LMFDB - Embedded newform 1075.4.a.b.1.3

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:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.847740$ 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)

$f(q)$	$=$	$q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} +O(q^{10})$	\(q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} -36.8506 q^{11} +43.5497 q^{12} -89.5430 q^{13} -48.1743 q^{14} -6.28309 q^{16} +28.8042 q^{17} -116.748 q^{18} -58.8677 q^{19} -247.594 q^{21} +68.0904 q^{22} -2.63139 q^{23} -220.846 q^{24} +165.452 q^{26} -343.624 q^{27} -119.563 q^{28} +173.812 q^{29} +57.9476 q^{31} -174.434 q^{32} +349.953 q^{33} -53.2227 q^{34} -289.753 q^{36} -52.0754 q^{37} +108.772 q^{38} +850.348 q^{39} +142.704 q^{41} +457.489 q^{42} +43.0000 q^{43} +168.992 q^{44} +4.86213 q^{46} +106.853 q^{47} +59.6676 q^{48} +336.750 q^{49} -273.540 q^{51} +410.631 q^{52} -244.652 q^{53} +634.928 q^{54} +606.315 q^{56} +559.039 q^{57} -321.160 q^{58} -127.799 q^{59} -443.613 q^{61} -107.072 q^{62} +1647.34 q^{63} +372.573 q^{64} -646.622 q^{66} +117.896 q^{67} -132.092 q^{68} +24.9891 q^{69} +816.799 q^{71} +1469.37 q^{72} +620.953 q^{73} +96.2217 q^{74} +269.959 q^{76} -960.770 q^{77} -1571.22 q^{78} +377.771 q^{79} +1557.27 q^{81} -263.680 q^{82} +1453.23 q^{83} +1135.43 q^{84} -79.4528 q^{86} -1650.62 q^{87} -856.975 q^{88} +627.993 q^{89} -2334.57 q^{91} +12.0672 q^{92} -550.302 q^{93} -197.436 q^{94} +1656.52 q^{96} +817.163 q^{97} -622.227 q^{98} -2328.38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.84774	−0.653275	−0.326637	−	0.945150i	$-0.605916\pi$
$2$	−1.84774	−0.653275	−0.326637	+	0.945150i	$0.605916\pi$
$3$	−9.49653	−1.82761	−0.913804	−	0.406154i	$-0.866870\pi$
$3$	−9.49653	−1.82761	−0.913804	+	0.406154i	$0.866870\pi$
$4$	−4.58586	−0.573232
$5$	0	0
$5$	0	0
$6$	17.5471	1.19393
$7$	26.0720	1.40776	0.703878	−	0.710321i	$-0.251450\pi$
$7$	26.0720	1.40776	0.703878	+	0.710321i	$0.251450\pi$
$8$	23.2554	1.02775
$9$	63.1842	2.34015
$10$	0	0
$11$	−36.8506	−1.01008	−0.505040	−	0.863096i	$-0.668522\pi$
$11$	−36.8506	−1.01008	−0.505040	+	0.863096i	$0.668522\pi$
$12$	43.5497	1.04764
$13$	−89.5430	−1.91037	−0.955183	−	0.296016i	$-0.904342\pi$
$13$	−89.5430	−1.91037	−0.955183	+	0.296016i	$0.904342\pi$
$14$	−48.1743	−0.919652
$15$	0	0
$16$	−6.28309	−0.0981733
$17$	28.8042	0.410944	0.205472	−	0.978663i	$-0.434127\pi$
$17$	28.8042	0.410944	0.205472	+	0.978663i	$0.434127\pi$
$18$	−116.748	−1.52876
$19$	−58.8677	−0.710799	−0.355400	−	0.934714i	$-0.615655\pi$
$19$	−58.8677	−0.710799	−0.355400	+	0.934714i	$0.615655\pi$
$20$	0	0
$21$	−247.594	−2.57283
$22$	68.0904	0.659860
$23$	−2.63139	−0.0238558	−0.0119279	−	0.999929i	$-0.503797\pi$
$23$	−2.63139	−0.0238558	−0.0119279	+	0.999929i	$0.503797\pi$
$24$	−220.846	−1.87833
$25$	0	0
$26$	165.452	1.24799
$27$	−343.624	−2.44928
$28$	−119.563	−0.806971
$29$	173.812	1.11297	0.556486	−	0.830857i	$-0.312149\pi$
$29$	173.812	1.11297	0.556486	+	0.830857i	$0.312149\pi$
$30$	0	0
$31$	57.9476	0.335732	0.167866	−	0.985810i	$-0.446312\pi$
$31$	57.9476	0.335732	0.167866	+	0.985810i	$0.446312\pi$
$32$	−174.434	−0.963619
$33$	349.953	1.84603
$34$	−53.2227	−0.268459
$35$	0	0
$36$	−289.753	−1.34145
$37$	−52.0754	−0.231382	−0.115691	−	0.993285i	$-0.536908\pi$
$37$	−52.0754	−0.231382	−0.115691	+	0.993285i	$0.536908\pi$
$38$	108.772	0.464347
$39$	850.348	3.49140
$40$	0	0
$41$	142.704	0.543577	0.271788	−	0.962357i	$-0.412385\pi$
$41$	142.704	0.543577	0.271788	+	0.962357i	$0.412385\pi$
$42$	457.489	1.68076
$43$	43.0000	0.152499
$43$	43.0000	0.152499
$44$	168.992	0.579010
$45$	0	0
$46$	4.86213	0.0155844
$47$	106.853	0.331618	0.165809	−	0.986158i	$-0.446976\pi$
$47$	106.853	0.331618	0.165809	+	0.986158i	$0.446976\pi$
$48$	59.6676	0.179422
$49$	336.750	0.981779
$50$	0	0
$51$	−273.540	−0.751045
$52$	410.631	1.09508
$53$	−244.652	−0.634067	−0.317033	−	0.948414i	$-0.602687\pi$
$53$	−244.652	−0.634067	−0.317033	+	0.948414i	$0.602687\pi$
$54$	634.928	1.60005
$55$	0	0
$56$	606.315	1.44683
$57$	559.039	1.29906
$58$	−321.160	−0.727076
$59$	−127.799	−0.281999	−0.141000	−	0.990010i	$-0.545032\pi$
$59$	−127.799	−0.281999	−0.141000	+	0.990010i	$0.545032\pi$
$60$	0	0
$61$	−443.613	−0.931128	−0.465564	−	0.885014i	$-0.654149\pi$
$61$	−443.613	−0.931128	−0.465564	+	0.885014i	$0.654149\pi$
$62$	−107.072	−0.219325
$63$	1647.34	3.29437
$64$	372.573	0.727681
$65$	0	0
$66$	−646.622	−1.20597
$67$	117.896	0.214975	0.107487	−	0.994206i	$-0.465720\pi$
$67$	117.896	0.214975	0.107487	+	0.994206i	$0.465720\pi$
$68$	−132.092	−0.235566
$69$	24.9891	0.0435991
$70$	0	0
$71$	816.799	1.36530	0.682650	−	0.730746i	$-0.260827\pi$
$71$	816.799	1.36530	0.682650	+	0.730746i	$0.260827\pi$
$72$	1469.37	2.40510
$73$	620.953	0.995576	0.497788	−	0.867299i	$-0.334146\pi$
$73$	620.953	0.995576	0.497788	+	0.867299i	$0.334146\pi$
$74$	96.2217	0.151156
$75$	0	0
$76$	269.959	0.407453
$77$	−960.770	−1.42195
$78$	−1571.22	−2.28085
$79$	377.771	0.538007	0.269003	−	0.963139i	$-0.413306\pi$
$79$	377.771	0.538007	0.269003	+	0.963139i	$0.413306\pi$
$80$	0	0
