LMFDB - Embedded newform 1183.2.a.n.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			$0.908891$ 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)

$f(q)$	$=$	$q-2.63777 q^{2} -2.71083 q^{3} +4.95781 q^{4} +2.08281 q^{5} +7.15053 q^{6} +1.00000 q^{7} -7.80201 q^{8} +4.34860 q^{9} +O(q^{10})$	\(q-2.63777 q^{2} -2.71083 q^{3} +4.95781 q^{4} +2.08281 q^{5} +7.15053 q^{6} +1.00000 q^{7} -7.80201 q^{8} +4.34860 q^{9} -5.49396 q^{10} +3.60559 q^{11} -13.4398 q^{12} -2.63777 q^{14} -5.64614 q^{15} +10.6643 q^{16} -5.76942 q^{17} -11.4706 q^{18} -1.36230 q^{19} +10.3262 q^{20} -2.71083 q^{21} -9.51070 q^{22} -4.22817 q^{23} +21.1499 q^{24} -0.661912 q^{25} -3.65581 q^{27} +4.95781 q^{28} -8.29095 q^{29} +14.8932 q^{30} +0.734580 q^{31} -12.5258 q^{32} -9.77414 q^{33} +15.2184 q^{34} +2.08281 q^{35} +21.5595 q^{36} -2.16348 q^{37} +3.59344 q^{38} -16.2501 q^{40} +2.86719 q^{41} +7.15053 q^{42} +4.26879 q^{43} +17.8758 q^{44} +9.05729 q^{45} +11.1529 q^{46} +8.68467 q^{47} -28.9090 q^{48} +1.00000 q^{49} +1.74597 q^{50} +15.6399 q^{51} -10.9872 q^{53} +9.64317 q^{54} +7.50975 q^{55} -7.80201 q^{56} +3.69297 q^{57} +21.8696 q^{58} -6.75315 q^{59} -27.9925 q^{60} +10.5003 q^{61} -1.93765 q^{62} +4.34860 q^{63} +11.7116 q^{64} +25.7819 q^{66} -4.70356 q^{67} -28.6037 q^{68} +11.4619 q^{69} -5.49396 q^{70} -13.3023 q^{71} -33.9278 q^{72} +4.36010 q^{73} +5.70675 q^{74} +1.79433 q^{75} -6.75404 q^{76} +3.60559 q^{77} -1.73764 q^{79} +22.2116 q^{80} -3.13551 q^{81} -7.56297 q^{82} -5.74467 q^{83} -13.4398 q^{84} -12.0166 q^{85} -11.2601 q^{86} +22.4754 q^{87} -28.1308 q^{88} +8.41205 q^{89} -23.8910 q^{90} -20.9625 q^{92} -1.99132 q^{93} -22.9081 q^{94} -2.83742 q^{95} +33.9553 q^{96} -6.20363 q^{97} -2.63777 q^{98} +15.6792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63777	−1.86518	−0.932591	−	0.360935i	$-0.882458\pi$
$2$	−2.63777	−1.86518	−0.932591	+	0.360935i	$0.882458\pi$
$3$	−2.71083	−1.56510	−0.782549	−	0.622589i	$-0.786081\pi$
$3$	−2.71083	−1.56510	−0.782549	+	0.622589i	$0.786081\pi$
$4$	4.95781	2.47890
$5$	2.08281	0.931460	0.465730	−	0.884927i	$-0.345792\pi$
$5$	2.08281	0.931460	0.465730	+	0.884927i	$0.345792\pi$
$6$	7.15053	2.91919
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−7.80201	−2.75843
$9$	4.34860	1.44953
$10$	−5.49396	−1.73734
$11$	3.60559	1.08713	0.543563	−	0.839368i	$-0.317075\pi$
$11$	3.60559	1.08713	0.543563	+	0.839368i	$0.317075\pi$
$12$	−13.4398	−3.87973
$13$	0	0
$13$	0	0
$14$	−2.63777	−0.704973
$15$	−5.64614	−1.45783
$16$	10.6643	2.66606
$17$	−5.76942	−1.39929	−0.699645	−	0.714491i	$-0.746659\pi$
$17$	−5.76942	−1.39929	−0.699645	+	0.714491i	$0.746659\pi$
$18$	−11.4706	−2.70364
$19$	−1.36230	−0.312534	−0.156267	−	0.987715i	$-0.549946\pi$
$19$	−1.36230	−0.312534	−0.156267	+	0.987715i	$0.549946\pi$
$20$	10.3262	2.30900
$21$	−2.71083	−0.591551
$22$	−9.51070	−2.02769
$23$	−4.22817	−0.881635	−0.440817	−	0.897597i	$-0.645311\pi$
$23$	−4.22817	−0.881635	−0.440817	+	0.897597i	$0.645311\pi$
$24$	21.1499	4.31721
$25$	−0.661912	−0.132382
$26$	0	0
$27$	−3.65581	−0.703561
$28$	4.95781	0.936938
$29$	−8.29095	−1.53959	−0.769796	−	0.638290i	$-0.779642\pi$
$29$	−8.29095	−1.53959	−0.769796	+	0.638290i	$0.779642\pi$
$30$	14.8932	2.71911
$31$	0.734580	0.131934	0.0659672	−	0.997822i	$-0.478987\pi$
$31$	0.734580	0.131934	0.0659672	+	0.997822i	$0.478987\pi$
$32$	−12.5258	−2.21427
$33$	−9.77414	−1.70146
$34$	15.2184	2.60993
$35$	2.08281	0.352059
$36$	21.5595	3.59325
$37$	−2.16348	−0.355674	−0.177837	−	0.984060i	$-0.556910\pi$
$37$	−2.16348	−0.355674	−0.177837	+	0.984060i	$0.556910\pi$
$38$	3.59344	0.582933
$39$	0	0
$40$	−16.2501	−2.56936
$41$	2.86719	0.447779	0.223890	−	0.974614i	$-0.428124\pi$
$41$	2.86719	0.447779	0.223890	+	0.974614i	$0.428124\pi$
$42$	7.15053	1.10335
$43$	4.26879	0.650984	0.325492	−	0.945545i	$-0.394470\pi$
$43$	4.26879	0.650984	0.325492	+	0.945545i	$0.394470\pi$
$44$	17.8758	2.69488
$45$	9.05729	1.35018
$46$	11.1529	1.64441
$47$	8.68467	1.26679	0.633395	−	0.773829i	$-0.281661\pi$
$47$	8.68467	1.26679	0.633395	+	0.773829i	$0.281661\pi$
$48$	−28.9090	−4.17265
$49$	1.00000	0.142857
$50$	1.74597	0.246917
$51$	15.6399	2.19003
$52$	0	0
$53$	−10.9872	−1.50921	−0.754603	−	0.656182i	$-0.772171\pi$
$53$	−10.9872	−1.50921	−0.754603	+	0.656182i	$0.772171\pi$
$54$	9.64317	1.31227
$55$	7.50975	1.01261
$56$	−7.80201	−1.04259
$57$	3.69297	0.489146
$58$	21.8696	2.87162
$59$	−6.75315	−0.879186	−0.439593	−	0.898197i	$-0.644877\pi$
$59$	−6.75315	−0.879186	−0.439593	+	0.898197i	$0.644877\pi$
$60$	−27.9925	−3.61381
$61$	10.5003	1.34443	0.672216	−	0.740355i	$-0.265343\pi$
$61$	10.5003	1.34443	0.672216	+	0.740355i	$0.265343\pi$
$62$	−1.93765	−0.246082
$63$	4.34860	0.547871
$64$	11.7116	1.46395
$65$	0	0
$66$	25.7819	3.17353
$67$	−4.70356	−0.574631	−0.287316	−	0.957836i	$-0.592763\pi$
$67$	−4.70356	−0.574631	−0.287316	+	0.957836i	$0.592763\pi$
$68$	−28.6037	−3.46871
$69$	11.4619	1.37984
$70$	−5.49396	−0.656654
$71$	−13.3023	−1.57869	−0.789345	−	0.613949i	$-0.789580\pi$
$71$	−13.3023	−1.57869	−0.789345	+	0.613949i	$0.789580\pi$
$72$	−33.9278	−3.99843
$73$	4.36010	0.510312	0.255156	−	0.966900i	$-0.417873\pi$
$73$	4.36010	0.510312	0.255156	+	0.966900i	$0.417873\pi$
$74$	5.70675	0.663396
$75$	1.79433	0.207191
$76$	−6.75404	−0.774742
$77$	3.60559	0.410895
$78$	0	0
$79$	−1.73764	−0.195500	−0.0977499	−	0.995211i	$-0.531165\pi$
