LMFDB - Embedded newform 725.6.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,6,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("725.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	725.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:	$116.278269364$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 $ x^7 - 3x^6 - 184x^5 + 584x^4 + 10145x^3 - 34491x^2 - 149754x + 524902
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.83960$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.83960 q^{2} -15.9679 q^{3} +2.10095 q^{4} +93.2461 q^{6} -106.304 q^{7} +174.599 q^{8} +11.9736 q^{9} +O(q^{10})$	\(q-5.83960 q^{2} -15.9679 q^{3} +2.10095 q^{4} +93.2461 q^{6} -106.304 q^{7} +174.599 q^{8} +11.9736 q^{9} -152.796 q^{11} -33.5477 q^{12} -325.745 q^{13} +620.776 q^{14} -1086.82 q^{16} +664.939 q^{17} -69.9212 q^{18} -1595.33 q^{19} +1697.46 q^{21} +892.268 q^{22} -719.327 q^{23} -2787.97 q^{24} +1902.22 q^{26} +3689.00 q^{27} -223.340 q^{28} +841.000 q^{29} +2059.61 q^{31} +759.420 q^{32} +2439.83 q^{33} -3882.98 q^{34} +25.1559 q^{36} -14948.4 q^{37} +9316.11 q^{38} +5201.47 q^{39} +14673.9 q^{41} -9912.48 q^{42} -10298.3 q^{43} -321.016 q^{44} +4200.58 q^{46} -4588.36 q^{47} +17354.2 q^{48} -5506.36 q^{49} -10617.7 q^{51} -684.373 q^{52} -8952.75 q^{53} -21542.3 q^{54} -18560.6 q^{56} +25474.1 q^{57} -4911.10 q^{58} -13734.5 q^{59} -33480.9 q^{61} -12027.3 q^{62} -1272.85 q^{63} +30343.4 q^{64} -14247.6 q^{66} -37519.2 q^{67} +1397.00 q^{68} +11486.1 q^{69} -14763.7 q^{71} +2090.58 q^{72} -63298.3 q^{73} +87292.9 q^{74} -3351.71 q^{76} +16242.9 q^{77} -30374.5 q^{78} -27148.9 q^{79} -61815.2 q^{81} -85689.7 q^{82} +54499.5 q^{83} +3566.27 q^{84} +60138.1 q^{86} -13429.0 q^{87} -26678.0 q^{88} -139829. q^{89} +34628.2 q^{91} -1511.27 q^{92} -32887.6 q^{93} +26794.2 q^{94} -12126.3 q^{96} -89845.2 q^{97} +32154.9 q^{98} -1829.52 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 4 q^{2} - 26 q^{3} + 154 q^{4} + 22 q^{6} - 184 q^{7} - 942 q^{8} + 1005 q^{9}+O(q^{10}) $ 7 * q - 4 * q^2 - 26 * q^3 + 154 * q^4 + 22 * q^6 - 184 * q^7 - 942 * q^8 + 1005 * q^9	\( 7 q - 4 q^{2} - 26 q^{3} + 154 q^{4} + 22 q^{6} - 184 q^{7} - 942 q^{8} + 1005 q^{9} + 1106 q^{11} - 214 q^{12} - 408 q^{13} - 2008 q^{14} + 242 q^{16} + 874 q^{17} + 5598 q^{18} + 4288 q^{19} - 4200 q^{21} + 6114 q^{22} + 4532 q^{23} - 4318 q^{24} - 19806 q^{26} - 5942 q^{27} + 496 q^{28} + 5887 q^{29} + 7794 q^{31} - 7898 q^{32} - 34410 q^{33} + 20840 q^{34} - 572 q^{36} - 5086 q^{37} - 23732 q^{38} + 33394 q^{39} + 19826 q^{41} + 55440 q^{42} - 19498 q^{43} - 6074 q^{44} - 12404 q^{46} - 14278 q^{47} + 16406 q^{48} + 38431 q^{49} + 23892 q^{51} + 34302 q^{52} + 58644 q^{53} - 31194 q^{54} - 79560 q^{56} + 88540 q^{57} - 3364 q^{58} + 12888 q^{59} + 102866 q^{61} + 42654 q^{62} + 88632 q^{63} - 10170 q^{64} + 7710 q^{66} - 102996 q^{67} - 85100 q^{68} - 107244 q^{69} - 51596 q^{71} - 135568 q^{72} + 17566 q^{73} + 12132 q^{74} + 360740 q^{76} + 94104 q^{77} - 46386 q^{78} + 212058 q^{79} - 128285 q^{81} - 201924 q^{82} + 122928 q^{83} - 12328 q^{84} - 63290 q^{86} - 21866 q^{87} - 136666 q^{88} - 66510 q^{89} + 194368 q^{91} + 110108 q^{92} + 474274 q^{93} + 438926 q^{94} - 117018 q^{96} + 118182 q^{97} + 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 26 * q^3 + 154 * q^4 + 22 * q^6 - 184 * q^7 - 942 * q^8 + 1005 * q^9 + 1106 * q^11 - 214 * q^12 - 408 * q^13 - 2008 * q^14 + 242 * q^16 + 874 * q^17 + 5598 * q^18 + 4288 * q^19 - 4200 * q^21 + 6114 * q^22 + 4532 * q^23 - 4318 * q^24 - 19806 * q^26 - 5942 * q^27 + 496 * q^28 + 5887 * q^29 + 7794 * q^31 - 7898 * q^32 - 34410 * q^33 + 20840 * q^34 - 572 * q^36 - 5086 * q^37 - 23732 * q^38 + 33394 * q^39 + 19826 * q^41 + 55440 * q^42 - 19498 * q^43 - 6074 * q^44 - 12404 * q^46 - 14278 * q^47 + 16406 * q^48 + 38431 * q^49 + 23892 * q^51 + 34302 * q^52 + 58644 * q^53 - 31194 * q^54 - 79560 * q^56 + 88540 * q^57 - 3364 * q^58 + 12888 * q^59 + 102866 * q^61 + 42654 * q^62 + 88632 * q^63 - 10170 * q^64 + 7710 * q^66 - 102996 * q^67 - 85100 * q^68 - 107244 * q^69 - 51596 * q^71 - 135568 * q^72 + 17566 * q^73 + 12132 * q^74 + 360740 * q^76 + 94104 * q^77 - 46386 * q^78 + 212058 * q^79 - 128285 * q^81 - 201924 * q^82 + 122928 * q^83 - 12328 * q^84 - 63290 * q^86 - 21866 * q^87 - 136666 * q^88 - 66510 * q^89 + 194368 * q^91 + 110108 * q^92 + 474274 * q^93 + 438926 * q^94 - 117018 * q^96 + 118182 * q^97 + 29132 * q^98 + 300668 * 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 $

$2$	−5.83960	−1.03231	−0.516153	−	0.856497i	$-0.672636\pi$
$2$	−5.83960	−1.03231	−0.516153	+	0.856497i	$0.672636\pi$
$3$	−15.9679	−1.02434	−0.512170	−	0.858884i	$-0.671158\pi$
$3$	−15.9679	−1.02434	−0.512170	+	0.858884i	$0.671158\pi$
$4$	2.10095	0.0656545
$5$	0	0
$5$	0	0
$6$	93.2461	1.05743
$7$	−106.304	−0.819986	−0.409993	−	0.912089i	$-0.634469\pi$
$7$	−106.304	−0.819986	−0.409993	+	0.912089i	$0.634469\pi$
$8$	174.599	0.964530
$9$	11.9736	0.0492742
$10$	0	0
$11$	−152.796	−0.380741	−0.190371	−	0.981712i	$-0.560969\pi$
$11$	−152.796	−0.380741	−0.190371	+	0.981712i	$0.560969\pi$
$12$	−33.5477	−0.0672526
$13$	−325.745	−0.534589	−0.267294	−	0.963615i	$-0.586130\pi$
$13$	−325.745	−0.534589	−0.267294	+	0.963615i	$0.586130\pi$
$14$	620.776	0.846476
$15$	0	0
$16$	−1086.82	−1.06134
$17$	664.939	0.558033	0.279016	−	0.960286i	$-0.409992\pi$
$17$	664.939	0.558033	0.279016	+	0.960286i	$0.409992\pi$
$18$	−69.9212	−0.0508660
$19$	−1595.33	−1.01383	−0.506917	−	0.861995i	$-0.669215\pi$
$19$	−1595.33	−1.01383	−0.506917	+	0.861995i	$0.669215\pi$
$20$	0	0
$21$	1697.46	0.839945
$22$	892.268	0.393041
$23$	−719.327	−0.283535	−0.141768	−	0.989900i	$-0.545279\pi$
$23$	−719.327	−0.283535	−0.141768	+	0.989900i	$0.545279\pi$
$24$	−2787.97	−0.988007
$25$	0	0
$26$	1902.22	0.551859
$27$	3689.00	0.973867
$28$	−223.340	−0.0538358
$29$	841.000	0.185695
$29$	841.000	0.185695
$30$	0	0
