44$	−0.692021	−0.104326
$45$	2.24698	0.334960
$46$	−0.753020	−0.111027
$47$	−2.10992	−0.307763	−0.153881	−	0.988089i	$-0.549177\pi$
$47$	−2.10992	−0.307763	−0.153881	+	0.988089i	$0.549177\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	0.0489173	0.00691796
$51$	2.44504	0.342374
$52$	0	0
$53$	−1.69202	−0.232417	−0.116209	−	0.993225i	$-0.537074\pi$
$53$	−1.69202	−0.232417	−0.116209	+	0.993225i	$0.537074\pi$
$54$	−1.00000	−0.136083
$55$	−1.55496	−0.209671
$56$	−1.00000	−0.133631
$57$	3.40581	0.451111
$58$	−3.66487	−0.481222
$59$	−4.96077	−0.645837	−0.322919	−	0.946427i	$-0.604664\pi$
$59$	−4.96077	−0.645837	−0.322919	+	0.946427i	$0.604664\pi$
$60$	−2.24698	−0.290084
$61$	−5.09783	−0.652711	−0.326355	−	0.945247i	$-0.605821\pi$
$61$	−5.09783	−0.652711	−0.326355	+	0.945247i	$0.605821\pi$
$62$	4.40581	0.559539
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	0.692021	0.0851820
$67$	−7.84117	−0.957951	−0.478975	−	0.877828i	$-0.658992\pi$
$67$	−7.84117	−0.957951	−0.478975	+	0.877828i	$0.658992\pi$
$68$	−2.44504	−0.296505
$69$	0.753020	0.0906530
$70$	−2.24698	−0.268565
$71$	8.76809	1.04058	0.520290	−	0.853990i	$-0.325824\pi$
$71$	8.76809	1.04058	0.520290	+	0.853990i	$0.325824\pi$
$72$	1.00000	0.117851
$73$	−11.2131	−1.31240	−0.656199	−	0.754588i	$-0.727837\pi$
$73$	−11.2131	−1.31240	−0.656199	+	0.754588i	$0.727837\pi$
$74$	−6.96077	−0.809173
$75$	−0.0489173	−0.00564849
$76$	−3.40581	−0.390674
$77$	0.692021	0.0788632
$78$	0	0
$79$	1.97285	0.221963	0.110982	−	0.993822i	$-0.464601\pi$
$79$	1.97285	0.221963	0.110982	+	0.993822i	$0.464601\pi$
$80$	2.24698	0.251220
$81$	1.00000	0.111111
$82$	−5.63102	−0.621842
$83$	9.22952	1.01307	0.506536	−	0.862219i	$-0.330926\pi$
$83$	9.22952	1.01307	0.506536	+	0.862219i	$0.330926\pi$
$84$	1.00000	0.109109
$85$	−5.49396	−0.595904
$86$	−1.64310	−0.177180
$87$	3.66487	0.392916
$88$	−0.692021	−0.0737697
$89$	3.44504	0.365174	0.182587	−	0.983190i	$-0.441553\pi$
$89$	3.44504	0.365174	0.182587	+	0.983190i	$0.441553\pi$
$90$	2.24698	0.236852
$91$	0	0
$92$	−0.753020	−0.0785078
$93$	−4.40581	−0.456862
$94$	−2.10992	−0.217621
$95$	−7.65279	−0.785160
$96$	−1.00000	−0.102062
$97$	−4.46681	−0.453536	−0.226768	−	0.973949i	$-0.572816\pi$
$97$	−4.46681	−0.453536	−0.226768	+	0.973949i	$0.572816\pi$
$98$	1.00000	0.101015
$99$	−0.692021	−0.0695508
$100$	0.0489173	0.00489173
$101$	6.48858	0.645638	0.322819	−	0.946461i	$-0.395369\pi$
$101$	6.48858	0.645638	0.322819	+	0.946461i	$0.395369\pi$
$102$	2.44504	0.242095
$103$	7.85623	0.774098	0.387049	−	0.922059i	$-0.373495\pi$
$103$	7.85623	0.774098	0.387049	+	0.922059i	$0.373495\pi$
$104$	0	0
$105$	2.24698	0.219283
$106$	−1.69202	−0.164344
$107$	−14.9215	−1.44252	−0.721260	−	0.692664i	$-0.756437\pi$
$107$	−14.9215	−1.44252	−0.721260	+	0.692664i	$0.756437\pi$
$108$	−1.00000	−0.0962250
$109$	12.6504	1.21169	0.605844	−	0.795583i	$-0.292835\pi$
$109$	12.6504	1.21169	0.605844	+	0.795583i	$0.292835\pi$
$110$	−1.55496	−0.148259
$111$	6.96077	0.660687
$112$	−1.00000	−0.0944911
$113$	−20.5526	−1.93342	−0.966711	−	0.255869i	$-0.917638\pi$
$113$	−20.5526	−1.93342	−0.966711	+	0.255869i	$0.917638\pi$
$114$	3.40581	0.318984
$115$	−1.69202	−0.157782
$116$	−3.66487	−0.340275
$117$	0	0
$118$	−4.96077	−0.456676
$119$	2.44504	0.224137
$120$	−2.24698	−0.205120
$121$	−10.5211	−0.956464
$122$	−5.09783	−0.461536
$123$	5.63102	0.507732
$124$	4.40581	0.395654
$125$	−11.1250	−0.995049
$126$	−1.00000	−0.0890871
$127$	2.66487	0.236469	0.118235	−	0.992986i	$-0.462276\pi$
$127$	2.66487	0.236469	0.118235	+	0.992986i	$0.462276\pi$
$128$	1.00000	0.0883883
$129$	1.64310	0.144667
$130$	0	0
$131$	3.37867	0.295195	0.147598	−	0.989047i	$-0.452846\pi$
$131$	3.37867	0.295195	0.147598	+	0.989047i	$0.452846\pi$
$132$	0.692021	0.0602327
$133$	3.40581	0.295321
$134$	−7.84117	−0.677374
$135$	−2.24698	−0.193389
$136$	−2.44504	−0.209661
$137$	−15.5646	−1.32978	−0.664889	−	0.746942i	$-0.731521\pi$
$137$	−15.5646	−1.32978	−0.664889	+	0.746942i	$0.731521\pi$
$138$	0.753020	0.0641014
$139$	−0.405813	−0.0344206	−0.0172103	−	0.999852i	$-0.505478\pi$
$139$	−0.405813	−0.0344206	−0.0172103	+	0.999852i	$0.505478\pi$
$140$	−2.24698	−0.189904
$141$	2.10992	0.177687
$142$	8.76809	0.735801
$143$	0	0
$144$	1.00000	0.0833333
$145$	−8.23490	−0.683871
$146$	−11.2131	−0.928005
$147$	−1.00000	−0.0824786
$148$	−6.96077	−0.572172
$149$	8.35019	0.684074	0.342037	−	0.939686i	$-0.388883\pi$
$149$	8.35019	0.684074	0.342037	+	0.939686i	$0.388883\pi$
$150$	−0.0489173	−0.00399408
$151$	−5.24160	−0.426556	−0.213278	−	0.976992i	$-0.568414\pi$
$151$	−5.24160	−0.426556	−0.213278	+	0.976992i	$0.568414\pi$
$152$	−3.40581	−0.276248
$153$	−2.44504	−0.197670
$154$	0.692021	0.0557647
$155$	9.89977	0.795169
$156$	0	0
$157$	10.4940	0.837509	0.418755	−	0.908099i	$-0.362467\pi$
$157$	10.4940	0.837509	0.418755	+	0.908099i	$0.362467\pi$
$158$	1.97285	0.156952
$159$	1.69202	0.134186
$160$	2.24698	0.177639
$161$	0.753020	0.0593463
$162$	1.00000	0.0785674
$163$	18.6993	1.46464	0.732322	−	0.680959i	$-0.238437\pi$
$163$	18.6993	1.46464	0.732322	+	0.680959i	$0.238437\pi$
