LMFDB - Embedded newform 2523.2.a.m.1.3

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 = [8,-1,8,11,-9] 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:	$1$
Dimension:	$8$
Coefficient field:	8.8.5878828125.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 13x^{6} + 7x^{5} + 55x^{4} + 3x^{3} - 78x^{2} - 54x - 9 $ x^8 - x^7 - 13x^6 + 7x^5 + 55x^4 + 3x^3 - 78x^2 - 54x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.758720$ 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)

$f(q)$	$=$	\(q-2.09698 q^{2} +1.00000 q^{3} +2.39733 q^{4} -1.13206 q^{5} -2.09698 q^{6} -0.0912936 q^{7} -0.833198 q^{8} +1.00000 q^{9} +2.37390 q^{10} -0.163949 q^{11} +2.39733 q^{12} +1.31599 q^{13} +0.191441 q^{14} -1.13206 q^{15} -3.04746 q^{16} +7.71760 q^{17} -2.09698 q^{18} -5.87961 q^{19} -2.71392 q^{20} -0.0912936 q^{21} +0.343799 q^{22} -7.17942 q^{23} -0.833198 q^{24} -3.71845 q^{25} -2.75960 q^{26} +1.00000 q^{27} -0.218861 q^{28} +2.37390 q^{30} -3.18098 q^{31} +8.05687 q^{32} -0.163949 q^{33} -16.1837 q^{34} +0.103350 q^{35} +2.39733 q^{36} -9.45882 q^{37} +12.3294 q^{38} +1.31599 q^{39} +0.943228 q^{40} +8.17236 q^{41} +0.191441 q^{42} +3.63682 q^{43} -0.393041 q^{44} -1.13206 q^{45} +15.0551 q^{46} +8.29212 q^{47} -3.04746 q^{48} -6.99167 q^{49} +7.79752 q^{50} +7.71760 q^{51} +3.15486 q^{52} -1.28693 q^{53} -2.09698 q^{54} +0.185600 q^{55} +0.0760657 q^{56} -5.87961 q^{57} -10.2612 q^{59} -2.71392 q^{60} -6.48785 q^{61} +6.67046 q^{62} -0.0912936 q^{63} -10.8002 q^{64} -1.48977 q^{65} +0.343799 q^{66} +4.74325 q^{67} +18.5017 q^{68} -7.17942 q^{69} -0.216722 q^{70} -0.498624 q^{71} -0.833198 q^{72} +9.30088 q^{73} +19.8350 q^{74} -3.71845 q^{75} -14.0954 q^{76} +0.0149675 q^{77} -2.75960 q^{78} +13.4381 q^{79} +3.44990 q^{80} +1.00000 q^{81} -17.1373 q^{82} +3.64859 q^{83} -0.218861 q^{84} -8.73677 q^{85} -7.62634 q^{86} +0.136602 q^{88} -9.56754 q^{89} +2.37390 q^{90} -0.120141 q^{91} -17.2115 q^{92} -3.18098 q^{93} -17.3884 q^{94} +6.65606 q^{95} +8.05687 q^{96} -12.6212 q^{97} +14.6614 q^{98} -0.163949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 8 q^{3} + 11 q^{4} - 9 q^{5} - q^{6} - 12 q^{7} - 15 q^{8} + 8 q^{9} - 2 q^{10} + 12 q^{11} + 11 q^{12} - 15 q^{13} - 11 q^{14} - 9 q^{15} + 13 q^{16} + 9 q^{17} - q^{18} - 9 q^{19} - 8 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) $ 8 * q - q^2 + 8 * q^3 + 11 * q^4 - 9 * q^5 - q^6 - 12 * q^7 - 15 * q^8 + 8 * q^9 - 2 * q^10 + 12 * q^11 + 11 * q^12 - 15 * q^13 - 11 * q^14 - 9 * q^15 + 13 * q^16 + 9 * q^17 - q^18 - 9 * q^19 - 8 * q^20 - 12 * q^21 - 24 * q^22 - 15 * q^23 - 15 * q^24 + 7 * q^25 + 5 * q^26 + 8 * q^27 - 39 * q^28 - 2 * q^30 - 20 * q^31 + 9 * q^32 + 12 * q^33 - 23 * q^34 + 6 * q^35 + 11 * q^36 - 17 * q^37 - 2 * q^38 - 15 * q^39 - 5 * q^40 - 20 * q^41 - 11 * q^42 - 20 * q^43 + 24 * q^44 - 9 * q^45 + 20 * q^46 - 9 * q^47 + 13 * q^48 + 2 * q^49 + 51 * q^50 + 9 * q^51 - 35 * q^52 - 39 * q^53 - q^54 - 36 * q^55 + 15 * q^56 - 9 * q^57 - 8 * q^60 - 34 * q^61 + 15 * q^62 - 12 * q^63 - 9 * q^64 - 25 * q^65 - 24 * q^66 - 21 * q^67 + 28 * q^68 - 15 * q^69 + 8 * q^70 + 15 * q^71 - 15 * q^72 + 2 * q^73 + 9 * q^74 + 7 * q^75 - 18 * q^76 - 3 * q^77 + 5 * q^78 - 6 * q^79 - 54 * q^80 + 8 * q^81 - 60 * q^82 + 17 * q^83 - 39 * q^84 - 22 * q^85 - 45 * q^86 - 60 * q^88 + 20 * q^89 - 2 * q^90 + 30 * q^91 - 70 * q^92 - 20 * q^93 - 2 * q^94 + 12 * q^95 + 9 * q^96 + 16 * q^97 + 51 * q^98 + 12 * 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 $

$2$	−2.09698	−1.48279	−0.741395	−	0.671069i	$-0.765835\pi$
$2$	−2.09698	−1.48279	−0.741395	+	0.671069i	$0.765835\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.39733	1.19867
$5$	−1.13206	−0.506271	−0.253136	−	0.967431i	$-0.581462\pi$
$5$	−1.13206	−0.506271	−0.253136	+	0.967431i	$0.581462\pi$
$6$	−2.09698	−0.856089
$7$	−0.0912936	−0.0345057	−0.0172529	−	0.999851i	$-0.505492\pi$
$7$	−0.0912936	−0.0345057	−0.0172529	+	0.999851i	$0.505492\pi$
$8$	−0.833198	−0.294580
$9$	1.00000	0.333333
$10$	2.37390	0.750694
$11$	−0.163949	−0.0494326	−0.0247163	−	0.999695i	$-0.507868\pi$
$11$	−0.163949	−0.0494326	−0.0247163	+	0.999695i	$0.507868\pi$
$12$	2.39733	0.692050
$13$	1.31599	0.364989	0.182495	−	0.983207i	$-0.441583\pi$
$13$	1.31599	0.364989	0.182495	+	0.983207i	$0.441583\pi$
$14$	0.191441	0.0511647
$15$	−1.13206	−0.292296
$16$	−3.04746	−0.761866
$17$	7.71760	1.87179	0.935897	−	0.352274i	$-0.114591\pi$
$17$	7.71760	1.87179	0.935897	+	0.352274i	$0.114591\pi$
$18$	−2.09698	−0.494263
$19$	−5.87961	−1.34888	−0.674438	−	0.738331i	$-0.735614\pi$
$19$	−5.87961	−1.34888	−0.674438	+	0.738331i	$0.735614\pi$
$20$	−2.71392	−0.606850
$21$	−0.0912936	−0.0199219
$22$	0.343799	0.0732981
$23$	−7.17942	−1.49701	−0.748507	−	0.663127i	$-0.769229\pi$
$23$	−7.17942	−1.49701	−0.748507	+	0.663127i	$0.769229\pi$
$24$	−0.833198	−0.170076
$25$	−3.71845	−0.743690
$26$	−2.75960	−0.541202
$27$	1.00000	0.192450
$28$	−0.218861	−0.0413608
$29$	0	0
$29$	0	0
$30$	2.37390	0.433413
$31$	−3.18098	−0.571321	−0.285661	−	0.958331i	$-0.592213\pi$
$31$	−3.18098	−0.571321	−0.285661	+	0.958331i	$0.592213\pi$
$32$	8.05687	1.42427
$33$	−0.163949	−0.0285399
$34$	−16.1837	−2.77548
$35$	0.103350	0.0174693
$36$	2.39733	0.399555
$37$	−9.45882	−1.55502	−0.777510	−	0.628871i	$-0.783518\pi$
$37$	−9.45882	−1.55502	−0.777510	+	0.628871i	$0.783518\pi$
$38$	12.3294	2.00010
$39$	1.31599	0.210727
$40$	0.943228	0.149137
$41$	8.17236	1.27631	0.638154	−	0.769909i	$-0.279698\pi$
$41$	8.17236	1.27631	0.638154	+	0.769909i	$0.279698\pi$
$42$	0.191441	0.0295400
$43$	3.63682	0.554610	0.277305	−	0.960782i	$-0.410559\pi$
$43$	3.63682	0.554610	0.277305	+	0.960782i	$0.410559\pi$
$44$	−0.393041	−0.0592531
$45$	−1.13206	−0.168757
$46$	15.0551	2.21976
$47$	8.29212	1.20953	0.604765	−	0.796404i	$-0.293267\pi$
$47$	8.29212	1.20953	0.604765	+	0.796404i	$0.293267\pi$
$48$	−3.04746	−0.439863
