LMFDB - Embedded newform 1075.4.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,4,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1075.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1075.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:	$63.4270532562$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 101 x^{13} + 85 x^{12} + 4104 x^{11} - 2826 x^{10} - 85598 x^{9} + 46269 x^{8} + \cdots + 110160 $ x^15 - x^14 - 101x^13 + 85x^12 + 4104x^11 - 2826x^10 - 85598x^9 + 46269x^8 + 964385x^7 - 383175x^6 - 5573805x^5 + 1453572x^4 + 13183622x^3 - 1740884x^2 - 2016128*x + 110160
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.04752$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.04752 q^{2} +4.47643 q^{3} +8.38240 q^{4} -18.1184 q^{6} -35.2850 q^{7} -1.54775 q^{8} -6.96159 q^{9} +O(q^{10})$	\(q-4.04752 q^{2} +4.47643 q^{3} +8.38240 q^{4} -18.1184 q^{6} -35.2850 q^{7} -1.54775 q^{8} -6.96159 q^{9} -21.9191 q^{11} +37.5232 q^{12} -70.3707 q^{13} +142.817 q^{14} -60.7946 q^{16} -107.764 q^{17} +28.1772 q^{18} +54.4585 q^{19} -157.951 q^{21} +88.7178 q^{22} -67.2934 q^{23} -6.92841 q^{24} +284.827 q^{26} -152.027 q^{27} -295.773 q^{28} -163.908 q^{29} -4.41635 q^{31} +258.449 q^{32} -98.1191 q^{33} +436.177 q^{34} -58.3548 q^{36} -147.963 q^{37} -220.422 q^{38} -315.009 q^{39} -397.564 q^{41} +639.308 q^{42} -43.0000 q^{43} -183.734 q^{44} +272.371 q^{46} +495.142 q^{47} -272.143 q^{48} +902.031 q^{49} -482.398 q^{51} -589.875 q^{52} +177.278 q^{53} +615.330 q^{54} +54.6125 q^{56} +243.780 q^{57} +663.422 q^{58} -126.013 q^{59} -297.662 q^{61} +17.8752 q^{62} +245.640 q^{63} -559.721 q^{64} +397.139 q^{66} +880.592 q^{67} -903.322 q^{68} -301.234 q^{69} -229.051 q^{71} +10.7748 q^{72} +394.100 q^{73} +598.882 q^{74} +456.493 q^{76} +773.414 q^{77} +1275.01 q^{78} +32.3392 q^{79} -492.573 q^{81} +1609.15 q^{82} +424.143 q^{83} -1324.01 q^{84} +174.043 q^{86} -733.725 q^{87} +33.9253 q^{88} -196.658 q^{89} +2483.03 q^{91} -564.080 q^{92} -19.7694 q^{93} -2004.10 q^{94} +1156.93 q^{96} -1515.69 q^{97} -3650.98 q^{98} +152.592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - q^{2} - 7 q^{3} + 83 q^{4} + 40 q^{6} - 36 q^{7} - 33 q^{8} + 242 q^{9}+O(q^{10}) $ 15 * q - q^2 - 7 * q^3 + 83 * q^4 + 40 * q^6 - 36 * q^7 - 33 * q^8 + 242 * q^9	\( 15 q - q^{2} - 7 q^{3} + 83 q^{4} + 40 q^{6} - 36 q^{7} - 33 q^{8} + 242 q^{9} + 87 q^{11} + 37 q^{12} + 35 q^{13} + 237 q^{14} + 139 q^{16} - 144 q^{17} + 325 q^{18} + 293 q^{19} + 208 q^{21} - 25 q^{22} - 22 q^{23} + 480 q^{24} + 127 q^{26} - 202 q^{27} - 187 q^{28} + 495 q^{29} + 408 q^{31} - 395 q^{32} - 308 q^{33} + 812 q^{34} + 1283 q^{36} - 1013 q^{37} - 251 q^{38} + 654 q^{39} + 820 q^{41} - 431 q^{42} - 645 q^{43} + 1244 q^{44} + 1416 q^{46} + 622 q^{47} - 70 q^{48} + 1525 q^{49} + 1760 q^{51} + 593 q^{52} - 276 q^{53} - 349 q^{54} + 822 q^{56} + 566 q^{57} - 1403 q^{58} - 1405 q^{59} + 1969 q^{61} + 3297 q^{62} + 2587 q^{63} - 1709 q^{64} - 3111 q^{66} + 439 q^{67} + 3412 q^{68} + 10 q^{69} + 494 q^{71} + 6476 q^{72} - 958 q^{73} - 6273 q^{74} + 1089 q^{76} + 918 q^{77} + 5438 q^{78} - 1846 q^{79} + 3655 q^{81} + 2693 q^{82} + 1524 q^{83} - 6283 q^{84} + 43 q^{86} + 2702 q^{87} + 2010 q^{88} + 1380 q^{89} + 3625 q^{91} + 3658 q^{92} - 1610 q^{93} - 274 q^{94} - 367 q^{96} - 3240 q^{97} + 6137 q^{98} - 3769 q^{99}+O(q^{100}) \) 15 * q - q^2 - 7 * q^3 + 83 * q^4 + 40 * q^6 - 36 * q^7 - 33 * q^8 + 242 * q^9 + 87 * q^11 + 37 * q^12 + 35 * q^13 + 237 * q^14 + 139 * q^16 - 144 * q^17 + 325 * q^18 + 293 * q^19 + 208 * q^21 - 25 * q^22 - 22 * q^23 + 480 * q^24 + 127 * q^26 - 202 * q^27 - 187 * q^28 + 495 * q^29 + 408 * q^31 - 395 * q^32 - 308 * q^33 + 812 * q^34 + 1283 * q^36 - 1013 * q^37 - 251 * q^38 + 654 * q^39 + 820 * q^41 - 431 * q^42 - 645 * q^43 + 1244 * q^44 + 1416 * q^46 + 622 * q^47 - 70 * q^48 + 1525 * q^49 + 1760 * q^51 + 593 * q^52 - 276 * q^53 - 349 * q^54 + 822 * q^56 + 566 * q^57 - 1403 * q^58 - 1405 * q^59 + 1969 * q^61 + 3297 * q^62 + 2587 * q^63 - 1709 * q^64 - 3111 * q^66 + 439 * q^67 + 3412 * q^68 + 10 * q^69 + 494 * q^71 + 6476 * q^72 - 958 * q^73 - 6273 * q^74 + 1089 * q^76 + 918 * q^77 + 5438 * q^78 - 1846 * q^79 + 3655 * q^81 + 2693 * q^82 + 1524 * q^83 - 6283 * q^84 + 43 * q^86 + 2702 * q^87 + 2010 * q^88 + 1380 * q^89 + 3625 * q^91 + 3658 * q^92 - 1610 * q^93 - 274 * q^94 - 367 * q^96 - 3240 * q^97 + 6137 * q^98 - 3769 * 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 $

$2$	−4.04752	−1.43101	−0.715507	−	0.698606i	$-0.753804\pi$
$2$	−4.04752	−1.43101	−0.715507	+	0.698606i	$0.753804\pi$
$3$	4.47643	0.861489	0.430744	−	0.902474i	$-0.358251\pi$
$3$	4.47643	0.861489	0.430744	+	0.902474i	$0.358251\pi$
$4$	8.38240	1.04780
$5$	0	0
$5$	0	0
$6$	−18.1184	−1.23280
$7$	−35.2850	−1.90521	−0.952605	−	0.304209i	$-0.901608\pi$
$7$	−35.2850	−1.90521	−0.952605	+	0.304209i	$0.901608\pi$
$8$	−1.54775	−0.0684017
$9$	−6.96159	−0.257837
$10$	0	0
$11$	−21.9191	−0.600804	−0.300402	−	0.953813i	$-0.597121\pi$
$11$	−21.9191	−0.600804	−0.300402	+	0.953813i	$0.597121\pi$
$12$	37.5232	0.902668
$13$	−70.3707	−1.50133	−0.750666	−	0.660681i	$-0.770267\pi$
$13$	−70.3707	−1.50133	−0.750666	+	0.660681i	$0.770267\pi$
$14$	142.817	2.72638
$15$	0	0
$16$	−60.7946	−0.949916
$17$	−107.764	−1.53745	−0.768725	−	0.639580i	$-0.779108\pi$
$17$	−107.764	−1.53745	−0.768725	+	0.639580i	$0.779108\pi$
$18$	28.1772	0.368968
$19$	54.4585	0.657560	0.328780	−	0.944407i	$-0.393363\pi$
$19$	54.4585	0.657560	0.328780	+	0.944407i	$0.393363\pi$
$20$	0	0
$21$	−157.951	−1.64132
$22$	88.7178	0.859759
$23$	−67.2934	−0.610071	−0.305036	−	0.952341i	$-0.598668\pi$
$23$	−67.2934	−0.610071	−0.305036	+	0.952341i	$0.598668\pi$
