LMFDB - Embedded newform 6025.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.385940$ 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)

$f(q)$	$=$	$q-1.20514 q^{2} -0.933583 q^{3} -0.547644 q^{4} +1.12510 q^{6} +2.09289 q^{7} +3.07026 q^{8} -2.12842 q^{9} +O(q^{10})$	\(q-1.20514 q^{2} -0.933583 q^{3} -0.547644 q^{4} +1.12510 q^{6} +2.09289 q^{7} +3.07026 q^{8} -2.12842 q^{9} -4.33455 q^{11} +0.511271 q^{12} -1.99281 q^{13} -2.52222 q^{14} -2.60480 q^{16} +2.99516 q^{17} +2.56504 q^{18} +0.142223 q^{19} -1.95388 q^{21} +5.22373 q^{22} -0.193698 q^{23} -2.86634 q^{24} +2.40162 q^{26} +4.78781 q^{27} -1.14616 q^{28} -0.0799482 q^{29} -9.71272 q^{31} -3.00138 q^{32} +4.04666 q^{33} -3.60958 q^{34} +1.16562 q^{36} -2.11450 q^{37} -0.171398 q^{38} +1.86046 q^{39} -1.74228 q^{41} +2.35470 q^{42} -0.129720 q^{43} +2.37379 q^{44} +0.233433 q^{46} -0.573558 q^{47} +2.43180 q^{48} -2.61983 q^{49} -2.79623 q^{51} +1.09135 q^{52} -4.38556 q^{53} -5.76997 q^{54} +6.42571 q^{56} -0.132777 q^{57} +0.0963486 q^{58} +11.2958 q^{59} +6.94029 q^{61} +11.7052 q^{62} -4.45455 q^{63} +8.82667 q^{64} -4.87679 q^{66} +8.70625 q^{67} -1.64028 q^{68} +0.180833 q^{69} -14.7777 q^{71} -6.53481 q^{72} +3.84543 q^{73} +2.54826 q^{74} -0.0778873 q^{76} -9.07172 q^{77} -2.24211 q^{78} +3.07277 q^{79} +1.91545 q^{81} +2.09968 q^{82} -12.2823 q^{83} +1.07003 q^{84} +0.156330 q^{86} +0.0746383 q^{87} -13.3082 q^{88} +9.15908 q^{89} -4.17074 q^{91} +0.106078 q^{92} +9.06763 q^{93} +0.691216 q^{94} +2.80204 q^{96} -9.88057 q^{97} +3.15725 q^{98} +9.22575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * 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 $

$2$	−1.20514	−0.852161	−0.426080	−	0.904685i	$-0.640106\pi$
$2$	−1.20514	−0.852161	−0.426080	+	0.904685i	$0.640106\pi$
$3$	−0.933583	−0.539005	−0.269502	−	0.963000i	$-0.586859\pi$
$3$	−0.933583	−0.539005	−0.269502	+	0.963000i	$0.586859\pi$
$4$	−0.547644	−0.273822
$5$	0	0
$5$	0	0
$6$	1.12510	0.459319
$7$	2.09289	0.791037	0.395518	−	0.918458i	$-0.370565\pi$
$7$	2.09289	0.791037	0.395518	+	0.918458i	$0.370565\pi$
$8$	3.07026	1.08550
$9$	−2.12842	−0.709474
$10$	0	0
$11$	−4.33455	−1.30692	−0.653458	−	0.756963i	$-0.726682\pi$
$11$	−4.33455	−1.30692	−0.653458	+	0.756963i	$0.726682\pi$
$12$	0.511271	0.147591
$13$	−1.99281	−0.552707	−0.276354	−	0.961056i	$-0.589126\pi$
$13$	−1.99281	−0.552707	−0.276354	+	0.961056i	$0.589126\pi$
$14$	−2.52222	−0.674091
$15$	0	0
$16$	−2.60480	−0.651200
$17$	2.99516	0.726433	0.363217	−	0.931705i	$-0.381679\pi$
$17$	2.99516	0.726433	0.363217	+	0.931705i	$0.381679\pi$
$18$	2.56504	0.604586
$19$	0.142223	0.0326281	0.0163140	−	0.999867i	$-0.494807\pi$
$19$	0.142223	0.0326281	0.0163140	+	0.999867i	$0.494807\pi$
$20$	0	0
$21$	−1.95388	−0.426373
$22$	5.22373	1.11370
$23$	−0.193698	−0.0403889	−0.0201944	−	0.999796i	$-0.506429\pi$
$23$	−0.193698	−0.0403889	−0.0201944	+	0.999796i	$0.506429\pi$
$24$	−2.86634	−0.585090
$25$	0	0
$26$	2.40162	0.470996
$27$	4.78781	0.921414
$28$	−1.14616	−0.216603
$29$	−0.0799482	−0.0148460	−0.00742301	−	0.999972i	$-0.502363\pi$
$29$	−0.0799482	−0.0148460	−0.00742301	+	0.999972i	$0.502363\pi$
$30$	0	0
$31$	−9.71272	−1.74446	−0.872228	−	0.489100i	$-0.837325\pi$
$31$	−9.71272	−1.74446	−0.872228	+	0.489100i	$0.837325\pi$
$32$	−3.00138	−0.530574
$33$	4.04666	0.704434
$34$	−3.60958	−0.619038
$35$	0	0
$36$	1.16562	0.194269
$37$	−2.11450	−0.347622	−0.173811	−	0.984779i	$-0.555608\pi$
$37$	−2.11450	−0.347622	−0.173811	+	0.984779i	$0.555608\pi$
$38$	−0.171398	−0.0278044
$39$	1.86046	0.297912
$40$	0	0
$41$	−1.74228	−0.272098	−0.136049	−	0.990702i	$-0.543440\pi$
$41$	−1.74228	−0.272098	−0.136049	+	0.990702i	$0.543440\pi$
$42$	2.35470	0.363338
$43$	−0.129720	−0.0197820	−0.00989102	−	0.999951i	$-0.503148\pi$
$43$	−0.129720	−0.0197820	−0.00989102	+	0.999951i	$0.503148\pi$
$44$	2.37379	0.357862
$45$	0	0
$46$	0.233433	0.0344178
$47$	−0.573558	−0.0836620	−0.0418310	−	0.999125i	$-0.513319\pi$
$47$	−0.573558	−0.0836620	−0.0418310	+	0.999125i	$0.513319\pi$
$48$	2.43180	0.351000
$49$	−2.61983	−0.374261
$50$	0	0
$51$	−2.79623	−0.391551
$52$	1.09135	0.151343
$53$	−4.38556	−0.602403	−0.301202	−	0.953560i	$-0.597388\pi$
$53$	−4.38556	−0.602403	−0.301202	+	0.953560i	$0.597388\pi$
$54$	−5.76997	−0.785193
$55$	0	0
$56$	6.42571	0.858671
$57$	−0.132777	−0.0175867
$58$	0.0963486	0.0126512
$59$	11.2958	1.47059	0.735293	−	0.677749i	$-0.237045\pi$
$59$	11.2958	1.47059	0.735293	+	0.677749i	$0.237045\pi$
$60$	0	0
$61$	6.94029	0.888613	0.444306	−	0.895875i	$-0.353450\pi$
$61$	6.94029	0.888613	0.444306	+	0.895875i	$0.353450\pi$
$62$	11.7052	1.48656
$63$	−4.45455	−0.561220
$64$	8.82667	1.10333
$65$	0	0
$66$	−4.87679	−0.600291
$67$	8.70625	1.06364	0.531819	−	0.846858i	$-0.321509\pi$
$67$	8.70625	1.06364	0.531819	+	0.846858i	$0.321509\pi$
$68$	−1.64028	−0.198913
$69$	0.180833	0.0217698
$70$	0	0
$71$	−14.7777	−1.75379	−0.876893	−	0.480685i	$-0.840388\pi$
$71$	−14.7777	−1.75379	−0.876893	+	0.480685i	$0.840388\pi$
$72$	−6.53481	−0.770135
$73$	3.84543	0.450073	0.225037	−	0.974350i	$-0.427750\pi$
$73$	3.84543	0.450073	0.225037	+	0.974350i	$0.427750\pi$
