LMFDB - Embedded newform 1183.2.a.o.1.1

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			1.1
Root			$-1.71083$ 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)

$f(q)$	$=$	$q-2.08281 q^{2} -0.0911085 q^{3} +2.33809 q^{4} +2.63777 q^{5} +0.189762 q^{6} -1.00000 q^{7} -0.704173 q^{8} -2.99170 q^{9} +O(q^{10})$	\(q-2.08281 q^{2} -0.0911085 q^{3} +2.33809 q^{4} +2.63777 q^{5} +0.189762 q^{6} -1.00000 q^{7} -0.704173 q^{8} -2.99170 q^{9} -5.49396 q^{10} +3.44676 q^{11} -0.213020 q^{12} +2.08281 q^{14} -0.240323 q^{15} -3.20952 q^{16} -4.83445 q^{17} +6.23113 q^{18} -2.42330 q^{19} +6.16733 q^{20} +0.0911085 q^{21} -7.17893 q^{22} -6.84789 q^{23} +0.0641561 q^{24} +1.95781 q^{25} +0.545895 q^{27} -2.33809 q^{28} +4.64785 q^{29} +0.500546 q^{30} -8.43394 q^{31} +8.09316 q^{32} -0.314029 q^{33} +10.0692 q^{34} -2.63777 q^{35} -6.99486 q^{36} +1.51646 q^{37} +5.04727 q^{38} -1.85744 q^{40} -10.4384 q^{41} -0.189762 q^{42} -0.451785 q^{43} +8.05882 q^{44} -7.89140 q^{45} +14.2628 q^{46} +2.56938 q^{47} +0.292415 q^{48} +1.00000 q^{49} -4.07774 q^{50} +0.440460 q^{51} -10.3402 q^{53} -1.13699 q^{54} +9.09173 q^{55} +0.704173 q^{56} +0.220783 q^{57} -9.68058 q^{58} +12.7994 q^{59} -0.561896 q^{60} -0.984619 q^{61} +17.5663 q^{62} +2.99170 q^{63} -10.4375 q^{64} +0.654061 q^{66} -1.28567 q^{67} -11.3034 q^{68} +0.623901 q^{69} +5.49396 q^{70} +12.0794 q^{71} +2.10667 q^{72} +5.18381 q^{73} -3.15850 q^{74} -0.178373 q^{75} -5.66589 q^{76} -3.44676 q^{77} +9.74733 q^{79} -8.46596 q^{80} +8.92536 q^{81} +21.7412 q^{82} -13.2658 q^{83} +0.213020 q^{84} -12.7522 q^{85} +0.940982 q^{86} -0.423459 q^{87} -2.42711 q^{88} -16.0403 q^{89} +16.4363 q^{90} -16.0110 q^{92} +0.768404 q^{93} -5.35152 q^{94} -6.39210 q^{95} -0.737356 q^{96} +14.9407 q^{97} -2.08281 q^{98} -10.3117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.08281	−1.47277	−0.736384	−	0.676564i	$-0.763468\pi$
$2$	−2.08281	−1.47277	−0.736384	+	0.676564i	$0.763468\pi$
$3$	−0.0911085	−0.0526015	−0.0263008	−	0.999654i	$-0.508373\pi$
$3$	−0.0911085	−0.0526015	−0.0263008	+	0.999654i	$0.508373\pi$
$4$	2.33809	1.16904
$5$	2.63777	1.17964	0.589822	−	0.807533i	$-0.299198\pi$
$5$	2.63777	1.17964	0.589822	+	0.807533i	$0.299198\pi$
$6$	0.189762	0.0774698
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.704173	−0.248963
$9$	−2.99170	−0.997233
$10$	−5.49396	−1.73734
$11$	3.44676	1.03924	0.519618	−	0.854399i	$-0.326074\pi$
$11$	3.44676	1.03924	0.519618	+	0.854399i	$0.326074\pi$
$12$	−0.213020	−0.0614935
$13$	0	0
$13$	0	0
$14$	2.08281	0.556654
$15$	−0.240323	−0.0620511
$16$	−3.20952	−0.802380
$17$	−4.83445	−1.17253	−0.586264	−	0.810120i	$-0.699402\pi$
$17$	−4.83445	−1.17253	−0.586264	+	0.810120i	$0.699402\pi$
$18$	6.23113	1.46869
$19$	−2.42330	−0.555944	−0.277972	−	0.960589i	$-0.589662\pi$
$19$	−2.42330	−0.555944	−0.277972	+	0.960589i	$0.589662\pi$
$20$	6.16733	1.37906
$21$	0.0911085	0.0198815
$22$	−7.17893	−1.53055
$23$	−6.84789	−1.42788	−0.713942	−	0.700205i	$-0.753092\pi$
$23$	−6.84789	−1.42788	−0.713942	+	0.700205i	$0.753092\pi$
$24$	0.0641561	0.0130958
$25$	1.95781	0.391562
$26$	0	0
$27$	0.545895	0.105057
$28$	−2.33809	−0.441857
$29$	4.64785	0.863084	0.431542	−	0.902093i	$-0.357970\pi$
$29$	4.64785	0.863084	0.431542	+	0.902093i	$0.357970\pi$
$30$	0.500546	0.0913869
$31$	−8.43394	−1.51478	−0.757390	−	0.652962i	$-0.773526\pi$
$31$	−8.43394	−1.51478	−0.757390	+	0.652962i	$0.773526\pi$
$32$	8.09316	1.43068
$33$	−0.314029	−0.0546654
$34$	10.0692	1.72686
$35$	−2.63777	−0.445864
$36$	−6.99486	−1.16581
$37$	1.51646	0.249305	0.124652	−	0.992200i	$-0.460218\pi$
$37$	1.51646	0.249305	0.124652	+	0.992200i	$0.460218\pi$
$38$	5.04727	0.818776
$39$	0	0
$40$	−1.85744	−0.293687
$41$	−10.4384	−1.63020	−0.815102	−	0.579317i	$-0.803319\pi$
$41$	−10.4384	−1.63020	−0.815102	+	0.579317i	$0.803319\pi$
$42$	−0.189762	−0.0292808
$43$	−0.451785	−0.0688966	−0.0344483	−	0.999406i	$-0.510967\pi$
$43$	−0.451785	−0.0688966	−0.0344483	+	0.999406i	$0.510967\pi$
$44$	8.05882	1.21491
$45$	−7.89140	−1.17638
$46$	14.2628	2.10294
$47$	2.56938	0.374782	0.187391	−	0.982285i	$-0.439997\pi$
$47$	2.56938	0.374782	0.187391	+	0.982285i	$0.439997\pi$
$48$	0.292415	0.0422064
$49$	1.00000	0.142857
$50$	−4.07774	−0.576679
$51$	0.440460	0.0616767
$52$	0	0
$53$	−10.3402	−1.42033	−0.710166	−	0.704035i	$-0.751380\pi$
$53$	−10.3402	−1.42033	−0.710166	+	0.704035i	$0.751380\pi$
$54$	−1.13699	−0.154725
$55$	9.09173	1.22593
$56$	0.704173	0.0940990
$57$	0.220783	0.0292435
$58$	−9.68058	−1.27112
$59$	12.7994	1.66634	0.833171	−	0.553016i	$-0.186523\pi$
$59$	12.7994	1.66634	0.833171	+	0.553016i	$0.186523\pi$
$60$	−0.561896	−0.0725405
$61$	−0.984619	−0.126068	−0.0630338	−	0.998011i	$-0.520078\pi$
$61$	−0.984619	−0.126068	−0.0630338	+	0.998011i	$0.520078\pi$
$62$	17.5663	2.23092
$63$	2.99170	0.376919
$64$	−10.4375	−1.30468
$65$	0	0
$66$	0.654061	0.0805094
$67$	−1.28567	−0.157069	−0.0785346	−	0.996911i	$-0.525024\pi$
$67$	−1.28567	−0.157069	−0.0785346	+	0.996911i	$0.525024\pi$
$68$	−11.3034	−1.37074
$69$	0.623901	0.0751089
$70$	5.49396	0.656654
$71$	12.0794	1.43356	0.716779	−	0.697301i	$-0.245616\pi$
$71$	12.0794	1.43356	0.716779	+	0.697301i	$0.245616\pi$
$72$	2.10667	0.248274
$73$	5.18381	0.606719	0.303360	−	0.952876i	$-0.401892\pi$
$73$	5.18381	0.606719	0.303360	+	0.952876i	$0.401892\pi$
$74$	−3.15850	−0.367168
$75$	−0.178373	−0.0205967
$76$	−5.66589	−0.649923
$77$	−3.44676	−0.392794
$78$	0	0