$24$	−6.92841	−0.0589273
$25$	0	0
$26$	284.827	2.14843
$27$	−152.027	−1.08361
$28$	−295.773	−1.99628
$29$	−163.908	−1.04955	−0.524777	−	0.851240i	$-0.675851\pi$
$29$	−163.908	−1.04955	−0.524777	+	0.851240i	$0.675851\pi$
$30$	0	0
$31$	−4.41635	−0.0255871	−0.0127935	−	0.999918i	$-0.504072\pi$
$31$	−4.41635	−0.0255871	−0.0127935	+	0.999918i	$0.504072\pi$
$32$	258.449	1.42774
$33$	−98.1191	−0.517586
$34$	436.177	2.20011
$35$	0	0
$36$	−58.3548	−0.270161
$37$	−147.963	−0.657431	−0.328715	−	0.944429i	$-0.606616\pi$
$37$	−147.963	−0.657431	−0.328715	+	0.944429i	$0.606616\pi$
$38$	−220.422	−0.940977
$39$	−315.009	−1.29338
$40$	0	0
$41$	−397.564	−1.51437	−0.757183	−	0.653202i	$-0.773425\pi$
$41$	−397.564	−1.51437	−0.757183	+	0.653202i	$0.773425\pi$
$42$	639.308	2.34875
$43$	−43.0000	−0.152499
$43$	−43.0000	−0.152499
$44$	−183.734	−0.629522
$45$	0	0
$46$	272.371	0.873020
$47$	495.142	1.53668	0.768340	−	0.640042i	$-0.221083\pi$
$47$	495.142	1.53668	0.768340	+	0.640042i	$0.221083\pi$
$48$	−272.143	−0.818342
$49$	902.031	2.62983
$50$	0	0
$51$	−482.398	−1.32450
$52$	−589.875	−1.57310
$53$	177.278	0.459453	0.229726	−	0.973255i	$-0.426217\pi$
$53$	177.278	0.459453	0.229726	+	0.973255i	$0.426217\pi$
$54$	615.330	1.55066
$55$	0	0
$56$	54.6125	0.130320
$57$	243.780	0.566481
$58$	663.422	1.50192
$59$	−126.013	−0.278060	−0.139030	−	0.990288i	$-0.544398\pi$
$59$	−126.013	−0.278060	−0.139030	+	0.990288i	$0.544398\pi$
$60$	0	0
$61$	−297.662	−0.624781	−0.312391	−	0.949954i	$-0.601130\pi$
$61$	−297.662	−0.624781	−0.312391	+	0.949954i	$0.601130\pi$
$62$	17.8752	0.0366154
$63$	245.640	0.491233
$64$	−559.721	−1.09321
$65$	0	0
$66$	397.139	0.740673
$67$	880.592	1.60569	0.802847	−	0.596185i	$-0.203318\pi$
$67$	880.592	1.60569	0.802847	+	0.596185i	$0.203318\pi$
$68$	−903.322	−1.61094
$69$	−301.234	−0.525570
$70$	0	0
$71$	−229.051	−0.382864	−0.191432	−	0.981506i	$-0.561313\pi$
$71$	−229.051	−0.382864	−0.191432	+	0.981506i	$0.561313\pi$
$72$	10.7748	0.0176365
$73$	394.100	0.631862	0.315931	−	0.948782i	$-0.397683\pi$
$73$	394.100	0.631862	0.315931	+	0.948782i	$0.397683\pi$
$74$	598.882	0.940792
$75$	0	0
$76$	456.493	0.688991
$77$	773.414	1.14466
$78$	1275.01	1.85085
$79$	32.3392	0.0460563	0.0230281	−	0.999735i	$-0.492669\pi$
$79$	32.3392	0.0460563	0.0230281	+	0.999735i	$0.492669\pi$
$80$	0	0
$81$	−492.573	−0.675683
$82$	1609.15	2.16708
$83$	424.143	0.560912	0.280456	−	0.959867i	$-0.409514\pi$
$83$	424.143	0.560912	0.280456	+	0.959867i	$0.409514\pi$
$84$	−1324.01	−1.71977
$85$	0	0
$86$	174.043	0.218228
$87$	−733.725	−0.904179
$88$	33.9253	0.0410960
$89$	−196.658	−0.234222	−0.117111	−	0.993119i	$-0.537363\pi$
$89$	−196.658	−0.234222	−0.117111	+	0.993119i	$0.537363\pi$
$90$	0	0
$91$	2483.03	2.86036
$92$	−564.080	−0.639233
$93$	−19.7694	−0.0220430
$94$	−2004.10	−2.19901
$95$	0	0
$96$	1156.93	1.22999
$97$	−1515.69	−1.58655	−0.793275	−	0.608863i	$-0.791626\pi$
$97$	−1515.69	−1.58655	−0.793275	+	0.608863i	$0.791626\pi$
$98$	−3650.98	−3.76332
$99$	152.592	0.154909
$100$	0	0
$101$	1105.03	1.08866	0.544331	−	0.838870i	$-0.316784\pi$
$101$	1105.03	1.08866	0.544331	+	0.838870i	$0.316784\pi$
$102$	1952.52	1.89537
$103$	−510.496	−0.488356	−0.244178	−	0.969730i	$-0.578518\pi$
$103$	−510.496	−0.488356	−0.244178	+	0.969730i	$0.578518\pi$
$104$	108.917	0.102694
$105$	0	0
$106$	−717.535	−0.657483
$107$	−1365.04	−1.23330	−0.616651	−	0.787237i	$-0.711511\pi$
$107$	−1365.04	−1.23330	−0.616651	+	0.787237i	$0.711511\pi$
$108$	−1274.35	−1.13541
$109$	−822.014	−0.722337	−0.361168	−	0.932501i	$-0.617622\pi$
$109$	−822.014	−0.722337	−0.361168	+	0.932501i	$0.617622\pi$
$110$	0	0
$111$	−662.345	−0.566369
$112$	2145.14	1.80979
$113$	−1152.54	−0.959484	−0.479742	−	0.877410i	$-0.659270\pi$
$113$	−1152.54	−0.959484	−0.479742	+	0.877410i	$0.659270\pi$
$114$	−986.702	−0.810641
$115$	0	0
$116$	−1373.95	−1.09972
$117$	489.892	0.387099
$118$	510.041	0.397908
$119$	3802.46	2.92916
$120$	0	0
$121$	−850.555	−0.639034
$122$	1204.79	0.894070
$123$	−1779.67	−1.30461
$124$	−37.0196	−0.0268101
$125$	0	0
$126$	−994.231	−0.702962
$127$	888.312	0.620669	0.310334	−	0.950627i	$-0.399559\pi$
$127$	888.312	0.620669	0.310334	+	0.950627i	$0.399559\pi$
$128$	197.886	0.136647
$129$	−192.486	−0.131376
$130$	0	0
$131$	−1787.49	−1.19216	−0.596082	−	0.802923i	$-0.703277\pi$
$131$	−1787.49	−1.19216	−0.596082	+	0.802923i	$0.703277\pi$
$132$	−822.473	−0.542326
$133$	−1921.57	−1.25279
$134$	−3564.21	−2.29777
$135$	0	0
$136$	166.792	0.105164
$137$	−738.607	−0.460609	−0.230304	−	0.973119i	$-0.573972\pi$
$137$	−738.607	−0.460609	−0.230304	+	0.973119i	$0.573972\pi$
$138$	1219.25	0.752097
$139$	−1479.35	−0.902711	−0.451355	−	0.892344i	$-0.649059\pi$
$139$	−1479.35	−0.902711	−0.451355	+	0.892344i	$0.649059\pi$
$140$	0	0
$141$	2216.47	1.32383
$142$	927.088	0.547884
$143$	1542.46	0.902007
$144$	423.227	0.244923
$145$	0	0
$146$	−1595.13	−0.904203
$147$	4037.87	2.26557
$148$	−1240.28	−0.688856
$149$	−3540.65	−1.94672	−0.973359	−	0.229286i	$-0.926361\pi$
$149$	−3540.65	−1.94672	−0.973359	+	0.229286i	$0.926361\pi$
$150$	0	0
$151$	1729.42	0.932041	0.466021	−	0.884774i	$-0.345687\pi$
$151$	1729.42	0.932041	0.466021	+	0.884774i	$0.345687\pi$
$152$	−84.2884	−0.0449782
$153$	750.210	0.396411
$154$	−3130.41	−1.63802
$155$	0	0
$156$	−2640.53	−1.35520
$157$	−3023.38	−1.53689	−0.768445	−	0.639916i	$-0.778969\pi$
$157$	−3023.38	−1.53689	−0.768445	+	0.639916i	$0.778969\pi$
$158$	−130.894	−0.0659072
$159$	793.572	0.395813
$160$	0	0
$161$	2374.45	1.16231
$162$	1993.70	0.966912
$163$	2337.01	1.12300	0.561498	−	0.827478i	$-0.310225\pi$
$163$	2337.01	1.12300	0.561498	+	0.827478i	$0.310225\pi$
$164$	−3332.54	−1.58675
$165$	0	0
$166$	−1716.73	−0.802673
$167$	765.636	0.354771	0.177385	−	0.984141i	$-0.443236\pi$