$49$	−6.99167	−0.998809
$50$	7.79752	1.10274
$51$	7.71760	1.08068
$52$	3.15486	0.437500
$53$	−1.28693	−0.176773	−0.0883866	−	0.996086i	$-0.528171\pi$
$53$	−1.28693	−0.176773	−0.0883866	+	0.996086i	$0.528171\pi$
$54$	−2.09698	−0.285363
$55$	0.185600	0.0250263
$56$	0.0760657	0.0101647
$57$	−5.87961	−0.778774
$58$	0	0
$59$	−10.2612	−1.33590	−0.667949	−	0.744207i	$-0.732827\pi$
$59$	−10.2612	−1.33590	−0.667949	+	0.744207i	$0.732827\pi$
$60$	−2.71392	−0.350365
$61$	−6.48785	−0.830684	−0.415342	−	0.909665i	$-0.636338\pi$
$61$	−6.48785	−0.830684	−0.415342	+	0.909665i	$0.636338\pi$
$62$	6.67046	0.847149
$63$	−0.0912936	−0.0115019
$64$	−10.8002	−1.35002
$65$	−1.48977	−0.184784
$66$	0.343799	0.0423187
$67$	4.74325	0.579480	0.289740	−	0.957105i	$-0.406431\pi$
$67$	4.74325	0.579480	0.289740	+	0.957105i	$0.406431\pi$
$68$	18.5017	2.24366
$69$	−7.17942	−0.864301
$70$	−0.216722	−0.0259032
$71$	−0.498624	−0.0591758	−0.0295879	−	0.999562i	$-0.509419\pi$
$71$	−0.498624	−0.0591758	−0.0295879	+	0.999562i	$0.509419\pi$
$72$	−0.833198	−0.0981934
$73$	9.30088	1.08859	0.544293	−	0.838895i	$-0.316798\pi$
$73$	9.30088	1.08859	0.544293	+	0.838895i	$0.316798\pi$
$74$	19.8350	2.30577
$75$	−3.71845	−0.429369
$76$	−14.0954	−1.61685
$77$	0.0149675	0.00170571
$78$	−2.75960	−0.312463
$79$	13.4381	1.51190	0.755952	−	0.654627i	$-0.227175\pi$
$79$	13.4381	1.51190	0.755952	+	0.654627i	$0.227175\pi$
$80$	3.44990	0.385711
$81$	1.00000	0.111111
$82$	−17.1373	−1.89250
$83$	3.64859	0.400484	0.200242	−	0.979746i	$-0.435827\pi$
$83$	3.64859	0.400484	0.200242	+	0.979746i	$0.435827\pi$
$84$	−0.218861	−0.0238797
$85$	−8.73677	−0.947635
$86$	−7.62634	−0.822370
$87$	0	0
$88$	0.136602	0.0145619
$89$	−9.56754	−1.01416	−0.507079	−	0.861900i	$-0.669275\pi$
$89$	−9.56754	−1.01416	−0.507079	+	0.861900i	$0.669275\pi$
$90$	2.37390	0.250231
$91$	−0.120141	−0.0125942
$92$	−17.2115	−1.79442
$93$	−3.18098	−0.329852
$94$	−17.3884	−1.79348
$95$	6.65606	0.682897
$96$	8.05687	0.822301
$97$	−12.6212	−1.28149	−0.640746	−	0.767753i	$-0.721375\pi$
$97$	−12.6212	−1.28149	−0.640746	+	0.767753i	$0.721375\pi$
$98$	14.6614	1.48102
$99$	−0.163949	−0.0164775
$100$	−8.91435	−0.891435
$101$	−7.21725	−0.718143	−0.359072	−	0.933310i	$-0.616907\pi$
$101$	−7.21725	−0.718143	−0.359072	+	0.933310i	$0.616907\pi$
$102$	−16.1837	−1.60242
$103$	−15.4950	−1.52677	−0.763383	−	0.645946i	$-0.776463\pi$
$103$	−15.4950	−1.52677	−0.763383	+	0.645946i	$0.776463\pi$
$104$	−1.09648	−0.107519
$105$	0.103350	0.0100859
$106$	2.69867	0.262118
$107$	−10.5923	−1.02400	−0.511998	−	0.858987i	$-0.671095\pi$
$107$	−10.5923	−1.02400	−0.511998	+	0.858987i	$0.671095\pi$
$108$	2.39733	0.230683
$109$	4.55678	0.436461	0.218230	−	0.975897i	$-0.429972\pi$
$109$	4.55678	0.436461	0.218230	+	0.975897i	$0.429972\pi$
$110$	−0.389200	−0.0371087
$111$	−9.45882	−0.897791
$112$	0.278214	0.0262887
$113$	−8.87084	−0.834498	−0.417249	−	0.908792i	$-0.637006\pi$
$113$	−8.87084	−0.834498	−0.417249	+	0.908792i	$0.637006\pi$
$114$	12.3294	1.15476
$115$	8.12751	0.757895
$116$	0	0
$117$	1.31599	0.121663
$118$	21.5176	1.98086
$119$	−0.704568	−0.0645876
$120$	0.943228	0.0861045
$121$	−10.9731	−0.997556
$122$	13.6049	1.23173
$123$	8.17236	0.736877
$124$	−7.62587	−0.684823
$125$	9.86978	0.882780
$126$	0.191441	0.0170549
$127$	8.09974	0.718736	0.359368	−	0.933196i	$-0.382992\pi$
$127$	8.09974	0.718736	0.359368	+	0.933196i	$0.382992\pi$
$128$	6.53405	0.577534
$129$	3.63682	0.320204
$130$	3.12403	0.273995
$131$	8.04982	0.703316	0.351658	−	0.936129i	$-0.385618\pi$
$131$	8.04982	0.703316	0.351658	+	0.936129i	$0.385618\pi$
$132$	−0.393041	−0.0342098
$133$	0.536771	0.0465440
$134$	−9.94651	−0.859248
$135$	−1.13206	−0.0974319
$136$	−6.43030	−0.551393
$137$	6.91181	0.590516	0.295258	−	0.955418i	$-0.404594\pi$
$137$	6.91181	0.590516	0.295258	+	0.955418i	$0.404594\pi$
$138$	15.0551	1.28158
$139$	7.66177	0.649863	0.324932	−	0.945738i	$-0.394659\pi$
$139$	7.66177	0.649863	0.324932	+	0.945738i	$0.394659\pi$
$140$	0.247763	0.0209398
$141$	8.29212	0.698322
$142$	1.04560	0.0877452
$143$	−0.215755	−0.0180424
$144$	−3.04746	−0.253955
$145$	0	0
$146$	−19.5038	−1.61414
$147$	−6.99167	−0.576663
$148$	−22.6759	−1.86395
$149$	−15.7867	−1.29330	−0.646649	−	0.762788i	$-0.723830\pi$
$149$	−15.7867	−1.29330	−0.646649	+	0.762788i	$0.723830\pi$
$150$	7.79752	0.636665
$151$	0.635934	0.0517516	0.0258758	−	0.999665i	$-0.491763\pi$
$151$	0.635934	0.0517516	0.0258758	+	0.999665i	$0.491763\pi$
$152$	4.89888	0.397352
$153$	7.71760	0.623931
$154$	−0.0313866	−0.00252921
$155$	3.60105	0.289243
$156$	3.15486	0.252591
$157$	−23.8012	−1.89954	−0.949771	−	0.312946i	$-0.898684\pi$
$157$	−23.8012	−1.89954	−0.949771	+	0.312946i	$0.898684\pi$
$158$	−28.1794	−2.24183
$159$	−1.28693	−0.102060
$160$	−9.12083	−0.721065
$161$	0.655435	0.0516555
$162$	−2.09698	−0.164754
$163$	3.91590	0.306717	0.153358	−	0.988171i	$-0.450991\pi$
$163$	3.91590	0.306717	0.153358	+	0.988171i	$0.450991\pi$
$164$	19.5919	1.52987
$165$	0.185600	0.0144489
$166$	−7.65102	−0.593834
$167$	10.8198	0.837264	0.418632	−	0.908156i	$-0.362510\pi$
$167$	10.8198	0.837264	0.418632	+	0.908156i	$0.362510\pi$
$168$	0.0760657	0.00586859
$169$	−11.2682	−0.866783
$170$	18.3208	1.40514
$171$	−5.87961	−0.449625
$172$	8.71866	0.664792
$173$	−9.24218	−0.702670	−0.351335	−	0.936250i	$-0.614272\pi$
$173$	−9.24218	−0.702670	−0.351335	+	0.936250i	$0.614272\pi$
$174$	0	0
$175$	0.339470	0.0256616
$176$	0.499629	0.0376610
$177$	−10.2612	−0.771281
$178$	20.0630	1.50378
$179$	23.1857	1.73298	0.866492	−	0.499192i	$-0.166370\pi$
$179$	23.1857	1.73298	0.866492	+	0.499192i	$0.166370\pi$
$180$	−2.71392	−0.202283
$181$	−9.10833	−0.677017	−0.338509	−	0.940963i	$-0.609922\pi$
$181$	−9.10833	−0.677017	−0.338509	+	0.940963i	$0.609922\pi$
$182$	0.251934	0.0186746
$183$	−6.48785	−0.479595
$184$	5.98188	0.440990
$185$	10.7079	0.787262
$186$	6.67046	0.489102
