LMFDB - Embedded newform 4025.2.a.t.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 $ x^8 - x^7 - 11x^6 + 9x^5 + 36x^4 - 23x^3 - 30x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.181467$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.181467 q^{2} -3.25071 q^{3} -1.96707 q^{4} +0.589897 q^{6} -1.00000 q^{7} +0.719892 q^{8} +7.56714 q^{9} +O(q^{10})$	\(q-0.181467 q^{2} -3.25071 q^{3} -1.96707 q^{4} +0.589897 q^{6} -1.00000 q^{7} +0.719892 q^{8} +7.56714 q^{9} -4.56129 q^{11} +6.39438 q^{12} -0.591570 q^{13} +0.181467 q^{14} +3.80350 q^{16} -6.55563 q^{17} -1.37319 q^{18} +2.17660 q^{19} +3.25071 q^{21} +0.827723 q^{22} -1.00000 q^{23} -2.34016 q^{24} +0.107350 q^{26} -14.8465 q^{27} +1.96707 q^{28} +3.00176 q^{29} -5.34448 q^{31} -2.13000 q^{32} +14.8274 q^{33} +1.18963 q^{34} -14.8851 q^{36} +8.46864 q^{37} -0.394981 q^{38} +1.92302 q^{39} -0.199340 q^{41} -0.589897 q^{42} -0.567912 q^{43} +8.97237 q^{44} +0.181467 q^{46} +2.66212 q^{47} -12.3641 q^{48} +1.00000 q^{49} +21.3105 q^{51} +1.16366 q^{52} +13.4576 q^{53} +2.69414 q^{54} -0.719892 q^{56} -7.07549 q^{57} -0.544721 q^{58} -1.38898 q^{59} -5.14656 q^{61} +0.969848 q^{62} -7.56714 q^{63} -7.22048 q^{64} -2.69069 q^{66} -9.43195 q^{67} +12.8954 q^{68} +3.25071 q^{69} +12.0746 q^{71} +5.44752 q^{72} +14.2499 q^{73} -1.53678 q^{74} -4.28152 q^{76} +4.56129 q^{77} -0.348965 q^{78} +3.39859 q^{79} +25.5602 q^{81} +0.0361737 q^{82} +16.4522 q^{83} -6.39438 q^{84} +0.103057 q^{86} -9.75788 q^{87} -3.28364 q^{88} -2.01173 q^{89} +0.591570 q^{91} +1.96707 q^{92} +17.3734 q^{93} -0.483086 q^{94} +6.92400 q^{96} +11.0458 q^{97} -0.181467 q^{98} -34.5159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * 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 $

$2$	−0.181467	−0.128317	−0.0641583	−	0.997940i	$-0.520436\pi$
$2$	−0.181467	−0.128317	−0.0641583	+	0.997940i	$0.520436\pi$
$3$	−3.25071	−1.87680	−0.938400	−	0.345551i	$-0.887692\pi$
$3$	−3.25071	−1.87680	−0.938400	+	0.345551i	$0.887692\pi$
$4$	−1.96707	−0.983535
$5$	0	0
$5$	0	0
$6$	0.589897	0.240825
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.719892	0.254520
$9$	7.56714	2.52238
$10$	0	0
$11$	−4.56129	−1.37528	−0.687640	−	0.726052i	$-0.741353\pi$
$11$	−4.56129	−1.37528	−0.687640	+	0.726052i	$0.741353\pi$
$12$	6.39438	1.84590
$13$	−0.591570	−0.164072	−0.0820360	−	0.996629i	$-0.526142\pi$
$13$	−0.591570	−0.164072	−0.0820360	+	0.996629i	$0.526142\pi$
$14$	0.181467	0.0484991
$15$	0	0
$16$	3.80350	0.950876
$17$	−6.55563	−1.58997	−0.794987	−	0.606626i	$-0.792522\pi$
$17$	−6.55563	−1.58997	−0.794987	+	0.606626i	$0.792522\pi$
$18$	−1.37319	−0.323663
$19$	2.17660	0.499346	0.249673	−	0.968330i	$-0.419677\pi$
$19$	2.17660	0.499346	0.249673	+	0.968330i	$0.419677\pi$
$20$	0	0
$21$	3.25071	0.709364
$22$	0.827723	0.176471
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.34016	−0.477684
$25$	0	0
$26$	0.107350	0.0210531
$27$	−14.8465	−2.85720
$28$	1.96707	0.371741
$29$	3.00176	0.557414	0.278707	−	0.960376i	$-0.410094\pi$
$29$	3.00176	0.557414	0.278707	+	0.960376i	$0.410094\pi$
$30$	0	0
$31$	−5.34448	−0.959898	−0.479949	−	0.877297i	$-0.659345\pi$
$31$	−5.34448	−0.959898	−0.479949	+	0.877297i	$0.659345\pi$
$32$	−2.13000	−0.376533
$33$	14.8274	2.58113
$34$	1.18963	0.204020
$35$	0	0
$36$	−14.8851	−2.48085
$37$	8.46864	1.39224	0.696118	−	0.717928i	$-0.254909\pi$
$37$	8.46864	1.39224	0.696118	+	0.717928i	$0.254909\pi$
$38$	−0.394981	−0.0640743
$39$	1.92302	0.307930
$40$	0	0
$41$	−0.199340	−0.0311318	−0.0155659	−	0.999879i	$-0.504955\pi$
$41$	−0.199340	−0.0311318	−0.0155659	+	0.999879i	$0.504955\pi$
$42$	−0.589897	−0.0910231
$43$	−0.567912	−0.0866057	−0.0433029	−	0.999062i	$-0.513788\pi$
$43$	−0.567912	−0.0866057	−0.0433029	+	0.999062i	$0.513788\pi$
$44$	8.97237	1.35264
$45$	0	0
$46$	0.181467	0.0267559
$47$	2.66212	0.388310	0.194155	−	0.980971i	$-0.437804\pi$
$47$	2.66212	0.388310	0.194155	+	0.980971i	$0.437804\pi$
$48$	−12.3641	−1.78460
$49$	1.00000	0.142857
$50$	0	0
$51$	21.3105	2.98406
$52$	1.16366	0.161370
$53$	13.4576	1.84855	0.924275	−	0.381728i	$-0.124671\pi$
$53$	13.4576	1.84855	0.924275	+	0.381728i	$0.124671\pi$
$54$	2.69414	0.366626
$55$	0	0
$56$	−0.719892	−0.0961997
$57$	−7.07549	−0.937172
$58$	−0.544721	−0.0715254
$59$	−1.38898	−0.180830	−0.0904150	−	0.995904i	$-0.528819\pi$
$59$	−1.38898	−0.180830	−0.0904150	+	0.995904i	$0.528819\pi$
$60$	0	0
$61$	−5.14656	−0.658950	−0.329475	−	0.944164i	$-0.606872\pi$
$61$	−5.14656	−0.658950	−0.329475	+	0.944164i	$0.606872\pi$
$62$	0.969848	0.123171
$63$	−7.56714	−0.953370
$64$	−7.22048	−0.902560
$65$	0	0
$66$	−2.69069	−0.331201
$67$	−9.43195	−1.15230	−0.576148	−	0.817345i	$-0.695445\pi$
$67$	−9.43195	−1.15230	−0.576148	+	0.817345i	$0.695445\pi$
$68$	12.8954	1.56380
$69$	3.25071	0.391340
$70$	0	0
$71$	12.0746	1.43299	0.716497	−	0.697590i	$-0.245744\pi$
$71$	12.0746	1.43299	0.716497	+	0.697590i	$0.245744\pi$
$72$	5.44752	0.641997
$73$	14.2499	1.66782	0.833911	−	0.551900i	$-0.186097\pi$
$73$	14.2499	1.66782	0.833911	+	0.551900i	$0.186097\pi$
$74$	−1.53678	−0.178647
$75$	0	0
$76$	−4.28152	−0.491124
$77$	4.56129	0.519807