$164$	−5.63102	−0.439709
$165$	1.55496	0.121053
$166$	9.22952	0.716350
$167$	11.9269	0.922933	0.461466	−	0.887158i	$-0.347323\pi$
$167$	11.9269	0.922933	0.461466	+	0.887158i	$0.347323\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−5.49396	−0.421367
$171$	−3.40581	−0.260449
$172$	−1.64310	−0.125286
$173$	−7.10992	−0.540557	−0.270278	−	0.962782i	$-0.587116\pi$
$173$	−7.10992	−0.540557	−0.270278	+	0.962782i	$0.587116\pi$
$174$	3.66487	0.277833
$175$	−0.0489173	−0.00369780
$176$	−0.692021	−0.0521631
$177$	4.96077	0.372874
$178$	3.44504	0.258217
$179$	−12.1642	−0.909196	−0.454598	−	0.890697i	$-0.650217\pi$
$179$	−12.1642	−0.909196	−0.454598	+	0.890697i	$0.650217\pi$
$180$	2.24698	0.167480
$181$	4.83877	0.359663	0.179832	−	0.983697i	$-0.442445\pi$
$181$	4.83877	0.359663	0.179832	+	0.983697i	$0.442445\pi$
$182$	0	0
$183$	5.09783	0.376843
$184$	−0.753020	−0.0555134
$185$	−15.6407	−1.14993
$186$	−4.40581	−0.323050
$187$	1.69202	0.123733
$188$	−2.10992	−0.153881
$189$	1.00000	0.0727393
$190$	−7.65279	−0.555192
$191$	−0.664874	−0.0481086	−0.0240543	−	0.999711i	$-0.507657\pi$
$191$	−0.664874	−0.0481086	−0.0240543	+	0.999711i	$0.507657\pi$
$192$	−1.00000	−0.0721688
$193$	−11.3013	−0.813483	−0.406742	−	0.913543i	$-0.633335\pi$
$193$	−11.3013	−0.813483	−0.406742	+	0.913543i	$0.633335\pi$
$194$	−4.46681	−0.320698
$195$	0	0
$196$	1.00000	0.0714286
$197$	−6.26875	−0.446630	−0.223315	−	0.974746i	$-0.571688\pi$
$197$	−6.26875	−0.446630	−0.223315	+	0.974746i	$0.571688\pi$
$198$	−0.692021	−0.0491798
$199$	−12.3937	−0.878568	−0.439284	−	0.898348i	$-0.644768\pi$
$199$	−12.3937	−0.878568	−0.439284	+	0.898348i	$0.644768\pi$
$200$	0.0489173	0.00345898
$201$	7.84117	0.553073
$202$	6.48858	0.456535
$203$	3.66487	0.257224
$204$	2.44504	0.171187
$205$	−12.6528	−0.883709
$206$	7.85623	0.547370
$207$	−0.753020	−0.0523385
$208$	0	0
$209$	2.35690	0.163030
$210$	2.24698	0.155056
$211$	7.65279	0.526840	0.263420	−	0.964681i	$-0.415150\pi$
$211$	7.65279	0.526840	0.263420	+	0.964681i	$0.415150\pi$
$212$	−1.69202	−0.116209
$213$	−8.76809	−0.600779
$214$	−14.9215	−1.02002
$215$	−3.69202	−0.251794
$216$	−1.00000	−0.0680414
$217$	−4.40581	−0.299086
$218$	12.6504	0.856793
$219$	11.2131	0.757713
$220$	−1.55496	−0.104835
$221$	0	0
$222$	6.96077	0.467176
$223$	−15.2905	−1.02393	−0.511964	−	0.859007i	$-0.671082\pi$
$223$	−15.2905	−1.02393	−0.511964	+	0.859007i	$0.671082\pi$
$224$	−1.00000	−0.0668153
$225$	0.0489173	0.00326116
$226$	−20.5526	−1.36714
$227$	−14.2808	−0.947852	−0.473926	−	0.880565i	$-0.657164\pi$
$227$	−14.2808	−0.947852	−0.473926	+	0.880565i	$0.657164\pi$
$228$	3.40581	0.225555
$229$	−6.30127	−0.416400	−0.208200	−	0.978086i	$-0.566760\pi$
$229$	−6.30127	−0.416400	−0.208200	+	0.978086i	$0.566760\pi$
$230$	−1.69202	−0.111569
$231$	−0.692021	−0.0455317
$232$	−3.66487	−0.240611
$233$	25.9071	1.69723	0.848614	−	0.529012i	$-0.177437\pi$
$233$	25.9071	1.69723	0.848614	+	0.529012i	$0.177437\pi$
$234$	0	0
$235$	−4.74094	−0.309265
$236$	−4.96077	−0.322919
$237$	−1.97285	−0.128151
$238$	2.44504	0.158489
$239$	0.811626	0.0524997	0.0262499	−	0.999655i	$-0.491643\pi$
$239$	0.811626	0.0524997	0.0262499	+	0.999655i	$0.491643\pi$
$240$	−2.24698	−0.145042
$241$	6.23490	0.401625	0.200813	−	0.979630i	$-0.435642\pi$
$241$	6.23490	0.401625	0.200813	+	0.979630i	$0.435642\pi$
$242$	−10.5211	−0.676322
$243$	−1.00000	−0.0641500
$244$	−5.09783	−0.326355
$245$	2.24698	0.143554
$246$	5.63102	0.359021
$247$	0	0
$248$	4.40581	0.279769
$249$	−9.22952	−0.584897
$250$	−11.1250	−0.703606
$251$	29.6045	1.86862	0.934309	−	0.356465i	$-0.116018\pi$
$251$	29.6045	1.86862	0.934309	+	0.356465i	$0.116018\pi$
$252$	−1.00000	−0.0629941
$253$	0.521106	0.0327617
$254$	2.66487	0.167209
$255$	5.49396	0.344045
$256$	1.00000	0.0625000
$257$	−9.24160	−0.576475	−0.288238	−	0.957559i	$-0.593069\pi$
$257$	−9.24160	−0.576475	−0.288238	+	0.957559i	$0.593069\pi$
$258$	1.64310	0.102295
$259$	6.96077	0.432521
$260$	0	0
$261$	−3.66487	−0.226850
$262$	3.37867	0.208735
$263$	1.09246	0.0673638	0.0336819	−	0.999433i	$-0.489277\pi$
$263$	1.09246	0.0673638	0.0336819	+	0.999433i	$0.489277\pi$
$264$	0.692021	0.0425910
$265$	−3.80194	−0.233551
$266$	3.40581	0.208824
$267$	−3.44504	−0.210833
$268$	−7.84117	−0.478975
$269$	−0.916166	−0.0558596	−0.0279298	−	0.999610i	$-0.508891\pi$
$269$	−0.916166	−0.0558596	−0.0279298	+	0.999610i	$0.508891\pi$
$270$	−2.24698	−0.136747
$271$	30.6655	1.86279	0.931397	−	0.364005i	$-0.118591\pi$
$271$	30.6655	1.86279	0.931397	+	0.364005i	$0.118591\pi$
$272$	−2.44504	−0.148252
$273$	0	0
$274$	−15.5646	−0.940295
$275$	−0.0338518	−0.00204134
$276$	0.753020	0.0453265
$277$	21.8146	1.31071	0.655356	−	0.755320i	$-0.272518\pi$
$277$	21.8146	1.31071	0.655356	+	0.755320i	$0.272518\pi$
$278$	−0.405813	−0.0243391
$279$	4.40581	0.263769
$280$	−2.24698	−0.134283
$281$	−6.67994	−0.398492	−0.199246	−	0.979950i	$-0.563849\pi$
$281$	−6.67994	−0.398492	−0.199246	+	0.979950i	$0.563849\pi$
$282$	2.10992	0.125644
$283$	26.2228	1.55878	0.779392	−	0.626536i	$-0.215528\pi$
$283$	26.2228	1.55878	0.779392	+	0.626536i	$0.215528\pi$