$187$	−1.26530	−0.0925276
$188$	19.8790	1.44982
$189$	−0.0912936	−0.00664063
$190$	−13.9576	−1.01259
$191$	−18.0224	−1.30405	−0.652027	−	0.758196i	$-0.726081\pi$
$191$	−18.0224	−1.30405	−0.652027	+	0.758196i	$0.726081\pi$
$192$	−10.8002	−0.779436
$193$	1.58339	0.113975	0.0569875	−	0.998375i	$-0.481850\pi$
$193$	1.58339	0.113975	0.0569875	+	0.998375i	$0.481850\pi$
$194$	26.4665	1.90018
$195$	−1.48977	−0.106685
$196$	−16.7613	−1.19724
$197$	−10.4546	−0.744863	−0.372431	−	0.928060i	$-0.621476\pi$
$197$	−10.4546	−0.744863	−0.372431	+	0.928060i	$0.621476\pi$
$198$	0.343799	0.0244327
$199$	3.74757	0.265658	0.132829	−	0.991139i	$-0.457594\pi$
$199$	3.74757	0.265658	0.132829	+	0.991139i	$0.457594\pi$
$200$	3.09820	0.219076
$201$	4.74325	0.334563
$202$	15.1344	1.06486
$203$	0	0
$204$	18.5017	1.29538
$205$	−9.25158	−0.646158
$206$	32.4927	2.26387
$207$	−7.17942	−0.499004
$208$	−4.01042	−0.278073
$209$	0.963959	0.0666784
$210$	−0.216722	−0.0149552
$211$	−26.1603	−1.80095	−0.900475	−	0.434907i	$-0.856781\pi$
$211$	−26.1603	−1.80095	−0.900475	+	0.434907i	$0.856781\pi$
$212$	−3.08519	−0.211892
$213$	−0.498624	−0.0341651
$214$	22.2119	1.51837
$215$	−4.11708	−0.280783
$216$	−0.833198	−0.0566920
$217$	0.290403	0.0197139
$218$	−9.55549	−0.647179
$219$	9.30088	0.628495
$220$	0.444945	0.0299982
$221$	10.1563	0.683185
$222$	19.8350	1.33124
$223$	25.9173	1.73555	0.867776	−	0.496956i	$-0.165549\pi$
$223$	25.9173	1.73555	0.867776	+	0.496956i	$0.165549\pi$
$224$	−0.735541	−0.0491454
$225$	−3.71845	−0.247897
$226$	18.6020	1.23739
$227$	9.08975	0.603308	0.301654	−	0.953417i	$-0.402461\pi$
$227$	9.08975	0.603308	0.301654	+	0.953417i	$0.402461\pi$
$228$	−14.0954	−0.933490
$229$	−9.16097	−0.605374	−0.302687	−	0.953090i	$-0.597884\pi$
$229$	−9.16097	−0.605374	−0.302687	+	0.953090i	$0.597884\pi$
$230$	−17.0432	−1.12380
$231$	0.0149675	0.000984790 0
$232$	0	0
$233$	−12.6349	−0.827739	−0.413869	−	0.910336i	$-0.635823\pi$
$233$	−12.6349	−0.827739	−0.413869	+	0.910336i	$0.635823\pi$
$234$	−2.75960	−0.180401
$235$	−9.38714	−0.612350
$236$	−24.5996	−1.60130
$237$	13.4381	0.872898
$238$	1.47747	0.0957699
$239$	11.3997	0.737388	0.368694	−	0.929551i	$-0.379805\pi$
$239$	11.3997	0.737388	0.368694	+	0.929551i	$0.379805\pi$
$240$	3.44990	0.222690
$241$	−20.1130	−1.29559	−0.647795	−	0.761814i	$-0.724309\pi$
$241$	−20.1130	−1.29559	−0.647795	+	0.761814i	$0.724309\pi$
$242$	23.0104	1.47917
$243$	1.00000	0.0641500
$244$	−15.5535	−0.995712
$245$	7.91496	0.505668
$246$	−17.1373	−1.09263
$247$	−7.73750	−0.492325
$248$	2.65039	0.168300
$249$	3.64859	0.231220
$250$	−20.6967	−1.30898
$251$	0.748847	0.0472668	0.0236334	−	0.999721i	$-0.492477\pi$
$251$	0.748847	0.0472668	0.0236334	+	0.999721i	$0.492477\pi$
$252$	−0.218861	−0.0137869
$253$	1.17706	0.0740012
$254$	−16.9850	−1.06573
$255$	−8.73677	−0.547118
$256$	7.89859	0.493662
$257$	9.30596	0.580490	0.290245	−	0.956952i	$-0.406263\pi$
$257$	9.30596	0.580490	0.290245	+	0.956952i	$0.406263\pi$
$258$	−7.62634	−0.474795
$259$	0.863529	0.0536571
$260$	−3.57148	−0.221494
$261$	0	0
$262$	−16.8803	−1.04287
$263$	−13.4886	−0.831740	−0.415870	−	0.909424i	$-0.636523\pi$
$263$	−13.4886	−0.831740	−0.415870	+	0.909424i	$0.636523\pi$
$264$	0.136602	0.00840729
$265$	1.45688	0.0894952
$266$	−1.12560	−0.0690149
$267$	−9.56754	−0.585524
$268$	11.3712	0.694604
$269$	−22.9084	−1.39675	−0.698375	−	0.715733i	$-0.746093\pi$
$269$	−22.9084	−1.39675	−0.698375	+	0.715733i	$0.746093\pi$
$270$	2.37390	0.144471
$271$	−0.252974	−0.0153671	−0.00768353	−	0.999970i	$-0.502446\pi$
$271$	−0.252974	−0.0153671	−0.00768353	+	0.999970i	$0.502446\pi$
$272$	−23.5191	−1.42606
$273$	−0.120141	−0.00727128
$274$	−14.4939	−0.875611
$275$	0.609637	0.0367625
$276$	−17.2115	−1.03601
$277$	−18.0655	−1.08545	−0.542726	−	0.839910i	$-0.682608\pi$
$277$	−18.0655	−1.08545	−0.542726	+	0.839910i	$0.682608\pi$
$278$	−16.0666	−0.963611
$279$	−3.18098	−0.190440
$280$	−0.0861106	−0.00514609
$281$	13.0549	0.778787	0.389394	−	0.921071i	$-0.372685\pi$
$281$	13.0549	0.778787	0.389394	+	0.921071i	$0.372685\pi$
$282$	−17.3884	−1.03546
$283$	−21.6748	−1.28843	−0.644216	−	0.764844i	$-0.722816\pi$
$283$	−21.6748	−1.28843	−0.644216	+	0.764844i	$0.722816\pi$
$284$	−1.19537	−0.0709320
$285$	6.65606	0.394271
$286$	0.452435	0.0267530
$287$	−0.746084	−0.0440400
$288$	8.05687	0.474756
$289$	42.5614	2.50361
$290$	0	0
$291$	−12.6212	−0.739870
$292$	22.2973	1.30485
$293$	−25.4395	−1.48619	−0.743097	−	0.669184i	$-0.766644\pi$
$293$	−25.4395	−1.48619	−0.743097	+	0.669184i	$0.766644\pi$
$294$	14.6614	0.855070
$295$	11.6163	0.676326
$296$	7.88107	0.458078
$297$	−0.163949	−0.00951330
$298$	33.1044	1.91769
$299$	−9.44803	−0.546394
$300$	−8.91435	−0.514670
$301$	−0.332018	−0.0191372
$302$	−1.33354	−0.0767367
$303$	−7.21725	−0.414620
$304$	17.9179	1.02766
$305$	7.34461	0.420551
$306$	−16.1837	−0.925159
$307$	−13.6331	−0.778083	−0.389041	−	0.921220i	$-0.627194\pi$
$307$	−13.6331	−0.778083	−0.389041	+	0.921220i	$0.627194\pi$
$308$	0.0358821	0.00204457
$309$	−15.4950	−0.881479
$310$	−7.55134	−0.428887
$311$	−27.3748	−1.55228	−0.776140	−	0.630560i	$-0.782825\pi$
$311$	−27.3748	−1.55228	−0.776140	+	0.630560i	$0.782825\pi$
$312$	−1.09648	−0.0620759
$313$	−17.7630	−1.00402	−0.502012	−	0.864861i	$-0.667407\pi$
$313$	−17.7630	−1.00402	−0.502012	+	0.864861i	$0.667407\pi$
$314$	49.9107	2.81662
$315$	0.103350	0.00582308
$316$	32.2156	1.81227
$317$	5.14271	0.288844	0.144422	−	0.989516i	$-0.453868\pi$
$317$	5.14271	0.288844	0.144422	+	0.989516i	$0.453868\pi$
$318$	2.69867	0.151334
$319$	0	0
$320$	12.2264	0.683478
$321$	−10.5923	−0.591204
$322$	−1.37444	−0.0765943
$323$	−45.3765	−2.52482
$324$	2.39733	0.133185
$325$	−4.89343	−0.271439
$326$	−8.21156	−0.454796
$327$	4.55678	0.251991
$328$	−6.80920	−0.375975
$329$	−0.757017	−0.0417357
$330$	−0.389200	−0.0214247
$331$	14.1996	0.780479	0.390239	−	0.920713i	$-0.372392\pi$