$78$	−0.348965	−0.0395125
$79$	3.39859	0.382371	0.191186	−	0.981554i	$-0.438767\pi$
$79$	3.39859	0.382371	0.191186	+	0.981554i	$0.438767\pi$
$80$	0	0
$81$	25.5602	2.84002
$82$	0.0361737	0.00399472
$83$	16.4522	1.80587	0.902933	−	0.429781i	$-0.141409\pi$
$83$	16.4522	1.80587	0.902933	+	0.429781i	$0.141409\pi$
$84$	−6.39438	−0.697684
$85$	0	0
$86$	0.103057	0.0111129
$87$	−9.75788	−1.04615
$88$	−3.28364	−0.350037
$89$	−2.01173	−0.213243	−0.106621	−	0.994300i	$-0.534003\pi$
$89$	−2.01173	−0.213243	−0.106621	+	0.994300i	$0.534003\pi$
$90$	0	0
$91$	0.591570	0.0620134
$92$	1.96707	0.205081
$93$	17.3734	1.80154
$94$	−0.483086	−0.0498266
$95$	0	0
$96$	6.92400	0.706678
$97$	11.0458	1.12153	0.560767	−	0.827974i	$-0.310507\pi$
$97$	11.0458	1.12153	0.560767	+	0.827974i	$0.310507\pi$
$98$	−0.181467	−0.0183309
$99$	−34.5159	−3.46898
$100$	0	0
$101$	−4.85692	−0.483282	−0.241641	−	0.970366i	$-0.577686\pi$
$101$	−4.85692	−0.483282	−0.241641	+	0.970366i	$0.577686\pi$
$102$	−3.86715	−0.382905
$103$	−6.30296	−0.621049	−0.310524	−	0.950565i	$-0.600505\pi$
$103$	−6.30296	−0.621049	−0.310524	+	0.950565i	$0.600505\pi$
$104$	−0.425867	−0.0417596
$105$	0	0
$106$	−2.44212	−0.237200
$107$	−4.96289	−0.479781	−0.239890	−	0.970800i	$-0.577112\pi$
$107$	−4.96289	−0.479781	−0.239890	+	0.970800i	$0.577112\pi$
$108$	29.2040	2.81016
$109$	2.19456	0.210201	0.105100	−	0.994462i	$-0.466484\pi$
$109$	2.19456	0.210201	0.105100	+	0.994462i	$0.466484\pi$
$110$	0	0
$111$	−27.5291	−2.61295
$112$	−3.80350	−0.359397
$113$	19.4541	1.83009	0.915044	−	0.403354i	$-0.132156\pi$
$113$	19.4541	1.83009	0.915044	+	0.403354i	$0.132156\pi$
$114$	1.28397	0.120255
$115$	0	0
$116$	−5.90468	−0.548236
$117$	−4.47649	−0.413852
$118$	0.252054	0.0232035
$119$	6.55563	0.600954
$120$	0	0
$121$	9.80534	0.891394
$122$	0.933931	0.0845541
$123$	0.647999	0.0584281
$124$	10.5130	0.944093
$125$	0	0
$126$	1.37319	0.122333
$127$	−8.46742	−0.751362	−0.375681	−	0.926749i	$-0.622591\pi$
$127$	−8.46742	−0.751362	−0.375681	+	0.926749i	$0.622591\pi$
$128$	5.57027	0.492347
$129$	1.84612	0.162542
$130$	0	0
$131$	13.3996	1.17073	0.585363	−	0.810771i	$-0.300952\pi$
$131$	13.3996	1.17073	0.585363	+	0.810771i	$0.300952\pi$
$132$	−29.1666	−2.53863
$133$	−2.17660	−0.188735
$134$	1.71159	0.147859
$135$	0	0
$136$	−4.71935	−0.404681
$137$	−19.1138	−1.63300	−0.816502	−	0.577343i	$-0.804089\pi$
$137$	−19.1138	−1.63300	−0.816502	+	0.577343i	$0.804089\pi$
$138$	−0.589897	−0.0502154
$139$	4.59581	0.389811	0.194906	−	0.980822i	$-0.437560\pi$
$139$	4.59581	0.389811	0.194906	+	0.980822i	$0.437560\pi$
$140$	0	0
$141$	−8.65378	−0.728780
$142$	−2.19115	−0.183877
$143$	2.69832	0.225645
$144$	28.7816	2.39847
$145$	0	0
$146$	−2.58588	−0.214009
$147$	−3.25071	−0.268114
$148$	−16.6584	−1.36931
$149$	1.34571	0.110244	0.0551222	−	0.998480i	$-0.482445\pi$
$149$	1.34571	0.110244	0.0551222	+	0.998480i	$0.482445\pi$
$150$	0	0
$151$	−18.9467	−1.54186	−0.770930	−	0.636920i	$-0.780208\pi$
$151$	−18.9467	−1.54186	−0.770930	+	0.636920i	$0.780208\pi$
$152$	1.56692	0.127094
$153$	−49.6074	−4.01052
$154$	−0.827723	−0.0666998
$155$	0	0
$156$	−3.78272	−0.302860
$157$	2.25478	0.179951	0.0899756	−	0.995944i	$-0.471321\pi$
$157$	2.25478	0.179951	0.0899756	+	0.995944i	$0.471321\pi$
$158$	−0.616732	−0.0490646
$159$	−43.7469	−3.46936
$160$	0	0
$161$	1.00000	0.0788110
$162$	−4.63832	−0.364421
$163$	−19.4427	−1.52287	−0.761435	−	0.648241i	$-0.775505\pi$
$163$	−19.4427	−1.52287	−0.761435	+	0.648241i	$0.775505\pi$
$164$	0.392117	0.0306192
$165$	0	0
$166$	−2.98554	−0.231723
$167$	14.9519	1.15701	0.578506	−	0.815678i	$-0.303636\pi$
$167$	14.9519	1.15701	0.578506	+	0.815678i	$0.303636\pi$
$168$	2.34016	0.180548
$169$	−12.6500	−0.973080
$170$	0	0
$171$	16.4706	1.25954
$172$	1.11712	0.0851797
$173$	−22.3266	−1.69746	−0.848731	−	0.528825i	$-0.822633\pi$
$173$	−22.3266	−1.69746	−0.848731	+	0.528825i	$0.822633\pi$
$174$	1.77073	0.134239
$175$	0	0
$176$	−17.3489	−1.30772
$177$	4.51518	0.339382
$178$	0.365062	0.0273626
$179$	20.1878	1.50891	0.754454	−	0.656353i	$-0.227902\pi$
$179$	20.1878	1.50891	0.754454	+	0.656353i	$0.227902\pi$
$180$	0	0
$181$	−20.4504	−1.52006	−0.760032	−	0.649886i	$-0.774817\pi$
$181$	−20.4504	−1.52006	−0.760032	+	0.649886i	$0.774817\pi$
$182$	−0.107350	−0.00795734
$183$	16.7300	1.23672
$184$	−0.719892	−0.0530712
$185$	0	0
$186$	−3.15270	−0.231167
$187$	29.9021	2.18666
$188$	−5.23657	−0.381916
$189$	14.8465	1.07992
$190$	0	0
$191$	−10.7195	−0.775637	−0.387819	−	0.921736i	$-0.626771\pi$
$191$	−10.7195	−0.775637	−0.387819	+	0.921736i	$0.626771\pi$
$192$	23.4717	1.69393
$193$	16.4424	1.18355	0.591776	−	0.806102i	$-0.298427\pi$
$193$	16.4424	1.18355	0.591776	+	0.806102i	$0.298427\pi$
$194$	−2.00445	−0.143911
$195$	0	0
$196$	−1.96707	−0.140505
$197$	16.7311	1.19204	0.596022	−	0.802968i	$-0.296747\pi$
$197$	16.7311	1.19204	0.596022	+	0.802968i	$0.296747\pi$
$198$	6.26349	0.445127
$199$	1.63152	0.115655	0.0578277	−	0.998327i	$-0.481583\pi$
$199$	1.63152	0.115655	0.0578277	+	0.998327i	$0.481583\pi$
$200$	0	0
$201$	30.6606	2.16263
$202$	0.881372	0.0620131
$203$	−3.00176	−0.210683
$204$	−41.9192	−2.93493
$205$	0	0
