LMFDB - Embedded newform 574.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(1,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("574.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
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			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	574.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.14134 q^{3} +1.00000 q^{4} -0.363328 q^{5} +3.14134 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.86799 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.14134 q^{3} +1.00000 q^{4} -0.363328 q^{5} +3.14134 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.86799 q^{9} -0.363328 q^{10} -1.50466 q^{11} +3.14134 q^{12} -1.00000 q^{14} -1.14134 q^{15} +1.00000 q^{16} -5.14134 q^{17} +6.86799 q^{18} -4.28267 q^{19} -0.363328 q^{20} -3.14134 q^{21} -1.50466 q^{22} +2.72666 q^{23} +3.14134 q^{24} -4.86799 q^{25} +12.1507 q^{27} -1.00000 q^{28} +2.36333 q^{29} -1.14134 q^{30} +5.14134 q^{31} +1.00000 q^{32} -4.72666 q^{33} -5.14134 q^{34} +0.363328 q^{35} +6.86799 q^{36} +2.00000 q^{37} -4.28267 q^{38} -0.363328 q^{40} -1.00000 q^{41} -3.14134 q^{42} -11.4240 q^{43} -1.50466 q^{44} -2.49534 q^{45} +2.72666 q^{46} +2.00000 q^{47} +3.14134 q^{48} +1.00000 q^{49} -4.86799 q^{50} -16.1507 q^{51} +5.37266 q^{53} +12.1507 q^{54} +0.546687 q^{55} -1.00000 q^{56} -13.4533 q^{57} +2.36333 q^{58} +4.23132 q^{59} -1.14134 q^{60} -10.6460 q^{61} +5.14134 q^{62} -6.86799 q^{63} +1.00000 q^{64} -4.72666 q^{66} +15.0607 q^{67} -5.14134 q^{68} +8.56534 q^{69} +0.363328 q^{70} -8.87732 q^{71} +6.86799 q^{72} -3.71733 q^{73} +2.00000 q^{74} -15.2920 q^{75} -4.28267 q^{76} +1.50466 q^{77} +2.13201 q^{79} -0.363328 q^{80} +17.5653 q^{81} -1.00000 q^{82} -6.77801 q^{83} -3.14134 q^{84} +1.86799 q^{85} -11.4240 q^{86} +7.42401 q^{87} -1.50466 q^{88} +11.8680 q^{89} -2.49534 q^{90} +2.72666 q^{92} +16.1507 q^{93} +2.00000 q^{94} +1.55602 q^{95} +3.14134 q^{96} -4.13201 q^{97} +1.00000 q^{98} -10.3340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + q^5 + q^6 - 3 * q^7 + 3 * q^8 + 8 * q^9	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 8 q^{9} + q^{10} + 6 q^{11} + q^{12} - 3 q^{14} + 5 q^{15} + 3 q^{16} - 7 q^{17} + 8 q^{18} + 4 q^{19} + q^{20} - q^{21} + 6 q^{22} + 4 q^{23} + q^{24} - 2 q^{25} + 7 q^{27} - 3 q^{28} + 5 q^{29} + 5 q^{30} + 7 q^{31} + 3 q^{32} - 10 q^{33} - 7 q^{34} - q^{35} + 8 q^{36} + 6 q^{37} + 4 q^{38} + q^{40} - 3 q^{41} - q^{42} - 9 q^{43} + 6 q^{44} - 18 q^{45} + 4 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} - 2 q^{50} - 19 q^{51} - 7 q^{53} + 7 q^{54} + 10 q^{55} - 3 q^{56} - 32 q^{57} + 5 q^{58} - 2 q^{59} + 5 q^{60} - 13 q^{61} + 7 q^{62} - 8 q^{63} + 3 q^{64} - 10 q^{66} + 22 q^{67} - 7 q^{68} - 8 q^{69} - q^{70} + 7 q^{71} + 8 q^{72} - 28 q^{73} + 6 q^{74} - 8 q^{75} + 4 q^{76} - 6 q^{77} + 19 q^{79} + q^{80} + 19 q^{81} - 3 q^{82} - 14 q^{83} - q^{84} - 7 q^{85} - 9 q^{86} - 3 q^{87} + 6 q^{88} + 23 q^{89} - 18 q^{90} + 4 q^{92} + 19 q^{93} + 6 q^{94} - 8 q^{95} + q^{96} - 25 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + q^5 + q^6 - 3 * q^7 + 3 * q^8 + 8 * q^9 + q^10 + 6 * q^11 + q^12 - 3 * q^14 + 5 * q^15 + 3 * q^16 - 7 * q^17 + 8 * q^18 + 4 * q^19 + q^20 - q^21 + 6 * q^22 + 4 * q^23 + q^24 - 2 * q^25 + 7 * q^27 - 3 * q^28 + 5 * q^29 + 5 * q^30 + 7 * q^31 + 3 * q^32 - 10 * q^33 - 7 * q^34 - q^35 + 8 * q^36 + 6 * q^37 + 4 * q^38 + q^40 - 3 * q^41 - q^42 - 9 * q^43 + 6 * q^44 - 18 * q^45 + 4 * q^46 + 6 * q^47 + q^48 + 3 * q^49 - 2 * q^50 - 19 * q^51 - 7 * q^53 + 7 * q^54 + 10 * q^55 - 3 * q^56 - 32 * q^57 + 5 * q^58 - 2 * q^59 + 5 * q^60 - 13 * q^61 + 7 * q^62 - 8 * q^63 + 3 * q^64 - 10 * q^66 + 22 * q^67 - 7 * q^68 - 8 * q^69 - q^70 + 7 * q^71 + 8 * q^72 - 28 * q^73 + 6 * q^74 - 8 * q^75 + 4 * q^76 - 6 * q^77 + 19 * q^79 + q^80 + 19 * q^81 - 3 * q^82 - 14 * q^83 - q^84 - 7 * q^85 - 9 * q^86 - 3 * q^87 + 6 * q^88 + 23 * q^89 - 18 * q^90 + 4 * q^92 + 19 * q^93 + 6 * q^94 - 8 * q^95 + q^96 - 25 * q^97 + 3 * q^98 - 12 * 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
$3$	3.14134	1.81365	0.906826	−	0.421506i	$-0.138498\pi$
$3$	3.14134	1.81365	0.906826	+	0.421506i	$0.138498\pi$
$4$	1.00000	0.500000
$5$	−0.363328	−0.162485	−0.0812427	−	0.996694i	$-0.525889\pi$
$5$	−0.363328	−0.162485	−0.0812427	+	0.996694i	$0.525889\pi$
$6$	3.14134	1.28245
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	6.86799	2.28933
$10$	−0.363328	−0.114894
$11$	−1.50466	−0.453673	−0.226837	−	0.973933i	$-0.572838\pi$
$11$	−1.50466	−0.453673	−0.226837	+	0.973933i	$0.572838\pi$
$12$	3.14134	0.906826
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−1.00000	−0.267261
$15$	−1.14134	−0.294692
$16$	1.00000	0.250000
$17$	−5.14134	−1.24696	−0.623479	−	0.781840i	$-0.714281\pi$
$17$	−5.14134	−1.24696	−0.623479	+	0.781840i	$0.714281\pi$
$18$	6.86799	1.61880
$19$	−4.28267	−0.982512	−0.491256	−	0.871015i	$-0.663462\pi$
$19$	−4.28267	−0.982512	−0.491256	+	0.871015i	$0.663462\pi$
$20$	−0.363328	−0.0812427
$21$	−3.14134	−0.685496
$22$	−1.50466	−0.320796
$23$	2.72666	0.568547	0.284274	−	0.958743i	$-0.408248\pi$
$23$	2.72666	0.568547	0.284274	+	0.958743i	$0.408248\pi$
$24$	3.14134	0.641223
$25$	−4.86799	−0.973599
$26$	0	0
$27$	12.1507	2.33840
$28$	−1.00000	−0.188982
$29$	2.36333	0.438859	0.219430	−	0.975628i	$-0.429580\pi$
$29$	2.36333	0.438859	0.219430	+	0.975628i	$0.429580\pi$
$30$	−1.14134	−0.208379
$31$	5.14134	0.923411	0.461706	−	0.887033i	$-0.347238\pi$
$31$	5.14134	0.923411	0.461706	+	0.887033i	$0.347238\pi$
$32$	1.00000	0.176777
$33$	−4.72666	−0.822805
$34$	−5.14134	−0.881732
$35$	0.363328	0.0614137
$36$	6.86799	1.14467
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−4.28267	−0.694741
$39$	0	0
$40$	−0.363328	−0.0574472
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	−3.14134	−0.484719
$43$	−11.4240	−1.74214	−0.871072	−	0.491155i	$-0.836575\pi$
