LMFDB - Embedded newform 6025.2.a.i.1.9

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:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 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			1.9
Root			$-0.227272$ 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)

$f(q)$	$=$	$q+0.227272 q^{2} -1.31252 q^{3} -1.94835 q^{4} -0.298298 q^{6} -4.34237 q^{7} -0.897348 q^{8} -1.27730 q^{9} +O(q^{10})$	\(q+0.227272 q^{2} -1.31252 q^{3} -1.94835 q^{4} -0.298298 q^{6} -4.34237 q^{7} -0.897348 q^{8} -1.27730 q^{9} -3.78752 q^{11} +2.55724 q^{12} +4.74890 q^{13} -0.986897 q^{14} +3.69275 q^{16} -1.90667 q^{17} -0.290294 q^{18} -4.94816 q^{19} +5.69943 q^{21} -0.860795 q^{22} +3.54164 q^{23} +1.17778 q^{24} +1.07929 q^{26} +5.61403 q^{27} +8.46044 q^{28} +3.95333 q^{29} +1.94023 q^{31} +2.63395 q^{32} +4.97118 q^{33} -0.433333 q^{34} +2.48862 q^{36} +10.4821 q^{37} -1.12458 q^{38} -6.23302 q^{39} -3.19721 q^{41} +1.29532 q^{42} +1.59123 q^{43} +7.37940 q^{44} +0.804915 q^{46} -9.45887 q^{47} -4.84680 q^{48} +11.8561 q^{49} +2.50254 q^{51} -9.25252 q^{52} +5.28147 q^{53} +1.27591 q^{54} +3.89661 q^{56} +6.49454 q^{57} +0.898480 q^{58} +2.44413 q^{59} -5.09098 q^{61} +0.440960 q^{62} +5.54650 q^{63} -6.78688 q^{64} +1.12981 q^{66} +9.56638 q^{67} +3.71486 q^{68} -4.64846 q^{69} -12.5342 q^{71} +1.14618 q^{72} +14.0282 q^{73} +2.38229 q^{74} +9.64074 q^{76} +16.4468 q^{77} -1.41659 q^{78} -4.86166 q^{79} -3.53661 q^{81} -0.726636 q^{82} -8.87655 q^{83} -11.1045 q^{84} +0.361643 q^{86} -5.18881 q^{87} +3.39872 q^{88} +9.16017 q^{89} -20.6215 q^{91} -6.90034 q^{92} -2.54659 q^{93} -2.14973 q^{94} -3.45711 q^{96} -5.17578 q^{97} +2.69457 q^{98} +4.83779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * 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 $

$2$	0.227272	0.160705	0.0803527	−	0.996766i	$-0.474395\pi$
$2$	0.227272	0.160705	0.0803527	+	0.996766i	$0.474395\pi$
$3$	−1.31252	−0.757782	−0.378891	−	0.925441i	$-0.623694\pi$
$3$	−1.31252	−0.757782	−0.378891	+	0.925441i	$0.623694\pi$
$4$	−1.94835	−0.974174
$5$	0	0
$5$	0	0
$6$	−0.298298	−0.121780
$7$	−4.34237	−1.64126	−0.820630	−	0.571460i	$-0.806377\pi$
$7$	−4.34237	−1.64126	−0.820630	+	0.571460i	$0.806377\pi$
$8$	−0.897348	−0.317260
$9$	−1.27730	−0.425766
$10$	0	0
$11$	−3.78752	−1.14198	−0.570989	−	0.820957i	$-0.693440\pi$
$11$	−3.78752	−1.14198	−0.570989	+	0.820957i	$0.693440\pi$
$12$	2.55724	0.738211
$13$	4.74890	1.31711	0.658555	−	0.752533i	$-0.271168\pi$
$13$	4.74890	1.31711	0.658555	+	0.752533i	$0.271168\pi$
$14$	−0.986897	−0.263759
$15$	0	0
$16$	3.69275	0.923188
$17$	−1.90667	−0.462436	−0.231218	−	0.972902i	$-0.574271\pi$
$17$	−1.90667	−0.462436	−0.231218	+	0.972902i	$0.574271\pi$
$18$	−0.290294	−0.0684230
$19$	−4.94816	−1.13519	−0.567593	−	0.823309i	$-0.692125\pi$
$19$	−4.94816	−1.13519	−0.567593	+	0.823309i	$0.692125\pi$
$20$	0	0
$21$	5.69943	1.24372
$22$	−0.860795	−0.183522
$23$	3.54164	0.738483	0.369241	−	0.929334i	$-0.379618\pi$
$23$	3.54164	0.738483	0.369241	+	0.929334i	$0.379618\pi$
$24$	1.17778	0.240414
$25$	0	0
$26$	1.07929	0.211667
$27$	5.61403	1.08042
$28$	8.46044	1.59887
$29$	3.95333	0.734114	0.367057	−	0.930198i	$-0.380365\pi$
$29$	3.95333	0.734114	0.367057	+	0.930198i	$0.380365\pi$
$30$	0	0
$31$	1.94023	0.348476	0.174238	−	0.984704i	$-0.444254\pi$
$31$	1.94023	0.348476	0.174238	+	0.984704i	$0.444254\pi$
$32$	2.63395	0.465622
$33$	4.97118	0.865371
$34$	−0.433333	−0.0743160
$35$	0	0
$36$	2.48862	0.414770
$37$	10.4821	1.72325	0.861626	−	0.507544i	$-0.169446\pi$
$37$	10.4821	1.72325	0.861626	+	0.507544i	$0.169446\pi$
$38$	−1.12458	−0.182431
$39$	−6.23302	−0.998082
$40$	0	0
$41$	−3.19721	−0.499320	−0.249660	−	0.968334i	$-0.580319\pi$
$41$	−3.19721	−0.499320	−0.249660	+	0.968334i	$0.580319\pi$
$42$	1.29532	0.199872
$43$	1.59123	0.242661	0.121330	−	0.992612i	$-0.461284\pi$
$43$	1.59123	0.242661	0.121330	+	0.992612i	$0.461284\pi$
$44$	7.37940	1.11249
$45$	0	0
$46$	0.804915	0.118678
$47$	−9.45887	−1.37972	−0.689859	−	0.723944i	$-0.742328\pi$
$47$	−9.45887	−1.37972	−0.689859	+	0.723944i	$0.742328\pi$
$48$	−4.84680	−0.699576
$49$	11.8561	1.69373
$50$	0	0
$51$	2.50254	0.350426
$52$	−9.25252	−1.28309
$53$	5.28147	0.725466	0.362733	−	0.931893i	$-0.381844\pi$
$53$	5.28147	0.725466	0.362733	+	0.931893i	$0.381844\pi$
$54$	1.27591	0.173629
$55$	0	0
$56$	3.89661	0.520707
$57$	6.49454	0.860223
$58$	0.898480	0.117976
$59$	2.44413	0.318198	0.159099	−	0.987263i	$-0.449141\pi$
$59$	2.44413	0.318198	0.159099	+	0.987263i	$0.449141\pi$
$60$	0	0
$61$	−5.09098	−0.651833	−0.325917	−	0.945398i	$-0.605673\pi$
$61$	−5.09098	−0.651833	−0.325917	+	0.945398i	$0.605673\pi$
$62$	0.440960	0.0560020
$63$	5.54650	0.698793
$64$	−6.78688	−0.848360
$65$	0	0
$66$	1.12981	0.139070
$67$	9.56638	1.16872	0.584359	−	0.811495i	$-0.301346\pi$
$67$	9.56638	1.16872	0.584359	+	0.811495i	$0.301346\pi$
$68$	3.71486	0.450493
$69$	−4.64846	−0.559609
$70$	0	0
$71$	−12.5342	−1.48753	−0.743765	−	0.668441i	$-0.766962\pi$
$71$	−12.5342	−1.48753	−0.743765	+	0.668441i	$0.766962\pi$
$72$	1.14618	0.135079
$73$	14.0282	1.64187	0.820937	−	0.571019i	$-0.193452\pi$