$79$	9.74733	1.09666	0.548330	−	0.836262i	$-0.315264\pi$
$79$	9.74733	1.09666	0.548330	+	0.836262i	$0.315264\pi$
$80$	−8.46596	−0.946523
$81$	8.92536	0.991707
$82$	21.7412	2.40091
$83$	−13.2658	−1.45611	−0.728054	−	0.685520i	$-0.759575\pi$
$83$	−13.2658	−1.45611	−0.728054	+	0.685520i	$0.759575\pi$
$84$	0.213020	0.0232424
$85$	−12.7522	−1.38317
$86$	0.940982	0.101469
$87$	−0.423459	−0.0453995
$88$	−2.42711	−0.258731
$89$	−16.0403	−1.70027	−0.850134	−	0.526567i	$-0.823479\pi$
$89$	−16.0403	−1.70027	−0.850134	+	0.526567i	$0.823479\pi$
$90$	16.4363	1.73254
$91$	0	0
$92$	−16.0110	−1.66926
$93$	0.768404	0.0796798
$94$	−5.35152	−0.551967
$95$	−6.39210	−0.655816
$96$	−0.737356	−0.0752560
$97$	14.9407	1.51700	0.758501	−	0.651672i	$-0.225932\pi$
$97$	14.9407	1.51700	0.758501	+	0.651672i	$0.225932\pi$
$98$	−2.08281	−0.210395
$99$	−10.3117	−1.03636
$100$	4.57753	0.457753
$101$	−5.58103	−0.555334	−0.277667	−	0.960677i	$-0.589561\pi$
$101$	−5.58103	−0.555334	−0.277667	+	0.960677i	$0.589561\pi$
$102$	−0.917393	−0.0908355
$103$	−15.0233	−1.48029	−0.740144	−	0.672448i	$-0.765243\pi$
$103$	−15.0233	−1.48029	−0.740144	+	0.672448i	$0.765243\pi$
$104$	0	0
$105$	0.240323	0.0234531
$106$	21.5366	2.09182
$107$	−12.0550	−1.16540	−0.582701	−	0.812687i	$-0.698004\pi$
$107$	−12.0550	−1.16540	−0.582701	+	0.812687i	$0.698004\pi$
$108$	1.27635	0.122817
$109$	−14.7918	−1.41679	−0.708397	−	0.705815i	$-0.750581\pi$
$109$	−14.7918	−1.41679	−0.708397	+	0.705815i	$0.750581\pi$
$110$	−18.9363	−1.80551
$111$	−0.138163	−0.0131138
$112$	3.20952	0.303271
$113$	−10.4878	−0.986608	−0.493304	−	0.869857i	$-0.664211\pi$
$113$	−10.4878	−0.986608	−0.493304	+	0.869857i	$0.664211\pi$
$114$	−0.459850	−0.0430689
$115$	−18.0631	−1.68440
$116$	10.8671	1.00898
$117$	0	0
$118$	−26.6587	−2.45413
$119$	4.83445	0.443174
$120$	0.169229	0.0154484
$121$	0.880123	0.0800112
$122$	2.05077	0.185668
$123$	0.951027	0.0857512
$124$	−19.7193	−1.77085
$125$	−8.02459	−0.717741
$126$	−6.23113	−0.555114
$127$	−5.86506	−0.520440	−0.260220	−	0.965549i	$-0.583795\pi$
$127$	−5.86506	−0.520440	−0.260220	+	0.965549i	$0.583795\pi$
$128$	5.55289	0.490811
$129$	0.0411615	0.00362407
$130$	0	0
$131$	1.38898	0.121356	0.0606778	−	0.998157i	$-0.480674\pi$
$131$	1.38898	0.121356	0.0606778	+	0.998157i	$0.480674\pi$
$132$	−0.734227	−0.0639062
$133$	2.42330	0.210127
$134$	2.67780	0.231326
$135$	1.43994	0.123931
$136$	3.40429	0.291915
$137$	−12.4476	−1.06347	−0.531736	−	0.846910i	$-0.678460\pi$
$137$	−12.4476	−1.06347	−0.531736	+	0.846910i	$0.678460\pi$
$138$	−1.29947	−0.110618
$139$	7.98054	0.676900	0.338450	−	0.940984i	$-0.390097\pi$
$139$	7.98054	0.676900	0.338450	+	0.940984i	$0.390097\pi$
$140$	−6.16733	−0.521234
$141$	−0.234092	−0.0197141
$142$	−25.1590	−2.11130
$143$	0	0
$144$	9.60192	0.800160
$145$	12.2599	1.01813
$146$	−10.7969	−0.893556
$147$	−0.0911085	−0.00751450
$148$	3.54562	0.291448
$149$	−9.36477	−0.767192	−0.383596	−	0.923501i	$-0.625314\pi$
$149$	−9.36477	−0.767192	−0.383596	+	0.923501i	$0.625314\pi$
$150$	0.371517	0.0303342
$151$	12.5890	1.02448	0.512239	−	0.858843i	$-0.328816\pi$
$151$	12.5890	1.02448	0.512239	+	0.858843i	$0.328816\pi$
$152$	1.70642	0.138409
$153$	14.4632	1.16928
$154$	7.17893	0.578495
$155$	−22.2468	−1.78690
$156$	0	0
$157$	6.31025	0.503613	0.251807	−	0.967778i	$-0.418975\pi$
$157$	6.31025	0.503613	0.251807	+	0.967778i	$0.418975\pi$
$158$	−20.3018	−1.61513
$159$	0.942077	0.0747116
$160$	21.3479	1.68770
$161$	6.84789	0.539690
$162$	−18.5898	−1.46055
$163$	−11.5904	−0.907829	−0.453915	−	0.891045i	$-0.649973\pi$
$163$	−11.5904	−0.907829	−0.453915	+	0.891045i	$0.649973\pi$
$164$	−24.4059	−1.90578
$165$	−0.828334	−0.0644857
$166$	27.6301	2.14451
$167$	−4.38945	−0.339666	−0.169833	−	0.985473i	$-0.554323\pi$
$167$	−4.38945	−0.339666	−0.169833	+	0.985473i	$0.554323\pi$
$168$	−0.0641561	−0.00494975
$169$	0	0
$170$	26.5603	2.03708
$171$	7.24979	0.554405
$172$	−1.05631	−0.0805432
$173$	−19.7818	−1.50398	−0.751990	−	0.659175i	$-0.770906\pi$
$173$	−19.7818	−1.50398	−0.751990	+	0.659175i	$0.770906\pi$
$174$	0.881983	0.0668630
$175$	−1.95781	−0.147996
$176$	−11.0624	−0.833862
$177$	−1.16614	−0.0876521
$178$	33.4088	2.50410
$179$	6.46685	0.483355	0.241678	−	0.970357i	$-0.422302\pi$
$179$	6.46685	0.483355	0.241678	+	0.970357i	$0.422302\pi$
$180$	−18.4508	−1.37524
$181$	20.9234	1.55522	0.777612	−	0.628745i	$-0.216431\pi$
$181$	20.9234	1.55522	0.777612	+	0.628745i	$0.216431\pi$
$182$	0	0
$183$	0.0897072	0.00663135
$184$	4.82210	0.355490
$185$	4.00007	0.294091
$186$	−1.60044	−0.117350
$187$	−16.6632	−1.21853
$188$	6.00743	0.438137
$189$	−0.545895	−0.0397080
$190$	13.3135	0.965865
$191$	−19.6754	−1.42366	−0.711831	−	0.702351i	$-0.752134\pi$
$191$	−19.6754	−1.42366	−0.711831	+	0.702351i	$0.752134\pi$
$192$	0.950941	0.0686282
$193$	14.8701	1.07038	0.535188	−	0.844733i	$-0.320241\pi$
$193$	14.8701	1.07038	0.535188	+	0.844733i	$0.320241\pi$
$194$	−31.1187	−2.23419
$195$	0	0
$196$	2.33809	0.167006
$197$	14.9442	1.06473	0.532365	−	0.846515i	$-0.321303\pi$
$197$	14.9442	1.06473	0.532365	+	0.846515i	$0.321303\pi$
$198$	21.4772	1.52632
$199$	9.08903	0.644305	0.322152	−	0.946688i	$-0.395594\pi$
$199$	9.08903	0.644305	0.322152	+	0.946688i	$0.395594\pi$
$200$	−1.37864	−0.0974842
$201$	0.117135	0.00826207
$202$	11.6242	0.817877
$203$	−4.64785	−0.326215
$204$	1.02983	0.0721028
$205$	−27.5341	−1.92306
$206$	31.2906	2.18012
$207$	20.4868	1.42393
$208$	0	0
$209$	−8.35253	−0.577757
