LMFDB - Embedded newform 2793.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,2,Mod(1,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2793.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2793 = 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2793.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:	$22.3022172845$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1240016.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 2x^{2} + 16x + 6 $ x^5 - x^4 - 8x^3 + 2x^2 + 16*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.91889$ of defining polynomial
Character	$\chi$	$=$	2793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23675 q^{2} -1.00000 q^{3} -0.470449 q^{4} +4.29208 q^{5} +1.23675 q^{6} +3.05533 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.23675 q^{2} -1.00000 q^{3} -0.470449 q^{4} +4.29208 q^{5} +1.23675 q^{6} +3.05533 q^{8} +1.00000 q^{9} -5.30823 q^{10} -3.83778 q^{11} +0.470449 q^{12} -4.47350 q^{13} -4.29208 q^{15} -2.83778 q^{16} -7.23298 q^{17} -1.23675 q^{18} -1.00000 q^{19} -2.01920 q^{20} +4.74638 q^{22} +3.83778 q^{23} -3.05533 q^{24} +13.4219 q^{25} +5.53260 q^{26} -1.00000 q^{27} -0.454298 q^{29} +5.30823 q^{30} +1.83778 q^{31} -2.60103 q^{32} +3.83778 q^{33} +8.94539 q^{34} -0.470449 q^{36} -3.64326 q^{37} +1.23675 q^{38} +4.47350 q^{39} +13.1137 q^{40} +0.467397 q^{41} +11.4810 q^{43} +1.80548 q^{44} +4.29208 q^{45} -4.74638 q^{46} -2.12986 q^{47} +2.83778 q^{48} -16.5996 q^{50} +7.23298 q^{51} +2.10455 q^{52} +10.1360 q^{53} +1.23675 q^{54} -16.4721 q^{55} +1.00000 q^{57} +0.561853 q^{58} +7.67556 q^{59} +2.01920 q^{60} +9.52505 q^{61} -2.27288 q^{62} +8.89239 q^{64} -19.2006 q^{65} -4.74638 q^{66} +7.21377 q^{67} +3.40274 q^{68} -3.83778 q^{69} +2.71546 q^{71} +3.05533 q^{72} +0.00610378 q^{73} +4.50580 q^{74} -13.4219 q^{75} +0.470449 q^{76} -5.53260 q^{78} +4.27288 q^{79} -12.1800 q^{80} +1.00000 q^{81} -0.578053 q^{82} +12.1238 q^{83} -31.0445 q^{85} -14.1992 q^{86} +0.454298 q^{87} -11.7257 q^{88} -16.7009 q^{89} -5.30823 q^{90} -1.80548 q^{92} -1.83778 q^{93} +2.63410 q^{94} -4.29208 q^{95} +2.60103 q^{96} -7.98074 q^{97} -3.83778 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 7 q^{12} - 8 q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 2 q^{23} - 3 q^{24} + 11 q^{25} + 32 q^{26} - 5 q^{27} - 8 q^{31} - 3 q^{32} + 2 q^{33} + 8 q^{34} + 7 q^{36} + 2 q^{37} - q^{38} + 8 q^{39} + 36 q^{40} - 2 q^{41} + 20 q^{43} + 6 q^{44} + 2 q^{45} - 2 q^{46} + 26 q^{47} - 3 q^{48} - q^{50} - 2 q^{51} - 4 q^{52} + 4 q^{53} - q^{54} + 4 q^{55} + 5 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} - 10 q^{61} - 4 q^{62} - 21 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} + 58 q^{68} - 2 q^{69} + 10 q^{71} + 3 q^{72} - 10 q^{73} - 6 q^{74} - 11 q^{75} - 7 q^{76} - 32 q^{78} + 14 q^{79} + 6 q^{80} + 5 q^{81} + 26 q^{82} + 34 q^{83} - 36 q^{85} + 8 q^{86} + 6 q^{88} - 10 q^{89} - 6 q^{92} + 8 q^{93} + 8 q^{94} - 2 q^{95} + 3 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 7 * q^12 - 8 * q^13 - 2 * q^15 + 3 * q^16 + 2 * q^17 + q^18 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 2 * q^23 - 3 * q^24 + 11 * q^25 + 32 * q^26 - 5 * q^27 - 8 * q^31 - 3 * q^32 + 2 * q^33 + 8 * q^34 + 7 * q^36 + 2 * q^37 - q^38 + 8 * q^39 + 36 * q^40 - 2 * q^41 + 20 * q^43 + 6 * q^44 + 2 * q^45 - 2 * q^46 + 26 * q^47 - 3 * q^48 - q^50 - 2 * q^51 - 4 * q^52 + 4 * q^53 - q^54 + 4 * q^55 + 5 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 - 10 * q^61 - 4 * q^62 - 21 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 + 58 * q^68 - 2 * q^69 + 10 * q^71 + 3 * q^72 - 10 * q^73 - 6 * q^74 - 11 * q^75 - 7 * q^76 - 32 * q^78 + 14 * q^79 + 6 * q^80 + 5 * q^81 + 26 * q^82 + 34 * q^83 - 36 * q^85 + 8 * q^86 + 6 * q^88 - 10 * q^89 - 6 * q^92 + 8 * q^93 + 8 * q^94 - 2 * q^95 + 3 * q^96 + 16 * q^97 - 2 * 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 $

$2$	−1.23675	−0.874515	−0.437257	−	0.899336i	$-0.644050\pi$
$2$	−1.23675	−0.874515	−0.437257	+	0.899336i	$0.644050\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.470449	−0.235224
$5$	4.29208	1.91948	0.959738	−	0.280897i	$-0.0906319\pi$
$5$	4.29208	1.91948	0.959738	+	0.280897i	$0.0906319\pi$
$6$	1.23675	0.504901
$7$	0	0
$7$	0	0
$8$	3.05533	1.08022
$9$	1.00000	0.333333
$10$	−5.30823	−1.67861
$11$	−3.83778	−1.15713	−0.578567	−	0.815635i	$-0.696388\pi$
$11$	−3.83778	−1.15713	−0.578567	+	0.815635i	$0.696388\pi$
$12$	0.470449	0.135807
$13$	−4.47350	−1.24073	−0.620363	−	0.784315i	$-0.713015\pi$
$13$	−4.47350	−1.24073	−0.620363	+	0.784315i	$0.713015\pi$
$14$	0	0
$15$	−4.29208	−1.10821
$16$	−2.83778	−0.709445
$17$	−7.23298	−1.75425	−0.877127	−	0.480258i	$-0.840543\pi$
$17$	−7.23298	−1.75425	−0.877127	+	0.480258i	$0.840543\pi$
$18$	−1.23675	−0.291505
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.01920	−0.451507
$21$	0	0
$22$	4.74638	1.01193
$23$	3.83778	0.800233	0.400116	−	0.916464i	$-0.368970\pi$
$23$	3.83778	0.800233	0.400116	+	0.916464i	$0.368970\pi$
$24$	−3.05533	−0.623666
$25$	13.4219	2.68439
$26$	5.53260	1.08503
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−0.454298	−0.0843610	−0.0421805	−	0.999110i	$-0.513430\pi$
$29$	−0.454298	−0.0843610	−0.0421805	+	0.999110i	$0.513430\pi$
$30$	5.30823	0.969146
$31$	1.83778	0.330075	0.165038	−	0.986287i	$-0.447225\pi$
$31$	1.83778	0.330075	0.165038	+	0.986287i	$0.447225\pi$
$32$	−2.60103	−0.459802
$33$	3.83778	0.668072
$34$	8.94539	1.53412
$35$	0	0
$36$	−0.470449	−0.0784081
$37$	−3.64326	−0.598948	−0.299474	−	0.954104i	$-0.596811\pi$
$37$	−3.64326	−0.598948	−0.299474	+	0.954104i	$0.596811\pi$
$38$	1.23675	0.200627
$39$	4.47350	0.716333
$40$	13.1137	2.07346
$41$	0.467397	0.0729951	0.0364976	−	0.999334i	$-0.488380\pi$
