LMFDB - Embedded newform 3549.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x - 1 $ x^3 - x^2 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.37720$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37720 q^{2} -1.00000 q^{3} +3.65109 q^{4} +4.02830 q^{5} -2.37720 q^{6} +1.00000 q^{7} +3.92498 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.37720 q^{2} -1.00000 q^{3} +3.65109 q^{4} +4.02830 q^{5} -2.37720 q^{6} +1.00000 q^{7} +3.92498 q^{8} +1.00000 q^{9} +9.57608 q^{10} +3.27389 q^{11} -3.65109 q^{12} +2.37720 q^{14} -4.02830 q^{15} +2.02830 q^{16} -0.377203 q^{17} +2.37720 q^{18} +3.54778 q^{19} +14.7077 q^{20} -1.00000 q^{21} +7.78270 q^{22} +1.89669 q^{23} -3.92498 q^{24} +11.2272 q^{25} -1.00000 q^{27} +3.65109 q^{28} -8.67939 q^{29} -9.57608 q^{30} -6.33048 q^{31} -3.02830 q^{32} -3.27389 q^{33} -0.896688 q^{34} +4.02830 q^{35} +3.65109 q^{36} -4.02830 q^{37} +8.43380 q^{38} +15.8110 q^{40} -7.50881 q^{41} -2.37720 q^{42} -8.65109 q^{43} +11.9533 q^{44} +4.02830 q^{45} +4.50881 q^{46} +12.1239 q^{47} -2.02830 q^{48} +1.00000 q^{49} +26.6893 q^{50} +0.377203 q^{51} +7.75441 q^{53} -2.37720 q^{54} +13.1882 q^{55} +3.92498 q^{56} -3.54778 q^{57} -20.6327 q^{58} +2.10331 q^{59} -14.7077 q^{60} +7.75441 q^{61} -15.0488 q^{62} +1.00000 q^{63} -11.2555 q^{64} -7.78270 q^{66} -5.58383 q^{67} -1.37720 q^{68} -1.89669 q^{69} +9.57608 q^{70} -3.99225 q^{71} +3.92498 q^{72} -7.50106 q^{73} -9.57608 q^{74} -11.2272 q^{75} +12.9533 q^{76} +3.27389 q^{77} -1.16283 q^{79} +8.17058 q^{80} +1.00000 q^{81} -17.8500 q^{82} -15.1805 q^{83} -3.65109 q^{84} -1.51948 q^{85} -20.5654 q^{86} +8.67939 q^{87} +12.8500 q^{88} -6.35878 q^{89} +9.57608 q^{90} +6.92498 q^{92} +6.33048 q^{93} +28.8209 q^{94} +14.2915 q^{95} +3.02830 q^{96} -4.97170 q^{97} +2.37720 q^{98} +3.27389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 13 q^{10} + 8 q^{11} - 4 q^{12} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 7 q^{19} + 13 q^{20} - 3 q^{21} + q^{22} + 9 q^{23} - 3 q^{24} + 11 q^{25} - 3 q^{27} + 4 q^{28} - 7 q^{29} - 13 q^{30} + 7 q^{31} + 3 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} - 4 q^{38} + 13 q^{40} - 2 q^{41} - 2 q^{42} - 19 q^{43} + 15 q^{44} - 7 q^{46} + 17 q^{47} + 6 q^{48} + 3 q^{49} + 16 q^{50} - 4 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} - 7 q^{57} - 22 q^{58} + 3 q^{59} - 13 q^{60} + 13 q^{61} - 17 q^{62} + 3 q^{63} + q^{64} - q^{66} - 5 q^{67} + q^{68} - 9 q^{69} + 13 q^{70} - 8 q^{71} + 3 q^{72} + 2 q^{73} - 13 q^{74} - 11 q^{75} + 18 q^{76} + 8 q^{77} - q^{79} + 26 q^{80} + 3 q^{81} - 36 q^{82} - 2 q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} + 7 q^{87} + 21 q^{88} + 19 q^{89} + 13 q^{90} + 12 q^{92} - 7 q^{93} + 7 q^{94} - 3 q^{96} - 27 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 13 * q^10 + 8 * q^11 - 4 * q^12 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 7 * q^19 + 13 * q^20 - 3 * q^21 + q^22 + 9 * q^23 - 3 * q^24 + 11 * q^25 - 3 * q^27 + 4 * q^28 - 7 * q^29 - 13 * q^30 + 7 * q^31 + 3 * q^32 - 8 * q^33 - 6 * q^34 + 4 * q^36 - 4 * q^38 + 13 * q^40 - 2 * q^41 - 2 * q^42 - 19 * q^43 + 15 * q^44 - 7 * q^46 + 17 * q^47 + 6 * q^48 + 3 * q^49 + 16 * q^50 - 4 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 - 7 * q^57 - 22 * q^58 + 3 * q^59 - 13 * q^60 + 13 * q^61 - 17 * q^62 + 3 * q^63 + q^64 - q^66 - 5 * q^67 + q^68 - 9 * q^69 + 13 * q^70 - 8 * q^71 + 3 * q^72 + 2 * q^73 - 13 * q^74 - 11 * q^75 + 18 * q^76 + 8 * q^77 - q^79 + 26 * q^80 + 3 * q^81 - 36 * q^82 - 2 * q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 + 7 * q^87 + 21 * q^88 + 19 * q^89 + 13 * q^90 + 12 * q^92 - 7 * q^93 + 7 * q^94 - 3 * q^96 - 27 * q^97 + 2 * q^98 + 8 * 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 $

$2$	2.37720	1.68094	0.840468	−	0.541861i	$-0.182280\pi$
$2$	2.37720	1.68094	0.840468	+	0.541861i	$0.182280\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.65109	1.82555
$5$	4.02830	1.80151	0.900754	−	0.434329i	$-0.143014\pi$
$5$	4.02830	1.80151	0.900754	+	0.434329i	$0.143014\pi$
$6$	−2.37720	−0.970489
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.92498	1.38769
$9$	1.00000	0.333333
$10$	9.57608	3.02822
$11$	3.27389	0.987115	0.493558	−	0.869713i	$-0.335696\pi$
$11$	3.27389	0.987115	0.493558	+	0.869713i	$0.335696\pi$
$12$	−3.65109	−1.05398
$13$	0	0
$13$	0	0
$14$	2.37720	0.635334
$15$	−4.02830	−1.04010
$16$	2.02830	0.507074
$17$	−0.377203	−0.0914851	−0.0457426	−	0.998953i	$-0.514565\pi$
$17$	−0.377203	−0.0914851	−0.0457426	+	0.998953i	$0.514565\pi$
$18$	2.37720	0.560312
$19$	3.54778	0.813917	0.406958	−	0.913447i	$-0.366589\pi$
$19$	3.54778	0.813917	0.406958	+	0.913447i	$0.366589\pi$
$20$	14.7077	3.28874
$21$	−1.00000	−0.218218
$22$	7.78270	1.65928
$23$	1.89669	0.395487	0.197743	−	0.980254i	$-0.436639\pi$
$23$	1.89669	0.395487	0.197743	+	0.980254i	$0.436639\pi$
$24$	−3.92498	−0.801184
$25$	11.2272	2.24543
$26$	0	0
$27$	−1.00000	−0.192450
$28$	3.65109	0.689992
$29$	−8.67939	−1.61172	−0.805861	−	0.592105i	$-0.798297\pi$
$29$	−8.67939	−1.61172	−0.805861	+	0.592105i	$0.798297\pi$
$30$	−9.57608	−1.74834
$31$	−6.33048	−1.13699	−0.568494	−	0.822687i	$-0.692474\pi$
$31$	−6.33048	−1.13699	−0.568494	+	0.822687i	$0.692474\pi$
$32$	−3.02830	−0.535332
$33$	−3.27389	−0.569911
$34$	−0.896688	−0.153781
$35$	4.02830	0.680906
$36$	3.65109	0.608516
$37$	−4.02830	−0.662248	−0.331124	−	0.943587i	$-0.607428\pi$
$37$	−4.02830	−0.662248	−0.331124	+	0.943587i	$0.607428\pi$
$38$	8.43380	1.36814
$39$	0	0
$40$	15.8110	2.49994
$41$	−7.50881	−1.17268	−0.586340	−	0.810065i	$-0.699432\pi$
$41$	−7.50881	−1.17268	−0.586340	+	0.810065i	$0.699432\pi$
$42$	−2.37720	−0.366810
$43$	−8.65109	−1.31928	−0.659640	−	0.751582i	$-0.729291\pi$
$43$	−8.65109	−1.31928	−0.659640	+	0.751582i	$0.729291\pi$
$44$	11.9533	1.80202
$45$	4.02830	0.600503
