LMFDB - Embedded newform 825.4.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$1$
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} - 44x^{5} + 118x^{4} + 515x^{3} - 1279x^{2} - 892x + 1840 $ x^7 - 3x^6 - 44x^5 + 118x^4 + 515x^3 - 1279x^2 - 892x + 1840
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.62783$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62783 q^{2} -3.00000 q^{3} -1.09451 q^{4} +7.88349 q^{6} +24.0582 q^{7} +23.8988 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.62783 q^{2} -3.00000 q^{3} -1.09451 q^{4} +7.88349 q^{6} +24.0582 q^{7} +23.8988 q^{8} +9.00000 q^{9} -11.0000 q^{11} +3.28354 q^{12} -70.7912 q^{13} -63.2207 q^{14} -54.0459 q^{16} +27.9494 q^{17} -23.6505 q^{18} +50.9926 q^{19} -72.1745 q^{21} +28.9061 q^{22} -201.498 q^{23} -71.6965 q^{24} +186.027 q^{26} -27.0000 q^{27} -26.3320 q^{28} +126.395 q^{29} +30.1877 q^{31} -49.1672 q^{32} +33.0000 q^{33} -73.4462 q^{34} -9.85063 q^{36} +7.32183 q^{37} -134.000 q^{38} +212.374 q^{39} +366.098 q^{41} +189.662 q^{42} +33.4661 q^{43} +12.0397 q^{44} +529.503 q^{46} +14.3267 q^{47} +162.138 q^{48} +235.795 q^{49} -83.8482 q^{51} +77.4820 q^{52} +154.671 q^{53} +70.9514 q^{54} +574.962 q^{56} -152.978 q^{57} -332.145 q^{58} +611.926 q^{59} -83.1222 q^{61} -79.3282 q^{62} +216.523 q^{63} +561.570 q^{64} -86.7184 q^{66} -737.743 q^{67} -30.5910 q^{68} +604.495 q^{69} -930.806 q^{71} +215.089 q^{72} -491.999 q^{73} -19.2405 q^{74} -55.8121 q^{76} -264.640 q^{77} -558.082 q^{78} +687.955 q^{79} +81.0000 q^{81} -962.043 q^{82} +712.253 q^{83} +78.9960 q^{84} -87.9431 q^{86} -379.186 q^{87} -262.887 q^{88} -1332.36 q^{89} -1703.11 q^{91} +220.543 q^{92} -90.5631 q^{93} -37.6482 q^{94} +147.502 q^{96} -598.852 q^{97} -619.630 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9	\( 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9} - 77 q^{11} - 123 q^{12} - 24 q^{13} + 142 q^{14} + 181 q^{16} - 38 q^{17} - 27 q^{18} + 26 q^{19} + 150 q^{21} + 33 q^{22} - 228 q^{23} + 63 q^{24} + 476 q^{26} - 189 q^{27} - 840 q^{28} + 572 q^{29} - 140 q^{31} - 991 q^{32} + 231 q^{33} - 806 q^{34} + 369 q^{36} + 104 q^{37} - 498 q^{38} + 72 q^{39} + 896 q^{41} - 426 q^{42} - 614 q^{43} - 451 q^{44} - 344 q^{46} - 520 q^{47} - 543 q^{48} + 295 q^{49} + 114 q^{51} + 26 q^{52} - 380 q^{53} + 81 q^{54} + 1522 q^{56} - 78 q^{57} - 1600 q^{58} + 1316 q^{59} - 386 q^{61} - 440 q^{62} - 450 q^{63} + 869 q^{64} - 99 q^{66} - 348 q^{67} - 332 q^{68} + 684 q^{69} + 804 q^{71} - 189 q^{72} - 468 q^{73} - 748 q^{74} - 1698 q^{76} + 550 q^{77} - 1428 q^{78} - 374 q^{79} + 567 q^{81} + 620 q^{82} - 3128 q^{83} + 2520 q^{84} - 2534 q^{86} - 1716 q^{87} + 231 q^{88} + 694 q^{89} - 3376 q^{91} + 1184 q^{92} + 420 q^{93} - 2920 q^{94} + 2973 q^{96} + 8 q^{97} - 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9 - 77 * q^11 - 123 * q^12 - 24 * q^13 + 142 * q^14 + 181 * q^16 - 38 * q^17 - 27 * q^18 + 26 * q^19 + 150 * q^21 + 33 * q^22 - 228 * q^23 + 63 * q^24 + 476 * q^26 - 189 * q^27 - 840 * q^28 + 572 * q^29 - 140 * q^31 - 991 * q^32 + 231 * q^33 - 806 * q^34 + 369 * q^36 + 104 * q^37 - 498 * q^38 + 72 * q^39 + 896 * q^41 - 426 * q^42 - 614 * q^43 - 451 * q^44 - 344 * q^46 - 520 * q^47 - 543 * q^48 + 295 * q^49 + 114 * q^51 + 26 * q^52 - 380 * q^53 + 81 * q^54 + 1522 * q^56 - 78 * q^57 - 1600 * q^58 + 1316 * q^59 - 386 * q^61 - 440 * q^62 - 450 * q^63 + 869 * q^64 - 99 * q^66 - 348 * q^67 - 332 * q^68 + 684 * q^69 + 804 * q^71 - 189 * q^72 - 468 * q^73 - 748 * q^74 - 1698 * q^76 + 550 * q^77 - 1428 * q^78 - 374 * q^79 + 567 * q^81 + 620 * q^82 - 3128 * q^83 + 2520 * q^84 - 2534 * q^86 - 1716 * q^87 + 231 * q^88 + 694 * q^89 - 3376 * q^91 + 1184 * q^92 + 420 * q^93 - 2920 * q^94 + 2973 * q^96 + 8 * q^97 - 4211 * q^98 - 693 * 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 $

$2$	−2.62783	−0.929078	−0.464539	−	0.885553i	$-0.653780\pi$
$2$	−2.62783	−0.929078	−0.464539	+	0.885553i	$0.653780\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−1.09451	−0.136814
$5$	0	0
$5$	0	0
$6$	7.88349	0.536403
$7$	24.0582	1.29902	0.649509	−	0.760354i	$-0.274974\pi$
$7$	24.0582	1.29902	0.649509	+	0.760354i	$0.274974\pi$
$8$	23.8988	1.05619
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	3.28354	0.0789898
$13$	−70.7912	−1.51030	−0.755152	−	0.655549i	$-0.772437\pi$
$13$	−70.7912	−1.51030	−0.755152	+	0.655549i	$0.772437\pi$
$14$	−63.2207	−1.20689
$15$	0	0
$16$	−54.0459	−0.844468
$17$	27.9494	0.398749	0.199374	−	0.979923i	$-0.436109\pi$
$17$	27.9494	0.398749	0.199374	+	0.979923i	$0.436109\pi$
$18$	−23.6505	−0.309693
$19$	50.9926	0.615711	0.307855	−	0.951433i	$-0.400389\pi$
$19$	50.9926	0.615711	0.307855	+	0.951433i	$0.400389\pi$
$20$	0	0
$21$	−72.1745	−0.749989
$22$	28.9061	0.280128
$23$	−201.498	−1.82675	−0.913376	−	0.407118i	$-0.866534\pi$
$23$	−201.498	−1.82675	−0.913376	+	0.407118i	$0.866534\pi$
$24$	−71.6965	−0.609791
$25$	0	0
$26$	186.027	1.40319
$27$	−27.0000	−0.192450
$28$	−26.3320	−0.177724
$29$	126.395	0.809345	0.404672	−	0.914462i	$-0.367386\pi$
$29$	126.395	0.809345	0.404672	+	0.914462i	$0.367386\pi$
$30$	0	0
$31$	30.1877	0.174899	0.0874496	−	0.996169i	$-0.472128\pi$
$31$	30.1877	0.174899	0.0874496	+	0.996169i	$0.472128\pi$
$32$	−49.1672	−0.271613
$33$	33.0000	0.174078
$34$	−73.4462	−0.370468
$35$	0	0
$36$	−9.85063	−0.0456048
$37$	7.32183	0.0325325	0.0162662	−	0.999868i	$-0.494822\pi$
$37$	7.32183	0.0325325	0.0162662	+	0.999868i	$0.494822\pi$
$38$	−134.000	−0.572043
$39$	212.374	0.871975
$40$	0	0
$41$	366.098	1.39451	0.697255	−	0.716824i	$-0.254405\pi$
$41$	366.098	1.39451	0.697255	+	0.716824i	$0.254405\pi$
$42$	189.662	0.696798
