LMFDB - Embedded newform 6025.2.a.i.1.4

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			1.4
Root			$1.92974$ 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)

$f(q)$	$=$	$q-1.92974 q^{2} -0.860854 q^{3} +1.72391 q^{4} +1.66123 q^{6} +4.27878 q^{7} +0.532780 q^{8} -2.25893 q^{9} +O(q^{10})$	\(q-1.92974 q^{2} -0.860854 q^{3} +1.72391 q^{4} +1.66123 q^{6} +4.27878 q^{7} +0.532780 q^{8} -2.25893 q^{9} -4.15941 q^{11} -1.48404 q^{12} -1.01359 q^{13} -8.25696 q^{14} -4.47595 q^{16} -5.08984 q^{17} +4.35916 q^{18} -0.226708 q^{19} -3.68341 q^{21} +8.02659 q^{22} +2.25775 q^{23} -0.458646 q^{24} +1.95598 q^{26} +4.52717 q^{27} +7.37624 q^{28} -0.0980765 q^{29} +5.03981 q^{31} +7.57188 q^{32} +3.58064 q^{33} +9.82208 q^{34} -3.89420 q^{36} +1.95298 q^{37} +0.437489 q^{38} +0.872557 q^{39} +1.64124 q^{41} +7.10804 q^{42} +10.2371 q^{43} -7.17045 q^{44} -4.35688 q^{46} -9.73665 q^{47} +3.85314 q^{48} +11.3080 q^{49} +4.38161 q^{51} -1.74735 q^{52} +8.87850 q^{53} -8.73628 q^{54} +2.27965 q^{56} +0.195163 q^{57} +0.189262 q^{58} -12.3589 q^{59} +5.46892 q^{61} -9.72554 q^{62} -9.66547 q^{63} -5.65989 q^{64} -6.90973 q^{66} +5.19583 q^{67} -8.77443 q^{68} -1.94359 q^{69} +2.82517 q^{71} -1.20351 q^{72} -12.6670 q^{73} -3.76874 q^{74} -0.390825 q^{76} -17.7972 q^{77} -1.68381 q^{78} -6.82909 q^{79} +2.87955 q^{81} -3.16717 q^{82} -0.598091 q^{83} -6.34987 q^{84} -19.7551 q^{86} +0.0844295 q^{87} -2.21605 q^{88} +4.03281 q^{89} -4.33695 q^{91} +3.89216 q^{92} -4.33854 q^{93} +18.7892 q^{94} -6.51829 q^{96} +6.64220 q^{97} -21.8215 q^{98} +9.39581 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.92974	−1.36453	−0.682267	−	0.731103i	$-0.739006\pi$
$2$	−1.92974	−1.36453	−0.682267	+	0.731103i	$0.739006\pi$
$3$	−0.860854	−0.497014	−0.248507	−	0.968630i	$-0.579940\pi$
$3$	−0.860854	−0.497014	−0.248507	+	0.968630i	$0.579940\pi$
$4$	1.72391	0.861956
$5$	0	0
$5$	0	0
$6$	1.66123	0.678194
$7$	4.27878	1.61723	0.808614	−	0.588339i	$-0.200218\pi$
$7$	4.27878	1.61723	0.808614	+	0.588339i	$0.200218\pi$
$8$	0.532780	0.188366
$9$	−2.25893	−0.752977
$10$	0	0
$11$	−4.15941	−1.25411	−0.627054	−	0.778976i	$-0.715740\pi$
$11$	−4.15941	−1.25411	−0.627054	+	0.778976i	$0.715740\pi$
$12$	−1.48404	−0.428404
$13$	−1.01359	−0.281120	−0.140560	−	0.990072i	$-0.544890\pi$
$13$	−1.01359	−0.281120	−0.140560	+	0.990072i	$0.544890\pi$
$14$	−8.25696	−2.20676
$15$	0	0
$16$	−4.47595	−1.11899
$17$	−5.08984	−1.23447	−0.617234	−	0.786780i	$-0.711747\pi$
$17$	−5.08984	−1.23447	−0.617234	+	0.786780i	$0.711747\pi$
$18$	4.35916	1.02746
$19$	−0.226708	−0.0520105	−0.0260052	−	0.999662i	$-0.508279\pi$
$19$	−0.226708	−0.0520105	−0.0260052	+	0.999662i	$0.508279\pi$
$20$	0	0
$21$	−3.68341	−0.803786
$22$	8.02659	1.71128
$23$	2.25775	0.470773	0.235387	−	0.971902i	$-0.424364\pi$
$23$	2.25775	0.470773	0.235387	+	0.971902i	$0.424364\pi$
$24$	−0.458646	−0.0936208
$25$	0	0
$26$	1.95598	0.383599
$27$	4.52717	0.871255
$28$	7.37624	1.39398
$29$	−0.0980765	−0.0182123	−0.00910617	−	0.999959i	$-0.502899\pi$
$29$	−0.0980765	−0.0182123	−0.00910617	+	0.999959i	$0.502899\pi$
$30$	0	0
$31$	5.03981	0.905176	0.452588	−	0.891720i	$-0.350501\pi$
$31$	5.03981	0.905176	0.452588	+	0.891720i	$0.350501\pi$
$32$	7.57188	1.33853
$33$	3.58064	0.623310
$34$	9.82208	1.68447
$35$	0	0
$36$	−3.89420	−0.649033
$37$	1.95298	0.321067	0.160534	−	0.987030i	$-0.448678\pi$
$37$	1.95298	0.321067	0.160534	+	0.987030i	$0.448678\pi$
$38$	0.437489	0.0709701
$39$	0.872557	0.139721
$40$	0	0
$41$	1.64124	0.256318	0.128159	−	0.991754i	$-0.459093\pi$
$41$	1.64124	0.256318	0.128159	+	0.991754i	$0.459093\pi$
$42$	7.10804	1.09679
$43$	10.2371	1.56115	0.780575	−	0.625063i	$-0.214927\pi$
$43$	10.2371	1.56115	0.780575	+	0.625063i	$0.214927\pi$
$44$	−7.17045	−1.08099
$45$	0	0
$46$	−4.35688	−0.642386
$47$	−9.73665	−1.42024	−0.710118	−	0.704082i	$-0.751359\pi$
$47$	−9.73665	−1.42024	−0.710118	+	0.704082i	$0.751359\pi$
$48$	3.85314	0.556153
$49$	11.3080	1.61543
$50$	0	0
$51$	4.38161	0.613548
$52$	−1.74735	−0.242313
$53$	8.87850	1.21956	0.609778	−	0.792573i	$-0.291259\pi$
$53$	8.87850	1.21956	0.609778	+	0.792573i	$0.291259\pi$
$54$	−8.73628	−1.18886
$55$	0	0
$56$	2.27965	0.304631
$57$	0.195163	0.0258499
$58$	0.189262	0.0248514
$59$	−12.3589	−1.60899	−0.804495	−	0.593959i	$-0.797564\pi$
$59$	−12.3589	−1.60899	−0.804495	+	0.593959i	$0.797564\pi$
$60$	0	0
$61$	5.46892	0.700223	0.350112	−	0.936708i	$-0.386144\pi$
$61$	5.46892	0.700223	0.350112	+	0.936708i	$0.386144\pi$
$62$	−9.72554	−1.23514
$63$	−9.66547	−1.21774
$64$	−5.65989	−0.707486
$65$	0	0
$66$	−6.90973	−0.850528
$67$	5.19583	0.634772	0.317386	−	0.948296i	$-0.397195\pi$
$67$	5.19583	0.634772	0.317386	+	0.948296i	$0.397195\pi$
$68$	−8.77443	−1.06406
$69$	−1.94359	−0.233981
$70$	0	0
$71$	2.82517	0.335287	0.167643	−	0.985848i	$-0.446384\pi$
$71$	2.82517	0.335287	0.167643	+	0.985848i	$0.446384\pi$
$72$	−1.20351	−0.141835
$73$	−12.6670	−1.48256	−0.741280	−	0.671195i	$-0.765781\pi$
$73$	−12.6670	−1.48256	−0.741280	+	0.671195i	$0.765781\pi$
$74$	−3.76874	−0.438108
$75$	0	0
$76$	−0.390825	−0.0448307
$77$	−17.7972	−2.02818
$78$	−1.68381	−0.190654