$46$	4.50881	0.664788
$47$	12.1239	1.76845	0.884223	−	0.467064i	$-0.154688\pi$
$47$	12.1239	1.76845	0.884223	+	0.467064i	$0.154688\pi$
$48$	−2.02830	−0.292759
$49$	1.00000	0.142857
$50$	26.6893	3.77443
$51$	0.377203	0.0528190
$52$	0	0
$53$	7.75441	1.06515	0.532575	−	0.846383i	$-0.321225\pi$
$53$	7.75441	1.06515	0.532575	+	0.846383i	$0.321225\pi$
$54$	−2.37720	−0.323496
$55$	13.1882	1.77830
$56$	3.92498	0.524498
$57$	−3.54778	−0.469915
$58$	−20.6327	−2.70920
$59$	2.10331	0.273828	0.136914	−	0.990583i	$-0.456282\pi$
$59$	2.10331	0.273828	0.136914	+	0.990583i	$0.456282\pi$
$60$	−14.7077	−1.89875
$61$	7.75441	0.992850	0.496425	−	0.868080i	$-0.334646\pi$
$61$	7.75441	0.992850	0.496425	+	0.868080i	$0.334646\pi$
$62$	−15.0488	−1.91120
$63$	1.00000	0.125988
$64$	−11.2555	−1.40693
$65$	0	0
$66$	−7.78270	−0.957984
$67$	−5.58383	−0.682173	−0.341087	−	0.940032i	$-0.610795\pi$
$67$	−5.58383	−0.682173	−0.341087	+	0.940032i	$0.610795\pi$
$68$	−1.37720	−0.167010
$69$	−1.89669	−0.228334
$70$	9.57608	1.14456
$71$	−3.99225	−0.473793	−0.236896	−	0.971535i	$-0.576130\pi$
$71$	−3.99225	−0.473793	−0.236896	+	0.971535i	$0.576130\pi$
$72$	3.92498	0.462564
$73$	−7.50106	−0.877933	−0.438966	−	0.898503i	$-0.644655\pi$
$73$	−7.50106	−0.877933	−0.438966	+	0.898503i	$0.644655\pi$
$74$	−9.57608	−1.11320
$75$	−11.2272	−1.29640
$76$	12.9533	1.48584
$77$	3.27389	0.373094
$78$	0	0
$79$	−1.16283	−0.130828	−0.0654142	−	0.997858i	$-0.520837\pi$
$79$	−1.16283	−0.130828	−0.0654142	+	0.997858i	$0.520837\pi$
$80$	8.17058	0.913498
$81$	1.00000	0.111111
$82$	−17.8500	−1.97120
$83$	−15.1805	−1.66627	−0.833135	−	0.553069i	$-0.813457\pi$
$83$	−15.1805	−1.66627	−0.833135	+	0.553069i	$0.813457\pi$
$84$	−3.65109	−0.398367
$85$	−1.51948	−0.164811
$86$	−20.5654	−2.21762
$87$	8.67939	0.930528
$88$	12.8500	1.36981
$89$	−6.35878	−0.674029	−0.337015	−	0.941499i	$-0.609417\pi$
$89$	−6.35878	−0.674029	−0.337015	+	0.941499i	$0.609417\pi$
$90$	9.57608	1.00941
$91$	0	0
$92$	6.92498	0.721979
$93$	6.33048	0.656441
$94$	28.8209	2.97265
$95$	14.2915	1.46628
$96$	3.02830	0.309074
$97$	−4.97170	−0.504800	−0.252400	−	0.967623i	$-0.581220\pi$
$97$	−4.97170	−0.504800	−0.252400	+	0.967623i	$0.581220\pi$
$98$	2.37720	0.240134
$99$	3.27389	0.329038
$100$	40.9914	4.09914
$101$	5.89669	0.586742	0.293371	−	0.955999i	$-0.405223\pi$
$101$	5.89669	0.586742	0.293371	+	0.955999i	$0.405223\pi$
$102$	0.896688	0.0887853
$103$	10.5654	1.04104	0.520520	−	0.853849i	$-0.325738\pi$
$103$	10.5654	1.04104	0.520520	+	0.853849i	$0.325738\pi$
$104$	0	0
$105$	−4.02830	−0.393121
$106$	18.4338	1.79045
$107$	−12.4055	−1.19928	−0.599642	−	0.800268i	$-0.704691\pi$
$107$	−12.4055	−1.19928	−0.599642	+	0.800268i	$0.704691\pi$
$108$	−3.65109	−0.351327
$109$	12.1316	1.16200	0.580999	−	0.813905i	$-0.302662\pi$
$109$	12.1316	1.16200	0.580999	+	0.813905i	$0.302662\pi$
$110$	31.3510	2.98920
$111$	4.02830	0.382349
$112$	2.02830	0.191656
$113$	−10.6716	−1.00390	−0.501952	−	0.864896i	$-0.667384\pi$
$113$	−10.6716	−1.00390	−0.501952	+	0.864896i	$0.667384\pi$
$114$	−8.43380	−0.789897
$115$	7.64042	0.712473
$116$	−31.6893	−2.94227
$117$	0	0
$118$	5.00000	0.460287
$119$	−0.377203	−0.0345781
$120$	−15.8110	−1.44334
$121$	−0.281641	−0.0256037
$122$	18.4338	1.66892
$123$	7.50881	0.677047
$124$	−23.1132	−2.07563
$125$	25.0849	2.24366
$126$	2.37720	0.211778
$127$	7.33048	0.650475	0.325238	−	0.945632i	$-0.394556\pi$
$127$	7.33048	0.650475	0.325238	+	0.945632i	$0.394556\pi$
$128$	−20.6999	−1.82963
$129$	8.65109	0.761686
$130$	0	0
$131$	11.4239	0.998113	0.499056	−	0.866570i	$-0.333680\pi$
$131$	11.4239	0.998113	0.499056	+	0.866570i	$0.333680\pi$
$132$	−11.9533	−1.04040
$133$	3.54778	0.307632
$134$	−13.2739	−1.14669
$135$	−4.02830	−0.346701
$136$	−1.48052	−0.126953
$137$	3.19112	0.272636	0.136318	−	0.990665i	$-0.456473\pi$
$137$	3.19112	0.272636	0.136318	+	0.990665i	$0.456473\pi$
$138$	−4.50881	−0.383816
$139$	5.37720	0.456088	0.228044	−	0.973651i	$-0.426767\pi$
$139$	5.37720	0.456088	0.228044	+	0.973651i	$0.426767\pi$
$140$	14.7077	1.24303
$141$	−12.1239	−1.02101
$142$	−9.49039	−0.796416
$143$	0	0
$144$	2.02830	0.169025
$145$	−34.9632	−2.90353
$146$	−17.8315	−1.47575
$147$	−1.00000	−0.0824786
$148$	−14.7077	−1.20896
$149$	10.0283	0.821550	0.410775	−	0.911737i	$-0.365258\pi$
$149$	10.0283	0.821550	0.410775	+	0.911737i	$0.365258\pi$
$150$	−26.6893	−2.17917
$151$	9.71544	0.790631	0.395315	−	0.918545i	$-0.370635\pi$
$151$	9.71544	0.790631	0.395315	+	0.918545i	$0.370635\pi$
$152$	13.9250	1.12947
$153$	−0.377203	−0.0304950
$154$	7.78270	0.627148
$155$	−25.5011	−2.04829
$156$	0	0
$157$	17.5761	1.40272	0.701362	−	0.712805i	$-0.252576\pi$
$157$	17.5761	1.40272	0.701362	+	0.712805i	$0.252576\pi$
$158$	−2.76428	−0.219914
$159$	−7.75441	−0.614964
$160$	−12.1989	−0.964406
$161$	1.89669	0.149480
$162$	2.37720	0.186771
$163$	5.49119	0.430103	0.215052	−	0.976603i	$-0.431008\pi$
$163$	5.49119	0.430103	0.215052	+	0.976603i	$0.431008\pi$
$164$	−27.4154	−2.14078
$165$	−13.1882	−1.02670
$166$	−36.0870	−2.80090
$167$	−4.43672	−0.343324	−0.171662	−	0.985156i	$-0.554914\pi$
$167$	−4.43672	−0.343324	−0.171662	+	0.985156i	$0.554914\pi$
$168$	−3.92498	−0.302819
$169$	0	0
$170$	−3.61212	−0.277037
$171$	3.54778	0.271306
$172$	−31.5860	−2.40841
$173$	22.1599	1.68479	0.842393	−	0.538863i	$-0.181146\pi$
$173$	22.1599	1.68479	0.842393	+	0.538863i	$0.181146\pi$
$174$	20.6327	1.56416
$175$	11.2272	0.848694
$176$	6.64042	0.500540
$177$	−2.10331	−0.158095
$178$	−15.1161	−1.13300
$179$	−1.94048	−0.145039	−0.0725193	−	0.997367i	$-0.523104\pi$
$179$	−1.94048	−0.145039	−0.0725193	+	0.997367i	$0.523104\pi$
$180$	14.7077	1.09625
$181$	−8.50106	−0.631879	−0.315939	−	0.948779i	$-0.602320\pi$
$181$	−8.50106	−0.631879	−0.315939	+	0.948779i	$0.602320\pi$
$182$	0	0
$183$	−7.75441	−0.573222
$184$	7.44447	0.548814
$185$	−16.2272	−1.19305