$206$	1.14378	0.0796908
$207$	−7.56714	−0.525952
$208$	−2.25004	−0.156012
$209$	−9.92808	−0.686740
$210$	0	0
$211$	−2.37196	−0.163293	−0.0816464	−	0.996661i	$-0.526018\pi$
$211$	−2.37196	−0.163293	−0.0816464	+	0.996661i	$0.526018\pi$
$212$	−26.4721	−1.81811
$213$	−39.2511	−2.68944
$214$	0.900601	0.0615638
$215$	0	0
$216$	−10.6878	−0.727216
$217$	5.34448	0.362807
$218$	−0.398241	−0.0269723
$219$	−46.3222	−3.13017
$220$	0	0
$221$	3.87811	0.260870
$222$	4.99563	0.335285
$223$	−4.84082	−0.324166	−0.162083	−	0.986777i	$-0.551821\pi$
$223$	−4.84082	−0.324166	−0.162083	+	0.986777i	$0.551821\pi$
$224$	2.13000	0.142316
$225$	0	0
$226$	−3.53028	−0.234831
$227$	−4.24806	−0.281953	−0.140977	−	0.990013i	$-0.545024\pi$
$227$	−4.24806	−0.281953	−0.140977	+	0.990013i	$0.545024\pi$
$228$	13.9180	0.921741
$229$	0.530171	0.0350347	0.0175173	−	0.999847i	$-0.494424\pi$
$229$	0.530171	0.0350347	0.0175173	+	0.999847i	$0.494424\pi$
$230$	0	0
$231$	−14.8274	−0.975574
$232$	2.16095	0.141873
$233$	−7.32565	−0.479919	−0.239960	−	0.970783i	$-0.577134\pi$
$233$	−7.32565	−0.479919	−0.239960	+	0.970783i	$0.577134\pi$
$234$	0.812335	0.0531040
$235$	0	0
$236$	2.73222	0.177853
$237$	−11.0478	−0.717635
$238$	−1.18963	−0.0771123
$239$	−6.20222	−0.401188	−0.200594	−	0.979674i	$-0.564287\pi$
$239$	−6.20222	−0.401188	−0.200594	+	0.979674i	$0.564287\pi$
$240$	0	0
$241$	−30.2652	−1.94955	−0.974775	−	0.223190i	$-0.928353\pi$
$241$	−30.2652	−1.94955	−0.974775	+	0.223190i	$0.928353\pi$
$242$	−1.77935	−0.114381
$243$	−38.5494	−2.47294
$244$	10.1236	0.648100
$245$	0	0
$246$	−0.117590	−0.00749729
$247$	−1.28761	−0.0819286
$248$	−3.84745	−0.244314
$249$	−53.4815	−3.38925
$250$	0	0
$251$	−4.76312	−0.300645	−0.150323	−	0.988637i	$-0.548031\pi$
$251$	−4.76312	−0.300645	−0.150323	+	0.988637i	$0.548031\pi$
$252$	14.8851	0.937672
$253$	4.56129	0.286766
$254$	1.53656	0.0964122
$255$	0	0
$256$	13.4301	0.839384
$257$	−27.3138	−1.70379	−0.851894	−	0.523715i	$-0.824546\pi$
$257$	−27.3138	−1.70379	−0.851894	+	0.523715i	$0.824546\pi$
$258$	−0.335010	−0.0208568
$259$	−8.46864	−0.526216
$260$	0	0
$261$	22.7148	1.40601
$262$	−2.43158	−0.150224
$263$	20.5490	1.26710	0.633552	−	0.773700i	$-0.281596\pi$
$263$	20.5490	1.26710	0.633552	+	0.773700i	$0.281596\pi$
$264$	10.6742	0.656949
$265$	0	0
$266$	0.394981	0.0242178
$267$	6.53955	0.400214
$268$	18.5533	1.13332
$269$	22.7340	1.38612	0.693059	−	0.720881i	$-0.256263\pi$
$269$	22.7340	1.38612	0.693059	+	0.720881i	$0.256263\pi$
$270$	0	0
$271$	−13.2983	−0.807815	−0.403907	−	0.914800i	$-0.632348\pi$
$271$	−13.2983	−0.807815	−0.403907	+	0.914800i	$0.632348\pi$
$272$	−24.9344	−1.51187
$273$	−1.92302	−0.116387
$274$	3.46853	0.209541
$275$	0	0
$276$	−6.39438	−0.384896
$277$	−3.16867	−0.190387	−0.0951935	−	0.995459i	$-0.530347\pi$
$277$	−3.16867	−0.190387	−0.0951935	+	0.995459i	$0.530347\pi$
$278$	−0.833988	−0.0500193
$279$	−40.4424	−2.42123
$280$	0	0
$281$	10.7570	0.641707	0.320853	−	0.947129i	$-0.396030\pi$
$281$	10.7570	0.641707	0.320853	+	0.947129i	$0.396030\pi$
$282$	1.57038	0.0935145
$283$	−23.8687	−1.41885	−0.709423	−	0.704783i	$-0.751044\pi$
$283$	−23.8687	−1.41885	−0.709423	+	0.704783i	$0.751044\pi$
$284$	−23.7516	−1.40940
$285$	0	0
$286$	−0.489656	−0.0289540
$287$	0.199340	0.0117667
$288$	−16.1180	−0.949760
$289$	25.9763	1.52802
$290$	0	0
$291$	−35.9068	−2.10489
$292$	−28.0305	−1.64036
$293$	−23.1413	−1.35193	−0.675964	−	0.736935i	$-0.736273\pi$
$293$	−23.1413	−1.35193	−0.675964	+	0.736935i	$0.736273\pi$
$294$	0.589897	0.0344035
$295$	0	0
$296$	6.09651	0.354352
$297$	67.7189	3.92945
$298$	−0.244201	−0.0141462
$299$	0.591570	0.0342114
$300$	0	0
$301$	0.567912	0.0327339
$302$	3.43820	0.197846
$303$	15.7885	0.907024
$304$	8.27869	0.474816
$305$	0	0
$306$	9.00210	0.514616
$307$	3.20792	0.183086	0.0915428	−	0.995801i	$-0.470820\pi$
$307$	3.20792	0.183086	0.0915428	+	0.995801i	$0.470820\pi$
$308$	−8.97237	−0.511248
$309$	20.4891	1.16558
$310$	0	0
$311$	−4.20969	−0.238710	−0.119355	−	0.992852i	$-0.538083\pi$
$311$	−4.20969	−0.238710	−0.119355	+	0.992852i	$0.538083\pi$
$312$	1.38437	0.0783745
$313$	4.83912	0.273523	0.136762	−	0.990604i	$-0.456331\pi$
$313$	4.83912	0.273523	0.136762	+	0.990604i	$0.456331\pi$
$314$	−0.409169	−0.0230907
$315$	0	0
$316$	−6.68527	−0.376076
$317$	0.128247	0.00720308	0.00360154	−	0.999994i	$-0.498854\pi$
$317$	0.128247	0.00720308	0.00360154	+	0.999994i	$0.498854\pi$
$318$	7.93863	0.445176
$319$	−13.6919	−0.766600
$320$	0	0
$321$	16.1329	0.900453
$322$	−0.181467	−0.0101128
$323$	−14.2690	−0.793947
$324$	−50.2786	−2.79326
$325$	0	0
$326$	3.52821	0.195410
$327$	−7.13389	−0.394505
$328$	−0.143504	−0.00792367
$329$	−2.66212	−0.146767
$330$	0	0
$331$	20.1989	1.11023	0.555115	−	0.831774i	$-0.312674\pi$
$331$	20.1989	1.11023	0.555115	+	0.831774i	$0.312674\pi$
$332$	−32.3627	−1.77613
$333$	64.0833	3.51175
$334$	−2.71328	−0.148464
$335$	0	0
$336$	12.3641	0.674517
$337$	31.5098	1.71645	0.858223	−	0.513277i	$-0.171569\pi$
$337$	31.5098	1.71645	0.858223	+	0.513277i	$0.171569\pi$
$338$	2.29557	0.124862
$339$	−63.2397	−3.43471
$340$	0	0
$341$	24.3777	1.32013
$342$	−2.98887	−0.161620
$343$	−1.00000	−0.0539949