$43$	−11.4240	−1.74214	−0.871072	+	0.491155i	$0.836575\pi$
$44$	−1.50466	−0.226837
$45$	−2.49534	−0.371983
$46$	2.72666	0.402024
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	3.14134	0.453413
$49$	1.00000	0.142857
$50$	−4.86799	−0.688438
$51$	−16.1507	−2.26155
$52$	0	0
$53$	5.37266	0.737991	0.368996	−	0.929431i	$-0.379702\pi$
$53$	5.37266	0.737991	0.368996	+	0.929431i	$0.379702\pi$
$54$	12.1507	1.65350
$55$	0.546687	0.0737153
$56$	−1.00000	−0.133631
$57$	−13.4533	−1.78193
$58$	2.36333	0.310320
$59$	4.23132	0.550871	0.275436	−	0.961320i	$-0.411178\pi$
$59$	4.23132	0.550871	0.275436	+	0.961320i	$0.411178\pi$
$60$	−1.14134	−0.147346
$61$	−10.6460	−1.36308	−0.681540	−	0.731781i	$-0.738690\pi$
$61$	−10.6460	−1.36308	−0.681540	+	0.731781i	$0.738690\pi$
$62$	5.14134	0.652950
$63$	−6.86799	−0.865286
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.72666	−0.581811
$67$	15.0607	1.83995	0.919977	−	0.391971i	$-0.128207\pi$
$67$	15.0607	1.83995	0.919977	+	0.391971i	$0.128207\pi$
$68$	−5.14134	−0.623479
$69$	8.56534	1.03115
$70$	0.363328	0.0434260
$71$	−8.87732	−1.05354	−0.526772	−	0.850007i	$-0.676598\pi$
$71$	−8.87732	−1.05354	−0.526772	+	0.850007i	$0.676598\pi$
$72$	6.86799	0.809401
$73$	−3.71733	−0.435080	−0.217540	−	0.976051i	$-0.569803\pi$
$73$	−3.71733	−0.435080	−0.217540	+	0.976051i	$0.569803\pi$
$74$	2.00000	0.232495
$75$	−15.2920	−1.76577
$76$	−4.28267	−0.491256
$77$	1.50466	0.171472
$78$	0	0
$79$	2.13201	0.239870	0.119935	−	0.992782i	$-0.461731\pi$
$79$	2.13201	0.239870	0.119935	+	0.992782i	$0.461731\pi$
$80$	−0.363328	−0.0406213
$81$	17.5653	1.95170
$82$	−1.00000	−0.110432
$83$	−6.77801	−0.743983	−0.371992	−	0.928236i	$-0.621325\pi$
$83$	−6.77801	−0.743983	−0.371992	+	0.928236i	$0.621325\pi$
$84$	−3.14134	−0.342748
$85$	1.86799	0.202612
$86$	−11.4240	−1.23188
$87$	7.42401	0.795937
$88$	−1.50466	−0.160398
$89$	11.8680	1.25800	0.629002	−	0.777403i	$-0.283464\pi$
$89$	11.8680	1.25800	0.629002	+	0.777403i	$0.283464\pi$
$90$	−2.49534	−0.263031
$91$	0	0
$92$	2.72666	0.284274
$93$	16.1507	1.67475
$94$	2.00000	0.206284
$95$	1.55602	0.159644
$96$	3.14134	0.320611
$97$	−4.13201	−0.419542	−0.209771	−	0.977751i	$-0.567272\pi$
$97$	−4.13201	−0.419542	−0.209771	+	0.977751i	$0.567272\pi$
$98$	1.00000	0.101015
$99$	−10.3340	−1.03861
$100$	−4.86799	−0.486799
$101$	10.1800	1.01294	0.506472	−	0.862256i	$-0.330949\pi$
$101$	10.1800	1.01294	0.506472	+	0.862256i	$0.330949\pi$
$102$	−16.1507	−1.59915
$103$	−5.97070	−0.588310	−0.294155	−	0.955758i	$-0.595038\pi$
$103$	−5.97070	−0.588310	−0.294155	+	0.955758i	$0.595038\pi$
$104$	0	0
$105$	1.14134	0.111383
$106$	5.37266	0.521839
$107$	−7.32131	−0.707777	−0.353889	−	0.935288i	$-0.615141\pi$
$107$	−7.32131	−0.707777	−0.353889	+	0.935288i	$0.615141\pi$
$108$	12.1507	1.16920
$109$	18.2500	1.74803	0.874015	−	0.485898i	$-0.161507\pi$
$109$	18.2500	1.74803	0.874015	+	0.485898i	$0.161507\pi$
$110$	0.546687	0.0521246
$111$	6.28267	0.596325
$112$	−1.00000	−0.0944911
$113$	10.4333	0.981486	0.490743	−	0.871304i	$-0.336725\pi$
$113$	10.4333	0.981486	0.490743	+	0.871304i	$0.336725\pi$
$114$	−13.4533	−1.26002
$115$	−0.990671	−0.0923806
$116$	2.36333	0.219430
$117$	0	0
$118$	4.23132	0.389525
$119$	5.14134	0.471306
$120$	−1.14134	−0.104189
$121$	−8.73599	−0.794180
$122$	−10.6460	−0.963844
$123$	−3.14134	−0.283245
$124$	5.14134	0.461706
$125$	3.58532	0.320681
$126$	−6.86799	−0.611849
$127$	1.00933	0.0895634	0.0447817	−	0.998997i	$-0.485741\pi$
$127$	1.00933	0.0895634	0.0447817	+	0.998997i	$0.485741\pi$
$128$	1.00000	0.0883883
$129$	−35.8867	−3.15964
$130$	0	0
$131$	−3.60737	−0.315177	−0.157589	−	0.987505i	$-0.550372\pi$
$131$	−3.60737	−0.315177	−0.157589	+	0.987505i	$0.550372\pi$
$132$	−4.72666	−0.411403
$133$	4.28267	0.371355
$134$	15.0607	1.30104
$135$	−4.41468	−0.379955
$136$	−5.14134	−0.440866
$137$	−12.7453	−1.08891	−0.544453	−	0.838791i	$-0.683263\pi$
$137$	−12.7453	−1.08891	−0.544453	+	0.838791i	$0.683263\pi$
$138$	8.56534	0.729131
$139$	−6.67531	−0.566192	−0.283096	−	0.959092i	$-0.591362\pi$
$139$	−6.67531	−0.566192	−0.283096	+	0.959092i	$0.591362\pi$
$140$	0.363328	0.0307068
$141$	6.28267	0.529096
$142$	−8.87732	−0.744968
$143$	0	0
$144$	6.86799	0.572333
$145$	−0.858664	−0.0713082
$146$	−3.71733	−0.307648
$147$	3.14134	0.259093
$148$	2.00000	0.164399
$149$	15.8166	1.29575	0.647875	−	0.761747i	$-0.275658\pi$
$149$	15.8166	1.29575	0.647875	+	0.761747i	$0.275658\pi$
$150$	−15.2920	−1.24859
$151$	15.4240	1.25519	0.627594	−	0.778541i	$-0.284040\pi$
$151$	15.4240	1.25519	0.627594	+	0.778541i	$0.284040\pi$
$152$	−4.28267	−0.347371
$153$	−35.3107	−2.85470
$154$	1.50466	0.121249
$155$	−1.86799	−0.150041
$156$	0	0
$157$	−8.00000	−0.638470	−0.319235	−	0.947676i	$-0.603426\pi$
$157$	−8.00000	−0.638470	−0.319235	+	0.947676i	$0.603426\pi$
$158$	2.13201	0.169613
$159$	16.8773	1.33846
$160$	−0.363328	−0.0287236
$161$	−2.72666	−0.214891
$162$	17.5653	1.38006
$163$	13.5560	1.06179	0.530895	−	0.847438i	$-0.321856\pi$
$163$	13.5560	1.06179	0.530895	+	0.847438i	$0.321856\pi$
$164$	−1.00000	−0.0780869
$165$	1.71733	0.133694
$166$	−6.77801	−0.526075
$167$	18.0187	1.39433	0.697163	−	0.716913i	$-0.254445\pi$
$167$	18.0187	1.39433	0.697163	+	0.716913i	$0.254445\pi$
$168$	−3.14134	−0.242359
$169$	−13.0000	−1.00000
$170$	1.86799	0.143268
$171$	−29.4134	−2.24930
$172$	−11.4240	−0.871072
$173$	−21.3913	−1.62635	−0.813176	−	0.582018i	$-0.802263\pi$
$173$	−21.3913	−1.62635	−0.813176	+	0.582018i	$0.802263\pi$
$174$	7.42401	0.562813
$175$	4.86799	0.367986
$176$	−1.50466	−0.113418
$177$	13.2920	0.999088
$178$	11.8680	0.889544
$179$	15.7873	1.18000	0.590000	−	0.807403i	$-0.299128\pi$
$179$	15.7873	1.18000	0.590000	+	0.807403i	$0.299128\pi$
$180$	−2.49534	−0.185991
$181$	−21.8573	−1.62464	−0.812322	−	0.583209i	$-0.801797\pi$
$181$	−21.8573	−1.62464	−0.812322	+	0.583209i	$0.801797\pi$
$182$	0	0
$183$	−33.4427	−2.47215
