LMFDB - Embedded newform 2175.4.a.n.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,4,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2175.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:	$128.329154262$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 $ x^7 - 2x^6 - 37x^5 + 55x^4 + 336x^3 - 227x^2 - 824x - 166
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 435)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$3.57720$ of defining polynomial
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.57720 q^{2} +3.00000 q^{3} +4.79637 q^{4} +10.7316 q^{6} -15.0281 q^{7} -11.4600 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.57720 q^{2} +3.00000 q^{3} +4.79637 q^{4} +10.7316 q^{6} -15.0281 q^{7} -11.4600 q^{8} +9.00000 q^{9} +70.8260 q^{11} +14.3891 q^{12} -62.2117 q^{13} -53.7587 q^{14} -79.3658 q^{16} +67.1848 q^{17} +32.1948 q^{18} +118.988 q^{19} -45.0844 q^{21} +253.359 q^{22} -72.5383 q^{23} -34.3801 q^{24} -222.544 q^{26} +27.0000 q^{27} -72.0804 q^{28} +29.0000 q^{29} -180.227 q^{31} -192.227 q^{32} +212.478 q^{33} +240.334 q^{34} +43.1673 q^{36} +47.8439 q^{37} +425.646 q^{38} -186.635 q^{39} +371.956 q^{41} -161.276 q^{42} +409.069 q^{43} +339.707 q^{44} -259.484 q^{46} -125.891 q^{47} -238.097 q^{48} -117.155 q^{49} +201.555 q^{51} -298.390 q^{52} +215.764 q^{53} +96.5844 q^{54} +172.223 q^{56} +356.965 q^{57} +103.739 q^{58} +356.919 q^{59} -466.115 q^{61} -644.707 q^{62} -135.253 q^{63} -52.7086 q^{64} +760.076 q^{66} +578.359 q^{67} +322.243 q^{68} -217.615 q^{69} +870.924 q^{71} -103.140 q^{72} -411.904 q^{73} +171.147 q^{74} +570.712 q^{76} -1064.38 q^{77} -667.631 q^{78} +1120.23 q^{79} +81.0000 q^{81} +1330.56 q^{82} -1079.28 q^{83} -216.241 q^{84} +1463.32 q^{86} +87.0000 q^{87} -811.668 q^{88} +388.993 q^{89} +934.926 q^{91} -347.920 q^{92} -540.680 q^{93} -450.339 q^{94} -576.681 q^{96} +1528.82 q^{97} -419.088 q^{98} +637.434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9	\( 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9} + 76 q^{11} + 66 q^{12} - 30 q^{13} + 89 q^{14} + 138 q^{16} + 140 q^{17} + 18 q^{18} + 90 q^{19} + 150 q^{21} - 61 q^{22} - 34 q^{23} + 99 q^{24} - 241 q^{26} + 189 q^{27} + 57 q^{28} + 203 q^{29} + 524 q^{31} + 6 q^{32} + 228 q^{33} + 255 q^{34} + 198 q^{36} + 28 q^{37} - 222 q^{38} - 90 q^{39} + 1532 q^{41} + 267 q^{42} + 464 q^{43} + 1475 q^{44} + 72 q^{46} + 360 q^{47} + 414 q^{48} + 569 q^{49} + 420 q^{51} + 205 q^{52} - 282 q^{53} + 54 q^{54} + 1102 q^{56} + 270 q^{57} + 58 q^{58} + 766 q^{59} + 1200 q^{61} - 2856 q^{62} + 450 q^{63} + 701 q^{64} - 183 q^{66} - 1546 q^{67} - 1801 q^{68} - 102 q^{69} + 1802 q^{71} + 297 q^{72} + 220 q^{73} + 1594 q^{74} + 1960 q^{76} - 3222 q^{77} - 723 q^{78} + 1298 q^{79} + 567 q^{81} - 856 q^{82} - 1652 q^{83} + 171 q^{84} + 7628 q^{86} + 609 q^{87} - 550 q^{88} + 2846 q^{89} - 816 q^{91} - 472 q^{92} + 1572 q^{93} + 745 q^{94} + 18 q^{96} - 1110 q^{97} + 761 q^{98} + 684 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9 + 76 * q^11 + 66 * q^12 - 30 * q^13 + 89 * q^14 + 138 * q^16 + 140 * q^17 + 18 * q^18 + 90 * q^19 + 150 * q^21 - 61 * q^22 - 34 * q^23 + 99 * q^24 - 241 * q^26 + 189 * q^27 + 57 * q^28 + 203 * q^29 + 524 * q^31 + 6 * q^32 + 228 * q^33 + 255 * q^34 + 198 * q^36 + 28 * q^37 - 222 * q^38 - 90 * q^39 + 1532 * q^41 + 267 * q^42 + 464 * q^43 + 1475 * q^44 + 72 * q^46 + 360 * q^47 + 414 * q^48 + 569 * q^49 + 420 * q^51 + 205 * q^52 - 282 * q^53 + 54 * q^54 + 1102 * q^56 + 270 * q^57 + 58 * q^58 + 766 * q^59 + 1200 * q^61 - 2856 * q^62 + 450 * q^63 + 701 * q^64 - 183 * q^66 - 1546 * q^67 - 1801 * q^68 - 102 * q^69 + 1802 * q^71 + 297 * q^72 + 220 * q^73 + 1594 * q^74 + 1960 * q^76 - 3222 * q^77 - 723 * q^78 + 1298 * q^79 + 567 * q^81 - 856 * q^82 - 1652 * q^83 + 171 * q^84 + 7628 * q^86 + 609 * q^87 - 550 * q^88 + 2846 * q^89 - 816 * q^91 - 472 * q^92 + 1572 * q^93 + 745 * q^94 + 18 * q^96 - 1110 * q^97 + 761 * q^98 + 684 * 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 $

$2$	3.57720	1.26473	0.632366	−	0.774670i	$-0.282084\pi$
$2$	3.57720	1.26473	0.632366	+	0.774670i	$0.282084\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.79637	0.599546
$5$	0	0
$5$	0	0
$6$	10.7316	0.730193
$7$	−15.0281	−0.811443	−0.405721	−	0.913997i	$-0.632980\pi$
$7$	−15.0281	−0.811443	−0.405721	+	0.913997i	$0.632980\pi$
$8$	−11.4600	−0.506467
$9$	9.00000	0.333333
$10$	0	0
$11$	70.8260	1.94135	0.970674	−	0.240399i	$-0.0772781\pi$
$11$	70.8260	1.94135	0.970674	+	0.240399i	$0.0772781\pi$
$12$	14.3891	0.346148
$13$	−62.2117	−1.32726	−0.663632	−	0.748059i	$-0.730986\pi$
$13$	−62.2117	−1.32726	−0.663632	+	0.748059i	$0.730986\pi$
$14$	−53.7587	−1.02626
$15$	0	0
$16$	−79.3658	−1.24009
$17$	67.1848	0.958513	0.479256	−	0.877675i	$-0.340906\pi$
$17$	67.1848	0.958513	0.479256	+	0.877675i	$0.340906\pi$
$18$	32.1948	0.421577
$19$	118.988	1.43673	0.718364	−	0.695667i	$-0.244891\pi$
$19$	118.988	1.43673	0.718364	+	0.695667i	$0.244891\pi$
$20$	0	0
$21$	−45.0844	−0.468487
$22$	253.359	2.45528
$23$	−72.5383	−0.657621	−0.328810	−	0.944396i	$-0.606648\pi$
$23$	−72.5383	−0.657621	−0.328810	+	0.944396i	$0.606648\pi$
$24$	−34.3801	−0.292409
$25$	0	0
$26$	−222.544	−1.67863
$27$	27.0000	0.192450
$28$	−72.0804	−0.486497
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	−180.227	−1.04418	−0.522092	−	0.852889i	$-0.674848\pi$
$31$	−180.227	−1.04418	−0.522092	+	0.852889i	$0.674848\pi$
$32$	−192.227	−1.06191
$33$	212.478	1.12084
$34$	240.334	1.21226
$35$	0	0
$36$	43.1673	0.199849
$37$	47.8439	0.212581	0.106290	−	0.994335i	$-0.466103\pi$