$31$	2059.61	0.384929	0.192464	−	0.981304i	$-0.438352\pi$
$31$	2059.61	0.384929	0.192464	+	0.981304i	$0.438352\pi$
$32$	759.420	0.131101
$33$	2439.83	0.390009
$34$	−3882.98	−0.576060
$35$	0	0
$36$	25.1559	0.00323508
$37$	−14948.4	−1.79511	−0.897556	−	0.440901i	$-0.854659\pi$
$37$	−14948.4	−1.79511	−0.897556	+	0.440901i	$0.854659\pi$
$38$	9316.11	1.04659
$39$	5201.47	0.547601
$40$	0	0
$41$	14673.9	1.36328	0.681641	−	0.731687i	$-0.261267\pi$
$41$	14673.9	1.36328	0.681641	+	0.731687i	$0.261267\pi$
$42$	−9912.48	−0.867080
$43$	−10298.3	−0.849367	−0.424683	−	0.905342i	$-0.639615\pi$
$43$	−10298.3	−0.849367	−0.424683	+	0.905342i	$0.639615\pi$
$44$	−321.016	−0.0249974
$45$	0	0
$46$	4200.58	0.292695
$47$	−4588.36	−0.302979	−0.151490	−	0.988459i	$-0.548407\pi$
$47$	−4588.36	−0.302979	−0.151490	+	0.988459i	$0.548407\pi$
$48$	17354.2	1.08718
$49$	−5506.36	−0.327623
$50$	0	0
$51$	−10617.7	−0.571616
$52$	−684.373	−0.0350982
$53$	−8952.75	−0.437791	−0.218896	−	0.975748i	$-0.570245\pi$
$53$	−8952.75	−0.437791	−0.218896	+	0.975748i	$0.570245\pi$
$54$	−21542.3	−1.00533
$55$	0	0
$56$	−18560.6	−0.790901
$57$	25474.1	1.03851
$58$	−4911.10	−0.191694
$59$	−13734.5	−0.513670	−0.256835	−	0.966455i	$-0.582680\pi$
$59$	−13734.5	−0.513670	−0.256835	+	0.966455i	$0.582680\pi$
$60$	0	0
$61$	−33480.9	−1.15205	−0.576026	−	0.817431i	$-0.695397\pi$
$61$	−33480.9	−1.15205	−0.576026	+	0.817431i	$0.695397\pi$
$62$	−12027.3	−0.397364
$63$	−1272.85	−0.0404042
$64$	30343.4	0.926007
$65$	0	0
$66$	−14247.6	−0.402608
$67$	−37519.2	−1.02110	−0.510548	−	0.859849i	$-0.670558\pi$
$67$	−37519.2	−1.02110	−0.510548	+	0.859849i	$0.670558\pi$
$68$	1397.00	0.0366374
$69$	11486.1	0.290437
$70$	0	0
$71$	−14763.7	−0.347576	−0.173788	−	0.984783i	$-0.555601\pi$
$71$	−14763.7	−0.347576	−0.173788	+	0.984783i	$0.555601\pi$
$72$	2090.58	0.0475264
$73$	−63298.3	−1.39022	−0.695112	−	0.718901i	$-0.744645\pi$
$73$	−63298.3	−1.39022	−0.695112	+	0.718901i	$0.744645\pi$
$74$	87292.9	1.85310
$75$	0	0
$76$	−3351.71	−0.0665629
$77$	16242.9	0.312203
$78$	−30374.5	−0.565292
$79$	−27148.9	−0.489423	−0.244711	−	0.969596i	$-0.578693\pi$
$79$	−27148.9	−0.489423	−0.244711	+	0.969596i	$0.578693\pi$
$80$	0	0
$81$	−61815.2	−1.04685
$82$	−85689.7	−1.40732
$83$	54499.5	0.868356	0.434178	−	0.900827i	$-0.357039\pi$
$83$	54499.5	0.868356	0.434178	+	0.900827i	$0.357039\pi$
$84$	3566.27	0.0551462
$85$	0	0
$86$	60138.1	0.876806
$87$	−13429.0	−0.190215
$88$	−26678.0	−0.367237
$89$	−139829.	−1.87120	−0.935602	−	0.353057i	$-0.885142\pi$
$89$	−139829.	−1.87120	−0.935602	+	0.353057i	$0.885142\pi$
$90$	0	0
$91$	34628.2	0.438355
$92$	−1511.27	−0.0186154
$93$	−32887.6	−0.394298
$94$	26794.2	0.312767
$95$	0	0
$96$	−12126.3	−0.134292
$97$	−89845.2	−0.969539	−0.484770	−	0.874642i	$-0.661097\pi$
$97$	−89845.2	−0.969539	−0.484770	+	0.874642i	$0.661097\pi$
$98$	32154.9	0.338207
$99$	−1829.52	−0.0187607
$100$	0	0
$101$	−107293.	−1.04657	−0.523285	−	0.852158i	$-0.675294\pi$
$101$	−107293.	−1.04657	−0.523285	+	0.852158i	$0.675294\pi$
$102$	62003.0	0.590082
$103$	−160302.	−1.48884	−0.744419	−	0.667713i	$-0.767273\pi$
$103$	−160302.	−1.48884	−0.744419	+	0.667713i	$0.767273\pi$
$104$	−56874.7	−0.515627
$105$	0	0
$106$	52280.5	0.451934
$107$	−79970.2	−0.675256	−0.337628	−	0.941280i	$-0.609625\pi$
$107$	−79970.2	−0.675256	−0.337628	+	0.941280i	$0.609625\pi$
$108$	7750.40	0.0639388
$109$	−97964.0	−0.789769	−0.394885	−	0.918731i	$-0.629215\pi$
$109$	−97964.0	−0.789769	−0.394885	+	0.918731i	$0.629215\pi$
$110$	0	0
$111$	238695.	1.83881
$112$	115533.	0.870287
$113$	237682.	1.75105	0.875527	−	0.483170i	$-0.160515\pi$
$113$	237682.	1.75105	0.875527	+	0.483170i	$0.160515\pi$
$114$	−148759.	−1.07206
$115$	0	0
$116$	1766.90	0.0121917
$117$	−3900.36	−0.0263414
$118$	80204.2	0.530264
$119$	−70686.0	−0.457579
$120$	0	0
$121$	−137704.	−0.855036
$122$	195515.	1.18927
$123$	−234311.	−1.39647
$124$	4327.12	0.0252723
$125$	0	0
$126$	7432.94	0.0417094
$127$	−194961.	−1.07260	−0.536299	−	0.844028i	$-0.680178\pi$
$127$	−194961.	−1.07260	−0.536299	+	0.844028i	$0.680178\pi$
$128$	−201495.	−1.08702
$129$	164442.	0.870041
$130$	0	0
$131$	350750.	1.78575	0.892873	−	0.450309i	$-0.148686\pi$
$131$	350750.	1.78575	0.892873	+	0.450309i	$0.148686\pi$
$132$	5125.95	0.0256059
$133$	169591.	0.831330
$134$	219097.	1.05408
$135$	0	0
$136$	116097.	0.538239
$137$	−185712.	−0.845356	−0.422678	−	0.906280i	$-0.638910\pi$
$137$	−185712.	−0.845356	−0.422678	+	0.906280i	$0.638910\pi$
$138$	−67074.5	−0.299819
$139$	−316673.	−1.39019	−0.695095	−	0.718918i	$-0.744638\pi$
$139$	−316673.	−1.39019	−0.695095	+	0.718918i	$0.744638\pi$
$140$	0	0
$141$	73266.4	0.310354
$142$	86214.2	0.358804
$143$	49772.6	0.203540
$144$	−13013.1	−0.0522969
$145$	0	0
$146$	369637.	1.43514
$147$	87925.0	0.335598
$148$	−31405.8	−0.117857
$149$	−326686.	−1.20549	−0.602747	−	0.797932i	$-0.705927\pi$
$149$	−326686.	−1.20549	−0.602747	+	0.797932i	$0.705927\pi$
$150$	0	0
$151$	427072.	1.52426	0.762130	−	0.647424i	$-0.224154\pi$
$151$	427072.	1.52426	0.762130	+	0.647424i	$0.224154\pi$
$152$	−278543.	−0.977874
$153$	7961.74	0.0274966
$154$	−94852.0	−0.322289
$155$	0	0
$156$	10928.0	0.0359525
$157$	−48668.5	−0.157579	−0.0787896	−	0.996891i	$-0.525106\pi$
$157$	−48668.5	−0.157579	−0.0787896	+	0.996891i	$0.525106\pi$
$158$	158539.	0.505234
$159$	142957.	0.448447
$160$	0	0
$161$	76467.7	0.232495
$162$	360976.	1.08067
$163$	149764.	0.441509	0.220755	−	0.975329i	$-0.429148\pi$
$163$	149764.	0.441509	0.220755	+	0.975329i	$0.429148\pi$
$164$	30829.0	0.0895056
$165$	0	0
$166$	−318256.	−0.896408
$167$	−371818.	−1.03167	−0.515833	−	0.856689i	$-0.672518\pi$
$167$	−371818.	−1.03167	−0.515833	+	0.856689i	$0.672518\pi$
$168$	296374.	0.810152
$169$	−265183.	−0.714215
$170$	0	0
$171$	−19101.9	−0.0499559
$172$	−21636.2	−0.0557648
$173$	434068.	1.10266	0.551331	−	0.834287i	$-0.314120\pi$
$173$	434068.	1.10266	0.551331	+	0.834287i	$0.314120\pi$
$174$	78420.0	0.196360
$175$	0	0
$176$	166061.	0.404098