$184$	2.72666	0.201012
$185$	−0.726656	−0.0534248
$186$	16.1507	1.18422
$187$	7.73599	0.565711
$188$	2.00000	0.145865
$189$	−12.1507	−0.883831
$190$	1.55602	0.112885
$191$	17.1413	1.24030	0.620152	−	0.784482i	$-0.287071\pi$
$191$	17.1413	1.24030	0.620152	+	0.784482i	$0.287071\pi$
$192$	3.14134	0.226706
$193$	−26.8667	−1.93391	−0.966953	−	0.254956i	$-0.917939\pi$
$193$	−26.8667	−1.93391	−0.966953	+	0.254956i	$0.917939\pi$
$194$	−4.13201	−0.296661
$195$	0	0
$196$	1.00000	0.0714286
$197$	1.27334	0.0907220	0.0453610	−	0.998971i	$-0.485556\pi$
$197$	1.27334	0.0907220	0.0453610	+	0.998971i	$0.485556\pi$
$198$	−10.3340	−0.734407
$199$	−19.1893	−1.36029	−0.680147	−	0.733076i	$-0.738084\pi$
$199$	−19.1893	−1.36029	−0.680147	+	0.733076i	$0.738084\pi$
$200$	−4.86799	−0.344219
$201$	47.3107	3.33704
$202$	10.1800	0.716260
$203$	−2.36333	−0.165873
$204$	−16.1507	−1.13077
$205$	0.363328	0.0253759
$206$	−5.97070	−0.415998
$207$	18.7267	1.30159
$208$	0	0
$209$	6.44398	0.445740
$210$	1.14134	0.0787597
$211$	4.67531	0.321861	0.160931	−	0.986966i	$-0.448550\pi$
$211$	4.67531	0.321861	0.160931	+	0.986966i	$0.448550\pi$
$212$	5.37266	0.368996
$213$	−27.8867	−1.91076
$214$	−7.32131	−0.500474
$215$	4.15066	0.283073
$216$	12.1507	0.826748
$217$	−5.14134	−0.349017
$218$	18.2500	1.23604
$219$	−11.6774	−0.789084
$220$	0.546687	0.0368576
$221$	0	0
$222$	6.28267	0.421665
$223$	1.03863	0.0695520	0.0347760	−	0.999395i	$-0.488928\pi$
$223$	1.03863	0.0695520	0.0347760	+	0.999395i	$0.488928\pi$
$224$	−1.00000	−0.0668153
$225$	−33.4333	−2.22889
$226$	10.4333	0.694015
$227$	14.1507	0.939213	0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1507	0.939213	0.469606	+	0.882876i	$0.344396\pi$
$228$	−13.4533	−0.890967
$229$	9.55602	0.631479	0.315740	−	0.948846i	$-0.397747\pi$
$229$	9.55602	0.631479	0.315740	+	0.948846i	$0.397747\pi$
$230$	−0.990671	−0.0653229
$231$	4.72666	0.310991
$232$	2.36333	0.155160
$233$	23.1307	1.51534	0.757671	−	0.652637i	$-0.226337\pi$
$233$	23.1307	1.51534	0.757671	+	0.652637i	$0.226337\pi$
$234$	0	0
$235$	−0.726656	−0.0474018
$236$	4.23132	0.275436
$237$	6.69735	0.435040
$238$	5.14134	0.333263
$239$	0.102703	0.00664329	0.00332165	−	0.999994i	$-0.498943\pi$
$239$	0.102703	0.00664329	0.00332165	+	0.999994i	$0.498943\pi$
$240$	−1.14134	−0.0736729
$241$	6.56534	0.422911	0.211456	−	0.977388i	$-0.432180\pi$
$241$	6.56534	0.422911	0.211456	+	0.977388i	$0.432180\pi$
$242$	−8.73599	−0.561570
$243$	18.7267	1.20132
$244$	−10.6460	−0.681540
$245$	−0.363328	−0.0232122
$246$	−3.14134	−0.200284
$247$	0	0
$248$	5.14134	0.326475
$249$	−21.2920	−1.34933
$250$	3.58532	0.226756
$251$	−20.5327	−1.29601	−0.648005	−	0.761636i	$-0.724396\pi$
$251$	−20.5327	−1.29601	−0.648005	+	0.761636i	$0.724396\pi$
$252$	−6.86799	−0.432643
$253$	−4.10270	−0.257935
$254$	1.00933	0.0633309
$255$	5.86799	0.367468
$256$	1.00000	0.0625000
$257$	−23.3400	−1.45591	−0.727953	−	0.685627i	$-0.759528\pi$
$257$	−23.3400	−1.45591	−0.727953	+	0.685627i	$0.759528\pi$
$258$	−35.8867	−2.23421
$259$	−2.00000	−0.124274
$260$	0	0
$261$	16.2313	1.00469
$262$	−3.60737	−0.222864
$263$	30.0187	1.85103	0.925515	−	0.378711i	$-0.123633\pi$
$263$	30.0187	1.85103	0.925515	+	0.378711i	$0.123633\pi$
$264$	−4.72666	−0.290906
$265$	−1.95204	−0.119913
$266$	4.28267	0.262587
$267$	37.2814	2.28158
$268$	15.0607	0.919977
$269$	4.61670	0.281485	0.140742	−	0.990046i	$-0.455051\pi$
$269$	4.61670	0.281485	0.140742	+	0.990046i	$0.455051\pi$
$270$	−4.41468	−0.268669
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−5.14134	−0.311739
$273$	0	0
$274$	−12.7453	−0.769973
$275$	7.32469	0.441696
$276$	8.56534	0.515573
$277$	24.1214	1.44931	0.724656	−	0.689111i	$-0.241999\pi$
$277$	24.1214	1.44931	0.724656	+	0.689111i	$0.241999\pi$
$278$	−6.67531	−0.400358
$279$	35.3107	2.11399
$280$	0.363328	0.0217130
$281$	11.4533	0.683247	0.341624	−	0.939837i	$-0.389023\pi$
$281$	11.4533	0.683247	0.341624	+	0.939837i	$0.389023\pi$
$282$	6.28267	0.374128
$283$	8.33402	0.495406	0.247703	−	0.968836i	$-0.420324\pi$
$283$	8.33402	0.495406	0.247703	+	0.968836i	$0.420324\pi$
$284$	−8.87732	−0.526772
$285$	4.88797	0.289538
$286$	0	0
$287$	1.00000	0.0590281
$288$	6.86799	0.404700
$289$	9.43334	0.554902
$290$	−0.858664	−0.0504225
$291$	−12.9800	−0.760902
$292$	−3.71733	−0.217540
$293$	−28.8667	−1.68641	−0.843205	−	0.537593i	$-0.819334\pi$
$293$	−28.8667	−1.68641	−0.843205	+	0.537593i	$0.819334\pi$
$294$	3.14134	0.183206
$295$	−1.53736	−0.0895085
$296$	2.00000	0.116248
$297$	−18.2827	−1.06087
$298$	15.8166	0.916233
$299$	0	0
$300$	−15.2920	−0.882884
$301$	11.4240	0.658469
$302$	15.4240	0.887552
$303$	31.9787	1.83713
$304$	−4.28267	−0.245628
$305$	3.86799	0.221481
$306$	−35.3107	−2.01858
$307$	22.9766	1.31135	0.655673	−	0.755045i	$-0.272385\pi$
$307$	22.9766	1.31135	0.655673	+	0.755045i	$0.272385\pi$
$308$	1.50466	0.0857362
$309$	−18.7560	−1.06699
$310$	−1.86799	−0.106095
$311$	7.65872	0.434286	0.217143	−	0.976140i	$-0.430326\pi$
$311$	7.65872	0.434286	0.217143	+	0.976140i	$0.430326\pi$
$312$	0	0
$313$	−12.1986	−0.689507	−0.344754	−	0.938693i	$-0.612038\pi$
$313$	−12.1986	−0.689507	−0.344754	+	0.938693i	$0.612038\pi$
$314$	−8.00000	−0.451466
$315$	2.49534	0.140596
$316$	2.13201	0.119935
$317$	26.2500	1.47435	0.737173	−	0.675704i	$-0.236160\pi$
$317$	26.2500	1.47435	0.737173	+	0.675704i	$0.236160\pi$
$318$	16.8773	0.946433
$319$	−3.55602	−0.199099
$320$	−0.363328	−0.0203107
$321$	−22.9987	−1.28366
$322$	−2.72666	−0.151951
$323$	22.0187	1.22515
$324$	17.5653	0.975852
$325$	0	0
$326$	13.5560	0.750798
$327$	57.3293	3.17032
$328$	−1.00000	−0.0552158
$329$	−2.00000	−0.110264
$330$	1.71733	0.0945358
$331$	−8.67531	−0.476838	−0.238419	−	0.971162i	$-0.576629\pi$
$331$	−8.67531	−0.476838	−0.238419	+	0.971162i	$0.576629\pi$
$332$	−6.77801	−0.371992
$333$	13.7360	0.752727
$334$	18.0187	0.985937
$335$	−5.47197	−0.298966
$336$	−3.14134	−0.171374