$331$	14.1996	0.780479	0.390239	+	0.920713i	$0.372392\pi$
$332$	8.74688	0.480047
$333$	−9.45882	−0.518340
$334$	−22.6890	−1.24149
$335$	−5.36963	−0.293374
$336$	0.278214	0.0151778
$337$	33.9954	1.85185	0.925925	−	0.377708i	$-0.123288\pi$
$337$	33.9954	1.85185	0.925925	+	0.377708i	$0.123288\pi$
$338$	23.6292	1.28526
$339$	−8.87084	−0.481798
$340$	−20.9449	−1.13590
$341$	0.521520	0.0282419
$342$	12.3294	0.666700
$343$	1.27735	0.0689704
$344$	−3.03019	−0.163377
$345$	8.12751	0.437571
$346$	19.3807	1.04191
$347$	−12.1147	−0.650351	−0.325175	−	0.945654i	$-0.605423\pi$
$347$	−12.1147	−0.650351	−0.325175	+	0.945654i	$0.605423\pi$
$348$	0	0
$349$	4.80123	0.257004	0.128502	−	0.991709i	$-0.458983\pi$
$349$	4.80123	0.257004	0.128502	+	0.991709i	$0.458983\pi$
$350$	−0.711863	−0.0380507
$351$	1.31599	0.0702422
$352$	−1.32092	−0.0704052
$353$	−17.7002	−0.942085	−0.471042	−	0.882111i	$-0.656122\pi$
$353$	−17.7002	−0.942085	−0.471042	+	0.882111i	$0.656122\pi$
$354$	21.5176	1.14365
$355$	0.564470	0.0299590
$356$	−22.9366	−1.21564
$357$	−0.704568	−0.0372897
$358$	−48.6201	−2.56965
$359$	−1.99568	−0.105328	−0.0526641	−	0.998612i	$-0.516771\pi$
$359$	−1.99568	−0.105328	−0.0526641	+	0.998612i	$0.516771\pi$
$360$	0.943228	0.0497125
$361$	15.5699	0.819467
$362$	19.1000	1.00387
$363$	−10.9731	−0.575939
$364$	−0.288018	−0.0150963
$365$	−10.5291	−0.551120
$366$	13.6049	0.711139
$367$	6.40827	0.334509	0.167255	−	0.985914i	$-0.446510\pi$
$367$	6.40827	0.334509	0.167255	+	0.985914i	$0.446510\pi$
$368$	21.8790	1.14052
$369$	8.17236	0.425436
$370$	−22.4543	−1.16734
$371$	0.117488	0.00609969
$372$	−7.62587	−0.395383
$373$	−37.9983	−1.96748	−0.983739	−	0.179605i	$-0.942518\pi$
$373$	−37.9983	−1.96748	−0.983739	+	0.179605i	$0.942518\pi$
$374$	2.65330	0.137199
$375$	9.86978	0.509673
$376$	−6.90898	−0.356303
$377$	0	0
$378$	0.191441	0.00984666
$379$	−34.1968	−1.75657	−0.878286	−	0.478136i	$-0.841313\pi$
$379$	−34.1968	−1.75657	−0.878286	+	0.478136i	$0.841313\pi$
$380$	15.9568	0.818565
$381$	8.09974	0.414962
$382$	37.7926	1.93364
$383$	−17.9240	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$383$	−17.9240	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$384$	6.53405	0.333439
$385$	−0.0169441	−0.000863550 0
$386$	−3.32034	−0.169001
$387$	3.63682	0.184870
$388$	−30.2573	−1.53608
$389$	−13.4961	−0.684280	−0.342140	−	0.939649i	$-0.611152\pi$
$389$	−13.4961	−0.684280	−0.342140	+	0.939649i	$0.611152\pi$
$390$	3.12403	0.158191
$391$	−55.4080	−2.80210
$392$	5.82544	0.294229
$393$	8.04982	0.406060
$394$	21.9232	1.10447
$395$	−15.2127	−0.765433
$396$	−0.393041	−0.0197510
$397$	−3.90554	−0.196014	−0.0980068	−	0.995186i	$-0.531247\pi$
$397$	−3.90554	−0.196014	−0.0980068	+	0.995186i	$0.531247\pi$
$398$	−7.85859	−0.393916
$399$	0.536771	0.0268722
$400$	11.3318	0.566592
$401$	−17.8068	−0.889231	−0.444616	−	0.895722i	$-0.646660\pi$
$401$	−17.8068	−0.889231	−0.444616	+	0.895722i	$0.646660\pi$
$402$	−9.94651	−0.496087
$403$	−4.18613	−0.208526
$404$	−17.3021	−0.860814
$405$	−1.13206	−0.0562523
$406$	0	0
$407$	1.55077	0.0768686
$408$	−6.43030	−0.318347
$409$	13.5378	0.669402	0.334701	−	0.942324i	$-0.391365\pi$
$409$	13.5378	0.669402	0.334701	+	0.942324i	$0.391365\pi$
$410$	19.4004	0.958117
$411$	6.91181	0.340935
$412$	−37.1466	−1.83008
$413$	0.936784	0.0460961
$414$	15.0551	0.739919
$415$	−4.13041	−0.202754
$416$	10.6027	0.519842
$417$	7.66177	0.375199
$418$	−2.02140	−0.0988701
$419$	28.2739	1.38127	0.690636	−	0.723203i	$-0.257331\pi$
$419$	28.2739	1.38127	0.690636	+	0.723203i	$0.257331\pi$
$420$	0.247763	0.0120896
$421$	18.0251	0.878490	0.439245	−	0.898367i	$-0.355246\pi$
$421$	18.0251	0.878490	0.439245	+	0.898367i	$0.355246\pi$
$422$	54.8577	2.67043
$423$	8.29212	0.403176
$424$	1.07227	0.0520739
$425$	−28.6975	−1.39203
$426$	1.04560	0.0506597
$427$	0.592299	0.0286633
$428$	−25.3933	−1.22743
$429$	−0.215755	−0.0104168
$430$	8.63345	0.416342
$431$	11.2989	0.544247	0.272124	−	0.962262i	$-0.412274\pi$
$431$	11.2989	0.544247	0.272124	+	0.962262i	$0.412274\pi$
$432$	−3.04746	−0.146621
$433$	−10.4849	−0.503874	−0.251937	−	0.967744i	$-0.581068\pi$
$433$	−10.4849	−0.503874	−0.251937	+	0.967744i	$0.581068\pi$
$434$	−0.608970	−0.0292315
$435$	0	0
$436$	10.9241	0.523170
$437$	42.2122	2.01929
$438$	−19.5038	−0.931927
$439$	−12.0658	−0.575869	−0.287934	−	0.957650i	$-0.592969\pi$
$439$	−12.0658	−0.575869	−0.287934	+	0.957650i	$0.592969\pi$
$440$	−0.154642	−0.00737225
$441$	−6.99167	−0.332936
$442$	−21.2975	−1.01302
$443$	23.2867	1.10639	0.553193	−	0.833053i	$-0.313409\pi$
$443$	23.2867	1.10639	0.553193	+	0.833053i	$0.313409\pi$
$444$	−22.6759	−1.07615
$445$	10.8310	0.513439
$446$	−54.3481	−2.57346
$447$	−15.7867	−0.746686
$448$	0.985987	0.0465835
$449$	34.3214	1.61973	0.809864	−	0.586617i	$-0.199541\pi$
$449$	34.3214	1.61973	0.809864	+	0.586617i	$0.199541\pi$
$450$	7.79752	0.367578
$451$	−1.33985	−0.0630912
$452$	−21.2663	−1.00028
$453$	0.635934	0.0298788
$454$	−19.0610	−0.894579
$455$	0.136007	0.00637609
$456$	4.89888	0.229411
$457$	−4.33538	−0.202801	−0.101400	−	0.994846i	$-0.532332\pi$
$457$	−4.33538	−0.202801	−0.101400	+	0.994846i	$0.532332\pi$
$458$	19.2104	0.897642
$459$	7.71760	0.360227
$460$	19.4844	0.908463
$461$	26.1946	1.22000	0.610002	−	0.792400i	$-0.291168\pi$
$461$	26.1946	1.22000	0.610002	+	0.792400i	$0.291168\pi$
$462$	−0.0313866	−0.00146024
$463$	−36.9851	−1.71884	−0.859422	−	0.511267i	$-0.829176\pi$
$463$	−36.9851	−1.71884	−0.859422	+	0.511267i	$0.829176\pi$
$464$	0	0
$465$	3.60105	0.166995
$466$	26.4951	1.22736
$467$	9.31884	0.431224	0.215612	−	0.976479i	$-0.430825\pi$
$467$	9.31884	0.431224	0.215612	+	0.976479i	$0.430825\pi$
$468$	3.15486	0.145833
$469$	−0.433028	−0.0199954
$470$	19.6847	0.907986
$471$	−23.8012	−1.09670
$472$	8.54963	0.393529
$473$	−0.596254	−0.0274158
$474$	−28.1794	−1.29432
$475$	21.8630	1.00314