$37$	47.8439	0.212581	0.106290	+	0.994335i	$0.466103\pi$
$38$	425.646	1.81708
$39$	−186.635	−0.766296
$40$	0	0
$41$	371.956	1.41682	0.708411	−	0.705800i	$-0.249412\pi$
$41$	371.956	1.41682	0.708411	+	0.705800i	$0.249412\pi$
$42$	−161.276	−0.592510
$43$	409.069	1.45075	0.725377	−	0.688352i	$-0.241666\pi$
$43$	409.069	1.45075	0.725377	+	0.688352i	$0.241666\pi$
$44$	339.707	1.16393
$45$	0	0
$46$	−259.484	−0.831714
$47$	−125.891	−0.390705	−0.195353	−	0.980733i	$-0.562585\pi$
$47$	−125.891	−0.390705	−0.195353	+	0.980733i	$0.562585\pi$
$48$	−238.097	−0.715967
$49$	−117.155	−0.341560
$50$	0	0
$51$	201.555	0.553398
$52$	−298.390	−0.795755
$53$	215.764	0.559198	0.279599	−	0.960117i	$-0.409798\pi$
$53$	215.764	0.559198	0.279599	+	0.960117i	$0.409798\pi$
$54$	96.5844	0.243398
$55$	0	0
$56$	172.223	0.410969
$57$	356.965	0.829495
$58$	103.739	0.234855
$59$	356.919	0.787575	0.393788	−	0.919201i	$-0.371165\pi$
$59$	356.919	0.787575	0.393788	+	0.919201i	$0.371165\pi$
$60$	0	0
$61$	−466.115	−0.978358	−0.489179	−	0.872183i	$-0.662704\pi$
$61$	−466.115	−0.978358	−0.489179	+	0.872183i	$0.662704\pi$
$62$	−644.707	−1.32061
$63$	−135.253	−0.270481
$64$	−52.7086	−0.102946
$65$	0	0
$66$	760.076	1.41756
$67$	578.359	1.05459	0.527297	−	0.849681i	$-0.323206\pi$
$67$	578.359	1.05459	0.527297	+	0.849681i	$0.323206\pi$
$68$	322.243	0.574672
$69$	−217.615	−0.379678
$70$	0	0
$71$	870.924	1.45577	0.727885	−	0.685699i	$-0.240503\pi$
$71$	870.924	1.45577	0.727885	+	0.685699i	$0.240503\pi$
$72$	−103.140	−0.168822
$73$	−411.904	−0.660407	−0.330204	−	0.943910i	$-0.607117\pi$
$73$	−411.904	−0.660407	−0.330204	+	0.943910i	$0.607117\pi$
$74$	171.147	0.268857
$75$	0	0
$76$	570.712	0.861384
$77$	−1064.38	−1.57529
$78$	−667.631	−0.969159
$79$	1120.23	1.59538	0.797692	−	0.603065i	$-0.206054\pi$
$79$	1120.23	1.59538	0.797692	+	0.603065i	$0.206054\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1330.56	1.79190
$83$	−1079.28	−1.42730	−0.713652	−	0.700501i	$-0.752960\pi$
$83$	−1079.28	−1.42730	−0.713652	+	0.700501i	$0.752960\pi$
$84$	−216.241	−0.280879
$85$	0	0
$86$	1463.32	1.83481
$87$	87.0000	0.107211
$88$	−811.668	−0.983229
$89$	388.993	0.463294	0.231647	−	0.972800i	$-0.425589\pi$
$89$	388.993	0.463294	0.231647	+	0.972800i	$0.425589\pi$
$90$	0	0
$91$	934.926	1.07700
$92$	−347.920	−0.394274
$93$	−540.680	−0.602859
$94$	−450.339	−0.494137
$95$	0	0
$96$	−576.681	−0.613097
$97$	1528.82	1.60029	0.800147	−	0.599803i	$-0.204755\pi$
$97$	1528.82	1.60029	0.800147	+	0.599803i	$0.204755\pi$
$98$	−419.088	−0.431982
$99$	637.434	0.647116
$100$	0	0
$101$	−1425.50	−1.40439	−0.702193	−	0.711987i	$-0.747796\pi$
$101$	−1425.50	−1.40439	−0.702193	+	0.711987i	$0.747796\pi$
$102$	721.001	0.699899
$103$	1595.68	1.52648	0.763240	−	0.646116i	$-0.223608\pi$
$103$	1595.68	1.52648	0.763240	+	0.646116i	$0.223608\pi$
$104$	712.949	0.672215
$105$	0	0
$106$	771.832	0.707236
$107$	155.104	0.140135	0.0700675	−	0.997542i	$-0.477679\pi$
$107$	155.104	0.140135	0.0700675	+	0.997542i	$0.477679\pi$
$108$	129.502	0.115383
$109$	1212.23	1.06524	0.532618	−	0.846356i	$-0.321208\pi$
$109$	1212.23	1.06524	0.532618	+	0.846356i	$0.321208\pi$
$110$	0	0
$111$	143.532	0.122733
$112$	1192.72	1.00626
$113$	1152.01	0.959043	0.479521	−	0.877530i	$-0.340810\pi$
$113$	1152.01	0.959043	0.479521	+	0.877530i	$0.340810\pi$
$114$	1276.94	1.04909
$115$	0	0
$116$	139.095	0.111333
$117$	−559.905	−0.442421
$118$	1276.77	0.996072
$119$	−1009.66	−0.777778
$120$	0	0
$121$	3685.32	2.76883
$122$	−1667.39	−1.23736
$123$	1115.87	0.818003
$124$	−864.434	−0.626036
$125$	0	0
$126$	−483.828	−0.342086
$127$	−398.743	−0.278604	−0.139302	−	0.990250i	$-0.544486\pi$
$127$	−398.743	−0.278604	−0.139302	+	0.990250i	$0.544486\pi$
$128$	1349.27	0.931715
$129$	1227.21	0.837593
$130$	0	0
$131$	−385.241	−0.256937	−0.128468	−	0.991714i	$-0.541006\pi$
$131$	−385.241	−0.256937	−0.128468	+	0.991714i	$0.541006\pi$
$132$	1019.12	0.671994
$133$	−1788.17	−1.16582
$134$	2068.90	1.33378
$135$	0	0
$136$	−769.941	−0.485455
$137$	351.877	0.219437	0.109719	−	0.993963i	$-0.465005\pi$
$137$	351.877	0.219437	0.109719	+	0.993963i	$0.465005\pi$
$138$	−778.452	−0.480190
$139$	1138.48	0.694711	0.347355	−	0.937734i	$-0.387080\pi$
$139$	1138.48	0.694711	0.347355	+	0.937734i	$0.387080\pi$
$140$	0	0
$141$	−377.674	−0.225574
$142$	3115.47	1.84116
$143$	−4406.21	−2.57668
$144$	−714.292	−0.413364
$145$	0	0
$146$	−1473.46	−0.835238
$147$	−351.466	−0.197200
$148$	229.477	0.127452
$149$	1200.59	0.660107	0.330053	−	0.943962i	$-0.392933\pi$
$149$	1200.59	0.660107	0.330053	+	0.943962i	$0.392933\pi$
$150$	0	0
$151$	−1539.35	−0.829605	−0.414802	−	0.909911i	$-0.636149\pi$
$151$	−1539.35	−0.829605	−0.414802	+	0.909911i	$0.636149\pi$
$152$	−1363.61	−0.727655
$153$	604.664	0.319504
$154$	−3807.51	−1.99232
$155$	0	0
$156$	−895.171	−0.459430
$157$	−223.134	−0.113427	−0.0567136	−	0.998390i	$-0.518062\pi$
$157$	−223.134	−0.113427	−0.0567136	+	0.998390i	$0.518062\pi$
$158$	4007.28	2.01773
$159$	647.293	0.322853
$160$	0	0
$161$	1090.11	0.533622
$162$	289.753	0.140526
$163$	3114.71	1.49671	0.748353	−	0.663301i	$-0.230845\pi$
$163$	3114.71	1.49671	0.748353	+	0.663301i	$0.230845\pi$
$164$	1784.04	0.849450
$165$	0	0
$166$	−3860.79	−1.80516
$167$	1720.78	0.797351	0.398676	−	0.917092i	$-0.369470\pi$
$167$	1720.78	0.797351	0.398676	+	0.917092i	$0.369470\pi$
$168$	516.669	0.237273
$169$	1673.30	0.761629
$170$	0	0
$171$	1070.90	0.478909
$172$	1962.04	0.869793
$173$	−2438.70	−1.07174	−0.535870	−	0.844301i	$-0.680016\pi$
$173$	−2438.70	−1.07174	−0.535870	+	0.844301i	$0.680016\pi$
$174$	311.216	0.135593
$175$	0	0
$176$	−5621.16	−2.40745
$177$	1070.76	0.454707
$178$	1391.50	0.585942