$344$	−0.408835	−0.0220429
$345$	0	0
$346$	4.05155	0.217812
$347$	−21.7940	−1.16996	−0.584981	−	0.811047i	$-0.698898\pi$
$347$	−21.7940	−1.16996	−0.584981	+	0.811047i	$0.698898\pi$
$348$	19.1944	1.02893
$349$	26.6695	1.42758	0.713792	−	0.700357i	$-0.246976\pi$
$349$	26.6695	1.42758	0.713792	+	0.700357i	$0.246976\pi$
$350$	0	0
$351$	8.78271	0.468786
$352$	9.71552	0.517839
$353$	−23.2531	−1.23764	−0.618818	−	0.785534i	$-0.712388\pi$
$353$	−23.2531	−1.23764	−0.618818	+	0.785534i	$0.712388\pi$
$354$	−0.819356	−0.0435483
$355$	0	0
$356$	3.95721	0.209732
$357$	−21.3105	−1.12787
$358$	−3.66342	−0.193618
$359$	2.39480	0.126393	0.0631965	−	0.998001i	$-0.479871\pi$
$359$	2.39480	0.126393	0.0631965	+	0.998001i	$0.479871\pi$
$360$	0	0
$361$	−14.2624	−0.750654
$362$	3.71107	0.195049
$363$	−31.8743	−1.67297
$364$	−1.16366	−0.0609923
$365$	0	0
$366$	−3.03594	−0.158691
$367$	16.9846	0.886587	0.443294	−	0.896376i	$-0.353810\pi$
$367$	16.9846	0.886587	0.443294	+	0.896376i	$0.353810\pi$
$368$	−3.80350	−0.198271
$369$	−1.50844	−0.0785261
$370$	0	0
$371$	−13.4576	−0.698686
$372$	−34.1747	−1.77187
$373$	18.8867	0.977918	0.488959	−	0.872307i	$-0.337377\pi$
$373$	18.8867	0.977918	0.488959	+	0.872307i	$0.337377\pi$
$374$	−5.42625	−0.280585
$375$	0	0
$376$	1.91644	0.0988327
$377$	−1.77575	−0.0914559
$378$	−2.69414	−0.138572
$379$	13.0987	0.672837	0.336418	−	0.941713i	$-0.390784\pi$
$379$	13.0987	0.672837	0.336418	+	0.941713i	$0.390784\pi$
$380$	0	0
$381$	27.5251	1.41016
$382$	1.94524	0.0995271
$383$	−19.4494	−0.993820	−0.496910	−	0.867802i	$-0.665532\pi$
$383$	−19.4494	−0.993820	−0.496910	+	0.867802i	$0.665532\pi$
$384$	−18.1073	−0.924037
$385$	0	0
$386$	−2.98376	−0.151869
$387$	−4.29746	−0.218452
$388$	−21.7279	−1.10307
$389$	−8.22505	−0.417027	−0.208513	−	0.978020i	$-0.566862\pi$
$389$	−8.22505	−0.417027	−0.208513	+	0.978020i	$0.566862\pi$
$390$	0	0
$391$	6.55563	0.331533
$392$	0.719892	0.0363601
$393$	−43.5582	−2.19722
$394$	−3.03615	−0.152959
$395$	0	0
$396$	67.8951	3.41186
$397$	−21.0576	−1.05685	−0.528426	−	0.848980i	$-0.677217\pi$
$397$	−21.0576	−1.05685	−0.528426	+	0.848980i	$0.677217\pi$
$398$	−0.296067	−0.0148405
$399$	7.07549	0.354218
$400$	0	0
$401$	−11.2843	−0.563510	−0.281755	−	0.959486i	$-0.590916\pi$
$401$	−11.2843	−0.563510	−0.281755	+	0.959486i	$0.590916\pi$
$402$	−5.56388	−0.277501
$403$	3.16163	0.157492
$404$	9.55391	0.475325
$405$	0	0
$406$	0.544721	0.0270341
$407$	−38.6279	−1.91471
$408$	15.3413	0.759505
$409$	−16.3548	−0.808692	−0.404346	−	0.914606i	$-0.632501\pi$
$409$	−16.3548	−0.808692	−0.404346	+	0.914606i	$0.632501\pi$
$410$	0	0
$411$	62.1335	3.06482
$412$	12.3984	0.610823
$413$	1.38898	0.0683473
$414$	1.37319	0.0674884
$415$	0	0
$416$	1.26004	0.0617786
$417$	−14.9397	−0.731598
$418$	1.80162	0.0881201
$419$	32.3264	1.57925	0.789623	−	0.613592i	$-0.210276\pi$
$419$	32.3264	1.57925	0.789623	+	0.613592i	$0.210276\pi$
$420$	0	0
$421$	−1.00012	−0.0487426	−0.0243713	−	0.999703i	$-0.507758\pi$
$421$	−1.00012	−0.0487426	−0.0243713	+	0.999703i	$0.507758\pi$
$422$	0.430433	0.0209532
$423$	20.1446	0.979464
$424$	9.68805	0.470494
$425$	0	0
$426$	7.12279	0.345100
$427$	5.14656	0.249060
$428$	9.76235	0.471881
$429$	−8.77146	−0.423490
$430$	0	0
$431$	35.3816	1.70427	0.852137	−	0.523319i	$-0.175306\pi$
$431$	35.3816	1.70427	0.852137	+	0.523319i	$0.175306\pi$
$432$	−56.4685	−2.71684
$433$	27.3443	1.31408	0.657041	−	0.753855i	$-0.271808\pi$
$433$	27.3443	1.31408	0.657041	+	0.753855i	$0.271808\pi$
$434$	−0.969848	−0.0465542
$435$	0	0
$436$	−4.31686	−0.206740
$437$	−2.17660	−0.104121
$438$	8.40596	0.401652
$439$	−23.8443	−1.13802	−0.569012	−	0.822329i	$-0.692674\pi$
$439$	−23.8443	−1.13802	−0.569012	+	0.822329i	$0.692674\pi$
$440$	0	0
$441$	7.56714	0.360340
$442$	−0.703750	−0.0334740
$443$	−4.32892	−0.205673	−0.102837	−	0.994698i	$-0.532792\pi$
$443$	−4.32892	−0.205673	−0.102837	+	0.994698i	$0.532792\pi$
$444$	54.1517	2.56993
$445$	0	0
$446$	0.878450	0.0415958
$447$	−4.37450	−0.206907
$448$	7.22048	0.341136
$449$	15.5938	0.735918	0.367959	−	0.929842i	$-0.380057\pi$
$449$	15.5938	0.735918	0.367959	+	0.929842i	$0.380057\pi$
$450$	0	0
$451$	0.909249	0.0428149
$452$	−38.2676	−1.79996
$453$	61.5902	2.89376
$454$	0.770882	0.0361793
$455$	0	0
$456$	−5.09359	−0.238529
$457$	−15.1257	−0.707552	−0.353776	−	0.935330i	$-0.615102\pi$
$457$	−15.1257	−0.707552	−0.353776	+	0.935330i	$0.615102\pi$
$458$	−0.0962085	−0.00449553
$459$	97.3279	4.54288
$460$	0	0
$461$	−1.76763	−0.0823265	−0.0411633	−	0.999152i	$-0.513106\pi$
$461$	−1.76763	−0.0823265	−0.0411633	+	0.999152i	$0.513106\pi$
$462$	2.69069	0.125182
$463$	−33.3807	−1.55133	−0.775667	−	0.631143i	$-0.782586\pi$
$463$	−33.3807	−1.55133	−0.775667	+	0.631143i	$0.782586\pi$
$464$	11.4172	0.530031
$465$	0	0
$466$	1.32936	0.0615816
$467$	−10.6221	−0.491530	−0.245765	−	0.969329i	$-0.579039\pi$
$467$	−10.6221	−0.491530	−0.245765	+	0.969329i	$0.579039\pi$
$468$	8.80557	0.407037
$469$	9.43195	0.435527
$470$	0	0
$471$	−7.32965	−0.337732
$472$	−0.999917	−0.0460249
$473$	2.59041	0.119107
$474$	2.00482	0.0920844
$475$	0	0
$476$	−12.8954	−0.591059
$477$	101.836	4.66274
