LMFDB - Embedded newform 6025.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.38569.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} + 4x - 1 $ x^5 - 5x^3 + 4x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.790734$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.526087 q^{2} +2.87779 q^{3} -1.72323 q^{4} +1.51397 q^{6} +4.16547 q^{7} -1.95874 q^{8} +5.28166 q^{9} +O(q^{10})$	\(q+0.526087 q^{2} +2.87779 q^{3} -1.72323 q^{4} +1.51397 q^{6} +4.16547 q^{7} -1.95874 q^{8} +5.28166 q^{9} +0.133130 q^{11} -4.95910 q^{12} +0.0230385 q^{13} +2.19140 q^{14} +2.41600 q^{16} +0.577908 q^{17} +2.77861 q^{18} +4.83079 q^{19} +11.9873 q^{21} +0.0700382 q^{22} -2.38566 q^{23} -5.63685 q^{24} +0.0121202 q^{26} +6.56614 q^{27} -7.17808 q^{28} +5.43622 q^{29} -6.98534 q^{31} +5.18851 q^{32} +0.383121 q^{33} +0.304030 q^{34} -9.10153 q^{36} -6.76040 q^{37} +2.54141 q^{38} +0.0662998 q^{39} +0.889908 q^{41} +6.30639 q^{42} -1.16427 q^{43} -0.229415 q^{44} -1.25506 q^{46} +7.26345 q^{47} +6.95272 q^{48} +10.3512 q^{49} +1.66310 q^{51} -0.0397006 q^{52} +8.72323 q^{53} +3.45436 q^{54} -8.15910 q^{56} +13.9020 q^{57} +2.85992 q^{58} +4.97322 q^{59} +6.87151 q^{61} -3.67490 q^{62} +22.0006 q^{63} -2.10238 q^{64} +0.201555 q^{66} +8.47916 q^{67} -0.995870 q^{68} -6.86542 q^{69} -6.49254 q^{71} -10.3454 q^{72} +3.09308 q^{73} -3.55656 q^{74} -8.32457 q^{76} +0.554551 q^{77} +0.0348795 q^{78} -2.01769 q^{79} +3.05097 q^{81} +0.468169 q^{82} +3.73923 q^{83} -20.6570 q^{84} -0.612508 q^{86} +15.6443 q^{87} -0.260768 q^{88} -14.8780 q^{89} +0.0959661 q^{91} +4.11104 q^{92} -20.1023 q^{93} +3.82120 q^{94} +14.9314 q^{96} +7.50238 q^{97} +5.44562 q^{98} +0.703150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9} - 3 q^{11} - 8 q^{12} + q^{13} - q^{14} + 15 q^{16} + 5 q^{17} - 4 q^{18} + 3 q^{19} + 11 q^{21} + 13 q^{22} + 8 q^{23} - 14 q^{24} + 14 q^{26} + 14 q^{27} + 17 q^{28} + 9 q^{29} - 16 q^{31} + 16 q^{32} - 23 q^{33} - 10 q^{34} - 17 q^{36} - 7 q^{37} + 22 q^{38} - 19 q^{39} + 9 q^{41} - 17 q^{42} + 32 q^{43} - 8 q^{44} + 5 q^{46} + 7 q^{47} + 6 q^{48} + 9 q^{49} - 8 q^{51} + 10 q^{52} + 32 q^{53} + 32 q^{54} - 18 q^{56} - 3 q^{57} - 11 q^{58} - 8 q^{59} - 12 q^{61} - 17 q^{62} + 11 q^{63} - 16 q^{64} + 15 q^{66} + 5 q^{67} + 2 q^{68} + 7 q^{69} - 11 q^{71} - 7 q^{72} + 29 q^{73} + 10 q^{74} - 8 q^{76} + 5 q^{77} - 2 q^{78} + 16 q^{79} - 15 q^{81} + 2 q^{82} + 10 q^{83} + 5 q^{84} + 14 q^{86} + 37 q^{87} - 10 q^{88} + 9 q^{89} + 12 q^{91} + 25 q^{92} - 15 q^{93} - 11 q^{94} - 3 q^{96} + 43 q^{97} - 30 q^{98} - 30 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9 - 3 * q^11 - 8 * q^12 + q^13 - q^14 + 15 * q^16 + 5 * q^17 - 4 * q^18 + 3 * q^19 + 11 * q^21 + 13 * q^22 + 8 * q^23 - 14 * q^24 + 14 * q^26 + 14 * q^27 + 17 * q^28 + 9 * q^29 - 16 * q^31 + 16 * q^32 - 23 * q^33 - 10 * q^34 - 17 * q^36 - 7 * q^37 + 22 * q^38 - 19 * q^39 + 9 * q^41 - 17 * q^42 + 32 * q^43 - 8 * q^44 + 5 * q^46 + 7 * q^47 + 6 * q^48 + 9 * q^49 - 8 * q^51 + 10 * q^52 + 32 * q^53 + 32 * q^54 - 18 * q^56 - 3 * q^57 - 11 * q^58 - 8 * q^59 - 12 * q^61 - 17 * q^62 + 11 * q^63 - 16 * q^64 + 15 * q^66 + 5 * q^67 + 2 * q^68 + 7 * q^69 - 11 * q^71 - 7 * q^72 + 29 * q^73 + 10 * q^74 - 8 * q^76 + 5 * q^77 - 2 * q^78 + 16 * q^79 - 15 * q^81 + 2 * q^82 + 10 * q^83 + 5 * q^84 + 14 * q^86 + 37 * q^87 - 10 * q^88 + 9 * q^89 + 12 * q^91 + 25 * q^92 - 15 * q^93 - 11 * q^94 - 3 * q^96 + 43 * q^97 - 30 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.526087	0.372000	0.186000	−	0.982550i	$-0.440448\pi$
$2$	0.526087	0.372000	0.186000	+	0.982550i	$0.440448\pi$
$3$	2.87779	1.66149	0.830746	−	0.556652i	$-0.187914\pi$
$3$	2.87779	1.66149	0.830746	+	0.556652i	$0.187914\pi$
$4$	−1.72323	−0.861616
$5$	0	0
$5$	0	0
$6$	1.51397	0.618074
$7$	4.16547	1.57440	0.787201	−	0.616697i	$-0.211530\pi$
$7$	4.16547	1.57440	0.787201	+	0.616697i	$0.211530\pi$
$8$	−1.95874	−0.692521
$9$	5.28166	1.76055
$10$	0	0
$11$	0.133130	0.0401403	0.0200702	−	0.999799i	$-0.493611\pi$
$11$	0.133130	0.0401403	0.0200702	+	0.999799i	$0.493611\pi$
$12$	−4.95910	−1.43157
$13$	0.0230385	0.00638972	0.00319486	−	0.999995i	$-0.498983\pi$
$13$	0.0230385	0.00638972	0.00319486	+	0.999995i	$0.498983\pi$
$14$	2.19140	0.585677
$15$	0	0
$16$	2.41600	0.603999
$17$	0.577908	0.140163	0.0700816	−	0.997541i	$-0.477674\pi$
$17$	0.577908	0.140163	0.0700816	+	0.997541i	$0.477674\pi$
$18$	2.77861	0.654926
$19$	4.83079	1.10826	0.554129	−	0.832431i	$-0.313051\pi$
$19$	4.83079	1.10826	0.554129	+	0.832431i	$0.313051\pi$
$20$	0	0
$21$	11.9873	2.61585
$22$	0.0700382	0.0149322
$23$	−2.38566	−0.497444	−0.248722	−	0.968575i	$-0.580011\pi$
$23$	−2.38566	−0.497444	−0.248722	+	0.968575i	$0.580011\pi$
$24$	−5.63685	−1.15062
$25$	0	0
$26$	0.0121202	0.00237697
$27$	6.56614	1.26365
$28$	−7.17808	−1.35653
$29$	5.43622	1.00948	0.504740	−	0.863271i	$-0.331588\pi$
$29$	5.43622	1.00948	0.504740	+	0.863271i	$0.331588\pi$
$30$	0	0
$31$	−6.98534	−1.25460	−0.627302	−	0.778776i	$-0.715841\pi$
$31$	−6.98534	−1.25460	−0.627302	+	0.778776i	$0.715841\pi$
$32$	5.18851	0.917208
$33$	0.383121	0.0666928
$34$	0.304030	0.0521407
$35$	0	0
$36$	−9.10153	−1.51692
$37$	−6.76040	−1.11140	−0.555701	−	0.831382i	$-0.687550\pi$
$37$	−6.76040	−1.11140	−0.555701	+	0.831382i	$0.687550\pi$
$38$	2.54141	0.412272
$39$	0.0662998	0.0106165
$40$	0	0
$41$	0.889908	0.138980	0.0694901	−	0.997583i	$-0.477863\pi$
$41$	0.889908	0.138980	0.0694901	+	0.997583i	$0.477863\pi$
$42$	6.30639	0.973097
$43$	−1.16427	−0.177550	−0.0887749	−	0.996052i	$-0.528295\pi$
