LMFDB - Embedded newform 931.2.a.p.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 57x^6 - 98x^5 - 93x^4 + 152x^3 + 39x^2 - 58*x - 7
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			1.9
Root			$-1.94026$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.94026 q^{2} -2.74246 q^{3} +1.76460 q^{4} +0.683496 q^{5} -5.32108 q^{6} -0.456739 q^{8} +4.52109 q^{9} +O(q^{10})$	\(q+1.94026 q^{2} -2.74246 q^{3} +1.76460 q^{4} +0.683496 q^{5} -5.32108 q^{6} -0.456739 q^{8} +4.52109 q^{9} +1.32616 q^{10} +0.192400 q^{11} -4.83934 q^{12} -6.05408 q^{13} -1.87446 q^{15} -4.41539 q^{16} +1.81259 q^{17} +8.77209 q^{18} -1.00000 q^{19} +1.20610 q^{20} +0.373305 q^{22} +2.34025 q^{23} +1.25259 q^{24} -4.53283 q^{25} -11.7465 q^{26} -4.17154 q^{27} -4.90426 q^{29} -3.63694 q^{30} -4.62466 q^{31} -7.65351 q^{32} -0.527649 q^{33} +3.51689 q^{34} +7.97792 q^{36} -11.2175 q^{37} -1.94026 q^{38} +16.6031 q^{39} -0.312180 q^{40} -8.35421 q^{41} -4.32517 q^{43} +0.339508 q^{44} +3.09015 q^{45} +4.54069 q^{46} +12.3525 q^{47} +12.1090 q^{48} -8.79486 q^{50} -4.97095 q^{51} -10.6830 q^{52} +10.1462 q^{53} -8.09387 q^{54} +0.131505 q^{55} +2.74246 q^{57} -9.51553 q^{58} -8.32878 q^{59} -3.30767 q^{60} +6.04778 q^{61} -8.97302 q^{62} -6.01901 q^{64} -4.13795 q^{65} -1.02378 q^{66} -9.96022 q^{67} +3.19849 q^{68} -6.41804 q^{69} +4.43250 q^{71} -2.06496 q^{72} +3.53551 q^{73} -21.7649 q^{74} +12.4311 q^{75} -1.76460 q^{76} +32.2143 q^{78} -3.94009 q^{79} -3.01790 q^{80} -2.12299 q^{81} -16.2093 q^{82} +8.38645 q^{83} +1.23890 q^{85} -8.39195 q^{86} +13.4498 q^{87} -0.0878765 q^{88} +5.73261 q^{89} +5.99569 q^{90} +4.12960 q^{92} +12.6829 q^{93} +23.9669 q^{94} -0.683496 q^{95} +20.9895 q^{96} -5.29649 q^{97} +0.869858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^3 + 10 * q^4 - 16 * q^5 - 8 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9} + 12 q^{10} - 12 q^{12} - 12 q^{13} + 2 q^{16} - 16 q^{17} + 2 q^{18} - 10 q^{19} - 32 q^{20} + 4 q^{22} + 12 q^{23} + 8 q^{24} + 14 q^{25} - 24 q^{26} - 16 q^{27} - 12 q^{29} - 12 q^{30} - 8 q^{31} - 34 q^{32} + 4 q^{33} - 16 q^{34} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 4 q^{39} + 20 q^{40} - 40 q^{41} + 4 q^{43} - 20 q^{44} - 24 q^{45} - 32 q^{46} - 16 q^{47} - 12 q^{48} - 34 q^{50} - 28 q^{51} + 40 q^{52} - 8 q^{54} - 16 q^{55} + 4 q^{57} - 8 q^{58} - 36 q^{59} + 32 q^{60} - 16 q^{61} + 16 q^{62} + 18 q^{64} + 8 q^{65} - 8 q^{66} - 28 q^{67} - 40 q^{68} - 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} + 32 q^{75} - 10 q^{76} + 28 q^{78} - 8 q^{79} - 8 q^{80} + 14 q^{81} + 8 q^{82} + 40 q^{85} - 52 q^{86} + 8 q^{87} - 4 q^{88} - 48 q^{89} + 64 q^{90} + 28 q^{92} + 40 q^{93} + 36 q^{94} + 16 q^{95} + 8 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^3 + 10 * q^4 - 16 * q^5 - 8 * q^6 - 6 * q^8 + 10 * q^9 + 12 * q^10 - 12 * q^12 - 12 * q^13 + 2 * q^16 - 16 * q^17 + 2 * q^18 - 10 * q^19 - 32 * q^20 + 4 * q^22 + 12 * q^23 + 8 * q^24 + 14 * q^25 - 24 * q^26 - 16 * q^27 - 12 * q^29 - 12 * q^30 - 8 * q^31 - 34 * q^32 + 4 * q^33 - 16 * q^34 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 4 * q^39 + 20 * q^40 - 40 * q^41 + 4 * q^43 - 20 * q^44 - 24 * q^45 - 32 * q^46 - 16 * q^47 - 12 * q^48 - 34 * q^50 - 28 * q^51 + 40 * q^52 - 8 * q^54 - 16 * q^55 + 4 * q^57 - 8 * q^58 - 36 * q^59 + 32 * q^60 - 16 * q^61 + 16 * q^62 + 18 * q^64 + 8 * q^65 - 8 * q^66 - 28 * q^67 - 40 * q^68 - 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 + 32 * q^75 - 10 * q^76 + 28 * q^78 - 8 * q^79 - 8 * q^80 + 14 * q^81 + 8 * q^82 + 40 * q^85 - 52 * q^86 + 8 * q^87 - 4 * q^88 - 48 * q^89 + 64 * q^90 + 28 * q^92 + 40 * q^93 + 36 * q^94 + 16 * q^95 + 8 * q^96 + 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.94026	1.37197	0.685985	−	0.727616i	$-0.259372\pi$
$2$	1.94026	1.37197	0.685985	+	0.727616i	$0.259372\pi$
$3$	−2.74246	−1.58336	−0.791680	−	0.610935i	$-0.790793\pi$
$3$	−2.74246	−1.58336	−0.791680	+	0.610935i	$0.790793\pi$
$4$	1.76460	0.882299
$5$	0.683496	0.305669	0.152834	−	0.988252i	$-0.451160\pi$
$5$	0.683496	0.305669	0.152834	+	0.988252i	$0.451160\pi$
$6$	−5.32108	−2.17232
$7$	0	0
$7$	0	0
$8$	−0.456739	−0.161482
$9$	4.52109	1.50703
$10$	1.32616	0.419368
$11$	0.192400	0.0580107	0.0290054	−	0.999579i	$-0.490766\pi$
$11$	0.192400	0.0580107	0.0290054	+	0.999579i	$0.490766\pi$
$12$	−4.83934	−1.39700
$13$	−6.05408	−1.67910	−0.839550	−	0.543282i	$-0.817182\pi$
$13$	−6.05408	−1.67910	−0.839550	+	0.543282i	$0.817182\pi$
$14$	0	0
$15$	−1.87446	−0.483984
$16$	−4.41539	−1.10385
$17$	1.81259	0.439617	0.219809	−	0.975543i	$-0.429457\pi$
$17$	1.81259	0.439617	0.219809	+	0.975543i	$0.429457\pi$
$18$	8.77209	2.06760
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.20610	0.269691
$21$	0	0
$22$	0.373305	0.0795889
$23$	2.34025	0.487976	0.243988	−	0.969778i	$-0.421544\pi$
$23$	2.34025	0.487976	0.243988	+	0.969778i	$0.421544\pi$
$24$	1.25259	0.255684
$25$	−4.53283	−0.906567
$26$	−11.7465	−2.30367
$27$	−4.17154	−0.802814
$28$	0	0
$29$	−4.90426	−0.910699	−0.455349	−	0.890313i	$-0.650486\pi$
$29$	−4.90426	−0.910699	−0.455349	+	0.890313i	$0.650486\pi$
$30$	−3.63694	−0.664011
$31$	−4.62466	−0.830613	−0.415306	−	0.909682i	$-0.636326\pi$
$31$	−4.62466	−0.830613	−0.415306	+	0.909682i	$0.636326\pi$
$32$	−7.65351	−1.35296
$33$	−0.527649	−0.0918519
$34$	3.51689	0.603141
$35$	0	0
$36$	7.97792	1.32965
$37$	−11.2175	−1.84415	−0.922075	−	0.387012i	$-0.873507\pi$
$37$	−11.2175	−1.84415	−0.922075	+	0.387012i	$0.873507\pi$
$38$	−1.94026	−0.314751
$39$	16.6031	2.65862
$40$	−0.312180	−0.0493599
$41$	−8.35421	−1.30471	−0.652354	−	0.757914i	$-0.726218\pi$
$41$	−8.35421	−1.30471	−0.652354	+	0.757914i	$0.726218\pi$
$42$	0	0
$43$	−4.32517	−0.659583	−0.329791	−	0.944054i	$-0.606978\pi$