$79$	−6.82909	−0.768333	−0.384167	−	0.923264i	$-0.625511\pi$
$79$	−6.82909	−0.768333	−0.384167	+	0.923264i	$0.625511\pi$
$80$	0	0
$81$	2.87955	0.319950
$82$	−3.16717	−0.349755
$83$	−0.598091	−0.0656491	−0.0328245	−	0.999461i	$-0.510450\pi$
$83$	−0.598091	−0.0656491	−0.0328245	+	0.999461i	$0.510450\pi$
$84$	−6.34987	−0.692828
$85$	0	0
$86$	−19.7551	−2.13024
$87$	0.0844295	0.00905180
$88$	−2.21605	−0.236232
$89$	4.03281	0.427477	0.213739	−	0.976891i	$-0.431436\pi$
$89$	4.03281	0.427477	0.213739	+	0.976891i	$0.431436\pi$
$90$	0	0
$91$	−4.33695	−0.454636
$92$	3.89216	0.405786
$93$	−4.33854	−0.449886
$94$	18.7892	1.93796
$95$	0	0
$96$	−6.51829	−0.665270
$97$	6.64220	0.674413	0.337207	−	0.941431i	$-0.390518\pi$
$97$	6.64220	0.674413	0.337207	+	0.941431i	$0.390518\pi$
$98$	−21.8215	−2.20431
$99$	9.39581	0.944315
$100$	0	0
$101$	0.208478	0.0207443	0.0103722	−	0.999946i	$-0.496698\pi$
$101$	0.208478	0.0207443	0.0103722	+	0.999946i	$0.496698\pi$
$102$	−8.45538	−0.837208
$103$	2.18940	0.215728	0.107864	−	0.994166i	$-0.465599\pi$
$103$	2.18940	0.215728	0.107864	+	0.994166i	$0.465599\pi$
$104$	−0.540023	−0.0529536
$105$	0	0
$106$	−17.1332	−1.66413
$107$	13.9628	1.34983	0.674916	−	0.737895i	$-0.264180\pi$
$107$	13.9628	1.34983	0.674916	+	0.737895i	$0.264180\pi$
$108$	7.80444	0.750983
$109$	−16.7010	−1.59967	−0.799833	−	0.600222i	$-0.795079\pi$
$109$	−16.7010	−1.59967	−0.799833	+	0.600222i	$0.795079\pi$
$110$	0	0
$111$	−1.68123	−0.159575
$112$	−19.1516	−1.80966
$113$	−14.9373	−1.40518	−0.702592	−	0.711593i	$-0.747974\pi$
$113$	−14.9373	−1.40518	−0.702592	+	0.711593i	$0.747974\pi$
$114$	−0.376614	−0.0352732
$115$	0	0
$116$	−0.169075	−0.0156982
$117$	2.28964	0.211677
$118$	23.8495	2.19552
$119$	−21.7783	−1.99642
$120$	0	0
$121$	6.30067	0.572788
$122$	−10.5536	−0.955479
$123$	−1.41287	−0.127394
$124$	8.68818	0.780222
$125$	0	0
$126$	18.6519	1.66164
$127$	7.99709	0.709627	0.354813	−	0.934937i	$-0.384544\pi$
$127$	7.99709	0.709627	0.354813	+	0.934937i	$0.384544\pi$
$128$	−4.22163	−0.373143
$129$	−8.81269	−0.775914
$130$	0	0
$131$	1.04129	0.0909775	0.0454887	−	0.998965i	$-0.485515\pi$
$131$	1.04129	0.0909775	0.0454887	+	0.998965i	$0.485515\pi$
$132$	6.17271	0.537266
$133$	−0.970036	−0.0841128
$134$	−10.0266	−0.866168
$135$	0	0
$136$	−2.71177	−0.232532
$137$	−0.348409	−0.0297666	−0.0148833	−	0.999889i	$-0.504738\pi$
$137$	−0.348409	−0.0297666	−0.0148833	+	0.999889i	$0.504738\pi$
$138$	3.75064	0.319275
$139$	0.755352	0.0640681	0.0320340	−	0.999487i	$-0.489802\pi$
$139$	0.755352	0.0640681	0.0320340	+	0.999487i	$0.489802\pi$
$140$	0	0
$141$	8.38184	0.705878
$142$	−5.45186	−0.457510
$143$	4.21595	0.352555
$144$	10.1109	0.842572
$145$	0	0
$146$	24.4441	2.02301
$147$	−9.73453	−0.802891
$148$	3.36676	0.276746
$149$	−17.7229	−1.45192	−0.725958	−	0.687739i	$-0.758604\pi$
$149$	−17.7229	−1.45192	−0.725958	+	0.687739i	$0.758604\pi$
$150$	0	0
$151$	7.38376	0.600882	0.300441	−	0.953800i	$-0.402866\pi$
$151$	7.38376	0.600882	0.300441	+	0.953800i	$0.402866\pi$
$152$	−0.120786	−0.00979702
$153$	11.4976	0.929525
$154$	34.3441	2.76752
$155$	0	0
$156$	1.50421	0.120433
$157$	−2.53136	−0.202024	−0.101012	−	0.994885i	$-0.532208\pi$
$157$	−2.53136	−0.202024	−0.101012	+	0.994885i	$0.532208\pi$
$158$	13.1784	1.04842
$159$	−7.64309	−0.606137
$160$	0	0
$161$	9.66042	0.761348
$162$	−5.55680	−0.436584
$163$	5.60586	0.439085	0.219543	−	0.975603i	$-0.429544\pi$
$163$	5.60586	0.439085	0.219543	+	0.975603i	$0.429544\pi$
$164$	2.82935	0.220935
$165$	0	0
$166$	1.15416	0.0895804
$167$	14.9994	1.16069	0.580344	−	0.814372i	$-0.302918\pi$
$167$	14.9994	1.16069	0.580344	+	0.814372i	$0.302918\pi$
$168$	−1.96245	−0.151406
$169$	−11.9726	−0.920971
$170$	0	0
$171$	0.512118	0.0391627
$172$	17.6479	1.34564
$173$	14.1212	1.07362	0.536808	−	0.843704i	$-0.319630\pi$
$173$	14.1212	1.07362	0.536808	+	0.843704i	$0.319630\pi$
$174$	−0.162927	−0.0123515
$175$	0	0
$176$	18.6173	1.40333
$177$	10.6392	0.799692
$178$	−7.78229	−0.583307
$179$	−23.0755	−1.72474	−0.862372	−	0.506275i	$-0.831022\pi$
$179$	−23.0755	−1.72474	−0.862372	+	0.506275i	$0.831022\pi$
$180$	0	0
$181$	−13.2453	−0.984517	−0.492258	−	0.870449i	$-0.663829\pi$
$181$	−13.2453	−0.984517	−0.492258	+	0.870449i	$0.663829\pi$
$182$	8.36920	0.620366
$183$	−4.70794	−0.348021
$184$	1.20288	0.0886778
$185$	0	0
$186$	8.37227	0.613885
$187$	21.1707	1.54816
$188$	−16.7851	−1.22418
$189$	19.3708	1.40902
$190$	0	0
$191$	21.9302	1.58681	0.793406	−	0.608693i	$-0.208306\pi$
$191$	21.9302	1.58681	0.793406	+	0.608693i	$0.208306\pi$
$192$	4.87234	0.351631
$193$	−20.0677	−1.44450	−0.722252	−	0.691630i	$-0.756893\pi$
$193$	−20.0677	−1.44450	−0.722252	+	0.691630i	$0.756893\pi$
$194$	−12.8177	−0.920260
$195$	0	0
$196$	19.4940	1.39243
$197$	−15.4880	−1.10348	−0.551738	−	0.834017i	$-0.686035\pi$
$197$	−15.4880	−1.10348	−0.551738	+	0.834017i	$0.686035\pi$
$198$	−18.1315	−1.28855
$199$	−12.6164	−0.894354	−0.447177	−	0.894445i	$-0.647571\pi$
$199$	−12.6164	−0.894354	−0.447177	+	0.894445i	$0.647571\pi$
$200$	0	0
$201$	−4.47285	−0.315491
$202$	−0.402309	−0.0283063
$203$	−0.419648	−0.0294535
$204$	7.55350	0.528851