$79$	−1.73764	−0.195500	−0.0977499	+	0.995211i	$0.531165\pi$
$80$	22.2116	2.48333
$81$	−3.13551	−0.348390
$82$	−7.56297	−0.835190
$83$	−5.74467	−0.630559	−0.315280	−	0.948999i	$-0.602098\pi$
$83$	−5.74467	−0.630559	−0.315280	+	0.948999i	$0.602098\pi$
$84$	−13.4398	−1.46640
$85$	−12.0166	−1.30338
$86$	−11.2601	−1.21420
$87$	22.4754	2.40961
$88$	−28.1308	−2.99876
$89$	8.41205	0.891675	0.445838	−	0.895114i	$-0.352906\pi$
$89$	8.41205	0.891675	0.445838	+	0.895114i	$0.352906\pi$
$90$	−23.8910	−2.51833
$91$	0	0
$92$	−20.9625	−2.18549
$93$	−1.99132	−0.206490
$94$	−22.9081	−2.36279
$95$	−2.83742	−0.291113
$96$	33.9553	3.46554
$97$	−6.20363	−0.629883	−0.314942	−	0.949111i	$-0.601985\pi$
$97$	−6.20363	−0.629883	−0.314942	+	0.949111i	$0.601985\pi$
$98$	−2.63777	−0.266455
$99$	15.6792	1.57582
$100$	−3.28163	−0.328163
$101$	−6.33082	−0.629940	−0.314970	−	0.949102i	$-0.601994\pi$
$101$	−6.33082	−0.629940	−0.314970	+	0.949102i	$0.601994\pi$
$102$	−41.2544	−4.08480
$103$	7.64462	0.753247	0.376623	−	0.926367i	$-0.377085\pi$
$103$	7.64462	0.753247	0.376623	+	0.926367i	$0.377085\pi$
$104$	0	0
$105$	−5.64614	−0.551006
$106$	28.9816	2.81494
$107$	2.75373	0.266213	0.133107	−	0.991102i	$-0.457505\pi$
$107$	2.75373	0.266213	0.133107	+	0.991102i	$0.457505\pi$
$108$	−18.1248	−1.74406
$109$	−4.89736	−0.469082	−0.234541	−	0.972106i	$-0.575359\pi$
$109$	−4.89736	−0.469082	−0.234541	+	0.972106i	$0.575359\pi$
$110$	−19.8090	−1.88871
$111$	5.86482	0.556664
$112$	10.6643	1.00768
$113$	−17.4120	−1.63798	−0.818991	−	0.573807i	$-0.805466\pi$
$113$	−17.4120	−1.63798	−0.818991	+	0.573807i	$0.805466\pi$
$114$	−9.74120	−0.912347
$115$	−8.80647	−0.821207
$116$	−41.1050	−3.81650
$117$	0	0
$118$	17.8132	1.63984
$119$	−5.76942	−0.528882
$120$	44.0512	4.02131
$121$	2.00027	0.181843
$122$	−27.6975	−2.50761
$123$	−7.77245	−0.700819
$124$	3.64191	0.327053
$125$	−11.7927	−1.05477
$126$	−11.4706	−1.02188
$127$	11.0903	0.984102	0.492051	−	0.870566i	$-0.336247\pi$
$127$	11.0903	0.984102	0.492051	+	0.870566i	$0.336247\pi$
$128$	−5.84084	−0.516262
$129$	−11.5720	−1.01885
$130$	0	0
$131$	15.2627	1.33351	0.666756	−	0.745276i	$-0.267682\pi$
$131$	15.2627	1.33351	0.666756	+	0.745276i	$0.267682\pi$
$132$	−48.4583	−4.21775
$133$	−1.36230	−0.118127
$134$	12.4069	1.07179
$135$	−7.61435	−0.655339
$136$	45.0131	3.85984
$137$	−10.9701	−0.937236	−0.468618	−	0.883401i	$-0.655248\pi$
$137$	−10.9701	−0.937236	−0.468618	+	0.883401i	$0.655248\pi$
$138$	−30.2337	−2.57366
$139$	−17.0445	−1.44570	−0.722849	−	0.691006i	$-0.757168\pi$
$139$	−17.0445	−1.44570	−0.722849	+	0.691006i	$0.757168\pi$
$140$	10.3262	0.872720
$141$	−23.5427	−1.98265
$142$	35.0883	2.94455
$143$	0	0
$144$	46.3745	3.86454
$145$	−17.2685	−1.43407
$146$	−11.5009	−0.951824
$147$	−2.71083	−0.223585
$148$	−10.7261	−0.881681
$149$	−21.0025	−1.72059	−0.860296	−	0.509795i	$-0.829721\pi$
$149$	−21.0025	−1.72059	−0.860296	+	0.509795i	$0.829721\pi$
$150$	−4.73302	−0.386450
$151$	9.14395	0.744124	0.372062	−	0.928208i	$-0.378651\pi$
$151$	9.14395	0.744124	0.372062	+	0.928208i	$0.378651\pi$
$152$	10.6287	0.862102
$153$	−25.0889	−2.02832
$154$	−9.51070	−0.766394
$155$	1.52999	0.122892
$156$	0	0
$157$	−19.4962	−1.55597	−0.777984	−	0.628284i	$-0.783758\pi$
$157$	−19.4962	−1.55597	−0.777984	+	0.628284i	$0.783758\pi$
$158$	4.58349	0.364643
$159$	29.7844	2.36206
$160$	−26.0888	−2.06250
$161$	−4.22817	−0.333227
$162$	8.27073	0.649810
$163$	21.0315	1.64732	0.823659	−	0.567086i	$-0.191929\pi$
$163$	21.0315	1.64732	0.823659	+	0.567086i	$0.191929\pi$
$164$	14.2150	1.11000
$165$	−20.3576	−1.58484
$166$	15.1531	1.17611
$167$	0.603845	0.0467269	0.0233634	−	0.999727i	$-0.492563\pi$
$167$	0.603845	0.0467269	0.0233634	+	0.999727i	$0.492563\pi$
$168$	21.1499	1.63175
$169$	0	0
$170$	31.6970	2.43105
$171$	−5.92411	−0.453028
$172$	21.1638	1.61373
$173$	13.4932	1.02587	0.512933	−	0.858429i	$-0.328559\pi$
$173$	13.4932	1.02587	0.512933	+	0.858429i	$0.328559\pi$
$174$	−59.2847	−4.49436
$175$	−0.661912	−0.0500358
$176$	38.4509	2.89835
$177$	18.3066	1.37601
$178$	−22.1890	−1.66314
$179$	1.74628	0.130523	0.0652614	−	0.997868i	$-0.479212\pi$
$179$	1.74628	0.130523	0.0652614	+	0.997868i	$0.479212\pi$
$180$	44.9043	3.34697
$181$	7.12074	0.529280	0.264640	−	0.964347i	$-0.414747\pi$
$181$	7.12074	0.529280	0.264640	+	0.964347i	$0.414747\pi$
$182$	0	0
$183$	−28.4647	−2.10417
$184$	32.9882	2.43192
$185$	−4.50611	−0.331296
$186$	5.25264	0.385142
$187$	−20.8022	−1.52120
$188$	43.0569	3.14025
$189$	−3.65581	−0.265921
$190$	7.48444	0.542978
$191$	10.4609	0.756927	0.378464	−	0.925616i	$-0.376452\pi$
$191$	10.4609	0.756927	0.378464	+	0.925616i	$0.376452\pi$
$192$	−31.7481	−2.29122
$193$	6.15874	0.443316	0.221658	−	0.975124i	$-0.428853\pi$
$193$	6.15874	0.443316	0.221658	+	0.975124i	$0.428853\pi$
$194$	16.3637	1.17485
$195$	0	0
$196$	4.95781	0.354129
$197$	14.7190	1.04869	0.524343	−	0.851507i	$-0.324311\pi$
$197$	14.7190	1.04869	0.524343	+	0.851507i	$0.324311\pi$
$198$	−41.3582	−2.93920
$199$	−9.37716	−0.664729	−0.332365	−	0.943151i	$-0.607846\pi$
$199$	−9.37716	−0.664729	−0.332365	+	0.943151i	$0.607846\pi$
$200$	5.16424	0.365167
$201$	12.7506	0.899354
$202$	16.6992	1.17495
$203$	−8.29095	−0.581911
$204$	77.5397	5.42887
$205$	5.97180	0.417089
$206$	−20.1647	−1.40494
$207$	−18.3866	−1.27796
$208$	0	0
$209$	−4.91191	−0.339764
$210$	14.8932	1.02773
