LMFDB - Embedded newform 187.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(1,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, 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("187.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.33844.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 2x + 2 $ x^4 - x^3 - 6x^2 + 2x + 2
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			1.4
Root			$2.79774$ of defining polynomial
Character	$\chi$	$=$	187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79774 q^{2} -1.08288 q^{3} +5.82737 q^{4} -1.79774 q^{5} -3.02962 q^{6} +10.7080 q^{8} -1.82737 q^{9} +O(q^{10})$	\(q+2.79774 q^{2} -1.08288 q^{3} +5.82737 q^{4} -1.79774 q^{5} -3.02962 q^{6} +10.7080 q^{8} -1.82737 q^{9} -5.02962 q^{10} -1.00000 q^{11} -6.31035 q^{12} -3.74449 q^{13} +1.94674 q^{15} +18.3035 q^{16} +1.00000 q^{17} -5.11251 q^{18} +0.314763 q^{19} -10.4761 q^{20} -2.79774 q^{22} -2.51261 q^{23} -11.5955 q^{24} -1.76812 q^{25} -10.4761 q^{26} +5.22747 q^{27} +5.02962 q^{29} +5.44649 q^{30} -8.42727 q^{31} +29.7925 q^{32} +1.08288 q^{33} +2.79774 q^{34} -10.6487 q^{36} +8.51261 q^{37} +0.880625 q^{38} +4.05483 q^{39} -19.2502 q^{40} +4.16576 q^{41} -7.48897 q^{43} -5.82737 q^{44} +3.28514 q^{45} -7.02962 q^{46} +4.88062 q^{47} -19.8205 q^{48} -7.00000 q^{49} -4.94674 q^{50} -1.08288 q^{51} -21.8205 q^{52} +10.8806 q^{53} +14.6251 q^{54} +1.79774 q^{55} -0.340851 q^{57} +14.0716 q^{58} +6.93388 q^{59} +11.3444 q^{60} +13.1910 q^{61} -23.5773 q^{62} +46.7447 q^{64} +6.73163 q^{65} +3.02962 q^{66} -7.07847 q^{67} +5.82737 q^{68} +2.72085 q^{69} -15.2137 q^{71} -19.5674 q^{72} -0.506613 q^{73} +23.8161 q^{74} +1.91466 q^{75} +1.83424 q^{76} +11.3444 q^{78} +4.05483 q^{79} -32.9050 q^{80} -0.178624 q^{81} +11.6547 q^{82} +10.5614 q^{83} -1.79774 q^{85} -20.9522 q^{86} -5.44649 q^{87} -10.7080 q^{88} -3.14654 q^{89} +9.19097 q^{90} -14.6419 q^{92} +9.12573 q^{93} +13.6547 q^{94} -0.565862 q^{95} -32.2617 q^{96} -4.84413 q^{97} -19.5842 q^{98} +1.82737 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} + 9 q^{8} + 11 q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 + 9 * q^8 + 11 * q^9	$ 4 q + q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} + 9 q^{8} + 11 q^{9} - 12 q^{10} - 4 q^{11} - 2 q^{13} + 5 q^{15} + 19 q^{16} + 4 q^{17} - 7 q^{18} - 2 q^{19} - 6 q^{20} - q^{22} + 5 q^{23} - 26 q^{24} - 5 q^{25} - 6 q^{26} + q^{27} + 12 q^{29} - 6 q^{30} - 17 q^{31} + 39 q^{32} - q^{33} + q^{34} - 25 q^{36} + 19 q^{37} - 12 q^{38} - 22 q^{39} - 20 q^{40} + 6 q^{41} - 4 q^{43} - 5 q^{44} + 18 q^{45} - 20 q^{46} + 4 q^{47} - 32 q^{48} - 28 q^{49} - 17 q^{50} + q^{51} - 40 q^{52} + 28 q^{53} + 30 q^{54} - 3 q^{55} - 16 q^{57} + 15 q^{59} + 34 q^{60} + 12 q^{61} + 6 q^{62} + 35 q^{64} + 4 q^{65} + 4 q^{66} - q^{67} + 5 q^{68} - 13 q^{69} + 17 q^{71} - 25 q^{72} - 6 q^{73} + 26 q^{74} + 6 q^{75} + 18 q^{76} + 34 q^{78} - 22 q^{79} - 38 q^{80} + 10 q^{82} + 8 q^{83} + 3 q^{85} - 12 q^{86} + 6 q^{87} - 9 q^{88} - 13 q^{89} - 4 q^{90} - 12 q^{92} + 31 q^{93} + 18 q^{94} + 10 q^{95} + 16 q^{96} + 17 q^{97} - 7 q^{98} - 11 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 + 9 * q^8 + 11 * q^9 - 12 * q^10 - 4 * q^11 - 2 * q^13 + 5 * q^15 + 19 * q^16 + 4 * q^17 - 7 * q^18 - 2 * q^19 - 6 * q^20 - q^22 + 5 * q^23 - 26 * q^24 - 5 * q^25 - 6 * q^26 + q^27 + 12 * q^29 - 6 * q^30 - 17 * q^31 + 39 * q^32 - q^33 + q^34 - 25 * q^36 + 19 * q^37 - 12 * q^38 - 22 * q^39 - 20 * q^40 + 6 * q^41 - 4 * q^43 - 5 * q^44 + 18 * q^45 - 20 * q^46 + 4 * q^47 - 32 * q^48 - 28 * q^49 - 17 * q^50 + q^51 - 40 * q^52 + 28 * q^53 + 30 * q^54 - 3 * q^55 - 16 * q^57 + 15 * q^59 + 34 * q^60 + 12 * q^61 + 6 * q^62 + 35 * q^64 + 4 * q^65 + 4 * q^66 - q^67 + 5 * q^68 - 13 * q^69 + 17 * q^71 - 25 * q^72 - 6 * q^73 + 26 * q^74 + 6 * q^75 + 18 * q^76 + 34 * q^78 - 22 * q^79 - 38 * q^80 + 10 * q^82 + 8 * q^83 + 3 * q^85 - 12 * q^86 + 6 * q^87 - 9 * q^88 - 13 * q^89 - 4 * q^90 - 12 * q^92 + 31 * q^93 + 18 * q^94 + 10 * q^95 + 16 * q^96 + 17 * q^97 - 7 * q^98 - 11 * 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 $

$2$	2.79774	1.97830	0.989152	−	0.146898i	$-0.0469289\pi$
$2$	2.79774	1.97830	0.989152	+	0.146898i	$0.0469289\pi$
$3$	−1.08288	−0.625202	−0.312601	−	0.949885i	$-0.601200\pi$
$3$	−1.08288	−0.625202	−0.312601	+	0.949885i	$0.601200\pi$
$4$	5.82737	2.91368
$5$	−1.79774	−0.803975	−0.401988	−	0.915645i	$-0.631681\pi$
$5$	−1.79774	−0.803975	−0.401988	+	0.915645i	$0.631681\pi$
$6$	−3.02962	−1.23684
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	10.7080	3.78585
$9$	−1.82737	−0.609123
$10$	−5.02962	−1.59051
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−6.31035	−1.82164
$13$	−3.74449	−1.03853	−0.519267	−	0.854612i	$-0.673795\pi$
$13$	−3.74449	−1.03853	−0.519267	+	0.854612i	$0.673795\pi$
$14$	0	0
$15$	1.94674	0.502647
$16$	18.3035	4.57587
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−5.11251	−1.20503
$19$	0.314763	0.0722115	0.0361057	−	0.999348i	$-0.488505\pi$
$19$	0.314763	0.0722115	0.0361057	+	0.999348i	$0.488505\pi$
$20$	−10.4761	−2.34253
$21$	0	0
$22$	−2.79774	−0.596481
$23$	−2.51261	−0.523914	−0.261957	−	0.965079i	$-0.584368\pi$
$23$	−2.51261	−0.523914	−0.261957	+	0.965079i	$0.584368\pi$
$24$	−11.5955	−2.36692
$25$	−1.76812	−0.353624
$26$	−10.4761	−2.05453
$27$	5.22747	1.00603
$28$	0	0
$29$	5.02962	0.933978	0.466989	−	0.884263i	$-0.345339\pi$
$29$	5.02962	0.933978	0.466989	+	0.884263i	$0.345339\pi$
$30$	5.44649	0.994388
$31$	−8.42727	−1.51358	−0.756791	−	0.653657i	$-0.773234\pi$
$31$	−8.42727	−1.51358	−0.756791	+	0.653657i	$0.773234\pi$
$32$	29.7925	5.26661
$33$	1.08288	0.188505
$34$	2.79774	0.479809
$35$	0	0
$36$	−10.6487	−1.77479
$37$	8.51261	1.39946	0.699732	−	0.714406i	$-0.253303\pi$
$37$	8.51261	1.39946	0.699732	+	0.714406i	$0.253303\pi$