$73$	14.0282	1.64187	0.820937	+	0.571019i	$0.193452\pi$
$74$	2.38229	0.276936
$75$	0	0
$76$	9.64074	1.10587
$77$	16.4468	1.87428
$78$	−1.41659	−0.160397
$79$	−4.86166	−0.546979	−0.273490	−	0.961875i	$-0.588178\pi$
$79$	−4.86166	−0.546979	−0.273490	+	0.961875i	$0.588178\pi$
$80$	0	0
$81$	−3.53661	−0.392957
$82$	−0.726636	−0.0802435
$83$	−8.87655	−0.974327	−0.487164	−	0.873311i	$-0.661969\pi$
$83$	−8.87655	−0.974327	−0.487164	+	0.873311i	$0.661969\pi$
$84$	−11.1045	−1.21160
$85$	0	0
$86$	0.361643	0.0389969
$87$	−5.18881	−0.556299
$88$	3.39872	0.362305
$89$	9.16017	0.970976	0.485488	−	0.874243i	$-0.338642\pi$
$89$	9.16017	0.970976	0.485488	+	0.874243i	$0.338642\pi$
$90$	0	0
$91$	−20.6215	−2.16172
$92$	−6.90034	−0.719411
$93$	−2.54659	−0.264069
$94$	−2.14973	−0.221728
$95$	0	0
$96$	−3.45711	−0.352840
$97$	−5.17578	−0.525520	−0.262760	−	0.964861i	$-0.584633\pi$
$97$	−5.17578	−0.525520	−0.262760	+	0.964861i	$0.584633\pi$
$98$	2.69457	0.272192
$99$	4.83779	0.486216
$100$	0	0
$101$	7.95979	0.792029	0.396015	−	0.918244i	$-0.370393\pi$
$101$	7.95979	0.792029	0.396015	+	0.918244i	$0.370393\pi$
$102$	0.568757	0.0563153
$103$	19.9054	1.96134	0.980671	−	0.195663i	$-0.0626860\pi$
$103$	19.9054	1.96134	0.980671	+	0.195663i	$0.0626860\pi$
$104$	−4.26142	−0.417867
$105$	0	0
$106$	1.20033	0.116586
$107$	−6.09395	−0.589125	−0.294562	−	0.955632i	$-0.595174\pi$
$107$	−6.09395	−0.589125	−0.294562	+	0.955632i	$0.595174\pi$
$108$	−10.9381	−1.05252
$109$	−9.05280	−0.867101	−0.433550	−	0.901129i	$-0.642739\pi$
$109$	−9.05280	−0.867101	−0.433550	+	0.901129i	$0.642739\pi$
$110$	0	0
$111$	−13.7580	−1.30585
$112$	−16.0353	−1.51519
$113$	7.64841	0.719501	0.359751	−	0.933048i	$-0.382862\pi$
$113$	7.64841	0.719501	0.359751	+	0.933048i	$0.382862\pi$
$114$	1.47603	0.138243
$115$	0	0
$116$	−7.70245	−0.715155
$117$	−6.06577	−0.560781
$118$	0.555482	0.0511362
$119$	8.27947	0.758978
$120$	0	0
$121$	3.34527	0.304115
$122$	−1.15704	−0.104753
$123$	4.19639	0.378376
$124$	−3.78025	−0.339476
$125$	0	0
$126$	1.26056	0.112300
$127$	−14.9702	−1.32839	−0.664194	−	0.747561i	$-0.731225\pi$
$127$	−14.9702	−1.32839	−0.664194	+	0.747561i	$0.731225\pi$
$128$	−6.81038	−0.601958
$129$	−2.08852	−0.183884
$130$	0	0
$131$	−3.51577	−0.307174	−0.153587	−	0.988135i	$-0.549083\pi$
$131$	−3.51577	−0.307174	−0.153587	+	0.988135i	$0.549083\pi$
$132$	−9.68558	−0.843022
$133$	21.4867	1.86314
$134$	2.17417	0.187819
$135$	0	0
$136$	1.71095	0.146713
$137$	−18.7336	−1.60052	−0.800260	−	0.599654i	$-0.795305\pi$
$137$	−18.7336	−1.60052	−0.800260	+	0.599654i	$0.795305\pi$
$138$	−1.05646	−0.0899322
$139$	−0.488165	−0.0414056	−0.0207028	−	0.999786i	$-0.506590\pi$
$139$	−0.488165	−0.0414056	−0.0207028	+	0.999786i	$0.506590\pi$
$140$	0	0
$141$	12.4149	1.04553
$142$	−2.84866	−0.239054
$143$	−17.9865	−1.50411
$144$	−4.71675	−0.393063
$145$	0	0
$146$	3.18821	0.263858
$147$	−15.5614	−1.28348
$148$	−20.4228	−1.67875
$149$	−13.6893	−1.12147	−0.560737	−	0.827994i	$-0.689482\pi$
$149$	−13.6893	−1.12147	−0.560737	+	0.827994i	$0.689482\pi$
$150$	0	0
$151$	21.6631	1.76291	0.881457	−	0.472264i	$-0.156563\pi$
$151$	21.6631	1.76291	0.881457	+	0.472264i	$0.156563\pi$
$152$	4.44022	0.360150
$153$	2.43539	0.196890
$154$	3.73789	0.301208
$155$	0	0
$156$	12.1441	0.972305
$157$	4.69612	0.374791	0.187396	−	0.982285i	$-0.439995\pi$
$157$	4.69612	0.374791	0.187396	+	0.982285i	$0.439995\pi$
$158$	−1.10492	−0.0879025
$159$	−6.93202	−0.549745
$160$	0	0
$161$	−15.3791	−1.21204
$162$	−0.803772	−0.0631503
$163$	−19.5560	−1.53174	−0.765870	−	0.642995i	$-0.777692\pi$
$163$	−19.5560	−1.53174	−0.765870	+	0.642995i	$0.777692\pi$
$164$	6.22928	0.486425
$165$	0	0
$166$	−2.01739	−0.156580
$167$	−8.28168	−0.640855	−0.320428	−	0.947273i	$-0.603827\pi$
$167$	−8.28168	−0.640855	−0.320428	+	0.947273i	$0.603827\pi$
$168$	−5.11437	−0.394582
$169$	9.55209	0.734776
$170$	0	0
$171$	6.32028	0.483324
$172$	−3.10028	−0.236394
$173$	11.6694	0.887211	0.443605	−	0.896222i	$-0.353699\pi$
$173$	11.6694	0.887211	0.443605	+	0.896222i	$0.353699\pi$
$174$	−1.17927	−0.0894002
$175$	0	0
$176$	−13.9864	−1.05426
$177$	−3.20796	−0.241125
$178$	2.08185	0.156041
$179$	1.56938	0.117301	0.0586504	−	0.998279i	$-0.481320\pi$
$179$	1.56938	0.117301	0.0586504	+	0.998279i	$0.481320\pi$
$180$	0	0
$181$	4.98176	0.370291	0.185146	−	0.982711i	$-0.440724\pi$
$181$	4.98176	0.370291	0.185146	+	0.982711i	$0.440724\pi$
$182$	−4.68668	−0.347400
$183$	6.68200	0.493948
$184$	−3.17808	−0.234291
$185$	0	0
$186$	−0.578768	−0.0424373
$187$	7.22155	0.528092
$188$	18.4292	1.34409
$189$	−24.3782	−1.77325
$190$	0	0
$191$	3.53891	0.256067	0.128033	−	0.991770i	$-0.459134\pi$
$191$	3.53891	0.256067	0.128033	+	0.991770i	$0.459134\pi$
$192$	8.90790	0.642872
$193$	11.7362	0.844793	0.422396	−	0.906411i	$-0.361189\pi$
$193$	11.7362	0.844793	0.422396	+	0.906411i	$0.361189\pi$
$194$	−1.17631	−0.0844540
$195$	0	0
$196$	−23.0999	−1.64999
$197$	0.411155	0.0292936	0.0146468	−	0.999893i	$-0.495338\pi$
$197$	0.411155	0.0292936	0.0146468	+	0.999893i	$0.495338\pi$
$198$	1.09949	0.0781376
$199$	23.6023	1.67312	0.836560	−	0.547876i	$-0.184563\pi$