$43$	−1.16427	−0.177550	−0.0887749	+	0.996052i	$0.528295\pi$
$44$	−0.229415	−0.0345856
$45$	0	0
$46$	−1.25506	−0.185049
$47$	7.26345	1.05948	0.529741	−	0.848159i	$-0.322289\pi$
$47$	7.26345	1.05948	0.529741	+	0.848159i	$0.322289\pi$
$48$	6.95272	1.00354
$49$	10.3512	1.47874
$50$	0	0
$51$	1.66310	0.232880
$52$	−0.0397006	−0.00550549
$53$	8.72323	1.19823	0.599114	−	0.800664i	$-0.295520\pi$
$53$	8.72323	1.19823	0.599114	+	0.800664i	$0.295520\pi$
$54$	3.45436	0.470079
$55$	0	0
$56$	−8.15910	−1.09031
$57$	13.9020	1.84136
$58$	2.85992	0.375526
$59$	4.97322	0.647459	0.323729	−	0.946150i	$-0.395063\pi$
$59$	4.97322	0.647459	0.323729	+	0.946150i	$0.395063\pi$
$60$	0	0
$61$	6.87151	0.879807	0.439904	−	0.898045i	$-0.355013\pi$
$61$	6.87151	0.879807	0.439904	+	0.898045i	$0.355013\pi$
$62$	−3.67490	−0.466713
$63$	22.0006	2.77182
$64$	−2.10238	−0.262798
$65$	0	0
$66$	0.201555	0.0248097
$67$	8.47916	1.03589	0.517947	−	0.855413i	$-0.326696\pi$
$67$	8.47916	1.03589	0.517947	+	0.855413i	$0.326696\pi$
$68$	−0.995870	−0.120767
$69$	−6.86542	−0.826499
$70$	0	0
$71$	−6.49254	−0.770523	−0.385261	−	0.922807i	$-0.625889\pi$
$71$	−6.49254	−0.770523	−0.385261	+	0.922807i	$0.625889\pi$
$72$	−10.3454	−1.21922
$73$	3.09308	0.362017	0.181009	−	0.983482i	$-0.442064\pi$
$73$	3.09308	0.362017	0.181009	+	0.983482i	$0.442064\pi$
$74$	−3.55656	−0.413441
$75$	0	0
$76$	−8.32457	−0.954894
$77$	0.554551	0.0631970
$78$	0.0348795	0.00394932
$79$	−2.01769	−0.227007	−0.113504	−	0.993538i	$-0.536207\pi$
$79$	−2.01769	−0.227007	−0.113504	+	0.993538i	$0.536207\pi$
$80$	0	0
$81$	3.05097	0.338997
$82$	0.468169	0.0517006
$83$	3.73923	0.410434	0.205217	−	0.978716i	$-0.434210\pi$
$83$	3.73923	0.410434	0.205217	+	0.978716i	$0.434210\pi$
$84$	−20.6570	−2.25386
$85$	0	0
$86$	−0.612508	−0.0660485
$87$	15.6443	1.67724
$88$	−0.260768	−0.0277980
$89$	−14.8780	−1.57707	−0.788534	−	0.614992i	$-0.789159\pi$
$89$	−14.8780	−1.57707	−0.788534	+	0.614992i	$0.789159\pi$
$90$	0	0
$91$	0.0959661	0.0100600
$92$	4.11104	0.428606
$93$	−20.1023	−2.08452
$94$	3.82120	0.394127
$95$	0	0
$96$	14.9314	1.52393
$97$	7.50238	0.761751	0.380876	−	0.924626i	$-0.375623\pi$
$97$	7.50238	0.761751	0.380876	+	0.924626i	$0.375623\pi$
$98$	5.44562	0.550090
$99$	0.703150	0.0706692
$100$	0	0
$101$	−12.1785	−1.21180	−0.605902	−	0.795540i	$-0.707187\pi$
$101$	−12.1785	−1.21180	−0.605902	+	0.795540i	$0.707187\pi$
$102$	0.874933	0.0866313
$103$	−14.8658	−1.46478	−0.732388	−	0.680888i	$-0.761594\pi$
$103$	−14.8658	−1.46478	−0.732388	+	0.680888i	$0.761594\pi$
$104$	−0.0451265	−0.00442501
$105$	0	0
$106$	4.58918	0.445740
$107$	5.10206	0.493235	0.246618	−	0.969113i	$-0.420681\pi$
$107$	5.10206	0.493235	0.246618	+	0.969113i	$0.420681\pi$
$108$	−11.3150	−1.08879
$109$	16.1730	1.54910	0.774548	−	0.632515i	$-0.217977\pi$
$109$	16.1730	1.54910	0.774548	+	0.632515i	$0.217977\pi$
$110$	0	0
$111$	−19.4550	−1.84659
$112$	10.0638	0.950936
$113$	−11.4629	−1.07834	−0.539172	−	0.842196i	$-0.681263\pi$
$113$	−11.4629	−1.07834	−0.539172	+	0.842196i	$0.681263\pi$
$114$	7.31365	0.684986
$115$	0	0
$116$	−9.36787	−0.869785
$117$	0.121681	0.0112495
$118$	2.61635	0.240854
$119$	2.40726	0.220673
$120$	0	0
$121$	−10.9823	−0.998389
$122$	3.61501	0.327288
$123$	2.56097	0.230915
$124$	12.0374	1.08099
$125$	0	0
$126$	11.5742	1.03112
$127$	7.34314	0.651598	0.325799	−	0.945439i	$-0.394367\pi$
$127$	7.34314	0.651598	0.325799	+	0.945439i	$0.394367\pi$
$128$	−11.4831	−1.01497
$129$	−3.35053	−0.294997
$130$	0	0
$131$	−9.41462	−0.822559	−0.411279	−	0.911509i	$-0.634918\pi$
$131$	−9.41462	−0.822559	−0.411279	+	0.911509i	$0.634918\pi$
$132$	−0.660207	−0.0574636
$133$	20.1225	1.74484
$134$	4.46078	0.385352
$135$	0	0
$136$	−1.13197	−0.0970659
$137$	−8.45752	−0.722575	−0.361288	−	0.932454i	$-0.617663\pi$
$137$	−8.45752	−0.722575	−0.361288	+	0.932454i	$0.617663\pi$
$138$	−3.61181	−0.307457
$139$	8.15428	0.691637	0.345818	−	0.938301i	$-0.387601\pi$
$139$	8.15428	0.691637	0.345818	+	0.938301i	$0.387601\pi$
$140$	0	0
$141$	20.9027	1.76032
$142$	−3.41564	−0.286634
$143$	0.00306712	0.000256486 0
$144$	12.7605	1.06337
$145$	0	0
$146$	1.62723	0.134670
$147$	29.7885	2.45691
$148$	11.6497	0.957602
$149$	13.0308	1.06753	0.533763	−	0.845634i	$-0.320777\pi$
$149$	13.0308	1.06753	0.533763	+	0.845634i	$0.320777\pi$
$150$	0	0
$151$	−14.1836	−1.15425	−0.577124	−	0.816656i	$-0.695825\pi$
$151$	−14.1836	−1.15425	−0.577124	+	0.816656i	$0.695825\pi$
$152$	−9.46228	−0.767492
$153$	3.05231	0.246765
$154$	0.291742	0.0235093
$155$	0	0
$156$	−0.114250	−0.00914732
$157$	10.4055	0.830448	0.415224	−	0.909719i	$-0.363703\pi$
$157$	10.4055	0.830448	0.415224	+	0.909719i	$0.363703\pi$
$158$	−1.06148	−0.0844467
$159$	25.1036	1.99085
$160$	0	0
$161$	−9.93739	−0.783176
$162$	1.60508	0.126107
$163$	1.74602	0.136759	0.0683794	−	0.997659i	$-0.478217\pi$
$163$	1.74602	0.136759	0.0683794	+	0.997659i	$0.478217\pi$
$164$	−1.53352	−0.119748
$165$	0	0
$166$	1.96716	0.152681
$167$	−3.27324	−0.253291	−0.126646	−	0.991948i	$-0.540421\pi$
$167$	−3.27324	−0.253291	−0.126646	+	0.991948i	$0.540421\pi$
$168$	−23.4802	−1.81153
$169$	−12.9995	−0.999959
$170$	0	0
$171$	25.5146	1.95115
$172$	2.00631	0.152980
$173$	19.6028	1.49037	0.745186	−	0.666857i	$-0.232361\pi$
$173$	19.6028	1.49037	0.745186	+	0.666857i	$0.232361\pi$
$174$	8.23025	0.623934
$175$	0	0
$176$	0.321642	0.0242447
$177$	14.3119	1.07575
$178$	−7.82713	−0.586668
$179$	11.4763	0.857781	0.428891	−	0.903356i	$-0.358905\pi$
$179$	11.4763	0.857781	0.428891	+	0.903356i	$0.358905\pi$
$180$	0	0
$181$	−2.56995	−0.191023	−0.0955116	−	0.995428i	$-0.530449\pi$