$38$	0.880625	0.142856
$39$	4.05483	0.649293
$40$	−19.2502	−3.04373
$41$	4.16576	0.650583	0.325291	−	0.945614i	$-0.394538\pi$
$41$	4.16576	0.650583	0.325291	+	0.945614i	$0.394538\pi$
$42$	0	0
$43$	−7.48897	−1.14206	−0.571029	−	0.820930i	$-0.693456\pi$
$43$	−7.48897	−1.14206	−0.571029	+	0.820930i	$0.693456\pi$
$44$	−5.82737	−0.878509
$45$	3.28514	0.489719
$46$	−7.02962	−1.03646
$47$	4.88062	0.711912	0.355956	−	0.934503i	$-0.384155\pi$
$47$	4.88062	0.711912	0.355956	+	0.934503i	$0.384155\pi$
$48$	−19.8205	−2.86084
$49$	−7.00000	−1.00000
$50$	−4.94674	−0.699575
$51$	−1.08288	−0.151634
$52$	−21.8205	−3.02596
$53$	10.8806	1.49457	0.747284	−	0.664504i	$-0.231357\pi$
$53$	10.8806	1.49457	0.747284	+	0.664504i	$0.231357\pi$
$54$	14.6251	1.99023
$55$	1.79774	0.242408
$56$	0	0
$57$	−0.340851	−0.0451468
$58$	14.0716	1.84769
$59$	6.93388	0.902715	0.451357	−	0.892343i	$-0.350940\pi$
$59$	6.93388	0.902715	0.451357	+	0.892343i	$0.350940\pi$
$60$	11.3444	1.46455
$61$	13.1910	1.68893	0.844466	−	0.535610i	$-0.179918\pi$
$61$	13.1910	1.68893	0.844466	+	0.535610i	$0.179918\pi$
$62$	−23.5773	−2.99432
$63$	0	0
$64$	46.7447	5.84308
$65$	6.73163	0.834955
$66$	3.02962	0.372921
$67$	−7.07847	−0.864772	−0.432386	−	0.901689i	$-0.642328\pi$
$67$	−7.07847	−0.864772	−0.432386	+	0.901689i	$0.642328\pi$
$68$	5.82737	0.706672
$69$	2.72085	0.327552
$70$	0	0
$71$	−15.2137	−1.80554	−0.902769	−	0.430126i	$-0.858469\pi$
$71$	−15.2137	−1.80554	−0.902769	+	0.430126i	$0.858469\pi$
$72$	−19.5674	−2.30604
$73$	−0.506613	−0.0592946	−0.0296473	−	0.999560i	$-0.509438\pi$
$73$	−0.506613	−0.0592946	−0.0296473	+	0.999560i	$0.509438\pi$
$74$	23.8161	2.76856
$75$	1.91466	0.221086
$76$	1.83424	0.210401
$77$	0	0
$78$	11.3444	1.28450
$79$	4.05483	0.456205	0.228102	−	0.973637i	$-0.426748\pi$
$79$	4.05483	0.456205	0.228102	+	0.973637i	$0.426748\pi$
$80$	−32.9050	−3.67889
$81$	−0.178624	−0.0198471
$82$	11.6547	1.28705
$83$	10.5614	1.15927	0.579635	−	0.814876i	$-0.303195\pi$
$83$	10.5614	1.15927	0.579635	+	0.814876i	$0.303195\pi$
$84$	0	0
$85$	−1.79774	−0.194993
$86$	−20.9522	−2.25934
$87$	−5.44649	−0.583925
$88$	−10.7080	−1.14148
$89$	−3.14654	−0.333533	−0.166767	−	0.985996i	$-0.553333\pi$
$89$	−3.14654	−0.333533	−0.166767	+	0.985996i	$0.553333\pi$
$90$	9.19097	0.968814
$91$	0	0
$92$	−14.6419	−1.52652
$93$	9.12573	0.946294
$94$	13.6547	1.40838
$95$	−0.565862	−0.0580562
$96$	−32.2617	−3.29270
$97$	−4.84413	−0.491847	−0.245923	−	0.969289i	$-0.579091\pi$
$97$	−4.84413	−0.491847	−0.245923	+	0.969289i	$0.579091\pi$
$98$	−19.5842	−1.97830
$99$	1.82737	0.183657
$100$	−10.3035	−1.03035
$101$	−14.1353	−1.40651	−0.703256	−	0.710937i	$-0.748271\pi$
$101$	−14.1353	−1.40651	−0.703256	+	0.710937i	$0.748271\pi$
$102$	−3.02962	−0.299978
$103$	−6.60835	−0.651140	−0.325570	−	0.945518i	$-0.605556\pi$
$103$	−6.60835	−0.651140	−0.325570	+	0.945518i	$0.605556\pi$
$104$	−40.0959	−3.93173
$105$	0	0
$106$	30.4412	2.95671
$107$	−4.97038	−0.480504	−0.240252	−	0.970711i	$-0.577230\pi$
$107$	−4.97038	−0.480504	−0.240252	+	0.970711i	$0.577230\pi$
$108$	30.4624	2.93124
$109$	−0.400099	−0.0383226	−0.0191613	−	0.999816i	$-0.506100\pi$
$109$	−0.400099	−0.0383226	−0.0191613	+	0.999816i	$0.506100\pi$
$110$	5.02962	0.479556
$111$	−9.21814	−0.874947
$112$	0	0
$113$	4.77253	0.448962	0.224481	−	0.974478i	$-0.427931\pi$
$113$	4.77253	0.448962	0.224481	+	0.974478i	$0.427931\pi$
$114$	−0.953612	−0.0893140
$115$	4.51702	0.421214
$116$	29.3095	2.72132
$117$	6.84255	0.632594
$118$	19.3992	1.78584
$119$	0	0
$120$	20.8457	1.90294
$121$	1.00000	0.0909091
$122$	36.9050	3.34122
$123$	−4.51103	−0.406746
$124$	−49.1088	−4.41010
$125$	12.1673	1.08828
$126$	0	0
$127$	−3.47699	−0.308533	−0.154266	−	0.988029i	$-0.549301\pi$
$127$	−3.47699	−0.308533	−0.154266	+	0.988029i	$0.549301\pi$
$128$	71.1947	6.29278
$129$	8.10967	0.714017
$130$	18.8334	1.65179
$131$	−12.2250	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$131$	−12.2250	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$132$	6.31035	0.549245
$133$	0	0
$134$	−19.8037	−1.71078
$135$	−9.39764	−0.808820
$136$	10.7080	0.918203
$137$	0.457770	0.0391100	0.0195550	−	0.999809i	$-0.493775\pi$
$137$	0.457770	0.0391100	0.0195550	+	0.999809i	$0.493775\pi$
$138$	7.61225	0.647998
$139$	−3.43414	−0.291280	−0.145640	−	0.989338i	$-0.546524\pi$
$139$	−3.43414	−0.291280	−0.145640	+	0.989338i	$0.546524\pi$
$140$	0	0
$141$	−5.28514	−0.445089
$142$	−42.5641	−3.57190
$143$	3.74449	0.313130
$144$	−33.4472	−2.78727
$145$	−9.04197	−0.750895
$146$	−1.41737	−0.117303
$147$	7.58017	0.625202
$148$	49.6061	4.07759
$149$	−2.01676	−0.165220	−0.0826098	−	0.996582i	$-0.526326\pi$
$149$	−2.01676	−0.165220	−0.0826098	+	0.996582i	$0.526326\pi$
$150$	5.35674	0.437376
$151$	−15.6242	−1.27148	−0.635741	−	0.771902i	$-0.719305\pi$
$151$	−15.6242	−1.27148	−0.635741	+	0.771902i	$0.719305\pi$
$152$	3.37047	0.273382
$153$	−1.82737	−0.147734
$154$	0	0
$155$	15.1501	1.21688
$156$	23.6290	1.89184
$157$	−0.682782	−0.0544919	−0.0272460	−	0.999629i	$-0.508674\pi$
$157$	−0.682782	−0.0544919	−0.0272460	+	0.999629i	$0.508674\pi$
$158$	11.3444	0.902511
$159$	−11.7824	−0.934407
$160$	−53.5592	−4.23423
$161$	0	0
$162$	−0.499744	−0.0392636
$163$	0.331526	0.0259671	0.0129836	−	0.999916i	$-0.495867\pi$
$163$	0.331526	0.0259671	0.0129836	+	0.999916i	$0.495867\pi$
$164$	24.2754	1.89559
$165$	−1.94674	−0.151554
$166$	29.5482	2.29339
$167$	3.14812	0.243609	0.121804	−	0.992554i	$-0.461132\pi$
$167$	3.14812	0.243609	0.121804	+	0.992554i	$0.461132\pi$
$168$	0	0
$169$	1.02118	0.0785521
$170$	−5.02962	−0.385755
$171$	−0.575187	−0.0439856
$172$	−43.6410	−3.32759
$173$	−3.53624	−0.268855	−0.134428	−	0.990923i	$-0.542920\pi$
$173$	−3.53624	−0.268855	−0.134428	+	0.990923i	$0.542920\pi$
$174$	−15.2379	−1.15518
$175$	0	0
$176$	−18.3035	−1.37968