$478$	1.12550	0.0514791
$479$	−30.8372	−1.40899	−0.704495	−	0.709709i	$-0.748826\pi$
$479$	−30.8372	−1.40899	−0.704495	+	0.709709i	$0.748826\pi$
$480$	0	0
$481$	−5.00979	−0.228427
$482$	5.49213	0.250160
$483$	−3.25071	−0.147913
$484$	−19.2878	−0.876717
$485$	0	0
$486$	6.99544	0.317320
$487$	18.7309	0.848777	0.424388	−	0.905480i	$-0.360489\pi$
$487$	18.7309	0.848777	0.424388	+	0.905480i	$0.360489\pi$
$488$	−3.70497	−0.167716
$489$	63.2027	2.85812
$490$	0	0
$491$	−0.931990	−0.0420601	−0.0210301	−	0.999779i	$-0.506695\pi$
$491$	−0.931990	−0.0420601	−0.0210301	+	0.999779i	$0.506695\pi$
$492$	−1.27466	−0.0574660
$493$	−19.6785	−0.886273
$494$	0.233659	0.0105128
$495$	0	0
$496$	−20.3278	−0.912743
$497$	−12.0746	−0.541621
$498$	9.70512	0.434897
$499$	−9.11453	−0.408022	−0.204011	−	0.978969i	$-0.565398\pi$
$499$	−9.11453	−0.408022	−0.204011	+	0.978969i	$0.565398\pi$
$500$	0	0
$501$	−48.6043	−2.17148
$502$	0.864349	0.0385778
$503$	−1.93145	−0.0861190	−0.0430595	−	0.999073i	$-0.513711\pi$
$503$	−1.93145	−0.0861190	−0.0430595	+	0.999073i	$0.513711\pi$
$504$	−5.44752	−0.242652
$505$	0	0
$506$	−0.827723	−0.0367968
$507$	41.1217	1.82628
$508$	16.6560	0.738990
$509$	14.0000	0.620541	0.310271	−	0.950648i	$-0.399580\pi$
$509$	14.0000	0.620541	0.310271	+	0.950648i	$0.399580\pi$
$510$	0	0
$511$	−14.2499	−0.630377
$512$	−13.5777	−0.600054
$513$	−32.3147	−1.42673
$514$	4.95655	0.218624
$515$	0	0
$516$	−3.63144	−0.159865
$517$	−12.1427	−0.534034
$518$	1.53678	0.0675222
$519$	72.5774	3.18580
$520$	0	0
$521$	24.5875	1.07720	0.538600	−	0.842562i	$-0.318954\pi$
$521$	24.5875	1.07720	0.538600	+	0.842562i	$0.318954\pi$
$522$	−4.12198	−0.180414
$523$	−28.1877	−1.23256	−0.616282	−	0.787526i	$-0.711362\pi$
$523$	−28.1877	−1.23256	−0.616282	+	0.787526i	$0.711362\pi$
$524$	−26.3579	−1.15145
$525$	0	0
$526$	−3.72896	−0.162591
$527$	35.0365	1.52621
$528$	56.3962	2.45433
$529$	1.00000	0.0434783
$530$	0	0
$531$	−10.5106	−0.456122
$532$	4.28152	0.185627
$533$	0.117924	0.00510785
$534$	−1.18671	−0.0513541
$535$	0	0
$536$	−6.78999	−0.293283
$537$	−65.6248	−2.83192
$538$	−4.12547	−0.177862
$539$	−4.56129	−0.196469
$540$	0	0
$541$	19.1419	0.822973	0.411487	−	0.911416i	$-0.365010\pi$
$541$	19.1419	0.822973	0.411487	+	0.911416i	$0.365010\pi$
$542$	2.41320	0.103656
$543$	66.4783	2.85285
$544$	13.9635	0.598679
$545$	0	0
$546$	0.348965	0.0149343
$547$	−6.36750	−0.272255	−0.136127	−	0.990691i	$-0.543466\pi$
$547$	−6.36750	−0.272255	−0.136127	+	0.990691i	$0.543466\pi$
$548$	37.5982	1.60612
$549$	−38.9447	−1.66212
$550$	0	0
$551$	6.53363	0.278342
$552$	2.34016	0.0996040
$553$	−3.39859	−0.144523
$554$	0.575009	0.0244298
$555$	0	0
$556$	−9.04028	−0.383393
$557$	36.1864	1.53327	0.766633	−	0.642085i	$-0.221930\pi$
$557$	36.1864	1.53327	0.766633	+	0.642085i	$0.221930\pi$
$558$	7.33897	0.310683
$559$	0.335959	0.0142096
$560$	0	0
$561$	−97.2032	−4.10392
$562$	−1.95203	−0.0823416
$563$	−14.8592	−0.626241	−0.313120	−	0.949713i	$-0.601374\pi$
$563$	−14.8592	−0.626241	−0.313120	+	0.949713i	$0.601374\pi$
$564$	17.0226	0.716780
$565$	0	0
$566$	4.33138	0.182061
$567$	−25.5602	−1.07343
$568$	8.69243	0.364726
$569$	26.0485	1.09201	0.546006	−	0.837781i	$-0.316148\pi$
$569$	26.0485	1.09201	0.546006	+	0.837781i	$0.316148\pi$
$570$	0	0
$571$	27.4939	1.15058	0.575292	−	0.817948i	$-0.304888\pi$
$571$	27.4939	1.15058	0.575292	+	0.817948i	$0.304888\pi$
$572$	−5.30778	−0.221930
$573$	34.8461	1.45572
$574$	−0.0361737	−0.00150986
$575$	0	0
$576$	−54.6384	−2.27660
$577$	−26.8005	−1.11572	−0.557859	−	0.829935i	$-0.688377\pi$
$577$	−26.8005	−1.11572	−0.557859	+	0.829935i	$0.688377\pi$
$578$	−4.71385	−0.196070
$579$	−53.4497	−2.22129
$580$	0	0
$581$	−16.4522	−0.682553
$582$	6.51590	0.270093
$583$	−61.3842	−2.54227
$584$	10.2584	0.424494
$585$	0	0
$586$	4.19938	0.173475
$587$	40.7182	1.68062	0.840310	−	0.542107i	$-0.182373\pi$
$587$	40.7182	1.68062	0.840310	+	0.542107i	$0.182373\pi$
$588$	6.39438	0.263700
$589$	−11.6328	−0.479321
$590$	0	0
$591$	−54.3881	−2.23723
$592$	32.2105	1.32384
$593$	−7.76852	−0.319015	−0.159507	−	0.987197i	$-0.550991\pi$
$593$	−7.76852	−0.319015	−0.159507	+	0.987197i	$0.550991\pi$
$594$	−12.2888	−0.504214
$595$	0	0
$596$	−2.64710	−0.108429
$597$	−5.30360	−0.217062
$598$	−0.107350	−0.00438988
$599$	25.3937	1.03756	0.518778	−	0.854909i	$-0.326387\pi$
$599$	25.3937	1.03756	0.518778	+	0.854909i	$0.326387\pi$
$600$	0	0
$601$	−46.4340	−1.89408	−0.947041	−	0.321112i	$-0.895943\pi$
$601$	−46.4340	−1.89408	−0.947041	+	0.321112i	$0.895943\pi$
$602$	−0.103057	−0.00420030
$603$	−71.3729	−2.90653
$604$	37.2695	1.51647
$605$	0	0
$606$	−2.86509	−0.116386
$607$	−11.4129	−0.463234	−0.231617	−	0.972807i	$-0.574402\pi$
$607$	−11.4129	−0.463234	−0.231617	+	0.972807i	$0.574402\pi$
$608$	−4.63614	−0.188020
$609$	9.75788	0.395409
$610$	0	0
$611$	−1.57483	−0.0637107
$612$	97.5812	3.94448
$613$	43.2800	1.74806	0.874031	−	0.485871i	$-0.161497\pi$
$613$	43.2800	1.74806	0.874031	+	0.485871i	$0.161497\pi$
$614$	−0.582131	−0.0234929
$615$	0	0
$616$	3.28364	0.132301
$617$	−47.7350	−1.92174	−0.960869	−	0.277002i	$-0.910659\pi$
$617$	−47.7350	−1.92174	−0.960869	+	0.277002i	$0.910659\pi$