$43$	−4.32517	−0.659583	−0.329791	+	0.944054i	$0.606978\pi$
$44$	0.339508	0.0511828
$45$	3.09015	0.460653
$46$	4.54069	0.669488
$47$	12.3525	1.80179	0.900896	−	0.434036i	$-0.142911\pi$
$47$	12.3525	1.80179	0.900896	+	0.434036i	$0.142911\pi$
$48$	12.1090	1.74779
$49$	0	0
$50$	−8.79486	−1.24378
$51$	−4.97095	−0.696073
$52$	−10.6830	−1.48147
$53$	10.1462	1.39369	0.696845	−	0.717222i	$-0.254587\pi$
$53$	10.1462	1.39369	0.696845	+	0.717222i	$0.254587\pi$
$54$	−8.09387	−1.10144
$55$	0.131505	0.0177321
$56$	0	0
$57$	2.74246	0.363248
$58$	−9.51553	−1.24945
$59$	−8.32878	−1.08431	−0.542157	−	0.840277i	$-0.682392\pi$
$59$	−8.32878	−1.08431	−0.542157	+	0.840277i	$0.682392\pi$
$60$	−3.30767	−0.427019
$61$	6.04778	0.774339	0.387169	−	0.922009i	$-0.373453\pi$
$61$	6.04778	0.774339	0.387169	+	0.922009i	$0.373453\pi$
$62$	−8.97302	−1.13958
$63$	0	0
$64$	−6.01901	−0.752376
$65$	−4.13795	−0.513249
$66$	−1.02378	−0.126018
$67$	−9.96022	−1.21683	−0.608417	−	0.793617i	$-0.708195\pi$
$67$	−9.96022	−1.21683	−0.608417	+	0.793617i	$0.708195\pi$
$68$	3.19849	0.387874
$69$	−6.41804	−0.772641
$70$	0	0
$71$	4.43250	0.526042	0.263021	−	0.964790i	$-0.415281\pi$
$71$	4.43250	0.526042	0.263021	+	0.964790i	$0.415281\pi$
$72$	−2.06496	−0.243358
$73$	3.53551	0.413800	0.206900	−	0.978362i	$-0.433663\pi$
$73$	3.53551	0.413800	0.206900	+	0.978362i	$0.433663\pi$
$74$	−21.7649	−2.53012
$75$	12.4311	1.43542
$76$	−1.76460	−0.202413
$77$	0	0
$78$	32.2143	3.64755
$79$	−3.94009	−0.443295	−0.221647	−	0.975127i	$-0.571143\pi$
$79$	−3.94009	−0.443295	−0.221647	+	0.975127i	$0.571143\pi$
$80$	−3.01790	−0.337412
$81$	−2.12299	−0.235888
$82$	−16.2093	−1.79002
$83$	8.38645	0.920532	0.460266	−	0.887781i	$-0.347754\pi$
$83$	8.38645	0.920532	0.460266	+	0.887781i	$0.347754\pi$
$84$	0	0
$85$	1.23890	0.134377
$86$	−8.39195	−0.904927
$87$	13.4498	1.44196
$88$	−0.0878765	−0.00936767
$89$	5.73261	0.607655	0.303828	−	0.952727i	$-0.401735\pi$
$89$	5.73261	0.607655	0.303828	+	0.952727i	$0.401735\pi$
$90$	5.99569	0.632001
$91$	0	0
$92$	4.12960	0.430541
$93$	12.6829	1.31516
$94$	23.9669	2.47200
$95$	−0.683496	−0.0701253
$96$	20.9895	2.14223
$97$	−5.29649	−0.537778	−0.268889	−	0.963171i	$-0.586656\pi$
$97$	−5.29649	−0.537778	−0.268889	+	0.963171i	$0.586656\pi$
$98$	0	0
$99$	0.869858	0.0874240
$100$	−7.99863	−0.799863
$101$	−18.5208	−1.84289	−0.921445	−	0.388508i	$-0.872990\pi$
$101$	−18.5208	−1.84289	−0.921445	+	0.388508i	$0.872990\pi$
$102$	−9.64493	−0.954990
$103$	16.9610	1.67122	0.835608	−	0.549326i	$-0.185115\pi$
$103$	16.9610	1.67122	0.835608	+	0.549326i	$0.185115\pi$
$104$	2.76514	0.271144
$105$	0	0
$106$	19.6863	1.91210
$107$	15.7135	1.51908	0.759541	−	0.650459i	$-0.225424\pi$
$107$	15.7135	1.51908	0.759541	+	0.650459i	$0.225424\pi$
$108$	−7.36110	−0.708322
$109$	9.56857	0.916503	0.458252	−	0.888823i	$-0.348476\pi$
$109$	9.56857	0.916503	0.458252	+	0.888823i	$0.348476\pi$
$110$	0.255153	0.0243279
$111$	30.7636	2.91995
$112$	0	0
$113$	4.48256	0.421684	0.210842	−	0.977520i	$-0.432379\pi$
$113$	4.48256	0.421684	0.210842	+	0.977520i	$0.432379\pi$
$114$	5.32108	0.498365
$115$	1.59955	0.149159
$116$	−8.65406	−0.803509
$117$	−27.3711	−2.53046
$118$	−16.1600	−1.48765
$119$	0	0
$120$	0.856140	0.0781546
$121$	−10.9630	−0.996635
$122$	11.7342	1.06237
$123$	22.9111	2.06582
$124$	−8.16066	−0.732849
$125$	−6.51566	−0.582778
$126$	0	0
$127$	10.7697	0.955657	0.477829	−	0.878453i	$-0.341424\pi$
$127$	10.7697	0.955657	0.477829	+	0.878453i	$0.341424\pi$
$128$	3.62860	0.320726
$129$	11.8616	1.04436
$130$	−8.02868	−0.704162
$131$	−10.6473	−0.930259	−0.465129	−	0.885243i	$-0.653992\pi$
$131$	−10.6473	−0.930259	−0.465129	+	0.885243i	$0.653992\pi$
$132$	−0.931089	−0.0810409
$133$	0	0
$134$	−19.3254	−1.66946
$135$	−2.85123	−0.245395
$136$	−0.827880	−0.0709901
$137$	−12.9027	−1.10236	−0.551178	−	0.834388i	$-0.685821\pi$
$137$	−12.9027	−1.10236	−0.551178	+	0.834388i	$0.685821\pi$
$138$	−12.4527	−1.06004
$139$	11.7659	0.997966	0.498983	−	0.866612i	$-0.333707\pi$
$139$	11.7659	0.997966	0.498983	+	0.866612i	$0.333707\pi$
$140$	0	0
$141$	−33.8761	−2.85289
$142$	8.60020	0.721713
$143$	−1.16480	−0.0974059
$144$	−19.9624	−1.66353
$145$	−3.35205	−0.278372
$146$	6.85979	0.567721
$147$	0	0
$148$	−19.7944	−1.62709
$149$	−2.04421	−0.167468	−0.0837342	−	0.996488i	$-0.526685\pi$
$149$	−2.04421	−0.167468	−0.0837342	+	0.996488i	$0.526685\pi$
$150$	24.1196	1.96935
$151$	17.4814	1.42262	0.711309	−	0.702879i	$-0.248102\pi$
$151$	17.4814	1.42262	0.711309	+	0.702879i	$0.248102\pi$
$152$	0.456739	0.0370464
$153$	8.19488	0.662517
$154$	0	0
$155$	−3.16094	−0.253892
$156$	29.2978	2.34570
$157$	8.10942	0.647202	0.323601	−	0.946194i	$-0.395106\pi$
$157$	8.10942	0.647202	0.323601	+	0.946194i	$0.395106\pi$
$158$	−7.64478	−0.608186
$159$	−27.8256	−2.20671
$160$	−5.23115	−0.413559
$161$	0	0
$162$	−4.11914	−0.323631
$163$	1.01030	0.0791324	0.0395662	−	0.999217i	$-0.487402\pi$
$163$	1.01030	0.0791324	0.0395662	+	0.999217i	$0.487402\pi$
$164$	−14.7418	−1.15114
$165$	−0.360646	−0.0280763
$166$	16.2719	1.26294
$167$	−15.1617	−1.17325	−0.586624	−	0.809859i	$-0.699543\pi$
$167$	−15.1617	−1.17325	−0.586624	+	0.809859i	$0.699543\pi$
$168$	0	0
$169$	23.6519	1.81938
$170$	2.40378	0.184362
$171$	−4.52109	−0.345737
$172$	−7.63219	−0.581949
$173$	6.50785	0.494783	0.247391	−	0.968916i	$-0.420427\pi$
$173$	6.50785	0.494783	0.247391	+	0.968916i	$0.420427\pi$
$174$	26.0960	1.97833
$175$	0	0
$176$	−0.849520	−0.0640350
$177$	22.8413	1.71686
$178$	11.1227	0.833684
$179$	9.81074	0.733289	0.366644	−	0.930361i	$-0.380507\pi$
$179$	9.81074	0.733289	0.366644	+	0.930361i	$0.380507\pi$
$180$	5.45288	0.406434
$181$	−14.1392	−1.05096	−0.525481	−	0.850806i	$-0.676115\pi$
$181$	−14.1392	−1.05096	−0.525481	+	0.850806i	$0.676115\pi$