$181$	−2.56995	−0.191023	−0.0955116	+	0.995428i	$0.530449\pi$
$182$	0.0504865	0.00374231
$183$	19.7748	1.46179
$184$	4.67289	0.344490
$185$	0	0
$186$	−10.5756	−0.775439
$187$	0.0769371	0.00562620
$188$	−12.5166	−0.912867
$189$	27.3511	1.98950
$190$	0	0
$191$	24.3793	1.76402	0.882011	−	0.471228i	$-0.156189\pi$
$191$	24.3793	1.76402	0.882011	+	0.471228i	$0.156189\pi$
$192$	−6.05021	−0.436636
$193$	−26.7168	−1.92312	−0.961560	−	0.274595i	$-0.911456\pi$
$193$	−26.7168	−1.92312	−0.961560	+	0.274595i	$0.911456\pi$
$194$	3.94690	0.283371
$195$	0	0
$196$	−17.8375	−1.27411
$197$	16.5398	1.17841	0.589204	−	0.807984i	$-0.299441\pi$
$197$	16.5398	1.17841	0.589204	+	0.807984i	$0.299441\pi$
$198$	0.369918	0.0262889
$199$	−1.67360	−0.118639	−0.0593193	−	0.998239i	$-0.518893\pi$
$199$	−1.67360	−0.118639	−0.0593193	+	0.998239i	$0.518893\pi$
$200$	0	0
$201$	24.4012	1.72113
$202$	−6.40694	−0.450790
$203$	22.6444	1.58933
$204$	−2.86590	−0.200653
$205$	0	0
$206$	−7.82073	−0.544896
$207$	−12.6002	−0.875777
$208$	0.0556608	0.00385938
$209$	0.643125	0.0444859
$210$	0	0
$211$	−14.3144	−0.985441	−0.492721	−	0.870188i	$-0.663998\pi$
$211$	−14.3144	−0.985441	−0.492721	+	0.870188i	$0.663998\pi$
$212$	−15.0322	−1.03241
$213$	−18.6842	−1.28022
$214$	2.68413	0.183483
$215$	0	0
$216$	−12.8614	−0.875107
$217$	−29.0973	−1.97525
$218$	8.50843	0.576264
$219$	8.90122	0.601489
$220$	0	0
$221$	0.0133141	0.000895604 0
$222$	−10.2350	−0.686929
$223$	−3.64090	−0.243812	−0.121906	−	0.992542i	$-0.538901\pi$
$223$	−3.64090	−0.243812	−0.121906	+	0.992542i	$0.538901\pi$
$224$	21.6126	1.44405
$225$	0	0
$226$	−6.03051	−0.401143
$227$	20.8343	1.38282	0.691409	−	0.722463i	$-0.256990\pi$
$227$	20.8343	1.38282	0.691409	+	0.722463i	$0.256990\pi$
$228$	−23.9563	−1.58655
$229$	13.5981	0.898590	0.449295	−	0.893384i	$-0.351675\pi$
$229$	13.5981	0.898590	0.449295	+	0.893384i	$0.351675\pi$
$230$	0	0
$231$	1.59588	0.105001
$232$	−10.6482	−0.699086
$233$	−5.90150	−0.386620	−0.193310	−	0.981138i	$-0.561922\pi$
$233$	−5.90150	−0.386620	−0.193310	+	0.981138i	$0.561922\pi$
$234$	0.0640150	0.00418479
$235$	0	0
$236$	−8.57002	−0.557861
$237$	−5.80647	−0.377171
$238$	1.26643	0.0820903
$239$	8.63878	0.558796	0.279398	−	0.960175i	$-0.409865\pi$
$239$	8.63878	0.558796	0.279398	+	0.960175i	$0.409865\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−5.77763	−0.371400
$243$	−10.9184	−0.700414
$244$	−11.8412	−0.758056
$245$	0	0
$246$	1.34729	0.0859001
$247$	0.111294	0.00708147
$248$	13.6825	0.868840
$249$	10.7607	0.681933
$250$	0	0
$251$	11.1515	0.703876	0.351938	−	0.936023i	$-0.385523\pi$
$251$	11.1515	0.703876	0.351938	+	0.936023i	$0.385523\pi$
$252$	−37.9122	−2.38824
$253$	−0.317604	−0.0199676
$254$	3.86313	0.242394
$255$	0	0
$256$	−1.83633	−0.114770
$257$	−26.0902	−1.62746	−0.813730	−	0.581244i	$-0.802566\pi$
$257$	−26.0902	−1.62746	−0.813730	+	0.581244i	$0.802566\pi$
$258$	−1.76267	−0.109739
$259$	−28.1603	−1.74979
$260$	0	0
$261$	28.7123	1.77724
$262$	−4.95291	−0.305992
$263$	15.6718	0.966367	0.483183	−	0.875519i	$-0.339480\pi$
$263$	15.6718	0.966367	0.483183	+	0.875519i	$0.339480\pi$
$264$	−0.750436	−0.0461862
$265$	0	0
$266$	10.5862	0.649081
$267$	−42.8158	−2.62028
$268$	−14.6116	−0.892543
$269$	−8.87409	−0.541063	−0.270531	−	0.962711i	$-0.587199\pi$
$269$	−8.87409	−0.541063	−0.270531	+	0.962711i	$0.587199\pi$
$270$	0	0
$271$	−27.8579	−1.69225	−0.846124	−	0.532985i	$-0.821070\pi$
$271$	−27.8579	−1.69225	−0.846124	+	0.532985i	$0.821070\pi$
$272$	1.39622	0.0846584
$273$	0.276170	0.0167146
$274$	−4.44939	−0.268798
$275$	0	0
$276$	11.8307	0.712125
$277$	13.9275	0.836820	0.418410	−	0.908258i	$-0.362588\pi$
$277$	13.9275	0.836820	0.418410	+	0.908258i	$0.362588\pi$
$278$	4.28986	0.257289
$279$	−36.8942	−2.20880
$280$	0	0
$281$	1.25527	0.0748831	0.0374415	−	0.999299i	$-0.488079\pi$
$281$	1.25527	0.0748831	0.0374415	+	0.999299i	$0.488079\pi$
$282$	10.9966	0.654839
$283$	15.6734	0.931686	0.465843	−	0.884867i	$-0.345751\pi$
$283$	15.6734	0.931686	0.465843	+	0.884867i	$0.345751\pi$
$284$	11.1882	0.663895
$285$	0	0
$286$	0.00161357	9.54126e−5 0
$287$	3.70689	0.218811
$288$	27.4040	1.61479
$289$	−16.6660	−0.980354
$290$	0	0
$291$	21.5902	1.26564
$292$	−5.33009	−0.311920
$293$	−6.93078	−0.404901	−0.202450	−	0.979293i	$-0.564890\pi$
$293$	−6.93078	−0.404901	−0.202450	+	0.979293i	$0.564890\pi$
$294$	15.6713	0.913970
$295$	0	0
$296$	13.2419	0.769669
$297$	0.874153	0.0507235
$298$	6.85535	0.397120
$299$	−0.0549619	−0.00317853
$300$	0	0
$301$	−4.84974	−0.279535
$302$	−7.46183	−0.429380
$303$	−35.0471	−2.01340
$304$	11.6712	0.669387
$305$	0	0
$306$	1.60578	0.0917965
$307$	30.5946	1.74613	0.873063	−	0.487607i	$-0.162130\pi$
$307$	30.5946	1.74613	0.873063	+	0.487607i	$0.162130\pi$
$308$	−0.955621	−0.0544515
$309$	−42.7807	−2.43371
$310$	0	0
$311$	8.93967	0.506922	0.253461	−	0.967346i	$-0.418431\pi$
$311$	8.93967	0.506922	0.253461	+	0.967346i	$0.418431\pi$
$312$	−0.129864	−0.00735212
$313$	18.1102	1.02365	0.511825	−	0.859090i	$-0.328970\pi$
$313$	18.1102	1.02365	0.511825	+	0.859090i	$0.328970\pi$
$314$	5.47419	0.308927
$315$	0	0
$316$	3.47694	0.195593
$317$	−9.60483	−0.539461	−0.269730	−	0.962936i	$-0.586935\pi$
$317$	−9.60483	−0.539461	−0.269730	+	0.962936i	$0.586935\pi$
$318$	13.2067	0.740594
$319$	0.723726	0.0405209
$320$	0	0
$321$	14.6827	0.819506
$322$	−5.22793	−0.291341
$323$	2.79175	0.155337
$324$	−5.25753	−0.292085
$325$	0	0
$326$	0.918558	0.0508742
$327$	46.5426	2.57381
$328$	−1.74310	−0.0962467
$329$	30.2557	1.66805
$330$	0	0
$331$	−22.7938	−1.25286	−0.626431	−	0.779477i	$-0.715485\pi$