$81$	1557.27	2.13617
$82$	−263.680	−0.355105
$83$	1453.23	1.92184	0.960919	−	0.276829i	$-0.0892835\pi$
$83$	1453.23	1.92184	0.960919	+	0.276829i	$0.0892835\pi$
$84$	1135.43	1.47483
$85$	0	0
$86$	−79.4528	−0.0996235
$87$	−1650.62	−2.03408
$88$	−856.975	−1.03811
$89$	627.993	0.747945	0.373973	−	0.927440i	$-0.377995\pi$
$89$	627.993	0.747945	0.373973	+	0.927440i	$0.377995\pi$
$90$	0	0
$91$	−2334.57	−2.68933
$92$	12.0672	0.0136749
$93$	−550.302	−0.613587
$94$	−197.436	−0.216638
$95$	0	0
$96$	1656.52	1.76112
$97$	817.163	0.855365	0.427682	−	0.903929i	$-0.359330\pi$
$97$	817.163	0.855365	0.427682	+	0.903929i	$0.359330\pi$
$98$	−622.227	−0.641372
$99$	−2328.38	−2.36374
$100$	0	0
$101$	513.438	0.505832	0.252916	−	0.967488i	$-0.418610\pi$
$101$	513.438	0.505832	0.252916	+	0.967488i	$0.418610\pi$
$102$	505.431	0.490639
$103$	−689.788	−0.659872	−0.329936	−	0.944003i	$-0.607027\pi$
$103$	−689.788	−0.659872	−0.329936	+	0.944003i	$0.607027\pi$
$104$	−2082.36	−1.96338
$105$	0	0
$106$	452.053	0.414220
$107$	−320.710	−0.289759	−0.144879	−	0.989449i	$-0.546279\pi$
$107$	−320.710	−0.289759	−0.144879	+	0.989449i	$0.546279\pi$
$108$	1575.81	1.40400
$109$	−1691.51	−1.48640	−0.743200	−	0.669069i	$-0.766693\pi$
$109$	−1691.51	−1.48640	−0.743200	+	0.669069i	$0.766693\pi$
$110$	0	0
$111$	494.535	0.422876
$112$	−163.813	−0.138204
$113$	−856.360	−0.712916	−0.356458	−	0.934311i	$-0.616016\pi$
$113$	−856.360	−0.712916	−0.356458	+	0.934311i	$0.616016\pi$
$114$	−1032.96	−0.848645
$115$	0	0
$116$	−797.079	−0.637990
$117$	−5657.70	−4.47055
$118$	236.139	0.184223
$119$	750.984	0.578509
$120$	0	0
$121$	26.9674	0.0202610
$122$	819.682	0.608283
$123$	−1355.19	−0.993445
$124$	−265.739	−0.192452
$125$	0	0
$126$	−3043.85	−2.15213
$127$	2233.72	1.56071	0.780357	−	0.625335i	$-0.215038\pi$
$127$	2233.72	1.56071	0.780357	+	0.625335i	$0.215038\pi$
$128$	707.051	0.488243
$129$	−408.351	−0.278708
$130$	0	0
$131$	−2051.51	−1.36825	−0.684126	−	0.729364i	$-0.739816\pi$
$131$	−2051.51	−1.36825	−0.684126	+	0.729364i	$0.739816\pi$
$132$	−1604.83	−1.05820
$133$	−1534.80	−1.00063
$134$	−217.841	−0.140437
$135$	0	0
$136$	669.853	0.422349
$137$	−2594.49	−1.61797	−0.808986	−	0.587827i	$-0.799983\pi$
$137$	−2594.49	−1.61797	−0.808986	+	0.587827i	$0.799983\pi$
$138$	−46.1734	−0.0284822
$139$	1140.44	0.695905	0.347953	−	0.937512i	$-0.386877\pi$
$139$	1140.44	0.695905	0.347953	+	0.937512i	$0.386877\pi$
$140$	0	0
$141$	−1014.73	−0.606068
$142$	−1509.23	−0.891916
$143$	3299.71	1.92962
$144$	−396.992	−0.229741
$145$	0	0
$146$	−1147.36	−0.650385
$147$	−3197.96	−1.79431
$148$	238.810	0.132636
$149$	−2112.03	−1.16124	−0.580618	−	0.814176i	$-0.697189\pi$
$149$	−2112.03	−1.16124	−0.580618	+	0.814176i	$0.697189\pi$
$150$	0	0
$151$	−1351.31	−0.728265	−0.364132	−	0.931347i	$-0.618634\pi$
$151$	−1351.31	−0.728265	−0.364132	+	0.931347i	$0.618634\pi$
$152$	−1368.99	−0.730526
$153$	1819.97	0.961672
$154$	1775.25	0.928922
$155$	0	0
$156$	−3899.57	−2.00138
$157$	1506.02	0.765562	0.382781	−	0.923839i	$-0.374966\pi$
$157$	1506.02	0.765562	0.382781	+	0.923839i	$0.374966\pi$
$158$	−698.022	−0.351466
$159$	2323.35	1.15883
$160$	0	0
$161$	−68.6057	−0.0335832
$162$	−2877.43	−1.39551
$163$	1258.30	0.604647	0.302323	−	0.953205i	$-0.402238\pi$
$163$	1258.30	0.604647	0.302323	+	0.953205i	$0.402238\pi$
$164$	−654.420	−0.311595
$165$	0	0
$166$	−2685.19	−1.25549
$167$	−2764.50	−1.28098	−0.640489	−	0.767967i	$-0.721268\pi$
$167$	−2764.50	−1.28098	−0.640489	+	0.767967i	$0.721268\pi$
$168$	−5757.89	−2.64423
$169$	5820.95	2.64950
$170$	0	0
$171$	−3719.51	−1.66338
$172$	−197.192	−0.0874170
$173$	−1004.21	−0.441322	−0.220661	−	0.975351i	$-0.570821\pi$
$173$	−1004.21	−0.441322	−0.220661	+	0.975351i	$0.570821\pi$
$174$	3049.91	1.32881
$175$	0	0
$176$	231.536	0.0991628
$177$	1213.64	0.515384
$178$	−1160.37	−0.488614
$179$	2666.39	1.11338	0.556692	−	0.830719i	$-0.312070\pi$
$179$	2666.39	1.11338	0.556692	+	0.830719i	$0.312070\pi$
$180$	0	0
$181$	3016.21	1.23863	0.619317	−	0.785141i	$-0.287409\pi$
$181$	3016.21	1.23863	0.619317	+	0.785141i	$0.287409\pi$
$182$	4313.67	1.75687
$183$	4212.79	1.70174
$184$	−61.1941	−0.0245179
$185$	0	0
$186$	1016.81	0.400841
$187$	−1061.45	−0.415086
$188$	−490.010	−0.190094
$189$	−8958.98	−3.44799
$190$	0	0
$191$	1413.15	0.535352	0.267676	−	0.963509i	$-0.413744\pi$
$191$	1413.15	0.535352	0.267676	+	0.963509i	$0.413744\pi$
$192$	−3538.15	−1.32992
$193$	1246.60	0.464934	0.232467	−	0.972604i	$-0.425320\pi$
$193$	1246.60	0.464934	0.232467	+	0.972604i	$0.425320\pi$
$194$	−1509.91	−0.558788
$195$	0	0
$196$	−1544.29	−0.562787
$197$	4931.17	1.78341	0.891704	−	0.452619i	$-0.149510\pi$
$197$	4931.17	1.78341	0.891704	+	0.452619i	$0.149510\pi$
$198$	4302.23	1.54417
$199$	552.461	0.196799	0.0983993	−	0.995147i	$-0.468628\pi$
$199$	552.461	0.196799	0.0983993	+	0.995147i	$0.468628\pi$
$200$	0	0
$201$	−1119.60	−0.392889
$202$	−948.700	−0.330447
$203$	4531.64	1.56679
$204$	1254.42	0.430523
$205$	0	0
$206$	1274.55	0.431078
$207$	−166.262	−0.0558263
$208$	562.607	0.187547
$209$	2169.31	0.717964
$210$	0	0
$211$	2302.22	0.751145	0.375572	−	0.926793i	$-0.377446\pi$