$210$	−0.500546	−0.0345410
$211$	−3.39540	−0.233749	−0.116875	−	0.993147i	$-0.537288\pi$
$211$	−3.39540	−0.233749	−0.116875	+	0.993147i	$0.537288\pi$
$212$	−24.1762	−1.66043
$213$	−1.10053	−0.0754073
$214$	25.1083	1.71637
$215$	−1.19170	−0.0812735
$216$	−0.384404	−0.0261554
$217$	8.43394	0.572533
$218$	30.8084	2.08661
$219$	−0.472289	−0.0319144
$220$	21.2573	1.43317
$221$	0	0
$222$	0.287766	0.0193136
$223$	−5.64878	−0.378270	−0.189135	−	0.981951i	$-0.560568\pi$
$223$	−5.64878	−0.378270	−0.189135	+	0.981951i	$0.560568\pi$
$224$	−8.09316	−0.540747
$225$	−5.85718	−0.390478
$226$	21.8440	1.45304
$227$	13.2468	0.879222	0.439611	−	0.898188i	$-0.355116\pi$
$227$	13.2468	0.879222	0.439611	+	0.898188i	$0.355116\pi$
$228$	0.516211	0.0341869
$229$	−1.66636	−0.110116	−0.0550580	−	0.998483i	$-0.517534\pi$
$229$	−1.66636	−0.110116	−0.0550580	+	0.998483i	$0.517534\pi$
$230$	37.6220	2.48072
$231$	0.314029	0.0206616
$232$	−3.27289	−0.214876
$233$	12.0833	0.791600	0.395800	−	0.918337i	$-0.370467\pi$
$233$	12.0833	0.791600	0.395800	+	0.918337i	$0.370467\pi$
$234$	0	0
$235$	6.77742	0.442110
$236$	29.9262	1.94803
$237$	−0.888065	−0.0576860
$238$	−10.0692	−0.652692
$239$	14.8457	0.960287	0.480143	−	0.877190i	$-0.340585\pi$
$239$	14.8457	0.960287	0.480143	+	0.877190i	$0.340585\pi$
$240$	0.771321	0.0497886
$241$	20.4472	1.31712	0.658560	−	0.752528i	$-0.271166\pi$
$241$	20.4472	1.31712	0.658560	+	0.752528i	$0.271166\pi$
$242$	−1.83313	−0.117838
$243$	−2.45086	−0.157223
$244$	−2.30213	−0.147379
$245$	2.63777	0.168521
$246$	−1.98081	−0.126292
$247$	0	0
$248$	5.93895	0.377124
$249$	1.20862	0.0765935
$250$	16.7137	1.05707
$251$	−6.03670	−0.381033	−0.190517	−	0.981684i	$-0.561016\pi$
$251$	−6.03670	−0.381033	−0.190517	+	0.981684i	$0.561016\pi$
$252$	6.99486	0.440635
$253$	−23.6030	−1.48391
$254$	12.2158	0.766487
$255$	1.16183	0.0727566
$256$	9.30930	0.581831
$257$	−1.99555	−0.124479	−0.0622396	−	0.998061i	$-0.519824\pi$
$257$	−1.99555	−0.124479	−0.0622396	+	0.998061i	$0.519824\pi$
$258$	−0.0857314	−0.00533741
$259$	−1.51646	−0.0942283
$260$	0	0
$261$	−13.9050	−0.860696
$262$	−2.89298	−0.178729
$263$	12.8872	0.794661	0.397331	−	0.917676i	$-0.369937\pi$
$263$	12.8872	0.794661	0.397331	+	0.917676i	$0.369937\pi$
$264$	0.221130	0.0136096
$265$	−27.2749	−1.67549
$266$	−5.04727	−0.309468
$267$	1.46141	0.0894367
$268$	−3.00600	−0.183621
$269$	−24.4694	−1.49193	−0.745963	−	0.665988i	$-0.768010\pi$
$269$	−24.4694	−1.49193	−0.745963	+	0.665988i	$0.768010\pi$
$270$	−2.99912	−0.182521
$271$	14.2847	0.867734	0.433867	−	0.900977i	$-0.357149\pi$
$271$	14.2847	0.867734	0.433867	+	0.900977i	$0.357149\pi$
$272$	15.5163	0.940813
$273$	0	0
$274$	25.9260	1.56625
$275$	6.74809	0.406925
$276$	1.45874	0.0878056
$277$	−26.5784	−1.59694	−0.798469	−	0.602035i	$-0.794357\pi$
$277$	−26.5784	−1.59694	−0.798469	+	0.602035i	$0.794357\pi$
$278$	−16.6219	−0.996917
$279$	25.2318	1.51059
$280$	1.85744	0.111003
$281$	−9.68696	−0.577876	−0.288938	−	0.957348i	$-0.593302\pi$
$281$	−9.68696	−0.577876	−0.288938	+	0.957348i	$0.593302\pi$
$282$	0.487569	0.0290343
$283$	−9.01853	−0.536096	−0.268048	−	0.963406i	$-0.586379\pi$
$283$	−9.01853	−0.536096	−0.268048	+	0.963406i	$0.586379\pi$
$284$	28.2426	1.67589
$285$	0.582375	0.0344969
$286$	0	0
$287$	10.4384	0.616159
$288$	−24.2123	−1.42672
$289$	6.37195	0.374820
$290$	−25.5351	−1.49947
$291$	−1.36123	−0.0797966
$292$	12.1202	0.709282
$293$	3.36723	0.196716	0.0983579	−	0.995151i	$-0.468641\pi$
$293$	3.36723	0.196716	0.0983579	+	0.995151i	$0.468641\pi$
$294$	0.189762	0.0110671
$295$	33.7619	1.96569
$296$	−1.06785	−0.0620675
$297$	1.88157	0.109180
$298$	19.5050	1.12989
$299$	0	0
$300$	−0.417052	−0.0240785
$301$	0.451785	0.0260405
$302$	−26.2204	−1.50882
$303$	0.508480	0.0292114
$304$	7.77764	0.446078
$305$	−2.59720	−0.148715
$306$	−30.1241	−1.72208
$307$	5.27364	0.300983	0.150491	−	0.988611i	$-0.451914\pi$
$307$	5.27364	0.300983	0.150491	+	0.988611i	$0.451914\pi$
$308$	−8.05882	−0.459194
$309$	1.36875	0.0778654
$310$	46.3357	2.63169
$311$	9.31654	0.528292	0.264146	−	0.964483i	$-0.414910\pi$
$311$	9.31654	0.528292	0.264146	+	0.964483i	$0.414910\pi$
$312$	0	0
$313$	−31.0327	−1.75407	−0.877037	−	0.480423i	$-0.840483\pi$
$313$	−31.0327	−1.75407	−0.877037	+	0.480423i	$0.840483\pi$
$314$	−13.1430	−0.741705
$315$	7.89140	0.444630
$316$	22.7901	1.28204
$317$	9.22067	0.517884	0.258942	−	0.965893i	$-0.416626\pi$
$317$	9.22067	0.517884	0.258942	+	0.965893i	$0.416626\pi$
$318$	−1.96217	−0.110033
$319$	16.0200	0.896948
$320$	−27.5316	−1.53906
$321$	1.09831	0.0613019
$322$	−14.2628	−0.794837
$323$	11.7153	0.651859
$324$	20.8683	1.15935
$325$	0	0
$326$	24.1406	1.33702
$327$	1.34765	0.0745255
$328$	7.35043	0.405860
$329$	−2.56938	−0.141654
$330$	1.72526	0.0949725
$331$	15.3888	0.845848	0.422924	−	0.906165i	$-0.361004\pi$
$331$	15.3888	0.845848	0.422924	+	0.906165i	$0.361004\pi$
$332$	−31.0166	−1.70225
$333$	−4.53680	−0.248615
$334$	9.14238	0.500249
$335$	−3.39129	−0.185286
$336$	−0.292415	−0.0159525
$337$	9.97038	0.543121	0.271561	−	0.962421i	$-0.412460\pi$
$337$	9.97038	0.543121	0.271561	+	0.962421i	$0.412460\pi$
$338$	0	0
$339$	0.955527	0.0518971
$340$	−29.8157	−1.61698
$341$	−29.0697	−1.57421
$342$	−15.0999	−0.816510
$343$	−1.00000	−0.0539949
$344$	0.318135	0.0171527
$345$	1.64571	0.0886018
$346$	41.2016	2.21501
$347$	18.3587	0.985547	0.492773	−	0.870158i	$-0.335983\pi$
$347$	18.3587	0.985547	0.492773	+	0.870158i	$0.335983\pi$