$182$	0	0
$183$	−16.5858	−1.22606
$184$	−1.06888	−0.0787991
$185$	−7.66714	−0.563699
$186$	24.6082	1.80436
$187$	0.348742	0.0255025
$188$	21.7971	1.58972
$189$	0	0
$190$	−1.32616	−0.0962097
$191$	7.93484	0.574145	0.287072	−	0.957909i	$-0.407318\pi$
$191$	7.93484	0.574145	0.287072	+	0.957909i	$0.407318\pi$
$192$	16.5069	1.19128
$193$	−4.22611	−0.304202	−0.152101	−	0.988365i	$-0.548604\pi$
$193$	−4.22611	−0.304202	−0.152101	+	0.988365i	$0.548604\pi$
$194$	−10.2766	−0.737814
$195$	11.3482	0.812658
$196$	0	0
$197$	−1.87072	−0.133283	−0.0666415	−	0.997777i	$-0.521228\pi$
$197$	−1.87072	−0.133283	−0.0666415	+	0.997777i	$0.521228\pi$
$198$	1.68775	0.119943
$199$	−17.6651	−1.25224	−0.626122	−	0.779725i	$-0.715359\pi$
$199$	−17.6651	−1.25224	−0.626122	+	0.779725i	$0.715359\pi$
$200$	2.07032	0.146394
$201$	27.3155	1.92669
$202$	−35.9352	−2.52839
$203$	0	0
$204$	−8.77174	−0.614144
$205$	−5.71007	−0.398809
$206$	32.9087	2.29286
$207$	10.5805	0.735395
$208$	26.7311	1.85347
$209$	−0.192400	−0.0133086
$210$	0	0
$211$	−14.4664	−0.995905	−0.497953	−	0.867204i	$-0.665915\pi$
$211$	−14.4664	−0.995905	−0.497953	+	0.867204i	$0.665915\pi$
$212$	17.9040	1.22965
$213$	−12.1560	−0.832914
$214$	30.4883	2.08413
$215$	−2.95624	−0.201614
$216$	1.90531	0.129640
$217$	0	0
$218$	18.5655	1.25741
$219$	−9.69599	−0.655194
$220$	0.232053	0.0156450
$221$	−10.9736	−0.738162
$222$	59.6893	4.00609
$223$	−13.0807	−0.875950	−0.437975	−	0.898987i	$-0.644304\pi$
$223$	−13.0807	−0.875950	−0.437975	+	0.898987i	$0.644304\pi$
$224$	0	0
$225$	−20.4934	−1.36622
$226$	8.69732	0.578537
$227$	−6.48777	−0.430609	−0.215304	−	0.976547i	$-0.569074\pi$
$227$	−6.48777	−0.430609	−0.215304	+	0.976547i	$0.569074\pi$
$228$	4.83934	0.320493
$229$	−20.6178	−1.36246	−0.681231	−	0.732068i	$-0.738555\pi$
$229$	−20.6178	−1.36246	−0.681231	+	0.732068i	$0.738555\pi$
$230$	3.10354	0.204642
$231$	0	0
$232$	2.23997	0.147061
$233$	26.7239	1.75074	0.875371	−	0.483452i	$-0.160617\pi$
$233$	26.7239	1.75074	0.875371	+	0.483452i	$0.160617\pi$
$234$	−53.1070	−3.47171
$235$	8.44286	0.550752
$236$	−14.6969	−0.956690
$237$	10.8055	0.701895
$238$	0	0
$239$	4.55886	0.294888	0.147444	−	0.989070i	$-0.452895\pi$
$239$	4.55886	0.294888	0.147444	+	0.989070i	$0.452895\pi$
$240$	8.27648	0.534245
$241$	−1.53700	−0.0990071	−0.0495035	−	0.998774i	$-0.515764\pi$
$241$	−1.53700	−0.0990071	−0.0495035	+	0.998774i	$0.515764\pi$
$242$	−21.2710	−1.36735
$243$	18.3368	1.17631
$244$	10.6719	0.683198
$245$	0	0
$246$	44.4534	2.83425
$247$	6.05408	0.385212
$248$	2.11226	0.134129
$249$	−22.9995	−1.45753
$250$	−12.6421	−0.799554
$251$	−11.2582	−0.710610	−0.355305	−	0.934750i	$-0.615623\pi$
$251$	−11.2582	−0.710610	−0.355305	+	0.934750i	$0.615623\pi$
$252$	0	0
$253$	0.450263	0.0283078
$254$	20.8960	1.31113
$255$	−3.39763	−0.212768
$256$	19.0784	1.19240
$257$	0.920862	0.0574418	0.0287209	−	0.999587i	$-0.490857\pi$
$257$	0.920862	0.0574418	0.0287209	+	0.999587i	$0.490857\pi$
$258$	23.0146	1.43283
$259$	0	0
$260$	−7.30181	−0.452839
$261$	−22.1726	−1.37245
$262$	−20.6585	−1.27629
$263$	−4.40823	−0.271823	−0.135912	−	0.990721i	$-0.543396\pi$
$263$	−4.40823	−0.271823	−0.135912	+	0.990721i	$0.543396\pi$
$264$	0.240998	0.0148324
$265$	6.93490	0.426007
$266$	0	0
$267$	−15.7215	−0.962137
$268$	−17.5758	−1.07361
$269$	−13.6786	−0.833997	−0.416999	−	0.908907i	$-0.636918\pi$
$269$	−13.6786	−0.833997	−0.416999	+	0.908907i	$0.636918\pi$
$270$	−5.53213	−0.336675
$271$	−19.1248	−1.16175	−0.580873	−	0.813994i	$-0.697289\pi$
$271$	−19.1248	−1.16175	−0.580873	+	0.813994i	$0.697289\pi$
$272$	−8.00328	−0.485270
$273$	0	0
$274$	−25.0346	−1.51240
$275$	−0.872116	−0.0525906
$276$	−11.3253	−0.681701
$277$	−31.3234	−1.88204	−0.941020	−	0.338351i	$-0.890131\pi$
$277$	−31.3234	−1.88204	−0.941020	+	0.338351i	$0.890131\pi$
$278$	22.8288	1.36918
$279$	−20.9085	−1.25176
$280$	0	0
$281$	−28.9148	−1.72491	−0.862455	−	0.506134i	$-0.831074\pi$
$281$	−28.9148	−1.72491	−0.862455	+	0.506134i	$0.831074\pi$
$282$	−65.7284	−3.91407
$283$	11.1470	0.662623	0.331311	−	0.943521i	$-0.392509\pi$
$283$	11.1470	0.662623	0.331311	+	0.943521i	$0.392509\pi$
$284$	7.82159	0.464126
$285$	1.87446	0.111034
$286$	−2.26002	−0.133638
$287$	0	0
$288$	−34.6023	−2.03896
$289$	−13.7145	−0.806737
$290$	−6.50383	−0.381918
$291$	14.5254	0.851496
$292$	6.23875	0.365095
$293$	−0.420121	−0.0245437	−0.0122719	−	0.999925i	$-0.503906\pi$
$293$	−0.420121	−0.0245437	−0.0122719	+	0.999925i	$0.503906\pi$
$294$	0	0
$295$	−5.69269	−0.331441
$296$	5.12348	0.297796
$297$	−0.802604	−0.0465718
$298$	−3.96630	−0.229762
$299$	−14.1681	−0.819360
$300$	21.9359	1.26647
$301$	0	0
$302$	33.9185	1.95179
$303$	50.7926	2.91796
$304$	4.41539	0.253240
$305$	4.13363	0.236691
$306$	15.9002	0.908953
$307$	7.37818	0.421095	0.210548	−	0.977584i	$-0.432475\pi$
$307$	7.37818	0.421095	0.210548	+	0.977584i	$0.432475\pi$
$308$	0	0
$309$	−46.5149	−2.64614
$310$	−6.13303	−0.348333
$311$	15.1051	0.856530	0.428265	−	0.903653i	$-0.359125\pi$
$311$	15.1051	0.856530	0.428265	+	0.903653i	$0.359125\pi$
$312$	−7.58328	−0.429319
$313$	7.86571	0.444596	0.222298	−	0.974979i	$-0.428644\pi$
$313$	7.86571	0.444596	0.222298	+	0.974979i	$0.428644\pi$
$314$	15.7344	0.887941
$315$	0	0
$316$	−6.95267	−0.391118
$317$	−6.56106	−0.368506	−0.184253	−	0.982879i	$-0.558987\pi$
$317$	−6.56106	−0.368506	−0.184253	+	0.982879i	$0.558987\pi$
$318$	−53.9888	−3.02754
$319$	−0.943579	−0.0528303
$320$	−4.11397	−0.229978
$321$	−43.0937	−2.40526
$322$	0	0
$323$	−1.81259	−0.100855
$324$	−3.74622	−0.208124
$325$	27.4422	1.52222
$326$	1.96023	0.108567
$327$	−26.2414	−1.45115
$328$	3.81569	0.210686
$329$	0	0
$330$	−0.699747	−0.0385198
$331$	−36.0045	−1.97899	−0.989494	−	0.144576i	$-0.953818\pi$