$43$	33.4661	0.118687	0.0593434	−	0.998238i	$-0.481099\pi$
$43$	33.4661	0.118687	0.0593434	+	0.998238i	$0.481099\pi$
$44$	12.0397	0.0412511
$45$	0	0
$46$	529.503	1.69719
$47$	14.3267	0.0444632	0.0222316	−	0.999753i	$-0.492923\pi$
$47$	14.3267	0.0444632	0.0222316	+	0.999753i	$0.492923\pi$
$48$	162.138	0.487554
$49$	235.795	0.687450
$50$	0	0
$51$	−83.8482	−0.230218
$52$	77.4820	0.206631
$53$	154.671	0.400863	0.200432	−	0.979708i	$-0.435766\pi$
$53$	154.671	0.400863	0.200432	+	0.979708i	$0.435766\pi$
$54$	70.9514	0.178801
$55$	0	0
$56$	574.962	1.37201
$57$	−152.978	−0.355481
$58$	−332.145	−0.751944
$59$	611.926	1.35027	0.675135	−	0.737694i	$-0.264085\pi$
$59$	611.926	1.35027	0.675135	+	0.737694i	$0.264085\pi$
$60$	0	0
$61$	−83.1222	−0.174471	−0.0872353	−	0.996188i	$-0.527803\pi$
$61$	−83.1222	−0.174471	−0.0872353	+	0.996188i	$0.527803\pi$
$62$	−79.3282	−0.162495
$63$	216.523	0.433006
$64$	561.570	1.09682
$65$	0	0
$66$	−86.7184	−0.161732
$67$	−737.743	−1.34522	−0.672609	−	0.739998i	$-0.734826\pi$
$67$	−737.743	−1.34522	−0.672609	+	0.739998i	$0.734826\pi$
$68$	−30.5910	−0.0545545
$69$	604.495	1.05468
$70$	0	0
$71$	−930.806	−1.55586	−0.777932	−	0.628348i	$-0.783731\pi$
$71$	−930.806	−1.55586	−0.777932	+	0.628348i	$0.783731\pi$
$72$	215.089	0.352063
$73$	−491.999	−0.788824	−0.394412	−	0.918934i	$-0.629052\pi$
$73$	−491.999	−0.788824	−0.394412	+	0.918934i	$0.629052\pi$
$74$	−19.2405	−0.0302252
$75$	0	0
$76$	−55.8121	−0.0842380
$77$	−264.640	−0.391669
$78$	−558.082	−0.810132
$79$	687.955	0.979759	0.489879	−	0.871790i	$-0.337041\pi$
$79$	687.955	0.979759	0.489879	+	0.871790i	$0.337041\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−962.043	−1.29561
$83$	712.253	0.941927	0.470963	−	0.882153i	$-0.343906\pi$
$83$	712.253	0.941927	0.470963	+	0.882153i	$0.343906\pi$
$84$	78.9960	0.102609
$85$	0	0
$86$	−87.9431	−0.110269
$87$	−379.186	−0.467275
$88$	−262.887	−0.318453
$89$	−1332.36	−1.58685	−0.793423	−	0.608670i	$-0.791703\pi$
$89$	−1332.36	−1.58685	−0.793423	+	0.608670i	$0.791703\pi$
$90$	0	0
$91$	−1703.11	−1.96191
$92$	220.543	0.249926
$93$	−90.5631	−0.100978
$94$	−37.6482	−0.0413097
$95$	0	0
$96$	147.502	0.156816
$97$	−598.852	−0.626847	−0.313424	−	0.949613i	$-0.601476\pi$
$97$	−598.852	−0.626847	−0.313424	+	0.949613i	$0.601476\pi$
$98$	−619.630	−0.638694
$99$	−99.0000	−0.100504
$100$	0	0
$101$	392.723	0.386905	0.193452	−	0.981110i	$-0.438032\pi$
$101$	392.723	0.386905	0.193452	+	0.981110i	$0.438032\pi$
$102$	220.339	0.213890
$103$	−889.816	−0.851225	−0.425613	−	0.904905i	$-0.639941\pi$
$103$	−889.816	−0.851225	−0.425613	+	0.904905i	$0.639941\pi$
$104$	−1691.83	−1.59517
$105$	0	0
$106$	−406.450	−0.372433
$107$	911.308	0.823360	0.411680	−	0.911328i	$-0.364942\pi$
$107$	911.308	0.823360	0.411680	+	0.911328i	$0.364942\pi$
$108$	29.5519	0.0263299
$109$	−1552.29	−1.36406	−0.682029	−	0.731325i	$-0.738902\pi$
$109$	−1552.29	−1.36406	−0.682029	+	0.731325i	$0.738902\pi$
$110$	0	0
$111$	−21.9655	−0.0187826
$112$	−1300.25	−1.09698
$113$	−457.867	−0.381173	−0.190586	−	0.981670i	$-0.561039\pi$
$113$	−457.867	−0.381173	−0.190586	+	0.981670i	$0.561039\pi$
$114$	401.999	0.330269
$115$	0	0
$116$	−138.341	−0.110730
$117$	−637.121	−0.503435
$118$	−1608.04	−1.25451
$119$	672.411	0.517982
$120$	0	0
$121$	121.000	0.0909091
$122$	218.431	0.162097
$123$	−1098.29	−0.805120
$124$	−33.0409	−0.0239287
$125$	0	0
$126$	−568.987	−0.402297
$127$	911.406	0.636805	0.318402	−	0.947956i	$-0.396854\pi$
$127$	911.406	0.636805	0.318402	+	0.947956i	$0.396854\pi$
$128$	−1082.37	−0.747416
$129$	−100.398	−0.0685238
$130$	0	0
$131$	2552.41	1.70233	0.851165	−	0.524898i	$-0.175897\pi$
$131$	2552.41	1.70233	0.851165	+	0.524898i	$0.175897\pi$
$132$	−36.1190	−0.0238163
$133$	1226.79	0.799820
$134$	1938.66	1.24981
$135$	0	0
$136$	667.958	0.421154
$137$	390.364	0.243438	0.121719	−	0.992565i	$-0.461159\pi$
$137$	390.364	0.243438	0.121719	+	0.992565i	$0.461159\pi$
$138$	−1588.51	−0.979876
$139$	−2657.82	−1.62182	−0.810912	−	0.585168i	$-0.801028\pi$
$139$	−2657.82	−1.62182	−0.810912	+	0.585168i	$0.801028\pi$
$140$	0	0
$141$	−42.9802	−0.0256708
$142$	2446.00	1.44552
$143$	778.704	0.455374
$144$	−486.413	−0.281489
$145$	0	0
$146$	1292.89	0.732879
$147$	−707.386	−0.396899
$148$	−8.01385	−0.00445091
$149$	−266.568	−0.146565	−0.0732823	−	0.997311i	$-0.523347\pi$
$149$	−266.568	−0.146565	−0.0732823	+	0.997311i	$0.523347\pi$
$150$	0	0
$151$	2565.20	1.38247	0.691235	−	0.722630i	$-0.257067\pi$
$151$	2565.20	1.38247	0.691235	+	0.722630i	$0.257067\pi$
$152$	1218.66	0.650307
$153$	251.545	0.132916
$154$	695.428	0.363891
$155$	0	0
$156$	−232.446	−0.119299
$157$	−483.922	−0.245995	−0.122997	−	0.992407i	$-0.539251\pi$
$157$	−483.922	−0.245995	−0.122997	+	0.992407i	$0.539251\pi$
$158$	−1807.83	−0.910272
$159$	−464.014	−0.231438
$160$	0	0
$161$	−4847.68	−2.37298
$162$	−212.854	−0.103231
$163$	−3701.47	−1.77866	−0.889330	−	0.457266i	$-0.848829\pi$
$163$	−3701.47	−1.77866	−0.889330	+	0.457266i	$0.848829\pi$
$164$	−400.699	−0.190789
$165$	0	0
$166$	−1871.68	−0.875123
$167$	−2361.35	−1.09417	−0.547086	−	0.837077i	$-0.684263\pi$
$167$	−2361.35	−1.09417	−0.547086	+	0.837077i	$0.684263\pi$
$168$	−1724.89	−0.792130
$169$	2814.40	1.28102
$170$	0	0
$171$	458.933	0.205237
$172$	−36.6291	−0.0162380
$173$	−3613.18	−1.58789	−0.793944	−	0.607990i	$-0.791976\pi$
$173$	−3613.18	−1.58789	−0.793944	+	0.607990i	$0.791976\pi$
$174$	996.435	0.434135
$175$	0	0
$176$	594.505	0.254617
$177$	−1835.78	−0.779579
$178$	3501.20	1.47430
$179$	2632.47	1.09922	0.549608	−	0.835422i	$-0.314777\pi$
$179$	2632.47	1.09922	0.549608	+	0.835422i	$0.314777\pi$
$180$	0	0
$181$	−3956.26	−1.62468	−0.812338	−	0.583187i	$-0.801806\pi$