$177$	219312.	0.526173
$178$	816543.	1.93165
$179$	341482.	0.796590	0.398295	−	0.917257i	$-0.369602\pi$
$179$	341482.	0.796590	0.398295	+	0.917257i	$0.369602\pi$
$180$	0	0
$181$	542203.	1.23017	0.615086	−	0.788460i	$-0.289121\pi$
$181$	542203.	1.23017	0.615086	+	0.788460i	$0.289121\pi$
$182$	−202215.	−0.452517
$183$	534619.	1.18009
$184$	−125593.	−0.273478
$185$	0	0
$186$	192050.	0.407036
$187$	−101600.	−0.212466
$188$	−9639.89	−0.0198920
$189$	−392158.	−0.798558
$190$	0	0
$191$	−454420.	−0.901310	−0.450655	−	0.892698i	$-0.648810\pi$
$191$	−454420.	−0.901310	−0.450655	+	0.892698i	$0.648810\pi$
$192$	−484520.	−0.948547
$193$	−791182.	−1.52891	−0.764457	−	0.644674i	$-0.776993\pi$
$193$	−791182.	−1.52891	−0.764457	+	0.644674i	$0.776993\pi$
$194$	524660.	1.00086
$195$	0	0
$196$	−11568.6	−0.0215099
$197$	519219.	0.953201	0.476601	−	0.879120i	$-0.341869\pi$
$197$	519219.	0.953201	0.476601	+	0.879120i	$0.341869\pi$
$198$	10683.7	0.0193668
$199$	−301548.	−0.539789	−0.269895	−	0.962890i	$-0.586989\pi$
$199$	−301548.	−0.539789	−0.269895	+	0.962890i	$0.586989\pi$
$200$	0	0
$201$	599103.	1.04595
$202$	626548.	1.08038
$203$	−89402.1	−0.152268
$204$	−22307.2	−0.0375292
$205$	0	0
$206$	936103.	1.53693
$207$	−8612.96	−0.0139710
$208$	354025.	0.567383
$209$	243760.	0.386009
$210$	0	0
$211$	−473908.	−0.732804	−0.366402	−	0.930457i	$-0.619410\pi$
$211$	−473908.	−0.732804	−0.366402	+	0.930457i	$0.619410\pi$
$212$	−18809.2	−0.0287430
$213$	235745.	0.356036
$214$	466994.	0.697071
$215$	0	0
$216$	644095.	0.939324
$217$	−218945.	−0.315636
$218$	572071.	0.815283
$219$	1.01074e6	1.42406
$220$	0	0
$221$	−216601.	−0.298318
$222$	−1.39388e6	−1.89821
$223$	135893.	0.182993	0.0914963	−	0.995805i	$-0.470835\pi$
$223$	135893.	0.182993	0.0914963	+	0.995805i	$0.470835\pi$
$224$	−80729.7	−0.107501
$225$	0	0
$226$	−1.38797e6	−1.80762
$227$	1.21029e6	1.55893	0.779464	−	0.626448i	$-0.215492\pi$
$227$	1.21029e6	1.55893	0.779464	+	0.626448i	$0.215492\pi$
$228$	53519.7	0.0681831
$229$	−577029.	−0.727125	−0.363563	−	0.931570i	$-0.618440\pi$
$229$	−577029.	−0.727125	−0.363563	+	0.931570i	$0.618440\pi$
$230$	0	0
$231$	−259365.	−0.319802
$232$	146837.	0.179109
$233$	966231.	1.16598	0.582990	−	0.812479i	$-0.301883\pi$
$233$	966231.	1.16598	0.582990	+	0.812479i	$0.301883\pi$
$234$	22776.5	0.0271924
$235$	0	0
$236$	−28855.5	−0.0337248
$237$	433510.	0.501336
$238$	412778.	0.472361
$239$	592337.	0.670771	0.335386	−	0.942081i	$-0.391133\pi$
$239$	592337.	0.670771	0.335386	+	0.942081i	$0.391133\pi$
$240$	0	0
$241$	405276.	0.449478	0.224739	−	0.974419i	$-0.427847\pi$
$241$	405276.	0.449478	0.224739	+	0.974419i	$0.427847\pi$
$242$	804139.	0.882658
$243$	90630.9	0.0984601
$244$	−70341.5	−0.0756374
$245$	0	0
$246$	1.36828e6	1.44158
$247$	519672.	0.541985
$248$	359605.	0.371275
$249$	−870243.	−0.889492
$250$	0	0
$251$	922052.	0.923785	0.461893	−	0.886936i	$-0.347171\pi$
$251$	922052.	0.923785	0.461893	+	0.886936i	$0.347171\pi$
$252$	−2674.19	−0.00265272
$253$	109910.	0.107954
$254$	1.13849e6	1.10725
$255$	0	0
$256$	205661.	0.196133
$257$	−461687.	−0.436028	−0.218014	−	0.975946i	$-0.569958\pi$
$257$	−461687.	−0.436028	−0.218014	+	0.975946i	$0.569958\pi$
$258$	−960279.	−0.898148
$259$	1.58909e6	1.47197
$260$	0	0
$261$	10069.8	0.00914999
$262$	−2.04824e6	−1.84344
$263$	1.78425e6	1.59062	0.795311	−	0.606202i	$-0.207308\pi$
$263$	1.78425e6	1.59062	0.795311	+	0.606202i	$0.207308\pi$
$264$	425991.	0.376175
$265$	0	0
$266$	−990344.	−0.858187
$267$	2.23277e6	1.91675
$268$	−78825.9	−0.0670396
$269$	−1.43033e6	−1.20519	−0.602596	−	0.798046i	$-0.705867\pi$
$269$	−1.43033e6	−1.20519	−0.602596	+	0.798046i	$0.705867\pi$
$270$	0	0
$271$	418695.	0.346318	0.173159	−	0.984894i	$-0.444603\pi$
$271$	418695.	0.346318	0.173159	+	0.984894i	$0.444603\pi$
$272$	−722667.	−0.592265
$273$	−552939.	−0.449025
$274$	1.08449e6	0.872666
$275$	0	0
$276$	24131.7	0.0190685
$277$	−319476.	−0.250172	−0.125086	−	0.992146i	$-0.539921\pi$
$277$	−319476.	−0.250172	−0.125086	+	0.992146i	$0.539921\pi$
$278$	1.84925e6	1.43510
$279$	24661.0	0.0189671
$280$	0	0
$281$	421076.	0.318123	0.159061	−	0.987269i	$-0.449153\pi$
$281$	421076.	0.318123	0.159061	+	0.987269i	$0.449153\pi$
$282$	−427847.	−0.320380
$283$	129444.	0.0960759	0.0480380	−	0.998846i	$-0.484703\pi$
$283$	129444.	0.0960759	0.0480380	+	0.998846i	$0.484703\pi$
$284$	−31017.7	−0.0228199
$285$	0	0
$286$	−290652.	−0.210116
$287$	−1.55990e6	−1.11787
$288$	9093.02	0.00645991
$289$	−977713.	−0.688600
$290$	0	0
$291$	1.43464e6	0.993139
$292$	−132986.	−0.0912746
$293$	−1.71643e6	−1.16804	−0.584020	−	0.811740i	$-0.698521\pi$
$293$	−1.71643e6	−1.16804	−0.584020	+	0.811740i	$0.698521\pi$
$294$	−513447.	−0.346439
$295$	0	0
$296$	−2.60998e6	−1.73144
$297$	−563665.	−0.370792
$298$	1.90772e6	1.24444
$299$	234317.	0.151575
$300$	0	0
$301$	1.09476e6	0.696469
$302$	−2.49393e6	−1.57350
$303$	1.71324e6	1.07204
$304$	1.73383e6	1.07603
$305$	0	0
$306$	−46493.4	−0.0283849
$307$	−2.88448e6	−1.74671	−0.873356	−	0.487083i	$-0.838061\pi$
$307$	−2.88448e6	−1.74671	−0.873356	+	0.487083i	$0.838061\pi$
$308$	34125.4	0.0204975
$309$	2.55969e6	1.52508
$310$	0	0
$311$	−2.59382e6	−1.52069	−0.760343	−	0.649522i	$-0.774969\pi$
$311$	−2.59382e6	−1.52069	−0.760343	+	0.649522i	$0.774969\pi$
$312$	908169.	0.528178
$313$	−1.47281e6	−0.849742	−0.424871	−	0.905254i	$-0.639681\pi$
$313$	−1.47281e6	−0.849742	−0.424871	+	0.905254i	$0.639681\pi$
$314$	284205.	0.162670
$315$	0	0
$316$	−57038.3	−0.0321328
$317$	−661940.	−0.369973	−0.184987	−	0.982741i	$-0.559224\pi$
$317$	−661940.	−0.369973	−0.184987	+	0.982741i	$0.559224\pi$
$318$	−834809.	−0.462935
$319$	−128501.	−0.0707019
$320$	0	0
$321$	1.27696e6	0.691693
$322$	−446541.	−0.240006
$323$	−1.06080e6	−0.565753
$324$	−129870.	−0.0687302
$325$	0	0
$326$	−874564.	−0.455772
$327$	1.56428e6	0.808993
$328$	2.56204e6	1.31493
$329$	487763.	0.248439
$330$	0	0
$331$	3.40774e6	1.70961	0.854805	−	0.518949i	$-0.173677\pi$
