LMFDB - Embedded newform 525.4.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.78066700.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 18x^{3} + 7x^{2} + 30x - 10 $ x^5 - x^4 - 18x^3 + 7x^2 + 30*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 5 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.71490$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.18660 q^{2} +3.00000 q^{3} +18.9008 q^{4} -15.5598 q^{6} -7.00000 q^{7} -56.5383 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.18660 q^{2} +3.00000 q^{3} +18.9008 q^{4} -15.5598 q^{6} -7.00000 q^{7} -56.5383 q^{8} +9.00000 q^{9} -35.9555 q^{11} +56.7025 q^{12} -45.2622 q^{13} +36.3062 q^{14} +142.035 q^{16} -113.154 q^{17} -46.6794 q^{18} +61.5906 q^{19} -21.0000 q^{21} +186.487 q^{22} +30.6108 q^{23} -169.615 q^{24} +234.757 q^{26} +27.0000 q^{27} -132.306 q^{28} +214.989 q^{29} +164.206 q^{31} -284.372 q^{32} -107.866 q^{33} +586.882 q^{34} +170.107 q^{36} +410.533 q^{37} -319.446 q^{38} -135.787 q^{39} -309.310 q^{41} +108.919 q^{42} +29.9519 q^{43} -679.589 q^{44} -158.766 q^{46} -483.790 q^{47} +426.104 q^{48} +49.0000 q^{49} -339.461 q^{51} -855.493 q^{52} +295.582 q^{53} -140.038 q^{54} +395.768 q^{56} +184.772 q^{57} -1115.06 q^{58} +416.191 q^{59} -151.196 q^{61} -851.670 q^{62} -63.0000 q^{63} +338.644 q^{64} +559.460 q^{66} -89.5253 q^{67} -2138.70 q^{68} +91.8324 q^{69} +714.265 q^{71} -508.844 q^{72} +1135.58 q^{73} -2129.27 q^{74} +1164.11 q^{76} +251.688 q^{77} +704.271 q^{78} -323.347 q^{79} +81.0000 q^{81} +1604.27 q^{82} -297.898 q^{83} -396.917 q^{84} -155.348 q^{86} +644.966 q^{87} +2032.86 q^{88} -90.2097 q^{89} +316.835 q^{91} +578.570 q^{92} +492.617 q^{93} +2509.23 q^{94} -853.115 q^{96} +492.101 q^{97} -254.143 q^{98} -323.599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9	$ 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9} + 66 q^{11} + 81 q^{12} + 2 q^{13} + 7 q^{14} + 155 q^{16} - 108 q^{17} - 9 q^{18} + 174 q^{19} - 105 q^{21} + 506 q^{22} + 116 q^{23} - 99 q^{24} + 446 q^{26} + 135 q^{27} - 189 q^{28} + 370 q^{29} + 342 q^{31} + 55 q^{32} + 198 q^{33} + 112 q^{34} + 243 q^{36} + 408 q^{37} + 34 q^{38} + 6 q^{39} + 802 q^{41} + 21 q^{42} + 584 q^{43} + 290 q^{44} + 640 q^{46} - 716 q^{47} + 465 q^{48} + 245 q^{49} - 324 q^{51} - 338 q^{52} - 98 q^{53} - 27 q^{54} + 231 q^{56} + 522 q^{57} - 482 q^{58} + 704 q^{59} + 650 q^{61} - 2070 q^{62} - 315 q^{63} + 75 q^{64} + 1518 q^{66} - 180 q^{67} - 4520 q^{68} + 348 q^{69} + 1470 q^{71} - 297 q^{72} + 534 q^{73} - 1312 q^{74} + 4370 q^{76} - 462 q^{77} + 1338 q^{78} - 820 q^{79} + 405 q^{81} + 1338 q^{82} - 1520 q^{83} - 567 q^{84} + 832 q^{86} + 1110 q^{87} + 3258 q^{88} + 286 q^{89} - 14 q^{91} - 1288 q^{92} + 1026 q^{93} + 2540 q^{94} + 165 q^{96} - 278 q^{97} - 49 q^{98} + 594 q^{99}+O(q^{100}) $ 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9 + 66 * q^11 + 81 * q^12 + 2 * q^13 + 7 * q^14 + 155 * q^16 - 108 * q^17 - 9 * q^18 + 174 * q^19 - 105 * q^21 + 506 * q^22 + 116 * q^23 - 99 * q^24 + 446 * q^26 + 135 * q^27 - 189 * q^28 + 370 * q^29 + 342 * q^31 + 55 * q^32 + 198 * q^33 + 112 * q^34 + 243 * q^36 + 408 * q^37 + 34 * q^38 + 6 * q^39 + 802 * q^41 + 21 * q^42 + 584 * q^43 + 290 * q^44 + 640 * q^46 - 716 * q^47 + 465 * q^48 + 245 * q^49 - 324 * q^51 - 338 * q^52 - 98 * q^53 - 27 * q^54 + 231 * q^56 + 522 * q^57 - 482 * q^58 + 704 * q^59 + 650 * q^61 - 2070 * q^62 - 315 * q^63 + 75 * q^64 + 1518 * q^66 - 180 * q^67 - 4520 * q^68 + 348 * q^69 + 1470 * q^71 - 297 * q^72 + 534 * q^73 - 1312 * q^74 + 4370 * q^76 - 462 * q^77 + 1338 * q^78 - 820 * q^79 + 405 * q^81 + 1338 * q^82 - 1520 * q^83 - 567 * q^84 + 832 * q^86 + 1110 * q^87 + 3258 * q^88 + 286 * q^89 - 14 * q^91 - 1288 * q^92 + 1026 * q^93 + 2540 * q^94 + 165 * q^96 - 278 * q^97 - 49 * q^98 + 594 * 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 $

$2$	−5.18660	−1.83374	−0.916870	−	0.399185i	$-0.869293\pi$
$2$	−5.18660	−1.83374	−0.916870	+	0.399185i	$0.869293\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	18.9008	2.36260
$5$	0	0
$5$	0	0
$6$	−15.5598	−1.05871
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−56.5383	−2.49866
$9$	9.00000	0.333333
$10$	0	0
$11$	−35.9555	−0.985545	−0.492772	−	0.870158i	$-0.664016\pi$
$11$	−35.9555	−0.985545	−0.492772	+	0.870158i	$0.664016\pi$
$12$	56.7025	1.36405
$13$	−45.2622	−0.965652	−0.482826	−	0.875716i	$-0.660390\pi$
$13$	−45.2622	−0.965652	−0.482826	+	0.875716i	$0.660390\pi$
$14$	36.3062	0.693089
$15$	0	0
$16$	142.035	2.21929
$17$	−113.154	−1.61434	−0.807170	−	0.590319i	$-0.799002\pi$
$17$	−113.154	−1.61434	−0.807170	+	0.590319i	$0.799002\pi$
$18$	−46.6794	−0.611247
$19$	61.5906	0.743677	0.371838	−	0.928297i	$-0.378728\pi$
$19$	61.5906	0.743677	0.371838	+	0.928297i	$0.378728\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	186.487	1.80723
$23$	30.6108	0.277513	0.138756	−	0.990327i	$-0.455690\pi$
$23$	30.6108	0.277513	0.138756	+	0.990327i	$0.455690\pi$
$24$	−169.615	−1.44260
$25$	0	0
$26$	234.757	1.77075
$27$	27.0000	0.192450
$28$	−132.306	−0.892980
$29$	214.989	1.37663	0.688317	−	0.725410i	$-0.258350\pi$
$29$	214.989	1.37663	0.688317	+	0.725410i	$0.258350\pi$
$30$	0	0
$31$	164.206	0.951362	0.475681	−	0.879618i	$-0.342202\pi$
$31$	164.206	0.951362	0.475681	+	0.879618i	$0.342202\pi$
$32$	−284.372	−1.57095
$33$	−107.866	−0.569004
$34$	586.882	2.96028
$35$	0	0
$36$	170.107	0.787535
$37$	410.533	1.82409	0.912043	−	0.410095i	$-0.134504\pi$
$37$	410.533	1.82409	0.912043	+	0.410095i	$0.134504\pi$
$38$	−319.446	−1.36371
$39$	−135.787	−0.557519
$40$	0	0
$41$	−309.310	−1.17820	−0.589100	−	0.808060i	$-0.700517\pi$