$181$	−3956.26	−1.62468	−0.812338	+	0.583187i	$0.801806\pi$
$182$	4475.48	1.82277
$183$	249.367	0.100731
$184$	−4815.57	−1.92939
$185$	0	0
$186$	237.984	0.0938165
$187$	−307.443	−0.120227
$188$	−15.6808	−0.00608320
$189$	−649.570	−0.249996
$190$	0	0
$191$	−2921.65	−1.10682	−0.553412	−	0.832908i	$-0.686674\pi$
$191$	−2921.65	−1.10682	−0.553412	+	0.832908i	$0.686674\pi$
$192$	−1684.71	−0.633248
$193$	−510.977	−0.190575	−0.0952875	−	0.995450i	$-0.530377\pi$
$193$	−510.977	−0.190575	−0.0952875	+	0.995450i	$0.530377\pi$
$194$	1573.68	0.582390
$195$	0	0
$196$	−258.081	−0.0940529
$197$	−2020.44	−0.730711	−0.365356	−	0.930868i	$-0.619053\pi$
$197$	−2020.44	−0.730711	−0.365356	+	0.930868i	$0.619053\pi$
$198$	260.155	0.0933758
$199$	−3608.68	−1.28549	−0.642745	−	0.766080i	$-0.722205\pi$
$199$	−3608.68	−1.28549	−0.642745	+	0.766080i	$0.722205\pi$
$200$	0	0
$201$	2213.23	0.776662
$202$	−1032.01	−0.359464
$203$	3040.84	1.05135
$204$	91.7730	0.0314970
$205$	0	0
$206$	2338.29	0.790855
$207$	−1813.48	−0.608917
$208$	3825.98	1.27540
$209$	−560.919	−0.185644
$210$	0	0
$211$	2279.36	0.743685	0.371842	−	0.928296i	$-0.378726\pi$
$211$	2279.36	0.743685	0.371842	+	0.928296i	$0.378726\pi$
$212$	−169.290	−0.0548438
$213$	2792.42	0.898279
$214$	−2394.76	−0.764965
$215$	0	0
$216$	−645.268	−0.203264
$217$	726.261	0.227197
$218$	4079.15	1.26732
$219$	1476.00	0.455428
$220$	0	0
$221$	−1978.57	−0.602232
$222$	57.7216	0.0174505
$223$	−6504.82	−1.95334	−0.976670	−	0.214744i	$-0.931108\pi$
$223$	−6504.82	−1.95334	−0.976670	+	0.214744i	$0.931108\pi$
$224$	−1182.87	−0.352830
$225$	0	0
$226$	1203.20	0.354139
$227$	5152.78	1.50662	0.753308	−	0.657668i	$-0.228457\pi$
$227$	5152.78	1.50662	0.753308	+	0.657668i	$0.228457\pi$
$228$	167.436	0.0486348
$229$	−5961.82	−1.72039	−0.860193	−	0.509969i	$-0.829657\pi$
$229$	−5961.82	−1.72039	−0.860193	+	0.509969i	$0.829657\pi$
$230$	0	0
$231$	793.919	0.226130
$232$	3020.70	0.854821
$233$	4516.75	1.26996	0.634982	−	0.772527i	$-0.281007\pi$
$233$	4516.75	1.26996	0.634982	+	0.772527i	$0.281007\pi$
$234$	1674.25	0.467730
$235$	0	0
$236$	−669.762	−0.184736
$237$	−2063.86	−0.565664
$238$	−1766.98	−0.481245
$239$	3298.29	0.892672	0.446336	−	0.894865i	$-0.352729\pi$
$239$	3298.29	0.892672	0.446336	+	0.894865i	$0.352729\pi$
$240$	0	0
$241$	−500.141	−0.133680	−0.0668400	−	0.997764i	$-0.521292\pi$
$241$	−500.141	−0.133680	−0.0668400	+	0.997764i	$0.521292\pi$
$242$	−317.967	−0.0844616
$243$	−243.000	−0.0641500
$244$	90.9784	0.0238701
$245$	0	0
$246$	2886.13	0.748019
$247$	−3609.83	−0.929911
$248$	721.451	0.184727
$249$	−2136.76	−0.543822
$250$	0	0
$251$	1070.12	0.269106	0.134553	−	0.990906i	$-0.457040\pi$
$251$	1070.12	0.269106	0.134553	+	0.990906i	$0.457040\pi$
$252$	−236.988	−0.0592414
$253$	2216.48	0.550786
$254$	−2395.02	−0.591641
$255$	0	0
$256$	−1648.27	−0.402410
$257$	−3868.69	−0.938997	−0.469499	−	0.882933i	$-0.655565\pi$
$257$	−3868.69	−0.938997	−0.469499	+	0.882933i	$0.655565\pi$
$258$	263.829	0.0636640
$259$	176.150	0.0422603
$260$	0	0
$261$	1137.56	0.269782
$262$	−6707.30	−1.58160
$263$	−7328.33	−1.71819	−0.859096	−	0.511815i	$-0.828974\pi$
$263$	−7328.33	−1.71819	−0.859096	+	0.511815i	$0.828974\pi$
$264$	788.661	0.183859
$265$	0	0
$266$	−3223.79	−0.743095
$267$	3997.07	0.916166
$268$	807.470	0.184045
$269$	2589.62	0.586960	0.293480	−	0.955965i	$-0.405187\pi$
$269$	2589.62	0.586960	0.293480	+	0.955965i	$0.405187\pi$
$270$	0	0
$271$	4148.33	0.929863	0.464932	−	0.885347i	$-0.346079\pi$
$271$	4148.33	0.929863	0.464932	+	0.885347i	$0.346079\pi$
$272$	−1510.55	−0.336730
$273$	5109.32	1.13271
$274$	−1025.81	−0.226173
$275$	0	0
$276$	−661.628	−0.144295
$277$	−839.252	−0.182042	−0.0910212	−	0.995849i	$-0.529013\pi$
$277$	−839.252	−0.182042	−0.0910212	+	0.995849i	$0.529013\pi$
$278$	6984.30	1.50680
$279$	271.689	0.0582997
$280$	0	0
$281$	737.536	0.156575	0.0782877	−	0.996931i	$-0.475055\pi$
$281$	737.536	0.156575	0.0782877	+	0.996931i	$0.475055\pi$
$282$	112.945	0.0238502
$283$	−2013.44	−0.422921	−0.211460	−	0.977387i	$-0.567822\pi$
$283$	−2013.44	−0.422921	−0.211460	+	0.977387i	$0.567822\pi$
$284$	1018.78	0.212864
$285$	0	0
$286$	−2046.30	−0.423078
$287$	8807.64	1.81149
$288$	−442.505	−0.0905376
$289$	−4131.83	−0.841000
$290$	0	0
$291$	1796.55	0.361910
$292$	538.500	0.107922
$293$	−4857.22	−0.968469	−0.484235	−	0.874938i	$-0.660902\pi$
$293$	−4857.22	−0.968469	−0.484235	+	0.874938i	$0.660902\pi$
$294$	1858.89	0.368750
$295$	0	0
$296$	174.983	0.0343605
$297$	297.000	0.0580259
$298$	700.496	0.136170
$299$	14264.3	2.75895
$300$	0	0
$301$	805.132	0.154176
$302$	−6740.91	−1.28442
$303$	−1178.17	−0.223379
$304$	−2755.94	−0.519948
$305$	0	0
$306$	−661.016	−0.123489
$307$	−10201.0	−1.89642	−0.948211	−	0.317641i	$-0.897109\pi$
$307$	−10201.0	−1.89642	−0.948211	+	0.317641i	$0.897109\pi$
$308$	289.652	0.0535859
$309$	2669.45	0.491455
$310$	0	0
$311$	−690.017	−0.125811	−0.0629056	−	0.998019i	$-0.520037\pi$
$311$	−690.017	−0.125811	−0.0629056	+	0.998019i	$0.520037\pi$
$312$	5075.48	0.920970
$313$	5360.35	0.968003	0.484002	−	0.875067i	$-0.339183\pi$
$313$	5360.35	0.968003	0.484002	+	0.875067i	$0.339183\pi$
$314$	1271.67	0.228548
$315$	0	0
$316$	−752.976	−0.134045
$317$	10817.5	1.91662	0.958312	−	0.285724i	$-0.0922341\pi$
$317$	10817.5	1.91662	0.958312	+	0.285724i	$0.0922341\pi$
$318$	1219.35	0.215024
$319$	−1390.35	−0.244027
$320$	0	0
$321$	−2733.93	−0.475367
$322$	12738.9	2.20469
$323$	1425.21	0.245514
$324$	−88.6556	−0.0152016
$325$	0	0
$326$	9726.83	1.65251
$327$	4656.86	0.787539
$328$	8749.31	1.47287
$329$	344.675	0.0577585
$330$	0	0
$331$	−10694.7	−1.77593	−0.887966	−	0.459909i	$-0.847882\pi$
$331$	−10694.7	−1.77593	−0.887966	+	0.459909i	$0.847882\pi$