$167$	765.636	0.354771	0.177385	+	0.984141i	$0.443236\pi$
$168$	244.469	0.112269
$169$	2755.04	1.25400
$170$	0	0
$171$	−379.118	−0.169543
$172$	−360.443	−0.159788
$173$	3740.17	1.64370	0.821849	−	0.569705i	$-0.192943\pi$
$173$	3740.17	1.64370	0.821849	+	0.569705i	$0.192943\pi$
$174$	2969.76	1.29389
$175$	0	0
$176$	1332.56	0.570713
$177$	−564.090	−0.239546
$178$	795.978	0.335175
$179$	1984.89	0.828815	0.414408	−	0.910091i	$-0.363989\pi$
$179$	1984.89	0.828815	0.414408	+	0.910091i	$0.363989\pi$
$180$	0	0
$181$	3272.15	1.34374	0.671870	−	0.740669i	$-0.265492\pi$
$181$	3272.15	1.34374	0.671870	+	0.740669i	$0.265492\pi$
$182$	−10050.1	−4.09321
$183$	−1332.46	−0.538242
$184$	104.154	0.0417299
$185$	0	0
$186$	80.0172	0.0315438
$187$	2362.09	0.923706
$188$	4150.48	1.61013
$189$	5364.26	2.06451
$190$	0	0
$191$	2851.55	1.08027	0.540134	−	0.841579i	$-0.318374\pi$
$191$	2851.55	1.08027	0.540134	+	0.841579i	$0.318374\pi$
$192$	−2505.55	−0.941784
$193$	−1437.13	−0.535996	−0.267998	−	0.963419i	$-0.586362\pi$
$193$	−1437.13	−0.535996	−0.267998	+	0.963419i	$0.586362\pi$
$194$	6134.80	2.27038
$195$	0	0
$196$	7561.18	2.75553
$197$	−2659.10	−0.961691	−0.480846	−	0.876805i	$-0.659670\pi$
$197$	−2659.10	−0.961691	−0.480846	+	0.876805i	$0.659670\pi$
$198$	−617.617	−0.221677
$199$	−3007.35	−1.07128	−0.535642	−	0.844445i	$-0.679930\pi$
$199$	−3007.35	−1.07128	−0.535642	+	0.844445i	$0.679930\pi$
$200$	0	0
$201$	3941.91	1.38329
$202$	−4472.64	−1.55789
$203$	5783.51	1.99962
$204$	−4043.65	−1.38781
$205$	0	0
$206$	2066.24	0.698844
$207$	468.469	0.157299
$208$	4278.16	1.42614
$209$	−1193.68	−0.395065
$210$	0	0
$211$	−4234.51	−1.38159	−0.690795	−	0.723050i	$-0.742739\pi$
$211$	−4234.51	−1.38159	−0.690795	+	0.723050i	$0.742739\pi$
$212$	1486.01	0.481414
$213$	−1025.33	−0.329833
$214$	5525.02	1.76487
$215$	0	0
$216$	235.300	0.0741210
$217$	155.831	0.0487487
$218$	3327.12	1.03367
$219$	1764.16	0.544342
$220$	0	0
$221$	7583.44	2.30822
$222$	2680.85	0.810482
$223$	240.530	0.0722291	0.0361145	−	0.999348i	$-0.488502\pi$
$223$	240.530	0.0722291	0.0361145	+	0.999348i	$0.488502\pi$
$224$	−9119.38	−2.72015
$225$	0	0
$226$	4664.92	1.37303
$227$	5343.90	1.56250	0.781249	−	0.624219i	$-0.214583\pi$
$227$	5343.90	1.56250	0.781249	+	0.624219i	$0.214583\pi$
$228$	2043.46	0.593558
$229$	2036.67	0.587715	0.293858	−	0.955849i	$-0.405061\pi$
$229$	2036.67	0.587715	0.293858	+	0.955849i	$0.405061\pi$
$230$	0	0
$231$	3462.13	0.986110
$232$	253.690	0.0717913
$233$	−2974.63	−0.836372	−0.418186	−	0.908361i	$-0.637334\pi$
$233$	−2974.63	−0.836372	−0.418186	+	0.908361i	$0.637334\pi$
$234$	−1982.85	−0.553944
$235$	0	0
$236$	−1056.29	−0.291351
$237$	144.764	0.0396770
$238$	−15390.5	−4.19167
$239$	2022.60	0.547411	0.273705	−	0.961814i	$-0.411751\pi$
$239$	2022.60	0.547411	0.273705	+	0.961814i	$0.411751\pi$
$240$	0	0
$241$	−5525.71	−1.47694	−0.738470	−	0.674286i	$-0.764451\pi$
$241$	−5525.71	−1.47694	−0.738470	+	0.674286i	$0.764451\pi$
$242$	3442.64	0.914467
$243$	1899.75	0.501519
$244$	−2495.12	−0.654645
$245$	0	0
$246$	7203.23	1.86691
$247$	−3832.29	−0.987216
$248$	6.83542	0.00175020
$249$	1898.64	0.483220
$250$	0	0
$251$	−6544.91	−1.64586	−0.822930	−	0.568142i	$-0.807662\pi$
$251$	−6544.91	−1.64586	−0.822930	+	0.568142i	$0.807662\pi$
$252$	2059.05	0.514714
$253$	1475.01	0.366533
$254$	−3595.46	−0.888186
$255$	0	0
$256$	3676.82	0.897661
$257$	−3003.85	−0.729086	−0.364543	−	0.931187i	$-0.618775\pi$
$257$	−3003.85	−0.729086	−0.364543	+	0.931187i	$0.618775\pi$
$258$	779.092	0.188001
$259$	5220.87	1.25254
$260$	0	0
$261$	1141.06	0.270613
$262$	7234.89	1.70600
$263$	−123.301	−0.0289090	−0.0144545	−	0.999896i	$-0.504601\pi$
$263$	−123.301	−0.0289090	−0.0144545	+	0.999896i	$0.504601\pi$
$264$	151.864	0.0354038
$265$	0	0
$266$	7777.58	1.79276
$267$	−880.327	−0.201780
$268$	7381.47	1.68245
$269$	7004.23	1.58757	0.793783	−	0.608201i	$-0.208109\pi$
$269$	7004.23	1.58757	0.793783	+	0.608201i	$0.208109\pi$
$270$	0	0
$271$	−2280.47	−0.511175	−0.255588	−	0.966786i	$-0.582269\pi$
$271$	−2280.47	−0.511175	−0.255588	+	0.966786i	$0.582269\pi$
$272$	6551.48	1.46045
$273$	11115.1	2.46416
$274$	2989.52	0.659137
$275$	0	0
$276$	−2525.06	−0.550692
$277$	5160.72	1.11941	0.559707	−	0.828690i	$-0.310914\pi$
$277$	5160.72	1.11941	0.559707	+	0.828690i	$0.310914\pi$
$278$	5987.69	1.29179
$279$	30.7448	0.00659729
$280$	0	0
$281$	5153.09	1.09398	0.546989	−	0.837140i	$-0.315774\pi$
$281$	5153.09	1.09398	0.546989	+	0.837140i	$0.315774\pi$
$282$	−8971.20	−1.89442
$283$	−2144.33	−0.450414	−0.225207	−	0.974311i	$-0.572306\pi$
$283$	−2144.33	−0.450414	−0.225207	+	0.974311i	$0.572306\pi$
$284$	−1920.00	−0.401165
$285$	0	0
$286$	−6243.13	−1.29078
$287$	14028.0	2.88519
$288$	−1799.22	−0.368125
$289$	6700.11	1.36375
$290$	0	0
$291$	−6784.90	−1.36680
$292$	3303.50	0.662065
$293$	−2639.76	−0.526336	−0.263168	−	0.964750i	$-0.584767\pi$
$293$	−2639.76	−0.526336	−0.263168	+	0.964750i	$0.584767\pi$
$294$	−16343.4	−3.24206
$295$	0	0
$296$	229.010	0.0449694
$297$	3332.28	0.651039
$298$	14330.8	2.78578
$299$	4735.49	0.915920
$300$	0	0
$301$	1517.25	0.290542
$302$	−6999.86	−1.33376
$303$	4946.60	0.937870
$304$	−3310.78	−0.624627
$305$	0	0
$306$	−3036.49	−0.567270
$307$	−5758.95	−1.07062	−0.535310	−	0.844656i	$-0.679805\pi$
$307$	−5758.95	−1.07062	−0.535310	+	0.844656i	$0.679805\pi$
$308$	6483.06	1.19937
$309$	−2285.20	−0.420714
$310$	0	0
$311$	967.329	0.176374	0.0881868	−	0.996104i	$-0.471893\pi$
$311$	967.329	0.176374	0.0881868	+	0.996104i	$0.471893\pi$
$312$	487.557	0.0884696
$313$	1380.96	0.249381	0.124691	−	0.992196i	$-0.460206\pi$
$313$	1380.96	0.249381	0.124691	+	0.992196i	$0.460206\pi$
$314$	12237.2	2.19931
$315$	0	0
$316$	271.080	0.0482578