$331$	−22.7938	−1.25286	−0.626431	+	0.779477i	$0.715485\pi$
$332$	−6.44357	−0.353637
$333$	−35.7061	−1.95668
$334$	−1.72201	−0.0942242
$335$	0	0
$336$	28.9614	1.57997
$337$	23.9052	1.30220	0.651101	−	0.758991i	$-0.274307\pi$
$337$	23.9052	1.30220	0.651101	+	0.758991i	$0.274307\pi$
$338$	−6.83885	−0.371985
$339$	−32.9879	−1.79166
$340$	0	0
$341$	−0.929962	−0.0503603
$342$	13.4229	0.725827
$343$	13.9592	0.753726
$344$	2.28051	0.122957
$345$	0	0
$346$	10.3128	0.554418
$347$	−3.71611	−0.199491	−0.0997456	−	0.995013i	$-0.531803\pi$
$347$	−3.71611	−0.199491	−0.0997456	+	0.995013i	$0.531803\pi$
$348$	−26.9587	−1.44514
$349$	−26.1173	−1.39803	−0.699014	−	0.715108i	$-0.746378\pi$
$349$	−26.1173	−1.39803	−0.699014	+	0.715108i	$0.746378\pi$
$350$	0	0
$351$	0.151274	0.00807440
$352$	0.690749	0.0368170
$353$	27.6130	1.46969	0.734846	−	0.678234i	$-0.237255\pi$
$353$	27.6130	1.46969	0.734846	+	0.678234i	$0.237255\pi$
$354$	7.52929	0.400177
$355$	0	0
$356$	25.6383	1.35883
$357$	6.92758	0.366647
$358$	6.03755	0.319094
$359$	14.6021	0.770668	0.385334	−	0.922777i	$-0.374086\pi$
$359$	14.6021	0.770668	0.385334	+	0.922777i	$0.374086\pi$
$360$	0	0
$361$	4.33651	0.228238
$362$	−1.35202	−0.0710605
$363$	−31.6047	−1.65881
$364$	−0.165372	−0.00866785
$365$	0	0
$366$	10.4032	0.543786
$367$	−1.02005	−0.0532463	−0.0266232	−	0.999646i	$-0.508475\pi$
$367$	−1.02005	−0.0532463	−0.0266232	+	0.999646i	$0.508475\pi$
$368$	−5.76374	−0.300456
$369$	4.70019	0.244682
$370$	0	0
$371$	36.3364	1.88649
$372$	34.6410	1.79605
$373$	6.95086	0.359902	0.179951	−	0.983676i	$-0.442406\pi$
$373$	6.95086	0.359902	0.179951	+	0.983676i	$0.442406\pi$
$374$	0.0404756	0.00209294
$375$	0	0
$376$	−14.2272	−0.733713
$377$	0.125242	0.00645030
$378$	14.3891	0.740093
$379$	−34.7457	−1.78477	−0.892384	−	0.451276i	$-0.850969\pi$
$379$	−34.7457	−1.78477	−0.892384	+	0.451276i	$0.850969\pi$
$380$	0	0
$381$	21.1320	1.08263
$382$	12.8256	0.656216
$383$	−10.3824	−0.530517	−0.265258	−	0.964177i	$-0.585457\pi$
$383$	−10.3824	−0.530517	−0.265258	+	0.964177i	$0.585457\pi$
$384$	−33.0458	−1.68636
$385$	0	0
$386$	−14.0554	−0.715400
$387$	−6.14929	−0.312586
$388$	−12.9283	−0.656337
$389$	−27.2475	−1.38150	−0.690750	−	0.723093i	$-0.742720\pi$
$389$	−27.2475	−1.38150	−0.690750	+	0.723093i	$0.742720\pi$
$390$	0	0
$391$	−1.37869	−0.0697234
$392$	−20.2753	−1.02406
$393$	−27.0933	−1.36667
$394$	8.70135	0.438368
$395$	0	0
$396$	−1.21169	−0.0608898
$397$	−20.2568	−1.01666	−0.508330	−	0.861162i	$-0.669737\pi$
$397$	−20.2568	−1.01666	−0.508330	+	0.861162i	$0.669737\pi$
$398$	−0.880461	−0.0441335
$399$	57.9083	2.89904
$400$	0	0
$401$	−26.1243	−1.30459	−0.652293	−	0.757967i	$-0.726193\pi$
$401$	−26.1243	−1.30459	−0.652293	+	0.757967i	$0.726193\pi$
$402$	12.8372	0.640260
$403$	−0.160932	−0.00801658
$404$	20.9863	1.04411
$405$	0	0
$406$	11.9129	0.591229
$407$	−0.900015	−0.0446121
$408$	−3.25758	−0.161274
$409$	−21.0462	−1.04067	−0.520334	−	0.853963i	$-0.674193\pi$
$409$	−21.0462	−1.04067	−0.520334	+	0.853963i	$0.674193\pi$
$410$	0	0
$411$	−24.3390	−1.20055
$412$	25.6173	1.26207
$413$	20.7158	1.01936
$414$	−6.62882	−0.325789
$415$	0	0
$416$	0.119535	0.00586070
$417$	23.4663	1.14915
$418$	0.338340	0.0165487
$419$	−38.3724	−1.87462	−0.937308	−	0.348502i	$-0.886691\pi$
$419$	−38.3724	−1.87462	−0.937308	+	0.348502i	$0.886691\pi$
$420$	0	0
$421$	32.3918	1.57868	0.789340	−	0.613956i	$-0.210423\pi$
$421$	32.3918	1.57868	0.789340	+	0.613956i	$0.210423\pi$
$422$	−7.53060	−0.366584
$423$	38.3631	1.86528
$424$	−17.0866	−0.829798
$425$	0	0
$426$	−9.82949	−0.476240
$427$	28.6231	1.38517
$428$	−8.79204	−0.424979
$429$	0.00882653	0.000426149 0
$430$	0	0
$431$	−11.0372	−0.531642	−0.265821	−	0.964022i	$-0.585643\pi$
$431$	−11.0372	−0.531642	−0.265821	+	0.964022i	$0.585643\pi$
$432$	15.8638	0.763246
$433$	−14.5128	−0.697441	−0.348720	−	0.937227i	$-0.613384\pi$
$433$	−14.5128	−0.697441	−0.348720	+	0.937227i	$0.613384\pi$
$434$	−15.3077	−0.734793
$435$	0	0
$436$	−27.8699	−1.33473
$437$	−11.5246	−0.551297
$438$	4.68282	0.223754
$439$	−9.31943	−0.444792	−0.222396	−	0.974956i	$-0.571388\pi$
$439$	−9.31943	−0.444792	−0.222396	+	0.974956i	$0.571388\pi$
$440$	0	0
$441$	54.6714	2.60340
$442$	0.00700438	0.000333165 0
$443$	28.9626	1.37606	0.688028	−	0.725684i	$-0.258477\pi$
$443$	28.9626	1.37606	0.688028	+	0.725684i	$0.258477\pi$
$444$	33.5255	1.59105
$445$	0	0
$446$	−1.91543	−0.0906982
$447$	37.4999	1.77369
$448$	−8.75741	−0.413749
$449$	6.57669	0.310373	0.155187	−	0.987885i	$-0.450402\pi$
$449$	6.57669	0.310373	0.155187	+	0.987885i	$0.450402\pi$
$450$	0	0
$451$	0.118474	0.00557872
$452$	19.7533	0.929118
$453$	−40.8175	−1.91777
$454$	10.9606	0.514408
$455$	0	0
$456$	−27.2304	−1.27518
$457$	37.0634	1.73375	0.866875	−	0.498525i	$-0.166125\pi$
$457$	37.0634	1.73375	0.866875	+	0.498525i	$0.166125\pi$
$458$	7.15380	0.334275
$459$	3.79462	0.177118
$460$	0	0
$461$	32.9360	1.53398	0.766992	−	0.641656i	$-0.221752\pi$
$461$	32.9360	1.53398	0.766992	+	0.641656i	$0.221752\pi$
$462$	0.839572	0.0390604
$463$	−15.1555	−0.704336	−0.352168	−	0.935937i	$-0.614555\pi$
$463$	−15.1555	−0.704336	−0.352168	+	0.935937i	$0.614555\pi$
$464$	13.1339	0.609725
$465$	0	0
$466$	−3.10470	−0.143823
$467$	−19.9616	−0.923712	−0.461856	−	0.886955i	$-0.652816\pi$
$467$	−19.9616	−0.923712	−0.461856	+	0.886955i	$0.652816\pi$
$468$	−0.209685	−0.00969271
$469$	35.3197	1.63091
$470$	0	0
$471$	29.9448	1.37978
$472$	−9.74127	−0.448378
$473$	−0.155000	−0.00712691
$474$	−3.05471	−0.140307
$475$	0	0
$476$	−4.14827	−0.190136
$477$	46.0732	2.10955
$478$	4.54475	0.207872