$41$	−309.310	−1.17820	−0.589100	+	0.808060i	$0.700517\pi$
$42$	108.919	0.400155
$43$	29.9519	0.106224	0.0531118	−	0.998589i	$-0.483086\pi$
$43$	29.9519	0.106224	0.0531118	+	0.998589i	$0.483086\pi$
$44$	−679.589	−2.32845
$45$	0	0
$46$	−158.766	−0.508886
$47$	−483.790	−1.50145	−0.750724	−	0.660616i	$-0.770295\pi$
$47$	−483.790	−1.50145	−0.750724	+	0.660616i	$0.770295\pi$
$48$	426.104	1.28131
$49$	49.0000	0.142857
$50$	0	0
$51$	−339.461	−0.932039
$52$	−855.493	−2.28145
$53$	295.582	0.766063	0.383031	−	0.923735i	$-0.374880\pi$
$53$	295.582	0.766063	0.383031	+	0.923735i	$0.374880\pi$
$54$	−140.038	−0.352904
$55$	0	0
$56$	395.768	0.944405
$57$	184.772	0.429362
$58$	−1115.06	−2.52439
$59$	416.191	0.918364	0.459182	−	0.888342i	$-0.348143\pi$
$59$	416.191	0.918364	0.459182	+	0.888342i	$0.348143\pi$
$60$	0	0
$61$	−151.196	−0.317355	−0.158677	−	0.987330i	$-0.550723\pi$
$61$	−151.196	−0.317355	−0.158677	+	0.987330i	$0.550723\pi$
$62$	−851.670	−1.74455
$63$	−63.0000	−0.125988
$64$	338.644	0.661415
$65$	0	0
$66$	559.460	1.04341
$67$	−89.5253	−0.163243	−0.0816213	−	0.996663i	$-0.526010\pi$
$67$	−89.5253	−0.163243	−0.0816213	+	0.996663i	$0.526010\pi$
$68$	−2138.70	−3.81404
$69$	91.8324	0.160222
$70$	0	0
$71$	714.265	1.19391	0.596955	−	0.802274i	$-0.296377\pi$
$71$	714.265	1.19391	0.596955	+	0.802274i	$0.296377\pi$
$72$	−508.844	−0.832887
$73$	1135.58	1.82068	0.910340	−	0.413861i	$-0.135820\pi$
$73$	1135.58	1.82068	0.910340	+	0.413861i	$0.135820\pi$
$74$	−2129.27	−3.34490
$75$	0	0
$76$	1164.11	1.75701
$77$	251.688	0.372501
$78$	704.271	1.02235
$79$	−323.347	−0.460498	−0.230249	−	0.973132i	$-0.573954\pi$
$79$	−323.347	−0.460498	−0.230249	+	0.973132i	$0.573954\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1604.27	2.16051
$83$	−297.898	−0.393959	−0.196979	−	0.980408i	$-0.563113\pi$
$83$	−297.898	−0.393959	−0.196979	+	0.980408i	$0.563113\pi$
$84$	−396.917	−0.515562
$85$	0	0
$86$	−155.348	−0.194787
$87$	644.966	0.794800
$88$	2032.86	2.46254
$89$	−90.2097	−0.107441	−0.0537203	−	0.998556i	$-0.517108\pi$
$89$	−90.2097	−0.107441	−0.0537203	+	0.998556i	$0.517108\pi$
$90$	0	0
$91$	316.835	0.364982
$92$	578.570	0.655653
$93$	492.617	0.549269
$94$	2509.23	2.75326
$95$	0	0
$96$	−853.115	−0.906986
$97$	492.101	0.515106	0.257553	−	0.966264i	$-0.417084\pi$
$97$	492.101	0.515106	0.257553	+	0.966264i	$0.417084\pi$
$98$	−254.143	−0.261963
$99$	−323.599	−0.328515
$100$	0	0
$101$	−272.636	−0.268597	−0.134299	−	0.990941i	$-0.542878\pi$
$101$	−272.636	−0.268597	−0.134299	+	0.990941i	$0.542878\pi$
$102$	1760.65	1.70912
$103$	628.179	0.600936	0.300468	−	0.953792i	$-0.402857\pi$
$103$	628.179	0.600936	0.300468	+	0.953792i	$0.402857\pi$
$104$	2559.05	2.41284
$105$	0	0
$106$	−1533.07	−1.40476
$107$	−908.469	−0.820794	−0.410397	−	0.911907i	$-0.634610\pi$
$107$	−908.469	−0.820794	−0.410397	+	0.911907i	$0.634610\pi$
$108$	510.322	0.454683
$109$	984.306	0.864948	0.432474	−	0.901646i	$-0.357641\pi$
$109$	984.306	0.864948	0.432474	+	0.901646i	$0.357641\pi$
$110$	0	0
$111$	1231.60	1.05314
$112$	−994.244	−0.838814
$113$	2228.79	1.85546	0.927730	−	0.373251i	$-0.121757\pi$
$113$	2228.79	1.85546	0.927730	+	0.373251i	$0.121757\pi$
$114$	−958.338	−0.787339
$115$	0	0
$116$	4063.47	3.25244
$117$	−407.360	−0.321884
$118$	−2158.62	−1.68404
$119$	792.075	0.610163
$120$	0	0
$121$	−38.2023	−0.0287019
$122$	784.193	0.581946
$123$	−927.931	−0.680234
$124$	3103.63	2.24769
$125$	0	0
$126$	326.756	0.231030
$127$	2860.78	1.99885	0.999423	−	0.0339770i	$-0.0108173\pi$
$127$	2860.78	1.99885	0.999423	+	0.0339770i	$0.0108173\pi$
$128$	518.561	0.358084
$129$	89.8556	0.0613283
$130$	0	0
$131$	−524.971	−0.350130	−0.175065	−	0.984557i	$-0.556013\pi$
$131$	−524.971	−0.350130	−0.175065	+	0.984557i	$0.556013\pi$
$132$	−2038.77	−1.34433
$133$	−431.134	−0.281083
$134$	464.332	0.299344
$135$	0	0
$136$	6397.51	4.03369
$137$	2149.03	1.34017	0.670087	−	0.742282i	$-0.266257\pi$
$137$	2149.03	1.34017	0.670087	+	0.742282i	$0.266257\pi$
$138$	−476.298	−0.293806
$139$	−1507.78	−0.920060	−0.460030	−	0.887903i	$-0.652161\pi$
$139$	−1507.78	−0.920060	−0.460030	+	0.887903i	$0.652161\pi$
$140$	0	0
$141$	−1451.37	−0.866861
$142$	−3704.61	−2.18932
$143$	1627.42	0.951693
$144$	1278.31	0.739765
$145$	0	0
$146$	−5889.80	−3.33865
$147$	147.000	0.0824786
$148$	7759.41	4.30959
$149$	−1013.61	−0.557304	−0.278652	−	0.960392i	$-0.589888\pi$
$149$	−1013.61	−0.557304	−0.278652	+	0.960392i	$0.589888\pi$
$150$	0	0
$151$	1663.70	0.896623	0.448312	−	0.893877i	$-0.352025\pi$
$151$	1663.70	0.896623	0.448312	+	0.893877i	$0.352025\pi$
$152$	−3482.23	−1.85820
$153$	−1018.38	−0.538113
$154$	−1305.41	−0.683070
$155$	0	0
$156$	−2566.48	−1.31720
$157$	−2399.48	−1.21974	−0.609872	−	0.792500i	$-0.708779\pi$
$157$	−2399.48	−1.21974	−0.609872	+	0.792500i	$0.708779\pi$
$158$	1677.07	0.844434
$159$	886.746	0.442286
$160$	0	0
$161$	−214.276	−0.104890
$162$	−420.115	−0.203749
$163$	−1415.81	−0.680337	−0.340168	−	0.940365i	$-0.610484\pi$
$163$	−1415.81	−0.680337	−0.340168	+	0.940365i	$0.610484\pi$
$164$	−5846.22	−2.78362
$165$	0	0
$166$	1545.08	0.722418
$167$	3543.86	1.64211	0.821055	−	0.570850i	$-0.193386\pi$
$167$	3543.86	1.64211	0.821055	+	0.570850i	$0.193386\pi$
$168$	1187.30	0.545253
$169$	−148.335	−0.0675170
$170$	0	0
$171$	554.316	0.247892
$172$	566.115	0.250964
$173$	95.6649	0.0420420	0.0210210	−	0.999779i	$-0.493308\pi$
$173$	95.6649	0.0420420	0.0210210	+	0.999779i	$0.493308\pi$
$174$	−3345.18	−1.45746
$175$	0	0
$176$	−5106.93	−2.18721
$177$	1248.57	0.530218
$178$	467.882	0.197018
$179$	2166.13	0.904491	0.452245	−	0.891894i	$-0.350623\pi$
$179$	2166.13	0.904491	0.452245	+	0.891894i	$0.350623\pi$
