LMFDB - Embedded newform 2523.2.a.r.1.6

Error: table mf_hecke_newspace_traces does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2523,2,Mod(1,2523)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2523.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2523, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2523.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,5,9,11,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$20.1462564300$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 6x^{7} + 33x^{6} + 6x^{5} - 90x^{4} + 21x^{3} + 84x^{2} - 36x - 8 $ x^9 - 4x^8 - 6x^7 + 33x^6 + 6x^5 - 90x^4 + 21x^3 + 84x^2 - 36x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.163909$ of defining polynomial
Character	$\chi$	$=$	2523.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.16391 q^{2} +1.00000 q^{3} -0.645316 q^{4} +3.11042 q^{5} +1.16391 q^{6} +1.74624 q^{7} -3.07891 q^{8} +1.00000 q^{9} +3.62025 q^{10} -2.77225 q^{11} -0.645316 q^{12} -1.15295 q^{13} +2.03246 q^{14} +3.11042 q^{15} -2.29294 q^{16} +2.64265 q^{17} +1.16391 q^{18} +7.22436 q^{19} -2.00720 q^{20} +1.74624 q^{21} -3.22665 q^{22} -2.81031 q^{23} -3.07891 q^{24} +4.67473 q^{25} -1.34193 q^{26} +1.00000 q^{27} -1.12688 q^{28} +3.62025 q^{30} +3.98533 q^{31} +3.48904 q^{32} -2.77225 q^{33} +3.07581 q^{34} +5.43154 q^{35} -0.645316 q^{36} +10.4698 q^{37} +8.40850 q^{38} -1.15295 q^{39} -9.57670 q^{40} +8.92649 q^{41} +2.03246 q^{42} +11.7961 q^{43} +1.78898 q^{44} +3.11042 q^{45} -3.27095 q^{46} -7.34522 q^{47} -2.29294 q^{48} -3.95065 q^{49} +5.44096 q^{50} +2.64265 q^{51} +0.744019 q^{52} -5.38657 q^{53} +1.16391 q^{54} -8.62288 q^{55} -5.37651 q^{56} +7.22436 q^{57} -8.20042 q^{59} -2.00720 q^{60} +4.90841 q^{61} +4.63856 q^{62} +1.74624 q^{63} +8.64680 q^{64} -3.58617 q^{65} -3.22665 q^{66} -0.453589 q^{67} -1.70534 q^{68} -2.81031 q^{69} +6.32182 q^{70} +11.6046 q^{71} -3.07891 q^{72} -12.8553 q^{73} +12.1859 q^{74} +4.67473 q^{75} -4.66199 q^{76} -4.84102 q^{77} -1.34193 q^{78} -15.4177 q^{79} -7.13200 q^{80} +1.00000 q^{81} +10.3896 q^{82} -4.21480 q^{83} -1.12688 q^{84} +8.21977 q^{85} +13.7296 q^{86} +8.53551 q^{88} -2.03195 q^{89} +3.62025 q^{90} -2.01333 q^{91} +1.81354 q^{92} +3.98533 q^{93} -8.54917 q^{94} +22.4708 q^{95} +3.48904 q^{96} +12.6660 q^{97} -4.59819 q^{98} -2.77225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 5 q^{2} + 9 q^{3} + 11 q^{4} - 4 q^{5} + 5 q^{6} + 5 q^{7} + 24 q^{8} + 9 q^{9} - q^{11} + 11 q^{12} + q^{13} + 9 q^{14} - 4 q^{15} + 35 q^{16} + 2 q^{17} + 5 q^{18} + 9 q^{19} - 18 q^{20} + 5 q^{21}+ \cdots - q^{99}+O(q^{100}) $ 9 * q + 5 * q^2 + 9 * q^3 + 11 * q^4 - 4 * q^5 + 5 * q^6 + 5 * q^7 + 24 * q^8 + 9 * q^9 - q^11 + 11 * q^12 + q^13 + 9 * q^14 - 4 * q^15 + 35 * q^16 + 2 * q^17 + 5 * q^18 + 9 * q^19 - 18 * q^20 + 5 * q^21 - 4 * q^22 - 4 * q^23 + 24 * q^24 + q^25 - 8 * q^26 + 9 * q^27 + 40 * q^28 + 8 * q^31 + 43 * q^32 - q^33 - 4 * q^34 + 22 * q^35 + 11 * q^36 + 27 * q^37 - 30 * q^38 + q^39 - 29 * q^40 + 12 * q^41 + 9 * q^42 + 16 * q^43 + 37 * q^44 - 4 * q^45 - 22 * q^46 - 8 * q^47 + 35 * q^48 - 6 * q^49 - 7 * q^50 + 2 * q^51 + 33 * q^52 - 8 * q^53 + 5 * q^54 + 9 * q^55 + 40 * q^56 + 9 * q^57 - 16 * q^59 - 18 * q^60 + 21 * q^61 - 32 * q^62 + 5 * q^63 + 36 * q^64 - 31 * q^65 - 4 * q^66 + 3 * q^67 + 33 * q^68 - 4 * q^69 - 6 * q^70 - 33 * q^71 + 24 * q^72 + 3 * q^73 + 28 * q^74 + q^75 - 26 * q^76 + 24 * q^77 - 8 * q^78 + 3 * q^79 - 64 * q^80 + 9 * q^81 + 13 * q^82 + 13 * q^83 + 40 * q^84 + 6 * q^85 + 58 * q^86 + 27 * q^88 + 6 * q^89 + q^91 - 29 * q^92 + 8 * q^93 - 18 * q^94 + 48 * q^95 + 43 * q^96 + 4 * q^97 - 30 * q^98 - q^99

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 $

$2$	1.16391	0.823008	0.411504	−	0.911408i	$-0.365004\pi$
$2$	1.16391	0.823008	0.411504	+	0.911408i	$0.365004\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.645316	−0.322658
$5$	3.11042	1.39102	0.695512	−	0.718515i	$-0.255178\pi$
$5$	3.11042	1.39102	0.695512	+	0.718515i	$0.255178\pi$
$6$	1.16391	0.475164
$7$	1.74624	0.660017	0.330008	−	0.943978i	$-0.392948\pi$
$7$	1.74624	0.660017	0.330008	+	0.943978i	$0.392948\pi$
$8$	−3.07891	−1.08856
$9$	1.00000	0.333333
$10$	3.62025	1.14482
$11$	−2.77225	−0.835866	−0.417933	−	0.908478i	$-0.637245\pi$
$11$	−2.77225	−0.835866	−0.417933	+	0.908478i	$0.637245\pi$
$12$	−0.645316	−0.186287
$13$	−1.15295	−0.319772	−0.159886	−	0.987136i	$-0.551113\pi$
$13$	−1.15295	−0.319772	−0.159886	+	0.987136i	$0.551113\pi$
$14$	2.03246	0.543199
$15$	3.11042	0.803108
$16$	−2.29294	−0.573234
$17$	2.64265	0.640937	0.320469	−	0.947259i	$-0.396160\pi$
$17$	2.64265	0.640937	0.320469	+	0.947259i	$0.396160\pi$
$18$	1.16391	0.274336
$19$	7.22436	1.65738	0.828691	−	0.559707i	$-0.189086\pi$
$19$	7.22436	1.65738	0.828691	+	0.559707i	$0.189086\pi$
$20$	−2.00720	−0.448824
$21$	1.74624	0.381061
$22$	−3.22665	−0.687925
$23$	−2.81031	−0.585991	−0.292995	−	0.956114i	$-0.594652\pi$
$23$	−2.81031	−0.585991	−0.292995	+	0.956114i	$0.594652\pi$
$24$	−3.07891	−0.628479
$25$	4.67473	0.934945
$26$	−1.34193	−0.263175
$27$	1.00000	0.192450
$28$	−1.12688	−0.212959
$29$	0	0
$29$	0	0
$30$	3.62025	0.660964
$31$	3.98533	0.715786	0.357893	−	0.933763i	$-0.383495\pi$
$31$	3.98533	0.715786	0.357893	+	0.933763i	$0.383495\pi$
$32$	3.48904	0.616782
$33$	−2.77225	−0.482588
$34$	3.07581	0.527497
$35$	5.43154	0.918098
$36$	−0.645316	−0.107553
$37$	10.4698	1.72123	0.860613	−	0.509260i	$-0.170081\pi$
$37$	10.4698	1.72123	0.860613	+	0.509260i	$0.170081\pi$
$38$	8.40850	1.36404
$39$	−1.15295	−0.184620
$40$	−9.57670	−1.51421
$41$	8.92649	1.39408	0.697041	−	0.717031i	$-0.254499\pi$
$41$	8.92649	1.39408	0.697041	+	0.717031i	$0.254499\pi$
$42$	2.03246	0.313616
$43$	11.7961	1.79889	0.899446	−	0.437031i	$-0.143970\pi$
$43$	11.7961	1.79889	0.899446	+	0.437031i	$0.143970\pi$
$44$	1.78898	0.269699
$45$	3.11042	0.463674
$46$	−3.27095	−0.482275
