LMFDB - Embedded newform 183.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [183,2,Mod(1,183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(183, 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("183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 183 = 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	183.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:	$1.46126235699$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.311108 q^{2} -1.00000 q^{3} -1.90321 q^{4} +2.00000 q^{5} -0.311108 q^{6} +4.42864 q^{7} -1.21432 q^{8} +1.00000 q^{9} +0.622216 q^{10} +2.90321 q^{11} +1.90321 q^{12} -2.42864 q^{13} +1.37778 q^{14} -2.00000 q^{15} +3.42864 q^{16} +6.28100 q^{17} +0.311108 q^{18} -2.62222 q^{19} -3.80642 q^{20} -4.42864 q^{21} +0.903212 q^{22} -5.95407 q^{23} +1.21432 q^{24} -1.00000 q^{25} -0.755569 q^{26} -1.00000 q^{27} -8.42864 q^{28} +3.52543 q^{29} -0.622216 q^{30} -7.18421 q^{31} +3.49532 q^{32} -2.90321 q^{33} +1.95407 q^{34} +8.85728 q^{35} -1.90321 q^{36} -10.8573 q^{37} -0.815792 q^{38} +2.42864 q^{39} -2.42864 q^{40} +5.05086 q^{41} -1.37778 q^{42} +0.133353 q^{43} -5.52543 q^{44} +2.00000 q^{45} -1.85236 q^{46} +1.24443 q^{47} -3.42864 q^{48} +12.6128 q^{49} -0.311108 q^{50} -6.28100 q^{51} +4.62222 q^{52} +10.5763 q^{53} -0.311108 q^{54} +5.80642 q^{55} -5.37778 q^{56} +2.62222 q^{57} +1.09679 q^{58} -13.5669 q^{59} +3.80642 q^{60} +1.00000 q^{61} -2.23506 q^{62} +4.42864 q^{63} -5.76986 q^{64} -4.85728 q^{65} -0.903212 q^{66} -8.99063 q^{67} -11.9541 q^{68} +5.95407 q^{69} +2.75557 q^{70} -1.95407 q^{71} -1.21432 q^{72} +8.10171 q^{73} -3.37778 q^{74} +1.00000 q^{75} +4.99063 q^{76} +12.8573 q^{77} +0.755569 q^{78} +4.99063 q^{79} +6.85728 q^{80} +1.00000 q^{81} +1.57136 q^{82} -11.6128 q^{83} +8.42864 q^{84} +12.5620 q^{85} +0.0414872 q^{86} -3.52543 q^{87} -3.52543 q^{88} -12.3827 q^{89} +0.622216 q^{90} -10.7556 q^{91} +11.3319 q^{92} +7.18421 q^{93} +0.387152 q^{94} -5.24443 q^{95} -3.49532 q^{96} +1.57136 q^{97} +3.92396 q^{98} +2.90321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - q^{6} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 2 q^{11} - q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} - 3 q^{16} + 12 q^{17} + q^{18} - 8 q^{19} + 2 q^{20} - 4 q^{22}+ \cdots + 2 q^{99}+O(q^{100}) $ 3 * q + q^2 - 3 * q^3 + q^4 + 6 * q^5 - q^6 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 2 * q^11 - q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 - 3 * q^16 + 12 * q^17 + q^18 - 8 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 - 3 * q^24 - 3 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 + 4 * q^29 - 2 * q^30 - 8 * q^31 - 3 * q^32 - 2 * q^33 - 14 * q^34 + q^36 - 6 * q^37 - 16 * q^38 - 6 * q^39 + 6 * q^40 + 2 * q^41 - 4 * q^42 - 10 * q^44 + 6 * q^45 - 12 * q^46 + 4 * q^47 + 3 * q^48 + 11 * q^49 - q^50 - 12 * q^51 + 14 * q^52 + 12 * q^53 - q^54 + 4 * q^55 - 16 * q^56 + 8 * q^57 + 10 * q^58 + 6 * q^59 - 2 * q^60 + 3 * q^61 + 20 * q^62 - 11 * q^64 + 12 * q^65 + 4 * q^66 - 16 * q^68 - 2 * q^69 + 8 * q^70 + 14 * q^71 + 3 * q^72 - 2 * q^73 - 10 * q^74 + 3 * q^75 - 12 * q^76 + 12 * q^77 + 2 * q^78 - 12 * q^79 - 6 * q^80 + 3 * q^81 + 18 * q^82 - 8 * q^83 + 12 * q^84 + 24 * q^85 - 40 * q^86 - 4 * q^87 - 4 * q^88 - 4 * q^89 + 2 * q^90 - 32 * q^91 + 14 * q^92 + 8 * q^93 + 28 * q^94 - 16 * q^95 + 3 * q^96 + 18 * q^97 - 15 * q^98 + 2 * q^99

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 $

$2$	0.311108	0.219986	0.109993	−	0.993932i	$-0.464917\pi$
$2$	0.311108	0.219986	0.109993	+	0.993932i	$0.464917\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.90321	−0.951606
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−0.311108	−0.127009
$7$	4.42864	1.67387	0.836934	−	0.547304i	$-0.184346\pi$
$7$	4.42864	1.67387	0.836934	+	0.547304i	$0.184346\pi$
$8$	−1.21432	−0.429327
$9$	1.00000	0.333333
$10$	0.622216	0.196762
$11$	2.90321	0.875351	0.437676	−	0.899133i	$-0.355802\pi$
$11$	2.90321	0.875351	0.437676	+	0.899133i	$0.355802\pi$
$12$	1.90321	0.549410
$13$	−2.42864	−0.673583	−0.336792	−	0.941579i	$-0.609342\pi$
$13$	−2.42864	−0.673583	−0.336792	+	0.941579i	$0.609342\pi$
$14$	1.37778	0.368228
$15$	−2.00000	−0.516398
$16$	3.42864	0.857160
$17$	6.28100	1.52337	0.761683	−	0.647950i	$-0.224374\pi$
$17$	6.28100	1.52337	0.761683	+	0.647950i	$0.224374\pi$
$18$	0.311108	0.0733288
$19$	−2.62222	−0.601578	−0.300789	−	0.953691i	$-0.597250\pi$
$19$	−2.62222	−0.601578	−0.300789	+	0.953691i	$0.597250\pi$
$20$	−3.80642	−0.851142
$21$	−4.42864	−0.966408
$22$	0.903212	0.192565
$23$	−5.95407	−1.24151	−0.620754	−	0.784005i	$-0.713174\pi$
$23$	−5.95407	−1.24151	−0.620754	+	0.784005i	$0.713174\pi$
$24$	1.21432	0.247872
$25$	−1.00000	−0.200000
$26$	−0.755569	−0.148179
$27$	−1.00000	−0.192450
$28$	−8.42864	−1.59286
$29$	3.52543	0.654655	0.327328	−	0.944911i	$-0.393852\pi$
$29$	3.52543	0.654655	0.327328	+	0.944911i	$0.393852\pi$
$30$	−0.622216	−0.113601
$31$	−7.18421	−1.29032	−0.645161	−	0.764047i	$-0.723210\pi$
$31$	−7.18421	−1.29032	−0.645161	+	0.764047i	$0.723210\pi$
$32$	3.49532	0.617890
$33$	−2.90321	−0.505384
$34$	1.95407	0.335120
$35$	8.85728	1.49715
$36$	−1.90321	−0.317202
$37$	−10.8573	−1.78493	−0.892463	−	0.451121i	$-0.851024\pi$
$37$	−10.8573	−1.78493	−0.892463	+	0.451121i	$0.851024\pi$
$38$	−0.815792	−0.132339
$39$	2.42864	0.388894
$40$	−2.42864	−0.384002
$41$	5.05086	0.788811	0.394406	−	0.918936i	$-0.370951\pi$
$41$	5.05086	0.788811	0.394406	+	0.918936i	$0.370951\pi$
$42$	−1.37778	−0.212597
$43$	0.133353	0.0203362	0.0101681	−	0.999948i	$-0.496763\pi$
$43$	0.133353	0.0203362	0.0101681	+	0.999948i	$0.496763\pi$
$44$	−5.52543	−0.832990
$45$	2.00000	0.298142
$46$	−1.85236	−0.273115
$47$	1.24443	0.181519	0.0907595	−	0.995873i	$-0.471071\pi$
$47$	1.24443	0.181519	0.0907595	+	0.995873i	$0.471071\pi$
$48$	−3.42864	−0.494881
$49$	12.6128	1.80184