$337$	35.2814	1.92190	0.960949	−	0.276726i	$-0.0892494\pi$
$337$	35.2814	1.92190	0.960949	+	0.276726i	$0.0892494\pi$
$338$	−13.0000	−0.707107
$339$	32.7746	1.78007
$340$	1.86799	0.101306
$341$	−7.73599	−0.418927
$342$	−29.4134	−1.59049
$343$	−1.00000	−0.0539949
$344$	−11.4240	−0.615941
$345$	−3.11203	−0.167546
$346$	−21.3913	−1.15000
$347$	3.68463	0.197802	0.0989008	−	0.995097i	$-0.468467\pi$
$347$	3.68463	0.197802	0.0989008	+	0.995097i	$0.468467\pi$
$348$	7.42401	0.397969
$349$	−36.5140	−1.95455	−0.977275	−	0.211977i	$-0.932010\pi$
$349$	−36.5140	−1.95455	−0.977275	+	0.211977i	$0.932010\pi$
$350$	4.86799	0.260205
$351$	0	0
$352$	−1.50466	−0.0801989
$353$	13.6333	0.725626	0.362813	−	0.931862i	$-0.381816\pi$
$353$	13.6333	0.725626	0.362813	+	0.931862i	$0.381816\pi$
$354$	13.2920	0.706462
$355$	3.22538	0.171185
$356$	11.8680	0.629002
$357$	16.1507	0.854784
$358$	15.7873	0.834387
$359$	−10.9066	−0.575630	−0.287815	−	0.957686i	$-0.592929\pi$
$359$	−10.9066	−0.575630	−0.287815	+	0.957686i	$0.592929\pi$
$360$	−2.49534	−0.131516
$361$	−0.658719	−0.0346694
$362$	−21.8573	−1.14880
$363$	−27.4427	−1.44037
$364$	0	0
$365$	1.35061	0.0706942
$366$	−33.4427	−1.74808
$367$	−0.150665	−0.00786464	−0.00393232	−	0.999992i	$-0.501252\pi$
$367$	−0.150665	−0.00786464	−0.00393232	+	0.999992i	$0.501252\pi$
$368$	2.72666	0.142137
$369$	−6.86799	−0.357533
$370$	−0.726656	−0.0377771
$371$	−5.37266	−0.278934
$372$	16.1507	0.837373
$373$	−22.9253	−1.18703	−0.593513	−	0.804824i	$-0.702259\pi$
$373$	−22.9253	−1.18703	−0.593513	+	0.804824i	$0.702259\pi$
$374$	7.73599	0.400018
$375$	11.2627	0.581603
$376$	2.00000	0.103142
$377$	0	0
$378$	−12.1507	−0.624963
$379$	−25.6040	−1.31519	−0.657594	−	0.753373i	$-0.728426\pi$
$379$	−25.6040	−1.31519	−0.657594	+	0.753373i	$0.728426\pi$
$380$	1.55602	0.0798219
$381$	3.17064	0.162437
$382$	17.1413	0.877027
$383$	4.82936	0.246769	0.123384	−	0.992359i	$-0.460625\pi$
$383$	4.82936	0.246769	0.123384	+	0.992359i	$0.460625\pi$
$384$	3.14134	0.160306
$385$	−0.546687	−0.0278618
$386$	−26.8667	−1.36748
$387$	−78.4600	−3.98835
$388$	−4.13201	−0.209771
$389$	−33.1493	−1.68074	−0.840369	−	0.542014i	$-0.817662\pi$
$389$	−33.1493	−1.68074	−0.840369	+	0.542014i	$0.817662\pi$
$390$	0	0
$391$	−14.0187	−0.708954
$392$	1.00000	0.0505076
$393$	−11.3320	−0.571621
$394$	1.27334	0.0641501
$395$	−0.774618	−0.0389753
$396$	−10.3340	−0.519304
$397$	4.10270	0.205909	0.102954	−	0.994686i	$-0.467170\pi$
$397$	4.10270	0.205909	0.102954	+	0.994686i	$0.467170\pi$
$398$	−19.1893	−0.961873
$399$	13.4533	0.673508
$400$	−4.86799	−0.243400
$401$	23.2627	1.16168	0.580842	−	0.814016i	$-0.302723\pi$
$401$	23.2627	1.16168	0.580842	+	0.814016i	$0.302723\pi$
$402$	47.3107	2.35964
$403$	0	0
$404$	10.1800	0.506472
$405$	−6.38199	−0.317123
$406$	−2.36333	−0.117290
$407$	−3.00933	−0.149167
$408$	−16.1507	−0.799577
$409$	22.0373	1.08968	0.544838	−	0.838542i	$-0.316591\pi$
$409$	22.0373	1.08968	0.544838	+	0.838542i	$0.316591\pi$
$410$	0.363328	0.0179435
$411$	−40.0373	−1.97490
$412$	−5.97070	−0.294155
$413$	−4.23132	−0.208210
$414$	18.7267	0.920365
$415$	2.46264	0.120886
$416$	0	0
$417$	−20.9694	−1.02687
$418$	6.44398	0.315186
$419$	18.9766	0.927069	0.463535	−	0.886079i	$-0.346581\pi$
$419$	18.9766	0.927069	0.463535	+	0.886079i	$0.346581\pi$
$420$	1.14134	0.0556915
$421$	−38.4006	−1.87153	−0.935766	−	0.352621i	$-0.885291\pi$
$421$	−38.4006	−1.87153	−0.935766	+	0.352621i	$0.885291\pi$
$422$	4.67531	0.227590
$423$	13.7360	0.667866
$424$	5.37266	0.260919
$425$	25.0280	1.21404
$426$	−27.8867	−1.35111
$427$	10.6460	0.515196
$428$	−7.32131	−0.353889
$429$	0	0
$430$	4.15066	0.200163
$431$	−23.2920	−1.12194	−0.560968	−	0.827837i	$-0.689571\pi$
$431$	−23.2920	−1.12194	−0.560968	+	0.827837i	$0.689571\pi$
$432$	12.1507	0.584599
$433$	−39.3947	−1.89319	−0.946594	−	0.322427i	$-0.895501\pi$
$433$	−39.3947	−1.89319	−0.946594	+	0.322427i	$0.895501\pi$
$434$	−5.14134	−0.246792
$435$	−2.69735	−0.129328
$436$	18.2500	0.874015
$437$	−11.6774	−0.558605
$438$	−11.6774	−0.557967
$439$	12.9066	0.616000	0.308000	−	0.951386i	$-0.400340\pi$
$439$	12.9066	0.616000	0.308000	+	0.951386i	$0.400340\pi$
$440$	0.546687	0.0260623
$441$	6.86799	0.327047
$442$	0	0
$443$	28.6133	1.35946	0.679730	−	0.733463i	$-0.262097\pi$
$443$	28.6133	1.35946	0.679730	+	0.733463i	$0.262097\pi$
$444$	6.28267	0.298162
$445$	−4.31198	−0.204407
$446$	1.03863	0.0491807
$447$	49.6854	2.35004
$448$	−1.00000	−0.0472456
$449$	1.28399	0.0605953	0.0302976	−	0.999541i	$-0.490354\pi$
$449$	1.28399	0.0605953	0.0302976	+	0.999541i	$0.490354\pi$
$450$	−33.4333	−1.57606
$451$	1.50466	0.0708519
$452$	10.4333	0.490743
$453$	48.4520	2.27647
$454$	14.1507	0.664124
$455$	0	0
$456$	−13.4533	−0.630009
$457$	−16.5467	−0.774021	−0.387011	−	0.922075i	$-0.626492\pi$
$457$	−16.5467	−0.774021	−0.387011	+	0.922075i	$0.626492\pi$
$458$	9.55602	0.446523
$459$	−62.4707	−2.91588
$460$	−0.990671	−0.0461903
$461$	12.5620	0.585069	0.292534	−	0.956255i	$-0.405501\pi$
$461$	12.5620	0.585069	0.292534	+	0.956255i	$0.405501\pi$
$462$	4.72666	0.219904
$463$	−1.98134	−0.0920808	−0.0460404	−	0.998940i	$-0.514660\pi$
$463$	−1.98134	−0.0920808	−0.0460404	+	0.998940i	$0.514660\pi$
$464$	2.36333	0.109715
$465$	−5.86799	−0.272122
$466$	23.1307	1.07151
$467$	13.3620	0.618320	0.309160	−	0.951010i	$-0.399952\pi$
$467$	13.3620	0.618320	0.309160	+	0.951010i	$0.399952\pi$
$468$	0	0
$469$	−15.0607	−0.695438
$470$	−0.726656	−0.0335182
$471$	−25.1307	−1.15796
$472$	4.23132	0.194762
$473$	17.1893	0.790365
$474$	6.69735	0.307620
$475$	20.8480	0.956573
$476$	5.14134	0.235653
$477$	36.8994	1.68951
$478$	0.102703	0.00469752
$479$	37.1493	1.69740	0.848698	−	0.528877i	$-0.177387\pi$
$479$	37.1493	1.69740	0.848698	+	0.528877i	$0.177387\pi$
$480$	−1.14134	−0.0520946
$481$	0	0
$482$	6.56534	0.299043
$483$	−8.56534	−0.389737
$484$	−8.73599	−0.397090
$485$	1.50127	0.0681694