$199$	23.6023	1.67312	0.836560	+	0.547876i	$0.184563\pi$
$200$	0	0
$201$	−12.5560	−0.885634
$202$	1.80904	0.127283
$203$	−17.1668	−1.20487
$204$	−4.87582	−0.341376
$205$	0	0
$206$	4.52395	0.315198
$207$	−4.52373	−0.314421
$208$	17.5365	1.21594
$209$	18.7412	1.29636
$210$	0	0
$211$	21.5367	1.48265	0.741324	−	0.671148i	$-0.234198\pi$
$211$	21.5367	1.48265	0.741324	+	0.671148i	$0.234198\pi$
$212$	−10.2901	−0.706730
$213$	16.4513	1.12722
$214$	−1.38498	−0.0946756
$215$	0	0
$216$	−5.03774	−0.342775
$217$	−8.42520	−0.571940
$218$	−2.05745	−0.139348
$219$	−18.4122	−1.24418
$220$	0	0
$221$	−9.05461	−0.609079
$222$	−3.12680	−0.209857
$223$	3.92517	0.262849	0.131424	−	0.991326i	$-0.458045\pi$
$223$	3.92517	0.262849	0.131424	+	0.991326i	$0.458045\pi$
$224$	−11.4376	−0.764206
$225$	0	0
$226$	1.73827	0.115628
$227$	−0.481838	−0.0319807	−0.0159903	−	0.999872i	$-0.505090\pi$
$227$	−0.481838	−0.0319807	−0.0159903	+	0.999872i	$0.505090\pi$
$228$	−12.6536	−0.838007
$229$	−13.9644	−0.922790	−0.461395	−	0.887195i	$-0.652651\pi$
$229$	−13.9644	−0.922790	−0.461395	+	0.887195i	$0.652651\pi$
$230$	0	0
$231$	−21.5867	−1.42030
$232$	−3.54751	−0.232905
$233$	−18.3864	−1.20453	−0.602265	−	0.798296i	$-0.705735\pi$
$233$	−18.3864	−1.20453	−0.602265	+	0.798296i	$0.705735\pi$
$234$	−1.37858	−0.0901205
$235$	0	0
$236$	−4.76201	−0.309981
$237$	6.38101	0.414491
$238$	1.88169	0.121972
$239$	15.5883	1.00832	0.504161	−	0.863609i	$-0.331802\pi$
$239$	15.5883	1.00832	0.504161	+	0.863609i	$0.331802\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	0.760286	0.0488730
$243$	−12.2002	−0.782645
$244$	9.91900	0.634999
$245$	0	0
$246$	0.953721	0.0608071
$247$	−23.4983	−1.49516
$248$	−1.74107	−0.110558
$249$	11.6506	0.738328
$250$	0	0
$251$	−31.3374	−1.97800	−0.989000	−	0.147915i	$-0.952744\pi$
$251$	−31.3374	−1.97800	−0.989000	+	0.147915i	$0.952744\pi$
$252$	−10.8065	−0.680746
$253$	−13.4140	−0.843332
$254$	−3.40230	−0.213479
$255$	0	0
$256$	12.0260	0.751622
$257$	17.7838	1.10932	0.554662	−	0.832076i	$-0.312848\pi$
$257$	17.7838	1.10932	0.554662	+	0.832076i	$0.312848\pi$
$258$	−0.474662	−0.0295512
$259$	−45.5173	−2.82830
$260$	0	0
$261$	−5.04958	−0.312561
$262$	−0.799035	−0.0493646
$263$	26.9582	1.66231	0.831157	−	0.556038i	$-0.187679\pi$
$263$	26.9582	1.66231	0.831157	+	0.556038i	$0.187679\pi$
$264$	−4.46088	−0.274548
$265$	0	0
$266$	4.88333	0.299416
$267$	−12.0229	−0.735788
$268$	−18.6386	−1.13854
$269$	25.0304	1.52613	0.763066	−	0.646320i	$-0.223693\pi$
$269$	25.0304	1.52613	0.763066	+	0.646320i	$0.223693\pi$
$270$	0	0
$271$	−11.7091	−0.711275	−0.355638	−	0.934624i	$-0.615736\pi$
$271$	−11.7091	−0.711275	−0.355638	+	0.934624i	$0.615736\pi$
$272$	−7.04087	−0.426916
$273$	27.0660	1.63811
$274$	−4.25762	−0.257212
$275$	0	0
$276$	9.05682	0.545156
$277$	14.3385	0.861517	0.430759	−	0.902467i	$-0.358246\pi$
$277$	14.3385	0.861517	0.430759	+	0.902467i	$0.358246\pi$
$278$	−0.110946	−0.00665410
$279$	−2.47826	−0.148369
$280$	0	0
$281$	−9.43973	−0.563127	−0.281564	−	0.959543i	$-0.590853\pi$
$281$	−9.43973	−0.563127	−0.281564	+	0.959543i	$0.590853\pi$
$282$	2.82156	0.168022
$283$	−19.8200	−1.17818	−0.589088	−	0.808069i	$-0.700513\pi$
$283$	−19.8200	−1.17818	−0.589088	+	0.808069i	$0.700513\pi$
$284$	24.4209	1.44911
$285$	0	0
$286$	−4.08783	−0.241719
$287$	13.8835	0.819514
$288$	−3.36435	−0.198246
$289$	−13.3646	−0.786153
$290$	0	0
$291$	6.79329	0.398230
$292$	−27.3318	−1.59947
$293$	−19.4034	−1.13356	−0.566779	−	0.823870i	$-0.691811\pi$
$293$	−19.4034	−1.13356	−0.566779	+	0.823870i	$0.691811\pi$
$294$	−3.53666	−0.206262
$295$	0	0
$296$	−9.40612	−0.546720
$297$	−21.2632	−1.23382
$298$	−3.11120	−0.180227
$299$	16.8189	0.972662
$300$	0	0
$301$	−6.90972	−0.398270
$302$	4.92340	0.283310
$303$	−10.4474	−0.600186
$304$	−18.2723	−1.04799
$305$	0	0
$306$	0.553496	0.0316413
$307$	−12.4782	−0.712169	−0.356084	−	0.934454i	$-0.615888\pi$
$307$	−12.4782	−0.712169	−0.356084	+	0.934454i	$0.615888\pi$
$308$	−32.0440	−1.82588
$309$	−26.1262	−1.48627
$310$	0	0
$311$	19.9330	1.13030	0.565148	−	0.824990i	$-0.308819\pi$
$311$	19.9330	1.13030	0.565148	+	0.824990i	$0.308819\pi$
$312$	5.59319	0.316652
$313$	−22.2646	−1.25847	−0.629236	−	0.777214i	$-0.716632\pi$
$313$	−22.2646	−1.25847	−0.629236	+	0.777214i	$0.716632\pi$
$314$	1.06730	0.0602310
$315$	0	0
$316$	9.47220	0.532853
$317$	−24.1166	−1.35452	−0.677261	−	0.735743i	$-0.736833\pi$
$317$	−24.1166	−1.35452	−0.677261	+	0.735743i	$0.736833\pi$
$318$	−1.57545	−0.0883470
$319$	−14.9733	−0.838343
$320$	0	0
$321$	7.99842	0.446428
$322$	−3.49523	−0.194782
$323$	9.43453	0.524951
$324$	6.89054	0.382808
$325$	0	0
$326$	−4.44452	−0.246159
$327$	11.8820	0.657073
$328$	2.86901	0.158415
$329$	41.0739	2.26448
$330$	0	0
$331$	2.58251	0.141948	0.0709738	−	0.997478i	$-0.477389\pi$
$331$	2.58251	0.141948	0.0709738	+	0.997478i	$0.477389\pi$
$332$	17.2946	0.949164
$333$	−13.3888	−0.733703
$334$	−1.88219	−0.102989
$335$	0	0
$336$	21.0466	1.14819
$337$	25.6170	1.39545	0.697723	−	0.716367i	$-0.254196\pi$
$337$	25.6170	1.39545	0.697723	+	0.716367i	$0.254196\pi$
$338$	2.17092	0.118083
$339$	−10.0387	−0.545225
$340$	0	0