$50$	−0.311108	−0.0439973
$51$	−6.28100	−0.879515
$52$	4.62222	0.640986
$53$	10.5763	1.45276	0.726382	−	0.687291i	$-0.241200\pi$
$53$	10.5763	1.45276	0.726382	+	0.687291i	$0.241200\pi$
$54$	−0.311108	−0.0423364
$55$	5.80642	0.782938
$56$	−5.37778	−0.718637
$57$	2.62222	0.347321
$58$	1.09679	0.144015
$59$	−13.5669	−1.76626	−0.883131	−	0.469127i	$-0.844569\pi$
$59$	−13.5669	−1.76626	−0.883131	+	0.469127i	$0.844569\pi$
$60$	3.80642	0.491407
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−2.23506	−0.283853
$63$	4.42864	0.557956
$64$	−5.76986	−0.721232
$65$	−4.85728	−0.602471
$66$	−0.903212	−0.111178
$67$	−8.99063	−1.09838	−0.549190	−	0.835697i	$-0.685064\pi$
$67$	−8.99063	−1.09838	−0.549190	+	0.835697i	$0.685064\pi$
$68$	−11.9541	−1.44964
$69$	5.95407	0.716785
$70$	2.75557	0.329353
$71$	−1.95407	−0.231905	−0.115953	−	0.993255i	$-0.536992\pi$
$71$	−1.95407	−0.231905	−0.115953	+	0.993255i	$0.536992\pi$
$72$	−1.21432	−0.143109
$73$	8.10171	0.948233	0.474117	−	0.880462i	$-0.342767\pi$
$73$	8.10171	0.948233	0.474117	+	0.880462i	$0.342767\pi$
$74$	−3.37778	−0.392659
$75$	1.00000	0.115470
$76$	4.99063	0.572465
$77$	12.8573	1.46522
$78$	0.755569	0.0855513
$79$	4.99063	0.561490	0.280745	−	0.959782i	$-0.409418\pi$
$79$	4.99063	0.561490	0.280745	+	0.959782i	$0.409418\pi$
$80$	6.85728	0.766667
$81$	1.00000	0.111111
$82$	1.57136	0.173528
$83$	−11.6128	−1.27468	−0.637338	−	0.770585i	$-0.719964\pi$
$83$	−11.6128	−1.27468	−0.637338	+	0.770585i	$0.719964\pi$
$84$	8.42864	0.919640
$85$	12.5620	1.36254
$86$	0.0414872	0.00447368
$87$	−3.52543	−0.377966
$88$	−3.52543	−0.375812
$89$	−12.3827	−1.31256	−0.656282	−	0.754516i	$-0.727872\pi$
$89$	−12.3827	−1.31256	−0.656282	+	0.754516i	$0.727872\pi$
$90$	0.622216	0.0655873
$91$	−10.7556	−1.12749
$92$	11.3319	1.18143
$93$	7.18421	0.744968
$94$	0.387152	0.0399317
$95$	−5.24443	−0.538067
$96$	−3.49532	−0.356739
$97$	1.57136	0.159547	0.0797737	−	0.996813i	$-0.474580\pi$
$97$	1.57136	0.159547	0.0797737	+	0.996813i	$0.474580\pi$
$98$	3.92396	0.396379
$99$	2.90321	0.291784
$100$	1.90321	0.190321
$101$	−0.0874201	−0.00869863	−0.00434931	−	0.999991i	$-0.501384\pi$
$101$	−0.0874201	−0.00869863	−0.00434931	+	0.999991i	$0.501384\pi$
$102$	−1.95407	−0.193481
$103$	1.37778	0.135757	0.0678786	−	0.997694i	$-0.478377\pi$
$103$	1.37778	0.135757	0.0678786	+	0.997694i	$0.478377\pi$
$104$	2.94914	0.289187
$105$	−8.85728	−0.864382
$106$	3.29036	0.319588
$107$	−1.24443	−0.120304	−0.0601519	−	0.998189i	$-0.519158\pi$
$107$	−1.24443	−0.120304	−0.0601519	+	0.998189i	$0.519158\pi$
$108$	1.90321	0.183137
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	1.80642	0.172236
$111$	10.8573	1.03053
$112$	15.1842	1.43477
$113$	19.4193	1.82681	0.913406	−	0.407050i	$-0.133443\pi$
$113$	19.4193	1.82681	0.913406	+	0.407050i	$0.133443\pi$
$114$	0.815792	0.0764059
$115$	−11.9081	−1.11044
$116$	−6.70964	−0.622974
$117$	−2.42864	−0.224528
$118$	−4.22077	−0.388554
$119$	27.8163	2.54991
$120$	2.42864	0.221703
$121$	−2.57136	−0.233760
$122$	0.311108	0.0281664
$123$	−5.05086	−0.455420
$124$	13.6731	1.22788
$125$	−12.0000	−1.07331
$126$	1.37778	0.122743
$127$	1.11108	0.0985922	0.0492961	−	0.998784i	$-0.484302\pi$
$127$	1.11108	0.0985922	0.0492961	+	0.998784i	$0.484302\pi$
$128$	−8.78568	−0.776552
$129$	−0.133353	−0.0117411
$130$	−1.51114	−0.132536
$131$	6.36842	0.556411	0.278206	−	0.960522i	$-0.410260\pi$
$131$	6.36842	0.556411	0.278206	+	0.960522i	$0.410260\pi$
$132$	5.52543	0.480927
$133$	−11.6128	−1.00696
$134$	−2.79706	−0.241629
$135$	−2.00000	−0.172133
$136$	−7.62714	−0.654022
$137$	−7.80642	−0.666948	−0.333474	−	0.942759i	$-0.608221\pi$
$137$	−7.80642	−0.666948	−0.333474	+	0.942759i	$0.608221\pi$
$138$	1.85236	0.157683
$139$	15.0923	1.28012	0.640058	−	0.768327i	$-0.278910\pi$
$139$	15.0923	1.28012	0.640058	+	0.768327i	$0.278910\pi$
$140$	−16.8573	−1.42470
$141$	−1.24443	−0.104800
$142$	−0.607926	−0.0510160
$143$	−7.05086	−0.589622
$144$	3.42864	0.285720
$145$	7.05086	0.585542
$146$	2.52051	0.208599
$147$	−12.6128	−1.04029
$148$	20.6637	1.69855
$149$	−13.0509	−1.06917	−0.534584	−	0.845115i	$-0.679532\pi$
$149$	−13.0509	−1.06917	−0.534584	+	0.845115i	$0.679532\pi$
$150$	0.311108	0.0254018
$151$	−15.7462	−1.28141	−0.640704	−	0.767788i	$-0.721357\pi$
$151$	−15.7462	−1.28141	−0.640704	+	0.767788i	$0.721357\pi$
$152$	3.18421	0.258273
$153$	6.28100	0.507788
$154$	4.00000	0.322329
$155$	−14.3684	−1.15410
$156$	−4.62222	−0.370073
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	1.55262	0.123520
$159$	−10.5763	−0.838754
$160$	6.99063	0.552658
$161$	−26.3684	−2.07812
$162$	0.311108	0.0244429
$163$	−7.86665	−0.616163	−0.308082	−	0.951360i	$-0.599687\pi$
$163$	−7.86665	−0.616163	−0.308082	+	0.951360i	$0.599687\pi$
$164$	−9.61285	−0.750637
$165$	−5.80642	−0.452029
$166$	−3.61285	−0.280411
$167$	9.80642	0.758844	0.379422	−	0.925224i	$-0.376123\pi$
$167$	9.80642	0.758844	0.379422	+	0.925224i	$0.376123\pi$
$168$	5.37778	0.414905
$169$	−7.10171	−0.546285
$170$	3.90813	0.299740
$171$	−2.62222	−0.200526
$172$	−0.253799	−0.0193520
$173$	14.1891	1.07878	0.539390	−	0.842056i	$-0.318655\pi$
$173$	14.1891	1.07878	0.539390	+	0.842056i	$0.318655\pi$
$174$	−1.09679	−0.0831473
$175$	−4.42864	−0.334774
$176$	9.95407	0.750316
$177$	13.5669	1.01975
$178$	−3.85236	−0.288746
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−3.80642	−0.283714
$181$	−6.94914	−0.516526	−0.258263	−	0.966075i	$-0.583150\pi$
$181$	−6.94914	−0.516526	−0.258263	+	0.966075i	$0.583150\pi$
$182$	−3.34614	−0.248033
$183$	−1.00000	−0.0739221
$184$	7.23014	0.533013
$185$	−21.7146	−1.59649
$186$	2.23506	0.163883
$187$	18.2351	1.33348
$188$	−2.36842	−0.172735
$189$	−4.42864	−0.322136
$190$	−1.63158	−0.118368
$191$	−13.0049	−0.941003	−0.470502	−	0.882399i	$-0.655927\pi$
$191$	−13.0049	−0.941003	−0.470502	+	0.882399i	$0.655927\pi$
$192$	5.76986	0.416404