$177$	−7.50857	−0.564379
$178$	−8.80322	−0.659829
$179$	−10.5674	−0.789848	−0.394924	−	0.918714i	$-0.629229\pi$
$179$	−10.5674	−0.789848	−0.394924	+	0.918714i	$0.629229\pi$
$180$	19.1437	1.42689
$181$	−10.5599	−0.784909	−0.392454	−	0.919771i	$-0.628374\pi$
$181$	−10.5599	−0.784909	−0.392454	+	0.919771i	$0.628374\pi$
$182$	0	0
$183$	−14.2843	−1.05592
$184$	−26.9050	−1.98346
$185$	−15.3035	−1.12513
$186$	25.5315	1.87206
$187$	−1.00000	−0.0731272
$188$	28.4412	2.07429
$189$	0	0
$190$	−1.58314	−0.114853
$191$	11.9330	0.863442	0.431721	−	0.902007i	$-0.357907\pi$
$191$	11.9330	0.863442	0.431721	+	0.902007i	$0.357907\pi$
$192$	−50.6189	−3.65311
$193$	−5.06315	−0.364454	−0.182227	−	0.983257i	$-0.558331\pi$
$193$	−5.06315	−0.364454	−0.182227	+	0.983257i	$0.558331\pi$
$194$	−13.5526	−0.973023
$195$	−7.28955	−0.522016
$196$	−40.7916	−2.91368
$197$	22.7909	1.62378	0.811891	−	0.583809i	$-0.198438\pi$
$197$	22.7909	1.62378	0.811891	+	0.583809i	$0.198438\pi$
$198$	5.11251	0.363330
$199$	15.6075	1.10638	0.553192	−	0.833054i	$-0.313410\pi$
$199$	15.6075	1.10638	0.553192	+	0.833054i	$0.313410\pi$
$200$	−18.9330	−1.33877
$201$	7.66514	0.540657
$202$	−39.5468	−2.78251
$203$	0	0
$204$	−6.31035	−0.441813
$205$	−7.48897	−0.523053
$206$	−18.4885	−1.28815
$207$	4.59145	0.319128
$208$	−68.5371	−4.75219
$209$	−0.314763	−0.0217726
$210$	0	0
$211$	−16.8122	−1.15740	−0.578699	−	0.815541i	$-0.696439\pi$
$211$	−16.8122	−1.15740	−0.578699	+	0.815541i	$0.696439\pi$
$212$	63.4054	4.35470
$213$	16.4747	1.12883
$214$	−13.9058	−0.950583
$215$	13.4633	0.918186
$216$	55.9757	3.80866
$217$	0	0
$218$	−1.11938	−0.0758137
$219$	0.548602	0.0370711
$220$	10.4761	0.706299
$221$	−3.74449	−0.251881
$222$	−25.7900	−1.73091
$223$	12.8866	0.862952	0.431476	−	0.902124i	$-0.357993\pi$
$223$	12.8866	0.862952	0.431476	+	0.902124i	$0.357993\pi$
$224$	0	0
$225$	3.23100	0.215400
$226$	13.3523	0.888183
$227$	−25.0071	−1.65978	−0.829888	−	0.557929i	$-0.811596\pi$
$227$	−25.0071	−1.65978	−0.829888	+	0.557929i	$0.811596\pi$
$228$	−1.98626	−0.131543
$229$	2.84111	0.187746	0.0938728	−	0.995584i	$-0.470075\pi$
$229$	2.84111	0.187746	0.0938728	+	0.995584i	$0.470075\pi$
$230$	12.6375	0.833289
$231$	0	0
$232$	53.8572	3.53590
$233$	0.527922	0.0345853	0.0172926	−	0.999850i	$-0.494495\pi$
$233$	0.527922	0.0345853	0.0172926	+	0.999850i	$0.494495\pi$
$234$	19.1437	1.25146
$235$	−8.77411	−0.572360
$236$	40.4063	2.63022
$237$	−4.39091	−0.285220
$238$	0	0
$239$	−14.1402	−0.914652	−0.457326	−	0.889299i	$-0.651193\pi$
$239$	−14.1402	−0.914652	−0.457326	+	0.889299i	$0.651193\pi$
$240$	35.6322	2.30005
$241$	−22.5142	−1.45027	−0.725133	−	0.688609i	$-0.758222\pi$
$241$	−22.5142	−1.45027	−0.725133	+	0.688609i	$0.758222\pi$
$242$	2.79774	0.179846
$243$	−15.4890	−0.993618
$244$	76.8687	4.92101
$245$	12.5842	0.803975
$246$	−12.6207	−0.804666
$247$	−1.17862	−0.0749940
$248$	−90.2391	−5.73019
$249$	−11.4368	−0.724778
$250$	34.0411	2.15295
$251$	12.2310	0.772014	0.386007	−	0.922496i	$-0.373854\pi$
$251$	12.2310	0.772014	0.386007	+	0.922496i	$0.373854\pi$
$252$	0	0
$253$	2.51261	0.157966
$254$	−9.72772	−0.610372
$255$	1.94674	0.121910
$256$	105.695	6.60595
$257$	25.2714	1.57639	0.788193	−	0.615428i	$-0.211017\pi$
$257$	25.2714	1.57639	0.788193	+	0.615428i	$0.211017\pi$
$258$	22.6888	1.41254
$259$	0	0
$260$	39.2277	2.43280
$261$	−9.19097	−0.568907
$262$	−34.2024	−2.11303
$263$	−2.77852	−0.171331	−0.0856656	−	0.996324i	$-0.527302\pi$
$263$	−2.77852	−0.171331	−0.0856656	+	0.996324i	$0.527302\pi$
$264$	11.5955	0.713653
$265$	−19.5606	−1.20160
$266$	0	0
$267$	3.40733	0.208525
$268$	−41.2488	−2.51967
$269$	10.9611	0.668307	0.334154	−	0.942519i	$-0.391550\pi$
$269$	10.9611	0.668307	0.334154	+	0.942519i	$0.391550\pi$
$270$	−26.2922	−1.60009
$271$	−2.37879	−0.144501	−0.0722506	−	0.997387i	$-0.523018\pi$
$271$	−2.37879	−0.144501	−0.0722506	+	0.997387i	$0.523018\pi$
$272$	18.3035	1.10981
$273$	0	0
$274$	1.28072	0.0773714
$275$	1.76812	0.106622
$276$	15.8554	0.954384
$277$	−27.8709	−1.67460	−0.837301	−	0.546743i	$-0.815868\pi$
$277$	−27.8709	−1.67460	−0.837301	+	0.546743i	$0.815868\pi$
$278$	−9.60784	−0.576240
$279$	15.3997	0.921957
$280$	0	0
$281$	−5.51456	−0.328971	−0.164486	−	0.986379i	$-0.552596\pi$
$281$	−5.51456	−0.328971	−0.164486	+	0.986379i	$0.552596\pi$
$282$	−14.7865	−0.880521
$283$	12.5994	0.748956	0.374478	−	0.927236i	$-0.377822\pi$
$283$	12.5994	0.748956	0.374478	+	0.927236i	$0.377822\pi$
$284$	−88.6560	−5.26077
$285$	0.612762	0.0362969
$286$	10.4761	0.619465
$287$	0	0
$288$	−54.4418	−3.20801
$289$	1.00000	0.0588235
$290$	−25.2971	−1.48550
$291$	5.24562	0.307504
$292$	−2.95222	−0.172766
$293$	15.3232	0.895191	0.447596	−	0.894236i	$-0.352280\pi$
$293$	15.3232	0.895191	0.447596	+	0.894236i	$0.352280\pi$
$294$	21.2074	1.23684
$295$	−12.4653	−0.725760
$296$	91.1529	5.29816
$297$	−5.22747	−0.303328
$298$	−5.64239	−0.326855
$299$	9.40842	0.544103
$300$	11.1574	0.644175
$301$	0	0
$302$	−43.7126	−2.51538
$303$	15.3068	0.879353
$304$	5.76125	0.330430
$305$	−23.7140	−1.35786
$306$	−5.11251	−0.292263
$307$	8.42443	0.480808	0.240404	−	0.970673i	$-0.422720\pi$
$307$	8.42443	0.480808	0.240404	+	0.970673i	$0.422720\pi$
$308$	0	0
$309$	7.15606	0.407094
$310$	42.3860	2.40736
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	43.4191	2.45812
$313$	16.1797	0.914530	0.457265	−	0.889330i	$-0.348829\pi$
$313$	16.1797	0.914530	0.457265	+	0.889330i	$0.348829\pi$
$314$	−1.91025	−0.107802
$315$	0	0
$316$	23.6290	1.32924
$317$	15.1210	0.849277	0.424639	−	0.905363i	$-0.360401\pi$
$317$	15.1210	0.849277	0.424639	+	0.905363i	$0.360401\pi$
$318$	−32.9642	−1.84854
$319$	−5.02962	−0.281605
$320$	−84.0349	−4.69770
$321$	5.38233	0.300412
$322$	0	0
$323$	0.314763	0.0175139
$324$	−1.04091	−0.0578282
$325$	6.62070	0.367250
$326$	0.927524	0.0513708
$327$	0.433260	0.0239593