$341$	−7.34866	−0.397953
$342$	1.43642	0.0776728
$343$	−21.0871	−1.13860
$344$	−1.42789	−0.0769867
$345$	0	0
$346$	2.65213	0.142580
$347$	8.55736	0.459383	0.229692	−	0.973263i	$-0.426228\pi$
$347$	8.55736	0.459383	0.229692	+	0.973263i	$0.426228\pi$
$348$	10.1096	0.541932
$349$	−17.5551	−0.939700	−0.469850	−	0.882746i	$-0.655692\pi$
$349$	−17.5551	−0.939700	−0.469850	+	0.882746i	$0.655692\pi$
$350$	0	0
$351$	26.6605	1.42303
$352$	−9.97614	−0.531730
$353$	−26.3356	−1.40170	−0.700852	−	0.713307i	$-0.747197\pi$
$353$	−26.3356	−1.40170	−0.700852	+	0.713307i	$0.747197\pi$
$354$	−0.729079	−0.0387501
$355$	0	0
$356$	−17.8472	−0.945900
$357$	−10.8669	−0.575140
$358$	0.356675	0.0188509
$359$	−32.5292	−1.71683	−0.858413	−	0.512959i	$-0.828549\pi$
$359$	−32.5292	−1.71683	−0.858413	+	0.512959i	$0.828549\pi$
$360$	0	0
$361$	5.48429	0.288647
$362$	1.13221	0.0595078
$363$	−4.39072	−0.230453
$364$	40.1778	2.10589
$365$	0	0
$366$	1.51863	0.0793801
$367$	21.6369	1.12943	0.564717	−	0.825284i	$-0.308985\pi$
$367$	21.6369	1.12943	0.564717	+	0.825284i	$0.308985\pi$
$368$	13.0784	0.681759
$369$	4.08379	0.212594
$370$	0	0
$371$	−22.9341	−1.19068
$372$	4.96164	0.257249
$373$	−5.61612	−0.290792	−0.145396	−	0.989374i	$-0.546446\pi$
$373$	−5.61612	−0.290792	−0.145396	+	0.989374i	$0.546446\pi$
$374$	1.64126	0.0848673
$375$	0	0
$376$	8.48790	0.437730
$377$	18.7740	0.966909
$378$	−5.54047	−0.284971
$379$	−0.510673	−0.0262315	−0.0131158	−	0.999914i	$-0.504175\pi$
$379$	−0.510673	−0.0262315	−0.0131158	+	0.999914i	$0.504175\pi$
$380$	0	0
$381$	19.6486	1.00663
$382$	0.804295	0.0411513
$383$	−3.40620	−0.174049	−0.0870244	−	0.996206i	$-0.527736\pi$
$383$	−3.40620	−0.174049	−0.0870244	+	0.996206i	$0.527736\pi$
$384$	8.93873	0.456153
$385$	0	0
$386$	2.66732	0.135763
$387$	−2.03248	−0.103317
$388$	10.0842	0.511948
$389$	8.84933	0.448679	0.224339	−	0.974511i	$-0.427978\pi$
$389$	8.84933	0.448679	0.224339	+	0.974511i	$0.427978\pi$
$390$	0	0
$391$	−6.75275	−0.341501
$392$	−10.6391	−0.537355
$393$	4.61451	0.232771
$394$	0.0934440	0.00470764
$395$	0	0
$396$	−9.42570	−0.473659
$397$	14.6504	0.735285	0.367642	−	0.929967i	$-0.380165\pi$
$397$	14.6504	0.735285	0.367642	+	0.929967i	$0.380165\pi$
$398$	5.36413	0.268879
$399$	−28.2017	−1.41185
$400$	0	0
$401$	5.02617	0.250995	0.125497	−	0.992094i	$-0.459947\pi$
$401$	5.02617	0.250995	0.125497	+	0.992094i	$0.459947\pi$
$402$	−2.85363	−0.142326
$403$	9.21398	0.458981
$404$	−15.5084	−0.771574
$405$	0	0
$406$	−3.90153	−0.193630
$407$	−39.7012	−1.96792
$408$	−2.24565	−0.111176
$409$	2.30631	0.114040	0.0570199	−	0.998373i	$-0.481840\pi$
$409$	2.30631	0.114040	0.0570199	+	0.998373i	$0.481840\pi$
$410$	0	0
$411$	24.5882	1.21284
$412$	−38.7827	−1.91069
$413$	−10.6133	−0.522246
$414$	−1.02812	−0.0505292
$415$	0	0
$416$	12.5084	0.613275
$417$	0.640724	0.0313764
$418$	4.25935	0.208332
$419$	−36.2002	−1.76850	−0.884249	−	0.467016i	$-0.845329\pi$
$419$	−36.2002	−1.76850	−0.884249	+	0.467016i	$0.845329\pi$
$420$	0	0
$421$	−19.3813	−0.944587	−0.472294	−	0.881441i	$-0.656574\pi$
$421$	−19.3813	−0.944587	−0.472294	+	0.881441i	$0.656574\pi$
$422$	4.89468	0.238269
$423$	12.0818	0.587438
$424$	−4.73932	−0.230162
$425$	0	0
$426$	3.73891	0.181151
$427$	22.1069	1.06983
$428$	11.8731	0.573910
$429$	23.6076	1.13979
$430$	0	0
$431$	24.5871	1.18432	0.592160	−	0.805821i	$-0.298275\pi$
$431$	24.5871	1.18432	0.592160	+	0.805821i	$0.298275\pi$
$432$	20.7312	0.997431
$433$	8.08635	0.388605	0.194303	−	0.980942i	$-0.437756\pi$
$433$	8.08635	0.388605	0.194303	+	0.980942i	$0.437756\pi$
$434$	−1.91481	−0.0919139
$435$	0	0
$436$	17.6380	0.844707
$437$	−17.5246	−0.838315
$438$	−4.18458	−0.199947
$439$	15.4558	0.737665	0.368833	−	0.929496i	$-0.379758\pi$
$439$	15.4558	0.737665	0.368833	+	0.929496i	$0.379758\pi$
$440$	0	0
$441$	−15.1438	−0.721135
$442$	−2.05786	−0.0978823
$443$	26.9418	1.28004	0.640022	−	0.768356i	$-0.278925\pi$
$443$	26.9418	1.28004	0.640022	+	0.768356i	$0.278925\pi$
$444$	26.8053	1.27212
$445$	0	0
$446$	0.892079	0.0422412
$447$	17.9675	0.849833
$448$	29.4711	1.39238
$449$	−0.178771	−0.00843672	−0.00421836	−	0.999991i	$-0.501343\pi$
$449$	−0.178771	−0.00843672	−0.00421836	+	0.999991i	$0.501343\pi$
$450$	0	0
$451$	12.1095	0.570213
$452$	−14.9018	−0.700919
$453$	−28.4331	−1.33591
$454$	−0.109508	−0.00513947
$455$	0	0
$456$	−5.82787	−0.272915
$457$	14.3591	0.671689	0.335845	−	0.941917i	$-0.390978\pi$
$457$	14.3591	0.671689	0.335845	+	0.941917i	$0.390978\pi$
$458$	−3.17370	−0.148297
$459$	−10.7041	−0.499625
$460$	0	0
$461$	30.9080	1.43953	0.719764	−	0.694219i	$-0.244250\pi$
$461$	30.9080	1.43953	0.719764	+	0.694219i	$0.244250\pi$
$462$	−4.90604	−0.228250
$463$	−0.604283	−0.0280834	−0.0140417	−	0.999901i	$-0.504470\pi$
$463$	−0.604283	−0.0280834	−0.0140417	+	0.999901i	$0.504470\pi$
$464$	14.5987	0.677726
$465$	0	0
$466$	−4.17870	−0.193575
$467$	−16.9907	−0.786234	−0.393117	−	0.919488i	$-0.628603\pi$
$467$	−16.9907	−0.786234	−0.393117	+	0.919488i	$0.628603\pi$
$468$	11.8182	0.546298
$469$	−41.5407	−1.91817
$470$	0	0
$471$	−6.16374	−0.284010
$472$	−2.19323	−0.100952
$473$	−6.02682	−0.277114
