LMFDB - Embedded newform 1183.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1279733.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 $ x^6 - 2x^5 - 6x^4 + 10x^3 + 10x^2 - 11*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.33192$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90785 q^{2} -1.08494 q^{3} +1.63989 q^{4} +1.10591 q^{5} +2.06989 q^{6} -1.00000 q^{7} +0.687029 q^{8} -1.82292 q^{9} +O(q^{10})$	\(q-1.90785 q^{2} -1.08494 q^{3} +1.63989 q^{4} +1.10591 q^{5} +2.06989 q^{6} -1.00000 q^{7} +0.687029 q^{8} -1.82292 q^{9} -2.10992 q^{10} +0.799816 q^{11} -1.77918 q^{12} +1.90785 q^{14} -1.19984 q^{15} -4.59054 q^{16} +2.63979 q^{17} +3.47785 q^{18} +1.84186 q^{19} +1.81358 q^{20} +1.08494 q^{21} -1.52593 q^{22} -3.82692 q^{23} -0.745382 q^{24} -3.77696 q^{25} +5.23255 q^{27} -1.63989 q^{28} -7.54322 q^{29} +2.28912 q^{30} +7.86730 q^{31} +7.38400 q^{32} -0.867749 q^{33} -5.03633 q^{34} -1.10591 q^{35} -2.98939 q^{36} -3.45786 q^{37} -3.51399 q^{38} +0.759794 q^{40} +10.9578 q^{41} -2.06989 q^{42} -2.63910 q^{43} +1.31161 q^{44} -2.01599 q^{45} +7.30119 q^{46} -5.22430 q^{47} +4.98044 q^{48} +1.00000 q^{49} +7.20587 q^{50} -2.86401 q^{51} +6.15957 q^{53} -9.98293 q^{54} +0.884527 q^{55} -0.687029 q^{56} -1.99830 q^{57} +14.3913 q^{58} -5.10250 q^{59} -1.96762 q^{60} +3.31543 q^{61} -15.0096 q^{62} +1.82292 q^{63} -4.90649 q^{64} +1.65553 q^{66} +13.9305 q^{67} +4.32898 q^{68} +4.15196 q^{69} +2.10992 q^{70} -6.69004 q^{71} -1.25240 q^{72} -15.0774 q^{73} +6.59708 q^{74} +4.09775 q^{75} +3.02045 q^{76} -0.799816 q^{77} -8.10529 q^{79} -5.07673 q^{80} -0.208236 q^{81} -20.9059 q^{82} -15.6338 q^{83} +1.77918 q^{84} +2.91938 q^{85} +5.03501 q^{86} +8.18390 q^{87} +0.549497 q^{88} +2.27897 q^{89} +3.84620 q^{90} -6.27574 q^{92} -8.53552 q^{93} +9.96718 q^{94} +2.03694 q^{95} -8.01116 q^{96} -16.4949 q^{97} -1.90785 q^{98} -1.45800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 8 q^{6} - 6 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 8 * q^6 - 6 * q^7 + 3 * q^8	$ 6 q + 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 8 q^{6} - 6 q^{7} + 3 q^{8} - 14 q^{10} + 8 q^{11} - 23 q^{12} - 2 q^{14} + 3 q^{15} - 23 q^{17} + 26 q^{18} - 13 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{22} - 18 q^{23} - 26 q^{24} - 10 q^{25} - 10 q^{27} - 8 q^{28} - 15 q^{29} + 14 q^{30} + 3 q^{31} + 28 q^{32} + 3 q^{33} - 29 q^{34} - 2 q^{35} + 22 q^{36} - 13 q^{37} - 11 q^{38} - 14 q^{40} - 4 q^{41} + 8 q^{42} - 18 q^{43} - 19 q^{45} + 10 q^{46} - 16 q^{47} - 11 q^{48} + 6 q^{49} - 10 q^{50} + 14 q^{51} - 25 q^{53} - 31 q^{54} - 3 q^{56} - 4 q^{57} - 13 q^{58} + 18 q^{59} + 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} + 16 q^{67} - 34 q^{68} - q^{69} + 14 q^{70} + 25 q^{71} + 39 q^{72} - 5 q^{73} - 14 q^{74} + 15 q^{75} + 7 q^{76} - 8 q^{77} + 2 q^{79} - 27 q^{80} - 6 q^{81} - 10 q^{82} - 7 q^{83} + 23 q^{84} + 9 q^{85} - 3 q^{86} + 13 q^{87} - 48 q^{88} - 10 q^{89} - 32 q^{92} + 35 q^{93} - 14 q^{94} - 7 q^{95} - 14 q^{96} - 5 q^{97} + 2 q^{98} - 15 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 8 * q^6 - 6 * q^7 + 3 * q^8 - 14 * q^10 + 8 * q^11 - 23 * q^12 - 2 * q^14 + 3 * q^15 - 23 * q^17 + 26 * q^18 - 13 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^22 - 18 * q^23 - 26 * q^24 - 10 * q^25 - 10 * q^27 - 8 * q^28 - 15 * q^29 + 14 * q^30 + 3 * q^31 + 28 * q^32 + 3 * q^33 - 29 * q^34 - 2 * q^35 + 22 * q^36 - 13 * q^37 - 11 * q^38 - 14 * q^40 - 4 * q^41 + 8 * q^42 - 18 * q^43 - 19 * q^45 + 10 * q^46 - 16 * q^47 - 11 * q^48 + 6 * q^49 - 10 * q^50 + 14 * q^51 - 25 * q^53 - 31 * q^54 - 3 * q^56 - 4 * q^57 - 13 * q^58 + 18 * q^59 + 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 + 16 * q^67 - 34 * q^68 - q^69 + 14 * q^70 + 25 * q^71 + 39 * q^72 - 5 * q^73 - 14 * q^74 + 15 * q^75 + 7 * q^76 - 8 * q^77 + 2 * q^79 - 27 * q^80 - 6 * q^81 - 10 * q^82 - 7 * q^83 + 23 * q^84 + 9 * q^85 - 3 * q^86 + 13 * q^87 - 48 * q^88 - 10 * q^89 - 32 * q^92 + 35 * q^93 - 14 * q^94 - 7 * q^95 - 14 * q^96 - 5 * q^97 + 2 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.90785	−1.34905	−0.674527	−	0.738250i	$-0.735652\pi$
$2$	−1.90785	−1.34905	−0.674527	+	0.738250i	$0.735652\pi$
$3$	−1.08494	−0.626388	−0.313194	−	0.949689i	$-0.601399\pi$
$3$	−1.08494	−0.626388	−0.313194	+	0.949689i	$0.601399\pi$
$4$	1.63989	0.819947
$5$	1.10591	0.494579	0.247290	−	0.968942i	$-0.420460\pi$
$5$	1.10591	0.494579	0.247290	+	0.968942i	$0.420460\pi$
$6$	2.06989	0.845031
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.687029	0.242902
$9$	−1.82292	−0.607638
$10$	−2.10992	−0.667214
$11$	0.799816	0.241154	0.120577	−	0.992704i	$-0.461526\pi$
$11$	0.799816	0.241154	0.120577	+	0.992704i	$0.461526\pi$
$12$	−1.77918	−0.513605
$13$	0	0
$13$	0	0
$14$	1.90785	0.509894
$15$	−1.19984	−0.309798
$16$	−4.59054	−1.14763
$17$	2.63979	0.640244	0.320122	−	0.947376i	$-0.396276\pi$
$17$	2.63979	0.640244	0.320122	+	0.947376i	$0.396276\pi$
$18$	3.47785	0.819737
$19$	1.84186	0.422552	0.211276	−	0.977426i	$-0.432238\pi$
$19$	1.84186	0.422552	0.211276	+	0.977426i	$0.432238\pi$
$20$	1.81358	0.405529
$21$	1.08494	0.236752
$22$	−1.52593	−0.325329
$23$	−3.82692	−0.797968	−0.398984	−	0.916958i	$-0.630637\pi$
$23$	−3.82692	−0.797968	−0.398984	+	0.916958i	$0.630637\pi$
$24$	−0.745382	−0.152151
$25$	−3.77696	−0.755391
$26$	0	0
$27$	5.23255	1.00701
$28$	−1.63989	−0.309911
$29$	−7.54322	−1.40074	−0.700370	−	0.713780i	$-0.746982\pi$
$29$	−7.54322	−1.40074	−0.700370	+	0.713780i	$0.746982\pi$
$30$	2.28912	0.417935
$31$	7.86730	1.41301	0.706505	−	0.707708i	$-0.250271\pi$
$31$	7.86730	1.41301	0.706505	+	0.707708i	$0.250271\pi$
$32$	7.38400	1.30532
$33$	−0.867749	−0.151056
$34$	−5.03633	−0.863724
$35$	−1.10591	−0.186933
$36$	−2.98939	−0.498231
$37$	−3.45786	−0.568469	−0.284234	−	0.958755i	$-0.591739\pi$
$37$	−3.45786	−0.568469	−0.284234	+	0.958755i	$0.591739\pi$
$38$	−3.51399	−0.570045
$39$	0	0
$40$	0.759794	0.120134