$328$	44.6070	2.46301
$329$	0	0
$330$	−5.44649	−0.299819
$331$	26.6010	1.46212	0.731061	−	0.682312i	$-0.239026\pi$
$331$	26.6010	1.46212	0.731061	+	0.682312i	$0.239026\pi$
$332$	61.5454	3.37774
$333$	−15.5557	−0.852445
$334$	8.80764	0.481932
$335$	12.7253	0.695256
$336$	0	0
$337$	21.1180	1.15037	0.575185	−	0.818023i	$-0.304930\pi$
$337$	21.1180	1.15037	0.575185	+	0.818023i	$0.304930\pi$
$338$	2.85699	0.155400
$339$	−5.16809	−0.280692
$340$	−10.4761	−0.568147
$341$	8.42727	0.456362
$342$	−1.60923	−0.0870169
$343$	0	0
$344$	−80.1919	−4.32366
$345$	−4.89140	−0.263344
$346$	−9.89349	−0.531877
$347$	0.0729875	0.00391817	0.00195909	−	0.999998i	$-0.499376\pi$
$347$	0.0729875	0.00391817	0.00195909	+	0.999998i	$0.499376\pi$
$348$	−31.7387	−1.70137
$349$	12.9138	0.691259	0.345630	−	0.938371i	$-0.387665\pi$
$349$	12.9138	0.691259	0.345630	+	0.938371i	$0.387665\pi$
$350$	0	0
$351$	−19.5742	−1.04479
$352$	−29.7925	−1.58794
$353$	11.4096	0.607273	0.303637	−	0.952788i	$-0.401799\pi$
$353$	11.4096	0.607273	0.303637	+	0.952788i	$0.401799\pi$
$354$	−21.0071	−1.11651
$355$	27.3504	1.45161
$356$	−18.3361	−0.971810
$357$	0	0
$358$	−29.5650	−1.56256
$359$	16.3059	0.860594	0.430297	−	0.902687i	$-0.358409\pi$
$359$	16.3059	0.860594	0.430297	+	0.902687i	$0.358409\pi$
$360$	35.1772	1.85400
$361$	−18.9009	−0.994786
$362$	−29.5438	−1.55279
$363$	−1.08288	−0.0568365
$364$	0	0
$365$	0.910761	0.0476714
$366$	−39.9637	−2.08894
$367$	32.5250	1.69779	0.848894	−	0.528562i	$-0.177269\pi$
$367$	32.5250	1.69779	0.848894	+	0.528562i	$0.177269\pi$
$368$	−45.9894	−2.39736
$369$	−7.61238	−0.396285
$370$	−42.8152	−2.22586
$371$	0	0
$372$	53.1790	2.75720
$373$	6.20825	0.321451	0.160725	−	0.986999i	$-0.448617\pi$
$373$	6.20825	0.321451	0.160725	+	0.986999i	$0.448617\pi$
$374$	−2.79774	−0.144668
$375$	−13.1758	−0.680395
$376$	52.2617	2.69519
$377$	−18.8334	−0.969967
$378$	0	0
$379$	27.0007	1.38693	0.693466	−	0.720489i	$-0.256083\pi$
$379$	27.0007	1.38693	0.693466	+	0.720489i	$0.256083\pi$
$380$	−3.29749	−0.169158
$381$	3.76517	0.192895
$382$	33.3855	1.70815
$383$	12.3375	0.630418	0.315209	−	0.949022i	$-0.397925\pi$
$383$	12.3375	0.630418	0.315209	+	0.949022i	$0.397925\pi$
$384$	−77.0954	−3.93426
$385$	0	0
$386$	−14.1654	−0.721000
$387$	13.6851	0.695653
$388$	−28.2285	−1.43309
$389$	38.6648	1.96038	0.980191	−	0.198057i	$-0.0634630\pi$
$389$	38.6648	1.96038	0.980191	+	0.198057i	$0.0634630\pi$
$390$	−20.3943	−1.03271
$391$	−2.51261	−0.127068
$392$	−74.9559	−3.78585
$393$	13.2382	0.667781
$394$	63.7630	3.21233
$395$	−7.28955	−0.366777
$396$	10.6487	0.535120
$397$	9.03756	0.453582	0.226791	−	0.973943i	$-0.427177\pi$
$397$	9.03756	0.453582	0.226791	+	0.973943i	$0.427177\pi$
$398$	43.6657	2.18876
$399$	0	0
$400$	−32.3627	−1.61814
$401$	14.2966	0.713939	0.356969	−	0.934116i	$-0.383810\pi$
$401$	14.2966	0.713939	0.356969	+	0.934116i	$0.383810\pi$
$402$	21.4451	1.06958
$403$	31.5558	1.57191
$404$	−82.3714	−4.09813
$405$	0.321120	0.0159566
$406$	0	0
$407$	−8.51261	−0.421954
$408$	−11.5955	−0.574062
$409$	−35.5255	−1.75662	−0.878312	−	0.478088i	$-0.841330\pi$
$409$	−35.5255	−1.75662	−0.878312	+	0.478088i	$0.841330\pi$
$410$	−20.9522	−1.03476
$411$	−0.495711	−0.0244516
$412$	−38.5093	−1.89722
$413$	0	0
$414$	12.8457	0.631332
$415$	−18.9868	−0.932024
$416$	−111.557	−5.46955
$417$	3.71876	0.182109
$418$	−0.880625	−0.0430728
$419$	−23.7781	−1.16164	−0.580819	−	0.814033i	$-0.697268\pi$
$419$	−23.7781	−1.16164	−0.580819	+	0.814033i	$0.697268\pi$
$420$	0	0
$421$	−30.8108	−1.50163	−0.750813	−	0.660515i	$-0.770338\pi$
$421$	−30.8108	−1.50163	−0.750813	+	0.660515i	$0.770338\pi$
$422$	−47.0362	−2.28968
$423$	−8.91870	−0.433642
$424$	116.510	5.65821
$425$	−1.76812	−0.0857664
$426$	46.0919	2.23316
$427$	0	0
$428$	−28.9642	−1.40004
$429$	−4.05483	−0.195769
$430$	37.6667	1.81645
$431$	−13.7826	−0.663882	−0.331941	−	0.943300i	$-0.607704\pi$
$431$	−13.7826	−0.663882	−0.331941	+	0.943300i	$0.607704\pi$
$432$	95.6808	4.60345
$433$	3.89984	0.187415	0.0937073	−	0.995600i	$-0.470128\pi$
$433$	3.89984	0.187415	0.0937073	+	0.995600i	$0.470128\pi$
$434$	0	0
$435$	9.79139	0.469461
$436$	−2.33153	−0.111660
$437$	−0.790874	−0.0378326
$438$	1.53485	0.0733379
$439$	−23.8023	−1.13602	−0.568012	−	0.823020i	$-0.692287\pi$
$439$	−23.8023	−1.13602	−0.568012	+	0.823020i	$0.692287\pi$
$440$	19.2502	0.917718
$441$	12.7916	0.609123
$442$	−10.4761	−0.498298
$443$	13.4618	0.639590	0.319795	−	0.947487i	$-0.396386\pi$
$443$	13.4618	0.639590	0.319795	+	0.947487i	$0.396386\pi$
$444$	−53.7175	−2.54932
$445$	5.65668	0.268152
$446$	36.0534	1.70718
$447$	2.18392	0.103296
$448$	0	0
$449$	−0.789793	−0.0372726	−0.0186363	−	0.999826i	$-0.505932\pi$
$449$	−0.789793	−0.0372726	−0.0186363	+	0.999826i	$0.505932\pi$
$450$	9.03952	0.426127
$451$	−4.16576	−0.196158
$452$	27.8113	1.30813
$453$	16.9192	0.794933
$454$	−69.9633	−3.28354
$455$	0	0
$456$	−3.64982	−0.170919
$457$	−12.9186	−0.604305	−0.302153	−	0.953260i	$-0.597705\pi$
$457$	−12.9186	−0.604305	−0.302153	+	0.953260i	$0.597705\pi$
$458$	7.94869	0.371418
$459$	5.22747	0.243997
$460$	26.3223	1.22729
$461$	35.3479	1.64632	0.823158	−	0.567812i	$-0.192210\pi$
$461$	35.3479	1.64632	0.823158	+	0.567812i	$0.192210\pi$
$462$	0	0
$463$	−19.7372	−0.917267	−0.458634	−	0.888625i	$-0.651661\pi$
$463$	−19.7372	−0.917267	−0.458634	+	0.888625i	$0.651661\pi$
$464$	92.0596	4.27376
$465$	−16.4057	−0.760797
$466$	1.47699	0.0684202
$467$	−8.14742	−0.377018	−0.188509	−	0.982071i	$-0.560365\pi$
$467$	−8.14742	−0.377018	−0.188509	+	0.982071i	$0.560365\pi$
$468$	39.8741	1.84318
$469$	0	0
$470$	−24.5477	−1.13230
$471$	0.739372	0.0340685
$472$	74.2480	3.41754
$473$	7.48897	0.344343
$474$	−12.2846	−0.564252
$475$	−0.556538	−0.0255357
$476$	0	0
$477$	−19.8829	−0.910376
$478$	−39.5606	−1.80946
$479$	−11.2333	−0.513264	−0.256632	−	0.966509i	$-0.582613\pi$