$47$	−7.34522	−1.07141	−0.535705	−	0.844405i	$-0.679954\pi$
$47$	−7.34522	−1.07141	−0.535705	+	0.844405i	$0.679954\pi$
$48$	−2.29294	−0.330957
$49$	−3.95065	−0.564378
$50$	5.44096	0.769468
$51$	2.64265	0.370045
$52$	0.744019	0.103177
$53$	−5.38657	−0.739903	−0.369951	−	0.929051i	$-0.620626\pi$
$53$	−5.38657	−0.739903	−0.369951	+	0.929051i	$0.620626\pi$
$54$	1.16391	0.158388
$55$	−8.62288	−1.16271
$56$	−5.37651	−0.718466
$57$	7.22436	0.956889
$58$	0	0
$59$	−8.20042	−1.06760	−0.533802	−	0.845610i	$-0.679237\pi$
$59$	−8.20042	−1.06760	−0.533802	+	0.845610i	$0.679237\pi$
$60$	−2.00720	−0.259129
$61$	4.90841	0.628458	0.314229	−	0.949347i	$-0.398254\pi$
$61$	4.90841	0.628458	0.314229	+	0.949347i	$0.398254\pi$
$62$	4.63856	0.589098
$63$	1.74624	0.220006
$64$	8.64680	1.08085
$65$	−3.58617	−0.444810
$66$	−3.22665	−0.397173
$67$	−0.453589	−0.0554147	−0.0277074	−	0.999616i	$-0.508821\pi$
$67$	−0.453589	−0.0554147	−0.0277074	+	0.999616i	$0.508821\pi$
$68$	−1.70534	−0.206803
$69$	−2.81031	−0.338322
$70$	6.32182	0.755602
$71$	11.6046	1.37721	0.688606	−	0.725136i	$-0.258223\pi$
$71$	11.6046	1.37721	0.688606	+	0.725136i	$0.258223\pi$
$72$	−3.07891	−0.362853
$73$	−12.8553	−1.50460	−0.752298	−	0.658823i	$-0.771055\pi$
$73$	−12.8553	−1.50460	−0.752298	+	0.658823i	$0.771055\pi$
$74$	12.1859	1.41658
$75$	4.67473	0.539791
$76$	−4.66199	−0.534767
$77$	−4.84102	−0.551686
$78$	−1.34193	−0.151944
$79$	−15.4177	−1.73463	−0.867314	−	0.497761i	$-0.834156\pi$
$79$	−15.4177	−1.73463	−0.867314	+	0.497761i	$0.834156\pi$
$80$	−7.13200	−0.797382
$81$	1.00000	0.111111
$82$	10.3896	1.14734
$83$	−4.21480	−0.462635	−0.231317	−	0.972878i	$-0.574304\pi$
$83$	−4.21480	−0.462635	−0.231317	+	0.972878i	$0.574304\pi$
$84$	−1.12688	−0.122952
$85$	8.21977	0.891559
$86$	13.7296	1.48050
$87$	0	0
$88$	8.53551	0.909889
$89$	−2.03195	−0.215386	−0.107693	−	0.994184i	$-0.534346\pi$
$89$	−2.03195	−0.215386	−0.107693	+	0.994184i	$0.534346\pi$
$90$	3.62025	0.381608
$91$	−2.01333	−0.211055
$92$	1.81354	0.189075
$93$	3.98533	0.413259
$94$	−8.54917	−0.881779
$95$	22.4708	2.30546
$96$	3.48904	0.356099
$97$	12.6660	1.28604	0.643018	−	0.765851i	$-0.277682\pi$
$97$	12.6660	1.28604	0.643018	+	0.765851i	$0.277682\pi$
$98$	−4.59819	−0.464488
$99$	−2.77225	−0.278622
$100$	−3.01667	−0.301667
$101$	3.16539	0.314968	0.157484	−	0.987522i	$-0.449662\pi$
$101$	3.16539	0.314968	0.157484	+	0.987522i	$0.449662\pi$
$102$	3.07581	0.304550
$103$	2.61991	0.258148	0.129074	−	0.991635i	$-0.458800\pi$
$103$	2.61991	0.258148	0.129074	+	0.991635i	$0.458800\pi$
$104$	3.54984	0.348090
$105$	5.43154	0.530064
$106$	−6.26948	−0.608946
$107$	−10.0408	−0.970685	−0.485343	−	0.874324i	$-0.661305\pi$
$107$	−10.0408	−0.970685	−0.485343	+	0.874324i	$0.661305\pi$
$108$	−0.645316	−0.0620955
$109$	−4.61764	−0.442290	−0.221145	−	0.975241i	$-0.570979\pi$
$109$	−4.61764	−0.442290	−0.221145	+	0.975241i	$0.570979\pi$
$110$	−10.0363	−0.956919
$111$	10.4698	0.993750
$112$	−4.00402	−0.378344
$113$	−5.18977	−0.488212	−0.244106	−	0.969749i	$-0.578495\pi$
$113$	−5.18977	−0.488212	−0.244106	+	0.969749i	$0.578495\pi$
$114$	8.40850	0.787528
$115$	−8.74126	−0.815127
$116$	0	0
$117$	−1.15295	−0.106591
$118$	−9.54454	−0.878646
$119$	4.61470	0.423029
$120$	−9.57670	−0.874229
$121$	−3.31460	−0.301328
$122$	5.71295	0.517226
$123$	8.92649	0.804874
$124$	−2.57179	−0.230954
$125$	−1.01174	−0.0904924
$126$	2.03246	0.181066
$127$	−15.0144	−1.33231	−0.666156	−	0.745812i	$-0.732062\pi$
$127$	−15.0144	−1.33231	−0.666156	+	0.745812i	$0.732062\pi$
$128$	3.08601	0.272767
$129$	11.7961	1.03859
$130$	−4.17398	−0.366082
$131$	−0.535351	−0.0467738	−0.0233869	−	0.999726i	$-0.507445\pi$
$131$	−0.535351	−0.0467738	−0.0233869	+	0.999726i	$0.507445\pi$
$132$	1.78898	0.155711
$133$	12.6155	1.09390
$134$	−0.527936	−0.0456068
$135$	3.11042	0.267703
$136$	−8.13648	−0.697697
$137$	12.4709	1.06546	0.532729	−	0.846286i	$-0.321167\pi$
$137$	12.4709	1.06546	0.532729	+	0.846286i	$0.321167\pi$
$138$	−3.27095	−0.278442
$139$	−8.68832	−0.736933	−0.368467	−	0.929641i	$-0.620117\pi$
$139$	−8.68832	−0.736933	−0.368467	+	0.929641i	$0.620117\pi$
$140$	−3.50506	−0.296232
$141$	−7.34522	−0.618579
$142$	13.5067	1.13346
$143$	3.19628	0.267286
$144$	−2.29294	−0.191078
$145$	0	0
$146$	−14.9624	−1.23830
$147$	−3.95065	−0.325844
$148$	−6.75633	−0.555367
$149$	−15.0304	−1.23134	−0.615668	−	0.788006i	$-0.711114\pi$
$149$	−15.0304	−1.23134	−0.615668	+	0.788006i	$0.711114\pi$
$150$	5.44096	0.444252
$151$	15.0837	1.22750	0.613749	−	0.789501i	$-0.289661\pi$
$151$	15.0837	1.22750	0.613749	+	0.789501i	$0.289661\pi$
$152$	−22.2431	−1.80416
$153$	2.64265	0.213646
$154$	−5.63451	−0.454042
$155$	12.3961	0.995675
$156$	0.744019	0.0595692
$157$	−9.94273	−0.793517	−0.396758	−	0.917923i	$-0.629865\pi$
$157$	−9.94273	−0.793517	−0.396758	+	0.917923i	$0.629865\pi$
$158$	−17.9448	−1.42761
$159$	−5.38657	−0.427183
$160$	10.8524	0.857958
$161$	−4.90748	−0.386764
$162$	1.16391	0.0914453
$163$	−2.74444	−0.214961	−0.107481	−	0.994207i	$-0.534278\pi$
$163$	−2.74444	−0.214961	−0.107481	+	0.994207i	$0.534278\pi$
$164$	−5.76040	−0.449812
$165$	−8.62288	−0.671291
$166$	−4.90565	−0.380752
$167$	−3.18949	−0.246810	−0.123405	−	0.992356i	$-0.539381\pi$
$167$	−3.18949	−0.246810	−0.123405	+	0.992356i	$0.539381\pi$
$168$	−5.37651	−0.414807
$169$	−11.6707	−0.897746
$170$	9.56706	0.733760
$171$	7.22436	0.552460
$172$	−7.61222	−0.580427
$173$	7.57784	0.576132	0.288066	−	0.957611i	$-0.406988\pi$
$173$	7.57784	0.576132	0.288066	+	0.957611i	$0.406988\pi$
$174$	0	0
$175$	8.16319	0.617079
$176$	6.35661	0.479147
$177$	−8.20042	−0.616381
$178$	−2.36501	−0.177265
$179$	−2.81192	−0.210173	−0.105086	−	0.994463i	$-0.533512\pi$
$179$	−2.81192	−0.210173	−0.105086	+	0.994463i	$0.533512\pi$
$180$	−2.00720	−0.149608
$181$	7.04070	0.523331	0.261666	−	0.965159i	$-0.415728\pi$
$181$	7.04070	0.523331	0.261666	+	0.965159i	$0.415728\pi$