$284$	8.76809	0.520290
$285$	7.65279	0.453312
$286$	0	0
$287$	5.63102	0.332389
$288$	1.00000	0.0589256
$289$	−11.0218	−0.648339
$290$	−8.23490	−0.483570
$291$	4.46681	0.261849
$292$	−11.2131	−0.656199
$293$	−13.2741	−0.775483	−0.387741	−	0.921768i	$-0.626745\pi$
$293$	−13.2741	−0.775483	−0.387741	+	0.921768i	$0.626745\pi$
$294$	−1.00000	−0.0583212
$295$	−11.1468	−0.648989
$296$	−6.96077	−0.404587
$297$	0.692021	0.0401552
$298$	8.35019	0.483714
$299$	0	0
$300$	−0.0489173	−0.00282424
$301$	1.64310	0.0947069
$302$	−5.24160	−0.301620
$303$	−6.48858	−0.372759
$304$	−3.40581	−0.195337
$305$	−11.4547	−0.655896
$306$	−2.44504	−0.139774
$307$	−32.3260	−1.84494	−0.922472	−	0.386064i	$-0.873834\pi$
$307$	−32.3260	−1.84494	−0.922472	+	0.386064i	$0.873834\pi$
$308$	0.692021	0.0394316
$309$	−7.85623	−0.446925
$310$	9.89977	0.562269
$311$	−9.89738	−0.561229	−0.280614	−	0.959821i	$-0.590538\pi$
$311$	−9.89738	−0.561229	−0.280614	+	0.959821i	$0.590538\pi$
$312$	0	0
$313$	−2.66786	−0.150796	−0.0753981	−	0.997154i	$-0.524023\pi$
$313$	−2.66786	−0.150796	−0.0753981	+	0.997154i	$0.524023\pi$
$314$	10.4940	0.592208
$315$	−2.24698	−0.126603
$316$	1.97285	0.110982
$317$	9.68425	0.543922	0.271961	−	0.962308i	$-0.412328\pi$
$317$	9.68425	0.543922	0.271961	+	0.962308i	$0.412328\pi$
$318$	1.69202	0.0948839
$319$	2.53617	0.141998
$320$	2.24698	0.125610
$321$	14.9215	0.832839
$322$	0.753020	0.0419642
$323$	8.32736	0.463346
$324$	1.00000	0.0555556
$325$	0	0
$326$	18.6993	1.03566
$327$	−12.6504	−0.699569
$328$	−5.63102	−0.310921
$329$	2.10992	0.116323
$330$	1.55496	0.0855976
$331$	1.38644	0.0762054	0.0381027	−	0.999274i	$-0.487869\pi$
$331$	1.38644	0.0762054	0.0381027	+	0.999274i	$0.487869\pi$
$332$	9.22952	0.506536
$333$	−6.96077	−0.381448
$334$	11.9269	0.652612
$335$	−17.6189	−0.962626
$336$	1.00000	0.0545545
$337$	−1.30260	−0.0709572	−0.0354786	−	0.999370i	$-0.511296\pi$
$337$	−1.30260	−0.0709572	−0.0354786	+	0.999370i	$0.511296\pi$
$338$	0	0
$339$	20.5526	1.11626
$340$	−5.49396	−0.297952
$341$	−3.04892	−0.165108
$342$	−3.40581	−0.184165
$343$	−1.00000	−0.0539949
$344$	−1.64310	−0.0885902
$345$	1.69202	0.0910954
$346$	−7.10992	−0.382231
$347$	−12.7506	−0.684490	−0.342245	−	0.939611i	$-0.611187\pi$
$347$	−12.7506	−0.684490	−0.342245	+	0.939611i	$0.611187\pi$
$348$	3.66487	0.196458
$349$	−26.8267	−1.43600	−0.718000	−	0.696043i	$-0.754942\pi$
$349$	−26.8267	−1.43600	−0.718000	+	0.696043i	$0.754942\pi$
$350$	−0.0489173	−0.00261474
$351$	0	0
$352$	−0.692021	−0.0368849
$353$	−18.1086	−0.963823	−0.481911	−	0.876220i	$-0.660057\pi$
$353$	−18.1086	−0.963823	−0.481911	+	0.876220i	$0.660057\pi$
$354$	4.96077	0.263662
$355$	19.7017	1.04566
$356$	3.44504	0.182587
$357$	−2.44504	−0.129405
$358$	−12.1642	−0.642898
$359$	7.46144	0.393799	0.196900	−	0.980424i	$-0.436913\pi$
$359$	7.46144	0.393799	0.196900	+	0.980424i	$0.436913\pi$
$360$	2.24698	0.118426
$361$	−7.40044	−0.389497
$362$	4.83877	0.254320
$363$	10.5211	0.552215
$364$	0	0
$365$	−25.1957	−1.31880
$366$	5.09783	0.266468
$367$	28.0194	1.46260	0.731300	−	0.682056i	$-0.238914\pi$
$367$	28.0194	1.46260	0.731300	+	0.682056i	$0.238914\pi$
$368$	−0.753020	−0.0392539
$369$	−5.63102	−0.293139
$370$	−15.6407	−0.813122
$371$	1.69202	0.0878454
$372$	−4.40581	−0.228431
$373$	−32.2868	−1.67175	−0.835874	−	0.548922i	$-0.815038\pi$
$373$	−32.2868	−1.67175	−0.835874	+	0.548922i	$0.815038\pi$
$374$	1.69202	0.0874923
$375$	11.1250	0.574492
$376$	−2.10992	−0.108811
$377$	0	0
$378$	1.00000	0.0514344
$379$	−27.0465	−1.38929	−0.694643	−	0.719354i	$-0.744438\pi$
$379$	−27.0465	−1.38929	−0.694643	+	0.719354i	$0.744438\pi$
$380$	−7.65279	−0.392580
$381$	−2.66487	−0.136526
$382$	−0.664874	−0.0340179
$383$	6.21552	0.317598	0.158799	−	0.987311i	$-0.449238\pi$
$383$	6.21552	0.317598	0.158799	+	0.987311i	$0.449238\pi$
$384$	−1.00000	−0.0510310
$385$	1.55496	0.0792480
$386$	−11.3013	−0.575220
$387$	−1.64310	−0.0835237
$388$	−4.46681	−0.226768
$389$	12.0683	0.611887	0.305943	−	0.952050i	$-0.401028\pi$
$389$	12.0683	0.611887	0.305943	+	0.952050i	$0.401028\pi$
$390$	0	0
$391$	1.84117	0.0931118
$392$	1.00000	0.0505076
$393$	−3.37867	−0.170431
$394$	−6.26875	−0.315815
$395$	4.43296	0.223046
$396$	−0.692021	−0.0347754
$397$	36.3551	1.82461	0.912305	−	0.409512i	$-0.134301\pi$
$397$	36.3551	1.82461	0.912305	+	0.409512i	$0.134301\pi$
$398$	−12.3937	−0.621242
$399$	−3.40581	−0.170504
$400$	0.0489173	0.00244587
$401$	−23.9463	−1.19582	−0.597910	−	0.801563i	$-0.704002\pi$
$401$	−23.9463	−1.19582	−0.597910	+	0.801563i	$0.704002\pi$
$402$	7.84117	0.391082
$403$	0	0
$404$	6.48858	0.322819
$405$	2.24698	0.111653
$406$	3.66487	0.181885
$407$	4.81700	0.238770
$408$	2.44504	0.121048
$409$	−19.6571	−0.971981	−0.485991	−	0.873964i	$-0.661541\pi$
$409$	−19.6571	−0.971981	−0.485991	+	0.873964i	$0.661541\pi$
$410$	−12.6528	−0.624877
$411$	15.5646	0.767747
$412$	7.85623	0.387049
$413$	4.96077	0.244104
$414$	−0.753020	−0.0370089
$415$	20.7385	1.01802
$416$	0	0
$417$	0.405813	0.0198728
$418$	2.35690	0.115280