$41$	0.467397	0.0729951	0.0364976	+	0.999334i	$0.488380\pi$
$42$	0	0
$43$	11.4810	1.75084	0.875421	−	0.483361i	$-0.160584\pi$
$43$	11.4810	1.75084	0.875421	+	0.483361i	$0.160584\pi$
$44$	1.80548	0.272186
$45$	4.29208	0.639825
$46$	−4.74638	−0.699815
$47$	−2.12986	−0.310672	−0.155336	−	0.987862i	$-0.549646\pi$
$47$	−2.12986	−0.310672	−0.155336	+	0.987862i	$0.549646\pi$
$48$	2.83778	0.409598
$49$	0	0
$50$	−16.5996	−2.34754
$51$	7.23298	1.01282
$52$	2.10455	0.291849
$53$	10.1360	1.39228	0.696141	−	0.717905i	$-0.254899\pi$
$53$	10.1360	1.39228	0.696141	+	0.717905i	$0.254899\pi$
$54$	1.23675	0.168300
$55$	−16.4721	−2.22109
$56$	0	0
$57$	1.00000	0.132453
$58$	0.561853	0.0737749
$59$	7.67556	0.999273	0.499636	−	0.866235i	$-0.333467\pi$
$59$	7.67556	0.999273	0.499636	+	0.866235i	$0.333467\pi$
$60$	2.01920	0.260678
$61$	9.52505	1.21956	0.609779	−	0.792571i	$-0.291258\pi$
$61$	9.52505	1.21956	0.609779	+	0.792571i	$0.291258\pi$
$62$	−2.27288	−0.288656
$63$	0	0
$64$	8.89239	1.11155
$65$	−19.2006	−2.38154
$66$	−4.74638	−0.584239
$67$	7.21377	0.881303	0.440651	−	0.897678i	$-0.354748\pi$
$67$	7.21377	0.881303	0.440651	+	0.897678i	$0.354748\pi$
$68$	3.40274	0.412643
$69$	−3.83778	−0.462014
$70$	0	0
$71$	2.71546	0.322266	0.161133	−	0.986933i	$-0.448485\pi$
$71$	2.71546	0.322266	0.161133	+	0.986933i	$0.448485\pi$
$72$	3.05533	0.360074
$73$	0.00610378	0.000714394 0	0.000357197	−	1.00000i	$-0.499886\pi$
$73$	0.00610378	0.000714394 0	0.000357197		1.00000i	$0.499886\pi$
$74$	4.50580	0.523789
$75$	−13.4219	−1.54983
$76$	0.470449	0.0539642
$77$	0	0
$78$	−5.53260	−0.626444
$79$	4.27288	0.480736	0.240368	−	0.970682i	$-0.422732\pi$
$79$	4.27288	0.480736	0.240368	+	0.970682i	$0.422732\pi$
$80$	−12.1800	−1.36176
$81$	1.00000	0.111111
$82$	−0.578053	−0.0638353
$83$	12.1238	1.33076	0.665378	−	0.746507i	$-0.268271\pi$
$83$	12.1238	1.33076	0.665378	+	0.746507i	$0.268271\pi$
$84$	0	0
$85$	−31.0445	−3.36725
$86$	−14.1992	−1.53114
$87$	0.454298	0.0487058
$88$	−11.7257	−1.24996
$89$	−16.7009	−1.77029	−0.885147	−	0.465312i	$-0.845942\pi$
$89$	−16.7009	−1.77029	−0.885147	+	0.465312i	$0.845942\pi$
$90$	−5.30823	−0.559536
$91$	0	0
$92$	−1.80548	−0.188234
$93$	−1.83778	−0.190569
$94$	2.63410	0.271687
$95$	−4.29208	−0.440358
$96$	2.60103	0.265467
$97$	−7.98074	−0.810321	−0.405161	−	0.914246i	$-0.632784\pi$
$97$	−7.98074	−0.810321	−0.405161	+	0.914246i	$0.632784\pi$
$98$	0	0
$99$	−3.83778	−0.385711
$100$	−6.31433	−0.631433
$101$	−0.442585	−0.0440389	−0.0220194	−	0.999758i	$-0.507010\pi$
$101$	−0.442585	−0.0440389	−0.0220194	+	0.999758i	$0.507010\pi$
$102$	−8.94539	−0.885725
$103$	14.8288	1.46112	0.730562	−	0.682846i	$-0.239258\pi$
$103$	14.8288	1.46112	0.730562	+	0.682846i	$0.239258\pi$
$104$	−13.6680	−1.34026
$105$	0	0
$106$	−12.5357	−1.21757
$107$	13.3319	1.28885	0.644423	−	0.764669i	$-0.277098\pi$
$107$	13.3319	1.28885	0.644423	+	0.764669i	$0.277098\pi$
$108$	0.470449	0.0452689
$109$	−14.2597	−1.36583	−0.682917	−	0.730496i	$-0.739289\pi$
$109$	−14.2597	−1.36583	−0.682917	+	0.730496i	$0.739289\pi$
$110$	20.3718	1.94238
$111$	3.64326	0.345803
$112$	0	0
$113$	−7.19507	−0.676855	−0.338427	−	0.940993i	$-0.609895\pi$
$113$	−7.19507	−0.676855	−0.338427	+	0.940993i	$0.609895\pi$
$114$	−1.23675	−0.115832
$115$	16.4721	1.53603
$116$	0.213724	0.0198438
$117$	−4.47350	−0.413575
$118$	−9.49275	−0.873879
$119$	0	0
$120$	−13.1137	−1.19711
$121$	3.72856	0.338960
$122$	−11.7801	−1.06652
$123$	−0.467397	−0.0421438
$124$	−0.864582	−0.0776417
$125$	36.1476	3.23314
$126$	0	0
$127$	2.66802	0.236749	0.118374	−	0.992969i	$-0.462232\pi$
$127$	2.66802	0.236749	0.118374	+	0.992969i	$0.462232\pi$
$128$	−5.79560	−0.512264
$129$	−11.4810	−1.01085
$130$	23.7464	2.08269
$131$	2.60480	0.227583	0.113791	−	0.993505i	$-0.463700\pi$
$131$	2.60480	0.227583	0.113791	+	0.993505i	$0.463700\pi$
$132$	−1.80548	−0.157147
$133$	0	0
$134$	−8.92164	−0.770712
$135$	−4.29208	−0.369403
$136$	−22.0991	−1.89498
$137$	9.15323	0.782014	0.391007	−	0.920388i	$-0.372127\pi$
$137$	9.15323	0.782014	0.391007	+	0.920388i	$0.372127\pi$
$138$	4.74638	0.404038
$139$	1.99390	0.169120	0.0845600	−	0.996418i	$-0.473052\pi$
$139$	1.99390	0.169120	0.0845600	+	0.996418i	$0.473052\pi$
$140$	0	0
$141$	2.12986	0.179366
$142$	−3.35835	−0.281826
$143$	17.1683	1.43569
$144$	−2.83778	−0.236482
$145$	−1.94988	−0.161929
$146$	−0.00754886	−0.000624748 0
$147$	0	0
$148$	1.71397	0.140887
$149$	22.2597	1.82359	0.911794	−	0.410649i	$-0.134698\pi$
$149$	22.2597	1.82359	0.911794	+	0.410649i	$0.134698\pi$
$150$	16.5996	1.35535
$151$	−1.58272	−0.128800	−0.0644000	−	0.997924i	$-0.520513\pi$
$151$	−1.58272	−0.128800	−0.0644000	+	0.997924i	$0.520513\pi$
$152$	−3.05533	−0.247820
$153$	−7.23298	−0.584751
$154$	0	0
$155$	7.88790	0.633571
$156$	−2.10455	−0.168499
$157$	−2.69626	−0.215185	−0.107592	−	0.994195i	$-0.534314\pi$
$157$	−2.69626	−0.215185	−0.107592	+	0.994195i	$0.534314\pi$
$158$	−5.28448	−0.420411
$159$	−10.1360	−0.803834
$160$	−11.1638	−0.882578
$161$	0	0
$162$	−1.23675	−0.0971683
$163$	4.74027	0.371287	0.185643	−	0.982617i	$-0.440563\pi$
$163$	4.74027	0.371287	0.185643	+	0.982617i	$0.440563\pi$
$164$	−0.219886	−0.0171702
$165$	16.4721	1.28235
$166$	−14.9941	−1.16376
$167$	8.36284	0.647136	0.323568	−	0.946205i	$-0.395118\pi$
$167$	8.36284	0.647136	0.323568	+	0.946205i	$0.395118\pi$
$168$	0	0
$169$	7.01221	0.539401
$170$	38.3943	2.94471
$171$	−1.00000	−0.0764719
$172$	−5.40124	−0.411841
$173$	8.14296	0.619098	0.309549	−	0.950884i	$-0.399822\pi$
$173$	8.14296	0.619098	0.309549	+	0.950884i	$0.399822\pi$
$174$	−0.561853	−0.0425940
$175$	0	0
$176$	10.8908	0.820923
$177$	−7.67556	−0.576931
$178$	20.6549	1.54815
$179$	7.90100	0.590548	0.295274	−	0.955413i	$-0.404589\pi$
$179$	7.90100	0.590548	0.295274	+	0.955413i	$0.404589\pi$