$193$	16.1017	1.15903	0.579513	−	0.814963i	$-0.303243\pi$
$193$	16.1017	1.15903	0.579513	+	0.814963i	$0.303243\pi$
$194$	0.488863	0.0350983
$195$	4.85728	0.347837
$196$	−24.0049	−1.71464
$197$	17.2257	1.22728	0.613640	−	0.789586i	$-0.289705\pi$
$197$	17.2257	1.22728	0.613640	+	0.789586i	$0.289705\pi$
$198$	0.903212	0.0641885
$199$	−6.10171	−0.432539	−0.216269	−	0.976334i	$-0.569389\pi$
$199$	−6.10171	−0.432539	−0.216269	+	0.976334i	$0.569389\pi$
$200$	1.21432	0.0858654
$201$	8.99063	0.634150
$202$	−0.0271971	−0.00191358
$203$	15.6128	1.09581
$204$	11.9541	0.836952
$205$	10.1017	0.705534
$206$	0.428639	0.0298647
$207$	−5.95407	−0.413836
$208$	−8.32693	−0.577369
$209$	−7.61285	−0.526592
$210$	−2.75557	−0.190152
$211$	−9.76494	−0.672246	−0.336123	−	0.941818i	$-0.609116\pi$
$211$	−9.76494	−0.672246	−0.336123	+	0.941818i	$0.609116\pi$
$212$	−20.1289	−1.38246
$213$	1.95407	0.133890
$214$	−0.387152	−0.0264652
$215$	0.266706	0.0181892
$216$	1.21432	0.0826240
$217$	−31.8163	−2.15983
$218$	−3.11108	−0.210709
$219$	−8.10171	−0.547463
$220$	−11.0509	−0.745049
$221$	−15.2543	−1.02611
$222$	3.37778	0.226702
$223$	17.9398	1.20134	0.600668	−	0.799498i	$-0.294901\pi$
$223$	17.9398	1.20134	0.600668	+	0.799498i	$0.294901\pi$
$224$	15.4795	1.03427
$225$	−1.00000	−0.0666667
$226$	6.04149	0.401874
$227$	27.1066	1.79913	0.899565	−	0.436787i	$-0.143883\pi$
$227$	27.1066	1.79913	0.899565	+	0.436787i	$0.143883\pi$
$228$	−4.99063	−0.330513
$229$	−8.53035	−0.563701	−0.281851	−	0.959458i	$-0.590948\pi$
$229$	−8.53035	−0.563701	−0.281851	+	0.959458i	$0.590948\pi$
$230$	−3.70471	−0.244282
$231$	−12.8573	−0.845947
$232$	−4.28100	−0.281061
$233$	−19.6084	−1.28459	−0.642295	−	0.766458i	$-0.722017\pi$
$233$	−19.6084	−1.28459	−0.642295	+	0.766458i	$0.722017\pi$
$234$	−0.755569	−0.0493931
$235$	2.48886	0.162355
$236$	25.8207	1.68079
$237$	−4.99063	−0.324176
$238$	8.65386	0.560946
$239$	6.48886	0.419730	0.209865	−	0.977730i	$-0.432698\pi$
$239$	6.48886	0.419730	0.209865	+	0.977730i	$0.432698\pi$
$240$	−6.85728	−0.442635
$241$	6.81579	0.439044	0.219522	−	0.975608i	$-0.429550\pi$
$241$	6.81579	0.439044	0.219522	+	0.975608i	$0.429550\pi$
$242$	−0.799970	−0.0514240
$243$	−1.00000	−0.0641500
$244$	−1.90321	−0.121841
$245$	25.2257	1.61161
$246$	−1.57136	−0.100186
$247$	6.36842	0.405213
$248$	8.72393	0.553970
$249$	11.6128	0.735934
$250$	−3.73329	−0.236114
$251$	12.4429	0.785391	0.392695	−	0.919669i	$-0.371543\pi$
$251$	12.4429	0.785391	0.392695	+	0.919669i	$0.371543\pi$
$252$	−8.42864	−0.530954
$253$	−17.2859	−1.08676
$254$	0.345665	0.0216890
$255$	−12.5620	−0.786662
$256$	8.80642	0.550401
$257$	23.1526	1.44422	0.722109	−	0.691780i	$-0.243173\pi$
$257$	23.1526	1.44422	0.722109	+	0.691780i	$0.243173\pi$
$258$	−0.0414872	−0.00258288
$259$	−48.0830	−2.98773
$260$	9.24443	0.573315
$261$	3.52543	0.218218
$262$	1.98126	0.122403
$263$	2.48886	0.153470	0.0767349	−	0.997052i	$-0.475550\pi$
$263$	2.48886	0.153470	0.0767349	+	0.997052i	$0.475550\pi$
$264$	3.52543	0.216975
$265$	21.1526	1.29939
$266$	−3.61285	−0.221518
$267$	12.3827	0.757809
$268$	17.1111	1.04523
$269$	2.47013	0.150606	0.0753031	−	0.997161i	$-0.476008\pi$
$269$	2.47013	0.150606	0.0753031	+	0.997161i	$0.476008\pi$
$270$	−0.622216	−0.0378668
$271$	31.8163	1.93270	0.966350	−	0.257230i	$-0.0828097\pi$
$271$	31.8163	1.93270	0.966350	+	0.257230i	$0.0828097\pi$
$272$	21.5353	1.30577
$273$	10.7556	0.650957
$274$	−2.42864	−0.146719
$275$	−2.90321	−0.175070
$276$	−11.3319	−0.682097
$277$	23.1526	1.39110	0.695551	−	0.718476i	$-0.255160\pi$
$277$	23.1526	1.39110	0.695551	+	0.718476i	$0.255160\pi$
$278$	4.69535	0.281608
$279$	−7.18421	−0.430107
$280$	−10.7556	−0.642768
$281$	15.4050	0.918984	0.459492	−	0.888182i	$-0.348031\pi$
$281$	15.4050	0.918984	0.459492	+	0.888182i	$0.348031\pi$
$282$	−0.387152	−0.0230546
$283$	16.4701	0.979047	0.489524	−	0.871990i	$-0.337171\pi$
$283$	16.4701	0.979047	0.489524	+	0.871990i	$0.337171\pi$
$284$	3.71900	0.220682
$285$	5.24443	0.310653
$286$	−2.19358	−0.129709
$287$	22.3684	1.32037
$288$	3.49532	0.205963
$289$	22.4509	1.32064
$290$	2.19358	0.128811
$291$	−1.57136	−0.0921148
$292$	−15.4193	−0.902345
$293$	−13.0509	−0.762439	−0.381220	−	0.924485i	$-0.624496\pi$
$293$	−13.0509	−0.762439	−0.381220	+	0.924485i	$0.624496\pi$
$294$	−3.92396	−0.228850
$295$	−27.1338	−1.57979
$296$	13.1842	0.766317
$297$	−2.90321	−0.168461
$298$	−4.06022	−0.235202
$299$	14.4603	0.836260
$300$	−1.90321	−0.109882
$301$	0.590573	0.0340400
$302$	−4.89877	−0.281892
$303$	0.0874201	0.00502216
$304$	−8.99063	−0.515648
$305$	2.00000	0.114520
$306$	1.95407	0.111707
$307$	−24.7239	−1.41107	−0.705534	−	0.708676i	$-0.749293\pi$
$307$	−24.7239	−1.41107	−0.705534	+	0.708676i	$0.749293\pi$
$308$	−24.4701	−1.39431
$309$	−1.37778	−0.0783794
$310$	−4.47013	−0.253886
$311$	−16.7096	−0.947517	−0.473758	−	0.880655i	$-0.657103\pi$
$311$	−16.7096	−0.947517	−0.473758	+	0.880655i	$0.657103\pi$
$312$	−2.94914	−0.166962
$313$	26.8573	1.51806	0.759032	−	0.651054i	$-0.225673\pi$
$313$	26.8573	1.51806	0.759032	+	0.651054i	$0.225673\pi$
$314$	1.86665	0.105341
$315$	8.85728	0.499051
$316$	−9.49823	−0.534317
$317$	−34.1748	−1.91945	−0.959725	−	0.280941i	$-0.909354\pi$
$317$	−34.1748	−1.91945	−0.959725	+	0.280941i	$0.909354\pi$
$318$	−3.29036	−0.184514
$319$	10.2351	0.573054
$320$	−11.5397	−0.645090
$321$	1.24443	0.0694574
$322$	−8.20342	−0.457159
$323$	−16.4701	−0.916422
$324$	−1.90321	−0.105734
$325$	2.42864	0.134717
$326$	−2.44738	−0.135548
$327$	10.0000	0.553001
$328$	−6.13335	−0.338658
$329$	5.51114	0.303839
$330$	−1.80642	−0.0994404
$331$	−25.5526	−1.40450	−0.702250	−	0.711931i	$-0.747821\pi$
$331$	−25.5526	−1.40450	−0.702250	+	0.711931i	$0.747821\pi$
$332$	22.1017	1.21299
$333$	−10.8573	−0.594975
$334$	3.05086	0.166935
$335$	−17.9813	−0.982421
$336$	−15.1842	−0.828366
$337$	−3.80642	−0.207349	−0.103675	−	0.994611i	$-0.533060\pi$