$74$	2.54826	0.296230
$75$	0	0
$76$	−0.0778873	−0.00893428
$77$	−9.07172	−1.03382
$78$	−2.24211	−0.253869
$79$	3.07277	0.345713	0.172857	−	0.984947i	$-0.444700\pi$
$79$	3.07277	0.345713	0.172857	+	0.984947i	$0.444700\pi$
$80$	0	0
$81$	1.91545	0.212827
$82$	2.09968	0.231871
$83$	−12.2823	−1.34816	−0.674078	−	0.738660i	$-0.735459\pi$
$83$	−12.2823	−1.34816	−0.674078	+	0.738660i	$0.735459\pi$
$84$	1.07003	0.116750
$85$	0	0
$86$	0.156330	0.0168575
$87$	0.0746383	0.00800207
$88$	−13.3082	−1.41866
$89$	9.15908	0.970861	0.485430	−	0.874275i	$-0.338663\pi$
$89$	9.15908	0.970861	0.485430	+	0.874275i	$0.338663\pi$
$90$	0	0
$91$	−4.17074	−0.437212
$92$	0.106078	0.0110593
$93$	9.06763	0.940270
$94$	0.691216	0.0712935
$95$	0	0
$96$	2.80204	0.285982
$97$	−9.88057	−1.00322	−0.501610	−	0.865094i	$-0.667259\pi$
$97$	−9.88057	−1.00322	−0.501610	+	0.865094i	$0.667259\pi$
$98$	3.15725	0.318930
$99$	9.22575	0.927223
$100$	0	0
$101$	−15.2256	−1.51500	−0.757500	−	0.652835i	$-0.773579\pi$
$101$	−15.2256	−1.51500	−0.757500	+	0.652835i	$0.773579\pi$
$102$	3.36984	0.333664
$103$	8.45018	0.832621	0.416310	−	0.909223i	$-0.363323\pi$
$103$	8.45018	0.832621	0.416310	+	0.909223i	$0.363323\pi$
$104$	−6.11846	−0.599964
$105$	0	0
$106$	5.28521	0.513345
$107$	−0.971724	−0.0939401	−0.0469700	−	0.998896i	$-0.514957\pi$
$107$	−0.971724	−0.0939401	−0.0469700	+	0.998896i	$0.514957\pi$
$108$	−2.62201	−0.252303
$109$	−9.82150	−0.940729	−0.470365	−	0.882472i	$-0.655878\pi$
$109$	−9.82150	−0.940729	−0.470365	+	0.882472i	$0.655878\pi$
$110$	0	0
$111$	1.97406	0.187370
$112$	−5.45155	−0.515123
$113$	0.695702	0.0654461	0.0327231	−	0.999464i	$-0.489582\pi$
$113$	0.695702	0.0654461	0.0327231	+	0.999464i	$0.489582\pi$
$114$	0.160014	0.0149867
$115$	0	0
$116$	0.0437831	0.00406516
$117$	4.24155	0.392132
$118$	−13.6130	−1.25318
$119$	6.26853	0.574635
$120$	0	0
$121$	7.78832	0.708029
$122$	−8.36400	−0.757241
$123$	1.62656	0.146662
$124$	5.31911	0.477670
$125$	0	0
$126$	5.36834	0.478250
$127$	12.7864	1.13461	0.567304	−	0.823508i	$-0.307986\pi$
$127$	12.7864	1.13461	0.567304	+	0.823508i	$0.307986\pi$
$128$	−4.63460	−0.409644
$129$	0.121104	0.0106626
$130$	0	0
$131$	0.999764	0.0873498	0.0436749	−	0.999046i	$-0.486093\pi$
$131$	0.999764	0.0873498	0.0436749	+	0.999046i	$0.486093\pi$
$132$	−2.21613	−0.192889
$133$	0.297656	0.0258100
$134$	−10.4922	−0.906391
$135$	0	0
$136$	9.19592	0.788544
$137$	18.6568	1.59396	0.796980	−	0.604006i	$-0.206430\pi$
$137$	18.6568	1.59396	0.796980	+	0.604006i	$0.206430\pi$
$138$	−0.217929	−0.0185514
$139$	−8.95713	−0.759733	−0.379867	−	0.925041i	$-0.624030\pi$
$139$	−8.95713	−0.759733	−0.379867	+	0.925041i	$0.624030\pi$
$140$	0	0
$141$	0.535464	0.0450942
$142$	17.8091	1.49451
$143$	8.63795	0.722342
$144$	5.54411	0.462009
$145$	0	0
$146$	−4.63427	−0.383535
$147$	2.44583	0.201728
$148$	1.15799	0.0951864
$149$	5.76386	0.472194	0.236097	−	0.971730i	$-0.424132\pi$
$149$	5.76386	0.472194	0.236097	+	0.971730i	$0.424132\pi$
$150$	0	0
$151$	−7.26625	−0.591319	−0.295660	−	0.955293i	$-0.595539\pi$
$151$	−7.26625	−0.591319	−0.295660	+	0.955293i	$0.595539\pi$
$152$	0.436660	0.0354178
$153$	−6.37497	−0.515385
$154$	10.9327	0.880980
$155$	0	0
$156$	−1.01887	−0.0815748
$157$	−17.0549	−1.36113	−0.680563	−	0.732690i	$-0.738265\pi$
$157$	−17.0549	−1.36113	−0.680563	+	0.732690i	$0.738265\pi$
$158$	−3.70311	−0.294603
$159$	4.09429	0.324698
$160$	0	0
$161$	−0.405388	−0.0319491
$162$	−2.30838	−0.181363
$163$	−2.40730	−0.188555	−0.0942773	−	0.995546i	$-0.530054\pi$
$163$	−2.40730	−0.188555	−0.0942773	+	0.995546i	$0.530054\pi$
$164$	0.954146	0.0745063
$165$	0	0
$166$	14.8018	1.14885
$167$	10.0949	0.781163	0.390582	−	0.920568i	$-0.372274\pi$
$167$	10.0949	0.781163	0.390582	+	0.920568i	$0.372274\pi$
$168$	−5.99893	−0.462828
$169$	−9.02869	−0.694515
$170$	0	0
$171$	−0.302710	−0.0231488
$172$	0.0710401	0.00541676
$173$	3.87402	0.294536	0.147268	−	0.989097i	$-0.452952\pi$
$173$	3.87402	0.294536	0.147268	+	0.989097i	$0.452952\pi$
$174$	−0.0899495	−0.00681905
$175$	0	0
$176$	11.2906	0.851063
$177$	−10.5456	−0.792653
$178$	−11.0380	−0.827330
$179$	8.50607	0.635774	0.317887	−	0.948129i	$-0.397027\pi$
$179$	8.50607	0.635774	0.317887	+	0.948129i	$0.397027\pi$
$180$	0	0
$181$	3.54372	0.263402	0.131701	−	0.991289i	$-0.457956\pi$
$181$	3.54372	0.263402	0.131701	+	0.991289i	$0.457956\pi$
$182$	5.02631	0.372575
$183$	−6.47934	−0.478966
$184$	−0.594704	−0.0438421
$185$	0	0
$186$	−10.9277	−0.801261
$187$	−12.9827	−0.949387
$188$	0.314105	0.0229085
$189$	10.0203	0.728873
$190$	0	0
$191$	−6.12284	−0.443033	−0.221516	−	0.975157i	$-0.571101\pi$
$191$	−6.12284	−0.443033	−0.221516	+	0.975157i	$0.571101\pi$
$192$	−8.24044	−0.594702
$193$	−17.9230	−1.29013	−0.645063	−	0.764129i	$-0.723169\pi$
$193$	−17.9230	−1.29013	−0.645063	+	0.764129i	$0.723169\pi$
$194$	11.9074	0.854904
$195$	0	0
$196$	1.43473	0.102481
$197$	−10.9703	−0.781601	−0.390800	−	0.920475i	$-0.627802\pi$
$197$	−10.9703	−0.781601	−0.390800	+	0.920475i	$0.627802\pi$
$198$	−11.1183	−0.790143
$199$	4.84399	0.343382	0.171691	−	0.985151i	$-0.445077\pi$
$199$	4.84399	0.343382	0.171691	+	0.985151i	$0.445077\pi$
$200$	0	0