$180$	−2.01920	−0.150502
$181$	−0.0838648	−0.00623362	−0.00311681	−	0.999995i	$-0.500992\pi$
$181$	−0.0838648	−0.00623362	−0.00311681	+	0.999995i	$0.500992\pi$
$182$	0	0
$183$	−9.52505	−0.704112
$184$	11.7257	0.864429
$185$	−15.6372	−1.14967
$186$	2.27288	0.166655
$187$	27.7586	2.02991
$188$	1.00199	0.0730776
$189$	0	0
$190$	5.30823	0.385099
$191$	18.2775	1.32252	0.661258	−	0.750159i	$-0.270023\pi$
$191$	18.2775	1.32252	0.661258	+	0.750159i	$0.270023\pi$
$192$	−8.89239	−0.641753
$193$	4.03230	0.290251	0.145126	−	0.989413i	$-0.453641\pi$
$193$	4.03230	0.290251	0.145126	+	0.989413i	$0.453641\pi$
$194$	9.87018	0.708638
$195$	19.2006	1.37498
$196$	0	0
$197$	14.1002	1.00460	0.502300	−	0.864693i	$-0.332487\pi$
$197$	14.1002	1.00460	0.502300	+	0.864693i	$0.332487\pi$
$198$	4.74638	0.337310
$199$	4.90860	0.347961	0.173981	−	0.984749i	$-0.444337\pi$
$199$	4.90860	0.347961	0.173981	+	0.984749i	$0.444337\pi$
$200$	41.0084	2.89973
$201$	−7.21377	−0.508820
$202$	0.547368	0.0385126
$203$	0	0
$204$	−3.40274	−0.238240
$205$	2.00610	0.140112
$206$	−18.3395	−1.27777
$207$	3.83778	0.266744
$208$	12.6948	0.880227
$209$	3.83778	0.265465
$210$	0	0
$211$	−27.1491	−1.86902	−0.934509	−	0.355940i	$-0.884161\pi$
$211$	−27.1491	−1.86902	−0.934509	+	0.355940i	$0.884161\pi$
$212$	−4.76845	−0.327499
$213$	−2.71546	−0.186060
$214$	−16.4883	−1.12711
$215$	49.2775	3.36070
$216$	−3.05533	−0.207889
$217$	0	0
$218$	17.6357	1.19444
$219$	−0.00610378	−0.000412456 0
$220$	7.74926	0.522455
$221$	32.3567	2.17655
$222$	−4.50580	−0.302410
$223$	−9.21233	−0.616903	−0.308452	−	0.951240i	$-0.599811\pi$
$223$	−9.21233	−0.616903	−0.308452	+	0.951240i	$0.599811\pi$
$224$	0	0
$225$	13.4219	0.894796
$226$	8.89850	0.591919
$227$	−22.1415	−1.46958	−0.734792	−	0.678293i	$-0.762720\pi$
$227$	−22.1415	−1.46958	−0.734792	+	0.678293i	$0.762720\pi$
$228$	−0.470449	−0.0311562
$229$	−11.5190	−0.761194	−0.380597	−	0.924741i	$-0.624281\pi$
$229$	−11.5190	−0.761194	−0.380597	+	0.924741i	$0.624281\pi$
$230$	−20.3718	−1.34328
$231$	0	0
$232$	−1.38803	−0.0911286
$233$	−6.59636	−0.432142	−0.216071	−	0.976378i	$-0.569324\pi$
$233$	−6.59636	−0.432142	−0.216071	+	0.976378i	$0.569324\pi$
$234$	5.53260	0.361678
$235$	−9.14152	−0.596327
$236$	−3.61096	−0.235053
$237$	−4.27288	−0.277553
$238$	0	0
$239$	9.26870	0.599543	0.299771	−	0.954011i	$-0.403090\pi$
$239$	9.26870	0.599543	0.299771	+	0.954011i	$0.403090\pi$
$240$	12.1800	0.786214
$241$	10.7215	0.690633	0.345316	−	0.938486i	$-0.387772\pi$
$241$	10.7215	0.690633	0.345316	+	0.938486i	$0.387772\pi$
$242$	−4.61130	−0.296425
$243$	−1.00000	−0.0641500
$244$	−4.48105	−0.286870
$245$	0	0
$246$	0.578053	0.0368553
$247$	4.47350	0.284642
$248$	5.61502	0.356554
$249$	−12.1238	−0.768312
$250$	−44.7056	−2.82743
$251$	16.3745	1.03355	0.516775	−	0.856122i	$-0.327133\pi$
$251$	16.3745	1.03355	0.516775	+	0.856122i	$0.327133\pi$
$252$	0	0
$253$	−14.7286	−0.925977
$254$	−3.29968	−0.207040
$255$	31.0445	1.94408
$256$	−10.6171	−0.663566
$257$	−20.1168	−1.25485	−0.627425	−	0.778677i	$-0.715891\pi$
$257$	−20.1168	−1.25485	−0.627425	+	0.778677i	$0.715891\pi$
$258$	14.1992	0.884002
$259$	0	0
$260$	9.03290	0.560197
$261$	−0.454298	−0.0281203
$262$	−3.22149	−0.199025
$263$	−18.3037	−1.12866	−0.564328	−	0.825551i	$-0.690865\pi$
$263$	−18.3037	−1.12866	−0.564328	+	0.825551i	$0.690865\pi$
$264$	11.7257	0.721666
$265$	43.5043	2.67245
$266$	0	0
$267$	16.7009	1.02208
$268$	−3.39371	−0.207304
$269$	2.23497	0.136268	0.0681341	−	0.997676i	$-0.478295\pi$
$269$	2.23497	0.136268	0.0681341	+	0.997676i	$0.478295\pi$
$270$	5.30823	0.323049
$271$	−0.784287	−0.0476420	−0.0238210	−	0.999716i	$-0.507583\pi$
$271$	−0.784287	−0.0476420	−0.0238210	+	0.999716i	$0.507583\pi$
$272$	20.5256	1.24455
$273$	0	0
$274$	−11.3203	−0.683882
$275$	−51.5105	−3.10620
$276$	1.80548	0.108677
$277$	−11.8996	−0.714978	−0.357489	−	0.933917i	$-0.616367\pi$
$277$	−11.8996	−0.714978	−0.357489	+	0.933917i	$0.616367\pi$
$278$	−2.46595	−0.147898
$279$	1.83778	0.110025
$280$	0	0
$281$	25.7731	1.53750	0.768748	−	0.639552i	$-0.220880\pi$
$281$	25.7731	1.53750	0.768748	+	0.639552i	$0.220880\pi$
$282$	−2.63410	−0.156859
$283$	−14.0535	−0.835393	−0.417696	−	0.908587i	$-0.637162\pi$
$283$	−14.0535	−0.835393	−0.417696	+	0.908587i	$0.637162\pi$
$284$	−1.27749	−0.0758048
$285$	4.29208	0.254241
$286$	−21.2329	−1.25553
$287$	0	0
$288$	−2.60103	−0.153267
$289$	35.3159	2.07741
$290$	2.41152	0.141609
$291$	7.98074	0.467839
$292$	−0.00287152	−0.000168043 0
$293$	−5.61229	−0.327873	−0.163937	−	0.986471i	$-0.552419\pi$
$293$	−5.61229	−0.327873	−0.163937	+	0.986471i	$0.552419\pi$
$294$	0	0
$295$	32.9441	1.91808
$296$	−11.1314	−0.646997
$297$	3.83778	0.222691
$298$	−27.5297	−1.59475
$299$	−17.1683	−0.992869
$300$	6.31433	0.364558
$301$	0	0
$302$	1.95743	0.112637
$303$	0.442585	0.0254259
$304$	2.83778	0.162758
$305$	40.8823	2.34091
$306$	8.94539	0.511374
$307$	11.7318	0.669568	0.334784	−	0.942295i	$-0.391337\pi$
$307$	11.7318	0.669568	0.334784	+	0.942295i	$0.391337\pi$
$308$	0	0
$309$	−14.8288	−0.843581
$310$	−9.75536	−0.554067
$311$	24.7201	1.40175	0.700875	−	0.713284i	$-0.252793\pi$
$311$	24.7201	1.40175	0.700875	+	0.713284i	$0.252793\pi$
$312$	13.6680	0.773799
$313$	−21.2006	−1.19833	−0.599165	−	0.800626i	$-0.704501\pi$
$313$	−21.2006	−1.19833	−0.599165	+	0.800626i	$0.704501\pi$
$314$	3.33460	0.188182
$315$	0	0
$316$	−2.01017	−0.113081
$317$	1.76414	0.0990842	0.0495421	−	0.998772i	$-0.484224\pi$
$317$	1.76414	0.0990842	0.0495421	+	0.998772i	$0.484224\pi$
$318$	12.5357	0.702965
$319$	1.74350	0.0976170
$320$	38.1668	2.13359
$321$	−13.3319	−0.744115
$322$	0	0
$323$	7.23298	0.402454
$324$	−0.470449	−0.0261360
$325$	−60.0430	−3.33059
$326$	−5.86253	−0.324696
$327$	14.2597	0.788564
$328$	1.42805	0.0788509