$179$	−2248.00	−0.938676	−0.469338	−	0.883018i	$-0.655507\pi$
$179$	−2248.00	−0.938676	−0.469338	+	0.883018i	$0.655507\pi$
$180$	0	0
$181$	−2357.13	−0.967977	−0.483989	−	0.875074i	$-0.660812\pi$
$181$	−2357.13	−0.967977	−0.483989	+	0.875074i	$0.660812\pi$
$182$	3344.42	1.36211
$183$	−1398.34	−0.564855
$184$	831.292	0.333063
$185$	0	0
$186$	−1934.12	−0.762455
$187$	4758.43	1.86081
$188$	−603.821	−0.234246
$189$	−405.760	−0.156162
$190$	0	0
$191$	1922.56	0.728331	0.364166	−	0.931334i	$-0.381354\pi$
$191$	1922.56	0.728331	0.364166	+	0.931334i	$0.381354\pi$
$192$	−158.126	−0.0594362
$193$	−1840.68	−0.686504	−0.343252	−	0.939243i	$-0.611528\pi$
$193$	−1840.68	−0.686504	−0.343252	+	0.939243i	$0.611528\pi$
$194$	5468.91	2.02394
$195$	0	0
$196$	−561.919	−0.204781
$197$	2712.79	0.981109	0.490555	−	0.871410i	$-0.336794\pi$
$197$	2712.79	0.981109	0.490555	+	0.871410i	$0.336794\pi$
$198$	2280.23	0.818428
$199$	224.631	0.0800185	0.0400093	−	0.999199i	$-0.487261\pi$
$199$	224.631	0.0800185	0.0400093	+	0.999199i	$0.487261\pi$
$200$	0	0
$201$	1735.08	0.608870
$202$	−5099.31	−1.77617
$203$	−435.816	−0.150681
$204$	966.729	0.331787
$205$	0	0
$206$	5708.08	1.93059
$207$	−652.845	−0.219207
$208$	4937.48	1.64593
$209$	8427.48	2.78919
$210$	0	0
$211$	−4160.10	−1.35731	−0.678656	−	0.734456i	$-0.737437\pi$
$211$	−4160.10	−1.35731	−0.678656	+	0.734456i	$0.737437\pi$
$212$	1034.88	0.335265
$213$	2612.77	0.840489
$214$	554.837	0.177233
$215$	0	0
$216$	−309.421	−0.0974696
$217$	2708.47	0.847295
$218$	4336.40	1.34724
$219$	−1235.71	−0.381286
$220$	0	0
$221$	−4179.68	−1.27220
$222$	513.441	0.155225
$223$	1746.41	0.524432	0.262216	−	0.965009i	$-0.415547\pi$
$223$	1746.41	0.524432	0.262216	+	0.965009i	$0.415547\pi$
$224$	2888.81	0.861683
$225$	0	0
$226$	4120.97	1.21293
$227$	−129.508	−0.0378666	−0.0189333	−	0.999821i	$-0.506027\pi$
$227$	−129.508	−0.0378666	−0.0189333	+	0.999821i	$0.506027\pi$
$228$	1712.14	0.497320
$229$	−682.166	−0.196851	−0.0984253	−	0.995144i	$-0.531381\pi$
$229$	−682.166	−0.196851	−0.0984253	+	0.995144i	$0.531381\pi$
$230$	0	0
$231$	−3193.15	−0.909496
$232$	−332.341	−0.0940486
$233$	−1731.11	−0.486732	−0.243366	−	0.969935i	$-0.578252\pi$
$233$	−1731.11	−0.486732	−0.243366	+	0.969935i	$0.578252\pi$
$234$	−2002.89	−0.559544
$235$	0	0
$236$	1711.92	0.472188
$237$	3360.68	0.921095
$238$	−3611.77	−0.983681
$239$	3308.38	0.895402	0.447701	−	0.894183i	$-0.352243\pi$
$239$	3308.38	0.895402	0.447701	+	0.894183i	$0.352243\pi$
$240$	0	0
$241$	3586.39	0.958588	0.479294	−	0.877654i	$-0.340893\pi$
$241$	3586.39	0.958588	0.479294	+	0.877654i	$0.340893\pi$
$242$	13183.1	3.50183
$243$	243.000	0.0641500
$244$	−2235.66	−0.586571
$245$	0	0
$246$	3991.68	1.03455
$247$	−7402.48	−1.90692
$248$	2065.41	0.528844
$249$	−3237.83	−0.824054
$250$	0	0
$251$	−2956.22	−0.743406	−0.371703	−	0.928352i	$-0.621226\pi$
$251$	−2956.22	−0.743406	−0.371703	+	0.928352i	$0.621226\pi$
$252$	−648.724	−0.162166
$253$	−5137.59	−1.27667
$254$	−1426.39	−0.352360
$255$	0	0
$256$	5248.27	1.28132
$257$	−2258.12	−0.548084	−0.274042	−	0.961718i	$-0.588361\pi$
$257$	−2258.12	−0.548084	−0.274042	+	0.961718i	$0.588361\pi$
$258$	4389.96	1.05933
$259$	−719.004	−0.172497
$260$	0	0
$261$	261.000	0.0618984
$262$	−1378.09	−0.324956
$263$	−2908.67	−0.681963	−0.340981	−	0.940070i	$-0.610759\pi$
$263$	−2908.67	−0.681963	−0.340981	+	0.940070i	$0.610759\pi$
$264$	−2435.01	−0.567667
$265$	0	0
$266$	−6396.66	−1.47445
$267$	1166.98	0.267483
$268$	2774.02	0.632277
$269$	−297.910	−0.0675238	−0.0337619	−	0.999430i	$-0.510749\pi$
$269$	−297.910	−0.0675238	−0.0337619	+	0.999430i	$0.510749\pi$
$270$	0	0
$271$	6993.04	1.56752	0.783758	−	0.621067i	$-0.213300\pi$
$271$	6993.04	1.56752	0.783758	+	0.621067i	$0.213300\pi$
$272$	−5332.18	−1.18864
$273$	2804.78	0.621805
$274$	1258.73	0.277529
$275$	0	0
$276$	−1043.76	−0.227634
$277$	−5701.84	−1.23679	−0.618394	−	0.785868i	$-0.712216\pi$
$277$	−5701.84	−1.23679	−0.618394	+	0.785868i	$0.712216\pi$
$278$	4072.58	0.878622
$279$	−1622.04	−0.348061
$280$	0	0
$281$	−1216.34	−0.258223	−0.129112	−	0.991630i	$-0.541213\pi$
$281$	−1216.34	−0.258223	−0.129112	+	0.991630i	$0.541213\pi$
$282$	−1351.02	−0.285290
$283$	−4096.17	−0.860396	−0.430198	−	0.902735i	$-0.641556\pi$
$283$	−4096.17	−0.860396	−0.430198	+	0.902735i	$0.641556\pi$
$284$	4177.27	0.872801
$285$	0	0
$286$	−15761.9	−3.25881
$287$	−5589.80	−1.14967
$288$	−1730.04	−0.353972
$289$	−399.197	−0.0812532
$290$	0	0
$291$	4586.47	0.923931
$292$	−1975.64	−0.395944
$293$	−5854.29	−1.16727	−0.583637	−	0.812015i	$-0.698371\pi$
$293$	−5854.29	−1.16727	−0.583637	+	0.812015i	$0.698371\pi$
$294$	−1257.26	−0.249405
$295$	0	0
$296$	−548.292	−0.107665
$297$	1912.30	0.373613
$298$	4294.74	0.834858
$299$	4512.73	0.872836
$300$	0	0
$301$	−6147.54	−1.17720
$302$	−5506.56	−1.04923
$303$	−4276.51	−0.810822
$304$	−9443.62	−1.78167
$305$	0	0
$306$	2163.00	0.404087
$307$	2748.38	0.510940	0.255470	−	0.966817i	$-0.417770\pi$
$307$	2748.38	0.510940	0.255470	+	0.966817i	$0.417770\pi$
$308$	−5105.17	−0.944461
$309$	4787.05	0.881313
$310$	0	0
$311$	−10289.0	−1.87600	−0.938000	−	0.346634i	$-0.887325\pi$
$311$	−10289.0	−1.87600	−0.938000	+	0.346634i	$0.887325\pi$
$312$	2138.85	0.388104
$313$	−8540.93	−1.54237	−0.771185	−	0.636611i	$-0.780336\pi$
$313$	−8540.93	−1.54237	−0.771185	+	0.636611i	$0.780336\pi$
$314$	−798.196	−0.143455
$315$	0	0
$316$	5373.02	0.956506
$317$	131.153	0.0232375	0.0116187	−	0.999933i	$-0.496302\pi$
$317$	131.153	0.0232375	0.0116187	+	0.999933i	$0.496302\pi$
$318$	2315.50	0.408323
$319$	2053.95	0.360499
$320$	0	0
$321$	465.311	0.0809070
$322$	3899.56	0.674888