$479$	−11.2333	−0.513264	−0.256632	+	0.966509i	$0.582613\pi$
$480$	57.9982	2.64725
$481$	−31.8753	−1.45339
$482$	−62.9889	−2.86907
$483$	0	0
$484$	5.82737	0.264880
$485$	8.70850	0.395433
$486$	−43.3342	−1.96568
$487$	22.0471	0.999049	0.499524	−	0.866300i	$-0.333508\pi$
$487$	22.0471	0.999049	0.499524	+	0.866300i	$0.333508\pi$
$488$	141.249	6.39403
$489$	−0.359003	−0.0162347
$490$	35.2074	1.59051
$491$	−16.3483	−0.737788	−0.368894	−	0.929471i	$-0.620263\pi$
$491$	−16.3483	−0.737788	−0.368894	+	0.929471i	$0.620263\pi$
$492$	−26.2874	−1.18513
$493$	5.02962	0.226523
$494$	−3.29749	−0.148361
$495$	−3.28514	−0.147656
$496$	−154.248	−6.92595
$497$	0	0
$498$	−31.9972	−1.43383
$499$	−24.1171	−1.07963	−0.539815	−	0.841784i	$-0.681506\pi$
$499$	−24.1171	−1.07963	−0.539815	+	0.841784i	$0.681506\pi$
$500$	70.9036	3.17090
$501$	−3.40904	−0.152305
$502$	34.2192	1.52728
$503$	12.9094	0.575600	0.287800	−	0.957690i	$-0.407076\pi$
$503$	12.9094	0.575600	0.287800	+	0.957690i	$0.407076\pi$
$504$	0	0
$505$	25.4116	1.13080
$506$	7.02962	0.312505
$507$	−1.10581	−0.0491109
$508$	−20.2617	−0.898967
$509$	23.9923	1.06344	0.531719	−	0.846921i	$-0.321546\pi$
$509$	23.9923	1.06344	0.531719	+	0.846921i	$0.321546\pi$
$510$	5.44649	0.241175
$511$	0	0
$512$	153.318	6.77578
$513$	1.64541	0.0726467
$514$	70.7029	3.11857
$515$	11.8801	0.523500
$516$	47.2580	2.08042
$517$	−4.88062	−0.214650
$518$	0	0
$519$	3.82933	0.168089
$520$	72.0822	3.16101
$521$	−40.2982	−1.76550	−0.882748	−	0.469847i	$-0.844309\pi$
$521$	−40.2982	−1.76550	−0.882748	+	0.469847i	$0.844309\pi$
$522$	−25.7140	−1.12547
$523$	1.01323	0.0443053	0.0221527	−	0.999755i	$-0.492948\pi$
$523$	1.01323	0.0443053	0.0221527	+	0.999755i	$0.492948\pi$
$524$	−71.2396	−3.11212
$525$	0	0
$526$	−7.77360	−0.338945
$527$	−8.42727	−0.367098
$528$	19.8205	0.862576
$529$	−16.6868	−0.725514
$530$	−54.7255	−2.37712
$531$	−12.6708	−0.549864
$532$	0	0
$533$	−15.5986	−0.675652
$534$	9.53285	0.412527
$535$	8.93546	0.386314
$536$	−75.7962	−3.27390
$537$	11.4433	0.493814
$538$	30.6662	1.32211
$539$	7.00000	0.301511
$540$	−54.7635	−2.35665
$541$	14.3744	0.618003	0.309001	−	0.951062i	$-0.400005\pi$
$541$	14.3744	0.618003	0.309001	+	0.951062i	$0.400005\pi$
$542$	−6.65525	−0.285867
$543$	11.4351	0.490727
$544$	29.7925	1.27734
$545$	0.719276	0.0308104
$546$	0	0
$547$	2.86877	0.122660	0.0613299	−	0.998118i	$-0.480466\pi$
$547$	2.86877	0.122660	0.0613299	+	0.998118i	$0.480466\pi$
$548$	2.66760	0.113954
$549$	−24.1048	−1.02877
$550$	4.94674	0.210930
$551$	1.58314	0.0674439
$552$	29.1349	1.24006
$553$	0	0
$554$	−77.9757	−3.31287
$555$	16.5719	0.703436
$556$	−20.0120	−0.848697
$557$	−8.57343	−0.363268	−0.181634	−	0.983366i	$-0.558139\pi$
$557$	−8.57343	−0.363268	−0.181634	+	0.983366i	$0.558139\pi$
$558$	43.0845	1.82391
$559$	28.0424	1.18607
$560$	0	0
$561$	1.08288	0.0457193
$562$	−15.4283	−0.650805
$563$	−30.6325	−1.29101	−0.645504	−	0.763757i	$-0.723353\pi$
$563$	−30.6325	−1.29101	−0.645504	+	0.763757i	$0.723353\pi$
$564$	−30.7984	−1.29685
$565$	−8.57979	−0.360954
$566$	35.2499	1.48166
$567$	0	0
$568$	−162.908	−6.83549
$569$	−10.3435	−0.433622	−0.216811	−	0.976214i	$-0.569566\pi$
$569$	−10.3435	−0.433622	−0.216811	+	0.976214i	$0.569566\pi$
$570$	1.71435	0.0718062
$571$	−36.4960	−1.52731	−0.763656	−	0.645624i	$-0.776597\pi$
$571$	−36.4960	−1.52731	−0.763656	+	0.645624i	$0.776597\pi$
$572$	21.8205	0.912361
$573$	−12.9220	−0.539826
$574$	0	0
$575$	4.44258	0.185269
$576$	−85.4197	−3.55915
$577$	−12.9384	−0.538634	−0.269317	−	0.963052i	$-0.586798\pi$
$577$	−12.9384	−0.538634	−0.269317	+	0.963052i	$0.586798\pi$
$578$	2.79774	0.116371
$579$	5.48279	0.227857
$580$	−52.6909	−2.18787
$581$	0	0
$582$	14.6759	0.608336
$583$	−10.8806	−0.450629
$584$	−5.42481	−0.224480
$585$	−12.3012	−0.508590
$586$	42.8704	1.77096
$587$	−27.1441	−1.12036	−0.560178	−	0.828372i	$-0.689267\pi$
$587$	−27.1441	−1.12036	−0.560178	+	0.828372i	$0.689267\pi$
$588$	44.1724	1.82164
$589$	−2.65259	−0.109298
$590$	−34.8748	−1.43577
$591$	−24.6798	−1.01519
$592$	155.810	6.40376
$593$	−6.09858	−0.250439	−0.125219	−	0.992129i	$-0.539963\pi$
$593$	−6.09858	−0.250439	−0.125219	+	0.992129i	$0.539963\pi$
$594$	−14.6251	−0.600076
$595$	0	0
$596$	−11.7524	−0.481398
$597$	−16.9010	−0.691714
$598$	26.3223	1.07640
$599$	5.09365	0.208121	0.104061	−	0.994571i	$-0.466816\pi$
$599$	5.09365	0.208121	0.104061	+	0.994571i	$0.466816\pi$
$600$	20.5022	0.836999
$601$	32.6525	1.33192	0.665961	−	0.745987i	$-0.268022\pi$
$601$	32.6525	1.33192	0.665961	+	0.745987i	$0.268022\pi$
$602$	0	0
$603$	12.9350	0.526752
$604$	−91.0482	−3.70470
$605$	−1.79774	−0.0730887
$606$	42.8245	1.73963
$607$	37.1349	1.50726	0.753629	−	0.657300i	$-0.228301\pi$
$607$	37.1349	1.50726	0.753629	+	0.657300i	$0.228301\pi$
$608$	9.37755	0.380310
$609$	0	0
$610$	−66.3456	−2.68626
$611$	−18.2754	−0.739345
$612$	−10.6487	−0.430450
$613$	13.6596	0.551708	0.275854	−	0.961200i	$-0.411039\pi$
$613$	13.6596	0.551708	0.275854	+	0.961200i	$0.411039\pi$
$614$	23.5694	0.951184
$615$	8.10967	0.327013
$616$	0	0
$617$	−13.9478	−0.561518	−0.280759	−	0.959778i	$-0.590586\pi$
$617$	−13.9478	−0.561518	−0.280759	+	0.959778i	$0.590586\pi$
$618$	20.0208	0.805355
$619$	16.9503	0.681289	0.340645	−	0.940192i	$-0.389355\pi$
$619$	16.9503	0.681289	0.340645	+	0.940192i	$0.389355\pi$
$620$	88.2850	3.54561
$621$	−13.1346	−0.527072
$622$	0	0
$623$	0	0
$624$	74.2176	2.97108
$625$	−13.0332	−0.521326
$626$	45.2666	1.80922
$627$	0.340851	0.0136123
$628$	−3.97882	−0.158772
$629$	8.51261	0.339420
$630$	0	0
$631$	1.94674	0.0774986	0.0387493	−	0.999249i	$-0.487663\pi$
$631$	1.94674	0.0774986	0.0387493	+	0.999249i	$0.487663\pi$
$632$	43.4191	1.72712
$633$	18.2056	0.723608
$634$	42.3045	1.68013
$635$	6.25073	0.248053
$636$	−68.6605	−2.72257
$637$	26.2114	1.03853