$41$	10.9578	1.71133	0.855664	−	0.517532i	$-0.173149\pi$
$41$	10.9578	1.71133	0.855664	+	0.517532i	$0.173149\pi$
$42$	−2.06989	−0.319392
$43$	−2.63910	−0.402459	−0.201230	−	0.979544i	$-0.564494\pi$
$43$	−2.63910	−0.402459	−0.201230	+	0.979544i	$0.564494\pi$
$44$	1.31161	0.197733
$45$	−2.01599	−0.300525
$46$	7.30119	1.07650
$47$	−5.22430	−0.762043	−0.381021	−	0.924566i	$-0.624428\pi$
$47$	−5.22430	−0.762043	−0.381021	+	0.924566i	$0.624428\pi$
$48$	4.98044	0.718864
$49$	1.00000	0.142857
$50$	7.20587	1.01906
$51$	−2.86401	−0.401041
$52$	0	0
$53$	6.15957	0.846082	0.423041	−	0.906111i	$-0.360963\pi$
$53$	6.15957	0.846082	0.423041	+	0.906111i	$0.360963\pi$
$54$	−9.98293	−1.35850
$55$	0.884527	0.119270
$56$	−0.687029	−0.0918081
$57$	−1.99830	−0.264681
$58$	14.3913	1.88967
$59$	−5.10250	−0.664288	−0.332144	−	0.943229i	$-0.607772\pi$
$59$	−5.10250	−0.664288	−0.332144	+	0.943229i	$0.607772\pi$
$60$	−1.96762	−0.254018
$61$	3.31543	0.424498	0.212249	−	0.977216i	$-0.431921\pi$
$61$	3.31543	0.424498	0.212249	+	0.977216i	$0.431921\pi$
$62$	−15.0096	−1.90623
$63$	1.82292	0.229666
$64$	−4.90649	−0.613312
$65$	0	0
$66$	1.65553	0.203782
$67$	13.9305	1.70188	0.850942	−	0.525260i	$-0.176032\pi$
$67$	13.9305	1.70188	0.850942	+	0.525260i	$0.176032\pi$
$68$	4.32898	0.524966
$69$	4.15196	0.499837
$70$	2.10992	0.252183
$71$	−6.69004	−0.793962	−0.396981	−	0.917827i	$-0.629942\pi$
$71$	−6.69004	−0.793962	−0.396981	+	0.917827i	$0.629942\pi$
$72$	−1.25240	−0.147596
$73$	−15.0774	−1.76467	−0.882336	−	0.470619i	$-0.844031\pi$
$73$	−15.0774	−1.76467	−0.882336	+	0.470619i	$0.844031\pi$
$74$	6.59708	0.766895
$75$	4.09775	0.473168
$76$	3.02045	0.346470
$77$	−0.799816	−0.0911475
$78$	0	0
$79$	−8.10529	−0.911916	−0.455958	−	0.890001i	$-0.650703\pi$
$79$	−8.10529	−0.911916	−0.455958	+	0.890001i	$0.650703\pi$
$80$	−5.07673	−0.567596
$81$	−0.208236	−0.0231373
$82$	−20.9059	−2.30867
$83$	−15.6338	−1.71603	−0.858016	−	0.513623i	$-0.828303\pi$
$83$	−15.6338	−1.71603	−0.858016	+	0.513623i	$0.828303\pi$
$84$	1.77918	0.194124
$85$	2.91938	0.316651
$86$	5.03501	0.542939
$87$	8.18390	0.877407
$88$	0.549497	0.0585766
$89$	2.27897	0.241570	0.120785	−	0.992679i	$-0.461459\pi$
$89$	2.27897	0.241570	0.120785	+	0.992679i	$0.461459\pi$
$90$	3.84620	0.405425
$91$	0	0
$92$	−6.27574	−0.654291
$93$	−8.53552	−0.885092
$94$	9.96718	1.02804
$95$	2.03694	0.208985
$96$	−8.01116	−0.817636
$97$	−16.4949	−1.67481	−0.837404	−	0.546585i	$-0.815927\pi$
$97$	−16.4949	−1.67481	−0.837404	+	0.546585i	$0.815927\pi$
$98$	−1.90785	−0.192722
$99$	−1.45800	−0.146534
$100$	−6.19381	−0.619381
$101$	−14.0686	−1.39988	−0.699940	−	0.714201i	$-0.746790\pi$
$101$	−14.0686	−1.39988	−0.699940	+	0.714201i	$0.746790\pi$
$102$	5.46409	0.541026
$103$	0.110230	0.0108613	0.00543063	−	0.999985i	$-0.498271\pi$
$103$	0.110230	0.0108613	0.00543063	+	0.999985i	$0.498271\pi$
$104$	0	0
$105$	1.19984	0.117093
$106$	−11.7515	−1.14141
$107$	−13.8071	−1.33478	−0.667389	−	0.744709i	$-0.732588\pi$
$107$	−13.8071	−1.33478	−0.667389	+	0.744709i	$0.732588\pi$
$108$	8.58083	0.825691
$109$	2.17385	0.208217	0.104108	−	0.994566i	$-0.466801\pi$
$109$	2.17385	0.208217	0.104108	+	0.994566i	$0.466801\pi$
$110$	−1.68754	−0.160901
$111$	3.75156	0.356082
$112$	4.59054	0.433765
$113$	−16.2026	−1.52421	−0.762105	−	0.647453i	$-0.775834\pi$
$113$	−16.2026	−1.52421	−0.762105	+	0.647453i	$0.775834\pi$
$114$	3.81245	0.357069
$115$	−4.23224	−0.394658
$116$	−12.3701	−1.14853
$117$	0	0
$118$	9.73480	0.896161
$119$	−2.63979	−0.241989
$120$	−0.824328	−0.0752505
$121$	−10.3603	−0.941845
$122$	−6.32535	−0.572670
$123$	−11.8886	−1.07195
$124$	12.9015	1.15859
$125$	−9.70655	−0.868180
$126$	−3.47785	−0.309831
$127$	19.9799	1.77293	0.886463	−	0.462800i	$-0.153155\pi$
$127$	19.9799	1.77293	0.886463	+	0.462800i	$0.153155\pi$
$128$	−5.40714	−0.477928
$129$	2.86325	0.252095
$130$	0	0
$131$	−18.3019	−1.59905	−0.799524	−	0.600634i	$-0.794915\pi$
$131$	−18.3019	−1.59905	−0.799524	+	0.600634i	$0.794915\pi$
$132$	−1.42302	−0.123858
$133$	−1.84186	−0.159709
$134$	−26.5773	−2.29593
$135$	5.78675	0.498044
$136$	1.81362	0.155516
$137$	−1.03858	−0.0887322	−0.0443661	−	0.999015i	$-0.514127\pi$
$137$	−1.03858	−0.0887322	−0.0443661	+	0.999015i	$0.514127\pi$
$138$	−7.92132	−0.674307
$139$	16.0516	1.36148	0.680738	−	0.732527i	$-0.261659\pi$
$139$	16.0516	1.36148	0.680738	+	0.732527i	$0.261659\pi$
$140$	−1.81358	−0.153275
$141$	5.66803	0.477334
$142$	12.7636	1.07110
$143$	0	0
$144$	8.36816	0.697346
$145$	−8.34214	−0.692777
$146$	28.7654	2.38064
$147$	−1.08494	−0.0894840
$148$	−5.67052	−0.466114
$149$	0.376052	0.0308074	0.0154037	−	0.999881i	$-0.495097\pi$
$149$	0.376052	0.0308074	0.0154037	+	0.999881i	$0.495097\pi$
$150$	−7.81790	−0.638329
$151$	0.149749	0.0121864	0.00609321	−	0.999981i	$-0.498060\pi$
$151$	0.149749	0.0121864	0.00609321	+	0.999981i	$0.498060\pi$
$152$	1.26541	0.102638
$153$	−4.81212	−0.389037
$154$	1.52593	0.122963
$155$	8.70055	0.698845
$156$	0	0
$157$	−7.22397	−0.576536	−0.288268	−	0.957550i	$-0.593079\pi$
$157$	−7.22397	−0.576536	−0.288268	+	0.957550i	$0.593079\pi$
$158$	15.4637	1.23022
$159$	−6.68274	−0.529976
$160$	8.16606	0.645584
$161$	3.82692	0.301603
$162$	0.397282	0.0312134
$163$	−3.83171	−0.300123	−0.150062	−	0.988677i	$-0.547947\pi$
$163$	−3.83171	−0.300123	−0.150062	+	0.988677i	$0.547947\pi$
$164$	17.9697	1.40320
$165$	−0.959654	−0.0747090
$166$	29.8269	2.31502
$167$	−1.83270	−0.141819	−0.0709094	−	0.997483i	$-0.522590\pi$
$167$	−1.83270	−0.141819	−0.0709094	+	0.997483i	$0.522590\pi$
$168$	0.745382	0.0575075
$169$	0	0
$170$	−5.56974	−0.427180
$171$	−3.35755	−0.256759
$172$	−4.32784	−0.329995
$173$	−22.0343	−1.67524	−0.837618	−	0.546256i	$-0.816053\pi$
$173$	−22.0343	−1.67524	−0.837618	+	0.546256i	$0.816053\pi$
$174$	−15.6137	−1.18367
$175$	3.77696	0.285511
$176$	−3.67158	−0.276756
$177$	5.53588	0.416102
$178$	−4.34793	−0.325891
$179$	5.62164	0.420181	0.210091	−	0.977682i	$-0.432624\pi$