$182$	−2.34334	−0.173700
$183$	4.90841	0.362840
$184$	8.65269	0.637885
$185$	32.5655	2.39426
$186$	4.63856	0.340116
$187$	−7.32611	−0.535738
$188$	4.73998	0.345699
$189$	1.74624	0.127020
$190$	26.1540	1.89741
$191$	4.42589	0.320246	0.160123	−	0.987097i	$-0.448811\pi$
$191$	4.42589	0.320246	0.160123	+	0.987097i	$0.448811\pi$
$192$	8.64680	0.624029
$193$	−4.03908	−0.290739	−0.145370	−	0.989377i	$-0.546437\pi$
$193$	−4.03908	−0.290739	−0.145370	+	0.989377i	$0.546437\pi$
$194$	14.7421	1.05842
$195$	−3.58617	−0.256811
$196$	2.54941	0.182101
$197$	11.9908	0.854309	0.427154	−	0.904179i	$-0.359516\pi$
$197$	11.9908	0.854309	0.427154	+	0.904179i	$0.359516\pi$
$198$	−3.22665	−0.229308
$199$	1.37703	0.0976152	0.0488076	−	0.998808i	$-0.484458\pi$
$199$	1.37703	0.0976152	0.0488076	+	0.998808i	$0.484458\pi$
$200$	−14.3931	−1.01774
$201$	−0.453589	−0.0319937
$202$	3.68422	0.259221
$203$	0	0
$204$	−1.70534	−0.119398
$205$	27.7651	1.93920
$206$	3.04934	0.212458
$207$	−2.81031	−0.195330
$208$	2.64365	0.183304
$209$	−20.0278	−1.38535
$210$	6.32182	0.436247
$211$	−17.3739	−1.19607	−0.598034	−	0.801471i	$-0.704051\pi$
$211$	−17.3739	−1.19607	−0.598034	+	0.801471i	$0.704051\pi$
$212$	3.47604	0.238735
$213$	11.6046	0.795133
$214$	−11.6866	−0.798882
$215$	36.6909	2.50230
$216$	−3.07891	−0.209493
$217$	6.95934	0.472430
$218$	−5.37451	−0.364008
$219$	−12.8553	−0.868679
$220$	5.56448	0.375157
$221$	−3.04685	−0.204954
$222$	12.1859	0.817864
$223$	13.8682	0.928686	0.464343	−	0.885655i	$-0.346290\pi$
$223$	13.8682	0.928686	0.464343	+	0.885655i	$0.346290\pi$
$224$	6.09271	0.407086
$225$	4.67473	0.311648
$226$	−6.04042	−0.401803
$227$	2.39052	0.158664	0.0793322	−	0.996848i	$-0.474721\pi$
$227$	2.39052	0.158664	0.0793322	+	0.996848i	$0.474721\pi$
$228$	−4.66199	−0.308748
$229$	1.06811	0.0705826	0.0352913	−	0.999377i	$-0.488764\pi$
$229$	1.06811	0.0705826	0.0352913	+	0.999377i	$0.488764\pi$
$230$	−10.1740	−0.670856
$231$	−4.84102	−0.318516
$232$	0	0
$233$	−25.6684	−1.68159	−0.840795	−	0.541353i	$-0.817912\pi$
$233$	−25.6684	−1.68159	−0.840795	+	0.541353i	$0.817912\pi$
$234$	−1.34193	−0.0877249
$235$	−22.8467	−1.49036
$236$	5.29186	0.344470
$237$	−15.4177	−1.00149
$238$	5.37110	0.348156
$239$	−7.85957	−0.508393	−0.254197	−	0.967153i	$-0.581811\pi$
$239$	−7.85957	−0.508393	−0.254197	+	0.967153i	$0.581811\pi$
$240$	−7.13200	−0.460369
$241$	24.4553	1.57531	0.787653	−	0.616119i	$-0.211296\pi$
$241$	24.4553	1.57531	0.787653	+	0.616119i	$0.211296\pi$
$242$	−3.85790	−0.247995
$243$	1.00000	0.0641500
$244$	−3.16747	−0.202777
$245$	−12.2882	−0.785063
$246$	10.3896	0.662418
$247$	−8.32935	−0.529984
$248$	−12.2705	−0.779174
$249$	−4.21480	−0.267102
$250$	−1.17757	−0.0744759
$251$	−5.97805	−0.377331	−0.188666	−	0.982041i	$-0.560416\pi$
$251$	−5.97805	−0.377331	−0.188666	+	0.982041i	$0.560416\pi$
$252$	−1.12688	−0.0709865
$253$	7.79091	0.489810
$254$	−17.4754	−1.09650
$255$	8.21977	0.514742
$256$	−13.7018	−0.856361
$257$	26.9440	1.68072	0.840361	−	0.542027i	$-0.182343\pi$
$257$	26.9440	1.68072	0.840361	+	0.542027i	$0.182343\pi$
$258$	13.7296	0.854769
$259$	18.2828	1.13604
$260$	2.31421	0.143521
$261$	0	0
$262$	−0.623100	−0.0384952
$263$	16.6334	1.02566	0.512829	−	0.858491i	$-0.328597\pi$
$263$	16.6334	1.02566	0.512829	+	0.858491i	$0.328597\pi$
$264$	8.53551	0.525325
$265$	−16.7545	−1.02922
$266$	14.6832	0.900288
$267$	−2.03195	−0.124353
$268$	0.292708	0.0178800
$269$	13.6354	0.831366	0.415683	−	0.909510i	$-0.363543\pi$
$269$	13.6354	0.831366	0.415683	+	0.909510i	$0.363543\pi$
$270$	3.62025	0.220321
$271$	−14.4025	−0.874892	−0.437446	−	0.899245i	$-0.644117\pi$
$271$	−14.4025	−0.874892	−0.437446	+	0.899245i	$0.644117\pi$
$272$	−6.05944	−0.367407
$273$	−2.01333	−0.121852
$274$	14.5149	0.876880
$275$	−12.9595	−0.781489
$276$	1.81354	0.109162
$277$	−13.7296	−0.824933	−0.412467	−	0.910973i	$-0.635333\pi$
$277$	−13.7296	−0.824933	−0.412467	+	0.910973i	$0.635333\pi$
$278$	−10.1124	−0.606502
$279$	3.98533	0.238595
$280$	−16.7232	−0.999403
$281$	−0.143690	−0.00857182	−0.00428591	−	0.999991i	$-0.501364\pi$
$281$	−0.143690	−0.00857182	−0.00428591	+	0.999991i	$0.501364\pi$
$282$	−8.54917	−0.509096
$283$	−8.83798	−0.525364	−0.262682	−	0.964883i	$-0.584607\pi$
$283$	−8.83798	−0.525364	−0.262682	+	0.964883i	$0.584607\pi$
$284$	−7.48862	−0.444368
$285$	22.4708	1.33106
$286$	3.72018	0.219979
$287$	15.5878	0.920118
$288$	3.48904	0.205594
$289$	−10.0164	−0.589199
$290$	0	0
$291$	12.6660	0.742493
$292$	8.29571	0.485470
$293$	−3.37386	−0.197103	−0.0985516	−	0.995132i	$-0.531421\pi$
$293$	−3.37386	−0.197103	−0.0985516	+	0.995132i	$0.531421\pi$
$294$	−4.59819	−0.268172
$295$	−25.5068	−1.48506
$296$	−32.2356	−1.87365
$297$	−2.77225	−0.160863
$298$	−17.4940	−1.01340
$299$	3.24016	0.187383
$300$	−3.01667	−0.174168
$301$	20.5989	1.18730
$302$	17.5561	1.01024
$303$	3.16539	0.181847
$304$	−16.5650	−0.950068
$305$	15.2672	0.874199
$306$	3.07581	0.175832
$307$	−0.230862	−0.0131760	−0.00658799	−	0.999978i	$-0.502097\pi$
$307$	−0.230862	−0.0131760	−0.00658799	+	0.999978i	$0.502097\pi$
$308$	3.12399	0.178006
$309$	2.61991	0.149042
$310$	14.4279	0.819448
$311$	−25.1762	−1.42761	−0.713806	−	0.700344i	$-0.753030\pi$
$311$	−25.1762	−1.42761	−0.713806	+	0.700344i	$0.753030\pi$
$312$	3.54984	0.200970
$313$	9.98229	0.564233	0.282116	−	0.959380i	$-0.408964\pi$
$313$	9.98229	0.564233	0.282116	+	0.959380i	$0.408964\pi$
$314$	−11.5724	−0.653071
$315$	5.43154	0.306033
$316$	9.94929	0.559691
$317$	−27.6956	−1.55554	−0.777770	−	0.628549i	$-0.783649\pi$
$317$	−27.6956	−1.55554	−0.777770	+	0.628549i	$0.783649\pi$
$318$	−6.26948	−0.351575
$319$	0	0
$320$	26.8952	1.50349
$321$	−10.0408	−0.560425
$322$	−5.71186	−0.318310
$323$	19.0915	1.06228
$324$	−0.645316	−0.0358509
$325$	−5.38974	−0.298969
$326$	−3.19428	−0.176915
$327$	−4.61764	−0.255356
$328$	−27.4838	−1.51754
$329$	−12.8265	−0.707149
$330$	−10.0363	−0.552478