$323$	7994.22	1.37712
$324$	388.506	0.0666162
$325$	0	0
$326$	11142.0	1.89293
$327$	3636.70	0.615014
$328$	−4262.63	−0.717574
$329$	1891.91	0.317035
$330$	0	0
$331$	−7274.79	−1.20803	−0.604016	−	0.796972i	$-0.706434\pi$
$331$	−7274.79	−1.20803	−0.604016	+	0.796972i	$0.706434\pi$
$332$	−5176.61	−0.855734
$333$	430.595	0.0708602
$334$	6155.56	1.00844
$335$	0	0
$336$	3578.16	0.580966
$337$	−4663.56	−0.753830	−0.376915	−	0.926248i	$-0.623015\pi$
$337$	−4663.56	−0.753830	−0.376915	+	0.926248i	$0.623015\pi$
$338$	5985.72	0.963256
$339$	3456.03	0.553704
$340$	0	0
$341$	−12764.7	−2.02712
$342$	3830.81	0.605692
$343$	6915.27	1.08860
$344$	−4687.94	−0.734759
$345$	0	0
$346$	−8723.72	−1.35546
$347$	−6050.81	−0.936093	−0.468046	−	0.883704i	$-0.655042\pi$
$347$	−6050.81	−0.936093	−0.468046	+	0.883704i	$0.655042\pi$
$348$	417.284	0.0642781
$349$	12824.0	1.96691	0.983455	−	0.181152i	$-0.0579825\pi$
$349$	12824.0	1.96691	0.983455	+	0.181152i	$0.0579825\pi$
$350$	0	0
$351$	−1679.72	−0.255432
$352$	−13614.7	−2.06155
$353$	−12514.5	−1.88691	−0.943457	−	0.331494i	$-0.892447\pi$
$353$	−12514.5	−1.88691	−0.943457	+	0.331494i	$0.892447\pi$
$354$	3830.32	0.575082
$355$	0	0
$356$	1865.75	0.277766
$357$	−3028.99	−0.449051
$358$	−8041.53	−1.18717
$359$	3394.70	0.499068	0.249534	−	0.968366i	$-0.419723\pi$
$359$	3394.70	0.499068	0.249534	+	0.968366i	$0.419723\pi$
$360$	0	0
$361$	7299.26	1.06419
$362$	−8431.92	−1.22423
$363$	11056.0	1.59859
$364$	4484.25	0.645710
$365$	0	0
$366$	−5002.16	−0.714391
$367$	9991.93	1.42118	0.710592	−	0.703604i	$-0.248427\pi$
$367$	9991.93	1.42118	0.710592	+	0.703604i	$0.248427\pi$
$368$	5757.06	0.815509
$369$	3347.60	0.472274
$370$	0	0
$371$	−3242.54	−0.453758
$372$	−2593.30	−0.361442
$373$	−7219.40	−1.00216	−0.501081	−	0.865400i	$-0.667064\pi$
$373$	−7219.40	−1.00216	−0.501081	+	0.865400i	$0.667064\pi$
$374$	17021.9	2.35342
$375$	0	0
$376$	1442.72	0.197879
$377$	−1804.14	−0.246467
$378$	−1451.48	−0.197503
$379$	10797.8	1.46345	0.731724	−	0.681601i	$-0.238716\pi$
$379$	10797.8	1.46345	0.731724	+	0.681601i	$0.238716\pi$
$380$	0	0
$381$	−1196.23	−0.160852
$382$	6877.37	0.921144
$383$	3396.75	0.453174	0.226587	−	0.973991i	$-0.427243\pi$
$383$	3396.75	0.453174	0.226587	+	0.973991i	$0.427243\pi$
$384$	4047.80	0.537926
$385$	0	0
$386$	−6584.49	−0.868243
$387$	3681.62	0.483585
$388$	7332.80	0.959450
$389$	−4927.07	−0.642192	−0.321096	−	0.947047i	$-0.604051\pi$
$389$	−4927.07	−0.642192	−0.321096	+	0.947047i	$0.604051\pi$
$390$	0	0
$391$	−4873.47	−0.630338
$392$	1342.60	0.172989
$393$	−1155.72	−0.148342
$394$	9704.21	1.24084
$395$	0	0
$396$	3057.37	0.387976
$397$	7777.55	0.983234	0.491617	−	0.870812i	$-0.336406\pi$
$397$	7777.55	0.983234	0.491617	+	0.870812i	$0.336406\pi$
$398$	803.551	0.101202
$399$	−5364.52	−0.673088
$400$	0	0
$401$	6058.22	0.754446	0.377223	−	0.926122i	$-0.376879\pi$
$401$	6058.22	0.754446	0.377223	+	0.926122i	$0.376879\pi$
$402$	6206.71	0.770057
$403$	11212.2	1.38591
$404$	−6837.24	−0.841994
$405$	0	0
$406$	−1559.00	−0.190571
$407$	3388.59	0.412693
$408$	−2309.82	−0.280278
$409$	−15078.2	−1.82291	−0.911454	−	0.411403i	$-0.865039\pi$
$409$	−15078.2	−1.82291	−0.911454	+	0.411403i	$0.865039\pi$
$410$	0	0
$411$	1055.63	0.126692
$412$	7653.48	0.915194
$413$	−5363.83	−0.639073
$414$	−2335.36	−0.277238
$415$	0	0
$416$	11958.8	1.40944
$417$	3415.45	0.401091
$418$	30146.8	3.52758
$419$	5698.22	0.664383	0.332192	−	0.943212i	$-0.392212\pi$
$419$	5698.22	0.664383	0.332192	+	0.943212i	$0.392212\pi$
$420$	0	0
$421$	846.838	0.0980341	0.0490171	−	0.998798i	$-0.484391\pi$
$421$	846.838	0.0980341	0.0490171	+	0.998798i	$0.484391\pi$
$422$	−14881.5	−1.71664
$423$	−1133.02	−0.130235
$424$	−2472.67	−0.283215
$425$	0	0
$426$	9346.41	1.06299
$427$	7004.83	0.793882
$428$	743.934	0.0840173
$429$	−13218.6	−1.48765
$430$	0	0
$431$	−7518.27	−0.840237	−0.420119	−	0.907469i	$-0.638012\pi$
$431$	−7518.27	−0.840237	−0.420119	+	0.907469i	$0.638012\pi$
$432$	−2142.88	−0.238656
$433$	−12686.0	−1.40797	−0.703987	−	0.710213i	$-0.748599\pi$
$433$	−12686.0	−1.40797	−0.703987	+	0.710213i	$0.748599\pi$
$434$	9688.75	1.07160
$435$	0	0
$436$	5814.31	0.638658
$437$	−8631.22	−0.944822
$438$	−4420.39	−0.482225
$439$	10530.4	1.14485	0.572424	−	0.819958i	$-0.306003\pi$
$439$	10530.4	1.14485	0.572424	+	0.819958i	$0.306003\pi$
$440$	0	0
$441$	−1054.40	−0.113853
$442$	−14951.6	−1.60899
$443$	5199.17	0.557608	0.278804	−	0.960348i	$-0.410062\pi$
$443$	5199.17	0.557608	0.278804	+	0.960348i	$0.410062\pi$
$444$	688.430	0.0735843
$445$	0	0
$446$	6247.27	0.663266
$447$	3601.76	0.381113
$448$	792.112	0.0835352
$449$	−11836.7	−1.24412	−0.622058	−	0.782971i	$-0.713703\pi$
$449$	−11836.7	−1.24412	−0.622058	+	0.782971i	$0.713703\pi$
$450$	0	0
$451$	26344.1	2.75055
$452$	5525.46	0.574990
$453$	−4618.04	−0.478973
$454$	−463.274	−0.0478911
$455$	0	0
$456$	−4090.84	−0.420112
$457$	−404.451	−0.0413992	−0.0206996	−	0.999786i	$-0.506589\pi$
$457$	−404.451	−0.0413992	−0.0206996	+	0.999786i	$0.506589\pi$
$458$	−2440.24	−0.248963
$459$	1813.99	0.184466
$460$	0	0
$461$	7072.59	0.714541	0.357270	−	0.934001i	$-0.383707\pi$
$461$	7072.59	0.714541	0.357270	+	0.934001i	$0.383707\pi$
$462$	−11422.5	−1.15027
$463$	6500.22	0.652464	0.326232	−	0.945290i	$-0.394221\pi$
$463$	6500.22	0.652464	0.326232	+	0.945290i	$0.394221\pi$
$464$	−2301.61	−0.230279
$465$	0	0
$466$	−6192.51	−0.615585
$467$	8850.61	0.876997	0.438498	−	0.898732i	$-0.355511\pi$
$467$	8850.61	0.876997	0.438498	+	0.898732i	$0.355511\pi$
$468$	−2685.51	−0.265252
$469$	−8691.65	−0.855742
$470$	0	0
$471$	−669.403	−0.0654872
$472$	−4090.31	−0.398881
$473$	28972.7	2.81642