$179$	5.62164	0.420181	0.210091	+	0.977682i	$0.432624\pi$
$180$	−3.30600	−0.246415
$181$	−4.44007	−0.330028	−0.165014	−	0.986291i	$-0.552767\pi$
$181$	−4.44007	−0.330028	−0.165014	+	0.986291i	$0.552767\pi$
$182$	0	0
$183$	−3.59703	−0.265900
$184$	−2.62920	−0.193828
$185$	−3.82409	−0.281153
$186$	16.2845	1.19404
$187$	2.11135	0.154397
$188$	−8.56730	−0.624834
$189$	−5.23255	−0.380612
$190$	−3.88617	−0.281932
$191$	−4.39741	−0.318186	−0.159093	−	0.987264i	$-0.550857\pi$
$191$	−4.39741	−0.318186	−0.159093	+	0.987264i	$0.550857\pi$
$192$	5.32323	0.384171
$193$	−25.2708	−1.81903	−0.909516	−	0.415669i	$-0.863548\pi$
$193$	−25.2708	−1.81903	−0.909516	+	0.415669i	$0.863548\pi$
$194$	31.4699	2.25941
$195$	0	0
$196$	1.63989	0.117135
$197$	−6.91860	−0.492930	−0.246465	−	0.969152i	$-0.579269\pi$
$197$	−6.91860	−0.492930	−0.246465	+	0.969152i	$0.579269\pi$
$198$	2.78164	0.197683
$199$	17.3958	1.23315	0.616577	−	0.787295i	$-0.288519\pi$
$199$	17.3958	1.23315	0.616577	+	0.787295i	$0.288519\pi$
$200$	−2.59488	−0.183486
$201$	−15.1137	−1.06604
$202$	26.8408	1.88851
$203$	7.54322	0.529430
$204$	−4.69666	−0.328832
$205$	12.1184	0.846387
$206$	−0.210302	−0.0146524
$207$	6.97615	0.484876
$208$	0	0
$209$	1.47315	0.101900
$210$	−2.28912	−0.157964
$211$	7.50167	0.516436	0.258218	−	0.966087i	$-0.416865\pi$
$211$	7.50167	0.516436	0.258218	+	0.966087i	$0.416865\pi$
$212$	10.1010	0.693742
$213$	7.25826	0.497328
$214$	26.3418	1.80069
$215$	−2.91862	−0.199048
$216$	3.59492	0.244603
$217$	−7.86730	−0.534067
$218$	−4.14738	−0.280896
$219$	16.3580	1.10537
$220$	1.45053	0.0977947
$221$	0	0
$222$	−7.15741	−0.480374
$223$	25.8645	1.73201	0.866007	−	0.500032i	$-0.166678\pi$
$223$	25.8645	1.73201	0.866007	+	0.500032i	$0.166678\pi$
$224$	−7.38400	−0.493364
$225$	6.88507	0.459005
$226$	30.9121	2.05624
$227$	−5.19695	−0.344933	−0.172467	−	0.985015i	$-0.555174\pi$
$227$	−5.19695	−0.344933	−0.172467	+	0.985015i	$0.555174\pi$
$228$	−3.27700	−0.217024
$229$	−5.03722	−0.332869	−0.166434	−	0.986053i	$-0.553225\pi$
$229$	−5.03722	−0.332869	−0.166434	+	0.986053i	$0.553225\pi$
$230$	8.07448	0.532415
$231$	0.867749	0.0570937
$232$	−5.18241	−0.340242
$233$	−16.2022	−1.06144	−0.530721	−	0.847546i	$-0.678079\pi$
$233$	−16.2022	−1.06144	−0.530721	+	0.847546i	$0.678079\pi$
$234$	0	0
$235$	−5.77762	−0.376890
$236$	−8.36755	−0.544681
$237$	8.79372	0.571213
$238$	5.03633	0.326457
$239$	−3.22405	−0.208546	−0.104273	−	0.994549i	$-0.533252\pi$
$239$	−3.22405	−0.208546	−0.104273	+	0.994549i	$0.533252\pi$
$240$	5.50793	0.355535
$241$	17.2522	1.11131	0.555655	−	0.831413i	$-0.312468\pi$
$241$	17.2522	1.11131	0.555655	+	0.831413i	$0.312468\pi$
$242$	19.7659	1.27060
$243$	−15.4717	−0.992512
$244$	5.43696	0.348065
$245$	1.10591	0.0706542
$246$	22.6816	1.44613
$247$	0	0
$248$	5.40507	0.343222
$249$	16.9617	1.07490
$250$	18.5186	1.17122
$251$	17.3864	1.09742	0.548711	−	0.836012i	$-0.315119\pi$
$251$	17.3864	1.09742	0.548711	+	0.836012i	$0.315119\pi$
$252$	2.98939	0.188314
$253$	−3.06083	−0.192433
$254$	−38.1186	−2.39177
$255$	−3.16734	−0.198347
$256$	20.1290	1.25806
$257$	−14.6189	−0.911901	−0.455950	−	0.890005i	$-0.650701\pi$
$257$	−14.6189	−0.911901	−0.455950	+	0.890005i	$0.650701\pi$
$258$	−5.46266	−0.340090
$259$	3.45786	0.214861
$260$	0	0
$261$	13.7506	0.851143
$262$	34.9174	2.15720
$263$	7.41229	0.457061	0.228531	−	0.973537i	$-0.426608\pi$
$263$	7.41229	0.457061	0.228531	+	0.973537i	$0.426608\pi$
$264$	−0.596169	−0.0366916
$265$	6.81195	0.418455
$266$	3.51399	0.215457
$267$	−2.47253	−0.151317
$268$	22.8446	1.39545
$269$	−4.58385	−0.279482	−0.139741	−	0.990188i	$-0.544627\pi$
$269$	−4.58385	−0.279482	−0.139741	+	0.990188i	$0.544627\pi$
$270$	−11.0402	−0.671888
$271$	3.62768	0.220366	0.110183	−	0.993911i	$-0.464856\pi$
$271$	3.62768	0.220366	0.110183	+	0.993911i	$0.464856\pi$
$272$	−12.1181	−0.734766
$273$	0	0
$274$	1.98146	0.119705
$275$	−3.02087	−0.182165
$276$	6.80877	0.409840
$277$	23.6739	1.42242	0.711212	−	0.702978i	$-0.248147\pi$
$277$	23.6739	1.42242	0.711212	+	0.702978i	$0.248147\pi$
$278$	−30.6240	−1.83670
$279$	−14.3414	−0.858599
$280$	−0.759794	−0.0454064
$281$	25.5415	1.52368	0.761838	−	0.647768i	$-0.224297\pi$
$281$	25.5415	1.52368	0.761838	+	0.647768i	$0.224297\pi$
$282$	−10.8138	−0.643950
$283$	−2.95356	−0.175571	−0.0877855	−	0.996139i	$-0.527979\pi$
$283$	−2.95356	−0.175571	−0.0877855	+	0.996139i	$0.527979\pi$
$284$	−10.9710	−0.651006
$285$	−2.20994	−0.130906
$286$	0	0
$287$	−10.9578	−0.646821
$288$	−13.4604	−0.793162
$289$	−10.0315	−0.590088
$290$	15.9156	0.934594
$291$	17.8959	1.04908
$292$	−24.7253	−1.44694
$293$	−22.6667	−1.32420	−0.662102	−	0.749414i	$-0.730335\pi$
$293$	−22.6667	−1.32420	−0.662102	+	0.749414i	$0.730335\pi$
$294$	2.06989	0.120719
$295$	−5.64291	−0.328543
$296$	−2.37565	−0.138082
$297$	4.18508	0.242843
$298$	−0.717451	−0.0415608
$299$	0	0
$300$	6.71988	0.387973
$301$	2.63910	0.152115
$302$	−0.285699	−0.0164401
$303$	15.2636	0.876868
$304$	−8.45512	−0.484934
$305$	3.66658	0.209948
$306$	9.18080	0.524832
$307$	−2.04932	−0.116961	−0.0584805	−	0.998289i	$-0.518626\pi$
$307$	−2.04932	−0.116961	−0.0584805	+	0.998289i	$0.518626\pi$
$308$	−1.31161	−0.0747361
$309$	−0.119592	−0.00680336
$310$	−16.5994	−0.942780
$311$	−15.4445	−0.875776	−0.437888	−	0.899030i	$-0.644273\pi$
$311$	−15.4445	−0.875776	−0.437888	+	0.899030i	$0.644273\pi$
$312$	0	0
$313$	−6.59184	−0.372593	−0.186296	−	0.982494i	$-0.559648\pi$
$313$	−6.59184	−0.372593	−0.186296	+	0.982494i	$0.559648\pi$
$314$	13.7823	0.777778
$315$	2.01599	0.113588
$316$	−13.2918	−0.747723
$317$	17.6182	0.989536	0.494768	−	0.869025i	$-0.335253\pi$
$317$	17.6182	0.989536	0.494768	+	0.869025i	$0.335253\pi$
$318$	12.7497	0.714966
$319$	−6.03319	−0.337794
$320$	−5.42615	−0.303331
$321$	14.9798	0.836089
$322$	−7.30119	−0.406879
$323$	4.86213	0.270536
$324$	−0.341484	−0.0189713
$325$	0	0
$326$	7.31034	0.404882
$327$	−2.35848	−0.130424
$328$	7.52836	0.415684
$329$	5.22430	0.288025
$330$	1.83088	0.100786