$332$	−779.571	−0.128869
$333$	65.8965	0.0108442
$334$	6205.22	1.01657
$335$	0	0
$336$	3900.74	0.633341
$337$	−656.983	−0.106196	−0.0530981	−	0.998589i	$-0.516910\pi$
$337$	−656.983	−0.106196	−0.0530981	+	0.998589i	$0.516910\pi$
$338$	−7395.76	−1.19017
$339$	1373.60	0.220070
$340$	0	0
$341$	−332.065	−0.0527341
$342$	−1206.00	−0.190681
$343$	−2579.15	−0.406009
$344$	799.800	0.125356
$345$	0	0
$346$	9494.81	1.47527
$347$	887.275	0.137266	0.0686331	−	0.997642i	$-0.478136\pi$
$347$	887.275	0.137266	0.0686331	+	0.997642i	$0.478136\pi$
$348$	415.024	0.0639299
$349$	5723.95	0.877925	0.438963	−	0.898505i	$-0.355346\pi$
$349$	5723.95	0.877925	0.438963	+	0.898505i	$0.355346\pi$
$350$	0	0
$351$	1911.36	0.290658
$352$	540.839	0.0818944
$353$	−3266.86	−0.492571	−0.246285	−	0.969197i	$-0.579210\pi$
$353$	−3266.86	−0.492571	−0.246285	+	0.969197i	$0.579210\pi$
$354$	4824.11	0.724290
$355$	0	0
$356$	1458.28	0.217103
$357$	−2017.23	−0.299057
$358$	−6917.67	−1.02126
$359$	−11275.9	−1.65771	−0.828854	−	0.559466i	$-0.811006\pi$
$359$	−11275.9	−1.65771	−0.828854	+	0.559466i	$0.811006\pi$
$360$	0	0
$361$	−4258.76	−0.620900
$362$	10396.4	1.50945
$363$	−363.000	−0.0524864
$364$	1864.08	0.268418
$365$	0	0
$366$	−655.293	−0.0935866
$367$	−2789.28	−0.396728	−0.198364	−	0.980128i	$-0.563563\pi$
$367$	−2789.28	−0.396728	−0.198364	+	0.980128i	$0.563563\pi$
$368$	10890.2	1.54263
$369$	3294.88	0.464836
$370$	0	0
$371$	3721.11	0.520729
$372$	99.1226	0.0138152
$373$	13032.2	1.80907	0.904533	−	0.426403i	$-0.140220\pi$
$373$	13032.2	1.80907	0.904533	+	0.426403i	$0.140220\pi$
$374$	807.909	0.111700
$375$	0	0
$376$	342.392	0.0469615
$377$	−8947.67	−1.22236
$378$	1706.96	0.232266
$379$	−3913.88	−0.530455	−0.265227	−	0.964186i	$-0.585447\pi$
$379$	−3913.88	−0.530455	−0.265227	+	0.964186i	$0.585447\pi$
$380$	0	0
$381$	−2734.22	−0.367659
$382$	7677.60	1.02833
$383$	−3589.82	−0.478932	−0.239466	−	0.970905i	$-0.576972\pi$
$383$	−3589.82	−0.478932	−0.239466	+	0.970905i	$0.576972\pi$
$384$	3247.12	0.431521
$385$	0	0
$386$	1342.76	0.177059
$387$	301.195	0.0395622
$388$	655.452	0.0857616
$389$	−5556.23	−0.724196	−0.362098	−	0.932140i	$-0.617939\pi$
$389$	−5556.23	−0.724196	−0.362098	+	0.932140i	$0.617939\pi$
$390$	0	0
$391$	−5631.75	−0.728414
$392$	5635.23	0.726077
$393$	−7657.23	−0.982841
$394$	5309.36	0.678887
$395$	0	0
$396$	108.357	0.0137504
$397$	−355.562	−0.0449500	−0.0224750	−	0.999747i	$-0.507155\pi$
$397$	−355.562	−0.0449500	−0.0224750	+	0.999747i	$0.507155\pi$
$398$	9482.99	1.19432
$399$	−3680.36	−0.461776
$400$	0	0
$401$	4439.53	0.552867	0.276434	−	0.961033i	$-0.410847\pi$
$401$	4439.53	0.552867	0.276434	+	0.961033i	$0.410847\pi$
$402$	−5815.99	−0.721580
$403$	−2137.03	−0.264151
$404$	−429.840	−0.0529341
$405$	0	0
$406$	−7990.80	−0.976790
$407$	−80.5402	−0.00980891
$408$	−2003.87	−0.243153
$409$	−7022.79	−0.849033	−0.424517	−	0.905420i	$-0.639556\pi$
$409$	−7022.79	−0.849033	−0.424517	+	0.905420i	$0.639556\pi$
$410$	0	0
$411$	−1171.09	−0.140549
$412$	973.917	0.116460
$413$	14721.8	1.75403
$414$	4765.53	0.565731
$415$	0	0
$416$	3480.61	0.410218
$417$	7973.46	0.936360
$418$	1474.00	0.172478
$419$	10786.9	1.25769	0.628847	−	0.777529i	$-0.283527\pi$
$419$	10786.9	1.25769	0.628847	+	0.777529i	$0.283527\pi$
$420$	0	0
$421$	−683.119	−0.0790812	−0.0395406	−	0.999218i	$-0.512589\pi$
$421$	−683.119	−0.0790812	−0.0395406	+	0.999218i	$0.512589\pi$
$422$	−5989.76	−0.690941
$423$	128.941	0.0148211
$424$	3696.46	0.423387
$425$	0	0
$426$	−7338.00	−0.834571
$427$	−1999.77	−0.226641
$428$	−997.440	−0.112647
$429$	−2336.11	−0.262910
$430$	0	0
$431$	−5515.28	−0.616384	−0.308192	−	0.951324i	$-0.599724\pi$
$431$	−5515.28	−0.616384	−0.308192	+	0.951324i	$0.599724\pi$
$432$	1459.24	0.162518
$433$	1021.73	0.113398	0.0566989	−	0.998391i	$-0.481942\pi$
$433$	1021.73	0.113398	0.0566989	+	0.998391i	$0.481942\pi$
$434$	−1908.49	−0.211084
$435$	0	0
$436$	1699.00	0.186623
$437$	−10274.9	−1.12475
$438$	−3878.67	−0.423128
$439$	−15902.3	−1.72887	−0.864435	−	0.502745i	$-0.832324\pi$
$439$	−15902.3	−1.72887	−0.864435	+	0.502745i	$0.832324\pi$
$440$	0	0
$441$	2122.16	0.229150
$442$	5199.35	0.559520
$443$	8290.70	0.889172	0.444586	−	0.895736i	$-0.353351\pi$
$443$	8290.70	0.889172	0.444586	+	0.895736i	$0.353351\pi$
$444$	24.0416	0.00256973
$445$	0	0
$446$	17093.6	1.81481
$447$	799.705	0.0846191
$448$	13510.4	1.42479
$449$	14375.1	1.51092	0.755461	−	0.655194i	$-0.227413\pi$
$449$	14375.1	1.51092	0.755461	+	0.655194i	$0.227413\pi$
$450$	0	0
$451$	−4027.08	−0.420460
$452$	501.142	0.0521499
$453$	−7695.60	−0.798169
$454$	−13540.6	−1.39976
$455$	0	0
$456$	−3655.99	−0.375455
$457$	2187.59	0.223919	0.111959	−	0.993713i	$-0.464287\pi$
$457$	2187.59	0.223919	0.111959	+	0.993713i	$0.464287\pi$
$458$	15666.6	1.59837
$459$	−754.634	−0.0767392
$460$	0	0
$461$	−1016.23	−0.102669	−0.0513344	−	0.998682i	$-0.516347\pi$
$461$	−1016.23	−0.102669	−0.0513344	+	0.998682i	$0.516347\pi$
$462$	−2086.28	−0.210093
$463$	9523.44	0.955921	0.477961	−	0.878381i	$-0.341376\pi$
$463$	9523.44	0.955921	0.477961	+	0.878381i	$0.341376\pi$
$464$	−6831.15	−0.683465
$465$	0	0
$466$	−11869.2	−1.17990
$467$	−7251.93	−0.718585	−0.359293	−	0.933225i	$-0.616982\pi$
$467$	−7251.93	−0.718585	−0.359293	+	0.933225i	$0.616982\pi$
$468$	697.338	0.0688771
$469$	−17748.7	−1.74746
$470$	0	0
$471$	1451.77	0.142025
$472$	14624.3	1.42614
$473$	−368.127	−0.0357854
$474$	5423.48	0.525546
$475$	0	0
$476$	−735.964	−0.0708673
$477$	1392.04	0.133621
$478$	−8667.34	−0.829362
$479$	−10523.6	−1.00383	−0.501916	−	0.864916i	$-0.667371\pi$
$479$	−10523.6	−1.00383	−0.501916	+	0.864916i	$0.667371\pi$
$480$	0	0
$481$	−518.322	−0.0491340