$486$	18.7267	0.849458
$487$	−18.9066	−0.856741	−0.428370	−	0.903603i	$-0.640912\pi$
$487$	−18.9066	−0.856741	−0.428370	+	0.903603i	$0.640912\pi$
$488$	−10.6460	−0.481922
$489$	42.5840	1.92572
$490$	−0.363328	−0.0164135
$491$	21.4054	0.966010	0.483005	−	0.875618i	$-0.339545\pi$
$491$	21.4054	0.966010	0.483005	+	0.875618i	$0.339545\pi$
$492$	−3.14134	−0.141622
$493$	−12.1507	−0.547238
$494$	0	0
$495$	3.75464	0.168759
$496$	5.14134	0.230853
$497$	8.87732	0.398202
$498$	−21.2920	−0.954117
$499$	10.0700	0.450796	0.225398	−	0.974267i	$-0.427632\pi$
$499$	10.0700	0.450796	0.225398	+	0.974267i	$0.427632\pi$
$500$	3.58532	0.160340
$501$	56.6027	2.52882
$502$	−20.5327	−0.916417
$503$	−7.47197	−0.333159	−0.166579	−	0.986028i	$-0.553272\pi$
$503$	−7.47197	−0.333159	−0.166579	+	0.986028i	$0.553272\pi$
$504$	−6.86799	−0.305925
$505$	−3.69867	−0.164589
$506$	−4.10270	−0.182387
$507$	−40.8374	−1.81365
$508$	1.00933	0.0447817
$509$	−10.8039	−0.478875	−0.239438	−	0.970912i	$-0.576963\pi$
$509$	−10.8039	−0.478875	−0.239438	+	0.970912i	$0.576963\pi$
$510$	5.86799	0.259839
$511$	3.71733	0.164445
$512$	1.00000	0.0441942
$513$	−52.0373	−2.29750
$514$	−23.3400	−1.02948
$515$	2.16932	0.0955918
$516$	−35.8867	−1.57982
$517$	−3.00933	−0.132350
$518$	−2.00000	−0.0878750
$519$	−67.1973	−2.94963
$520$	0	0
$521$	23.2733	1.01962	0.509812	−	0.860286i	$-0.329715\pi$
$521$	23.2733	1.01962	0.509812	+	0.860286i	$0.329715\pi$
$522$	16.2313	0.710426
$523$	−7.40196	−0.323665	−0.161833	−	0.986818i	$-0.551740\pi$
$523$	−7.40196	−0.323665	−0.161833	+	0.986818i	$0.551740\pi$
$524$	−3.60737	−0.157589
$525$	15.2920	0.667398
$526$	30.0187	1.30888
$527$	−26.4333	−1.15145
$528$	−4.72666	−0.205701
$529$	−15.5653	−0.676754
$530$	−1.95204	−0.0847911
$531$	29.0607	1.26113
$532$	4.28267	0.185677
$533$	0	0
$534$	37.2814	1.61332
$535$	2.66004	0.115003
$536$	15.0607	0.650522
$537$	49.5933	2.14011
$538$	4.61670	0.199040
$539$	−1.50466	−0.0648105
$540$	−4.41468	−0.189978
$541$	−19.4533	−0.836363	−0.418182	−	0.908363i	$-0.637332\pi$
$541$	−19.4533	−0.836363	−0.418182	+	0.908363i	$0.637332\pi$
$542$	20.0000	0.859074
$543$	−68.6613	−2.94654
$544$	−5.14134	−0.220433
$545$	−6.63073	−0.284029
$546$	0	0
$547$	−8.15405	−0.348642	−0.174321	−	0.984689i	$-0.555773\pi$
$547$	−8.15405	−0.348642	−0.174321	+	0.984689i	$0.555773\pi$
$548$	−12.7453	−0.544453
$549$	−73.1167	−3.12054
$550$	7.32469	0.312326
$551$	−10.1214	−0.431184
$552$	8.56534	0.364565
$553$	−2.13201	−0.0906622
$554$	24.1214	1.02482
$555$	−2.28267	−0.0968940
$556$	−6.67531	−0.283096
$557$	6.30472	0.267140	0.133570	−	0.991039i	$-0.457356\pi$
$557$	6.30472	0.267140	0.133570	+	0.991039i	$0.457356\pi$
$558$	35.3107	1.49482
$559$	0	0
$560$	0.363328	0.0153534
$561$	24.3013	1.02600
$562$	11.4533	0.483129
$563$	−26.2640	−1.10690	−0.553448	−	0.832884i	$-0.686688\pi$
$563$	−26.2640	−1.10690	−0.553448	+	0.832884i	$0.686688\pi$
$564$	6.28267	0.264548
$565$	−3.79073	−0.159477
$566$	8.33402	0.350305
$567$	−17.5653	−0.737675
$568$	−8.87732	−0.372484
$569$	−17.8680	−0.749065	−0.374533	−	0.927214i	$-0.622197\pi$
$569$	−17.8680	−0.749065	−0.374533	+	0.927214i	$0.622197\pi$
$570$	4.88797	0.204734
$571$	−0.675305	−0.0282606	−0.0141303	−	0.999900i	$-0.504498\pi$
$571$	−0.675305	−0.0282606	−0.0141303	+	0.999900i	$0.504498\pi$
$572$	0	0
$573$	53.8467	2.24948
$574$	1.00000	0.0417392
$575$	−13.2733	−0.553537
$576$	6.86799	0.286166
$577$	−20.7267	−0.862862	−0.431431	−	0.902146i	$-0.641991\pi$
$577$	−20.7267	−0.862862	−0.431431	+	0.902146i	$0.641991\pi$
$578$	9.43334	0.392375
$579$	−84.3973	−3.50743
$580$	−0.858664	−0.0356541
$581$	6.77801	0.281199
$582$	−12.9800	−0.538039
$583$	−8.08405	−0.334807
$584$	−3.71733	−0.153824
$585$	0	0
$586$	−28.8667	−1.19247
$587$	1.95204	0.0805692	0.0402846	−	0.999188i	$-0.487174\pi$
$587$	1.95204	0.0805692	0.0402846	+	0.999188i	$0.487174\pi$
$588$	3.14134	0.129547
$589$	−22.0187	−0.907263
$590$	−1.53736	−0.0632920
$591$	4.00000	0.164538
$592$	2.00000	0.0821995
$593$	−48.4333	−1.98892	−0.994459	−	0.105122i	$-0.966477\pi$
$593$	−48.4333	−1.98892	−0.994459	+	0.105122i	$0.966477\pi$
$594$	−18.2827	−0.750147
$595$	−1.86799	−0.0765802
$596$	15.8166	0.647875
$597$	−60.2800	−2.46710
$598$	0	0
$599$	−18.9066	−0.772504	−0.386252	−	0.922393i	$-0.626230\pi$
$599$	−18.9066	−0.772504	−0.386252	+	0.922393i	$0.626230\pi$
$600$	−15.2920	−0.624293
$601$	−15.4826	−0.631549	−0.315775	−	0.948834i	$-0.602264\pi$
$601$	−15.4826	−0.631549	−0.315775	+	0.948834i	$0.602264\pi$
$602$	11.4240	0.465608
$603$	103.437	4.21227
$604$	15.4240	0.627594
$605$	3.17403	0.129043
$606$	31.9787	1.29905
$607$	−40.8119	−1.65651	−0.828253	−	0.560355i	$-0.810665\pi$
$607$	−40.8119	−1.65651	−0.828253	+	0.560355i	$0.810665\pi$
$608$	−4.28267	−0.173685
$609$	−7.42401	−0.300836
$610$	3.86799	0.156610
$611$	0	0
$612$	−35.3107	−1.42735
$613$	−11.4974	−0.464376	−0.232188	−	0.972671i	$-0.574588\pi$
$613$	−11.4974	−0.464376	−0.232188	+	0.972671i	$0.574588\pi$
$614$	22.9766	0.927262
$615$	1.14134	0.0460231
$616$	1.50466	0.0606247
$617$	−15.2080	−0.612249	−0.306125	−	0.951991i	$-0.599032\pi$
$617$	−15.2080	−0.612249	−0.306125	+	0.951991i	$0.599032\pi$
$618$	−18.7560	−0.754475
$619$	19.0793	0.766863	0.383432	−	0.923569i	$-0.374742\pi$
$619$	19.0793	0.766863	0.383432	+	0.923569i	$0.374742\pi$
$620$	−1.86799	−0.0750204
$621$	33.1307	1.32949
$622$	7.65872	0.307087
$623$	−11.8680	−0.475481
$624$	0	0
$625$	23.0373	0.921493
$626$	−12.1986	−0.487555
$627$	20.2427	0.808416
$628$	−8.00000	−0.319235
$629$	−10.2827	−0.409997
$630$	2.49534	0.0994166
$631$	−26.6680	−1.06164	−0.530819	−	0.847485i	$-0.678116\pi$
$631$	−26.6680	−1.06164	−0.530819	+	0.847485i	$0.678116\pi$
$632$	2.13201	0.0848067
$633$	14.6867	0.583744
$634$	26.2500	1.04252
$635$	−0.366718	−0.0145527
$636$	16.8773	0.669229
$637$	0	0
$638$	−3.55602	−0.140784
$639$	−60.9694	−2.41191
$640$	−0.363328	−0.0143618