$638$	−14.0716	−0.557100
$639$	27.8011	1.09979
$640$	−127.990	−5.05924
$641$	−2.01532	−0.0796002	−0.0398001	−	0.999208i	$-0.512672\pi$
$641$	−2.01532	−0.0796002	−0.0398001	+	0.999208i	$0.512672\pi$
$642$	15.0584	0.594307
$643$	−26.0471	−1.02720	−0.513598	−	0.858031i	$-0.671688\pi$
$643$	−26.0471	−1.02720	−0.513598	+	0.858031i	$0.671688\pi$
$644$	0	0
$645$	−14.5791	−0.574052
$646$	0.880625	0.0346477
$647$	−5.72917	−0.225237	−0.112618	−	0.993638i	$-0.535924\pi$
$647$	−5.72917	−0.225237	−0.112618	+	0.993638i	$0.535924\pi$
$648$	−1.91270	−0.0751381
$649$	−6.93388	−0.272179
$650$	18.5230	0.726532
$651$	0	0
$652$	1.93192	0.0756599
$653$	−14.9838	−0.586362	−0.293181	−	0.956057i	$-0.594714\pi$
$653$	−14.9838	−0.586362	−0.293181	+	0.956057i	$0.594714\pi$
$654$	1.21215	0.0473988
$655$	21.9774	0.858729
$656$	76.2480	2.97698
$657$	0.925769	0.0361177
$658$	0	0
$659$	24.8745	0.968971	0.484486	−	0.874799i	$-0.339007\pi$
$659$	24.8745	0.968971	0.484486	+	0.874799i	$0.339007\pi$
$660$	−11.3444	−0.441580
$661$	−34.3450	−1.33586	−0.667932	−	0.744222i	$-0.732820\pi$
$661$	−34.3450	−1.33586	−0.667932	+	0.744222i	$0.732820\pi$
$662$	74.4227	2.89252
$663$	4.05483	0.157477
$664$	113.092	4.38882
$665$	0	0
$666$	−43.5207	−1.68639
$667$	−12.6375	−0.489324
$668$	18.3453	0.709800
$669$	−13.9547	−0.539519
$670$	35.6020	1.37543
$671$	−13.1910	−0.509232
$672$	0	0
$673$	0.400099	0.0154227	0.00771135	−	0.999970i	$-0.497545\pi$
$673$	0.400099	0.0154227	0.00771135	+	0.999970i	$0.497545\pi$
$674$	59.0827	2.27578
$675$	−9.24278	−0.355755
$676$	5.95078	0.228876
$677$	−30.2918	−1.16421	−0.582105	−	0.813114i	$-0.697771\pi$
$677$	−30.2918	−1.16421	−0.582105	+	0.813114i	$0.697771\pi$
$678$	−14.4590	−0.555294
$679$	0	0
$680$	−19.2502	−0.738212
$681$	27.0797	1.03770
$682$	23.5773	0.902823
$683$	13.0795	0.500475	0.250238	−	0.968184i	$-0.419491\pi$
$683$	13.0795	0.500475	0.250238	+	0.968184i	$0.419491\pi$
$684$	−3.35183	−0.128160
$685$	−0.822954	−0.0314434
$686$	0	0
$687$	−3.07658	−0.117379
$688$	−137.074	−5.22591
$689$	−40.7424	−1.55216
$690$	−13.6849	−0.520974
$691$	−11.1041	−0.422418	−0.211209	−	0.977441i	$-0.567740\pi$
$691$	−11.1041	−0.422418	−0.211209	+	0.977441i	$0.567740\pi$
$692$	−20.6070	−0.783359
$693$	0	0
$694$	0.204200	0.00775133
$695$	6.17370	0.234182
$696$	−58.3209	−2.21065
$697$	4.16576	0.157790
$698$	36.1295	1.36752
$699$	−0.571676	−0.0216228
$700$	0	0
$701$	−23.1861	−0.875726	−0.437863	−	0.899042i	$-0.644264\pi$
$701$	−23.1861	−0.875726	−0.437863	+	0.899042i	$0.644264\pi$
$702$	−54.7635	−2.06692
$703$	2.67945	0.101057
$704$	−46.7447	−1.76176
$705$	9.50132	0.357840
$706$	31.9212	1.20137
$707$	0	0
$708$	−43.7552	−1.64442
$709$	−21.9967	−0.826102	−0.413051	−	0.910708i	$-0.635537\pi$
$709$	−21.9967	−0.826102	−0.413051	+	0.910708i	$0.635537\pi$
$710$	76.5193	2.87172
$711$	−7.40967	−0.277884
$712$	−33.6932	−1.26271
$713$	21.1744	0.792987
$714$	0	0
$715$	−6.73163	−0.251749
$716$	−61.5804	−2.30137
$717$	15.3121	0.571842
$718$	45.6198	1.70252
$719$	−46.4516	−1.73235	−0.866176	−	0.499739i	$-0.833429\pi$
$719$	−46.4516	−1.73235	−0.866176	+	0.499739i	$0.833429\pi$
$720$	60.1295	2.24089
$721$	0	0
$722$	−52.8799	−1.96799
$723$	24.3802	0.906709
$724$	−61.5362	−2.28698
$725$	−8.89297	−0.330277
$726$	−3.02962	−0.112440
$727$	37.4692	1.38966	0.694829	−	0.719175i	$-0.255480\pi$
$727$	37.4692	1.38966	0.694829	+	0.719175i	$0.255480\pi$
$728$	0	0
$729$	17.3086	0.641059
$730$	2.54808	0.0943085
$731$	−7.48897	−0.276990
$732$	−83.2396	−3.07663
$733$	42.9247	1.58546	0.792731	−	0.609572i	$-0.208659\pi$
$733$	42.9247	1.58546	0.792731	+	0.609572i	$0.208659\pi$
$734$	90.9965	3.35874
$735$	−13.6272	−0.502647
$736$	−74.8567	−2.75925
$737$	7.07847	0.260739
$738$	−21.2975	−0.783971
$739$	−18.4470	−0.678584	−0.339292	−	0.940681i	$-0.610187\pi$
$739$	−18.4470	−0.678584	−0.339292	+	0.940681i	$0.610187\pi$
$740$	−89.1790	−3.27829
$741$	1.27631	0.0468864
$742$	0	0
$743$	8.34035	0.305978	0.152989	−	0.988228i	$-0.451110\pi$
$743$	8.34035	0.305978	0.152989	+	0.988228i	$0.451110\pi$
$744$	97.7183	3.58253
$745$	3.62562	0.132833
$746$	17.3691	0.635927
$747$	−19.2996	−0.706137
$748$	−5.82737	−0.213070
$749$	0	0
$750$	−36.8625	−1.34603
$751$	18.1885	0.663708	0.331854	−	0.943331i	$-0.392326\pi$
$751$	18.1885	0.663708	0.331854	+	0.943331i	$0.392326\pi$
$752$	89.3324	3.25762
$753$	−13.2447	−0.482665
$754$	−52.6909	−1.91889
$755$	28.0884	1.02224
$756$	0	0
$757$	39.5119	1.43609	0.718043	−	0.695999i	$-0.245038\pi$
$757$	39.5119	1.43609	0.718043	+	0.695999i	$0.245038\pi$
$758$	75.5410	2.74377
$759$	−2.72085	−0.0987607
$760$	−6.05925	−0.219792
$761$	−12.0305	−0.436105	−0.218053	−	0.975937i	$-0.569970\pi$
$761$	−12.0305	−0.436105	−0.218053	+	0.975937i	$0.569970\pi$
$762$	10.5340	0.381606
$763$	0	0
$764$	69.5380	2.51580
$765$	3.28514	0.118774
$766$	34.5172	1.24716
$767$	−25.9638	−0.937499
$768$	−114.455	−4.13005
$769$	5.19980	0.187510	0.0937548	−	0.995595i	$-0.470113\pi$
$769$	5.19980	0.187510	0.0937548	+	0.995595i	$0.470113\pi$
$770$	0	0
$771$	−27.3659	−0.985560
$772$	−29.5048	−1.06190
$773$	−15.3642	−0.552611	−0.276305	−	0.961070i	$-0.589110\pi$
$773$	−15.3642	−0.552611	−0.276305	+	0.961070i	$0.589110\pi$
$774$	38.2874	1.37621
$775$	14.9004	0.535239
$776$	−51.8709	−1.86206
$777$	0	0
$778$	108.174	3.87823
$779$	1.31123	0.0469796
$780$	−42.4789	−1.52099
$781$	15.2137	0.544390
$782$	−7.02962	−0.251379
$783$	26.2922	0.939606
$784$	−128.124	−4.57587
$785$	1.22747	0.0438102
$786$	37.0372	1.32107
$787$	−8.24632	−0.293950	−0.146975	−	0.989140i	$-0.546954\pi$
$787$	−8.24632	−0.293950	−0.146975	+	0.989140i	$0.546954\pi$
$788$	132.811	4.73119
$789$	3.00881	0.107117
$790$	−20.3943	−0.725596
$791$	0	0
$792$	19.5674	0.695299
$793$	−49.3934	−1.75401
$794$	25.2848	0.897323
$795$	21.1818	0.751240
$796$	90.9505	3.22365
$797$	0.646100	0.0228860	0.0114430	−	0.999935i	$-0.496357\pi$