$180$	0	0
$181$	−1859.24	−0.763514	−0.381757	−	0.924263i	$-0.624681\pi$
$181$	−1859.24	−0.763514	−0.381757	+	0.924263i	$0.624681\pi$
$182$	−1643.30	−0.669282
$183$	−453.588	−0.183225
$184$	−1730.68	−0.693411
$185$	0	0
$186$	−2555.01	−1.00722
$187$	4068.49	1.59100
$188$	−9144.03	−3.54733
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−2661.60	−1.00831	−0.504154	−	0.863614i	$-0.668195\pi$
$191$	−2661.60	−1.00831	−0.504154	+	0.863614i	$0.668195\pi$
$192$	1015.93	0.381868
$193$	−1952.03	−0.728033	−0.364016	−	0.931393i	$-0.618595\pi$
$193$	−1952.03	−0.728033	−0.364016	+	0.931393i	$0.618595\pi$
$194$	−2552.33	−0.944570
$195$	0	0
$196$	926.141	0.337515
$197$	3587.80	1.29757	0.648783	−	0.760974i	$-0.275278\pi$
$197$	3587.80	1.29757	0.648783	+	0.760974i	$0.275278\pi$
$198$	1678.38	0.602411
$199$	−767.691	−0.273468	−0.136734	−	0.990608i	$-0.543661\pi$
$199$	−767.691	−0.273468	−0.136734	+	0.990608i	$0.543661\pi$
$200$	0	0
$201$	−268.576	−0.0942481
$202$	1414.06	0.492538
$203$	−1504.92	−0.520319
$204$	−6416.09	−2.20204
$205$	0	0
$206$	−3258.12	−1.10196
$207$	275.497	0.0925042
$208$	−6428.81	−2.14306
$209$	−2214.52	−0.732927
$210$	0	0
$211$	−1199.84	−0.391472	−0.195736	−	0.980657i	$-0.562710\pi$
$211$	−1199.84	−0.391472	−0.195736	+	0.980657i	$0.562710\pi$
$212$	5586.75	1.80990
$213$	2142.79	0.689305
$214$	4711.87	1.50512
$215$	0	0
$216$	−1526.53	−0.480868
$217$	−1149.44	−0.359581
$218$	−5105.20	−1.58609
$219$	3406.74	1.05117
$220$	0	0
$221$	5121.58	1.55889
$222$	−6387.81	−1.93118
$223$	2917.84	0.876203	0.438101	−	0.898926i	$-0.355651\pi$
$223$	2917.84	0.876203	0.438101	+	0.898926i	$0.355651\pi$
$224$	1990.60	0.593762
$225$	0	0
$226$	−11559.9	−3.40243
$227$	612.679	0.179141	0.0895703	−	0.995981i	$-0.471451\pi$
$227$	612.679	0.179141	0.0895703	+	0.995981i	$0.471451\pi$
$228$	3492.34	1.01441
$229$	2641.51	0.762253	0.381126	−	0.924523i	$-0.375536\pi$
$229$	2641.51	0.762253	0.381126	+	0.924523i	$0.375536\pi$
$230$	0	0
$231$	755.065	0.215063
$232$	−12155.1	−3.43974
$233$	−2322.87	−0.653117	−0.326558	−	0.945177i	$-0.605889\pi$
$233$	−2322.87	−0.653117	−0.326558	+	0.945177i	$0.605889\pi$
$234$	2112.81	0.590251
$235$	0	0
$236$	7866.36	2.16973
$237$	−970.041	−0.265869
$238$	−4108.18	−1.11888
$239$	5372.54	1.45406	0.727030	−	0.686605i	$-0.240900\pi$
$239$	5372.54	1.45406	0.727030	+	0.686605i	$0.240900\pi$
$240$	0	0
$241$	−1412.33	−0.377494	−0.188747	−	0.982026i	$-0.560443\pi$
$241$	−1412.33	−0.377494	−0.188747	+	0.982026i	$0.560443\pi$
$242$	198.140	0.0526319
$243$	243.000	0.0641500
$244$	−2857.73	−0.749784
$245$	0	0
$246$	4812.81	1.24737
$247$	−2787.73	−0.718133
$248$	−9283.91	−2.37713
$249$	−893.694	−0.227452
$250$	0	0
$251$	5676.06	1.42737	0.713684	−	0.700467i	$-0.247025\pi$
$251$	5676.06	1.42737	0.713684	+	0.700467i	$0.247025\pi$
$252$	−1190.75	−0.297660
$253$	−1100.63	−0.273501
$254$	−14837.7	−3.66536
$255$	0	0
$256$	−5398.72	−1.31805
$257$	−3939.60	−0.956207	−0.478104	−	0.878303i	$-0.658676\pi$
$257$	−3939.60	−0.956207	−0.478104	+	0.878303i	$0.658676\pi$
$258$	−466.045	−0.112460
$259$	−2873.73	−0.689440
$260$	0	0
$261$	1934.90	0.458878
$262$	2722.82	0.642047
$263$	−5397.68	−1.26553	−0.632766	−	0.774343i	$-0.718081\pi$
$263$	−5397.68	−1.26553	−0.632766	+	0.774343i	$0.718081\pi$
$264$	6098.58	1.42175
$265$	0	0
$266$	2236.12	0.515434
$267$	−270.629	−0.0620308
$268$	−1692.10	−0.385678
$269$	4973.60	1.12731	0.563654	−	0.826011i	$-0.309395\pi$
$269$	4973.60	1.12731	0.563654	+	0.826011i	$0.309395\pi$
$270$	0	0
$271$	4147.48	0.929672	0.464836	−	0.885397i	$-0.346113\pi$
$271$	4147.48	0.929672	0.464836	+	0.885397i	$0.346113\pi$
$272$	−16071.7	−3.58269
$273$	950.506	0.210722
$274$	−11146.2	−2.45753
$275$	0	0
$276$	1735.71	0.378541
$277$	−2616.79	−0.567609	−0.283805	−	0.958882i	$-0.591597\pi$
$277$	−2616.79	−0.567609	−0.283805	+	0.958882i	$0.591597\pi$
$278$	7820.26	1.68715
$279$	1477.85	0.317121
$280$	0	0
$281$	2866.89	0.608628	0.304314	−	0.952572i	$-0.401573\pi$
$281$	2866.89	0.608628	0.304314	+	0.952572i	$0.401573\pi$
$282$	7527.68	1.58960
$283$	3015.40	0.633381	0.316691	−	0.948529i	$-0.397428\pi$
$283$	3015.40	0.633381	0.316691	+	0.948529i	$0.397428\pi$
$284$	13500.2	2.82074
$285$	0	0
$286$	−8440.80	−1.74516
$287$	2165.17	0.445318
$288$	−2559.35	−0.523649
$289$	7890.73	1.60609
$290$	0	0
$291$	1476.30	0.297396
$292$	21463.4	4.30155
$293$	3580.41	0.713890	0.356945	−	0.934125i	$-0.383818\pi$
$293$	3580.41	0.713890	0.356945	+	0.934125i	$0.383818\pi$
$294$	−762.430	−0.151244
$295$	0	0
$296$	−23210.8	−4.55777
$297$	−970.798	−0.189668
$298$	5257.20	1.02195
$299$	−1385.51	−0.267981
$300$	0	0
$301$	−209.663	−0.0401488
$302$	−8628.96	−1.64417
$303$	−817.909	−0.155075
$304$	8748.01	1.65044
$305$	0	0
$306$	5281.94	0.986760
$307$	−1432.92	−0.266389	−0.133194	−	0.991090i	$-0.542523\pi$
$307$	−1432.92	−0.266389	−0.133194	+	0.991090i	$0.542523\pi$
$308$	4757.12	0.880072
$309$	1884.54	0.346950
$310$	0	0
$311$	5488.33	1.00069	0.500345	−	0.865826i	$-0.333206\pi$
$311$	5488.33	1.00069	0.500345	+	0.865826i	$0.333206\pi$
$312$	7677.14	1.39305
$313$	2461.68	0.444545	0.222272	−	0.974985i	$-0.428653\pi$
$313$	2461.68	0.444545	0.222272	+	0.974985i	$0.428653\pi$
$314$	12445.2	2.23669
$315$	0	0
$316$	−6111.53	−1.08798
$317$	−3113.12	−0.551579	−0.275789	−	0.961218i	$-0.588939\pi$
$317$	−3113.12	−0.551579	−0.275789	+	0.961218i	$0.588939\pi$
$318$	−4599.20	−0.811038
$319$	−7730.03	−1.35673
$320$	0	0
$321$	−2725.41	−0.473886
$322$	1111.36	0.192341
$323$	−6969.20	−1.20055
$324$	1530.97	0.262512
$325$	0	0
$326$	7343.25	1.24756
$327$	2952.92	0.499378
$328$	17487.9	2.94392
$329$	3386.53	0.567494
$330$	0	0
$331$	−6364.21	−1.05682	−0.528411	−	0.848988i	$-0.677212\pi$