$479$	−5.21508	−0.238283	−0.119142	−	0.992877i	$-0.538014\pi$
$479$	−5.21508	−0.238283	−0.119142	+	0.992877i	$0.538014\pi$
$480$	0	0
$481$	−0.155749	−0.00710155
$482$	0.526087	0.0239626
$483$	−28.5977	−1.30124
$484$	18.9250	0.860228
$485$	0	0
$486$	−5.74401	−0.260554
$487$	−26.7458	−1.21197	−0.605985	−	0.795476i	$-0.707221\pi$
$487$	−26.7458	−1.21197	−0.605985	+	0.795476i	$0.707221\pi$
$488$	−13.4595	−0.609285
$489$	5.02467	0.227224
$490$	0	0
$491$	11.0728	0.499708	0.249854	−	0.968284i	$-0.419617\pi$
$491$	11.0728	0.499708	0.249854	+	0.968284i	$0.419617\pi$
$492$	−4.41314	−0.198960
$493$	3.14163	0.141492
$494$	0.0585503	0.00263430
$495$	0	0
$496$	−16.8766	−0.757780
$497$	−27.0445	−1.21311
$498$	5.66107	0.253679
$499$	8.73572	0.391065	0.195532	−	0.980697i	$-0.437357\pi$
$499$	8.73572	0.391065	0.195532	+	0.980697i	$0.437357\pi$
$500$	0	0
$501$	−9.41970	−0.420841
$502$	5.86665	0.261842
$503$	−30.3059	−1.35127	−0.675637	−	0.737235i	$-0.736131\pi$
$503$	−30.3059	−1.35127	−0.675637	+	0.737235i	$0.736131\pi$
$504$	−43.0936	−1.91954
$505$	0	0
$506$	−0.167087	−0.00742793
$507$	−37.4097	−1.66142
$508$	−12.6539	−0.561428
$509$	2.00658	0.0889402	0.0444701	−	0.999011i	$-0.485840\pi$
$509$	2.00658	0.0889402	0.0444701	+	0.999011i	$0.485840\pi$
$510$	0	0
$511$	12.8841	0.569960
$512$	22.0001	0.972274
$513$	31.7196	1.40046
$514$	−13.7257	−0.605414
$515$	0	0
$516$	5.77374	0.254175
$517$	0.966986	0.0425280
$518$	−14.8147	−0.650922
$519$	56.4126	2.47624
$520$	0	0
$521$	11.0737	0.485146	0.242573	−	0.970133i	$-0.422009\pi$
$521$	11.0737	0.485146	0.242573	+	0.970133i	$0.422009\pi$
$522$	15.1052	0.661135
$523$	−13.9476	−0.609884	−0.304942	−	0.952371i	$-0.598637\pi$
$523$	−13.9476	−0.609884	−0.304942	+	0.952371i	$0.598637\pi$
$524$	16.2236	0.708730
$525$	0	0
$526$	8.24475	0.359488
$527$	−4.03689	−0.175849
$528$	0.925619	0.0402824
$529$	−17.3086	−0.752549
$530$	0	0
$531$	26.2669	1.13989
$532$	−34.6758	−1.50339
$533$	0.0205021	0.000888045 0
$534$	−22.5248	−0.974745
$535$	0	0
$536$	−16.6085	−0.717378
$537$	33.0264	1.42520
$538$	−4.66854	−0.201275
$539$	1.37806	0.0593571
$540$	0	0
$541$	−30.9415	−1.33028	−0.665140	−	0.746718i	$-0.731628\pi$
$541$	−30.9415	−1.33028	−0.665140	+	0.746718i	$0.731628\pi$
$542$	−14.6557	−0.629516
$543$	−7.39578	−0.317383
$544$	2.99848	0.128559
$545$	0	0
$546$	0.145290	0.00621782
$547$	−27.0127	−1.15498	−0.577489	−	0.816398i	$-0.695967\pi$
$547$	−27.0127	−1.15498	−0.577489	+	0.816398i	$0.695967\pi$
$548$	14.5743	0.622582
$549$	36.2930	1.54895
$550$	0	0
$551$	26.2612	1.11877
$552$	13.4476	0.572368
$553$	−8.40462	−0.357401
$554$	7.32705	0.311297
$555$	0	0
$556$	−14.0517	−0.595925
$557$	−14.6384	−0.620247	−0.310124	−	0.950696i	$-0.600370\pi$
$557$	−14.6384	−0.620247	−0.310124	+	0.950696i	$0.600370\pi$
$558$	−19.4096	−0.821673
$559$	−0.0268230	−0.00113449
$560$	0	0
$561$	0.221409	0.00934788
$562$	0.660381	0.0278565
$563$	42.5825	1.79464	0.897319	−	0.441383i	$-0.145512\pi$
$563$	42.5825	1.79464	0.897319	+	0.441383i	$0.145512\pi$
$564$	−36.0201	−1.51672
$565$	0	0
$566$	8.24556	0.346587
$567$	12.7087	0.533717
$568$	12.7172	0.533603
$569$	−34.3236	−1.43892	−0.719459	−	0.694535i	$-0.755610\pi$
$569$	−34.3236	−1.43892	−0.719459	+	0.694535i	$0.755610\pi$
$570$	0	0
$571$	39.0213	1.63299	0.816494	−	0.577353i	$-0.195914\pi$
$571$	39.0213	1.63299	0.816494	+	0.577353i	$0.195914\pi$
$572$	−0.00528536	−0.000220992 0
$573$	70.1584	2.93091
$574$	1.95015	0.0813975
$575$	0	0
$576$	−11.1041	−0.462670
$577$	−19.7992	−0.824252	−0.412126	−	0.911127i	$-0.635214\pi$
$577$	−19.7992	−0.824252	−0.412126	+	0.911127i	$0.635214\pi$
$578$	−8.76778	−0.364691
$579$	−76.8854	−3.19525
$580$	0	0
$581$	15.5757	0.646188
$582$	11.3583	0.470819
$583$	1.16133	0.0480973
$584$	−6.05855	−0.250704
$585$	0	0
$586$	−3.64620	−0.150623
$587$	−7.66765	−0.316478	−0.158239	−	0.987401i	$-0.550582\pi$
$587$	−7.66765	−0.316478	−0.158239	+	0.987401i	$0.550582\pi$
$588$	−51.3325	−2.11691
$589$	−33.7447	−1.39043
$590$	0	0
$591$	47.5979	1.95792
$592$	−16.3331	−0.671286
$593$	24.8266	1.01951	0.509754	−	0.860320i	$-0.329736\pi$
$593$	24.8266	1.01951	0.509754	+	0.860320i	$0.329736\pi$
$594$	0.459881	0.0188691
$595$	0	0
$596$	−22.4551	−0.919798
$597$	−4.81627	−0.197117
$598$	−0.0289147	−0.00118241
$599$	−13.6077	−0.555995	−0.277997	−	0.960582i	$-0.589671\pi$
$599$	−13.6077	−0.555995	−0.277997	+	0.960582i	$0.589671\pi$
$600$	0	0
$601$	−48.4269	−1.97538	−0.987688	−	0.156439i	$-0.949998\pi$
$601$	−48.4269	−1.97538	−0.987688	+	0.156439i	$0.949998\pi$
$602$	−2.55139	−0.103987
$603$	44.7841	1.82375
$604$	24.4417	0.994519
$605$	0	0
$606$	−18.4378	−0.748984
$607$	23.4132	0.950313	0.475156	−	0.879901i	$-0.342391\pi$
$607$	23.4132	0.950313	0.475156	+	0.879901i	$0.342391\pi$
$608$	25.0646	1.01650
$609$	65.1658	2.64065
$610$	0	0
$611$	0.167339	0.00676980
$612$	−5.25985	−0.212617
$613$	−12.9653	−0.523665	−0.261832	−	0.965113i	$-0.584327\pi$
$613$	−12.9653	−0.523665	−0.261832	+	0.965113i	$0.584327\pi$
$614$	16.0954	0.649558
$615$	0	0
$616$	−1.08622	−0.0437652
$617$	−15.4470	−0.621871	−0.310936	−	0.950431i	$-0.600642\pi$
$617$	−15.4470	−0.621871	−0.310936	+	0.950431i	$0.600642\pi$
$618$	−22.5064	−0.905340
$619$	−27.8396	−1.11897	−0.559483	−	0.828842i	$-0.689000\pi$
$619$	−27.8396	−1.11897	−0.559483	+	0.828842i	$0.689000\pi$
$620$	0	0
$621$	−15.6646	−0.628597
$622$	4.70304	0.188575
$623$	−61.9740	−2.48294
$624$	0.160180	0.00641233
$625$	0	0
$626$	9.52754	0.380797
$627$	1.85078	0.0739129
$628$	−17.9311	−0.715528
$629$	−3.90689	−0.155778
$630$	0	0
$631$	1.78050	0.0708807	0.0354403	−	0.999372i	$-0.488717\pi$