$337$	−3.80642	−0.207349	−0.103675	+	0.994611i	$0.533060\pi$
$338$	−2.20940	−0.120175
$339$	−19.4193	−1.05471
$340$	−23.9081	−1.29660
$341$	−20.8573	−1.12948
$342$	−0.815792	−0.0441130
$343$	24.8573	1.34217
$344$	−0.161933	−0.00873086
$345$	11.9081	0.641112
$346$	4.41435	0.237317
$347$	18.6637	1.00192	0.500960	−	0.865470i	$-0.332980\pi$
$347$	18.6637	1.00192	0.500960	+	0.865470i	$0.332980\pi$
$348$	6.70964	0.359674
$349$	22.8573	1.22352	0.611761	−	0.791043i	$-0.290461\pi$
$349$	22.8573	1.22352	0.611761	+	0.791043i	$0.290461\pi$
$350$	−1.37778	−0.0736457
$351$	2.42864	0.129631
$352$	10.1476	0.540871
$353$	7.12399	0.379171	0.189586	−	0.981864i	$-0.439286\pi$
$353$	7.12399	0.379171	0.189586	+	0.981864i	$0.439286\pi$
$354$	4.22077	0.224332
$355$	−3.90813	−0.207422
$356$	23.5669	1.24904
$357$	−27.8163	−1.47219
$358$	0	0
$359$	13.1798	0.695601	0.347801	−	0.937569i	$-0.386929\pi$
$359$	13.1798	0.695601	0.347801	+	0.937569i	$0.386929\pi$
$360$	−2.42864	−0.128001
$361$	−12.1240	−0.638104
$362$	−2.16193	−0.113629
$363$	2.57136	0.134961
$364$	20.4701	1.07293
$365$	16.2034	0.848126
$366$	−0.311108	−0.0162619
$367$	7.74620	0.404348	0.202174	−	0.979350i	$-0.435199\pi$
$367$	7.74620	0.404348	0.202174	+	0.979350i	$0.435199\pi$
$368$	−20.4143	−1.06417
$369$	5.05086	0.262937
$370$	−6.75557	−0.351205
$371$	46.8385	2.43174
$372$	−13.6731	−0.708916
$373$	−21.6128	−1.11907	−0.559535	−	0.828806i	$-0.689020\pi$
$373$	−21.6128	−1.11907	−0.559535	+	0.828806i	$0.689020\pi$
$374$	5.67307	0.293348
$375$	12.0000	0.619677
$376$	−1.51114	−0.0779310
$377$	−8.56199	−0.440965
$378$	−1.37778	−0.0708656
$379$	−5.89829	−0.302975	−0.151487	−	0.988459i	$-0.548406\pi$
$379$	−5.89829	−0.302975	−0.151487	+	0.988459i	$0.548406\pi$
$380$	9.98126	0.512028
$381$	−1.11108	−0.0569223
$382$	−4.04593	−0.207008
$383$	−16.6178	−0.849128	−0.424564	−	0.905398i	$-0.639573\pi$
$383$	−16.6178	−0.849128	−0.424564	+	0.905398i	$0.639573\pi$
$384$	8.78568	0.448342
$385$	25.7146	1.31054
$386$	5.00937	0.254970
$387$	0.133353	0.00677872
$388$	−2.99063	−0.151826
$389$	−35.3131	−1.79045	−0.895223	−	0.445618i	$-0.852984\pi$
$389$	−35.3131	−1.79045	−0.895223	+	0.445618i	$0.852984\pi$
$390$	1.51114	0.0765194
$391$	−37.3975	−1.89127
$392$	−15.3160	−0.773576
$393$	−6.36842	−0.321244
$394$	5.35905	0.269985
$395$	9.98126	0.502212
$396$	−5.52543	−0.277663
$397$	1.34614	0.0675609	0.0337805	−	0.999429i	$-0.489245\pi$
$397$	1.34614	0.0675609	0.0337805	+	0.999429i	$0.489245\pi$
$398$	−1.89829	−0.0951527
$399$	11.6128	0.581370
$400$	−3.42864	−0.171432
$401$	7.25872	0.362483	0.181242	−	0.983439i	$-0.441988\pi$
$401$	7.25872	0.362483	0.181242	+	0.983439i	$0.441988\pi$
$402$	2.79706	0.139504
$403$	17.4479	0.869139
$404$	0.166379	0.00827767
$405$	2.00000	0.0993808
$406$	4.85728	0.241063
$407$	−31.5210	−1.56244
$408$	7.62714	0.377600
$409$	−20.3970	−1.00857	−0.504283	−	0.863538i	$-0.668243\pi$
$409$	−20.3970	−1.00857	−0.504283	+	0.863538i	$0.668243\pi$
$410$	3.14272	0.155208
$411$	7.80642	0.385062
$412$	−2.62222	−0.129187
$413$	−60.0830	−2.95649
$414$	−1.85236	−0.0910384
$415$	−23.2257	−1.14010
$416$	−8.48886	−0.416201
$417$	−15.0923	−0.739075
$418$	−2.36842	−0.115843
$419$	27.7605	1.35619	0.678094	−	0.734975i	$-0.262806\pi$
$419$	27.7605	1.35619	0.678094	+	0.734975i	$0.262806\pi$
$420$	16.8573	0.822551
$421$	12.0731	0.588408	0.294204	−	0.955743i	$-0.404945\pi$
$421$	12.0731	0.588408	0.294204	+	0.955743i	$0.404945\pi$
$422$	−3.03795	−0.147885
$423$	1.24443	0.0605063
$424$	−12.8430	−0.623711
$425$	−6.28100	−0.304673
$426$	0.607926	0.0294541
$427$	4.42864	0.214317
$428$	2.36842	0.114482
$429$	7.05086	0.340418
$430$	0.0829744	0.00400138
$431$	1.63158	0.0785906	0.0392953	−	0.999228i	$-0.487489\pi$
$431$	1.63158	0.0785906	0.0392953	+	0.999228i	$0.487489\pi$
$432$	−3.42864	−0.164960
$433$	38.4701	1.84876	0.924378	−	0.381477i	$-0.124585\pi$
$433$	38.4701	1.84876	0.924378	+	0.381477i	$0.124585\pi$
$434$	−9.89829	−0.475133
$435$	−7.05086	−0.338063
$436$	19.0321	0.911473
$437$	15.6128	0.746864
$438$	−2.52051	−0.120434
$439$	−9.12399	−0.435464	−0.217732	−	0.976009i	$-0.569866\pi$
$439$	−9.12399	−0.435464	−0.217732	+	0.976009i	$0.569866\pi$
$440$	−7.05086	−0.336136
$441$	12.6128	0.600612
$442$	−4.74572	−0.225731
$443$	−23.9911	−1.13985	−0.569926	−	0.821696i	$-0.693028\pi$
$443$	−23.9911	−1.13985	−0.569926	+	0.821696i	$0.693028\pi$
$444$	−20.6637	−0.980656
$445$	−24.7654	−1.17399
$446$	5.58120	0.264278
$447$	13.0509	0.617284
$448$	−25.5526	−1.20725
$449$	24.0098	1.13309	0.566547	−	0.824029i	$-0.308279\pi$
$449$	24.0098	1.13309	0.566547	+	0.824029i	$0.308279\pi$
$450$	−0.311108	−0.0146658
$451$	14.6637	0.690487
$452$	−36.9590	−1.73840
$453$	15.7462	0.739821
$454$	8.43309	0.395784
$455$	−21.5111	−1.00846
$456$	−3.18421	−0.149114
$457$	25.5210	1.19382	0.596911	−	0.802308i	$-0.296395\pi$
$457$	25.5210	1.19382	0.596911	+	0.802308i	$0.296395\pi$
$458$	−2.65386	−0.124007
$459$	−6.28100	−0.293172
$460$	22.6637	1.05670
$461$	−12.5807	−0.585943	−0.292971	−	0.956121i	$-0.594644\pi$
$461$	−12.5807	−0.585943	−0.292971	+	0.956121i	$0.594644\pi$
$462$	−4.00000	−0.186097
$463$	−9.64449	−0.448217	−0.224109	−	0.974564i	$-0.571947\pi$
$463$	−9.64449	−0.448217	−0.224109	+	0.974564i	$0.571947\pi$
$464$	12.0874	0.561144
$465$	14.3684	0.666319
$466$	−6.10033	−0.282592
$467$	6.99508	0.323694	0.161847	−	0.986816i	$-0.448255\pi$
$467$	6.99508	0.323694	0.161847	+	0.986816i	$0.448255\pi$
$468$	4.62222	0.213662
$469$	−39.8163	−1.83854
$470$	0.774305	0.0357160
$471$	−6.00000	−0.276465
$472$	16.4746	0.758304
$473$	0.387152	0.0178013
$474$	−1.55262	−0.0713144
$475$	2.62222	0.120316
$476$	−52.9403	−2.42651
$477$	10.5763	0.484255
$478$	2.01874	0.0923348
$479$	22.2766	1.01784	0.508921	−	0.860813i	$-0.330045\pi$
$479$	22.2766	1.01784	0.508921	+	0.860813i	$0.330045\pi$
$480$	−6.99063	−0.319077
$481$	26.3684	1.20230