$331$	3.40774e6	1.70961	0.854805	+	0.518949i	$0.173677\pi$
$332$	114501.	0.0570115
$333$	−178987.	−0.0884527
$334$	2.17127e6	1.06499
$335$	0	0
$336$	−1.84483e6	−0.891471
$337$	2.52588e6	1.21154	0.605771	−	0.795639i	$-0.292865\pi$
$337$	2.52588e6	1.21154	0.605771	+	0.795639i	$0.292865\pi$
$338$	1.54856e6	0.737288
$339$	−3.79527e6	−1.79368
$340$	0	0
$341$	−314700.	−0.146558
$342$	111548.	0.0515698
$343$	2.37201e6	1.08863
$344$	−1.79807e6	−0.819240
$345$	0	0
$346$	−2.53478e6	−1.13828
$347$	2.09340e6	0.933317	0.466658	−	0.884438i	$-0.345458\pi$
$347$	2.09340e6	0.933317	0.466658	+	0.884438i	$0.345458\pi$
$348$	−28213.6	−0.0124885
$349$	2.90749e6	1.27777	0.638887	−	0.769300i	$-0.279395\pi$
$349$	2.90749e6	1.27777	0.638887	+	0.769300i	$0.279395\pi$
$350$	0	0
$351$	−1.20168e6	−0.520619
$352$	−116036.	−0.0499157
$353$	8176.61	0.00349250	0.00174625	−	0.999998i	$-0.499444\pi$
$353$	8176.61	0.00349250	0.00174625	+	0.999998i	$0.499444\pi$
$354$	−1.28069e6	−0.543171
$355$	0	0
$356$	−293772.	−0.122853
$357$	1.12871e6	0.468717
$358$	−1.99412e6	−0.822324
$359$	457001.	0.187146	0.0935732	−	0.995612i	$-0.470171\pi$
$359$	457001.	0.187146	0.0935732	+	0.995612i	$0.470171\pi$
$360$	0	0
$361$	68986.9	0.0278611
$362$	−3.16625e6	−1.26991
$363$	2.19885e6	0.875848
$364$	72752.0	0.0287800
$365$	0	0
$366$	−3.12196e6	−1.21822
$367$	−3.50049e6	−1.35664	−0.678318	−	0.734768i	$-0.737291\pi$
$367$	−3.50049e6	−1.35664	−0.678318	+	0.734768i	$0.737291\pi$
$368$	781776.	0.300928
$369$	175700.	0.0671746
$370$	0	0
$371$	951717.	0.358983
$372$	−69095.0	−0.0258875
$373$	2.17554e6	0.809645	0.404822	−	0.914395i	$-0.367333\pi$
$373$	2.17554e6	0.809645	0.404822	+	0.914395i	$0.367333\pi$
$374$	593304.	0.219330
$375$	0	0
$376$	−801121.	−0.292232
$377$	−273952.	−0.0992707
$378$	2.29004e6	0.824355
$379$	1.97581e6	0.706557	0.353278	−	0.935518i	$-0.385067\pi$
$379$	1.97581e6	0.706557	0.353278	+	0.935518i	$0.385067\pi$
$380$	0	0
$381$	3.11311e6	1.09871
$382$	2.65363e6	0.930428
$383$	−2.77434e6	−0.966412	−0.483206	−	0.875507i	$-0.660528\pi$
$383$	−2.77434e6	−0.966412	−0.483206	+	0.875507i	$0.660528\pi$
$384$	3.21745e6	1.11348
$385$	0	0
$386$	4.62019e6	1.57831
$387$	−123308.	−0.0418519
$388$	−188760.	−0.0636547
$389$	2.12869e6	0.713245	0.356622	−	0.934249i	$-0.383928\pi$
$389$	2.12869e6	0.713245	0.356622	+	0.934249i	$0.383928\pi$
$390$	0	0
$391$	−478309.	−0.158222
$392$	−961402.	−0.316002
$393$	−5.60074e6	−1.82921
$394$	−3.03203e6	−0.983995
$395$	0	0
$396$	−3843.73	−0.00123173
$397$	−2.73423e6	−0.870680	−0.435340	−	0.900266i	$-0.643372\pi$
$397$	−2.73423e6	−0.870680	−0.435340	+	0.900266i	$0.643372\pi$
$398$	1.76092e6	0.557228
$399$	−2.70801e6	−0.851566
$400$	0	0
$401$	−1.29206e6	−0.401257	−0.200628	−	0.979667i	$-0.564298\pi$
$401$	−1.29206e6	−0.401257	−0.200628	+	0.979667i	$0.564298\pi$
$402$	−3.49852e6	−1.07974
$403$	−670908.	−0.205779
$404$	−225417.	−0.0687120
$405$	0	0
$406$	522072.	0.157187
$407$	2.28406e6	0.683473
$408$	−1.85383e6	−0.551340
$409$	−2.78691e6	−0.823787	−0.411894	−	0.911232i	$-0.635132\pi$
$409$	−2.78691e6	−0.823787	−0.411894	+	0.911232i	$0.635132\pi$
$410$	0	0
$411$	2.96544e6	0.865933
$412$	−336787.	−0.0977489
$413$	1.46004e6	0.421202
$414$	50296.2	0.0144223
$415$	0	0
$416$	−247378.	−0.0700853
$417$	5.05660e6	1.42403
$418$	−1.42346e6	−0.398479
$419$	−1.51265e6	−0.420924	−0.210462	−	0.977602i	$-0.567497\pi$
$419$	−1.51265e6	−0.420924	−0.210462	+	0.977602i	$0.567497\pi$
$420$	0	0
$421$	2.55990e6	0.703911	0.351955	−	0.936017i	$-0.385517\pi$
$421$	2.55990e6	0.703911	0.351955	+	0.936017i	$0.385517\pi$
$422$	2.76743e6	0.756477
$423$	−54939.3	−0.0149291
$424$	−1.56314e6	−0.422263
$425$	0	0
$426$	−1.37666e6	−0.367538
$427$	3.55917e6	0.944666
$428$	−168013.	−0.0443336
$429$	−794763.	−0.208495
$430$	0	0
$431$	−5.38406e6	−1.39610	−0.698051	−	0.716048i	$-0.745949\pi$
$431$	−5.38406e6	−1.39610	−0.698051	+	0.716048i	$0.745949\pi$
$432$	−4.00927e6	−1.03361
$433$	−1.90699e6	−0.488797	−0.244398	−	0.969675i	$-0.578590\pi$
$433$	−1.90699e6	−0.488797	−0.244398	+	0.969675i	$0.578590\pi$
$434$	1.27855e6	0.325833
$435$	0	0
$436$	−205817.	−0.0518520
$437$	1.14757e6	0.287458
$438$	−5.90232e6	−1.47007
$439$	−3.84641e6	−0.952565	−0.476283	−	0.879292i	$-0.658016\pi$
$439$	−3.84641e6	−0.952565	−0.476283	+	0.879292i	$0.658016\pi$
$440$	0	0
$441$	−65931.1	−0.0161434
$442$	1.26486e6	0.307955
$443$	−1.43911e6	−0.348406	−0.174203	−	0.984710i	$-0.555735\pi$
$443$	−1.43911e6	−0.348406	−0.174203	+	0.984710i	$0.555735\pi$
$444$	501485.	0.120726
$445$	0	0
$446$	−793558.	−0.188904
$447$	5.21649e6	1.23484
$448$	−3.22564e6	−0.759313
$449$	−5.05146e6	−1.18250	−0.591249	−	0.806489i	$-0.701365\pi$
$449$	−5.05146e6	−1.18250	−0.591249	+	0.806489i	$0.701365\pi$
$450$	0	0
$451$	−2.24211e6	−0.519058
$452$	499356.	0.114965
$453$	−6.81945e6	−1.56136
$454$	−7.06763e6	−1.60929
$455$	0	0
$456$	4.44774e6	1.00168
$457$	3.02849e6	0.678323	0.339161	−	0.940728i	$-0.389857\pi$
$457$	3.02849e6	0.678323	0.339161	+	0.940728i	$0.389857\pi$
$458$	3.36962e6	0.750615
$459$	2.45296e6	0.543450
$460$	0	0
$461$	−3.54068e6	−0.775951	−0.387976	−	0.921670i	$-0.626826\pi$
$461$	−3.54068e6	−0.775951	−0.387976	+	0.921670i	$0.626826\pi$
$462$	1.51459e6	0.330133
$463$	−3.78475e6	−0.820512	−0.410256	−	0.911970i	$-0.634561\pi$
$463$	−3.78475e6	−0.820512	−0.410256	+	0.911970i	$0.634561\pi$
$464$	−914012.	−0.197087
$465$	0	0
$466$	−5.64240e6	−1.20365
$467$	3.93030e6	0.833938	0.416969	−	0.908921i	$-0.363092\pi$
$467$	3.93030e6	0.833938	0.416969	+	0.908921i	$0.363092\pi$
$468$	−8194.44	−0.00172944
$469$	3.98846e6	0.837285
$470$	0	0
$471$	777134.	0.161415
$472$	−2.39803e6	−0.495450
$473$	1.57354e6	0.323389
$474$	−2.53153e6	−0.517531
$475$	0	0
$476$	−148507.	−0.0300421
$477$	−107197.	−0.0215718
$478$	−3.45901e6	−0.692441
$479$	−3.65493e6	−0.727848	−0.363924	−	0.931429i	$-0.618563\pi$
$479$	−3.65493e6	−0.727848	−0.363924	+	0.931429i	$0.618563\pi$
$480$	0	0
$481$	4.86938e6	0.959647