$482$	1314.28	0.124199
$483$	14543.0	1.37004
$484$	−132.436	−0.0124377
$485$	0	0
$486$	638.562	0.0596004
$487$	−555.512	−0.0516892	−0.0258446	−	0.999666i	$-0.508228\pi$
$487$	−555.512	−0.0516892	−0.0258446	+	0.999666i	$0.508228\pi$
$488$	−1986.52	−0.184274
$489$	11104.4	1.02691
$490$	0	0
$491$	−19782.4	−1.81826	−0.909132	−	0.416509i	$-0.863253\pi$
$491$	−19782.4	−1.81826	−0.909132	+	0.416509i	$0.863253\pi$
$492$	1202.10	0.110152
$493$	3532.67	0.322725
$494$	9486.01	0.863959
$495$	0	0
$496$	−1631.52	−0.147697
$497$	−22393.5	−2.02110
$498$	5615.04	0.505253
$499$	−2749.43	−0.246657	−0.123328	−	0.992366i	$-0.539357\pi$
$499$	−2749.43	−0.246657	−0.123328	+	0.992366i	$0.539357\pi$
$500$	0	0
$501$	7084.05	0.631720
$502$	−2812.10	−0.250020
$503$	−13224.1	−1.17223	−0.586116	−	0.810227i	$-0.699344\pi$
$503$	−13224.1	−1.17223	−0.586116	+	0.810227i	$0.699344\pi$
$504$	5174.66	0.457336
$505$	0	0
$506$	−5824.53	−0.511723
$507$	−8443.20	−0.739597
$508$	−997.547	−0.0871240
$509$	−2851.62	−0.248322	−0.124161	−	0.992262i	$-0.539624\pi$
$509$	−2851.62	−0.248322	−0.124161	+	0.992262i	$0.539624\pi$
$510$	0	0
$511$	−11836.6	−1.02470
$512$	12990.4	1.12129
$513$	−1376.80	−0.118494
$514$	10166.3	0.872402
$515$	0	0
$516$	109.887	0.00937504
$517$	−157.594	−0.0134061
$518$	−462.892	−0.0392631
$519$	10839.5	0.916768
$520$	0	0
$521$	18549.3	1.55980	0.779902	−	0.625901i	$-0.215269\pi$
$521$	18549.3	1.55980	0.779902	+	0.625901i	$0.215269\pi$
$522$	−2989.30	−0.250648
$523$	−11766.4	−0.983760	−0.491880	−	0.870663i	$-0.663690\pi$
$523$	−11766.4	−0.983760	−0.491880	+	0.870663i	$0.663690\pi$
$524$	−2793.65	−0.232903
$525$	0	0
$526$	19257.6	1.59633
$527$	843.729	0.0697408
$528$	−1783.52	−0.147003
$529$	28434.5	2.33702
$530$	0	0
$531$	5507.33	0.450090
$532$	−1342.74	−0.109427
$533$	−25916.5	−2.10613
$534$	−10503.6	−0.851190
$535$	0	0
$536$	−17631.2	−1.42080
$537$	−7897.40	−0.634633
$538$	−6805.09	−0.545331
$539$	−2593.75	−0.207274
$540$	0	0
$541$	13561.9	1.07777	0.538884	−	0.842380i	$-0.318846\pi$
$541$	13561.9	1.07777	0.538884	+	0.842380i	$0.318846\pi$
$542$	−10901.1	−0.863915
$543$	11868.8	0.938007
$544$	−1374.19	−0.108305
$545$	0	0
$546$	−13426.4	−1.05238
$547$	16092.5	1.25789	0.628944	−	0.777451i	$-0.283487\pi$
$547$	16092.5	1.25789	0.628944	+	0.777451i	$0.283487\pi$
$548$	−427.259	−0.0333058
$549$	−748.100	−0.0581569
$550$	0	0
$551$	6445.22	0.498322
$552$	14446.7	1.11394
$553$	16550.9	1.27273
$554$	2205.41	0.169132
$555$	0	0
$556$	2909.02	0.221889
$557$	−19100.1	−1.45296	−0.726478	−	0.687190i	$-0.758844\pi$
$557$	−19100.1	−1.45296	−0.726478	+	0.687190i	$0.758844\pi$
$558$	−713.953	−0.0541650
$559$	−2369.11	−0.179253
$560$	0	0
$561$	922.330	0.0694132
$562$	−1938.12	−0.145471
$563$	−6898.73	−0.516424	−0.258212	−	0.966088i	$-0.583133\pi$
$563$	−6898.73	−0.516424	−0.258212	+	0.966088i	$0.583133\pi$
$564$	47.0424	0.00351213
$565$	0	0
$566$	5290.98	0.392926
$567$	1948.71	0.144335
$568$	−22245.2	−1.64329
$569$	−161.850	−0.0119246	−0.00596231	−	0.999982i	$-0.501898\pi$
$569$	−161.850	−0.0119246	−0.00596231	+	0.999982i	$0.501898\pi$
$570$	0	0
$571$	19826.3	1.45307	0.726537	−	0.687127i	$-0.241128\pi$
$571$	19826.3	1.45307	0.726537	+	0.687127i	$0.241128\pi$
$572$	−852.302	−0.0623017
$573$	8764.96	0.639025
$574$	−23145.0	−1.68302
$575$	0	0
$576$	5054.13	0.365606
$577$	25367.5	1.83027	0.915134	−	0.403150i	$-0.132085\pi$
$577$	25367.5	1.83027	0.915134	+	0.403150i	$0.132085\pi$
$578$	10857.7	0.781354
$579$	1532.93	0.110028
$580$	0	0
$581$	17135.5	1.22358
$582$	−4721.04	−0.336243
$583$	−1701.39	−0.120865
$584$	−11758.2	−0.833147
$585$	0	0
$586$	12763.9	0.899784
$587$	−14760.7	−1.03789	−0.518943	−	0.854809i	$-0.673674\pi$
$587$	−14760.7	−1.03789	−0.518943	+	0.854809i	$0.673674\pi$
$588$	774.244	0.0543015
$589$	1539.35	0.107687
$590$	0	0
$591$	6061.31	0.421876
$592$	−395.715	−0.0274726
$593$	10705.6	0.741357	0.370679	−	0.928761i	$-0.379125\pi$
$593$	10705.6	0.741357	0.370679	+	0.928761i	$0.379125\pi$
$594$	−780.465	−0.0539106
$595$	0	0
$596$	291.763	0.0200521
$597$	10826.0	0.742178
$598$	−37484.2	−2.56328
$599$	−14015.0	−0.955986	−0.477993	−	0.878364i	$-0.658636\pi$
$599$	−14015.0	−0.955986	−0.477993	+	0.878364i	$0.658636\pi$
$600$	0	0
$601$	−27307.6	−1.85341	−0.926706	−	0.375788i	$-0.877372\pi$
$601$	−27307.6	−1.85341	−0.926706	+	0.375788i	$0.877372\pi$
$602$	−2115.75	−0.143242
$603$	−6639.69	−0.448406
$604$	−2807.65	−0.189142
$605$	0	0
$606$	3096.02	0.207537
$607$	−4494.13	−0.300513	−0.150256	−	0.988647i	$-0.548010\pi$
$607$	−4494.13	−0.300513	−0.150256	+	0.988647i	$0.548010\pi$
$608$	−2507.16	−0.167235
$609$	−9122.51	−0.607000
$610$	0	0
$611$	−1014.21	−0.0671529
$612$	−275.319	−0.0181848
$613$	9965.04	0.656581	0.328291	−	0.944577i	$-0.393528\pi$
$613$	9965.04	0.656581	0.328291	+	0.944577i	$0.393528\pi$
$614$	26806.5	1.76192
$615$	0	0
$616$	−6324.58	−0.413676
$617$	−20508.4	−1.33815	−0.669075	−	0.743195i	$-0.733309\pi$
$617$	−20508.4	−1.33815	−0.669075	+	0.743195i	$0.733309\pi$
$618$	−7014.86	−0.456600
$619$	6213.15	0.403437	0.201718	−	0.979444i	$-0.435347\pi$
$619$	6213.15	0.403437	0.201718	+	0.979444i	$0.435347\pi$
$620$	0	0
$621$	5440.45	0.351558
$622$	1813.25	0.116888
$623$	−32054.0	−2.06134
$624$	−11477.9	−0.736354
$625$	0	0
$626$	−14086.1	−0.899350
$627$	1682.76	0.107181
$628$	529.660	0.0336556
$629$	204.641	0.0129723
$630$	0	0
$631$	−26557.9	−1.67552	−0.837762	−	0.546036i	$-0.816136\pi$
$631$	−26557.9	−1.67552	−0.837762	+	0.546036i	$0.816136\pi$
$632$	16441.3	1.03481
$633$	−6838.07	−0.429367
$634$	−28426.5	−1.78069
$635$	0	0
$636$	507.870	0.0316641
$637$	−16692.2	−1.03826
$638$	3653.59	0.226720
$639$	−8377.25	−0.518621
$640$	0	0