$631$	1.78050	0.0708807	0.0354403	+	0.999372i	$0.488717\pi$
$632$	3.95213	0.157207
$633$	−41.1937	−1.63730
$634$	−5.05297	−0.200679
$635$	0	0
$636$	−43.2594	−1.71535
$637$	0.238475	0.00944873
$638$	0.380743	0.0150738
$639$	−34.2914	−1.35655
$640$	0	0
$641$	−38.0663	−1.50353	−0.751764	−	0.659432i	$-0.770797\pi$
$641$	−38.0663	−1.50353	−0.751764	+	0.659432i	$0.770797\pi$
$642$	7.72435	0.304856
$643$	−8.15567	−0.321628	−0.160814	−	0.986985i	$-0.551412\pi$
$643$	−8.15567	−0.321628	−0.160814	+	0.986985i	$0.551412\pi$
$644$	17.1244	0.674797
$645$	0	0
$646$	1.46870	0.0577854
$647$	4.49633	0.176769	0.0883844	−	0.996086i	$-0.471830\pi$
$647$	4.49633	0.176769	0.0883844	+	0.996086i	$0.471830\pi$
$648$	−5.97607	−0.234762
$649$	0.662087	0.0259892
$650$	0	0
$651$	−83.7357	−3.28186
$652$	−3.00880	−0.117834
$653$	39.6742	1.55257	0.776286	−	0.630381i	$-0.217101\pi$
$653$	39.6742	1.55257	0.776286	+	0.630381i	$0.217101\pi$
$654$	24.4855	0.957457
$655$	0	0
$656$	2.15001	0.0839439
$657$	16.3366	0.637351
$658$	15.9171	0.620514
$659$	−41.8801	−1.63142	−0.815708	−	0.578464i	$-0.803652\pi$
$659$	−41.8801	−1.63142	−0.815708	+	0.578464i	$0.803652\pi$
$660$	0	0
$661$	−29.1433	−1.13354	−0.566771	−	0.823875i	$-0.691808\pi$
$661$	−29.1433	−1.13354	−0.566771	+	0.823875i	$0.691808\pi$
$662$	−11.9915	−0.466064
$663$	0.0383152	0.00148804
$664$	−7.32420	−0.284234
$665$	0	0
$666$	−18.7845	−0.727886
$667$	−12.9690	−0.502160
$668$	5.64056	0.218240
$669$	−10.4777	−0.405092
$670$	0	0
$671$	0.914808	0.0353158
$672$	62.1965	2.39928
$673$	33.5490	1.29322	0.646610	−	0.762821i	$-0.276186\pi$
$673$	33.5490	1.29322	0.646610	+	0.762821i	$0.276186\pi$
$674$	12.5762	0.484419
$675$	0	0
$676$	22.4011	0.861581
$677$	17.9719	0.690718	0.345359	−	0.938471i	$-0.387757\pi$
$677$	17.9719	0.690718	0.345359	+	0.938471i	$0.387757\pi$
$678$	−17.3545	−0.666496
$679$	31.2510	1.19930
$680$	0	0
$681$	59.9566	2.29754
$682$	−0.489241	−0.0187340
$683$	−37.3229	−1.42812	−0.714061	−	0.700084i	$-0.753146\pi$
$683$	−37.3229	−1.42812	−0.714061	+	0.700084i	$0.753146\pi$
$684$	−43.9676	−1.68114
$685$	0	0
$686$	7.34376	0.280386
$687$	39.1325	1.49300
$688$	−2.81287	−0.107240
$689$	0.200970	0.00765635
$690$	0	0
$691$	−6.54978	−0.249165	−0.124583	−	0.992209i	$-0.539759\pi$
$691$	−6.54978	−0.249165	−0.124583	+	0.992209i	$0.539759\pi$
$692$	−33.7801	−1.28413
$693$	2.92895	0.111262
$694$	−1.95500	−0.0742107
$695$	0	0
$696$	−30.6431	−1.16153
$697$	0.514285	0.0194799
$698$	−13.7400	−0.520066
$699$	−16.9833	−0.642366
$700$	0	0
$701$	−1.12219	−0.0423846	−0.0211923	−	0.999775i	$-0.506746\pi$
$701$	−1.12219	−0.0423846	−0.0211923	+	0.999775i	$0.506746\pi$
$702$	0.0795832	0.00300367
$703$	−32.6580	−1.23172
$704$	−0.279891	−0.0105488
$705$	0	0
$706$	14.5268	0.546725
$707$	−50.7291	−1.90786
$708$	−24.6627	−0.926881
$709$	35.1438	1.31985	0.659927	−	0.751330i	$-0.270587\pi$
$709$	35.1438	1.31985	0.659927	+	0.751330i	$0.270587\pi$
$710$	0	0
$711$	−10.6567	−0.399659
$712$	29.1422	1.09215
$713$	16.6646	0.624096
$714$	3.64451	0.136392
$715$	0	0
$716$	−19.7764	−0.739078
$717$	24.8606	0.928435
$718$	7.68197	0.286688
$719$	−37.7313	−1.40714	−0.703569	−	0.710627i	$-0.748411\pi$
$719$	−37.7313	−1.40714	−0.703569	+	0.710627i	$0.748411\pi$
$720$	0	0
$721$	−61.9233	−2.30614
$722$	2.28138	0.0849043
$723$	2.87779	0.107026
$724$	4.42863	0.164589
$725$	0	0
$726$	−16.6268	−0.617078
$727$	−10.8104	−0.400935	−0.200468	−	0.979700i	$-0.564246\pi$
$727$	−10.8104	−0.400935	−0.200468	+	0.979700i	$0.564246\pi$
$728$	−0.187973	−0.00696675
$729$	−40.5737	−1.50273
$730$	0	0
$731$	−0.672842	−0.0248859
$732$	−34.0765	−1.25950
$733$	11.0318	0.407468	0.203734	−	0.979026i	$-0.434692\pi$
$733$	11.0318	0.407468	0.203734	+	0.979026i	$0.434692\pi$
$734$	−0.536636	−0.0198076
$735$	0	0
$736$	−12.3780	−0.456260
$737$	1.12883	0.0415812
$738$	2.47271	0.0910217
$739$	18.1704	0.668409	0.334204	−	0.942501i	$-0.391532\pi$
$739$	18.1704	0.668409	0.334204	+	0.942501i	$0.391532\pi$
$740$	0	0
$741$	0.320280	0.0117658
$742$	19.1161	0.701774
$743$	−21.5543	−0.790752	−0.395376	−	0.918519i	$-0.629386\pi$
$743$	−21.5543	−0.790752	−0.395376	+	0.918519i	$0.629386\pi$
$744$	39.3753	1.44357
$745$	0	0
$746$	3.65676	0.133883
$747$	19.7494	0.722591
$748$	−0.132581	−0.00484763
$749$	21.2525	0.776550
$750$	0	0
$751$	2.66683	0.0973139	0.0486569	−	0.998816i	$-0.484506\pi$
$751$	2.66683	0.0973139	0.0486569	+	0.998816i	$0.484506\pi$
$752$	17.5484	0.639926
$753$	32.0916	1.16948
$754$	0.0658883	0.00239951
$755$	0	0
$756$	−47.1323	−1.71418
$757$	−23.4553	−0.852497	−0.426248	−	0.904606i	$-0.640165\pi$
$757$	−23.4553	−0.852497	−0.426248	+	0.904606i	$0.640165\pi$
$758$	−18.2793	−0.663933
$759$	−0.913996	−0.0331759
$760$	0	0
$761$	−18.9433	−0.686692	−0.343346	−	0.939209i	$-0.611560\pi$
$761$	−18.9433	−0.686692	−0.343346	+	0.939209i	$0.611560\pi$
$762$	11.1173	0.402736
$763$	67.3684	2.43890
$764$	−42.0112	−1.51991
$765$	0	0
$766$	−5.46205	−0.197352
$767$	0.114575	0.00413708
$768$	−5.28456	−0.190690
$769$	29.2771	1.05576	0.527880	−	0.849319i	$-0.322987\pi$
$769$	29.2771	1.05576	0.527880	+	0.849319i	$0.322987\pi$
$770$	0	0
$771$	−75.0819	−2.70401
$772$	46.0393	1.65699
$773$	−35.9819	−1.29418	−0.647089	−	0.762415i	$-0.724014\pi$
$773$	−35.9819	−1.29418	−0.647089	+	0.762415i	$0.724014\pi$
$774$	−3.23506	−0.116282
$775$	0	0
$776$	−14.6952	−0.527528
$777$	−81.0392	−2.90727
$778$	−14.3345	−0.513918
$779$	4.29896	0.154026
$780$	0	0
$781$	−0.864355	−0.0309291
$782$	−0.725311	−0.0259371
$783$	35.6950	1.27563
$784$	25.0084	0.893156
$785$	0	0
$786$	−14.2534	−0.508402