$186$	15.0488	1.10343
$187$	−1.23492	−0.0903064
$188$	44.2653	3.22838
$189$	−1.00000	−0.0727393
$190$	33.9738	2.46472
$191$	0.651093	0.0471115	0.0235557	−	0.999723i	$-0.492501\pi$
$191$	0.651093	0.0471115	0.0235557	+	0.999723i	$0.492501\pi$
$192$	11.2555	0.812293
$193$	−19.0643	−1.37228	−0.686141	−	0.727469i	$-0.740697\pi$
$193$	−19.0643	−1.37228	−0.686141	+	0.727469i	$0.740697\pi$
$194$	−11.8187	−0.848537
$195$	0	0
$196$	3.65109	0.260792
$197$	−24.7098	−1.76050	−0.880250	−	0.474509i	$-0.842626\pi$
$197$	−24.7098	−1.76050	−0.880250	+	0.474509i	$0.842626\pi$
$198$	7.78270	0.553093
$199$	13.1444	0.931782	0.465891	−	0.884842i	$-0.345734\pi$
$199$	13.1444	0.931782	0.465891	+	0.884842i	$0.345734\pi$
$200$	44.0665	3.11597
$201$	5.58383	0.393853
$202$	14.0176	0.986277
$203$	−8.67939	−0.609174
$204$	1.37720	0.0964235
$205$	−30.2477	−2.11259
$206$	25.1161	1.74992
$207$	1.89669	0.131829
$208$	0	0
$209$	11.6150	0.803430
$210$	−9.57608	−0.660812
$211$	−19.5966	−1.34909	−0.674544	−	0.738235i	$-0.735660\pi$
$211$	−19.5966	−1.34909	−0.674544	+	0.738235i	$0.735660\pi$
$212$	28.3121	1.94448
$213$	3.99225	0.273544
$214$	−29.4904	−2.01592
$215$	−34.8492	−2.37669
$216$	−3.92498	−0.267061
$217$	−6.33048	−0.429741
$218$	28.8393	1.95324
$219$	7.50106	0.506875
$220$	48.1514	3.24636
$221$	0	0
$222$	9.57608	0.642704
$223$	27.8676	1.86615	0.933076	−	0.359679i	$-0.117114\pi$
$223$	27.8676	1.86615	0.933076	+	0.359679i	$0.117114\pi$
$224$	−3.02830	−0.202337
$225$	11.2272	0.748478
$226$	−25.3687	−1.68750
$227$	−12.0304	−0.798487	−0.399243	−	0.916845i	$-0.630727\pi$
$227$	−12.0304	−0.798487	−0.399243	+	0.916845i	$0.630727\pi$
$228$	−12.9533	−0.857852
$229$	9.19887	0.607879	0.303939	−	0.952691i	$-0.401698\pi$
$229$	9.19887	0.607879	0.303939	+	0.952691i	$0.401698\pi$
$230$	18.1628	1.19762
$231$	−3.27389	−0.215406
$232$	−34.0665	−2.23657
$233$	−12.4522	−0.815772	−0.407886	−	0.913033i	$-0.633734\pi$
$233$	−12.4522	−0.815772	−0.407886	+	0.913033i	$0.633734\pi$
$234$	0	0
$235$	48.8385	3.18587
$236$	7.67939	0.499886
$237$	1.16283	0.0755338
$238$	−0.896688	−0.0581236
$239$	3.24559	0.209940	0.104970	−	0.994475i	$-0.466525\pi$
$239$	3.24559	0.209940	0.104970	+	0.994475i	$0.466525\pi$
$240$	−8.17058	−0.527409
$241$	−9.42605	−0.607185	−0.303592	−	0.952802i	$-0.598186\pi$
$241$	−9.42605	−0.607185	−0.303592	+	0.952802i	$0.598186\pi$
$242$	−0.669517	−0.0430382
$243$	−1.00000	−0.0641500
$244$	28.3121	1.81249
$245$	4.02830	0.257358
$246$	17.8500	1.13807
$247$	0	0
$248$	−24.8470	−1.57779
$249$	15.1805	0.962022
$250$	59.6319	3.77145
$251$	−11.9893	−0.756760	−0.378380	−	0.925650i	$-0.623519\pi$
$251$	−11.9893	−0.756760	−0.378380	+	0.925650i	$0.623519\pi$
$252$	3.65109	0.229997
$253$	6.20955	0.390391
$254$	17.4260	1.09341
$255$	1.51948	0.0951538
$256$	−26.6970	−1.66856
$257$	14.5966	0.910512	0.455256	−	0.890360i	$-0.349548\pi$
$257$	14.5966	0.910512	0.455256	+	0.890360i	$0.349548\pi$
$258$	20.5654	1.28035
$259$	−4.02830	−0.250306
$260$	0	0
$261$	−8.67939	−0.537241
$262$	27.1570	1.67776
$263$	22.6532	1.39686	0.698429	−	0.715680i	$-0.253883\pi$
$263$	22.6532	1.39686	0.698429	+	0.715680i	$0.253883\pi$
$264$	−12.8500	−0.790861
$265$	31.2370	1.91888
$266$	8.43380	0.517109
$267$	6.35878	0.389151
$268$	−20.3871	−1.24534
$269$	−27.9893	−1.70654	−0.853270	−	0.521470i	$-0.825384\pi$
$269$	−27.9893	−1.70654	−0.853270	+	0.521470i	$0.825384\pi$
$270$	−9.57608	−0.582782
$271$	7.60730	0.462110	0.231055	−	0.972941i	$-0.425782\pi$
$271$	7.60730	0.462110	0.231055	+	0.972941i	$0.425782\pi$
$272$	−0.765079	−0.0463897
$273$	0	0
$274$	7.58595	0.458284
$275$	36.7565	2.21650
$276$	−6.92498	−0.416835
$277$	−6.88894	−0.413916	−0.206958	−	0.978350i	$-0.566356\pi$
$277$	−6.88894	−0.413916	−0.206958	+	0.978350i	$0.566356\pi$
$278$	12.7827	0.766656
$279$	−6.33048	−0.378996
$280$	15.8110	0.944888
$281$	−10.8062	−0.644642	−0.322321	−	0.946630i	$-0.604463\pi$
$281$	−10.8062	−0.644642	−0.322321	+	0.946630i	$0.604463\pi$
$282$	−28.8209	−1.71626
$283$	−7.62492	−0.453254	−0.226627	−	0.973982i	$-0.572770\pi$
$283$	−7.62492	−0.453254	−0.226627	+	0.973982i	$0.572770\pi$
$284$	−14.5761	−0.864931
$285$	−14.2915	−0.846556
$286$	0	0
$287$	−7.50881	−0.443231
$288$	−3.02830	−0.178444
$289$	−16.8577	−0.991630
$290$	−83.1145	−4.88065
$291$	4.97170	0.291446
$292$	−27.3871	−1.60271
$293$	22.2915	1.30228	0.651142	−	0.758956i	$-0.274290\pi$
$293$	22.2915	1.30228	0.651142	+	0.758956i	$0.274290\pi$
$294$	−2.37720	−0.138641
$295$	8.47277	0.493303
$296$	−15.8110	−0.918996
$297$	−3.27389	−0.189970
$298$	23.8393	1.38097
$299$	0	0
$300$	−40.9914	−2.36664
$301$	−8.65109	−0.498641
$302$	23.0956	1.32900
$303$	−5.89669	−0.338756
$304$	7.19595	0.412716
$305$	31.2370	1.78863
$306$	−0.896688	−0.0512602
$307$	28.2448	1.61202	0.806008	−	0.591905i	$-0.201624\pi$
$307$	28.2448	1.61202	0.806008	+	0.591905i	$0.201624\pi$
$308$	11.9533	0.681101
$309$	−10.5654	−0.601045
$310$	−60.6212	−3.44305
$311$	−2.66177	−0.150935	−0.0754675	−	0.997148i	$-0.524045\pi$
$311$	−2.66177	−0.150935	−0.0754675	+	0.997148i	$0.524045\pi$
$312$	0	0
$313$	−22.4826	−1.27079	−0.635397	−	0.772186i	$-0.719163\pi$
$313$	−22.4826	−1.27079	−0.635397	+	0.772186i	$0.719163\pi$
$314$	41.7819	2.35789
$315$	4.02830	0.226969
$316$	−4.24559	−0.238833
$317$	−18.8315	−1.05768	−0.528842	−	0.848720i	$-0.677374\pi$
$317$	−18.8315	−1.05768	−0.528842	+	0.848720i	$0.677374\pi$
$318$	−18.4338	−1.03372
$319$	−28.4154	−1.59096
$320$	−45.3404	−2.53460
$321$	12.4055	0.692407
$322$	4.50881	0.251266
$323$	−1.33823	−0.0744613
$324$	3.65109	0.202839
$325$	0	0
$326$	13.0537	0.722976
$327$	−12.1316	−0.670879
$328$	−29.4720	−1.62732
$329$	12.1239	0.668410
$330$	−31.3510	−1.72582
$331$	17.8315	0.980110	0.490055	−	0.871691i	$-0.336977\pi$
$331$	17.8315	0.980110	0.490055	+	0.871691i	$0.336977\pi$
$332$	−55.4252	−3.04186
$333$	−4.02830	−0.220749