$482$	−2.36665e6	−0.463999
$483$	−1.22103e6	−0.238154
$484$	−289309.	−0.0561370
$485$	0	0
$486$	−529248.	−0.101641
$487$	3.90232e6	0.745591	0.372796	−	0.927913i	$-0.378399\pi$
$487$	3.90232e6	0.745591	0.372796	+	0.927913i	$0.378399\pi$
$488$	−5.84571e6	−1.11119
$489$	−2.39142e6	−0.452256
$490$	0	0
$491$	8.22645e6	1.53996	0.769979	−	0.638069i	$-0.220267\pi$
$491$	8.22645e6	1.53996	0.769979	+	0.638069i	$0.220267\pi$
$492$	−492275.	−0.0916843
$493$	559214.	0.103624
$494$	−3.03468e6	−0.559494
$495$	0	0
$496$	−2.23841e6	−0.408542
$497$	1.56945e6	0.285007
$498$	5.08187e6	0.918228
$499$	1.95126e6	0.350803	0.175401	−	0.984497i	$-0.443878\pi$
$499$	1.95126e6	0.350803	0.175401	+	0.984497i	$0.443878\pi$
$500$	0	0
$501$	5.93715e6	1.05678
$502$	−5.38442e6	−0.953629
$503$	−6.74097e6	−1.18796	−0.593981	−	0.804479i	$-0.702445\pi$
$503$	−6.74097e6	−1.18796	−0.593981	+	0.804479i	$0.702445\pi$
$504$	−222238.	−0.0389710
$505$	0	0
$506$	−641832.	−0.111441
$507$	4.23441e6	0.731599
$508$	−409601.	−0.0704210
$509$	2.57165e6	0.439964	0.219982	−	0.975504i	$-0.429400\pi$
$509$	2.57165e6	0.439964	0.219982	+	0.975504i	$0.429400\pi$
$510$	0	0
$511$	6.72889e6	1.13996
$512$	5.24686e6	0.884554
$513$	−5.88519e6	−0.987341
$514$	2.69607e6	0.450114
$515$	0	0
$516$	345485.	0.0571221
$517$	701083.	0.115357
$518$	−9.27963e6	−1.51952
$519$	−6.93115e6	−1.12950
$520$	0	0
$521$	1.25025e6	0.201791	0.100896	−	0.994897i	$-0.467829\pi$
$521$	1.25025e6	0.201791	0.100896	+	0.994897i	$0.467829\pi$
$522$	−58803.8	−0.00944559
$523$	188395.	0.0301172	0.0150586	−	0.999887i	$-0.495207\pi$
$523$	188395.	0.0301172	0.0150586	+	0.999887i	$0.495207\pi$
$524$	736907.	0.117242
$525$	0	0
$526$	−1.04193e7	−1.64201
$527$	1.36951e6	0.214803
$528$	−2.65165e6	−0.413934
$529$	−5.91891e6	−0.919608
$530$	0	0
$531$	−164452.	−0.0253107
$532$	356301.	0.0545806
$533$	−4.77995e6	−0.728795
$534$	−1.30385e7	−1.97867
$535$	0	0
$536$	−6.55080e6	−0.984878
$537$	−5.45274e6	−0.815980
$538$	8.35258e6	1.24413
$539$	841349.	0.124740
$540$	0	0
$541$	−7.69990e6	−1.13108	−0.565538	−	0.824722i	$-0.691331\pi$
$541$	−7.69990e6	−1.13108	−0.565538	+	0.824722i	$0.691331\pi$
$542$	−2.44501e6	−0.357506
$543$	−8.65785e6	−1.26012
$544$	504968.	0.0731588
$545$	0	0
$546$	3.22895e6	0.463531
$547$	−1.21820e7	−1.74081	−0.870406	−	0.492334i	$-0.836144\pi$
$547$	−1.21820e7	−1.74081	−0.870406	+	0.492334i	$0.836144\pi$
$548$	−390172.	−0.0555015
$549$	−400888.	−0.0567664
$550$	0	0
$551$	−1.34167e6	−0.188264
$552$	2.00546e6	0.280135
$553$	2.88605e6	0.401320
$554$	1.86561e6	0.258254
$555$	0	0
$556$	−665313.	−0.0912723
$557$	−5.21687e6	−0.712479	−0.356239	−	0.934395i	$-0.615941\pi$
$557$	−5.21687e6	−0.712479	−0.356239	+	0.934395i	$0.615941\pi$
$558$	−144010.	−0.0195798
$559$	3.35463e6	0.454062
$560$	0	0
$561$	1.62234e6	0.217638
$562$	−2.45892e6	−0.328400
$563$	782547.	0.104049	0.0520247	−	0.998646i	$-0.483433\pi$
$563$	782547.	0.104049	0.0520247	+	0.998646i	$0.483433\pi$
$564$	153929.	0.0203761
$565$	0	0
$566$	−755899.	−0.0991797
$567$	6.57123e6	0.858399
$568$	−2.57772e6	−0.335247
$569$	1.01820e7	1.31841	0.659206	−	0.751962i	$-0.270893\pi$
$569$	1.01820e7	1.31841	0.659206	+	0.751962i	$0.270893\pi$
$570$	0	0
$571$	−1.56900e6	−0.201388	−0.100694	−	0.994917i	$-0.532106\pi$
$571$	−1.56900e6	−0.201388	−0.100694	+	0.994917i	$0.532106\pi$
$572$	104569.	0.0133633
$573$	7.25614e6	0.923249
$574$	9.10919e6	1.15399
$575$	0	0
$576$	363321.	0.0456283
$577$	1.53116e7	1.91462	0.957308	−	0.289069i	$-0.0933458\pi$
$577$	1.53116e7	1.91462	0.957308	+	0.289069i	$0.0933458\pi$
$578$	5.70945e6	0.710845
$579$	1.26335e7	1.56613
$580$	0	0
$581$	−5.79355e6	−0.712040
$582$	−8.37771e6	−1.02522
$583$	1.36794e6	0.166685
$584$	−1.10518e7	−1.34091
$585$	0	0
$586$	1.00233e7	1.20577
$587$	−3.65745e6	−0.438110	−0.219055	−	0.975712i	$-0.570297\pi$
$587$	−3.65745e6	−0.438110	−0.219055	+	0.975712i	$0.570297\pi$
$588$	184726.	0.0220335
$589$	−3.28576e6	−0.390254
$590$	0	0
$591$	−8.29083e6	−0.976403
$592$	1.62462e7	1.90523
$593$	7.18479e6	0.839029	0.419515	−	0.907749i	$-0.362200\pi$
$593$	7.18479e6	0.839029	0.419515	+	0.907749i	$0.362200\pi$
$594$	3.29158e6	0.382770
$595$	0	0
$596$	−686350.	−0.0791462
$597$	4.81509e6	0.552928
$598$	−1.36832e6	−0.156471
$599$	2.35482e6	0.268158	0.134079	−	0.990971i	$-0.457192\pi$
$599$	2.35482e6	0.268158	0.134079	+	0.990971i	$0.457192\pi$
$600$	0	0
$601$	−7.49135e6	−0.846007	−0.423003	−	0.906128i	$-0.639024\pi$
$601$	−7.49135e6	−0.846007	−0.423003	+	0.906128i	$0.639024\pi$
$602$	−6.39295e6	−0.718969
$603$	−449241.	−0.0503137
$604$	897256.	0.100075
$605$	0	0
$606$	−1.00047e7	−1.10668
$607$	−248110.	−0.0273320	−0.0136660	−	0.999907i	$-0.504350\pi$
$607$	−248110.	−0.0273320	−0.0136660	+	0.999907i	$0.504350\pi$
$608$	−1.21153e6	−0.132915
$609$	1.42756e6	0.155974
$610$	0	0
$611$	1.49464e6	0.161969
$612$	16727.2	0.00180528
$613$	1.97712e6	0.212511	0.106256	−	0.994339i	$-0.466114\pi$
$613$	1.97712e6	0.212511	0.106256	+	0.994339i	$0.466114\pi$
$614$	1.68442e7	1.80314
$615$	0	0
$616$	2.83599e6	0.301129
$617$	−1.43605e7	−1.51865	−0.759323	−	0.650714i	$-0.774470\pi$
$617$	−1.43605e7	−1.51865	−0.759323	+	0.650714i	$0.774470\pi$
$618$	−1.49476e7	−1.57435
$619$	−3.63487e6	−0.381297	−0.190648	−	0.981658i	$-0.561059\pi$
$619$	−3.63487e6	−0.381297	−0.190648	+	0.981658i	$0.561059\pi$
$620$	0	0
$621$	−2.65360e6	−0.276126
$622$	1.51469e7	1.56981
$623$	1.48644e7	1.53436
$624$	−5.65304e6	−0.581193
$625$	0	0
$626$	8.60065e6	0.877193
$627$	−3.89234e6	−0.395405
$628$	−102250.	−0.0103458
$629$	−9.93980e6	−1.00173
$630$	0	0
$631$	−1.71093e6	−0.171065	−0.0855323	−	0.996335i	$-0.527259\pi$
$631$	−1.71093e6	−0.171065	−0.0855323	+	0.996335i	$0.527259\pi$
$632$	−4.74015e6	−0.472063
$633$	7.56731e6	0.750641
$634$	3.86547e6	0.381926
$635$	0	0
$636$	300344.	0.0294426
$637$	1.79367e6	0.175144
$638$	750397.	0.0729860
$639$	−176775.	−0.0171265
$640$	0	0
$641$	−7.33888e6	−0.705480	−0.352740	−	0.935721i	$-0.614750\pi$