$797$	0.646100	0.0228860	0.0114430	+	0.999935i	$0.496357\pi$
$798$	0	0
$799$	4.88062	0.172664
$800$	−52.6766	−1.86240
$801$	5.74989	0.203162
$802$	39.9982	1.41239
$803$	0.506613	0.0178780
$804$	44.6676	1.57530
$805$	0	0
$806$	88.2850	3.10971
$807$	−11.8695	−0.417827
$808$	−151.360	−5.32484
$809$	−43.0406	−1.51323	−0.756613	−	0.653863i	$-0.773147\pi$
$809$	−43.0406	−1.51323	−0.756613	+	0.653863i	$0.773147\pi$
$810$	0.898412	0.0315670
$811$	33.7639	1.18561	0.592806	−	0.805346i	$-0.298020\pi$
$811$	33.7639	1.18561	0.592806	+	0.805346i	$0.298020\pi$
$812$	0	0
$813$	2.57595	0.0903425
$814$	−23.8161	−0.834753
$815$	−0.595998	−0.0208769
$816$	−19.8205	−0.693856
$817$	−2.35725	−0.0824697
$818$	−99.3913	−3.47514
$819$	0	0
$820$	−43.6410	−1.52401
$821$	46.2069	1.61263	0.806315	−	0.591486i	$-0.201459\pi$
$821$	46.2069	1.61263	0.806315	+	0.591486i	$0.201459\pi$
$822$	−1.38687	−0.0483727
$823$	−4.59794	−0.160274	−0.0801371	−	0.996784i	$-0.525536\pi$
$823$	−4.59794	−0.160274	−0.0801371	+	0.996784i	$0.525536\pi$
$824$	−70.7621	−2.46512
$825$	−1.91466	−0.0666600
$826$	0	0
$827$	24.6388	0.856777	0.428388	−	0.903595i	$-0.359082\pi$
$827$	24.6388	0.856777	0.428388	+	0.903595i	$0.359082\pi$
$828$	26.7561	0.929838
$829$	−32.6465	−1.13386	−0.566930	−	0.823766i	$-0.691869\pi$
$829$	−32.6465	−1.13386	−0.566930	+	0.823766i	$0.691869\pi$
$830$	−53.1201	−1.84383
$831$	30.1809	1.04696
$832$	−175.035	−6.06824
$833$	−7.00000	−0.242536
$834$	10.4041	0.360266
$835$	−5.65952	−0.195856
$836$	−1.83424	−0.0634384
$837$	−44.0533	−1.52270
$838$	−66.5251	−2.29807
$839$	37.5608	1.29674	0.648371	−	0.761325i	$-0.275451\pi$
$839$	37.5608	1.29674	0.648371	+	0.761325i	$0.275451\pi$
$840$	0	0
$841$	−3.70288	−0.127685
$842$	−86.2007	−2.97067
$843$	5.97162	0.205673
$844$	−97.9708	−3.37229
$845$	−1.83581	−0.0631539
$846$	−24.9522	−0.857875
$847$	0	0
$848$	199.153	6.83895
$849$	−13.6436	−0.468249
$850$	−4.94674	−0.169672
$851$	−21.3888	−0.733199
$852$	96.0039	3.28904
$853$	−15.3661	−0.526124	−0.263062	−	0.964779i	$-0.584732\pi$
$853$	−15.3661	−0.526124	−0.263062	+	0.964779i	$0.584732\pi$
$854$	0	0
$855$	1.03404	0.0353634
$856$	−53.2227	−1.81912
$857$	−2.10034	−0.0717464	−0.0358732	−	0.999356i	$-0.511421\pi$
$857$	−2.10034	−0.0717464	−0.0358732	+	0.999356i	$0.511421\pi$
$858$	−11.3444	−0.387291
$859$	50.5661	1.72529	0.862646	−	0.505809i	$-0.168806\pi$
$859$	50.5661	1.72529	0.862646	+	0.505809i	$0.168806\pi$
$860$	78.4553	2.67530
$861$	0	0
$862$	−38.5601	−1.31336
$863$	5.72318	0.194819	0.0974096	−	0.995244i	$-0.468944\pi$
$863$	5.72318	0.194819	0.0974096	+	0.995244i	$0.468944\pi$
$864$	155.739	5.29835
$865$	6.35725	0.216153
$866$	10.9108	0.370763
$867$	−1.08288	−0.0367766
$868$	0	0
$869$	−4.05483	−0.137551
$870$	27.3938	0.928736
$871$	26.5052	0.898095
$872$	−4.28426	−0.145083
$873$	8.85201	0.299595
$874$	−2.21266	−0.0748444
$875$	0	0
$876$	3.19691	0.108013
$877$	1.79630	0.0606566	0.0303283	−	0.999540i	$-0.490345\pi$
$877$	1.79630	0.0606566	0.0303283	+	0.999540i	$0.490345\pi$
$878$	−66.5929	−2.24740
$879$	−16.5932	−0.559675
$880$	32.9050	1.10923
$881$	29.7822	1.00339	0.501695	−	0.865045i	$-0.332710\pi$
$881$	29.7822	1.00339	0.501695	+	0.865045i	$0.332710\pi$
$882$	35.7875	1.20503
$883$	−19.8540	−0.668141	−0.334071	−	0.942548i	$-0.608422\pi$
$883$	−19.8540	−0.668141	−0.334071	+	0.942548i	$0.608422\pi$
$884$	−21.8205	−0.733903
$885$	13.4985	0.453747
$886$	37.6627	1.26530
$887$	−28.4077	−0.953836	−0.476918	−	0.878948i	$-0.658246\pi$
$887$	−28.4077	−0.953836	−0.476918	+	0.878948i	$0.658246\pi$
$888$	−98.7078	−3.31242
$889$	0	0
$890$	15.8259	0.530487
$891$	0.178624	0.00598413
$892$	75.0951	2.51437
$893$	1.53624	0.0514082
$894$	6.11004	0.204350
$895$	18.9975	0.635018
$896$	0	0
$897$	−10.1882	−0.340174
$898$	−2.20964	−0.0737366
$899$	−42.3860	−1.41365
$900$	18.8282	0.627608
$901$	10.8806	0.362486
$902$	−11.6547	−0.388060
$903$	0	0
$904$	51.1042	1.69970
$905$	18.9839	0.631047
$906$	47.3356	1.57262
$907$	54.2874	1.80258	0.901292	−	0.433212i	$-0.142620\pi$
$907$	54.2874	1.80258	0.901292	+	0.433212i	$0.142620\pi$
$908$	−145.725	−4.83606
$909$	25.8303	0.856738
$910$	0	0
$911$	7.20724	0.238787	0.119393	−	0.992847i	$-0.461905\pi$
$911$	7.20724	0.238787	0.119393	+	0.992847i	$0.461905\pi$
$912$	−6.23875	−0.206586
$913$	−10.5614	−0.349533
$914$	−36.1428	−1.19550
$915$	25.6794	0.848936
$916$	16.5562	0.547031
$917$	0	0
$918$	14.6251	0.482701
$919$	−0.791371	−0.0261049	−0.0130525	−	0.999915i	$-0.504155\pi$
$919$	−0.791371	−0.0261049	−0.0130525	+	0.999915i	$0.504155\pi$
$920$	48.3682	1.59465
$921$	−9.12266	−0.300602
$922$	98.8944	3.25691
$923$	56.9676	1.87511
$924$	0	0
$925$	−15.0513	−0.494884
$926$	−55.2197	−1.81463
$927$	12.0759	0.396624
$928$	149.845	4.91890
$929$	−48.7374	−1.59902	−0.799512	−	0.600650i	$-0.794908\pi$
$929$	−48.7374	−1.59902	−0.799512	+	0.600650i	$0.794908\pi$
$930$	−45.8990	−1.50509
$931$	−2.20334	−0.0722115
$932$	3.07639	0.100771
$933$	0	0
$934$	−22.7944	−0.745855
$935$	1.79774	0.0587925
$936$	73.2700	2.39491
$937$	−4.25551	−0.139022	−0.0695108	−	0.997581i	$-0.522144\pi$
$937$	−4.25551	−0.139022	−0.0695108	+	0.997581i	$0.522144\pi$
$938$	0	0
$939$	−17.5207	−0.571766
$940$	−51.1300	−1.66768
$941$	31.5817	1.02954	0.514768	−	0.857330i	$-0.327878\pi$
$941$	31.5817	1.02954	0.514768	+	0.857330i	$0.327878\pi$
$942$	2.06857	0.0673978
$943$	−10.4669	−0.340850
$944$	126.914	4.13070
$945$	0	0
$946$	20.9522	0.681216
$947$	24.4184	0.793493	0.396746	−	0.917928i	$-0.370139\pi$
$947$	24.4184	0.793493	0.396746	+	0.917928i	$0.370139\pi$
$948$	−25.5874	−0.831041
$949$	1.89701	0.0615795
$950$	−1.55705	−0.0505174
$951$	−16.3742	−0.530970
$952$	0	0
$953$	−47.3324	−1.53325	−0.766624	−	0.642097i	$-0.778065\pi$
$953$	−47.3324	−1.53325	−0.766624	+	0.642097i	$0.778065\pi$
$954$	−55.6273	−1.80100