$201$	−8.12802	−0.573306
$202$	18.3489	1.29102
$203$	−0.167323	−0.0117437
$204$	1.53134	0.107215
$205$	0	0
$206$	−10.1836	−0.709527
$207$	0.412271	0.0286548
$208$	5.19088	0.359923
$209$	−0.616471	−0.0426422
$210$	0	0
$211$	2.14918	0.147955	0.0739777	−	0.997260i	$-0.476431\pi$
$211$	2.14918	0.147955	0.0739777	+	0.997260i	$0.476431\pi$
$212$	2.40173	0.164951
$213$	13.7962	0.945299
$214$	1.17106	0.0800521
$215$	0	0
$216$	14.6998	1.00020
$217$	−20.3276	−1.37993
$218$	11.8363	0.801653
$219$	−3.59003	−0.242592
$220$	0	0
$221$	−5.96880	−0.401505
$222$	−2.37902	−0.159669
$223$	−0.141794	−0.00949523	−0.00474762	−	0.999989i	$-0.501511\pi$
$223$	−0.141794	−0.00949523	−0.00474762	+	0.999989i	$0.501511\pi$
$224$	−6.28155	−0.419704
$225$	0	0
$226$	−0.838416	−0.0557706
$227$	−14.6935	−0.975242	−0.487621	−	0.873056i	$-0.662135\pi$
$227$	−14.6935	−0.975242	−0.487621	+	0.873056i	$0.662135\pi$
$228$	0.0727143	0.00481562
$229$	8.84936	0.584782	0.292391	−	0.956299i	$-0.405549\pi$
$229$	8.84936	0.584782	0.292391	+	0.956299i	$0.405549\pi$
$230$	0	0
$231$	8.46921	0.557233
$232$	−0.245462	−0.0161154
$233$	1.45610	0.0953925	0.0476963	−	0.998862i	$-0.484812\pi$
$233$	1.45610	0.0953925	0.0476963	+	0.998862i	$0.484812\pi$
$234$	−5.11165	−0.334159
$235$	0	0
$236$	−6.18606	−0.402678
$237$	−2.86869	−0.186341
$238$	−7.55444	−0.489682
$239$	−7.75249	−0.501467	−0.250733	−	0.968056i	$-0.580672\pi$
$239$	−7.75249	−0.501467	−0.250733	+	0.968056i	$0.580672\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−9.38600	−0.603355
$243$	−16.1517	−1.03613
$244$	−3.80080	−0.243322
$245$	0	0
$246$	−1.96023	−0.124980
$247$	−0.283423	−0.0180338
$248$	−29.8206	−1.89361
$249$	11.4665	0.726662
$250$	0	0
$251$	−10.2633	−0.647816	−0.323908	−	0.946089i	$-0.604997\pi$
$251$	−10.2633	−0.647816	−0.323908	+	0.946089i	$0.604997\pi$
$252$	2.43950	0.153674
$253$	0.839594	0.0527848
$254$	−15.4094	−0.966869
$255$	0	0
$256$	−12.0680	−0.754251
$257$	0.949866	0.0592510	0.0296255	−	0.999561i	$-0.490569\pi$
$257$	0.949866	0.0592510	0.0296255	+	0.999561i	$0.490569\pi$
$258$	−0.145947	−0.00908626
$259$	−4.42541	−0.274982
$260$	0	0
$261$	0.170164	0.0105329
$262$	−1.20485	−0.0744361
$263$	25.7389	1.58713	0.793565	−	0.608485i	$-0.208223\pi$
$263$	25.7389	1.58713	0.793565	+	0.608485i	$0.208223\pi$
$264$	12.4243	0.764664
$265$	0	0
$266$	−0.358716	−0.0219943
$267$	−8.55077	−0.523298
$268$	−4.76792	−0.291247
$269$	28.3508	1.72858	0.864290	−	0.502993i	$-0.167768\pi$
$269$	28.3508	1.72858	0.864290	+	0.502993i	$0.167768\pi$
$270$	0	0
$271$	5.17827	0.314558	0.157279	−	0.987554i	$-0.449728\pi$
$271$	5.17827	0.314558	0.157279	+	0.987554i	$0.449728\pi$
$272$	−7.80179	−0.473053
$273$	3.89373	0.235659
$274$	−22.4840	−1.35831
$275$	0	0
$276$	−0.0990322	−0.00596104
$277$	26.3629	1.58399	0.791997	−	0.610525i	$-0.209041\pi$
$277$	26.3629	1.58399	0.791997	+	0.610525i	$0.209041\pi$
$278$	10.7946	0.647415
$279$	20.6728	1.23765
$280$	0	0
$281$	−16.3915	−0.977834	−0.488917	−	0.872330i	$-0.662608\pi$
$281$	−16.3915	−0.977834	−0.488917	+	0.872330i	$0.662608\pi$
$282$	−0.645308	−0.0384275
$283$	−2.29929	−0.136678	−0.0683392	−	0.997662i	$-0.521770\pi$
$283$	−2.29929	−0.136678	−0.0683392	+	0.997662i	$0.521770\pi$
$284$	8.09289	0.480225
$285$	0	0
$286$	−10.4099	−0.615552
$287$	−3.64639	−0.215239
$288$	6.38820	0.376429
$289$	−8.02901	−0.472295
$290$	0	0
$291$	9.22433	0.540740
$292$	−2.10592	−0.123240
$293$	13.3127	0.777736	0.388868	−	0.921293i	$-0.372866\pi$
$293$	13.3127	0.777736	0.388868	+	0.921293i	$0.372866\pi$
$294$	−2.94756	−0.171905
$295$	0	0
$296$	−6.49207	−0.377344
$297$	−20.7530	−1.20421
$298$	−6.94624	−0.402385
$299$	0.386005	0.0223232
$300$	0	0
$301$	−0.271488	−0.0156483
$302$	8.75683	0.503899
$303$	14.2143	0.816592
$304$	−0.370461	−0.0212474
$305$	0	0
$306$	7.68271	0.439191
$307$	11.9598	0.682583	0.341291	−	0.939958i	$-0.389136\pi$
$307$	11.9598	0.682583	0.341291	+	0.939958i	$0.389136\pi$
$308$	4.96807	0.283082
$309$	−7.88894	−0.448786
$310$	0	0
$311$	19.3765	1.09874	0.549371	−	0.835579i	$-0.314868\pi$
$311$	19.3765	1.09874	0.549371	+	0.835579i	$0.314868\pi$
$312$	5.71209	0.323384
$313$	−4.58076	−0.258920	−0.129460	−	0.991585i	$-0.541324\pi$
$313$	−4.58076	−0.258920	−0.129460	+	0.991585i	$0.541324\pi$
$314$	20.5534	1.15990
$315$	0	0
$316$	−1.68278	−0.0946639
$317$	16.0333	0.900519	0.450260	−	0.892898i	$-0.351331\pi$
$317$	16.0333	0.900519	0.450260	+	0.892898i	$0.351331\pi$
$318$	−4.93418	−0.276695
$319$	0.346539	0.0194025
$320$	0	0
$321$	0.907185	0.0506341
$322$	0.488549	0.0272257
$323$	0.425979	0.0237021
$324$	−1.04898	−0.0582768
$325$	0	0
$326$	2.90113	0.160679
$327$	9.16919	0.507058
$328$	−5.34924	−0.295362
$329$	−1.20039	−0.0661797
$330$	0	0
$331$	−23.5291	−1.29328	−0.646639	−	0.762796i	$-0.723826\pi$
$331$	−23.5291	−1.29328	−0.646639	+	0.762796i	$0.723826\pi$
$332$	6.72631	0.369154
$333$	4.50055	0.246629
$334$	−12.1657	−0.665677
$335$	0	0
$336$	5.08948	0.277654
$337$	19.9386	1.08613	0.543063	−	0.839692i	$-0.317265\pi$
$337$	19.9386	1.08613	0.543063	+	0.839692i	$0.317265\pi$
$338$	10.8808	0.591838
$339$	−0.649496	−0.0352758
$340$	0	0
$341$	42.1002	2.27986
$342$	0.364807	0.0197265