$334$	−10.5470	−0.577105
$335$	−22.4933	−1.22894
$336$	−2.02830	−0.110653
$337$	7.57608	0.412695	0.206348	−	0.978479i	$-0.433842\pi$
$337$	7.57608	0.412695	0.206348	+	0.978479i	$0.433842\pi$
$338$	0	0
$339$	10.6716	0.579604
$340$	−5.54778	−0.300871
$341$	−20.7253	−1.12234
$342$	8.43380	0.456047
$343$	1.00000	0.0539949
$344$	−33.9554	−1.83075
$345$	−7.64042	−0.411346
$346$	52.6786	2.83202
$347$	7.88814	0.423457	0.211729	−	0.977328i	$-0.432091\pi$
$347$	7.88814	0.423457	0.211729	+	0.977328i	$0.432091\pi$
$348$	31.6893	1.69872
$349$	11.7339	0.628099	0.314050	−	0.949407i	$-0.398314\pi$
$349$	11.7339	0.628099	0.314050	+	0.949407i	$0.398314\pi$
$350$	26.6893	1.42660
$351$	0	0
$352$	−9.91431	−0.528435
$353$	12.5371	0.667283	0.333641	−	0.942700i	$-0.391723\pi$
$353$	12.5371	0.667283	0.333641	+	0.942700i	$0.391723\pi$
$354$	−5.00000	−0.265747
$355$	−16.0820	−0.853542
$356$	−23.2165	−1.23047
$357$	0.377203	0.0199637
$358$	−4.61292	−0.243801
$359$	5.01762	0.264820	0.132410	−	0.991195i	$-0.457728\pi$
$359$	5.01762	0.264820	0.132410	+	0.991195i	$0.457728\pi$
$360$	15.8110	0.833313
$361$	−6.41325	−0.337539
$362$	−20.2087	−1.06215
$363$	0.281641	0.0147823
$364$	0	0
$365$	−30.2165	−1.58160
$366$	−18.4338	−0.963550
$367$	23.7098	1.23764	0.618821	−	0.785532i	$-0.287611\pi$
$367$	23.7098	1.23764	0.618821	+	0.785532i	$0.287611\pi$
$368$	3.84704	0.200541
$369$	−7.50881	−0.390893
$370$	−38.5753	−2.00543
$371$	7.75441	0.402589
$372$	23.1132	1.19836
$373$	−9.95328	−0.515361	−0.257681	−	0.966230i	$-0.582958\pi$
$373$	−9.95328	−0.515361	−0.257681	+	0.966230i	$0.582958\pi$
$374$	−2.93566	−0.151799
$375$	−25.0849	−1.29538
$376$	47.5860	2.45406
$377$	0	0
$378$	−2.37720	−0.122270
$379$	27.8500	1.43056	0.715278	−	0.698840i	$-0.246300\pi$
$379$	27.8500	1.43056	0.715278	+	0.698840i	$0.246300\pi$
$380$	52.1797	2.67676
$381$	−7.33048	−0.375552
$382$	1.54778	0.0791914
$383$	6.90444	0.352800	0.176400	−	0.984319i	$-0.443555\pi$
$383$	6.90444	0.352800	0.176400	+	0.984319i	$0.443555\pi$
$384$	20.6999	1.05634
$385$	13.1882	0.672133
$386$	−45.3198	−2.30672
$387$	−8.65109	−0.439760
$388$	−18.1522	−0.921536
$389$	−28.3764	−1.43874	−0.719370	−	0.694627i	$-0.755570\pi$
$389$	−28.3764	−1.43874	−0.719370	+	0.694627i	$0.755570\pi$
$390$	0	0
$391$	−0.715436	−0.0361812
$392$	3.92498	0.198242
$393$	−11.4239	−0.576261
$394$	−58.7402	−2.95929
$395$	−4.68422	−0.235689
$396$	11.9533	0.600675
$397$	4.76720	0.239259	0.119630	−	0.992819i	$-0.461829\pi$
$397$	4.76720	0.239259	0.119630	+	0.992819i	$0.461829\pi$
$398$	31.2469	1.56627
$399$	−3.54778	−0.177611
$400$	22.7720	1.13860
$401$	8.26614	0.412791	0.206396	−	0.978469i	$-0.433827\pi$
$401$	8.26614	0.412791	0.206396	+	0.978469i	$0.433827\pi$
$402$	13.2739	0.662041
$403$	0	0
$404$	21.5294	1.07113
$405$	4.02830	0.200168
$406$	−20.6327	−1.02398
$407$	−13.1882	−0.653715
$408$	1.48052	0.0732964
$409$	−21.4338	−1.05983	−0.529916	−	0.848050i	$-0.677777\pi$
$409$	−21.4338	−1.05983	−0.529916	+	0.848050i	$0.677777\pi$
$410$	−71.9050	−3.55113
$411$	−3.19112	−0.157407
$412$	38.5753	1.90047
$413$	2.10331	0.103497
$414$	4.50881	0.221596
$415$	−61.1514	−3.00180
$416$	0	0
$417$	−5.37720	−0.263323
$418$	27.6113	1.35051
$419$	−2.29151	−0.111948	−0.0559739	−	0.998432i	$-0.517826\pi$
$419$	−2.29151	−0.111948	−0.0559739	+	0.998432i	$0.517826\pi$
$420$	−14.7077	−0.717662
$421$	−7.61292	−0.371031	−0.185516	−	0.982641i	$-0.559396\pi$
$421$	−7.61292	−0.371031	−0.185516	+	0.982641i	$0.559396\pi$
$422$	−46.5851	−2.26773
$423$	12.1239	0.589482
$424$	30.4359	1.47810
$425$	−4.23492	−0.205424
$426$	9.49039	0.459811
$427$	7.75441	0.375262
$428$	−45.2936	−2.18935
$429$	0	0
$430$	−82.8435	−3.99507
$431$	−20.8628	−1.00492	−0.502462	−	0.864599i	$-0.667572\pi$
$431$	−20.8628	−1.00492	−0.502462	+	0.864599i	$0.667572\pi$
$432$	−2.02830	−0.0975864
$433$	−23.3764	−1.12340	−0.561699	−	0.827342i	$-0.689852\pi$
$433$	−23.3764	−1.12340	−0.561699	+	0.827342i	$0.689852\pi$
$434$	−15.0488	−0.722368
$435$	34.9632	1.67635
$436$	44.2936	2.12128
$437$	6.72903	0.321893
$438$	17.8315	0.852024
$439$	9.15508	0.436948	0.218474	−	0.975843i	$-0.429892\pi$
$439$	9.15508	0.436948	0.218474	+	0.975843i	$0.429892\pi$
$440$	51.7635	2.46773
$441$	1.00000	0.0476190
$442$	0	0
$443$	11.2632	0.535132	0.267566	−	0.963540i	$-0.413781\pi$
$443$	11.2632	0.535132	0.267566	+	0.963540i	$0.413781\pi$
$444$	14.7077	0.697996
$445$	−25.6150	−1.21427
$446$	66.2469	3.13688
$447$	−10.0283	−0.474322
$448$	−11.2555	−0.531771
$449$	33.7848	1.59440	0.797202	−	0.603712i	$-0.206312\pi$
$449$	33.7848	1.59440	0.797202	+	0.603712i	$0.206312\pi$
$450$	26.6893	1.25814
$451$	−24.5830	−1.15757
$452$	−38.9632	−1.83267
$453$	−9.71544	−0.456471
$454$	−28.5987	−1.34221
$455$	0	0
$456$	−13.9250	−0.652097
$457$	−34.2944	−1.60423	−0.802113	−	0.597172i	$-0.796291\pi$
$457$	−34.2944	−1.60423	−0.802113	+	0.597172i	$0.796291\pi$
$458$	21.8676	1.02181
$459$	0.377203	0.0176063
$460$	27.8959	1.30065
$461$	−19.3326	−0.900409	−0.450205	−	0.892925i	$-0.648649\pi$
$461$	−19.3326	−0.900409	−0.450205	+	0.892925i	$0.648649\pi$
$462$	−7.78270	−0.362084
$463$	−6.29444	−0.292527	−0.146264	−	0.989246i	$-0.546725\pi$
$463$	−6.29444	−0.292527	−0.146264	+	0.989246i	$0.546725\pi$
$464$	−17.6044	−0.817263
$465$	25.5011	1.18258
$466$	−29.6015	−1.37126
$467$	24.2293	1.12120	0.560599	−	0.828087i	$-0.310571\pi$
$467$	24.2293	1.12120	0.560599	+	0.828087i	$0.310571\pi$
$468$	0	0
$469$	−5.58383	−0.257837
$470$	116.099	5.35525
$471$	−17.5761	−0.809863
$472$	8.25547	0.379989
$473$	−28.3227	−1.30228
$474$	2.76428	0.126968
$475$	39.8315	1.82760
$476$	−1.37720	−0.0631240
$477$	7.75441	0.355050
$478$	7.71544	0.352896
$479$	33.6297	1.53658	0.768291	−	0.640101i	$-0.221107\pi$
$479$	33.6297	1.53658	0.768291	+	0.640101i	$0.221107\pi$
$480$	12.1989	0.556800
$481$	0	0
$482$	−22.4076	−1.02064
$483$	−1.89669	−0.0863023