$787$	−40.5775	−1.44643	−0.723216	−	0.690622i	$-0.757337\pi$
$787$	−40.5775	−1.44643	−0.723216	+	0.690622i	$0.757337\pi$
$788$	−28.5018	−1.01534
$789$	45.1002	1.60561
$790$	0	0
$791$	−47.7486	−1.69775
$792$	−1.37729	−0.0489399
$793$	0.158309	0.00562172
$794$	−10.6568	−0.378197
$795$	0	0
$796$	2.88401	0.102221
$797$	48.7905	1.72825	0.864125	−	0.503278i	$-0.167873\pi$
$797$	48.7905	1.72825	0.864125	+	0.503278i	$0.167873\pi$
$798$	30.4648	1.07844
$799$	4.19760	0.148500
$800$	0	0
$801$	−78.5807	−2.77651
$802$	−13.7437	−0.485306
$803$	0.411783	0.0145315
$804$	−42.0490	−1.48295
$805$	0	0
$806$	−0.0846640	−0.00298216
$807$	−25.5377	−0.898971
$808$	23.8545	0.839199
$809$	36.8207	1.29455	0.647273	−	0.762258i	$-0.275909\pi$
$809$	36.8207	1.29455	0.647273	+	0.762258i	$0.275909\pi$
$810$	0	0
$811$	30.8842	1.08449	0.542245	−	0.840221i	$-0.317575\pi$
$811$	30.8842	1.08449	0.542245	+	0.840221i	$0.317575\pi$
$812$	−39.0216	−1.36939
$813$	−80.1692	−2.81166
$814$	−0.473486	−0.0165957
$815$	0	0
$816$	4.01803	0.140659
$817$	−5.62435	−0.196771
$818$	−11.0721	−0.387128
$819$	0.506861	0.0177111
$820$	0	0
$821$	−0.333148	−0.0116269	−0.00581347	−	0.999983i	$-0.501850\pi$
$821$	−0.333148	−0.0116269	−0.00581347	+	0.999983i	$0.501850\pi$
$822$	−12.8044	−0.446605
$823$	−40.1393	−1.39917	−0.699584	−	0.714550i	$-0.746632\pi$
$823$	−40.1393	−1.39917	−0.699584	+	0.714550i	$0.746632\pi$
$824$	29.1184	1.01439
$825$	0	0
$826$	10.8983	0.379201
$827$	−27.6716	−0.962236	−0.481118	−	0.876656i	$-0.659769\pi$
$827$	−27.6716	−0.962236	−0.481118	+	0.876656i	$0.659769\pi$
$828$	21.7131	0.754584
$829$	−9.07416	−0.315159	−0.157579	−	0.987506i	$-0.550369\pi$
$829$	−9.07416	−0.315159	−0.157579	+	0.987506i	$0.550369\pi$
$830$	0	0
$831$	40.0803	1.39037
$832$	−0.0484357	−0.00167920
$833$	5.98202	0.207265
$834$	12.3453	0.427483
$835$	0	0
$836$	−1.10825	−0.0383298
$837$	−45.8667	−1.58539
$838$	−20.1872	−0.697357
$839$	22.6685	0.782603	0.391301	−	0.920263i	$-0.372025\pi$
$839$	22.6685	0.782603	0.391301	+	0.920263i	$0.372025\pi$
$840$	0	0
$841$	0.552465	0.0190505
$842$	17.0409	0.587269
$843$	3.61240	0.124418
$844$	24.6670	0.849072
$845$	0	0
$846$	20.1823	0.693882
$847$	−45.7464	−1.57186
$848$	21.0753	0.723728
$849$	45.1047	1.54799
$850$	0	0
$851$	16.1280	0.552860
$852$	32.1971	1.10306
$853$	−18.7783	−0.642956	−0.321478	−	0.946917i	$-0.604180\pi$
$853$	−18.7783	−0.642956	−0.321478	+	0.946917i	$0.604180\pi$
$854$	15.0582	0.515283
$855$	0	0
$856$	−9.99364	−0.341575
$857$	−34.1855	−1.16775	−0.583877	−	0.811842i	$-0.698465\pi$
$857$	−34.1855	−1.16775	−0.583877	+	0.811842i	$0.698465\pi$
$858$	0.00464352	0.000158527 0
$859$	−46.0644	−1.57170	−0.785849	−	0.618418i	$-0.787774\pi$
$859$	−46.0644	−1.57170	−0.785849	+	0.618418i	$0.787774\pi$
$860$	0	0
$861$	10.6676	0.363552
$862$	−5.80651	−0.197771
$863$	−2.66377	−0.0906757	−0.0453379	−	0.998972i	$-0.514436\pi$
$863$	−2.66377	−0.0906757	−0.0453379	+	0.998972i	$0.514436\pi$
$864$	34.0685	1.15903
$865$	0	0
$866$	−7.63500	−0.259448
$867$	−47.9613	−1.62885
$868$	50.1413	1.70191
$869$	−0.268615	−0.00911216
$870$	0	0
$871$	0.195347	0.00661908
$872$	−31.6789	−1.07278
$873$	39.6250	1.34110
$874$	−6.06295	−0.205082
$875$	0	0
$876$	−15.3389	−0.518252
$877$	7.96747	0.269042	0.134521	−	0.990911i	$-0.457050\pi$
$877$	7.96747	0.269042	0.134521	+	0.990911i	$0.457050\pi$
$878$	−4.90283	−0.165463
$879$	−19.9453	−0.672739
$880$	0	0
$881$	28.5600	0.962210	0.481105	−	0.876663i	$-0.340236\pi$
$881$	28.5600	0.962210	0.481105	+	0.876663i	$0.340236\pi$
$882$	28.7619	0.968464
$883$	11.8316	0.398167	0.199083	−	0.979983i	$-0.436204\pi$
$883$	11.8316	0.398167	0.199083	+	0.979983i	$0.436204\pi$
$884$	−0.0229433	−0.000771667 0
$885$	0	0
$886$	15.2369	0.511892
$887$	−58.5821	−1.96700	−0.983498	−	0.180919i	$-0.942093\pi$
$887$	−58.5821	−1.96700	−0.983498	+	0.180919i	$0.942093\pi$
$888$	38.1073	1.27880
$889$	30.5877	1.02588
$890$	0	0
$891$	0.406177	0.0136074
$892$	6.27411	0.210073
$893$	35.0882	1.17418
$894$	19.7282	0.659811
$895$	0	0
$896$	−47.8324	−1.59797
$897$	−0.158169	−0.00528110
$898$	3.45991	0.115459
$899$	−37.9738	−1.26650
$900$	0	0
$901$	5.04122	0.167948
$902$	0.0623275	0.00207528
$903$	−13.9565	−0.464444
$904$	22.4530	0.746775
$905$	0	0
$906$	−21.4736	−0.713412
$907$	−7.83669	−0.260213	−0.130106	−	0.991500i	$-0.541532\pi$
$907$	−7.83669	−0.260213	−0.130106	+	0.991500i	$0.541532\pi$
$908$	−35.9023	−1.19146
$909$	−64.3226	−2.13345
$910$	0	0
$911$	1.70766	0.0565773	0.0282886	−	0.999600i	$-0.490994\pi$
$911$	1.70766	0.0565773	0.0282886	+	0.999600i	$0.490994\pi$
$912$	33.5871	1.11218
$913$	0.497806	0.0164750
$914$	19.4985	0.644955
$915$	0	0
$916$	−23.4327	−0.774240
$917$	−39.2163	−1.29504
$918$	1.99630	0.0658878
$919$	45.1214	1.48842	0.744208	−	0.667948i	$-0.232827\pi$
$919$	45.1214	1.48842	0.744208	+	0.667948i	$0.232827\pi$
$920$	0	0
$921$	88.0448	2.90117
$922$	17.3272	0.570642
$923$	−0.149578	−0.00492343
$924$	−2.75007	−0.0904708
$925$	0	0
$926$	−7.97311	−0.262013
$927$	−78.5164	−2.57882
$928$	28.2059	0.925903
$929$	24.9370	0.818157	0.409078	−	0.912499i	$-0.365850\pi$
$929$	24.9370	0.818157	0.409078	+	0.912499i	$0.365850\pi$
$930$	0	0
$931$	50.0043	1.63883
$932$	10.1697	0.333118
$933$	25.7265	0.842247
$934$	−10.5015	−0.343621
$935$	0	0
$936$	−0.238343	−0.00779048
$937$	−8.58983	−0.280617	−0.140309	−	0.990108i	$-0.544810\pi$
$937$	−8.58983	−0.280617	−0.140309	+	0.990108i	$0.544810\pi$
$938$	18.5812	0.606699
$939$	52.1173	1.70078
$940$	0	0
$941$	−16.8201	−0.548320	−0.274160	−	0.961684i	$-0.588400\pi$
$941$	−16.8201	−0.548320	−0.274160	+	0.961684i	$0.588400\pi$