$348$	−0.990084	−0.0530741
$349$	−3.91068	−0.209334	−0.104667	−	0.994507i	$-0.533378\pi$
$349$	−3.91068	−0.209334	−0.104667	+	0.994507i	$0.533378\pi$
$350$	4.07774	0.217964
$351$	0	0
$352$	27.8951	1.48682
$353$	−25.6384	−1.36459	−0.682297	−	0.731075i	$-0.739019\pi$
$353$	−25.6384	−1.36459	−0.682297	+	0.731075i	$0.739019\pi$
$354$	2.42884	0.129091
$355$	31.8625	1.69109
$356$	−37.5036	−1.98769
$357$	−0.440460	−0.0233116
$358$	−13.4692	−0.711870
$359$	−17.5435	−0.925908	−0.462954	−	0.886382i	$-0.653210\pi$
$359$	−17.5435	−0.925908	−0.462954	+	0.886382i	$0.653210\pi$
$360$	5.55691	0.292875
$361$	−13.1276	−0.690927
$362$	−43.5794	−2.29048
$363$	−0.0801867	−0.00420871
$364$	0	0
$365$	13.6737	0.715713
$366$	−0.186843	−0.00976643
$367$	12.0095	0.626890	0.313445	−	0.949606i	$-0.398517\pi$
$367$	12.0095	0.626890	0.313445	+	0.949606i	$0.398517\pi$
$368$	21.9784	1.14571
$369$	31.2286	1.62569
$370$	−8.33138	−0.433128
$371$	10.3402	0.536835
$372$	1.79660	0.0931492
$373$	6.58590	0.341005	0.170503	−	0.985357i	$-0.445461\pi$
$373$	6.58590	0.341005	0.170503	+	0.985357i	$0.445461\pi$
$374$	34.7062	1.79461
$375$	0.731108	0.0377543
$376$	−1.80929	−0.0933068
$377$	0	0
$378$	1.13699	0.0584807
$379$	11.1382	0.572130	0.286065	−	0.958210i	$-0.407653\pi$
$379$	11.1382	0.572130	0.286065	+	0.958210i	$0.407653\pi$
$380$	−14.9453	−0.766678
$381$	0.534357	0.0273759
$382$	40.9801	2.09672
$383$	−5.16337	−0.263836	−0.131918	−	0.991261i	$-0.542114\pi$
$383$	−5.16337	−0.263836	−0.131918	+	0.991261i	$0.542114\pi$
$384$	−0.505916	−0.0258174
$385$	−9.09173	−0.463358
$386$	−30.9716	−1.57642
$387$	1.35161	0.0687060
$388$	34.9327	1.77344
$389$	−3.90202	−0.197840	−0.0989200	−	0.995095i	$-0.531539\pi$
$389$	−3.90202	−0.197840	−0.0989200	+	0.995095i	$0.531539\pi$
$390$	0	0
$391$	33.1058	1.67423
$392$	−0.704173	−0.0355661
$393$	−0.126548	−0.00638349
$394$	−31.1259	−1.56810
$395$	25.7112	1.29367
$396$	−24.1096	−1.21155
$397$	−6.09215	−0.305756	−0.152878	−	0.988245i	$-0.548854\pi$
$397$	−6.09215	−0.305756	−0.152878	+	0.988245i	$0.548854\pi$
$398$	−18.9307	−0.948911
$399$	−0.220783	−0.0110530
$400$	−6.28363	−0.314181
$401$	14.5534	0.726761	0.363380	−	0.931641i	$-0.381623\pi$
$401$	14.5534	0.726761	0.363380	+	0.931641i	$0.381623\pi$
$402$	−0.243970	−0.0121681
$403$	0	0
$404$	−13.0489	−0.649210
$405$	23.5430	1.16986
$406$	9.68058	0.480439
$407$	5.22687	0.259086
$408$	−0.310160	−0.0153552
$409$	29.5278	1.46006	0.730028	−	0.683417i	$-0.239507\pi$
$409$	29.5278	1.46006	0.730028	+	0.683417i	$0.239507\pi$
$410$	57.3481	2.83222
$411$	1.13408	0.0559403
$412$	−35.1258	−1.73052
$413$	−12.7994	−0.629818
$414$	−42.6701	−2.09712
$415$	−34.9920	−1.71769
$416$	0	0
$417$	−0.727095	−0.0356060
$418$	17.3967	0.850901
$419$	31.8847	1.55767	0.778835	−	0.627229i	$-0.215811\pi$
$419$	31.8847	1.55767	0.778835	+	0.627229i	$0.215811\pi$
$420$	0.561896	0.0274177
$421$	−16.0318	−0.781344	−0.390672	−	0.920530i	$-0.627757\pi$
$421$	−16.0318	−0.781344	−0.390672	+	0.920530i	$0.627757\pi$
$422$	7.07197	0.344258
$423$	−7.68681	−0.373745
$424$	7.28126	0.353609
$425$	−9.46494	−0.459117
$426$	2.29220	0.111057
$427$	0.984619	0.0476491
$428$	−28.1857	−1.36241
$429$	0	0
$430$	2.48209	0.119697
$431$	20.3260	0.979069	0.489535	−	0.871984i	$-0.337167\pi$
$431$	20.3260	0.979069	0.489535	+	0.871984i	$0.337167\pi$
$432$	−1.75206	−0.0842960
$433$	−13.9077	−0.668364	−0.334182	−	0.942509i	$-0.608460\pi$
$433$	−13.9077	−0.668364	−0.334182	+	0.942509i	$0.608460\pi$
$434$	−17.5663	−0.843208
$435$	−1.11698	−0.0535553
$436$	−34.5844	−1.65629
$437$	16.5945	0.793823
$438$	0.983688	0.0470024
$439$	−11.3492	−0.541669	−0.270835	−	0.962626i	$-0.587300\pi$
$439$	−11.3492	−0.541669	−0.270835	+	0.962626i	$0.587300\pi$
$440$	−6.40215	−0.305210
$441$	−2.99170	−0.142462
$442$	0	0
$443$	−21.8184	−1.03662	−0.518311	−	0.855192i	$-0.673439\pi$
$443$	−21.8184	−1.03662	−0.518311	+	0.855192i	$0.673439\pi$
$444$	−0.323036	−0.0153306
$445$	−42.3105	−2.00571
$446$	11.7653	0.557104
$447$	0.853210	0.0403554
$448$	10.4375	0.493123
$449$	−11.0754	−0.522680	−0.261340	−	0.965247i	$-0.584164\pi$
$449$	−11.0754	−0.522680	−0.261340	+	0.965247i	$0.584164\pi$
$450$	12.1994	0.575084
$451$	−35.9786	−1.69417
$452$	−24.5214	−1.15339
$453$	−1.14696	−0.0538891
$454$	−27.5906	−1.29489
$455$	0	0
$456$	−0.155470	−0.00728053
$457$	6.02903	0.282026	0.141013	−	0.990008i	$-0.454964\pi$
$457$	6.02903	0.282026	0.141013	+	0.990008i	$0.454964\pi$
$458$	3.47070	0.162175
$459$	−2.63910	−0.123183
$460$	−42.2332	−1.96913
$461$	−31.2543	−1.45566	−0.727829	−	0.685759i	$-0.759471\pi$
$461$	−31.2543	−1.45566	−0.727829	+	0.685759i	$0.759471\pi$
$462$	−0.654061	−0.0304297
$463$	−16.0896	−0.747746	−0.373873	−	0.927480i	$-0.621970\pi$
$463$	−16.0896	−0.747746	−0.373873	+	0.927480i	$0.621970\pi$
$464$	−14.9174	−0.692521
$465$	2.02687	0.0939938
$466$	−25.1671	−1.16584
$467$	−5.18604	−0.239981	−0.119991	−	0.992775i	$-0.538286\pi$
$467$	−5.18604	−0.239981	−0.119991	+	0.992775i	$0.538286\pi$
$468$	0	0
$469$	1.28567	0.0593665
$470$	−14.1161	−0.651125
$471$	−0.574918	−0.0264908
$472$	−9.01299	−0.414857
$473$	−1.55719	−0.0715998
$474$	1.84967	0.0849581
$475$	−4.74436	−0.217686
$476$	11.3034	0.518090
$477$	30.9347	1.41640
$478$	−30.9207	−1.41428
$479$	4.15275	0.189744	0.0948720	−	0.995489i	$-0.469756\pi$
$479$	4.15275	0.189744	0.0948720	+	0.995489i	$0.469756\pi$
$480$	−1.94497	−0.0887754
$481$	0	0
$482$	−42.5876	−1.93981
$483$	−0.623901	−0.0283885