$211$	−11.3257	−0.779692	−0.389846	−	0.920880i	$-0.627472\pi$
$211$	−11.3257	−0.779692	−0.389846	+	0.920880i	$0.627472\pi$
$212$	−54.4724	−3.74118
$213$	36.0602	2.47081
$214$	−7.26370	−0.496536
$215$	8.89107	0.606366
$216$	28.5227	1.94072
$217$	0.734580	0.0498665
$218$	12.9181	0.874923
$219$	−11.8195	−0.798688
$220$	37.2319	2.51017
$221$	0	0
$222$	−15.4700	−1.03828
$223$	−13.1511	−0.880663	−0.440331	−	0.897835i	$-0.645139\pi$
$223$	−13.1511	−0.880663	−0.440331	+	0.897835i	$0.645139\pi$
$224$	−12.5258	−0.836914
$225$	−2.87839	−0.191892
$226$	45.9287	3.05513
$227$	6.15435	0.408479	0.204239	−	0.978921i	$-0.434528\pi$
$227$	6.15435	0.408479	0.204239	+	0.978921i	$0.434528\pi$
$228$	18.3091	1.21255
$229$	−17.2159	−1.13766	−0.568831	−	0.822455i	$-0.692604\pi$
$229$	−17.2159	−1.13766	−0.568831	+	0.822455i	$0.692604\pi$
$230$	23.2294	1.53170
$231$	−9.77414	−0.643091
$232$	64.6861	4.24685
$233$	−19.1225	−1.25276	−0.626378	−	0.779520i	$-0.715463\pi$
$233$	−19.1225	−1.25276	−0.626378	+	0.779520i	$0.715463\pi$
$234$	0	0
$235$	18.0885	1.17996
$236$	−33.4808	−2.17942
$237$	4.71044	0.305976
$238$	15.2184	0.986461
$239$	8.98811	0.581393	0.290696	−	0.956815i	$-0.406113\pi$
$239$	8.98811	0.581393	0.290696	+	0.956815i	$0.406113\pi$
$240$	−60.2118	−3.88666
$241$	8.52326	0.549032	0.274516	−	0.961583i	$-0.411482\pi$
$241$	8.52326	0.549032	0.274516	+	0.961583i	$0.411482\pi$
$242$	−5.27625	−0.339170
$243$	19.4673	1.24882
$244$	52.0587	3.33272
$245$	2.08281	0.133066
$246$	20.5019	1.30715
$247$	0	0
$248$	−5.73120	−0.363932
$249$	15.5728	0.986887
$250$	31.1063	1.96734
$251$	−18.4820	−1.16657	−0.583287	−	0.812266i	$-0.698234\pi$
$251$	−18.4820	−1.16657	−0.583287	+	0.812266i	$0.698234\pi$
$252$	21.5595	1.35812
$253$	−15.2450	−0.958448
$254$	−29.2535	−1.83553
$255$	32.5749	2.03992
$256$	−8.01639	−0.501024
$257$	−28.5202	−1.77904	−0.889520	−	0.456896i	$-0.848961\pi$
$257$	−28.5202	−1.77904	−0.889520	+	0.456896i	$0.848961\pi$
$258$	30.5241	1.90035
$259$	−2.16348	−0.134432
$260$	0	0
$261$	−36.0540	−2.23169
$262$	−40.2596	−2.48724
$263$	−11.9385	−0.736162	−0.368081	−	0.929794i	$-0.619985\pi$
$263$	−11.9385	−0.736162	−0.368081	+	0.929794i	$0.619985\pi$
$264$	76.2579	4.69335
$265$	−22.8842	−1.40577
$266$	3.59344	0.220328
$267$	−22.8036	−1.39556
$268$	−23.3194	−1.42446
$269$	−1.05171	−0.0641239	−0.0320619	−	0.999486i	$-0.510207\pi$
$269$	−1.05171	−0.0641239	−0.0320619	+	0.999486i	$0.510207\pi$
$270$	20.0849	1.22233
$271$	4.18149	0.254008	0.127004	−	0.991902i	$-0.459464\pi$
$271$	4.18149	0.254008	0.127004	+	0.991902i	$0.459464\pi$
$272$	−61.5266	−3.73060
$273$	0	0
$274$	28.9365	1.74811
$275$	−2.38658	−0.143916
$276$	56.8257	3.42050
$277$	−1.79552	−0.107882	−0.0539412	−	0.998544i	$-0.517178\pi$
$277$	−1.79552	−0.107882	−0.0539412	+	0.998544i	$0.517178\pi$
$278$	44.9594	2.69649
$279$	3.19439	0.191243
$280$	−16.2501	−0.971128
$281$	−21.2449	−1.26736	−0.633682	−	0.773593i	$-0.718457\pi$
$281$	−21.2449	−1.26736	−0.633682	+	0.773593i	$0.718457\pi$
$282$	62.1000	3.69800
$283$	27.3633	1.62658	0.813291	−	0.581857i	$-0.197674\pi$
$283$	27.3633	1.62658	0.813291	+	0.581857i	$0.197674\pi$
$284$	−65.9502	−3.91342
$285$	7.69175	0.455620
$286$	0	0
$287$	2.86719	0.169245
$288$	−54.4696	−3.20965
$289$	16.2862	0.958013
$290$	45.5502	2.67480
$291$	16.8170	0.985829
$292$	21.6166	1.26501
$293$	25.9939	1.51858	0.759291	−	0.650751i	$-0.225546\pi$
$293$	25.9939	1.51858	0.759291	+	0.650751i	$0.225546\pi$
$294$	7.15053	0.417028
$295$	−14.0655	−0.818926
$296$	16.8795	0.981100
$297$	−13.1814	−0.764860
$298$	55.3997	3.20922
$299$	0	0
$300$	8.89595	0.513608
$301$	4.26879	0.246049
$302$	−24.1196	−1.38793
$303$	17.1618	0.985918
$304$	−14.5279	−0.833235
$305$	21.8702	1.25228
$306$	66.1786	3.78318
$307$	−6.54230	−0.373389	−0.186694	−	0.982418i	$-0.559777\pi$
$307$	−6.54230	−0.373389	−0.186694	+	0.982418i	$0.559777\pi$
$308$	17.8758	1.01857
$309$	−20.7233	−1.17890
$310$	−4.03575	−0.229215
$311$	−14.7482	−0.836292	−0.418146	−	0.908380i	$-0.637320\pi$
$311$	−14.7482	−0.836292	−0.418146	+	0.908380i	$0.637320\pi$
$312$	0	0
$313$	−26.8881	−1.51980	−0.759902	−	0.650038i	$-0.774753\pi$
$313$	−26.8881	−1.51980	−0.759902	+	0.650038i	$0.774753\pi$
$314$	51.4265	2.90217
$315$	9.05729	0.510320
$316$	−8.61489	−0.484625
$317$	−19.6995	−1.10644	−0.553218	−	0.833036i	$-0.686601\pi$
$317$	−19.6995	−1.10644	−0.553218	+	0.833036i	$0.686601\pi$
$318$	−78.5642	−4.40566
$319$	−29.8938	−1.67373
$320$	24.3930	1.36361
$321$	−7.46490	−0.416650
$322$	11.1529	0.621528
$323$	7.85970	0.437326
$324$	−15.5452	−0.863624
$325$	0	0
$326$	−55.4763	−3.07255
$327$	13.2759	0.734159
$328$	−22.3698	−1.23517
$329$	8.68467	0.478801
$330$	53.6987	2.95602
$331$	−27.2645	−1.49859	−0.749297	−	0.662234i	$-0.769609\pi$
$331$	−27.2645	−1.49859	−0.749297	+	0.662234i	$0.769609\pi$
$332$	−28.4810	−1.56310
$333$	−9.40809	−0.515560
$334$	−1.59280	−0.0871542
$335$	−9.79661	−0.535246
$336$	−28.9090	−1.57711
$337$	−11.9935	−0.653326	−0.326663	−	0.945141i	$-0.605924\pi$
$337$	−11.9935	−0.653326	−0.326663	+	0.945141i	$0.605924\pi$
$338$	0	0
$339$	47.2009	2.56360
$340$	−59.5760	−3.23096
$341$	2.64859	0.143429
$342$	15.6264	0.844979
$343$	1.00000	0.0539949
$344$	−33.3051	−1.79569
$345$	23.8728	1.28527
$346$	−35.5918	−1.91343
$347$	0.180455	0.00968735	0.00484368	−	0.999988i	$-0.498458\pi$
$347$	0.180455	0.00968735	0.00484368	+	0.999988i	$0.498458\pi$