$641$	−15431.3	−0.950859	−0.475430	−	0.879754i	$-0.657707\pi$
$641$	−15431.3	−0.950859	−0.475430	+	0.879754i	$0.657707\pi$
$642$	7184.29	0.441653
$643$	19148.5	1.17441	0.587204	−	0.809439i	$-0.300229\pi$
$643$	19148.5	1.17441	0.587204	+	0.809439i	$0.300229\pi$
$644$	5305.85	0.324658
$645$	0	0
$646$	−3745.21	−0.228101
$647$	15497.7	0.941699	0.470849	−	0.882214i	$-0.343948\pi$
$647$	15497.7	0.941699	0.470849	+	0.882214i	$0.343948\pi$
$648$	1935.81	0.117354
$649$	−6731.19	−0.407122
$650$	0	0
$651$	−2178.78	−0.131172
$652$	4051.31	0.243346
$653$	−11208.7	−0.671716	−0.335858	−	0.941913i	$-0.609026\pi$
$653$	−11208.7	−0.671716	−0.335858	+	0.941913i	$0.609026\pi$
$654$	−12237.4	−0.731685
$655$	0	0
$656$	−19786.1	−1.17762
$657$	−4427.99	−0.262941
$658$	−905.747	−0.0536621
$659$	−12671.7	−0.749045	−0.374523	−	0.927218i	$-0.622193\pi$
$659$	−12671.7	−0.749045	−0.374523	+	0.927218i	$0.622193\pi$
$660$	0	0
$661$	29609.9	1.74235	0.871173	−	0.490977i	$-0.163360\pi$
$661$	29609.9	1.74235	0.871173	+	0.490977i	$0.163360\pi$
$662$	28103.8	1.64998
$663$	5935.72	0.347699
$664$	17022.0	0.994853
$665$	0	0
$666$	−173.165	−0.0100751
$667$	−25468.4	−1.47847
$668$	2584.53	0.149698
$669$	19514.5	1.12776
$670$	0	0
$671$	914.344	0.0526049
$672$	3548.62	0.203707
$673$	−4928.54	−0.282290	−0.141145	−	0.989989i	$-0.545078\pi$
$673$	−4928.54	−0.282290	−0.141145	+	0.989989i	$0.545078\pi$
$674$	1726.44	0.0986646
$675$	0	0
$676$	−3080.40	−0.175262
$677$	−17239.1	−0.978659	−0.489330	−	0.872099i	$-0.662759\pi$
$677$	−17239.1	−0.978659	−0.489330	+	0.872099i	$0.662759\pi$
$678$	−3609.59	−0.204462
$679$	−14407.3	−0.814286
$680$	0	0
$681$	−15458.3	−0.869845
$682$	872.610	0.0489941
$683$	−16810.9	−0.941804	−0.470902	−	0.882185i	$-0.656071\pi$
$683$	−16810.9	−0.941804	−0.470902	+	0.882185i	$0.656071\pi$
$684$	−502.309	−0.0280793
$685$	0	0
$686$	6777.56	0.377214
$687$	17885.5	0.993265
$688$	−1808.71	−0.100227
$689$	−10949.4	−0.605425
$690$	0	0
$691$	11163.7	0.614597	0.307298	−	0.951613i	$-0.400575\pi$
$691$	11163.7	0.614597	0.307298	+	0.951613i	$0.400575\pi$
$692$	3954.67	0.217246
$693$	−2381.76	−0.130556
$694$	−2331.61	−0.127531
$695$	0	0
$696$	−9062.09	−0.493531
$697$	10232.2	0.556059
$698$	−15041.6	−0.815661
$699$	−13550.2	−0.733215
$700$	0	0
$701$	28098.2	1.51391	0.756956	−	0.653466i	$-0.226686\pi$
$701$	28098.2	1.51391	0.756956	+	0.653466i	$0.226686\pi$
$702$	−5022.74	−0.270044
$703$	373.359	0.0200306
$704$	−6177.27	−0.330703
$705$	0	0
$706$	8584.75	0.457637
$707$	9448.18	0.502596
$708$	2009.28	0.106658
$709$	−23232.4	−1.23062	−0.615310	−	0.788285i	$-0.710969\pi$
$709$	−23232.4	−1.23062	−0.615310	+	0.788285i	$0.710969\pi$
$710$	0	0
$711$	6191.59	0.326586
$712$	−31841.7	−1.67601
$713$	−6082.77	−0.319497
$714$	5300.95	0.277847
$715$	0	0
$716$	−2881.27	−0.150389
$717$	−9894.87	−0.515384
$718$	29631.0	1.54014
$719$	24964.9	1.29490	0.647450	−	0.762108i	$-0.275835\pi$
$719$	24964.9	1.29490	0.647450	+	0.762108i	$0.275835\pi$
$720$	0	0
$721$	−21407.3	−1.10576
$722$	11191.3	0.576865
$723$	1500.42	0.0771802
$724$	4330.18	0.222279
$725$	0	0
$726$	953.902	0.0487639
$727$	12425.8	0.633904	0.316952	−	0.948442i	$-0.397341\pi$
$727$	12425.8	0.633904	0.316952	+	0.948442i	$0.397341\pi$
$728$	−40702.3	−2.07215
$729$	729.000	0.0370370
$730$	0	0
$731$	935.357	0.0473262
$732$	−272.935	−0.0137814
$733$	3632.29	0.183031	0.0915154	−	0.995804i	$-0.470829\pi$
$733$	3632.29	0.183031	0.0915154	+	0.995804i	$0.470829\pi$
$734$	7329.74	0.368591
$735$	0	0
$736$	9907.10	0.496169
$737$	8115.17	0.405599
$738$	−8658.38	−0.431869
$739$	15663.6	0.779693	0.389847	−	0.920880i	$-0.372528\pi$
$739$	15663.6	0.779693	0.389847	+	0.920880i	$0.372528\pi$
$740$	0	0
$741$	10829.5	0.536884
$742$	−9778.44	−0.483798
$743$	−20450.2	−1.00975	−0.504875	−	0.863193i	$-0.668461\pi$
$743$	−20450.2	−1.00975	−0.504875	+	0.863193i	$0.668461\pi$
$744$	−2164.35	−0.106652
$745$	0	0
$746$	−34246.4	−1.68076
$747$	6410.28	0.313976
$748$	336.501	0.0164488
$749$	21924.4	1.06956
$750$	0	0
$751$	−18814.2	−0.914168	−0.457084	−	0.889424i	$-0.651106\pi$
$751$	−18814.2	−0.914168	−0.457084	+	0.889424i	$0.651106\pi$
$752$	−774.302	−0.0375477
$753$	−3210.37	−0.155368
$754$	23513.0	1.13566
$755$	0	0
$756$	710.964	0.0342031
$757$	−1994.60	−0.0957663	−0.0478831	−	0.998853i	$-0.515248\pi$
$757$	−1994.60	−0.0957663	−0.0478831	+	0.998853i	$0.515248\pi$
$758$	10285.0	0.492834
$759$	−6649.44	−0.317997
$760$	0	0
$761$	−3002.11	−0.143004	−0.0715021	−	0.997440i	$-0.522779\pi$
$761$	−3002.11	−0.143004	−0.0715021	+	0.997440i	$0.522779\pi$
$762$	7185.06	0.341584
$763$	−37345.2	−1.77194
$764$	3197.79	0.151429
$765$	0	0
$766$	9433.43	0.444966
$767$	−43319.0	−2.03932
$768$	4944.81	0.232331
$769$	5156.00	0.241781	0.120891	−	0.992666i	$-0.461425\pi$
$769$	5156.00	0.241781	0.120891	+	0.992666i	$0.461425\pi$
$770$	0	0
$771$	11606.1	0.542130
$772$	559.272	0.0260734
$773$	13932.5	0.648276	0.324138	−	0.946010i	$-0.394926\pi$
$773$	13932.5	0.648276	0.324138	+	0.946010i	$0.394926\pi$
$774$	−791.488	−0.0367564
$775$	0	0
$776$	−14311.9	−0.662069
$777$	−528.450	−0.0243990
$778$	14600.8	0.672834
$779$	18668.3	0.858614
$780$	0	0
$781$	10238.9	0.469111
$782$	14799.3	0.676754
$783$	−3412.67	−0.155758
$784$	−12743.8	−0.580529
$785$	0	0
$786$	20121.9	0.913136
$787$	−30180.5	−1.36699	−0.683493	−	0.729957i	$-0.739540\pi$
$787$	−30180.5	−1.36699	−0.683493	+	0.729957i	$0.739540\pi$
$788$	2211.40	0.0999717
$789$	21985.0	0.991999
$790$	0	0
$791$	−11015.4	−0.495151
$792$	−2365.98	−0.106151
$793$	5884.32	0.263504
$794$	934.357	0.0417621
$795$	0	0
$796$	3949.75	0.175873
$797$	−19931.9	−0.885853	−0.442927	−	0.896558i	$-0.646060\pi$
$797$	−19931.9	−0.885853	−0.442927	+	0.896558i	$0.646060\pi$