$205$	0	0
$206$	−4.22498	−0.294368
$207$	−5.10010	−0.354481
$208$	4.53680	0.314570
$209$	0.942972	0.0652268
$210$	0	0
$211$	15.4401	1.06294	0.531470	−	0.847077i	$-0.321640\pi$
$211$	15.4401	1.06294	0.531470	+	0.847077i	$0.321640\pi$
$212$	15.3057	1.05120
$213$	−2.43206	−0.166642
$214$	−26.9446	−1.84189
$215$	0	0
$216$	2.41199	0.164115
$217$	21.5643	1.46388
$218$	32.2287	2.18280
$219$	10.9044	0.736854
$220$	0	0
$221$	5.15903	0.347034
$222$	3.24434	0.217746
$223$	−4.61995	−0.309375	−0.154687	−	0.987963i	$-0.549437\pi$
$223$	−4.61995	−0.309375	−0.154687	+	0.987963i	$0.549437\pi$
$224$	32.3984	2.16471
$225$	0	0
$226$	28.8252	1.91742
$227$	−15.7557	−1.04574	−0.522870	−	0.852413i	$-0.675139\pi$
$227$	−15.7557	−1.04574	−0.522870	+	0.852413i	$0.675139\pi$
$228$	0.336443	0.0222815
$229$	10.3167	0.681744	0.340872	−	0.940110i	$-0.389278\pi$
$229$	10.3167	0.681744	0.340872	+	0.940110i	$0.389278\pi$
$230$	0	0
$231$	15.3208	1.00803
$232$	−0.0522532	−0.00343059
$233$	28.7950	1.88642	0.943210	−	0.332197i	$-0.107790\pi$
$233$	28.7950	1.88642	0.943210	+	0.332197i	$0.107790\pi$
$234$	−4.41841	−0.288841
$235$	0	0
$236$	−21.3056	−1.38688
$237$	5.87885	0.381873
$238$	42.0266	2.72418
$239$	2.11916	0.137077	0.0685385	−	0.997648i	$-0.478166\pi$
$239$	2.11916	0.137077	0.0685385	+	0.997648i	$0.478166\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−12.1587	−0.781590
$243$	−16.0604	−1.03027
$244$	9.42793	0.603561
$245$	0	0
$246$	2.72647	0.173833
$247$	0.229790	0.0146212
$248$	2.68511	0.170505
$249$	0.514869	0.0326285
$250$	0	0
$251$	14.7992	0.934116	0.467058	−	0.884227i	$-0.345314\pi$
$251$	14.7992	0.934116	0.467058	+	0.884227i	$0.345314\pi$
$252$	−16.6624	−1.04963
$253$	−9.39090	−0.590401
$254$	−15.4323	−0.968310
$255$	0	0
$256$	19.4664	1.21665
$257$	−3.44087	−0.214635	−0.107318	−	0.994225i	$-0.534226\pi$
$257$	−3.44087	−0.214635	−0.107318	+	0.994225i	$0.534226\pi$
$258$	17.0062	1.05876
$259$	8.35636	0.519239
$260$	0	0
$261$	0.221548	0.0137135
$262$	−2.00941	−0.124142
$263$	−15.0960	−0.930856	−0.465428	−	0.885086i	$-0.654100\pi$
$263$	−15.0960	−0.930856	−0.465428	+	0.885086i	$0.654100\pi$
$264$	1.90770	0.117411
$265$	0	0
$266$	1.87192	0.114775
$267$	−3.47166	−0.212462
$268$	8.95715	0.547145
$269$	−19.7140	−1.20198	−0.600990	−	0.799256i	$-0.705227\pi$
$269$	−19.7140	−1.20198	−0.600990	+	0.799256i	$0.705227\pi$
$270$	0	0
$271$	6.40136	0.388855	0.194427	−	0.980917i	$-0.437715\pi$
$271$	6.40136	0.388855	0.194427	+	0.980917i	$0.437715\pi$
$272$	22.7819	1.38135
$273$	3.73348	0.225961
$274$	0.672341	0.0406176
$275$	0	0
$276$	−3.35058	−0.201681
$277$	−0.0900030	−0.00540775	−0.00270388	−	0.999996i	$-0.500861\pi$
$277$	−0.0900030	−0.00540775	−0.00270388	+	0.999996i	$0.500861\pi$
$278$	−1.45763	−0.0874231
$279$	−11.3846	−0.681577
$280$	0	0
$281$	−32.2937	−1.92648	−0.963241	−	0.268639i	$-0.913426\pi$
$281$	−32.2937	−1.92648	−0.963241	+	0.268639i	$0.913426\pi$
$282$	−16.1748	−0.963196
$283$	20.5936	1.22416	0.612082	−	0.790794i	$-0.290332\pi$
$283$	20.5936	1.22416	0.612082	+	0.790794i	$0.290332\pi$
$284$	4.87035	0.289002
$285$	0	0
$286$	−8.13570	−0.481074
$287$	7.02250	0.414525
$288$	−17.1043	−1.00788
$289$	8.90645	0.523909
$290$	0	0
$291$	−5.71797	−0.335193
$292$	−21.8368	−1.27790
$293$	−30.9657	−1.80904	−0.904519	−	0.426433i	$-0.859770\pi$
$293$	−30.9657	−1.80904	−0.904519	+	0.426433i	$0.859770\pi$
$294$	18.7852	1.09557
$295$	0	0
$296$	1.04051	0.0604782
$297$	−18.8304	−1.09265
$298$	34.2007	1.98119
$299$	−2.28844	−0.132344
$300$	0	0
$301$	43.8025	2.52474
$302$	−14.2488	−0.819924
$303$	−0.179469	−0.0103102
$304$	1.01474	0.0581991
$305$	0	0
$306$	−22.1874	−1.26837
$307$	5.68955	0.324720	0.162360	−	0.986732i	$-0.448089\pi$
$307$	5.68955	0.324720	0.162360	+	0.986732i	$0.448089\pi$
$308$	−30.6808	−1.74820
$309$	−1.88475	−0.107220
$310$	0	0
$311$	10.2738	0.582571	0.291285	−	0.956636i	$-0.405917\pi$
$311$	10.2738	0.582571	0.291285	+	0.956636i	$0.405917\pi$
$312$	0.464881	0.0263187
$313$	6.76087	0.382147	0.191074	−	0.981576i	$-0.438803\pi$
$313$	6.76087	0.382147	0.191074	+	0.981576i	$0.438803\pi$
$314$	4.88487	0.275669
$315$	0	0
$316$	−11.7728	−0.662269
$317$	−13.1784	−0.740175	−0.370088	−	0.928997i	$-0.620672\pi$
$317$	−13.1784	−0.740175	−0.370088	+	0.928997i	$0.620672\pi$
$318$	14.7492	0.827095
$319$	0.407940	0.0228403
$320$	0	0
$321$	−12.0199	−0.670886
$322$	−18.6421	−1.03889
$323$	1.15391	0.0642052
$324$	4.96410	0.275783
$325$	0	0
$326$	−10.8179	−0.599147
$327$	14.3771	0.795057
$328$	0.874419	0.0482817
$329$	−41.6610	−2.29685
$330$	0	0
$331$	−27.3929	−1.50565	−0.752824	−	0.658222i	$-0.771309\pi$
$331$	−27.3929	−1.50565	−0.752824	+	0.658222i	$0.771309\pi$
$332$	−1.03106	−0.0565866
$333$	−4.41164	−0.241756
$334$	−28.9450	−1.58380
$335$	0	0
$336$	16.4868	0.899427
$337$	−0.450778	−0.0245554	−0.0122777	−	0.999925i	$-0.503908\pi$
$337$	−0.450778	−0.0245554	−0.0122777	+	0.999925i	$0.503908\pi$
$338$	23.1041	1.25670
$339$	12.8589	0.698397
$340$	0	0
$341$	−20.9626	−1.13519
$342$	−0.988257	−0.0534388
$343$	18.4330	0.995287
$344$	5.45415	0.294068
$345$	0	0
$346$	−27.2503	−1.46499
$347$	−11.8401	−0.635610	−0.317805	−	0.948156i	$-0.602946\pi$