$348$	111.429	5.97320
$349$	35.4438	1.89726	0.948632	−	0.316381i	$-0.102468\pi$
$349$	35.4438	1.89726	0.948632	+	0.316381i	$0.102468\pi$
$350$	1.74597	0.0933259
$351$	0	0
$352$	−45.1628	−2.40719
$353$	−21.7983	−1.16021	−0.580103	−	0.814543i	$-0.696988\pi$
$353$	−21.7983	−1.16021	−0.580103	+	0.814543i	$0.696988\pi$
$354$	−48.2886	−2.56651
$355$	−27.7061	−1.47049
$356$	41.7053	2.21038
$357$	15.6399	0.827752
$358$	−4.60627	−0.243449
$359$	−2.89545	−0.152816	−0.0764079	−	0.997077i	$-0.524345\pi$
$359$	−2.89545	−0.152816	−0.0764079	+	0.997077i	$0.524345\pi$
$360$	−70.6650	−3.72437
$361$	−17.1441	−0.902323
$362$	−18.7828	−0.987204
$363$	−5.42240	−0.284602
$364$	0	0
$365$	9.08126	0.475335
$366$	75.0831	3.92466
$367$	−25.7297	−1.34308	−0.671540	−	0.740968i	$-0.734367\pi$
$367$	−25.7297	−1.34308	−0.671540	+	0.740968i	$0.734367\pi$
$368$	−45.0903	−2.35049
$369$	12.4682	0.649070
$370$	11.8861	0.617927
$371$	−10.9872	−0.570426
$372$	−9.87259	−0.511870
$373$	−12.7012	−0.657643	−0.328821	−	0.944392i	$-0.606651\pi$
$373$	−12.7012	−0.657643	−0.328821	+	0.944392i	$0.606651\pi$
$374$	54.8712	2.83732
$375$	31.9679	1.65082
$376$	−67.7579	−3.49435
$377$	0	0
$378$	9.64317	0.495991
$379$	−15.1801	−0.779748	−0.389874	−	0.920868i	$-0.627482\pi$
$379$	−15.1801	−0.779748	−0.389874	+	0.920868i	$0.627482\pi$
$380$	−14.0674	−0.721641
$381$	−30.0638	−1.54022
$382$	−27.5935	−1.41181
$383$	23.4381	1.19763	0.598816	−	0.800887i	$-0.295638\pi$
$383$	23.4381	1.19763	0.598816	+	0.800887i	$0.295638\pi$
$384$	15.8335	0.808001
$385$	7.50975	0.382732
$386$	−16.2453	−0.826865
$387$	18.5632	0.943622
$388$	−30.7564	−1.56142
$389$	0.0433907	0.00220000	0.00110000	−	0.999999i	$-0.499650\pi$
$389$	0.0433907	0.00220000	0.00110000	+	0.999999i	$0.499650\pi$
$390$	0	0
$391$	24.3941	1.23366
$392$	−7.80201	−0.394061
$393$	−41.3747	−2.08708
$394$	−38.8253	−1.95599
$395$	−3.61917	−0.182100
$396$	77.7347	3.90632
$397$	3.70335	0.185866	0.0929328	−	0.995672i	$-0.470376\pi$
$397$	3.70335	0.185866	0.0929328	+	0.995672i	$0.470376\pi$
$398$	24.7348	1.23984
$399$	3.69297	0.184880
$400$	−7.05879	−0.352940
$401$	30.2889	1.51256	0.756279	−	0.654250i	$-0.227015\pi$
$401$	30.2889	1.51256	0.756279	+	0.654250i	$0.227015\pi$
$402$	−33.6330	−1.67746
$403$	0	0
$404$	−31.3870	−1.56156
$405$	−6.53066	−0.324511
$406$	21.8696	1.08537
$407$	−7.80062	−0.386662
$408$	−122.023	−6.04103
$409$	7.03924	0.348068	0.174034	−	0.984740i	$-0.444320\pi$
$409$	7.03924	0.348068	0.174034	+	0.984740i	$0.444320\pi$
$410$	−15.7522	−0.777946
$411$	29.7380	1.46687
$412$	37.9006	1.86723
$413$	−6.75315	−0.332301
$414$	48.4996	2.38362
$415$	−11.9650	−0.587341
$416$	0	0
$417$	46.2048	2.26266
$418$	12.9565	0.633721
$419$	15.9101	0.777258	0.388629	−	0.921394i	$-0.372949\pi$
$419$	15.9101	0.777258	0.388629	+	0.921394i	$0.372949\pi$
$420$	−27.9925	−1.36589
$421$	9.91446	0.483201	0.241601	−	0.970376i	$-0.422328\pi$
$421$	9.91446	0.483201	0.241601	+	0.970376i	$0.422328\pi$
$422$	29.8745	1.45427
$423$	37.7661	1.83625
$424$	85.7221	4.16303
$425$	3.81885	0.185241
$426$	−95.1184	−4.60850
$427$	10.5003	0.508147
$428$	13.6525	0.659917
$429$	0	0
$430$	−23.4525	−1.13098
$431$	−18.3787	−0.885270	−0.442635	−	0.896702i	$-0.645956\pi$
$431$	−18.3787	−0.885270	−0.442635	+	0.896702i	$0.645956\pi$
$432$	−38.9865	−1.87574
$433$	−11.4478	−0.550147	−0.275074	−	0.961423i	$-0.588702\pi$
$433$	−11.4478	−0.550147	−0.275074	+	0.961423i	$0.588702\pi$
$434$	−1.93765	−0.0930102
$435$	46.8119	2.24446
$436$	−24.2802	−1.16281
$437$	5.76005	0.275541
$438$	31.1771	1.48970
$439$	−21.1811	−1.01092	−0.505459	−	0.862851i	$-0.668677\pi$
$439$	−21.1811	−1.01092	−0.505459	+	0.862851i	$0.668677\pi$
$440$	−58.5911	−2.79322
$441$	4.34860	0.207076
$442$	0	0
$443$	35.4959	1.68646	0.843231	−	0.537552i	$-0.180651\pi$
$443$	35.4959	1.68646	0.843231	+	0.537552i	$0.180651\pi$
$444$	29.0767	1.37992
$445$	17.5207	0.830560
$446$	34.6895	1.64260
$447$	56.9342	2.69289
$448$	11.7116	0.553320
$449$	−9.93940	−0.469069	−0.234535	−	0.972108i	$-0.575357\pi$
$449$	−9.93940	−0.469069	−0.234535	+	0.972108i	$0.575357\pi$
$450$	7.59251	0.357914
$451$	10.3379	0.486793
$452$	−86.3253	−4.06040
$453$	−24.7877	−1.16463
$454$	−16.2337	−0.761887
$455$	0	0
$456$	−28.8126	−1.34927
$457$	−6.51624	−0.304817	−0.152409	−	0.988318i	$-0.548703\pi$
$457$	−6.51624	−0.304817	−0.152409	+	0.988318i	$0.548703\pi$
$458$	45.4116	2.12195
$459$	21.0919	0.984486
$460$	−43.6608	−2.03569
$461$	17.9564	0.836314	0.418157	−	0.908375i	$-0.362676\pi$
$461$	17.9564	0.836314	0.418157	+	0.908375i	$0.362676\pi$
$462$	25.7819	1.19948
$463$	27.0873	1.25885	0.629427	−	0.777059i	$-0.283290\pi$
$463$	27.0873	1.25885	0.629427	+	0.777059i	$0.283290\pi$
$464$	−88.4168	−4.10465
$465$	−4.14754	−0.192338
$466$	50.4406	2.33662
$467$	24.6940	1.14270	0.571351	−	0.820706i	$-0.306419\pi$
$467$	24.6940	1.14270	0.571351	+	0.820706i	$0.306419\pi$
$468$	0	0
$469$	−4.70356	−0.217190
$470$	−47.7132	−2.20085
$471$	52.8510	2.43524
$472$	52.6881	2.42517
$473$	15.3915	0.707702
$474$	−12.4250	−0.570701
$475$	0.901725	0.0413740
$476$	−28.6037	−1.31105
$477$	−47.7788	−2.18764
$478$	−23.7085	−1.08440
$479$	−22.5936	−1.03233	−0.516163	−	0.856490i	$-0.672640\pi$
$479$	−22.5936	−1.03233	−0.516163	+	0.856490i	$0.672640\pi$
$480$	70.7223	3.22802
$481$	0	0
$482$	−22.4824	−1.02404
$483$	11.4619	0.521532
$484$	9.91697	0.450771
$485$	−12.9210	−0.586711