$331$	−36.0045	−1.97899	−0.989494	+	0.144576i	$0.953818\pi$
$332$	14.7987	0.812185
$333$	−50.7155	−2.77919
$334$	−29.4176	−1.60966
$335$	−6.80778	−0.371949
$336$	0	0
$337$	1.38628	0.0755153	0.0377576	−	0.999287i	$-0.487979\pi$
$337$	1.38628	0.0755153	0.0377576	+	0.999287i	$0.487979\pi$
$338$	45.8909	2.49613
$339$	−12.2932	−0.667677
$340$	2.18616	0.118561
$341$	−0.889783	−0.0481844
$342$	−8.77209	−0.474340
$343$	0	0
$344$	1.97548	0.106510
$345$	−4.38671	−0.236172
$346$	12.6269	0.678827
$347$	−28.8673	−1.54968	−0.774839	−	0.632158i	$-0.782169\pi$
$347$	−28.8673	−1.54968	−0.774839	+	0.632158i	$0.782169\pi$
$348$	23.7334	1.27224
$349$	8.84813	0.473629	0.236815	−	0.971555i	$-0.423897\pi$
$349$	8.84813	0.473629	0.236815	+	0.971555i	$0.423897\pi$
$350$	0	0
$351$	25.2549	1.34801
$352$	−1.47253	−0.0784863
$353$	3.62348	0.192859	0.0964293	−	0.995340i	$-0.469258\pi$
$353$	3.62348	0.192859	0.0964293	+	0.995340i	$0.469258\pi$
$354$	44.3181	2.35548
$355$	3.02960	0.160795
$356$	10.1157	0.536134
$357$	0	0
$358$	19.0354	1.00605
$359$	−30.5675	−1.61329	−0.806645	−	0.591036i	$-0.798719\pi$
$359$	−30.5675	−1.61329	−0.806645	+	0.591036i	$0.798719\pi$
$360$	−1.41139	−0.0743869
$361$	1.00000	0.0526316
$362$	−27.4338	−1.44189
$363$	30.0656	1.57803
$364$	0	0
$365$	2.41651	0.126486
$366$	−32.1807	−1.68211
$367$	0.660235	0.0344640	0.0172320	−	0.999852i	$-0.494515\pi$
$367$	0.660235	0.0344640	0.0172320	+	0.999852i	$0.494515\pi$
$368$	−10.3331	−0.538651
$369$	−37.7702	−1.96624
$370$	−14.8762	−0.773378
$371$	0	0
$372$	22.3803	1.16036
$373$	30.1867	1.56301	0.781504	−	0.623900i	$-0.214453\pi$
$373$	30.1867	1.56301	0.781504	+	0.623900i	$0.214453\pi$
$374$	0.676648	0.0349887
$375$	17.8689	0.922748
$376$	−5.64185	−0.290956
$377$	29.6908	1.52916
$378$	0	0
$379$	33.2831	1.70964	0.854818	−	0.518927i	$-0.173668\pi$
$379$	33.2831	1.70964	0.854818	+	0.518927i	$0.173668\pi$
$380$	−1.20610	−0.0618715
$381$	−29.5355	−1.51315
$382$	15.3956	0.787709
$383$	−18.8985	−0.965669	−0.482835	−	0.875712i	$-0.660393\pi$
$383$	−18.8985	−0.965669	−0.482835	+	0.875712i	$0.660393\pi$
$384$	−9.95130	−0.507825
$385$	0	0
$386$	−8.19973	−0.417355
$387$	−19.5545	−0.994012
$388$	−9.34619	−0.474481
$389$	0.0893791	0.00453170	0.00226585	−	0.999997i	$-0.499279\pi$
$389$	0.0893791	0.00453170	0.00226585	+	0.999997i	$0.499279\pi$
$390$	22.0183	1.11494
$391$	4.24191	0.214522
$392$	0	0
$393$	29.1998	1.47294
$394$	−3.62967	−0.182860
$395$	−2.69304	−0.135501
$396$	1.53495	0.0771341
$397$	6.78478	0.340518	0.170259	−	0.985399i	$-0.445540\pi$
$397$	6.78478	0.340518	0.170259	+	0.985399i	$0.445540\pi$
$398$	−34.2748	−1.71804
$399$	0	0
$400$	20.0142	1.00071
$401$	20.3795	1.01770	0.508852	−	0.860854i	$-0.330070\pi$
$401$	20.3795	1.01770	0.508852	+	0.860854i	$0.330070\pi$
$402$	52.9992	2.64336
$403$	27.9981	1.39468
$404$	−32.6818	−1.62598
$405$	−1.45106	−0.0721035
$406$	0	0
$407$	−2.15825	−0.106980
$408$	2.27043	0.112403
$409$	−16.1675	−0.799433	−0.399717	−	0.916639i	$-0.630891\pi$
$409$	−16.1675	−0.799433	−0.399717	+	0.916639i	$0.630891\pi$
$410$	−11.0790	−0.547153
$411$	35.3853	1.74543
$412$	29.9293	1.47451
$413$	0	0
$414$	20.5289	1.00894
$415$	5.73211	0.281378
$416$	46.3350	2.27176
$417$	−32.2674	−1.58014
$418$	−0.373305	−0.0182590
$419$	17.1797	0.839285	0.419643	−	0.907689i	$-0.362155\pi$
$419$	17.1797	0.839285	0.419643	+	0.907689i	$0.362155\pi$
$420$	0	0
$421$	4.11849	0.200723	0.100361	−	0.994951i	$-0.468000\pi$
$421$	4.11849	0.200723	0.100361	+	0.994951i	$0.468000\pi$
$422$	−28.0685	−1.36635
$423$	55.8466	2.71536
$424$	−4.63417	−0.225055
$425$	−8.21616	−0.398542
$426$	−23.5857	−1.14273
$427$	0	0
$428$	27.7280	1.34029
$429$	3.19443	0.154229
$430$	−5.73587	−0.276608
$431$	−8.05167	−0.387835	−0.193918	−	0.981018i	$-0.562119\pi$
$431$	−8.05167	−0.387835	−0.193918	+	0.981018i	$0.562119\pi$
$432$	18.4190	0.886184
$433$	−33.5669	−1.61312	−0.806560	−	0.591152i	$-0.798673\pi$
$433$	−33.5669	−1.61312	−0.806560	+	0.591152i	$0.798673\pi$
$434$	0	0
$435$	9.19286	0.440764
$436$	16.8847	0.808630
$437$	−2.34025	−0.111949
$438$	−18.8127	−0.898907
$439$	20.0028	0.954683	0.477342	−	0.878718i	$-0.341600\pi$
$439$	20.0028	0.954683	0.477342	+	0.878718i	$0.341600\pi$
$440$	−0.0600633	−0.00286340
$441$	0	0
$442$	−21.2915	−1.01273
$443$	−24.8213	−1.17930	−0.589648	−	0.807660i	$-0.700734\pi$
$443$	−24.8213	−1.17930	−0.589648	+	0.807660i	$0.700734\pi$
$444$	54.2854	2.57627
$445$	3.91822	0.185741
$446$	−25.3800	−1.20178
$447$	5.60618	0.265163
$448$	0	0
$449$	34.9167	1.64782	0.823910	−	0.566720i	$-0.191788\pi$
$449$	34.9167	1.64782	0.823910	+	0.566720i	$0.191788\pi$
$450$	−39.7624	−1.87442
$451$	−1.60735	−0.0756871
$452$	7.90992	0.372051
$453$	−47.9422	−2.25252
$454$	−12.5880	−0.590782
$455$	0	0
$456$	−1.25259	−0.0586579
$457$	−5.91930	−0.276893	−0.138447	−	0.990370i	$-0.544211\pi$
$457$	−5.91930	−0.276893	−0.138447	+	0.990370i	$0.544211\pi$
$458$	−40.0038	−1.86926
$459$	−7.56129	−0.352931
$460$	2.82257	0.131603
$461$	−6.26645	−0.291858	−0.145929	−	0.989295i	$-0.546617\pi$
$461$	−6.26645	−0.291858	−0.145929	+	0.989295i	$0.546617\pi$
$462$	0	0
$463$	−2.31327	−0.107507	−0.0537533	−	0.998554i	$-0.517118\pi$
$463$	−2.31327	−0.107507	−0.0537533	+	0.998554i	$0.517118\pi$
$464$	21.6542	1.00527
$465$	8.66874	0.402003
$466$	51.8513	2.40196
$467$	26.9171	1.24557	0.622786	−	0.782392i	$-0.286001\pi$
$467$	26.9171	1.24557	0.622786	+	0.782392i	$0.286001\pi$
$468$	−48.2990	−2.23262
$469$	0	0
$470$	16.3813	0.755614
$471$	−22.2398	−1.02475
$472$	3.80408	0.175097
$473$	−0.832162	−0.0382629
$474$	20.9655	0.962979
$475$	4.53283	0.207981
$476$	0	0
$477$	45.8720	2.10033
$478$	8.84536	0.404577
$479$	22.4276	1.02474	0.512372	−	0.858763i	$-0.328767\pi$
$479$	22.4276	1.02474	0.512372	+	0.858763i	$0.328767\pi$
$480$	14.3462	0.654813