$317$	367.287	0.0650753	0.0325376	−	0.999471i	$-0.489641\pi$
$317$	367.287	0.0650753	0.0325376	+	0.999471i	$0.489641\pi$
$318$	−3211.99	−0.566414
$319$	3592.72	0.630576
$320$	0	0
$321$	−6110.50	−1.06248
$322$	−9610.62	−1.66329
$323$	−5868.67	−1.01097
$324$	−4128.94	−0.707981
$325$	0	0
$326$	−9459.08	−1.60702
$327$	−3679.69	−0.622285
$328$	615.331	0.103585
$329$	−17471.1	−2.92770
$330$	0	0
$331$	−9138.75	−1.51756	−0.758778	−	0.651349i	$-0.774203\pi$
$331$	−9138.75	−1.51756	−0.758778	+	0.651349i	$0.774203\pi$
$332$	3555.33	0.587724
$333$	1030.06	0.169510
$334$	−3098.92	−0.507681
$335$	0	0
$336$	9602.55	1.55911
$337$	−2278.19	−0.368252	−0.184126	−	0.982903i	$-0.558945\pi$
$337$	−2278.19	−0.368252	−0.184126	+	0.982903i	$0.558945\pi$
$338$	−11151.1	−1.79449
$339$	−5159.25	−0.826584
$340$	0	0
$341$	96.8021	0.0153728
$342$	1534.49	0.242619
$343$	−19725.4	−3.10516
$344$	66.5535	0.0104312
$345$	0	0
$346$	−15138.4	−2.35215
$347$	12314.0	1.90505	0.952526	−	0.304459i	$-0.0984755\pi$
$347$	12314.0	1.90505	0.952526	+	0.304459i	$0.0984755\pi$
$348$	−6150.37	−0.947398
$349$	5093.12	0.781170	0.390585	−	0.920567i	$-0.372273\pi$
$349$	5093.12	0.781170	0.390585	+	0.920567i	$0.372273\pi$
$350$	0	0
$351$	10698.2	1.62686
$352$	−5664.96	−0.857794
$353$	9361.75	1.41155	0.705773	−	0.708438i	$-0.250600\pi$
$353$	9361.75	1.41155	0.705773	+	0.708438i	$0.250600\pi$
$354$	2283.16	0.342793
$355$	0	0
$356$	−1648.47	−0.245418
$357$	17021.4	2.52344
$358$	−8033.89	−1.18605
$359$	−6955.89	−1.02261	−0.511306	−	0.859399i	$-0.670838\pi$
$359$	−6955.89	−1.02261	−0.511306	+	0.859399i	$0.670838\pi$
$360$	0	0
$361$	−3893.27	−0.567615
$362$	−13244.1	−1.92291
$363$	−3807.45	−0.550521
$364$	20813.7	2.99708
$365$	0	0
$366$	5393.16	0.770232
$367$	620.019	0.0881873	0.0440936	−	0.999027i	$-0.485960\pi$
$367$	620.019	0.0881873	0.0440936	+	0.999027i	$0.485960\pi$
$368$	4091.08	0.579516
$369$	2767.68	0.390460
$370$	0	0
$371$	−6255.25	−0.875354
$372$	−165.715	−0.0230966
$373$	7527.83	1.04498	0.522488	−	0.852647i	$-0.325004\pi$
$373$	7527.83	1.04498	0.522488	+	0.852647i	$0.325004\pi$
$374$	−9560.59	−1.32184
$375$	0	0
$376$	−766.359	−0.105112
$377$	11534.4	1.57573
$378$	−21711.9	−2.95434
$379$	−478.221	−0.0648141	−0.0324070	−	0.999475i	$-0.510317\pi$
$379$	−478.221	−0.0648141	−0.0324070	+	0.999475i	$0.510317\pi$
$380$	0	0
$381$	3976.47	0.534699
$382$	−11541.7	−1.54588
$383$	−6247.78	−0.833542	−0.416771	−	0.909012i	$-0.636838\pi$
$383$	−6247.78	−0.833542	−0.416771	+	0.909012i	$0.636838\pi$
$384$	885.824	0.117720
$385$	0	0
$386$	5816.83	0.767017
$387$	299.349	0.0393197
$388$	−12705.1	−1.66239
$389$	5939.31	0.774125	0.387063	−	0.922053i	$-0.373490\pi$
$389$	5939.31	0.774125	0.387063	+	0.922053i	$0.373490\pi$
$390$	0	0
$391$	7251.81	0.937954
$392$	−1396.12	−0.179885
$393$	−8001.56	−1.02704
$394$	10762.8	1.37619
$395$	0	0
$396$	1279.08	0.162314
$397$	−14686.0	−1.85659	−0.928296	−	0.371842i	$-0.878726\pi$
$397$	−14686.0	−1.85659	−0.928296	+	0.371842i	$0.878726\pi$
$398$	12172.3	1.53302
$399$	−8601.76	−1.07926
$400$	0	0
$401$	6580.66	0.819507	0.409753	−	0.912196i	$-0.365615\pi$
$401$	6580.66	0.819507	0.409753	+	0.912196i	$0.365615\pi$
$402$	−15954.9	−1.97950
$403$	310.781	0.0384147
$404$	9262.82	1.14070
$405$	0	0
$406$	−23408.9	−2.86148
$407$	3243.21	0.394987
$408$	746.634	0.0905978
$409$	−12135.7	−1.46717	−0.733586	−	0.679596i	$-0.762155\pi$
$409$	−12135.7	−1.46717	−0.733586	+	0.679596i	$0.762155\pi$
$410$	0	0
$411$	−3306.32	−0.396809
$412$	−4279.18	−0.511700
$413$	4446.38	0.529763
$414$	−1896.14	−0.225097
$415$	0	0
$416$	−18187.3	−2.14352
$417$	−6622.20	−0.777675
$418$	4831.44	0.565343
$419$	−1561.29	−0.182038	−0.0910190	−	0.995849i	$-0.529012\pi$
$419$	−1561.29	−0.182038	−0.0910190	+	0.995849i	$0.529012\pi$
$420$	0	0
$421$	516.899	0.0598387	0.0299194	−	0.999552i	$-0.490475\pi$
$421$	516.899	0.0598387	0.0299194	+	0.999552i	$0.490475\pi$
$422$	17139.3	1.97708
$423$	−3446.98	−0.396213
$424$	−274.383	−0.0314274
$425$	0	0
$426$	4150.04	0.471996
$427$	10503.0	1.19034
$428$	−11442.3	−1.29225
$429$	6904.71	0.777069
$430$	0	0
$431$	−13618.7	−1.52201	−0.761007	−	0.648743i	$-0.775295\pi$
$431$	−13618.7	−1.52201	−0.761007	+	0.648743i	$0.775295\pi$
$432$	9242.40	1.02934
$433$	−9864.27	−1.09480	−0.547398	−	0.836873i	$-0.684382\pi$
$433$	−9864.27	−1.09480	−0.547398	+	0.836873i	$0.684382\pi$
$434$	−630.727	−0.0697601
$435$	0	0
$436$	−6890.45	−0.756864
$437$	−3664.70	−0.401159
$438$	−7140.47	−0.778961
$439$	3507.60	0.381341	0.190670	−	0.981654i	$-0.438934\pi$
$439$	3507.60	0.381341	0.190670	+	0.981654i	$0.438934\pi$
$440$	0	0
$441$	−6279.57	−0.678066
$442$	−30694.1	−3.30310
$443$	4414.65	0.473469	0.236734	−	0.971574i	$-0.423923\pi$
$443$	4414.65	0.473469	0.236734	+	0.971574i	$0.423923\pi$
$444$	−5552.04	−0.593442
$445$	0	0
$446$	−973.549	−0.103361
$447$	−15849.4	−1.67708
$448$	19749.7	2.08279
$449$	18901.6	1.98669	0.993344	−	0.115184i	$-0.0367457\pi$
$449$	18901.6	1.98669	0.993344	+	0.115184i	$0.0367457\pi$
$450$	0	0
$451$	8714.23	0.909838
$452$	−9661.03	−1.00535
$453$	7741.62	0.802943
$454$	−21629.5	−2.23596
$455$	0	0
$456$	−377.311	−0.0387483
$457$	−13249.2	−1.35617	−0.678086	−	0.734983i	$-0.737190\pi$
$457$	−13249.2	−1.35617	−0.678086	+	0.734983i	$0.737190\pi$
$458$	−8243.45	−0.841028
$459$	16383.0	1.66600
$460$	0	0
$461$	−3962.15	−0.400294	−0.200147	−	0.979766i	$-0.564142\pi$
$461$	−3962.15	−0.400294	−0.200147	+	0.979766i	$0.564142\pi$
$462$	−14013.0	−1.41114
$463$	−16243.9	−1.63049	−0.815245	−	0.579117i	$-0.803398\pi$
$463$	−16243.9	−1.63049	−0.815245	+	0.579117i	$0.803398\pi$
$464$	9964.75	0.996987
$465$	0	0
$466$	12039.9	1.19686
$467$	14413.7	1.42824	0.714119	−	0.700024i	$-0.246827\pi$
$467$	14413.7	1.42824	0.714119	+	0.700024i	$0.246827\pi$