$331$	14.0822	0.774027	0.387014	−	0.922074i	$-0.373507\pi$
$331$	14.0822	0.774027	0.387014	+	0.922074i	$0.373507\pi$
$332$	−25.6378	−1.40706
$333$	6.30339	0.345423
$334$	3.49652	0.191321
$335$	15.4059	0.841716
$336$	−4.98044	−0.271705
$337$	2.73318	0.148886	0.0744429	−	0.997225i	$-0.476282\pi$
$337$	2.73318	0.148886	0.0744429	+	0.997225i	$0.476282\pi$
$338$	0	0
$339$	17.5788	0.954747
$340$	4.78747	0.259637
$341$	6.29240	0.340752
$342$	6.40571	0.346381
$343$	−1.00000	−0.0539949
$344$	−1.81314	−0.0977579
$345$	4.59171	0.247209
$346$	42.0382	2.25999
$347$	−2.90684	−0.156047	−0.0780236	−	0.996952i	$-0.524861\pi$
$347$	−2.90684	−0.156047	−0.0780236	+	0.996952i	$0.524861\pi$
$348$	13.4207	0.719427
$349$	−7.10583	−0.380366	−0.190183	−	0.981749i	$-0.560908\pi$
$349$	−7.10583	−0.380366	−0.190183	+	0.981749i	$0.560908\pi$
$350$	−7.20587	−0.385170
$351$	0	0
$352$	5.90584	0.314782
$353$	6.18844	0.329378	0.164689	−	0.986346i	$-0.447338\pi$
$353$	6.18844	0.329378	0.164689	+	0.986346i	$0.447338\pi$
$354$	−10.5616	−0.561344
$355$	−7.39860	−0.392677
$356$	3.73726	0.198075
$357$	2.86401	0.151579
$358$	−10.7253	−0.566847
$359$	25.8517	1.36440	0.682201	−	0.731165i	$-0.261023\pi$
$359$	25.8517	1.36440	0.682201	+	0.731165i	$0.261023\pi$
$360$	−1.38504	−0.0729981
$361$	−15.6076	−0.821450
$362$	8.47099	0.445225
$363$	11.2403	0.589960
$364$	0	0
$365$	−16.6743	−0.872770
$366$	6.86260	0.358714
$367$	−34.7499	−1.81393	−0.906964	−	0.421207i	$-0.861606\pi$
$367$	−34.7499	−1.81393	−0.906964	+	0.421207i	$0.861606\pi$
$368$	17.5676	0.915775
$369$	−19.9752	−1.03987
$370$	7.29580	0.379290
$371$	−6.15957	−0.319789
$372$	−13.9973	−0.725728
$373$	−26.1368	−1.35331	−0.676656	−	0.736299i	$-0.736572\pi$
$373$	−26.1368	−1.35331	−0.676656	+	0.736299i	$0.736572\pi$
$374$	−4.02814	−0.208290
$375$	10.5310	0.543817
$376$	−3.58925	−0.185101
$377$	0	0
$378$	9.98293	0.513466
$379$	−18.1562	−0.932623	−0.466311	−	0.884621i	$-0.654417\pi$
$379$	−18.1562	−0.932623	−0.466311	+	0.884621i	$0.654417\pi$
$380$	3.34036	0.171357
$381$	−21.6769	−1.11054
$382$	8.38961	0.429250
$383$	7.68219	0.392541	0.196271	−	0.980550i	$-0.437117\pi$
$383$	7.68219	0.392541	0.196271	+	0.980550i	$0.437117\pi$
$384$	5.86640	0.299368
$385$	−0.884527	−0.0450797
$386$	48.2129	2.45397
$387$	4.81086	0.244550
$388$	−27.0499	−1.37325
$389$	−9.23745	−0.468357	−0.234179	−	0.972194i	$-0.575240\pi$
$389$	−9.23745	−0.468357	−0.234179	+	0.972194i	$0.575240\pi$
$390$	0	0
$391$	−10.1023	−0.510894
$392$	0.687029	0.0347002
$393$	19.8564	1.00162
$394$	13.1997	0.664989
$395$	−8.96374	−0.451015
$396$	−2.39096	−0.120150
$397$	16.7052	0.838410	0.419205	−	0.907892i	$-0.362309\pi$
$397$	16.7052	0.838410	0.419205	+	0.907892i	$0.362309\pi$
$398$	−33.1885	−1.66359
$399$	1.99830	0.100040
$400$	17.3383	0.866913
$401$	28.3934	1.41790	0.708950	−	0.705258i	$-0.249169\pi$
$401$	28.3934	1.41790	0.708950	+	0.705258i	$0.249169\pi$
$402$	28.8347	1.43814
$403$	0	0
$404$	−23.0710	−1.14783
$405$	−0.230290	−0.0114432
$406$	−14.3913	−0.714230
$407$	−2.76565	−0.137088
$408$	−1.96766	−0.0974135
$409$	25.8721	1.27929	0.639647	−	0.768669i	$-0.279081\pi$
$409$	25.8721	1.27929	0.639647	+	0.768669i	$0.279081\pi$
$410$	−23.1201	−1.14182
$411$	1.12680	0.0555808
$412$	0.180765	0.00890565
$413$	5.10250	0.251077
$414$	−13.3094	−0.654124
$415$	−17.2896	−0.848714
$416$	0	0
$417$	−17.4149	−0.852811
$418$	−2.81055	−0.137468
$419$	−6.55673	−0.320317	−0.160158	−	0.987091i	$-0.551201\pi$
$419$	−6.55673	−0.320317	−0.160158	+	0.987091i	$0.551201\pi$
$420$	1.96762	0.0960099
$421$	14.4100	0.702300	0.351150	−	0.936319i	$-0.385791\pi$
$421$	14.4100	0.702300	0.351150	+	0.936319i	$0.385791\pi$
$422$	−14.3121	−0.696700
$423$	9.52346	0.463046
$424$	4.23181	0.205515
$425$	−9.97039	−0.483635
$426$	−13.8477	−0.670922
$427$	−3.31543	−0.160445
$428$	−22.6421	−1.09445
$429$	0	0
$430$	5.56828	0.268526
$431$	−14.7027	−0.708204	−0.354102	−	0.935207i	$-0.615213\pi$
$431$	−14.7027	−0.708204	−0.354102	+	0.935207i	$0.615213\pi$
$432$	−24.0202	−1.15567
$433$	−20.6178	−0.990830	−0.495415	−	0.868656i	$-0.664984\pi$
$433$	−20.6178	−0.990830	−0.495415	+	0.868656i	$0.664984\pi$
$434$	15.0096	0.720486
$435$	9.05068	0.433947
$436$	3.56488	0.170727
$437$	−7.04865	−0.337182
$438$	−31.2086	−1.49120
$439$	20.3424	0.970892	0.485446	−	0.874267i	$-0.338657\pi$
$439$	20.3424	0.970892	0.485446	+	0.874267i	$0.338657\pi$
$440$	0.607696	0.0289708
$441$	−1.82292	−0.0868055
$442$	0	0
$443$	13.8195	0.656582	0.328291	−	0.944577i	$-0.393527\pi$
$443$	13.8195	0.656582	0.328291	+	0.944577i	$0.393527\pi$
$444$	6.15215	0.291968
$445$	2.52034	0.119476
$446$	−49.3456	−2.33658
$447$	−0.407992	−0.0192974
$448$	4.90649	0.231810
$449$	18.2060	0.859193	0.429596	−	0.903021i	$-0.358656\pi$
$449$	18.2060	0.859193	0.429596	+	0.903021i	$0.358656\pi$
$450$	−13.1357	−0.619222
$451$	8.76426	0.412693
$452$	−26.5705	−1.24977
$453$	−0.162468	−0.00763342
$454$	9.91500	0.465334
$455$	0	0
$456$	−1.37289	−0.0642914
$457$	8.94689	0.418518	0.209259	−	0.977860i	$-0.432895\pi$
$457$	8.94689	0.418518	0.209259	+	0.977860i	$0.432895\pi$
$458$	9.61025	0.449058
$459$	13.8129	0.644729
$460$	−6.94042	−0.323599
$461$	−8.68811	−0.404645	−0.202323	−	0.979319i	$-0.564849\pi$
$461$	−8.68811	−0.404645	−0.202323	+	0.979319i	$0.564849\pi$
$462$	−1.65553	−0.0770225
$463$	−20.2019	−0.938864	−0.469432	−	0.882969i	$-0.655541\pi$
$463$	−20.2019	−0.938864	−0.469432	+	0.882969i	$0.655541\pi$
$464$	34.6274	1.60754
$465$	−9.43954	−0.437748
$466$	30.9114	1.43194
$467$	−10.5588	−0.488601	−0.244300	−	0.969700i	$-0.578558\pi$
$467$	−10.5588	−0.488601	−0.244300	+	0.969700i	$0.578558\pi$
$468$	0	0
$469$	−13.9305	−0.643252
$470$	11.0228	0.508446
$471$	7.83754	0.361135
$472$	−3.50556	−0.161357
$473$	−2.11079	−0.0970545
$474$	−16.7771	−0.770597
$475$	−6.95662	−0.319192
$476$	−4.32898	−0.198418
$477$	−11.2284	−0.514112
$478$	6.15100	0.281340
$479$	38.1404	1.74268	0.871340	−	0.490680i	$-0.163252\pi$