$481$	67.9118	3.09651
$482$	−2.98218	−0.135835
$483$	0	0
$484$	−19.3453	−0.879330
$485$	−3.62014	−0.164382
$486$	35.5782	1.61386
$487$	21.9354	0.993988	0.496994	−	0.867754i	$-0.334437\pi$
$487$	21.9354	0.993988	0.496994	+	0.867754i	$0.334437\pi$
$488$	−2.76226	−0.125041
$489$	−2.77070	−0.125295
$490$	0	0
$491$	11.8512	0.534835	0.267418	−	0.963581i	$-0.413830\pi$
$491$	11.8512	0.534835	0.267418	+	0.963581i	$0.413830\pi$
$492$	40.4289	1.82268
$493$	−8.88941	−0.400359
$494$	11.7465	0.528499
$495$	0.594545	0.0267228
$496$	20.4197	0.916870
$497$	0	0
$498$	−44.6250	−1.99969
$499$	9.09498	0.407147	0.203574	−	0.979060i	$-0.434744\pi$
$499$	9.09498	0.407147	0.203574	+	0.979060i	$0.434744\pi$
$500$	−11.4975	−0.514185
$501$	41.5804	1.85768
$502$	−21.8438	−0.974935
$503$	−25.2730	−1.12687	−0.563434	−	0.826161i	$-0.690520\pi$
$503$	−25.2730	−1.12687	−0.563434	+	0.826161i	$0.690520\pi$
$504$	0	0
$505$	−12.6589	−0.563314
$506$	0.873627	0.0388375
$507$	−64.8645	−2.88074
$508$	19.0042	0.843176
$509$	−38.5816	−1.71010	−0.855049	−	0.518547i	$-0.826473\pi$
$509$	−38.5816	−1.71010	−0.855049	+	0.518547i	$0.826473\pi$
$510$	−6.59227	−0.291911
$511$	0	0
$512$	29.7599	1.31521
$513$	4.17154	0.184178
$514$	1.78671	0.0788084
$515$	11.5928	0.510839
$516$	20.9310	0.921436
$517$	2.37661	0.104523
$518$	0	0
$519$	−17.8475	−0.783420
$520$	1.88996	0.0828803
$521$	21.1781	0.927829	0.463915	−	0.885880i	$-0.346444\pi$
$521$	21.1781	0.927829	0.463915	+	0.885880i	$0.346444\pi$
$522$	−43.0206	−1.88296
$523$	−4.00891	−0.175298	−0.0876488	−	0.996151i	$-0.527935\pi$
$523$	−4.00891	−0.175298	−0.0876488	+	0.996151i	$0.527935\pi$
$524$	−18.7882	−0.820767
$525$	0	0
$526$	−8.55310	−0.372933
$527$	−8.38260	−0.365152
$528$	2.32978	0.101390
$529$	−17.5232	−0.761880
$530$	13.4555	0.584469
$531$	−37.6552	−1.63410
$532$	0	0
$533$	50.5771	2.19074
$534$	−30.5037	−1.32002
$535$	10.7401	0.464336
$536$	4.54922	0.196497
$537$	−26.9056	−1.16106
$538$	−26.5399	−1.14422
$539$	0	0
$540$	−5.03128	−0.216512
$541$	23.1629	0.995852	0.497926	−	0.867220i	$-0.334095\pi$
$541$	23.1629	0.995852	0.497926	+	0.867220i	$0.334095\pi$
$542$	−37.1070	−1.59388
$543$	38.7763	1.66405
$544$	−13.8727	−0.594786
$545$	6.54009	0.280146
$546$	0	0
$547$	15.0084	0.641712	0.320856	−	0.947128i	$-0.396029\pi$
$547$	15.0084	0.641712	0.320856	+	0.947128i	$0.396029\pi$
$548$	−22.7682	−0.972608
$549$	27.3426	1.16695
$550$	−1.69213	−0.0721527
$551$	4.90426	0.208929
$552$	2.93137	0.124767
$553$	0	0
$554$	−60.7754	−2.58210
$555$	21.0268	0.892539
$556$	20.7620	0.880505
$557$	19.7653	0.837482	0.418741	−	0.908106i	$-0.362472\pi$
$557$	19.7653	0.837482	0.418741	+	0.908106i	$0.362472\pi$
$558$	−40.5679	−1.71738
$559$	26.1850	1.10751
$560$	0	0
$561$	−0.956410	−0.0403797
$562$	−56.1021	−2.36652
$563$	−27.7154	−1.16807	−0.584033	−	0.811730i	$-0.698526\pi$
$563$	−27.7154	−1.16807	−0.584033	+	0.811730i	$0.698526\pi$
$564$	−59.7778	−2.51710
$565$	3.06381	0.128896
$566$	21.6281	0.909098
$567$	0	0
$568$	−2.02450	−0.0849460
$569$	18.3936	0.771101	0.385551	−	0.922687i	$-0.374011\pi$
$569$	18.3936	0.771101	0.385551	+	0.922687i	$0.374011\pi$
$570$	3.63694	0.152335
$571$	−31.9250	−1.33602	−0.668011	−	0.744152i	$-0.732854\pi$
$571$	−31.9250	−1.33602	−0.668011	+	0.744152i	$0.732854\pi$
$572$	−2.05541	−0.0859411
$573$	−21.7610	−0.909078
$574$	0	0
$575$	−10.6080	−0.442382
$576$	−27.2125	−1.13385
$577$	−8.17595	−0.340369	−0.170185	−	0.985412i	$-0.554436\pi$
$577$	−8.17595	−0.340369	−0.170185	+	0.985412i	$0.554436\pi$
$578$	−26.6097	−1.10682
$579$	11.5899	0.481661
$580$	−5.91502	−0.245608
$581$	0	0
$582$	28.1831	1.16823
$583$	1.95213	0.0808489
$584$	−1.61480	−0.0668211
$585$	−18.7080	−0.773482
$586$	−0.815143	−0.0336732
$587$	20.7599	0.856853	0.428427	−	0.903577i	$-0.359068\pi$
$587$	20.7599	0.856853	0.428427	+	0.903577i	$0.359068\pi$
$588$	0	0
$589$	4.62466	0.190556
$590$	−11.0453	−0.454727
$591$	5.13037	0.211035
$592$	49.5297	2.03566
$593$	−6.95346	−0.285544	−0.142772	−	0.989756i	$-0.545602\pi$
$593$	−6.95346	−0.285544	−0.142772	+	0.989756i	$0.545602\pi$
$594$	−1.55726	−0.0638951
$595$	0	0
$596$	−3.60722	−0.147757
$597$	48.4458	1.98275
$598$	−27.4897	−1.12414
$599$	−3.03769	−0.124117	−0.0620583	−	0.998073i	$-0.519766\pi$
$599$	−3.03769	−0.124117	−0.0620583	+	0.998073i	$0.519766\pi$
$600$	−5.67778	−0.231794
$601$	44.2423	1.80468	0.902341	−	0.431022i	$-0.141847\pi$
$601$	44.2423	1.80468	0.902341	+	0.431022i	$0.141847\pi$
$602$	0	0
$603$	−45.0311	−1.83381
$604$	30.8477	1.25518
$605$	−7.49316	−0.304640
$606$	98.5508	4.00335
$607$	−20.8333	−0.845596	−0.422798	−	0.906224i	$-0.638952\pi$
$607$	−20.8333	−0.845596	−0.422798	+	0.906224i	$0.638952\pi$
$608$	7.65351	0.310391
$609$	0	0
$610$	8.02032	0.324733
$611$	−74.7828	−3.02539
$612$	14.4607	0.584538
$613$	−37.3213	−1.50739	−0.753696	−	0.657223i	$-0.771731\pi$
$613$	−37.3213	−1.50739	−0.753696	+	0.657223i	$0.771731\pi$
$614$	14.3156	0.577729
$615$	15.6597	0.631458
$616$	0	0
$617$	11.5064	0.463231	0.231616	−	0.972807i	$-0.425599\pi$
$617$	11.5064	0.463231	0.231616	+	0.972807i	$0.425599\pi$
$618$	−90.2508	−3.63042
$619$	−7.48008	−0.300650	−0.150325	−	0.988637i	$-0.548032\pi$
$619$	−7.48008	−0.300650	−0.150325	+	0.988637i	$0.548032\pi$
$620$	−5.57778	−0.224009
$621$	−9.76245	−0.391754
$622$	29.3077	1.17513
$623$	0	0
$624$	−73.3091	−2.93471
$625$	18.2107	0.728429
$626$	15.2615	0.609973
$627$	0.527649	0.0210723
$628$	14.3099	0.571026
$629$	−20.3327	−0.810720
$630$	0	0
$631$	−7.94530	−0.316298	−0.158149	−	0.987415i	$-0.550553\pi$
$631$	−7.94530	−0.316298	−0.158149	+	0.987415i	$0.550553\pi$
$632$	1.79959	0.0715839
$633$	39.6734	1.57688
$634$	−12.7301	−0.505579
$635$	7.36106	0.292115
$636$	−49.1010	−1.94698
$637$	0	0
$638$	−1.83079	−0.0724815
$639$	20.0398	0.792761