$484$	2.05780	0.0935366
$485$	39.4101	1.78952
$486$	5.10467	0.231553
$487$	−6.52104	−0.295496	−0.147748	−	0.989025i	$-0.547203\pi$
$487$	−6.52104	−0.295496	−0.147748	+	0.989025i	$0.547203\pi$
$488$	0.693342	0.0313861
$489$	1.05598	0.0477532
$490$	−5.49396	−0.248192
$491$	18.9254	0.854091	0.427046	−	0.904230i	$-0.359554\pi$
$491$	18.9254	0.854091	0.427046	+	0.904230i	$0.359554\pi$
$492$	2.22358	0.100247
$493$	−22.4698	−1.01199
$494$	0	0
$495$	−27.1997	−1.22254
$496$	27.0689	1.21543
$497$	−12.0794	−0.541834
$498$	−2.51733	−0.112804
$499$	36.1116	1.61658	0.808290	−	0.588785i	$-0.200394\pi$
$499$	36.1116	1.61658	0.808290	+	0.588785i	$0.200394\pi$
$500$	−18.7622	−0.839071
$501$	0.399916	0.0178669
$502$	12.5733	0.561173
$503$	13.8545	0.617743	0.308872	−	0.951104i	$-0.400049\pi$
$503$	13.8545	0.617743	0.308872	+	0.951104i	$0.400049\pi$
$504$	−2.10667	−0.0938386
$505$	−14.7215	−0.655096
$506$	49.1605	2.18545
$507$	0	0
$508$	−13.7130	−0.608417
$509$	10.1964	0.451948	0.225974	−	0.974133i	$-0.427444\pi$
$509$	10.1964	0.451948	0.225974	+	0.974133i	$0.427444\pi$
$510$	−2.41987	−0.107154
$511$	−5.18381	−0.229318
$512$	−30.4953	−1.34771
$513$	−1.32287	−0.0584061
$514$	4.15635	0.183329
$515$	−39.6279	−1.74621
$516$	0.0962392	0.00423669
$517$	8.85602	0.389487
$518$	3.15850	0.138776
$519$	1.80229	0.0791116
$520$	0	0
$521$	−40.6356	−1.78028	−0.890139	−	0.455688i	$-0.849393\pi$
$521$	−40.6356	−1.78028	−0.890139	+	0.455688i	$0.849393\pi$
$522$	28.9614	1.26760
$523$	25.0743	1.09642	0.548210	−	0.836340i	$-0.315309\pi$
$523$	25.0743	1.09642	0.548210	+	0.836340i	$0.315309\pi$
$524$	3.24755	0.141870
$525$	0.178373	0.00778484
$526$	−26.8416	−1.17035
$527$	40.7735	1.77612
$528$	1.00788	0.0438624
$529$	23.8936	1.03885
$530$	56.8085	2.46760
$531$	−38.2920	−1.66173
$532$	5.66589	0.245648
$533$	0	0
$534$	−3.04383	−0.131719
$535$	−31.7983	−1.37476
$536$	0.905331	0.0391043
$537$	−0.589185	−0.0254252
$538$	50.9650	2.19726
$539$	3.44676	0.148462
$540$	3.36671	0.144880
$541$	22.0722	0.948959	0.474479	−	0.880267i	$-0.342636\pi$
$541$	22.0722	0.948959	0.474479	+	0.880267i	$0.342636\pi$
$542$	−29.7523	−1.27797
$543$	−1.90630	−0.0818071
$544$	−39.1260	−1.67751
$545$	−39.0172	−1.67131
$546$	0	0
$547$	−12.9107	−0.552022	−0.276011	−	0.961154i	$-0.589013\pi$
$547$	−12.9107	−0.552022	−0.276011	+	0.961154i	$0.589013\pi$
$548$	−29.1036	−1.24325
$549$	2.94568	0.125719
$550$	−14.0550	−0.599306
$551$	−11.2631	−0.479826
$552$	−0.439334	−0.0186993
$553$	−9.74733	−0.414499
$554$	55.3576	2.35192
$555$	−0.364440	−0.0154696
$556$	18.6592	0.791326
$557$	23.4061	0.991746	0.495873	−	0.868395i	$-0.334848\pi$
$557$	23.4061	0.991746	0.495873	+	0.868395i	$0.334848\pi$
$558$	−52.5530	−2.22475
$559$	0	0
$560$	8.46596	0.357752
$561$	1.51816	0.0640967
$562$	20.1761	0.851077
$563$	42.3634	1.78541	0.892703	−	0.450645i	$-0.148806\pi$
$563$	42.3634	1.78541	0.892703	+	0.450645i	$0.148806\pi$
$564$	−0.547328	−0.0230467
$565$	−27.6643	−1.16385
$566$	18.7839	0.789545
$567$	−8.92536	−0.374830
$568$	−8.50596	−0.356902
$569$	24.3356	1.02020	0.510101	−	0.860115i	$-0.329608\pi$
$569$	24.3356	1.02020	0.510101	+	0.860115i	$0.329608\pi$
$570$	−1.21298	−0.0508059
$571$	9.71777	0.406676	0.203338	−	0.979109i	$-0.434821\pi$
$571$	9.71777	0.406676	0.203338	+	0.979109i	$0.434821\pi$
$572$	0	0
$573$	1.79260	0.0748868
$574$	−21.7412	−0.907459
$575$	−13.4069	−0.559105
$576$	31.2257	1.30107
$577$	4.39680	0.183041	0.0915206	−	0.995803i	$-0.470827\pi$
$577$	4.39680	0.183041	0.0915206	+	0.995803i	$0.470827\pi$
$578$	−13.2715	−0.552023
$579$	−1.35480	−0.0563034
$580$	28.6648	1.19024
$581$	13.2658	0.550357
$582$	2.83518	0.117522
$583$	−35.6400	−1.47606
$584$	−3.65030	−0.151050
$585$	0	0
$586$	−7.01330	−0.289717
$587$	−13.2174	−0.545540	−0.272770	−	0.962079i	$-0.587940\pi$
$587$	−13.2174	−0.545540	−0.272770	+	0.962079i	$0.587940\pi$
$588$	−0.213020	−0.00878479
$589$	20.4380	0.842133
$590$	−70.3194	−2.89501
$591$	−1.36154	−0.0560065
$592$	−4.86711	−0.200037
$593$	5.35235	0.219795	0.109897	−	0.993943i	$-0.464948\pi$
$593$	5.35235	0.219795	0.109897	+	0.993943i	$0.464948\pi$
$594$	−3.91894	−0.160796
$595$	12.7522	0.522787
$596$	−21.8957	−0.896881
$597$	−0.828088	−0.0338914
$598$	0	0
$599$	9.81933	0.401207	0.200604	−	0.979673i	$-0.435710\pi$
$599$	9.81933	0.401207	0.200604	+	0.979673i	$0.435710\pi$
$600$	0.125605	0.00512782
$601$	−28.2788	−1.15352	−0.576758	−	0.816915i	$-0.695682\pi$
$601$	−28.2788	−1.15352	−0.576758	+	0.816915i	$0.695682\pi$
$602$	−0.940982	−0.0383516
$603$	3.84633	0.156635
$604$	29.4342	1.19766
$605$	2.32156	0.0943848
$606$	−1.05907	−0.0430216
$607$	8.70338	0.353259	0.176630	−	0.984277i	$-0.443480\pi$
$607$	8.70338	0.353259	0.176630	+	0.984277i	$0.443480\pi$
$608$	−19.6122	−0.795379
$609$	0.423459	0.0171594
$610$	5.40946	0.219023
$611$	0	0
$612$	33.8163	1.36694
$613$	−28.8798	−1.16644	−0.583222	−	0.812313i	$-0.698208\pi$
$613$	−28.8798	−1.16644	−0.583222	+	0.812313i	$0.698208\pi$
$614$	−10.9840	−0.443277
$615$	2.50859	0.101156
$616$	2.42711	0.0977911
$617$	24.5573	0.988641	0.494320	−	0.869280i	$-0.335417\pi$
$617$	24.5573	0.988641	0.494320	+	0.869280i	$0.335417\pi$
$618$	−2.85084	−0.114678
$619$	−16.7008	−0.671262	−0.335631	−	0.941994i	$-0.608949\pi$
$619$	−16.7008	−0.671262	−0.335631	+	0.941994i	$0.608949\pi$
$620$	−52.0149	−2.08897
$621$	−3.73823	−0.150010
$622$	−19.4046	−0.778052
$623$	16.0403	0.642641
$624$	0	0
$625$	−30.9560	−1.23824
$626$	64.6352	2.58334