$343$	−20.1332	−1.08709
$344$	−0.398273	−0.0214734
$345$	0	0
$346$	−4.66872	−0.250992
$347$	20.4785	1.09934	0.549672	−	0.835381i	$-0.314753\pi$
$347$	20.4785	1.09934	0.549672	+	0.835381i	$0.314753\pi$
$348$	−0.0408752	−0.00219114
$349$	−12.3728	−0.662303	−0.331152	−	0.943578i	$-0.607437\pi$
$349$	−12.3728	−0.662303	−0.331152	+	0.943578i	$0.607437\pi$
$350$	0	0
$351$	−9.54122	−0.509273
$352$	13.0096	0.693416
$353$	−1.01586	−0.0540687	−0.0270344	−	0.999635i	$-0.508606\pi$
$353$	−1.01586	−0.0540687	−0.0270344	+	0.999635i	$0.508606\pi$
$354$	12.7088	0.675468
$355$	0	0
$356$	−5.01591	−0.265843
$357$	−5.85220	−0.309731
$358$	−10.2510	−0.541781
$359$	7.21033	0.380547	0.190273	−	0.981731i	$-0.439063\pi$
$359$	7.21033	0.380547	0.190273	+	0.981731i	$0.439063\pi$
$360$	0	0
$361$	−18.9798	−0.998935
$362$	−4.27066	−0.224461
$363$	−7.27105	−0.381631
$364$	2.28408	0.119718
$365$	0	0
$366$	7.80849	0.408156
$367$	18.8263	0.982727	0.491363	−	0.870955i	$-0.336499\pi$
$367$	18.8263	0.982727	0.491363	+	0.870955i	$0.336499\pi$
$368$	0.504545	0.0263012
$369$	3.70830	0.193046
$370$	0	0
$371$	−9.17849	−0.476523
$372$	−4.96583	−0.257466
$373$	−15.2297	−0.788562	−0.394281	−	0.918990i	$-0.629006\pi$
$373$	−15.2297	−0.788562	−0.394281	+	0.918990i	$0.629006\pi$
$374$	15.6459	0.809030
$375$	0	0
$376$	−1.76097	−0.0908152
$377$	0.159322	0.00820550
$378$	−12.0759	−0.621117
$379$	7.64481	0.392688	0.196344	−	0.980535i	$-0.437093\pi$
$379$	7.64481	0.392688	0.196344	+	0.980535i	$0.437093\pi$
$380$	0	0
$381$	−11.9372	−0.611559
$382$	7.37886	0.377535
$383$	19.5782	1.00040	0.500199	−	0.865910i	$-0.333260\pi$
$383$	19.5782	1.00040	0.500199	+	0.865910i	$0.333260\pi$
$384$	4.32678	0.220800
$385$	0	0
$386$	21.5997	1.09940
$387$	0.276098	0.0140348
$388$	5.41103	0.274703
$389$	20.0734	1.01776	0.508880	−	0.860838i	$-0.330060\pi$
$389$	20.0734	1.01776	0.508880	+	0.860838i	$0.330060\pi$
$390$	0	0
$391$	−0.580157	−0.0293398
$392$	−8.04355	−0.406261
$393$	−0.933363	−0.0470819
$394$	13.2207	0.666050
$395$	0	0
$396$	−5.05242	−0.253894
$397$	−1.10932	−0.0556753	−0.0278376	−	0.999612i	$-0.508862\pi$
$397$	−1.10932	−0.0556753	−0.0278376	+	0.999612i	$0.508862\pi$
$398$	−5.83768	−0.292616
$399$	−0.277886	−0.0139117
$400$	0	0
$401$	30.9488	1.54551	0.772754	−	0.634705i	$-0.218878\pi$
$401$	30.9488	1.54551	0.772754	+	0.634705i	$0.218878\pi$
$402$	9.79538	0.488549
$403$	19.3556	0.964173
$404$	8.33818	0.414840
$405$	0	0
$406$	0.201647	0.0100076
$407$	9.16541	0.454312
$408$	−8.58516	−0.425029
$409$	22.1618	1.09583	0.547915	−	0.836534i	$-0.315422\pi$
$409$	22.1618	1.09583	0.547915	+	0.836534i	$0.315422\pi$
$410$	0	0
$411$	−17.4177	−0.859152
$412$	−4.62768	−0.227990
$413$	23.6408	1.16329
$414$	−0.496844	−0.0244185
$415$	0	0
$416$	5.98120	0.293252
$417$	8.36222	0.409500
$418$	0.742932	0.0363380
$419$	−9.25893	−0.452329	−0.226164	−	0.974089i	$-0.572619\pi$
$419$	−9.25893	−0.452329	−0.226164	+	0.974089i	$0.572619\pi$
$420$	0	0
$421$	22.9469	1.11836	0.559181	−	0.829046i	$-0.311116\pi$
$421$	22.9469	1.11836	0.559181	+	0.829046i	$0.311116\pi$
$422$	−2.59005	−0.126082
$423$	1.22077	0.0593560
$424$	−13.4648	−0.653910
$425$	0	0
$426$	−16.6263	−0.805547
$427$	14.5252	0.702925
$428$	0.532158	0.0257228
$429$	−8.06425	−0.389346
$430$	0	0
$431$	28.4237	1.36912	0.684562	−	0.728955i	$-0.259994\pi$
$431$	28.4237	1.36912	0.684562	+	0.728955i	$0.259994\pi$
$432$	−12.4713	−0.600025
$433$	28.8613	1.38698	0.693492	−	0.720464i	$-0.256071\pi$
$433$	28.8613	1.38698	0.693492	+	0.720464i	$0.256071\pi$
$434$	24.4976	1.17592
$435$	0	0
$436$	5.37868	0.257592
$437$	−0.0275482	−0.00131781
$438$	4.32648	0.206727
$439$	−15.8606	−0.756983	−0.378492	−	0.925605i	$-0.623557\pi$
$439$	−15.8606	−0.756983	−0.378492	+	0.925605i	$0.623557\pi$
$440$	0	0
$441$	5.57609	0.265528
$442$	7.19322	0.342147
$443$	−13.4827	−0.640583	−0.320291	−	0.947319i	$-0.603781\pi$
$443$	−13.4827	−0.640583	−0.320291	+	0.947319i	$0.603781\pi$
$444$	−1.08108	−0.0513059
$445$	0	0
$446$	0.170881	0.00809146
$447$	−5.38104	−0.254515
$448$	18.4732	0.872778
$449$	−9.34552	−0.441042	−0.220521	−	0.975382i	$-0.570776\pi$
$449$	−9.34552	−0.441042	−0.220521	+	0.975382i	$0.570776\pi$
$450$	0	0
$451$	7.55198	0.355609
$452$	−0.380997	−0.0179206
$453$	6.78365	0.318724
$454$	17.7077	0.831063
$455$	0	0
$456$	−0.407659	−0.0190904
$457$	24.2071	1.13236	0.566180	−	0.824282i	$-0.308421\pi$
$457$	24.2071	1.13236	0.566180	+	0.824282i	$0.308421\pi$
$458$	−10.6647	−0.498328
$459$	14.3403	0.669346
$460$	0	0
$461$	−23.6044	−1.09936	−0.549682	−	0.835374i	$-0.685251\pi$
$461$	−23.6044	−1.09936	−0.549682	+	0.835374i	$0.685251\pi$
$462$	−10.2066	−0.474852
$463$	7.67600	0.356734	0.178367	−	0.983964i	$-0.442919\pi$
$463$	7.67600	0.356734	0.178367	+	0.983964i	$0.442919\pi$
$464$	0.208249	0.00966772
$465$	0	0
$466$	−1.75480	−0.0812898
$467$	22.8944	1.05942	0.529712	−	0.848177i	$-0.322300\pi$
$467$	22.8944	1.05942	0.529712	+	0.848177i	$0.322300\pi$
$468$	−2.32286	−0.107374
$469$	18.2212	0.841377
$470$	0	0
$471$	15.9221	0.733653
$472$	34.6810	1.59632
$473$	0.562276	0.0258535
$474$	3.45716	0.158793
$475$	0	0
$476$	−3.43292	−0.157348
$477$	9.33433	0.427390