$640$	2.48014	0.0980360
$641$	−38.8592	−1.53485	−0.767423	−	0.641141i	$-0.778461\pi$
$641$	−38.8592	−1.53485	−0.767423	+	0.641141i	$0.778461\pi$
$642$	−83.6129	−3.29994
$643$	29.2448	1.15330	0.576652	−	0.816990i	$-0.304359\pi$
$643$	29.2448	1.15330	0.576652	+	0.816990i	$0.304359\pi$
$644$	0	0
$645$	8.10737	0.319228
$646$	−3.51689	−0.138370
$647$	−19.0372	−0.748428	−0.374214	−	0.927342i	$-0.622088\pi$
$647$	−19.0372	−0.748428	−0.374214	+	0.927342i	$0.622088\pi$
$648$	0.969652	0.0380915
$649$	−1.60245	−0.0629019
$650$	53.2448	2.08843
$651$	0	0
$652$	1.78277	0.0698185
$653$	−17.8384	−0.698069	−0.349034	−	0.937110i	$-0.613490\pi$
$653$	−17.8384	−0.698069	−0.349034	+	0.937110i	$0.613490\pi$
$654$	−50.9151	−1.99094
$655$	−7.27739	−0.284351
$656$	36.8871	1.44020
$657$	15.9844	0.623609
$658$	0	0
$659$	9.81202	0.382222	0.191111	−	0.981568i	$-0.438791\pi$
$659$	9.81202	0.382222	0.191111	+	0.981568i	$0.438791\pi$
$660$	−0.636396	−0.0247717
$661$	−32.9225	−1.28054	−0.640268	−	0.768152i	$-0.721177\pi$
$661$	−32.9225	−1.28054	−0.640268	+	0.768152i	$0.721177\pi$
$662$	−69.8580	−2.71511
$663$	30.0946	1.16878
$664$	−3.83042	−0.148649
$665$	0	0
$666$	−98.4011	−3.81296
$667$	−11.4772	−0.444399
$668$	−26.7543	−1.03516
$669$	35.8734	1.38694
$670$	−13.2088	−0.510302
$671$	1.16359	0.0449199
$672$	0	0
$673$	21.4834	0.828125	0.414063	−	0.910248i	$-0.364109\pi$
$673$	21.4834	0.828125	0.414063	+	0.910248i	$0.364109\pi$
$674$	2.68973	0.103605
$675$	18.9089	0.727804
$676$	41.7362	1.60524
$677$	5.36805	0.206311	0.103156	−	0.994665i	$-0.467106\pi$
$677$	5.36805	0.206311	0.103156	+	0.994665i	$0.467106\pi$
$678$	−23.8521	−0.916033
$679$	0	0
$680$	−0.565853	−0.0216995
$681$	17.7925	0.681809
$682$	−1.72641	−0.0661076
$683$	−10.2705	−0.392991	−0.196495	−	0.980505i	$-0.562956\pi$
$683$	−10.2705	−0.392991	−0.196495	+	0.980505i	$0.562956\pi$
$684$	−7.97792	−0.305043
$685$	−8.81898	−0.336956
$686$	0	0
$687$	56.5435	2.15727
$688$	19.0973	0.728078
$689$	−61.4260	−2.34014
$690$	−8.51135	−0.324021
$691$	−7.85169	−0.298692	−0.149346	−	0.988785i	$-0.547717\pi$
$691$	−7.85169	−0.298692	−0.149346	+	0.988785i	$0.547717\pi$
$692$	11.4837	0.436547
$693$	0	0
$694$	−56.0100	−2.12611
$695$	8.04192	0.305047
$696$	−6.14303	−0.232851
$697$	−15.1427	−0.573572
$698$	17.1676	0.649805
$699$	−73.2893	−2.77206
$700$	0	0
$701$	10.6944	0.403921	0.201961	−	0.979394i	$-0.435269\pi$
$701$	10.6944	0.403921	0.201961	+	0.979394i	$0.435269\pi$
$702$	49.0010	1.84942
$703$	11.2175	0.423077
$704$	−1.15806	−0.0436459
$705$	−23.1542	−0.872038
$706$	7.03049	0.264596
$707$	0	0
$708$	40.3058	1.51479
$709$	−19.3737	−0.727594	−0.363797	−	0.931478i	$-0.618520\pi$
$709$	−19.3737	−0.727594	−0.363797	+	0.931478i	$0.618520\pi$
$710$	5.87821	0.220605
$711$	−17.8135	−0.668059
$712$	−2.61830	−0.0981251
$713$	−10.8228	−0.405319
$714$	0	0
$715$	−0.796140	−0.0297739
$716$	17.3120	0.646980
$717$	−12.5025	−0.466914
$718$	−59.3088	−2.21338
$719$	16.8116	0.626966	0.313483	−	0.949594i	$-0.398504\pi$
$719$	16.8116	0.626966	0.313483	+	0.949594i	$0.398504\pi$
$720$	−13.6442	−0.508490
$721$	0	0
$722$	1.94026	0.0722089
$723$	4.21517	0.156764
$724$	−24.9501	−0.927263
$725$	22.2302	0.825609
$726$	58.3349	2.16501
$727$	−3.96696	−0.147126	−0.0735632	−	0.997291i	$-0.523437\pi$
$727$	−3.96696	−0.147126	−0.0735632	+	0.997291i	$0.523437\pi$
$728$	0	0
$729$	−43.9191	−1.62663
$730$	4.68865	0.173535
$731$	−7.83976	−0.289964
$732$	−29.2673	−1.08175
$733$	32.3771	1.19587	0.597937	−	0.801543i	$-0.295987\pi$
$733$	32.3771	1.19587	0.597937	+	0.801543i	$0.295987\pi$
$734$	1.28103	0.0472836
$735$	0	0
$736$	−17.9111	−0.660213
$737$	−1.91635	−0.0705895
$738$	−73.2838	−2.69762
$739$	−22.7528	−0.836975	−0.418487	−	0.908223i	$-0.637440\pi$
$739$	−22.7528	−0.836975	−0.418487	+	0.908223i	$0.637440\pi$
$740$	−13.5294	−0.497351
$741$	−16.6031	−0.609930
$742$	0	0
$743$	−33.2593	−1.22017	−0.610084	−	0.792337i	$-0.708864\pi$
$743$	−33.2593	−1.22017	−0.610084	+	0.792337i	$0.708864\pi$
$744$	−5.79279	−0.212374
$745$	−1.39721	−0.0511899
$746$	58.5700	2.14440
$747$	37.9159	1.38727
$748$	0.615389	0.0225009
$749$	0	0
$750$	34.6703	1.26598
$751$	37.1867	1.35696	0.678481	−	0.734618i	$-0.262639\pi$
$751$	37.1867	1.35696	0.678481	+	0.734618i	$0.262639\pi$
$752$	−54.5409	−1.98890
$753$	30.8751	1.12515
$754$	57.6078	2.09795
$755$	11.9485	0.434850
$756$	0	0
$757$	−16.7204	−0.607715	−0.303857	−	0.952718i	$-0.598275\pi$
$757$	−16.7204	−0.607715	−0.303857	+	0.952718i	$0.598275\pi$
$758$	64.5777	2.34557
$759$	−1.23483	−0.0448215
$760$	0.312180	0.0113239
$761$	−24.5306	−0.889232	−0.444616	−	0.895721i	$-0.646660\pi$
$761$	−24.5306	−0.889232	−0.444616	+	0.895721i	$0.646660\pi$
$762$	−57.3065	−2.07599
$763$	0	0
$764$	14.0018	0.506567
$765$	5.60117	0.202511
$766$	−36.6680	−1.32487
$767$	50.4231	1.82067
$768$	−52.3219	−1.88800
$769$	36.8874	1.33019	0.665097	−	0.746757i	$-0.268390\pi$
$769$	36.8874	1.33019	0.665097	+	0.746757i	$0.268390\pi$
$770$	0	0
$771$	−2.52543	−0.0909511
$772$	−7.45738	−0.268397
$773$	−52.7373	−1.89683	−0.948414	−	0.317034i	$-0.897313\pi$
$773$	−52.7373	−1.89683	−0.948414	+	0.317034i	$0.897313\pi$
$774$	−37.9408	−1.36375
$775$	20.9628	0.753006
$776$	2.41912	0.0868412
$777$	0	0
$778$	0.173419	0.00621736
$779$	8.35421	0.299321
$780$	20.0249	0.717008
$781$	0.852813	0.0305161
$782$	8.23039	0.294318
$783$	20.4583	0.731122
$784$	0	0
$785$	5.54276	0.197829
$786$	56.6551	2.02082
$787$	23.4819	0.837038	0.418519	−	0.908208i	$-0.362549\pi$
$787$	23.4819	0.837038	0.418519	+	0.908208i	$0.362549\pi$
$788$	−3.30106	−0.117596
$789$	12.0894	0.430394
$790$	−5.22518	−0.185904
$791$	0	0
$792$	−0.397298	−0.0141174
$793$	−36.6138	−1.30019
$794$	13.1642	0.467180
$795$	−19.0187	−0.674523
$796$	−31.1717	−1.10485