$474$	12021.8	1.16494
$475$	0	0
$476$	−4842.71	−0.466314
$477$	1941.88	0.186399
$478$	11834.7	1.13244
$479$	−8582.91	−0.818712	−0.409356	−	0.912375i	$-0.634247\pi$
$479$	−8582.91	−0.818712	−0.409356	+	0.912375i	$0.634247\pi$
$480$	0	0
$481$	−2976.45	−0.282150
$482$	12829.2	1.21236
$483$	3270.34	0.308087
$484$	17676.1	1.66004
$485$	0	0
$486$	869.260	0.0811326
$487$	2823.62	0.262732	0.131366	−	0.991334i	$-0.458064\pi$
$487$	2823.62	0.262732	0.131366	+	0.991334i	$0.458064\pi$
$488$	5341.69	0.495506
$489$	9344.14	0.864124
$490$	0	0
$491$	−13116.2	−1.20555	−0.602776	−	0.797911i	$-0.705939\pi$
$491$	−13116.2	−1.20555	−0.602776	+	0.797911i	$0.705939\pi$
$492$	5352.11	0.490430
$493$	1948.36	0.177991
$494$	−26480.2	−2.41174
$495$	0	0
$496$	14303.8	1.29488
$497$	−13088.4	−1.18127
$498$	−11582.4	−1.04221
$499$	−16495.4	−1.47983	−0.739916	−	0.672699i	$-0.765135\pi$
$499$	−16495.4	−1.47983	−0.739916	+	0.672699i	$0.765135\pi$
$500$	0	0
$501$	5162.33	0.460351
$502$	−10575.0	−0.940209
$503$	16677.3	1.47834	0.739169	−	0.673520i	$-0.235219\pi$
$503$	16677.3	1.47834	0.739169	+	0.673520i	$0.235219\pi$
$504$	1550.01	0.136990
$505$	0	0
$506$	−18378.2	−1.61465
$507$	5019.89	0.439726
$508$	−1912.52	−0.167036
$509$	9386.35	0.817373	0.408686	−	0.912675i	$-0.365987\pi$
$509$	9386.35	0.817373	0.408686	+	0.912675i	$0.365987\pi$
$510$	0	0
$511$	6190.15	0.535883
$512$	7979.98	0.688806
$513$	3212.69	0.276498
$514$	−8077.75	−0.693180
$515$	0	0
$516$	5886.13	0.502175
$517$	−8916.37	−0.758495
$518$	−2572.02	−0.218162
$519$	−7316.10	−0.618769
$520$	0	0
$521$	−16530.2	−1.39002	−0.695009	−	0.719001i	$-0.744600\pi$
$521$	−16530.2	−1.39002	−0.695009	+	0.719001i	$0.744600\pi$
$522$	933.649	0.0782849
$523$	18295.9	1.52968	0.764842	−	0.644217i	$-0.222817\pi$
$523$	18295.9	1.52968	0.764842	+	0.644217i	$0.222817\pi$
$524$	−1847.76	−0.154045
$525$	0	0
$526$	−10404.9	−0.862500
$527$	−12108.5	−1.00086
$528$	−16863.5	−1.38994
$529$	−6905.20	−0.567535
$530$	0	0
$531$	3212.27	0.262525
$532$	−8576.74	−0.698964
$533$	−23140.0	−1.88050
$534$	4174.51	0.338294
$535$	0	0
$536$	−6628.01	−0.534117
$537$	−6743.99	−0.541945
$538$	−1065.68	−0.0853994
$539$	−8297.63	−0.663088
$540$	0	0
$541$	−949.695	−0.0754724	−0.0377362	−	0.999288i	$-0.512015\pi$
$541$	−949.695	−0.0754724	−0.0377362	+	0.999288i	$0.512015\pi$
$542$	25015.5	1.98249
$543$	−7071.38	−0.558862
$544$	−12914.7	−1.01786
$545$	0	0
$546$	10033.3	0.786417
$547$	−18017.4	−1.40835	−0.704177	−	0.710024i	$-0.748684\pi$
$547$	−18017.4	−1.40835	−0.704177	+	0.710024i	$0.748684\pi$
$548$	1687.73	0.131563
$549$	−4195.03	−0.326119
$550$	0	0
$551$	3450.67	0.266794
$552$	2493.87	0.192294
$553$	−16834.9	−1.29456
$554$	−20396.6	−1.56420
$555$	0	0
$556$	5460.58	0.416511
$557$	11387.6	0.866263	0.433131	−	0.901331i	$-0.357409\pi$
$557$	11387.6	0.866263	0.433131	+	0.901331i	$0.357409\pi$
$558$	−5802.37	−0.440204
$559$	−25448.9	−1.92553
$560$	0	0
$561$	14275.3	1.07434
$562$	−4351.09	−0.326583
$563$	277.822	0.0207971	0.0103986	−	0.999946i	$-0.496690\pi$
$563$	277.822	0.0207971	0.0103986	+	0.999946i	$0.496690\pi$
$564$	−1811.46	−0.135242
$565$	0	0
$566$	−14652.8	−1.08817
$567$	−1217.28	−0.0901603
$568$	−9980.82	−0.737299
$569$	15475.5	1.14019	0.570093	−	0.821580i	$-0.306907\pi$
$569$	15475.5	1.14019	0.570093	+	0.821580i	$0.306907\pi$
$570$	0	0
$571$	−3245.82	−0.237887	−0.118944	−	0.992901i	$-0.537951\pi$
$571$	−3245.82	−0.237887	−0.118944	+	0.992901i	$0.537951\pi$
$572$	−21133.8	−1.54484
$573$	5767.67	0.420502
$574$	−19995.8	−1.45402
$575$	0	0
$576$	−474.377	−0.0343155
$577$	23087.9	1.66579	0.832895	−	0.553430i	$-0.186682\pi$
$577$	23087.9	1.66579	0.832895	+	0.553430i	$0.186682\pi$
$578$	−1428.01	−0.102764
$579$	−5522.05	−0.396353
$580$	0	0
$581$	16219.5	1.15818
$582$	16406.7	1.16852
$583$	15281.7	1.08560
$584$	4720.44	0.334474
$585$	0	0
$586$	−20942.0	−1.47629
$587$	−13526.1	−0.951075	−0.475537	−	0.879696i	$-0.657746\pi$
$587$	−13526.1	−0.951075	−0.475537	+	0.879696i	$0.657746\pi$
$588$	−1685.76	−0.118230
$589$	−21444.9	−1.50021
$590$	0	0
$591$	8138.38	0.566444
$592$	−3797.17	−0.263619
$593$	−15964.6	−1.10554	−0.552770	−	0.833334i	$-0.686429\pi$
$593$	−15964.6	−1.10554	−0.552770	+	0.833334i	$0.686429\pi$
$594$	6840.69	0.472520
$595$	0	0
$596$	5758.46	0.395764
$597$	673.894	0.0461987
$598$	16142.9	1.10390
$599$	22.9584	0.00156603	0.000783017	−	1.00000i	$-0.499751\pi$
$599$	22.9584	0.00156603	0.000783017		1.00000i	$0.499751\pi$
$600$	0	0
$601$	−7471.32	−0.507090	−0.253545	−	0.967324i	$-0.581597\pi$
$601$	−7471.32	−0.507090	−0.253545	+	0.967324i	$0.581597\pi$
$602$	−21991.0	−1.48885
$603$	5205.23	0.351531
$604$	−7383.28	−0.497386
$605$	0	0
$606$	−15297.9	−1.02547
$607$	−23036.9	−1.54042	−0.770212	−	0.637788i	$-0.779849\pi$
$607$	−23036.9	−1.54042	−0.770212	+	0.637788i	$0.779849\pi$
$608$	−22872.8	−1.52568
$609$	−1307.45	−0.0869958
$610$	0	0
$611$	7831.91	0.518569
$612$	2900.19	0.191557
$613$	20040.0	1.32040	0.660202	−	0.751088i	$-0.270470\pi$
$613$	20040.0	1.32040	0.660202	+	0.751088i	$0.270470\pi$
$614$	9831.52	0.646202
$615$	0	0
$616$	12197.9	0.797834
$617$	27464.4	1.79202	0.896010	−	0.444035i	$-0.146453\pi$
$617$	27464.4	1.79202	0.896010	+	0.444035i	$0.146453\pi$
$618$	17124.2	1.11462
$619$	3585.29	0.232803	0.116402	−	0.993202i	$-0.462864\pi$
$619$	3585.29	0.232803	0.116402	+	0.993202i	$0.462864\pi$
$620$	0	0
$621$	−1958.53	−0.126559
$622$	−36805.9	−2.37264
$623$	−5845.83	−0.375936
$624$	14812.4	0.950276
$625$	0	0
$626$	−30552.6	−1.95069
$627$	25282.4	1.61034
$628$	−1070.23	−0.0680048
$629$	3214.38	0.203761
$630$	0	0
$631$	−27135.3	−1.71195	−0.855973	−	0.517020i	$-0.827041\pi$