$482$	2.12045	0.0965837
$483$	26.3684	1.19980
$484$	4.89384	0.222447
$485$	3.14272	0.142704
$486$	−0.311108	−0.0141121
$487$	2.48886	0.112781	0.0563906	−	0.998409i	$-0.482041\pi$
$487$	2.48886	0.112781	0.0563906	+	0.998409i	$0.482041\pi$
$488$	−1.21432	−0.0549697
$489$	7.86665	0.355742
$490$	7.84791	0.354532
$491$	6.84743	0.309020	0.154510	−	0.987991i	$-0.450620\pi$
$491$	6.84743	0.309020	0.154510	+	0.987991i	$0.450620\pi$
$492$	9.61285	0.433381
$493$	22.1432	0.997279
$494$	1.98126	0.0891413
$495$	5.80642	0.260979
$496$	−24.6321	−1.10601
$497$	−8.65386	−0.388179
$498$	3.61285	0.161896
$499$	−34.6222	−1.54990	−0.774952	−	0.632021i	$-0.782226\pi$
$499$	−34.6222	−1.54990	−0.774952	+	0.632021i	$0.782226\pi$
$500$	22.8385	1.02137
$501$	−9.80642	−0.438119
$502$	3.87109	0.172775
$503$	7.87955	0.351332	0.175666	−	0.984450i	$-0.443792\pi$
$503$	7.87955	0.351332	0.175666	+	0.984450i	$0.443792\pi$
$504$	−5.37778	−0.239546
$505$	−0.174840	−0.00778029
$506$	−5.37778	−0.239072
$507$	7.10171	0.315398
$508$	−2.11462	−0.0938210
$509$	1.80198	0.0798713	0.0399356	−	0.999202i	$-0.487285\pi$
$509$	1.80198	0.0798713	0.0399356	+	0.999202i	$0.487285\pi$
$510$	−3.90813	−0.173055
$511$	35.8796	1.58722
$512$	20.3111	0.897633
$513$	2.62222	0.115774
$514$	7.20294	0.317708
$515$	2.75557	0.121425
$516$	0.253799	0.0111729
$517$	3.61285	0.158893
$518$	−14.9590	−0.657260
$519$	−14.1891	−0.622834
$520$	5.89829	0.258657
$521$	12.3541	0.541244	0.270622	−	0.962686i	$-0.412771\pi$
$521$	12.3541	0.541244	0.270622	+	0.962686i	$0.412771\pi$
$522$	1.09679	0.0480051
$523$	18.3269	0.801381	0.400690	−	0.916214i	$-0.368770\pi$
$523$	18.3269	0.801381	0.400690	+	0.916214i	$0.368770\pi$
$524$	−12.1204	−0.529484
$525$	4.42864	0.193282
$526$	0.774305	0.0337613
$527$	−45.1240	−1.96563
$528$	−9.95407	−0.433195
$529$	12.4509	0.541344
$530$	6.58073	0.285849
$531$	−13.5669	−0.588754
$532$	22.1017	0.958231
$533$	−12.2667	−0.531330
$534$	3.85236	0.166708
$535$	−2.48886	−0.107603
$536$	10.9175	0.471564
$537$	0	0
$538$	0.768476	0.0331313
$539$	36.6178	1.57724
$540$	3.80642	0.163802
$541$	−25.2543	−1.08577	−0.542883	−	0.839808i	$-0.682667\pi$
$541$	−25.2543	−1.08577	−0.542883	+	0.839808i	$0.682667\pi$
$542$	9.89829	0.425168
$543$	6.94914	0.298216
$544$	21.9541	0.941273
$545$	−20.0000	−0.856706
$546$	3.34614	0.143202
$547$	−4.54909	−0.194505	−0.0972524	−	0.995260i	$-0.531005\pi$
$547$	−4.54909	−0.194505	−0.0972524	+	0.995260i	$0.531005\pi$
$548$	14.8573	0.634672
$549$	1.00000	0.0426790
$550$	−0.903212	−0.0385131
$551$	−9.24443	−0.393826
$552$	−7.23014	−0.307735
$553$	22.1017	0.939860
$554$	7.20294	0.306024
$555$	21.7146	0.921732
$556$	−28.7239	−1.21817
$557$	16.8528	0.714077	0.357039	−	0.934090i	$-0.383786\pi$
$557$	16.8528	0.714077	0.357039	+	0.934090i	$0.383786\pi$
$558$	−2.23506	−0.0946178
$559$	−0.323867	−0.0136981
$560$	30.3684	1.28330
$561$	−18.2351	−0.769885
$562$	4.79261	0.202164
$563$	−21.1240	−0.890270	−0.445135	−	0.895464i	$-0.646844\pi$
$563$	−21.1240	−0.890270	−0.445135	+	0.895464i	$0.646844\pi$
$564$	2.36842	0.0997283
$565$	38.8385	1.63395
$566$	5.12399	0.215377
$567$	4.42864	0.185985
$568$	2.37286	0.0995631
$569$	6.56199	0.275093	0.137547	−	0.990495i	$-0.456078\pi$
$569$	6.56199	0.275093	0.137547	+	0.990495i	$0.456078\pi$
$570$	1.63158	0.0683395
$571$	13.3778	0.559843	0.279921	−	0.960023i	$-0.409692\pi$
$571$	13.3778	0.559843	0.279921	+	0.960023i	$0.409692\pi$
$572$	13.4193	0.561088
$573$	13.0049	0.543288
$574$	6.95899	0.290463
$575$	5.95407	0.248302
$576$	−5.76986	−0.240411
$577$	−35.9180	−1.49529	−0.747643	−	0.664101i	$-0.768814\pi$
$577$	−35.9180	−1.49529	−0.747643	+	0.664101i	$0.768814\pi$
$578$	6.98465	0.290523
$579$	−16.1017	−0.669164
$580$	−13.4193	−0.557205
$581$	−51.4291	−2.13364
$582$	−0.488863	−0.0202640
$583$	30.7052	1.27168
$584$	−9.83807	−0.407102
$585$	−4.85728	−0.200824
$586$	−4.06022	−0.167726
$587$	33.0968	1.36605	0.683025	−	0.730395i	$-0.260664\pi$
$587$	33.0968	1.36605	0.683025	+	0.730395i	$0.260664\pi$
$588$	24.0049	0.989946
$589$	18.8385	0.776229
$590$	−8.44155	−0.347533
$591$	−17.2257	−0.708570
$592$	−37.2257	−1.52997
$593$	16.9161	0.694662	0.347331	−	0.937743i	$-0.387088\pi$
$593$	16.9161	0.694662	0.347331	+	0.937743i	$0.387088\pi$
$594$	−0.903212	−0.0370592
$595$	55.6325	2.28071
$596$	24.8385	1.01743
$597$	6.10171	0.249726
$598$	4.49871	0.183966
$599$	42.3323	1.72965	0.864826	−	0.502072i	$-0.167429\pi$
$599$	42.3323	1.72965	0.864826	+	0.502072i	$0.167429\pi$
$600$	−1.21432	−0.0495744
$601$	−38.7783	−1.58180	−0.790900	−	0.611945i	$-0.790387\pi$
$601$	−38.7783	−1.58180	−0.790900	+	0.611945i	$0.790387\pi$
$602$	0.183732	0.00748835
$603$	−8.99063	−0.366127
$604$	29.9684	1.21940
$605$	−5.14272	−0.209081
$606$	0.0271971	0.00110481
$607$	9.63158	0.390934	0.195467	−	0.980710i	$-0.437378\pi$
$607$	9.63158	0.390934	0.195467	+	0.980710i	$0.437378\pi$
$608$	−9.16547	−0.371709
$609$	−15.6128	−0.632665
$610$	0.622216	0.0251928
$611$	−3.02227	−0.122268
$612$	−11.9541	−0.483215
$613$	−40.6133	−1.64036	−0.820178	−	0.572108i	$-0.806126\pi$
$613$	−40.6133	−1.64036	−0.820178	+	0.572108i	$0.806126\pi$
$614$	−7.69181	−0.310416
$615$	−10.1017	−0.407340
$616$	−15.6128	−0.629060
$617$	−41.1195	−1.65541	−0.827705	−	0.561163i	$-0.810354\pi$
$617$	−41.1195	−1.65541	−0.827705	+	0.561163i	$0.810354\pi$
$618$	−0.428639	−0.0172424
$619$	−28.3368	−1.13895	−0.569476	−	0.822008i	$-0.692854\pi$
$619$	−28.3368	−1.13895	−0.569476	+	0.822008i	$0.692854\pi$
$620$	27.3461	1.09825
$621$	5.95407	0.238928
$622$	−5.19850	−0.208441
$623$	−54.8385	−2.19706
$624$	8.32693	0.333344
$625$	−19.0000	−0.760000
$626$	8.35551	0.333953
$627$	7.61285	0.304028
$628$	−11.4193	−0.455679
$629$	−68.1945	−2.71909
$630$	2.75557	0.109784
$631$	6.06022	0.241254	0.120627	−	0.992698i	$-0.461510\pi$
$631$	6.06022	0.241254	0.120627	+	0.992698i	$0.461510\pi$
$632$	−6.06022	−0.241063