$476$	−1.68908	−0.0774190
$477$	−1.28693	−0.0589244
$478$	−23.9050	−1.09339
$479$	27.7692	1.26881	0.634403	−	0.773002i	$-0.281246\pi$
$479$	27.7692	1.26881	0.634403	+	0.773002i	$0.281246\pi$
$480$	−9.12083	−0.416307
$481$	−12.4477	−0.567566
$482$	42.1765	1.92109
$483$	0.655435	0.0298233
$484$	−26.3062	−1.19574
$485$	14.2880	0.648783
$486$	−2.09698	−0.0951210
$487$	−16.4009	−0.743196	−0.371598	−	0.928394i	$-0.621190\pi$
$487$	−16.4009	−0.743196	−0.371598	+	0.928394i	$0.621190\pi$
$488$	5.40566	0.244703
$489$	3.91590	0.177083
$490$	−16.5975	−0.749800
$491$	10.3115	0.465352	0.232676	−	0.972554i	$-0.425252\pi$
$491$	10.3115	0.465352	0.232676	+	0.972554i	$0.425252\pi$
$492$	19.5919	0.883269
$493$	0	0
$494$	16.2254	0.730015
$495$	0.185600	0.00834209
$496$	9.69392	0.435270
$497$	0.0455211	0.00204190
$498$	−7.65102	−0.342850
$499$	23.6561	1.05899	0.529497	−	0.848312i	$-0.322381\pi$
$499$	23.6561	1.05899	0.529497	+	0.848312i	$0.322381\pi$
$500$	23.6611	1.05816
$501$	10.8198	0.483394
$502$	−1.57032	−0.0700868
$503$	−22.3591	−0.996944	−0.498472	−	0.866906i	$-0.666105\pi$
$503$	−22.3591	−0.996944	−0.498472	+	0.866906i	$0.666105\pi$
$504$	0.0760657	0.00338823
$505$	8.17034	0.363575
$506$	−2.46828	−0.109728
$507$	−11.2682	−0.500437
$508$	19.4178	0.861524
$509$	−6.26755	−0.277804	−0.138902	−	0.990306i	$-0.544357\pi$
$509$	−6.26755	−0.277804	−0.138902	+	0.990306i	$0.544357\pi$
$510$	18.3208	0.811260
$511$	−0.849111	−0.0375624
$512$	−29.6313	−1.30953
$513$	−5.87961	−0.259591
$514$	−19.5144	−0.860745
$515$	17.5412	0.772957
$516$	8.71866	0.383818
$517$	−1.35949	−0.0597901
$518$	−1.81081	−0.0795622
$519$	−9.24218	−0.405687
$520$	1.24128	0.0544335
$521$	7.10042	0.311075	0.155537	−	0.987830i	$-0.450289\pi$
$521$	7.10042	0.311075	0.155537	+	0.987830i	$0.450289\pi$
$522$	0	0
$523$	34.1343	1.49259	0.746295	−	0.665616i	$-0.231831\pi$
$523$	34.1343	1.49259	0.746295	+	0.665616i	$0.231831\pi$
$524$	19.2981	0.843041
$525$	0.339470	0.0148157
$526$	28.2853	1.23330
$527$	−24.5496	−1.06940
$528$	0.499629	0.0217436
$529$	28.5441	1.24105
$530$	−3.05504	−0.132703
$531$	−10.2612	−0.445299
$532$	1.28682	0.0557907
$533$	10.7547	0.465839
$534$	20.0630	0.868209
$535$	11.9911	0.518420
$536$	−3.95207	−0.170703
$537$	23.1857	1.00054
$538$	48.0385	2.07109
$539$	1.14628	0.0493737
$540$	−2.71392	−0.116788
$541$	21.3516	0.917979	0.458990	−	0.888442i	$-0.348212\pi$
$541$	21.3516	0.917979	0.458990	+	0.888442i	$0.348212\pi$
$542$	0.530481	0.0227861
$543$	−9.10833	−0.390876
$544$	62.1797	2.66593
$545$	−5.15854	−0.220967
$546$	0.251934	0.0107818
$547$	−1.57848	−0.0674909	−0.0337455	−	0.999430i	$-0.510744\pi$
$547$	−1.57848	−0.0674909	−0.0337455	+	0.999430i	$0.510744\pi$
$548$	16.5699	0.707832
$549$	−6.48785	−0.276895
$550$	−1.27840	−0.0545110
$551$	0	0
$552$	5.98188	0.254606
$553$	−1.22681	−0.0521693
$554$	37.8831	1.60950
$555$	10.7079	0.454526
$556$	18.3678	0.778969
$557$	10.8029	0.457733	0.228866	−	0.973458i	$-0.426498\pi$
$557$	10.8029	0.457733	0.228866	+	0.973458i	$0.426498\pi$
$558$	6.67046	0.282383
$559$	4.78601	0.202427
$560$	−0.314954	−0.0133092
$561$	−1.26530	−0.0534208
$562$	−27.3758	−1.15478
$563$	9.00865	0.379669	0.189835	−	0.981816i	$-0.439205\pi$
$563$	9.00865	0.379669	0.189835	+	0.981816i	$0.439205\pi$
$564$	19.8790	0.837055
$565$	10.0423	0.422482
$566$	45.4516	1.91047
$567$	−0.0912936	−0.00383397
$568$	0.415452	0.0174320
$569$	−4.88055	−0.204603	−0.102302	−	0.994753i	$-0.532621\pi$
$569$	−4.88055	−0.204603	−0.102302	+	0.994753i	$0.532621\pi$
$570$	−13.9576	−0.584621
$571$	−12.4919	−0.522770	−0.261385	−	0.965235i	$-0.584179\pi$
$571$	−12.4919	−0.522770	−0.261385	+	0.965235i	$0.584179\pi$
$572$	−0.517237	−0.0216268
$573$	−18.0224	−0.752895
$574$	1.56452	0.0653020
$575$	26.6963	1.11331
$576$	−10.8002	−0.450008
$577$	−1.29103	−0.0537461	−0.0268730	−	0.999639i	$-0.508555\pi$
$577$	−1.29103	−0.0537461	−0.0268730	+	0.999639i	$0.508555\pi$
$578$	−89.2505	−3.71233
$579$	1.58339	0.0658035
$580$	0	0
$581$	−0.333093	−0.0138190
$582$	26.4665	1.09707
$583$	0.210991	0.00873835
$584$	−7.74948	−0.320676
$585$	−1.48977	−0.0615945
$586$	53.3462	2.20371
$587$	20.6154	0.850888	0.425444	−	0.904985i	$-0.360118\pi$
$587$	20.6154	0.850888	0.425444	+	0.904985i	$0.360118\pi$
$588$	−16.7613	−0.691226
$589$	18.7029	0.770641
$590$	−24.3591	−1.00285
$591$	−10.4546	−0.430047
$592$	28.8254	1.18472
$593$	12.4617	0.511742	0.255871	−	0.966711i	$-0.417638\pi$
$593$	12.4617	0.511742	0.255871	+	0.966711i	$0.417638\pi$
$594$	0.343799	0.0141062
$595$	0.797611	0.0326988
$596$	−37.8460	−1.55023
$597$	3.74757	0.153378
$598$	19.8123	0.810187
$599$	10.8545	0.443502	0.221751	−	0.975103i	$-0.428823\pi$
$599$	10.8545	0.443502	0.221751	+	0.975103i	$0.428823\pi$
$600$	3.09820	0.126484
$601$	40.9778	1.67152	0.835761	−	0.549094i	$-0.185027\pi$
$601$	40.9778	1.67152	0.835761	+	0.549094i	$0.185027\pi$
$602$	0.696236	0.0283765
$603$	4.74325	0.193160
$604$	1.52455	0.0620329
$605$	12.4222	0.505034
$606$	15.1344	0.614795
$607$	−3.25085	−0.131948	−0.0659740	−	0.997821i	$-0.521015\pi$
$607$	−3.25085	−0.131948	−0.0659740	+	0.997821i	$0.521015\pi$
$608$	−47.3713	−1.92116
$609$	0	0
$610$	−15.4015	−0.623589
$611$	10.9123	0.441465
$612$	18.5017	0.747885
$613$	23.5901	0.952797	0.476398	−	0.879230i	$-0.341942\pi$
$613$	23.5901	0.952797	0.476398	+	0.879230i	$0.341942\pi$
$614$	28.5884	1.15373
$615$	−9.25158	−0.373060
$616$	−0.0124709	−0.000502467 0
$617$	−0.947410	−0.0381413	−0.0190706	−	0.999818i	$-0.506071\pi$
$617$	−0.947410	−0.0381413	−0.0190706	+	0.999818i	$0.506071\pi$
$618$	32.4927	1.30705
$619$	−17.6721	−0.710300	−0.355150	−	0.934809i	$-0.615570\pi$
$619$	−17.6721	−0.710300	−0.355150	+	0.934809i	$0.615570\pi$
$620$	8.63292	0.346706
$621$	−7.17942	−0.288100
$622$	57.4044	2.30171
$623$	0.873455	0.0349942
$624$	−4.01042	−0.160545
$625$	7.41909	0.296764
$626$	37.2487	1.48876
$627$	0.963959	0.0384968