$331$	−6364.21	−1.05682	−0.528411	+	0.848988i	$0.677212\pi$
$332$	−5630.52	−0.930768
$333$	3694.79	0.608029
$334$	−18380.6	−3.01120
$335$	0	0
$336$	−2982.73	−0.484290
$337$	5163.25	0.834600	0.417300	−	0.908769i	$-0.362976\pi$
$337$	5163.25	0.834600	0.417300	+	0.908769i	$0.362976\pi$
$338$	769.353	0.123809
$339$	6686.37	1.07125
$340$	0	0
$341$	−5904.10	−0.937610
$342$	−2875.01	−0.454570
$343$	−343.000	−0.0539949
$344$	−1693.43	−0.265417
$345$	0	0
$346$	−496.176	−0.0770941
$347$	−305.000	−0.0471851	−0.0235926	−	0.999722i	$-0.507510\pi$
$347$	−305.000	−0.0471851	−0.0235926	+	0.999722i	$0.507510\pi$
$348$	12190.4	1.87780
$349$	−8233.50	−1.26283	−0.631417	−	0.775443i	$-0.717526\pi$
$349$	−8233.50	−1.26283	−0.631417	+	0.775443i	$0.717526\pi$
$350$	0	0
$351$	−1222.08	−0.185840
$352$	10224.7	1.54824
$353$	1064.37	0.160483	0.0802415	−	0.996775i	$-0.474431\pi$
$353$	1064.37	0.160483	0.0802415	+	0.996775i	$0.474431\pi$
$354$	−6475.85	−0.972281
$355$	0	0
$356$	−1705.04	−0.253839
$357$	2376.22	0.352278
$358$	−11234.8	−1.65860
$359$	−3915.59	−0.575646	−0.287823	−	0.957684i	$-0.592931\pi$
$359$	−3915.59	−0.575646	−0.287823	+	0.957684i	$0.592931\pi$
$360$	0	0
$361$	−3065.59	−0.446945
$362$	9643.13	1.40009
$363$	−114.607	−0.0165711
$364$	5988.45	0.862308
$365$	0	0
$366$	2352.58	0.335987
$367$	−7430.70	−1.05689	−0.528446	−	0.848967i	$-0.677225\pi$
$367$	−7430.70	−1.05689	−0.528446	+	0.848967i	$0.677225\pi$
$368$	4347.80	0.615882
$369$	−2783.79	−0.392733
$370$	0	0
$371$	−2069.07	−0.289544
$372$	9310.88	1.29771
$373$	3275.71	0.454718	0.227359	−	0.973811i	$-0.426991\pi$
$373$	3275.71	0.454718	0.227359	+	0.973811i	$0.426991\pi$
$374$	−21101.6	−2.91749
$375$	0	0
$376$	27352.7	3.75161
$377$	−9730.86	−1.32935
$378$	980.268	0.133385
$379$	5745.18	0.778655	0.389327	−	0.921099i	$-0.372707\pi$
$379$	5745.18	0.778655	0.389327	+	0.921099i	$0.372707\pi$
$380$	0	0
$381$	8582.35	1.15403
$382$	13804.7	1.84897
$383$	−101.844	−0.0135874	−0.00679372	−	0.999977i	$-0.502163\pi$
$383$	−101.844	−0.0135874	−0.00679372	+	0.999977i	$0.502163\pi$
$384$	1555.68	0.206740
$385$	0	0
$386$	10124.4	1.33502
$387$	269.567	0.0354079
$388$	9301.11	1.21699
$389$	3047.72	0.397237	0.198619	−	0.980077i	$-0.436354\pi$
$389$	3047.72	0.397237	0.198619	+	0.980077i	$0.436354\pi$
$390$	0	0
$391$	−3463.72	−0.448000
$392$	−2770.38	−0.356952
$393$	−1574.91	−0.202147
$394$	−18608.5	−2.37940
$395$	0	0
$396$	−6116.30	−0.776151
$397$	−9830.23	−1.24273	−0.621367	−	0.783520i	$-0.713422\pi$
$397$	−9830.23	−1.24273	−0.621367	+	0.783520i	$0.713422\pi$
$398$	3981.71	0.501470
$399$	−1293.40	−0.162284
$400$	0	0
$401$	3693.01	0.459900	0.229950	−	0.973202i	$-0.426144\pi$
$401$	3693.01	0.459900	0.229950	+	0.973202i	$0.426144\pi$
$402$	1393.00	0.172827
$403$	−7432.31	−0.918684
$404$	−5153.06	−0.634589
$405$	0	0
$406$	7805.43	0.954130
$407$	−14760.9	−1.79772
$408$	19192.5	2.32885
$409$	8815.07	1.06571	0.532857	−	0.846205i	$-0.321118\pi$
$409$	8815.07	1.06571	0.532857	+	0.846205i	$0.321118\pi$
$410$	0	0
$411$	6447.09	0.773750
$412$	11873.1	1.41977
$413$	−2913.34	−0.347109
$414$	−1428.89	−0.169629
$415$	0	0
$416$	12871.3	1.51699
$417$	−4523.35	−0.531197
$418$	11485.8	1.34400
$419$	3746.84	0.436862	0.218431	−	0.975852i	$-0.429906\pi$
$419$	3746.84	0.436862	0.218431	+	0.975852i	$0.429906\pi$
$420$	0	0
$421$	−10554.5	−1.22184	−0.610922	−	0.791690i	$-0.709201\pi$
$421$	−10554.5	−1.22184	−0.610922	+	0.791690i	$0.709201\pi$
$422$	6223.10	0.717858
$423$	−4354.11	−0.500482
$424$	−16711.7	−1.91413
$425$	0	0
$426$	−11113.8	−1.26401
$427$	1058.37	0.119949
$428$	−17170.8	−1.93921
$429$	4882.27	0.549460
$430$	0	0
$431$	−14029.9	−1.56797	−0.783986	−	0.620778i	$-0.786817\pi$
$431$	−14029.9	−1.56797	−0.783986	+	0.620778i	$0.786817\pi$
$432$	3834.94	0.427103
$433$	9639.08	1.06980	0.534901	−	0.844915i	$-0.320349\pi$
$433$	9639.08	1.06980	0.534901	+	0.844915i	$0.320349\pi$
$434$	5961.69	0.659378
$435$	0	0
$436$	18604.2	2.04353
$437$	1885.34	0.206380
$438$	−17669.4	−1.92757
$439$	3936.53	0.427974	0.213987	−	0.976837i	$-0.431355\pi$
$439$	3936.53	0.427974	0.213987	+	0.976837i	$0.431355\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	−26563.6	−2.85860
$443$	10812.5	1.15963	0.579817	−	0.814746i	$-0.303124\pi$
$443$	10812.5	1.15963	0.579817	+	0.814746i	$0.303124\pi$
$444$	23278.2	2.48814
$445$	0	0
$446$	−15133.7	−1.60673
$447$	−3040.84	−0.321760
$448$	−2370.51	−0.249991
$449$	8154.86	0.857131	0.428565	−	0.903511i	$-0.359019\pi$
$449$	8154.86	0.857131	0.428565	+	0.903511i	$0.359019\pi$
$450$	0	0
$451$	11121.4	1.16117
$452$	42126.0	4.38372
$453$	4991.11	0.517666
$454$	−3177.72	−0.328497
$455$	0	0
$456$	−10446.7	−1.07283
$457$	17787.5	1.82071	0.910353	−	0.413833i	$-0.135810\pi$
$457$	17787.5	1.82071	0.910353	+	0.413833i	$0.135810\pi$
$458$	−13700.5	−1.39777
$459$	−3055.15	−0.310680
$460$	0	0
$461$	13192.1	1.33280	0.666398	−	0.745596i	$-0.267835\pi$
$461$	13192.1	1.33280	0.666398	+	0.745596i	$0.267835\pi$
$462$	−3916.22	−0.394371
$463$	542.568	0.0544607	0.0272303	−	0.999629i	$-0.491331\pi$
$463$	542.568	0.0544607	0.0272303	+	0.999629i	$0.491331\pi$
$464$	30535.9	3.05516
$465$	0	0
$466$	12047.8	1.19765
$467$	5962.51	0.590818	0.295409	−	0.955371i	$-0.404544\pi$
$467$	5962.51	0.590818	0.295409	+	0.955371i	$0.404544\pi$
$468$	−7699.44	−0.760484
$469$	626.677	0.0616999
$470$	0	0
$471$	−7198.45	−0.704219
$472$	−23530.7	−2.29468
$473$	−1076.93	−0.104688
$474$	5031.21	0.487534
$475$	0	0
$476$	14970.9	1.44157
$477$	2660.24	0.255354
$478$	−27865.2	−2.66637
$479$	−1317.66	−0.125690	−0.0628451	−	0.998023i	$-0.520017\pi$
$479$	−1317.66	−0.125690	−0.0628451	+	0.998023i	$0.520017\pi$