$486$	−51.3501	−2.32929
$487$	−20.6049	−0.933696	−0.466848	−	0.884338i	$-0.654610\pi$
$487$	−20.6049	−0.933696	−0.466848	+	0.884338i	$0.654610\pi$
$488$	−81.9238	−3.70852
$489$	−57.0129	−2.57821
$490$	−5.49396	−0.248192
$491$	2.14396	0.0967555	0.0483778	−	0.998829i	$-0.484595\pi$
$491$	2.14396	0.0967555	0.0483778	+	0.998829i	$0.484595\pi$
$492$	−38.5343	−1.73726
$493$	47.8340	2.15434
$494$	0	0
$495$	32.6569	1.46782
$496$	7.83375	0.351746
$497$	−13.3023	−0.596689
$498$	−41.0774	−1.84072
$499$	0.962977	0.0431088	0.0215544	−	0.999768i	$-0.493138\pi$
$499$	0.962977	0.0431088	0.0215544	+	0.999768i	$0.493138\pi$
$500$	−58.4658	−2.61467
$501$	−1.63692	−0.0731322
$502$	48.7512	2.17587
$503$	−14.0985	−0.628623	−0.314311	−	0.949320i	$-0.601774\pi$
$503$	−14.0985	−0.628623	−0.314311	+	0.949320i	$0.601774\pi$
$504$	−33.9278	−1.51126
$505$	−13.1859	−0.586764
$506$	40.2129	1.78768
$507$	0	0
$508$	54.9834	2.43950
$509$	−14.6607	−0.649823	−0.324912	−	0.945744i	$-0.605335\pi$
$509$	−14.6607	−0.649823	−0.324912	+	0.945744i	$0.605335\pi$
$510$	−85.9251	−3.80483
$511$	4.36010	0.192880
$512$	32.8270	1.45076
$513$	4.98032	0.219887
$514$	75.2295	3.31823
$515$	15.9223	0.701619
$516$	−57.3715	−2.52564
$517$	31.3134	1.37716
$518$	5.70675	0.250740
$519$	−36.5777	−1.60558
$520$	0	0
$521$	34.0043	1.48976	0.744878	−	0.667200i	$-0.232507\pi$
$521$	34.0043	1.48976	0.744878	+	0.667200i	$0.232507\pi$
$522$	95.1020	4.16250
$523$	−32.7639	−1.43266	−0.716332	−	0.697759i	$-0.754181\pi$
$523$	−32.7639	−1.43266	−0.716332	+	0.697759i	$0.754181\pi$
$524$	75.6698	3.30565
$525$	1.79433	0.0783110
$526$	31.4911	1.37308
$527$	−4.23810	−0.184615
$528$	−104.234	−4.53620
$529$	−5.12256	−0.222720
$530$	60.3632	2.62201
$531$	−29.3667	−1.27441
$532$	−6.75404	−0.292825
$533$	0	0
$534$	60.1506	2.60297
$535$	5.73550	0.247967
$536$	36.6972	1.58508
$537$	−4.73386	−0.204281
$538$	2.77416	0.119603
$539$	3.60559	0.155304
$540$	−37.7505	−1.62452
$541$	−9.58117	−0.411926	−0.205963	−	0.978560i	$-0.566033\pi$
$541$	−9.58117	−0.411926	−0.205963	+	0.978560i	$0.566033\pi$
$542$	−11.0298	−0.473770
$543$	−19.3031	−0.828376
$544$	72.2665	3.09840
$545$	−10.2003	−0.436931
$546$	0	0
$547$	−22.1667	−0.947779	−0.473889	−	0.880584i	$-0.657150\pi$
$547$	−22.1667	−0.947779	−0.473889	+	0.880584i	$0.657150\pi$
$548$	−54.3875	−2.32332
$549$	45.6618	1.94880
$550$	6.29525	0.268430
$551$	11.2948	0.481174
$552$	−89.4255	−3.80620
$553$	−1.73764	−0.0738920
$554$	4.73616	0.201220
$555$	12.2153	0.518510
$556$	−84.5035	−3.58375
$557$	18.6947	0.792118	0.396059	−	0.918225i	$-0.370378\pi$
$557$	18.6947	0.792118	0.396059	+	0.918225i	$0.370378\pi$
$558$	−8.42606	−0.356703
$559$	0	0
$560$	22.2116	0.938611
$561$	56.3911	2.38083
$562$	56.0391	2.36387
$563$	0.984350	0.0414854	0.0207427	−	0.999785i	$-0.493397\pi$
$563$	0.984350	0.0414854	0.0207427	+	0.999785i	$0.493397\pi$
$564$	−116.720	−4.91480
$565$	−36.2658	−1.52571
$566$	−72.1781	−3.03387
$567$	−3.13551	−0.131679
$568$	103.785	4.35470
$569$	20.4218	0.856128	0.428064	−	0.903748i	$-0.359196\pi$
$569$	20.4218	0.856128	0.428064	+	0.903748i	$0.359196\pi$
$570$	−20.2890	−0.849814
$571$	−29.6858	−1.24231	−0.621157	−	0.783686i	$-0.713337\pi$
$571$	−29.6858	−1.24231	−0.621157	+	0.783686i	$0.713337\pi$
$572$	0	0
$573$	−28.3578	−1.18467
$574$	−7.56297	−0.315672
$575$	2.79868	0.116713
$576$	50.9289	2.12204
$577$	−11.8652	−0.493957	−0.246978	−	0.969021i	$-0.579438\pi$
$577$	−11.8652	−0.493957	−0.246978	+	0.969021i	$0.579438\pi$
$578$	−42.9592	−1.78687
$579$	−16.6953	−0.693833
$580$	−85.6137	−3.55492
$581$	−5.74467	−0.238329
$582$	−44.3593	−1.83875
$583$	−39.6153	−1.64070
$584$	−34.0176	−1.40766
$585$	0	0
$586$	−68.5659	−2.83243
$587$	48.3763	1.99670	0.998352	−	0.0573787i	$-0.0182743\pi$
$587$	48.3763	1.99670	0.998352	+	0.0573787i	$0.0182743\pi$
$588$	−13.4398	−0.554247
$589$	−1.00072	−0.0412340
$590$	37.1015	1.52745
$591$	−39.9007	−1.64130
$592$	−23.0719	−0.948248
$593$	−34.3228	−1.40947	−0.704734	−	0.709471i	$-0.748934\pi$
$593$	−34.3228	−1.40947	−0.704734	+	0.709471i	$0.748934\pi$
$594$	34.7693	1.42660
$595$	−12.0166	−0.492632
$596$	−104.126	−4.26518
$597$	25.4199	1.04037
$598$	0	0
$599$	−22.8086	−0.931933	−0.465967	−	0.884802i	$-0.654293\pi$
$599$	−22.8086	−0.931933	−0.465967	+	0.884802i	$0.654293\pi$
$600$	−13.9994	−0.571522
$601$	15.6032	0.636467	0.318233	−	0.948012i	$-0.396910\pi$
$601$	15.6032	0.636467	0.318233	+	0.948012i	$0.396910\pi$
$602$	−11.2601	−0.458926
$603$	−20.4539	−0.832946
$604$	45.3339	1.84461
$605$	4.16618	0.169379
$606$	−45.2687	−1.83892
$607$	−5.67517	−0.230348	−0.115174	−	0.993345i	$-0.536743\pi$
$607$	−5.67517	−0.230348	−0.115174	+	0.993345i	$0.536743\pi$
$608$	17.0639	0.692033
$609$	22.4754	0.910748
$610$	−57.6885	−2.33574
$611$	0	0
$612$	−124.386	−5.02800
$613$	28.5664	1.15379	0.576894	−	0.816819i	$-0.304265\pi$
$613$	28.5664	1.15379	0.576894	+	0.816819i	$0.304265\pi$
$614$	17.2570	0.696438
$615$	−16.1885	−0.652784
$616$	−28.1308	−1.13342
$617$	12.3751	0.498201	0.249101	−	0.968478i	$-0.419865\pi$
$617$	12.3751	0.498201	0.249101	+	0.968478i	$0.419865\pi$
$618$	54.6631	2.19887
$619$	−23.9715	−0.963494	−0.481747	−	0.876310i	$-0.659998\pi$
$619$	−23.9715	−0.963494	−0.481747	+	0.876310i	$0.659998\pi$
$620$	7.58539	0.304637
$621$	15.4574	0.620284
$622$	38.9022	1.55984
$623$	8.41205	0.337022
$624$	0	0
$625$	−21.2523	−0.850093
$626$	70.9244	2.83471