$641$	−9.67738	−0.382233	−0.191117	−	0.981567i	$-0.561211\pi$
$641$	−9.67738	−0.382233	−0.191117	+	0.981567i	$0.561211\pi$
$642$	−22.9987	−0.907686
$643$	25.6226	1.01046	0.505229	−	0.862985i	$-0.331408\pi$
$643$	25.6226	1.01046	0.505229	+	0.862985i	$0.331408\pi$
$644$	−2.72666	−0.107445
$645$	13.0386	0.513396
$646$	22.0187	0.866312
$647$	18.9546	0.745182	0.372591	−	0.927996i	$-0.378469\pi$
$647$	18.9546	0.745182	0.372591	+	0.927996i	$0.378469\pi$
$648$	17.5653	0.690032
$649$	−6.36672	−0.249916
$650$	0	0
$651$	−16.1507	−0.632994
$652$	13.5560	0.530895
$653$	−0.543298	−0.0212609	−0.0106304	−	0.999943i	$-0.503384\pi$
$653$	−0.543298	−0.0212609	−0.0106304	+	0.999943i	$0.503384\pi$
$654$	57.3293	2.24175
$655$	1.31066	0.0512117
$656$	−1.00000	−0.0390434
$657$	−25.5306	−0.996043
$658$	−2.00000	−0.0779681
$659$	−19.4647	−0.758238	−0.379119	−	0.925348i	$-0.623773\pi$
$659$	−19.4647	−0.758238	−0.379119	+	0.925348i	$0.623773\pi$
$660$	1.71733	0.0668469
$661$	33.9673	1.32118	0.660588	−	0.750749i	$-0.270307\pi$
$661$	33.9673	1.32118	0.660588	+	0.750749i	$0.270307\pi$
$662$	−8.67531	−0.337175
$663$	0	0
$664$	−6.77801	−0.263038
$665$	−1.55602	−0.0603397
$666$	13.7360	0.532259
$667$	6.44398	0.249512
$668$	18.0187	0.697163
$669$	3.26270	0.126143
$670$	−5.47197	−0.211401
$671$	16.0187	0.618393
$672$	−3.14134	−0.121180
$673$	−42.7054	−1.64617	−0.823085	−	0.567918i	$-0.807749\pi$
$673$	−42.7054	−1.64617	−0.823085	+	0.567918i	$0.807749\pi$
$674$	35.2814	1.35899
$675$	−59.1493	−2.27666
$676$	−13.0000	−0.500000
$677$	−5.14473	−0.197728	−0.0988639	−	0.995101i	$-0.531521\pi$
$677$	−5.14473	−0.197728	−0.0988639	+	0.995101i	$0.531521\pi$
$678$	32.7746	1.25870
$679$	4.13201	0.158572
$680$	1.86799	0.0716342
$681$	44.4520	1.70340
$682$	−7.73599	−0.296226
$683$	2.89937	0.110941	0.0554706	−	0.998460i	$-0.482334\pi$
$683$	2.89937	0.110941	0.0554706	+	0.998460i	$0.482334\pi$
$684$	−29.4134	−1.12465
$685$	4.63073	0.176931
$686$	−1.00000	−0.0381802
$687$	30.0187	1.14528
$688$	−11.4240	−0.435536
$689$	0	0
$690$	−3.11203	−0.118473
$691$	−1.95204	−0.0742590	−0.0371295	−	0.999310i	$-0.511821\pi$
$691$	−1.95204	−0.0742590	−0.0371295	+	0.999310i	$0.511821\pi$
$692$	−21.3913	−0.813176
$693$	10.3340	0.392557
$694$	3.68463	0.139867
$695$	2.42533	0.0919979
$696$	7.42401	0.281406
$697$	5.14134	0.194742
$698$	−36.5140	−1.38208
$699$	72.6613	2.74830
$700$	4.86799	0.183993
$701$	35.3947	1.33684	0.668420	−	0.743784i	$-0.266971\pi$
$701$	35.3947	1.33684	0.668420	+	0.743784i	$0.266971\pi$
$702$	0	0
$703$	−8.56534	−0.323048
$704$	−1.50466	−0.0567092
$705$	−2.28267	−0.0859704
$706$	13.6333	0.513095
$707$	−10.1800	−0.382857
$708$	13.2920	0.499544
$709$	−8.68332	−0.326109	−0.163054	−	0.986617i	$-0.552135\pi$
$709$	−8.68332	−0.326109	−0.163054	+	0.986617i	$0.552135\pi$
$710$	3.22538	0.121046
$711$	14.6426	0.549141
$712$	11.8680	0.444772
$713$	14.0187	0.525003
$714$	16.1507	0.604423
$715$	0	0
$716$	15.7873	0.590000
$717$	0.322624	0.0120486
$718$	−10.9066	−0.407032
$719$	−38.7894	−1.44660	−0.723300	−	0.690534i	$-0.757376\pi$
$719$	−38.7894	−1.44660	−0.723300	+	0.690534i	$0.757376\pi$
$720$	−2.49534	−0.0929957
$721$	5.97070	0.222360
$722$	−0.658719	−0.0245150
$723$	20.6240	0.767013
$724$	−21.8573	−0.812322
$725$	−11.5047	−0.427273
$726$	−27.4427	−1.01849
$727$	29.1307	1.08040	0.540199	−	0.841537i	$-0.318349\pi$
$727$	29.1307	1.08040	0.540199	+	0.841537i	$0.318349\pi$
$728$	0	0
$729$	6.13069	0.227063
$730$	1.35061	0.0499883
$731$	58.7347	2.17238
$732$	−33.4427	−1.23608
$733$	53.8540	1.98914	0.994571	−	0.104064i	$-0.0331846\pi$
$733$	53.8540	1.98914	0.994571	+	0.104064i	$0.0331846\pi$
$734$	−0.150665	−0.00556114
$735$	−1.14134	−0.0420988
$736$	2.72666	0.100506
$737$	−22.6613	−0.834739
$738$	−6.86799	−0.252814
$739$	−5.61076	−0.206395	−0.103198	−	0.994661i	$-0.532907\pi$
$739$	−5.61076	−0.206395	−0.103198	+	0.994661i	$0.532907\pi$
$740$	−0.726656	−0.0267124
$741$	0	0
$742$	−5.37266	−0.197236
$743$	−12.5653	−0.460978	−0.230489	−	0.973075i	$-0.574033\pi$
$743$	−12.5653	−0.460978	−0.230489	+	0.973075i	$0.574033\pi$
$744$	16.1507	0.592112
$745$	−5.74663	−0.210540
$746$	−22.9253	−0.839354
$747$	−46.5513	−1.70322
$748$	7.73599	0.282856
$749$	7.32131	0.267515
$750$	11.2627	0.411256
$751$	35.0466	1.27887	0.639435	−	0.768845i	$-0.279168\pi$
$751$	35.0466	1.27887	0.639435	+	0.768845i	$0.279168\pi$
$752$	2.00000	0.0729325
$753$	−64.5000	−2.35051
$754$	0	0
$755$	−5.60398	−0.203950
$756$	−12.1507	−0.441915
$757$	−27.4499	−0.997684	−0.498842	−	0.866693i	$-0.666241\pi$
$757$	−27.4499	−0.997684	−0.498842	+	0.866693i	$0.666241\pi$
$758$	−25.6040	−0.929978
$759$	−12.8880	−0.467804
$760$	1.55602	0.0564426
$761$	5.53736	0.200729	0.100365	−	0.994951i	$-0.467999\pi$
$761$	5.53736	0.200729	0.100365	+	0.994951i	$0.467999\pi$
$762$	3.17064	0.114860
$763$	−18.2500	−0.660694
$764$	17.1413	0.620152
$765$	12.8294	0.463846
$766$	4.82936	0.174492
$767$	0	0
$768$	3.14134	0.113353
$769$	−20.1587	−0.726940	−0.363470	−	0.931606i	$-0.618408\pi$
$769$	−20.1587	−0.726940	−0.363470	+	0.931606i	$0.618408\pi$
$770$	−0.546687	−0.0197012
$771$	−73.3187	−2.64051
$772$	−26.8667	−0.966953
$773$	−27.9414	−1.00498	−0.502491	−	0.864582i	$-0.667583\pi$
$773$	−27.9414	−1.00498	−0.502491	+	0.864582i	$0.667583\pi$
$774$	−78.4600	−2.82019
$775$	−25.0280	−0.899032
$776$	−4.13201	−0.148330
$777$	−6.28267	−0.225390
$778$	−33.1493	−1.18846
$779$	4.28267	0.153443
$780$	0	0
$781$	13.3574	0.477965
$782$	−14.0187	−0.501306
$783$	28.7160	1.02623
$784$	1.00000	0.0357143
$785$	2.90663	0.103742
$786$	−11.3320	−0.404197
$787$	−37.5233	−1.33756	−0.668781	−	0.743459i	$-0.733184\pi$
$787$	−37.5233	−1.33756	−0.668781	+	0.743459i	$0.733184\pi$
$788$	1.27334	0.0453610
$789$	94.2987	3.35712
$790$	−0.774618	−0.0275597
$791$	−10.4333	−0.370967
$792$	−10.3340	−0.367204
$793$	0	0
$794$	4.10270	0.145599
$795$	−6.13201	−0.217480
$796$	−19.1893	−0.680147