$468$	4106.47	0.405602
$469$	−31071.7	−3.05918
$470$	0	0
$471$	−13533.9	−1.32401
$472$	195.038	0.0190198
$473$	942.519	0.0916218
$474$	−585.936	−0.0567783
$475$	0	0
$476$	31873.7	3.06918
$477$	−1234.14	−0.118464
$478$	−8186.51	−0.783352
$479$	9358.60	0.892704	0.446352	−	0.894857i	$-0.352723\pi$
$479$	9358.60	0.892704	0.446352	+	0.894857i	$0.352723\pi$
$480$	0	0
$481$	10412.3	0.987023
$482$	22365.4	2.11352
$483$	10629.0	1.00132
$484$	−7129.69	−0.669580
$485$	0	0
$486$	−7689.27	−0.717680
$487$	−1232.17	−0.114651	−0.0573256	−	0.998356i	$-0.518257\pi$
$487$	−1232.17	−0.114651	−0.0573256	+	0.998356i	$0.518257\pi$
$488$	460.707	0.0427361
$489$	10461.4	0.967449
$490$	0	0
$491$	−13427.0	−1.23412	−0.617058	−	0.786917i	$-0.711676\pi$
$491$	−13427.0	−1.23412	−0.617058	+	0.786917i	$0.711676\pi$
$492$	−14917.9	−1.36697
$493$	17663.5	1.61363
$494$	15511.2	1.41272
$495$	0	0
$496$	268.490	0.0243056
$497$	8082.06	0.729437
$498$	−7684.80	−0.691494
$499$	5135.13	0.460682	0.230341	−	0.973110i	$-0.426016\pi$
$499$	5135.13	0.460682	0.230341	+	0.973110i	$0.426016\pi$
$500$	0	0
$501$	3427.31	0.305631
$502$	26490.6	2.35525
$503$	12121.7	1.07451	0.537256	−	0.843419i	$-0.319461\pi$
$503$	12121.7	1.07451	0.537256	+	0.843419i	$0.319461\pi$
$504$	−380.190	−0.0336012
$505$	0	0
$506$	−5970.12	−0.524514
$507$	12332.7	1.08031
$508$	7446.18	0.650337
$509$	−202.127	−0.0176014	−0.00880070	−	0.999961i	$-0.502801\pi$
$509$	−202.127	−0.0176014	−0.00880070	+	0.999961i	$0.502801\pi$
$510$	0	0
$511$	−13905.8	−1.20383
$512$	−16465.1	−1.42121
$513$	−8279.14	−0.712540
$514$	12158.1	1.04333
$515$	0	0
$516$	−1613.50	−0.137656
$517$	−10853.1	−0.923243
$518$	−21131.6	−1.79241
$519$	16742.6	1.41603
$520$	0	0
$521$	4956.22	0.416768	0.208384	−	0.978047i	$-0.433180\pi$
$521$	4956.22	0.416768	0.208384	+	0.978047i	$0.433180\pi$
$522$	−4618.48	−0.387252
$523$	−6931.85	−0.579557	−0.289779	−	0.957094i	$-0.593582\pi$
$523$	−6931.85	−0.579557	−0.289779	+	0.957094i	$0.593582\pi$
$524$	−14983.4	−1.24915
$525$	0	0
$526$	499.064	0.0413692
$527$	475.924	0.0393388
$528$	5965.11	0.491663
$529$	−7638.60	−0.627813
$530$	0	0
$531$	877.254	0.0716941
$532$	−16107.3	−1.31267
$533$	27976.9	2.27357
$534$	3563.14	0.288749
$535$	0	0
$536$	−1362.94	−0.109832
$537$	8885.23	0.714015
$538$	−28349.7	−2.27183
$539$	−19771.7	−1.58001
$540$	0	0
$541$	7161.41	0.569118	0.284559	−	0.958658i	$-0.408153\pi$
$541$	7161.41	0.569118	0.284559	+	0.958658i	$0.408153\pi$
$542$	9230.23	0.731498
$543$	14647.5	1.15762
$544$	−27851.6	−2.19508
$545$	0	0
$546$	−44988.6	−3.52625
$547$	−7432.45	−0.580966	−0.290483	−	0.956880i	$-0.593816\pi$
$547$	−7432.45	−0.580966	−0.290483	+	0.956880i	$0.593816\pi$
$548$	−6191.29	−0.482626
$549$	2072.20	0.161092
$550$	0	0
$551$	−8926.21	−0.690144
$552$	466.236	0.0359499
$553$	−1141.09	−0.0877469
$554$	−20888.1	−1.60190
$555$	0	0
$556$	−12400.5	−0.945860
$557$	11940.5	0.908320	0.454160	−	0.890920i	$-0.349939\pi$
$557$	11940.5	0.908320	0.454160	+	0.890920i	$0.349939\pi$
$558$	−124.440	−0.00944081
$559$	3025.94	0.228951
$560$	0	0
$561$	10573.7	0.795762
$562$	−20857.2	−1.56550
$563$	−6917.09	−0.517799	−0.258899	−	0.965904i	$-0.583360\pi$
$563$	−6917.09	−0.517799	−0.258899	+	0.965904i	$0.583360\pi$
$564$	18579.3	1.38711
$565$	0	0
$566$	8679.22	0.644549
$567$	17380.4	1.28732
$568$	354.515	0.0261886
$569$	15803.8	1.16437	0.582186	−	0.813055i	$-0.302197\pi$
$569$	15803.8	1.16437	0.582186	+	0.813055i	$0.302197\pi$
$570$	0	0
$571$	−14949.1	−1.09562	−0.547812	−	0.836601i	$-0.684539\pi$
$571$	−14949.1	−1.09562	−0.547812	+	0.836601i	$0.684539\pi$
$572$	12929.5	0.945122
$573$	12764.8	0.930639
$574$	−56778.7	−4.12874
$575$	0	0
$576$	3896.55	0.281869
$577$	1029.70	0.0742928	0.0371464	−	0.999310i	$-0.488173\pi$
$577$	1029.70	0.0742928	0.0371464	+	0.999310i	$0.488173\pi$
$578$	−27118.8	−1.95155
$579$	−6433.23	−0.461755
$580$	0	0
$581$	−14965.9	−1.06866
$582$	27462.0	1.95590
$583$	−3885.76	−0.276041
$584$	−609.970	−0.0432205
$585$	0	0
$586$	10684.5	0.753193
$587$	−25190.1	−1.77122	−0.885609	−	0.464432i	$-0.846259\pi$
$587$	−25190.1	−1.77122	−0.885609	+	0.464432i	$0.846259\pi$
$588$	33847.1	2.37386
$589$	−240.508	−0.0168250
$590$	0	0
$591$	−11903.3	−0.828486
$592$	8995.34	0.624504
$593$	−25617.2	−1.77398	−0.886992	−	0.461785i	$-0.847209\pi$
$593$	−25617.2	−1.77398	−0.886992	+	0.461785i	$0.847209\pi$
$594$	−13487.5	−0.931645
$595$	0	0
$596$	−29679.1	−2.03977
$597$	−13462.2	−0.922899
$598$	−19167.0	−1.31069
$599$	5615.73	0.383059	0.191530	−	0.981487i	$-0.438655\pi$
$599$	5615.73	0.383059	0.191530	+	0.981487i	$0.438655\pi$
$600$	0	0
$601$	16414.7	1.11409	0.557045	−	0.830482i	$-0.311935\pi$
$601$	16414.7	1.11409	0.557045	+	0.830482i	$0.311935\pi$
$602$	−6141.11	−0.415769
$603$	−6130.33	−0.414007
$604$	14496.7	0.976592
$605$	0	0
$606$	−20021.4	−1.34211
$607$	−9880.24	−0.660670	−0.330335	−	0.943864i	$-0.607162\pi$
$607$	−9880.24	−0.660670	−0.330335	+	0.943864i	$0.607162\pi$
$608$	14074.8	0.938827
$609$	25889.5	1.72265
$610$	0	0
$611$	−34843.5	−2.30707
$612$	6288.56	0.415359
$613$	−11909.7	−0.784714	−0.392357	−	0.919813i	$-0.628340\pi$
$613$	−11909.7	−0.784714	−0.392357	+	0.919813i	$0.628340\pi$
$614$	23309.4	1.53207
$615$	0	0
$616$	−1197.05	−0.0782966
$617$	−2191.99	−0.143025	−0.0715124	−	0.997440i	$-0.522783\pi$
$617$	−2191.99	−0.143025	−0.0715124	+	0.997440i	$0.522783\pi$
$618$	9249.39	0.602047
$619$	−3676.20	−0.238706	−0.119353	−	0.992852i	$-0.538082\pi$
$619$	−3676.20	−0.238706	−0.119353	+	0.992852i	$0.538082\pi$
$620$	0	0
$621$	10230.4	0.661081
$622$	−3915.28	−0.252393
$623$	6939.09	0.446242
$624$	19150.9	1.22860
$625$	0	0
$626$	−5589.45	−0.356868
$627$	−5343.42	−0.340344
$628$	−25343.1	−1.61035
$629$	15945.1	1.01077