$331$	−23.2748	−1.27930	−0.639650	−	0.768666i	$-0.720921\pi$
$331$	−23.2748	−1.27930	−0.639650	+	0.768666i	$0.720921\pi$
$332$	2.71988	0.149273
$333$	10.4698	0.573742
$334$	−3.71228	−0.203127
$335$	−1.41085	−0.0770831
$336$	−4.00402	−0.218437
$337$	18.8302	1.02574	0.512872	−	0.858465i	$-0.328581\pi$
$337$	18.8302	1.02574	0.512872	+	0.858465i	$0.328581\pi$
$338$	−13.5836	−0.738852
$339$	−5.18977	−0.281869
$340$	−5.30434	−0.287668
$341$	−11.0483	−0.598301
$342$	8.40850	0.454679
$343$	−19.1225	−1.03252
$344$	−36.3192	−1.95820
$345$	−8.74126	−0.470614
$346$	8.81991	0.474161
$347$	−19.4007	−1.04148	−0.520741	−	0.853715i	$-0.674344\pi$
$347$	−19.4007	−1.04148	−0.520741	+	0.853715i	$0.674344\pi$
$348$	0	0
$349$	9.57141	0.512346	0.256173	−	0.966631i	$-0.417538\pi$
$349$	9.57141	0.512346	0.256173	+	0.966631i	$0.417538\pi$
$350$	9.50122	0.507861
$351$	−1.15295	−0.0615401
$352$	−9.67252	−0.515547
$353$	−32.7562	−1.74344	−0.871718	−	0.490008i	$-0.836994\pi$
$353$	−32.7562	−1.74344	−0.871718	+	0.490008i	$0.836994\pi$
$354$	−9.54454	−0.507287
$355$	36.0952	1.91573
$356$	1.31125	0.0694961
$357$	4.61470	0.244236
$358$	−3.27282	−0.172974
$359$	14.5169	0.766172	0.383086	−	0.923713i	$-0.374861\pi$
$359$	14.5169	0.766172	0.383086	+	0.923713i	$0.374861\pi$
$360$	−9.57670	−0.504736
$361$	33.1913	1.74691
$362$	8.19473	0.430706
$363$	−3.31460	−0.173972
$364$	1.29923	0.0680984
$365$	−39.9854	−2.09293
$366$	5.71295	0.298620
$367$	17.2024	0.897959	0.448979	−	0.893542i	$-0.351788\pi$
$367$	17.2024	0.897959	0.448979	+	0.893542i	$0.351788\pi$
$368$	6.44387	0.335910
$369$	8.92649	0.464694
$370$	37.9033	1.97050
$371$	−9.40625	−0.488348
$372$	−2.57179	−0.133341
$373$	8.53262	0.441802	0.220901	−	0.975296i	$-0.429100\pi$
$373$	8.53262	0.441802	0.220901	+	0.975296i	$0.429100\pi$
$374$	−8.52692	−0.440917
$375$	−1.01174	−0.0522458
$376$	22.6152	1.16629
$377$	0	0
$378$	2.03246	0.104539
$379$	−10.8270	−0.556147	−0.278074	−	0.960560i	$-0.589696\pi$
$379$	−10.8270	−0.556147	−0.278074	+	0.960560i	$0.589696\pi$
$380$	−14.5008	−0.743873
$381$	−15.0144	−0.769211
$382$	5.15134	0.263565
$383$	20.0319	1.02358	0.511791	−	0.859110i	$-0.328982\pi$
$383$	20.0319	1.02358	0.511791	+	0.859110i	$0.328982\pi$
$384$	3.08601	0.157482
$385$	−15.0576	−0.767407
$386$	−4.70112	−0.239281
$387$	11.7961	0.599631
$388$	−8.17355	−0.414949
$389$	−30.9606	−1.56976	−0.784881	−	0.619646i	$-0.787276\pi$
$389$	−30.9606	−1.56976	−0.784881	+	0.619646i	$0.787276\pi$
$390$	−4.17398	−0.211358
$391$	−7.42668	−0.375583
$392$	12.1637	0.614358
$393$	−0.535351	−0.0270049
$394$	13.9562	0.703103
$395$	−47.9556	−2.41291
$396$	1.78898	0.0898996
$397$	19.7641	0.991933	0.495966	−	0.868342i	$-0.334814\pi$
$397$	19.7641	0.991933	0.495966	+	0.868342i	$0.334814\pi$
$398$	1.60274	0.0803381
$399$	12.6155	0.631563
$400$	−10.7189	−0.535943
$401$	18.5889	0.928285	0.464143	−	0.885760i	$-0.346362\pi$
$401$	18.5889	0.928285	0.464143	+	0.885760i	$0.346362\pi$
$402$	−0.527936	−0.0263311
$403$	−4.59490	−0.228888
$404$	−2.04267	−0.101627
$405$	3.11042	0.154558
$406$	0	0
$407$	−29.0250	−1.43871
$408$	−8.13648	−0.402816
$409$	31.5490	1.56000	0.779999	−	0.625780i	$-0.215219\pi$
$409$	31.5490	1.56000	0.779999	+	0.625780i	$0.215219\pi$
$410$	32.3161	1.59598
$411$	12.4709	0.615142
$412$	−1.69067	−0.0832934
$413$	−14.3199	−0.704636
$414$	−3.27095	−0.160758
$415$	−13.1098	−0.643536
$416$	−4.02270	−0.197229
$417$	−8.68832	−0.425469
$418$	−23.3105	−1.14015
$419$	−23.4046	−1.14339	−0.571695	−	0.820466i	$-0.693714\pi$
$419$	−23.4046	−1.14339	−0.571695	+	0.820466i	$0.693714\pi$
$420$	−3.50506	−0.171029
$421$	−0.394623	−0.0192327	−0.00961637	−	0.999954i	$-0.503061\pi$
$421$	−0.394623	−0.0192327	−0.00961637	+	0.999954i	$0.503061\pi$
$422$	−20.2216	−0.984373
$423$	−7.34522	−0.357137
$424$	16.5848	0.805427
$425$	12.3537	0.599241
$426$	13.5067	0.654401
$427$	8.57126	0.414792
$428$	6.47952	0.313199
$429$	3.19628	0.154318
$430$	42.7049	2.05941
$431$	−20.8177	−1.00275	−0.501376	−	0.865230i	$-0.667173\pi$
$431$	−20.8177	−1.00275	−0.501376	+	0.865230i	$0.667173\pi$
$432$	−2.29294	−0.110319
$433$	0.298803	0.0143596	0.00717978	−	0.999974i	$-0.497715\pi$
$433$	0.298803	0.0143596	0.00717978	+	0.999974i	$0.497715\pi$
$434$	8.10003	0.388814
$435$	0	0
$436$	2.97983	0.142708
$437$	−20.3027	−0.971210
$438$	−14.9624	−0.714930
$439$	25.9002	1.23615	0.618075	−	0.786119i	$-0.287913\pi$
$439$	25.9002	1.23615	0.618075	+	0.786119i	$0.287913\pi$
$440$	26.5491	1.26568
$441$	−3.95065	−0.188126
$442$	−3.54626	−0.168678
$443$	4.17054	0.198149	0.0990743	−	0.995080i	$-0.468412\pi$
$443$	4.17054	0.198149	0.0990743	+	0.995080i	$0.468412\pi$
$444$	−6.75633	−0.320641
$445$	−6.32022	−0.299607
$446$	16.1414	0.764316
$447$	−15.0304	−0.710912
$448$	15.0994	0.713379
$449$	−21.4255	−1.01113	−0.505566	−	0.862788i	$-0.668716\pi$
$449$	−21.4255	−1.01113	−0.505566	+	0.862788i	$0.668716\pi$
$450$	5.44096	0.256489
$451$	−24.7465	−1.16527
$452$	3.34904	0.157525
$453$	15.0837	0.708696
$454$	2.78235	0.130582
$455$	−6.26231	−0.293582
$456$	−22.2431	−1.04163
$457$	15.2181	0.711875	0.355937	−	0.934510i	$-0.384162\pi$
$457$	15.2181	0.711875	0.355937	+	0.934510i	$0.384162\pi$
$458$	1.24318	0.0580900
$459$	2.64265	0.123348
$460$	5.64087	0.263007
$461$	−3.40687	−0.158674	−0.0793370	−	0.996848i	$-0.525280\pi$
$461$	−3.40687	−0.158674	−0.0793370	+	0.996848i	$0.525280\pi$
$462$	−5.63451	−0.262141
$463$	−20.8584	−0.969374	−0.484687	−	0.874688i	$-0.661066\pi$
$463$	−20.8584	−0.969374	−0.484687	+	0.874688i	$0.661066\pi$
$464$	0	0
$465$	12.3961	0.574853
$466$	−29.8757	−1.38396
$467$	17.3430	0.802536	0.401268	−	0.915961i	$-0.368570\pi$
$467$	17.3430	0.802536	0.401268	+	0.915961i	$0.368570\pi$
$468$	0.744019	0.0343923
$469$	−0.792075	−0.0365746
$470$	−26.5915	−1.22658
$471$	−9.94273	−0.458137
$472$	25.2483	1.16215
$473$	−32.7019	−1.50363
$474$	−17.9448	−0.824233
$475$	33.7719	1.54956