$628$	−57.0594	−2.27692
$629$	−72.9994	−2.91068
$630$	−0.216722	−0.00863441
$631$	41.0803	1.63538	0.817689	−	0.575660i	$-0.195255\pi$
$631$	41.0803	1.63538	0.817689	+	0.575660i	$0.195255\pi$
$632$	−11.1966	−0.445377
$633$	−26.1603	−1.03978
$634$	−10.7842	−0.428294
$635$	−9.16936	−0.363875
$636$	−3.08519	−0.122336
$637$	−9.20094	−0.364555
$638$	0	0
$639$	−0.498624	−0.0197253
$640$	−7.39691	−0.292389
$641$	−13.7121	−0.541597	−0.270798	−	0.962636i	$-0.587288\pi$
$641$	−13.7121	−0.541597	−0.270798	+	0.962636i	$0.587288\pi$
$642$	22.2119	0.876632
$643$	6.81932	0.268928	0.134464	−	0.990918i	$-0.457069\pi$
$643$	6.81932	0.268928	0.134464	+	0.990918i	$0.457069\pi$
$644$	1.57130	0.0619177
$645$	−4.11708	−0.162110
$646$	95.1538	3.74378
$647$	−1.97113	−0.0774931	−0.0387465	−	0.999249i	$-0.512336\pi$
$647$	−1.97113	−0.0774931	−0.0387465	+	0.999249i	$0.512336\pi$
$648$	−0.833198	−0.0327311
$649$	1.68232	0.0660369
$650$	10.2614	0.402487
$651$	0.290403	0.0113818
$652$	9.38771	0.367651
$653$	36.9164	1.44465	0.722325	−	0.691554i	$-0.243074\pi$
$653$	36.9164	1.44465	0.722325	+	0.691554i	$0.243074\pi$
$654$	−9.55549	−0.373649
$655$	−9.11285	−0.356068
$656$	−24.9050	−0.972376
$657$	9.30088	0.362862
$658$	1.58745	0.0618853
$659$	3.59139	0.139901	0.0699503	−	0.997550i	$-0.477716\pi$
$659$	3.59139	0.139901	0.0699503	+	0.997550i	$0.477716\pi$
$660$	0.444945	0.0173194
$661$	−0.738752	−0.0287341	−0.0143671	−	0.999897i	$-0.504573\pi$
$661$	−0.738752	−0.0287341	−0.0143671	+	0.999897i	$0.504573\pi$
$662$	−29.7762	−1.15729
$663$	10.1563	0.394437
$664$	−3.04000	−0.117975
$665$	−0.607655	−0.0235639
$666$	19.8350	0.768589
$667$	0	0
$668$	25.9387	1.00360
$669$	25.9173	1.00202
$670$	11.2600	0.435012
$671$	1.06368	0.0410628
$672$	−0.735541	−0.0283741
$673$	0.0479660	0.00184895	0.000924476	−	1.00000i	$-0.499706\pi$
$673$	0.0479660	0.00184895	0.000924476		1.00000i	$0.499706\pi$
$674$	−71.2878	−2.74590
$675$	−3.71845	−0.143123
$676$	−27.0136	−1.03898
$677$	14.3152	0.550176	0.275088	−	0.961419i	$-0.411293\pi$
$677$	14.3152	0.550176	0.275088	+	0.961419i	$0.411293\pi$
$678$	18.6020	0.714405
$679$	1.15224	0.0442188
$680$	7.27946	0.279155
$681$	9.08975	0.348320
$682$	−1.09362	−0.0418768
$683$	3.42727	0.131141	0.0655705	−	0.997848i	$-0.479113\pi$
$683$	3.42727	0.131141	0.0655705	+	0.997848i	$0.479113\pi$
$684$	−14.0954	−0.538951
$685$	−7.82456	−0.298961
$686$	−2.67858	−0.102269
$687$	−9.16097	−0.349513
$688$	−11.0831	−0.422538
$689$	−1.69358	−0.0645203
$690$	−17.0432	−0.648825
$691$	−11.4442	−0.435359	−0.217680	−	0.976020i	$-0.569849\pi$
$691$	−11.4442	−0.435359	−0.217680	+	0.976020i	$0.569849\pi$
$692$	−22.1566	−0.842266
$693$	0.0149675	0.000568569 0
$694$	25.4043	0.964334
$695$	−8.67356	−0.329007
$696$	0	0
$697$	63.0711	2.38899
$698$	−10.0681	−0.381083
$699$	−12.6349	−0.477895
$700$	0.813823	0.0307596
$701$	−2.53939	−0.0959115	−0.0479558	−	0.998849i	$-0.515271\pi$
$701$	−2.53939	−0.0959115	−0.0479558	+	0.998849i	$0.515271\pi$
$702$	−2.75960	−0.104154
$703$	55.6142	2.09753
$704$	1.77068	0.0667351
$705$	−9.38714	−0.353540
$706$	37.1169	1.39691
$707$	0.658889	0.0247801
$708$	−24.5996	−0.924508
$709$	−2.88169	−0.108224	−0.0541121	−	0.998535i	$-0.517233\pi$
$709$	−2.88169	−0.108224	−0.0541121	+	0.998535i	$0.517233\pi$
$710$	−1.18368	−0.0444229
$711$	13.4381	0.503968
$712$	7.97166	0.298751
$713$	22.8376	0.855275
$714$	1.47747	0.0552928
$715$	0.244247	0.00913432
$716$	55.5839	2.07727
$717$	11.3997	0.425731
$718$	4.18491	0.156179
$719$	2.19420	0.0818298	0.0409149	−	0.999163i	$-0.486973\pi$
$719$	2.19420	0.0818298	0.0409149	+	0.999163i	$0.486973\pi$
$720$	3.44990	0.128570
$721$	1.41459	0.0526822
$722$	−32.6497	−1.21510
$723$	−20.1130	−0.748010
$724$	−21.8357	−0.811518
$725$	0	0
$726$	23.0104	0.853997
$727$	−42.0925	−1.56112	−0.780562	−	0.625079i	$-0.785067\pi$
$727$	−42.0925	−1.56112	−0.780562	+	0.625079i	$0.785067\pi$
$728$	0.100101	0.00371001
$729$	1.00000	0.0370370
$730$	22.0794	0.817195
$731$	28.0675	1.03812
$732$	−15.5535	−0.574875
$733$	−13.3636	−0.493597	−0.246799	−	0.969067i	$-0.579379\pi$
$733$	−13.3636	−0.493597	−0.246799	+	0.969067i	$0.579379\pi$
$734$	−13.4380	−0.496007
$735$	7.91496	0.291948
$736$	−57.8437	−2.13215
$737$	−0.777653	−0.0286452
$738$	−17.1373	−0.630832
$739$	7.77219	0.285905	0.142952	−	0.989730i	$-0.454340\pi$
$739$	7.77219	0.285905	0.142952	+	0.989730i	$0.454340\pi$
$740$	25.6704	0.943664
$741$	−7.73750	−0.284244
$742$	−0.246371	−0.00904456
$743$	45.6074	1.67317	0.836587	−	0.547835i	$-0.184548\pi$
$743$	45.6074	1.67317	0.836587	+	0.547835i	$0.184548\pi$
$744$	2.65039	0.0971680
$745$	17.8714	0.654759
$746$	79.6818	2.91736
$747$	3.64859	0.133495
$748$	−3.03333	−0.110910
$749$	0.967009	0.0353337
$750$	−20.6967	−0.755738
$751$	11.5520	0.421538	0.210769	−	0.977536i	$-0.432403\pi$
$751$	11.5520	0.421538	0.210769	+	0.977536i	$0.432403\pi$
$752$	−25.2699	−0.921499
$753$	0.748847	0.0272895
$754$	0	0
$755$	−0.719913	−0.0262003
$756$	−0.218861	−0.00795990
$757$	43.4744	1.58010	0.790052	−	0.613039i	$-0.210053\pi$
$757$	43.4744	1.58010	0.790052	+	0.613039i	$0.210053\pi$
$758$	71.7101	2.60463
$759$	1.17706	0.0427246
$760$	−5.54582	−0.201168
$761$	−12.9622	−0.469878	−0.234939	−	0.972010i	$-0.575489\pi$
$761$	−12.9622	−0.469878	−0.234939	+	0.972010i	$0.575489\pi$
$762$	−16.9850	−0.615302
$763$	−0.416005	−0.0150604
$764$	−43.2056	−1.56312
$765$	−8.73677	−0.315878
$766$	37.5862	1.35805
$767$	−13.5036	−0.487588
$768$	7.89859	0.285016
$769$	−21.3281	−0.769112	−0.384556	−	0.923102i	$-0.625646\pi$
$769$	−21.3281	−0.769112	−0.384556	+	0.923102i	$0.625646\pi$
$770$	0.0355314	0.00128046
$771$	9.30596	0.335146
$772$	3.79591	0.136618
$773$	−47.2378	−1.69903	−0.849514	−	0.527567i	$-0.823104\pi$
$773$	−47.2378	−1.69903	−0.849514	+	0.527567i	$0.823104\pi$
$774$	−7.62634	−0.274123
$775$	11.8283	0.424886
$776$	10.5160	0.377502
$777$	0.863529	0.0309789