$627$	0.760987	0.0303909
$628$	14.7539	0.588746
$629$	−7.33126	−0.292317
$630$	−16.4363	−0.654837
$631$	26.7848	1.06629	0.533143	−	0.846025i	$-0.321011\pi$
$631$	26.7848	1.06629	0.533143	+	0.846025i	$0.321011\pi$
$632$	−6.86380	−0.273027
$633$	0.309350	0.0122956
$634$	−19.2049	−0.762723
$635$	−15.4707	−0.613934
$636$	2.20266	0.0873411
$637$	0	0
$638$	−33.3666	−1.32100
$639$	−36.1378	−1.42959
$640$	14.6472	0.578982
$641$	2.23814	0.0884012	0.0442006	−	0.999023i	$-0.485926\pi$
$641$	2.23814	0.0884012	0.0442006	+	0.999023i	$0.485926\pi$
$642$	−2.28758	−0.0902834
$643$	−34.6442	−1.36623	−0.683117	−	0.730309i	$-0.739376\pi$
$643$	−34.6442	−1.36623	−0.683117	+	0.730309i	$0.739376\pi$
$644$	16.0110	0.630921
$645$	0.108574	0.00427511
$646$	−24.4008	−0.960037
$647$	−19.0383	−0.748473	−0.374236	−	0.927333i	$-0.622095\pi$
$647$	−19.0383	−0.748473	−0.374236	+	0.927333i	$0.622095\pi$
$648$	−6.28499	−0.246898
$649$	44.1164	1.73172
$650$	0	0
$651$	−0.768404	−0.0301161
$652$	−27.0994	−1.06129
$653$	0.112802	0.00441429	0.00220715	−	0.999998i	$-0.499297\pi$
$653$	0.112802	0.00441429	0.00220715	+	0.999998i	$0.499297\pi$
$654$	−2.80691	−0.109759
$655$	3.66380	0.143157
$656$	33.5023	1.30804
$657$	−15.5084	−0.605041
$658$	5.35152	0.208624
$659$	8.44907	0.329129	0.164565	−	0.986366i	$-0.447378\pi$
$659$	8.44907	0.329129	0.164565	+	0.986366i	$0.447378\pi$
$660$	−1.93672	−0.0753867
$661$	−19.0576	−0.741256	−0.370628	−	0.928781i	$-0.620858\pi$
$661$	−19.0576	−0.741256	−0.370628	+	0.928781i	$0.620858\pi$
$662$	−32.0520	−1.24574
$663$	0	0
$664$	9.34139	0.362516
$665$	6.39210	0.247875
$666$	9.44927	0.366152
$667$	−31.8280	−1.23238
$668$	−10.2629	−0.397084
$669$	0.514652	0.0198976
$670$	7.06340	0.272883
$671$	−3.39374	−0.131014
$672$	0.737356	0.0284441
$673$	4.66145	0.179686	0.0898428	−	0.995956i	$-0.471364\pi$
$673$	4.66145	0.179686	0.0898428	+	0.995956i	$0.471364\pi$
$674$	−20.7664	−0.799891
$675$	1.06876	0.0411365
$676$	0	0
$677$	−14.2159	−0.546360	−0.273180	−	0.961963i	$-0.588075\pi$
$677$	−14.2159	−0.546360	−0.273180	+	0.961963i	$0.588075\pi$
$678$	−1.99018	−0.0764323
$679$	−14.9407	−0.573373
$680$	8.97972	0.344357
$681$	−1.20690	−0.0462484
$682$	60.5467	2.31845
$683$	−47.4878	−1.81707	−0.908536	−	0.417807i	$-0.862799\pi$
$683$	−47.4878	−1.81707	−0.908536	+	0.417807i	$0.862799\pi$
$684$	16.9507	0.648124
$685$	−32.8339	−1.25452
$686$	2.08281	0.0795220
$687$	0.151819	0.00579227
$688$	1.45001	0.0552813
$689$	0	0
$690$	−3.42769	−0.130490
$691$	6.11055	0.232456	0.116228	−	0.993223i	$-0.462920\pi$
$691$	6.11055	0.232456	0.116228	+	0.993223i	$0.462920\pi$
$692$	−46.2515	−1.75822
$693$	10.3117	0.391707
$694$	−38.2376	−1.45148
$695$	21.0508	0.798502
$696$	0.298188	0.0113028
$697$	50.4640	1.91146
$698$	8.14519	0.308300
$699$	−1.10089	−0.0416394
$700$	−4.57753	−0.173014
$701$	46.9469	1.77316	0.886580	−	0.462575i	$-0.153074\pi$
$701$	46.9469	1.77316	0.886580	+	0.462575i	$0.153074\pi$
$702$	0	0
$703$	−3.67484	−0.138599
$704$	−35.9753	−1.35587
$705$	−0.617481	−0.0232557
$706$	53.3998	2.00973
$707$	5.58103	0.209896
$708$	−2.72653	−0.102469
$709$	42.2551	1.58692	0.793462	−	0.608620i	$-0.208276\pi$
$709$	42.2551	1.58692	0.793462	+	0.608620i	$0.208276\pi$
$710$	−66.3635	−2.49058
$711$	−29.1611	−1.09363
$712$	11.2951	0.423303
$713$	57.7547	2.16293
$714$	0.917393	0.0343326
$715$	0	0
$716$	15.1201	0.565063
$717$	−1.35257	−0.0505125
$718$	36.5396	1.36365
$719$	29.1865	1.08847	0.544237	−	0.838932i	$-0.316819\pi$
$719$	29.1865	1.08847	0.544237	+	0.838932i	$0.316819\pi$
$720$	25.3276	0.943904
$721$	15.0233	0.559496
$722$	27.3423	1.01757
$723$	−1.86291	−0.0692825
$724$	48.9207	1.81812
$725$	9.09960	0.337951
$726$	0.167013	0.00619845
$727$	−21.5693	−0.799961	−0.399981	−	0.916524i	$-0.630983\pi$
$727$	−21.5693	−0.799961	−0.399981	+	0.916524i	$0.630983\pi$
$728$	0	0
$729$	−26.5528	−0.983437
$730$	−28.4796	−1.05408
$731$	2.18413	0.0807831
$732$	0.209743	0.00775234
$733$	−7.73466	−0.285686	−0.142843	−	0.989745i	$-0.545624\pi$
$733$	−7.73466	−0.285686	−0.142843	+	0.989745i	$0.545624\pi$
$734$	−25.0135	−0.923263
$735$	−0.240323	−0.00886444
$736$	−55.4211	−2.04285
$737$	−4.43138	−0.163232
$738$	−65.0431	−2.39427
$739$	−17.0608	−0.627591	−0.313796	−	0.949491i	$-0.601601\pi$
$739$	−17.0608	−0.627591	−0.313796	+	0.949491i	$0.601601\pi$
$740$	9.35251	0.343805
$741$	0	0
$742$	−21.5366	−0.790633
$743$	42.3773	1.55467	0.777337	−	0.629085i	$-0.216570\pi$
$743$	42.3773	1.55467	0.777337	+	0.629085i	$0.216570\pi$
$744$	−0.541089	−0.0198373
$745$	−24.7021	−0.905014
$746$	−13.7172	−0.502221
$747$	39.6872	1.45208
$748$	−38.9600	−1.42452
$749$	12.0550	0.440480
$750$	−1.52276	−0.0556033
$751$	13.6368	0.497615	0.248807	−	0.968553i	$-0.419961\pi$
$751$	13.6368	0.497615	0.248807	+	0.968553i	$0.419961\pi$
$752$	−8.24647	−0.300718
$753$	0.549995	0.0200429
$754$	0	0
$755$	33.2068	1.20852
$756$	−1.27635	−0.0464204
$757$	−3.57825	−0.130054	−0.0650269	−	0.997884i	$-0.520713\pi$
$757$	−3.57825	−0.130054	−0.0650269	+	0.997884i	$0.520713\pi$
$758$	−23.1987	−0.842614
$759$	2.15044	0.0780558
$760$	4.50114	0.163274
$761$	−10.5161	−0.381207	−0.190603	−	0.981667i	$-0.561044\pi$
$761$	−10.5161	−0.381207	−0.190603	+	0.981667i	$0.561044\pi$
$762$	−1.11296	−0.0403184
$763$	14.7918	0.535497
$764$	−46.0028	−1.66432
$765$	38.1506	1.37934
$766$	10.7543	0.388569
$767$	0	0
$768$	−0.848157	−0.0306052
$769$	19.9912	0.720901	0.360451	−	0.932778i	$-0.382623\pi$