$797$	−5.19269	−0.183934	−0.0919672	−	0.995762i	$-0.529315\pi$
$797$	−5.19269	−0.183934	−0.0919672	+	0.995762i	$0.529315\pi$
$798$	13.4533	0.476242
$799$	−10.2827	−0.363775
$800$	−4.86799	−0.172110
$801$	81.5093	2.87999
$802$	23.2627	0.821434
$803$	5.59333	0.197384
$804$	47.3107	1.66852
$805$	0.990671	0.0349166
$806$	0	0
$807$	14.5026	0.510515
$808$	10.1800	0.358130
$809$	36.5840	1.28623	0.643113	−	0.765772i	$-0.277643\pi$
$809$	36.5840	1.28623	0.643113	+	0.765772i	$0.277643\pi$
$810$	−6.38199	−0.224240
$811$	−35.0793	−1.23180	−0.615901	−	0.787824i	$-0.711208\pi$
$811$	−35.0793	−1.23180	−0.615901	+	0.787824i	$0.711208\pi$
$812$	−2.36333	−0.0829366
$813$	62.8267	2.20343
$814$	−3.00933	−0.105477
$815$	−4.92528	−0.172525
$816$	−16.1507	−0.565386
$817$	48.9253	1.71168
$818$	22.0373	0.770517
$819$	0	0
$820$	0.363328	0.0126880
$821$	−26.1986	−0.914338	−0.457169	−	0.889380i	$-0.651137\pi$
$821$	−26.1986	−0.914338	−0.457169	+	0.889380i	$0.651137\pi$
$822$	−40.0373	−1.39646
$823$	17.1413	0.597509	0.298755	−	0.954330i	$-0.403429\pi$
$823$	17.1413	0.597509	0.298755	+	0.954330i	$0.403429\pi$
$824$	−5.97070	−0.207999
$825$	23.0093	0.801082
$826$	−4.23132	−0.147226
$827$	35.5233	1.23527	0.617633	−	0.786466i	$-0.288092\pi$
$827$	35.5233	1.23527	0.617633	+	0.786466i	$0.288092\pi$
$828$	18.7267	0.650796
$829$	−12.7233	−0.441897	−0.220949	−	0.975285i	$-0.570915\pi$
$829$	−12.7233	−0.441897	−0.220949	+	0.975285i	$0.570915\pi$
$830$	2.46264	0.0854795
$831$	75.7733	2.62855
$832$	0	0
$833$	−5.14134	−0.178137
$834$	−20.9694	−0.726110
$835$	−6.54669	−0.226557
$836$	6.44398	0.222870
$837$	62.4707	2.15930
$838$	18.9766	0.655537
$839$	−5.47197	−0.188913	−0.0944567	−	0.995529i	$-0.530111\pi$
$839$	−5.47197	−0.188913	−0.0944567	+	0.995529i	$0.530111\pi$
$840$	1.14134	0.0393798
$841$	−23.4147	−0.807403
$842$	−38.4006	−1.32337
$843$	35.9787	1.23917
$844$	4.67531	0.160931
$845$	4.72327	0.162485
$846$	13.7360	0.472253
$847$	8.73599	0.300172
$848$	5.37266	0.184498
$849$	26.1800	0.898494
$850$	25.0280	0.858453
$851$	5.45331	0.186937
$852$	−27.8867	−0.955381
$853$	16.3047	0.558263	0.279131	−	0.960253i	$-0.409953\pi$
$853$	16.3047	0.558263	0.279131	+	0.960253i	$0.409953\pi$
$854$	10.6460	0.364299
$855$	10.6867	0.365478
$856$	−7.32131	−0.250237
$857$	−30.0373	−1.02606	−0.513028	−	0.858372i	$-0.671476\pi$
$857$	−30.0373	−1.02606	−0.513028	+	0.858372i	$0.671476\pi$
$858$	0	0
$859$	0.817960	0.0279084	0.0139542	−	0.999903i	$-0.495558\pi$
$859$	0.817960	0.0279084	0.0139542	+	0.999903i	$0.495558\pi$
$860$	4.15066	0.141536
$861$	3.14134	0.107056
$862$	−23.2920	−0.793329
$863$	−6.22406	−0.211870	−0.105935	−	0.994373i	$-0.533783\pi$
$863$	−6.22406	−0.211870	−0.105935	+	0.994373i	$0.533783\pi$
$864$	12.1507	0.413374
$865$	7.77207	0.264258
$866$	−39.3947	−1.33869
$867$	29.6333	1.00640
$868$	−5.14134	−0.174508
$869$	−3.20796	−0.108822
$870$	−2.69735	−0.0914488
$871$	0	0
$872$	18.2500	0.618022
$873$	−28.3786	−0.960470
$874$	−11.6774	−0.394993
$875$	−3.58532	−0.121206
$876$	−11.6774	−0.394542
$877$	10.4040	0.351319	0.175660	−	0.984451i	$-0.443794\pi$
$877$	10.4040	0.351319	0.175660	+	0.984451i	$0.443794\pi$
$878$	12.9066	0.435578
$879$	−90.6799	−3.05856
$880$	0.546687	0.0184288
$881$	2.93206	0.0987837	0.0493918	−	0.998779i	$-0.484272\pi$
$881$	2.93206	0.0987837	0.0493918	+	0.998779i	$0.484272\pi$
$882$	6.86799	0.231257
$883$	44.7567	1.50618	0.753092	−	0.657916i	$-0.228562\pi$
$883$	44.7567	1.50618	0.753092	+	0.657916i	$0.228562\pi$
$884$	0	0
$885$	−4.82936	−0.162337
$886$	28.6133	0.961283
$887$	−42.3013	−1.42034	−0.710170	−	0.704030i	$-0.751382\pi$
$887$	−42.3013	−1.42034	−0.710170	+	0.704030i	$0.751382\pi$
$888$	6.28267	0.210833
$889$	−1.00933	−0.0338518
$890$	−4.31198	−0.144538
$891$	−26.4299	−0.885437
$892$	1.03863	0.0347760
$893$	−8.56534	−0.286628
$894$	49.6854	1.66173
$895$	−5.73599	−0.191733
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	1.28399	0.0428473
$899$	12.1507	0.405247
$900$	−33.4333	−1.11444
$901$	−27.6226	−0.920243
$902$	1.50466	0.0500998
$903$	35.8867	1.19423
$904$	10.4333	0.347008
$905$	7.94139	0.263981
$906$	48.4520	1.60971
$907$	20.9359	0.695166	0.347583	−	0.937649i	$-0.387002\pi$
$907$	20.9359	0.695166	0.347583	+	0.937649i	$0.387002\pi$
$908$	14.1507	0.469606
$909$	69.9160	2.31897
$910$	0	0
$911$	28.6494	0.949197	0.474598	−	0.880202i	$-0.342593\pi$
$911$	28.6494	0.949197	0.474598	+	0.880202i	$0.342593\pi$
$912$	−13.4533	−0.445484
$913$	10.1986	0.337525
$914$	−16.5467	−0.547316
$915$	12.1507	0.401689
$916$	9.55602	0.315740
$917$	3.60737	0.119126
$918$	−62.4707	−2.06184
$919$	51.4613	1.69755	0.848776	−	0.528752i	$-0.177340\pi$
$919$	51.4613	1.69755	0.848776	+	0.528752i	$0.177340\pi$
$920$	−0.990671	−0.0326615
$921$	72.1773	2.37832
$922$	12.5620	0.413706
$923$	0	0
$924$	4.72666	0.155496
$925$	−9.73599	−0.320117
$926$	−1.98134	−0.0651110
$927$	−41.0067	−1.34684
$928$	2.36333	0.0775801
$929$	−9.43466	−0.309541	−0.154771	−	0.987950i	$-0.549464\pi$
$929$	−9.43466	−0.309541	−0.154771	+	0.987950i	$0.549464\pi$
$930$	−5.86799	−0.192419
$931$	−4.28267	−0.140359
$932$	23.1307	0.757671
$933$	24.0586	0.787644
$934$	13.3620	0.437218
$935$	−2.81070	−0.0919198
$936$	0	0
$937$	7.33996	0.239786	0.119893	−	0.992787i	$-0.461745\pi$
$937$	7.33996	0.239786	0.119893	+	0.992787i	$0.461745\pi$
$938$	−15.0607	−0.491749
$939$	−38.3200	−1.25053
$940$	−0.726656	−0.0237009
$941$	24.6167	0.802481	0.401241	−	0.915973i	$-0.368579\pi$
$941$	24.6167	0.802481	0.401241	+	0.915973i	$0.368579\pi$
$942$	−25.1307	−0.818802
$943$	−2.72666	−0.0887922
$944$	4.23132	0.137718
$945$	4.41468	0.143610
$946$	17.1893	0.558872
$947$	−34.3786	−1.11715	−0.558577	−	0.829453i	$-0.688653\pi$
$947$	−34.3786	−1.11715	−0.558577	+	0.829453i	$0.688653\pi$
$948$	6.69735	0.217520
$949$	0	0
$950$	20.8480	0.676399
$951$	82.4600	2.67395
$952$	5.14134	0.166632
$953$	−45.0721	−1.46003	−0.730014	−	0.683432i	$-0.760486\pi$