$631$	−27135.3	−1.71195	−0.855973	+	0.517020i	$0.827041\pi$
$632$	−12837.8	−0.808009
$633$	−12480.3	−0.783645
$634$	469.160	0.0293892
$635$	0	0
$636$	3104.65	0.193565
$637$	7288.43	0.453341
$638$	7347.40	0.455935
$639$	7838.32	0.485257
$640$	0	0
$641$	23443.5	1.44456	0.722278	−	0.691603i	$-0.243095\pi$
$641$	23443.5	1.44456	0.722278	+	0.691603i	$0.243095\pi$
$642$	1664.51	0.102326
$643$	9339.29	0.572792	0.286396	−	0.958111i	$-0.407543\pi$
$643$	9339.29	0.572792	0.286396	+	0.958111i	$0.407543\pi$
$644$	5228.59	0.319931
$645$	0	0
$646$	28596.9	1.74169
$647$	−1103.56	−0.0670562	−0.0335281	−	0.999438i	$-0.510674\pi$
$647$	−1103.56	−0.0670562	−0.0335281	+	0.999438i	$0.510674\pi$
$648$	−928.263	−0.0562741
$649$	25279.2	1.52896
$650$	0	0
$651$	8125.41	0.489186
$652$	14939.3	0.897344
$653$	3127.51	0.187425	0.0937127	−	0.995599i	$-0.470126\pi$
$653$	3127.51	0.187425	0.0937127	+	0.995599i	$0.470126\pi$
$654$	13009.2	0.777828
$655$	0	0
$656$	−29520.6	−1.75699
$657$	−3707.14	−0.220136
$658$	6767.75	0.400964
$659$	16004.5	0.946050	0.473025	−	0.881049i	$-0.343162\pi$
$659$	16004.5	0.946050	0.473025	+	0.881049i	$0.343162\pi$
$660$	0	0
$661$	10807.3	0.635939	0.317970	−	0.948101i	$-0.396999\pi$
$661$	10807.3	0.635939	0.317970	+	0.948101i	$0.396999\pi$
$662$	−26023.4	−1.52784
$663$	−12539.1	−0.734504
$664$	12368.6	0.722882
$665$	0	0
$666$	1540.32	0.0896191
$667$	−2103.61	−0.122117
$668$	8253.47	0.478049
$669$	5239.24	0.302781
$670$	0	0
$671$	−33013.0	−1.89933
$672$	8666.44	0.497493
$673$	−23835.6	−1.36522	−0.682612	−	0.730781i	$-0.739156\pi$
$673$	−23835.6	−1.36522	−0.682612	+	0.730781i	$0.739156\pi$
$674$	−16682.5	−0.953392
$675$	0	0
$676$	8025.75	0.456631
$677$	−5081.10	−0.288453	−0.144227	−	0.989545i	$-0.546069\pi$
$677$	−5081.10	−0.288453	−0.144227	+	0.989545i	$0.546069\pi$
$678$	12362.9	0.700286
$679$	−22975.4	−1.29855
$680$	0	0
$681$	−388.523	−0.0218623
$682$	−45662.0	−2.56377
$683$	−7815.19	−0.437833	−0.218917	−	0.975744i	$-0.570252\pi$
$683$	−7815.19	−0.437833	−0.218917	+	0.975744i	$0.570252\pi$
$684$	5136.41	0.287128
$685$	0	0
$686$	24737.3	1.37679
$687$	−2046.50	−0.113652
$688$	−32466.1	−1.79907
$689$	−13423.1	−0.742204
$690$	0	0
$691$	8815.96	0.485347	0.242674	−	0.970108i	$-0.421976\pi$
$691$	8815.96	0.485347	0.242674	+	0.970108i	$0.421976\pi$
$692$	−11696.9	−0.642557
$693$	−9579.44	−0.525098
$694$	−21644.9	−1.18391
$695$	0	0
$696$	−997.023	−0.0542990
$697$	24989.8	1.35804
$698$	45873.9	2.48761
$699$	−5193.32	−0.281015
$700$	0	0
$701$	−4100.40	−0.220927	−0.110464	−	0.993880i	$-0.535234\pi$
$701$	−4100.40	−0.220927	−0.110464	+	0.993880i	$0.535234\pi$
$702$	−6008.68	−0.323053
$703$	5692.87	0.305420
$704$	−3733.14	−0.199855
$705$	0	0
$706$	−44767.0	−2.38644
$707$	21422.7	1.13958
$708$	5135.75	0.272618
$709$	−17803.3	−0.943042	−0.471521	−	0.881855i	$-0.656295\pi$
$709$	−17803.3	−0.943042	−0.471521	+	0.881855i	$0.656295\pi$
$710$	0	0
$711$	10082.0	0.531795
$712$	−4457.87	−0.234643
$713$	13073.3	0.686677
$714$	−10835.3	−0.567928
$715$	0	0
$716$	−10782.2	−0.562780
$717$	9925.13	0.516961
$718$	12143.5	0.631187
$719$	−4213.37	−0.218543	−0.109271	−	0.994012i	$-0.534852\pi$
$719$	−4213.37	−0.218543	−0.109271	+	0.994012i	$0.534852\pi$
$720$	0	0
$721$	−23980.1	−1.23865
$722$	26110.9	1.34591
$723$	10759.2	0.553441
$724$	−11305.6	−0.580347
$725$	0	0
$726$	39549.4	2.02178
$727$	−29559.3	−1.50797	−0.753984	−	0.656893i	$-0.771870\pi$
$727$	−29559.3	−1.50797	−0.753984	+	0.656893i	$0.771870\pi$
$728$	−10714.3	−0.545464
$729$	729.000	0.0370370
$730$	0	0
$731$	27483.2	1.39057
$732$	−6706.97	−0.338657
$733$	−23312.9	−1.17474	−0.587369	−	0.809319i	$-0.699836\pi$
$733$	−23312.9	−1.17474	−0.587369	+	0.809319i	$0.699836\pi$
$734$	35743.1	1.79742
$735$	0	0
$736$	13943.8	0.698337
$737$	40962.8	2.04733
$738$	11975.0	0.597300
$739$	27985.2	1.39303	0.696517	−	0.717540i	$-0.254732\pi$
$739$	27985.2	1.39303	0.696517	+	0.717540i	$0.254732\pi$
$740$	0	0
$741$	−22207.4	−1.10096
$742$	−11599.2	−0.573881
$743$	2542.48	0.125538	0.0627690	−	0.998028i	$-0.480007\pi$
$743$	2542.48	0.125538	0.0627690	+	0.998028i	$0.480007\pi$
$744$	6196.22	0.305328
$745$	0	0
$746$	−25825.3	−1.26747
$747$	−9713.50	−0.475768
$748$	22823.2	1.11564
$749$	−2330.92	−0.113712
$750$	0	0
$751$	33600.2	1.63261	0.816305	−	0.577622i	$-0.196019\pi$
$751$	33600.2	1.63261	0.816305	+	0.577622i	$0.196019\pi$
$752$	9991.46	0.484510
$753$	−8868.65	−0.429206
$754$	−6453.77	−0.311714
$755$	0	0
$756$	−1946.17	−0.0936264
$757$	34022.4	1.63351	0.816754	−	0.576986i	$-0.195771\pi$
$757$	34022.4	1.63351	0.816754	+	0.576986i	$0.195771\pi$
$758$	38626.0	1.85087
$759$	−15412.8	−0.737086
$760$	0	0
$761$	15032.8	0.716084	0.358042	−	0.933705i	$-0.383444\pi$
$761$	15032.8	0.716084	0.358042	+	0.933705i	$0.383444\pi$
$762$	−4279.16	−0.203435
$763$	−18217.6	−0.864378
$764$	9221.28	0.436668
$765$	0	0
$766$	12150.8	0.573144
$767$	−22204.6	−1.04532
$768$	15744.8	0.739768
$769$	−24042.9	−1.12745	−0.563725	−	0.825963i	$-0.690632\pi$
$769$	−24042.9	−1.12745	−0.563725	+	0.825963i	$0.690632\pi$
$770$	0	0
$771$	−6774.36	−0.316437
$772$	−8828.59	−0.411590
$773$	−17441.1	−0.811530	−0.405765	−	0.913977i	$-0.632995\pi$
$773$	−17441.1	−0.811530	−0.405765	+	0.913977i	$0.632995\pi$
$774$	13169.9	0.611605
$775$	0	0
$776$	−17520.4	−0.810496
$777$	−2157.01	−0.0995912
$778$	−17625.1	−0.812200
$779$	44258.5	2.03559
$780$	0	0
$781$	61684.0	2.82616
$782$	−17433.4	−0.797208
$783$	783.000	0.0357371
$784$	9298.12	0.423566
$785$	0	0
$786$	−4134.26	−0.187613
$787$	38211.9	1.73076	0.865379	−	0.501119i	$-0.167078\pi$
$787$	38211.9	1.73076	0.865379	+	0.501119i	$0.167078\pi$
$788$	13011.6	0.588220
$789$	−8726.00	−0.393731