$627$	13.3153	0.531763
$628$	−96.6586	−3.85710
$629$	12.4820	0.497691
$630$	−23.8910	−0.951840
$631$	3.79928	0.151247	0.0756236	−	0.997136i	$-0.475905\pi$
$631$	3.79928	0.151247	0.0756236	+	0.997136i	$0.475905\pi$
$632$	13.5571	0.539272
$633$	30.7020	1.22029
$634$	51.9628	2.06371
$635$	23.0989	0.916652
$636$	147.665	5.85531
$637$	0	0
$638$	78.8528	3.12181
$639$	−57.8462	−2.28836
$640$	−12.1653	−0.480878
$641$	2.98792	0.118016	0.0590080	−	0.998258i	$-0.481206\pi$
$641$	2.98792	0.118016	0.0590080	+	0.998258i	$0.481206\pi$
$642$	19.6907	0.777128
$643$	−34.0839	−1.34414	−0.672069	−	0.740489i	$-0.734594\pi$
$643$	−34.0839	−1.34414	−0.672069	+	0.740489i	$0.734594\pi$
$644$	−20.9625	−0.826037
$645$	−24.1022	−0.949022
$646$	−20.7321	−0.815692
$647$	1.79132	0.0704240	0.0352120	−	0.999380i	$-0.488789\pi$
$647$	1.79132	0.0704240	0.0352120	+	0.999380i	$0.488789\pi$
$648$	24.4632	0.961007
$649$	−24.3491	−0.955786
$650$	0	0
$651$	−1.99132	−0.0780460
$652$	104.270	4.08354
$653$	−23.6436	−0.925245	−0.462623	−	0.886555i	$-0.653092\pi$
$653$	−23.6436	−0.925245	−0.462623	+	0.886555i	$0.653092\pi$
$654$	−35.0187	−1.36934
$655$	31.7894	1.24211
$656$	30.5764	1.19381
$657$	18.9603	0.739713
$658$	−22.9081	−0.893052
$659$	14.8861	0.579878	0.289939	−	0.957045i	$-0.406365\pi$
$659$	14.8861	0.579878	0.289939	+	0.957045i	$0.406365\pi$
$660$	−100.929	−3.92867
$661$	−23.7725	−0.924643	−0.462322	−	0.886712i	$-0.652983\pi$
$661$	−23.7725	−0.924643	−0.462322	+	0.886712i	$0.652983\pi$
$662$	71.9175	2.79515
$663$	0	0
$664$	44.8199	1.73935
$665$	−2.83742	−0.110030
$666$	24.8163	0.961614
$667$	35.0556	1.35736
$668$	2.99375	0.115832
$669$	35.6504	1.37832
$670$	25.8412	0.998332
$671$	37.8599	1.46157
$672$	33.9553	1.30985
$673$	0.690661	0.0266230	0.0133115	−	0.999911i	$-0.495763\pi$
$673$	0.690661	0.0266230	0.0133115	+	0.999911i	$0.495763\pi$
$674$	31.6360	1.21857
$675$	2.41982	0.0931391
$676$	0	0
$677$	24.4126	0.938252	0.469126	−	0.883131i	$-0.344569\pi$
$677$	24.4126	0.938252	0.469126	+	0.883131i	$0.344569\pi$
$678$	−124.505	−4.78158
$679$	−6.20363	−0.238073
$680$	93.7536	3.59529
$681$	−16.6834	−0.639309
$682$	−6.98637	−0.267522
$683$	34.4983	1.32004	0.660020	−	0.751248i	$-0.270548\pi$
$683$	34.4983	1.32004	0.660020	+	0.751248i	$0.270548\pi$
$684$	−29.3706	−1.12301
$685$	−22.8485	−0.872997
$686$	−2.63777	−0.100710
$687$	46.6695	1.78055
$688$	45.5234	1.73556
$689$	0	0
$690$	−62.9709	−2.39726
$691$	44.2084	1.68177	0.840883	−	0.541217i	$-0.182036\pi$
$691$	44.2084	1.68177	0.840883	+	0.541217i	$0.182036\pi$
$692$	66.8965	2.54302
$693$	15.6792	0.595605
$694$	−0.475999	−0.0180687
$695$	−35.5005	−1.34661
$696$	−175.353	−6.64674
$697$	−16.5420	−0.626573
$698$	−93.4925	−3.53874
$699$	51.8378	1.96068
$700$	−3.28163	−0.124034
$701$	20.6216	0.778866	0.389433	−	0.921055i	$-0.372671\pi$
$701$	20.6216	0.778866	0.389433	+	0.921055i	$0.372671\pi$
$702$	0	0
$703$	2.94731	0.111160
$704$	42.2271	1.59150
$705$	−49.0348	−1.84676
$706$	57.4987	2.16399
$707$	−6.33082	−0.238095
$708$	90.7608	3.41100
$709$	−18.9972	−0.713456	−0.356728	−	0.934208i	$-0.616108\pi$
$709$	−18.9972	−0.713456	−0.356728	+	0.934208i	$0.616108\pi$
$710$	73.0822	2.74273
$711$	−7.55629	−0.283383
$712$	−65.6308	−2.45962
$713$	−3.10593	−0.116318
$714$	−41.2544	−1.54391
$715$	0	0
$716$	8.65771	0.323554
$717$	−24.3652	−0.909937
$718$	7.63751	0.285029
$719$	−34.2107	−1.27584	−0.637921	−	0.770101i	$-0.720206\pi$
$719$	−34.2107	−1.27584	−0.637921	+	0.770101i	$0.720206\pi$
$720$	96.5892	3.59967
$721$	7.64462	0.284700
$722$	45.2222	1.68300
$723$	−23.1051	−0.859288
$724$	35.3033	1.31204
$725$	5.48788	0.203815
$726$	14.3030	0.530835
$727$	21.3777	0.792855	0.396427	−	0.918066i	$-0.370250\pi$
$727$	21.3777	0.792855	0.396427	+	0.918066i	$0.370250\pi$
$728$	0	0
$729$	−43.3659	−1.60614
$730$	−23.9542	−0.886586
$731$	−24.6284	−0.910916
$732$	−141.122	−5.21603
$733$	5.24309	0.193658	0.0968290	−	0.995301i	$-0.469130\pi$
$733$	5.24309	0.193658	0.0968290	+	0.995301i	$0.469130\pi$
$734$	67.8690	2.50509
$735$	−5.64614	−0.208261
$736$	52.9612	1.95217
$737$	−16.9591	−0.624697
$738$	−32.8883	−1.21063
$739$	−30.1907	−1.11058	−0.555291	−	0.831656i	$-0.687393\pi$
$739$	−30.1907	−1.11058	−0.555291	+	0.831656i	$0.687393\pi$
$740$	−22.3404	−0.821251
$741$	0	0
$742$	28.9816	1.06395
$743$	−17.0073	−0.623937	−0.311969	−	0.950092i	$-0.600988\pi$
$743$	−17.0073	−0.623937	−0.311969	+	0.950092i	$0.600988\pi$
$744$	15.5363	0.569589
$745$	−43.7442	−1.60266
$746$	33.5028	1.22662
$747$	−24.9812	−0.914016
$748$	−103.133	−3.77092
$749$	2.75373	0.100619
$750$	−84.3239	−3.07907
$751$	36.9314	1.34765	0.673823	−	0.738893i	$-0.264651\pi$
$751$	36.9314	1.34765	0.673823	+	0.738893i	$0.264651\pi$
$752$	92.6155	3.37734
$753$	50.1016	1.82580
$754$	0	0
$755$	19.0451	0.693121
$756$	−18.1248	−0.659193
$757$	32.6360	1.18618	0.593088	−	0.805138i	$-0.297909\pi$
$757$	32.6360	1.18618	0.593088	+	0.805138i	$0.297909\pi$
$758$	40.0415	1.45437
$759$	41.3267	1.50007
$760$	22.1375	0.803013
$761$	29.2956	1.06196	0.530982	−	0.847383i	$-0.321823\pi$
$761$	29.2956	1.06196	0.530982	+	0.847383i	$0.321823\pi$
$762$	79.3013	2.87278
$763$	−4.89736	−0.177296
$764$	51.8634	1.87635
$765$	−52.2553	−1.88929
$766$	−61.8243	−2.23380
$767$	0	0
$768$	21.7311	0.784152
$769$	31.3796	1.13158	0.565788	−	0.824551i	$-0.308572\pi$
$769$	31.3796	1.13158	0.565788	+	0.824551i	$0.308572\pi$