$329$	0	0
$330$	−20.3718	−1.12143
$331$	−21.7918	−1.19779	−0.598894	−	0.800829i	$-0.704393\pi$
$331$	−21.7918	−1.19779	−0.598894	+	0.800829i	$0.704393\pi$
$332$	−5.70360	−0.313026
$333$	−3.64326	−0.199649
$334$	−10.3428	−0.565930
$335$	30.9621	1.69164
$336$	0	0
$337$	19.1187	1.04146	0.520731	−	0.853721i	$-0.325660\pi$
$337$	19.1187	1.04146	0.520731	+	0.853721i	$0.325660\pi$
$338$	−8.67235	−0.471714
$339$	7.19507	0.390782
$340$	14.6048	0.792059
$341$	−7.05300	−0.381941
$342$	1.23675	0.0668758
$343$	0	0
$344$	35.0783	1.89130
$345$	−16.4721	−0.886826
$346$	−10.0708	−0.541410
$347$	−10.2035	−0.547752	−0.273876	−	0.961765i	$-0.588306\pi$
$347$	−10.2035	−0.547752	−0.273876	+	0.961765i	$0.588306\pi$
$348$	−0.213724	−0.0114568
$349$	28.1031	1.50432	0.752162	−	0.658978i	$-0.229011\pi$
$349$	28.1031	1.50432	0.752162	+	0.658978i	$0.229011\pi$
$350$	0	0
$351$	4.47350	0.238778
$352$	9.98218	0.532052
$353$	32.0941	1.70820	0.854098	−	0.520113i	$-0.174110\pi$
$353$	32.0941	1.70820	0.854098	+	0.520113i	$0.174110\pi$
$354$	9.49275	0.504534
$355$	11.6550	0.618582
$356$	7.85692	0.416416
$357$	0	0
$358$	−9.77156	−0.516443
$359$	−17.6315	−0.930557	−0.465279	−	0.885164i	$-0.654046\pi$
$359$	−17.6315	−0.930557	−0.465279	+	0.885164i	$0.654046\pi$
$360$	13.1137	0.691153
$361$	1.00000	0.0526316
$362$	0.103720	0.00545139
$363$	−3.72856	−0.195699
$364$	0	0
$365$	0.0261979	0.00137126
$366$	11.7801	0.615756
$367$	7.41584	0.387104	0.193552	−	0.981090i	$-0.437999\pi$
$367$	7.41584	0.387104	0.193552	+	0.981090i	$0.437999\pi$
$368$	−10.8908	−0.567721
$369$	0.467397	0.0243317
$370$	19.3393	1.00540
$371$	0	0
$372$	0.864582	0.0448265
$373$	−25.9737	−1.34487	−0.672433	−	0.740158i	$-0.734751\pi$
$373$	−25.9737	−1.34487	−0.672433	+	0.740158i	$0.734751\pi$
$374$	−34.3304	−1.77518
$375$	−36.1476	−1.86665
$376$	−6.50742	−0.335594
$377$	2.03230	0.104669
$378$	0	0
$379$	20.9338	1.07530	0.537650	−	0.843168i	$-0.319312\pi$
$379$	20.9338	1.07530	0.537650	+	0.843168i	$0.319312\pi$
$380$	2.01920	0.103583
$381$	−2.66802	−0.136687
$382$	−22.6047	−1.15656
$383$	8.36284	0.427321	0.213661	−	0.976908i	$-0.431461\pi$
$383$	8.36284	0.427321	0.213661	+	0.976908i	$0.431461\pi$
$384$	5.79560	0.295756
$385$	0	0
$386$	−4.98695	−0.253829
$387$	11.4810	0.583614
$388$	3.75453	0.190607
$389$	−30.8701	−1.56517	−0.782587	−	0.622541i	$-0.786101\pi$
$389$	−30.8701	−1.56517	−0.782587	+	0.622541i	$0.786101\pi$
$390$	−23.7464	−1.20244
$391$	−27.7586	−1.40381
$392$	0	0
$393$	−2.60480	−0.131395
$394$	−17.4385	−0.878537
$395$	18.3395	0.922761
$396$	1.80548	0.0907287
$397$	17.8969	0.898218	0.449109	−	0.893477i	$-0.351741\pi$
$397$	17.8969	0.898218	0.449109	+	0.893477i	$0.351741\pi$
$398$	−6.07071	−0.304297
$399$	0	0
$400$	−38.0885	−1.90443
$401$	−4.92635	−0.246010	−0.123005	−	0.992406i	$-0.539253\pi$
$401$	−4.92635	−0.246010	−0.123005	+	0.992406i	$0.539253\pi$
$402$	8.92164	0.444971
$403$	−8.22131	−0.409533
$404$	0.208214	0.0103590
$405$	4.29208	0.213275
$406$	0	0
$407$	13.9820	0.693064
$408$	22.0991	1.09407
$409$	−24.7950	−1.22604	−0.613018	−	0.790069i	$-0.710045\pi$
$409$	−24.7950	−1.22604	−0.613018	+	0.790069i	$0.710045\pi$
$410$	−2.48105	−0.122530
$411$	−9.15323	−0.451496
$412$	−6.97619	−0.343692
$413$	0	0
$414$	−4.74638	−0.233272
$415$	52.0361	2.55435
$416$	11.6357	0.570488
$417$	−1.99390	−0.0976415
$418$	−4.74638	−0.232153
$419$	−9.54281	−0.466197	−0.233098	−	0.972453i	$-0.574886\pi$
$419$	−9.54281	−0.466197	−0.233098	+	0.972453i	$0.574886\pi$
$420$	0	0
$421$	−13.7999	−0.672565	−0.336282	−	0.941761i	$-0.609170\pi$
$421$	−13.7999	−0.672565	−0.336282	+	0.941761i	$0.609170\pi$
$422$	33.5766	1.63448
$423$	−2.12986	−0.103557
$424$	30.9687	1.50397
$425$	−97.0806	−4.70910
$426$	3.35835	0.162712
$427$	0	0
$428$	−6.27198	−0.303168
$429$	−17.1683	−0.828894
$430$	−60.9440	−2.93898
$431$	−35.4969	−1.70982	−0.854912	−	0.518773i	$-0.826389\pi$
$431$	−35.4969	−1.70982	−0.854912	+	0.518773i	$0.826389\pi$
$432$	2.83778	0.136533
$433$	10.3203	0.495960	0.247980	−	0.968765i	$-0.420233\pi$
$433$	10.3203	0.495960	0.247980	+	0.968765i	$0.420233\pi$
$434$	0	0
$435$	1.94988	0.0934897
$436$	6.70847	0.321277
$437$	−3.83778	−0.183586
$438$	0.00754886	0.000360698 0
$439$	12.2653	0.585392	0.292696	−	0.956206i	$-0.405448\pi$
$439$	12.2653	0.585392	0.292696	+	0.956206i	$0.405448\pi$
$440$	−50.3275	−2.39927
$441$	0	0
$442$	−40.0172	−1.90342
$443$	13.2658	0.630278	0.315139	−	0.949046i	$-0.397949\pi$
$443$	13.2658	0.630278	0.315139	+	0.949046i	$0.397949\pi$
$444$	−1.71397	−0.0813413
$445$	−71.6816	−3.39804
$446$	11.3933	0.539491
$447$	−22.2597	−1.05285
$448$	0	0
$449$	3.17388	0.149785	0.0748924	−	0.997192i	$-0.476139\pi$
$449$	3.17388	0.149785	0.0748924	+	0.997192i	$0.476139\pi$
$450$	−16.5996	−0.782512
$451$	−1.79377	−0.0844652
$452$	3.38491	0.159213
$453$	1.58272	0.0743627
$454$	27.3835	1.28517
$455$	0	0
$456$	3.05533	0.143079
$457$	5.47206	0.255972	0.127986	−	0.991776i	$-0.459149\pi$
$457$	5.47206	0.255972	0.127986	+	0.991776i	$0.459149\pi$
$458$	14.2461	0.665675
$459$	7.23298	0.337606
$460$	−7.74926	−0.361311
$461$	−18.0880	−0.842441	−0.421220	−	0.906958i	$-0.638398\pi$
$461$	−18.0880	−0.842441	−0.421220	+	0.906958i	$0.638398\pi$
$462$	0	0
$463$	2.11821	0.0984413	0.0492207	−	0.998788i	$-0.484326\pi$
$463$	2.11821	0.0984413	0.0492207	+	0.998788i	$0.484326\pi$
$464$	1.28920	0.0598495
$465$	−7.88790	−0.365793
$466$	8.15806	0.377915
$467$	23.8611	1.10416	0.552081	−	0.833790i	$-0.313834\pi$
$467$	23.8611	1.10416	0.552081	+	0.833790i	$0.313834\pi$
$468$	2.10455	0.0972830
$469$	0	0
$470$	11.3058	0.521497
$471$	2.69626	0.124237
$472$	23.4514	1.07944
$473$	−44.0617	−2.02596
$474$	5.28448	0.242724
$475$	−13.4219	−0.615841
$476$	0	0
$477$	10.1360	0.464094
$478$	−11.4631	−0.524309