$790$	0	0
$791$	−17312.5	−0.778208
$792$	−7305.02	−0.327743
$793$	28997.8	1.29854
$794$	27821.8	1.24353
$795$	0	0
$796$	1077.41	0.0479748
$797$	−18149.9	−0.806655	−0.403327	−	0.915056i	$-0.632146\pi$
$797$	−18149.9	−0.806655	−0.403327	+	0.915056i	$0.632146\pi$
$798$	−19190.0	−0.851276
$799$	−8457.99	−0.374496
$800$	0	0
$801$	3500.93	0.154431
$802$	21671.5	0.954172
$803$	−29173.5	−1.28208
$804$	8322.06	0.365045
$805$	0	0
$806$	40108.3	1.75280
$807$	−893.730	−0.0389849
$808$	16336.3	0.711275
$809$	−339.522	−0.0147552	−0.00737759	−	0.999973i	$-0.502348\pi$
$809$	−339.522	−0.0147552	−0.00737759	+	0.999973i	$0.502348\pi$
$810$	0	0
$811$	26295.4	1.13854	0.569270	−	0.822151i	$-0.307226\pi$
$811$	26295.4	1.13854	0.569270	+	0.822151i	$0.307226\pi$
$812$	−2090.33	−0.0903403
$813$	20979.1	0.905005
$814$	12121.7	0.521946
$815$	0	0
$816$	−15996.5	−0.686263
$817$	48674.5	2.08434
$818$	−53937.8	−2.30549
$819$	8414.33	0.359000
$820$	0	0
$821$	−46289.6	−1.96775	−0.983873	−	0.178867i	$-0.942757\pi$
$821$	−46289.6	−1.96775	−0.983873	+	0.178867i	$0.942757\pi$
$822$	3776.20	0.160231
$823$	28099.3	1.19013	0.595067	−	0.803676i	$-0.297126\pi$
$823$	28099.3	1.19013	0.595067	+	0.803676i	$0.297126\pi$
$824$	−18286.6	−0.773111
$825$	0	0
$826$	−19187.5	−0.808255
$827$	38732.3	1.62860	0.814301	−	0.580443i	$-0.197121\pi$
$827$	38732.3	1.62860	0.814301	+	0.580443i	$0.197121\pi$
$828$	−3131.28	−0.131425
$829$	−9334.33	−0.391067	−0.195534	−	0.980697i	$-0.562644\pi$
$829$	−9334.33	−0.391067	−0.195534	+	0.980697i	$0.562644\pi$
$830$	0	0
$831$	−17105.5	−0.714060
$832$	3279.09	0.136637
$833$	−7871.06	−0.327390
$834$	12217.7	0.507273
$835$	0	0
$836$	40421.3	1.67225
$837$	−4866.12	−0.200953
$838$	20383.7	0.840266
$839$	−40742.1	−1.67649	−0.838245	−	0.545294i	$-0.816418\pi$
$839$	−40742.1	−1.67649	−0.838245	+	0.545294i	$0.816418\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	3029.31	0.123987
$843$	−3649.02	−0.149085
$844$	−19953.4	−0.813771
$845$	0	0
$846$	−4053.05	−0.164712
$847$	−55383.5	−2.24675
$848$	−17124.3	−0.693457
$849$	−12288.5	−0.496750
$850$	0	0
$851$	−3470.51	−0.139797
$852$	12531.8	0.503912
$853$	29088.9	1.16762	0.583812	−	0.811889i	$-0.301560\pi$
$853$	29088.9	1.16762	0.583812	+	0.811889i	$0.301560\pi$
$854$	25057.7	1.00405
$855$	0	0
$856$	−1777.49	−0.0709737
$857$	−31564.0	−1.25812	−0.629059	−	0.777357i	$-0.716560\pi$
$857$	−31564.0	−1.25812	−0.629059	+	0.777357i	$0.716560\pi$
$858$	−47285.6	−1.88147
$859$	21654.5	0.860120	0.430060	−	0.902800i	$-0.358492\pi$
$859$	21654.5	0.860120	0.430060	+	0.902800i	$0.358492\pi$
$860$	0	0
$861$	−16769.4	−0.663763
$862$	−26894.4	−1.06267
$863$	−2304.51	−0.0908996	−0.0454498	−	0.998967i	$-0.514472\pi$
$863$	−2304.51	−0.0908996	−0.0454498	+	0.998967i	$0.514472\pi$
$864$	−5190.13	−0.204366
$865$	0	0
$866$	−45380.5	−1.78071
$867$	−1197.59	−0.0469116
$868$	12990.8	0.507992
$869$	79341.1	3.09720
$870$	0	0
$871$	−35980.7	−1.39972
$872$	−13892.2	−0.539507
$873$	13759.4	0.533432
$874$	−30875.6	−1.19495
$875$	0	0
$876$	−5926.93	−0.228599
$877$	−42141.0	−1.62258	−0.811289	−	0.584645i	$-0.801234\pi$
$877$	−42141.0	−1.62258	−0.811289	+	0.584645i	$0.801234\pi$
$878$	37669.4	1.44793
$879$	−17562.9	−0.673926
$880$	0	0
$881$	3482.39	0.133172	0.0665861	−	0.997781i	$-0.478789\pi$
$881$	3482.39	0.133172	0.0665861	+	0.997781i	$0.478789\pi$
$882$	−3771.79	−0.143994
$883$	−28559.6	−1.08846	−0.544229	−	0.838937i	$-0.683178\pi$
$883$	−28559.6	−1.08846	−0.544229	+	0.838937i	$0.683178\pi$
$884$	−20047.3	−0.762742
$885$	0	0
$886$	18598.5	0.705224
$887$	42485.5	1.60826	0.804128	−	0.594456i	$-0.202633\pi$
$887$	42485.5	1.60826	0.804128	+	0.594456i	$0.202633\pi$
$888$	−1644.88	−0.0621604
$889$	5992.37	0.226072
$890$	0	0
$891$	5736.90	0.215705
$892$	8376.43	0.314421
$893$	−14979.6	−0.561337
$894$	12884.2	0.482005
$895$	0	0
$896$	−20277.0	−0.756034
$897$	13538.2	0.503932
$898$	−42342.3	−1.57347
$899$	−5226.58	−0.193900
$900$	0	0
$901$	14496.1	0.535999
$902$	94238.2	3.47870
$903$	−18442.6	−0.679659
$904$	−13202.1	−0.485724
$905$	0	0
$906$	−16519.7	−0.605772
$907$	22359.4	0.818559	0.409280	−	0.912409i	$-0.365780\pi$
$907$	22359.4	0.818559	0.409280	+	0.912409i	$0.365780\pi$
$908$	−621.166	−0.0227028
$909$	−12829.5	−0.468128
$910$	0	0
$911$	−14833.6	−0.539471	−0.269735	−	0.962934i	$-0.586936\pi$
$911$	−14833.6	−0.539471	−0.269735	+	0.962934i	$0.586936\pi$
$912$	−28330.9	−1.02865
$913$	−76440.9	−2.77089
$914$	−1446.80	−0.0523588
$915$	0	0
$916$	−3271.92	−0.118021
$917$	5789.46	0.208489
$918$	6489.01	0.233300
$919$	−41161.8	−1.47748	−0.738740	−	0.673991i	$-0.764579\pi$
$919$	−41161.8	−1.47748	−0.738740	+	0.673991i	$0.764579\pi$
$920$	0	0
$921$	8245.15	0.294991
$922$	25300.1	0.903702
$923$	−54181.7	−1.93219
$924$	−15315.5	−0.545285
$925$	0	0
$926$	23252.6	0.825192
$927$	14361.2	0.508826
$928$	−5574.59	−0.197193
$929$	29321.8	1.03554	0.517771	−	0.855519i	$-0.326762\pi$
$929$	29321.8	1.03554	0.517771	+	0.855519i	$0.326762\pi$
$930$	0	0
$931$	−13940.1	−0.490729
$932$	−8303.02	−0.291818
$933$	−30867.0	−1.08311
$934$	31660.4	1.10917
$935$	0	0
$936$	6416.54	0.224072
$937$	42922.5	1.49650	0.748249	−	0.663418i	$-0.230895\pi$
$937$	42922.5	1.49650	0.748249	+	0.663418i	$0.230895\pi$
$938$	−31091.8	−1.08228
$939$	−25622.8	−0.890488
$940$	0	0
$941$	−13239.3	−0.458650	−0.229325	−	0.973350i	$-0.573652\pi$
$941$	−13239.3	−0.458650	−0.229325	+	0.973350i	$0.573652\pi$
$942$	−2394.59	−0.0828237
$943$	−26981.0	−0.931732
$944$	−28327.2	−0.976665
$945$	0	0
$946$	103641.	3.56201
$947$	19266.8	0.661126	0.330563	−	0.943784i	$-0.392761\pi$
$947$	19266.8	0.661126	0.330563	+	0.943784i	$0.392761\pi$