$484$	−1.02830	−0.0467407
$485$	−20.0275	−0.909402
$486$	−2.37720	−0.107832
$487$	7.92498	0.359115	0.179558	−	0.983747i	$-0.442533\pi$
$487$	7.92498	0.359115	0.179558	+	0.983747i	$0.442533\pi$
$488$	30.4359	1.37777
$489$	−5.49119	−0.248320
$490$	9.57608	0.432603
$491$	2.43167	0.109740	0.0548699	−	0.998494i	$-0.482526\pi$
$491$	2.43167	0.109740	0.0548699	+	0.998494i	$0.482526\pi$
$492$	27.4154	1.23598
$493$	3.27389	0.147449
$494$	0	0
$495$	13.1882	0.592766
$496$	−12.8401	−0.576537
$497$	−3.99225	−0.179077
$498$	36.0870	1.61710
$499$	18.5838	0.831926	0.415963	−	0.909381i	$-0.363445\pi$
$499$	18.5838	0.831926	0.415963	+	0.909381i	$0.363445\pi$
$500$	91.5873	4.09591
$501$	4.43672	0.198218
$502$	−28.5011	−1.27206
$503$	−17.4543	−0.778251	−0.389125	−	0.921185i	$-0.627223\pi$
$503$	−17.4543	−0.778251	−0.389125	+	0.921185i	$0.627223\pi$
$504$	3.92498	0.174833
$505$	23.7536	1.05702
$506$	14.7614	0.656222
$507$	0	0
$508$	26.7643	1.18747
$509$	−2.76991	−0.122774	−0.0613870	−	0.998114i	$-0.519552\pi$
$509$	−2.76991	−0.122774	−0.0613870	+	0.998114i	$0.519552\pi$
$510$	3.61212	0.159948
$511$	−7.50106	−0.331827
$512$	−22.0643	−0.975115
$513$	−3.54778	−0.156638
$514$	34.6991	1.53051
$515$	42.5606	1.87544
$516$	31.5860	1.39049
$517$	39.6922	1.74566
$518$	−9.57608	−0.420749
$519$	−22.1599	−0.972712
$520$	0	0
$521$	−26.2816	−1.15142	−0.575710	−	0.817654i	$-0.695274\pi$
$521$	−26.2816	−1.15142	−0.575710	+	0.817654i	$0.695274\pi$
$522$	−20.6327	−0.903067
$523$	5.25042	0.229585	0.114792	−	0.993389i	$-0.463380\pi$
$523$	5.25042	0.229585	0.114792	+	0.993389i	$0.463380\pi$
$524$	41.7098	1.82210
$525$	−11.2272	−0.489994
$526$	53.8513	2.34803
$527$	2.38788	0.104018
$528$	−6.64042	−0.288987
$529$	−19.4026	−0.843590
$530$	74.2568	3.22551
$531$	2.10331	0.0912760
$532$	12.9533	0.561596
$533$	0	0
$534$	15.1161	0.654138
$535$	−49.9730	−2.16052
$536$	−21.9164	−0.946646
$537$	1.94048	0.0837381
$538$	−66.5363	−2.86858
$539$	3.27389	0.141016
$540$	−14.7077	−0.632918
$541$	0.111863	0.00480937	0.00240468	−	0.999997i	$-0.499235\pi$
$541$	0.111863	0.00480937	0.00240468	+	0.999997i	$0.499235\pi$
$542$	18.0841	0.776778
$543$	8.50106	0.364815
$544$	1.14228	0.0489749
$545$	48.8697	2.09335
$546$	0	0
$547$	−33.7515	−1.44311	−0.721555	−	0.692358i	$-0.756572\pi$
$547$	−33.7515	−1.44311	−0.721555	+	0.692358i	$0.756572\pi$
$548$	11.6511	0.497710
$549$	7.75441	0.330950
$550$	87.3777	3.72580
$551$	−30.7926	−1.31181
$552$	−7.44447	−0.316858
$553$	−1.16283	−0.0494485
$554$	−16.3764	−0.695767
$555$	16.2272	0.688805
$556$	19.6327	0.832611
$557$	−29.0147	−1.22939	−0.614696	−	0.788764i	$-0.710721\pi$
$557$	−29.0147	−1.22939	−0.614696	+	0.788764i	$0.710721\pi$
$558$	−15.0488	−0.637068
$559$	0	0
$560$	8.17058	0.345270
$561$	1.23492	0.0521384
$562$	−25.6885	−1.08360
$563$	1.43167	0.0603378	0.0301689	−	0.999545i	$-0.490395\pi$
$563$	1.43167	0.0603378	0.0301689	+	0.999545i	$0.490395\pi$
$564$	−44.2653	−1.86391
$565$	−42.9885	−1.80854
$566$	−18.1260	−0.761892
$567$	1.00000	0.0419961
$568$	−15.6695	−0.657478
$569$	−24.5011	−1.02714	−0.513569	−	0.858048i	$-0.671677\pi$
$569$	−24.5011	−1.02714	−0.513569	+	0.858048i	$0.671677\pi$
$570$	−33.9738	−1.42301
$571$	−47.3735	−1.98252	−0.991259	−	0.131929i	$-0.957883\pi$
$571$	−47.3735	−1.98252	−0.991259	+	0.131929i	$0.957883\pi$
$572$	0	0
$573$	−0.651093	−0.0271998
$574$	−17.8500	−0.745043
$575$	21.2944	0.888039
$576$	−11.2555	−0.468978
$577$	−27.4055	−1.14091	−0.570453	−	0.821330i	$-0.693232\pi$
$577$	−27.4055	−1.14091	−0.570453	+	0.821330i	$0.693232\pi$
$578$	−40.0742	−1.66687
$579$	19.0643	0.792287
$580$	−127.654	−5.30053
$581$	−15.1805	−0.629791
$582$	11.8187	0.489903
$583$	25.3871	1.05143
$584$	−29.4415	−1.21830
$585$	0	0
$586$	52.9914	2.18906
$587$	−27.8959	−1.15139	−0.575693	−	0.817666i	$-0.695268\pi$
$587$	−27.8959	−1.15139	−0.575693	+	0.817666i	$0.695268\pi$
$588$	−3.65109	−0.150569
$589$	−22.4592	−0.925414
$590$	20.1415	0.829212
$591$	24.7098	1.01643
$592$	−8.17058	−0.335809
$593$	16.6015	0.681740	0.340870	−	0.940110i	$-0.389278\pi$
$593$	16.6015	0.681740	0.340870	+	0.940110i	$0.389278\pi$
$594$	−7.78270	−0.319328
$595$	−1.51948	−0.0622928
$596$	36.6142	1.49978
$597$	−13.1444	−0.537965
$598$	0	0
$599$	11.7913	0.481778	0.240889	−	0.970553i	$-0.422561\pi$
$599$	11.7913	0.481778	0.240889	+	0.970553i	$0.422561\pi$
$600$	−44.0665	−1.79901
$601$	13.8217	0.563798	0.281899	−	0.959444i	$-0.409036\pi$
$601$	13.8217	0.563798	0.281899	+	0.959444i	$0.409036\pi$
$602$	−20.5654	−0.838183
$603$	−5.58383	−0.227391
$604$	35.4720	1.44333
$605$	−1.13453	−0.0461253
$606$	−14.0176	−0.569427
$607$	−21.0948	−0.856210	−0.428105	−	0.903729i	$-0.640819\pi$
$607$	−21.0948	−0.856210	−0.428105	+	0.903729i	$0.640819\pi$
$608$	−10.7437	−0.435716
$609$	8.67939	0.351707
$610$	74.2568	3.00657
$611$	0	0
$612$	−1.37720	−0.0556701
$613$	−2.19383	−0.0886079	−0.0443039	−	0.999018i	$-0.514107\pi$
$613$	−2.19383	−0.0886079	−0.0443039	+	0.999018i	$0.514107\pi$
$614$	67.1436	2.70970
$615$	30.2477	1.21971
$616$	12.8500	0.517740
$617$	6.34811	0.255565	0.127783	−	0.991802i	$-0.459214\pi$
$617$	6.34811	0.255565	0.127783	+	0.991802i	$0.459214\pi$
$618$	−25.1161	−1.01032
$619$	7.77203	0.312384	0.156192	−	0.987727i	$-0.450078\pi$
$619$	7.77203	0.312384	0.156192	+	0.987727i	$0.450078\pi$
$620$	−93.1068	−3.73926
$621$	−1.89669	−0.0761115
$622$	−6.32756	−0.253712
$623$	−6.35878	−0.254759
$624$	0	0
$625$	44.9135	1.79654
$626$	−53.4458	−2.13612
$627$	−11.6150	−0.463860
$628$	64.1719	2.56074
$629$	1.51948	0.0605858
$630$	9.57608	0.381520
$631$	−34.2624	−1.36397	−0.681983	−	0.731368i	$-0.738882\pi$
$631$	−34.2624	−1.36397	−0.681983	+	0.731368i	$0.738882\pi$
$632$	−4.56408	−0.181549
$633$	19.5966	0.778896
$634$	−44.7664	−1.77790
$635$	29.5294	1.17184
$636$	−28.3121	−1.12265
$637$	0	0
$638$	−67.5491	−2.67429
$639$	−3.99225	−0.157931