$211$	2302.22	0.751145	0.375572	+	0.926793i	$0.377446\pi$
$212$	1121.94	0.363467
$213$	−7756.76	−2.49523
$214$	592.588	0.189292
$215$	0	0
$216$	−7991.12	−2.51725
$217$	1510.81	0.472629
$218$	3125.48	0.971028
$219$	−5896.90	−1.81952
$220$	0	0
$221$	−2579.21	−0.785053
$222$	−913.773	−0.276254
$223$	−2558.41	−0.768269	−0.384135	−	0.923277i	$-0.625500\pi$
$223$	−2558.41	−0.768269	−0.384135	+	0.923277i	$0.625500\pi$
$224$	−4547.84	−1.35654
$225$	0	0
$226$	1582.33	0.465730
$227$	−3622.76	−1.05926	−0.529628	−	0.848230i	$-0.677669\pi$
$227$	−3622.76	−1.05926	−0.529628	+	0.848230i	$0.677669\pi$
$228$	−2563.67	−0.744664
$229$	1155.46	0.333428	0.166714	−	0.986005i	$-0.446684\pi$
$229$	1155.46	0.333428	0.166714	+	0.986005i	$0.446684\pi$
$230$	0	0
$231$	9123.98	2.59876
$232$	4042.08	1.14386
$233$	−527.800	−0.148401	−0.0742003	−	0.997243i	$-0.523640\pi$
$233$	−527.800	−0.148401	−0.0742003	+	0.997243i	$0.523640\pi$
$234$	10454.0	2.92050
$235$	0	0
$236$	586.066	0.161651
$237$	−3587.51	−0.983266
$238$	−1387.62	−0.377925
$239$	−1341.41	−0.363048	−0.181524	−	0.983387i	$-0.558103\pi$
$239$	−1341.41	−0.363048	−0.181524	+	0.983387i	$0.558103\pi$
$240$	0	0
$241$	−3738.93	−0.999361	−0.499680	−	0.866210i	$-0.666549\pi$
$241$	−3738.93	−0.999361	−0.499680	+	0.866210i	$0.666549\pi$
$242$	−49.8287	−0.0132360
$243$	−5510.79	−1.45480
$244$	2034.34	0.533752
$245$	0	0
$246$	2504.05	0.648993
$247$	5271.19	1.35789
$248$	1347.59	0.345050
$249$	−13800.6	−3.51237
$250$	0	0
$251$	−1741.62	−0.437969	−0.218985	−	0.975728i	$-0.570274\pi$
$251$	−1741.62	−0.437969	−0.218985	+	0.975728i	$0.570274\pi$
$252$	−7554.46	−1.88844
$253$	96.9684	0.0240963
$254$	−4127.33	−1.01957
$255$	0	0
$256$	−4287.03	−1.04664
$257$	−4121.68	−1.00040	−0.500200	−	0.865910i	$-0.666740\pi$
$257$	−4121.68	−1.00040	−0.500200	+	0.865910i	$0.666740\pi$
$258$	754.527	0.182073
$259$	−1357.71	−0.325730
$260$	0	0
$261$	10982.2	2.60452
$262$	3790.65	0.893844
$263$	−4315.46	−1.01180	−0.505898	−	0.862593i	$-0.668839\pi$
$263$	−4315.46	−1.01180	−0.505898	+	0.862593i	$0.668839\pi$
$264$	8138.30	1.89726
$265$	0	0
$266$	2835.91	0.653688
$267$	−5963.76	−1.36695
$268$	−540.654	−0.123230
$269$	5195.44	1.17759	0.588794	−	0.808283i	$-0.299603\pi$
$269$	5195.44	1.17759	0.588794	+	0.808283i	$0.299603\pi$
$270$	0	0
$271$	−7874.15	−1.76502	−0.882510	−	0.470294i	$-0.844148\pi$
$271$	−7874.15	−1.76502	−0.882510	+	0.470294i	$0.844148\pi$
$272$	−180.979	−0.0403437
$273$	22170.3	4.91504
$274$	4793.94	1.05698
$275$	0	0
$276$	−114.596	−0.0249924
$277$	175.471	0.0380615	0.0190307	−	0.999819i	$-0.493942\pi$
$277$	175.471	0.0380615	0.0190307	+	0.999819i	$0.493942\pi$
$278$	−2107.24	−0.454617
$279$	3661.37	0.785665
$280$	0	0
$281$	7263.01	1.54190	0.770951	−	0.636894i	$-0.219781\pi$
$281$	7263.01	1.54190	0.770951	+	0.636894i	$0.219781\pi$
$282$	1874.96	0.395929
$283$	−2314.68	−0.486196	−0.243098	−	0.970002i	$-0.578164\pi$
$283$	−2314.68	−0.486196	−0.243098	+	0.970002i	$0.578164\pi$
$284$	−3745.72	−0.782633
$285$	0	0
$286$	−6097.01	−1.26057
$287$	3720.58	0.765224
$288$	−11021.4	−2.25502
$289$	−4083.32	−0.831125
$290$	0	0
$291$	−7760.22	−1.56327
$292$	−2847.60	−0.570696
$293$	−8723.52	−1.73936	−0.869681	−	0.493614i	$-0.835676\pi$
$293$	−8723.52	−1.73936	−0.869681	+	0.493614i	$0.835676\pi$
$294$	5909.00	1.17218
$295$	0	0
$296$	−1211.03	−0.237804
$297$	12662.8	2.47397
$298$	3902.48	0.758607
$299$	235.623	0.0455733
$300$	0	0
$301$	1121.10	0.214681
$302$	2496.87	0.475757
$303$	−4875.88	−0.924462
$304$	369.871	0.0697815
$305$	0	0
$306$	−3362.83	−0.628236
$307$	−1579.68	−0.293672	−0.146836	−	0.989161i	$-0.546909\pi$
$307$	−1579.68	−0.293672	−0.146836	+	0.989161i	$0.546909\pi$
$308$	4405.95	0.815105
$309$	6550.59	1.20599
$310$	0	0
$311$	−5604.24	−1.02182	−0.510912	−	0.859633i	$-0.670692\pi$
$311$	−5604.24	−1.02182	−0.510912	+	0.859633i	$0.670692\pi$
$312$	19775.2	3.58830
$313$	−3429.86	−0.619384	−0.309692	−	0.950837i	$-0.600226\pi$
$313$	−3429.86	−0.619384	−0.309692	+	0.950837i	$0.600226\pi$
$314$	−2782.73	−0.500123
$315$	0	0
$316$	−1732.40	−0.308403
$317$	−4493.00	−0.796064	−0.398032	−	0.917372i	$-0.630307\pi$
$317$	−4493.00	−0.796064	−0.398032	+	0.917372i	$0.630307\pi$
$318$	−4292.94	−0.757032
$319$	−6405.09	−1.12419
$320$	0	0
$321$	3045.63	0.529566
$322$	126.766	0.0219390
$323$	−1695.64	−0.292098
$324$	−7141.40	−1.22452
$325$	0	0
$326$	−2325.01	−0.395001
$327$	16063.5	2.71656
$328$	3318.64	0.558662
$329$	2785.86	0.466837
$330$	0	0
$331$	4433.87	0.736277	0.368139	−	0.929771i	$-0.379995\pi$
$331$	4433.87	0.736277	0.368139	+	0.929771i	$0.379995\pi$
$332$	−6664.30	−1.10166
$333$	−3290.34	−0.541470
$334$	5108.07	0.836831
$335$	0	0
$336$	1555.65	0.252583
$337$	−6498.33	−1.05040	−0.525202	−	0.850977i	$-0.676010\pi$
$337$	−6498.33	−1.05040	−0.525202	+	0.850977i	$0.676010\pi$
$338$	−10755.6	−1.73085
$339$	8132.45	1.30293
$340$	0	0
$341$	−2135.41	−0.339116
$342$	6872.69	1.08664
$343$	−162.945	−0.0256507
$344$	999.982	0.156731
$345$	0	0
$346$	1855.52	0.288305
$347$	11973.6	1.85237	0.926187	−	0.377064i	$-0.123066\pi$