$948$	16119.1	0.552239
$949$	25625.3	0.876534
$950$	0	0
$951$	393.459	0.0134162
$952$	11570.8	0.393919
$953$	14816.2	0.503615	0.251807	−	0.967777i	$-0.418975\pi$
$953$	14816.2	0.503615	0.251807	+	0.967777i	$0.418975\pi$
$954$	6946.49	0.235745
$955$	0	0
$956$	15868.2	0.536835
$957$	6161.86	0.208134
$958$	−30702.8	−1.03545
$959$	−5288.05	−0.178061
$960$	0	0
$961$	2690.68	0.0903185
$962$	−10647.4	−0.356845
$963$	1395.93	0.0467117
$964$	17201.6	0.574717
$965$	0	0
$966$	11698.7	0.389647
$967$	−1342.65	−0.0446502	−0.0223251	−	0.999751i	$-0.507107\pi$
$967$	−1342.65	−0.0446502	−0.0223251	+	0.999751i	$0.507107\pi$
$968$	−42233.9	−1.40232
$969$	23982.7	0.795082
$970$	0	0
$971$	−11211.1	−0.370526	−0.185263	−	0.982689i	$-0.559314\pi$
$971$	−11211.1	−0.370526	−0.185263	+	0.982689i	$0.559314\pi$
$972$	1165.52	0.0384609
$973$	−17109.3	−0.563718
$974$	10100.7	0.332285
$975$	0	0
$976$	36993.6	1.21325
$977$	−30870.2	−1.01088	−0.505438	−	0.862863i	$-0.668669\pi$
$977$	−30870.2	−1.01088	−0.505438	+	0.862863i	$0.668669\pi$
$978$	33425.9	1.09288
$979$	27550.8	0.899414
$980$	0	0
$981$	10910.1	0.355079
$982$	−46919.3	−1.52470
$983$	−28549.4	−0.926332	−0.463166	−	0.886272i	$-0.653287\pi$
$983$	−28549.4	−0.926332	−0.463166	+	0.886272i	$0.653287\pi$
$984$	−12787.9	−0.414292
$985$	0	0
$986$	6969.68	0.225111
$987$	5675.73	0.183040
$988$	−35505.0	−1.14328
$989$	−29673.1	−0.954046
$990$	0	0
$991$	−20806.0	−0.666927	−0.333464	−	0.942763i	$-0.608217\pi$
$991$	−20806.0	−0.666927	−0.333464	+	0.942763i	$0.608217\pi$
$992$	34644.5	1.10883
$993$	−21824.4	−0.697458
$994$	−46819.7	−1.49399
$995$	0	0
$996$	−15529.8	−0.494058
$997$	−57999.9	−1.84240	−0.921201	−	0.389088i	$-0.872790\pi$
$997$	−57999.9	−1.84240	−0.921201	+	0.389088i	$0.872790\pi$
$998$	−59007.4	−1.87159
$999$	1291.78	0.0409112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.4.a.n.1.6		7
5.4	even	2		435.4.a.i.1.2	✓	7
15.14	odd	2		1305.4.a.n.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.i.1.2	✓	7	5.4	even	2
1305.4.a.n.1.6		7	15.14	odd	2
2175.4.a.n.1.6		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

\(f(q)\)	\(=\)	\(q+3.57720 q^{2} +3.00000 q^{3} +4.79637 q^{4} +10.7316 q^{6} -15.0281 q^{7} -11.4600 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.57720 q^{2} +3.00000 q^{3} +4.79637 q^{4} +10.7316 q^{6} -15.0281 q^{7} -11.4600 q^{8} +9.00000 q^{9} +70.8260 q^{11} +14.3891 q^{12} -62.2117 q^{13} -53.7587 q^{14} -79.3658 q^{16} +67.1848 q^{17} +32.1948 q^{18} +118.988 q^{19} -45.0844 q^{21} +253.359 q^{22} -72.5383 q^{23} -34.3801 q^{24} -222.544 q^{26} +27.0000 q^{27} -72.0804 q^{28} +29.0000 q^{29} -180.227 q^{31} -192.227 q^{32} +212.478 q^{33} +240.334 q^{34} +43.1673 q^{36} +47.8439 q^{37} +425.646 q^{38} -186.635 q^{39} +371.956 q^{41} -161.276 q^{42} +409.069 q^{43} +339.707 q^{44} -259.484 q^{46} -125.891 q^{47} -238.097 q^{48} -117.155 q^{49} +201.555 q^{51} -298.390 q^{52} +215.764 q^{53} +96.5844 q^{54} +172.223 q^{56} +356.965 q^{57} +103.739 q^{58} +356.919 q^{59} -466.115 q^{61} -644.707 q^{62} -135.253 q^{63} -52.7086 q^{64} +760.076 q^{66} +578.359 q^{67} +322.243 q^{68} -217.615 q^{69} +870.924 q^{71} -103.140 q^{72} -411.904 q^{73} +171.147 q^{74} +570.712 q^{76} -1064.38 q^{77} -667.631 q^{78} +1120.23 q^{79} +81.0000 q^{81} +1330.56 q^{82} -1079.28 q^{83} -216.241 q^{84} +1463.32 q^{86} +87.0000 q^{87} -811.668 q^{88} +388.993 q^{89} +934.926 q^{91} -347.920 q^{92} -540.680 q^{93} -450.339 q^{94} -576.681 q^{96} +1528.82 q^{97} -419.088 q^{98} +637.434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9	\( 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9} + 76 q^{11} + 66 q^{12} - 30 q^{13} + 89 q^{14} + 138 q^{16} + 140 q^{17} + 18 q^{18} + 90 q^{19} + 150 q^{21} - 61 q^{22} - 34 q^{23} + 99 q^{24} - 241 q^{26} + 189 q^{27} + 57 q^{28} + 203 q^{29} + 524 q^{31} + 6 q^{32} + 228 q^{33} + 255 q^{34} + 198 q^{36} + 28 q^{37} - 222 q^{38} - 90 q^{39} + 1532 q^{41} + 267 q^{42} + 464 q^{43} + 1475 q^{44} + 72 q^{46} + 360 q^{47} + 414 q^{48} + 569 q^{49} + 420 q^{51} + 205 q^{52} - 282 q^{53} + 54 q^{54} + 1102 q^{56} + 270 q^{57} + 58 q^{58} + 766 q^{59} + 1200 q^{61} - 2856 q^{62} + 450 q^{63} + 701 q^{64} - 183 q^{66} - 1546 q^{67} - 1801 q^{68} - 102 q^{69} + 1802 q^{71} + 297 q^{72} + 220 q^{73} + 1594 q^{74} + 1960 q^{76} - 3222 q^{77} - 723 q^{78} + 1298 q^{79} + 567 q^{81} - 856 q^{82} - 1652 q^{83} + 171 q^{84} + 7628 q^{86} + 609 q^{87} - 550 q^{88} + 2846 q^{89} - 816 q^{91} - 472 q^{92} + 1572 q^{93} + 745 q^{94} + 18 q^{96} - 1110 q^{97} + 761 q^{98} + 684 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9 + 76 * q^11 + 66 * q^12 - 30 * q^13 + 89 * q^14 + 138 * q^16 + 140 * q^17 + 18 * q^18 + 90 * q^19 + 150 * q^21 - 61 * q^22 - 34 * q^23 + 99 * q^24 - 241 * q^26 + 189 * q^27 + 57 * q^28 + 203 * q^29 + 524 * q^31 + 6 * q^32 + 228 * q^33 + 255 * q^34 + 198 * q^36 + 28 * q^37 - 222 * q^38 - 90 * q^39 + 1532 * q^41 + 267 * q^42 + 464 * q^43 + 1475 * q^44 + 72 * q^46 + 360 * q^47 + 414 * q^48 + 569 * q^49 + 420 * q^51 + 205 * q^52 - 282 * q^53 + 54 * q^54 + 1102 * q^56 + 270 * q^57 + 58 * q^58 + 766 * q^59 + 1200 * q^61 - 2856 * q^62 + 450 * q^63 + 701 * q^64 - 183 * q^66 - 1546 * q^67 - 1801 * q^68 - 102 * q^69 + 1802 * q^71 + 297 * q^72 + 220 * q^73 + 1594 * q^74 + 1960 * q^76 - 3222 * q^77 - 723 * q^78 + 1298 * q^79 + 567 * q^81 - 856 * q^82 - 1652 * q^83 + 171 * q^84 + 7628 * q^86 + 609 * q^87 - 550 * q^88 + 2846 * q^89 - 816 * q^91 - 472 * q^92 + 1572 * q^93 + 745 * q^94 + 18 * q^96 - 1110 * q^97 + 761 * q^98 + 684 * q^99

Introduction

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