$479$	38.1404	1.74268	0.871340	+	0.490680i	$0.163252\pi$
$480$	−8.85965	−0.404386
$481$	0	0
$482$	−32.9146	−1.49922
$483$	−4.15196	−0.188921
$484$	−16.9898	−0.772263
$485$	−18.2420	−0.828325
$486$	29.5178	1.33895
$487$	4.23947	0.192109	0.0960544	−	0.995376i	$-0.469378\pi$
$487$	4.23947	0.192109	0.0960544	+	0.995376i	$0.469378\pi$
$488$	2.27780	0.103111
$489$	4.15716	0.187993
$490$	−2.10992	−0.0953163
$491$	16.0662	0.725057	0.362529	−	0.931973i	$-0.381913\pi$
$491$	16.0662	0.725057	0.362529	+	0.931973i	$0.381913\pi$
$492$	−19.4960	−0.878946
$493$	−19.9125	−0.896815
$494$	0	0
$495$	−1.61242	−0.0724728
$496$	−36.1151	−1.62162
$497$	6.69004	0.300089
$498$	−32.3603	−1.45010
$499$	−28.9437	−1.29570	−0.647848	−	0.761769i	$-0.724331\pi$
$499$	−28.9437	−1.29570	−0.647848	+	0.761769i	$0.724331\pi$
$500$	−15.9177	−0.711862
$501$	1.98837	0.0888336
$502$	−33.1707	−1.48048
$503$	−26.9087	−1.19980	−0.599901	−	0.800075i	$-0.704793\pi$
$503$	−26.9087	−1.19980	−0.599901	+	0.800075i	$0.704793\pi$
$504$	1.25240	0.0557861
$505$	−15.5587	−0.692352
$506$	5.83961	0.259602
$507$	0	0
$508$	32.7648	1.45370
$509$	−20.0963	−0.890755	−0.445377	−	0.895343i	$-0.646930\pi$
$509$	−20.0963	−0.890755	−0.445377	+	0.895343i	$0.646930\pi$
$510$	6.04281	0.267580
$511$	15.0774	0.666984
$512$	−27.5888	−1.21927
$513$	9.63762	0.425511
$514$	27.8906	1.23020
$515$	0.121904	0.00537175
$516$	4.69543	0.206705
$517$	−4.17848	−0.183769
$518$	−6.59708	−0.289859
$519$	23.9058	1.04935
$520$	0	0
$521$	30.2678	1.32605	0.663027	−	0.748595i	$-0.269271\pi$
$521$	30.2678	1.32605	0.663027	+	0.748595i	$0.269271\pi$
$522$	−26.2342	−1.14824
$523$	41.6444	1.82098	0.910491	−	0.413529i	$-0.135704\pi$
$523$	41.6444	1.82098	0.910491	+	0.413529i	$0.135704\pi$
$524$	−30.0132	−1.31113
$525$	−4.09775	−0.178841
$526$	−14.1415	−0.616600
$527$	20.7681	0.904671
$528$	3.98343	0.173357
$529$	−8.35469	−0.363248
$530$	−12.9962	−0.564518
$531$	9.30142	0.403647
$532$	−3.02045	−0.130953
$533$	0	0
$534$	4.71722	0.204134
$535$	−15.2694	−0.660154
$536$	9.57067	0.413390
$537$	−6.09912	−0.263196
$538$	8.74531	0.377037
$539$	0.799816	0.0344505
$540$	9.48965	0.408369
$541$	−9.64131	−0.414512	−0.207256	−	0.978287i	$-0.566453\pi$
$541$	−9.64131	−0.414512	−0.207256	+	0.978287i	$0.566453\pi$
$542$	−6.92107	−0.297285
$543$	4.81719	0.206725
$544$	19.4922	0.835723
$545$	2.40409	0.102980
$546$	0	0
$547$	−21.0811	−0.901362	−0.450681	−	0.892685i	$-0.648819\pi$
$547$	−21.0811	−0.901362	−0.450681	+	0.892685i	$0.648819\pi$
$548$	−1.70317	−0.0727557
$549$	−6.04375	−0.257941
$550$	5.76337	0.245751
$551$	−13.8935	−0.591885
$552$	2.85252	0.121411
$553$	8.10529	0.344672
$554$	−45.1662	−1.91893
$555$	4.14889	0.176111
$556$	26.3228	1.11634
$557$	−16.5044	−0.699313	−0.349657	−	0.936878i	$-0.613702\pi$
$557$	−16.5044	−0.699313	−0.349657	+	0.936878i	$0.613702\pi$
$558$	27.3613	1.15830
$559$	0	0
$560$	5.07673	0.214531
$561$	−2.29068	−0.0967125
$562$	−48.7293	−2.05552
$563$	−10.7950	−0.454954	−0.227477	−	0.973784i	$-0.573048\pi$
$563$	−10.7950	−0.454954	−0.227477	+	0.973784i	$0.573048\pi$
$564$	9.29496	0.391389
$565$	−17.9186	−0.753843
$566$	5.63495	0.236855
$567$	0.208236	0.00874507
$568$	−4.59625	−0.192854
$569$	−39.8672	−1.67132	−0.835660	−	0.549247i	$-0.814915\pi$
$569$	−39.8672	−1.67132	−0.835660	+	0.549247i	$0.814915\pi$
$570$	4.21624	0.176599
$571$	42.8074	1.79143	0.895717	−	0.444624i	$-0.146663\pi$
$571$	42.8074	1.79143	0.895717	+	0.444624i	$0.146663\pi$
$572$	0	0
$573$	4.77091	0.199308
$574$	20.9059	0.872597
$575$	14.4541	0.602778
$576$	8.94412	0.372672
$577$	−0.199664	−0.00831211	−0.00415606	−	0.999991i	$-0.501323\pi$
$577$	−0.199664	−0.00831211	−0.00415606	+	0.999991i	$0.501323\pi$
$578$	19.1386	0.796060
$579$	27.4172	1.13942
$580$	−13.6802	−0.568040
$581$	15.6338	0.648599
$582$	−34.1428	−1.41526
$583$	4.92652	0.204036
$584$	−10.3586	−0.428642
$585$	0	0
$586$	43.2447	1.78642
$587$	−1.12962	−0.0466244	−0.0233122	−	0.999728i	$-0.507421\pi$
$587$	−1.12962	−0.0466244	−0.0233122	+	0.999728i	$0.507421\pi$
$588$	−1.77918	−0.0733721
$589$	14.4905	0.597069
$590$	10.7658	0.443223
$591$	7.50624	0.308765
$592$	15.8734	0.652394
$593$	−16.5142	−0.678158	−0.339079	−	0.940758i	$-0.610115\pi$
$593$	−16.5142	−0.678158	−0.339079	+	0.940758i	$0.610115\pi$
$594$	−7.98450	−0.327608
$595$	−2.91938	−0.119683
$596$	0.616685	0.0252604
$597$	−18.8733	−0.772432
$598$	0	0
$599$	7.44907	0.304361	0.152180	−	0.988353i	$-0.451371\pi$
$599$	7.44907	0.304361	0.152180	+	0.988353i	$0.451371\pi$
$600$	2.81528	0.114933
$601$	−20.8286	−0.849618	−0.424809	−	0.905283i	$-0.639659\pi$
$601$	−20.8286	−0.849618	−0.424809	+	0.905283i	$0.639659\pi$
$602$	−5.03501	−0.205212
$603$	−25.3942	−1.03413
$604$	0.245573	0.00999221
$605$	−11.4576	−0.465817
$606$	−29.1206	−1.18294
$607$	35.4304	1.43808	0.719038	−	0.694970i	$-0.244583\pi$
$607$	35.4304	1.43808	0.719038	+	0.694970i	$0.244583\pi$
$608$	13.6003	0.551564
$609$	−8.18390	−0.331628
$610$	−6.99529	−0.283231
$611$	0	0
$612$	−7.89136	−0.318989
$613$	−19.1451	−0.773263	−0.386632	−	0.922234i	$-0.626362\pi$
$613$	−19.1451	−0.773263	−0.386632	+	0.922234i	$0.626362\pi$
$614$	3.90980	0.157787
$615$	−13.1477	−0.530167
$616$	−0.549497	−0.0221399
$617$	−3.52481	−0.141904	−0.0709518	−	0.997480i	$-0.522604\pi$
$617$	−3.52481	−0.141904	−0.0709518	+	0.997480i	$0.522604\pi$
$618$	0.228164	0.00917810
$619$	−40.1768	−1.61484	−0.807421	−	0.589976i	$-0.799137\pi$
$619$	−40.1768	−1.61484	−0.807421	+	0.589976i	$0.799137\pi$
$620$	14.2680	0.573016
$621$	−20.0245	−0.803557
$622$	29.4657	1.18147
$623$	−2.27897	−0.0913049
$624$	0	0
$625$	8.15019	0.326008
$626$	12.5762	0.502648
$627$	−1.59827	−0.0638288
$628$	−11.8465	−0.472728
$629$	−9.12804	−0.363959
$630$	−3.84620	−0.153236
$631$	6.33561	0.252217	0.126108	−	0.992016i	$-0.459751\pi$
$631$	6.33561	0.252217	0.126108	+	0.992016i	$0.459751\pi$
$632$	−5.56857	−0.221506
$633$	−8.13883	−0.323489
$634$	−33.6129	−1.33494
$635$	22.0960	0.876852
$636$	−10.9590	−0.434552
$637$	0	0