$347$	11973.6	1.85237	0.926187	+	0.377064i	$0.123066\pi$
$348$	7569.49	1.16600
$349$	5611.30	0.860648	0.430324	−	0.902674i	$-0.358399\pi$
$349$	5611.30	0.860648	0.430324	+	0.902674i	$0.358399\pi$
$350$	0	0
$351$	30769.1	4.67902
$352$	6427.99	0.973332
$353$	2022.00	0.304874	0.152437	−	0.988313i	$-0.451288\pi$
$353$	2022.00	0.304874	0.152437	+	0.988313i	$0.451288\pi$
$354$	−2242.50	−0.336688
$355$	0	0
$356$	−2879.88	−0.428746
$357$	−7131.74	−1.05729
$358$	−4926.81	−0.727346
$359$	10135.3	1.49003	0.745014	−	0.667049i	$-0.232443\pi$
$359$	10135.3	1.49003	0.745014	+	0.667049i	$0.232443\pi$
$360$	0	0
$361$	−3393.59	−0.494765
$362$	−5573.17	−0.809169
$363$	−256.097	−0.0370292
$364$	10706.0	1.54161
$365$	0	0
$366$	−7784.13	−1.11170
$367$	4379.58	0.622922	0.311461	−	0.950259i	$-0.399182\pi$
$367$	4379.58	0.622922	0.311461	+	0.950259i	$0.399182\pi$
$368$	16.5333	0.00234200
$369$	9016.64	1.27205
$370$	0	0
$371$	−6378.57	−0.892612
$372$	2523.60	0.351728
$373$	−4392.98	−0.609813	−0.304906	−	0.952382i	$-0.598625\pi$
$373$	−4392.98	−0.609813	−0.304906	+	0.952382i	$0.598625\pi$
$374$	1961.29	0.271165
$375$	0	0
$376$	2484.90	0.340821
$377$	−15563.7	−2.12618
$378$	16553.9	2.25248
$379$	−878.629	−0.119082	−0.0595411	−	0.998226i	$-0.518964\pi$
$379$	−878.629	−0.119082	−0.0595411	+	0.998226i	$0.518964\pi$
$380$	0	0
$381$	−21212.6	−2.85237
$382$	−2611.14	−0.349732
$383$	−5061.60	−0.675289	−0.337644	−	0.941274i	$-0.609630\pi$
$383$	−5061.60	−0.675289	−0.337644	+	0.941274i	$0.609630\pi$
$384$	−6714.54	−0.892317
$385$	0	0
$386$	−2303.39	−0.303730
$387$	2716.92	0.356870
$388$	−3747.39	−0.490322
$389$	−3417.17	−0.445392	−0.222696	−	0.974888i	$-0.571486\pi$
$389$	−3417.17	−0.445392	−0.222696	+	0.974888i	$0.571486\pi$
$390$	0	0
$391$	−75.7952	−0.00980339
$392$	7831.26	1.00903
$393$	19482.2	2.50063
$394$	−9111.52	−1.16506
$395$	0	0
$396$	10677.6	1.35497
$397$	−7634.34	−0.965130	−0.482565	−	0.875860i	$-0.660295\pi$
$397$	−7634.34	−0.965130	−0.482565	+	0.875860i	$0.660295\pi$
$398$	−1020.80	−0.128564
$399$	14575.3	1.82876
$400$	0	0
$401$	−8402.74	−1.04642	−0.523208	−	0.852205i	$-0.675265\pi$
$401$	−8402.74	−1.04642	−0.523208	+	0.852205i	$0.675265\pi$
$402$	2068.74	0.256665
$403$	−5188.80	−0.641372
$404$	−2354.55	−0.289959
$405$	0	0
$406$	−8373.30	−1.02355
$407$	1919.01	0.233714
$408$	−6361.28	−0.771888
$409$	−11792.8	−1.42571	−0.712857	−	0.701310i	$-0.752599\pi$
$409$	−11792.8	−1.42571	−0.712857	+	0.701310i	$0.752599\pi$
$410$	0	0
$411$	24638.7	2.95702
$412$	3163.27	0.378260
$413$	−3331.97	−0.396986
$414$	307.210	0.0364699
$415$	0	0
$416$	15619.3	1.84086
$417$	−10830.2	−1.27184
$418$	−4008.32	−0.469028
$419$	−10631.9	−1.23962	−0.619811	−	0.784751i	$-0.712791\pi$
$419$	−10631.9	−1.23962	−0.619811	+	0.784751i	$0.712791\pi$
$420$	0	0
$421$	−3136.52	−0.363099	−0.181550	−	0.983382i	$-0.558111\pi$
$421$	−3136.52	−0.363099	−0.181550	+	0.983382i	$0.558111\pi$
$422$	−4253.91	−0.490704
$423$	6751.39	0.776037
$424$	−5689.48	−0.651664
$425$	0	0
$426$	14332.5	1.63007
$427$	−11565.9	−1.31080
$428$	1470.73	0.166099
$429$	−31335.8	−3.52659
$430$	0	0
$431$	−170.380	−0.0190416	−0.00952080	−	0.999955i	$-0.503031\pi$
$431$	−170.380	−0.0190416	−0.00952080	+	0.999955i	$0.503031\pi$
$432$	2159.02	0.240454
$433$	−2093.65	−0.232365	−0.116183	−	0.993228i	$-0.537066\pi$
$433$	−2093.65	−0.232365	−0.116183	+	0.993228i	$0.537066\pi$
$434$	−2791.59	−0.308757
$435$	0	0
$436$	7757.04	0.852052
$437$	154.904	0.0169567
$438$	10895.9	1.18865
$439$	−10860.1	−1.18070	−0.590348	−	0.807149i	$-0.701010\pi$
$439$	−10860.1	−1.18070	−0.590348	+	0.807149i	$0.701010\pi$
$440$	0	0
$441$	21277.3	2.29751
$442$	4765.72	0.512855
$443$	−8256.28	−0.885480	−0.442740	−	0.896650i	$-0.645994\pi$
$443$	−8256.28	−0.885480	−0.442740	+	0.896650i	$0.645994\pi$
$444$	−2267.87	−0.242406
$445$	0	0
$446$	4727.29	0.501891
$447$	20057.0	2.12229
$448$	9713.73	1.02440
$449$	−6792.03	−0.713888	−0.356944	−	0.934126i	$-0.616181\pi$
$449$	−6792.03	−0.713888	−0.356944	+	0.934126i	$0.616181\pi$
$450$	0	0
$451$	−5258.73	−0.549056
$452$	3927.14	0.408666
$453$	12832.8	1.33098
$454$	6693.93	0.691986
$455$	0	0
$456$	13000.7	1.33512
$457$	−4004.62	−0.409908	−0.204954	−	0.978772i	$-0.565705\pi$
$457$	−4004.62	−0.409908	−0.204954	+	0.978772i	$0.565705\pi$
$458$	−2134.99	−0.217820
$459$	−9897.82	−1.00652
$460$	0	0
$461$	1164.36	0.117635	0.0588175	−	0.998269i	$-0.481267\pi$
$461$	1164.36	0.117635	0.0588175	+	0.998269i	$0.481267\pi$
$462$	−16858.8	−1.69771
$463$	−2566.99	−0.257664	−0.128832	−	0.991666i	$-0.541123\pi$
$463$	−2566.99	−0.257664	−0.128832	+	0.991666i	$0.541123\pi$
$464$	−1092.08	−0.109264
$465$	0	0
$466$	975.237	0.0969463
$467$	7654.43	0.758469	0.379234	−	0.925301i	$-0.376187\pi$
$467$	7654.43	0.758469	0.379234	+	0.925301i	$0.376187\pi$
$468$	25945.4	2.56266
$469$	3073.79	0.302632
$470$	0	0
$471$	−14301.9	−1.39915
$472$	−2972.01	−0.289826
$473$	−1584.58	−0.154036
$474$	6628.79	0.642343
$475$	0	0
$476$	−3443.90	−0.331620
$477$	−15458.1	−1.48381
$478$	2478.57	0.237170
$479$	−8754.20	−0.835051	−0.417526	−	0.908665i	$-0.637103\pi$