$798$	9671.37	0.429026
$799$	400.424	0.0177296
$800$	0	0
$801$	−11991.2	−0.528949
$802$	−11666.3	−0.513657
$803$	5411.99	0.237839
$804$	−2422.41	−0.106258
$805$	0	0
$806$	5615.74	0.245417
$807$	−7768.87	−0.338881
$808$	9385.61	0.408644
$809$	−10844.1	−0.471272	−0.235636	−	0.971841i	$-0.575717\pi$
$809$	−10844.1	−0.471272	−0.235636	+	0.971841i	$0.575717\pi$
$810$	0	0
$811$	8058.46	0.348916	0.174458	−	0.984665i	$-0.444183\pi$
$811$	8058.46	0.348916	0.174458	+	0.984665i	$0.444183\pi$
$812$	−3328.24	−0.143840
$813$	−12445.0	−0.536857
$814$	211.646	0.00911325
$815$	0	0
$816$	4531.65	0.194411
$817$	1706.52	0.0730767
$818$	18454.7	0.788818
$819$	−15328.0	−0.653971
$820$	0	0
$821$	19340.1	0.822136	0.411068	−	0.911605i	$-0.365156\pi$
$821$	19340.1	0.822136	0.411068	+	0.911605i	$0.365156\pi$
$822$	3077.43	0.130581
$823$	−10347.7	−0.438271	−0.219135	−	0.975694i	$-0.570324\pi$
$823$	−10347.7	−0.438271	−0.219135	+	0.975694i	$0.570324\pi$
$824$	−21265.6	−0.899055
$825$	0	0
$826$	−38686.4	−1.62963
$827$	−4117.22	−0.173119	−0.0865597	−	0.996247i	$-0.527587\pi$
$827$	−4117.22	−0.173119	−0.0865597	+	0.996247i	$0.527587\pi$
$828$	1984.88	0.0833085
$829$	35735.0	1.49714	0.748569	−	0.663057i	$-0.230741\pi$
$829$	35735.0	1.49714	0.748569	+	0.663057i	$0.230741\pi$
$830$	0	0
$831$	2517.76	0.105102
$832$	−39754.3	−1.65653
$833$	6590.34	0.274120
$834$	−20952.9	−0.869952
$835$	0	0
$836$	613.933	0.0253987
$837$	−815.068	−0.0336594
$838$	−28346.1	−1.16850
$839$	9919.13	0.408160	0.204080	−	0.978954i	$-0.434580\pi$
$839$	9919.13	0.408160	0.204080	+	0.978954i	$0.434580\pi$
$840$	0	0
$841$	−8413.25	−0.344961
$842$	1795.12	0.0734726
$843$	−2212.61	−0.0903989
$844$	−2494.79	−0.101747
$845$	0	0
$846$	−338.834	−0.0137699
$847$	2911.04	0.118093
$848$	−8359.36	−0.338516
$849$	6040.32	0.244173
$850$	0	0
$851$	−1475.34	−0.0594288
$852$	−3056.34	−0.122897
$853$	14138.6	0.567523	0.283761	−	0.958895i	$-0.408418\pi$
$853$	14138.6	0.567523	0.283761	+	0.958895i	$0.408418\pi$
$854$	5255.05	0.210567
$855$	0	0
$856$	21779.2	0.869624
$857$	9474.85	0.377660	0.188830	−	0.982010i	$-0.439530\pi$
$857$	9474.85	0.377660	0.188830	+	0.982010i	$0.439530\pi$
$858$	6138.90	0.244264
$859$	14024.6	0.557059	0.278529	−	0.960428i	$-0.410153\pi$
$859$	14024.6	0.557059	0.278529	+	0.960428i	$0.410153\pi$
$860$	0	0
$861$	−26422.9	−1.04587
$862$	14493.2	0.572669
$863$	−32886.7	−1.29719	−0.648596	−	0.761133i	$-0.724643\pi$
$863$	−32886.7	−1.29719	−0.648596	+	0.761133i	$0.724643\pi$
$864$	1327.51	0.0522719
$865$	0	0
$866$	−2684.93	−0.105355
$867$	12395.5	0.485551
$868$	−794.903	−0.0310838
$869$	−7567.50	−0.295408
$870$	0	0
$871$	52225.7	2.03169
$872$	−37097.9	−1.44070
$873$	−5389.66	−0.208949
$874$	27000.7	1.04498
$875$	0	0
$876$	−1615.50	−0.0623090
$877$	−7459.91	−0.287233	−0.143616	−	0.989633i	$-0.545873\pi$
$877$	−7459.91	−0.287233	−0.143616	+	0.989633i	$0.545873\pi$
$878$	41788.5	1.60625
$879$	14571.6	0.559146
$880$	0	0
$881$	6549.49	0.250463	0.125231	−	0.992128i	$-0.460033\pi$
$881$	6549.49	0.250463	0.125231	+	0.992128i	$0.460033\pi$
$882$	−5576.67	−0.212898
$883$	433.667	0.0165278	0.00826391	−	0.999966i	$-0.497369\pi$
$883$	433.667	0.0165278	0.00826391	+	0.999966i	$0.497369\pi$
$884$	2165.58	0.0823939
$885$	0	0
$886$	−21786.5	−0.826110
$887$	8848.55	0.334955	0.167478	−	0.985876i	$-0.446438\pi$
$887$	8848.55	0.334955	0.167478	+	0.985876i	$0.446438\pi$
$888$	−524.950	−0.0198380
$889$	21926.8	0.827222
$890$	0	0
$891$	−891.000	−0.0335013
$892$	7119.62	0.267245
$893$	730.557	0.0273764
$894$	−2101.49	−0.0786177
$895$	0	0
$896$	−26039.9	−0.970907
$897$	−42792.9	−1.59288
$898$	−37775.4	−1.40376
$899$	3815.58	0.141554
$900$	0	0
$901$	4322.97	0.159844
$902$	10582.5	0.390640
$903$	−2415.40	−0.0890137
$904$	−10942.5	−0.402591
$905$	0	0
$906$	20222.7	0.741562
$907$	36540.9	1.33773	0.668865	−	0.743384i	$-0.266781\pi$
$907$	36540.9	1.33773	0.668865	+	0.743384i	$0.266781\pi$
$908$	−5639.79	−0.206127
$909$	3534.50	0.128968
$910$	0	0
$911$	13231.9	0.481220	0.240610	−	0.970622i	$-0.422653\pi$
$911$	13231.9	0.481220	0.240610	+	0.970622i	$0.422653\pi$
$912$	8267.83	0.300192
$913$	−7834.78	−0.284002
$914$	−5748.60	−0.208038
$915$	0	0
$916$	6525.30	0.235373
$917$	61406.3	2.21136
$918$	1983.05	0.0712967
$919$	15568.9	0.558838	0.279419	−	0.960169i	$-0.409858\pi$
$919$	15568.9	0.558838	0.279419	+	0.960169i	$0.409858\pi$
$920$	0	0
$921$	30603.0	1.09490
$922$	2670.47	0.0953874
$923$	65892.9	2.34983
$924$	−868.956	−0.0309378
$925$	0	0
$926$	−25026.0	−0.888125
$927$	−8008.35	−0.283742
$928$	−6214.49	−0.219828
$929$	−19507.9	−0.688950	−0.344475	−	0.938795i	$-0.611943\pi$
$929$	−19507.9	−0.688950	−0.344475	+	0.938795i	$0.611943\pi$
$930$	0	0
$931$	12023.8	0.423270
$932$	−4943.64	−0.173749
$933$	2070.05	0.0726371
$934$	19056.8	0.667622
$935$	0	0
$936$	−15226.5	−0.531722
$937$	9493.57	0.330994	0.165497	−	0.986210i	$-0.447077\pi$
$937$	9493.57	0.330994	0.165497	+	0.986210i	$0.447077\pi$
$938$	46640.6	1.62353
$939$	−16081.1	−0.558877
$940$	0	0
$941$	39841.1	1.38022	0.690108	−	0.723706i	$-0.257563\pi$
$941$	39841.1	1.38022	0.690108	+	0.723706i	$0.257563\pi$
$942$	−3815.00	−0.131953
$943$	−73768.1	−2.54742
$944$	−33072.1	−1.14026
$945$	0	0
$946$	967.374	0.0332474
$947$	−8119.72	−0.278622	−0.139311	−	0.990249i	$-0.544489\pi$
$947$	−8119.72	−0.278622	−0.139311	+	0.990249i	$0.544489\pi$
$948$	2258.93	0.0773909
$949$	34829.2	1.19136
$950$	0	0
$951$	−32452.4	−1.10656
$952$	16069.8	0.547087
$953$	−21781.7	−0.740376	−0.370188	−	0.928957i	$-0.620707\pi$
$953$	−21781.7	−0.740376	−0.370188	+	0.928957i	$0.620707\pi$
$954$	−3658.05	−0.124144
$955$	0	0
$956$	−3610.02	−0.122130
$957$	4171.04	0.140889