$479$	−13.4660	−0.615277	−0.307639	−	0.951503i	$-0.599539\pi$
$479$	−13.4660	−0.615277	−0.307639	+	0.951503i	$0.599539\pi$
$480$	11.1638	0.509557
$481$	16.2981	0.743130
$482$	−13.2598	−0.603969
$483$	0	0
$484$	−1.75410	−0.0797316
$485$	−34.2540	−1.55539
$486$	1.23675	0.0561001
$487$	−10.1841	−0.461486	−0.230743	−	0.973015i	$-0.574116\pi$
$487$	−10.1841	−0.461486	−0.230743	+	0.973015i	$0.574116\pi$
$488$	29.1022	1.31739
$489$	−4.74027	−0.214363
$490$	0	0
$491$	−35.4486	−1.59977	−0.799887	−	0.600151i	$-0.795107\pi$
$491$	−35.4486	−1.59977	−0.799887	+	0.600151i	$0.795107\pi$
$492$	0.219886	0.00991324
$493$	3.28593	0.147991
$494$	−5.53260	−0.248924
$495$	−16.4721	−0.740364
$496$	−5.21522	−0.234170
$497$	0	0
$498$	14.9941	0.671900
$499$	19.4514	0.870762	0.435381	−	0.900246i	$-0.356614\pi$
$499$	19.4514	0.870762	0.435381	+	0.900246i	$0.356614\pi$
$500$	−17.0056	−0.760514
$501$	−8.36284	−0.373624
$502$	−20.2512	−0.903854
$503$	32.1978	1.43563	0.717814	−	0.696235i	$-0.245143\pi$
$503$	32.1978	1.43563	0.717814	+	0.696235i	$0.245143\pi$
$504$	0	0
$505$	−1.89961	−0.0845316
$506$	18.2156	0.809780
$507$	−7.01221	−0.311423
$508$	−1.25517	−0.0556890
$509$	8.11676	0.359769	0.179885	−	0.983688i	$-0.442428\pi$
$509$	8.11676	0.359769	0.179885	+	0.983688i	$0.442428\pi$
$510$	−38.3943	−1.70013
$511$	0	0
$512$	24.7219	1.09256
$513$	1.00000	0.0441511
$514$	24.8794	1.09738
$515$	63.6464	2.80459
$516$	5.40124	0.237776
$517$	8.17393	0.359489
$518$	0	0
$519$	−8.14296	−0.357436
$520$	−58.6642	−2.57259
$521$	21.6741	0.949560	0.474780	−	0.880104i	$-0.342528\pi$
$521$	21.6741	0.949560	0.474780	+	0.880104i	$0.342528\pi$
$522$	0.561853	0.0245916
$523$	−30.8850	−1.35051	−0.675254	−	0.737585i	$-0.735966\pi$
$523$	−30.8850	−1.35051	−0.675254	+	0.737585i	$0.735966\pi$
$524$	−1.22543	−0.0535330
$525$	0	0
$526$	22.6371	0.987026
$527$	−13.2926	−0.579036
$528$	−10.8908	−0.473960
$529$	−8.27144	−0.359628
$530$	−53.8040	−2.33710
$531$	7.67556	0.333091
$532$	0	0
$533$	−2.09090	−0.0905669
$534$	−20.6549	−0.893823
$535$	57.2216	2.47391
$536$	22.0404	0.952002
$537$	−7.90100	−0.340953
$538$	−2.76409	−0.119169
$539$	0	0
$540$	2.01920	0.0868927
$541$	19.2207	0.826363	0.413181	−	0.910649i	$-0.364418\pi$
$541$	19.2207	0.826363	0.413181	+	0.910649i	$0.364418\pi$
$542$	0.969967	0.0416636
$543$	0.0838648	0.00359898
$544$	18.8132	0.806609
$545$	−61.2038	−2.62168
$546$	0	0
$547$	−4.90765	−0.209836	−0.104918	−	0.994481i	$-0.533458\pi$
$547$	−4.90765	−0.209836	−0.104918	+	0.994481i	$0.533458\pi$
$548$	−4.30613	−0.183949
$549$	9.52505	0.406519
$550$	63.7056	2.71641
$551$	0.454298	0.0193537
$552$	−11.7257	−0.499078
$553$	0	0
$554$	14.7168	0.625259
$555$	15.6372	0.663760
$556$	−0.938026	−0.0397812
$557$	−35.5958	−1.50824	−0.754120	−	0.656736i	$-0.771937\pi$
$557$	−35.5958	−1.50824	−0.754120	+	0.656736i	$0.771937\pi$
$558$	−2.27288	−0.0962185
$559$	−51.3604	−2.17232
$560$	0	0
$561$	−27.7586	−1.17197
$562$	−31.8749	−1.34456
$563$	31.1765	1.31393	0.656967	−	0.753919i	$-0.271839\pi$
$563$	31.1765	1.31393	0.656967	+	0.753919i	$0.271839\pi$
$564$	−1.00199	−0.0421914
$565$	−30.8818	−1.29921
$566$	17.3807	0.730563
$567$	0	0
$568$	8.29662	0.348119
$569$	−10.5786	−0.443477	−0.221739	−	0.975106i	$-0.571173\pi$
$569$	−10.5786	−0.443477	−0.221739	+	0.975106i	$0.571173\pi$
$570$	−5.30823	−0.222337
$571$	−2.35173	−0.0984166	−0.0492083	−	0.998789i	$-0.515670\pi$
$571$	−2.35173	−0.0984166	−0.0492083	+	0.998789i	$0.515670\pi$
$572$	−8.07681	−0.337708
$573$	−18.2775	−0.763555
$574$	0	0
$575$	51.5105	2.14813
$576$	8.89239	0.370516
$577$	38.3811	1.59783	0.798914	−	0.601446i	$-0.205408\pi$
$577$	38.3811	1.59783	0.798914	+	0.601446i	$0.205408\pi$
$578$	−43.6770	−1.81672
$579$	−4.03230	−0.167577
$580$	0.917319	0.0380896
$581$	0	0
$582$	−9.87018	−0.409132
$583$	−38.8996	−1.61106
$584$	0.0186491	0.000771704 0
$585$	−19.2006	−0.793848
$586$	6.94100	0.286730
$587$	21.6337	0.892920	0.446460	−	0.894804i	$-0.352685\pi$
$587$	21.6337	0.892920	0.446460	+	0.894804i	$0.352685\pi$
$588$	0	0
$589$	−1.83778	−0.0757244
$590$	−40.7436	−1.67739
$591$	−14.1002	−0.580006
$592$	10.3388	0.424921
$593$	38.3165	1.57347	0.786735	−	0.617292i	$-0.211770\pi$
$593$	38.3165	1.57347	0.786735	+	0.617292i	$0.211770\pi$
$594$	−4.74638	−0.194746
$595$	0	0
$596$	−10.4721	−0.428952
$597$	−4.90860	−0.200895
$598$	21.2329	0.868279
$599$	−4.94288	−0.201961	−0.100980	−	0.994888i	$-0.532198\pi$
$599$	−4.94288	−0.201961	−0.100980	+	0.994888i	$0.532198\pi$
$600$	−41.0084	−1.67416
$601$	−28.6145	−1.16721	−0.583605	−	0.812037i	$-0.698358\pi$
$601$	−28.6145	−1.16721	−0.583605	+	0.812037i	$0.698358\pi$
$602$	0	0
$603$	7.21377	0.293768
$604$	0.744589	0.0302969
$605$	16.0033	0.650626
$606$	−0.547368	−0.0222353
$607$	−0.324439	−0.0131686	−0.00658428	−	0.999978i	$-0.502096\pi$
$607$	−0.324439	−0.0131686	−0.00658428	+	0.999978i	$0.502096\pi$
$608$	2.60103	0.105486
$609$	0	0
$610$	−50.5612	−2.04716
$611$	9.52793	0.385459
$612$	3.40274	0.137548
$613$	42.2250	1.70545	0.852726	−	0.522358i	$-0.174948\pi$
$613$	42.2250	1.70545	0.852726	+	0.522358i	$0.174948\pi$
$614$	−14.5093	−0.585547
$615$	−2.00610	−0.0808939
$616$	0	0
$617$	17.9849	0.724045	0.362022	−	0.932169i	$-0.382086\pi$
$617$	17.9849	0.724045	0.362022	+	0.932169i	$0.382086\pi$
$618$	18.3395	0.737724
$619$	−18.8612	−0.758095	−0.379048	−	0.925377i	$-0.623748\pi$
$619$	−18.8612	−0.758095	−0.379048	+	0.925377i	$0.623748\pi$
$620$	−3.71085	−0.149031
$621$	−3.83778	−0.154005
$622$	−30.5726	−1.22585
$623$	0	0
$624$	−12.6948	−0.508199
$625$	88.0387	3.52155
$626$	26.2199	1.04796
$627$	−3.83778	−0.153266
$628$	1.26845	0.0506167
$629$	26.3516	1.05071
$630$	0	0
$631$	−20.0512	−0.798226	−0.399113	−	0.916902i	$-0.630682\pi$
$631$	−20.0512	−0.798226	−0.399113	+	0.916902i	$0.630682\pi$