$640$	−83.3855	−3.29610
$641$	−23.2186	−0.917080	−0.458540	−	0.888674i	$-0.651627\pi$
$641$	−23.2186	−0.917080	−0.458540	+	0.888674i	$0.651627\pi$
$642$	29.4904	1.16389
$643$	−20.0801	−0.791880	−0.395940	−	0.918276i	$-0.629581\pi$
$643$	−20.0801	−0.791880	−0.395940	+	0.918276i	$0.629581\pi$
$644$	6.92498	0.272883
$645$	34.8492	1.37218
$646$	−3.18125	−0.125165
$647$	−16.5294	−0.649836	−0.324918	−	0.945742i	$-0.605337\pi$
$647$	−16.5294	−0.649836	−0.324918	+	0.945742i	$0.605337\pi$
$648$	3.92498	0.154188
$649$	6.88601	0.270300
$650$	0	0
$651$	6.33048	0.248111
$652$	20.0488	0.785173
$653$	−0.927907	−0.0363118	−0.0181559	−	0.999835i	$-0.505780\pi$
$653$	−0.927907	−0.0363118	−0.0181559	+	0.999835i	$0.505780\pi$
$654$	−28.8393	−1.12771
$655$	46.0189	1.79811
$656$	−15.2301	−0.594635
$657$	−7.50106	−0.292644
$658$	28.8209	1.12355
$659$	32.2568	1.25655	0.628273	−	0.777993i	$-0.283762\pi$
$659$	32.2568	1.25655	0.628273	+	0.777993i	$0.283762\pi$
$660$	−48.1514	−1.87429
$661$	22.8569	0.889031	0.444516	−	0.895771i	$-0.353376\pi$
$661$	22.8569	0.889031	0.444516	+	0.895771i	$0.353376\pi$
$662$	42.3892	1.64750
$663$	0	0
$664$	−59.5830	−2.31227
$665$	14.2915	0.554201
$666$	−9.57608	−0.371065
$667$	−16.4621	−0.637415
$668$	−16.1989	−0.626753
$669$	−27.8676	−1.07742
$670$	−53.4712	−2.06577
$671$	25.3871	0.980057
$672$	3.02830	0.116819
$673$	1.08569	0.0418503	0.0209251	−	0.999781i	$-0.493339\pi$
$673$	1.08569	0.0418503	0.0209251	+	0.999781i	$0.493339\pi$
$674$	18.0099	0.693714
$675$	−11.2272	−0.432134
$676$	0	0
$677$	−8.60730	−0.330805	−0.165403	−	0.986226i	$-0.552892\pi$
$677$	−8.60730	−0.330805	−0.165403	+	0.986226i	$0.552892\pi$
$678$	25.3687	0.974277
$679$	−4.97170	−0.190796
$680$	−5.96395	−0.228707
$681$	12.0304	0.461007
$682$	−49.2683	−1.88658
$683$	−33.4621	−1.28039	−0.640196	−	0.768212i	$-0.721147\pi$
$683$	−33.4621	−1.28039	−0.640196	+	0.768212i	$0.721147\pi$
$684$	12.9533	0.495281
$685$	12.8548	0.491156
$686$	2.37720	0.0907620
$687$	−9.19887	−0.350959
$688$	−17.5470	−0.668972
$689$	0	0
$690$	−18.1628	−0.691447
$691$	4.69219	0.178499	0.0892496	−	0.996009i	$-0.471553\pi$
$691$	4.69219	0.178499	0.0892496	+	0.996009i	$0.471553\pi$
$692$	80.9079	3.07566
$693$	3.27389	0.124365
$694$	18.7517	0.711805
$695$	21.6610	0.821647
$696$	34.0665	1.29129
$697$	2.83235	0.107283
$698$	27.8938	1.05579
$699$	12.4522	0.470986
$700$	40.9914	1.54933
$701$	41.4535	1.56568	0.782839	−	0.622224i	$-0.213771\pi$
$701$	41.4535	1.56568	0.782839	+	0.622224i	$0.213771\pi$
$702$	0	0
$703$	−14.2915	−0.539015
$704$	−36.8492	−1.38881
$705$	−48.8385	−1.83936
$706$	29.8032	1.12166
$707$	5.89669	0.221768
$708$	−7.67939	−0.288609
$709$	−3.84222	−0.144298	−0.0721488	−	0.997394i	$-0.522986\pi$
$709$	−3.84222	−0.144298	−0.0721488	+	0.997394i	$0.522986\pi$
$710$	−38.2301	−1.43475
$711$	−1.16283	−0.0436095
$712$	−24.9581	−0.935345
$713$	−12.0069	−0.449664
$714$	0.896688	0.0335577
$715$	0	0
$716$	−7.08489	−0.264775
$717$	−3.24559	−0.121209
$718$	11.9279	0.445146
$719$	8.91219	0.332369	0.166184	−	0.986095i	$-0.446855\pi$
$719$	8.91219	0.332369	0.166184	+	0.986095i	$0.446855\pi$
$720$	8.17058	0.304499
$721$	10.5654	0.393476
$722$	−15.2456	−0.567382
$723$	9.42605	0.350558
$724$	−31.0382	−1.15352
$725$	−97.4450	−3.61902
$726$	0.669517	0.0248481
$727$	29.6815	1.10083	0.550413	−	0.834892i	$-0.314470\pi$
$727$	29.6815	1.10083	0.550413	+	0.834892i	$0.314470\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−71.8307	−2.65858
$731$	3.26322	0.120694
$732$	−28.3121	−1.04644
$733$	−5.30299	−0.195870	−0.0979352	−	0.995193i	$-0.531224\pi$
$733$	−5.30299	−0.195870	−0.0979352	+	0.995193i	$0.531224\pi$
$734$	56.3630	2.08040
$735$	−4.02830	−0.148586
$736$	−5.74373	−0.211717
$737$	−18.2808	−0.673383
$738$	−17.8500	−0.657066
$739$	20.9143	0.769345	0.384673	−	0.923053i	$-0.374314\pi$
$739$	20.9143	0.769345	0.384673	+	0.923053i	$0.374314\pi$
$740$	−59.2469	−2.17796
$741$	0	0
$742$	18.4338	0.676726
$743$	0.318488	0.0116842	0.00584209	−	0.999983i	$-0.498140\pi$
$743$	0.318488	0.0116842	0.00584209	+	0.999983i	$0.498140\pi$
$744$	24.8470	0.910937
$745$	40.3969	1.48003
$746$	−23.6610	−0.866290
$747$	−15.1805	−0.555424
$748$	−4.50881	−0.164858
$749$	−12.4055	−0.453287
$750$	−59.6319	−2.17745
$751$	39.5881	1.44459	0.722295	−	0.691585i	$-0.243087\pi$
$751$	39.5881	1.44459	0.722295	+	0.691585i	$0.243087\pi$
$752$	24.5908	0.896733
$753$	11.9893	0.436915
$754$	0	0
$755$	39.1367	1.42433
$756$	−3.65109	−0.132789
$757$	−10.2533	−0.372664	−0.186332	−	0.982487i	$-0.559660\pi$
$757$	−10.2533	−0.372664	−0.186332	+	0.982487i	$0.559660\pi$
$758$	66.2050	2.40467
$759$	−6.20955	−0.225392
$760$	56.0940	2.03474
$761$	17.4784	0.633591	0.316796	−	0.948494i	$-0.397393\pi$
$761$	17.4784	0.633591	0.316796	+	0.948494i	$0.397393\pi$
$762$	−17.4260	−0.631279
$763$	12.1316	0.439194
$764$	2.37720	0.0860042
$765$	−1.51948	−0.0549371
$766$	16.4132	0.593035
$767$	0	0
$768$	26.6970	0.963345
$769$	−36.0566	−1.30023	−0.650117	−	0.759834i	$-0.725280\pi$
$769$	−36.0566	−1.30023	−0.650117	+	0.759834i	$0.725280\pi$
$770$	31.3510	1.12981
$771$	−14.5966	−0.525685
$772$	−69.6057	−2.50516
$773$	10.7184	0.385513	0.192756	−	0.981247i	$-0.438257\pi$
$773$	10.7184	0.385513	0.192756	+	0.981247i	$0.438257\pi$
$774$	−20.5654	−0.739208
$775$	−71.0734	−2.55303
$776$	−19.5139	−0.700507
$777$	4.02830	0.144514
$778$	−67.4565	−2.41843
$779$	−26.6396	−0.954463
$780$	0	0
$781$	−13.0702	−0.467688
$782$	−1.70074	−0.0608182
$783$	8.67939	0.310176
$784$	2.02830	0.0724392
$785$	70.8016	2.52702
$786$	−27.1570	−0.968657
$787$	8.95811	0.319322	0.159661	−	0.987172i	$-0.448960\pi$
$787$	8.95811	0.319322	0.159661	+	0.987172i	$0.448960\pi$
$788$	−90.2178	−3.21388
$789$	−22.6532	−0.806476
$790$	−11.1353	−0.396177
$791$	−10.6716	−0.379440
$792$	12.8500	0.456604
$793$	0	0
$794$	11.3326	0.402179
$795$	−31.2370	−1.10786