$474$	1.45022	0.0666109
$475$	0	0
$476$	−16.1313	−0.739377
$477$	−6.74602	−0.308879
$478$	3.54278	0.162043
$479$	−22.5236	−1.02913	−0.514564	−	0.857452i	$-0.672046\pi$
$479$	−22.5236	−1.02913	−0.514564	+	0.857452i	$0.672046\pi$
$480$	0	0
$481$	49.7786	2.26971
$482$	−0.227272	−0.0103519
$483$	20.1853	0.918464
$484$	−6.51775	−0.296261
$485$	0	0
$486$	−2.77277	−0.125775
$487$	−16.9242	−0.766908	−0.383454	−	0.923560i	$-0.625266\pi$
$487$	−16.9242	−0.766908	−0.383454	+	0.923560i	$0.625266\pi$
$488$	4.56838	0.206801
$489$	25.6675	1.16073
$490$	0	0
$491$	14.8980	0.672335	0.336168	−	0.941802i	$-0.390869\pi$
$491$	14.8980	0.672335	0.336168	+	0.941802i	$0.390869\pi$
$492$	−8.17603	−0.368604
$493$	−7.53770	−0.339481
$494$	−5.34051	−0.240281
$495$	0	0
$496$	7.16480	0.321709
$497$	54.4279	2.44142
$498$	2.64786	0.118653
$499$	−29.5477	−1.32274	−0.661369	−	0.750061i	$-0.730024\pi$
$499$	−29.5477	−1.32274	−0.661369	+	0.750061i	$0.730024\pi$
$500$	0	0
$501$	10.8698	0.485629
$502$	−7.12211	−0.317875
$503$	18.5081	0.825234	0.412617	−	0.910905i	$-0.364615\pi$
$503$	18.5081	0.825234	0.412617	+	0.910905i	$0.364615\pi$
$504$	−4.97714	−0.221699
$505$	0	0
$506$	−3.04863	−0.135528
$507$	−12.5373	−0.556800
$508$	29.1671	1.29408
$509$	21.9225	0.971696	0.485848	−	0.874043i	$-0.338511\pi$
$509$	21.9225	0.971696	0.485848	+	0.874043i	$0.338511\pi$
$510$	0	0
$511$	−60.9155	−2.69474
$512$	16.3539	0.722748
$513$	−27.7791	−1.22648
$514$	4.04176	0.178274
$515$	0	0
$516$	4.06917	0.179135
$517$	35.8256	1.57561
$518$	−10.3448	−0.454524
$519$	−15.3163	−0.672312
$520$	0	0
$521$	9.12624	0.399828	0.199914	−	0.979813i	$-0.435934\pi$
$521$	9.12624	0.399828	0.199914	+	0.979813i	$0.435934\pi$
$522$	−1.14763	−0.0502303
$523$	29.6684	1.29731	0.648654	−	0.761084i	$-0.275332\pi$
$523$	29.6684	1.29731	0.648654	+	0.761084i	$0.275332\pi$
$524$	6.84994	0.299241
$525$	0	0
$526$	6.12684	0.267143
$527$	−3.69939	−0.161148
$528$	18.3573	0.798900
$529$	−10.4568	−0.454643
$530$	0	0
$531$	−3.12188	−0.135478
$532$	−41.8636	−1.81502
$533$	−15.1832	−0.657659
$534$	−2.73246	−0.118245
$535$	0	0
$536$	−8.58437	−0.370788
$537$	−2.05983	−0.0888884
$538$	5.68871	0.245258
$539$	−44.9053	−1.93421
$540$	0	0
$541$	−25.7764	−1.10821	−0.554107	−	0.832445i	$-0.686940\pi$
$541$	−25.7764	−1.10821	−0.554107	+	0.832445i	$0.686940\pi$
$542$	−2.66114	−0.114306
$543$	−6.53864	−0.280600
$544$	−5.02209	−0.215320
$545$	0	0
$546$	6.15135	0.263253
$547$	19.3946	0.829254	0.414627	−	0.909992i	$-0.363912\pi$
$547$	19.3946	0.829254	0.414627	+	0.909992i	$0.363912\pi$
$548$	36.4996	1.55918
$549$	6.50271	0.277529
$550$	0	0
$551$	−19.5617	−0.833356
$552$	4.17129	0.177542
$553$	21.1111	0.897735
$554$	3.25874	0.138450
$555$	0	0
$556$	0.951114	0.0403362
$557$	15.7916	0.669113	0.334557	−	0.942376i	$-0.391413\pi$
$557$	15.7916	0.669113	0.334557	+	0.942376i	$0.391413\pi$
$558$	−0.563238	−0.0238438
$559$	7.55662	0.319611
$560$	0	0
$561$	−9.47841	−0.400179
$562$	−2.14538	−0.0904976
$563$	42.7874	1.80327	0.901637	−	0.432493i	$-0.142366\pi$
$563$	42.7874	1.80327	0.901637	+	0.432493i	$0.142366\pi$
$564$	−24.1886	−1.01852
$565$	0	0
$566$	−4.50452	−0.189339
$567$	15.3573	0.644944
$568$	11.2475	0.471934
$569$	−11.5414	−0.483841	−0.241921	−	0.970296i	$-0.577777\pi$
$569$	−11.5414	−0.483841	−0.241921	+	0.970296i	$0.577777\pi$
$570$	0	0
$571$	−22.0691	−0.923563	−0.461782	−	0.886994i	$-0.652790\pi$
$571$	−22.0691	−0.923563	−0.461782	+	0.886994i	$0.652790\pi$
$572$	35.0440	1.46527
$573$	−4.64489	−0.194043
$574$	3.15532	0.131700
$575$	0	0
$576$	8.66888	0.361203
$577$	−39.8416	−1.65863	−0.829314	−	0.558783i	$-0.811269\pi$
$577$	−39.8416	−1.65863	−0.829314	+	0.558783i	$0.811269\pi$
$578$	−3.03740	−0.126339
$579$	−15.4040	−0.640169
$580$	0	0
$581$	38.5452	1.59912
$582$	1.54392	0.0639977
$583$	−20.0036	−0.828466
$584$	−12.5882	−0.520902
$585$	0	0
$586$	−4.40984	−0.182169
$587$	−5.57560	−0.230130	−0.115065	−	0.993358i	$-0.536708\pi$
$587$	−5.57560	−0.230130	−0.115065	+	0.993358i	$0.536708\pi$
$588$	30.3190	1.25033
$589$	−9.60059	−0.395585
$590$	0	0
$591$	−0.539648	−0.0221982
$592$	38.7079	1.59089
$593$	−35.7773	−1.46920	−0.734599	−	0.678502i	$-0.762630\pi$
$593$	−35.7773	−1.46920	−0.734599	+	0.678502i	$0.762630\pi$
$594$	−4.83253	−0.198281
$595$	0	0
$596$	26.6716	1.09251
$597$	−30.9784	−1.26786
$598$	3.82246	0.156312
$599$	−21.4396	−0.875998	−0.437999	−	0.898975i	$-0.644313\pi$
$599$	−21.4396	−0.875998	−0.437999	+	0.898975i	$0.644313\pi$
$600$	0	0
$601$	−16.0030	−0.652774	−0.326387	−	0.945236i	$-0.605831\pi$
$601$	−16.0030	−0.652774	−0.326387	+	0.945236i	$0.605831\pi$
$602$	−1.57038	−0.0640041
$603$	−12.2191	−0.497601
$604$	−42.2072	−1.71739
$605$	0	0
$606$	−2.37439	−0.0964531
$607$	−27.0156	−1.09653	−0.548264	−	0.836305i	$-0.684711\pi$
$607$	−27.0156	−1.09653	−0.548264	+	0.836305i	$0.684711\pi$
$608$	−13.0332	−0.528567
$609$	22.5317	0.913031
$610$	0	0
$611$	−44.9193	−1.81724
$612$	−4.74499	−0.191805
$613$	−7.49953	−0.302903	−0.151452	−	0.988465i	$-0.548395\pi$
$613$	−7.49953	−0.302903	−0.151452	+	0.988465i	$0.548395\pi$
$614$	−2.83594	−0.114449
$615$	0	0
$616$	−14.7585	−0.594636