$778$	28.3011	1.01464
$779$	−48.0503	−1.72158
$780$	−3.57148	−0.127879
$781$	0.0817490	0.00292521
$782$	116.189	4.15493
$783$	0	0
$784$	21.3068	0.760959
$785$	26.9443	0.961683
$786$	−16.8803	−0.602101
$787$	4.70797	0.167821	0.0839105	−	0.996473i	$-0.473259\pi$
$787$	4.70797	0.167821	0.0839105	+	0.996473i	$0.473259\pi$
$788$	−25.0633	−0.892842
$789$	−13.4886	−0.480205
$790$	31.9007	1.13498
$791$	0.809850	0.0287950
$792$	0.136602	0.00485395
$793$	−8.53792	−0.303191
$794$	8.18985	0.290647
$795$	1.45688	0.0516701
$796$	8.98418	0.318436
$797$	−34.6119	−1.22602	−0.613008	−	0.790076i	$-0.710041\pi$
$797$	−34.6119	−1.22602	−0.613008	+	0.790076i	$0.710041\pi$
$798$	−1.12560	−0.0398458
$799$	63.9953	2.26399
$800$	−29.9591	−1.05921
$801$	−9.56754	−0.338053
$802$	37.3406	1.31854
$803$	−1.52487	−0.0538116
$804$	11.3712	0.401030
$805$	−0.741990	−0.0261517
$806$	8.77824	0.309200
$807$	−22.9084	−0.806413
$808$	6.01340	0.211551
$809$	48.7335	1.71338	0.856689	−	0.515834i	$-0.172518\pi$
$809$	48.7335	1.71338	0.856689	+	0.515834i	$0.172518\pi$
$810$	2.37390	0.0834104
$811$	−12.0087	−0.421684	−0.210842	−	0.977520i	$-0.567621\pi$
$811$	−12.0087	−0.421684	−0.210842	+	0.977520i	$0.567621\pi$
$812$	0	0
$813$	−0.252974	−0.00887217
$814$	−3.25193	−0.113980
$815$	−4.43302	−0.155282
$816$	−23.5191	−0.823334
$817$	−21.3831	−0.748100
$818$	−28.3886	−0.992583
$819$	−0.120141	−0.00419807
$820$	−22.1791	−0.774528
$821$	−11.1177	−0.388012	−0.194006	−	0.981000i	$-0.562148\pi$
$821$	−11.1177	−0.388012	−0.194006	+	0.981000i	$0.562148\pi$
$822$	−14.4939	−0.505534
$823$	−9.56608	−0.333452	−0.166726	−	0.986003i	$-0.553320\pi$
$823$	−9.56608	−0.333452	−0.166726	+	0.986003i	$0.553320\pi$
$824$	12.9104	0.449755
$825$	0.609637	0.0212248
$826$	−1.96442	−0.0683509
$827$	−37.1375	−1.29140	−0.645698	−	0.763593i	$-0.723434\pi$
$827$	−37.1375	−1.29140	−0.645698	+	0.763593i	$0.723434\pi$
$828$	−17.2115	−0.598140
$829$	37.8359	1.31409	0.657047	−	0.753850i	$-0.271805\pi$
$829$	37.8359	1.31409	0.657047	+	0.753850i	$0.271805\pi$
$830$	8.66139	0.300641
$831$	−18.0655	−0.626686
$832$	−14.2129	−0.492744
$833$	−53.9589	−1.86957
$834$	−16.0666	−0.556341
$835$	−12.2487	−0.423882
$836$	2.31093	0.0799252
$837$	−3.18098	−0.109951
$838$	−59.2899	−2.04814
$839$	47.4370	1.63771	0.818854	−	0.574001i	$-0.194610\pi$
$839$	47.4370	1.63771	0.818854	+	0.574001i	$0.194610\pi$
$840$	−0.0861106	−0.00297110
$841$	0	0
$842$	−37.7983	−1.30262
$843$	13.0549	0.449633
$844$	−62.7150	−2.15874
$845$	12.7562	0.438827
$846$	−17.3884	−0.597826
$847$	1.00178	0.0344214
$848$	3.92187	0.134677
$849$	−21.6748	−0.743877
$850$	60.1782	2.06409
$851$	67.9089	2.32789
$852$	−1.19537	−0.0409526
$853$	27.5050	0.941754	0.470877	−	0.882199i	$-0.343938\pi$
$853$	27.5050	0.941754	0.470877	+	0.882199i	$0.343938\pi$
$854$	−1.24204	−0.0425017
$855$	6.65606	0.227632
$856$	8.82549	0.301649
$857$	−23.0151	−0.786180	−0.393090	−	0.919500i	$-0.628594\pi$
$857$	−23.0151	−0.786180	−0.393090	+	0.919500i	$0.628594\pi$
$858$	0.452435	0.0154459
$859$	−22.6058	−0.771299	−0.385650	−	0.922645i	$-0.626023\pi$
$859$	−22.6058	−0.771299	−0.385650	+	0.922645i	$0.626023\pi$
$860$	−9.87002	−0.336565
$861$	−0.746084	−0.0254265
$862$	−23.6935	−0.807005
$863$	−31.9619	−1.08800	−0.543998	−	0.839086i	$-0.683090\pi$
$863$	−31.9619	−1.08800	−0.543998	+	0.839086i	$0.683090\pi$
$864$	8.05687	0.274100
$865$	10.4627	0.355741
$866$	21.9867	0.747139
$867$	42.5614	1.44546
$868$	0.696193	0.0236303
$869$	−2.20317	−0.0747373
$870$	0	0
$871$	6.24206	0.211504
$872$	−3.79670	−0.128573
$873$	−12.6212	−0.427164
$874$	−88.5183	−2.99418
$875$	−0.901047	−0.0304610
$876$	22.2973	0.753356
$877$	−44.7188	−1.51005	−0.755023	−	0.655699i	$-0.772374\pi$
$877$	−44.7188	−1.51005	−0.755023	+	0.655699i	$0.772374\pi$
$878$	25.3017	0.853892
$879$	−25.4395	−0.858054
$880$	−0.565609	−0.0190667
$881$	19.3000	0.650233	0.325117	−	0.945674i	$-0.394596\pi$
$881$	19.3000	0.650233	0.325117	+	0.945674i	$0.394596\pi$
$882$	14.6614	0.493675
$883$	−43.7898	−1.47365	−0.736823	−	0.676086i	$-0.763675\pi$
$883$	−43.7898	−1.47365	−0.736823	+	0.676086i	$0.763675\pi$
$884$	24.3480	0.818910
$885$	11.6163	0.390477
$886$	−48.8319	−1.64054
$887$	3.50632	0.117731	0.0588653	−	0.998266i	$-0.481252\pi$
$887$	3.50632	0.117731	0.0588653	+	0.998266i	$0.481252\pi$
$888$	7.88107	0.264471
$889$	−0.739454	−0.0248005
$890$	−22.7124	−0.761322
$891$	−0.163949	−0.00549251
$892$	62.1324	2.08035
$893$	−48.7544	−1.63151
$894$	33.1044	1.10718
$895$	−26.2476	−0.877359
$896$	−0.596517	−0.0199282
$897$	−9.44803	−0.315461
$898$	−71.9714	−2.40172
$899$	0	0
$900$	−8.91435	−0.297145
$901$	−9.93201	−0.330883
$902$	2.80965	0.0935510
$903$	−0.332018	−0.0110489
$904$	7.39117	0.245827
$905$	10.3112	0.342754
$906$	−1.33354	−0.0443040
$907$	30.6917	1.01910	0.509551	−	0.860441i	$-0.329812\pi$
$907$	30.6917	1.01910	0.509551	+	0.860441i	$0.329812\pi$
$908$	21.7912	0.723165
$909$	−7.21725	−0.239381
$910$	−0.285203	−0.00945440
$911$	13.4661	0.446151	0.223075	−	0.974801i	$-0.428390\pi$
$911$	13.4661	0.446151	0.223075	+	0.974801i	$0.428390\pi$
$912$	17.9179	0.593321
$913$	−0.598183	−0.0197970
$914$	9.09121	0.300711
$915$	7.34461	0.242805
$916$	−21.9619	−0.725641
$917$	−0.734897	−0.0242684
$918$	−16.1837	−0.534141
$919$	12.3778	0.408308	0.204154	−	0.978939i	$-0.434556\pi$
$919$	12.3778	0.408308	0.204154	+	0.978939i	$0.434556\pi$
$920$	−6.77183	−0.223261
$921$	−13.6331	−0.449226
$922$	−54.9296	−1.80901
$923$	−0.656183	−0.0215985
$924$	0.0358821	0.00118043
$925$	35.1721	1.15645
$926$	77.5571	2.54868
$927$	−15.4950	−0.508922
$928$	0	0
$929$	−20.2666	−0.664927	−0.332464	−	0.943116i	$-0.607880\pi$
$929$	−20.2666	−0.664927	−0.332464	+	0.943116i	$0.607880\pi$
$930$	−7.55134	−0.247618
$931$	41.1083	1.34727
$932$	−30.2900	−0.992183
$933$	−27.3748	−0.896210
$934$	−19.5414	−0.639415
$935$	1.43239	0.0468441
$936$	−1.09648	−0.0358395