$347$	−11.8401	−0.635610	−0.317805	+	0.948156i	$0.602946\pi$
$348$	0.145549	0.00780225
$349$	16.6656	0.892087	0.446044	−	0.895011i	$-0.352833\pi$
$349$	16.6656	0.892087	0.446044	+	0.895011i	$0.352833\pi$
$350$	0	0
$351$	−4.58871	−0.244927
$352$	−31.4945	−1.67866
$353$	−23.4430	−1.24775	−0.623873	−	0.781526i	$-0.714442\pi$
$353$	−23.4430	−1.24775	−0.623873	+	0.781526i	$0.714442\pi$
$354$	−20.5309	−1.09121
$355$	0	0
$356$	6.95221	0.368466
$357$	18.7480	0.992247
$358$	44.5298	2.35347
$359$	−20.3446	−1.07375	−0.536875	−	0.843662i	$-0.680395\pi$
$359$	−20.3446	−1.07375	−0.536875	+	0.843662i	$0.680395\pi$
$360$	0	0
$361$	−18.9486	−0.997295
$362$	25.5601	1.34341
$363$	−5.42396	−0.284684
$364$	−7.47652	−0.391876
$365$	0	0
$366$	9.08512	0.474887
$367$	−33.0454	−1.72495	−0.862477	−	0.506096i	$-0.831088\pi$
$367$	−33.0454	−1.72495	−0.862477	+	0.506096i	$0.831088\pi$
$368$	−10.1056	−0.526790
$369$	−3.70744	−0.193002
$370$	0	0
$371$	37.9892	1.97230
$372$	−7.47926	−0.387782
$373$	−24.2843	−1.25740	−0.628698	−	0.777650i	$-0.716412\pi$
$373$	−24.2843	−1.25740	−0.628698	+	0.777650i	$0.716412\pi$
$374$	−40.8541	−2.11251
$375$	0	0
$376$	−5.18750	−0.267525
$377$	0.0994097	0.00511986
$378$	−37.3807	−1.92265
$379$	−26.0547	−1.33834	−0.669170	−	0.743110i	$-0.733350\pi$
$379$	−26.0547	−1.33834	−0.669170	+	0.743110i	$0.733350\pi$
$380$	0	0
$381$	−6.88433	−0.352695
$382$	−42.3196	−2.16526
$383$	−23.6290	−1.20738	−0.603692	−	0.797218i	$-0.706304\pi$
$383$	−23.6290	−1.20738	−0.603692	+	0.797218i	$0.706304\pi$
$384$	3.63421	0.185457
$385$	0	0
$386$	38.7255	1.97108
$387$	−23.1250	−1.17551
$388$	11.4506	0.581314
$389$	25.6016	1.29805	0.649026	−	0.760766i	$-0.275176\pi$
$389$	25.6016	1.29805	0.649026	+	0.760766i	$0.275176\pi$
$390$	0	0
$391$	−11.4916	−0.581154
$392$	6.02468	0.304292
$393$	−0.896395	−0.0452171
$394$	29.8879	1.50573
$395$	0	0
$396$	16.1975	0.813957
$397$	−3.25969	−0.163599	−0.0817996	−	0.996649i	$-0.526067\pi$
$397$	−3.25969	−0.163599	−0.0817996	+	0.996649i	$0.526067\pi$
$398$	24.3465	1.22038
$399$	0.835060	0.0418053
$400$	0	0
$401$	−27.9043	−1.39347	−0.696736	−	0.717327i	$-0.745365\pi$
$401$	−27.9043	−1.39347	−0.696736	+	0.717327i	$0.745365\pi$
$402$	8.63146	0.430498
$403$	−5.10832	−0.254463
$404$	0.359397	0.0178807
$405$	0	0
$406$	0.809813	0.0401904
$407$	−8.12322	−0.402653
$408$	2.33443	0.115572
$409$	2.75895	0.136421	0.0682107	−	0.997671i	$-0.478271\pi$
$409$	2.75895	0.136421	0.0682107	+	0.997671i	$0.478271\pi$
$410$	0	0
$411$	0.299930	0.0147944
$412$	3.77433	0.185948
$413$	−52.8810	−2.60211
$414$	9.84188	0.483702
$415$	0	0
$416$	−7.67481	−0.376289
$417$	−0.650248	−0.0318428
$418$	−1.81970	−0.0890042
$419$	6.53907	0.319454	0.159727	−	0.987161i	$-0.448939\pi$
$419$	6.53907	0.319454	0.159727	+	0.987161i	$0.448939\pi$
$420$	0	0
$421$	−19.0767	−0.929741	−0.464871	−	0.885379i	$-0.653899\pi$
$421$	−19.0767	−0.929741	−0.464871	+	0.885379i	$0.653899\pi$
$422$	−29.7954	−1.45042
$423$	21.9944	1.06941
$424$	4.73029	0.229723
$425$	0	0
$426$	4.69326	0.227389
$427$	23.4003	1.13242
$428$	24.0706	1.16349
$429$	−3.62932	−0.175225
$430$	0	0
$431$	12.2304	0.589117	0.294559	−	0.955633i	$-0.404827\pi$
$431$	12.2304	0.589117	0.294559	+	0.955633i	$0.404827\pi$
$432$	−20.2634	−0.974924
$433$	36.0938	1.73456	0.867278	−	0.497824i	$-0.165868\pi$
$433$	36.0938	1.73456	0.867278	+	0.497824i	$0.165868\pi$
$434$	−41.6135	−1.99751
$435$	0	0
$436$	−28.7911	−1.37884
$437$	−0.511850	−0.0244851
$438$	−21.0428	−1.00546
$439$	22.7319	1.08494	0.542468	−	0.840077i	$-0.317490\pi$
$439$	22.7319	1.08494	0.542468	+	0.840077i	$0.317490\pi$
$440$	0	0
$441$	−25.5440	−1.21638
$442$	−9.95560	−0.473540
$443$	35.9263	1.70691	0.853454	−	0.521168i	$-0.174503\pi$
$443$	35.9263	1.70691	0.853454	+	0.521168i	$0.174503\pi$
$444$	−2.89829	−0.137547
$445$	0	0
$446$	8.91531	0.422152
$447$	15.2568	0.721624
$448$	−24.2174	−1.14417
$449$	32.4537	1.53159	0.765793	−	0.643088i	$-0.222347\pi$
$449$	32.4537	1.53159	0.765793	+	0.643088i	$0.222347\pi$
$450$	0	0
$451$	−6.82658	−0.321451
$452$	−25.7506	−1.21121
$453$	−6.35634	−0.298647
$454$	30.4044	1.42695
$455$	0	0
$456$	0.103979	0.00486926
$457$	19.2139	0.898787	0.449394	−	0.893334i	$-0.351640\pi$
$457$	19.2139	0.898787	0.449394	+	0.893334i	$0.351640\pi$
$458$	−19.9085	−0.930263
$459$	−23.0426	−1.07554
$460$	0	0
$461$	−39.6176	−1.84517	−0.922587	−	0.385789i	$-0.873929\pi$
$461$	−39.6176	−1.84517	−0.922587	+	0.385789i	$0.873929\pi$
$462$	−29.5652	−1.37550
$463$	9.54990	0.443821	0.221911	−	0.975067i	$-0.428771\pi$
$463$	9.54990	0.443821	0.221911	+	0.975067i	$0.428771\pi$
$464$	0.438986	0.0203794
$465$	0	0
$466$	−55.5669	−2.57409
$467$	15.3884	0.712089	0.356044	−	0.934469i	$-0.384125\pi$
$467$	15.3884	0.712089	0.356044	+	0.934469i	$0.384125\pi$
$468$	3.94713	0.182456
$469$	22.2318	1.02657
$470$	0	0
$471$	2.17913	0.100409
$472$	−6.58457	−0.303080
$473$	−42.5804	−1.95785
$474$	−11.3447	−0.521079
$475$	0	0
$476$	−37.5439	−1.72082
$477$	−20.0559	−0.918297
$478$	−4.08943	−0.187046
$479$	−12.3599	−0.564738	−0.282369	−	0.959306i	$-0.591120\pi$
$479$	−12.3599	−0.564738	−0.282369	+	0.959306i	$0.591120\pi$