$617$	28.8447	1.16124	0.580622	−	0.814173i	$-0.302809\pi$
$617$	28.8447	1.16124	0.580622	+	0.814173i	$0.302809\pi$
$618$	−5.93776	−0.238852
$619$	−40.8872	−1.64339	−0.821697	−	0.569925i	$-0.806972\pi$
$619$	−40.8872	−1.64339	−0.821697	+	0.569925i	$0.806972\pi$
$620$	0	0
$621$	19.8829	0.797872
$622$	4.53021	0.181645
$623$	−39.7768	−1.59362
$624$	−23.0170	−0.921417
$625$	0	0
$626$	−5.06013	−0.202243
$627$	−24.5982	−0.982357
$628$	−9.14967	−0.365112
$629$	−19.9860	−0.796894
$630$	0	0
$631$	17.7011	0.704669	0.352335	−	0.935874i	$-0.385388\pi$
$631$	17.7011	0.704669	0.352335	+	0.935874i	$0.385388\pi$
$632$	4.36260	0.173535
$633$	−28.2673	−1.12352
$634$	−5.48102	−0.217679
$635$	0	0
$636$	13.5060	0.535547
$637$	56.3037	2.23083
$638$	−3.40300	−0.134726
$639$	16.0099	0.633340
$640$	0	0
$641$	−12.0209	−0.474798	−0.237399	−	0.971412i	$-0.576295\pi$
$641$	−12.0209	−0.474798	−0.237399	+	0.971412i	$0.576295\pi$
$642$	1.81782	0.0717434
$643$	−5.96370	−0.235185	−0.117593	−	0.993062i	$-0.537518\pi$
$643$	−5.96370	−0.235185	−0.117593	+	0.993062i	$0.537518\pi$
$644$	29.9638	1.18074
$645$	0	0
$646$	2.14420	0.0843625
$647$	−24.1163	−0.948109	−0.474055	−	0.880495i	$-0.657210\pi$
$647$	−24.1163	−0.948109	−0.474055	+	0.880495i	$0.657210\pi$
$648$	3.17357	0.124670
$649$	−9.25717	−0.363376
$650$	0	0
$651$	11.0582	0.433406
$652$	38.1018	1.49218
$653$	−44.0774	−1.72488	−0.862442	−	0.506156i	$-0.831066\pi$
$653$	−44.0774	−1.72488	−0.862442	+	0.506156i	$0.831066\pi$
$654$	2.70043	0.105595
$655$	0	0
$656$	−11.8065	−0.460967
$657$	−17.9182	−0.699055
$658$	9.33493	0.363914
$659$	26.7646	1.04260	0.521301	−	0.853373i	$-0.325447\pi$
$659$	26.7646	1.04260	0.521301	+	0.853373i	$0.325447\pi$
$660$	0	0
$661$	13.6194	0.529733	0.264867	−	0.964285i	$-0.414672\pi$
$661$	13.6194	0.529733	0.264867	+	0.964285i	$0.414672\pi$
$662$	0.586931	0.0228117
$663$	11.8843	0.461549
$664$	7.96535	0.309116
$665$	0	0
$666$	−3.04290	−0.117910
$667$	14.0013	0.542131
$668$	16.1356	0.624304
$669$	−5.15185	−0.199182
$670$	0	0
$671$	19.2822	0.744380
$672$	15.0120	0.579102
$673$	12.1077	0.466717	0.233359	−	0.972391i	$-0.425028\pi$
$673$	12.1077	0.466717	0.233359	+	0.972391i	$0.425028\pi$
$674$	5.82202	0.224256
$675$	0	0
$676$	−18.6108	−0.715800
$677$	25.5650	0.982543	0.491271	−	0.871007i	$-0.336532\pi$
$677$	25.5650	0.982543	0.491271	+	0.871007i	$0.336532\pi$
$678$	−2.28150	−0.0876207
$679$	22.4751	0.862516
$680$	0	0
$681$	0.632420	0.0242344
$682$	−1.67014	−0.0639531
$683$	−23.4168	−0.896018	−0.448009	−	0.894029i	$-0.647867\pi$
$683$	−23.4168	−0.896018	−0.448009	+	0.894029i	$0.647867\pi$
$684$	−12.3141	−0.470842
$685$	0	0
$686$	−4.79251	−0.182979
$687$	18.3284	0.699274
$688$	5.87604	0.224022
$689$	25.0812	0.955517
$690$	0	0
$691$	−40.5856	−1.54395	−0.771975	−	0.635653i	$-0.780731\pi$
$691$	−40.5856	−1.54395	−0.771975	+	0.635653i	$0.780731\pi$
$692$	−22.7361	−0.864297
$693$	−21.0075	−0.798007
$694$	1.94485	0.0738254
$695$	0	0
$696$	4.65617	0.176492
$697$	6.09603	0.230904
$698$	−3.98977	−0.151015
$699$	24.1324	0.912772
$700$	0	0
$701$	−12.9134	−0.487734	−0.243867	−	0.969809i	$-0.578416\pi$
$701$	−12.9134	−0.487734	−0.243867	+	0.969809i	$0.578416\pi$
$702$	6.05918	0.228689
$703$	−51.8673	−1.95621
$704$	25.7054	0.968809
$705$	0	0
$706$	−5.98534	−0.225261
$707$	−34.5643	−1.29993
$708$	6.25022	0.234898
$709$	22.1153	0.830556	0.415278	−	0.909695i	$-0.363684\pi$
$709$	22.1153	0.830556	0.415278	+	0.909695i	$0.363684\pi$
$710$	0	0
$711$	6.20979	0.232885
$712$	−8.21986	−0.308052
$713$	6.87161	0.257344
$714$	−2.46975	−0.0924281
$715$	0	0
$716$	−3.05769	−0.114271
$717$	−20.4599	−0.764089
$718$	−7.39298	−0.275903
$719$	−18.7175	−0.698044	−0.349022	−	0.937115i	$-0.613486\pi$
$719$	−18.7175	−0.698044	−0.349022	+	0.937115i	$0.613486\pi$
$720$	0	0
$721$	−86.4367	−3.21907
$722$	1.24642	0.0463871
$723$	1.31252	0.0488130
$724$	−9.70620	−0.360728
$725$	0	0
$726$	−0.997888	−0.0370351
$727$	47.1613	1.74912	0.874558	−	0.484921i	$-0.161152\pi$
$727$	47.1613	1.74912	0.874558	+	0.484921i	$0.161152\pi$
$728$	18.5046	0.685828
$729$	26.6228	0.986031
$730$	0	0
$731$	−3.03396	−0.112215
$732$	−13.0189	−0.481191
$733$	52.0609	1.92291	0.961457	−	0.274955i	$-0.0886629\pi$
$733$	52.0609	1.92291	0.961457	+	0.274955i	$0.0886629\pi$
$734$	4.91745	0.181506
$735$	0	0
$736$	9.32852	0.343854
$737$	−36.2328	−1.33465
$738$	0.928131	0.0341650
$739$	−24.4909	−0.900911	−0.450456	−	0.892799i	$-0.648738\pi$
$739$	−24.4909	−0.900911	−0.450456	+	0.892799i	$0.648738\pi$
$740$	0	0
$741$	30.8420	1.13301
$742$	−5.21227	−0.191348
$743$	26.3398	0.966313	0.483157	−	0.875534i	$-0.339490\pi$
$743$	26.3398	0.966313	0.483157	+	0.875534i	$0.339490\pi$
$744$	2.28518	0.0837787
$745$	0	0
$746$	−1.27639	−0.0467318
$747$	11.3380	0.414836
$748$	−14.0701	−0.514454
$749$	26.4622	0.966907
$750$	0	0
$751$	48.9803	1.78731	0.893657	−	0.448750i	$-0.148131\pi$
$751$	48.9803	1.78731	0.893657	+	0.448750i	$0.148131\pi$
$752$	−34.9293	−1.27374
$753$	41.1309	1.49889
$754$	4.26679	0.155387
$755$	0	0
$756$	47.4971	1.72745
$757$	−4.91565	−0.178662	−0.0893312	−	0.996002i	$-0.528473\pi$
$757$	−4.91565	−0.178662	−0.0893312	+	0.996002i	$0.528473\pi$