$479$	−8754.20	−0.835051	−0.417526	+	0.908665i	$0.637103\pi$
$480$	0	0
$481$	4662.98	0.442024
$482$	6908.58	0.652857
$483$	651.517	0.0613769
$484$	−123.668	−0.0116142
$485$	0	0
$486$	10182.5	0.950386
$487$	9406.39	0.875245	0.437623	−	0.899159i	$-0.355821\pi$
$487$	9406.39	0.875245	0.437623	+	0.899159i	$0.355821\pi$
$488$	−10316.4	−0.956970
$489$	−11949.5	−1.10506
$490$	0	0
$491$	6362.18	0.584768	0.292384	−	0.956301i	$-0.405551\pi$
$491$	6362.18	0.584768	0.292384	+	0.956301i	$0.405551\pi$
$492$	6214.73	0.569475
$493$	5006.53	0.457369
$494$	−9739.80	−0.887073
$495$	0	0
$496$	−364.090	−0.0329599
$497$	21295.6	1.92201
$498$	25500.0	2.29454
$499$	11574.8	1.03840	0.519198	−	0.854654i	$-0.326231\pi$
$499$	11574.8	1.03840	0.519198	+	0.854654i	$0.326231\pi$
$500$	0	0
$501$	26253.2	2.34113
$502$	3218.07	0.286114
$503$	−11443.5	−1.01439	−0.507196	−	0.861831i	$-0.669318\pi$
$503$	−11443.5	−1.01439	−0.507196	+	0.861831i	$0.669318\pi$
$504$	38309.5	3.38580
$505$	0	0
$506$	−179.172	−0.0157415
$507$	−55278.8	−4.84225
$508$	−10243.5	−0.894651
$509$	−17397.9	−1.51502	−0.757511	−	0.652822i	$-0.773585\pi$
$509$	−17397.9	−1.51502	−0.757511	+	0.652822i	$0.773585\pi$
$510$	0	0
$511$	16189.5	1.40153
$512$	2264.91	0.195499
$513$	20228.4	1.74095
$514$	7615.79	0.653537
$515$	0	0
$516$	1872.64	0.159764
$517$	−3937.58	−0.334961
$518$	2508.70	0.212791
$519$	9536.53	0.806565
$520$	0	0
$521$	−23236.4	−1.95394	−0.976972	−	0.213369i	$-0.931556\pi$
$521$	−23236.4	−1.95394	−0.976972	+	0.213369i	$0.931556\pi$
$522$	−20292.2	−1.70147
$523$	6523.69	0.545432	0.272716	−	0.962095i	$-0.412078\pi$
$523$	6523.69	0.545432	0.272716	+	0.962095i	$0.412078\pi$
$524$	9407.91	0.784325
$525$	0	0
$526$	7973.85	0.660981
$527$	1669.13	0.137967
$528$	−2198.79	−0.181231
$529$	−12160.1	−0.999431
$530$	0	0
$531$	−8074.85	−0.659922
$532$	7038.37	0.573594
$533$	−12778.2	−1.03843
$534$	11019.5	0.892995
$535$	0	0
$536$	2741.72	0.220941
$537$	−25321.5	−2.03483
$538$	−9599.82	−0.769289
$539$	−12409.5	−0.991675
$540$	0	0
$541$	−13311.4	−1.05786	−0.528930	−	0.848666i	$-0.677406\pi$
$541$	−13311.4	−1.05786	−0.528930	+	0.848666i	$0.677406\pi$
$542$	14549.4	1.15304
$543$	−28643.5	−2.26374
$544$	−5024.42	−0.395993
$545$	0	0
$546$	−40964.9	−3.21088
$547$	24529.8	1.91740	0.958700	−	0.284420i	$-0.0918010\pi$
$547$	24529.8	1.91740	0.958700	+	0.284420i	$0.0918010\pi$
$548$	11898.0	0.927474
$549$	−28029.3	−2.17898
$550$	0	0
$551$	−10231.9	−0.791099
$552$	581.132	0.0448091
$553$	9849.25	0.757383
$554$	−324.225	−0.0248646
$555$	0	0
$556$	−5229.89	−0.398915
$557$	1732.87	0.131821	0.0659104	−	0.997826i	$-0.479005\pi$
$557$	1732.87	0.131821	0.0659104	+	0.997826i	$0.479005\pi$
$558$	−6765.27	−0.513255
$559$	−3850.35	−0.291328
$560$	0	0
$561$	10080.1	0.758615
$562$	−13420.1	−1.00729
$563$	−13482.0	−1.00924	−0.504618	−	0.863343i	$-0.668366\pi$
$563$	−13482.0	−1.00924	−0.504618	+	0.863343i	$0.668366\pi$
$564$	4653.40	0.347417
$565$	0	0
$566$	4276.92	0.317619
$567$	40601.1	3.00721
$568$	18995.0	1.40319
$569$	23053.6	1.69852	0.849261	−	0.527973i	$-0.177048\pi$
$569$	23053.6	1.69852	0.849261	+	0.527973i	$0.177048\pi$
$570$	0	0
$571$	8791.94	0.644363	0.322181	−	0.946678i	$-0.395584\pi$
$571$	8791.94	0.644363	0.322181	+	0.946678i	$0.395584\pi$
$572$	−15132.0	−1.10612
$573$	−13420.1	−0.978414
$574$	−6874.68	−0.499901
$575$	0	0
$576$	23540.7	1.70289
$577$	12464.3	0.899302	0.449651	−	0.893204i	$-0.351548\pi$
$577$	12464.3	0.899302	0.449651	+	0.893204i	$0.351548\pi$
$578$	7544.91	0.542953
$579$	−11838.4	−0.849718
$580$	0	0
$581$	37888.6	2.70548
$582$	14338.9	1.02125
$583$	9015.58	0.640458
$584$	14440.5	1.02321
$585$	0	0
$586$	16118.8	1.13628
$587$	24395.5	1.71535	0.857674	−	0.514193i	$-0.171909\pi$
$587$	24395.5	1.71535	0.857674	+	0.514193i	$0.171909\pi$
$588$	14665.4	1.02855
$589$	−3411.24	−0.238638
$590$	0	0
$591$	−46829.0	−3.25937
$592$	327.194	0.0227155
$593$	8779.99	0.608012	0.304006	−	0.952670i	$-0.401676\pi$
$593$	8779.99	0.608012	0.304006	+	0.952670i	$0.401676\pi$
$594$	−23397.5	−1.61618
$595$	0	0
$596$	9685.46	0.665658
$597$	−5246.46	−0.359671
$598$	−435.370	−0.0297719
$599$	−14440.3	−0.985001	−0.492501	−	0.870312i	$-0.663917\pi$
$599$	−14440.3	−0.985001	−0.492501	+	0.870312i	$0.663917\pi$
$600$	0	0
$601$	7456.08	0.506056	0.253028	−	0.967459i	$-0.418573\pi$
$601$	7456.08	0.506056	0.253028	+	0.967459i	$0.418573\pi$
$602$	−2071.50	−0.140246
$603$	7449.16	0.503074
$604$	6196.91	0.417464
$605$	0	0
$606$	9009.37	0.603928
$607$	6832.01	0.456842	0.228421	−	0.973563i	$-0.426644\pi$
$607$	6832.01	0.456842	0.228421	+	0.973563i	$0.426644\pi$
$608$	10268.5	0.684939
$609$	−43034.9	−2.86348
$610$	0	0
$611$	−9567.89	−0.633512
$612$	−8346.12	−0.551261
$613$	−12239.8	−0.806460	−0.403230	−	0.915099i	$-0.632113\pi$
$613$	−12239.8	−0.806460	−0.403230	+	0.915099i	$0.632113\pi$
$614$	2918.84	0.191849
$615$	0	0
$616$	−22343.1	−1.46141
$617$	−4307.99	−0.281091	−0.140546	−	0.990074i	$-0.544886\pi$
$617$	−4307.99	−0.281091	−0.140546	+	0.990074i	$0.544886\pi$
$618$	−12103.8	−0.787842
$619$	21923.8	1.42357	0.711786	−	0.702396i	$-0.247887\pi$
$619$	21923.8	1.42357	0.711786	+	0.702396i	$0.247887\pi$