$480$	0	0
$481$	−1.97952	−0.0902585
$482$	1.92974	0.0878974
$483$	−8.31621	−0.378401
$484$	10.8618	0.493718
$485$	0	0
$486$	30.9924	1.40585
$487$	−13.2006	−0.598176	−0.299088	−	0.954226i	$-0.596682\pi$
$487$	−13.2006	−0.598176	−0.299088	+	0.954226i	$0.596682\pi$
$488$	2.91373	0.131898
$489$	−4.82583	−0.218232
$490$	0	0
$491$	1.26409	0.0570475	0.0285237	−	0.999593i	$-0.490919\pi$
$491$	1.26409	0.0570475	0.0285237	+	0.999593i	$0.490919\pi$
$492$	−2.43566	−0.109808
$493$	0.499193	0.0224825
$494$	−0.443436	−0.0199511
$495$	0	0
$496$	−22.5579	−1.01288
$497$	12.0883	0.542235
$498$	−0.993566	−0.0445228
$499$	−15.3594	−0.687582	−0.343791	−	0.939046i	$-0.611711\pi$
$499$	−15.3594	−0.687582	−0.343791	+	0.939046i	$0.611711\pi$
$500$	0	0
$501$	−12.9123	−0.576878
$502$	−28.5586	−1.27463
$503$	34.7267	1.54839	0.774194	−	0.632949i	$-0.218156\pi$
$503$	34.7267	1.54839	0.774194	+	0.632949i	$0.218156\pi$
$504$	−5.14957	−0.229380
$505$	0	0
$506$	18.1220	0.805622
$507$	10.3067	0.457736
$508$	13.7863	0.611667
$509$	−1.23400	−0.0546960	−0.0273480	−	0.999626i	$-0.508706\pi$
$509$	−1.23400	−0.0546960	−0.0273480	+	0.999626i	$0.508706\pi$
$510$	0	0
$511$	−54.1994	−2.39764
$512$	−29.1220	−1.28702
$513$	−1.02635	−0.0453144
$514$	6.63999	0.292877
$515$	0	0
$516$	−15.1923	−0.668803
$517$	40.4987	1.78113
$518$	−16.1256	−0.708520
$519$	−12.1563	−0.533603
$520$	0	0
$521$	41.5523	1.82044	0.910219	−	0.414128i	$-0.135913\pi$
$521$	41.5523	1.82044	0.910219	+	0.414128i	$0.135913\pi$
$522$	−0.427531	−0.0187125
$523$	1.16999	0.0511601	0.0255801	−	0.999673i	$-0.491857\pi$
$523$	1.16999	0.0511601	0.0255801	+	0.999673i	$0.491857\pi$
$524$	1.79508	0.0784186
$525$	0	0
$526$	29.1313	1.27019
$527$	−25.6518	−1.11741
$528$	−16.0268	−0.697477
$529$	−17.9026	−0.778373
$530$	0	0
$531$	27.9179	1.21153
$532$	−1.67226	−0.0725015
$533$	−1.66355	−0.0720563
$534$	6.69942	0.289912
$535$	0	0
$536$	2.76824	0.119570
$537$	19.8646	0.857223
$538$	38.0429	1.64014
$539$	−47.0346	−2.02592
$540$	0	0
$541$	13.4142	0.576722	0.288361	−	0.957522i	$-0.406890\pi$
$541$	13.4142	0.576722	0.288361	+	0.957522i	$0.406890\pi$
$542$	−12.3530	−0.530606
$543$	11.4023	0.489319
$544$	−38.5396	−1.65237
$545$	0	0
$546$	−7.20466	−0.308331
$547$	−15.1917	−0.649550	−0.324775	−	0.945791i	$-0.605289\pi$
$547$	−15.1917	−0.649550	−0.324775	+	0.945791i	$0.605289\pi$
$548$	−0.600627	−0.0256575
$549$	−12.3539	−0.527252
$550$	0	0
$551$	0.0222348	0.000947232 0
$552$	−1.03551	−0.0440741
$553$	−29.2202	−1.24257
$554$	0.173683	0.00737907
$555$	0	0
$556$	1.30216	0.0552238
$557$	−39.8802	−1.68978	−0.844888	−	0.534943i	$-0.820333\pi$
$557$	−39.8802	−1.68978	−0.844888	+	0.534943i	$0.820333\pi$
$558$	21.9693	0.930035
$559$	−10.3763	−0.438871
$560$	0	0
$561$	−18.2249	−0.769456
$562$	62.3186	2.62875
$563$	−0.395018	−0.0166480	−0.00832401	−	0.999965i	$-0.502650\pi$
$563$	−0.395018	−0.0166480	−0.00832401	+	0.999965i	$0.502650\pi$
$564$	14.4495	0.608436
$565$	0	0
$566$	−39.7404	−1.67042
$567$	12.3210	0.517433
$568$	1.50520	0.0631567
$569$	0.348736	0.0146198	0.00730989	−	0.999973i	$-0.497673\pi$
$569$	0.348736	0.0146198	0.00730989	+	0.999973i	$0.497673\pi$
$570$	0	0
$571$	42.4391	1.77602	0.888010	−	0.459825i	$-0.152088\pi$
$571$	42.4391	1.77602	0.888010	+	0.459825i	$0.152088\pi$
$572$	7.26792	0.303887
$573$	−18.8787	−0.788668
$574$	−13.5516	−0.565634
$575$	0	0
$576$	12.7853	0.532720
$577$	−12.1367	−0.505257	−0.252628	−	0.967563i	$-0.581295\pi$
$577$	−12.1367	−0.505257	−0.252628	+	0.967563i	$0.581295\pi$
$578$	−17.1872	−0.714892
$579$	17.2754	0.717939
$580$	0	0
$581$	−2.55910	−0.106170
$582$	11.0342	0.457383
$583$	−36.9293	−1.52945
$584$	−6.74873	−0.279264
$585$	0	0
$586$	59.7560	2.46850
$587$	−1.30593	−0.0539013	−0.0269507	−	0.999637i	$-0.508580\pi$
$587$	−1.30593	−0.0539013	−0.0269507	+	0.999637i	$0.508580\pi$
$588$	−16.7815	−0.692056
$589$	−1.14257	−0.0470786
$590$	0	0
$591$	13.3329	0.548444
$592$	−8.74143	−0.359270
$593$	7.46971	0.306744	0.153372	−	0.988169i	$-0.450987\pi$
$593$	7.46971	0.306744	0.153372	+	0.988169i	$0.450987\pi$
$594$	36.3378	1.49096
$595$	0	0
$596$	−30.5527	−1.25149
$597$	10.8609	0.444507
$598$	4.41610	0.180588
$599$	20.9641	0.856569	0.428285	−	0.903644i	$-0.359118\pi$
$599$	20.9641	0.856569	0.428285	+	0.903644i	$0.359118\pi$
$600$	0	0
$601$	−32.4369	−1.32313	−0.661565	−	0.749888i	$-0.730108\pi$
$601$	−32.4369	−1.32313	−0.661565	+	0.749888i	$0.730108\pi$
$602$	−84.5276	−3.44509
$603$	−11.7370	−0.477968
$604$	12.7289	0.517933
$605$	0	0
$606$	0.346329	0.0140687
$607$	−2.08203	−0.0845071	−0.0422536	−	0.999107i	$-0.513454\pi$
$607$	−2.08203	−0.0845071	−0.0422536	+	0.999107i	$0.513454\pi$
$608$	−1.71661	−0.0696177
$609$	0.361256	0.0146388
$610$	0	0
$611$	9.86901	0.399257
$612$	19.8208	0.801209
$613$	18.2956	0.738953	0.369476	−	0.929240i	$-0.379537\pi$
$613$	18.2956	0.738953	0.369476	+	0.929240i	$0.379537\pi$
$614$	−10.9794	−0.443091
$615$	0	0
$616$	−9.48200	−0.382041
$617$	−40.2177	−1.61911	−0.809553	−	0.587047i	$-0.800290\pi$
$617$	−40.2177	−1.61911	−0.809553	+	0.587047i	$0.800290\pi$
$618$	3.63709	0.146305
$619$	−18.5221	−0.744468	−0.372234	−	0.928139i	$-0.621408\pi$