$630$	0	0
$631$	−209.068	−0.0131900	−0.00659499	−	0.999978i	$-0.502099\pi$
$631$	−209.068	−0.0131900	−0.00659499	+	0.999978i	$0.502099\pi$
$632$	−50.0532	−0.00315033
$633$	−18955.5	−1.19023
$634$	−1486.60	−0.0931236
$635$	0	0
$636$	6652.03	0.414733
$637$	−63476.6	−3.94825
$638$	−14541.6	−0.902363
$639$	1594.56	0.0987165
$640$	0	0
$641$	−26729.7	−1.64705	−0.823526	−	0.567279i	$-0.807996\pi$
$641$	−26729.7	−1.64705	−0.823526	+	0.567279i	$0.807996\pi$
$642$	24732.3	1.52042
$643$	19152.3	1.17464	0.587319	−	0.809355i	$-0.300183\pi$
$643$	19152.3	1.17464	0.587319	+	0.809355i	$0.300183\pi$
$644$	19903.6	1.21787
$645$	0	0
$646$	23753.6	1.44670
$647$	5208.81	0.316506	0.158253	−	0.987399i	$-0.449414\pi$
$647$	5208.81	0.316506	0.158253	+	0.987399i	$0.449414\pi$
$648$	762.382	0.0462179
$649$	2762.09	0.167060
$650$	0	0
$651$	697.565	0.0419965
$652$	19589.7	1.17668
$653$	853.809	0.0511671	0.0255836	−	0.999673i	$-0.491856\pi$
$653$	853.809	0.0511671	0.0255836	+	0.999673i	$0.491856\pi$
$654$	14893.6	0.890498
$655$	0	0
$656$	24169.7	1.43852
$657$	−2743.57	−0.162917
$658$	70714.5	4.18957
$659$	6239.14	0.368805	0.184403	−	0.982851i	$-0.440965\pi$
$659$	6239.14	0.368805	0.184403	+	0.982851i	$0.440965\pi$
$660$	0	0
$661$	−23578.1	−1.38742	−0.693708	−	0.720257i	$-0.744024\pi$
$661$	−23578.1	−1.38742	−0.693708	+	0.720257i	$0.744024\pi$
$662$	36989.2	2.17164
$663$	33946.7	1.98851
$664$	−656.469	−0.0383674
$665$	0	0
$666$	−4169.17	−0.242571
$667$	11030.0	0.640302
$668$	6417.86	0.371728
$669$	1076.72	0.0622245
$670$	0	0
$671$	6524.46	0.375371
$672$	−40822.2	−2.34338
$673$	21431.2	1.22750	0.613752	−	0.789499i	$-0.289659\pi$
$673$	21431.2	1.22750	0.613752	+	0.789499i	$0.289659\pi$
$674$	9221.02	0.526974
$675$	0	0
$676$	23093.8	1.31394
$677$	4319.50	0.245217	0.122608	−	0.992455i	$-0.460874\pi$
$677$	4319.50	0.245217	0.122608	+	0.992455i	$0.460874\pi$
$678$	20882.2	1.18285
$679$	53481.3	3.02271
$680$	0	0
$681$	23921.6	1.34608
$682$	−391.808	−0.0219987
$683$	−20556.5	−1.15164	−0.575821	−	0.817576i	$-0.695317\pi$
$683$	−20556.5	−1.15164	−0.575821	+	0.817576i	$0.695317\pi$
$684$	−3177.92	−0.177647
$685$	0	0
$686$	79838.9	4.44353
$687$	9116.99	0.506310
$688$	2614.17	0.144861
$689$	−12475.2	−0.689791
$690$	0	0
$691$	9737.74	0.536094	0.268047	−	0.963406i	$-0.413622\pi$
$691$	9737.74	0.536094	0.268047	+	0.963406i	$0.413622\pi$
$692$	31351.6	1.72227
$693$	−5384.19	−0.295135
$694$	−49841.3	−2.72615
$695$	0	0
$696$	1135.63	0.0618474
$697$	42843.1	2.32826
$698$	−20614.5	−1.11786
$699$	−13315.7	−0.720525
$700$	0	0
$701$	−34574.5	−1.86286	−0.931428	−	0.363925i	$-0.881436\pi$
$701$	−34574.5	−1.86286	−0.931428	+	0.363925i	$0.881436\pi$
$702$	−43301.2	−2.32806
$703$	−8057.84	−0.432300
$704$	12268.6	0.656802
$705$	0	0
$706$	−37891.8	−2.01994
$707$	−38991.1	−2.07413
$708$	−4728.42	−0.250996
$709$	−6994.85	−0.370518	−0.185259	−	0.982690i	$-0.559312\pi$
$709$	−6994.85	−0.370518	−0.185259	+	0.982690i	$0.559312\pi$
$710$	0	0
$711$	−225.133	−0.0118750
$712$	304.379	0.0160212
$713$	297.191	0.0156099
$714$	−68894.5	−3.61108
$715$	0	0
$716$	16638.2	0.868432
$717$	9054.03	0.471588
$718$	28154.1	1.46337
$719$	−27154.2	−1.40846	−0.704229	−	0.709972i	$-0.748707\pi$
$719$	−27154.2	−1.40846	−0.704229	+	0.709972i	$0.748707\pi$
$720$	0	0
$721$	18012.9	0.930422
$722$	15758.1	0.812265
$723$	−24735.5	−1.27237
$724$	27428.4	1.40797
$725$	0	0
$726$	15410.7	0.787803
$727$	21058.0	1.07427	0.537137	−	0.843495i	$-0.319506\pi$
$727$	21058.0	1.07427	0.537137	+	0.843495i	$0.319506\pi$
$728$	−3843.12	−0.195653
$729$	21803.6	1.10774
$730$	0	0
$731$	4633.86	0.234459
$732$	−11169.2	−0.563970
$733$	20006.7	1.00814	0.504069	−	0.863664i	$-0.331836\pi$
$733$	20006.7	1.00814	0.504069	+	0.863664i	$0.331836\pi$
$734$	−2509.54	−0.126197
$735$	0	0
$736$	−17391.9	−0.871026
$737$	−19301.8	−0.964707
$738$	−11202.2	−0.558753
$739$	−4208.73	−0.209500	−0.104750	−	0.994499i	$-0.533404\pi$
$739$	−4208.73	−0.209500	−0.104750	+	0.994499i	$0.533404\pi$
$740$	0	0
$741$	−17154.9	−0.850476
$742$	25318.2	1.25264
$743$	2209.58	0.109101	0.0545503	−	0.998511i	$-0.482627\pi$
$743$	2209.58	0.109101	0.0545503	+	0.998511i	$0.482627\pi$
$744$	30.5983	0.00150778
$745$	0	0
$746$	−30469.0	−1.49537
$747$	−2952.71	−0.144624
$748$	19800.0	0.967858
$749$	48165.4	2.34970
$750$	0	0
$751$	40524.3	1.96905	0.984523	−	0.175253i	$-0.0560744\pi$
$751$	40524.3	1.96905	0.984523	+	0.175253i	$0.0560744\pi$
$752$	−30102.0	−1.45972
$753$	−29297.8	−1.41789
$754$	−46685.5	−2.25489
$755$	0	0
$756$	44965.3	2.16319
$757$	−32196.0	−1.54582	−0.772909	−	0.634517i	$-0.781199\pi$
$757$	−32196.0	−1.54582	−0.772909	+	0.634517i	$0.781199\pi$
$758$	1935.61	0.0927498
$759$	6602.77	0.315764
$760$	0	0
$761$	7769.67	0.370106	0.185053	−	0.982729i	$-0.440754\pi$
$761$	7769.67	0.370106	0.185053	+	0.982729i	$0.440754\pi$
$762$	−16094.8	−0.765162
$763$	29004.8	1.37620
$764$	23902.8	1.13190
$765$	0	0
$766$	25288.0	1.19281
$767$	8867.65	0.417461
$768$	16459.0	0.773325
$769$	−4179.79	−0.196004	−0.0980020	−	0.995186i	$-0.531245\pi$
$769$	−4179.79	−0.196004	−0.0980020	+	0.995186i	$0.531245\pi$
$770$	0	0
$771$	−13446.5	−0.628100
$772$	−12046.6	−0.561616
$773$	8662.16	0.403048	0.201524	−	0.979484i	$-0.435411\pi$
$773$	8662.16	0.403048	0.201524	+	0.979484i	$0.435411\pi$
$774$	−1211.62	−0.0562671
$775$	0	0
$776$	2345.92	0.108523
$777$	23370.8	1.07905
$778$	−24039.4	−1.10778
$779$	−21650.7	−0.995787
$780$	0	0
$781$	5020.58	0.230026
$782$	−29351.8	−1.34222
$783$	24918.5	1.13731
$784$	−54838.6	−2.49811
$785$	0	0
$786$	32386.5	1.46970
$787$	−19036.1	−0.862216	−0.431108	−	0.902300i	$-0.641877\pi$
$787$	−19036.1	−0.862216	−0.431108	+	0.902300i	$0.641877\pi$
$788$	−22289.6	−1.00766
$789$	−551.949	−0.0249048
$790$	0	0