$641$	−7.33888e6	−0.705480	−0.352740	+	0.935721i	$0.614750\pi$
$642$	−7.45691e6	−0.714038
$643$	−1.65108e7	−1.57485	−0.787426	−	0.616409i	$-0.788587\pi$
$643$	−1.65108e7	−1.57485	−0.787426	+	0.616409i	$0.788587\pi$
$644$	160654.	0.0152643
$645$	0	0
$646$	6.19464e6	0.584030
$647$	4.75302e6	0.446384	0.223192	−	0.974774i	$-0.428352\pi$
$647$	4.75302e6	0.446384	0.223192	+	0.974774i	$0.428352\pi$
$648$	−1.07928e7	−1.00971
$649$	2.09858e6	0.195575
$650$	0	0
$651$	3.49610e6	0.323319
$652$	314647.	0.0289871
$653$	−2.06957e7	−1.89932	−0.949658	−	0.313290i	$-0.898569\pi$
$653$	−2.06957e7	−1.89932	−0.949658	+	0.313290i	$0.898569\pi$
$654$	−9.13477e6	−0.835128
$655$	0	0
$656$	−1.59478e7	−1.44691
$657$	−757911.	−0.0685022
$658$	−2.84834e6	−0.256465
$659$	1.75250e7	1.57197	0.785987	−	0.618244i	$-0.212155\pi$
$659$	1.75250e7	1.57197	0.785987	+	0.618244i	$0.212155\pi$
$660$	0	0
$661$	5.06876e6	0.451230	0.225615	−	0.974217i	$-0.427561\pi$
$661$	5.06876e6	0.451230	0.225615	+	0.974217i	$0.427561\pi$
$662$	−1.98999e7	−1.76484
$663$	3.45866e6	0.305579
$664$	9.51554e6	0.837555
$665$	0	0
$666$	1.04521e6	0.0913102
$667$	−604954.	−0.0526511
$668$	−781170.	−0.0677336
$669$	−2.16992e6	−0.187447
$670$	0	0
$671$	5.11574e6	0.438634
$672$	1.28908e6	0.110118
$673$	−1.07503e7	−0.914922	−0.457461	−	0.889230i	$-0.651241\pi$
$673$	−1.07503e7	−0.914922	−0.457461	+	0.889230i	$0.651241\pi$
$674$	−1.47501e7	−1.25068
$675$	0	0
$676$	−557135.	−0.0468914
$677$	6.95239e6	0.582992	0.291496	−	0.956572i	$-0.405847\pi$
$677$	6.95239e6	0.582992	0.291496	+	0.956572i	$0.405847\pi$
$678$	2.21629e7	1.85162
$679$	9.55094e6	0.795009
$680$	0	0
$681$	−1.93258e7	−1.59687
$682$	1.83772e6	0.151293
$683$	1.26571e7	1.03821	0.519103	−	0.854711i	$-0.326266\pi$
$683$	1.26571e7	1.03821	0.519103	+	0.854711i	$0.326266\pi$
$684$	−40132.1	−0.00327983
$685$	0	0
$686$	−1.38516e7	−1.12380
$687$	9.21394e6	0.744824
$688$	1.11924e7	0.901470
$689$	2.91632e6	0.234038
$690$	0	0
$691$	−7.61067e6	−0.606356	−0.303178	−	0.952934i	$-0.598048\pi$
$691$	−7.61067e6	−0.606356	−0.303178	+	0.952934i	$0.598048\pi$
$692$	911952.	0.0723947
$693$	194486.	0.0153835
$694$	−1.22246e7	−0.963468
$695$	0	0
$696$	−2.34468e6	−0.183468
$697$	9.75724e6	0.760756
$698$	−1.69786e7	−1.31905
$699$	−1.54287e7	−1.19436
$700$	0	0
$701$	−1.63413e7	−1.25600	−0.628002	−	0.778211i	$-0.716127\pi$
$701$	−1.63413e7	−1.25600	−0.628002	+	0.778211i	$0.716127\pi$
$702$	7.01731e6	0.537437
$703$	2.38477e7	1.81995
$704$	−4.63635e6	−0.352569
$705$	0	0
$706$	−47748.1	−0.00360533
$707$	1.14057e7	0.858172
$708$	460762.	0.0345456
$709$	1.11269e7	0.831300	0.415650	−	0.909525i	$-0.363554\pi$
$709$	1.11269e7	0.831300	0.415650	+	0.909525i	$0.363554\pi$
$710$	0	0
$711$	−325071.	−0.0241159
$712$	−2.44139e7	−1.80483
$713$	−1.48153e6	−0.109141
$714$	−6.59120e6	−0.483859
$715$	0	0
$716$	717434.	0.0522997
$717$	−9.45838e6	−0.687098
$718$	−2.66871e6	−0.193192
$719$	1.28895e7	0.929849	0.464924	−	0.885350i	$-0.346081\pi$
$719$	1.28895e7	0.929849	0.464924	+	0.885350i	$0.346081\pi$
$720$	0	0
$721$	1.70409e7	1.22083
$722$	−402856.	−0.0287612
$723$	−6.47141e6	−0.460419
$724$	1.13914e6	0.0807664
$725$	0	0
$726$	−1.28404e7	−0.904143
$727$	2.32214e7	1.62949	0.814745	−	0.579820i	$-0.196877\pi$
$727$	2.32214e7	1.62949	0.814745	+	0.579820i	$0.196877\pi$
$728$	6.04603e6	0.422807
$729$	1.35739e7	0.945990
$730$	0	0
$731$	−6.84776e6	−0.473974
$732$	1.12321e6	0.0774785
$733$	8.72009e6	0.599461	0.299731	−	0.954024i	$-0.403103\pi$
$733$	8.72009e6	0.599461	0.299731	+	0.954024i	$0.403103\pi$
$734$	2.04415e7	1.40046
$735$	0	0
$736$	−546271.	−0.0371718
$737$	5.73279e6	0.388774
$738$	−1.02602e6	−0.0693447
$739$	2.49740e7	1.68220	0.841098	−	0.540882i	$-0.181910\pi$
$739$	2.49740e7	1.68220	0.841098	+	0.540882i	$0.181910\pi$
$740$	0	0
$741$	−8.29807e6	−0.555177
$742$	−5.55765e6	−0.370580
$743$	288063.	0.0191433	0.00957164	−	0.999954i	$-0.496953\pi$
$743$	288063.	0.0191433	0.00957164	+	0.999954i	$0.496953\pi$
$744$	−5.74213e6	−0.380312
$745$	0	0
$746$	−1.27043e7	−0.835801
$747$	652558.	0.0427875
$748$	−213456.	−0.0139494
$749$	8.50119e6	0.553701
$750$	0	0
$751$	2.19870e7	1.42255	0.711274	−	0.702915i	$-0.248119\pi$
$751$	2.19870e7	1.42255	0.711274	+	0.702915i	$0.248119\pi$
$752$	4.98670e6	0.321565
$753$	−1.47232e7	−0.946271
$754$	1.59977e6	0.102478
$755$	0	0
$756$	−823902.	−0.0524289
$757$	6.72062e6	0.426255	0.213128	−	0.977024i	$-0.431635\pi$
$757$	6.72062e6	0.426255	0.213128	+	0.977024i	$0.431635\pi$
$758$	−1.15379e7	−0.729382
$759$	−1.75504e6	−0.110581
$760$	0	0
$761$	−1.10936e7	−0.694400	−0.347200	−	0.937791i	$-0.612868\pi$
$761$	−1.10936e7	−0.694400	−0.347200	+	0.937791i	$0.612868\pi$
$762$	−1.81793e7	−1.13420
$763$	1.04140e7	0.647600
$764$	−954712.	−0.0591751
$765$	0	0
$766$	1.62010e7	0.997632
$767$	4.47396e6	0.274602
$768$	−3.28397e6	−0.200907
$769$	6.42928e6	0.392054	0.196027	−	0.980598i	$-0.437196\pi$
$769$	6.42928e6	0.392054	0.196027	+	0.980598i	$0.437196\pi$
$770$	0	0
$771$	7.37217e6	0.446642
$772$	−1.66223e6	−0.100380
$773$	1.38614e7	0.834371	0.417185	−	0.908821i	$-0.363017\pi$
$773$	1.38614e7	0.834371	0.417185	+	0.908821i	$0.363017\pi$
$774$	720071.	0.0432039
$775$	0	0
$776$	−1.56868e7	−0.935150
$777$	−2.53743e7	−1.50780
$778$	−1.24307e7	−0.736287
$779$	−2.34097e7	−1.38214
$780$	0	0
$781$	2.25584e6	0.132337
$782$	2.79313e6	0.163333
$783$	3.10245e6	0.180843
$784$	5.98440e6	0.347721
$785$	0	0
$786$	3.27061e7	1.88831
$787$	−2.48798e7	−1.43189	−0.715945	−	0.698157i	$-0.754004\pi$
$787$	−2.48798e7	−1.43189	−0.715945	+	0.698157i	$0.754004\pi$
$788$	1.09085e6	0.0625820
$789$	−2.84907e7	−1.62934
$790$	0	0
$791$	−2.52666e7	−1.43584
$792$	−319432.	−0.0180953
$793$	1.09062e7	0.615874
$794$	1.59668e7	0.898808
$795$	0	0
$796$	−633537.	−0.0354396
$797$	−2.80418e7	−1.56372	−0.781861	−	0.623453i	$-0.785729\pi$
$797$	−2.80418e7	−1.56372	−0.781861	+	0.623453i	$0.785729\pi$
$798$	1.58137e7	0.879076
$799$	−3.05098e6	−0.169072
$800$	0	0