$618$	−3.71810	−0.149564
$619$	4.94685	0.198831	0.0994154	−	0.995046i	$-0.468303\pi$
$619$	4.94685	0.198831	0.0994154	+	0.995046i	$0.468303\pi$
$620$	0	0
$621$	14.8465	0.595768
$622$	0.763920	0.0306304
$623$	2.01173	0.0805981
$624$	7.31423	0.292803
$625$	0	0
$626$	−0.878140	−0.0350975
$627$	32.2733	1.28887
$628$	−4.43531	−0.176988
$629$	−55.5173	−2.21362
$630$	0	0
$631$	−15.0640	−0.599687	−0.299844	−	0.953988i	$-0.596935\pi$
$631$	−15.0640	−0.599687	−0.299844	+	0.953988i	$0.596935\pi$
$632$	2.44662	0.0973213
$633$	7.71058	0.306468
$634$	−0.0232726	−0.000924275 0
$635$	0	0
$636$	86.0533	3.41223
$637$	−0.591570	−0.0234388
$638$	2.48463	0.0983674
$639$	91.3703	3.61455
$640$	0	0
$641$	19.4897	0.769795	0.384898	−	0.922959i	$-0.374237\pi$
$641$	19.4897	0.769795	0.384898	+	0.922959i	$0.374237\pi$
$642$	−2.92760	−0.115543
$643$	−19.5714	−0.771822	−0.385911	−	0.922536i	$-0.626113\pi$
$643$	−19.5714	−0.771822	−0.385911	+	0.922536i	$0.626113\pi$
$644$	−1.96707	−0.0775134
$645$	0	0
$646$	2.58935	0.101877
$647$	−14.0491	−0.552328	−0.276164	−	0.961111i	$-0.589063\pi$
$647$	−14.0491	−0.552328	−0.276164	+	0.961111i	$0.589063\pi$
$648$	18.4006	0.722842
$649$	6.33554	0.248692
$650$	0	0
$651$	−17.3734	−0.680917
$652$	38.2452	1.49780
$653$	−18.2223	−0.713094	−0.356547	−	0.934277i	$-0.616046\pi$
$653$	−18.2223	−0.713094	−0.356547	+	0.934277i	$0.616046\pi$
$654$	1.29457	0.0506215
$655$	0	0
$656$	−0.758192	−0.0296024
$657$	107.831	4.20688
$658$	0.483086	0.0188327
$659$	−25.5241	−0.994278	−0.497139	−	0.867671i	$-0.665616\pi$
$659$	−25.5241	−0.994278	−0.497139	+	0.867671i	$0.665616\pi$
$660$	0	0
$661$	3.99411	0.155353	0.0776764	−	0.996979i	$-0.475250\pi$
$661$	3.99411	0.155353	0.0776764	+	0.996979i	$0.475250\pi$
$662$	−3.66543	−0.142461
$663$	−12.6066	−0.489601
$664$	11.8438	0.459630
$665$	0	0
$666$	−11.6290	−0.450615
$667$	−3.00176	−0.116229
$668$	−29.4114	−1.13796
$669$	15.7361	0.608394
$670$	0	0
$671$	23.4749	0.906240
$672$	−6.92400	−0.267099
$673$	5.65721	0.218070	0.109035	−	0.994038i	$-0.465224\pi$
$673$	5.65721	0.218070	0.109035	+	0.994038i	$0.465224\pi$
$674$	−5.71798	−0.220248
$675$	0	0
$676$	24.8835	0.957058
$677$	0.329430	0.0126610	0.00633052	−	0.999980i	$-0.497985\pi$
$677$	0.329430	0.0126610	0.00633052	+	0.999980i	$0.497985\pi$
$678$	11.4759	0.440730
$679$	−11.0458	−0.423900
$680$	0	0
$681$	13.8092	0.529170
$682$	−4.42375	−0.169394
$683$	−23.8354	−0.912036	−0.456018	−	0.889971i	$-0.650725\pi$
$683$	−23.8354	−0.912036	−0.456018	+	0.889971i	$0.650725\pi$
$684$	−32.3988	−1.23880
$685$	0	0
$686$	0.181467	0.00692844
$687$	−1.72343	−0.0657531
$688$	−2.16005	−0.0823513
$689$	−7.96113	−0.303295
$690$	0	0
$691$	0.100329	0.00381671	0.00190835	−	0.999998i	$-0.499393\pi$
$691$	0.100329	0.00381671	0.00190835	+	0.999998i	$0.499393\pi$
$692$	43.9180	1.66951
$693$	34.5159	1.31115
$694$	3.95489	0.150125
$695$	0	0
$696$	−7.02462	−0.266268
$697$	1.30680	0.0494987
$698$	−4.83963	−0.183183
$699$	23.8136	0.900713
$700$	0	0
$701$	−28.6267	−1.08121	−0.540607	−	0.841275i	$-0.681806\pi$
$701$	−28.6267	−1.08121	−0.540607	+	0.841275i	$0.681806\pi$
$702$	−1.59377	−0.0601531
$703$	18.4328	0.695207
$704$	32.9347	1.24127
$705$	0	0
$706$	4.21967	0.158809
$707$	4.85692	0.182663
$708$	−8.88167	−0.333794
$709$	0.604266	0.0226937	0.0113469	−	0.999936i	$-0.496388\pi$
$709$	0.604266	0.0226937	0.0113469	+	0.999936i	$0.496388\pi$
$710$	0	0
$711$	25.7176	0.964486
$712$	−1.44823	−0.0542746
$713$	5.34448	0.200152
$714$	3.86715	0.144724
$715$	0	0
$716$	−39.7108	−1.48406
$717$	20.1616	0.752950
$718$	−0.434578	−0.0162183
$719$	−33.2430	−1.23976	−0.619878	−	0.784698i	$-0.712818\pi$
$719$	−33.2430	−1.23976	−0.619878	+	0.784698i	$0.712818\pi$
$720$	0	0
$721$	6.30296	0.234734
$722$	2.58816	0.0963214
$723$	98.3833	3.65892
$724$	40.2273	1.49504
$725$	0	0
$726$	5.78414	0.214670
$727$	−15.0611	−0.558587	−0.279293	−	0.960206i	$-0.590100\pi$
$727$	−15.0611	−0.558587	−0.279293	+	0.960206i	$0.590100\pi$
$728$	0.425867	0.0157837
$729$	48.6325	1.80120
$730$	0	0
$731$	3.72302	0.137701
$732$	−32.9091	−1.21635
$733$	7.69286	0.284142	0.142071	−	0.989856i	$-0.454624\pi$
$733$	7.69286	0.284142	0.142071	+	0.989856i	$0.454624\pi$
$734$	−3.08214	−0.113764
$735$	0	0
$736$	2.13000	0.0785127
$737$	43.0218	1.58473
$738$	0.273732	0.0100762
$739$	−36.8381	−1.35511	−0.677555	−	0.735472i	$-0.736960\pi$
$739$	−36.8381	−1.35511	−0.677555	+	0.735472i	$0.736960\pi$
$740$	0	0
$741$	4.18565	0.153764
$742$	2.44212	0.0896530
$743$	31.7003	1.16297	0.581485	−	0.813557i	$-0.302472\pi$
$743$	31.7003	1.16297	0.581485	+	0.813557i	$0.302472\pi$
$744$	12.5070	0.458528
$745$	0	0
$746$	−3.42732	−0.125483
$747$	124.496	4.55508
$748$	−58.8196	−2.15066
$749$	4.96289	0.181340
$750$	0	0
$751$	15.0507	0.549206	0.274603	−	0.961558i	$-0.411453\pi$
$751$	15.0507	0.549206	0.274603	+	0.961558i	$0.411453\pi$
$752$	10.1254	0.369234
$753$	15.4835	0.564251
$754$	0.322241	0.0117353
$755$	0	0
$756$	−29.2040	−1.06214
$757$	−14.1607	−0.514681	−0.257341	−	0.966321i	$-0.582846\pi$
$757$	−14.1607	−0.514681	−0.257341	+	0.966321i	$0.582846\pi$
$758$	−2.37699	−0.0863361
$759$	−14.8274	−0.538202