$769$	19.9912	0.720901	0.360451	+	0.932778i	$0.382623\pi$
$770$	18.9363	0.682418
$771$	0.181812	0.00654779
$772$	34.7677	1.25132
$773$	−44.5679	−1.60300	−0.801498	−	0.597998i	$-0.795963\pi$
$773$	−44.5679	−1.60300	−0.801498	+	0.597998i	$0.795963\pi$
$774$	−2.81513	−0.101188
$775$	−16.5120	−0.593130
$776$	−10.5209	−0.377677
$777$	0.138163	0.00495655
$778$	8.12715	0.291372
$779$	25.2954	0.906302
$780$	0	0
$781$	41.6346	1.48980
$782$	−68.9531	−2.46576
$783$	2.53724	0.0906734
$784$	−3.20952	−0.114626
$785$	16.6450	0.594085
$786$	0.263575	0.00940140
$787$	37.0091	1.31923	0.659617	−	0.751602i	$-0.270719\pi$
$787$	37.0091	1.31923	0.659617	+	0.751602i	$0.270719\pi$
$788$	34.9409	1.24472
$789$	−1.17414	−0.0418004
$790$	−53.5514	−1.90527
$791$	10.4878	0.372903
$792$	7.26118	0.258015
$793$	0	0
$794$	12.6888	0.450308
$795$	2.48498	0.0881331
$796$	21.2510	0.753220
$797$	−5.86398	−0.207713	−0.103856	−	0.994592i	$-0.533118\pi$
$797$	−5.86398	−0.207713	−0.103856	+	0.994592i	$0.533118\pi$
$798$	0.459850	0.0162785
$799$	−12.4215	−0.439443
$800$	15.8449	0.560200
$801$	47.9877	1.69556
$802$	−30.3119	−1.07035
$803$	17.8673	0.630524
$804$	0.273872	0.00965873
$805$	18.0631	0.636642
$806$	0	0
$807$	2.22937	0.0784775
$808$	3.93001	0.138257
$809$	1.17991	0.0414835	0.0207417	−	0.999785i	$-0.493397\pi$
$809$	1.17991	0.0414835	0.0207417	+	0.999785i	$0.493397\pi$
$810$	−49.0356	−1.72293
$811$	24.4596	0.858894	0.429447	−	0.903092i	$-0.358708\pi$
$811$	24.4596	0.858894	0.429447	+	0.903092i	$0.358708\pi$
$812$	−10.8671	−0.381360
$813$	−1.30146	−0.0456441
$814$	−10.8866	−0.381574
$815$	−30.5727	−1.07092
$816$	−1.41366	−0.0494882
$817$	1.09481	0.0383026
$818$	−61.5008	−2.15032
$819$	0	0
$820$	−64.3770	−2.24814
$821$	45.2922	1.58071	0.790354	−	0.612651i	$-0.209897\pi$
$821$	45.2922	1.58071	0.790354	+	0.612651i	$0.209897\pi$
$822$	−2.36208	−0.0823870
$823$	−28.5033	−0.993563	−0.496781	−	0.867876i	$-0.665485\pi$
$823$	−28.5033	−0.993563	−0.496781	+	0.867876i	$0.665485\pi$
$824$	10.5790	0.368536
$825$	−0.614808	−0.0214049
$826$	26.6587	0.927575
$827$	−0.594562	−0.0206749	−0.0103375	−	0.999947i	$-0.503291\pi$
$827$	−0.594562	−0.0206749	−0.0103375	+	0.999947i	$0.503291\pi$
$828$	47.9000	1.66464
$829$	−40.7651	−1.41583	−0.707915	−	0.706298i	$-0.750364\pi$
$829$	−40.7651	−1.41583	−0.707915	+	0.706298i	$0.750364\pi$
$830$	72.8816	2.52976
$831$	2.42151	0.0840014
$832$	0	0
$833$	−4.83445	−0.167504
$834$	1.51440	0.0524393
$835$	−11.5783	−0.400685
$836$	−19.5290	−0.675423
$837$	−4.60404	−0.159139
$838$	−66.4097	−2.29408
$839$	−48.1410	−1.66201	−0.831005	−	0.556264i	$-0.812234\pi$
$839$	−48.1410	−1.66201	−0.831005	+	0.556264i	$0.812234\pi$
$840$	−0.169229	−0.00583895
$841$	−7.39749	−0.255086
$842$	33.3912	1.15074
$843$	0.882565	0.0303971
$844$	−7.93875	−0.273263
$845$	0	0
$846$	16.0101	0.550440
$847$	−0.880123	−0.0302414
$848$	33.1870	1.13965
$849$	0.821665	0.0281995
$850$	19.7136	0.676172
$851$	−10.3846	−0.355978
$852$	−2.57314	−0.0881544
$853$	−15.8090	−0.541291	−0.270645	−	0.962679i	$-0.587237\pi$
$853$	−15.8090	−0.541291	−0.270645	+	0.962679i	$0.587237\pi$
$854$	−2.05077	−0.0701760
$855$	19.1233	0.654002
$856$	8.48880	0.290141
$857$	−43.5809	−1.48870	−0.744348	−	0.667792i	$-0.767239\pi$
$857$	−43.5809	−1.48870	−0.744348	+	0.667792i	$0.767239\pi$
$858$	0	0
$859$	57.5101	1.96222	0.981110	−	0.193449i	$-0.0619673\pi$
$859$	57.5101	1.96222	0.981110	+	0.193449i	$0.0619673\pi$
$860$	−2.78631	−0.0950123
$861$	−0.951027	−0.0324109
$862$	−42.3352	−1.44194
$863$	16.1116	0.548444	0.274222	−	0.961666i	$-0.411580\pi$
$863$	16.1116	0.548444	0.274222	+	0.961666i	$0.411580\pi$
$864$	4.41801	0.150304
$865$	−52.1797	−1.77416
$866$	28.9672	0.984344
$867$	−0.580538	−0.0197161
$868$	19.7193	0.669317
$869$	33.5967	1.13969
$870$	2.32646	0.0788745
$871$	0	0
$872$	10.4159	0.352728
$873$	−44.6982	−1.51280
$874$	−34.5632	−1.16912
$875$	8.02459	0.271281
$876$	−1.10425	−0.0373093
$877$	−44.0382	−1.48706	−0.743532	−	0.668700i	$-0.766851\pi$
$877$	−44.0382	−1.48706	−0.743532	+	0.668700i	$0.766851\pi$
$878$	23.6383	0.797753
$879$	−0.306784	−0.0103476
$880$	−29.1801	−0.983661
$881$	−21.2905	−0.717295	−0.358647	−	0.933473i	$-0.616762\pi$
$881$	−21.2905	−0.717295	−0.358647	+	0.933473i	$0.616762\pi$
$882$	6.23113	0.209813
$883$	4.28392	0.144165	0.0720827	−	0.997399i	$-0.477035\pi$
$883$	4.28392	0.144165	0.0720827	+	0.997399i	$0.477035\pi$
$884$	0	0
$885$	−3.07599	−0.103398
$886$	45.4434	1.52670
$887$	−37.0660	−1.24455	−0.622276	−	0.782798i	$-0.713792\pi$
$887$	−37.0660	−1.24455	−0.622276	+	0.782798i	$0.713792\pi$
$888$	0.0972902	0.00326485
$889$	5.86506	0.196708
$890$	88.1247	2.95395
$891$	30.7635	1.03062
$892$	−13.2073	−0.442215
$893$	−6.22638	−0.208358
$894$	−1.77707	−0.0594342
$895$	17.0580	0.570187
$896$	−5.55289	−0.185509
$897$	0	0
$898$	23.0679	0.769787
$899$	−39.1997	−1.30738
$900$	−13.6946	−0.456486
$901$	49.9891	1.66538
$902$	74.9365	2.49511
$903$	−0.0411615	−0.00136977
$904$	7.38521	0.245629
$905$	55.1910	1.83461
$906$	2.38891	0.0793661
$907$	−0.906355	−0.0300950	−0.0150475	−	0.999887i	$-0.504790\pi$
$907$	−0.906355	−0.0300950	−0.0150475	+	0.999887i	$0.504790\pi$
$908$	30.9722	1.02785
$909$	16.6968	0.553797
$910$	0	0
$911$	47.1318	1.56155	0.780773	−	0.624815i	$-0.214826\pi$
$911$	47.1318	1.56155	0.780773	+	0.624815i	$0.214826\pi$
$912$	−0.708609	−0.0234644
$913$	−45.7239	−1.51324
$914$	−12.5573	−0.415359
$915$	0.236627	0.00782263
$916$	−3.89609	−0.128730
$917$	−1.38898	−0.0458681