$796$	47.9914	1.70101
$797$	−36.0686	−1.27761	−0.638807	−	0.769367i	$-0.720572\pi$
$797$	−36.0686	−1.27761	−0.638807	+	0.769367i	$0.720572\pi$
$798$	−8.43380	−0.298553
$799$	−4.57315	−0.161787
$800$	−33.9992	−1.20205
$801$	−6.35878	−0.224676
$802$	19.6503	0.693876
$803$	−24.5577	−0.866621
$804$	20.3871	0.718997
$805$	7.64042	0.269289
$806$	0	0
$807$	27.9893	0.985271
$808$	23.1444	0.814217
$809$	47.5294	1.67104	0.835522	−	0.549458i	$-0.185166\pi$
$809$	47.5294	1.67104	0.835522	+	0.549458i	$0.185166\pi$
$810$	9.57608	0.336469
$811$	5.34678	0.187751	0.0938755	−	0.995584i	$-0.470074\pi$
$811$	5.34678	0.187751	0.0938755	+	0.995584i	$0.470074\pi$
$812$	−31.6893	−1.11208
$813$	−7.60730	−0.266800
$814$	−31.3510	−1.09885
$815$	22.1201	0.774835
$816$	0.765079	0.0267831
$817$	−30.6922	−1.07378
$818$	−50.9525	−1.78151
$819$	0	0
$820$	−110.437	−3.85664
$821$	21.8697	0.763258	0.381629	−	0.924316i	$-0.375363\pi$
$821$	21.8697	0.763258	0.381629	+	0.924316i	$0.375363\pi$
$822$	−7.58595	−0.264590
$823$	22.9942	0.801526	0.400763	−	0.916182i	$-0.368745\pi$
$823$	22.9942	0.801526	0.400763	+	0.916182i	$0.368745\pi$
$824$	41.4690	1.44464
$825$	−36.7565	−1.27970
$826$	5.00000	0.173972
$827$	−21.3425	−0.742151	−0.371075	−	0.928603i	$-0.621011\pi$
$827$	−21.3425	−0.742151	−0.371075	+	0.928603i	$0.621011\pi$
$828$	6.92498	0.240660
$829$	27.4309	0.952714	0.476357	−	0.879252i	$-0.341957\pi$
$829$	27.4309	0.952714	0.476357	+	0.879252i	$0.341957\pi$
$830$	−145.369	−5.04584
$831$	6.88894	0.238975
$832$	0	0
$833$	−0.377203	−0.0130693
$834$	−12.7827	−0.442629
$835$	−17.8724	−0.618501
$836$	42.4076	1.46670
$837$	6.33048	0.218814
$838$	−5.44739	−0.188177
$839$	4.43167	0.152998	0.0764992	−	0.997070i	$-0.475626\pi$
$839$	4.43167	0.152998	0.0764992	+	0.997070i	$0.475626\pi$
$840$	−15.8110	−0.545531
$841$	46.3318	1.59765
$842$	−18.0975	−0.623680
$843$	10.8062	0.372184
$844$	−71.5491	−2.46282
$845$	0	0
$846$	28.8209	0.990882
$847$	−0.281641	−0.00967729
$848$	15.7282	0.540110
$849$	7.62492	0.261687
$850$	−10.0673	−0.345304
$851$	−7.64042	−0.261910
$852$	14.5761	0.499368
$853$	−43.0040	−1.47243	−0.736215	−	0.676748i	$-0.763389\pi$
$853$	−43.0040	−1.47243	−0.736215	+	0.676748i	$0.763389\pi$
$854$	18.4338	0.630791
$855$	14.2915	0.488759
$856$	−48.6914	−1.66424
$857$	0.866269	0.0295912	0.0147956	−	0.999891i	$-0.495290\pi$
$857$	0.866269	0.0295912	0.0147956	+	0.999891i	$0.495290\pi$
$858$	0	0
$859$	−15.3481	−0.523671	−0.261835	−	0.965113i	$-0.584328\pi$
$859$	−15.3481	−0.523671	−0.261835	+	0.965113i	$0.584328\pi$
$860$	−127.238	−4.33876
$861$	7.50881	0.255900
$862$	−49.5950	−1.68921
$863$	37.0275	1.26043	0.630215	−	0.776420i	$-0.282967\pi$
$863$	37.0275	1.26043	0.630215	+	0.776420i	$0.282967\pi$
$864$	3.02830	0.103025
$865$	89.2667	3.03516
$866$	−55.5704	−1.88836
$867$	16.8577	0.572518
$868$	−23.1132	−0.784513
$869$	−3.80697	−0.129143
$870$	83.1145	2.81785
$871$	0	0
$872$	47.6164	1.61249
$873$	−4.97170	−0.168267
$874$	15.9963	0.541082
$875$	25.0849	0.848024
$876$	27.3871	0.925324
$877$	−23.0205	−0.777349	−0.388674	−	0.921375i	$-0.627067\pi$
$877$	−23.0205	−0.777349	−0.388674	+	0.921375i	$0.627067\pi$
$878$	21.7635	0.734482
$879$	−22.2915	−0.751874
$880$	26.7496	0.901728
$881$	38.0168	1.28082	0.640410	−	0.768034i	$-0.278765\pi$
$881$	38.0168	1.28082	0.640410	+	0.768034i	$0.278765\pi$
$882$	2.37720	0.0800446
$883$	−6.95620	−0.234095	−0.117047	−	0.993126i	$-0.537343\pi$
$883$	−6.95620	−0.234095	−0.117047	+	0.993126i	$0.537343\pi$
$884$	0	0
$885$	−8.47277	−0.284809
$886$	26.7750	0.899522
$887$	−25.8131	−0.866720	−0.433360	−	0.901221i	$-0.642672\pi$
$887$	−25.8131	−0.866720	−0.433360	+	0.901221i	$0.642672\pi$
$888$	15.8110	0.530582
$889$	7.33048	0.245857
$890$	−60.8922	−2.04111
$891$	3.27389	0.109679
$892$	101.747	3.40675
$893$	43.0128	1.43937
$894$	−23.8393	−0.797305
$895$	−7.81684	−0.261288
$896$	−20.6999	−0.691536
$897$	0	0
$898$	80.3134	2.68009
$899$	54.9447	1.83251
$900$	40.9914	1.36638
$901$	−2.92498	−0.0974453
$902$	−58.4388	−1.94580
$903$	8.65109	0.287890
$904$	−41.8860	−1.39311
$905$	−34.2448	−1.13834
$906$	−23.0956	−0.767299
$907$	−2.59158	−0.0860519	−0.0430260	−	0.999074i	$-0.513700\pi$
$907$	−2.59158	−0.0860519	−0.0430260	+	0.999074i	$0.513700\pi$
$908$	−43.9242	−1.45768
$909$	5.89669	0.195581
$910$	0	0
$911$	36.7507	1.21760	0.608802	−	0.793322i	$-0.291650\pi$
$911$	36.7507	1.21760	0.608802	+	0.793322i	$0.291650\pi$
$912$	−7.19595	−0.238282
$913$	−49.6991	−1.64480
$914$	−81.5248	−2.69660
$915$	−31.2370	−1.03266
$916$	33.5860	1.10971
$917$	11.4239	0.377251
$918$	0.896688	0.0295951
$919$	−3.16283	−0.104332	−0.0521660	−	0.998638i	$-0.516613\pi$
$919$	−3.16283	−0.104332	−0.0521660	+	0.998638i	$0.516613\pi$
$920$	29.9885	0.988692
$921$	−28.2448	−0.930698
$922$	−45.9575	−1.51353
$923$	0	0
$924$	−11.9533	−0.393234
$925$	−45.2264	−1.48703
$926$	−14.9632	−0.491720
$927$	10.5654	0.347013
$928$	26.2838	0.862807
$929$	−39.5929	−1.29900	−0.649500	−	0.760361i	$-0.725022\pi$
$929$	−39.5929	−1.29900	−0.649500	+	0.760361i	$0.725022\pi$
$930$	60.6212	1.98785
$931$	3.54778	0.116274
$932$	−45.4642	−1.48923
$933$	2.66177	0.0871423
$934$	57.5979	1.88466
$935$	−4.97463	−0.162688
$936$	0	0
$937$	2.94553	0.0962263	0.0481131	−	0.998842i	$-0.484679\pi$
$937$	2.94553	0.0962263	0.0481131	+	0.998842i	$0.484679\pi$
$938$	−13.2739	−0.433408
$939$	22.4826	0.733693
$940$	178.314	5.81596
$941$	−20.9893	−0.684232	−0.342116	−	0.939658i	$-0.611144\pi$
$941$	−20.9893	−0.684232	−0.342116	+	0.939658i	$0.611144\pi$
$942$	−41.7819	−1.36133
$943$	−14.2419	−0.463779
$944$	4.26614	0.138851
$945$	−4.02830	−0.131040
$946$	−67.3289	−2.18905
$947$	6.36733	0.206910	0.103455	−	0.994634i	$-0.467010\pi$
$947$	6.36733	0.206910	0.103455	+	0.994634i	$0.467010\pi$
$948$	4.24559	0.137890
$949$	0	0
$950$	94.6877	3.07207
$951$	18.8315	0.610655
$952$	−1.48052	−0.0479838