$633$	9.76494	0.388121
$634$	−10.6321	−0.422253
$635$	2.22216	0.0881836
$636$	20.1289	0.798163
$637$	−30.6321	−1.21369
$638$	3.18421	0.126064
$639$	−1.95407	−0.0773017
$640$	−17.5714	−0.694569
$641$	9.12843	0.360551	0.180276	−	0.983616i	$-0.442301\pi$
$641$	9.12843	0.360551	0.180276	+	0.983616i	$0.442301\pi$
$642$	0.387152	0.0152797
$643$	10.3269	0.407254	0.203627	−	0.979049i	$-0.434727\pi$
$643$	10.3269	0.407254	0.203627	+	0.979049i	$0.434727\pi$
$644$	50.1847	1.97755
$645$	−0.266706	−0.0105015
$646$	−5.12399	−0.201600
$647$	−26.3323	−1.03523	−0.517615	−	0.855613i	$-0.673180\pi$
$647$	−26.3323	−1.03523	−0.517615	+	0.855613i	$0.673180\pi$
$648$	−1.21432	−0.0477030
$649$	−39.3876	−1.54610
$650$	0.755569	0.0296358
$651$	31.8163	1.24698
$652$	14.9719	0.586345
$653$	43.1294	1.68778	0.843892	−	0.536514i	$-0.180259\pi$
$653$	43.1294	1.68778	0.843892	+	0.536514i	$0.180259\pi$
$654$	3.11108	0.121653
$655$	12.7368	0.497669
$656$	17.3176	0.676137
$657$	8.10171	0.316078
$658$	1.71456	0.0668404
$659$	−18.1017	−0.705143	−0.352571	−	0.935785i	$-0.614693\pi$
$659$	−18.1017	−0.705143	−0.352571	+	0.935785i	$0.614693\pi$
$660$	11.0509	0.430154
$661$	8.83854	0.343779	0.171890	−	0.985116i	$-0.445013\pi$
$661$	8.83854	0.343779	0.171890	+	0.985116i	$0.445013\pi$
$662$	−7.94962	−0.308971
$663$	15.2543	0.592427
$664$	14.1017	0.547252
$665$	−23.2257	−0.900654
$666$	−3.37778	−0.130886
$667$	−20.9906	−0.812761
$668$	−18.6637	−0.722120
$669$	−17.9398	−0.693592
$670$	−5.59411	−0.216119
$671$	2.90321	0.112077
$672$	−15.4795	−0.597134
$673$	−6.26671	−0.241564	−0.120782	−	0.992679i	$-0.538540\pi$
$673$	−6.26671	−0.241564	−0.120782	+	0.992679i	$0.538540\pi$
$674$	−1.18421	−0.0456140
$675$	1.00000	0.0384900
$676$	13.5161	0.519848
$677$	−32.0874	−1.23322	−0.616610	−	0.787269i	$-0.711494\pi$
$677$	−32.0874	−1.23322	−0.616610	+	0.787269i	$0.711494\pi$
$678$	−6.04149	−0.232022
$679$	6.95899	0.267061
$680$	−15.2543	−0.584975
$681$	−27.1066	−1.03873
$682$	−6.48886	−0.248471
$683$	−13.1526	−0.503269	−0.251634	−	0.967822i	$-0.580968\pi$
$683$	−13.1526	−0.503269	−0.251634	+	0.967822i	$0.580968\pi$
$684$	4.99063	0.190822
$685$	−15.6128	−0.596536
$686$	7.73329	0.295259
$687$	8.53035	0.325453
$688$	0.457220	0.0174313
$689$	−25.6860	−0.978558
$690$	3.70471	0.141036
$691$	16.9906	0.646354	0.323177	−	0.946339i	$-0.395249\pi$
$691$	16.9906	0.646354	0.323177	+	0.946339i	$0.395249\pi$
$692$	−27.0049	−1.02657
$693$	12.8573	0.488408
$694$	5.80642	0.220409
$695$	30.1847	1.14497
$696$	4.28100	0.162271
$697$	31.7244	1.20165
$698$	7.11108	0.269158
$699$	19.6084	0.741658
$700$	8.42864	0.318573
$701$	21.0651	0.795620	0.397810	−	0.917468i	$-0.369770\pi$
$701$	21.0651	0.795620	0.397810	+	0.917468i	$0.369770\pi$
$702$	0.755569	0.0285171
$703$	28.4701	1.07377
$704$	−16.7511	−0.631332
$705$	−2.48886	−0.0937360
$706$	2.21633	0.0834126
$707$	−0.387152	−0.0145604
$708$	−25.8207	−0.970402
$709$	14.8859	0.559050	0.279525	−	0.960138i	$-0.409823\pi$
$709$	14.8859	0.559050	0.279525	+	0.960138i	$0.409823\pi$
$710$	−1.21585	−0.0456301
$711$	4.99063	0.187163
$712$	15.0366	0.563519
$713$	42.7753	1.60195
$714$	−8.65386	−0.323863
$715$	−14.1017	−0.527374
$716$	0	0
$717$	−6.48886	−0.242331
$718$	4.10033	0.153023
$719$	−17.4479	−0.650695	−0.325348	−	0.945595i	$-0.605481\pi$
$719$	−17.4479	−0.650695	−0.325348	+	0.945595i	$0.605481\pi$
$720$	6.85728	0.255556
$721$	6.10171	0.227240
$722$	−3.77187	−0.140374
$723$	−6.81579	−0.253482
$724$	13.2257	0.491529
$725$	−3.52543	−0.130931
$726$	0.799970	0.0296897
$727$	20.4572	0.758716	0.379358	−	0.925250i	$-0.376145\pi$
$727$	20.4572	0.758716	0.379358	+	0.925250i	$0.376145\pi$
$728$	13.0607	0.484062
$729$	1.00000	0.0370370
$730$	5.04101	0.186576
$731$	0.837590	0.0309794
$732$	1.90321	0.0703447
$733$	−48.4514	−1.78959	−0.894796	−	0.446474i	$-0.852679\pi$
$733$	−48.4514	−1.78959	−0.894796	+	0.446474i	$0.852679\pi$
$734$	2.40990	0.0889512
$735$	−25.2257	−0.930464
$736$	−20.8113	−0.767116
$737$	−26.1017	−0.961469
$738$	1.57136	0.0578426
$739$	−20.3368	−0.748100	−0.374050	−	0.927408i	$-0.622031\pi$
$739$	−20.3368	−0.748100	−0.374050	+	0.927408i	$0.622031\pi$
$740$	41.3274	1.51923
$741$	−6.36842	−0.233950
$742$	14.5718	0.534949
$743$	−5.65878	−0.207601	−0.103800	−	0.994598i	$-0.533100\pi$
$743$	−5.65878	−0.207601	−0.103800	+	0.994598i	$0.533100\pi$
$744$	−8.72393	−0.319835
$745$	−26.1017	−0.956293
$746$	−6.72393	−0.246180
$747$	−11.6128	−0.424892
$748$	−34.7052	−1.26895
$749$	−5.51114	−0.201373
$750$	3.73329	0.136321
$751$	−10.4889	−0.382744	−0.191372	−	0.981518i	$-0.561294\pi$
$751$	−10.4889	−0.382744	−0.191372	+	0.981518i	$0.561294\pi$
$752$	4.26671	0.155591
$753$	−12.4429	−0.453446
$754$	−2.66370	−0.0970063
$755$	−31.4924	−1.14613
$756$	8.42864	0.306547
$757$	13.2257	0.480696	0.240348	−	0.970687i	$-0.422738\pi$
$757$	13.2257	0.480696	0.240348	+	0.970687i	$0.422738\pi$
$758$	−1.83500	−0.0666503
$759$	17.2859	0.627439
$760$	6.36842	0.231007
$761$	8.74128	0.316871	0.158436	−	0.987369i	$-0.449355\pi$
$761$	8.74128	0.316871	0.158436	+	0.987369i	$0.449355\pi$
$762$	−0.345665	−0.0125221
$763$	−44.2864	−1.60328
$764$	24.7511	0.895464
$765$	12.5620	0.454180
$766$	−5.16992	−0.186797
$767$	32.9491	1.18972
$768$	−8.80642	−0.317774
$769$	−13.4924	−0.486548	−0.243274	−	0.969958i	$-0.578221\pi$
$769$	−13.4924	−0.486548	−0.243274	+	0.969958i	$0.578221\pi$
$770$	8.00000	0.288300
$771$	−23.1526	−0.833819
$772$	−30.6450	−1.10294
$773$	12.9304	0.465074	0.232537	−	0.972587i	$-0.425297\pi$
$773$	12.9304	0.465074	0.232537	+	0.972587i	$0.425297\pi$
$774$	0.0414872	0.00149123
$775$	7.18421	0.258064
$776$	−1.90813	−0.0684980
$777$	48.0830	1.72497
$778$	−10.9862	−0.393874
$779$	−13.2444	−0.474531
$780$	−9.24443	−0.331004
$781$	−5.67307	−0.202998
$782$	−11.6346	−0.416054
$783$	−3.52543	−0.125989
$784$	43.2449	1.54446
$785$	12.0000	0.428298
$786$	−1.98126	−0.0706694