$419$	−22.4228	−1.09543	−0.547713	−	0.836666i	$-0.684501\pi$
$419$	−22.4228	−1.09543	−0.547713	+	0.836666i	$0.684501\pi$
$420$	2.24698	0.109641
$421$	−19.1317	−0.932421	−0.466211	−	0.884674i	$-0.654381\pi$
$421$	−19.1317	−0.932421	−0.466211	+	0.884674i	$0.654381\pi$
$422$	7.65279	0.372532
$423$	−2.10992	−0.102588
$424$	−1.69202	−0.0821718
$425$	−0.119605	−0.00580169
$426$	−8.76809	−0.424815
$427$	5.09783	0.246702
$428$	−14.9215	−0.721260
$429$	0	0
$430$	−3.69202	−0.178045
$431$	−16.0224	−0.771770	−0.385885	−	0.922547i	$-0.626104\pi$
$431$	−16.0224	−0.771770	−0.385885	+	0.922547i	$0.626104\pi$
$432$	−1.00000	−0.0481125
$433$	20.1933	0.970427	0.485213	−	0.874396i	$-0.338742\pi$
$433$	20.1933	0.970427	0.485213	+	0.874396i	$0.338742\pi$
$434$	−4.40581	−0.211486
$435$	8.23490	0.394833
$436$	12.6504	0.605844
$437$	2.56465	0.122684
$438$	11.2131	0.535784
$439$	2.28190	0.108909	0.0544545	−	0.998516i	$-0.482658\pi$
$439$	2.28190	0.108909	0.0544545	+	0.998516i	$0.482658\pi$
$440$	−1.55496	−0.0741297
$441$	1.00000	0.0476190
$442$	0	0
$443$	−14.1129	−0.670524	−0.335262	−	0.942125i	$-0.608825\pi$
$443$	−14.1129	−0.670524	−0.335262	+	0.942125i	$0.608825\pi$
$444$	6.96077	0.330344
$445$	7.74094	0.366956
$446$	−15.2905	−0.724027
$447$	−8.35019	−0.394950
$448$	−1.00000	−0.0472456
$449$	−21.8732	−1.03226	−0.516130	−	0.856510i	$-0.672628\pi$
$449$	−21.8732	−1.03226	−0.516130	+	0.856510i	$0.672628\pi$
$450$	0.0489173	0.00230599
$451$	3.89679	0.183493
$452$	−20.5526	−0.966711
$453$	5.24160	0.246272
$454$	−14.2808	−0.670233
$455$	0	0
$456$	3.40581	0.159492
$457$	−27.8280	−1.30174	−0.650870	−	0.759189i	$-0.725596\pi$
$457$	−27.8280	−1.30174	−0.650870	+	0.759189i	$0.725596\pi$
$458$	−6.30127	−0.294439
$459$	2.44504	0.114125
$460$	−1.69202	−0.0788909
$461$	−5.81833	−0.270987	−0.135493	−	0.990778i	$-0.543262\pi$
$461$	−5.81833	−0.270987	−0.135493	+	0.990778i	$0.543262\pi$
$462$	−0.692021	−0.0321958
$463$	−20.0218	−0.930491	−0.465245	−	0.885182i	$-0.654034\pi$
$463$	−20.0218	−0.930491	−0.465245	+	0.885182i	$0.654034\pi$
$464$	−3.66487	−0.170138
$465$	−9.89977	−0.459091
$466$	25.9071	1.20012
$467$	15.7791	0.730170	0.365085	−	0.930974i	$-0.381040\pi$
$467$	15.7791	0.730170	0.365085	+	0.930974i	$0.381040\pi$
$468$	0	0
$469$	7.84117	0.362071
$470$	−4.74094	−0.218683
$471$	−10.4940	−0.483536
$472$	−4.96077	−0.228338
$473$	1.13706	0.0522822
$474$	−1.97285	−0.0906161
$475$	−0.166603	−0.00764428
$476$	2.44504	0.112068
$477$	−1.69202	−0.0774723
$478$	0.811626	0.0371229
$479$	−1.31575	−0.0601181	−0.0300590	−	0.999548i	$-0.509570\pi$
$479$	−1.31575	−0.0601181	−0.0300590	+	0.999548i	$0.509570\pi$
$480$	−2.24698	−0.102560
$481$	0	0
$482$	6.23490	0.283992
$483$	−0.753020	−0.0342636
$484$	−10.5211	−0.478232
$485$	−10.0368	−0.455749
$486$	−1.00000	−0.0453609
$487$	−19.1618	−0.868305	−0.434152	−	0.900839i	$-0.642952\pi$
$487$	−19.1618	−0.868305	−0.434152	+	0.900839i	$0.642952\pi$
$488$	−5.09783	−0.230768
$489$	−18.6993	−0.845612
$490$	2.24698	0.101508
$491$	32.3860	1.46156	0.730779	−	0.682614i	$-0.239157\pi$
$491$	32.3860	1.46156	0.730779	+	0.682614i	$0.239157\pi$
$492$	5.63102	0.253866
$493$	8.96077	0.403573
$494$	0	0
$495$	−1.55496	−0.0698902
$496$	4.40581	0.197827
$497$	−8.76809	−0.393302
$498$	−9.22952	−0.413585
$499$	−8.55363	−0.382913	−0.191457	−	0.981501i	$-0.561321\pi$
$499$	−8.55363	−0.382913	−0.191457	+	0.981501i	$0.561321\pi$
$500$	−11.1250	−0.497524
$501$	−11.9269	−0.532855
$502$	29.6045	1.32131
$503$	−1.30319	−0.0581065	−0.0290532	−	0.999578i	$-0.509249\pi$
$503$	−1.30319	−0.0581065	−0.0290532	+	0.999578i	$0.509249\pi$
$504$	−1.00000	−0.0445435
$505$	14.5797	0.648789
$506$	0.521106	0.0231660
$507$	0	0
$508$	2.66487	0.118235
$509$	10.3720	0.459729	0.229865	−	0.973223i	$-0.426172\pi$
$509$	10.3720	0.459729	0.229865	+	0.973223i	$0.426172\pi$
$510$	5.49396	0.243277
$511$	11.2131	0.496040
$512$	1.00000	0.0441942
$513$	3.40581	0.150370
$514$	−9.24160	−0.407630
$515$	17.6528	0.777875
$516$	1.64310	0.0723336
$517$	1.46011	0.0642154
$518$	6.96077	0.305839
$519$	7.10992	0.312091
$520$	0	0
$521$	30.0183	1.31513	0.657563	−	0.753399i	$-0.271587\pi$
$521$	30.0183	1.31513	0.657563	+	0.753399i	$0.271587\pi$
$522$	−3.66487	−0.160407
$523$	37.3250	1.63211	0.816053	−	0.577977i	$-0.196158\pi$
$523$	37.3250	1.63211	0.816053	+	0.577977i	$0.196158\pi$
$524$	3.37867	0.147598
$525$	0.0489173	0.00213493
$526$	1.09246	0.0476334
$527$	−10.7724	−0.469253
$528$	0.692021	0.0301164
$529$	−22.4330	−0.975346
$530$	−3.80194	−0.165146
$531$	−4.96077	−0.215279
$532$	3.40581	0.147661
$533$	0	0
$534$	−3.44504	−0.149082
$535$	−33.5284	−1.44956
$536$	−7.84117	−0.338687
$537$	12.1642	0.524924
$538$	−0.916166	−0.0394987
$539$	−0.692021	−0.0298075
$540$	−2.24698	−0.0966946
$541$	1.98015	0.0851332	0.0425666	−	0.999094i	$-0.486447\pi$
$541$	1.98015	0.0851332	0.0425666	+	0.999094i	$0.486447\pi$
$542$	30.6655	1.31719
$543$	−4.83877	−0.207652
$544$	−2.44504	−0.104830
$545$	28.4252	1.21760
$546$	0	0
$547$	18.2862	0.781862	0.390931	−	0.920420i	$-0.372153\pi$
$547$	18.2862	0.781862	0.390931	+	0.920420i	$0.372153\pi$
$548$	−15.5646	−0.664889