$480$	0	0
$481$	−18581.6	−1.76143
$482$	7325.19	0.692227
$483$	−642.827	−0.0605582
$484$	−722.054	−0.0678113
$485$	0	0
$486$	−1260.34	−0.117635
$487$	−5976.21	−0.556074	−0.278037	−	0.960570i	$-0.589684\pi$
$487$	−5976.21	−0.556074	−0.278037	+	0.960570i	$0.589684\pi$
$488$	8548.35	0.792962
$489$	−4247.43	−0.392793
$490$	0	0
$491$	10338.9	0.950285	0.475143	−	0.879909i	$-0.342396\pi$
$491$	10338.9	0.950285	0.475143	+	0.879909i	$0.342396\pi$
$492$	−17538.7	−1.60712
$493$	−24326.7	−2.22236
$494$	14458.8	1.31687
$495$	0	0
$496$	23322.9	2.11135
$497$	−4999.85	−0.451256
$498$	4635.24	0.417088
$499$	−4161.74	−0.373357	−0.186678	−	0.982421i	$-0.559772\pi$
$499$	−4161.74	−0.373357	−0.186678	+	0.982421i	$0.559772\pi$
$500$	0	0
$501$	10631.6	0.948072
$502$	−29439.4	−2.61742
$503$	−7556.24	−0.669813	−0.334907	−	0.942251i	$-0.608705\pi$
$503$	−7556.24	−0.669813	−0.334907	+	0.942251i	$0.608705\pi$
$504$	3561.91	0.314802
$505$	0	0
$506$	5708.51	0.501530
$507$	−445.004	−0.0389809
$508$	54071.2	4.72248
$509$	7231.12	0.629693	0.314847	−	0.949143i	$-0.398047\pi$
$509$	7231.12	0.629693	0.314847	+	0.949143i	$0.398047\pi$
$510$	0	0
$511$	−7949.06	−0.688152
$512$	23852.5	2.05887
$513$	1662.95	0.143121
$514$	20433.1	1.75344
$515$	0	0
$516$	1698.35	0.144894
$517$	17394.9	1.47974
$518$	14904.9	1.26425
$519$	286.995	0.0242730
$520$	0	0
$521$	−7378.54	−0.620460	−0.310230	−	0.950661i	$-0.600406\pi$
$521$	−7378.54	−0.620460	−0.310230	+	0.950661i	$0.600406\pi$
$522$	−10035.5	−0.841464
$523$	−2200.53	−0.183982	−0.0919909	−	0.995760i	$-0.529323\pi$
$523$	−2200.53	−0.183982	−0.0919909	+	0.995760i	$0.529323\pi$
$524$	−9922.40	−0.827217
$525$	0	0
$526$	27995.6	2.32066
$527$	−18580.5	−1.53582
$528$	−15320.8	−1.26279
$529$	−11230.0	−0.922987
$530$	0	0
$531$	3745.72	0.306121
$532$	−8148.80	−0.664089
$533$	14000.1	1.13773
$534$	1403.64	0.113748
$535$	0	0
$536$	5061.60	0.407888
$537$	6498.38	0.522208
$538$	−25796.1	−2.06719
$539$	−1761.82	−0.140792
$540$	0	0
$541$	−23797.3	−1.89118	−0.945588	−	0.325365i	$-0.894513\pi$
$541$	−23797.3	−1.89118	−0.945588	+	0.325365i	$0.894513\pi$
$542$	−21511.3	−1.70478
$543$	−5577.72	−0.440815
$544$	32177.7	2.53604
$545$	0	0
$546$	−4929.89	−0.386410
$547$	−6586.46	−0.514839	−0.257419	−	0.966300i	$-0.582872\pi$
$547$	−6586.46	−0.514839	−0.257419	+	0.966300i	$0.582872\pi$
$548$	40618.4	3.16630
$549$	−1360.76	−0.105785
$550$	0	0
$551$	13241.3	1.02377
$552$	−5192.04	−0.400341
$553$	2263.43	0.174052
$554$	13572.3	1.04085
$555$	0	0
$556$	−28498.3	−2.17374
$557$	−23522.6	−1.78938	−0.894691	−	0.446686i	$-0.852604\pi$
$557$	−23522.6	−1.78938	−0.894691	+	0.446686i	$0.852604\pi$
$558$	−7665.03	−0.581517
$559$	−1355.69	−0.102575
$560$	0	0
$561$	12205.5	0.918566
$562$	−14869.4	−1.11607
$563$	−17654.3	−1.32156	−0.660782	−	0.750578i	$-0.729775\pi$
$563$	−17654.3	−1.32156	−0.660782	+	0.750578i	$0.729775\pi$
$564$	−27432.1	−2.04805
$565$	0	0
$566$	−15639.7	−1.16146
$567$	−567.000	−0.0419961
$568$	−40383.3	−2.98318
$569$	−13453.6	−0.991223	−0.495611	−	0.868544i	$-0.665056\pi$
$569$	−13453.6	−0.991223	−0.495611	+	0.868544i	$0.665056\pi$
$570$	0	0
$571$	9019.88	0.661069	0.330534	−	0.943794i	$-0.392771\pi$
$571$	9019.88	0.661069	0.330534	+	0.943794i	$0.392771\pi$
$572$	30759.7	2.24847
$573$	−7984.80	−0.582146
$574$	−11229.9	−0.816597
$575$	0	0
$576$	3047.80	0.220472
$577$	−1328.73	−0.0958680	−0.0479340	−	0.998851i	$-0.515264\pi$
$577$	−1328.73	−0.0958680	−0.0479340	+	0.998851i	$0.515264\pi$
$578$	−40926.1	−2.94516
$579$	−5856.09	−0.420330
$580$	0	0
$581$	2085.29	0.148902
$582$	−7656.99	−0.545348
$583$	−10627.8	−0.754989
$584$	−64203.8	−4.54926
$585$	0	0
$586$	−18570.2	−1.30909
$587$	−13927.3	−0.979283	−0.489642	−	0.871924i	$-0.662872\pi$
$587$	−13927.3	−0.979283	−0.489642	+	0.871924i	$0.662872\pi$
$588$	2778.42	0.194864
$589$	10113.5	0.707506
$590$	0	0
$591$	10763.4	0.749150
$592$	58309.9	4.04818
$593$	5684.69	0.393663	0.196831	−	0.980437i	$-0.436935\pi$
$593$	5684.69	0.393663	0.196831	+	0.980437i	$0.436935\pi$
$594$	5035.14	0.347802
$595$	0	0
$596$	−19158.1	−1.31669
$597$	−2303.07	−0.157887
$598$	7186.10	0.491407
$599$	27961.5	1.90730	0.953651	−	0.300914i	$-0.0972916\pi$
$599$	27961.5	1.90730	0.953651	+	0.300914i	$0.0972916\pi$
$600$	0	0
$601$	−12396.7	−0.841386	−0.420693	−	0.907203i	$-0.638213\pi$
$601$	−12396.7	−0.841386	−0.420693	+	0.907203i	$0.638213\pi$
$602$	1087.44	0.0736224
$603$	−805.727	−0.0544142
$604$	31445.3	2.11837
$605$	0	0
$606$	4242.17	0.284367
$607$	−3124.52	−0.208930	−0.104465	−	0.994529i	$-0.533313\pi$
$607$	−3124.52	−0.208930	−0.104465	+	0.994529i	$0.533313\pi$
$608$	−17514.6	−1.16828
$609$	−4514.76	−0.300406
$610$	0	0
$611$	21897.4	1.44988
$612$	−19248.3	−1.27135
$613$	9531.29	0.628002	0.314001	−	0.949423i	$-0.398330\pi$
$613$	9531.29	0.628002	0.314001	+	0.949423i	$0.398330\pi$
$614$	7432.01	0.488488
$615$	0	0
$616$	−14230.0	−0.930754
$617$	5410.37	0.353020	0.176510	−	0.984299i	$-0.443519\pi$
$617$	5410.37	0.353020	0.176510	+	0.984299i	$0.443519\pi$
$618$	−9774.35	−0.636217
$619$	−10244.9	−0.665228	−0.332614	−	0.943063i	$-0.607931\pi$
$619$	−10244.9	−0.665228	−0.332614	+	0.943063i	$0.607931\pi$
$620$	0	0
$621$	826.492	0.0534074
$622$	−28465.8	−1.83501
$623$	631.468	0.0406087
$624$	−19286.4	−1.23730
$625$	0	0
$626$	−12767.8	−0.815180
$627$	−6643.57	−0.423155
$628$	−45352.3	−2.88177
$629$	−46453.2	−2.94469
$630$	0	0
$631$	−10342.8	−0.652522	−0.326261	−	0.945280i	$-0.605789\pi$
$631$	−10342.8	−0.652522	−0.326261	+	0.945280i	$0.605789\pi$
$632$	18281.5	1.15063
$633$	−3599.53	−0.226016
$634$	16146.5	1.01145
$635$	0	0
$636$	16760.2	1.04495
$637$	−2217.85	−0.137950
$638$	40092.6	2.48790