$632$	13.0550	0.519302
$633$	27.1491	1.07908
$634$	−2.18180	−0.0866505
$635$	11.4514	0.454433
$636$	4.76845	0.189081
$637$	0	0
$638$	−2.15627	−0.0853675
$639$	2.71546	0.107422
$640$	−24.8752	−0.983278
$641$	10.9493	0.432473	0.216236	−	0.976341i	$-0.430622\pi$
$641$	10.9493	0.432473	0.216236	+	0.976341i	$0.430622\pi$
$642$	16.4883	0.650740
$643$	−4.14153	−0.163326	−0.0816630	−	0.996660i	$-0.526023\pi$
$643$	−4.14153	−0.163326	−0.0816630	+	0.996660i	$0.526023\pi$
$644$	0	0
$645$	−49.2775	−1.94030
$646$	−8.94539	−0.351951
$647$	7.19398	0.282824	0.141412	−	0.989951i	$-0.454836\pi$
$647$	7.19398	0.282824	0.141412	+	0.989951i	$0.454836\pi$
$648$	3.05533	0.120025
$649$	−29.4571	−1.15629
$650$	74.2583	2.91265
$651$	0	0
$652$	−2.23006	−0.0873357
$653$	17.2865	0.676474	0.338237	−	0.941061i	$-0.390169\pi$
$653$	17.2865	0.676474	0.338237	+	0.941061i	$0.390169\pi$
$654$	−17.6357	−0.689611
$655$	11.1800	0.436840
$656$	−1.32637	−0.0517860
$657$	0.00610378	0.000238131 0
$658$	0	0
$659$	14.3404	0.558623	0.279312	−	0.960201i	$-0.409894\pi$
$659$	14.3404	0.558623	0.279312	+	0.960201i	$0.409894\pi$
$660$	−7.74926	−0.301639
$661$	−47.1233	−1.83289	−0.916443	−	0.400165i	$-0.868953\pi$
$661$	−47.1233	−1.83289	−0.916443	+	0.400165i	$0.868953\pi$
$662$	26.9510	1.04748
$663$	−32.3567	−1.25663
$664$	37.0421	1.43751
$665$	0	0
$666$	4.50580	0.174596
$667$	−1.74350	−0.0675084
$668$	−3.93429	−0.152222
$669$	9.21233	0.356169
$670$	−38.2924	−1.47936
$671$	−36.5551	−1.41119
$672$	0	0
$673$	35.4040	1.36472	0.682361	−	0.731015i	$-0.260953\pi$
$673$	35.4040	1.36472	0.682361	+	0.731015i	$0.260953\pi$
$674$	−23.6450	−0.910773
$675$	−13.4219	−0.516611
$676$	−3.29888	−0.126880
$677$	−0.842449	−0.0323779	−0.0161890	−	0.999869i	$-0.505153\pi$
$677$	−0.842449	−0.0323779	−0.0161890	+	0.999869i	$0.505153\pi$
$678$	−8.89850	−0.341745
$679$	0	0
$680$	−94.8511	−3.63737
$681$	22.1415	0.848465
$682$	8.72280	0.334013
$683$	41.6151	1.59236	0.796178	−	0.605062i	$-0.206852\pi$
$683$	41.6151	1.59236	0.796178	+	0.605062i	$0.206852\pi$
$684$	0.470449	0.0179881
$685$	39.2864	1.50106
$686$	0	0
$687$	11.5190	0.439475
$688$	−32.5807	−1.24213
$689$	−45.3432	−1.72744
$690$	20.3718	0.775542
$691$	38.7731	1.47500	0.737498	−	0.675349i	$-0.236007\pi$
$691$	38.7731	1.47500	0.737498	+	0.675349i	$0.236007\pi$
$692$	−3.83084	−0.145627
$693$	0	0
$694$	12.6192	0.479017
$695$	8.55796	0.324622
$696$	1.38803	0.0526131
$697$	−3.38067	−0.128052
$698$	−34.7565	−1.31555
$699$	6.59636	0.249497
$700$	0	0
$701$	14.1333	0.533807	0.266903	−	0.963723i	$-0.414000\pi$
$701$	14.1333	0.533807	0.266903	+	0.963723i	$0.414000\pi$
$702$	−5.53260	−0.208815
$703$	3.64326	0.137408
$704$	−34.1270	−1.28621
$705$	9.14152	0.344290
$706$	−39.6924	−1.49384
$707$	0	0
$708$	3.61096	0.135708
$709$	14.2279	0.534340	0.267170	−	0.963649i	$-0.413911\pi$
$709$	14.2279	0.534340	0.267170	+	0.963649i	$0.413911\pi$
$710$	−14.4143	−0.540959
$711$	4.27288	0.160245
$712$	−51.0268	−1.91231
$713$	7.05300	0.264137
$714$	0	0
$715$	73.6878	2.75577
$716$	−3.71701	−0.138911
$717$	−9.26870	−0.346146
$718$	21.8058	0.813786
$719$	2.54556	0.0949333	0.0474667	−	0.998873i	$-0.484885\pi$
$719$	2.54556	0.0949333	0.0474667	+	0.998873i	$0.484885\pi$
$720$	−12.1800	−0.453921
$721$	0	0
$722$	−1.23675	−0.0460271
$723$	−10.7215	−0.398737
$724$	0.0394541	0.00146630
$725$	−6.09756	−0.226458
$726$	4.61130	0.171141
$727$	5.40974	0.200636	0.100318	−	0.994955i	$-0.468014\pi$
$727$	5.40974	0.200636	0.100318	+	0.994955i	$0.468014\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.0324003	−0.00119919
$731$	−83.0421	−3.07142
$732$	4.48105	0.165624
$733$	−7.21173	−0.266371	−0.133186	−	0.991091i	$-0.542521\pi$
$733$	−7.21173	−0.266371	−0.133186	+	0.991091i	$0.542521\pi$
$734$	−9.17155	−0.338528
$735$	0	0
$736$	−9.98218	−0.367948
$737$	−27.6849	−1.01979
$738$	−0.578053	−0.0212784
$739$	−46.1945	−1.69929	−0.849646	−	0.527353i	$-0.823184\pi$
$739$	−46.1945	−1.69929	−0.849646	+	0.527353i	$0.823184\pi$
$740$	7.35648	0.270430
$741$	−4.47350	−0.164338
$742$	0	0
$743$	−1.30572	−0.0479023	−0.0239511	−	0.999713i	$-0.507625\pi$
$743$	−1.30572	−0.0479023	−0.0239511	+	0.999713i	$0.507625\pi$
$744$	−5.61502	−0.205857
$745$	95.5405	3.50033
$746$	32.1230	1.17611
$747$	12.1238	0.443585
$748$	−13.0590	−0.477484
$749$	0	0
$750$	44.7056	1.63242
$751$	−20.8185	−0.759678	−0.379839	−	0.925053i	$-0.624021\pi$
$751$	−20.8185	−0.759678	−0.379839	+	0.925053i	$0.624021\pi$
$752$	6.04407	0.220405
$753$	−16.3745	−0.596720
$754$	−2.51345	−0.0915344
$755$	−6.79316	−0.247229
$756$	0	0
$757$	28.4398	1.03366	0.516830	−	0.856088i	$-0.327112\pi$
$757$	28.4398	1.03366	0.516830	+	0.856088i	$0.327112\pi$
$758$	−25.8899	−0.940365
$759$	14.7286	0.534613
$760$	−13.1137	−0.475684
$761$	−5.69284	−0.206365	−0.103183	−	0.994662i	$-0.532903\pi$
$761$	−5.69284	−0.206365	−0.103183	+	0.994662i	$0.532903\pi$
$762$	3.29968	0.119535
$763$	0	0
$764$	−8.59864	−0.311088
$765$	−31.0445	−1.12242
$766$	−10.3428	−0.373699
$767$	−34.3366	−1.23982
$768$	10.6171	0.383110
$769$	−30.6175	−1.10410	−0.552048	−	0.833812i	$-0.686154\pi$
$769$	−30.6175	−1.10410	−0.552048	+	0.833812i	$0.686154\pi$
$770$	0	0
$771$	20.1168	0.724487
$772$	−1.89699	−0.0682742
$773$	−10.8949	−0.391864	−0.195932	−	0.980617i	$-0.562773\pi$
$773$	−10.8949	−0.391864	−0.195932	+	0.980617i	$0.562773\pi$
$774$	−14.1992	−0.510379
$775$	24.6666	0.886050
$776$	−24.3838	−0.875327
$777$	0	0
$778$	38.1786	1.36877
$779$	−0.467397	−0.0167462
$780$	−9.03290	−0.323430
$781$	−10.4213	−0.372905
$782$	34.3304	1.22765
$783$	0.454298	0.0162353
$784$	0	0
$785$	−11.5726	−0.413042
$786$	3.22149	0.114907
$787$	10.4481	0.372436	0.186218	−	0.982508i	$-0.440377\pi$
$787$	10.4481	0.372436	0.186218	+	0.982508i	$0.440377\pi$
$788$	−6.63344	−0.236306