$549$	−5.09783	−0.217570
$550$	−0.0338518	−0.00144345
$551$	12.4819	0.531746
$552$	0.753020	0.0320507
$553$	−1.97285	−0.0838942
$554$	21.8146	0.926814
$555$	15.6407	0.663911
$556$	−0.405813	−0.0172103
$557$	−40.6612	−1.72287	−0.861434	−	0.507869i	$-0.830433\pi$
$557$	−40.6612	−1.72287	−0.861434	+	0.507869i	$0.830433\pi$
$558$	4.40581	0.186513
$559$	0	0
$560$	−2.24698	−0.0949522
$561$	−1.69202	−0.0714372
$562$	−6.67994	−0.281776
$563$	19.8780	0.837758	0.418879	−	0.908042i	$-0.362423\pi$
$563$	19.8780	0.837758	0.418879	+	0.908042i	$0.362423\pi$
$564$	2.10992	0.0888435
$565$	−46.1812	−1.94286
$566$	26.2228	1.10223
$567$	−1.00000	−0.0419961
$568$	8.76809	0.367901
$569$	18.9801	0.795689	0.397845	−	0.917453i	$-0.369758\pi$
$569$	18.9801	0.795689	0.397845	+	0.917453i	$0.369758\pi$
$570$	7.65279	0.320540
$571$	−30.2355	−1.26532	−0.632658	−	0.774431i	$-0.718036\pi$
$571$	−30.2355	−1.26532	−0.632658	+	0.774431i	$0.718036\pi$
$572$	0	0
$573$	0.664874	0.0277755
$574$	5.63102	0.235034
$575$	−0.0368358	−0.00153616
$576$	1.00000	0.0416667
$577$	−16.0707	−0.669031	−0.334516	−	0.942390i	$-0.608573\pi$
$577$	−16.0707	−0.669031	−0.334516	+	0.942390i	$0.608573\pi$
$578$	−11.0218	−0.458445
$579$	11.3013	0.469665
$580$	−8.23490	−0.341936
$581$	−9.22952	−0.382905
$582$	4.46681	0.185155
$583$	1.17092	0.0484944
$584$	−11.2131	−0.464003
$585$	0	0
$586$	−13.2741	−0.548349
$587$	−26.0793	−1.07641	−0.538204	−	0.842814i	$-0.680897\pi$
$587$	−26.0793	−1.07641	−0.538204	+	0.842814i	$0.680897\pi$
$588$	−1.00000	−0.0412393
$589$	−15.0054	−0.618286
$590$	−11.1468	−0.458905
$591$	6.26875	0.257862
$592$	−6.96077	−0.286086
$593$	46.4131	1.90596	0.952979	−	0.303036i	$-0.0980004\pi$
$593$	46.4131	1.90596	0.952979	+	0.303036i	$0.0980004\pi$
$594$	0.692021	0.0283940
$595$	5.49396	0.225230
$596$	8.35019	0.342037
$597$	12.3937	0.507242
$598$	0	0
$599$	17.9269	0.732474	0.366237	−	0.930522i	$-0.380646\pi$
$599$	17.9269	0.732474	0.366237	+	0.930522i	$0.380646\pi$
$600$	−0.0489173	−0.00199704
$601$	−27.6829	−1.12921	−0.564605	−	0.825361i	$-0.690971\pi$
$601$	−27.6829	−1.12921	−0.564605	+	0.825361i	$0.690971\pi$
$602$	1.64310	0.0669679
$603$	−7.84117	−0.319317
$604$	−5.24160	−0.213278
$605$	−23.6407	−0.961132
$606$	−6.48858	−0.263581
$607$	−13.8659	−0.562800	−0.281400	−	0.959591i	$-0.590799\pi$
$607$	−13.8659	−0.562800	−0.281400	+	0.959591i	$0.590799\pi$
$608$	−3.40581	−0.138124
$609$	−3.66487	−0.148508
$610$	−11.4547	−0.463788
$611$	0	0
$612$	−2.44504	−0.0988350
$613$	6.21744	0.251120	0.125560	−	0.992086i	$-0.459927\pi$
$613$	6.21744	0.251120	0.125560	+	0.992086i	$0.459927\pi$
$614$	−32.3260	−1.30457
$615$	12.6528	0.510210
$616$	0.692021	0.0278823
$617$	47.5900	1.91590	0.957950	−	0.286934i	$-0.0926359\pi$
$617$	47.5900	1.91590	0.957950	+	0.286934i	$0.0926359\pi$
$618$	−7.85623	−0.316024
$619$	34.7241	1.39568	0.697839	−	0.716255i	$-0.254145\pi$
$619$	34.7241	1.39568	0.697839	+	0.716255i	$0.254145\pi$
$620$	9.89977	0.397584
$621$	0.753020	0.0302177
$622$	−9.89738	−0.396849
$623$	−3.44504	−0.138023
$624$	0	0
$625$	−25.2422	−1.00969
$626$	−2.66786	−0.106629
$627$	−2.35690	−0.0941254
$628$	10.4940	0.418755
$629$	17.0194	0.678607
$630$	−2.24698	−0.0895218
$631$	15.6601	0.623418	0.311709	−	0.950178i	$-0.399099\pi$
$631$	15.6601	0.623418	0.311709	+	0.950178i	$0.399099\pi$
$632$	1.97285	0.0784759
$633$	−7.65279	−0.304171
$634$	9.68425	0.384611
$635$	5.98792	0.237623
$636$	1.69202	0.0670930
$637$	0	0
$638$	2.53617	0.100408
$639$	8.76809	0.346860
$640$	2.24698	0.0888197
$641$	−27.9869	−1.10541	−0.552707	−	0.833376i	$-0.686405\pi$
$641$	−27.9869	−1.10541	−0.552707	+	0.833376i	$0.686405\pi$
$642$	14.9215	0.588906
$643$	−16.1032	−0.635049	−0.317524	−	0.948250i	$-0.602852\pi$
$643$	−16.1032	−0.635049	−0.317524	+	0.948250i	$0.602852\pi$
$644$	0.753020	0.0296732
$645$	3.69202	0.145373
$646$	8.32736	0.327635
$647$	12.2397	0.481192	0.240596	−	0.970625i	$-0.422657\pi$
$647$	12.2397	0.481192	0.240596	+	0.970625i	$0.422657\pi$
$648$	1.00000	0.0392837
$649$	3.43296	0.134755
$650$	0	0
$651$	4.40581	0.172677
$652$	18.6993	0.732322
$653$	−4.60281	−0.180122	−0.0900609	−	0.995936i	$-0.528706\pi$
$653$	−4.60281	−0.180122	−0.0900609	+	0.995936i	$0.528706\pi$
$654$	−12.6504	−0.494670
$655$	7.59179	0.296636
$656$	−5.63102	−0.219854
$657$	−11.2131	−0.437466
$658$	2.10992	0.0822531
$659$	7.58450	0.295450	0.147725	−	0.989028i	$-0.452805\pi$
$659$	7.58450	0.295450	0.147725	+	0.989028i	$0.452805\pi$
$660$	1.55496	0.0605267
$661$	−33.4233	−1.30001	−0.650007	−	0.759928i	$-0.725234\pi$
$661$	−33.4233	−1.30001	−0.650007	+	0.759928i	$0.725234\pi$
$662$	1.38644	0.0538854
$663$	0	0
$664$	9.22952	0.358175
$665$	7.65279	0.296763
$666$	−6.96077	−0.269724
$667$	2.75973	0.106857
$668$	11.9269	0.461466
$669$	15.2905	0.591166
$670$	−17.6189	−0.680679
$671$	3.52781	0.136190
$672$	1.00000	0.0385758
$673$	30.0140	1.15695	0.578477	−	0.815698i	$-0.303647\pi$
$673$	30.0140	1.15695	0.578477	+	0.815698i	$0.303647\pi$
$674$	−1.30260	−0.0501743
$675$	−0.0489173	−0.00188283
$676$	0	0
$677$	43.0780	1.65562	0.827811	−	0.561008i	$-0.189586\pi$