$638$	11.5104	0.455702
$639$	12.1954	0.482442
$640$	−5.97983	−0.236373
$641$	−27.5697	−1.08894	−0.544469	−	0.838781i	$-0.683269\pi$
$641$	−27.5697	−1.08894	−0.544469	+	0.838781i	$0.683269\pi$
$642$	−28.5792	−1.12793
$643$	15.7718	0.621977	0.310989	−	0.950414i	$-0.399340\pi$
$643$	15.7718	0.621977	0.310989	+	0.950414i	$0.399340\pi$
$644$	6.27574	0.247299
$645$	3.16651	0.124681
$646$	−9.27621	−0.364968
$647$	7.55988	0.297210	0.148605	−	0.988897i	$-0.452522\pi$
$647$	7.55988	0.297210	0.148605	+	0.988897i	$0.452522\pi$
$648$	−0.143064	−0.00562008
$649$	−4.08106	−0.160196
$650$	0	0
$651$	8.53552	0.334533
$652$	−6.28360	−0.246085
$653$	27.2957	1.06816	0.534082	−	0.845432i	$-0.320657\pi$
$653$	27.2957	1.06816	0.534082	+	0.845432i	$0.320657\pi$
$654$	4.49964	0.175950
$655$	−20.2403	−0.790856
$656$	−50.3024	−1.96398
$657$	27.4848	1.07228
$658$	−9.96718	−0.388561
$659$	26.4906	1.03193	0.515963	−	0.856611i	$-0.327434\pi$
$659$	26.4906	1.03193	0.515963	+	0.856611i	$0.327434\pi$
$660$	−1.57373	−0.0612574
$661$	−9.13946	−0.355484	−0.177742	−	0.984077i	$-0.556879\pi$
$661$	−9.13946	−0.355484	−0.177742	+	0.984077i	$0.556879\pi$
$662$	−26.8667	−1.04420
$663$	0	0
$664$	−10.7409	−0.416827
$665$	−2.03694	−0.0789890
$666$	−12.0259	−0.465995
$667$	28.8673	1.11775
$668$	−3.00544	−0.116284
$669$	−28.0613	−1.08491
$670$	−29.3922	−1.13552
$671$	2.65174	0.102369
$672$	8.01116	0.309037
$673$	−9.03859	−0.348412	−0.174206	−	0.984709i	$-0.555736\pi$
$673$	−9.03859	−0.348412	−0.174206	+	0.984709i	$0.555736\pi$
$674$	−5.21450	−0.200855
$675$	−19.7631	−0.760683
$676$	0	0
$677$	−6.04397	−0.232289	−0.116144	−	0.993232i	$-0.537054\pi$
$677$	−6.04397	−0.232289	−0.116144	+	0.993232i	$0.537054\pi$
$678$	−33.5376	−1.28800
$679$	16.4949	0.633018
$680$	2.00570	0.0769151
$681$	5.63835	0.216062
$682$	−12.0050	−0.459693
$683$	−43.9978	−1.68353	−0.841764	−	0.539846i	$-0.818482\pi$
$683$	−43.9978	−1.68353	−0.841764	+	0.539846i	$0.818482\pi$
$684$	−5.50603	−0.210528
$685$	−1.14858	−0.0438851
$686$	1.90785	0.0728421
$687$	5.46505	0.208505
$688$	12.1149	0.461876
$689$	0	0
$690$	−8.76029	−0.333498
$691$	−22.7816	−0.866651	−0.433326	−	0.901237i	$-0.642660\pi$
$691$	−22.7816	−0.866651	−0.433326	+	0.901237i	$0.642660\pi$
$692$	−36.1339	−1.37361
$693$	1.45800	0.0553847
$694$	5.54581	0.210516
$695$	17.7516	0.673357
$696$	5.62258	0.213123
$697$	28.9264	1.09567
$698$	13.5569	0.513135
$699$	17.5784	0.664875
$700$	6.19381	0.234104
$701$	−30.4001	−1.14820	−0.574098	−	0.818786i	$-0.694647\pi$
$701$	−30.4001	−1.14820	−0.574098	+	0.818786i	$0.694647\pi$
$702$	0	0
$703$	−6.36889	−0.240207
$704$	−3.92429	−0.147902
$705$	6.26835	0.236080
$706$	−11.8066	−0.444348
$707$	14.0686	0.529105
$708$	9.07825	0.341182
$709$	30.0571	1.12882	0.564409	−	0.825495i	$-0.309104\pi$
$709$	30.0571	1.12882	0.564409	+	0.825495i	$0.309104\pi$
$710$	14.1154	0.529742
$711$	14.7753	0.554115
$712$	1.56572	0.0586777
$713$	−30.1075	−1.12754
$714$	−5.46409	−0.204489
$715$	0	0
$716$	9.21890	0.344526
$717$	3.49789	0.130631
$718$	−49.3212	−1.84065
$719$	17.5716	0.655308	0.327654	−	0.944798i	$-0.393742\pi$
$719$	17.5716	0.655308	0.327654	+	0.944798i	$0.393742\pi$
$720$	9.25445	0.344893
$721$	−0.110230	−0.00410517
$722$	29.7769	1.10818
$723$	−18.7175	−0.696111
$724$	−7.28124	−0.270605
$725$	28.4904	1.05811
$726$	−21.4447	−0.795888
$727$	24.8988	0.923446	0.461723	−	0.887024i	$-0.347231\pi$
$727$	24.8988	0.923446	0.461723	+	0.887024i	$0.347231\pi$
$728$	0	0
$729$	17.4105	0.644835
$730$	31.8120	1.17741
$731$	−6.96668	−0.257672
$732$	−5.89875	−0.218024
$733$	31.8923	1.17797	0.588984	−	0.808145i	$-0.299528\pi$
$733$	31.8923	1.17797	0.588984	+	0.808145i	$0.299528\pi$
$734$	66.2976	2.44709
$735$	−1.19984	−0.0442569
$736$	−28.2580	−1.04160
$737$	11.1419	0.410415
$738$	38.1097	1.40284
$739$	−18.0548	−0.664157	−0.332078	−	0.943252i	$-0.607750\pi$
$739$	−18.0548	−0.664157	−0.332078	+	0.943252i	$0.607750\pi$
$740$	−6.27110	−0.230530
$741$	0	0
$742$	11.7515	0.431413
$743$	43.5109	1.59626	0.798129	−	0.602486i	$-0.205823\pi$
$743$	43.5109	1.59626	0.798129	+	0.602486i	$0.205823\pi$
$744$	−5.86415	−0.214990
$745$	0.415881	0.0152367
$746$	49.8651	1.82569
$747$	28.4991	1.04273
$748$	3.46239	0.126597
$749$	13.8071	0.504499
$750$	−20.0915	−0.733639
$751$	−49.5788	−1.80916	−0.904578	−	0.426307i	$-0.859814\pi$
$751$	−49.5788	−1.80916	−0.904578	+	0.426307i	$0.859814\pi$
$752$	23.9823	0.874546
$753$	−18.8632	−0.687412
$754$	0	0
$755$	0.165610	0.00602715
$756$	−8.58083	−0.312082
$757$	51.8824	1.88570	0.942850	−	0.333218i	$-0.108135\pi$
$757$	51.8824	1.88570	0.942850	+	0.333218i	$0.108135\pi$
$758$	34.6394	1.25816
$759$	3.32080	0.120538
$760$	1.39943	0.0507628
$761$	8.00874	0.290317	0.145158	−	0.989408i	$-0.453631\pi$
$761$	8.00874	0.290317	0.145158	+	0.989408i	$0.453631\pi$
$762$	41.3562	1.49818
$763$	−2.17385	−0.0786986
$764$	−7.21129	−0.260895
$765$	−5.32178	−0.192410
$766$	−14.6565	−0.529560
$767$	0	0
$768$	−21.8387	−0.788035
$769$	−22.7156	−0.819147	−0.409573	−	0.912277i	$-0.634322\pi$
$769$	−22.7156	−0.819147	−0.409573	+	0.912277i	$0.634322\pi$
$770$	1.68754	0.0608149
$771$	15.8605	0.571204
$772$	−41.4414	−1.49151
$773$	24.4370	0.878937	0.439468	−	0.898258i	$-0.355167\pi$
$773$	24.4370	0.878937	0.439468	+	0.898258i	$0.355167\pi$
$774$	−9.17839	−0.329911
$775$	−29.7145	−1.06738
$776$	−11.3325	−0.406813
$777$	−3.75156	−0.134586
$778$	17.6237	0.631839
$779$	20.1828	0.723124
$780$	0	0
$781$	−5.35080	−0.191467
$782$	19.2736	0.689224
$783$	−39.4703	−1.41055
$784$	−4.59054	−0.163948
$785$	−7.98908	−0.285142
$786$	−37.8831	−1.35124
$787$	−3.70522	−0.132077	−0.0660385	−	0.997817i	$-0.521036\pi$
$787$	−3.70522	−0.132077	−0.0660385	+	0.997817i	$0.521036\pi$
$788$	−11.3458	−0.404176
$789$	−8.04186	−0.286298
$790$	17.1015	0.608443
$791$	16.2026	0.576097
$792$	−1.00169	−0.0355934
$793$	0	0
$794$	−31.8710	−1.13106
$795$	−7.39052	−0.262115
$796$	28.5272	1.01112
$797$	−47.2016	−1.67197	−0.835984	−	0.548754i	$-0.815102\pi$