$791$	40667.3	1.82802
$792$	−236.174	−0.0105961
$793$	20946.7	0.938005
$794$	59441.7	2.65681
$795$	0	0
$796$	−25208.8	−1.12249
$797$	−5094.80	−0.226433	−0.113216	−	0.993570i	$-0.536115\pi$
$797$	−5094.80	−0.226433	−0.113216	+	0.993570i	$0.536115\pi$
$798$	34815.8	1.54444
$799$	−53358.6	−2.36257
$800$	0	0
$801$	1369.06	0.0603910
$802$	−26635.3	−1.17273
$803$	−8638.30	−0.379625
$804$	33042.6	1.44941
$805$	0	0
$806$	−1257.89	−0.0549720
$807$	31353.9	1.36767
$808$	−1710.32	−0.0744664
$809$	−4085.55	−0.177553	−0.0887764	−	0.996052i	$-0.528296\pi$
$809$	−4085.55	−0.177553	−0.0887764	+	0.996052i	$0.528296\pi$
$810$	0	0
$811$	36520.8	1.58128	0.790641	−	0.612280i	$-0.209748\pi$
$811$	36520.8	1.58128	0.790641	+	0.612280i	$0.209748\pi$
$812$	48479.7	2.09520
$813$	−10208.3	−0.440372
$814$	−13126.9	−0.565232
$815$	0	0
$816$	29327.2	1.25816
$817$	−2341.72	−0.100277
$818$	49119.6	2.09954
$819$	−17285.9	−0.737505
$820$	0	0
$821$	14383.6	0.611440	0.305720	−	0.952121i	$-0.401103\pi$
$821$	14383.6	0.611440	0.305720	+	0.952121i	$0.401103\pi$
$822$	13382.4	0.567840
$823$	−22404.5	−0.948932	−0.474466	−	0.880274i	$-0.657359\pi$
$823$	−22404.5	−0.948932	−0.474466	+	0.880274i	$0.657359\pi$
$824$	790.123	0.0334044
$825$	0	0
$826$	−17996.8	−0.758098
$827$	−929.994	−0.0391040	−0.0195520	−	0.999809i	$-0.506224\pi$
$827$	−929.994	−0.0391040	−0.0195520	+	0.999809i	$0.506224\pi$
$828$	3926.90	0.164818
$829$	16490.4	0.690873	0.345437	−	0.938442i	$-0.387731\pi$
$829$	16490.4	0.690873	0.345437	+	0.938442i	$0.387731\pi$
$830$	0	0
$831$	23101.6	0.964363
$832$	39388.0	1.64126
$833$	−97206.5	−4.04323
$834$	26803.5	1.11286
$835$	0	0
$836$	−10005.9	−0.413949
$837$	671.402	0.0277265
$838$	6319.34	0.260499
$839$	41770.6	1.71881	0.859405	−	0.511295i	$-0.170834\pi$
$839$	41770.6	1.71881	0.859405	+	0.511295i	$0.170834\pi$
$840$	0	0
$841$	2477.00	0.101562
$842$	−2092.16	−0.0856300
$843$	23067.4	0.942449
$844$	−35495.3	−1.44763
$845$	0	0
$846$	13951.7	0.566985
$847$	30011.8	1.21750
$848$	−10777.5	−0.436441
$849$	−9598.94	−0.388027
$850$	0	0
$851$	9956.92	0.401080
$852$	−8594.73	−0.345599
$853$	12895.9	0.517642	0.258821	−	0.965925i	$-0.416666\pi$
$853$	12895.9	0.517642	0.258821	+	0.965925i	$0.416666\pi$
$854$	−42511.0	−1.70339
$855$	0	0
$856$	2112.74	0.0843600
$857$	2463.33	0.0981863	0.0490931	−	0.998794i	$-0.484367\pi$
$857$	2463.33	0.0981863	0.0490931	+	0.998794i	$0.484367\pi$
$858$	−27946.9	−1.11200
$859$	−4156.92	−0.165113	−0.0825566	−	0.996586i	$-0.526309\pi$
$859$	−4156.92	−0.165113	−0.0825566	+	0.996586i	$0.526309\pi$
$860$	0	0
$861$	62795.5	2.48556
$862$	55121.8	2.17802
$863$	18623.0	0.734572	0.367286	−	0.930108i	$-0.380287\pi$
$863$	18623.0	0.734572	0.367286	+	0.930108i	$0.380287\pi$
$864$	−39291.2	−1.54712
$865$	0	0
$866$	39925.8	1.56667
$867$	29992.5	1.17486
$868$	1306.23	0.0510789
$869$	−708.845	−0.0276708
$870$	0	0
$871$	−61967.9	−2.41068
$872$	1272.28	0.0494091
$873$	10551.6	0.409071
$874$	14832.9	0.574063
$875$	0	0
$876$	14787.9	0.570361
$877$	−44474.8	−1.71244	−0.856219	−	0.516613i	$-0.827193\pi$
$877$	−44474.8	−1.71244	−0.856219	+	0.516613i	$0.827193\pi$
$878$	−14197.1	−0.545704
$879$	−11816.7	−0.453432
$880$	0	0
$881$	−22188.5	−0.848524	−0.424262	−	0.905539i	$-0.639467\pi$
$881$	−22188.5	−0.848524	−0.424262	+	0.905539i	$0.639467\pi$
$882$	25416.7	0.970322
$883$	22096.8	0.842149	0.421074	−	0.907026i	$-0.361653\pi$
$883$	22096.8	0.842149	0.421074	+	0.907026i	$0.361653\pi$
$884$	63567.4	2.41856
$885$	0	0
$886$	−17868.4	−0.677540
$887$	2797.36	0.105892	0.0529459	−	0.998597i	$-0.483139\pi$
$887$	2797.36	0.105892	0.0529459	+	0.998597i	$0.483139\pi$
$888$	1025.15	0.0387407
$889$	−31344.1	−1.18250
$890$	0	0
$891$	10796.7	0.405953
$892$	2016.22	0.0756816
$893$	26964.7	1.01046
$894$	64150.9	2.39992
$895$	0	0
$896$	−6982.42	−0.260342
$897$	21198.1	0.789055
$898$	−76504.7	−2.84298
$899$	723.876	0.0268550
$900$	0	0
$901$	−19104.2	−0.706385
$902$	−35271.0	−1.30199
$903$	6791.88	0.250299
$904$	1783.85	0.0656303
$905$	0	0
$906$	−31334.4	−1.14902
$907$	−25176.3	−0.921683	−0.460842	−	0.887482i	$-0.652452\pi$
$907$	−25176.3	−0.921683	−0.460842	+	0.887482i	$0.652452\pi$
$908$	44794.7	1.63719
$909$	−7692.79	−0.280697
$910$	0	0
$911$	27032.6	0.983127	0.491563	−	0.870842i	$-0.336426\pi$
$911$	27032.6	0.983127	0.491563	+	0.870842i	$0.336426\pi$
$912$	−14820.5	−0.538109
$913$	−9296.81	−0.336998
$914$	53626.3	1.94070
$915$	0	0
$916$	17072.2	0.615808
$917$	63071.5	2.27132
$918$	−66310.5	−2.38407
$919$	48383.7	1.73670	0.868351	−	0.495950i	$-0.165180\pi$
$919$	48383.7	1.73670	0.868351	+	0.495950i	$0.165180\pi$
$920$	0	0
$921$	−25779.5	−0.922327
$922$	16036.9	0.572827
$923$	16118.5	0.574807
$924$	29021.0	1.03325
$925$	0	0
$926$	65747.3	2.33325
$927$	3553.87	0.125916
$928$	−42362.0	−1.49849
$929$	−16500.5	−0.582738	−0.291369	−	0.956611i	$-0.594111\pi$
$929$	−16500.5	−0.582738	−0.291369	+	0.956611i	$0.594111\pi$
$930$	0	0
$931$	49123.2	1.72927
$932$	−24934.6	−0.876350
$933$	4330.18	0.151944
$934$	−58339.8	−2.04383
$935$	0	0
$936$	−758.233	−0.0264782
$937$	−31016.7	−1.08140	−0.540700	−	0.841215i	$-0.681841\pi$
$937$	−31016.7	−1.08140	−0.540700	+	0.841215i	$0.681841\pi$
$938$	125763.	4.37773
$939$	6181.76	0.214839
$940$	0	0
$941$	−18073.8	−0.626131	−0.313065	−	0.949732i	$-0.601356\pi$
$941$	−18073.8	−0.626131	−0.313065	+	0.949732i	$0.601356\pi$
$942$	54778.8	1.89468
$943$	26753.4	0.923872
$944$	7660.93	0.264134
$945$	0	0
$946$	−3814.86	−0.131112
$947$	−27378.2	−0.939465	−0.469732	−	0.882809i	$-0.655650\pi$
$947$	−27378.2	−0.939465	−0.469732	+	0.882809i	$0.655650\pi$
$948$	1213.47	0.0415735
$949$	−27733.1	−0.948635
$950$	0	0
$951$	1644.13	0.0560616
$952$	−5885.27	−0.200360
$953$	9637.52	0.327586	0.163793	−	0.986495i	$-0.447627\pi$