$677$	43.0780	1.65562	0.827811	+	0.561008i	$0.189586\pi$
$678$	20.5526	0.789317
$679$	4.46681	0.171421
$680$	−5.49396	−0.210684
$681$	14.2808	0.547243
$682$	−3.04892	−0.116749
$683$	−40.6262	−1.55452	−0.777260	−	0.629180i	$-0.783391\pi$
$683$	−40.6262	−1.55452	−0.777260	+	0.629180i	$0.783391\pi$
$684$	−3.40581	−0.130225
$685$	−34.9734	−1.33627
$686$	−1.00000	−0.0381802
$687$	6.30127	0.240409
$688$	−1.64310	−0.0626428
$689$	0	0
$690$	1.69202	0.0644142
$691$	8.62266	0.328022	0.164011	−	0.986459i	$-0.447557\pi$
$691$	8.62266	0.328022	0.164011	+	0.986459i	$0.447557\pi$
$692$	−7.10992	−0.270278
$693$	0.692021	0.0262877
$694$	−12.7506	−0.484007
$695$	−0.911854	−0.0345886
$696$	3.66487	0.138917
$697$	13.7681	0.521503
$698$	−26.8267	−1.01541
$699$	−25.9071	−0.979895
$700$	−0.0489173	−0.00184890
$701$	−0.259652	−0.00980693	−0.00490346	−	0.999988i	$-0.501561\pi$
$701$	−0.259652	−0.00980693	−0.00490346	+	0.999988i	$0.501561\pi$
$702$	0	0
$703$	23.7071	0.894130
$704$	−0.692021	−0.0260815
$705$	4.74094	0.178554
$706$	−18.1086	−0.681526
$707$	−6.48858	−0.244028
$708$	4.96077	0.186437
$709$	28.6189	1.07481	0.537403	−	0.843325i	$-0.319405\pi$
$709$	28.6189	1.07481	0.537403	+	0.843325i	$0.319405\pi$
$710$	19.7017	0.739392
$711$	1.97285	0.0739878
$712$	3.44504	0.129108
$713$	−3.31767	−0.124248
$714$	−2.44504	−0.0915034
$715$	0	0
$716$	−12.1642	−0.454598
$717$	−0.811626	−0.0303107
$718$	7.46144	0.278458
$719$	40.6937	1.51762	0.758809	−	0.651313i	$-0.225782\pi$
$719$	40.6937	1.51762	0.758809	+	0.651313i	$0.225782\pi$
$720$	2.24698	0.0837400
$721$	−7.85623	−0.292581
$722$	−7.40044	−0.275416
$723$	−6.23490	−0.231878
$724$	4.83877	0.179832
$725$	−0.179276	−0.00665814
$726$	10.5211	0.390475
$727$	−38.3817	−1.42350	−0.711748	−	0.702435i	$-0.752096\pi$
$727$	−38.3817	−1.42350	−0.711748	+	0.702435i	$0.752096\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−25.1957	−0.932534
$731$	4.01746	0.148591
$732$	5.09783	0.188421
$733$	−20.7006	−0.764596	−0.382298	−	0.924039i	$-0.624867\pi$
$733$	−20.7006	−0.764596	−0.382298	+	0.924039i	$0.624867\pi$
$734$	28.0194	1.03421
$735$	−2.24698	−0.0828811
$736$	−0.753020	−0.0277567
$737$	5.42626	0.199879
$738$	−5.63102	−0.207281
$739$	−6.15990	−0.226596	−0.113298	−	0.993561i	$-0.536141\pi$
$739$	−6.15990	−0.226596	−0.113298	+	0.993561i	$0.536141\pi$
$740$	−15.6407	−0.574964
$741$	0	0
$742$	1.69202	0.0621161
$743$	9.15644	0.335917	0.167959	−	0.985794i	$-0.446283\pi$
$743$	9.15644	0.335917	0.167959	+	0.985794i	$0.446283\pi$
$744$	−4.40581	−0.161525
$745$	18.7627	0.687412
$746$	−32.2868	−1.18210
$747$	9.22952	0.337691
$748$	1.69202	0.0618664
$749$	14.9215	0.545221
$750$	11.1250	0.406227
$751$	21.5362	0.785866	0.392933	−	0.919567i	$-0.371460\pi$
$751$	21.5362	0.785866	0.392933	+	0.919567i	$0.371460\pi$
$752$	−2.10992	−0.0769407
$753$	−29.6045	−1.07885
$754$	0	0
$755$	−11.7778	−0.428637
$756$	1.00000	0.0363696
$757$	30.1648	1.09636	0.548179	−	0.836361i	$-0.315321\pi$
$757$	30.1648	1.09636	0.548179	+	0.836361i	$0.315321\pi$
$758$	−27.0465	−0.982374
$759$	−0.521106	−0.0189150
$760$	−7.65279	−0.277596
$761$	1.03193	0.0374075	0.0187038	−	0.999825i	$-0.494046\pi$
$761$	1.03193	0.0374075	0.0187038	+	0.999825i	$0.494046\pi$
$762$	−2.66487	−0.0965382
$763$	−12.6504	−0.457975
$764$	−0.664874	−0.0240543
$765$	−5.49396	−0.198635
$766$	6.21552	0.224576
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	32.8605	1.18498	0.592491	−	0.805577i	$-0.298145\pi$
$769$	32.8605	1.18498	0.592491	+	0.805577i	$0.298145\pi$
$770$	1.55496	0.0560368
$771$	9.24160	0.332828
$772$	−11.3013	−0.406742
$773$	−24.2717	−0.872994	−0.436497	−	0.899706i	$-0.643781\pi$
$773$	−24.2717	−0.872994	−0.436497	+	0.899706i	$0.643781\pi$
$774$	−1.64310	−0.0590602
$775$	0.215521	0.00774173
$776$	−4.46681	−0.160349
$777$	−6.96077	−0.249716
$778$	12.0683	0.432669
$779$	19.1782	0.687131
$780$	0	0
$781$	−6.06770	−0.217120
$782$	1.84117	0.0658400
$783$	3.66487	0.130972
$784$	1.00000	0.0357143
$785$	23.5797	0.841596
$786$	−3.37867	−0.120513
$787$	−35.9506	−1.28150	−0.640750	−	0.767749i	$-0.721377\pi$
$787$	−35.9506	−1.28150	−0.640750	+	0.767749i	$0.721377\pi$
$788$	−6.26875	−0.223315
$789$	−1.09246	−0.0388925
$790$	4.43296	0.157718
$791$	20.5526	0.730765
$792$	−0.692021	−0.0245899
$793$	0	0
$794$	36.3551	1.29019
$795$	3.80194	0.134841
$796$	−12.3937	−0.439284
$797$	8.11960	0.287611	0.143806	−	0.989606i	$-0.454066\pi$
$797$	8.11960	0.287611	0.143806	+	0.989606i	$0.454066\pi$
$798$	−3.40581	−0.120564
$799$	5.15883	0.182506
$800$	0.0489173	0.00172949
$801$	3.44504	0.121725
$802$	−23.9463	−0.845573
$803$	7.75973	0.273835
$804$	7.84117	0.276537
$805$	1.69202	0.0596359
$806$	0	0
$807$	0.916166	0.0322506
$808$	6.48858	0.228268
$809$	−4.10215	−0.144224	−0.0721119	−	0.997397i	$-0.522974\pi$
$809$	−4.10215	−0.144224	−0.0721119	+	0.997397i	$0.522974\pi$
$810$	2.24698	0.0789508
$811$	−24.0358	−0.844010	−0.422005	−	0.906593i	$-0.638674\pi$
$811$	−24.0358	−0.844010	−0.422005	+	0.906593i	$0.638674\pi$
$812$	3.66487	0.128612
$813$	−30.6655	−1.07548
$814$	4.81700	0.168836