$797$	−47.2016	−1.67197	−0.835984	+	0.548754i	$0.815102\pi$
$798$	−3.81245	−0.134959
$799$	−13.7911	−0.487893
$800$	−27.8890	−0.986027
$801$	−4.15436	−0.146787
$802$	−54.1704	−1.91282
$803$	−12.0591	−0.425557
$804$	−24.7849	−0.874095
$805$	4.23224	0.149167
$806$	0	0
$807$	4.97319	0.175064
$808$	−9.66556	−0.340033
$809$	−15.3631	−0.540139	−0.270070	−	0.962841i	$-0.587047\pi$
$809$	−15.3631	−0.540139	−0.270070	+	0.962841i	$0.587047\pi$
$810$	0.439359	0.0154375
$811$	38.2892	1.34452	0.672258	−	0.740317i	$-0.265324\pi$
$811$	38.2892	1.34452	0.672258	+	0.740317i	$0.265324\pi$
$812$	12.3701	0.434104
$813$	−3.93580	−0.138034
$814$	5.27645	0.184940
$815$	−4.23754	−0.148435
$816$	13.1473	0.460248
$817$	−4.86085	−0.170060
$818$	−49.3601	−1.72584
$819$	0	0
$820$	19.8729	0.693993
$821$	18.0178	0.628824	0.314412	−	0.949287i	$-0.398193\pi$
$821$	18.0178	0.628824	0.314412	+	0.949287i	$0.398193\pi$
$822$	−2.14976	−0.0749815
$823$	12.2209	0.425995	0.212998	−	0.977053i	$-0.431677\pi$
$823$	12.2209	0.425995	0.212998	+	0.977053i	$0.431677\pi$
$824$	0.0757310	0.00263821
$825$	3.27745	0.114106
$826$	−9.73480	−0.338717
$827$	50.2854	1.74859	0.874297	−	0.485390i	$-0.161323\pi$
$827$	50.2854	1.74859	0.874297	+	0.485390i	$0.161323\pi$
$828$	11.4401	0.397572
$829$	−41.3255	−1.43530	−0.717648	−	0.696407i	$-0.754781\pi$
$829$	−41.3255	−1.43530	−0.717648	+	0.696407i	$0.754781\pi$
$830$	32.9860	1.14496
$831$	−25.6846	−0.890989
$832$	0	0
$833$	2.63979	0.0914634
$834$	33.2250	1.15049
$835$	−2.02681	−0.0701407
$836$	2.41581	0.0835524
$837$	41.1661	1.42291
$838$	12.5093	0.432125
$839$	−44.8612	−1.54878	−0.774391	−	0.632708i	$-0.781943\pi$
$839$	−44.8612	−1.54878	−0.774391	+	0.632708i	$0.781943\pi$
$840$	0.824328	0.0284420
$841$	27.9001	0.962073
$842$	−27.4921	−0.947441
$843$	−27.7108	−0.954412
$844$	12.3019	0.423450
$845$	0	0
$846$	−18.1693	−0.624674
$847$	10.3603	0.355984
$848$	−28.2757	−0.970993
$849$	3.20442	0.109976
$850$	19.0220	0.652449
$851$	13.2330	0.453620
$852$	11.9028	0.407782
$853$	38.3749	1.31393	0.656966	−	0.753920i	$-0.271840\pi$
$853$	38.3749	1.31393	0.656966	+	0.753920i	$0.271840\pi$
$854$	6.32535	0.216449
$855$	−3.71316	−0.126987
$856$	−9.48585	−0.324220
$857$	6.20663	0.212015	0.106007	−	0.994365i	$-0.466193\pi$
$857$	6.20663	0.212015	0.106007	+	0.994365i	$0.466193\pi$
$858$	0	0
$859$	43.0183	1.46777	0.733884	−	0.679275i	$-0.237706\pi$
$859$	43.0183	1.46777	0.733884	+	0.679275i	$0.237706\pi$
$860$	−4.78622	−0.163209
$861$	11.8886	0.405161
$862$	28.0506	0.955406
$863$	−19.4927	−0.663540	−0.331770	−	0.943360i	$-0.607646\pi$
$863$	−19.4927	−0.663540	−0.331770	+	0.943360i	$0.607646\pi$
$864$	38.6372	1.31446
$865$	−24.3680	−0.828537
$866$	39.3358	1.33668
$867$	10.8835	0.369624
$868$	−12.9015	−0.437907
$869$	−6.48274	−0.219912
$870$	−17.2674	−0.585418
$871$	0	0
$872$	1.49350	0.0505762
$873$	30.0689	1.01768
$874$	13.4478	0.454877
$875$	9.70655	0.328141
$876$	26.8253	0.906344
$877$	33.2003	1.12109	0.560547	−	0.828123i	$-0.310591\pi$
$877$	33.2003	1.12109	0.560547	+	0.828123i	$0.310591\pi$
$878$	−38.8103	−1.30979
$879$	24.5919	0.829465
$880$	−4.06045	−0.136878
$881$	50.5588	1.70337	0.851684	−	0.524055i	$-0.175582\pi$
$881$	50.5588	1.70337	0.851684	+	0.524055i	$0.175582\pi$
$882$	3.47785	0.117105
$883$	7.17013	0.241294	0.120647	−	0.992695i	$-0.461503\pi$
$883$	7.17013	0.241294	0.120647	+	0.992695i	$0.461503\pi$
$884$	0	0
$885$	6.12220	0.205795
$886$	−26.3654	−0.885764
$887$	−31.0525	−1.04264	−0.521320	−	0.853361i	$-0.674560\pi$
$887$	−31.0525	−1.04264	−0.521320	+	0.853361i	$0.674560\pi$
$888$	2.57743	0.0864928
$889$	−19.9799	−0.670103
$890$	−4.80843	−0.161179
$891$	−0.166550	−0.00557964
$892$	42.4150	1.42016
$893$	−9.62243	−0.322002
$894$	0.778388	0.0260332
$895$	6.21705	0.207813
$896$	5.40714	0.180640
$897$	0	0
$898$	−34.7343	−1.15910
$899$	−59.3448	−1.97926
$900$	11.2908	0.376359
$901$	16.2600	0.541699
$902$	−16.7209	−0.556745
$903$	−2.86325	−0.0952831
$904$	−11.1316	−0.370233
$905$	−4.91033	−0.163225
$906$	0.309965	0.0102979
$907$	−21.6888	−0.720165	−0.360082	−	0.932921i	$-0.617251\pi$
$907$	−21.6888	−0.720165	−0.360082	+	0.932921i	$0.617251\pi$
$908$	−8.52244	−0.282827
$909$	25.6459	0.850621
$910$	0	0
$911$	−28.0626	−0.929756	−0.464878	−	0.885375i	$-0.653902\pi$
$911$	−28.0626	−0.929756	−0.464878	+	0.885375i	$0.653902\pi$
$912$	9.17326	0.303757
$913$	−12.5042	−0.413827
$914$	−17.0693	−0.564603
$915$	−3.97800	−0.131509
$916$	−8.26050	−0.272935
$917$	18.3019	0.604383
$918$	−26.3529	−0.869774
$919$	−1.09050	−0.0359724	−0.0179862	−	0.999838i	$-0.505725\pi$
$919$	−1.09050	−0.0359724	−0.0179862	+	0.999838i	$0.505725\pi$
$920$	−2.90767	−0.0958631
$921$	2.22338	0.0732629
$922$	16.5756	0.545889
$923$	0	0
$924$	1.42302	0.0468138
$925$	13.0602	0.429416
$926$	38.5423	1.26658
$927$	−0.200939	−0.00659971
$928$	−55.6991	−1.82841
$929$	25.7716	0.845540	0.422770	−	0.906237i	$-0.361058\pi$
$929$	25.7716	0.845540	0.422770	+	0.906237i	$0.361058\pi$
$930$	18.0092	0.590546
$931$	1.84186	0.0603645
$932$	−26.5699	−0.870327
$933$	16.7563	0.548575
$934$	20.1445	0.659149
$935$	2.33497	0.0763616
$936$	0	0
$937$	−5.39284	−0.176176	−0.0880882	−	0.996113i	$-0.528076\pi$
$937$	−5.39284	−0.176176	−0.0880882	+	0.996113i	$0.528076\pi$
$938$	26.5773	0.867781
$939$	7.15172	0.233388
$940$	−9.47468	−0.309030
$941$	59.3354	1.93428	0.967139	−	0.254248i	$-0.0818279\pi$
$941$	59.3354	1.93428	0.967139	+	0.254248i	$0.0818279\pi$
$942$	−14.9529	−0.487190
$943$	−41.9348	−1.36558
$944$	23.4232	0.762360
$945$	−5.78675	−0.188243
$946$	4.02708	0.130932
$947$	29.0891	0.945270	0.472635	−	0.881258i	$-0.343303\pi$
$947$	29.0891	0.945270	0.472635	+	0.881258i	$0.343303\pi$
$948$	14.4208	0.468364
$949$	0	0
$950$	13.2722	0.430607
$951$	−19.1146	−0.619833
$952$	−1.81362	−0.0587796
$953$	11.0404	0.357633	0.178816	−	0.983882i	$-0.442773\pi$
$953$	11.0404	0.357633	0.178816	+	0.983882i	$0.442773\pi$
$954$	21.4221	0.693565
$955$	−4.86315	−0.157368