$639$	6428.38	0.397970
$640$	0	0
$641$	−981.309	−0.0604671	−0.0302335	−	0.999543i	$-0.509625\pi$
$641$	−981.309	−0.0604671	−0.0302335	+	0.999543i	$0.509625\pi$
$642$	14135.6	0.868984
$643$	16289.5	0.999062	0.499531	−	0.866296i	$-0.333506\pi$
$643$	16289.5	0.999062	0.499531	+	0.866296i	$0.333506\pi$
$644$	−4049.99	−0.247813
$645$	0	0
$646$	36146.5	2.20149
$647$	11349.5	0.689634	0.344817	−	0.938670i	$-0.387941\pi$
$647$	11349.5	0.689634	0.344817	+	0.938670i	$0.387941\pi$
$648$	−4579.60	−0.277629
$649$	−14964.4	−0.905088
$650$	0	0
$651$	−3448.32	−0.207604
$652$	−26760.0	−1.60737
$653$	−20510.7	−1.22917	−0.614583	−	0.788852i	$-0.710676\pi$
$653$	−20510.7	−1.22917	−0.614583	+	0.788852i	$0.710676\pi$
$654$	−15315.6	−0.915730
$655$	0	0
$656$	−43932.8	−2.61477
$657$	10220.2	0.606893
$658$	−17564.6	−1.04064
$659$	15480.4	0.915070	0.457535	−	0.889191i	$-0.348732\pi$
$659$	15480.4	0.915070	0.457535	+	0.889191i	$0.348732\pi$
$660$	0	0
$661$	3720.51	0.218928	0.109464	−	0.993991i	$-0.465087\pi$
$661$	3720.51	0.218928	0.109464	+	0.993991i	$0.465087\pi$
$662$	33008.6	1.93794
$663$	15364.7	0.900025
$664$	16842.6	0.984369
$665$	0	0
$666$	−19163.4	−1.11497
$667$	6580.98	0.382034
$668$	66981.9	3.87965
$669$	8753.53	0.505876
$670$	0	0
$671$	5436.32	0.312767
$672$	5971.81	0.342809
$673$	−17977.2	−1.02967	−0.514837	−	0.857288i	$-0.672147\pi$
$673$	−17977.2	−1.02967	−0.514837	+	0.857288i	$0.672147\pi$
$674$	−26779.7	−1.53044
$675$	0	0
$676$	−2803.65	−0.159516
$677$	13079.2	0.742505	0.371253	−	0.928532i	$-0.378928\pi$
$677$	13079.2	0.742505	0.371253	+	0.928532i	$0.378928\pi$
$678$	−34679.6	−1.96440
$679$	−3444.70	−0.194692
$680$	0	0
$681$	1838.04	0.103427
$682$	30622.2	1.71933
$683$	22608.2	1.26659	0.633293	−	0.773912i	$-0.281703\pi$
$683$	22608.2	1.26659	0.633293	+	0.773912i	$0.281703\pi$
$684$	10477.0	0.585671
$685$	0	0
$686$	1779.00	0.0990127
$687$	7924.53	0.440087
$688$	4254.21	0.235742
$689$	−13378.7	−0.739749
$690$	0	0
$691$	26262.2	1.44582	0.722910	−	0.690942i	$-0.242804\pi$
$691$	26262.2	1.44582	0.722910	+	0.690942i	$0.242804\pi$
$692$	1808.15	0.0993286
$693$	2265.20	0.124167
$694$	1581.91	0.0865253
$695$	0	0
$696$	−36465.3	−1.98594
$697$	34999.6	1.90201
$698$	42703.9	2.31571
$699$	−6968.61	−0.377077
$700$	0	0
$701$	−15831.3	−0.852982	−0.426491	−	0.904492i	$-0.640250\pi$
$701$	−15831.3	−0.852982	−0.426491	+	0.904492i	$0.640250\pi$
$702$	6338.44	0.340782
$703$	25285.0	1.35653
$704$	−12176.1	−0.651853
$705$	0	0
$706$	−5520.44	−0.294284
$707$	1908.46	0.101520
$708$	23599.1	1.25269
$709$	−874.284	−0.0463109	−0.0231554	−	0.999732i	$-0.507371\pi$
$709$	−874.284	−0.0463109	−0.0231554	+	0.999732i	$0.507371\pi$
$710$	0	0
$711$	−2910.12	−0.153499
$712$	5100.30	0.268458
$713$	5026.47	0.264015
$714$	−12324.5	−0.645986
$715$	0	0
$716$	40941.6	2.13695
$717$	16117.6	0.839502
$718$	20308.6	1.05559
$719$	103.934	0.00539091	0.00269546	−	0.999996i	$-0.499142\pi$
$719$	103.934	0.00539091	0.00269546	+	0.999996i	$0.499142\pi$
$720$	0	0
$721$	−4397.26	−0.227132
$722$	15900.0	0.819580
$723$	−4236.99	−0.217946
$724$	−35141.2	−1.80388
$725$	0	0
$726$	594.420	0.0303870
$727$	−20972.0	−1.06989	−0.534945	−	0.844887i	$-0.679668\pi$
$727$	−20972.0	−1.06989	−0.534945	+	0.844887i	$0.679668\pi$
$728$	−17913.3	−0.911967
$729$	729.000	0.0370370
$730$	0	0
$731$	−3389.16	−0.171481
$732$	−8573.18	−0.432888
$733$	−32298.2	−1.62750	−0.813751	−	0.581213i	$-0.802578\pi$
$733$	−32298.2	−1.62750	−0.813751	+	0.581213i	$0.802578\pi$
$734$	38540.1	1.93807
$735$	0	0
$736$	−8704.85	−0.435958
$737$	3218.93	0.160883
$738$	14438.4	0.720171
$739$	19402.4	0.965804	0.482902	−	0.875674i	$-0.339583\pi$
$739$	19402.4	0.965804	0.482902	+	0.875674i	$0.339583\pi$
$740$	0	0
$741$	−8363.18	−0.414614
$742$	10731.5	0.530949
$743$	28784.0	1.42124	0.710621	−	0.703575i	$-0.248414\pi$
$743$	28784.0	1.42124	0.710621	+	0.703575i	$0.248414\pi$
$744$	−27851.7	−1.37244
$745$	0	0
$746$	−16989.8	−0.833834
$747$	−2681.08	−0.131320
$748$	76897.9	3.75891
$749$	6359.28	0.310231
$750$	0	0
$751$	4382.70	0.212952	0.106476	−	0.994315i	$-0.466043\pi$
$751$	4382.70	0.212952	0.106476	+	0.994315i	$0.466043\pi$
$752$	−68715.0	−3.33215
$753$	17028.2	0.824092
$754$	50470.1	2.43768
$755$	0	0
$756$	−3572.26	−0.171854
$757$	−13669.8	−0.656326	−0.328163	−	0.944621i	$-0.606430\pi$
$757$	−13669.8	−0.656326	−0.328163	+	0.944621i	$0.606430\pi$
$758$	−29798.0	−1.42785
$759$	−3301.88	−0.157906
$760$	0	0
$761$	−25216.4	−1.20117	−0.600586	−	0.799560i	$-0.705066\pi$
$761$	−25216.4	−1.20117	−0.600586	+	0.799560i	$0.705066\pi$
$762$	−44513.2	−2.11620
$763$	−6890.14	−0.326920
$764$	−50306.5	−2.38223
$765$	0	0
$766$	528.225	0.0249158
$767$	−18837.7	−0.886819
$768$	−16196.2	−0.760975
$769$	15930.6	0.747038	0.373519	−	0.927622i	$-0.378151\pi$
$769$	15930.6	0.747038	0.373519	+	0.927622i	$0.378151\pi$
$770$	0	0
$771$	−11818.8	−0.552066
$772$	−36895.0	−1.72005
$773$	−28154.5	−1.31002	−0.655012	−	0.755618i	$-0.727336\pi$
$773$	−28154.5	−1.31002	−0.655012	+	0.755618i	$0.727336\pi$
$774$	−1398.14	−0.0649289
$775$	0	0
$776$	−27822.5	−1.28708
$777$	−8621.19	−0.398048
$778$	−15807.3	−0.728430
$779$	−19050.6	−0.876200
$780$	0	0
$781$	−25681.8	−1.17665
$782$	17964.9	0.821515
$783$	5804.70	0.264933
$784$	6959.71	0.317042
$785$	0	0
$786$	8168.45	0.370686
$787$	16392.1	0.742461	0.371231	−	0.928541i	$-0.378936\pi$
$787$	16392.1	0.742461	0.371231	+	0.928541i	$0.378936\pi$
$788$	67812.5	3.06563
$789$	−16193.0	−0.730656
$790$	0	0
$791$	−15601.5	−0.701298
$792$	18295.8	0.820848
$793$	6843.45	0.306454
$794$	50985.5	2.27885
$795$	0	0
$796$	−14510.0	−0.646097
$797$	−2966.12	−0.131826	−0.0659129	−	0.997825i	$-0.520996\pi$