$789$	18.3037	0.651630
$790$	−22.6814	−0.806968
$791$	0	0
$792$	−11.7257	−0.416654
$793$	−42.6103	−1.51314
$794$	−22.1340	−0.785505
$795$	−43.5043	−1.54294
$796$	−2.30924	−0.0818489
$797$	−41.2326	−1.46053	−0.730266	−	0.683163i	$-0.760604\pi$
$797$	−41.2326	−1.46053	−0.730266	+	0.683163i	$0.760604\pi$
$798$	0	0
$799$	15.4052	0.544997
$800$	−34.9109	−1.23429
$801$	−16.7009	−0.590098
$802$	6.09267	0.215140
$803$	−0.0234250	−0.000826650 0
$804$	3.39371	0.119687
$805$	0	0
$806$	10.1677	0.358142
$807$	−2.23497	−0.0786745
$808$	−1.35224	−0.0475718
$809$	8.04952	0.283006	0.141503	−	0.989938i	$-0.454806\pi$
$809$	8.04952	0.283006	0.141503	+	0.989938i	$0.454806\pi$
$810$	−5.30823	−0.186512
$811$	−35.4269	−1.24401	−0.622004	−	0.783014i	$-0.713681\pi$
$811$	−35.4269	−1.24401	−0.622004	+	0.783014i	$0.713681\pi$
$812$	0	0
$813$	0.784287	0.0275061
$814$	−17.2923	−0.606094
$815$	20.3456	0.712676
$816$	−20.5256	−0.718540
$817$	−11.4810	−0.401671
$818$	30.6653	1.07219
$819$	0	0
$820$	−0.943769	−0.0329578
$821$	0.805488	0.0281117	0.0140559	−	0.999901i	$-0.495526\pi$
$821$	0.805488	0.0281117	0.0140559	+	0.999901i	$0.495526\pi$
$822$	11.3203	0.394840
$823$	24.3070	0.847288	0.423644	−	0.905829i	$-0.360751\pi$
$823$	24.3070	0.847288	0.423644	+	0.905829i	$0.360751\pi$
$824$	45.3068	1.57834
$825$	51.5105	1.79336
$826$	0	0
$827$	−2.20812	−0.0767837	−0.0383918	−	0.999263i	$-0.512224\pi$
$827$	−2.20812	−0.0767837	−0.0383918	+	0.999263i	$0.512224\pi$
$828$	−1.80548	−0.0627447
$829$	48.9248	1.69923	0.849615	−	0.527403i	$-0.176834\pi$
$829$	48.9248	1.69923	0.849615	+	0.527403i	$0.176834\pi$
$830$	−64.3557	−2.23382
$831$	11.8996	0.412793
$832$	−39.7801	−1.37913
$833$	0	0
$834$	2.46595	0.0853889
$835$	35.8940	1.24216
$836$	−1.80548	−0.0624438
$837$	−1.83778	−0.0635230
$838$	11.8021	0.407696
$839$	52.6197	1.81663	0.908316	−	0.418284i	$-0.137368\pi$
$839$	52.6197	1.81663	0.908316	+	0.418284i	$0.137368\pi$
$840$	0	0
$841$	−28.7936	−0.992883
$842$	17.0670	0.588167
$843$	−25.7731	−0.887673
$844$	12.7722	0.439639
$845$	30.0969	1.03537
$846$	2.63410	0.0905624
$847$	0	0
$848$	−28.7636	−0.987747
$849$	14.0535	0.482314
$850$	120.064	4.11817
$851$	−13.9820	−0.479298
$852$	1.27749	0.0437659
$853$	17.9120	0.613294	0.306647	−	0.951823i	$-0.400793\pi$
$853$	17.9120	0.613294	0.306647	+	0.951823i	$0.400793\pi$
$854$	0	0
$855$	−4.29208	−0.146786
$856$	40.7334	1.39224
$857$	−52.5770	−1.79599	−0.897997	−	0.440001i	$-0.854978\pi$
$857$	−52.5770	−1.79599	−0.897997	+	0.440001i	$0.854978\pi$
$858$	21.2329	0.724880
$859$	−11.6110	−0.396161	−0.198080	−	0.980186i	$-0.563471\pi$
$859$	−11.6110	−0.396161	−0.198080	+	0.980186i	$0.563471\pi$
$860$	−23.1825	−0.790518
$861$	0	0
$862$	43.9007	1.49527
$863$	36.5922	1.24561	0.622807	−	0.782375i	$-0.285992\pi$
$863$	36.5922	1.24561	0.622807	+	0.782375i	$0.285992\pi$
$864$	2.60103	0.0884888
$865$	34.9502	1.18834
$866$	−12.7636	−0.433724
$867$	−35.3159	−1.19939
$868$	0	0
$869$	−16.3984	−0.556276
$870$	−2.41152	−0.0817581
$871$	−32.2708	−1.09345
$872$	−43.5681	−1.47540
$873$	−7.98074	−0.270107
$874$	4.74638	0.160549
$875$	0	0
$876$	0.00287152	9.70196e−5 0
$877$	−38.8795	−1.31287	−0.656434	−	0.754384i	$-0.727936\pi$
$877$	−38.8795	−1.31287	−0.656434	+	0.754384i	$0.727936\pi$
$878$	−15.1691	−0.511934
$879$	5.61229	0.189298
$880$	46.7441	1.57574
$881$	9.43419	0.317846	0.158923	−	0.987291i	$-0.449198\pi$
$881$	9.43419	0.317846	0.158923	+	0.987291i	$0.449198\pi$
$882$	0	0
$883$	14.5195	0.488619	0.244309	−	0.969697i	$-0.421439\pi$
$883$	14.5195	0.488619	0.244309	+	0.969697i	$0.421439\pi$
$884$	−15.2222	−0.511977
$885$	−32.9441	−1.10740
$886$	−16.4065	−0.551187
$887$	27.8350	0.934609	0.467305	−	0.884096i	$-0.345225\pi$
$887$	27.8350	0.934609	0.467305	+	0.884096i	$0.345225\pi$
$888$	11.1314	0.373544
$889$	0	0
$890$	88.6523	2.97163
$891$	−3.83778	−0.128570
$892$	4.33393	0.145111
$893$	2.12986	0.0712730
$894$	27.5297	0.920731
$895$	33.9117	1.13354
$896$	0	0
$897$	17.1683	0.573233
$898$	−3.92530	−0.130989
$899$	−0.834900	−0.0278455
$900$	−6.31433	−0.210478
$901$	−73.3132	−2.44242
$902$	2.21844	0.0738660
$903$	0	0
$904$	−21.9833	−0.731153
$905$	−0.359954	−0.0119653
$906$	−1.95743	−0.0650313
$907$	12.1346	0.402922	0.201461	−	0.979497i	$-0.435431\pi$
$907$	12.1346	0.402922	0.201461	+	0.979497i	$0.435431\pi$
$908$	10.4164	0.345682
$909$	−0.442585	−0.0146796
$910$	0	0
$911$	−38.0759	−1.26151	−0.630755	−	0.775982i	$-0.717255\pi$
$911$	−38.0759	−1.26151	−0.630755	+	0.775982i	$0.717255\pi$
$912$	−2.83778	−0.0939683
$913$	−46.5283	−1.53986
$914$	−6.76758	−0.223852
$915$	−40.8823	−1.35153
$916$	5.41908	0.179051
$917$	0	0
$918$	−8.94539	−0.295242
$919$	−29.9242	−0.987107	−0.493553	−	0.869715i	$-0.664302\pi$
$919$	−29.9242	−0.987107	−0.493553	+	0.869715i	$0.664302\pi$
$920$	50.3275	1.65925
$921$	−11.7318	−0.386575
$922$	22.3703	0.736727
$923$	−12.1476	−0.399844
$924$	0	0
$925$	−48.8996	−1.60781
$926$	−2.61969	−0.0860884
$927$	14.8288	0.487042
$928$	1.18164	0.0387893
$929$	39.4140	1.29313	0.646565	−	0.762859i	$-0.276205\pi$
$929$	39.4140	1.29313	0.646565	+	0.762859i	$0.276205\pi$
$930$	9.75536	0.319891
$931$	0	0
$932$	3.10325	0.101650
$933$	−24.7201	−0.809300
$934$	−29.5103	−0.965606
$935$	119.142	3.89636
$936$	−13.6680	−0.446753
$937$	12.7286	0.415824	0.207912	−	0.978148i	$-0.433333\pi$
$937$	12.7286	0.415824	0.207912	+	0.978148i	$0.433333\pi$
$938$	0	0
$939$	21.2006	0.691856
$940$	4.30062	0.140271
$941$	−24.5151	−0.799170	−0.399585	−	0.916696i	$-0.630846\pi$
$941$	−24.5151	−0.799170	−0.399585	+	0.916696i	$0.630846\pi$
$942$	−3.33460	−0.108647
$943$	1.79377	0.0584131
$944$	−21.7816	−0.708929
$945$	0	0
$946$	54.4933	1.77173
$947$	−21.5162	−0.699183	−0.349591	−	0.936902i	$-0.613680\pi$
$947$	−21.5162	−0.699183	−0.349591	+	0.936902i	$0.613680\pi$