$770$	−19.8090	−0.713865
$771$	77.3133	2.78437
$772$	30.5339	1.09894
$773$	12.6440	0.454774	0.227387	−	0.973804i	$-0.426982\pi$
$773$	12.6440	0.454774	0.227387	+	0.973804i	$0.426982\pi$
$774$	−48.9655	−1.76003
$775$	−0.486227	−0.0174658
$776$	48.4008	1.73749
$777$	5.86482	0.210399
$778$	−0.114455	−0.00410340
$779$	−3.90598	−0.139946
$780$	0	0
$781$	−47.9626	−1.71624
$782$	−64.3459	−2.30101
$783$	30.3102	1.08320
$784$	10.6643	0.380866
$785$	−40.6069	−1.44932
$786$	109.137	3.89278
$787$	47.8788	1.70669	0.853347	−	0.521343i	$-0.174569\pi$
$787$	47.8788	1.70669	0.853347	+	0.521343i	$0.174569\pi$
$788$	72.9740	2.59959
$789$	32.3634	1.15217
$790$	9.54652	0.339650
$791$	−17.4120	−0.619099
$792$	−122.330	−4.34679
$793$	0	0
$794$	−9.76856	−0.346673
$795$	62.0352	2.20016
$796$	−46.4902	−1.64780
$797$	−0.670274	−0.0237423	−0.0118712	−	0.999930i	$-0.503779\pi$
$797$	−0.670274	−0.0237423	−0.0118712	+	0.999930i	$0.503779\pi$
$798$	−9.74120	−0.344835
$799$	−50.1055	−1.77261
$800$	8.29096	0.293130
$801$	36.5806	1.29251
$802$	−79.8951	−2.82120
$803$	15.7207	0.554773
$804$	63.2148	2.22941
$805$	−8.80647	−0.310387
$806$	0	0
$807$	2.85101	0.100360
$808$	49.3931	1.73764
$809$	−4.18768	−0.147231	−0.0736155	−	0.997287i	$-0.523454\pi$
$809$	−4.18768	−0.147231	−0.0736155	+	0.997287i	$0.523454\pi$
$810$	17.2263	0.605272
$811$	−35.4890	−1.24619	−0.623094	−	0.782147i	$-0.714125\pi$
$811$	−35.4890	−1.24619	−0.623094	+	0.782147i	$0.714125\pi$
$812$	−41.1050	−1.44250
$813$	−11.3353	−0.397547
$814$	20.5762	0.721195
$815$	43.8046	1.53441
$816$	166.788	5.83875
$817$	−5.81539	−0.203455
$818$	−18.5679	−0.649210
$819$	0	0
$820$	29.6070	1.03392
$821$	−47.5099	−1.65811	−0.829053	−	0.559170i	$-0.811120\pi$
$821$	−47.5099	−1.65811	−0.829053	+	0.559170i	$0.811120\pi$
$822$	−78.4418	−2.73597
$823$	1.31971	0.0460023	0.0230011	−	0.999735i	$-0.492678\pi$
$823$	1.31971	0.0460023	0.0230011	+	0.999735i	$0.492678\pi$
$824$	−59.6434	−2.07777
$825$	6.46962	0.225243
$826$	17.8132	0.619802
$827$	−32.9254	−1.14493	−0.572464	−	0.819930i	$-0.694012\pi$
$827$	−32.9254	−1.14493	−0.572464	+	0.819930i	$0.694012\pi$
$828$	−91.1573	−3.16793
$829$	38.3442	1.33175	0.665874	−	0.746064i	$-0.268059\pi$
$829$	38.3442	1.33175	0.665874	+	0.746064i	$0.268059\pi$
$830$	31.5610	1.09550
$831$	4.86735	0.168846
$832$	0	0
$833$	−5.76942	−0.199899
$834$	−121.877	−4.22027
$835$	1.25769	0.0435242
$836$	−24.3523	−0.842242
$837$	−2.68549	−0.0928240
$838$	−41.9670	−1.44973
$839$	−49.6084	−1.71267	−0.856335	−	0.516420i	$-0.827264\pi$
$839$	−49.6084	−1.71267	−0.856335	+	0.516420i	$0.827264\pi$
$840$	44.0512	1.51991
$841$	39.7399	1.37034
$842$	−26.1520	−0.901258
$843$	57.5913	1.98355
$844$	−56.1506	−1.93278
$845$	0	0
$846$	−99.6182	−3.42494
$847$	2.00027	0.0687302
$848$	−117.170	−4.02364
$849$	−74.1773	−2.54576
$850$	−10.0732	−0.345509
$851$	9.14756	0.313574
$852$	178.780	6.12489
$853$	−3.85470	−0.131982	−0.0659912	−	0.997820i	$-0.521021\pi$
$853$	−3.85470	−0.131982	−0.0659912	+	0.997820i	$0.521021\pi$
$854$	−27.6975	−0.947788
$855$	−12.3388	−0.421977
$856$	−21.4846	−0.734330
$857$	37.5468	1.28257	0.641287	−	0.767301i	$-0.278401\pi$
$857$	37.5468	1.28257	0.641287	+	0.767301i	$0.278401\pi$
$858$	0	0
$859$	4.89387	0.166977	0.0834883	−	0.996509i	$-0.473394\pi$
$859$	4.89387	0.166977	0.0834883	+	0.996509i	$0.473394\pi$
$860$	44.0802	1.50312
$861$	−7.77245	−0.264885
$862$	48.4787	1.65119
$863$	−17.9815	−0.612097	−0.306049	−	0.952016i	$-0.599007\pi$
$863$	−17.9815	−0.612097	−0.306049	+	0.952016i	$0.599007\pi$
$864$	45.7919	1.55787
$865$	28.1037	0.955553
$866$	30.1967	1.02612
$867$	−44.1492	−1.49938
$868$	3.64191	0.123614
$869$	−6.26521	−0.212533
$870$	−123.479	−4.18632
$871$	0	0
$872$	38.2092	1.29393
$873$	−26.9771	−0.913036
$874$	−15.1937	−0.513934
$875$	−11.7927	−0.398665
$876$	−58.5988	−1.97987
$877$	21.6582	0.731347	0.365674	−	0.930743i	$-0.380839\pi$
$877$	21.6582	0.731347	0.365674	+	0.930743i	$0.380839\pi$
$878$	55.8708	1.88555
$879$	−70.4651	−2.37673
$880$	80.0858	2.69969
$881$	−4.96810	−0.167379	−0.0836897	−	0.996492i	$-0.526670\pi$
$881$	−4.96810	−0.167379	−0.0836897	+	0.996492i	$0.526670\pi$
$882$	−11.4706	−0.386234
$883$	9.13265	0.307338	0.153669	−	0.988122i	$-0.450891\pi$
$883$	9.13265	0.307338	0.153669	+	0.988122i	$0.450891\pi$
$884$	0	0
$885$	38.1292	1.28170
$886$	−93.6299	−3.14556
$887$	17.4343	0.585388	0.292694	−	0.956206i	$-0.405448\pi$
$887$	17.4343	0.585388	0.292694	+	0.956206i	$0.405448\pi$
$888$	−45.7574	−1.53552
$889$	11.0903	0.371956
$890$	−46.2154	−1.54915
$891$	−11.3053	−0.378743
$892$	−65.2006	−2.18308
$893$	−11.8312	−0.395915
$894$	−150.179	−5.02274
$895$	3.63716	0.121577
$896$	−5.84084	−0.195129
$897$	0	0
$898$	26.2178	0.874900
$899$	−6.09037	−0.203125
$900$	−14.2705	−0.475683
$901$	63.3897	2.11182
$902$	−27.2690	−0.907957
$903$	−11.5720	−0.385091
$904$	135.848	4.51825
$905$	14.8311	0.493003
$906$	65.3841	2.17224
$907$	2.02670	0.0672954	0.0336477	−	0.999434i	$-0.489288\pi$
$907$	2.02670	0.0672954	0.0336477	+	0.999434i	$0.489288\pi$
$908$	30.5121	1.01258
$909$	−27.5302	−0.913118
$910$	0	0
$911$	11.4856	0.380535	0.190268	−	0.981732i	$-0.439064\pi$
$911$	11.4856	0.380535	0.190268	+	0.981732i	$0.439064\pi$
$912$	39.3828	1.30409
$913$	−20.7129	−0.685497
$914$	17.1883	0.568539
$915$	−59.2864	−1.95995
$916$	−85.3533	−2.82015
$917$	15.2627	0.504020
$918$	−55.6355	−1.83625