$797$	−2966.12	−0.131826	−0.0659129	+	0.997825i	$0.520996\pi$
$798$	6708.37	0.297586
$799$	54742.6	2.42385
$800$	0	0
$801$	−811.887	−0.0358135
$802$	−19154.2	−0.843338
$803$	−40830.4	−1.79436
$804$	−5076.31	−0.222671
$805$	0	0
$806$	38548.4	1.68463
$807$	14920.8	0.650851
$808$	15414.4	0.671134
$809$	−14712.3	−0.639378	−0.319689	−	0.947523i	$-0.603578\pi$
$809$	−14712.3	−0.639378	−0.319689	+	0.947523i	$0.603578\pi$
$810$	0	0
$811$	5794.69	0.250899	0.125450	−	0.992100i	$-0.459963\pi$
$811$	5794.69	0.250899	0.125450	+	0.992100i	$0.459963\pi$
$812$	−28444.3	−1.22931
$813$	12442.4	0.536747
$814$	76559.0	3.29655
$815$	0	0
$816$	−48215.2	−2.06847
$817$	1844.75	0.0789961
$818$	−45720.3	−1.95424
$819$	2851.52	0.121661
$820$	0	0
$821$	34345.7	1.46002	0.730009	−	0.683438i	$-0.239516\pi$
$821$	34345.7	1.46002	0.730009	+	0.683438i	$0.239516\pi$
$822$	−33438.5	−1.41886
$823$	17454.4	0.739274	0.369637	−	0.929176i	$-0.379482\pi$
$823$	17454.4	0.739274	0.369637	+	0.929176i	$0.379482\pi$
$824$	−35516.2	−1.50153
$825$	0	0
$826$	15110.3	0.636508
$827$	1378.54	0.0579645	0.0289822	−	0.999580i	$-0.490773\pi$
$827$	1378.54	0.0579645	0.0289822	+	0.999580i	$0.490773\pi$
$828$	5207.13	0.218551
$829$	36714.7	1.53818	0.769092	−	0.639138i	$-0.220709\pi$
$829$	36714.7	1.53818	0.769092	+	0.639138i	$0.220709\pi$
$830$	0	0
$831$	−7850.38	−0.327709
$832$	−15327.8	−0.638696
$833$	−5544.52	−0.230620
$834$	23460.8	0.974078
$835$	0	0
$836$	−41856.3	−1.73162
$837$	4433.55	0.183090
$838$	−19433.4	−0.801091
$839$	3191.34	0.131320	0.0656598	−	0.997842i	$-0.479085\pi$
$839$	3191.34	0.131320	0.0656598	+	0.997842i	$0.479085\pi$
$840$	0	0
$841$	21831.2	0.895123
$842$	54742.2	2.24055
$843$	8600.68	0.351392
$844$	−22678.0	−0.924893
$845$	0	0
$846$	22583.0	0.917755
$847$	267.416	0.0108483
$848$	41982.9	1.70012
$849$	9046.20	0.365683
$850$	0	0
$851$	12566.7	0.506207
$852$	40500.6	1.62855
$853$	42221.5	1.69477	0.847384	−	0.530980i	$-0.178176\pi$
$853$	42221.5	1.69477	0.847384	+	0.530980i	$0.178176\pi$
$854$	−5489.35	−0.219955
$855$	0	0
$856$	51363.3	2.05089
$857$	5849.17	0.233143	0.116572	−	0.993182i	$-0.462810\pi$
$857$	5849.17	0.233143	0.116572	+	0.993182i	$0.462810\pi$
$858$	−25322.4	−1.00757
$859$	−45756.1	−1.81744	−0.908719	−	0.417409i	$-0.862938\pi$
$859$	−45756.1	−1.81744	−0.908719	+	0.417409i	$0.862938\pi$
$860$	0	0
$861$	6495.52	0.257104
$862$	72767.5	2.87526
$863$	33012.0	1.30213	0.651067	−	0.759020i	$-0.274322\pi$
$863$	33012.0	1.30213	0.651067	+	0.759020i	$0.274322\pi$
$864$	−7678.04	−0.302329
$865$	0	0
$866$	−49994.1	−1.96174
$867$	23672.2	0.927278
$868$	−21725.4	−0.849548
$869$	11626.1	0.453842
$870$	0	0
$871$	4052.11	0.157635
$872$	−55650.9	−2.16121
$873$	4428.91	0.171702
$874$	−9778.50	−0.378447
$875$	0	0
$876$	64390.3	2.48350
$877$	20709.9	0.797404	0.398702	−	0.917080i	$-0.369461\pi$
$877$	20709.9	0.797404	0.398702	+	0.917080i	$0.369461\pi$
$878$	−20417.2	−0.784793
$879$	10741.2	0.412164
$880$	0	0
$881$	−13604.5	−0.520258	−0.260129	−	0.965574i	$-0.583765\pi$
$881$	−13604.5	−0.520258	−0.260129	+	0.965574i	$0.583765\pi$
$882$	−2287.29	−0.0873210
$883$	47582.7	1.81346	0.906729	−	0.421713i	$-0.138571\pi$
$883$	47582.7	1.81346	0.906729	+	0.421713i	$0.138571\pi$
$884$	96802.1	3.68304
$885$	0	0
$886$	−56080.2	−2.12647
$887$	−25132.9	−0.951386	−0.475693	−	0.879611i	$-0.657803\pi$
$887$	−25132.9	−0.951386	−0.475693	+	0.879611i	$0.657803\pi$
$888$	−69632.4	−2.63143
$889$	−20025.5	−0.755492
$890$	0	0
$891$	−2912.40	−0.109505
$892$	55149.7	2.07012
$893$	−29796.9	−1.11659
$894$	15771.6	0.590024
$895$	0	0
$896$	−3629.93	−0.135343
$897$	−4156.53	−0.154719
$898$	−42296.0	−1.57176
$899$	35302.4	1.30968
$900$	0	0
$901$	−33446.2	−1.23668
$902$	−57682.3	−2.12928
$903$	−628.989	−0.0231799
$904$	−126012.	−4.63617
$905$	0	0
$906$	−25886.9	−0.949265
$907$	36233.4	1.32647	0.663235	−	0.748411i	$-0.269183\pi$
$907$	36233.4	1.32647	0.663235	+	0.748411i	$0.269183\pi$
$908$	11580.1	0.423238
$909$	−2453.73	−0.0895325
$910$	0	0
$911$	16912.4	0.615076	0.307538	−	0.951536i	$-0.400495\pi$
$911$	16912.4	0.615076	0.307538	+	0.951536i	$0.400495\pi$
$912$	26244.0	0.952881
$913$	10711.1	0.388264
$914$	−92256.5	−3.33870
$915$	0	0
$916$	49926.7	1.80090
$917$	3674.80	0.132337
$918$	15845.8	0.569706
$919$	−49589.9	−1.78000	−0.890001	−	0.455959i	$-0.849296\pi$
$919$	−49589.9	−1.78000	−0.890001	+	0.455959i	$0.849296\pi$
$920$	0	0
$921$	−4298.77	−0.153800
$922$	−68422.4	−2.44400
$923$	−32329.2	−1.15290
$924$	14271.4	0.508110
$925$	0	0
$926$	−2814.09	−0.0998668
$927$	5653.62	0.200312
$928$	−61136.7	−2.16262
$929$	−40649.1	−1.43558	−0.717789	−	0.696261i	$-0.754846\pi$
$929$	−40649.1	−1.43558	−0.717789	+	0.696261i	$0.754846\pi$
$930$	0	0
$931$	3017.94	0.106240
$932$	−43904.2	−1.54306
$933$	16465.0	0.577749
$934$	−30925.1	−1.08341
$935$	0	0
$936$	23031.4	0.804279
$937$	3678.18	0.128240	0.0641200	−	0.997942i	$-0.479576\pi$
$937$	3678.18	0.128240	0.0641200	+	0.997942i	$0.479576\pi$
$938$	−3250.32	−0.113142
$939$	7385.05	0.256658
$940$	0	0
$941$	−4835.12	−0.167503	−0.0837516	−	0.996487i	$-0.526690\pi$
$941$	−4835.12	−0.167503	−0.0837516	+	0.996487i	$0.526690\pi$
$942$	37335.5	1.29136
$943$	−9468.24	−0.326965
$944$	59113.6	2.03812
$945$	0	0
$946$	5585.63	0.191971
$947$	31497.4	1.08081	0.540405	−	0.841405i	$-0.318271\pi$
$947$	31497.4	1.08081	0.540405	+	0.841405i	$0.318271\pi$
$948$	−18334.6	−0.628143
$949$	−51398.9	−1.75814
$950$	0	0
$951$	−9339.37	−0.318454
$952$	−44782.5	−1.52459
$953$	−26365.5	−0.896183	−0.448092	−	0.893988i	$-0.647896\pi$
$953$	−26365.5	−0.896183	−0.448092	+	0.893988i	$0.647896\pi$
$954$	−13797.6	−0.468253
$955$	0	0
$956$	101545.	3.43537
$957$	−23190.1	−0.783311