$758$	−0.116062	−0.00421555
$759$	17.6061	0.639062
$760$	0	0
$761$	11.3270	0.410603	0.205301	−	0.978699i	$-0.434183\pi$
$761$	11.3270	0.410603	0.205301	+	0.978699i	$0.434183\pi$
$762$	4.46557	0.161771
$763$	39.3106	1.42314
$764$	−6.89503	−0.249454
$765$	0	0
$766$	−0.774134	−0.0279706
$767$	11.6069	0.419102
$768$	−15.7843	−0.569566
$769$	−28.9152	−1.04271	−0.521354	−	0.853341i	$-0.674573\pi$
$769$	−28.9152	−1.04271	−0.521354	+	0.853341i	$0.674573\pi$
$770$	0	0
$771$	−23.3415	−0.840625
$772$	−22.8663	−0.822975
$773$	31.2067	1.12243	0.561214	−	0.827671i	$-0.310334\pi$
$773$	31.2067	1.12243	0.561214	+	0.827671i	$0.310334\pi$
$774$	−0.461926	−0.0166036
$775$	0	0
$776$	4.64447	0.166727
$777$	59.7422	2.14324
$778$	2.01120	0.0721051
$779$	15.8203	0.566821
$780$	0	0
$781$	47.4733	1.69873
$782$	−1.53471	−0.0548811
$783$	22.1941	0.793152
$784$	43.7818	1.56364
$785$	0	0
$786$	1.04875	0.0374076
$787$	−38.5271	−1.37334	−0.686671	−	0.726968i	$-0.740929\pi$
$787$	−38.5271	−1.37334	−0.686671	+	0.726968i	$0.740929\pi$
$788$	−0.801074	−0.0285371
$789$	−35.3831	−1.25967
$790$	0	0
$791$	−33.2122	−1.18089
$792$	−4.34118	−0.154257
$793$	−24.1766	−0.858536
$794$	3.32963	0.118164
$795$	0	0
$796$	−45.9854	−1.62991
$797$	−27.0593	−0.958490	−0.479245	−	0.877681i	$-0.659090\pi$
$797$	−27.0593	−0.958490	−0.479245	+	0.877681i	$0.659090\pi$
$798$	−6.40945	−0.226892
$799$	18.0350	0.638032
$800$	0	0
$801$	−11.7003	−0.413409
$802$	1.14231	0.0403363
$803$	−53.1319	−1.87499
$804$	24.4635	0.862762
$805$	0	0
$806$	2.09408	0.0737608
$807$	−32.8529	−1.15648
$808$	−7.14271	−0.251280
$809$	0.814932	0.0286515	0.0143257	−	0.999897i	$-0.495440\pi$
$809$	0.814932	0.0286515	0.0143257	+	0.999897i	$0.495440\pi$
$810$	0	0
$811$	−38.0343	−1.33556	−0.667782	−	0.744357i	$-0.732756\pi$
$811$	−38.0343	−1.33556	−0.667782	+	0.744357i	$0.732756\pi$
$812$	33.4469	1.17376
$813$	15.3684	0.538992
$814$	−9.02297	−0.316255
$815$	0	0
$816$	9.24127	0.323509
$817$	−7.87368	−0.275465
$818$	0.524159	0.0183268
$819$	26.3398	0.920387
$820$	0	0
$821$	−46.4606	−1.62149	−0.810744	−	0.585402i	$-0.800937\pi$
$821$	−46.4606	−1.62149	−0.810744	+	0.585402i	$0.800937\pi$
$822$	5.58820	0.194911
$823$	−6.51064	−0.226947	−0.113473	−	0.993541i	$-0.536198\pi$
$823$	−6.51064	−0.226947	−0.113473	+	0.993541i	$0.536198\pi$
$824$	−17.8621	−0.622256
$825$	0	0
$826$	−2.41210	−0.0839278
$827$	52.8190	1.83670	0.918348	−	0.395775i	$-0.129524\pi$
$827$	52.8190	1.83670	0.918348	+	0.395775i	$0.129524\pi$
$828$	8.81380	0.306301
$829$	24.2819	0.843346	0.421673	−	0.906748i	$-0.361443\pi$
$829$	24.2819	0.843346	0.421673	+	0.906748i	$0.361443\pi$
$830$	0	0
$831$	−18.8195	−0.652842
$832$	−32.2303	−1.11738
$833$	−22.6058	−0.783244
$834$	0.145619	0.00504236
$835$	0	0
$836$	−36.5144	−1.26288
$837$	10.8925	0.376501
$838$	−8.22729	−0.284207
$839$	−22.7561	−0.785628	−0.392814	−	0.919618i	$-0.628498\pi$
$839$	−22.7561	−0.785628	−0.392814	+	0.919618i	$0.628498\pi$
$840$	0	0
$841$	−13.3712	−0.461076
$842$	−4.40483	−0.151800
$843$	12.3898	0.426728
$844$	−41.9610	−1.44436
$845$	0	0
$846$	2.74585	0.0944044
$847$	−14.5264	−0.499133
$848$	19.5032	0.669741
$849$	26.0141	0.892801
$850$	0	0
$851$	37.1239	1.27259
$852$	−32.0528	−1.09811
$853$	−31.6817	−1.08476	−0.542380	−	0.840133i	$-0.682477\pi$
$853$	−31.6817	−1.08476	−0.542380	+	0.840133i	$0.682477\pi$
$854$	5.02428	0.171927
$855$	0	0
$856$	5.46840	0.186906
$857$	−51.1977	−1.74888	−0.874440	−	0.485134i	$-0.838771\pi$
$857$	−51.1977	−1.74888	−0.874440	+	0.485134i	$0.838771\pi$
$858$	5.36535	0.183170
$859$	−18.6822	−0.637430	−0.318715	−	0.947851i	$-0.603251\pi$
$859$	−18.6822	−0.637430	−0.318715	+	0.947851i	$0.603251\pi$
$860$	0	0
$861$	−18.2223	−0.621013
$862$	5.58796	0.190327
$863$	23.9124	0.813986	0.406993	−	0.913431i	$-0.366577\pi$
$863$	23.9124	0.813986	0.406993	+	0.913431i	$0.366577\pi$
$864$	14.7871	0.503067
$865$	0	0
$866$	1.83780	0.0624510
$867$	17.5413	0.595732
$868$	16.4152	0.557169
$869$	18.4136	0.624638
$870$	0	0
$871$	45.4298	1.53933
$872$	8.12351	0.275097
$873$	6.61101	0.223749
$874$	−3.98285	−0.134722
$875$	0	0
$876$	35.8734	1.21205
$877$	17.3811	0.586917	0.293459	−	0.955972i	$-0.405194\pi$
$877$	17.3811	0.586917	0.293459	+	0.955972i	$0.405194\pi$
$878$	3.51267	0.118547
$879$	25.4673	0.858989
$880$	0	0
$881$	37.7831	1.27294	0.636472	−	0.771299i	$-0.280393\pi$
$881$	37.7831	1.27294	0.636472	+	0.771299i	$0.280393\pi$
$882$	−3.44177	−0.115890
$883$	−14.1483	−0.476130	−0.238065	−	0.971249i	$-0.576513\pi$
$883$	−14.1483	−0.476130	−0.238065	+	0.971249i	$0.576513\pi$
$884$	17.6415	0.593349
$885$	0	0
$886$	6.12312	0.205710
$887$	28.0464	0.941705	0.470852	−	0.882212i	$-0.343946\pi$
$887$	28.0464	0.941705	0.470852	+	0.882212i	$0.343946\pi$
$888$	12.3457	0.414294
$889$	65.0059	2.18023
$890$	0	0
$891$	13.3950	0.448748
$892$	−7.64759	−0.256060
$893$	46.8040	1.56624
$894$	4.08350	0.136573
$895$	0	0
$896$	29.5731	0.987969
$897$	−22.0751	−0.737066
$898$	−0.0406296	−0.00135583
$899$	7.67038	0.255821
$900$	0	0
$901$	−10.0700	−0.335482
$902$	2.75214	0.0916363
$903$	9.06913	0.301802
$904$	−6.86328	−0.228269
$905$	0	0
$906$	−6.46205	−0.214687