$797$	−3.94848	−0.139862	−0.0699312	−	0.997552i	$-0.522278\pi$
$797$	−3.94848	−0.139862	−0.0699312	+	0.997552i	$0.522278\pi$
$798$	0	0
$799$	22.3899	0.792098
$800$	34.6921	1.22655
$801$	25.9177	0.915755
$802$	39.5415	1.39626
$803$	0.680231	0.0240048
$804$	48.2009	1.69992
$805$	0	0
$806$	54.3234	1.91346
$807$	37.5129	1.32052
$808$	8.45918	0.297593
$809$	47.7250	1.67792	0.838960	−	0.544193i	$-0.183164\pi$
$809$	47.7250	1.67792	0.838960	+	0.544193i	$0.183164\pi$
$810$	−2.81542	−0.0989238
$811$	4.50835	0.158310	0.0791548	−	0.996862i	$-0.474778\pi$
$811$	4.50835	0.158310	0.0791548	+	0.996862i	$0.474778\pi$
$812$	0	0
$813$	52.4489	1.83946
$814$	−4.18756	−0.146774
$815$	0.690533	0.0241883
$816$	21.9487	0.768358
$817$	4.32517	0.151319
$818$	−31.3692	−1.09680
$819$	0	0
$820$	−10.0760	−0.351869
$821$	−40.0565	−1.39798	−0.698991	−	0.715131i	$-0.746367\pi$
$821$	−40.0565	−1.39798	−0.698991	+	0.715131i	$0.746367\pi$
$822$	68.6565	2.39467
$823$	28.5747	0.996052	0.498026	−	0.867162i	$-0.334058\pi$
$823$	28.5747	0.996052	0.498026	+	0.867162i	$0.334058\pi$
$824$	−7.74675	−0.269871
$825$	2.39174	0.0832699
$826$	0	0
$827$	−10.2227	−0.355479	−0.177739	−	0.984078i	$-0.556878\pi$
$827$	−10.2227	−0.355479	−0.177739	+	0.984078i	$0.556878\pi$
$828$	18.6703	0.648838
$829$	31.1782	1.08286	0.541432	−	0.840744i	$-0.317882\pi$
$829$	31.1782	1.08286	0.541432	+	0.840744i	$0.317882\pi$
$830$	11.1218	0.386042
$831$	85.9032	2.97995
$832$	36.4396	1.26332
$833$	0	0
$834$	−62.6070	−2.16790
$835$	−10.3630	−0.358625
$836$	−0.339508	−0.0117421
$837$	19.2919	0.666827
$838$	33.3331	1.15147
$839$	−19.7223	−0.680890	−0.340445	−	0.940264i	$-0.610578\pi$
$839$	−19.7223	−0.680890	−0.340445	+	0.940264i	$0.610578\pi$
$840$	0	0
$841$	−4.94820	−0.170628
$842$	7.99092	0.275385
$843$	79.2976	2.73115
$844$	−25.5273	−0.878687
$845$	16.1660	0.556128
$846$	108.357	3.72538
$847$	0	0
$848$	−44.7995	−1.53842
$849$	−30.5703	−1.04917
$850$	−15.9415	−0.546788
$851$	−26.2518	−0.899900
$852$	−21.4504	−0.734879
$853$	15.2285	0.521413	0.260706	−	0.965418i	$-0.416045\pi$
$853$	15.2285	0.521413	0.260706	+	0.965418i	$0.416045\pi$
$854$	0	0
$855$	−3.09015	−0.105681
$856$	−7.17697	−0.245304
$857$	4.92849	0.168354	0.0841770	−	0.996451i	$-0.473174\pi$
$857$	4.92849	0.168354	0.0841770	+	0.996451i	$0.473174\pi$
$858$	6.19802	0.211597
$859$	15.2063	0.518831	0.259416	−	0.965766i	$-0.416470\pi$
$859$	15.2063	0.518831	0.259416	+	0.965766i	$0.416470\pi$
$860$	−5.21658	−0.177884
$861$	0	0
$862$	−15.6223	−0.532098
$863$	11.4634	0.390219	0.195109	−	0.980781i	$-0.437494\pi$
$863$	11.4634	0.390219	0.195109	+	0.980781i	$0.437494\pi$
$864$	31.9270	1.08618
$865$	4.44809	0.151240
$866$	−65.1283	−2.21315
$867$	37.6116	1.27736
$868$	0	0
$869$	−0.758072	−0.0257158
$870$	17.8365	0.604714
$871$	60.3000	2.04319
$872$	−4.37034	−0.147998
$873$	−23.9460	−0.810448
$874$	−4.54069	−0.153591
$875$	0	0
$876$	−17.1095	−0.578078
$877$	36.5395	1.23385	0.616925	−	0.787022i	$-0.288378\pi$
$877$	36.5395	1.23385	0.616925	+	0.787022i	$0.288378\pi$
$878$	38.8107	1.30980
$879$	1.15217	0.0388616
$880$	−0.580644	−0.0195735
$881$	5.82572	0.196273	0.0981367	−	0.995173i	$-0.468712\pi$
$881$	5.82572	0.196273	0.0981367	+	0.995173i	$0.468712\pi$
$882$	0	0
$883$	−43.7455	−1.47215	−0.736076	−	0.676898i	$-0.763324\pi$
$883$	−43.7455	−1.47215	−0.736076	+	0.676898i	$0.763324\pi$
$884$	−19.3639	−0.651280
$885$	15.6120	0.524791
$886$	−48.1598	−1.61796
$887$	−47.7565	−1.60351	−0.801754	−	0.597654i	$-0.796100\pi$
$887$	−47.7565	−1.60351	−0.801754	+	0.597654i	$0.796100\pi$
$888$	−14.0509	−0.471519
$889$	0	0
$890$	7.60235	0.254831
$891$	−0.408463	−0.0136840
$892$	−23.0822	−0.772850
$893$	−12.3525	−0.413359
$894$	10.8774	0.363795
$895$	6.70560	0.224144
$896$	0	0
$897$	38.8554	1.29734
$898$	67.7474	2.26076
$899$	22.6805	0.756438
$900$	−36.1626	−1.20542
$901$	18.3909	0.612690
$902$	−3.11867	−0.103840
$903$	0	0
$904$	−2.04736	−0.0680942
$905$	−9.66412	−0.321246
$906$	−93.0201	−3.09039
$907$	−56.9266	−1.89022	−0.945109	−	0.326755i	$-0.894045\pi$
$907$	−56.9266	−1.89022	−0.945109	+	0.326755i	$0.894045\pi$
$908$	−11.4483	−0.379926
$909$	−83.7344	−2.77729
$910$	0	0
$911$	−44.6183	−1.47827	−0.739135	−	0.673557i	$-0.764766\pi$
$911$	−44.6183	−1.47827	−0.739135	+	0.673557i	$0.764766\pi$
$912$	−12.1090	−0.400970
$913$	1.61355	0.0534007
$914$	−11.4850	−0.379889
$915$	−11.3363	−0.374768
$916$	−36.3821	−1.20210
$917$	0	0
$918$	−14.6708	−0.484210
$919$	14.5614	0.480337	0.240169	−	0.970731i	$-0.422797\pi$
$919$	14.5614	0.480337	0.240169	+	0.970731i	$0.422797\pi$
$920$	−0.730578	−0.0240864
$921$	−20.2344	−0.666745
$922$	−12.1585	−0.400420
$923$	−26.8348	−0.883277
$924$	0	0
$925$	50.8472	1.67184
$926$	−4.48833	−0.147496
$927$	76.6822	2.51858
$928$	37.5348	1.23214
$929$	−14.4906	−0.475421	−0.237710	−	0.971336i	$-0.576397\pi$
$929$	−14.4906	−0.475421	−0.237710	+	0.971336i	$0.576397\pi$
$930$	16.8196	0.551536
$931$	0	0
$932$	47.1570	1.54468
$933$	−41.4251	−1.35620
$934$	52.2260	1.70889
$935$	0.238364	0.00779533
$936$	12.5014	0.408622
$937$	50.1757	1.63917	0.819584	−	0.572959i	$-0.194205\pi$
$937$	50.1757	1.63917	0.819584	+	0.572959i	$0.194205\pi$
$938$	0	0
$939$	−21.5714	−0.703957
$940$	14.8983	0.485928
$941$	−20.1827	−0.657937	−0.328969	−	0.944341i	$-0.606701\pi$
$941$	−20.1827	−0.657937	−0.328969	+	0.944341i	$0.606701\pi$
$942$	−43.1509	−1.40593
$943$	−19.5509	−0.636666
$944$	36.7748	1.19692
$945$	0	0
$946$	−1.61461	−0.0524955
$947$	−14.1489	−0.459779	−0.229889	−	0.973217i	$-0.573836\pi$
$947$	−14.1489	−0.459779	−0.229889	+	0.973217i	$0.573836\pi$
$948$	19.0674	0.619282
$949$	−21.4043	−0.694812
$950$	8.79486	0.285343
$951$	17.9935	0.583478
$952$	0	0
$953$	−40.2838	−1.30492	−0.652460	−	0.757823i	$-0.726263\pi$