$478$	9.34282	0.427330
$479$	38.2924	1.74962	0.874811	−	0.484464i	$-0.160985\pi$
$479$	38.2924	1.74962	0.874811	+	0.484464i	$0.160985\pi$
$480$	0	0
$481$	4.21381	0.192133
$482$	−1.20514	−0.0548925
$483$	0.378464	0.0172207
$484$	−4.26522	−0.193874
$485$	0	0
$486$	19.4650	0.882949
$487$	32.0061	1.45033	0.725166	−	0.688574i	$-0.241763\pi$
$487$	32.0061	1.45033	0.725166	+	0.688574i	$0.241763\pi$
$488$	21.3085	0.964590
$489$	2.24742	0.101632
$490$	0	0
$491$	41.3053	1.86408	0.932042	−	0.362351i	$-0.118026\pi$
$491$	41.3053	1.86408	0.932042	+	0.362351i	$0.118026\pi$
$492$	−0.890775	−0.0401592
$493$	−0.239458	−0.0107846
$494$	0.341564	0.0153677
$495$	0	0
$496$	25.2997	1.13599
$497$	−30.9280	−1.38731
$498$	−13.8188	−0.619233
$499$	8.90573	0.398675	0.199338	−	0.979931i	$-0.436121\pi$
$499$	8.90573	0.398675	0.199338	+	0.979931i	$0.436121\pi$
$500$	0	0
$501$	−9.42439	−0.421051
$502$	12.3687	0.552043
$503$	−13.4974	−0.601818	−0.300909	−	0.953653i	$-0.597290\pi$
$503$	−13.4974	−0.601818	−0.300909	+	0.953653i	$0.597290\pi$
$504$	−13.6766	−0.609205
$505$	0	0
$506$	−1.01183	−0.0449812
$507$	8.42903	0.374347
$508$	−7.00238	−0.310680
$509$	42.6925	1.89231	0.946156	−	0.323711i	$-0.104931\pi$
$509$	42.6925	1.89231	0.946156	+	0.323711i	$0.104931\pi$
$510$	0	0
$511$	8.04805	0.356025
$512$	23.8128	1.05239
$513$	0.680934	0.0300640
$514$	−1.14472	−0.0504914
$515$	0	0
$516$	−0.0663218	−0.00291966
$517$	2.48611	0.109339
$518$	5.33323	0.234329
$519$	−3.61672	−0.158756
$520$	0	0
$521$	7.41290	0.324765	0.162382	−	0.986728i	$-0.448082\pi$
$521$	7.41290	0.324765	0.162382	+	0.986728i	$0.448082\pi$
$522$	−0.205070	−0.00897569
$523$	26.9602	1.17889	0.589443	−	0.807810i	$-0.299347\pi$
$523$	26.9602	1.17889	0.589443	+	0.807810i	$0.299347\pi$
$524$	−0.547514	−0.0239183
$525$	0	0
$526$	−31.0189	−1.35249
$527$	−29.0911	−1.26723
$528$	−10.5407	−0.458727
$529$	−22.9625	−0.998369
$530$	0	0
$531$	−24.0422	−1.04334
$532$	−0.163009	−0.00706735
$533$	3.47203	0.150390
$534$	10.3049	0.445934
$535$	0	0
$536$	26.7305	1.15458
$537$	−7.94113	−0.342685
$538$	−34.1667	−1.47303
$539$	11.3558	0.489127
$540$	0	0
$541$	13.3555	0.574200	0.287100	−	0.957901i	$-0.407309\pi$
$541$	13.3555	0.574200	0.287100	+	0.957901i	$0.407309\pi$
$542$	−6.24053	−0.268054
$543$	−3.30835	−0.141975
$544$	−8.98962	−0.385427
$545$	0	0
$546$	−4.69248	−0.200820
$547$	−23.5947	−1.00884	−0.504418	−	0.863459i	$-0.668293\pi$
$547$	−23.5947	−1.00884	−0.504418	+	0.863459i	$0.668293\pi$
$548$	−10.2173	−0.436461
$549$	−14.7719	−0.630448
$550$	0	0
$551$	−0.0113704	−0.000484397 0
$552$	0.555206	0.0236311
$553$	6.43096	0.273472
$554$	−31.7709	−1.34982
$555$	0	0
$556$	4.90531	0.208032
$557$	16.8597	0.714368	0.357184	−	0.934034i	$-0.383737\pi$
$557$	16.8597	0.714368	0.357184	+	0.934034i	$0.383737\pi$
$558$	−24.9135	−1.05467
$559$	0.258507	0.0109337
$560$	0	0
$561$	12.1204	0.511724
$562$	19.7540	0.833272
$563$	28.4822	1.20038	0.600192	−	0.799856i	$-0.295091\pi$
$563$	28.4822	1.20038	0.600192	+	0.799856i	$0.295091\pi$
$564$	−0.293243	−0.0123478
$565$	0	0
$566$	2.77096	0.116472
$567$	4.00881	0.168354
$568$	−45.3713	−1.90374
$569$	−32.5855	−1.36605	−0.683027	−	0.730393i	$-0.739337\pi$
$569$	−32.5855	−1.36605	−0.683027	+	0.730393i	$0.739337\pi$
$570$	0	0
$571$	−36.5027	−1.52759	−0.763795	−	0.645459i	$-0.776666\pi$
$571$	−36.5027	−1.52759	−0.763795	+	0.645459i	$0.776666\pi$
$572$	−4.73052	−0.197793
$573$	5.71618	0.238797
$574$	4.39440	0.183419
$575$	0	0
$576$	−18.7869	−0.782787
$577$	24.5415	1.02168	0.510838	−	0.859677i	$-0.329335\pi$
$577$	24.5415	1.02168	0.510838	+	0.859677i	$0.329335\pi$
$578$	9.67607	0.402471
$579$	16.7326	0.695384
$580$	0	0
$581$	−25.7054	−1.06644
$582$	−11.1166	−0.460797
$583$	19.0094	0.787291
$584$	11.8065	0.488555
$585$	0	0
$586$	−16.0436	−0.662756
$587$	−30.0912	−1.24200	−0.620999	−	0.783811i	$-0.713273\pi$
$587$	−30.0912	−1.24200	−0.620999	+	0.783811i	$0.713273\pi$
$588$	−1.33944	−0.0552376
$589$	−1.38137	−0.0569182
$590$	0	0
$591$	10.2417	0.421286
$592$	5.50785	0.226371
$593$	36.2006	1.48658	0.743291	−	0.668969i	$-0.233264\pi$
$593$	36.2006	1.48658	0.743291	+	0.668969i	$0.233264\pi$
$594$	25.0102	1.02618
$595$	0	0
$596$	−3.15654	−0.129297
$597$	−4.52227	−0.185084
$598$	−0.465189	−0.0190230
$599$	−41.6664	−1.70244	−0.851222	−	0.524805i	$-0.824138\pi$
$599$	−41.6664	−1.70244	−0.851222	+	0.524805i	$0.824138\pi$
$600$	0	0
$601$	1.89333	0.0772307	0.0386153	−	0.999254i	$-0.487705\pi$
$601$	1.89333	0.0772307	0.0386153	+	0.999254i	$0.487705\pi$
$602$	0.327181	0.0133349
$603$	−18.5306	−0.754624
$604$	3.97932	0.161916
$605$	0	0
$606$	−17.1302	−0.695868
$607$	30.0183	1.21841	0.609203	−	0.793015i	$-0.291490\pi$
$607$	30.0183	1.21841	0.609203	+	0.793015i	$0.291490\pi$
$608$	−0.426864	−0.0173116
$609$	0.156210	0.00632993
$610$	0	0
$611$	1.14299	0.0462406
$612$	3.49121	0.141124
$613$	−2.43759	−0.0984534	−0.0492267	−	0.998788i	$-0.515676\pi$
$613$	−2.43759	−0.0984534	−0.0492267	+	0.998788i	$0.515676\pi$
$614$	−14.4132	−0.581670
$615$	0	0
$616$	−27.8525	−1.12221
$617$	35.4406	1.42678	0.713392	−	0.700765i	$-0.247158\pi$
$617$	35.4406	1.42678	0.713392	+	0.700765i	$0.247158\pi$