$937$	−26.4354	−0.863607	−0.431804	−	0.901968i	$-0.642123\pi$
$937$	−26.4354	−0.863607	−0.431804	+	0.901968i	$0.642123\pi$
$938$	0.908053	0.0296490
$939$	−17.7630	−0.579673
$940$	−22.5041	−0.734003
$941$	−21.6605	−0.706111	−0.353055	−	0.935602i	$-0.614857\pi$
$941$	−21.6605	−0.706111	−0.353055	+	0.935602i	$0.614857\pi$
$942$	49.9107	1.62618
$943$	−58.6728	−1.91065
$944$	31.2707	1.01777
$945$	0.103350	0.00336196
$946$	1.25033	0.0406518
$947$	52.6021	1.70934	0.854669	−	0.519173i	$-0.173760\pi$
$947$	52.6021	1.70934	0.854669	+	0.519173i	$0.173760\pi$
$948$	32.2156	1.04631
$949$	12.2398	0.397322
$950$	−45.8464	−1.48745
$951$	5.14271	0.166764
$952$	0.587045	0.0190262
$953$	−29.7867	−0.964887	−0.482444	−	0.875927i	$-0.660251\pi$
$953$	−29.7867	−0.964887	−0.482444	+	0.875927i	$0.660251\pi$
$954$	2.69867	0.0873725
$955$	20.4023	0.660204
$956$	27.3290	0.883882
$957$	0	0
$958$	−58.2315	−1.88137
$959$	−0.631004	−0.0203762
$960$	12.2264	0.394606
$961$	−20.8814	−0.673592
$962$	26.1026	0.841581
$963$	−10.5923	−0.341332
$964$	−48.2175	−1.55298
$965$	−1.79249	−0.0577022
$966$	−1.37444	−0.0442217
$967$	37.1267	1.19391	0.596956	−	0.802274i	$-0.296377\pi$
$967$	37.1267	1.19391	0.596956	+	0.802274i	$0.296377\pi$
$968$	9.14279	0.293860
$969$	−45.3765	−1.45770
$970$	−29.9616	−0.962008
$971$	−3.73862	−0.119978	−0.0599890	−	0.998199i	$-0.519107\pi$
$971$	−3.73862	−0.119978	−0.0599890	+	0.998199i	$0.519107\pi$
$972$	2.39733	0.0768945
$973$	−0.699471	−0.0224240
$974$	34.3924	1.10200
$975$	−4.89343	−0.156715
$976$	19.7715	0.632869
$977$	9.85004	0.315131	0.157565	−	0.987509i	$-0.449636\pi$
$977$	9.85004	0.315131	0.157565	+	0.987509i	$0.449636\pi$
$978$	−8.21156	−0.262577
$979$	1.56859	0.0501324
$980$	18.9748	0.606127
$981$	4.55678	0.145487
$982$	−21.6231	−0.690020
$983$	9.42634	0.300653	0.150327	−	0.988636i	$-0.451967\pi$
$983$	9.42634	0.300653	0.150327	+	0.988636i	$0.451967\pi$
$984$	−6.80920	−0.217069
$985$	11.8353	0.377102
$986$	0	0
$987$	−0.757017	−0.0240961
$988$	−18.5494	−0.590134
$989$	−26.1103	−0.830258
$990$	−0.389200	−0.0123696
$991$	33.7698	1.07273	0.536367	−	0.843985i	$-0.319796\pi$
$991$	33.7698	1.07273	0.536367	+	0.843985i	$0.319796\pi$
$992$	−25.6288	−0.813714
$993$	14.1996	0.450610
$994$	−0.0954570	−0.00302771
$995$	−4.24246	−0.134495
$996$	8.74688	0.277155
$997$	5.94070	0.188144	0.0940719	−	0.995565i	$-0.470012\pi$
$997$	5.94070	0.188144	0.0940719	+	0.995565i	$0.470012\pi$
$998$	−49.6064	−1.57026
$999$	−9.45882	−0.299264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.2.a.m.1.3	✓	8
3.2	odd	2		7569.2.a.bh.1.6		8
29.28	even	2		2523.2.a.n.1.6	yes	8
87.86	odd	2		7569.2.a.be.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2523.2.a.m.1.3	✓	8	1.1	even	1	trivial
2523.2.a.n.1.6	yes	8	29.28	even	2
7569.2.a.be.1.3		8	87.86	odd	2
7569.2.a.bh.1.6		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.09698 q^{2} +1.00000 q^{3} +2.39733 q^{4} -1.13206 q^{5} -2.09698 q^{6} -0.0912936 q^{7} -0.833198 q^{8} +1.00000 q^{9} +2.37390 q^{10} -0.163949 q^{11} +2.39733 q^{12} +1.31599 q^{13} +0.191441 q^{14} -1.13206 q^{15} -3.04746 q^{16} +7.71760 q^{17} -2.09698 q^{18} -5.87961 q^{19} -2.71392 q^{20} -0.0912936 q^{21} +0.343799 q^{22} -7.17942 q^{23} -0.833198 q^{24} -3.71845 q^{25} -2.75960 q^{26} +1.00000 q^{27} -0.218861 q^{28} +2.37390 q^{30} -3.18098 q^{31} +8.05687 q^{32} -0.163949 q^{33} -16.1837 q^{34} +0.103350 q^{35} +2.39733 q^{36} -9.45882 q^{37} +12.3294 q^{38} +1.31599 q^{39} +0.943228 q^{40} +8.17236 q^{41} +0.191441 q^{42} +3.63682 q^{43} -0.393041 q^{44} -1.13206 q^{45} +15.0551 q^{46} +8.29212 q^{47} -3.04746 q^{48} -6.99167 q^{49} +7.79752 q^{50} +7.71760 q^{51} +3.15486 q^{52} -1.28693 q^{53} -2.09698 q^{54} +0.185600 q^{55} +0.0760657 q^{56} -5.87961 q^{57} -10.2612 q^{59} -2.71392 q^{60} -6.48785 q^{61} +6.67046 q^{62} -0.0912936 q^{63} -10.8002 q^{64} -1.48977 q^{65} +0.343799 q^{66} +4.74325 q^{67} +18.5017 q^{68} -7.17942 q^{69} -0.216722 q^{70} -0.498624 q^{71} -0.833198 q^{72} +9.30088 q^{73} +19.8350 q^{74} -3.71845 q^{75} -14.0954 q^{76} +0.0149675 q^{77} -2.75960 q^{78} +13.4381 q^{79} +3.44990 q^{80} +1.00000 q^{81} -17.1373 q^{82} +3.64859 q^{83} -0.218861 q^{84} -8.73677 q^{85} -7.62634 q^{86} +0.136602 q^{88} -9.56754 q^{89} +2.37390 q^{90} -0.120141 q^{91} -17.2115 q^{92} -3.18098 q^{93} -17.3884 q^{94} +6.65606 q^{95} +8.05687 q^{96} -12.6212 q^{97} +14.6614 q^{98} -0.163949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 8 q^{3} + 11 q^{4} - 9 q^{5} - q^{6} - 12 q^{7} - 15 q^{8} + 8 q^{9} - 2 q^{10} + 12 q^{11} + 11 q^{12} - 15 q^{13} - 11 q^{14} - 9 q^{15} + 13 q^{16} + 9 q^{17} - q^{18} - 9 q^{19} - 8 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) \) 8 * q - q^2 + 8 * q^3 + 11 * q^4 - 9 * q^5 - q^6 - 12 * q^7 - 15 * q^8 + 8 * q^9 - 2 * q^10 + 12 * q^11 + 11 * q^12 - 15 * q^13 - 11 * q^14 - 9 * q^15 + 13 * q^16 + 9 * q^17 - q^18 - 9 * q^19 - 8 * q^20 - 12 * q^21 - 24 * q^22 - 15 * q^23 - 15 * q^24 + 7 * q^25 + 5 * q^26 + 8 * q^27 - 39 * q^28 - 2 * q^30 - 20 * q^31 + 9 * q^32 + 12 * q^33 - 23 * q^34 + 6 * q^35 + 11 * q^36 - 17 * q^37 - 2 * q^38 - 15 * q^39 - 5 * q^40 - 20 * q^41 - 11 * q^42 - 20 * q^43 + 24 * q^44 - 9 * q^45 + 20 * q^46 - 9 * q^47 + 13 * q^48 + 2 * q^49 + 51 * q^50 + 9 * q^51 - 35 * q^52 - 39 * q^53 - q^54 - 36 * q^55 + 15 * q^56 - 9 * q^57 - 8 * q^60 - 34 * q^61 + 15 * q^62 - 12 * q^63 - 9 * q^64 - 25 * q^65 - 24 * q^66 - 21 * q^67 + 28 * q^68 - 15 * q^69 + 8 * q^70 + 15 * q^71 - 15 * q^72 + 2 * q^73 + 9 * q^74 + 7 * q^75 - 18 * q^76 - 3 * q^77 + 5 * q^78 - 6 * q^79 - 54 * q^80 + 8 * q^81 - 60 * q^82 + 17 * q^83 - 39 * q^84 - 22 * q^85 - 45 * q^86 - 60 * q^88 + 20 * q^89 - 2 * q^90 + 30 * q^91 - 70 * q^92 - 20 * q^93 - 2 * q^94 + 12 * q^95 + 9 * q^96 + 16 * q^97 + 51 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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