$476$	−2.97794	−0.136494
$477$	−5.38657	−0.246634
$478$	−9.14783	−0.418412
$479$	−36.0650	−1.64785	−0.823927	−	0.566696i	$-0.808221\pi$
$479$	−36.0650	−1.64785	−0.823927	+	0.566696i	$0.808221\pi$
$480$	10.8524	0.495342
$481$	−12.0712	−0.550399
$482$	28.4638	1.29649
$483$	−4.90748	−0.223298
$484$	2.13896	0.0972257
$485$	39.3966	1.78891
$486$	1.16391	0.0527960
$487$	13.2004	0.598167	0.299083	−	0.954227i	$-0.403319\pi$
$487$	13.2004	0.598167	0.299083	+	0.954227i	$0.403319\pi$
$488$	−15.1125	−0.684113
$489$	−2.74444	−0.124108
$490$	−14.3023	−0.646113
$491$	−24.7678	−1.11776	−0.558878	−	0.829250i	$-0.688768\pi$
$491$	−24.7678	−1.11776	−0.558878	+	0.829250i	$0.688768\pi$
$492$	−5.76040	−0.259699
$493$	0	0
$494$	−9.69460	−0.436181
$495$	−8.62288	−0.387570
$496$	−9.13810	−0.410313
$497$	20.2644	0.908982
$498$	−4.90565	−0.219827
$499$	15.8147	0.707963	0.353981	−	0.935252i	$-0.384828\pi$
$499$	15.8147	0.707963	0.353981	+	0.935252i	$0.384828\pi$
$500$	0.652889	0.0291981
$501$	−3.18949	−0.142496
$502$	−6.95791	−0.310547
$503$	−23.4528	−1.04571	−0.522854	−	0.852422i	$-0.675133\pi$
$503$	−23.4528	−1.04571	−0.522854	+	0.852422i	$0.675133\pi$
$504$	−5.37651	−0.239489
$505$	9.84569	0.438127
$506$	9.06791	0.403118
$507$	−11.6707	−0.518314
$508$	9.68903	0.429881
$509$	6.97756	0.309275	0.154638	−	0.987971i	$-0.450579\pi$
$509$	6.97756	0.309275	0.154638	+	0.987971i	$0.450579\pi$
$510$	9.56706	0.423637
$511$	−22.4484	−0.993059
$512$	−22.1196	−0.977559
$513$	7.22436	0.318963
$514$	31.3604	1.38325
$515$	8.14904	0.359090
$516$	−7.61222	−0.335109
$517$	20.3628	0.895556
$518$	21.2795	0.934968
$519$	7.57784	0.332630
$520$	11.0415	0.484201
$521$	−20.4524	−0.896037	−0.448019	−	0.894024i	$-0.647870\pi$
$521$	−20.4524	−0.896037	−0.448019	+	0.894024i	$0.647870\pi$
$522$	0	0
$523$	−19.8313	−0.867162	−0.433581	−	0.901115i	$-0.642750\pi$
$523$	−19.8313	−0.867162	−0.433581	+	0.901115i	$0.642750\pi$
$524$	0.345470	0.0150919
$525$	8.16319	0.356271
$526$	19.3597	0.844125
$527$	10.5318	0.458774
$528$	6.35661	0.276636
$529$	−15.1021	−0.656615
$530$	−19.5007	−0.847058
$531$	−8.20042	−0.355868
$532$	−8.14095	−0.352955
$533$	−10.2918	−0.445788
$534$	−2.36501	−0.102344
$535$	−31.2313	−1.35025
$536$	1.39656	0.0603221
$537$	−2.81192	−0.121343
$538$	15.8704	0.684221
$539$	10.9522	0.471745
$540$	−2.00720	−0.0863763
$541$	35.7048	1.53507	0.767535	−	0.641007i	$-0.221483\pi$
$541$	35.7048	1.53507	0.767535	+	0.641007i	$0.221483\pi$
$542$	−16.7633	−0.720043
$543$	7.04070	0.302145
$544$	9.22033	0.395318
$545$	−14.3628	−0.615235
$546$	−2.34334	−0.100286
$547$	−9.88299	−0.422566	−0.211283	−	0.977425i	$-0.567764\pi$
$547$	−9.88299	−0.422566	−0.211283	+	0.977425i	$0.567764\pi$
$548$	−8.04764	−0.343778
$549$	4.90841	0.209486
$550$	−15.0837	−0.643172
$551$	0	0
$552$	8.65269	0.368283
$553$	−26.9230	−1.14488
$554$	−15.9800	−0.678927
$555$	32.5655	1.38233
$556$	5.60671	0.237777
$557$	−31.8798	−1.35079	−0.675395	−	0.737457i	$-0.736027\pi$
$557$	−31.8798	−1.35079	−0.675395	+	0.737457i	$0.736027\pi$
$558$	4.63856	0.196366
$559$	−13.6004	−0.575235
$560$	−12.4542	−0.526285
$561$	−7.32611	−0.309308
$562$	−0.167242	−0.00705468
$563$	−9.06052	−0.381855	−0.190928	−	0.981604i	$-0.561150\pi$
$563$	−9.06052	−0.381855	−0.190928	+	0.981604i	$0.561150\pi$
$564$	4.73998	0.199589
$565$	−16.1424	−0.679114
$566$	−10.2866	−0.432378
$567$	1.74624	0.0733352
$568$	−35.7294	−1.49917
$569$	−16.7232	−0.701073	−0.350537	−	0.936549i	$-0.614001\pi$
$569$	−16.7232	−0.701073	−0.350537	+	0.936549i	$0.614001\pi$
$570$	26.1540	1.09547
$571$	−23.2770	−0.974113	−0.487057	−	0.873370i	$-0.661929\pi$
$571$	−23.2770	−0.974113	−0.487057	+	0.873370i	$0.661929\pi$
$572$	−2.06261	−0.0862420
$573$	4.42589	0.184894
$574$	18.1428	0.757264
$575$	−13.1375	−0.547870
$576$	8.64680	0.360283
$577$	18.9370	0.788358	0.394179	−	0.919034i	$-0.371029\pi$
$577$	18.9370	0.788358	0.394179	+	0.919034i	$0.371029\pi$
$578$	−11.6582	−0.484916
$579$	−4.03908	−0.167858
$580$	0	0
$581$	−7.36006	−0.305347
$582$	14.7421	0.611078
$583$	14.9330	0.618460
$584$	39.5802	1.63784
$585$	−3.58617	−0.148270
$586$	−3.92687	−0.162218
$587$	−0.0227550	−0.000939198 0	−0.000469599	−	1.00000i	$-0.500149\pi$
$587$	−0.0227550	−0.000939198 0	−0.000469599		1.00000i	$0.500149\pi$
$588$	2.54941	0.105136
$589$	28.7914	1.18633
$590$	−29.6875	−1.22222
$591$	11.9908	0.493235
$592$	−24.0066	−0.986665
$593$	0.352611	0.0144800	0.00724000	−	0.999974i	$-0.497695\pi$
$593$	0.352611	0.0144800	0.00724000	+	0.999974i	$0.497695\pi$
$594$	−3.22665	−0.132391
$595$	14.3537	0.588443
$596$	9.69933	0.397300
$597$	1.37703	0.0563582
$598$	3.77125	0.154218
$599$	8.06663	0.329594	0.164797	−	0.986328i	$-0.447303\pi$
$599$	8.06663	0.329594	0.164797	+	0.986328i	$0.447303\pi$
$600$	−14.3931	−0.587594
$601$	−21.8761	−0.892347	−0.446173	−	0.894947i	$-0.647213\pi$
$601$	−21.8761	−0.892347	−0.446173	+	0.894947i	$0.647213\pi$
$602$	23.9752	0.977157
$603$	−0.453589	−0.0184716
$604$	−9.73378	−0.396062
$605$	−10.3098	−0.419154
$606$	3.68422	0.149661
$607$	−3.24534	−0.131724	−0.0658622	−	0.997829i	$-0.520980\pi$
$607$	−3.24534	−0.131724	−0.0658622	+	0.997829i	$0.520980\pi$
$608$	25.2061	1.02224
$609$	0	0
$610$	17.7697	0.719473
$611$	8.46869	0.342607
$612$	−1.70534	−0.0689345
$613$	−9.33554	−0.377059	−0.188529	−	0.982068i	$-0.560372\pi$
$613$	−9.33554	−0.377059	−0.188529	+	0.982068i	$0.560372\pi$
$614$	−0.268702	−0.0108439
$615$	27.7651	1.11960
$616$	14.9051	0.600542
$617$	22.1616	0.892192	0.446096	−	0.894985i	$-0.352814\pi$
$617$	22.1616	0.892192	0.446096	+	0.894985i	$0.352814\pi$
$618$	3.04934	0.122663
$619$	−6.51815	−0.261987	−0.130993	−	0.991383i	$-0.541817\pi$
$619$	−6.51815	−0.261987	−0.130993	+	0.991383i	$0.541817\pi$
$620$	−7.99936	−0.321262
$621$	−2.81031	−0.112774
$622$	−29.3028	−1.17494
$623$	−3.54827	−0.142159
$624$	2.64365	0.105831
$625$	−26.5206	−1.06082
$626$	11.6185	0.464368
$627$	−20.0278	−0.799832