$618$	9.50726	0.382438
$619$	−1.11427	−0.0447865	−0.0223932	−	0.999749i	$-0.507129\pi$
$619$	−1.11427	−0.0447865	−0.0223932	+	0.999749i	$0.507129\pi$
$620$	0	0
$621$	−0.927390	−0.0372149
$622$	−23.3514	−0.936304
$623$	19.1689	0.767987
$624$	−4.84612	−0.194000
$625$	0	0
$626$	5.52044	0.220641
$627$	0.575527	0.0229843
$628$	9.33998	0.372706
$629$	−6.33327	−0.252524
$630$	0	0
$631$	−11.8586	−0.472084	−0.236042	−	0.971743i	$-0.575850\pi$
$631$	−11.8586	−0.472084	−0.236042	+	0.971743i	$0.575850\pi$
$632$	9.43420	0.375272
$633$	−2.00644	−0.0797487
$634$	−19.3223	−0.767387
$635$	0	0
$636$	−2.24221	−0.0889095
$637$	5.22083	0.206857
$638$	−0.417628	−0.0165340
$639$	31.4531	1.24427
$640$	0	0
$641$	5.06970	0.200241	0.100121	−	0.994975i	$-0.468077\pi$
$641$	5.06970	0.200241	0.100121	+	0.994975i	$0.468077\pi$
$642$	−1.09328	−0.0431484
$643$	17.9849	0.709256	0.354628	−	0.935008i	$-0.384608\pi$
$643$	17.9849	0.709256	0.354628	+	0.935008i	$0.384608\pi$
$644$	0.222008	0.00874835
$645$	0	0
$646$	−0.513364	−0.0201980
$647$	24.5507	0.965187	0.482593	−	0.875845i	$-0.339695\pi$
$647$	24.5507	0.965187	0.482593	+	0.875845i	$0.339695\pi$
$648$	5.88092	0.231024
$649$	−48.9621	−1.92193
$650$	0	0
$651$	18.9775	0.743788
$652$	1.31834	0.0516303
$653$	−19.2378	−0.752832	−0.376416	−	0.926451i	$-0.622844\pi$
$653$	−19.2378	−0.752832	−0.376416	+	0.926451i	$0.622844\pi$
$654$	−11.0501	−0.432095
$655$	0	0
$656$	4.53828	0.177190
$657$	−8.18469	−0.319315
$658$	1.44664	0.0563957
$659$	14.3392	0.558576	0.279288	−	0.960207i	$-0.409902\pi$
$659$	14.3392	0.558576	0.279288	+	0.960207i	$0.409902\pi$
$660$	0	0
$661$	15.6676	0.609400	0.304700	−	0.952448i	$-0.401444\pi$
$661$	15.6676	0.609400	0.304700	+	0.952448i	$0.401444\pi$
$662$	28.3558	1.10208
$663$	5.57237	0.216413
$664$	−37.7098	−1.46342
$665$	0	0
$666$	−5.42378	−0.210167
$667$	0.0154858	0.000599613 0
$668$	−5.52838	−0.213900
$669$	0.132377	0.00511797
$670$	0	0
$671$	−30.0830	−1.16134
$672$	5.86435	0.226222
$673$	−24.4034	−0.940683	−0.470342	−	0.882484i	$-0.655869\pi$
$673$	−24.4034	−0.940683	−0.470342	+	0.882484i	$0.655869\pi$
$674$	−24.0288	−0.925554
$675$	0	0
$676$	4.94450	0.190173
$677$	−12.3212	−0.473542	−0.236771	−	0.971566i	$-0.576089\pi$
$677$	−12.3212	−0.473542	−0.236771	+	0.971566i	$0.576089\pi$
$678$	0.782732	0.0300606
$679$	−20.6789	−0.793584
$680$	0	0
$681$	13.7176	0.525660
$682$	−50.7366	−1.94280
$683$	11.9987	0.459116	0.229558	−	0.973295i	$-0.426272\pi$
$683$	11.9987	0.459116	0.229558	+	0.973295i	$0.426272\pi$
$684$	0.165777	0.00633864
$685$	0	0
$686$	24.2633	0.926376
$687$	−8.26161	−0.315200
$688$	0.337893	0.0128821
$689$	8.73962	0.332953
$690$	0	0
$691$	48.6812	1.85192	0.925959	−	0.377624i	$-0.123259\pi$
$691$	48.6812	1.85192	0.925959	+	0.377624i	$0.123259\pi$
$692$	−2.12158	−0.0806504
$693$	19.3084	0.733467
$694$	−24.6794	−0.936817
$695$	0	0
$696$	0.229159	0.00868626
$697$	−5.21839	−0.197661
$698$	14.9110	0.564389
$699$	−1.35939	−0.0514170
$700$	0	0
$701$	22.3201	0.843017	0.421509	−	0.906824i	$-0.361501\pi$
$701$	22.3201	0.843017	0.421509	+	0.906824i	$0.361501\pi$
$702$	11.4985	0.433982
$703$	−0.300730	−0.0113422
$704$	−38.2597	−1.44197
$705$	0	0
$706$	1.22425	0.0460752
$707$	−31.8654	−1.19842
$708$	5.77521	0.217046
$709$	−34.1343	−1.28194	−0.640971	−	0.767565i	$-0.721468\pi$
$709$	−34.1343	−1.28194	−0.640971	+	0.767565i	$0.721468\pi$
$710$	0	0
$711$	−6.54015	−0.245275
$712$	28.1208	1.05387
$713$	1.88134	0.0704565
$714$	7.05270	0.263941
$715$	0	0
$716$	−4.65830	−0.174089
$717$	7.23760	0.270293
$718$	−8.68944	−0.324287
$719$	7.17280	0.267500	0.133750	−	0.991015i	$-0.457298\pi$
$719$	7.17280	0.267500	0.133750	+	0.991015i	$0.457298\pi$
$720$	0	0
$721$	17.6853	0.658634
$722$	22.8732	0.851254
$723$	−0.933583	−0.0347203
$724$	−1.94069	−0.0721253
$725$	0	0
$726$	8.76261	0.325211
$727$	38.1644	1.41544	0.707720	−	0.706493i	$-0.249724\pi$
$727$	38.1644	1.41544	0.707720	+	0.706493i	$0.249724\pi$
$728$	−12.8052	−0.474594
$729$	9.33258	0.345651
$730$	0	0
$731$	−0.388531	−0.0143703
$732$	3.54837	0.131151
$733$	2.89393	0.106890	0.0534448	−	0.998571i	$-0.482980\pi$
$733$	2.89393	0.106890	0.0534448	+	0.998571i	$0.482980\pi$
$734$	−22.6883	−0.837441
$735$	0	0
$736$	0.581362	0.0214293
$737$	−37.7377	−1.39009
$738$	−4.46901	−0.164506
$739$	15.4162	0.567095	0.283548	−	0.958958i	$-0.408489\pi$
$739$	15.4162	0.567095	0.283548	+	0.958958i	$0.408489\pi$
$740$	0	0
$741$	0.264599	0.00972029
$742$	11.0613	0.406074
$743$	−54.0481	−1.98283	−0.991416	−	0.130742i	$-0.958264\pi$
$743$	−54.0481	−1.98283	−0.991416	+	0.130742i	$0.958264\pi$
$744$	27.8400	1.02066
$745$	0	0
$746$	18.3538	0.671982
$747$	26.1419	0.956481
$748$	7.10988	0.259963
$749$	−2.03371	−0.0743101
$750$	0	0
$751$	5.77777	0.210834	0.105417	−	0.994428i	$-0.466382\pi$
$751$	5.77777	0.210834	0.105417	+	0.994428i	$0.466382\pi$
$752$	1.49400	0.0544807
$753$	9.58167	0.349176
$754$	−0.192005	−0.00699241
$755$	0	0
$756$	−5.48758	−0.199581
$757$	−23.6041	−0.857906	−0.428953	−	0.903327i	$-0.641117\pi$
$757$	−23.6041	−0.857906	−0.428953	+	0.903327i	$0.641117\pi$
$758$	−9.21305	−0.334633
$759$	−0.783831	−0.0284513
$760$	0	0