$953$	60.4535	1.95828	0.979141	−	0.203181i	$-0.0651281\pi$
$953$	60.4535	1.95828	0.979141	+	0.203181i	$0.0651281\pi$
$954$	18.4338	0.596816
$955$	2.62280	0.0848717
$956$	11.8500	0.383255
$957$	28.4154	0.918539
$958$	79.9447	2.58290
$959$	3.19112	0.103047
$960$	45.3404	1.46335
$961$	9.07502	0.292742
$962$	0	0
$963$	−12.4055	−0.399762
$964$	−34.4154	−1.10844
$965$	−76.7968	−2.47218
$966$	−4.50881	−0.145069
$967$	−48.1719	−1.54910	−0.774552	−	0.632510i	$-0.782025\pi$
$967$	−48.1719	−1.54910	−0.774552	+	0.632510i	$0.782025\pi$
$968$	−1.10543	−0.0355300
$969$	1.33823	0.0429902
$970$	−47.6094	−1.52865
$971$	17.9653	0.576533	0.288267	−	0.957550i	$-0.406921\pi$
$971$	17.9653	0.576533	0.288267	+	0.957550i	$0.406921\pi$
$972$	−3.65109	−0.117109
$973$	5.37720	0.172385
$974$	18.8393	0.603650
$975$	0	0
$976$	15.7282	0.503448
$977$	2.82672	0.0904347	0.0452174	−	0.998977i	$-0.485602\pi$
$977$	2.82672	0.0904347	0.0452174	+	0.998977i	$0.485602\pi$
$978$	−13.0537	−0.417410
$979$	−20.8179	−0.665344
$980$	14.7077	0.469820
$981$	12.1316	0.387332
$982$	5.78058	0.184466
$983$	29.8873	0.953258	0.476629	−	0.879105i	$-0.341859\pi$
$983$	29.8873	0.953258	0.476629	+	0.879105i	$0.341859\pi$
$984$	29.4720	0.939532
$985$	−99.5384	−3.17156
$986$	7.78270	0.247852
$987$	−12.1239	−0.385907
$988$	0	0
$989$	−16.4084	−0.521757
$990$	31.3510	0.996401
$991$	36.9469	1.17366	0.586828	−	0.809712i	$-0.300377\pi$
$991$	36.9469	1.17366	0.586828	+	0.809712i	$0.300377\pi$
$992$	19.1706	0.608666
$993$	−17.8315	−0.565867
$994$	−9.49039	−0.301017
$995$	52.9496	1.67861
$996$	55.4252	1.75622
$997$	10.7176	0.339428	0.169714	−	0.985493i	$-0.445716\pi$
$997$	10.7176	0.339428	0.169714	+	0.985493i	$0.445716\pi$
$998$	44.1775	1.39842
$999$	4.02830	0.127450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.s.1.3		3
13.4	even	6		273.2.k.d.211.3	yes	6
13.10	even	6		273.2.k.d.22.3	✓	6
13.12	even	2		3549.2.a.h.1.1		3
39.17	odd	6		819.2.o.d.757.1		6
39.23	odd	6		819.2.o.d.568.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.3	✓	6	13.10	even	6
273.2.k.d.211.3	yes	6	13.4	even	6
819.2.o.d.568.1		6	39.23	odd	6
819.2.o.d.757.1		6	39.17	odd	6
3549.2.a.h.1.1		3	13.12	even	2
3549.2.a.s.1.3		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+2.37720 q^{2} -1.00000 q^{3} +3.65109 q^{4} +4.02830 q^{5} -2.37720 q^{6} +1.00000 q^{7} +3.92498 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.37720 q^{2} -1.00000 q^{3} +3.65109 q^{4} +4.02830 q^{5} -2.37720 q^{6} +1.00000 q^{7} +3.92498 q^{8} +1.00000 q^{9} +9.57608 q^{10} +3.27389 q^{11} -3.65109 q^{12} +2.37720 q^{14} -4.02830 q^{15} +2.02830 q^{16} -0.377203 q^{17} +2.37720 q^{18} +3.54778 q^{19} +14.7077 q^{20} -1.00000 q^{21} +7.78270 q^{22} +1.89669 q^{23} -3.92498 q^{24} +11.2272 q^{25} -1.00000 q^{27} +3.65109 q^{28} -8.67939 q^{29} -9.57608 q^{30} -6.33048 q^{31} -3.02830 q^{32} -3.27389 q^{33} -0.896688 q^{34} +4.02830 q^{35} +3.65109 q^{36} -4.02830 q^{37} +8.43380 q^{38} +15.8110 q^{40} -7.50881 q^{41} -2.37720 q^{42} -8.65109 q^{43} +11.9533 q^{44} +4.02830 q^{45} +4.50881 q^{46} +12.1239 q^{47} -2.02830 q^{48} +1.00000 q^{49} +26.6893 q^{50} +0.377203 q^{51} +7.75441 q^{53} -2.37720 q^{54} +13.1882 q^{55} +3.92498 q^{56} -3.54778 q^{57} -20.6327 q^{58} +2.10331 q^{59} -14.7077 q^{60} +7.75441 q^{61} -15.0488 q^{62} +1.00000 q^{63} -11.2555 q^{64} -7.78270 q^{66} -5.58383 q^{67} -1.37720 q^{68} -1.89669 q^{69} +9.57608 q^{70} -3.99225 q^{71} +3.92498 q^{72} -7.50106 q^{73} -9.57608 q^{74} -11.2272 q^{75} +12.9533 q^{76} +3.27389 q^{77} -1.16283 q^{79} +8.17058 q^{80} +1.00000 q^{81} -17.8500 q^{82} -15.1805 q^{83} -3.65109 q^{84} -1.51948 q^{85} -20.5654 q^{86} +8.67939 q^{87} +12.8500 q^{88} -6.35878 q^{89} +9.57608 q^{90} +6.92498 q^{92} +6.33048 q^{93} +28.8209 q^{94} +14.2915 q^{95} +3.02830 q^{96} -4.97170 q^{97} +2.37720 q^{98} +3.27389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 13 q^{10} + 8 q^{11} - 4 q^{12} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 7 q^{19} + 13 q^{20} - 3 q^{21} + q^{22} + 9 q^{23} - 3 q^{24} + 11 q^{25} - 3 q^{27} + 4 q^{28} - 7 q^{29} - 13 q^{30} + 7 q^{31} + 3 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} - 4 q^{38} + 13 q^{40} - 2 q^{41} - 2 q^{42} - 19 q^{43} + 15 q^{44} - 7 q^{46} + 17 q^{47} + 6 q^{48} + 3 q^{49} + 16 q^{50} - 4 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} - 7 q^{57} - 22 q^{58} + 3 q^{59} - 13 q^{60} + 13 q^{61} - 17 q^{62} + 3 q^{63} + q^{64} - q^{66} - 5 q^{67} + q^{68} - 9 q^{69} + 13 q^{70} - 8 q^{71} + 3 q^{72} + 2 q^{73} - 13 q^{74} - 11 q^{75} + 18 q^{76} + 8 q^{77} - q^{79} + 26 q^{80} + 3 q^{81} - 36 q^{82} - 2 q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} + 7 q^{87} + 21 q^{88} + 19 q^{89} + 13 q^{90} + 12 q^{92} - 7 q^{93} + 7 q^{94} - 3 q^{96} - 27 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 13 * q^10 + 8 * q^11 - 4 * q^12 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 7 * q^19 + 13 * q^20 - 3 * q^21 + q^22 + 9 * q^23 - 3 * q^24 + 11 * q^25 - 3 * q^27 + 4 * q^28 - 7 * q^29 - 13 * q^30 + 7 * q^31 + 3 * q^32 - 8 * q^33 - 6 * q^34 + 4 * q^36 - 4 * q^38 + 13 * q^40 - 2 * q^41 - 2 * q^42 - 19 * q^43 + 15 * q^44 - 7 * q^46 + 17 * q^47 + 6 * q^48 + 3 * q^49 + 16 * q^50 - 4 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 - 7 * q^57 - 22 * q^58 + 3 * q^59 - 13 * q^60 + 13 * q^61 - 17 * q^62 + 3 * q^63 + q^64 - q^66 - 5 * q^67 + q^68 - 9 * q^69 + 13 * q^70 - 8 * q^71 + 3 * q^72 + 2 * q^73 - 13 * q^74 - 11 * q^75 + 18 * q^76 + 8 * q^77 - q^79 + 26 * q^80 + 3 * q^81 - 36 * q^82 - 2 * q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 + 7 * q^87 + 21 * q^88 + 19 * q^89 + 13 * q^90 + 12 * q^92 - 7 * q^93 + 7 * q^94 - 3 * q^96 - 27 * q^97 + 2 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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