$619$	−18.5221	−0.744468	−0.372234	+	0.928139i	$0.621408\pi$
$620$	0	0
$621$	10.2212	0.410163
$622$	−19.8257	−0.794938
$623$	17.2555	0.691328
$624$	−3.90552	−0.156346
$625$	0	0
$626$	−13.0468	−0.521453
$627$	−0.811762	−0.0324186
$628$	−4.36383	−0.174136
$629$	−9.94033	−0.396347
$630$	0	0
$631$	−16.1932	−0.644640	−0.322320	−	0.946631i	$-0.604463\pi$
$631$	−16.1932	−0.644640	−0.322320	+	0.946631i	$0.604463\pi$
$632$	−3.63841	−0.144728
$633$	−13.2917	−0.528296
$634$	25.4310	1.01000
$635$	0	0
$636$	−13.1760	−0.522463
$637$	−11.4617	−0.454130
$638$	−0.787220	−0.0311663
$639$	−6.38187	−0.252463
$640$	0	0
$641$	−12.5279	−0.494823	−0.247411	−	0.968911i	$-0.579580\pi$
$641$	−12.5279	−0.494823	−0.247411	+	0.968911i	$0.579580\pi$
$642$	23.1953	0.915447
$643$	−3.68823	−0.145450	−0.0727248	−	0.997352i	$-0.523169\pi$
$643$	−3.68823	−0.145450	−0.0727248	+	0.997352i	$0.523169\pi$
$644$	16.6537	0.656248
$645$	0	0
$646$	−2.22675	−0.0876102
$647$	2.22030	0.0872889	0.0436445	−	0.999047i	$-0.486103\pi$
$647$	2.22030	0.0872889	0.0436445	+	0.999047i	$0.486103\pi$
$648$	1.53417	0.0602679
$649$	51.4057	2.01785
$650$	0	0
$651$	−18.5637	−0.727568
$652$	9.66401	0.378472
$653$	11.1287	0.435499	0.217750	−	0.976005i	$-0.430128\pi$
$653$	11.1287	0.435499	0.217750	+	0.976005i	$0.430128\pi$
$654$	−27.7442	−1.08488
$655$	0	0
$656$	−7.34610	−0.286817
$657$	28.6139	1.11633
$658$	80.3951	3.13413
$659$	−48.7913	−1.90064	−0.950320	−	0.311274i	$-0.899244\pi$
$659$	−48.7913	−1.90064	−0.950320	+	0.311274i	$0.899244\pi$
$660$	0	0
$661$	9.83428	0.382509	0.191255	−	0.981540i	$-0.438744\pi$
$661$	9.83428	0.382509	0.191255	+	0.981540i	$0.438744\pi$
$662$	52.8612	2.05451
$663$	−4.44117	−0.172481
$664$	−0.318651	−0.0123661
$665$	0	0
$666$	8.51333	0.329885
$667$	−0.221432	−0.00857388
$668$	25.8576	1.00046
$669$	3.97710	0.153764
$670$	0	0
$671$	−22.7475	−0.878156
$672$	−27.8903	−1.07589
$673$	−7.68732	−0.296325	−0.148162	−	0.988963i	$-0.547336\pi$
$673$	−7.68732	−0.296325	−0.148162	+	0.988963i	$0.547336\pi$
$674$	0.869886	0.0335068
$675$	0	0
$676$	−20.6397	−0.793837
$677$	−14.6186	−0.561840	−0.280920	−	0.959731i	$-0.590639\pi$
$677$	−14.6186	−0.561840	−0.280920	+	0.959731i	$0.590639\pi$
$678$	−24.8143	−0.952987
$679$	28.4205	1.09068
$680$	0	0
$681$	13.5633	0.519748
$682$	40.4525	1.54901
$683$	−27.4320	−1.04966	−0.524828	−	0.851209i	$-0.675870\pi$
$683$	−27.4320	−1.04966	−0.524828	+	0.851209i	$0.675870\pi$
$684$	0.882846	0.0337565
$685$	0	0
$686$	−35.5709	−1.35810
$687$	−8.88113	−0.338836
$688$	−45.8210	−1.74691
$689$	−8.99919	−0.342842
$690$	0	0
$691$	−20.6077	−0.783955	−0.391977	−	0.919975i	$-0.628209\pi$
$691$	−20.6077	−0.783955	−0.391977	+	0.919975i	$0.628209\pi$
$692$	24.3437	0.925410
$693$	40.2026	1.52717
$694$	22.8484	0.867312
$695$	0	0
$696$	0.0449824	0.00170505
$697$	−8.35364	−0.316417
$698$	−32.1603	−1.21728
$699$	−24.7883	−0.937578
$700$	0	0
$701$	−4.40290	−0.166295	−0.0831476	−	0.996537i	$-0.526497\pi$
$701$	−4.40290	−0.166295	−0.0831476	+	0.996537i	$0.526497\pi$
$702$	8.85504	0.334212
$703$	−0.442756	−0.0166989
$704$	23.5418	0.887264
$705$	0	0
$706$	45.2390	1.70259
$707$	0.892032	0.0335483
$708$	18.3410	0.689299
$709$	14.6396	0.549803	0.274901	−	0.961472i	$-0.411355\pi$
$709$	14.6396	0.549803	0.274901	+	0.961472i	$0.411355\pi$
$710$	0	0
$711$	15.4264	0.578537
$712$	2.14860	0.0805223
$713$	11.3786	0.426133
$714$	−36.1788	−1.35396
$715$	0	0
$716$	−39.7801	−1.48665
$717$	−1.82429	−0.0681292
$718$	39.2599	1.46517
$719$	−10.3659	−0.386582	−0.193291	−	0.981141i	$-0.561916\pi$
$719$	−10.3659	−0.386582	−0.193291	+	0.981141i	$0.561916\pi$
$720$	0	0
$721$	9.36796	0.348881
$722$	36.5660	1.36084
$723$	0.860854	0.0320155
$724$	−22.8338	−0.848610
$725$	0	0
$726$	10.4669	0.388461
$727$	20.6367	0.765375	0.382687	−	0.923878i	$-0.374999\pi$
$727$	20.6367	0.765375	0.382687	+	0.923878i	$0.374999\pi$
$728$	−2.31064	−0.0856381
$729$	5.18699	0.192111
$730$	0	0
$731$	−52.1054	−1.92719
$732$	−8.11607	−0.299979
$733$	14.1693	0.523355	0.261677	−	0.965155i	$-0.415724\pi$
$733$	14.1693	0.523355	0.261677	+	0.965155i	$0.415724\pi$
$734$	63.7691	2.35376
$735$	0	0
$736$	17.0954	0.630145
$737$	−21.6116	−0.796073
$738$	7.15441	0.263358
$739$	−50.7411	−1.86654	−0.933270	−	0.359175i	$-0.883058\pi$
$739$	−50.7411	−1.86654	−0.933270	+	0.359175i	$0.883058\pi$
$740$	0	0
$741$	−0.197816	−0.00726695
$742$	−73.3094	−2.69127
$743$	12.3212	0.452020	0.226010	−	0.974125i	$-0.427432\pi$
$743$	12.3212	0.452020	0.226010	+	0.974125i	$0.427432\pi$
$744$	−2.31149	−0.0847433
$745$	0	0
$746$	46.8626	1.71576
$747$	1.35105	0.0494322
$748$	36.4964	1.33444
$749$	59.7436	2.18299
$750$	0	0
$751$	−14.0863	−0.514018	−0.257009	−	0.966409i	$-0.582737\pi$
$751$	−14.0863	−0.514018	−0.257009	+	0.966409i	$0.582737\pi$
$752$	43.5808	1.58923
$753$	−12.7399	−0.464269
$754$	−0.191835	−0.00698623
$755$	0	0
$756$	33.3935	1.21451
$757$	−39.3962	−1.43188	−0.715940	−	0.698162i	$-0.754002\pi$
$757$	−39.3962	−1.43188	−0.715940	+	0.698162i	$0.754002\pi$
$758$	50.2789	1.82621
$759$	8.08419	0.293438
$760$	0	0
$761$	−11.4776	−0.416064	−0.208032	−	0.978122i	$-0.566706\pi$