$787$	10.1432	0.361566	0.180783	−	0.983523i	$-0.442137\pi$
$787$	10.1432	0.361566	0.180783	+	0.983523i	$0.442137\pi$
$788$	−32.7841	−1.16789
$789$	−2.48886	−0.0886059
$790$	3.10525	0.110480
$791$	86.0010	3.05784
$792$	−3.52543	−0.125271
$793$	−2.42864	−0.0862435
$794$	0.418795	0.0148625
$795$	−21.1526	−0.750204
$796$	11.6128	0.411606
$797$	4.75557	0.168451	0.0842254	−	0.996447i	$-0.473158\pi$
$797$	4.75557	0.168451	0.0842254	+	0.996447i	$0.473158\pi$
$798$	3.61285	0.127893
$799$	7.81627	0.276520
$800$	−3.49532	−0.123578
$801$	−12.3827	−0.437521
$802$	2.25824	0.0797414
$803$	23.5210	0.830037
$804$	−17.1111	−0.603461
$805$	−52.7368	−1.85873
$806$	5.42816	0.191199
$807$	−2.47013	−0.0869526
$808$	0.106156	0.00373456
$809$	27.0321	0.950399	0.475199	−	0.879878i	$-0.342376\pi$
$809$	27.0321	0.950399	0.475199	+	0.879878i	$0.342376\pi$
$810$	0.622216	0.0218624
$811$	43.7748	1.53714	0.768570	−	0.639765i	$-0.220969\pi$
$811$	43.7748	1.53714	0.768570	+	0.639765i	$0.220969\pi$
$812$	−29.7146	−1.04278
$813$	−31.8163	−1.11585
$814$	−9.80642	−0.343715
$815$	−15.7333	−0.551113
$816$	−21.5353	−0.753885
$817$	−0.349681	−0.0122338
$818$	−6.34567	−0.221871
$819$	−10.7556	−0.375830
$820$	−19.2257	−0.671390
$821$	−27.3417	−0.954232	−0.477116	−	0.878840i	$-0.658318\pi$
$821$	−27.3417	−0.954232	−0.477116	+	0.878840i	$0.658318\pi$
$822$	2.42864	0.0847085
$823$	−47.8292	−1.66722	−0.833610	−	0.552353i	$-0.813730\pi$
$823$	−47.8292	−1.66722	−0.833610	+	0.552353i	$0.813730\pi$
$824$	−1.67307	−0.0582842
$825$	2.90321	0.101077
$826$	−18.6923	−0.650388
$827$	16.8573	0.586185	0.293093	−	0.956084i	$-0.405316\pi$
$827$	16.8573	0.586185	0.293093	+	0.956084i	$0.405316\pi$
$828$	11.3319	0.393809
$829$	−5.02227	−0.174431	−0.0872154	−	0.996189i	$-0.527797\pi$
$829$	−5.02227	−0.174431	−0.0872154	+	0.996189i	$0.527797\pi$
$830$	−7.22570	−0.250808
$831$	−23.1526	−0.803154
$832$	14.0129	0.485810
$833$	79.2212	2.74485
$834$	−4.69535	−0.162587
$835$	19.6128	0.678731
$836$	14.4889	0.501108
$837$	7.18421	0.248323
$838$	8.63651	0.298343
$839$	−24.8573	−0.858169	−0.429084	−	0.903264i	$-0.641164\pi$
$839$	−24.8573	−0.858169	−0.429084	+	0.903264i	$0.641164\pi$
$840$	10.7556	0.371102
$841$	−16.5714	−0.571426
$842$	3.75605	0.129442
$843$	−15.4050	−0.530576
$844$	18.5847	0.639713
$845$	−14.2034	−0.488613
$846$	0.387152	0.0133106
$847$	−11.3876	−0.391284
$848$	36.2623	1.24525
$849$	−16.4701	−0.565253
$850$	−1.95407	−0.0670239
$851$	64.6450	2.21600
$852$	−3.71900	−0.127411
$853$	0.838543	0.0287112	0.0143556	−	0.999897i	$-0.495430\pi$
$853$	0.838543	0.0287112	0.0143556	+	0.999897i	$0.495430\pi$
$854$	1.37778	0.0471468
$855$	−5.24443	−0.179356
$856$	1.51114	0.0516496
$857$	42.1116	1.43850	0.719252	−	0.694750i	$-0.244485\pi$
$857$	42.1116	1.43850	0.719252	+	0.694750i	$0.244485\pi$
$858$	2.19358	0.0748875
$859$	−5.98126	−0.204078	−0.102039	−	0.994780i	$-0.532537\pi$
$859$	−5.98126	−0.204078	−0.102039	+	0.994780i	$0.532537\pi$
$860$	−0.507598	−0.0173090
$861$	−22.3684	−0.762314
$862$	0.507598	0.0172889
$863$	−23.8796	−0.812869	−0.406435	−	0.913680i	$-0.633228\pi$
$863$	−23.8796	−0.812869	−0.406435	+	0.913680i	$0.633228\pi$
$864$	−3.49532	−0.118913
$865$	28.3783	0.964890
$866$	11.9684	0.406701
$867$	−22.4509	−0.762473
$868$	60.5531	2.05531
$869$	14.4889	0.491501
$870$	−2.19358	−0.0743692
$871$	21.8350	0.739851
$872$	12.1432	0.411221
$873$	1.57136	0.0531825
$874$	4.85728	0.164300
$875$	−53.1437	−1.79658
$876$	15.4193	0.520969
$877$	−13.3461	−0.450667	−0.225334	−	0.974282i	$-0.572347\pi$
$877$	−13.3461	−0.450667	−0.225334	+	0.974282i	$0.572347\pi$
$878$	−2.83854	−0.0957962
$879$	13.0509	0.440194
$880$	19.9081	0.671103
$881$	31.9813	1.07748	0.538738	−	0.842473i	$-0.318901\pi$
$881$	31.9813	1.07748	0.538738	+	0.842473i	$0.318901\pi$
$882$	3.92396	0.132126
$883$	42.9719	1.44612	0.723060	−	0.690786i	$-0.242735\pi$
$883$	42.9719	1.44612	0.723060	+	0.690786i	$0.242735\pi$
$884$	29.0321	0.976456
$885$	27.1338	0.912094
$886$	−7.46382	−0.250752
$887$	−35.9353	−1.20659	−0.603295	−	0.797518i	$-0.706146\pi$
$887$	−35.9353	−1.20659	−0.603295	+	0.797518i	$0.706146\pi$
$888$	−13.1842	−0.442433
$889$	4.92056	0.165030
$890$	−7.70471	−0.258263
$891$	2.90321	0.0972613
$892$	−34.1432	−1.14320
$893$	−3.26317	−0.109198
$894$	4.06022	0.135794
$895$	0	0
$896$	−38.9086	−1.29985
$897$	−14.4603	−0.482815
$898$	7.46965	0.249265
$899$	−25.3274	−0.844716
$900$	1.90321	0.0634404
$901$	66.4296	2.21309
$902$	4.56199	0.151898
$903$	−0.590573	−0.0196530
$904$	−23.5812	−0.784299
$905$	−13.8983	−0.461995
$906$	4.89877	0.162751
$907$	14.5303	0.482472	0.241236	−	0.970466i	$-0.422447\pi$
$907$	14.5303	0.482472	0.241236	+	0.970466i	$0.422447\pi$
$908$	−51.5897	−1.71206
$909$	−0.0874201	−0.00289954
$910$	−6.69228	−0.221847
$911$	59.3087	1.96498	0.982492	−	0.186305i	$-0.0596513\pi$
$911$	59.3087	1.96498	0.982492	+	0.186305i	$0.0596513\pi$
$912$	8.99063	0.297710
$913$	−33.7146	−1.11579
$914$	7.93978	0.262624
$915$	−2.00000	−0.0661180
$916$	16.2351	0.536422
$917$	28.2034	0.931359
$918$	−1.95407	−0.0644938
$919$	−15.8163	−0.521731	−0.260865	−	0.965375i	$-0.584008\pi$
$919$	−15.8163	−0.521731	−0.260865	+	0.965375i	$0.584008\pi$
$920$	14.4603	0.476741
$921$	24.7239	0.814681
$922$	−3.91396	−0.128900
$923$	4.74572	0.156207
$924$	24.4701	0.805008
$925$	10.8573	0.356985
$926$	−3.00048	−0.0986018
$927$	1.37778	0.0452524
$928$	12.3225	0.404505
$929$	−38.9117	−1.27665	−0.638325	−	0.769767i	$-0.720373\pi$
$929$	−38.9117	−1.27665	−0.638325	+	0.769767i	$0.720373\pi$
$930$	4.47013	0.146581
$931$	−33.0736	−1.08394
$932$	37.3189	1.22242
$933$	16.7096	0.547049
$934$	2.17622	0.0712082
$935$	36.4701	1.19270
$936$	2.94914	0.0963958
$937$	12.3269	0.402703	0.201352	−	0.979519i	$-0.435467\pi$
$937$	12.3269	0.402703	0.201352	+	0.979519i	$0.435467\pi$
$938$	−12.3872	−0.404455
$939$	−26.8573	−0.876454
$940$	−4.73683	−0.154498