$955$	−21.4525	−0.694186
$956$	−82.4000	−2.66501
$957$	5.44649	0.176060
$958$	−31.4280	−1.01539
$959$	0	0
$960$	90.9999	2.93701
$961$	40.0189	1.29093
$962$	−89.1790	−2.87525
$963$	9.08270	0.292686
$964$	−131.198	−4.22562
$965$	9.10225	0.293012
$966$	0	0
$967$	−17.9360	−0.576782	−0.288391	−	0.957513i	$-0.593120\pi$
$967$	−17.9360	−0.576782	−0.288391	+	0.957513i	$0.593120\pi$
$968$	10.7080	0.344168
$969$	−0.340851	−0.0109497
$970$	24.3642	0.782286
$971$	−8.27863	−0.265674	−0.132837	−	0.991138i	$-0.542409\pi$
$971$	−8.27863	−0.265674	−0.132837	+	0.991138i	$0.542409\pi$
$972$	−90.2599	−2.89509
$973$	0	0
$974$	61.6821	1.97642
$975$	−7.16943	−0.229606
$976$	241.441	7.72833
$977$	53.0555	1.69740	0.848698	−	0.528877i	$-0.177387\pi$
$977$	53.0555	1.69740	0.848698	+	0.528877i	$0.177387\pi$
$978$	−1.00440	−0.0321171
$979$	3.14654	0.100564
$980$	73.3328	2.34253
$981$	0.731129	0.0233431
$982$	−45.7383	−1.45957
$983$	−20.4361	−0.651810	−0.325905	−	0.945402i	$-0.605669\pi$
$983$	−20.4361	−0.651810	−0.325905	+	0.945402i	$0.605669\pi$
$984$	−48.3040	−1.53988
$985$	−40.9721	−1.30548
$986$	14.0716	0.448131
$987$	0	0
$988$	−6.86828	−0.218509
$989$	18.8168	0.598340
$990$	−9.19097	−0.292108
$991$	−0.203469	−0.00646339	−0.00323170	−	0.999995i	$-0.501029\pi$
$991$	−0.203469	−0.00646339	−0.00323170	+	0.999995i	$0.501029\pi$
$992$	−251.069	−7.97145
$993$	−28.8057	−0.914121
$994$	0	0
$995$	−28.0582	−0.889506
$996$	−66.6464	−2.11177
$997$	−7.62738	−0.241561	−0.120781	−	0.992679i	$-0.538540\pi$
$997$	−7.62738	−0.241561	−0.120781	+	0.992679i	$0.538540\pi$
$998$	−67.4735	−2.13584
$999$	44.4994	1.40790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.a.f.1.4	✓	4
3.2	odd	2		1683.2.a.y.1.1		4
4.3	odd	2		2992.2.a.v.1.3		4
5.4	even	2		4675.2.a.bd.1.1		4
7.6	odd	2		9163.2.a.l.1.4		4
11.10	odd	2		2057.2.a.s.1.1		4
17.16	even	2		3179.2.a.w.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.a.f.1.4	✓	4	1.1	even	1	trivial
1683.2.a.y.1.1		4	3.2	odd	2
2057.2.a.s.1.1		4	11.10	odd	2
2992.2.a.v.1.3		4	4.3	odd	2
3179.2.a.w.1.4		4	17.16	even	2
4675.2.a.bd.1.1		4	5.4	even	2
9163.2.a.l.1.4		4	7.6	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.a (trivial)

\(f(q)\)	\(=\)	\(q+2.79774 q^{2} -1.08288 q^{3} +5.82737 q^{4} -1.79774 q^{5} -3.02962 q^{6} +10.7080 q^{8} -1.82737 q^{9} +O(q^{10})\)	\(q+2.79774 q^{2} -1.08288 q^{3} +5.82737 q^{4} -1.79774 q^{5} -3.02962 q^{6} +10.7080 q^{8} -1.82737 q^{9} -5.02962 q^{10} -1.00000 q^{11} -6.31035 q^{12} -3.74449 q^{13} +1.94674 q^{15} +18.3035 q^{16} +1.00000 q^{17} -5.11251 q^{18} +0.314763 q^{19} -10.4761 q^{20} -2.79774 q^{22} -2.51261 q^{23} -11.5955 q^{24} -1.76812 q^{25} -10.4761 q^{26} +5.22747 q^{27} +5.02962 q^{29} +5.44649 q^{30} -8.42727 q^{31} +29.7925 q^{32} +1.08288 q^{33} +2.79774 q^{34} -10.6487 q^{36} +8.51261 q^{37} +0.880625 q^{38} +4.05483 q^{39} -19.2502 q^{40} +4.16576 q^{41} -7.48897 q^{43} -5.82737 q^{44} +3.28514 q^{45} -7.02962 q^{46} +4.88062 q^{47} -19.8205 q^{48} -7.00000 q^{49} -4.94674 q^{50} -1.08288 q^{51} -21.8205 q^{52} +10.8806 q^{53} +14.6251 q^{54} +1.79774 q^{55} -0.340851 q^{57} +14.0716 q^{58} +6.93388 q^{59} +11.3444 q^{60} +13.1910 q^{61} -23.5773 q^{62} +46.7447 q^{64} +6.73163 q^{65} +3.02962 q^{66} -7.07847 q^{67} +5.82737 q^{68} +2.72085 q^{69} -15.2137 q^{71} -19.5674 q^{72} -0.506613 q^{73} +23.8161 q^{74} +1.91466 q^{75} +1.83424 q^{76} +11.3444 q^{78} +4.05483 q^{79} -32.9050 q^{80} -0.178624 q^{81} +11.6547 q^{82} +10.5614 q^{83} -1.79774 q^{85} -20.9522 q^{86} -5.44649 q^{87} -10.7080 q^{88} -3.14654 q^{89} +9.19097 q^{90} -14.6419 q^{92} +9.12573 q^{93} +13.6547 q^{94} -0.565862 q^{95} -32.2617 q^{96} -4.84413 q^{97} -19.5842 q^{98} +1.82737 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 + 9 * q^8 + 11 * q^9	\( 4 q + q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} + 9 q^{8} + 11 q^{9} - 12 q^{10} - 4 q^{11} - 2 q^{13} + 5 q^{15} + 19 q^{16} + 4 q^{17} - 7 q^{18} - 2 q^{19} - 6 q^{20} - q^{22} + 5 q^{23} - 26 q^{24} - 5 q^{25} - 6 q^{26} + q^{27} + 12 q^{29} - 6 q^{30} - 17 q^{31} + 39 q^{32} - q^{33} + q^{34} - 25 q^{36} + 19 q^{37} - 12 q^{38} - 22 q^{39} - 20 q^{40} + 6 q^{41} - 4 q^{43} - 5 q^{44} + 18 q^{45} - 20 q^{46} + 4 q^{47} - 32 q^{48} - 28 q^{49} - 17 q^{50} + q^{51} - 40 q^{52} + 28 q^{53} + 30 q^{54} - 3 q^{55} - 16 q^{57} + 15 q^{59} + 34 q^{60} + 12 q^{61} + 6 q^{62} + 35 q^{64} + 4 q^{65} + 4 q^{66} - q^{67} + 5 q^{68} - 13 q^{69} + 17 q^{71} - 25 q^{72} - 6 q^{73} + 26 q^{74} + 6 q^{75} + 18 q^{76} + 34 q^{78} - 22 q^{79} - 38 q^{80} + 10 q^{82} + 8 q^{83} + 3 q^{85} - 12 q^{86} + 6 q^{87} - 9 q^{88} - 13 q^{89} - 4 q^{90} - 12 q^{92} + 31 q^{93} + 18 q^{94} + 10 q^{95} + 16 q^{96} + 17 q^{97} - 7 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 + 9 * q^8 + 11 * q^9 - 12 * q^10 - 4 * q^11 - 2 * q^13 + 5 * q^15 + 19 * q^16 + 4 * q^17 - 7 * q^18 - 2 * q^19 - 6 * q^20 - q^22 + 5 * q^23 - 26 * q^24 - 5 * q^25 - 6 * q^26 + q^27 + 12 * q^29 - 6 * q^30 - 17 * q^31 + 39 * q^32 - q^33 + q^34 - 25 * q^36 + 19 * q^37 - 12 * q^38 - 22 * q^39 - 20 * q^40 + 6 * q^41 - 4 * q^43 - 5 * q^44 + 18 * q^45 - 20 * q^46 + 4 * q^47 - 32 * q^48 - 28 * q^49 - 17 * q^50 + q^51 - 40 * q^52 + 28 * q^53 + 30 * q^54 - 3 * q^55 - 16 * q^57 + 15 * q^59 + 34 * q^60 + 12 * q^61 + 6 * q^62 + 35 * q^64 + 4 * q^65 + 4 * q^66 - q^67 + 5 * q^68 - 13 * q^69 + 17 * q^71 - 25 * q^72 - 6 * q^73 + 26 * q^74 + 6 * q^75 + 18 * q^76 + 34 * q^78 - 22 * q^79 - 38 * q^80 + 10 * q^82 + 8 * q^83 + 3 * q^85 - 12 * q^86 + 6 * q^87 - 9 * q^88 - 13 * q^89 - 4 * q^90 - 12 * q^92 + 31 * q^93 + 18 * q^94 + 10 * q^95 + 16 * q^96 + 17 * q^97 - 7 * q^98 - 11 * q^99

Introduction

L-functions

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Database

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