$628$	6.41620	0.256034
$629$	27.6681	1.10320
$630$	6.32182	0.251867
$631$	−23.9791	−0.954593	−0.477297	−	0.878742i	$-0.658383\pi$
$631$	−23.9791	−0.954593	−0.477297	+	0.878742i	$0.658383\pi$
$632$	47.4697	1.88824
$633$	−17.3739	−0.690550
$634$	−32.2352	−1.28022
$635$	−46.7011	−1.85328
$636$	3.47604	0.137834
$637$	4.55491	0.180472
$638$	0	0
$639$	11.6046	0.459070
$640$	9.59878	0.379425
$641$	43.9700	1.73671	0.868355	−	0.495943i	$-0.165177\pi$
$641$	43.9700	1.73671	0.868355	+	0.495943i	$0.165177\pi$
$642$	−11.6866	−0.461235
$643$	16.5216	0.651549	0.325775	−	0.945447i	$-0.394375\pi$
$643$	16.5216	0.651549	0.325775	+	0.945447i	$0.394375\pi$
$644$	3.16687	0.124792
$645$	36.6909	1.44470
$646$	22.2207	0.874263
$647$	−35.2719	−1.38668	−0.693340	−	0.720611i	$-0.743862\pi$
$647$	−35.2719	−1.38668	−0.693340	+	0.720611i	$0.743862\pi$
$648$	−3.07891	−0.120951
$649$	22.7336	0.892374
$650$	−6.27317	−0.246054
$651$	6.95934	0.272758
$652$	1.77103	0.0693590
$653$	16.8156	0.658045	0.329023	−	0.944322i	$-0.393281\pi$
$653$	16.8156	0.658045	0.329023	+	0.944322i	$0.393281\pi$
$654$	−5.37451	−0.210160
$655$	−1.66517	−0.0650635
$656$	−20.4679	−0.799136
$657$	−12.8553	−0.501532
$658$	−14.9289	−0.581989
$659$	3.00399	0.117019	0.0585094	−	0.998287i	$-0.481365\pi$
$659$	3.00399	0.117019	0.0585094	+	0.998287i	$0.481365\pi$
$660$	5.56448	0.216597
$661$	38.3135	1.49022	0.745111	−	0.666940i	$-0.232396\pi$
$661$	38.3135	1.49022	0.745111	+	0.666940i	$0.232396\pi$
$662$	−27.0898	−1.05287
$663$	−3.04685	−0.118330
$664$	12.9770	0.503605
$665$	39.2394	1.52164
$666$	12.1859	0.472194
$667$	0	0
$668$	2.05823	0.0796353
$669$	13.8682	0.536177
$670$	−1.64211	−0.0634401
$671$	−13.6074	−0.525307
$672$	6.09271	0.235031
$673$	−27.3818	−1.05549	−0.527745	−	0.849403i	$-0.676962\pi$
$673$	−27.3818	−1.05549	−0.527745	+	0.849403i	$0.676962\pi$
$674$	21.9166	0.844196
$675$	4.67473	0.179930
$676$	7.53128	0.289665
$677$	28.6366	1.10059	0.550297	−	0.834969i	$-0.314514\pi$
$677$	28.6366	1.10059	0.550297	+	0.834969i	$0.314514\pi$
$678$	−6.04042	−0.231981
$679$	22.1178	0.848805
$680$	−25.3079	−0.970513
$681$	2.39052	0.0916049
$682$	−12.8593	−0.492407
$683$	12.5885	0.481686	0.240843	−	0.970564i	$-0.422576\pi$
$683$	12.5885	0.481686	0.240843	+	0.970564i	$0.422576\pi$
$684$	−4.66199	−0.178256
$685$	38.7896	1.48208
$686$	−22.2568	−0.849769
$687$	1.06811	0.0407509
$688$	−27.0478	−1.03119
$689$	6.21047	0.236600
$690$	−10.1740	−0.387319
$691$	40.0195	1.52241	0.761207	−	0.648509i	$-0.224607\pi$
$691$	40.0195	1.52241	0.761207	+	0.648509i	$0.224607\pi$
$692$	−4.89009	−0.185894
$693$	−4.84102	−0.183895
$694$	−22.5806	−0.857148
$695$	−27.0243	−1.02509
$696$	0	0
$697$	23.5896	0.893520
$698$	11.1403	0.421665
$699$	−25.6684	−0.970867
$700$	−5.26784	−0.199105
$701$	−12.8864	−0.486711	−0.243356	−	0.969937i	$-0.578248\pi$
$701$	−12.8864	−0.486711	−0.243356	+	0.969937i	$0.578248\pi$
$702$	−1.34193	−0.0506480
$703$	75.6376	2.85273
$704$	−23.9711	−0.903446
$705$	−22.8467	−0.860458
$706$	−38.1252	−1.43486
$707$	5.52752	0.207884
$708$	5.29186	0.198880
$709$	−0.627021	−0.0235483	−0.0117741	−	0.999931i	$-0.503748\pi$
$709$	−0.627021	−0.0235483	−0.0117741	+	0.999931i	$0.503748\pi$
$710$	42.0115	1.57666
$711$	−15.4177	−0.578209
$712$	6.25619	0.234460
$713$	−11.2000	−0.419444
$714$	5.37110	0.201008
$715$	9.94178	0.371802
$716$	1.81458	0.0678139
$717$	−7.85957	−0.293521
$718$	16.8963	0.630566
$719$	35.4279	1.32124	0.660619	−	0.750722i	$-0.270294\pi$
$719$	35.4279	1.32124	0.660619	+	0.750722i	$0.270294\pi$
$720$	−7.13200	−0.265794
$721$	4.57500	0.170382
$722$	38.6317	1.43772
$723$	24.4553	0.909504
$724$	−4.54347	−0.168857
$725$	0	0
$726$	−3.85790	−0.143180
$727$	−19.4235	−0.720377	−0.360189	−	0.932879i	$-0.617288\pi$
$727$	−19.4235	−0.720377	−0.360189	+	0.932879i	$0.617288\pi$
$728$	6.19886	0.229745
$729$	1.00000	0.0370370
$730$	−46.5393	−1.72250
$731$	31.1731	1.15298
$732$	−3.16747	−0.117073
$733$	−25.0806	−0.926374	−0.463187	−	0.886261i	$-0.653294\pi$
$733$	−25.0806	−0.926374	−0.463187	+	0.886261i	$0.653294\pi$
$734$	20.0220	0.739027
$735$	−12.2882	−0.453256
$736$	−9.80531	−0.361428
$737$	1.25746	0.0463193
$738$	10.3896	0.382447
$739$	52.8524	1.94421	0.972104	−	0.234550i	$-0.0753617\pi$
$739$	52.8524	1.94421	0.972104	+	0.234550i	$0.0753617\pi$
$740$	−21.0150	−0.772528
$741$	−8.32935	−0.305986
$742$	−10.9480	−0.401914
$743$	15.8786	0.582528	0.291264	−	0.956643i	$-0.405924\pi$
$743$	15.8786	0.582528	0.291264	+	0.956643i	$0.405924\pi$
$744$	−12.2705	−0.449857
$745$	−46.7508	−1.71282
$746$	9.93119	0.363607
$747$	−4.21480	−0.154212
$748$	4.72765	0.172860
$749$	−17.5337	−0.640668
$750$	−1.17757	−0.0429987
$751$	−9.27637	−0.338500	−0.169250	−	0.985573i	$-0.554134\pi$
$751$	−9.27637	−0.338500	−0.169250	+	0.985573i	$0.554134\pi$
$752$	16.8421	0.614169
$753$	−5.97805	−0.217852
$754$	0	0
$755$	46.9168	1.70748
$756$	−1.12688	−0.0409841
$757$	−5.98504	−0.217530	−0.108765	−	0.994067i	$-0.534690\pi$
$757$	−5.98504	−0.217530	−0.108765	+	0.994067i	$0.534690\pi$
$758$	−12.6017	−0.457714
$759$	7.79091	0.282792
$760$	−69.1855	−2.50962
$761$	21.1614	0.767100	0.383550	−	0.923520i	$-0.374701\pi$
$761$	21.1614	0.767100	0.383550	+	0.923520i	$0.374701\pi$
$762$	−17.4754	−0.633067
$763$	−8.06351	−0.291918
$764$	−2.85610	−0.103330
$765$	8.21977	0.297186
$766$	23.3153	0.842415
$767$	9.45470	0.341389
$768$	−13.7018	−0.494420
$769$	24.3858	0.879373	0.439686	−	0.898151i	$-0.355090\pi$
$769$	24.3858	0.879373	0.439686	+	0.898151i	$0.355090\pi$
$770$	−17.5257	−0.631582
$771$	26.9440	0.970366
$772$	2.60648	0.0938093
$773$	54.2116	1.94985	0.974927	−	0.222524i	$-0.0714294\pi$
$773$	54.2116	1.94985	0.974927	+	0.222524i	$0.0714294\pi$
$774$	13.7296	0.493501
$775$	18.6303	0.669221
$776$	−38.9974	−1.39992
$777$	18.2828	0.655891
$778$	−36.0353	−1.29193
$779$	64.4881	2.31053
$780$	2.31421	0.0828621
$781$	−32.1709	−1.15116
$782$	−8.64398	−0.309108