$941$	−16.2623	−0.530135	−0.265067	−	0.964230i	$-0.585394\pi$
$941$	−16.2623	−0.530135	−0.265067	+	0.964230i	$0.585394\pi$
$942$	−1.86665	−0.0608186
$943$	−30.0731	−0.979316
$944$	−46.5161	−1.51397
$945$	−8.85728	−0.288127
$946$	0.120446	0.00391604
$947$	49.7703	1.61732	0.808659	−	0.588277i	$-0.200194\pi$
$947$	49.7703	1.61732	0.808659	+	0.588277i	$0.200194\pi$
$948$	9.49823	0.308488
$949$	−19.6761	−0.638714
$950$	0.815792	0.0264678
$951$	34.1748	1.10820
$952$	−33.7778	−1.09475
$953$	38.0973	1.23409	0.617046	−	0.786927i	$-0.288329\pi$
$953$	38.0973	1.23409	0.617046	+	0.786927i	$0.288329\pi$
$954$	3.29036	0.106529
$955$	−26.0098	−0.841659
$956$	−12.3497	−0.399417
$957$	−10.2351	−0.330853
$958$	6.93041	0.223911
$959$	−34.5718	−1.11638
$960$	11.5397	0.372443
$961$	20.6128	0.664931
$962$	8.20342	0.264489
$963$	−1.24443	−0.0401012
$964$	−12.9719	−0.417797
$965$	32.2034	1.03666
$966$	8.20342	0.263941
$967$	−2.75557	−0.0886131	−0.0443066	−	0.999018i	$-0.514108\pi$
$967$	−2.75557	−0.0886131	−0.0443066	+	0.999018i	$0.514108\pi$
$968$	3.12245	0.100359
$969$	16.4701	0.529097
$970$	0.977725	0.0313929
$971$	25.7146	0.825219	0.412610	−	0.910908i	$-0.364617\pi$
$971$	25.7146	0.825219	0.412610	+	0.910908i	$0.364617\pi$
$972$	1.90321	0.0610456
$973$	66.8385	2.14275
$974$	0.774305	0.0248103
$975$	−2.42864	−0.0777787
$976$	3.42864	0.109748
$977$	25.1427	0.804387	0.402193	−	0.915555i	$-0.368248\pi$
$977$	25.1427	0.804387	0.402193	+	0.915555i	$0.368248\pi$
$978$	2.44738	0.0782584
$979$	−35.9496	−1.14895
$980$	−48.0098	−1.53362
$981$	−10.0000	−0.319275
$982$	2.13029	0.0679803
$983$	47.2815	1.50804	0.754022	−	0.656849i	$-0.228111\pi$
$983$	47.2815	1.50804	0.754022	+	0.656849i	$0.228111\pi$
$984$	6.13335	0.195524
$985$	34.4514	1.09771
$986$	6.88892	0.219388
$987$	−5.51114	−0.175421
$988$	−12.1204	−0.385603
$989$	−0.793993	−0.0252475
$990$	1.80642	0.0574119
$991$	49.1941	1.56270	0.781350	−	0.624093i	$-0.214531\pi$
$991$	49.1941	1.56270	0.781350	+	0.624093i	$0.214531\pi$
$992$	−25.1111	−0.797278
$993$	25.5526	0.810888
$994$	−2.69228	−0.0853940
$995$	−12.2034	−0.386874
$996$	−22.1017	−0.700319
$997$	4.55215	0.144168	0.0720840	−	0.997399i	$-0.477035\pi$
$997$	4.55215	0.144168	0.0720840	+	0.997399i	$0.477035\pi$
$998$	−10.7712	−0.340958
$999$	10.8573	0.343509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	183.2.a.b.1.2	✓	3
3.2	odd	2		549.2.a.f.1.2		3
4.3	odd	2		2928.2.a.y.1.1		3
5.4	even	2		4575.2.a.j.1.2		3
7.6	odd	2		8967.2.a.s.1.2		3
12.11	even	2		8784.2.a.bk.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.a.b.1.2	✓	3	1.1	even	1	trivial
549.2.a.f.1.2		3	3.2	odd	2
2928.2.a.y.1.1		3	4.3	odd	2
4575.2.a.j.1.2		3	5.4	even	2
8784.2.a.bk.1.1		3	12.11	even	2
8967.2.a.s.1.2		3	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	183.a (trivial)

\(f(q)\)	\(=\)	\(q+0.311108 q^{2} -1.00000 q^{3} -1.90321 q^{4} +2.00000 q^{5} -0.311108 q^{6} +4.42864 q^{7} -1.21432 q^{8} +1.00000 q^{9} +0.622216 q^{10} +2.90321 q^{11} +1.90321 q^{12} -2.42864 q^{13} +1.37778 q^{14} -2.00000 q^{15} +3.42864 q^{16} +6.28100 q^{17} +0.311108 q^{18} -2.62222 q^{19} -3.80642 q^{20} -4.42864 q^{21} +0.903212 q^{22} -5.95407 q^{23} +1.21432 q^{24} -1.00000 q^{25} -0.755569 q^{26} -1.00000 q^{27} -8.42864 q^{28} +3.52543 q^{29} -0.622216 q^{30} -7.18421 q^{31} +3.49532 q^{32} -2.90321 q^{33} +1.95407 q^{34} +8.85728 q^{35} -1.90321 q^{36} -10.8573 q^{37} -0.815792 q^{38} +2.42864 q^{39} -2.42864 q^{40} +5.05086 q^{41} -1.37778 q^{42} +0.133353 q^{43} -5.52543 q^{44} +2.00000 q^{45} -1.85236 q^{46} +1.24443 q^{47} -3.42864 q^{48} +12.6128 q^{49} -0.311108 q^{50} -6.28100 q^{51} +4.62222 q^{52} +10.5763 q^{53} -0.311108 q^{54} +5.80642 q^{55} -5.37778 q^{56} +2.62222 q^{57} +1.09679 q^{58} -13.5669 q^{59} +3.80642 q^{60} +1.00000 q^{61} -2.23506 q^{62} +4.42864 q^{63} -5.76986 q^{64} -4.85728 q^{65} -0.903212 q^{66} -8.99063 q^{67} -11.9541 q^{68} +5.95407 q^{69} +2.75557 q^{70} -1.95407 q^{71} -1.21432 q^{72} +8.10171 q^{73} -3.37778 q^{74} +1.00000 q^{75} +4.99063 q^{76} +12.8573 q^{77} +0.755569 q^{78} +4.99063 q^{79} +6.85728 q^{80} +1.00000 q^{81} +1.57136 q^{82} -11.6128 q^{83} +8.42864 q^{84} +12.5620 q^{85} +0.0414872 q^{86} -3.52543 q^{87} -3.52543 q^{88} -12.3827 q^{89} +0.622216 q^{90} -10.7556 q^{91} +11.3319 q^{92} +7.18421 q^{93} +0.387152 q^{94} -5.24443 q^{95} -3.49532 q^{96} +1.57136 q^{97} +3.92396 q^{98} +2.90321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - q^{6} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 2 q^{11} - q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} - 3 q^{16} + 12 q^{17} + q^{18} - 8 q^{19} + 2 q^{20} - 4 q^{22}+ \cdots + 2 q^{99}+O(q^{100}) \) 3 * q + q^2 - 3 * q^3 + q^4 + 6 * q^5 - q^6 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 2 * q^11 - q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 - 3 * q^16 + 12 * q^17 + q^18 - 8 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 - 3 * q^24 - 3 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 + 4 * q^29 - 2 * q^30 - 8 * q^31 - 3 * q^32 - 2 * q^33 - 14 * q^34 + q^36 - 6 * q^37 - 16 * q^38 - 6 * q^39 + 6 * q^40 + 2 * q^41 - 4 * q^42 - 10 * q^44 + 6 * q^45 - 12 * q^46 + 4 * q^47 + 3 * q^48 + 11 * q^49 - q^50 - 12 * q^51 + 14 * q^52 + 12 * q^53 - q^54 + 4 * q^55 - 16 * q^56 + 8 * q^57 + 10 * q^58 + 6 * q^59 - 2 * q^60 + 3 * q^61 + 20 * q^62 - 11 * q^64 + 12 * q^65 + 4 * q^66 - 16 * q^68 - 2 * q^69 + 8 * q^70 + 14 * q^71 + 3 * q^72 - 2 * q^73 - 10 * q^74 + 3 * q^75 - 12 * q^76 + 12 * q^77 + 2 * q^78 - 12 * q^79 - 6 * q^80 + 3 * q^81 + 18 * q^82 - 8 * q^83 + 12 * q^84 + 24 * q^85 - 40 * q^86 - 4 * q^87 - 4 * q^88 - 4 * q^89 + 2 * q^90 - 32 * q^91 + 14 * q^92 + 8 * q^93 + 28 * q^94 - 16 * q^95 + 3 * q^96 + 18 * q^97 - 15 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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