$761$	−11.4776	−0.416064	−0.208032	+	0.978122i	$0.566706\pi$
$762$	13.2850	0.481264
$763$	−71.4600	−2.58703
$764$	37.8057	1.36776
$765$	0	0
$766$	45.5978	1.64752
$767$	12.5269	0.452320
$768$	−16.7578	−0.604694
$769$	−23.4598	−0.845983	−0.422991	−	0.906134i	$-0.639020\pi$
$769$	−23.4598	−0.845983	−0.422991	+	0.906134i	$0.639020\pi$
$770$	0	0
$771$	2.96208	0.106677
$772$	−34.5949	−1.24510
$773$	43.3955	1.56083	0.780414	−	0.625263i	$-0.215008\pi$
$773$	43.3955	1.56083	0.780414	+	0.625263i	$0.215008\pi$
$774$	44.6253	1.60402
$775$	0	0
$776$	3.53883	0.127037
$777$	−7.19361	−0.258069
$778$	−49.4045	−1.77124
$779$	−0.372082	−0.0133312
$780$	0	0
$781$	−11.7511	−0.420486
$782$	22.1758	0.793005
$783$	−0.444009	−0.0158676
$784$	−50.6140	−1.80764
$785$	0	0
$786$	1.72981	0.0617004
$787$	6.18560	0.220493	0.110246	−	0.993904i	$-0.464836\pi$
$787$	6.18560	0.220493	0.110246	+	0.993904i	$0.464836\pi$
$788$	−26.7000	−0.951148
$789$	12.9954	0.462649
$790$	0	0
$791$	−63.9136	−2.27250
$792$	5.00590	0.177877
$793$	−5.54326	−0.196847
$794$	6.29037	0.223237
$795$	0	0
$796$	−21.7496	−0.770894
$797$	33.9504	1.20259	0.601293	−	0.799029i	$-0.294653\pi$
$797$	33.9504	1.20259	0.601293	+	0.799029i	$0.294653\pi$
$798$	−1.61145	−0.0570448
$799$	49.5580	1.75324
$800$	0	0
$801$	−9.10984	−0.321880
$802$	53.8481	1.90144
$803$	52.6872	1.85929
$804$	−7.71080	−0.271939
$805$	0	0
$806$	9.85775	0.347224
$807$	16.9708	0.597402
$808$	0.111073	0.00390753
$809$	−17.0245	−0.598550	−0.299275	−	0.954167i	$-0.596745\pi$
$809$	−17.0245	−0.598550	−0.299275	+	0.954167i	$0.596745\pi$
$810$	0	0
$811$	−35.1615	−1.23469	−0.617344	−	0.786694i	$-0.711791\pi$
$811$	−35.1615	−1.23469	−0.617344	+	0.786694i	$0.711791\pi$
$812$	−0.723436	−0.0253876
$813$	−5.51064	−0.193266
$814$	15.6757	0.549434
$815$	0	0
$816$	−19.6119	−0.686553
$817$	−2.32085	−0.0811961
$818$	−5.32407	−0.186152
$819$	9.79686	0.342330
$820$	0	0
$821$	7.68686	0.268273	0.134137	−	0.990963i	$-0.457174\pi$
$821$	7.68686	0.268273	0.134137	+	0.990963i	$0.457174\pi$
$822$	−0.578787	−0.0201875
$823$	26.4535	0.922113	0.461056	−	0.887371i	$-0.347471\pi$
$823$	26.4535	0.922113	0.461056	+	0.887371i	$0.347471\pi$
$824$	1.16647	0.0406359
$825$	0	0
$826$	102.047	3.55066
$827$	−22.4623	−0.781090	−0.390545	−	0.920584i	$-0.627713\pi$
$827$	−22.4623	−0.781090	−0.390545	+	0.920584i	$0.627713\pi$
$828$	−8.79211	−0.305547
$829$	48.1972	1.67396	0.836979	−	0.547236i	$-0.184320\pi$
$829$	48.1972	1.67396	0.836979	+	0.547236i	$0.184320\pi$
$830$	0	0
$831$	0.0774794	0.00268773
$832$	5.73683	0.198889
$833$	−57.5559	−1.99419
$834$	1.25481	0.0434506
$835$	0	0
$836$	1.62560	0.0562226
$837$	22.8161	0.788639
$838$	−12.6187	−0.435907
$839$	−10.6726	−0.368459	−0.184229	−	0.982883i	$-0.558979\pi$
$839$	−10.6726	−0.368459	−0.184229	+	0.982883i	$0.558979\pi$
$840$	0	0
$841$	−28.9904	−0.999668
$842$	36.8131	1.26866
$843$	27.8002	0.957489
$844$	26.6173	0.916207
$845$	0	0
$846$	−42.4436	−1.45924
$847$	26.9592	0.926330
$848$	−39.7397	−1.36467
$849$	−17.7281	−0.608428
$850$	0	0
$851$	4.40933	0.151150
$852$	−4.19266	−0.143638
$853$	−15.2826	−0.523265	−0.261633	−	0.965168i	$-0.584261\pi$
$853$	−15.2826	−0.523265	−0.261633	+	0.965168i	$0.584261\pi$
$854$	−45.1566	−1.54523
$855$	0	0
$856$	7.43908	0.254263
$857$	−30.6509	−1.04701	−0.523507	−	0.852021i	$-0.675377\pi$
$857$	−30.6509	−1.04701	−0.523507	+	0.852021i	$0.675377\pi$
$858$	7.00366	0.239101
$859$	−14.1900	−0.484157	−0.242078	−	0.970257i	$-0.577829\pi$
$859$	−14.1900	−0.484157	−0.242078	+	0.970257i	$0.577829\pi$
$860$	0	0
$861$	−6.04535	−0.206025
$862$	−23.6015	−0.803871
$863$	−55.4190	−1.88649	−0.943243	−	0.332104i	$-0.892242\pi$
$863$	−55.4190	−1.88649	−0.943243	+	0.332104i	$0.892242\pi$
$864$	34.2792	1.16620
$865$	0	0
$866$	−69.6517	−2.36686
$867$	−7.66715	−0.260390
$868$	37.1749	1.26180
$869$	28.4050	0.963573
$870$	0	0
$871$	−5.26646	−0.178447
$872$	−8.89797	−0.301323
$873$	−15.0043	−0.507817
$874$	0.987740	0.0334108
$875$	0	0
$876$	18.7983	0.635136
$877$	49.2029	1.66147	0.830733	−	0.556672i	$-0.187922\pi$
$877$	49.2029	1.66147	0.830733	+	0.556672i	$0.187922\pi$
$878$	−43.8668	−1.48043
$879$	26.6570	0.899118
$880$	0	0
$881$	−16.9549	−0.571226	−0.285613	−	0.958345i	$-0.592197\pi$
$881$	−16.9549	−0.571226	−0.285613	+	0.958345i	$0.592197\pi$
$882$	49.2933	1.65979
$883$	4.68142	0.157542	0.0787712	−	0.996893i	$-0.474900\pi$
$883$	4.68142	0.157542	0.0787712	+	0.996893i	$0.474900\pi$
$884$	8.89371	0.299128
$885$	0	0
$886$	−69.3285	−2.32914
$887$	−49.3729	−1.65778	−0.828889	−	0.559413i	$-0.811027\pi$
$887$	−49.3729	−1.65778	−0.828889	+	0.559413i	$0.811027\pi$
$888$	−0.895725	−0.0300586
$889$	34.2178	1.14763
$890$	0	0
$891$	−11.9772	−0.401253
$892$	−7.96438	−0.266667
$893$	2.20738	0.0738672
$894$	−29.4418	−0.984681
$895$	0	0
$896$	−18.0634	−0.603457
$897$	1.97001	0.0657768
$898$	−62.6274	−2.08990
$899$	−0.494287	−0.0164854
$900$	0	0
$901$	−45.1901	−1.50550
$902$	13.1736	0.438631
$903$	−37.7076	−1.25483
$904$	−7.95831	−0.264689
$905$	0	0
$906$	12.2661	0.407514
$907$	13.0437	0.433108	0.216554	−	0.976271i	$-0.430518\pi$
$907$	13.0437	0.433108	0.216554	+	0.976271i	$0.430518\pi$