$918$	5.49674	0.181420
$919$	52.5207	1.73250	0.866249	−	0.499613i	$-0.166524\pi$
$919$	52.5207	1.73250	0.866249	+	0.499613i	$0.166524\pi$
$920$	12.7196	0.419352
$921$	−0.480474	−0.0158321
$922$	65.0967	2.14385
$923$	0	0
$924$	0.734227	0.0241543
$925$	2.96894	0.0976182
$926$	33.5115	1.10126
$927$	44.9451	1.47619
$928$	37.6158	1.23480
$929$	4.76389	0.156298	0.0781491	−	0.996942i	$-0.475099\pi$
$929$	4.76389	0.156298	0.0781491	+	0.996942i	$0.475099\pi$
$930$	−4.22158	−0.138431
$931$	−2.42330	−0.0794205
$932$	28.2517	0.925415
$933$	−0.848816	−0.0277890
$934$	10.8015	0.353437
$935$	−43.9536	−1.43744
$936$	0	0
$937$	47.8844	1.56432	0.782158	−	0.623080i	$-0.214119\pi$
$937$	47.8844	1.56432	0.782158	+	0.623080i	$0.214119\pi$
$938$	−2.67780	−0.0874331
$939$	2.82735	0.0922670
$940$	15.8462	0.516846
$941$	8.54785	0.278652	0.139326	−	0.990247i	$-0.455506\pi$
$941$	8.54785	0.278652	0.139326	+	0.990247i	$0.455506\pi$
$942$	1.19744	0.0390148
$943$	71.4810	2.32774
$944$	−41.0800	−1.33704
$945$	−1.43994	−0.0468413
$946$	3.24333	0.105450
$947$	−11.7381	−0.381437	−0.190718	−	0.981645i	$-0.561082\pi$
$947$	−11.7381	−0.381437	−0.190718	+	0.981645i	$0.561082\pi$
$948$	−2.07637	−0.0674375
$949$	0	0
$950$	9.88160	0.320601
$951$	−0.840081	−0.0272415
$952$	−3.40429	−0.110334
$953$	−39.2912	−1.27277	−0.636383	−	0.771373i	$-0.719570\pi$
$953$	−39.2912	−1.27277	−0.636383	+	0.771373i	$0.719570\pi$
$954$	−64.4310	−2.08603
$955$	−51.8991	−1.67942
$956$	34.7105	1.12262
$957$	−1.45956	−0.0471808
$958$	−8.64938	−0.279449
$959$	12.4476	0.401955
$960$	2.50836	0.0809569
$961$	40.1314	1.29456
$962$	0	0
$963$	36.0650	1.16218
$964$	47.8073	1.53977
$965$	39.2240	1.26266
$966$	1.29947	0.0418096
$967$	6.78097	0.218061	0.109031	−	0.994038i	$-0.465225\pi$
$967$	6.78097	0.218061	0.109031	+	0.994038i	$0.465225\pi$
$968$	−0.619758	−0.0199198
$969$	−1.06737	−0.0342888
$970$	−82.0838	−2.63555
$971$	−5.36908	−0.172302	−0.0861511	−	0.996282i	$-0.527457\pi$
$971$	−5.36908	−0.172302	−0.0861511	+	0.996282i	$0.527457\pi$
$972$	−5.73033	−0.183800
$973$	−7.98054	−0.255844
$974$	13.5821	0.435197
$975$	0	0
$976$	3.16016	0.101154
$977$	22.6247	0.723828	0.361914	−	0.932212i	$-0.382123\pi$
$977$	22.6247	0.723828	0.361914	+	0.932212i	$0.382123\pi$
$978$	−2.19941	−0.0703294
$979$	−55.2870	−1.76698
$980$	6.16733	0.197008
$981$	44.2525	1.41287
$982$	−39.4180	−1.25788
$983$	−25.8113	−0.823254	−0.411627	−	0.911352i	$-0.635039\pi$
$983$	−25.8113	−0.823254	−0.411627	+	0.911352i	$0.635039\pi$
$984$	−0.669687	−0.0213488
$985$	39.4193	1.25600
$986$	46.8003	1.49043
$987$	0.234092	0.00745124
$988$	0	0
$989$	3.09378	0.0983764
$990$	56.6518	1.80051
$991$	45.2014	1.43587	0.717936	−	0.696110i	$-0.245087\pi$
$991$	45.2014	1.43587	0.717936	+	0.696110i	$0.245087\pi$
$992$	−68.2572	−2.16717
$993$	−1.40206	−0.0444929
$994$	25.1590	0.797995
$995$	23.9747	0.760050
$996$	2.82587	0.0895412
$997$	12.9965	0.411604	0.205802	−	0.978594i	$-0.434020\pi$
$997$	12.9965	0.411604	0.205802	+	0.978594i	$0.434020\pi$
$998$	−75.2136	−2.38085
$999$	0.827828	0.0261913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.o.1.1	yes	6
7.6	odd	2		8281.2.a.cg.1.1		6
13.5	odd	4		1183.2.c.h.337.11		12
13.8	odd	4		1183.2.c.h.337.2		12
13.12	even	2		1183.2.a.n.1.6	✓	6
91.90	odd	2		8281.2.a.cb.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.6	✓	6	13.12	even	2
1183.2.a.o.1.1	yes	6	1.1	even	1	trivial
1183.2.c.h.337.2		12	13.8	odd	4
1183.2.c.h.337.11		12	13.5	odd	4
8281.2.a.cb.1.6		6	91.90	odd	2
8281.2.a.cg.1.1		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)

\(f(q)\)	\(=\)	\(q-2.08281 q^{2} -0.0911085 q^{3} +2.33809 q^{4} +2.63777 q^{5} +0.189762 q^{6} -1.00000 q^{7} -0.704173 q^{8} -2.99170 q^{9} +O(q^{10})\)	\(q-2.08281 q^{2} -0.0911085 q^{3} +2.33809 q^{4} +2.63777 q^{5} +0.189762 q^{6} -1.00000 q^{7} -0.704173 q^{8} -2.99170 q^{9} -5.49396 q^{10} +3.44676 q^{11} -0.213020 q^{12} +2.08281 q^{14} -0.240323 q^{15} -3.20952 q^{16} -4.83445 q^{17} +6.23113 q^{18} -2.42330 q^{19} +6.16733 q^{20} +0.0911085 q^{21} -7.17893 q^{22} -6.84789 q^{23} +0.0641561 q^{24} +1.95781 q^{25} +0.545895 q^{27} -2.33809 q^{28} +4.64785 q^{29} +0.500546 q^{30} -8.43394 q^{31} +8.09316 q^{32} -0.314029 q^{33} +10.0692 q^{34} -2.63777 q^{35} -6.99486 q^{36} +1.51646 q^{37} +5.04727 q^{38} -1.85744 q^{40} -10.4384 q^{41} -0.189762 q^{42} -0.451785 q^{43} +8.05882 q^{44} -7.89140 q^{45} +14.2628 q^{46} +2.56938 q^{47} +0.292415 q^{48} +1.00000 q^{49} -4.07774 q^{50} +0.440460 q^{51} -10.3402 q^{53} -1.13699 q^{54} +9.09173 q^{55} +0.704173 q^{56} +0.220783 q^{57} -9.68058 q^{58} +12.7994 q^{59} -0.561896 q^{60} -0.984619 q^{61} +17.5663 q^{62} +2.99170 q^{63} -10.4375 q^{64} +0.654061 q^{66} -1.28567 q^{67} -11.3034 q^{68} +0.623901 q^{69} +5.49396 q^{70} +12.0794 q^{71} +2.10667 q^{72} +5.18381 q^{73} -3.15850 q^{74} -0.178373 q^{75} -5.66589 q^{76} -3.44676 q^{77} +9.74733 q^{79} -8.46596 q^{80} +8.92536 q^{81} +21.7412 q^{82} -13.2658 q^{83} +0.213020 q^{84} -12.7522 q^{85} +0.940982 q^{86} -0.423459 q^{87} -2.42711 q^{88} -16.0403 q^{89} +16.4363 q^{90} -16.0110 q^{92} +0.768404 q^{93} -5.35152 q^{94} -6.39210 q^{95} -0.737356 q^{96} +14.9407 q^{97} -2.08281 q^{98} -10.3117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{5} - 8 q^{6} - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 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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