$907$	−21.2010	−0.703969	−0.351984	−	0.936006i	$-0.614493\pi$
$907$	−21.2010	−0.703969	−0.351984	+	0.936006i	$0.614493\pi$
$908$	0.938787	0.0311548
$909$	−10.1670	−0.337219
$910$	0	0
$911$	−9.34808	−0.309716	−0.154858	−	0.987937i	$-0.549492\pi$
$911$	−9.34808	−0.309716	−0.154858	+	0.987937i	$0.549492\pi$
$912$	23.9827	0.794148
$913$	33.6201	1.11266
$914$	3.26341	0.107944
$915$	0	0
$916$	27.2074	0.898958
$917$	15.2668	0.504153
$918$	−2.43274	−0.0802925
$919$	−26.7315	−0.881790	−0.440895	−	0.897559i	$-0.645339\pi$
$919$	−26.7315	−0.881790	−0.440895	+	0.897559i	$0.645339\pi$
$920$	0	0
$921$	16.3779	0.539669
$922$	7.02451	0.231340
$923$	−59.5235	−1.95924
$924$	42.0583	1.38362
$925$	0	0
$926$	−0.137336	−0.00451316
$927$	−25.4252	−0.835074
$928$	10.4129	0.341820
$929$	−41.8736	−1.37383	−0.686915	−	0.726738i	$-0.741035\pi$
$929$	−41.8736	−1.37383	−0.686915	+	0.726738i	$0.741035\pi$
$930$	0	0
$931$	−58.6661	−1.92270
$932$	35.8230	1.17342
$933$	−26.1624	−0.856518
$934$	−3.86150	−0.126352
$935$	0	0
$936$	5.44311	0.177914
$937$	0.711560	0.0232457	0.0116228	−	0.999932i	$-0.496300\pi$
$937$	0.711560	0.0232457	0.0116228	+	0.999932i	$0.496300\pi$
$938$	−9.44103	−0.308261
$939$	29.2227	0.953648
$940$	0	0
$941$	49.8155	1.62394	0.811970	−	0.583700i	$-0.198395\pi$
$941$	49.8155	1.62394	0.811970	+	0.583700i	$0.198395\pi$
$942$	−1.40084	−0.0456419
$943$	−11.3234	−0.368739
$944$	9.02556	0.293757
$945$	0	0
$946$	−1.36973	−0.0445337
$947$	41.0373	1.33353	0.666766	−	0.745267i	$-0.267678\pi$
$947$	41.0373	1.33353	0.666766	+	0.745267i	$0.267678\pi$
$948$	−12.4324	−0.403786
$949$	66.6185	2.16253
$950$	0	0
$951$	31.6534	1.02643
$952$	−7.42957	−0.240794
$953$	−21.3229	−0.690717	−0.345359	−	0.938471i	$-0.612243\pi$
$953$	−21.3229	−0.690717	−0.345359	+	0.938471i	$0.612243\pi$
$954$	−1.53318	−0.0496385
$955$	0	0
$956$	−30.3714	−0.982281
$957$	19.6527	0.635281
$958$	−5.11897	−0.165387
$959$	81.3481	2.62687
$960$	0	0
$961$	−27.2355	−0.878564
$962$	11.3133	0.364755
$963$	7.78380	0.250830
$964$	1.94835	0.0627520
$965$	0	0
$966$	4.58755	0.147602
$967$	45.7866	1.47240	0.736199	−	0.676765i	$-0.236619\pi$
$967$	45.7866	1.47240	0.736199	+	0.676765i	$0.236619\pi$
$968$	−3.00187	−0.0964838
$969$	−12.3830	−0.397798
$970$	0	0
$971$	31.8832	1.02318	0.511591	−	0.859229i	$-0.329056\pi$
$971$	31.8832	1.02318	0.511591	+	0.859229i	$0.329056\pi$
$972$	23.7703	0.762432
$973$	2.11979	0.0679573
$974$	−3.84639	−0.123246
$975$	0	0
$976$	−18.7997	−0.601765
$977$	4.09437	0.130990	0.0654952	−	0.997853i	$-0.479137\pi$
$977$	4.09437	0.130990	0.0654952	+	0.997853i	$0.479137\pi$
$978$	5.83350	0.186535
$979$	−34.6943	−1.10883
$980$	0	0
$981$	11.5631	0.369182
$982$	3.38589	0.108048
$983$	−3.78443	−0.120705	−0.0603523	−	0.998177i	$-0.519222\pi$
$983$	−3.78443	−0.120705	−0.0603523	+	0.998177i	$0.519222\pi$
$984$	−3.76562	−0.120044
$985$	0	0
$986$	−1.71311	−0.0545564
$987$	−53.9102	−1.71598
$988$	45.7829	1.45655
$989$	5.63558	0.179201
$990$	0	0
$991$	18.4592	0.586375	0.293188	−	0.956055i	$-0.405284\pi$
$991$	18.4592	0.586375	0.293188	+	0.956055i	$0.405284\pi$
$992$	5.11049	0.162258
$993$	−3.38959	−0.107565
$994$	12.3699	0.392350
$995$	0	0
$996$	−22.6995	−0.719260
$997$	33.7309	1.06827	0.534134	−	0.845400i	$-0.320638\pi$
$997$	33.7309	1.06827	0.534134	+	0.845400i	$0.320638\pi$
$998$	−6.71536	−0.212571
$999$	58.8470	1.86184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.i.1.9		15
5.4	even	2		1205.2.a.c.1.7	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.7	✓	15	5.4	even	2
6025.2.a.i.1.9		15	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)

\(f(q)\)	\(=\)	\(q+0.227272 q^{2} -1.31252 q^{3} -1.94835 q^{4} -0.298298 q^{6} -4.34237 q^{7} -0.897348 q^{8} -1.27730 q^{9} +O(q^{10})\)	\(q+0.227272 q^{2} -1.31252 q^{3} -1.94835 q^{4} -0.298298 q^{6} -4.34237 q^{7} -0.897348 q^{8} -1.27730 q^{9} -3.78752 q^{11} +2.55724 q^{12} +4.74890 q^{13} -0.986897 q^{14} +3.69275 q^{16} -1.90667 q^{17} -0.290294 q^{18} -4.94816 q^{19} +5.69943 q^{21} -0.860795 q^{22} +3.54164 q^{23} +1.17778 q^{24} +1.07929 q^{26} +5.61403 q^{27} +8.46044 q^{28} +3.95333 q^{29} +1.94023 q^{31} +2.63395 q^{32} +4.97118 q^{33} -0.433333 q^{34} +2.48862 q^{36} +10.4821 q^{37} -1.12458 q^{38} -6.23302 q^{39} -3.19721 q^{41} +1.29532 q^{42} +1.59123 q^{43} +7.37940 q^{44} +0.804915 q^{46} -9.45887 q^{47} -4.84680 q^{48} +11.8561 q^{49} +2.50254 q^{51} -9.25252 q^{52} +5.28147 q^{53} +1.27591 q^{54} +3.89661 q^{56} +6.49454 q^{57} +0.898480 q^{58} +2.44413 q^{59} -5.09098 q^{61} +0.440960 q^{62} +5.54650 q^{63} -6.78688 q^{64} +1.12981 q^{66} +9.56638 q^{67} +3.71486 q^{68} -4.64846 q^{69} -12.5342 q^{71} +1.14618 q^{72} +14.0282 q^{73} +2.38229 q^{74} +9.64074 q^{76} +16.4468 q^{77} -1.41659 q^{78} -4.86166 q^{79} -3.53661 q^{81} -0.726636 q^{82} -8.87655 q^{83} -11.1045 q^{84} +0.361643 q^{86} -5.18881 q^{87} +3.39872 q^{88} +9.16017 q^{89} -20.6215 q^{91} -6.90034 q^{92} -2.54659 q^{93} -2.14973 q^{94} -3.45711 q^{96} -5.17578 q^{97} +2.69457 q^{98} +4.83779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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