$620$	0	0
$621$	904.210	0.0584295
$622$	10355.2	0.667531
$623$	16373.0	1.05292
$624$	−5342.81	−0.342762
$625$	0	0
$626$	6337.49	0.404628
$627$	−20600.9	−1.31216
$628$	−6906.38	−0.438845
$629$	−1499.99	−0.0950850
$630$	0	0
$631$	13249.3	0.835891	0.417945	−	0.908472i	$-0.362750\pi$
$631$	13249.3	0.835891	0.417945	+	0.908472i	$0.362750\pi$
$632$	8785.21	0.552938
$633$	−21863.1	−1.37280
$634$	8301.91	0.520049
$635$	0	0
$636$	−10654.5	−0.664276
$637$	−30153.6	−1.87556
$638$	11835.0	0.734405
$639$	51608.8	3.19501
$640$	0	0
$641$	−6897.79	−0.425033	−0.212517	−	0.977157i	$-0.568166\pi$
$641$	−6897.79	−0.425033	−0.212517	+	0.977157i	$0.568166\pi$
$642$	−5627.54	−0.345952
$643$	570.068	0.0349631	0.0174816	−	0.999847i	$-0.494435\pi$
$643$	570.068	0.0349631	0.0174816	+	0.999847i	$0.494435\pi$
$644$	314.616	0.0192509
$645$	0	0
$646$	3133.10	0.190821
$647$	−15788.1	−0.959341	−0.479670	−	0.877449i	$-0.659244\pi$
$647$	−15788.1	−0.959341	−0.479670	+	0.877449i	$0.659244\pi$
$648$	36214.9	2.19545
$649$	4709.46	0.284842
$650$	0	0
$651$	−14347.5	−0.863782
$652$	−5770.37	−0.346603
$653$	−21960.3	−1.31604	−0.658019	−	0.753001i	$-0.728606\pi$
$653$	−21960.3	−1.31604	−0.658019	+	0.753001i	$0.728606\pi$
$654$	−29681.2	−1.77466
$655$	0	0
$656$	−896.623	−0.0533647
$657$	39234.4	2.32980
$658$	−5147.55	−0.304973
$659$	−12142.6	−0.717766	−0.358883	−	0.933383i	$-0.616842\pi$
$659$	−12142.6	−0.717766	−0.358883	+	0.933383i	$0.616842\pi$
$660$	0	0
$661$	3554.01	0.209130	0.104565	−	0.994518i	$-0.466655\pi$
$661$	3554.01	0.209130	0.104565	+	0.994518i	$0.466655\pi$
$662$	−8192.65	−0.480992
$663$	24493.6	1.43477
$664$	33795.4	1.97518
$665$	0	0
$666$	6079.69	0.353729
$667$	−457.369	−0.0265508
$668$	12677.6	0.734297
$669$	24296.1	1.40410
$670$	0	0
$671$	16347.4	0.940514
$672$	43188.7	2.47923
$673$	−20271.0	−1.16106	−0.580528	−	0.814240i	$-0.697154\pi$
$673$	−20271.0	−1.16106	−0.580528	+	0.814240i	$0.697154\pi$
$674$	12007.2	0.686203
$675$	0	0
$676$	−26694.0	−1.51878
$677$	−26668.2	−1.51395	−0.756973	−	0.653447i	$-0.773322\pi$
$677$	−26668.2	−1.51395	−0.756973	+	0.653447i	$0.773322\pi$
$678$	−15026.7	−0.851173
$679$	21305.1	1.20415
$680$	0	0
$681$	34403.7	1.93591
$682$	3945.67	0.221536
$683$	5584.15	0.312843	0.156421	−	0.987690i	$-0.450004\pi$
$683$	5584.15	0.312843	0.156421	+	0.987690i	$0.450004\pi$
$684$	17057.1	0.953502
$685$	0	0
$686$	301.079	0.0167569
$687$	−10972.9	−0.609377
$688$	−270.173	−0.0149713
$689$	21906.9	1.21130
$690$	0	0
$691$	−2702.39	−0.148776	−0.0743878	−	0.997229i	$-0.523700\pi$
$691$	−2702.39	−0.148776	−0.0743878	+	0.997229i	$0.523700\pi$
$692$	4605.17	0.252980
$693$	−60705.4	−3.32757
$694$	−22124.0	−1.21011
$695$	0	0
$696$	−38385.7	−2.09053
$697$	4110.48	0.223379
$698$	−10368.2	−0.562240
$699$	5012.27	0.271218
$700$	0	0
$701$	−19885.1	−1.07140	−0.535700	−	0.844408i	$-0.679952\pi$
$701$	−19885.1	−1.07140	−0.535700	+	0.844408i	$0.679952\pi$
$702$	−56853.4	−3.05669
$703$	3065.56	0.164466
$704$	−13729.5	−0.735016
$705$	0	0
$706$	−3736.14	−0.199166
$707$	13386.4	0.712088
$708$	−5565.59	−0.295435
$709$	−7798.56	−0.413090	−0.206545	−	0.978437i	$-0.566222\pi$
$709$	−7798.56	−0.413090	−0.206545	+	0.978437i	$0.566222\pi$
$710$	0	0
$711$	23869.1	1.25902
$712$	14604.2	0.768703
$713$	−152.483	−0.00800916
$714$	13177.6	0.690700
$715$	0	0
$716$	−12227.7	−0.638227
$717$	12738.7	0.663509
$718$	−18727.4	−0.973398
$719$	1118.09	0.0579939	0.0289970	−	0.999579i	$-0.490769\pi$
$719$	1118.09	0.0579939	0.0289970	+	0.999579i	$0.490769\pi$
$720$	0	0
$721$	−17984.2	−0.928939
$722$	6270.47	0.323217
$723$	35506.9	1.82644
$724$	−13831.9	−0.710025
$725$	0	0
$726$	473.200	0.0241902
$727$	1741.54	0.0888449	0.0444225	−	0.999013i	$-0.485855\pi$
$727$	1741.54	0.0888449	0.0444225	+	0.999013i	$0.485855\pi$
$728$	−54291.3	−2.76397
$729$	10287.2	0.522642
$730$	0	0
$731$	1238.58	0.0626683
$732$	−19319.2	−0.975491
$733$	9461.10	0.476744	0.238372	−	0.971174i	$-0.423386\pi$
$733$	9461.10	0.476744	0.238372	+	0.971174i	$0.423386\pi$
$734$	−8092.33	−0.406939
$735$	0	0
$736$	459.003	0.0229879
$737$	−4344.54	−0.217141
$738$	−16660.4	−0.831000
$739$	30605.3	1.52346	0.761728	−	0.647897i	$-0.224351\pi$
$739$	30605.3	1.52346	0.761728	+	0.647897i	$0.224351\pi$
$740$	0	0
$741$	−50058.1	−2.48169
$742$	11785.9	0.583121
$743$	−14556.5	−0.718745	−0.359373	−	0.933194i	$-0.617009\pi$
$743$	−14556.5	−0.718745	−0.359373	+	0.933194i	$0.617009\pi$
$744$	−12797.5	−0.630616
$745$	0	0
$746$	8117.10	0.398375
$747$	91821.1	4.49740
$748$	4867.67	0.237941
$749$	−8361.55	−0.407910
$750$	0	0
$751$	−17528.3	−0.851685	−0.425843	−	0.904797i	$-0.640022\pi$
$751$	−17528.3	−0.851685	−0.425843	+	0.904797i	$0.640022\pi$
$752$	−671.364	−0.0325560
$753$	16539.4	0.800436
$754$	28757.7	1.38898
$755$	0	0
$756$	41084.6	1.97650
$757$	37789.1	1.81436	0.907179	−	0.420744i	$-0.138231\pi$
$757$	37789.1	1.81436	0.907179	+	0.420744i	$0.138231\pi$
$758$	1623.48	0.0777934
$759$	−920.864	−0.0440385
$760$	0	0
$761$	3292.90	0.156856	0.0784281	−	0.996920i	$-0.475010\pi$
$761$	3292.90	0.156856	0.0784281	+	0.996920i	$0.475010\pi$