$783$	0	0
$784$	9.05858	0.323521
$785$	−30.9261	−1.10380
$786$	−0.623100	−0.0222252
$787$	−0.547155	−0.0195040	−0.00975198	−	0.999952i	$-0.503104\pi$
$787$	−0.547155	−0.0195040	−0.00975198	+	0.999952i	$0.503104\pi$
$788$	−7.73785	−0.275649
$789$	16.6334	0.592164
$790$	−55.8160	−1.98584
$791$	−9.06258	−0.322228
$792$	8.53551	0.303296
$793$	−5.65917	−0.200963
$794$	23.0036	0.816369
$795$	−16.7545	−0.594222
$796$	−0.888620	−0.0314963
$797$	−24.5501	−0.869610	−0.434805	−	0.900525i	$-0.643183\pi$
$797$	−24.5501	−0.869610	−0.434805	+	0.900525i	$0.643183\pi$
$798$	14.6832	0.519781
$799$	−19.4109	−0.686707
$800$	16.3103	0.576657
$801$	−2.03195	−0.0717954
$802$	21.6358	0.763986
$803$	35.6381	1.25764
$804$	0.292708	0.0103230
$805$	−15.2643	−0.537997
$806$	−5.34804	−0.188377
$807$	13.6354	0.479989
$808$	−9.74593	−0.342861
$809$	26.3716	0.927175	0.463588	−	0.886051i	$-0.346562\pi$
$809$	26.3716	0.927175	0.463588	+	0.886051i	$0.346562\pi$
$810$	3.62025	0.127203
$811$	31.8364	1.11793	0.558964	−	0.829192i	$-0.311199\pi$
$811$	31.8364	1.11793	0.558964	+	0.829192i	$0.311199\pi$
$812$	0	0
$813$	−14.4025	−0.505119
$814$	−33.7824	−1.18407
$815$	−8.53638	−0.299016
$816$	−6.05944	−0.212123
$817$	85.2194	2.98145
$818$	36.7202	1.28389
$819$	−2.01333	−0.0703515
$820$	−17.9173	−0.625698
$821$	13.1414	0.458640	0.229320	−	0.973351i	$-0.426350\pi$
$821$	13.1414	0.458640	0.229320	+	0.973351i	$0.426350\pi$
$822$	14.5149	0.506267
$823$	−52.3889	−1.82616	−0.913081	−	0.407778i	$-0.866304\pi$
$823$	−52.3889	−1.82616	−0.913081	+	0.407778i	$0.866304\pi$
$824$	−8.06647	−0.281009
$825$	−12.9595	−0.451193
$826$	−16.6671	−0.579921
$827$	−22.6892	−0.788981	−0.394491	−	0.918900i	$-0.629079\pi$
$827$	−22.6892	−0.788981	−0.394491	+	0.918900i	$0.629079\pi$
$828$	1.81354	0.0630248
$829$	20.0998	0.698094	0.349047	−	0.937105i	$-0.386505\pi$
$829$	20.0998	0.698094	0.349047	+	0.937105i	$0.386505\pi$
$830$	−15.2586	−0.529635
$831$	−13.7296	−0.476276
$832$	−9.96936	−0.345625
$833$	−10.4402	−0.361731
$834$	−10.1124	−0.350164
$835$	−9.92067	−0.343319
$836$	12.9242	0.446994
$837$	3.98533	0.137753
$838$	−27.2408	−0.941019
$839$	8.22035	0.283798	0.141899	−	0.989881i	$-0.454679\pi$
$839$	8.22035	0.283798	0.141899	+	0.989881i	$0.454679\pi$
$840$	−16.7232	−0.577006
$841$	0	0
$842$	−0.459305	−0.0158287
$843$	−0.143690	−0.00494895
$844$	11.2116	0.385920
$845$	−36.3008	−1.24879
$846$	−8.54917	−0.293926
$847$	−5.78809	−0.198881
$848$	12.3511	0.424138
$849$	−8.83798	−0.303319
$850$	14.3786	0.493181
$851$	−29.4234	−1.00862
$852$	−7.48862	−0.256556
$853$	20.7111	0.709136	0.354568	−	0.935030i	$-0.384628\pi$
$853$	20.7111	0.709136	0.354568	+	0.935030i	$0.384628\pi$
$854$	9.97617	0.341378
$855$	22.4708	0.768485
$856$	30.9148	1.05665
$857$	−6.13652	−0.209620	−0.104810	−	0.994492i	$-0.533423\pi$
$857$	−6.13652	−0.209620	−0.104810	+	0.994492i	$0.533423\pi$
$858$	3.72018	0.127005
$859$	15.9653	0.544730	0.272365	−	0.962194i	$-0.412194\pi$
$859$	15.9653	0.544730	0.272365	+	0.962194i	$0.412194\pi$
$860$	−23.6772	−0.807387
$861$	15.5878	0.531230
$862$	−24.2299	−0.825273
$863$	−20.5055	−0.698014	−0.349007	−	0.937120i	$-0.613481\pi$
$863$	−20.5055	−0.698014	−0.349007	+	0.937120i	$0.613481\pi$
$864$	3.48904	0.118700
$865$	23.5703	0.801413
$866$	0.347780	0.0118180
$867$	−10.0164	−0.340174
$868$	−4.49097	−0.152433
$869$	42.7418	1.44992
$870$	0	0
$871$	0.522967	0.0177201
$872$	14.2173	0.481458
$873$	12.6660	0.428679
$874$	−23.6305	−0.799314
$875$	−1.76673	−0.0597265
$876$	8.29571	0.280286
$877$	−26.7528	−0.903378	−0.451689	−	0.892175i	$-0.649178\pi$
$877$	−26.7528	−0.903378	−0.451689	+	0.892175i	$0.649178\pi$
$878$	30.1455	1.01736
$879$	−3.37386	−0.113798
$880$	19.7717	0.666505
$881$	20.0351	0.675001	0.337501	−	0.941325i	$-0.390418\pi$
$881$	20.0351	0.675001	0.337501	+	0.941325i	$0.390418\pi$
$882$	−4.59819	−0.154829
$883$	−34.9210	−1.17518	−0.587592	−	0.809157i	$-0.699924\pi$
$883$	−34.9210	−1.17518	−0.587592	+	0.809157i	$0.699924\pi$
$884$	1.96618	0.0661299
$885$	−25.5068	−0.857400
$886$	4.85413	0.163078
$887$	−16.0686	−0.539530	−0.269765	−	0.962926i	$-0.586946\pi$
$887$	−16.0686	−0.539530	−0.269765	+	0.962926i	$0.586946\pi$
$888$	−32.2356	−1.08175
$889$	−26.2187	−0.879348
$890$	−7.35617	−0.246579
$891$	−2.77225	−0.0928740
$892$	−8.94939	−0.299648
$893$	−53.0645	−1.77574
$894$	−17.4940	−0.585087
$895$	−8.74627	−0.292355
$896$	5.38891	0.180031
$897$	3.24016	0.108186
$898$	−24.9373	−0.832170
$899$	0	0
$900$	−3.01667	−0.100556
$901$	−14.2348	−0.474231
$902$	−28.8027	−0.959024
$903$	20.5989	0.685487
$904$	15.9788	0.531447
$905$	21.8995	0.727966
$906$	17.5561	0.583263
$907$	26.8790	0.892501	0.446251	−	0.894908i	$-0.352759\pi$
$907$	26.8790	0.892501	0.446251	+	0.894908i	$0.352759\pi$
$908$	−1.54264	−0.0511943
$909$	3.16539	0.104989
$910$	−7.28876	−0.241620
$911$	−29.9706	−0.992969	−0.496485	−	0.868045i	$-0.665376\pi$
$911$	−29.9706	−0.992969	−0.496485	+	0.868045i	$0.665376\pi$
$912$	−16.5650	−0.548522
$913$	11.6845	0.386701
$914$	17.7125	0.585879
$915$	15.2672	0.504719
$916$	−0.689267	−0.0227740
$917$	−0.934851	−0.0308715
$918$	3.07581	0.101517
$919$	34.5424	1.13945	0.569725	−	0.821835i	$-0.307050\pi$
$919$	34.5424	1.13945	0.569725	+	0.821835i	$0.307050\pi$
$920$	26.9135	0.887313
$921$	−0.230862	−0.00760715
$922$	−3.96529	−0.130590
$923$	−13.3795	−0.440393
$924$	3.12399	0.102772
$925$	48.9435	1.60925
$926$	−24.2773	−0.797803
$927$	2.61991	0.0860493
$928$	0	0
$929$	−55.5508	−1.82256	−0.911282	−	0.411783i	$-0.864906\pi$
$929$	−55.5508	−1.82256	−0.911282	+	0.411783i	$0.864906\pi$
$930$	14.4279	0.473109
$931$	−28.5409	−0.935390
$932$	16.5642	0.542578
$933$	−25.1762	−0.824232
$934$	20.1856	0.660494
$935$	−22.7873	−0.745224
$936$	3.54984	0.116030
$937$	−4.11223	−0.134341	−0.0671703	−	0.997742i	$-0.521397\pi$
$937$	−4.11223	−0.134341	−0.0671703	+	0.997742i	$0.521397\pi$
$938$	−0.921903	−0.0301012