$908$	−27.1614	−0.901381
$909$	−0.470937	−0.0156200
$910$	0	0
$911$	2.93310	0.0971779	0.0485889	−	0.998819i	$-0.484528\pi$
$911$	2.93310	0.0971779	0.0485889	+	0.998819i	$0.484528\pi$
$912$	−0.873540	−0.0289258
$913$	2.48771	0.0823310
$914$	−37.0779	−1.22643
$915$	0	0
$916$	17.7850	0.587633
$917$	4.45543	0.147131
$918$	44.4663	1.46761
$919$	−53.4647	−1.76364	−0.881820	−	0.471587i	$-0.843681\pi$
$919$	−53.4647	−1.76364	−0.881820	+	0.471587i	$0.843681\pi$
$920$	0	0
$921$	−4.89787	−0.161390
$922$	76.4518	2.51780
$923$	−2.86358	−0.0942559
$924$	26.4117	0.868881
$925$	0	0
$926$	−18.4289	−0.605610
$927$	−4.94570	−0.162438
$928$	−0.742623	−0.0243778
$929$	3.79205	0.124413	0.0622065	−	0.998063i	$-0.480186\pi$
$929$	3.79205	0.124413	0.0622065	+	0.998063i	$0.480186\pi$
$930$	0	0
$931$	−2.56362	−0.0840191
$932$	49.6400	1.62601
$933$	−8.84420	−0.289546
$934$	−29.6956	−0.971670
$935$	0	0
$936$	1.21987	0.0398728
$937$	39.6163	1.29421	0.647103	−	0.762402i	$-0.275980\pi$
$937$	39.6163	1.29421	0.647103	+	0.762402i	$0.275980\pi$
$938$	−42.9018	−1.40079
$939$	−5.82013	−0.189933
$940$	0	0
$941$	39.7620	1.29620	0.648101	−	0.761554i	$-0.275563\pi$
$941$	39.7620	1.29620	0.648101	+	0.761554i	$0.275563\pi$
$942$	−4.20516	−0.137011
$943$	3.70550	0.120668
$944$	55.3178	1.80044
$945$	0	0
$946$	82.1694	2.67156
$947$	−18.8648	−0.613024	−0.306512	−	0.951867i	$-0.599162\pi$
$947$	−18.8648	−0.613024	−0.306512	+	0.951867i	$0.599162\pi$
$948$	10.1346	0.329157
$949$	12.8392	0.416778
$950$	0	0
$951$	11.3447	0.367878
$952$	−11.6031	−0.376057
$953$	27.6442	0.895484	0.447742	−	0.894163i	$-0.352228\pi$
$953$	27.6442	0.895484	0.447742	+	0.894163i	$0.352228\pi$
$954$	38.7028	1.25305
$955$	0	0
$956$	3.65324	0.118154
$957$	−0.351177	−0.0113519
$958$	23.8514	0.770605
$959$	−1.49077	−0.0481394
$960$	0	0
$961$	−5.60033	−0.180656
$962$	3.81997	0.123161
$963$	−31.5409	−1.01639
$964$	−1.72391	−0.0555234
$965$	0	0
$966$	16.0482	0.516341
$967$	−2.13869	−0.0687757	−0.0343878	−	0.999409i	$-0.510948\pi$
$967$	−2.13869	−0.0687757	−0.0343878	+	0.999409i	$0.510948\pi$
$968$	3.35687	0.107894
$969$	−0.993347	−0.0319109
$970$	0	0
$971$	34.3123	1.10113	0.550567	−	0.834791i	$-0.314412\pi$
$971$	34.3123	1.10113	0.550567	+	0.834791i	$0.314412\pi$
$972$	−27.6867	−0.888051
$973$	3.23199	0.103613
$974$	25.4738	0.816232
$975$	0	0
$976$	−24.4786	−0.783541
$977$	43.8976	1.40441	0.702204	−	0.711976i	$-0.252200\pi$
$977$	43.8976	1.40441	0.702204	+	0.711976i	$0.252200\pi$
$978$	9.31262	0.297785
$979$	−16.7741	−0.536103
$980$	0	0
$981$	37.7264	1.20451
$982$	−2.43936	−0.0778432
$983$	−24.2230	−0.772594	−0.386297	−	0.922374i	$-0.626246\pi$
$983$	−24.2230	−0.772594	−0.386297	+	0.922374i	$0.626246\pi$
$984$	−0.752748	−0.0239967
$985$	0	0
$986$	−0.963315	−0.0306782
$987$	35.8641	1.14157
$988$	0.396138	0.0126028
$989$	23.1129	0.734947
$990$	0	0
$991$	−51.0189	−1.62067	−0.810335	−	0.585967i	$-0.800715\pi$
$991$	−51.0189	−1.62067	−0.810335	+	0.585967i	$0.800715\pi$
$992$	38.1608	1.21161
$993$	23.5813	0.748329
$994$	−23.3273	−0.739899
$995$	0	0
$996$	0.887589	0.0281243
$997$	12.2863	0.389112	0.194556	−	0.980891i	$-0.437673\pi$
$997$	12.2863	0.389112	0.194556	+	0.980891i	$0.437673\pi$
$998$	29.6397	0.938230
$999$	8.84146	0.279731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.i.1.4		15
5.4	even	2		1205.2.a.c.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.12	✓	15	5.4	even	2
6025.2.a.i.1.4		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)

\(f(q)\)	\(=\)	\(q-1.92974 q^{2} -0.860854 q^{3} +1.72391 q^{4} +1.66123 q^{6} +4.27878 q^{7} +0.532780 q^{8} -2.25893 q^{9} +O(q^{10})\)	\(q-1.92974 q^{2} -0.860854 q^{3} +1.72391 q^{4} +1.66123 q^{6} +4.27878 q^{7} +0.532780 q^{8} -2.25893 q^{9} -4.15941 q^{11} -1.48404 q^{12} -1.01359 q^{13} -8.25696 q^{14} -4.47595 q^{16} -5.08984 q^{17} +4.35916 q^{18} -0.226708 q^{19} -3.68341 q^{21} +8.02659 q^{22} +2.25775 q^{23} -0.458646 q^{24} +1.95598 q^{26} +4.52717 q^{27} +7.37624 q^{28} -0.0980765 q^{29} +5.03981 q^{31} +7.57188 q^{32} +3.58064 q^{33} +9.82208 q^{34} -3.89420 q^{36} +1.95298 q^{37} +0.437489 q^{38} +0.872557 q^{39} +1.64124 q^{41} +7.10804 q^{42} +10.2371 q^{43} -7.17045 q^{44} -4.35688 q^{46} -9.73665 q^{47} +3.85314 q^{48} +11.3080 q^{49} +4.38161 q^{51} -1.74735 q^{52} +8.87850 q^{53} -8.73628 q^{54} +2.27965 q^{56} +0.195163 q^{57} +0.189262 q^{58} -12.3589 q^{59} +5.46892 q^{61} -9.72554 q^{62} -9.66547 q^{63} -5.65989 q^{64} -6.90973 q^{66} +5.19583 q^{67} -8.77443 q^{68} -1.94359 q^{69} +2.82517 q^{71} -1.20351 q^{72} -12.6670 q^{73} -3.76874 q^{74} -0.390825 q^{76} -17.7972 q^{77} -1.68381 q^{78} -6.82909 q^{79} +2.87955 q^{81} -3.16717 q^{82} -0.598091 q^{83} -6.34987 q^{84} -19.7551 q^{86} +0.0844295 q^{87} -2.21605 q^{88} +4.03281 q^{89} -4.33695 q^{91} +3.89216 q^{92} -4.33854 q^{93} +18.7892 q^{94} -6.51829 q^{96} +6.64220 q^{97} -21.8215 q^{98} +9.39581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 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

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Database

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