$956$	−5.28710	−0.170997
$957$	6.54562	0.211590
$958$	−72.7662	−2.35097
$959$	1.03858	0.0335376
$960$	5.88703	0.190003
$961$	30.8945	0.996596
$962$	0	0
$963$	25.1691	0.811063
$964$	28.2917	0.911215
$965$	−27.9473	−0.899656
$966$	7.92132	0.254864
$967$	−15.3720	−0.494330	−0.247165	−	0.968973i	$-0.579499\pi$
$967$	−15.3720	−0.494330	−0.247165	+	0.968973i	$0.579499\pi$
$968$	−7.11782	−0.228776
$969$	−5.27510	−0.169460
$970$	34.8029	1.11745
$971$	45.8252	1.47060	0.735300	−	0.677741i	$-0.237041\pi$
$971$	45.8252	1.47060	0.735300	+	0.677741i	$0.237041\pi$
$972$	−25.3720	−0.813807
$973$	−16.0516	−0.514589
$974$	−8.08828	−0.259165
$975$	0	0
$976$	−15.2196	−0.487168
$977$	30.9623	0.990572	0.495286	−	0.868730i	$-0.335063\pi$
$977$	30.9623	0.990572	0.495286	+	0.868730i	$0.335063\pi$
$978$	−7.93125	−0.253613
$979$	1.82275	0.0582555
$980$	1.81358	0.0579327
$981$	−3.96274	−0.126521
$982$	−30.6519	−0.978142
$983$	−27.6460	−0.881769	−0.440884	−	0.897564i	$-0.645335\pi$
$983$	−27.6460	−0.881769	−0.440884	+	0.897564i	$0.645335\pi$
$984$	−8.16778	−0.260379
$985$	−7.65137	−0.243793
$986$	37.9901	1.20985
$987$	−5.66803	−0.180415
$988$	0	0
$989$	10.0996	0.321149
$990$	3.07625	0.0977697
$991$	−29.7267	−0.944301	−0.472151	−	0.881518i	$-0.656522\pi$
$991$	−29.7267	−0.944301	−0.472151	+	0.881518i	$0.656522\pi$
$992$	58.0922	1.84443
$993$	−15.2783	−0.484841
$994$	−12.7636	−0.404837
$995$	19.2382	0.609892
$996$	27.8153	0.881362
$997$	24.6552	0.780838	0.390419	−	0.920637i	$-0.372330\pi$
$997$	24.6552	0.780838	0.390419	+	0.920637i	$0.372330\pi$
$998$	55.2202	1.74797
$999$	−18.0934	−0.572451

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.o.1.2	yes	6
7.6	odd	2		8281.2.a.cg.1.2		6
13.5	odd	4		1183.2.c.h.337.9		12
13.8	odd	4		1183.2.c.h.337.4		12
13.12	even	2		1183.2.a.n.1.5	✓	6
91.90	odd	2		8281.2.a.cb.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.5	✓	6	13.12	even	2
1183.2.a.o.1.2	yes	6	1.1	even	1	trivial
1183.2.c.h.337.4		12	13.8	odd	4
1183.2.c.h.337.9		12	13.5	odd	4
8281.2.a.cb.1.5		6	91.90	odd	2
8281.2.a.cg.1.2		6	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-1.90785 q^{2} -1.08494 q^{3} +1.63989 q^{4} +1.10591 q^{5} +2.06989 q^{6} -1.00000 q^{7} +0.687029 q^{8} -1.82292 q^{9} +O(q^{10})\)	\(q-1.90785 q^{2} -1.08494 q^{3} +1.63989 q^{4} +1.10591 q^{5} +2.06989 q^{6} -1.00000 q^{7} +0.687029 q^{8} -1.82292 q^{9} -2.10992 q^{10} +0.799816 q^{11} -1.77918 q^{12} +1.90785 q^{14} -1.19984 q^{15} -4.59054 q^{16} +2.63979 q^{17} +3.47785 q^{18} +1.84186 q^{19} +1.81358 q^{20} +1.08494 q^{21} -1.52593 q^{22} -3.82692 q^{23} -0.745382 q^{24} -3.77696 q^{25} +5.23255 q^{27} -1.63989 q^{28} -7.54322 q^{29} +2.28912 q^{30} +7.86730 q^{31} +7.38400 q^{32} -0.867749 q^{33} -5.03633 q^{34} -1.10591 q^{35} -2.98939 q^{36} -3.45786 q^{37} -3.51399 q^{38} +0.759794 q^{40} +10.9578 q^{41} -2.06989 q^{42} -2.63910 q^{43} +1.31161 q^{44} -2.01599 q^{45} +7.30119 q^{46} -5.22430 q^{47} +4.98044 q^{48} +1.00000 q^{49} +7.20587 q^{50} -2.86401 q^{51} +6.15957 q^{53} -9.98293 q^{54} +0.884527 q^{55} -0.687029 q^{56} -1.99830 q^{57} +14.3913 q^{58} -5.10250 q^{59} -1.96762 q^{60} +3.31543 q^{61} -15.0096 q^{62} +1.82292 q^{63} -4.90649 q^{64} +1.65553 q^{66} +13.9305 q^{67} +4.32898 q^{68} +4.15196 q^{69} +2.10992 q^{70} -6.69004 q^{71} -1.25240 q^{72} -15.0774 q^{73} +6.59708 q^{74} +4.09775 q^{75} +3.02045 q^{76} -0.799816 q^{77} -8.10529 q^{79} -5.07673 q^{80} -0.208236 q^{81} -20.9059 q^{82} -15.6338 q^{83} +1.77918 q^{84} +2.91938 q^{85} +5.03501 q^{86} +8.18390 q^{87} +0.549497 q^{88} +2.27897 q^{89} +3.84620 q^{90} -6.27574 q^{92} -8.53552 q^{93} +9.96718 q^{94} +2.03694 q^{95} -8.01116 q^{96} -16.4949 q^{97} -1.90785 q^{98} -1.45800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 8 q^{6} - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 8 * q^6 - 6 * q^7 + 3 * q^8	\( 6 q + 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 8 q^{6} - 6 q^{7} + 3 q^{8} - 14 q^{10} + 8 q^{11} - 23 q^{12} - 2 q^{14} + 3 q^{15} - 23 q^{17} + 26 q^{18} - 13 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{22} - 18 q^{23} - 26 q^{24} - 10 q^{25} - 10 q^{27} - 8 q^{28} - 15 q^{29} + 14 q^{30} + 3 q^{31} + 28 q^{32} + 3 q^{33} - 29 q^{34} - 2 q^{35} + 22 q^{36} - 13 q^{37} - 11 q^{38} - 14 q^{40} - 4 q^{41} + 8 q^{42} - 18 q^{43} - 19 q^{45} + 10 q^{46} - 16 q^{47} - 11 q^{48} + 6 q^{49} - 10 q^{50} + 14 q^{51} - 25 q^{53} - 31 q^{54} - 3 q^{56} - 4 q^{57} - 13 q^{58} + 18 q^{59} + 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} + 16 q^{67} - 34 q^{68} - q^{69} + 14 q^{70} + 25 q^{71} + 39 q^{72} - 5 q^{73} - 14 q^{74} + 15 q^{75} + 7 q^{76} - 8 q^{77} + 2 q^{79} - 27 q^{80} - 6 q^{81} - 10 q^{82} - 7 q^{83} + 23 q^{84} + 9 q^{85} - 3 q^{86} + 13 q^{87} - 48 q^{88} - 10 q^{89} - 32 q^{92} + 35 q^{93} - 14 q^{94} - 7 q^{95} - 14 q^{96} - 5 q^{97} + 2 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^5 - 8 * q^6 - 6 * q^7 + 3 * q^8 - 14 * q^10 + 8 * q^11 - 23 * q^12 - 2 * q^14 + 3 * q^15 - 23 * q^17 + 26 * q^18 - 13 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^22 - 18 * q^23 - 26 * q^24 - 10 * q^25 - 10 * q^27 - 8 * q^28 - 15 * q^29 + 14 * q^30 + 3 * q^31 + 28 * q^32 + 3 * q^33 - 29 * q^34 - 2 * q^35 + 22 * q^36 - 13 * q^37 - 11 * q^38 - 14 * q^40 - 4 * q^41 + 8 * q^42 - 18 * q^43 - 19 * q^45 + 10 * q^46 - 16 * q^47 - 11 * q^48 + 6 * q^49 - 10 * q^50 + 14 * q^51 - 25 * q^53 - 31 * q^54 - 3 * q^56 - 4 * q^57 - 13 * q^58 + 18 * q^59 + 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 + 16 * q^67 - 34 * q^68 - q^69 + 14 * q^70 + 25 * q^71 + 39 * q^72 - 5 * q^73 - 14 * q^74 + 15 * q^75 + 7 * q^76 - 8 * q^77 + 2 * q^79 - 27 * q^80 - 6 * q^81 - 10 * q^82 - 7 * q^83 + 23 * q^84 + 9 * q^85 - 3 * q^86 + 13 * q^87 - 48 * q^88 - 10 * q^89 - 32 * q^92 + 35 * q^93 - 14 * q^94 - 7 * q^95 - 14 * q^96 - 5 * q^97 + 2 * q^98 - 15 * q^99

Introduction

L-functions

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