$815$	42.0170	1.47179
$816$	2.44504	0.0855936
$817$	5.59611	0.195783
$818$	−19.6571	−0.687295
$819$	0	0
$820$	−12.6528	−0.441855
$821$	2.01102	0.0701850	0.0350925	−	0.999384i	$-0.488827\pi$
$821$	2.01102	0.0701850	0.0350925	+	0.999384i	$0.488827\pi$
$822$	15.5646	0.542879
$823$	31.1511	1.08586	0.542929	−	0.839779i	$-0.317315\pi$
$823$	31.1511	1.08586	0.542929	+	0.839779i	$0.317315\pi$
$824$	7.85623	0.273685
$825$	0.0338518	0.00117857
$826$	4.96077	0.172607
$827$	−16.7646	−0.582963	−0.291482	−	0.956576i	$-0.594148\pi$
$827$	−16.7646	−0.582963	−0.291482	+	0.956576i	$0.594148\pi$
$828$	−0.753020	−0.0261693
$829$	25.9842	0.902468	0.451234	−	0.892406i	$-0.350984\pi$
$829$	25.9842	0.902468	0.451234	+	0.892406i	$0.350984\pi$
$830$	20.7385	0.719845
$831$	−21.8146	−0.756740
$832$	0	0
$833$	−2.44504	−0.0847157
$834$	0.405813	0.0140522
$835$	26.7995	0.927436
$836$	2.35690	0.0815149
$837$	−4.40581	−0.152287
$838$	−22.4228	−0.774583
$839$	16.1511	0.557597	0.278798	−	0.960350i	$-0.410064\pi$
$839$	16.1511	0.557597	0.278798	+	0.960350i	$0.410064\pi$
$840$	2.24698	0.0775282
$841$	−15.5687	−0.536852
$842$	−19.1317	−0.659321
$843$	6.67994	0.230069
$844$	7.65279	0.263420
$845$	0	0
$846$	−2.10992	−0.0725404
$847$	10.5211	0.361509
$848$	−1.69202	−0.0581043
$849$	−26.2228	−0.899965
$850$	−0.119605	−0.00410242
$851$	5.24160	0.179680
$852$	−8.76809	−0.300390
$853$	5.35450	0.183335	0.0916673	−	0.995790i	$-0.470780\pi$
$853$	5.35450	0.183335	0.0916673	+	0.995790i	$0.470780\pi$
$854$	5.09783	0.174444
$855$	−7.65279	−0.261720
$856$	−14.9215	−0.510008
$857$	−36.7948	−1.25689	−0.628443	−	0.777856i	$-0.716307\pi$
$857$	−36.7948	−1.25689	−0.628443	+	0.777856i	$0.716307\pi$
$858$	0	0
$859$	−4.73019	−0.161392	−0.0806959	−	0.996739i	$-0.525714\pi$
$859$	−4.73019	−0.161392	−0.0806959	+	0.996739i	$0.525714\pi$
$860$	−3.69202	−0.125897
$861$	−5.63102	−0.191905
$862$	−16.0224	−0.545724
$863$	54.0170	1.83876	0.919380	−	0.393371i	$-0.128691\pi$
$863$	54.0170	1.83876	0.919380	+	0.393371i	$0.128691\pi$
$864$	−1.00000	−0.0340207
$865$	−15.9758	−0.543195
$866$	20.1933	0.686195
$867$	11.0218	0.374319
$868$	−4.40581	−0.149543
$869$	−1.36526	−0.0463132
$870$	8.23490	0.279189
$871$	0	0
$872$	12.6504	0.428397
$873$	−4.46681	−0.151179
$874$	2.56465	0.0867505
$875$	11.1250	0.376093
$876$	11.2131	0.378856
$877$	50.5368	1.70651	0.853253	−	0.521498i	$-0.174627\pi$
$877$	50.5368	1.70651	0.853253	+	0.521498i	$0.174627\pi$
$878$	2.28190	0.0770103
$879$	13.2741	0.447725
$880$	−1.55496	−0.0524176
$881$	38.0133	1.28070	0.640350	−	0.768084i	$-0.278789\pi$
$881$	38.0133	1.28070	0.640350	+	0.768084i	$0.278789\pi$
$882$	1.00000	0.0336718
$883$	4.70815	0.158442	0.0792210	−	0.996857i	$-0.474757\pi$
$883$	4.70815	0.158442	0.0792210	+	0.996857i	$0.474757\pi$
$884$	0	0
$885$	11.1468	0.374694
$886$	−14.1129	−0.474132
$887$	47.4010	1.59157	0.795785	−	0.605579i	$-0.207058\pi$
$887$	47.4010	1.59157	0.795785	+	0.605579i	$0.207058\pi$
$888$	6.96077	0.233588
$889$	−2.66487	−0.0893770
$890$	7.74094	0.259477
$891$	−0.692021	−0.0231836
$892$	−15.2905	−0.511964
$893$	7.18598	0.240470
$894$	−8.35019	−0.279272
$895$	−27.3327	−0.913632
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−21.8732	−0.729919
$899$	−16.1468	−0.538524
$900$	0.0489173	0.00163058
$901$	4.13706	0.137826
$902$	3.89679	0.129749
$903$	−1.64310	−0.0546791
$904$	−20.5526	−0.683568
$905$	10.8726	0.361418
$906$	5.24160	0.174141
$907$	12.9317	0.429390	0.214695	−	0.976681i	$-0.431124\pi$
$907$	12.9317	0.429390	0.214695	+	0.976681i	$0.431124\pi$
$908$	−14.2808	−0.473926
$909$	6.48858	0.215213
$910$	0	0
$911$	0.499336	0.0165437	0.00827187	−	0.999966i	$-0.497367\pi$
$911$	0.499336	0.0165437	0.00827187	+	0.999966i	$0.497367\pi$
$912$	3.40581	0.112778
$913$	−6.38703	−0.211380
$914$	−27.8280	−0.920469
$915$	11.4547	0.378682
$916$	−6.30127	−0.208200
$917$	−3.37867	−0.111573
$918$	2.44504	0.0806984
$919$	−13.5439	−0.446773	−0.223387	−	0.974730i	$-0.571711\pi$
$919$	−13.5439	−0.446773	−0.223387	+	0.974730i	$0.571711\pi$
$920$	−1.69202	−0.0557843
$921$	32.3260	1.06518
$922$	−5.81833	−0.191617
$923$	0	0
$924$	−0.692021	−0.0227658
$925$	−0.340502	−0.0111957
$926$	−20.0218	−0.657956
$927$	7.85623	0.258033
$928$	−3.66487	−0.120305
$929$	−12.8278	−0.420865	−0.210433	−	0.977608i	$-0.567487\pi$
$929$	−12.8278	−0.420865	−0.210433	+	0.977608i	$0.567487\pi$
$930$	−9.89977	−0.324626
$931$	−3.40581	−0.111621
$932$	25.9071	0.848614
$933$	9.89738	0.324026
$934$	15.7791	0.516308
$935$	3.80194	0.124337
$936$	0	0
$937$	−18.0194	−0.588667	−0.294334	−	0.955703i	$-0.595098\pi$
$937$	−18.0194	−0.588667	−0.294334	+	0.955703i	$0.595098\pi$
$938$	7.84117	0.256023
$939$	2.66786	0.0870623
$940$	−4.74094	−0.154632
$941$	43.8611	1.42983	0.714916	−	0.699210i	$-0.246465\pi$
$941$	43.8611	1.42983	0.714916	+	0.699210i	$0.246465\pi$
$942$	−10.4940	−0.341912
$943$	4.24027	0.138082
$944$	−4.96077	−0.161459
$945$	2.24698	0.0730943
$946$	1.13706	0.0369691
$947$	−38.7991	−1.26080	−0.630400	−	0.776270i	$-0.717109\pi$
$947$	−38.7991	−1.26080	−0.630400	+	0.776270i	$0.717109\pi$