$919$	−21.7918	−0.718846	−0.359423	−	0.933175i	$-0.617027\pi$
$919$	−21.7918	−0.718846	−0.359423	+	0.933175i	$0.617027\pi$
$920$	68.7081	2.26524
$921$	17.7350	0.584390
$922$	−47.3649	−1.55988
$923$	0	0
$924$	−48.4583	−1.59416
$925$	1.43203	0.0470849
$926$	−71.4500	−2.34799
$927$	33.2433	1.09185
$928$	103.851	3.40907
$929$	39.9819	1.31176	0.655882	−	0.754863i	$-0.272297\pi$
$929$	39.9819	1.31176	0.655882	+	0.754863i	$0.272297\pi$
$930$	10.9402	0.358745
$931$	−1.36230	−0.0446477
$932$	−94.8056	−3.10546
$933$	39.9798	1.30888
$934$	−65.1370	−2.13135
$935$	−43.3269	−1.41694
$936$	0	0
$937$	−37.2739	−1.21768	−0.608842	−	0.793292i	$-0.708366\pi$
$937$	−37.2739	−1.21768	−0.608842	+	0.793292i	$0.708366\pi$
$938$	12.4069	0.405099
$939$	72.8890	2.37864
$940$	89.6793	2.92502
$941$	12.8373	0.418484	0.209242	−	0.977864i	$-0.432900\pi$
$941$	12.8373	0.418484	0.209242	+	0.977864i	$0.432900\pi$
$942$	−139.408	−4.54217
$943$	−12.1230	−0.394778
$944$	−72.0173	−2.34396
$945$	−7.61435	−0.247695
$946$	−40.5992	−1.31999
$947$	−17.6547	−0.573702	−0.286851	−	0.957975i	$-0.592608\pi$
$947$	−17.6547	−0.573702	−0.286851	+	0.957975i	$0.592608\pi$
$948$	23.3535	0.758486
$949$	0	0
$950$	−2.37854	−0.0771700
$951$	53.4021	1.73168
$952$	45.0131	1.45888
$953$	−19.3254	−0.626011	−0.313005	−	0.949751i	$-0.601336\pi$
$953$	−19.3254	−0.626011	−0.313005	+	0.949751i	$0.601336\pi$
$954$	126.029	4.08035
$955$	21.7881	0.705048
$956$	44.5613	1.44122
$957$	81.0369	2.61955
$958$	59.5965	1.92548
$959$	−10.9701	−0.354242
$960$	−66.1252	−2.13418
$961$	−30.4604	−0.982593
$962$	0	0
$963$	11.9749	0.385885
$964$	42.2567	1.36100
$965$	12.8275	0.412931
$966$	−30.2337	−0.972753
$967$	−47.1716	−1.51693	−0.758467	−	0.651711i	$-0.774052\pi$
$967$	−47.1716	−1.51693	−0.758467	+	0.651711i	$0.774052\pi$
$968$	−15.6061	−0.501600
$969$	−21.3063	−0.684457
$970$	34.0825	1.09432
$971$	17.7036	0.568136	0.284068	−	0.958804i	$-0.408316\pi$
$971$	17.7036	0.568136	0.284068	+	0.958804i	$0.408316\pi$
$972$	96.5149	3.09572
$973$	−17.0445	−0.546422
$974$	54.3508	1.74151
$975$	0	0
$976$	111.978	3.58434
$977$	47.7932	1.52904	0.764520	−	0.644600i	$-0.222976\pi$
$977$	47.7932	1.52904	0.764520	+	0.644600i	$0.222976\pi$
$978$	150.387	4.80884
$979$	30.3304	0.969363
$980$	10.3262	0.329857
$981$	−21.2966	−0.679949
$982$	−5.65526	−0.180467
$983$	7.81325	0.249204	0.124602	−	0.992207i	$-0.460235\pi$
$983$	7.81325	0.249204	0.124602	+	0.992207i	$0.460235\pi$
$984$	60.6407	1.93316
$985$	30.6569	0.976808
$986$	−126.175	−4.01823
$987$	−23.5427	−0.749371
$988$	0	0
$989$	−18.0492	−0.573930
$990$	−86.1411	−2.73775
$991$	9.77365	0.310470	0.155235	−	0.987878i	$-0.450386\pi$
$991$	9.77365	0.310470	0.155235	+	0.987878i	$0.450386\pi$
$992$	−9.20119	−0.292138
$993$	73.9095	2.34545
$994$	35.0883	1.11293
$995$	−19.5308	−0.619169
$996$	77.2070	2.44640
$997$	18.3134	0.579990	0.289995	−	0.957028i	$-0.406346\pi$
$997$	18.3134	0.579990	0.289995	+	0.957028i	$0.406346\pi$
$998$	−2.54011	−0.0804057
$999$	7.90927	0.250238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.n.1.1	✓	6
7.6	odd	2		8281.2.a.cb.1.1		6
13.5	odd	4		1183.2.c.h.337.12		12
13.8	odd	4		1183.2.c.h.337.1		12
13.12	even	2		1183.2.a.o.1.6	yes	6
91.90	odd	2		8281.2.a.cg.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.1	✓	6	1.1	even	1	trivial
1183.2.a.o.1.6	yes	6	13.12	even	2
1183.2.c.h.337.1		12	13.8	odd	4
1183.2.c.h.337.12		12	13.5	odd	4
8281.2.a.cb.1.1		6	7.6	odd	2
8281.2.a.cg.1.6		6	91.90	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)

\(f(q)\)	\(=\)	\(q-2.63777 q^{2} -2.71083 q^{3} +4.95781 q^{4} +2.08281 q^{5} +7.15053 q^{6} +1.00000 q^{7} -7.80201 q^{8} +4.34860 q^{9} +O(q^{10})\)	\(q-2.63777 q^{2} -2.71083 q^{3} +4.95781 q^{4} +2.08281 q^{5} +7.15053 q^{6} +1.00000 q^{7} -7.80201 q^{8} +4.34860 q^{9} -5.49396 q^{10} +3.60559 q^{11} -13.4398 q^{12} -2.63777 q^{14} -5.64614 q^{15} +10.6643 q^{16} -5.76942 q^{17} -11.4706 q^{18} -1.36230 q^{19} +10.3262 q^{20} -2.71083 q^{21} -9.51070 q^{22} -4.22817 q^{23} +21.1499 q^{24} -0.661912 q^{25} -3.65581 q^{27} +4.95781 q^{28} -8.29095 q^{29} +14.8932 q^{30} +0.734580 q^{31} -12.5258 q^{32} -9.77414 q^{33} +15.2184 q^{34} +2.08281 q^{35} +21.5595 q^{36} -2.16348 q^{37} +3.59344 q^{38} -16.2501 q^{40} +2.86719 q^{41} +7.15053 q^{42} +4.26879 q^{43} +17.8758 q^{44} +9.05729 q^{45} +11.1529 q^{46} +8.68467 q^{47} -28.9090 q^{48} +1.00000 q^{49} +1.74597 q^{50} +15.6399 q^{51} -10.9872 q^{53} +9.64317 q^{54} +7.50975 q^{55} -7.80201 q^{56} +3.69297 q^{57} +21.8696 q^{58} -6.75315 q^{59} -27.9925 q^{60} +10.5003 q^{61} -1.93765 q^{62} +4.34860 q^{63} +11.7116 q^{64} +25.7819 q^{66} -4.70356 q^{67} -28.6037 q^{68} +11.4619 q^{69} -5.49396 q^{70} -13.3023 q^{71} -33.9278 q^{72} +4.36010 q^{73} +5.70675 q^{74} +1.79433 q^{75} -6.75404 q^{76} +3.60559 q^{77} -1.73764 q^{79} +22.2116 q^{80} -3.13551 q^{81} -7.56297 q^{82} -5.74467 q^{83} -13.4398 q^{84} -12.0166 q^{85} -11.2601 q^{86} +22.4754 q^{87} -28.1308 q^{88} +8.41205 q^{89} -23.8910 q^{90} -20.9625 q^{92} -1.99132 q^{93} -22.9081 q^{94} -2.83742 q^{95} +33.9553 q^{96} -6.20363 q^{97} -2.63777 q^{98} +15.6792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8}+O(q^{10}) \) 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

Modular forms

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Database

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