$760$	0	0
$761$	−46.7288	−1.69392	−0.846959	−	0.531657i	$-0.821569\pi$
$761$	−46.7288	−1.69392	−0.846959	+	0.531657i	$0.821569\pi$
$762$	−4.99491	−0.180946
$763$	−2.19456	−0.0794485
$764$	21.0860	0.762866
$765$	0	0
$766$	3.52943	0.127524
$767$	0.821679	0.0296691
$768$	−43.6575	−1.57536
$769$	−29.5115	−1.06421	−0.532107	−	0.846677i	$-0.678599\pi$
$769$	−29.5115	−1.06421	−0.532107	+	0.846677i	$0.678599\pi$
$770$	0	0
$771$	88.7893	3.19767
$772$	−32.3434	−1.16407
$773$	37.2145	1.33851	0.669257	−	0.743031i	$-0.266613\pi$
$773$	37.2145	1.33851	0.669257	+	0.743031i	$0.266613\pi$
$774$	0.779848	0.0280311
$775$	0	0
$776$	7.95180	0.285453
$777$	27.5291	0.987602
$778$	1.49258	0.0535115
$779$	−0.433884	−0.0155455
$780$	0	0
$781$	−55.0758	−1.97077
$782$	−1.18963	−0.0425411
$783$	−44.5656	−1.59264
$784$	3.80350	0.135839
$785$	0	0
$786$	7.90438	0.281940
$787$	−23.3356	−0.831824	−0.415912	−	0.909405i	$-0.636538\pi$
$787$	−23.3356	−0.831824	−0.415912	+	0.909405i	$0.636538\pi$
$788$	−32.9113	−1.17242
$789$	−66.7989	−2.37810
$790$	0	0
$791$	−19.4541	−0.691708
$792$	−24.8477	−0.882925
$793$	3.04455	0.108115
$794$	3.82126	0.135611
$795$	0	0
$796$	−3.20931	−0.113751
$797$	19.4945	0.690529	0.345265	−	0.938505i	$-0.387789\pi$
$797$	19.4945	0.690529	0.345265	+	0.938505i	$0.387789\pi$
$798$	−1.28397	−0.0454520
$799$	−17.4519	−0.617402
$800$	0	0
$801$	−15.2230	−0.537879
$802$	2.04772	0.0723076
$803$	−64.9977	−2.29372
$804$	−60.3115	−2.12702
$805$	0	0
$806$	−0.573732	−0.0202089
$807$	−73.9018	−2.60146
$808$	−3.49646	−0.123005
$809$	23.2122	0.816098	0.408049	−	0.912960i	$-0.366209\pi$
$809$	23.2122	0.816098	0.408049	+	0.912960i	$0.366209\pi$
$810$	0	0
$811$	33.4342	1.17403	0.587017	−	0.809575i	$-0.300302\pi$
$811$	33.4342	1.17403	0.587017	+	0.809575i	$0.300302\pi$
$812$	5.90468	0.207214
$813$	43.2290	1.51611
$814$	7.00969	0.245689
$815$	0	0
$816$	81.0545	2.83747
$817$	−1.23611	−0.0432462
$818$	2.96785	0.103769
$819$	4.47649	0.156421
$820$	0	0
$821$	14.0135	0.489075	0.244537	−	0.969640i	$-0.421364\pi$
$821$	14.0135	0.489075	0.244537	+	0.969640i	$0.421364\pi$
$822$	−11.2752	−0.393267
$823$	−1.61509	−0.0562986	−0.0281493	−	0.999604i	$-0.508961\pi$
$823$	−1.61509	−0.0562986	−0.0281493	+	0.999604i	$0.508961\pi$
$824$	−4.53745	−0.158070
$825$	0	0
$826$	−0.252054	−0.00877009
$827$	−42.5043	−1.47802	−0.739010	−	0.673694i	$-0.764707\pi$
$827$	−42.5043	−1.47802	−0.739010	+	0.673694i	$0.764707\pi$
$828$	14.8851	0.517292
$829$	49.1433	1.70682	0.853409	−	0.521242i	$-0.174531\pi$
$829$	49.1433	1.70682	0.853409	+	0.521242i	$0.174531\pi$
$830$	0	0
$831$	10.3004	0.357318
$832$	4.27142	0.148085
$833$	−6.55563	−0.227139
$834$	2.71106	0.0938762
$835$	0	0
$836$	19.5292	0.675433
$837$	79.3466	2.74262
$838$	−5.86617	−0.202644
$839$	29.0707	1.00363	0.501817	−	0.864974i	$-0.332665\pi$
$839$	29.0707	1.00363	0.501817	+	0.864974i	$0.332665\pi$
$840$	0	0
$841$	−19.9894	−0.689290
$842$	0.181488	0.00625449
$843$	−34.9678	−1.20435
$844$	4.66582	0.160604
$845$	0	0
$846$	−3.65558	−0.125681
$847$	−9.80534	−0.336915
$848$	51.1862	1.75774
$849$	77.5903	2.66289
$850$	0	0
$851$	−8.46864	−0.290301
$852$	77.2097	2.64516
$853$	42.0018	1.43811	0.719057	−	0.694951i	$-0.244574\pi$
$853$	42.0018	1.43811	0.719057	+	0.694951i	$0.244574\pi$
$854$	−0.933931	−0.0319585
$855$	0	0
$856$	−3.57275	−0.122114
$857$	−36.6803	−1.25298	−0.626488	−	0.779431i	$-0.715508\pi$
$857$	−36.6803	−1.25298	−0.626488	+	0.779431i	$0.715508\pi$
$858$	1.59173	0.0543408
$859$	12.1909	0.415950	0.207975	−	0.978134i	$-0.433313\pi$
$859$	12.1909	0.415950	0.207975	+	0.978134i	$0.433313\pi$
$860$	0	0
$861$	−0.647999	−0.0220837
$862$	−6.42060	−0.218687
$863$	5.90721	0.201084	0.100542	−	0.994933i	$-0.467942\pi$
$863$	5.90721	0.201084	0.100542	+	0.994933i	$0.467942\pi$
$864$	31.6229	1.07583
$865$	0	0
$866$	−4.96208	−0.168618
$867$	−84.4416	−2.86779
$868$	−10.5130	−0.356834
$869$	−15.5019	−0.525868
$870$	0	0
$871$	5.57966	0.189059
$872$	1.57985	0.0535004
$873$	83.5852	2.82893
$874$	0.394981	0.0133604
$875$	0	0
$876$	91.1191	3.07863
$877$	−23.5706	−0.795924	−0.397962	−	0.917402i	$-0.630282\pi$
$877$	−23.5706	−0.795924	−0.397962	+	0.917402i	$0.630282\pi$
$878$	4.32695	0.146027
$879$	75.2257	2.53730
$880$	0	0
$881$	−9.47202	−0.319120	−0.159560	−	0.987188i	$-0.551008\pi$
$881$	−9.47202	−0.319120	−0.159560	+	0.987188i	$0.551008\pi$
$882$	−1.37319	−0.0462376
$883$	8.96960	0.301851	0.150926	−	0.988545i	$-0.451775\pi$
$883$	8.96960	0.301851	0.150926	+	0.988545i	$0.451775\pi$
$884$	−7.62852	−0.256575
$885$	0	0
$886$	0.785556	0.0263913
$887$	4.22865	0.141984	0.0709921	−	0.997477i	$-0.477383\pi$
$887$	4.22865	0.141984	0.0709921	+	0.997477i	$0.477383\pi$
$888$	−19.8180	−0.665049
$889$	8.46742	0.283988
$890$	0	0
$891$	−116.587	−3.90582
$892$	9.52224	0.318828
$893$	5.79436	0.193901
$894$	0.793828	0.0265496
$895$	0	0
$896$	−5.57027	−0.186090
$897$	−1.92302	−0.0642079
$898$	−2.82977	−0.0944305
$899$	−16.0429	−0.535060
$900$	0	0
$901$	−88.2234	−2.93915
$902$	−0.164999	−0.00549386
$903$	−1.84612	−0.0614350
$904$	14.0049	0.465795
$905$	0	0
$906$	−11.1766	−0.371318
$907$	47.6935	1.58364	0.791818	−	0.610757i	$-0.209135\pi$