$953$	−45.0721	−1.46003	−0.730014	+	0.683432i	$0.760486\pi$
$954$	36.8994	1.19466
$955$	−6.22793	−0.201531
$956$	0.102703	0.00332165
$957$	−11.1706	−0.361096
$958$	37.1493	1.20024
$959$	12.7453	0.411568
$960$	−1.14134	−0.0368365
$961$	−4.56666	−0.147312
$962$	0	0
$963$	−50.2827	−1.62034
$964$	6.56534	0.211456
$965$	9.76142	0.314231
$966$	−8.56534	−0.275585
$967$	−18.6387	−0.599382	−0.299691	−	0.954036i	$-0.596884\pi$
$967$	−18.6387	−0.599382	−0.299691	+	0.954036i	$0.596884\pi$
$968$	−8.73599	−0.280785
$969$	69.1680	2.22200
$970$	1.50127	0.0482030
$971$	−28.7933	−0.924020	−0.462010	−	0.886875i	$-0.652872\pi$
$971$	−28.7933	−0.924020	−0.462010	+	0.886875i	$0.652872\pi$
$972$	18.7267	0.600658
$973$	6.67531	0.214000
$974$	−18.9066	−0.605807
$975$	0	0
$976$	−10.6460	−0.340770
$977$	−23.9160	−0.765139	−0.382570	−	0.923927i	$-0.624961\pi$
$977$	−23.9160	−0.765139	−0.382570	+	0.923927i	$0.624961\pi$
$978$	42.5840	1.36169
$979$	−17.8573	−0.570723
$980$	−0.363328	−0.0116061
$981$	125.341	4.00182
$982$	21.4054	0.683072
$983$	−14.3306	−0.457076	−0.228538	−	0.973535i	$-0.573395\pi$
$983$	−14.3306	−0.457076	−0.228538	+	0.973535i	$0.573395\pi$
$984$	−3.14134	−0.100142
$985$	−0.462642	−0.0147410
$986$	−12.1507	−0.386956
$987$	−6.28267	−0.199980
$988$	0	0
$989$	−31.1493	−0.990492
$990$	3.75464	0.119330
$991$	7.21473	0.229184	0.114592	−	0.993413i	$-0.463444\pi$
$991$	7.21473	0.229184	0.114592	+	0.993413i	$0.463444\pi$
$992$	5.14134	0.163238
$993$	−27.2520	−0.864818
$994$	8.87732	0.281572
$995$	6.97201	0.221028
$996$	−21.2920	−0.674663
$997$	5.35061	0.169456	0.0847278	−	0.996404i	$-0.472998\pi$
$997$	5.35061	0.169456	0.0847278	+	0.996404i	$0.472998\pi$
$998$	10.0700	0.318761
$999$	24.3013	0.768860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.a.l.1.3	✓	3
3.2	odd	2		5166.2.a.bt.1.2		3
4.3	odd	2		4592.2.a.s.1.1		3
7.6	odd	2		4018.2.a.bg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.l.1.3	✓	3	1.1	even	1	trivial
4018.2.a.bg.1.1		3	7.6	odd	2
4592.2.a.s.1.1		3	4.3	odd	2
5166.2.a.bt.1.2		3	3.2	odd	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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.14134 q^{3} +1.00000 q^{4} -0.363328 q^{5} +3.14134 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.86799 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.14134 q^{3} +1.00000 q^{4} -0.363328 q^{5} +3.14134 q^{6} -1.00000 q^{7} +1.00000 q^{8} +6.86799 q^{9} -0.363328 q^{10} -1.50466 q^{11} +3.14134 q^{12} -1.00000 q^{14} -1.14134 q^{15} +1.00000 q^{16} -5.14134 q^{17} +6.86799 q^{18} -4.28267 q^{19} -0.363328 q^{20} -3.14134 q^{21} -1.50466 q^{22} +2.72666 q^{23} +3.14134 q^{24} -4.86799 q^{25} +12.1507 q^{27} -1.00000 q^{28} +2.36333 q^{29} -1.14134 q^{30} +5.14134 q^{31} +1.00000 q^{32} -4.72666 q^{33} -5.14134 q^{34} +0.363328 q^{35} +6.86799 q^{36} +2.00000 q^{37} -4.28267 q^{38} -0.363328 q^{40} -1.00000 q^{41} -3.14134 q^{42} -11.4240 q^{43} -1.50466 q^{44} -2.49534 q^{45} +2.72666 q^{46} +2.00000 q^{47} +3.14134 q^{48} +1.00000 q^{49} -4.86799 q^{50} -16.1507 q^{51} +5.37266 q^{53} +12.1507 q^{54} +0.546687 q^{55} -1.00000 q^{56} -13.4533 q^{57} +2.36333 q^{58} +4.23132 q^{59} -1.14134 q^{60} -10.6460 q^{61} +5.14134 q^{62} -6.86799 q^{63} +1.00000 q^{64} -4.72666 q^{66} +15.0607 q^{67} -5.14134 q^{68} +8.56534 q^{69} +0.363328 q^{70} -8.87732 q^{71} +6.86799 q^{72} -3.71733 q^{73} +2.00000 q^{74} -15.2920 q^{75} -4.28267 q^{76} +1.50466 q^{77} +2.13201 q^{79} -0.363328 q^{80} +17.5653 q^{81} -1.00000 q^{82} -6.77801 q^{83} -3.14134 q^{84} +1.86799 q^{85} -11.4240 q^{86} +7.42401 q^{87} -1.50466 q^{88} +11.8680 q^{89} -2.49534 q^{90} +2.72666 q^{92} +16.1507 q^{93} +2.00000 q^{94} +1.55602 q^{95} +3.14134 q^{96} -4.13201 q^{97} +1.00000 q^{98} -10.3340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + q^5 + q^6 - 3 * q^7 + 3 * q^8 + 8 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 8 q^{9} + q^{10} + 6 q^{11} + q^{12} - 3 q^{14} + 5 q^{15} + 3 q^{16} - 7 q^{17} + 8 q^{18} + 4 q^{19} + q^{20} - q^{21} + 6 q^{22} + 4 q^{23} + q^{24} - 2 q^{25} + 7 q^{27} - 3 q^{28} + 5 q^{29} + 5 q^{30} + 7 q^{31} + 3 q^{32} - 10 q^{33} - 7 q^{34} - q^{35} + 8 q^{36} + 6 q^{37} + 4 q^{38} + q^{40} - 3 q^{41} - q^{42} - 9 q^{43} + 6 q^{44} - 18 q^{45} + 4 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} - 2 q^{50} - 19 q^{51} - 7 q^{53} + 7 q^{54} + 10 q^{55} - 3 q^{56} - 32 q^{57} + 5 q^{58} - 2 q^{59} + 5 q^{60} - 13 q^{61} + 7 q^{62} - 8 q^{63} + 3 q^{64} - 10 q^{66} + 22 q^{67} - 7 q^{68} - 8 q^{69} - q^{70} + 7 q^{71} + 8 q^{72} - 28 q^{73} + 6 q^{74} - 8 q^{75} + 4 q^{76} - 6 q^{77} + 19 q^{79} + q^{80} + 19 q^{81} - 3 q^{82} - 14 q^{83} - q^{84} - 7 q^{85} - 9 q^{86} - 3 q^{87} + 6 q^{88} + 23 q^{89} - 18 q^{90} + 4 q^{92} + 19 q^{93} + 6 q^{94} - 8 q^{95} + q^{96} - 25 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + q^5 + q^6 - 3 * q^7 + 3 * q^8 + 8 * q^9 + q^10 + 6 * q^11 + q^12 - 3 * q^14 + 5 * q^15 + 3 * q^16 - 7 * q^17 + 8 * q^18 + 4 * q^19 + q^20 - q^21 + 6 * q^22 + 4 * q^23 + q^24 - 2 * q^25 + 7 * q^27 - 3 * q^28 + 5 * q^29 + 5 * q^30 + 7 * q^31 + 3 * q^32 - 10 * q^33 - 7 * q^34 - q^35 + 8 * q^36 + 6 * q^37 + 4 * q^38 + q^40 - 3 * q^41 - q^42 - 9 * q^43 + 6 * q^44 - 18 * q^45 + 4 * q^46 + 6 * q^47 + q^48 + 3 * q^49 - 2 * q^50 - 19 * q^51 - 7 * q^53 + 7 * q^54 + 10 * q^55 - 3 * q^56 - 32 * q^57 + 5 * q^58 - 2 * q^59 + 5 * q^60 - 13 * q^61 + 7 * q^62 - 8 * q^63 + 3 * q^64 - 10 * q^66 + 22 * q^67 - 7 * q^68 - 8 * q^69 - q^70 + 7 * q^71 + 8 * q^72 - 28 * q^73 + 6 * q^74 - 8 * q^75 + 4 * q^76 - 6 * q^77 + 19 * q^79 + q^80 + 19 * q^81 - 3 * q^82 - 14 * q^83 - q^84 - 7 * q^85 - 9 * q^86 - 3 * q^87 + 6 * q^88 + 23 * q^89 - 18 * q^90 + 4 * q^92 + 19 * q^93 + 6 * q^94 - 8 * q^95 + q^96 - 25 * q^97 + 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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