$942$	15.7536	0.513279
$943$	−2.12302	−0.0691349
$944$	12.0153	0.391064
$945$	0	0
$946$	−0.0815435	−0.00265121
$947$	38.3644	1.24667	0.623337	−	0.781953i	$-0.285777\pi$
$947$	38.3644	1.24667	0.623337	+	0.781953i	$0.285777\pi$
$948$	10.0059	0.324977
$949$	0.0712598	0.00231319
$950$	0	0
$951$	−27.6406	−0.896309
$952$	−4.71521	−0.152821
$953$	−21.9180	−0.709993	−0.354996	−	0.934868i	$-0.615518\pi$
$953$	−21.9180	−0.709993	−0.354996	+	0.934868i	$0.615518\pi$
$954$	24.2385	0.784750
$955$	0	0
$956$	−14.8866	−0.481468
$957$	2.08273	0.0673251
$958$	−2.74359	−0.0886413
$959$	−35.2296	−1.13762
$960$	0	0
$961$	17.7950	0.574033
$962$	−0.0819376	−0.00264178
$963$	26.9474	0.868367
$964$	−1.72323	−0.0555016
$965$	0	0
$966$	−15.0449	−0.484061
$967$	31.5117	1.01335	0.506674	−	0.862138i	$-0.330875\pi$
$967$	31.5117	1.01335	0.506674	+	0.862138i	$0.330875\pi$
$968$	21.5115	0.691405
$969$	8.03407	0.258091
$970$	0	0
$971$	−7.30306	−0.234366	−0.117183	−	0.993110i	$-0.537386\pi$
$971$	−7.30306	−0.234366	−0.117183	+	0.993110i	$0.537386\pi$
$972$	18.8149	0.603488
$973$	33.9664	1.08891
$974$	−14.0706	−0.450852
$975$	0	0
$976$	16.6015	0.531402
$977$	−22.6288	−0.723958	−0.361979	−	0.932186i	$-0.617899\pi$
$977$	−22.6288	−0.723958	−0.361979	+	0.932186i	$0.617899\pi$
$978$	2.64342	0.0845271
$979$	−1.98072	−0.0633040
$980$	0	0
$981$	85.4206	2.72727
$982$	5.82525	0.185891
$983$	35.5075	1.13251	0.566257	−	0.824229i	$-0.308391\pi$
$983$	35.5075	1.13251	0.566257	+	0.824229i	$0.308391\pi$
$984$	−5.01628	−0.159913
$985$	0	0
$986$	1.65277	0.0526350
$987$	87.0695	2.77145
$988$	−0.191785	−0.00610151
$989$	2.77755	0.0883211
$990$	0	0
$991$	−22.2090	−0.705492	−0.352746	−	0.935719i	$-0.614752\pi$
$991$	−22.2090	−0.705492	−0.352746	+	0.935719i	$0.614752\pi$
$992$	−36.2435	−1.15073
$993$	−65.5958	−2.08162
$994$	−14.2278	−0.451277
$995$	0	0
$996$	−18.5432	−0.587564
$997$	35.8975	1.13688	0.568442	−	0.822723i	$-0.307546\pi$
$997$	35.8975	1.13688	0.568442	+	0.822723i	$0.307546\pi$
$998$	4.59575	0.145476
$999$	−44.3897	−1.40443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.e.1.3		5
5.4	even	2		1205.2.a.a.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.a.1.3	✓	5	5.4	even	2
6025.2.a.e.1.3		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.526087 q^{2} +2.87779 q^{3} -1.72323 q^{4} +1.51397 q^{6} +4.16547 q^{7} -1.95874 q^{8} +5.28166 q^{9} +O(q^{10})\)	\(q+0.526087 q^{2} +2.87779 q^{3} -1.72323 q^{4} +1.51397 q^{6} +4.16547 q^{7} -1.95874 q^{8} +5.28166 q^{9} +0.133130 q^{11} -4.95910 q^{12} +0.0230385 q^{13} +2.19140 q^{14} +2.41600 q^{16} +0.577908 q^{17} +2.77861 q^{18} +4.83079 q^{19} +11.9873 q^{21} +0.0700382 q^{22} -2.38566 q^{23} -5.63685 q^{24} +0.0121202 q^{26} +6.56614 q^{27} -7.17808 q^{28} +5.43622 q^{29} -6.98534 q^{31} +5.18851 q^{32} +0.383121 q^{33} +0.304030 q^{34} -9.10153 q^{36} -6.76040 q^{37} +2.54141 q^{38} +0.0662998 q^{39} +0.889908 q^{41} +6.30639 q^{42} -1.16427 q^{43} -0.229415 q^{44} -1.25506 q^{46} +7.26345 q^{47} +6.95272 q^{48} +10.3512 q^{49} +1.66310 q^{51} -0.0397006 q^{52} +8.72323 q^{53} +3.45436 q^{54} -8.15910 q^{56} +13.9020 q^{57} +2.85992 q^{58} +4.97322 q^{59} +6.87151 q^{61} -3.67490 q^{62} +22.0006 q^{63} -2.10238 q^{64} +0.201555 q^{66} +8.47916 q^{67} -0.995870 q^{68} -6.86542 q^{69} -6.49254 q^{71} -10.3454 q^{72} +3.09308 q^{73} -3.55656 q^{74} -8.32457 q^{76} +0.554551 q^{77} +0.0348795 q^{78} -2.01769 q^{79} +3.05097 q^{81} +0.468169 q^{82} +3.73923 q^{83} -20.6570 q^{84} -0.612508 q^{86} +15.6443 q^{87} -0.260768 q^{88} -14.8780 q^{89} +0.0959661 q^{91} +4.11104 q^{92} -20.1023 q^{93} +3.82120 q^{94} +14.9314 q^{96} +7.50238 q^{97} +5.44562 q^{98} +0.703150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9} - 3 q^{11} - 8 q^{12} + q^{13} - q^{14} + 15 q^{16} + 5 q^{17} - 4 q^{18} + 3 q^{19} + 11 q^{21} + 13 q^{22} + 8 q^{23} - 14 q^{24} + 14 q^{26} + 14 q^{27} + 17 q^{28} + 9 q^{29} - 16 q^{31} + 16 q^{32} - 23 q^{33} - 10 q^{34} - 17 q^{36} - 7 q^{37} + 22 q^{38} - 19 q^{39} + 9 q^{41} - 17 q^{42} + 32 q^{43} - 8 q^{44} + 5 q^{46} + 7 q^{47} + 6 q^{48} + 9 q^{49} - 8 q^{51} + 10 q^{52} + 32 q^{53} + 32 q^{54} - 18 q^{56} - 3 q^{57} - 11 q^{58} - 8 q^{59} - 12 q^{61} - 17 q^{62} + 11 q^{63} - 16 q^{64} + 15 q^{66} + 5 q^{67} + 2 q^{68} + 7 q^{69} - 11 q^{71} - 7 q^{72} + 29 q^{73} + 10 q^{74} - 8 q^{76} + 5 q^{77} - 2 q^{78} + 16 q^{79} - 15 q^{81} + 2 q^{82} + 10 q^{83} + 5 q^{84} + 14 q^{86} + 37 q^{87} - 10 q^{88} + 9 q^{89} + 12 q^{91} + 25 q^{92} - 15 q^{93} - 11 q^{94} - 3 q^{96} + 43 q^{97} - 30 q^{98} - 30 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9 - 3 * q^11 - 8 * q^12 + q^13 - q^14 + 15 * q^16 + 5 * q^17 - 4 * q^18 + 3 * q^19 + 11 * q^21 + 13 * q^22 + 8 * q^23 - 14 * q^24 + 14 * q^26 + 14 * q^27 + 17 * q^28 + 9 * q^29 - 16 * q^31 + 16 * q^32 - 23 * q^33 - 10 * q^34 - 17 * q^36 - 7 * q^37 + 22 * q^38 - 19 * q^39 + 9 * q^41 - 17 * q^42 + 32 * q^43 - 8 * q^44 + 5 * q^46 + 7 * q^47 + 6 * q^48 + 9 * q^49 - 8 * q^51 + 10 * q^52 + 32 * q^53 + 32 * q^54 - 18 * q^56 - 3 * q^57 - 11 * q^58 - 8 * q^59 - 12 * q^61 - 17 * q^62 + 11 * q^63 - 16 * q^64 + 15 * q^66 + 5 * q^67 + 2 * q^68 + 7 * q^69 - 11 * q^71 - 7 * q^72 + 29 * q^73 + 10 * q^74 - 8 * q^76 + 5 * q^77 - 2 * q^78 + 16 * q^79 - 15 * q^81 + 2 * q^82 + 10 * q^83 + 5 * q^84 + 14 * q^86 + 37 * q^87 - 10 * q^88 + 9 * q^89 + 12 * q^91 + 25 * q^92 - 15 * q^93 - 11 * q^94 - 3 * q^96 + 43 * q^97 - 30 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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