$907$	47.6935	1.58364	0.791818	+	0.610757i	$0.209135\pi$
$908$	8.35622	0.277311
$909$	−36.7530	−1.21902
$910$	0	0
$911$	−39.9998	−1.32525	−0.662626	−	0.748951i	$-0.730558\pi$
$911$	−39.9998	−1.32525	−0.662626	+	0.748951i	$0.730558\pi$
$912$	−26.9117	−0.891134
$913$	−75.0433	−2.48357
$914$	2.74482	0.0907906
$915$	0	0
$916$	−1.04288	−0.0344578
$917$	−13.3996	−0.442493
$918$	−17.6618	−0.582926
$919$	−38.9176	−1.28377	−0.641887	−	0.766799i	$-0.721848\pi$
$919$	−38.9176	−1.28377	−0.641887	+	0.766799i	$0.721848\pi$
$920$	0	0
$921$	−10.4280	−0.343615
$922$	0.320766	0.0105639
$923$	−7.14298	−0.235114
$924$	29.1666	0.959511
$925$	0	0
$926$	6.05750	0.199062
$927$	−47.6953	−1.56652
$928$	−6.39374	−0.209885
$929$	38.1203	1.25069	0.625344	−	0.780349i	$-0.284959\pi$
$929$	38.1203	1.25069	0.625344	+	0.780349i	$0.284959\pi$
$930$	0	0
$931$	2.17660	0.0713351
$932$	14.4101	0.472017
$933$	13.6845	0.448010
$934$	1.92755	0.0630714
$935$	0	0
$936$	−3.22259	−0.105334
$937$	−11.1990	−0.365854	−0.182927	−	0.983126i	$-0.558557\pi$
$937$	−11.1990	−0.365854	−0.182927	+	0.983126i	$0.558557\pi$
$938$	−1.71159	−0.0558853
$939$	−15.7306	−0.513348
$940$	0	0
$941$	45.0673	1.46915	0.734576	−	0.678526i	$-0.237381\pi$
$941$	45.0673	1.46915	0.734576	+	0.678526i	$0.237381\pi$
$942$	1.33009	0.0433367
$943$	0.199340	0.00649142
$944$	−5.28299	−0.171947
$945$	0	0
$946$	−0.470074	−0.0152834
$947$	−41.7814	−1.35771	−0.678856	−	0.734272i	$-0.737524\pi$
$947$	−41.7814	−1.35771	−0.678856	+	0.734272i	$0.737524\pi$
$948$	21.7319	0.705819
$949$	−8.42979	−0.273643
$950$	0	0
$951$	−0.416895	−0.0135187
$952$	4.71935	0.152955
$953$	27.3759	0.886791	0.443395	−	0.896326i	$-0.353774\pi$
$953$	27.3759	0.886791	0.443395	+	0.896326i	$0.353774\pi$
$954$	−18.4798	−0.598307
$955$	0	0
$956$	12.2002	0.394582
$957$	44.5085	1.43875
$958$	5.59594	0.180797
$959$	19.1138	0.617217
$960$	0	0
$961$	−2.43650	−0.0785966
$962$	0.909112	0.0293109
$963$	−37.5549	−1.21019
$964$	59.5337	1.91745
$965$	0	0
$966$	0.589897	0.0189796
$967$	−44.9484	−1.44544	−0.722722	−	0.691139i	$-0.757109\pi$
$967$	−44.9484	−1.44544	−0.722722	+	0.691139i	$0.757109\pi$
$968$	7.05879	0.226878
$969$	46.3843	1.49008
$970$	0	0
$971$	−15.0456	−0.482837	−0.241418	−	0.970421i	$-0.577613\pi$
$971$	−15.0456	−0.482837	−0.241418	+	0.970421i	$0.577613\pi$
$972$	75.8293	2.43223
$973$	−4.59581	−0.147335
$974$	−3.39903	−0.108912
$975$	0	0
$976$	−19.5750	−0.626579
$977$	19.6423	0.628411	0.314206	−	0.949355i	$-0.398262\pi$
$977$	19.6423	0.628411	0.314206	+	0.949355i	$0.398262\pi$
$978$	−11.4692	−0.366745
$979$	9.17606	0.293268
$980$	0	0
$981$	16.6066	0.530206
$982$	0.169125	0.00539701
$983$	10.2902	0.328207	0.164103	−	0.986443i	$-0.447527\pi$
$983$	10.2902	0.328207	0.164103	+	0.986443i	$0.447527\pi$
$984$	0.466489	0.0148711
$985$	0	0
$986$	3.57099	0.113724
$987$	8.65378	0.275453
$988$	2.53282	0.0805796
$989$	0.567912	0.0180585
$990$	0	0
$991$	−48.6869	−1.54659	−0.773295	−	0.634047i	$-0.781393\pi$
$991$	−48.6869	−1.54659	−0.773295	+	0.634047i	$0.781393\pi$
$992$	11.3837	0.361434
$993$	−65.6607	−2.08368
$994$	2.19115	0.0694989
$995$	0	0
$996$	105.202	3.33345
$997$	46.5354	1.47379	0.736895	−	0.676008i	$-0.236291\pi$
$997$	46.5354	1.47379	0.736895	+	0.676008i	$0.236291\pi$
$998$	1.65399	0.0523560
$999$	−125.729	−3.97790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.t.1.5		8
5.4	even	2		805.2.a.m.1.4	✓	8
15.14	odd	2		7245.2.a.bp.1.5		8
35.34	odd	2		5635.2.a.bb.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.4	✓	8	5.4	even	2
4025.2.a.t.1.5		8	1.1	even	1	trivial
5635.2.a.bb.1.4		8	35.34	odd	2
7245.2.a.bp.1.5		8	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.181467 q^{2} -3.25071 q^{3} -1.96707 q^{4} +0.589897 q^{6} -1.00000 q^{7} +0.719892 q^{8} +7.56714 q^{9} +O(q^{10})\)	\(q-0.181467 q^{2} -3.25071 q^{3} -1.96707 q^{4} +0.589897 q^{6} -1.00000 q^{7} +0.719892 q^{8} +7.56714 q^{9} -4.56129 q^{11} +6.39438 q^{12} -0.591570 q^{13} +0.181467 q^{14} +3.80350 q^{16} -6.55563 q^{17} -1.37319 q^{18} +2.17660 q^{19} +3.25071 q^{21} +0.827723 q^{22} -1.00000 q^{23} -2.34016 q^{24} +0.107350 q^{26} -14.8465 q^{27} +1.96707 q^{28} +3.00176 q^{29} -5.34448 q^{31} -2.13000 q^{32} +14.8274 q^{33} +1.18963 q^{34} -14.8851 q^{36} +8.46864 q^{37} -0.394981 q^{38} +1.92302 q^{39} -0.199340 q^{41} -0.589897 q^{42} -0.567912 q^{43} +8.97237 q^{44} +0.181467 q^{46} +2.66212 q^{47} -12.3641 q^{48} +1.00000 q^{49} +21.3105 q^{51} +1.16366 q^{52} +13.4576 q^{53} +2.69414 q^{54} -0.719892 q^{56} -7.07549 q^{57} -0.544721 q^{58} -1.38898 q^{59} -5.14656 q^{61} +0.969848 q^{62} -7.56714 q^{63} -7.22048 q^{64} -2.69069 q^{66} -9.43195 q^{67} +12.8954 q^{68} +3.25071 q^{69} +12.0746 q^{71} +5.44752 q^{72} +14.2499 q^{73} -1.53678 q^{74} -4.28152 q^{76} +4.56129 q^{77} -0.348965 q^{78} +3.39859 q^{79} +25.5602 q^{81} +0.0361737 q^{82} +16.4522 q^{83} -6.39438 q^{84} +0.103057 q^{86} -9.75788 q^{87} -3.28364 q^{88} -2.01173 q^{89} +0.591570 q^{91} +1.96707 q^{92} +17.3734 q^{93} -0.483086 q^{94} +6.92400 q^{96} +11.0458 q^{97} -0.181467 q^{98} -34.5159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more