$801$	−1.67426e6	−0.0922021
$802$	7.54513e6	0.414220
$803$	9.67173e6	0.529316
$804$	1.25868e6	0.0686714
$805$	0	0
$806$	3.91783e6	0.212426
$807$	2.28394e7	1.23453
$808$	−1.87332e7	−1.00945
$809$	2.45320e7	1.31784	0.658919	−	0.752214i	$-0.271014\pi$
$809$	2.45320e7	1.31784	0.658919	+	0.752214i	$0.271014\pi$
$810$	0	0
$811$	2.44306e7	1.30431	0.652156	−	0.758084i	$-0.273865\pi$
$811$	2.44306e7	1.30431	0.652156	+	0.758084i	$0.273865\pi$
$812$	−187829.	−0.00999706
$813$	−6.68568e6	−0.354748
$814$	−1.33380e7	−0.705553
$815$	0	0
$816$	1.15395e7	0.606681
$817$	1.64292e7	0.861118
$818$	1.62745e7	0.850400
$819$	414625.	0.0215996
$820$	0	0
$821$	−4.22220e6	−0.218615	−0.109308	−	0.994008i	$-0.534863\pi$
$821$	−4.22220e6	−0.218615	−0.109308	+	0.994008i	$0.534863\pi$
$822$	−1.73170e7	−0.893907
$823$	2.11475e7	1.08833	0.544165	−	0.838979i	$-0.316847\pi$
$823$	2.11475e7	1.08833	0.544165	+	0.838979i	$0.316847\pi$
$824$	−2.79886e7	−1.43603
$825$	0	0
$826$	−8.52607e6	−0.434809
$827$	−2.31990e6	−0.117952	−0.0589761	−	0.998259i	$-0.518784\pi$
$827$	−2.31990e6	−0.117952	−0.0589761	+	0.998259i	$0.518784\pi$
$828$	−18095.4	−0.000917257 0
$829$	2.89837e7	1.46476	0.732381	−	0.680895i	$-0.238409\pi$
$829$	2.89837e7	1.46476	0.732381	+	0.680895i	$0.238409\pi$
$830$	0	0
$831$	5.10137e6	0.256262
$832$	−9.88423e6	−0.495033
$833$	−3.66139e6	−0.182824
$834$	−2.95286e7	−1.47003
$835$	0	0
$836$	512127.	0.0253432
$837$	7.59790e6	0.374869
$838$	8.83328e6	0.434522
$839$	3.32541e7	1.63095	0.815473	−	0.578795i	$-0.196477\pi$
$839$	3.32541e7	1.63095	0.815473	+	0.578795i	$0.196477\pi$
$840$	0	0
$841$	707281.	0.0344828
$842$	−1.49488e7	−0.726651
$843$	−6.72370e6	−0.325866
$844$	−995655.	−0.0481119
$845$	0	0
$846$	320824.	0.0154113
$847$	1.46386e7	0.701118
$848$	9.73000e6	0.464647
$849$	−2.06694e6	−0.0984145
$850$	0	0
$851$	1.07528e7	0.508977
$852$	495288.	0.0233754
$853$	−1.48503e7	−0.698816	−0.349408	−	0.936971i	$-0.613617\pi$
$853$	−1.48503e7	−0.698816	−0.349408	+	0.936971i	$0.613617\pi$
$854$	−2.07841e7	−0.975184
$855$	0	0
$856$	−1.39627e7	−0.651305
$857$	−2.15523e7	−1.00240	−0.501201	−	0.865331i	$-0.667108\pi$
$857$	−2.15523e7	−1.00240	−0.501201	+	0.865331i	$0.667108\pi$
$858$	4.64110e6	0.215230
$859$	−1.84444e7	−0.852867	−0.426434	−	0.904519i	$-0.640230\pi$
$859$	−1.84444e7	−0.852867	−0.426434	+	0.904519i	$0.640230\pi$
$860$	0	0
$861$	2.49083e7	1.14508
$862$	3.14408e7	1.44120
$863$	2.12674e7	0.972046	0.486023	−	0.873946i	$-0.338447\pi$
$863$	2.12674e7	0.972046	0.486023	+	0.873946i	$0.338447\pi$
$864$	2.80150e6	0.127675
$865$	0	0
$866$	1.11360e7	0.504587
$867$	1.56120e7	0.705361
$868$	−459993.	−0.0207229
$869$	4.14824e6	0.186343
$870$	0	0
$871$	1.22217e7	0.545867
$872$	−1.71044e7	−0.761756
$873$	−1.07577e6	−0.0477733
$874$	−6.70133e6	−0.296744
$875$	0	0
$876$	2.12351e6	0.0934963
$877$	2.51615e7	1.10468	0.552342	−	0.833618i	$-0.313734\pi$
$877$	2.51615e7	1.10468	0.552342	+	0.833618i	$0.313734\pi$
$878$	2.24615e7	0.983338
$879$	2.74078e7	1.19647
$880$	0	0
$881$	1.60794e7	0.697961	0.348980	−	0.937130i	$-0.386528\pi$
$881$	1.60794e7	0.697961	0.348980	+	0.937130i	$0.386528\pi$
$882$	385011.	0.0166649
$883$	7.09137e6	0.306075	0.153038	−	0.988220i	$-0.451094\pi$
$883$	7.09137e6	0.306075	0.153038	+	0.988220i	$0.451094\pi$
$884$	−455067.	−0.0195859
$885$	0	0
$886$	8.40384e6	0.359661
$887$	1.00313e7	0.428103	0.214051	−	0.976822i	$-0.431334\pi$
$887$	1.00313e7	0.428103	0.214051	+	0.976822i	$0.431334\pi$
$888$	4.16758e7	1.77358
$889$	2.07252e7	0.879516
$890$	0	0
$891$	9.44512e6	0.398578
$892$	285503.	0.0120143
$893$	7.31996e6	0.307171
$894$	−3.04622e7	−1.27473
$895$	0	0
$896$	2.14198e7	0.891344
$897$	−3.74156e6	−0.155264
$898$	2.94985e7	1.22070
$899$	1.73213e6	0.0714795
$900$	0	0
$901$	−5.95304e6	−0.244302
$902$	1.30930e7	0.535826
$903$	−1.74810e7	−0.713421
$904$	4.14989e7	1.68894
$905$	0	0
$906$	3.98228e7	1.61180
$907$	2.99381e7	1.20839	0.604193	−	0.796838i	$-0.293495\pi$
$907$	2.99381e7	1.20839	0.604193	+	0.796838i	$0.293495\pi$
$908$	2.54276e6	0.102351
$909$	−1.28469e6	−0.0515689
$910$	0	0
$911$	2.83738e7	1.13272	0.566360	−	0.824158i	$-0.308351\pi$
$911$	2.83738e7	1.13272	0.566360	+	0.824158i	$0.308351\pi$
$912$	−2.76857e7	−1.10222
$913$	−8.32731e6	−0.330619
$914$	−1.76852e7	−0.700236
$915$	0	0
$916$	−1.21231e6	−0.0477391
$917$	−3.72863e7	−1.46429
$918$	−1.43243e7	−0.561006
$919$	−3.91491e7	−1.52909	−0.764545	−	0.644570i	$-0.777036\pi$
$919$	−3.91491e7	−1.52909	−0.764545	+	0.644570i	$0.777036\pi$
$920$	0	0
$921$	4.60590e7	1.78923
$922$	2.06762e7	0.801019
$923$	4.80921e6	0.185810
$924$	−544911.	−0.0209965
$925$	0	0
$926$	2.21014e7	0.847019
$927$	−1.91940e6	−0.0733613
$928$	638672.	0.0243449
$929$	3.44851e6	0.131097	0.0655484	−	0.997849i	$-0.479120\pi$
$929$	3.44851e6	0.131097	0.0655484	+	0.997849i	$0.479120\pi$
$930$	0	0
$931$	8.78447e6	0.332156
$932$	2.03000e6	0.0765519
$933$	4.14179e7	1.55770
$934$	−2.29514e7	−0.860879
$935$	0	0
$936$	−680997.	−0.0254071
$937$	3.55183e7	1.32161	0.660805	−	0.750558i	$-0.270215\pi$
$937$	3.55183e7	1.32161	0.660805	+	0.750558i	$0.270215\pi$
$938$	−2.32910e7	−0.864334
$939$	2.35177e7	0.870425
$940$	0	0
$941$	−8.10962e6	−0.298557	−0.149278	−	0.988795i	$-0.547695\pi$
$941$	−8.10962e6	−0.298557	−0.149278	+	0.988795i	$0.547695\pi$
$942$	−4.53815e6	−0.166629
$943$	−1.05553e7	−0.386538
$944$	1.49269e7	0.545180
$945$	0	0
$946$	−9.18886e6	−0.333836
$947$	−1.58835e7	−0.575535	−0.287767	−	0.957700i	$-0.592913\pi$
$947$	−1.58835e7	−0.575535	−0.287767	+	0.957700i	$0.592913\pi$
$948$	910781.	0.0329150
$949$	2.06191e7	0.743199
$950$	0	0
$951$	1.05698e7	0.378979
$952$	−1.23417e7	−0.441349
$953$	1.76043e7	0.627893	0.313946	−	0.949441i	$-0.398349\pi$
$953$	1.76043e7	0.627893	0.313946	+	0.949441i	$0.398349\pi$
$954$	625988.	0.0222687
$955$	0	0
$956$	1.24447e6	0.0440392
$957$	2.05190e6	0.0724229
$958$	2.13433e7	0.751361
$959$	1.97421e7	0.693180
$960$	0	0
$961$	−2.43872e7	−0.851830
$962$	−2.84353e7	−0.990649