$761$	24.4216	0.885284	0.442642	−	0.896699i	$-0.354041\pi$
$761$	24.4216	0.885284	0.442642	+	0.896699i	$0.354041\pi$
$762$	14.3859	0.521147
$763$	−20.5553	−0.744152
$764$	3.35313	0.121312
$765$	0	0
$766$	−23.5944	−0.852501
$767$	−22.5104	−0.812804
$768$	11.2665	0.406545
$769$	−12.6875	−0.457524	−0.228762	−	0.973482i	$-0.573468\pi$
$769$	−12.6875	−0.457524	−0.228762	+	0.973482i	$0.573468\pi$
$770$	0	0
$771$	−0.886779	−0.0319366
$772$	9.81542	0.353265
$773$	−9.60185	−0.345354	−0.172677	−	0.984978i	$-0.555242\pi$
$773$	−9.60185	−0.345354	−0.172677	+	0.984978i	$0.555242\pi$
$774$	−0.332736	−0.0119599
$775$	0	0
$776$	−30.3359	−1.08900
$777$	4.13149	0.148216
$778$	−24.1912	−0.867295
$779$	−0.247791	−0.00887803
$780$	0	0
$781$	64.0545	2.29205
$782$	0.699169	0.0250022
$783$	−0.382777	−0.0136793
$784$	6.82412	0.243719
$785$	0	0
$786$	1.12483	0.0401214
$787$	23.8447	0.849970	0.424985	−	0.905200i	$-0.360279\pi$
$787$	23.8447	0.849970	0.424985	+	0.905200i	$0.360279\pi$
$788$	6.00781	0.214019
$789$	−24.0294	−0.855471
$790$	0	0
$791$	1.45603	0.0517703
$792$	28.3255	1.00650
$793$	−13.8307	−0.491143
$794$	1.33689	0.0474443
$795$	0	0
$796$	−2.65278	−0.0940253
$797$	−22.3491	−0.791645	−0.395823	−	0.918327i	$-0.629541\pi$
$797$	−22.3491	−0.791645	−0.395823	+	0.918327i	$0.629541\pi$
$798$	0.334891	0.0118550
$799$	−1.71790	−0.0607748
$800$	0	0
$801$	−19.4944	−0.688800
$802$	−37.2976	−1.31702
$803$	−16.6682	−0.588208
$804$	4.45126	0.156984
$805$	0	0
$806$	−23.3262	−0.821631
$807$	−26.4679	−0.931713
$808$	−46.7464	−1.64453
$809$	23.9412	0.841729	0.420865	−	0.907123i	$-0.361727\pi$
$809$	23.9412	0.841729	0.420865	+	0.907123i	$0.361727\pi$
$810$	0	0
$811$	−21.0275	−0.738374	−0.369187	−	0.929355i	$-0.620364\pi$
$811$	−21.0275	−0.738374	−0.369187	+	0.929355i	$0.620364\pi$
$812$	0.0916331	0.00321569
$813$	−4.83435	−0.169548
$814$	−11.0456	−0.387147
$815$	0	0
$816$	7.28362	0.254978
$817$	−0.0184490	−0.000645450 0
$818$	−26.7080	−0.933823
$819$	8.87709	0.310190
$820$	0	0
$821$	14.3293	0.500096	0.250048	−	0.968233i	$-0.419554\pi$
$821$	14.3293	0.500096	0.250048	+	0.968233i	$0.419554\pi$
$822$	20.9907	0.732136
$823$	19.7168	0.687285	0.343642	−	0.939101i	$-0.388339\pi$
$823$	19.7168	0.687285	0.343642	+	0.939101i	$0.388339\pi$
$824$	25.9442	0.903811
$825$	0	0
$826$	−28.4904	−0.991308
$827$	19.0592	0.662754	0.331377	−	0.943498i	$-0.392487\pi$
$827$	19.0592	0.662754	0.331377	+	0.943498i	$0.392487\pi$
$828$	−0.225778	−0.00784632
$829$	−22.0563	−0.766047	−0.383023	−	0.923739i	$-0.625117\pi$
$829$	−22.0563	−0.766047	−0.383023	+	0.923739i	$0.625117\pi$
$830$	0	0
$831$	−24.6120	−0.853780
$832$	−17.5899	−0.609821
$833$	−7.84680	−0.271875
$834$	−10.0776	−0.348960
$835$	0	0
$836$	0.337606	0.0116764
$837$	−46.5026	−1.60737
$838$	11.1583	0.385457
$839$	−35.3291	−1.21970	−0.609848	−	0.792518i	$-0.708770\pi$
$839$	−35.3291	−1.21970	−0.609848	+	0.792518i	$0.708770\pi$
$840$	0	0
$841$	−28.9936	−0.999780
$842$	−27.6541	−0.953024
$843$	15.3028	0.527057
$844$	−1.17698	−0.0405134
$845$	0	0
$846$	−1.47120	−0.0505809
$847$	16.3001	0.560077
$848$	11.4235	0.392285
$849$	2.14658	0.0736703
$850$	0	0
$851$	0.409575	0.0140400
$852$	−7.55539	−0.258843
$853$	23.5480	0.806268	0.403134	−	0.915141i	$-0.367921\pi$
$853$	23.5480	0.806268	0.403134	+	0.915141i	$0.367921\pi$
$854$	−17.5049	−0.599006
$855$	0	0
$856$	−2.98345	−0.101972
$857$	−29.7827	−1.01736	−0.508679	−	0.860956i	$-0.669866\pi$
$857$	−29.7827	−1.01736	−0.508679	+	0.860956i	$0.669866\pi$
$858$	9.71853	0.331785
$859$	4.27244	0.145774	0.0728869	−	0.997340i	$-0.476779\pi$
$859$	4.27244	0.145774	0.0728869	+	0.997340i	$0.476779\pi$
$860$	0	0
$861$	3.40420	0.116015
$862$	−34.2545	−1.16671
$863$	31.9210	1.08660	0.543301	−	0.839538i	$-0.317174\pi$
$863$	31.9210	1.08660	0.543301	+	0.839538i	$0.317174\pi$
$864$	−14.3700	−0.488879
$865$	0	0
$866$	−34.7818	−1.18193
$867$	7.49575	0.254569
$868$	11.1323	0.377854
$869$	−13.3191	−0.451818
$870$	0	0
$871$	−17.3500	−0.587881
$872$	−30.1546	−1.02116
$873$	21.0300	0.711758
$874$	0.0331994	0.00112299
$875$	0	0
$876$	1.96606	0.0664269
$877$	−45.1093	−1.52323	−0.761616	−	0.648028i	$-0.775594\pi$
$877$	−45.1093	−1.52323	−0.761616	+	0.648028i	$0.775594\pi$
$878$	19.1142	0.645071
$879$	−12.4285	−0.419203
$880$	0	0
$881$	13.2174	0.445305	0.222653	−	0.974898i	$-0.428528\pi$
$881$	13.2174	0.445305	0.222653	+	0.974898i	$0.428528\pi$
$882$	−6.71996	−0.226273
$883$	−38.4879	−1.29522	−0.647610	−	0.761972i	$-0.724231\pi$
$883$	−38.4879	−1.29522	−0.647610	+	0.761972i	$0.724231\pi$
$884$	3.26878	0.109941
$885$	0	0
$886$	16.2485	0.545880
$887$	−43.4635	−1.45936	−0.729681	−	0.683788i	$-0.760331\pi$
$887$	−43.4635	−1.45936	−0.729681	+	0.683788i	$0.760331\pi$
$888$	6.06089	0.203390
$889$	26.7605	0.897517
$890$	0	0
$891$	−8.30260	−0.278147
$892$	0.0776526	0.00260000
$893$	−0.0815728	−0.00272973
$894$	6.48490	0.216887
$895$	0	0
$896$	−9.69968	−0.324044
$897$	−0.360367	−0.0120323
$898$	11.2626	0.375839
$899$	0.776514	0.0258982
$900$	0	0
$901$	−13.1355	−0.437606
$902$	−9.10117	−0.303036
$903$	0.253457	0.00843452
$904$	2.13599	0.0710418
$905$	0	0
$906$	−8.17523	−0.271604
$907$	−3.08770	−0.102525	−0.0512627	−	0.998685i	$-0.516325\pi$