$939$	9.98229	0.325760
$940$	14.7434	0.480875
$941$	3.81681	0.124425	0.0622123	−	0.998063i	$-0.480184\pi$
$941$	3.81681	0.124425	0.0622123	+	0.998063i	$0.480184\pi$
$942$	−11.5724	−0.377050
$943$	−25.0862	−0.816920
$944$	18.8030	0.611987
$945$	5.43154	0.176688
$946$	−38.0620	−1.23750
$947$	22.8259	0.741743	0.370871	−	0.928684i	$-0.379059\pi$
$947$	22.8259	0.741743	0.370871	+	0.928684i	$0.379059\pi$
$948$	9.94929	0.323138
$949$	14.8215	0.481127
$950$	39.3074	1.27530
$951$	−27.6956	−0.898092
$952$	−14.2082	−0.460492
$953$	−44.6142	−1.44520	−0.722598	−	0.691268i	$-0.757052\pi$
$953$	−44.6142	−1.44520	−0.722598	+	0.691268i	$0.757052\pi$
$954$	−6.26948	−0.202982
$955$	13.7664	0.445470
$956$	5.07190	0.164037
$957$	0	0
$958$	−41.9764	−1.35620
$959$	21.7771	0.703219
$960$	26.8952	0.868039
$961$	−15.1172	−0.487651
$962$	−14.0498	−0.452983
$963$	−10.0408	−0.323562
$964$	−15.7814	−0.508285
$965$	−12.5632	−0.404425
$966$	−5.71186	−0.183776
$967$	55.1136	1.77233	0.886167	−	0.463366i	$-0.153358\pi$
$967$	55.1136	1.77233	0.886167	+	0.463366i	$0.153358\pi$
$968$	10.2054	0.328013
$969$	19.0915	0.613306
$970$	45.8540	1.47228
$971$	−13.2980	−0.426753	−0.213377	−	0.976970i	$-0.568446\pi$
$971$	−13.2980	−0.426753	−0.213377	+	0.976970i	$0.568446\pi$
$972$	−0.645316	−0.0206985
$973$	−15.1719	−0.486388
$974$	15.3640	0.492296
$975$	−5.38974	−0.172610
$976$	−11.2547	−0.360253
$977$	2.11659	0.0677156	0.0338578	−	0.999427i	$-0.489221\pi$
$977$	2.11659	0.0677156	0.0338578	+	0.999427i	$0.489221\pi$
$978$	−3.19428	−0.102142
$979$	5.63308	0.180034
$980$	7.92975	0.253307
$981$	−4.61764	−0.147430
$982$	−28.8275	−0.919922
$983$	−9.53887	−0.304243	−0.152121	−	0.988362i	$-0.548610\pi$
$983$	−9.53887	−0.304243	−0.152121	+	0.988362i	$0.548610\pi$
$984$	−27.4838	−0.876152
$985$	37.2964	1.18836
$986$	0	0
$987$	−12.8265	−0.408272
$988$	5.37506	0.171003
$989$	−33.1508	−1.05413
$990$	−10.0363	−0.318973
$991$	−11.7197	−0.372288	−0.186144	−	0.982522i	$-0.559599\pi$
$991$	−11.7197	−0.372288	−0.186144	+	0.982522i	$0.559599\pi$
$992$	13.9050	0.441484
$993$	−23.2748	−0.738604
$994$	23.5859	0.748100
$995$	4.28315	0.135785
$996$	2.71988	0.0861826
$997$	48.5074	1.53624	0.768122	−	0.640303i	$-0.221191\pi$
$997$	48.5074	1.53624	0.768122	+	0.640303i	$0.221191\pi$
$998$	18.4069	0.582659
$999$	10.4698	0.331250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.2.a.r.1.6		9
3.2	odd	2		7569.2.a.bj.1.4		9
29.7	even	7		87.2.g.a.49.2	yes	18
29.25	even	7		87.2.g.a.16.2	✓	18
29.28	even	2		2523.2.a.o.1.4		9
87.65	odd	14		261.2.k.c.136.2		18
87.83	odd	14		261.2.k.c.190.2		18
87.86	odd	2		7569.2.a.bm.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.16.2	✓	18	29.25	even	7
87.2.g.a.49.2	yes	18	29.7	even	7
261.2.k.c.136.2		18	87.65	odd	14
261.2.k.c.190.2		18	87.83	odd	14
2523.2.a.o.1.4		9	29.28	even	2
2523.2.a.r.1.6		9	1.1	even	1	trivial
7569.2.a.bj.1.4		9	3.2	odd	2
7569.2.a.bm.1.6		9	87.86	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2523.a (trivial)

\(f(q)\)	\(=\)	\(q+1.16391 q^{2} +1.00000 q^{3} -0.645316 q^{4} +3.11042 q^{5} +1.16391 q^{6} +1.74624 q^{7} -3.07891 q^{8} +1.00000 q^{9} +3.62025 q^{10} -2.77225 q^{11} -0.645316 q^{12} -1.15295 q^{13} +2.03246 q^{14} +3.11042 q^{15} -2.29294 q^{16} +2.64265 q^{17} +1.16391 q^{18} +7.22436 q^{19} -2.00720 q^{20} +1.74624 q^{21} -3.22665 q^{22} -2.81031 q^{23} -3.07891 q^{24} +4.67473 q^{25} -1.34193 q^{26} +1.00000 q^{27} -1.12688 q^{28} +3.62025 q^{30} +3.98533 q^{31} +3.48904 q^{32} -2.77225 q^{33} +3.07581 q^{34} +5.43154 q^{35} -0.645316 q^{36} +10.4698 q^{37} +8.40850 q^{38} -1.15295 q^{39} -9.57670 q^{40} +8.92649 q^{41} +2.03246 q^{42} +11.7961 q^{43} +1.78898 q^{44} +3.11042 q^{45} -3.27095 q^{46} -7.34522 q^{47} -2.29294 q^{48} -3.95065 q^{49} +5.44096 q^{50} +2.64265 q^{51} +0.744019 q^{52} -5.38657 q^{53} +1.16391 q^{54} -8.62288 q^{55} -5.37651 q^{56} +7.22436 q^{57} -8.20042 q^{59} -2.00720 q^{60} +4.90841 q^{61} +4.63856 q^{62} +1.74624 q^{63} +8.64680 q^{64} -3.58617 q^{65} -3.22665 q^{66} -0.453589 q^{67} -1.70534 q^{68} -2.81031 q^{69} +6.32182 q^{70} +11.6046 q^{71} -3.07891 q^{72} -12.8553 q^{73} +12.1859 q^{74} +4.67473 q^{75} -4.66199 q^{76} -4.84102 q^{77} -1.34193 q^{78} -15.4177 q^{79} -7.13200 q^{80} +1.00000 q^{81} +10.3896 q^{82} -4.21480 q^{83} -1.12688 q^{84} +8.21977 q^{85} +13.7296 q^{86} +8.53551 q^{88} -2.03195 q^{89} +3.62025 q^{90} -2.01333 q^{91} +1.81354 q^{92} +3.98533 q^{93} -8.54917 q^{94} +22.4708 q^{95} +3.48904 q^{96} +12.6660 q^{97} -4.59819 q^{98} -2.77225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 5 q^{2} + 9 q^{3} + 11 q^{4} - 4 q^{5} + 5 q^{6} + 5 q^{7} + 24 q^{8} + 9 q^{9} - q^{11} + 11 q^{12} + q^{13} + 9 q^{14} - 4 q^{15} + 35 q^{16} + 2 q^{17} + 5 q^{18} + 9 q^{19} - 18 q^{20} + 5 q^{21}+ \cdots - q^{99}+O(q^{100}) \) 9 * q + 5 * q^2 + 9 * q^3 + 11 * q^4 - 4 * q^5 + 5 * q^6 + 5 * q^7 + 24 * q^8 + 9 * q^9 - q^11 + 11 * q^12 + q^13 + 9 * q^14 - 4 * q^15 + 35 * q^16 + 2 * q^17 + 5 * q^18 + 9 * q^19 - 18 * q^20 + 5 * q^21 - 4 * q^22 - 4 * q^23 + 24 * q^24 + q^25 - 8 * q^26 + 9 * q^27 + 40 * q^28 + 8 * q^31 + 43 * q^32 - q^33 - 4 * q^34 + 22 * q^35 + 11 * q^36 + 27 * q^37 - 30 * q^38 + q^39 - 29 * q^40 + 12 * q^41 + 9 * q^42 + 16 * q^43 + 37 * q^44 - 4 * q^45 - 22 * q^46 - 8 * q^47 + 35 * q^48 - 6 * q^49 - 7 * q^50 + 2 * q^51 + 33 * q^52 - 8 * q^53 + 5 * q^54 + 9 * q^55 + 40 * q^56 + 9 * q^57 - 16 * q^59 - 18 * q^60 + 21 * q^61 - 32 * q^62 + 5 * q^63 + 36 * q^64 - 31 * q^65 - 4 * q^66 + 3 * q^67 + 33 * q^68 - 4 * q^69 - 6 * q^70 - 33 * q^71 + 24 * q^72 + 3 * q^73 + 28 * q^74 + q^75 - 26 * q^76 + 24 * q^77 - 8 * q^78 + 3 * q^79 - 64 * q^80 + 9 * q^81 + 13 * q^82 + 13 * q^83 + 40 * q^84 + 6 * q^85 + 58 * q^86 + 27 * q^88 + 6 * q^89 + q^91 - 29 * q^92 + 8 * q^93 - 18 * q^94 + 48 * q^95 + 43 * q^96 + 4 * q^97 - 30 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more