$953$	9637.52	0.327586	0.163793	+	0.986495i	$0.447627\pi$
$954$	4995.19	0.169523
$955$	0	0
$956$	16954.2	0.573577
$957$	16082.6	0.543234
$958$	−37879.1	−1.27747
$959$	26061.7	0.877557
$960$	0	0
$961$	−29771.5	−0.999345
$962$	−42143.8	−1.41244
$963$	9502.84	0.317991
$964$	−46318.7	−1.54754
$965$	0	0
$966$	−43021.2	−1.43290
$967$	6478.05	0.215429	0.107715	−	0.994182i	$-0.465647\pi$
$967$	6478.05	0.215429	0.107715	+	0.994182i	$0.465647\pi$
$968$	1316.45	0.0437111
$969$	−26270.7	−0.870935
$970$	0	0
$971$	−28924.6	−0.955959	−0.477979	−	0.878371i	$-0.658631\pi$
$971$	−28924.6	−0.955959	−0.477979	+	0.878371i	$0.658631\pi$
$972$	15924.5	0.525491
$973$	52198.8	1.71985
$974$	4987.25	0.164067
$975$	0	0
$976$	18096.2	0.593489
$977$	14362.8	0.470325	0.235162	−	0.971956i	$-0.424438\pi$
$977$	14362.8	0.470325	0.235162	+	0.971956i	$0.424438\pi$
$978$	−42342.9	−1.38443
$979$	4310.57	0.140721
$980$	0	0
$981$	5722.53	0.186245
$982$	54345.9	1.76604
$983$	−39806.8	−1.29160	−0.645798	−	0.763508i	$-0.723475\pi$
$983$	−39806.8	−1.29160	−0.645798	+	0.763508i	$0.723475\pi$
$984$	2754.49	0.0892376
$985$	0	0
$986$	−71493.1	−2.30913
$987$	−78208.1	−2.52218
$988$	−32123.7	−1.03440
$989$	2893.62	0.0930350
$990$	0	0
$991$	35617.3	1.14170	0.570848	−	0.821056i	$-0.306615\pi$
$991$	35617.3	1.14170	0.570848	+	0.821056i	$0.306615\pi$
$992$	−1141.40	−0.0365318
$993$	−40909.0	−1.30736
$994$	−32712.3	−1.04383
$995$	0	0
$996$	15915.2	0.506317
$997$	5365.76	0.170447	0.0852234	−	0.996362i	$-0.472840\pi$
$997$	5365.76	0.170447	0.0852234	+	0.996362i	$0.472840\pi$
$998$	−20784.5	−0.659242
$999$	22494.3	0.712400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.4.a.f.1.4		15
5.4	even	2		215.4.a.d.1.12	✓	15
15.14	odd	2		1935.4.a.n.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.4.a.d.1.12	✓	15	5.4	even	2
1075.4.a.f.1.4		15	1.1	even	1	trivial
1935.4.a.n.1.4		15	15.14	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-4.04752 q^{2} +4.47643 q^{3} +8.38240 q^{4} -18.1184 q^{6} -35.2850 q^{7} -1.54775 q^{8} -6.96159 q^{9} +O(q^{10})\)	\(q-4.04752 q^{2} +4.47643 q^{3} +8.38240 q^{4} -18.1184 q^{6} -35.2850 q^{7} -1.54775 q^{8} -6.96159 q^{9} -21.9191 q^{11} +37.5232 q^{12} -70.3707 q^{13} +142.817 q^{14} -60.7946 q^{16} -107.764 q^{17} +28.1772 q^{18} +54.4585 q^{19} -157.951 q^{21} +88.7178 q^{22} -67.2934 q^{23} -6.92841 q^{24} +284.827 q^{26} -152.027 q^{27} -295.773 q^{28} -163.908 q^{29} -4.41635 q^{31} +258.449 q^{32} -98.1191 q^{33} +436.177 q^{34} -58.3548 q^{36} -147.963 q^{37} -220.422 q^{38} -315.009 q^{39} -397.564 q^{41} +639.308 q^{42} -43.0000 q^{43} -183.734 q^{44} +272.371 q^{46} +495.142 q^{47} -272.143 q^{48} +902.031 q^{49} -482.398 q^{51} -589.875 q^{52} +177.278 q^{53} +615.330 q^{54} +54.6125 q^{56} +243.780 q^{57} +663.422 q^{58} -126.013 q^{59} -297.662 q^{61} +17.8752 q^{62} +245.640 q^{63} -559.721 q^{64} +397.139 q^{66} +880.592 q^{67} -903.322 q^{68} -301.234 q^{69} -229.051 q^{71} +10.7748 q^{72} +394.100 q^{73} +598.882 q^{74} +456.493 q^{76} +773.414 q^{77} +1275.01 q^{78} +32.3392 q^{79} -492.573 q^{81} +1609.15 q^{82} +424.143 q^{83} -1324.01 q^{84} +174.043 q^{86} -733.725 q^{87} +33.9253 q^{88} -196.658 q^{89} +2483.03 q^{91} -564.080 q^{92} -19.7694 q^{93} -2004.10 q^{94} +1156.93 q^{96} -1515.69 q^{97} -3650.98 q^{98} +152.592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - q^{2} - 7 q^{3} + 83 q^{4} + 40 q^{6} - 36 q^{7} - 33 q^{8} + 242 q^{9}+O(q^{10}) \) 15 * q - q^2 - 7 * q^3 + 83 * q^4 + 40 * q^6 - 36 * q^7 - 33 * q^8 + 242 * q^9	\( 15 q - q^{2} - 7 q^{3} + 83 q^{4} + 40 q^{6} - 36 q^{7} - 33 q^{8} + 242 q^{9} + 87 q^{11} + 37 q^{12} + 35 q^{13} + 237 q^{14} + 139 q^{16} - 144 q^{17} + 325 q^{18} + 293 q^{19} + 208 q^{21} - 25 q^{22} - 22 q^{23} + 480 q^{24} + 127 q^{26} - 202 q^{27} - 187 q^{28} + 495 q^{29} + 408 q^{31} - 395 q^{32} - 308 q^{33} + 812 q^{34} + 1283 q^{36} - 1013 q^{37} - 251 q^{38} + 654 q^{39} + 820 q^{41} - 431 q^{42} - 645 q^{43} + 1244 q^{44} + 1416 q^{46} + 622 q^{47} - 70 q^{48} + 1525 q^{49} + 1760 q^{51} + 593 q^{52} - 276 q^{53} - 349 q^{54} + 822 q^{56} + 566 q^{57} - 1403 q^{58} - 1405 q^{59} + 1969 q^{61} + 3297 q^{62} + 2587 q^{63} - 1709 q^{64} - 3111 q^{66} + 439 q^{67} + 3412 q^{68} + 10 q^{69} + 494 q^{71} + 6476 q^{72} - 958 q^{73} - 6273 q^{74} + 1089 q^{76} + 918 q^{77} + 5438 q^{78} - 1846 q^{79} + 3655 q^{81} + 2693 q^{82} + 1524 q^{83} - 6283 q^{84} + 43 q^{86} + 2702 q^{87} + 2010 q^{88} + 1380 q^{89} + 3625 q^{91} + 3658 q^{92} - 1610 q^{93} - 274 q^{94} - 367 q^{96} - 3240 q^{97} + 6137 q^{98} - 3769 q^{99}+O(q^{100}) \) 15 * q - q^2 - 7 * q^3 + 83 * q^4 + 40 * q^6 - 36 * q^7 - 33 * q^8 + 242 * q^9 + 87 * q^11 + 37 * q^12 + 35 * q^13 + 237 * q^14 + 139 * q^16 - 144 * q^17 + 325 * q^18 + 293 * q^19 + 208 * q^21 - 25 * q^22 - 22 * q^23 + 480 * q^24 + 127 * q^26 - 202 * q^27 - 187 * q^28 + 495 * q^29 + 408 * q^31 - 395 * q^32 - 308 * q^33 + 812 * q^34 + 1283 * q^36 - 1013 * q^37 - 251 * q^38 + 654 * q^39 + 820 * q^41 - 431 * q^42 - 645 * q^43 + 1244 * q^44 + 1416 * q^46 + 622 * q^47 - 70 * q^48 + 1525 * q^49 + 1760 * q^51 + 593 * q^52 - 276 * q^53 - 349 * q^54 + 822 * q^56 + 566 * q^57 - 1403 * q^58 - 1405 * q^59 + 1969 * q^61 + 3297 * q^62 + 2587 * q^63 - 1709 * q^64 - 3111 * q^66 + 439 * q^67 + 3412 * q^68 + 10 * q^69 + 494 * q^71 + 6476 * q^72 - 958 * q^73 - 6273 * q^74 + 1089 * q^76 + 918 * q^77 + 5438 * q^78 - 1846 * q^79 + 3655 * q^81 + 2693 * q^82 + 1524 * q^83 - 6283 * q^84 + 43 * q^86 + 2702 * q^87 + 2010 * q^88 + 1380 * q^89 + 3625 * q^91 + 3658 * q^92 - 1610 * q^93 - 274 * q^94 - 367 * q^96 - 3240 * q^97 + 6137 * q^98 - 3769 * q^99

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