$963$	−957534.	−0.0332727
$964$	851464.	0.0295103
$965$	0	0
$966$	7.13032e6	0.245848
$967$	5.37843e7	1.84965	0.924825	−	0.380393i	$-0.124211\pi$
$967$	5.37843e7	1.84965	0.924825	+	0.380393i	$0.124211\pi$
$968$	−2.40430e7	−0.824708
$969$	1.69387e7	0.579524
$970$	0	0
$971$	1.22227e7	0.416026	0.208013	−	0.978126i	$-0.433300\pi$
$971$	1.22227e7	0.416026	0.208013	+	0.978126i	$0.433300\pi$
$972$	190410.	0.00646435
$973$	3.36638e7	1.13994
$974$	−2.27880e7	−0.769678
$975$	0	0
$976$	3.63875e7	1.22272
$977$	−4.33000e6	−0.145128	−0.0725640	−	0.997364i	$-0.523118\pi$
$977$	−4.33000e6	−0.145128	−0.0725640	+	0.997364i	$0.523118\pi$
$978$	1.39650e7	0.466866
$979$	2.13652e7	0.712445
$980$	0	0
$981$	−1.17299e6	−0.0389153
$982$	−4.80392e7	−1.58971
$983$	−4.71098e7	−1.55499	−0.777494	−	0.628890i	$-0.783510\pi$
$983$	−4.71098e7	−1.55499	−0.777494	+	0.628890i	$0.783510\pi$
$984$	−4.09104e7	−1.34693
$985$	0	0
$986$	−3.26559e6	−0.106972
$987$	−7.78855e6	−0.254486
$988$	1.09180e6	0.0355838
$989$	7.40786e6	0.240825
$990$	0	0
$991$	−2.09978e7	−0.679187	−0.339594	−	0.940572i	$-0.610290\pi$
$991$	−2.09978e7	−0.679187	−0.339594	+	0.940572i	$0.610290\pi$
$992$	1.56411e6	0.0504647
$993$	−5.44145e7	−1.75122
$994$	−9.16495e6	−0.294215
$995$	0	0
$996$	−1.82833e6	−0.0583992
$997$	4.51805e7	1.43951	0.719753	−	0.694231i	$-0.244255\pi$
$997$	4.51805e7	1.43951	0.719753	+	0.694231i	$0.244255\pi$
$998$	−1.13946e7	−0.362136
$999$	−5.51448e7	−1.74820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.6.a.b.1.3		7
5.4	even	2		29.6.a.b.1.5	✓	7
15.14	odd	2		261.6.a.e.1.3		7
20.19	odd	2		464.6.a.k.1.3		7
145.144	even	2		841.6.a.b.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.b.1.5	✓	7	5.4	even	2
261.6.a.e.1.3		7	15.14	odd	2
464.6.a.k.1.3		7	20.19	odd	2
725.6.a.b.1.3		7	1.1	even	1	trivial
841.6.a.b.1.3		7	145.144	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q-5.83960 q^{2} -15.9679 q^{3} +2.10095 q^{4} +93.2461 q^{6} -106.304 q^{7} +174.599 q^{8} +11.9736 q^{9} +O(q^{10})\)	\(q-5.83960 q^{2} -15.9679 q^{3} +2.10095 q^{4} +93.2461 q^{6} -106.304 q^{7} +174.599 q^{8} +11.9736 q^{9} -152.796 q^{11} -33.5477 q^{12} -325.745 q^{13} +620.776 q^{14} -1086.82 q^{16} +664.939 q^{17} -69.9212 q^{18} -1595.33 q^{19} +1697.46 q^{21} +892.268 q^{22} -719.327 q^{23} -2787.97 q^{24} +1902.22 q^{26} +3689.00 q^{27} -223.340 q^{28} +841.000 q^{29} +2059.61 q^{31} +759.420 q^{32} +2439.83 q^{33} -3882.98 q^{34} +25.1559 q^{36} -14948.4 q^{37} +9316.11 q^{38} +5201.47 q^{39} +14673.9 q^{41} -9912.48 q^{42} -10298.3 q^{43} -321.016 q^{44} +4200.58 q^{46} -4588.36 q^{47} +17354.2 q^{48} -5506.36 q^{49} -10617.7 q^{51} -684.373 q^{52} -8952.75 q^{53} -21542.3 q^{54} -18560.6 q^{56} +25474.1 q^{57} -4911.10 q^{58} -13734.5 q^{59} -33480.9 q^{61} -12027.3 q^{62} -1272.85 q^{63} +30343.4 q^{64} -14247.6 q^{66} -37519.2 q^{67} +1397.00 q^{68} +11486.1 q^{69} -14763.7 q^{71} +2090.58 q^{72} -63298.3 q^{73} +87292.9 q^{74} -3351.71 q^{76} +16242.9 q^{77} -30374.5 q^{78} -27148.9 q^{79} -61815.2 q^{81} -85689.7 q^{82} +54499.5 q^{83} +3566.27 q^{84} +60138.1 q^{86} -13429.0 q^{87} -26678.0 q^{88} -139829. q^{89} +34628.2 q^{91} -1511.27 q^{92} -32887.6 q^{93} +26794.2 q^{94} -12126.3 q^{96} -89845.2 q^{97} +32154.9 q^{98} -1829.52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 4 q^{2} - 26 q^{3} + 154 q^{4} + 22 q^{6} - 184 q^{7} - 942 q^{8} + 1005 q^{9}+O(q^{10}) \) 7 * q - 4 * q^2 - 26 * q^3 + 154 * q^4 + 22 * q^6 - 184 * q^7 - 942 * q^8 + 1005 * q^9	\( 7 q - 4 q^{2} - 26 q^{3} + 154 q^{4} + 22 q^{6} - 184 q^{7} - 942 q^{8} + 1005 q^{9} + 1106 q^{11} - 214 q^{12} - 408 q^{13} - 2008 q^{14} + 242 q^{16} + 874 q^{17} + 5598 q^{18} + 4288 q^{19} - 4200 q^{21} + 6114 q^{22} + 4532 q^{23} - 4318 q^{24} - 19806 q^{26} - 5942 q^{27} + 496 q^{28} + 5887 q^{29} + 7794 q^{31} - 7898 q^{32} - 34410 q^{33} + 20840 q^{34} - 572 q^{36} - 5086 q^{37} - 23732 q^{38} + 33394 q^{39} + 19826 q^{41} + 55440 q^{42} - 19498 q^{43} - 6074 q^{44} - 12404 q^{46} - 14278 q^{47} + 16406 q^{48} + 38431 q^{49} + 23892 q^{51} + 34302 q^{52} + 58644 q^{53} - 31194 q^{54} - 79560 q^{56} + 88540 q^{57} - 3364 q^{58} + 12888 q^{59} + 102866 q^{61} + 42654 q^{62} + 88632 q^{63} - 10170 q^{64} + 7710 q^{66} - 102996 q^{67} - 85100 q^{68} - 107244 q^{69} - 51596 q^{71} - 135568 q^{72} + 17566 q^{73} + 12132 q^{74} + 360740 q^{76} + 94104 q^{77} - 46386 q^{78} + 212058 q^{79} - 128285 q^{81} - 201924 q^{82} + 122928 q^{83} - 12328 q^{84} - 63290 q^{86} - 21866 q^{87} - 136666 q^{88} - 66510 q^{89} + 194368 q^{91} + 110108 q^{92} + 474274 q^{93} + 438926 q^{94} - 117018 q^{96} + 118182 q^{97} + 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 26 * q^3 + 154 * q^4 + 22 * q^6 - 184 * q^7 - 942 * q^8 + 1005 * q^9 + 1106 * q^11 - 214 * q^12 - 408 * q^13 - 2008 * q^14 + 242 * q^16 + 874 * q^17 + 5598 * q^18 + 4288 * q^19 - 4200 * q^21 + 6114 * q^22 + 4532 * q^23 - 4318 * q^24 - 19806 * q^26 - 5942 * q^27 + 496 * q^28 + 5887 * q^29 + 7794 * q^31 - 7898 * q^32 - 34410 * q^33 + 20840 * q^34 - 572 * q^36 - 5086 * q^37 - 23732 * q^38 + 33394 * q^39 + 19826 * q^41 + 55440 * q^42 - 19498 * q^43 - 6074 * q^44 - 12404 * q^46 - 14278 * q^47 + 16406 * q^48 + 38431 * q^49 + 23892 * q^51 + 34302 * q^52 + 58644 * q^53 - 31194 * q^54 - 79560 * q^56 + 88540 * q^57 - 3364 * q^58 + 12888 * q^59 + 102866 * q^61 + 42654 * q^62 + 88632 * q^63 - 10170 * q^64 + 7710 * q^66 - 102996 * q^67 - 85100 * q^68 - 107244 * q^69 - 51596 * q^71 - 135568 * q^72 + 17566 * q^73 + 12132 * q^74 + 360740 * q^76 + 94104 * q^77 - 46386 * q^78 + 212058 * q^79 - 128285 * q^81 - 201924 * q^82 + 122928 * q^83 - 12328 * q^84 - 63290 * q^86 - 21866 * q^87 - 136666 * q^88 - 66510 * q^89 + 194368 * q^91 + 110108 * q^92 + 474274 * q^93 + 438926 * q^94 - 117018 * q^96 + 118182 * q^97 + 29132 * q^98 + 300668 * q^99

Introduction

L-functions

Modular forms

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