$953$	−40.2838	−1.30492	−0.652460	+	0.757823i	$0.726263\pi$
$954$	89.0034	2.88159
$955$	5.42343	0.175498
$956$	8.04456	0.260180
$957$	2.58773	0.0836494
$958$	43.5154	1.40592
$959$	0	0
$960$	11.2824	0.364138
$961$	−9.61256	−0.310083
$962$	131.766	4.24832
$963$	71.0423	2.28930
$964$	−2.71219	−0.0873539
$965$	−2.88853	−0.0929850
$966$	0	0
$967$	−14.9434	−0.480546	−0.240273	−	0.970705i	$-0.577237\pi$
$967$	−14.9434	−0.480546	−0.240273	+	0.970705i	$0.577237\pi$
$968$	5.00722	0.160938
$969$	4.97095	0.159690
$970$	−7.02399	−0.225527
$971$	30.3798	0.974935	0.487468	−	0.873141i	$-0.337921\pi$
$971$	30.3798	0.974935	0.487468	+	0.873141i	$0.337921\pi$
$972$	32.3572	1.03786
$973$	0	0
$974$	42.5603	1.36372
$975$	−75.2590	−2.41022
$976$	−26.7033	−0.854751
$977$	32.9069	1.05279	0.526393	−	0.850241i	$-0.323544\pi$
$977$	32.9069	1.05279	0.526393	+	0.850241i	$0.323544\pi$
$978$	−5.37586	−0.171901
$979$	1.10295	0.0352505
$980$	0	0
$981$	43.2604	1.38120
$982$	22.9943	0.733777
$983$	39.0681	1.24608	0.623039	−	0.782191i	$-0.285898\pi$
$983$	39.0681	1.24608	0.623039	+	0.782191i	$0.285898\pi$
$984$	−10.4644	−0.333593
$985$	−1.27863	−0.0407405
$986$	−17.2477	−0.549280
$987$	0	0
$988$	10.6830	0.339872
$989$	−10.1220	−0.321860
$990$	1.15357	0.0366629
$991$	−10.3408	−0.328485	−0.164243	−	0.986420i	$-0.552518\pi$
$991$	−10.3408	−0.328485	−0.164243	+	0.986420i	$0.552518\pi$
$992$	35.3949	1.12379
$993$	98.7410	3.13345
$994$	0	0
$995$	−12.0740	−0.382772
$996$	−40.5849	−1.28598
$997$	21.5137	0.681344	0.340672	−	0.940182i	$-0.389345\pi$
$997$	21.5137	0.681344	0.340672	+	0.940182i	$0.389345\pi$
$998$	17.6466	0.558594
$999$	46.7944	1.48051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.p.1.9	✓	10
3.2	odd	2		8379.2.a.ct.1.2		10
7.2	even	3		931.2.f.r.704.2		20
7.3	odd	6		931.2.f.q.324.2		20
7.4	even	3		931.2.f.r.324.2		20
7.5	odd	6		931.2.f.q.704.2		20
7.6	odd	2		931.2.a.q.1.9	yes	10
21.20	even	2		8379.2.a.cs.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.9	✓	10	1.1	even	1	trivial
931.2.a.q.1.9	yes	10	7.6	odd	2
931.2.f.q.324.2		20	7.3	odd	6
931.2.f.q.704.2		20	7.5	odd	6
931.2.f.r.324.2		20	7.4	even	3
931.2.f.r.704.2		20	7.2	even	3
8379.2.a.cs.1.2		10	21.20	even	2
8379.2.a.ct.1.2		10	3.2	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q+1.94026 q^{2} -2.74246 q^{3} +1.76460 q^{4} +0.683496 q^{5} -5.32108 q^{6} -0.456739 q^{8} +4.52109 q^{9} +O(q^{10})\)	\(q+1.94026 q^{2} -2.74246 q^{3} +1.76460 q^{4} +0.683496 q^{5} -5.32108 q^{6} -0.456739 q^{8} +4.52109 q^{9} +1.32616 q^{10} +0.192400 q^{11} -4.83934 q^{12} -6.05408 q^{13} -1.87446 q^{15} -4.41539 q^{16} +1.81259 q^{17} +8.77209 q^{18} -1.00000 q^{19} +1.20610 q^{20} +0.373305 q^{22} +2.34025 q^{23} +1.25259 q^{24} -4.53283 q^{25} -11.7465 q^{26} -4.17154 q^{27} -4.90426 q^{29} -3.63694 q^{30} -4.62466 q^{31} -7.65351 q^{32} -0.527649 q^{33} +3.51689 q^{34} +7.97792 q^{36} -11.2175 q^{37} -1.94026 q^{38} +16.6031 q^{39} -0.312180 q^{40} -8.35421 q^{41} -4.32517 q^{43} +0.339508 q^{44} +3.09015 q^{45} +4.54069 q^{46} +12.3525 q^{47} +12.1090 q^{48} -8.79486 q^{50} -4.97095 q^{51} -10.6830 q^{52} +10.1462 q^{53} -8.09387 q^{54} +0.131505 q^{55} +2.74246 q^{57} -9.51553 q^{58} -8.32878 q^{59} -3.30767 q^{60} +6.04778 q^{61} -8.97302 q^{62} -6.01901 q^{64} -4.13795 q^{65} -1.02378 q^{66} -9.96022 q^{67} +3.19849 q^{68} -6.41804 q^{69} +4.43250 q^{71} -2.06496 q^{72} +3.53551 q^{73} -21.7649 q^{74} +12.4311 q^{75} -1.76460 q^{76} +32.2143 q^{78} -3.94009 q^{79} -3.01790 q^{80} -2.12299 q^{81} -16.2093 q^{82} +8.38645 q^{83} +1.23890 q^{85} -8.39195 q^{86} +13.4498 q^{87} -0.0878765 q^{88} +5.73261 q^{89} +5.99569 q^{90} +4.12960 q^{92} +12.6829 q^{93} +23.9669 q^{94} -0.683496 q^{95} +20.9895 q^{96} -5.29649 q^{97} +0.869858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^3 + 10 * q^4 - 16 * q^5 - 8 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9} + 12 q^{10} - 12 q^{12} - 12 q^{13} + 2 q^{16} - 16 q^{17} + 2 q^{18} - 10 q^{19} - 32 q^{20} + 4 q^{22} + 12 q^{23} + 8 q^{24} + 14 q^{25} - 24 q^{26} - 16 q^{27} - 12 q^{29} - 12 q^{30} - 8 q^{31} - 34 q^{32} + 4 q^{33} - 16 q^{34} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 4 q^{39} + 20 q^{40} - 40 q^{41} + 4 q^{43} - 20 q^{44} - 24 q^{45} - 32 q^{46} - 16 q^{47} - 12 q^{48} - 34 q^{50} - 28 q^{51} + 40 q^{52} - 8 q^{54} - 16 q^{55} + 4 q^{57} - 8 q^{58} - 36 q^{59} + 32 q^{60} - 16 q^{61} + 16 q^{62} + 18 q^{64} + 8 q^{65} - 8 q^{66} - 28 q^{67} - 40 q^{68} - 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} + 32 q^{75} - 10 q^{76} + 28 q^{78} - 8 q^{79} - 8 q^{80} + 14 q^{81} + 8 q^{82} + 40 q^{85} - 52 q^{86} + 8 q^{87} - 4 q^{88} - 48 q^{89} + 64 q^{90} + 28 q^{92} + 40 q^{93} + 36 q^{94} + 16 q^{95} + 8 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^3 + 10 * q^4 - 16 * q^5 - 8 * q^6 - 6 * q^8 + 10 * q^9 + 12 * q^10 - 12 * q^12 - 12 * q^13 + 2 * q^16 - 16 * q^17 + 2 * q^18 - 10 * q^19 - 32 * q^20 + 4 * q^22 + 12 * q^23 + 8 * q^24 + 14 * q^25 - 24 * q^26 - 16 * q^27 - 12 * q^29 - 12 * q^30 - 8 * q^31 - 34 * q^32 + 4 * q^33 - 16 * q^34 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 4 * q^39 + 20 * q^40 - 40 * q^41 + 4 * q^43 - 20 * q^44 - 24 * q^45 - 32 * q^46 - 16 * q^47 - 12 * q^48 - 34 * q^50 - 28 * q^51 + 40 * q^52 - 8 * q^54 - 16 * q^55 + 4 * q^57 - 8 * q^58 - 36 * q^59 + 32 * q^60 - 16 * q^61 + 16 * q^62 + 18 * q^64 + 8 * q^65 - 8 * q^66 - 28 * q^67 - 40 * q^68 - 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 + 32 * q^75 - 10 * q^76 + 28 * q^78 - 8 * q^79 - 8 * q^80 + 14 * q^81 + 8 * q^82 + 40 * q^85 - 52 * q^86 + 8 * q^87 - 4 * q^88 - 48 * q^89 + 64 * q^90 + 28 * q^92 + 40 * q^93 + 36 * q^94 + 16 * q^95 + 8 * q^96 + 16 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more