$948$	2.01017	0.0652872
$949$	−0.0273053	−0.000886367 0
$950$	16.5996	0.538562
$951$	−1.76414	−0.0572063
$952$	0	0
$953$	7.15164	0.231665	0.115832	−	0.993269i	$-0.463046\pi$
$953$	7.15164	0.231665	0.115832	+	0.993269i	$0.463046\pi$
$954$	−12.5357	−0.405857
$955$	78.4486	2.53854
$956$	−4.36045	−0.141027
$957$	−1.74350	−0.0563592
$958$	16.6541	0.538069
$959$	0	0
$960$	−38.1668	−1.23183
$961$	−27.6226	−0.891050
$962$	−20.1567	−0.649878
$963$	13.3319	0.429615
$964$	−5.04392	−0.162454
$965$	17.3070	0.557131
$966$	0	0
$967$	−9.09487	−0.292471	−0.146236	−	0.989250i	$-0.546716\pi$
$967$	−9.09487	−0.292471	−0.146236	+	0.989250i	$0.546716\pi$
$968$	11.3920	0.366152
$969$	−7.23298	−0.232357
$970$	42.3636	1.36021
$971$	−24.6750	−0.791857	−0.395929	−	0.918281i	$-0.629577\pi$
$971$	−24.6750	−0.791857	−0.395929	+	0.918281i	$0.629577\pi$
$972$	0.470449	0.0150896
$973$	0	0
$974$	12.5952	0.403576
$975$	60.0430	1.92292
$976$	−27.0300	−0.865210
$977$	38.8796	1.24387	0.621934	−	0.783069i	$-0.286347\pi$
$977$	38.8796	1.24387	0.621934	+	0.783069i	$0.286347\pi$
$978$	5.86253	0.187463
$979$	64.0945	2.04847
$980$	0	0
$981$	−14.2597	−0.455278
$982$	43.8411	1.39903
$983$	32.6884	1.04260	0.521298	−	0.853375i	$-0.325448\pi$
$983$	32.6884	1.04260	0.521298	+	0.853375i	$0.325448\pi$
$984$	−1.42805	−0.0455246
$985$	60.5193	1.92831
$986$	−4.06387	−0.129420
$987$	0	0
$988$	−2.10455	−0.0669547
$989$	44.0617	1.40108
$990$	20.3718	0.647459
$991$	−35.2493	−1.11973	−0.559865	−	0.828584i	$-0.689147\pi$
$991$	−35.2493	−1.11973	−0.559865	+	0.828584i	$0.689147\pi$
$992$	−4.78012	−0.151769
$993$	21.7918	0.691543
$994$	0	0
$995$	21.0681	0.667903
$996$	5.70360	0.180726
$997$	9.98278	0.316158	0.158079	−	0.987426i	$-0.449470\pi$
$997$	9.98278	0.316158	0.158079	+	0.987426i	$0.449470\pi$
$998$	−24.0565	−0.761494
$999$	3.64326	0.115268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2793.2.a.be.1.2		5
3.2	odd	2		8379.2.a.ce.1.4		5
7.6	odd	2		399.2.a.f.1.2	✓	5
21.20	even	2		1197.2.a.p.1.4		5
28.27	even	2		6384.2.a.cc.1.1		5
35.34	odd	2		9975.2.a.bq.1.4		5
133.132	even	2		7581.2.a.x.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.a.f.1.2	✓	5	7.6	odd	2
1197.2.a.p.1.4		5	21.20	even	2
2793.2.a.be.1.2		5	1.1	even	1	trivial
6384.2.a.cc.1.1		5	28.27	even	2
7581.2.a.x.1.4		5	133.132	even	2
8379.2.a.ce.1.4		5	3.2	odd	2
9975.2.a.bq.1.4		5	35.34	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:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2793.a (trivial)

\(f(q)\)	\(=\)	\(q-1.23675 q^{2} -1.00000 q^{3} -0.470449 q^{4} +4.29208 q^{5} +1.23675 q^{6} +3.05533 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.23675 q^{2} -1.00000 q^{3} -0.470449 q^{4} +4.29208 q^{5} +1.23675 q^{6} +3.05533 q^{8} +1.00000 q^{9} -5.30823 q^{10} -3.83778 q^{11} +0.470449 q^{12} -4.47350 q^{13} -4.29208 q^{15} -2.83778 q^{16} -7.23298 q^{17} -1.23675 q^{18} -1.00000 q^{19} -2.01920 q^{20} +4.74638 q^{22} +3.83778 q^{23} -3.05533 q^{24} +13.4219 q^{25} +5.53260 q^{26} -1.00000 q^{27} -0.454298 q^{29} +5.30823 q^{30} +1.83778 q^{31} -2.60103 q^{32} +3.83778 q^{33} +8.94539 q^{34} -0.470449 q^{36} -3.64326 q^{37} +1.23675 q^{38} +4.47350 q^{39} +13.1137 q^{40} +0.467397 q^{41} +11.4810 q^{43} +1.80548 q^{44} +4.29208 q^{45} -4.74638 q^{46} -2.12986 q^{47} +2.83778 q^{48} -16.5996 q^{50} +7.23298 q^{51} +2.10455 q^{52} +10.1360 q^{53} +1.23675 q^{54} -16.4721 q^{55} +1.00000 q^{57} +0.561853 q^{58} +7.67556 q^{59} +2.01920 q^{60} +9.52505 q^{61} -2.27288 q^{62} +8.89239 q^{64} -19.2006 q^{65} -4.74638 q^{66} +7.21377 q^{67} +3.40274 q^{68} -3.83778 q^{69} +2.71546 q^{71} +3.05533 q^{72} +0.00610378 q^{73} +4.50580 q^{74} -13.4219 q^{75} +0.470449 q^{76} -5.53260 q^{78} +4.27288 q^{79} -12.1800 q^{80} +1.00000 q^{81} -0.578053 q^{82} +12.1238 q^{83} -31.0445 q^{85} -14.1992 q^{86} +0.454298 q^{87} -11.7257 q^{88} -16.7009 q^{89} -5.30823 q^{90} -1.80548 q^{92} -1.83778 q^{93} +2.63410 q^{94} -4.29208 q^{95} +2.60103 q^{96} -7.98074 q^{97} -3.83778 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 7 q^{12} - 8 q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 2 q^{23} - 3 q^{24} + 11 q^{25} + 32 q^{26} - 5 q^{27} - 8 q^{31} - 3 q^{32} + 2 q^{33} + 8 q^{34} + 7 q^{36} + 2 q^{37} - q^{38} + 8 q^{39} + 36 q^{40} - 2 q^{41} + 20 q^{43} + 6 q^{44} + 2 q^{45} - 2 q^{46} + 26 q^{47} - 3 q^{48} - q^{50} - 2 q^{51} - 4 q^{52} + 4 q^{53} - q^{54} + 4 q^{55} + 5 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} - 10 q^{61} - 4 q^{62} - 21 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} + 58 q^{68} - 2 q^{69} + 10 q^{71} + 3 q^{72} - 10 q^{73} - 6 q^{74} - 11 q^{75} - 7 q^{76} - 32 q^{78} + 14 q^{79} + 6 q^{80} + 5 q^{81} + 26 q^{82} + 34 q^{83} - 36 q^{85} + 8 q^{86} + 6 q^{88} - 10 q^{89} - 6 q^{92} + 8 q^{93} + 8 q^{94} - 2 q^{95} + 3 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 7 * q^12 - 8 * q^13 - 2 * q^15 + 3 * q^16 + 2 * q^17 + q^18 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 2 * q^23 - 3 * q^24 + 11 * q^25 + 32 * q^26 - 5 * q^27 - 8 * q^31 - 3 * q^32 + 2 * q^33 + 8 * q^34 + 7 * q^36 + 2 * q^37 - q^38 + 8 * q^39 + 36 * q^40 - 2 * q^41 + 20 * q^43 + 6 * q^44 + 2 * q^45 - 2 * q^46 + 26 * q^47 - 3 * q^48 - q^50 - 2 * q^51 - 4 * q^52 + 4 * q^53 - q^54 + 4 * q^55 + 5 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 - 10 * q^61 - 4 * q^62 - 21 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 + 58 * q^68 - 2 * q^69 + 10 * q^71 + 3 * q^72 - 10 * q^73 - 6 * q^74 - 11 * q^75 - 7 * q^76 - 32 * q^78 + 14 * q^79 + 6 * q^80 + 5 * q^81 + 26 * q^82 + 34 * q^83 - 36 * q^85 + 8 * q^86 + 6 * q^88 - 10 * q^89 - 6 * q^92 + 8 * q^93 + 8 * q^94 - 2 * q^95 + 3 * q^96 + 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more