$762$	39195.4	1.86338
$763$	−44101.2	−2.09249
$764$	−6480.52	−0.306881
$765$	0	0
$766$	9352.52	0.441149
$767$	11443.5	0.538722
$768$	40711.9	1.91285
$769$	−28023.9	−1.31413	−0.657065	−	0.753834i	$-0.728202\pi$
$769$	−28023.9	−1.31413	−0.657065	+	0.753834i	$0.728202\pi$
$770$	0	0
$771$	39141.6	1.82834
$772$	−5716.73	−0.266515
$773$	−22131.0	−1.02975	−0.514875	−	0.857265i	$-0.672162\pi$
$773$	−22131.0	−1.02975	−0.514875	+	0.857265i	$0.672162\pi$
$774$	−5020.16	−0.233134
$775$	0	0
$776$	19003.5	0.879103
$777$	12893.5	0.595306
$778$	6314.04	0.290963
$779$	−8400.67	−0.386374
$780$	0	0
$781$	−30099.6	−1.37906
$782$	140.050	0.00640431
$783$	−59726.2	−2.72598
$784$	−2115.83	−0.0963845
$785$	0	0
$786$	−35998.0	−1.63360
$787$	−5390.88	−0.244173	−0.122087	−	0.992519i	$-0.538959\pi$
$787$	−5390.88	−0.244173	−0.122087	+	0.992519i	$0.538959\pi$
$788$	−22613.6	−1.02231
$789$	40981.9	1.84917
$790$	0	0
$791$	−22327.0	−1.00361
$792$	−54147.3	−2.42934
$793$	39722.4	1.77880
$794$	14106.3	0.630495
$795$	0	0
$796$	−2533.51	−0.112811
$797$	−43815.4	−1.94733	−0.973664	−	0.227986i	$-0.926786\pi$
$797$	−43815.4	−1.94733	−0.973664	+	0.227986i	$0.926786\pi$
$798$	−26931.3	−1.19469
$799$	3077.80	0.136276
$800$	0	0
$801$	39679.2	1.75031
$802$	15526.1	0.683597
$803$	−22882.5	−1.00561
$804$	5134.34	0.225217
$805$	0	0
$806$	9587.56	0.418992
$807$	−49338.6	−2.15217
$808$	11940.2	0.519870
$809$	−19752.4	−0.858415	−0.429208	−	0.903206i	$-0.641207\pi$
$809$	−19752.4	−0.858415	−0.429208	+	0.903206i	$0.641207\pi$
$810$	0	0
$811$	21280.3	0.921398	0.460699	−	0.887556i	$-0.347599\pi$
$811$	21280.3	0.921398	0.460699	+	0.887556i	$0.347599\pi$
$812$	−20781.5	−0.898135
$813$	74777.1	3.22577
$814$	−3545.83	−0.152680
$815$	0	0
$816$	1718.68	0.0737325
$817$	−2531.31	−0.108396
$818$	21790.0	0.931383
$819$	−147508.	−6.29345
$820$	0	0
$821$	−19716.5	−0.838136	−0.419068	−	0.907955i	$-0.637643\pi$
$821$	−19716.5	−0.838136	−0.419068	+	0.907955i	$0.637643\pi$
$822$	−45525.9	−1.93175
$823$	−16269.0	−0.689065	−0.344532	−	0.938774i	$-0.611963\pi$
$823$	−16269.0	−0.689065	−0.344532	+	0.938774i	$0.611963\pi$
$824$	−16041.3	−0.678185
$825$	0	0
$826$	6156.61	0.259341
$827$	27410.0	1.15253	0.576263	−	0.817264i	$-0.304510\pi$
$827$	27410.0	1.15253	0.576263	+	0.817264i	$0.304510\pi$
$828$	762.455	0.0320014
$829$	−25392.8	−1.06385	−0.531923	−	0.846792i	$-0.678531\pi$
$829$	−25392.8	−1.06385	−0.531923	+	0.846792i	$0.678531\pi$
$830$	0	0
$831$	−1666.37	−0.0695615
$832$	−33361.3	−1.39014
$833$	9699.82	0.403456
$834$	20011.4	0.830863
$835$	0	0
$836$	−9948.15	−0.411560
$837$	−19912.2	−0.822302
$838$	19645.0	0.809814
$839$	−20579.5	−0.846823	−0.423412	−	0.905937i	$-0.639168\pi$
$839$	−20579.5	−0.846823	−0.423412	+	0.905937i	$0.639168\pi$
$840$	0	0
$841$	5821.76	0.238704
$842$	5795.48	0.237203
$843$	−68973.4	−2.81799
$844$	−10557.7	−0.430580
$845$	0	0
$846$	−12474.8	−0.506966
$847$	703.094	0.0285225
$848$	1537.17	0.0622484
$849$	21981.4	0.888575
$850$	0	0
$851$	137.031	0.00551980
$852$	35571.4	1.43035
$853$	−6873.98	−0.275921	−0.137961	−	0.990438i	$-0.544055\pi$
$853$	−6873.98	−0.275921	−0.137961	+	0.990438i	$0.544055\pi$
$854$	21370.8	0.856314
$855$	0	0
$856$	−7458.23	−0.297800
$857$	20623.8	0.822049	0.411025	−	0.911624i	$-0.365171\pi$
$857$	20623.8	0.822049	0.411025	+	0.911624i	$0.365171\pi$
$858$	57900.5	2.30384
$859$	40959.1	1.62690	0.813450	−	0.581635i	$-0.197587\pi$
$859$	40959.1	1.62690	0.813450	+	0.581635i	$0.197587\pi$
$860$	0	0
$861$	−35332.7	−1.39853
$862$	314.819	0.0124394
$863$	−33784.0	−1.33258	−0.666292	−	0.745691i	$-0.732120\pi$
$863$	−33784.0	−1.33258	−0.666292	+	0.745691i	$0.732120\pi$
$864$	59939.6	2.36017
$865$	0	0
$866$	3868.52	0.151799
$867$	38777.4	1.51897
$868$	−6928.36	−0.270926
$869$	−13921.1	−0.543430
$870$	0	0
$871$	−10556.8	−0.410680
$872$	−39336.8	−1.52765
$873$	51631.8	2.00169
$874$	−286.223	−0.0110774
$875$	0	0
$876$	27042.3	1.04301
$877$	37125.7	1.42947	0.714736	−	0.699395i	$-0.246547\pi$
$877$	37125.7	1.42947	0.714736	+	0.699395i	$0.246547\pi$
$878$	20066.7	0.771319
$879$	82843.2	3.17887
$880$	0	0
$881$	−108.651	−0.00415499	−0.00207749	−	0.999998i	$-0.500661\pi$
$881$	−108.651	−0.00415499	−0.00207749	+	0.999998i	$0.500661\pi$
$882$	−39314.9	−1.50091
$883$	19622.4	0.747843	0.373921	−	0.927460i	$-0.378013\pi$
$883$	19622.4	0.747843	0.373921	+	0.927460i	$0.378013\pi$
$884$	11827.9	0.450017
$885$	0	0
$886$	15255.5	0.578462
$887$	26012.1	0.984668	0.492334	−	0.870406i	$-0.336144\pi$
$887$	26012.1	0.984668	0.492334	+	0.870406i	$0.336144\pi$
$888$	11500.6	0.434612
$889$	58237.6	2.19710
$890$	0	0
$891$	−57386.2	−2.15770
$892$	11732.5	0.440397
$893$	−6290.17	−0.235714
$894$	−37060.1	−1.38644
$895$	0	0
$896$	18434.3	0.687327
$897$	−2237.60	−0.0832902
$898$	12549.9	0.466365
$899$	10072.0	0.373660
$900$	0	0
$901$	−7047.01	−0.260566
$902$	9716.78	0.358684
$903$	−10646.5	−0.392353
$904$	−19915.0	−0.732702
$905$	0	0
$906$	−23711.6	−0.869498
$907$	42258.2	1.54703	0.773517	−	0.633776i	$-0.218496\pi$
$907$	42258.2	1.54703	0.773517	+	0.633776i	$0.218496\pi$
$908$	16613.5	0.607200
$909$	32441.2	1.18372