$948$	−1.97285	−0.0640753
$949$	0	0
$950$	−0.166603	−0.00540533
$951$	−9.68425	−0.314033
$952$	2.44504	0.0792443
$953$	−33.6853	−1.09117	−0.545587	−	0.838054i	$-0.683693\pi$
$953$	−33.6853	−1.09117	−0.545587	+	0.838054i	$0.683693\pi$
$954$	−1.69202	−0.0547812
$955$	−1.49396	−0.0483434
$956$	0.811626	0.0262499
$957$	−2.53617	−0.0819828
$958$	−1.31575	−0.0425099
$959$	15.5646	0.502609
$960$	−2.24698	−0.0725210
$961$	−11.5888	−0.373833
$962$	0	0
$963$	−14.9215	−0.480840
$964$	6.23490	0.200813
$965$	−25.3937	−0.817453
$966$	−0.753020	−0.0242280
$967$	−40.1371	−1.29072	−0.645360	−	0.763878i	$-0.723293\pi$
$967$	−40.1371	−1.29072	−0.645360	+	0.763878i	$0.723293\pi$
$968$	−10.5211	−0.338161
$969$	−8.32736	−0.267513
$970$	−10.0368	−0.322263
$971$	37.6273	1.20752	0.603759	−	0.797167i	$-0.293669\pi$
$971$	37.6273	1.20752	0.603759	+	0.797167i	$0.293669\pi$
$972$	−1.00000	−0.0320750
$973$	0.405813	0.0130098
$974$	−19.1618	−0.613984
$975$	0	0
$976$	−5.09783	−0.163178
$977$	52.5182	1.68021	0.840104	−	0.542426i	$-0.182494\pi$
$977$	52.5182	1.68021	0.840104	+	0.542426i	$0.182494\pi$
$978$	−18.6993	−0.597938
$979$	−2.38404	−0.0761943
$980$	2.24698	0.0717771
$981$	12.6504	0.403896
$982$	32.3860	1.03348
$983$	−39.6222	−1.26375	−0.631876	−	0.775070i	$-0.717715\pi$
$983$	−39.6222	−1.26375	−0.631876	+	0.775070i	$0.717715\pi$
$984$	5.63102	0.179510
$985$	−14.0858	−0.448809
$986$	8.96077	0.285369
$987$	−2.10992	−0.0671594
$988$	0	0
$989$	1.23729	0.0393436
$990$	−1.55496	−0.0494198
$991$	46.4553	1.47570	0.737851	−	0.674964i	$-0.235841\pi$
$991$	46.4553	1.47570	0.737851	+	0.674964i	$0.235841\pi$
$992$	4.40581	0.139885
$993$	−1.38644	−0.0439972
$994$	−8.76809	−0.278107
$995$	−27.8485	−0.882856
$996$	−9.22952	−0.292449
$997$	−22.6631	−0.717747	−0.358873	−	0.933386i	$-0.616839\pi$
$997$	−22.6631	−0.717747	−0.358873	+	0.933386i	$0.616839\pi$
$998$	−8.55363	−0.270760
$999$	6.96077	0.220229

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cc.1.1	✓	3	13.12	even	2
7098.2.a.cj.1.3	yes	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.24698 q^{10} -0.692021 q^{11} -1.00000 q^{12} -1.00000 q^{14} -2.24698 q^{15} +1.00000 q^{16} -2.44504 q^{17} +1.00000 q^{18} -3.40581 q^{19} +2.24698 q^{20} +1.00000 q^{21} -0.692021 q^{22} -0.753020 q^{23} -1.00000 q^{24} +0.0489173 q^{25} -1.00000 q^{27} -1.00000 q^{28} -3.66487 q^{29} -2.24698 q^{30} +4.40581 q^{31} +1.00000 q^{32} +0.692021 q^{33} -2.44504 q^{34} -2.24698 q^{35} +1.00000 q^{36} -6.96077 q^{37} -3.40581 q^{38} +2.24698 q^{40} -5.63102 q^{41} +1.00000 q^{42} -1.64310 q^{43} -0.692021 q^{44} +2.24698 q^{45} -0.753020 q^{46} -2.10992 q^{47} -1.00000 q^{48} +1.00000 q^{49} +0.0489173 q^{50} +2.44504 q^{51} -1.69202 q^{53} -1.00000 q^{54} -1.55496 q^{55} -1.00000 q^{56} +3.40581 q^{57} -3.66487 q^{58} -4.96077 q^{59} -2.24698 q^{60} -5.09783 q^{61} +4.40581 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.692021 q^{66} -7.84117 q^{67} -2.44504 q^{68} +0.753020 q^{69} -2.24698 q^{70} +8.76809 q^{71} +1.00000 q^{72} -11.2131 q^{73} -6.96077 q^{74} -0.0489173 q^{75} -3.40581 q^{76} +0.692021 q^{77} +1.97285 q^{79} +2.24698 q^{80} +1.00000 q^{81} -5.63102 q^{82} +9.22952 q^{83} +1.00000 q^{84} -5.49396 q^{85} -1.64310 q^{86} +3.66487 q^{87} -0.692021 q^{88} +3.44504 q^{89} +2.24698 q^{90} -0.753020 q^{92} -4.40581 q^{93} -2.10992 q^{94} -7.65279 q^{95} -1.00000 q^{96} -4.46681 q^{97} +1.00000 q^{98} -0.692021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} + 3 q^{21} + 3 q^{22} - 7 q^{23} - 3 q^{24} - 9 q^{25} - 3 q^{27} - 3 q^{28} - 12 q^{29} - 2 q^{30} + 3 q^{32} - 3 q^{33} - 7 q^{34} - 2 q^{35} + 3 q^{36} - 8 q^{37} + 3 q^{38} + 2 q^{40} - 2 q^{41} + 3 q^{42} - 9 q^{43} + 3 q^{44} + 2 q^{45} - 7 q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} - 9 q^{50} + 7 q^{51} - 3 q^{54} - 5 q^{55} - 3 q^{56} - 3 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{63} + 3 q^{64} - 3 q^{66} - 32 q^{67} - 7 q^{68} + 7 q^{69} - 2 q^{70} + 6 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} + 9 q^{75} + 3 q^{76} - 3 q^{77} + 12 q^{79} + 2 q^{80} + 3 q^{81} - 2 q^{82} + 7 q^{83} + 3 q^{84} - 7 q^{85} - 9 q^{86} + 12 q^{87} + 3 q^{88} + 10 q^{89} + 2 q^{90} - 7 q^{92} - 7 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 + 3 * q^21 + 3 * q^22 - 7 * q^23 - 3 * q^24 - 9 * q^25 - 3 * q^27 - 3 * q^28 - 12 * q^29 - 2 * q^30 + 3 * q^32 - 3 * q^33 - 7 * q^34 - 2 * q^35 + 3 * q^36 - 8 * q^37 + 3 * q^38 + 2 * q^40 - 2 * q^41 + 3 * q^42 - 9 * q^43 + 3 * q^44 + 2 * q^45 - 7 * q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 - 9 * q^50 + 7 * q^51 - 3 * q^54 - 5 * q^55 - 3 * q^56 - 3 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^63 + 3 * q^64 - 3 * q^66 - 32 * q^67 - 7 * q^68 + 7 * q^69 - 2 * q^70 + 6 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 + 9 * q^75 + 3 * q^76 - 3 * q^77 + 12 * q^79 + 2 * q^80 + 3 * q^81 - 2 * q^82 + 7 * q^83 + 3 * q^84 - 7 * q^85 - 9 * q^86 + 12 * q^87 + 3 * q^88 + 10 * q^89 + 2 * q^90 - 7 * q^92 - 7 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more