$907$	−3.08770	−0.102525	−0.0512627	+	0.998685i	$0.516325\pi$
$908$	8.04680	0.267042
$909$	32.4064	1.07485
$910$	0	0
$911$	−22.9439	−0.760164	−0.380082	−	0.924953i	$-0.624104\pi$
$911$	−22.9439	−0.760164	−0.380082	+	0.924953i	$0.624104\pi$
$912$	0.345856	0.0114525
$913$	53.2382	1.76193
$914$	−29.1729	−0.964953
$915$	0	0
$916$	−4.84629	−0.160126
$917$	2.09239	0.0690969
$918$	−17.2820	−0.570390
$919$	−2.80199	−0.0924292	−0.0462146	−	0.998932i	$-0.514716\pi$
$919$	−2.80199	−0.0924292	−0.0462146	+	0.998932i	$0.514716\pi$
$920$	0	0
$921$	−11.1655	−0.367915
$922$	28.4465	0.936835
$923$	29.4492	0.969331
$924$	−4.63811	−0.152583
$925$	0	0
$926$	−9.25063	−0.303995
$927$	−17.9855	−0.590723
$928$	0.239955	0.00787691
$929$	−40.9814	−1.34456	−0.672279	−	0.740298i	$-0.734684\pi$
$929$	−40.9814	−1.34456	−0.672279	+	0.740298i	$0.734684\pi$
$930$	0	0
$931$	−0.372598	−0.0122114
$932$	−0.797426	−0.0261205
$933$	−18.0896	−0.592227
$934$	−27.5909	−0.902800
$935$	0	0
$936$	13.0227	0.425659
$937$	−4.54354	−0.148431	−0.0742154	−	0.997242i	$-0.523645\pi$
$937$	−4.54354	−0.148431	−0.0742154	+	0.997242i	$0.523645\pi$
$938$	−21.9591	−0.716989
$939$	4.27652	0.139559
$940$	0	0
$941$	6.97695	0.227442	0.113721	−	0.993513i	$-0.463723\pi$
$941$	6.97695	0.227442	0.113721	+	0.993513i	$0.463723\pi$
$942$	−19.1884	−0.625190
$943$	0.337476	0.0109897
$944$	−29.4233	−0.957645
$945$	0	0
$946$	−0.677620	−0.0220313
$947$	41.8354	1.35947	0.679735	−	0.733458i	$-0.262095\pi$
$947$	41.8354	1.35947	0.679735	+	0.733458i	$0.262095\pi$
$948$	1.57102	0.0510243
$949$	−7.66323	−0.248759
$950$	0	0
$951$	−14.9684	−0.485384
$952$	19.2460	0.623767
$953$	6.40091	0.207346	0.103673	−	0.994611i	$-0.466940\pi$
$953$	6.40091	0.207346	0.103673	+	0.994611i	$0.466940\pi$
$954$	−11.2491	−0.364205
$955$	0	0
$956$	4.24560	0.137313
$957$	−0.323524	−0.0104580
$958$	−46.1476	−1.49096
$959$	39.0466	1.26088
$960$	0	0
$961$	63.3369	2.04312
$962$	−5.07822	−0.163728
$963$	2.06824	0.0666481
$964$	−0.547644	−0.0176384
$965$	0	0
$966$	−0.456101	−0.0146748
$967$	−8.83238	−0.284030	−0.142015	−	0.989864i	$-0.545358\pi$
$967$	−8.83238	−0.284030	−0.142015	+	0.989864i	$0.545358\pi$
$968$	23.9122	0.768566
$969$	−0.397687	−0.0127756
$970$	0	0
$971$	10.3150	0.331023	0.165511	−	0.986208i	$-0.447073\pi$
$971$	10.3150	0.331023	0.165511	+	0.986208i	$0.447073\pi$
$972$	8.84535	0.283715
$973$	−18.7462	−0.600977
$974$	−38.5717	−1.23592
$975$	0	0
$976$	−18.0781	−0.578664
$977$	−2.59318	−0.0829630	−0.0414815	−	0.999139i	$-0.513208\pi$
$977$	−2.59318	−0.0829630	−0.0414815	+	0.999139i	$0.513208\pi$
$978$	−2.70845	−0.0866066
$979$	−39.7005	−1.26883
$980$	0	0
$981$	20.9043	0.667423
$982$	−49.7786	−1.58850
$983$	28.6126	0.912601	0.456301	−	0.889826i	$-0.349174\pi$
$983$	28.6126	0.912601	0.456301	+	0.889826i	$0.349174\pi$
$984$	4.99396	0.159202
$985$	0	0
$986$	0.288579	0.00919024
$987$	1.12067	0.0356712
$988$	0.155215	0.00493804
$989$	0.0251264	0.000798974 0
$990$	0	0
$991$	51.5276	1.63683	0.818414	−	0.574629i	$-0.194853\pi$
$991$	51.5276	1.63683	0.818414	+	0.574629i	$0.194853\pi$
$992$	29.1516	0.925563
$993$	21.9664	0.697083
$994$	37.2725	1.18221
$995$	0	0
$996$	−6.27957	−0.198976
$997$	−32.7082	−1.03588	−0.517940	−	0.855417i	$-0.673301\pi$
$997$	−32.7082	−1.03588	−0.517940	+	0.855417i	$0.673301\pi$
$998$	−10.7326	−0.339735
$999$	−10.1238	−0.320304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.3		11
5.4	even	2		1205.2.a.b.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.9	✓	11	5.4	even	2
6025.2.a.g.1.3		11	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)

\(f(q)\)	\(=\)	\(q-1.20514 q^{2} -0.933583 q^{3} -0.547644 q^{4} +1.12510 q^{6} +2.09289 q^{7} +3.07026 q^{8} -2.12842 q^{9} +O(q^{10})\)	\(q-1.20514 q^{2} -0.933583 q^{3} -0.547644 q^{4} +1.12510 q^{6} +2.09289 q^{7} +3.07026 q^{8} -2.12842 q^{9} -4.33455 q^{11} +0.511271 q^{12} -1.99281 q^{13} -2.52222 q^{14} -2.60480 q^{16} +2.99516 q^{17} +2.56504 q^{18} +0.142223 q^{19} -1.95388 q^{21} +5.22373 q^{22} -0.193698 q^{23} -2.86634 q^{24} +2.40162 q^{26} +4.78781 q^{27} -1.14616 q^{28} -0.0799482 q^{29} -9.71272 q^{31} -3.00138 q^{32} +4.04666 q^{33} -3.60958 q^{34} +1.16562 q^{36} -2.11450 q^{37} -0.171398 q^{38} +1.86046 q^{39} -1.74228 q^{41} +2.35470 q^{42} -0.129720 q^{43} +2.37379 q^{44} +0.233433 q^{46} -0.573558 q^{47} +2.43180 q^{48} -2.61983 q^{49} -2.79623 q^{51} +1.09135 q^{52} -4.38556 q^{53} -5.76997 q^{54} +6.42571 q^{56} -0.132777 q^{57} +0.0963486 q^{58} +11.2958 q^{59} +6.94029 q^{61} +11.7052 q^{62} -4.45455 q^{63} +8.82667 q^{64} -4.87679 q^{66} +8.70625 q^{67} -1.64028 q^{68} +0.180833 q^{69} -14.7777 q^{71} -6.53481 q^{72} +3.84543 q^{73} +2.54826 q^{74} -0.0778873 q^{76} -9.07172 q^{77} -2.24211 q^{78} +3.07277 q^{79} +1.91545 q^{81} +2.09968 q^{82} -12.2823 q^{83} +1.07003 q^{84} +0.156330 q^{86} +0.0746383 q^{87} -13.3082 q^{88} +9.15908 q^{89} -4.17074 q^{91} +0.106078 q^{92} +9.06763 q^{93} +0.691216 q^{94} +2.80204 q^{96} -9.88057 q^{97} +3.15725 q^{98} +9.22575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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