$910$	0	0
$911$	6717.75	0.244313	0.122156	−	0.992511i	$-0.461019\pi$
$911$	6717.75	0.244313	0.122156	+	0.992511i	$0.461019\pi$
$912$	−3512.50	−0.127533
$913$	−53552.4	−1.94121
$914$	7399.49	0.267783
$915$	0	0
$916$	−5298.78	−0.191132
$917$	−53486.9	−1.92616
$918$	18288.6	0.657532
$919$	46824.2	1.68073	0.840364	−	0.542023i	$-0.182341\pi$
$919$	46824.2	1.68073	0.840364	+	0.542023i	$0.182341\pi$
$920$	0	0
$921$	15001.5	0.536717
$922$	−2151.44	−0.0768479
$923$	−73138.7	−2.60822
$924$	−41841.3	−1.48969
$925$	0	0
$926$	4743.14	0.168325
$927$	−43583.7	−1.54420
$928$	−30318.7	−1.07248
$929$	14300.0	0.505025	0.252513	−	0.967594i	$-0.418743\pi$
$929$	14300.0	0.505025	0.252513	+	0.967594i	$0.418743\pi$
$930$	0	0
$931$	−19823.7	−0.697848
$932$	2420.41	0.0850679
$933$	53220.8	1.86749
$934$	−14143.4	−0.495489
$935$	0	0
$936$	−131572.	−4.59462
$937$	−44630.3	−1.55604	−0.778019	−	0.628241i	$-0.783775\pi$
$937$	−44630.3	−1.55604	−0.778019	+	0.628241i	$0.783775\pi$
$938$	−5679.56	−0.197702
$939$	32571.8	1.13199
$940$	0	0
$941$	−12069.3	−0.418116	−0.209058	−	0.977903i	$-0.567040\pi$
$941$	−12069.3	−0.418116	−0.209058	+	0.977903i	$0.567040\pi$
$942$	26426.3	0.914028
$943$	−375.511	−0.0129675
$944$	802.970	0.0276848
$945$	0	0
$946$	2927.89	0.100628
$947$	−23634.0	−0.810984	−0.405492	−	0.914099i	$-0.632900\pi$
$947$	−23634.0	−0.810984	−0.405492	+	0.914099i	$0.632900\pi$
$948$	16451.8	0.563640
$949$	−55602.0	−1.90192
$950$	0	0
$951$	42668.0	1.45489
$952$	17464.4	0.594564
$953$	31376.9	1.06652	0.533262	−	0.845950i	$-0.320966\pi$
$953$	31376.9	1.06652	0.533262	+	0.845950i	$0.320966\pi$
$954$	28562.6	0.969339
$955$	0	0
$956$	6151.50	0.208110
$957$	60826.2	2.05458
$958$	16175.5	0.545518
$959$	−67643.6	−2.27771
$960$	0	0
$961$	−26433.1	−0.887284
$962$	−8615.98	−0.288763
$963$	−20263.8	−0.678080
$964$	17146.2	0.572865
$965$	0	0
$966$	−1203.83	−0.0400960
$967$	−32665.7	−1.08631	−0.543154	−	0.839633i	$-0.682770\pi$
$967$	−32665.7	−1.08631	−0.543154	+	0.839633i	$0.682770\pi$
$968$	627.137	0.0208233
$969$	16102.7	0.533842
$970$	0	0
$971$	−41567.8	−1.37381	−0.686907	−	0.726745i	$-0.741032\pi$
$971$	−41567.8	−1.37381	−0.686907	+	0.726745i	$0.741032\pi$
$972$	25271.7	0.833940
$973$	29733.6	0.979665
$974$	−17380.6	−0.571776
$975$	0	0
$976$	2787.26	0.0914119
$977$	25363.2	0.830542	0.415271	−	0.909698i	$-0.363687\pi$
$977$	25363.2	0.830542	0.415271	+	0.909698i	$0.363687\pi$
$978$	22079.5	0.721907
$979$	−23141.9	−0.755484
$980$	0	0
$981$	−106877.	−3.47841
$982$	−11755.7	−0.382014
$983$	3961.23	0.128528	0.0642642	−	0.997933i	$-0.479530\pi$
$983$	3961.23	0.128528	0.0642642	+	0.997933i	$0.479530\pi$
$984$	−31515.6	−1.02102
$985$	0	0
$986$	−9250.76	−0.298787
$987$	−26456.0	−0.853196
$988$	−24172.9	−0.778384
$989$	−113.150	−0.00363798
$990$	0	0
$991$	27940.2	0.895610	0.447805	−	0.894131i	$-0.352206\pi$
$991$	27940.2	0.895610	0.447805	+	0.894131i	$0.352206\pi$
$992$	−10108.0	−0.323518
$993$	−42106.4	−1.34563
$994$	−39348.8	−1.25560
$995$	0	0
$996$	63287.7	2.01340
$997$	15531.3	0.493363	0.246681	−	0.969097i	$-0.420660\pi$
$997$	15531.3	0.493363	0.246681	+	0.969097i	$0.420660\pi$
$998$	−21387.2	−0.678357
$999$	17894.4	0.566719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.4.a.b.1.3		6
5.4	even	2		43.4.a.b.1.4	✓	6
15.14	odd	2		387.4.a.h.1.3		6
20.19	odd	2		688.4.a.i.1.1		6
35.34	odd	2		2107.4.a.c.1.4		6
215.214	odd	2		1849.4.a.c.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.4	✓	6	5.4	even	2
387.4.a.h.1.3		6	15.14	odd	2
688.4.a.i.1.1		6	20.19	odd	2
1075.4.a.b.1.3		6	1.1	even	1	trivial
1849.4.a.c.1.3		6	215.214	odd	2
2107.4.a.c.1.4		6	35.34	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)

\(f(q)\)	\(=\)	\(q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} +O(q^{10})\)	\(q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} -36.8506 q^{11} +43.5497 q^{12} -89.5430 q^{13} -48.1743 q^{14} -6.28309 q^{16} +28.8042 q^{17} -116.748 q^{18} -58.8677 q^{19} -247.594 q^{21} +68.0904 q^{22} -2.63139 q^{23} -220.846 q^{24} +165.452 q^{26} -343.624 q^{27} -119.563 q^{28} +173.812 q^{29} +57.9476 q^{31} -174.434 q^{32} +349.953 q^{33} -53.2227 q^{34} -289.753 q^{36} -52.0754 q^{37} +108.772 q^{38} +850.348 q^{39} +142.704 q^{41} +457.489 q^{42} +43.0000 q^{43} +168.992 q^{44} +4.86213 q^{46} +106.853 q^{47} +59.6676 q^{48} +336.750 q^{49} -273.540 q^{51} +410.631 q^{52} -244.652 q^{53} +634.928 q^{54} +606.315 q^{56} +559.039 q^{57} -321.160 q^{58} -127.799 q^{59} -443.613 q^{61} -107.072 q^{62} +1647.34 q^{63} +372.573 q^{64} -646.622 q^{66} +117.896 q^{67} -132.092 q^{68} +24.9891 q^{69} +816.799 q^{71} +1469.37 q^{72} +620.953 q^{73} +96.2217 q^{74} +269.959 q^{76} -960.770 q^{77} -1571.22 q^{78} +377.771 q^{79} +1557.27 q^{81} -263.680 q^{82} +1453.23 q^{83} +1135.43 q^{84} -79.4528 q^{86} -1650.62 q^{87} -856.975 q^{88} +627.993 q^{89} -2334.57 q^{91} +12.0672 q^{92} -550.302 q^{93} -197.436 q^{94} +1656.52 q^{96} +817.163 q^{97} -622.227 q^{98} -2328.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * q^99

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