$958$	6834.20	0.230483
$959$	−15043.2	−0.506538
$960$	0	0
$961$	−2827.48	−0.0949104
$962$	96375.4	3.23001
$963$	−8176.22	−0.273598
$964$	−26694.2	−0.891870
$965$	0	0
$966$	3334.09	0.111048
$967$	2307.07	0.0767221	0.0383611	−	0.999264i	$-0.487786\pi$
$967$	2307.07	0.0767221	0.0383611	+	0.999264i	$0.487786\pi$
$968$	2159.89	0.0717164
$969$	−20907.6	−0.693136
$970$	0	0
$971$	−48345.5	−1.59782	−0.798909	−	0.601452i	$-0.794589\pi$
$971$	−48345.5	−1.59782	−0.798909	+	0.601452i	$0.794589\pi$
$972$	4592.90	0.151561
$973$	10554.5	0.347750
$974$	30996.2	1.01969
$975$	0	0
$976$	−21475.1	−0.704304
$977$	−25534.5	−0.836153	−0.418076	−	0.908412i	$-0.637296\pi$
$977$	−25534.5	−0.836153	−0.418076	+	0.908412i	$0.637296\pi$
$978$	22029.7	0.720280
$979$	3243.53	0.105887
$980$	0	0
$981$	8858.75	0.288316
$982$	−53624.0	−1.74258
$983$	41611.3	1.35015	0.675074	−	0.737750i	$-0.264112\pi$
$983$	41611.3	1.35015	0.675074	+	0.737750i	$0.264112\pi$
$984$	52463.6	1.69967
$985$	0	0
$986$	126173.	4.07522
$987$	10159.6	0.327643
$988$	−52690.4	−1.69666
$989$	916.851	0.0294784
$990$	0	0
$991$	9963.65	0.319380	0.159690	−	0.987167i	$-0.448950\pi$
$991$	9963.65	0.319380	0.159690	+	0.987167i	$0.448950\pi$
$992$	−46695.5	−1.49454
$993$	−19092.6	−0.610157
$994$	25932.3	0.827486
$995$	0	0
$996$	−16891.6	−0.537379
$997$	−15960.8	−0.507005	−0.253502	−	0.967335i	$-0.581583\pi$
$997$	−15960.8	−0.507005	−0.253502	+	0.967335i	$0.581583\pi$
$998$	21585.3	0.684639
$999$	11084.4	0.351045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.w.1.1		5
3.2	odd	2		1575.4.a.bp.1.5		5
5.2	odd	4		105.4.d.b.64.1	✓	10
5.3	odd	4		105.4.d.b.64.10	yes	10
5.4	even	2		525.4.a.x.1.5		5
15.2	even	4		315.4.d.b.64.10		10
15.8	even	4		315.4.d.b.64.1		10
15.14	odd	2		1575.4.a.bo.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.1	✓	10	5.2	odd	4
105.4.d.b.64.10	yes	10	5.3	odd	4
315.4.d.b.64.1		10	15.8	even	4
315.4.d.b.64.10		10	15.2	even	4
525.4.a.w.1.1		5	1.1	even	1	trivial
525.4.a.x.1.5		5	5.4	even	2
1575.4.a.bo.1.1		5	15.14	odd	2
1575.4.a.bp.1.5		5	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q-5.18660 q^{2} +3.00000 q^{3} +18.9008 q^{4} -15.5598 q^{6} -7.00000 q^{7} -56.5383 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.18660 q^{2} +3.00000 q^{3} +18.9008 q^{4} -15.5598 q^{6} -7.00000 q^{7} -56.5383 q^{8} +9.00000 q^{9} -35.9555 q^{11} +56.7025 q^{12} -45.2622 q^{13} +36.3062 q^{14} +142.035 q^{16} -113.154 q^{17} -46.6794 q^{18} +61.5906 q^{19} -21.0000 q^{21} +186.487 q^{22} +30.6108 q^{23} -169.615 q^{24} +234.757 q^{26} +27.0000 q^{27} -132.306 q^{28} +214.989 q^{29} +164.206 q^{31} -284.372 q^{32} -107.866 q^{33} +586.882 q^{34} +170.107 q^{36} +410.533 q^{37} -319.446 q^{38} -135.787 q^{39} -309.310 q^{41} +108.919 q^{42} +29.9519 q^{43} -679.589 q^{44} -158.766 q^{46} -483.790 q^{47} +426.104 q^{48} +49.0000 q^{49} -339.461 q^{51} -855.493 q^{52} +295.582 q^{53} -140.038 q^{54} +395.768 q^{56} +184.772 q^{57} -1115.06 q^{58} +416.191 q^{59} -151.196 q^{61} -851.670 q^{62} -63.0000 q^{63} +338.644 q^{64} +559.460 q^{66} -89.5253 q^{67} -2138.70 q^{68} +91.8324 q^{69} +714.265 q^{71} -508.844 q^{72} +1135.58 q^{73} -2129.27 q^{74} +1164.11 q^{76} +251.688 q^{77} +704.271 q^{78} -323.347 q^{79} +81.0000 q^{81} +1604.27 q^{82} -297.898 q^{83} -396.917 q^{84} -155.348 q^{86} +644.966 q^{87} +2032.86 q^{88} -90.2097 q^{89} +316.835 q^{91} +578.570 q^{92} +492.617 q^{93} +2509.23 q^{94} -853.115 q^{96} +492.101 q^{97} -254.143 q^{98} -323.599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9	\( 5 q - q^{2} + 15 q^{3} + 27 q^{4} - 3 q^{6} - 35 q^{7} - 33 q^{8} + 45 q^{9} + 66 q^{11} + 81 q^{12} + 2 q^{13} + 7 q^{14} + 155 q^{16} - 108 q^{17} - 9 q^{18} + 174 q^{19} - 105 q^{21} + 506 q^{22} + 116 q^{23} - 99 q^{24} + 446 q^{26} + 135 q^{27} - 189 q^{28} + 370 q^{29} + 342 q^{31} + 55 q^{32} + 198 q^{33} + 112 q^{34} + 243 q^{36} + 408 q^{37} + 34 q^{38} + 6 q^{39} + 802 q^{41} + 21 q^{42} + 584 q^{43} + 290 q^{44} + 640 q^{46} - 716 q^{47} + 465 q^{48} + 245 q^{49} - 324 q^{51} - 338 q^{52} - 98 q^{53} - 27 q^{54} + 231 q^{56} + 522 q^{57} - 482 q^{58} + 704 q^{59} + 650 q^{61} - 2070 q^{62} - 315 q^{63} + 75 q^{64} + 1518 q^{66} - 180 q^{67} - 4520 q^{68} + 348 q^{69} + 1470 q^{71} - 297 q^{72} + 534 q^{73} - 1312 q^{74} + 4370 q^{76} - 462 q^{77} + 1338 q^{78} - 820 q^{79} + 405 q^{81} + 1338 q^{82} - 1520 q^{83} - 567 q^{84} + 832 q^{86} + 1110 q^{87} + 3258 q^{88} + 286 q^{89} - 14 q^{91} - 1288 q^{92} + 1026 q^{93} + 2540 q^{94} + 165 q^{96} - 278 q^{97} - 49 q^{98} + 594 q^{99}+O(q^{100}) \) 5 * q - q^2 + 15 * q^3 + 27 * q^4 - 3 * q^6 - 35 * q^7 - 33 * q^8 + 45 * q^9 + 66 * q^11 + 81 * q^12 + 2 * q^13 + 7 * q^14 + 155 * q^16 - 108 * q^17 - 9 * q^18 + 174 * q^19 - 105 * q^21 + 506 * q^22 + 116 * q^23 - 99 * q^24 + 446 * q^26 + 135 * q^27 - 189 * q^28 + 370 * q^29 + 342 * q^31 + 55 * q^32 + 198 * q^33 + 112 * q^34 + 243 * q^36 + 408 * q^37 + 34 * q^38 + 6 * q^39 + 802 * q^41 + 21 * q^42 + 584 * q^43 + 290 * q^44 + 640 * q^46 - 716 * q^47 + 465 * q^48 + 245 * q^49 - 324 * q^51 - 338 * q^52 - 98 * q^53 - 27 * q^54 + 231 * q^56 + 522 * q^57 - 482 * q^58 + 704 * q^59 + 650 * q^61 - 2070 * q^62 - 315 * q^63 + 75 * q^64 + 1518 * q^66 - 180 * q^67 - 4520 * q^68 + 348 * q^69 + 1470 * q^71 - 297 * q^72 + 534 * q^73 - 1312 * q^74 + 4370 * q^76 - 462 * q^77 + 1338 * q^78 - 820 * q^79 + 405 * q^81 + 1338 * q^82 - 1520 * q^83 - 567 * q^84 + 832 * q^86 + 1110 * q^87 + 3258 * q^88 + 286 * q^89 - 14 * q^91 - 1288 * q^92 + 1026 * q^93 + 2540 * q^94 + 165 * q^96 - 278 * q^97 - 49 * q^98 + 594 * q^99

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