$958$	27654.2	0.932638
$959$	9391.43	0.316231
$960$	0	0
$961$	−28879.7	−0.969410
$962$	1362.06	0.0456493
$963$	8201.78	0.274453
$964$	547.411	0.0182893
$965$	0	0
$966$	−38216.6	−1.27288
$967$	−9740.88	−0.323936	−0.161968	−	0.986796i	$-0.551784\pi$
$967$	−9740.88	−0.323936	−0.161968	+	0.986796i	$0.551784\pi$
$968$	2891.76	0.0960172
$969$	−4275.64	−0.141747
$970$	0	0
$971$	−9950.95	−0.328879	−0.164439	−	0.986387i	$-0.552581\pi$
$971$	−9950.95	−0.328879	−0.164439	+	0.986387i	$0.552581\pi$
$972$	265.967	0.00877664
$973$	−63942.3	−2.10678
$974$	1459.79	0.0480233
$975$	0	0
$976$	4492.41	0.147335
$977$	43872.0	1.43663	0.718317	−	0.695716i	$-0.244913\pi$
$977$	43872.0	1.43663	0.718317	+	0.695716i	$0.244913\pi$
$978$	−29180.5	−0.954079
$979$	14655.9	0.478452
$980$	0	0
$981$	−13970.6	−0.454686
$982$	51984.8	1.68931
$983$	−6647.35	−0.215684	−0.107842	−	0.994168i	$-0.534394\pi$
$983$	−6647.35	−0.215684	−0.107842	+	0.994168i	$0.534394\pi$
$984$	−26247.9	−0.850359
$985$	0	0
$986$	−9283.25	−0.299837
$987$	−1034.02	−0.0333469
$988$	3951.01	0.127225
$989$	−6743.35	−0.216811
$990$	0	0
$991$	−13097.7	−0.419840	−0.209920	−	0.977719i	$-0.567320\pi$
$991$	−13097.7	−0.419840	−0.209920	+	0.977719i	$0.567320\pi$
$992$	−1484.24	−0.0475049
$993$	32084.1	1.02533
$994$	58846.3	1.87776
$995$	0	0
$996$	2338.71	0.0744026
$997$	27231.3	0.865019	0.432510	−	0.901629i	$-0.357628\pi$
$997$	27231.3	0.865019	0.432510	+	0.901629i	$0.357628\pi$
$998$	7225.05	0.229163
$999$	−197.690	−0.00626088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.bb.1.3		7
3.2	odd	2		2475.4.a.br.1.5		7
5.2	odd	4		165.4.c.a.34.5	✓	14
5.3	odd	4		165.4.c.a.34.10	yes	14
5.4	even	2		825.4.a.bc.1.5		7
15.2	even	4		495.4.c.c.199.10		14
15.8	even	4		495.4.c.c.199.5		14
15.14	odd	2		2475.4.a.bq.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.5	✓	14	5.2	odd	4
165.4.c.a.34.10	yes	14	5.3	odd	4
495.4.c.c.199.5		14	15.8	even	4
495.4.c.c.199.10		14	15.2	even	4
825.4.a.bb.1.3		7	1.1	even	1	trivial
825.4.a.bc.1.5		7	5.4	even	2
2475.4.a.bq.1.3		7	15.14	odd	2
2475.4.a.br.1.5		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62783 q^{2} -3.00000 q^{3} -1.09451 q^{4} +7.88349 q^{6} +24.0582 q^{7} +23.8988 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.62783 q^{2} -3.00000 q^{3} -1.09451 q^{4} +7.88349 q^{6} +24.0582 q^{7} +23.8988 q^{8} +9.00000 q^{9} -11.0000 q^{11} +3.28354 q^{12} -70.7912 q^{13} -63.2207 q^{14} -54.0459 q^{16} +27.9494 q^{17} -23.6505 q^{18} +50.9926 q^{19} -72.1745 q^{21} +28.9061 q^{22} -201.498 q^{23} -71.6965 q^{24} +186.027 q^{26} -27.0000 q^{27} -26.3320 q^{28} +126.395 q^{29} +30.1877 q^{31} -49.1672 q^{32} +33.0000 q^{33} -73.4462 q^{34} -9.85063 q^{36} +7.32183 q^{37} -134.000 q^{38} +212.374 q^{39} +366.098 q^{41} +189.662 q^{42} +33.4661 q^{43} +12.0397 q^{44} +529.503 q^{46} +14.3267 q^{47} +162.138 q^{48} +235.795 q^{49} -83.8482 q^{51} +77.4820 q^{52} +154.671 q^{53} +70.9514 q^{54} +574.962 q^{56} -152.978 q^{57} -332.145 q^{58} +611.926 q^{59} -83.1222 q^{61} -79.3282 q^{62} +216.523 q^{63} +561.570 q^{64} -86.7184 q^{66} -737.743 q^{67} -30.5910 q^{68} +604.495 q^{69} -930.806 q^{71} +215.089 q^{72} -491.999 q^{73} -19.2405 q^{74} -55.8121 q^{76} -264.640 q^{77} -558.082 q^{78} +687.955 q^{79} +81.0000 q^{81} -962.043 q^{82} +712.253 q^{83} +78.9960 q^{84} -87.9431 q^{86} -379.186 q^{87} -262.887 q^{88} -1332.36 q^{89} -1703.11 q^{91} +220.543 q^{92} -90.5631 q^{93} -37.6482 q^{94} +147.502 q^{96} -598.852 q^{97} -619.630 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9	\( 7 q - 3 q^{2} - 21 q^{3} + 41 q^{4} + 9 q^{6} - 50 q^{7} - 21 q^{8} + 63 q^{9} - 77 q^{11} - 123 q^{12} - 24 q^{13} + 142 q^{14} + 181 q^{16} - 38 q^{17} - 27 q^{18} + 26 q^{19} + 150 q^{21} + 33 q^{22} - 228 q^{23} + 63 q^{24} + 476 q^{26} - 189 q^{27} - 840 q^{28} + 572 q^{29} - 140 q^{31} - 991 q^{32} + 231 q^{33} - 806 q^{34} + 369 q^{36} + 104 q^{37} - 498 q^{38} + 72 q^{39} + 896 q^{41} - 426 q^{42} - 614 q^{43} - 451 q^{44} - 344 q^{46} - 520 q^{47} - 543 q^{48} + 295 q^{49} + 114 q^{51} + 26 q^{52} - 380 q^{53} + 81 q^{54} + 1522 q^{56} - 78 q^{57} - 1600 q^{58} + 1316 q^{59} - 386 q^{61} - 440 q^{62} - 450 q^{63} + 869 q^{64} - 99 q^{66} - 348 q^{67} - 332 q^{68} + 684 q^{69} + 804 q^{71} - 189 q^{72} - 468 q^{73} - 748 q^{74} - 1698 q^{76} + 550 q^{77} - 1428 q^{78} - 374 q^{79} + 567 q^{81} + 620 q^{82} - 3128 q^{83} + 2520 q^{84} - 2534 q^{86} - 1716 q^{87} + 231 q^{88} + 694 q^{89} - 3376 q^{91} + 1184 q^{92} + 420 q^{93} - 2920 q^{94} + 2973 q^{96} + 8 q^{97} - 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 - 21 * q^3 + 41 * q^4 + 9 * q^6 - 50 * q^7 - 21 * q^8 + 63 * q^9 - 77 * q^11 - 123 * q^12 - 24 * q^13 + 142 * q^14 + 181 * q^16 - 38 * q^17 - 27 * q^18 + 26 * q^19 + 150 * q^21 + 33 * q^22 - 228 * q^23 + 63 * q^24 + 476 * q^26 - 189 * q^27 - 840 * q^28 + 572 * q^29 - 140 * q^31 - 991 * q^32 + 231 * q^33 - 806 * q^34 + 369 * q^36 + 104 * q^37 - 498 * q^38 + 72 * q^39 + 896 * q^41 - 426 * q^42 - 614 * q^43 - 451 * q^44 - 344 * q^46 - 520 * q^47 - 543 * q^48 + 295 * q^49 + 114 * q^51 + 26 * q^52 - 380 * q^53 + 81 * q^54 + 1522 * q^56 - 78 * q^57 - 1600 * q^58 + 1316 * q^59 - 386 * q^61 - 440 * q^62 - 450 * q^63 + 869 * q^64 - 99 * q^66 - 348 * q^67 - 332 * q^68 + 684 * q^69 + 804 * q^71 - 189 * q^72 - 468 * q^73 - 748 * q^74 - 1698 * q^76 + 550 * q^77 - 1428 * q^78 - 374 * q^79 + 567 * q^81 + 620 * q^82 - 3128 * q^83 + 2520 * q^84 - 2534 * q^86 - 1716 * q^87 + 231 * q^88 + 694 * q^89 - 3376 * q^91 + 1184 * q^92 + 420 * q^93 - 2920 * q^94 + 2973 * q^96 + 8 * q^97 - 4211 * q^98 - 693 * q^99

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