LMFDB - Embedded newform 1875.4.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,4,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1875.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:	$110.628581261$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + \cdots + 42064 $ x^14 - 81x^12 - 7x^11 + 2512x^10 + 517x^9 - 36970x^8 - 12987x^7 + 257291x^6 + 125779x^5 - 718713x^4 - 371750x^3 + 579848x^2 + 394896x + 42064
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{3} $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$4.65416$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.65416 q^{2} +3.00000 q^{3} +13.6612 q^{4} +13.9625 q^{6} -26.0445 q^{7} +26.3483 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.65416 q^{2} +3.00000 q^{3} +13.6612 q^{4} +13.9625 q^{6} -26.0445 q^{7} +26.3483 q^{8} +9.00000 q^{9} +2.51593 q^{11} +40.9837 q^{12} +39.6201 q^{13} -121.215 q^{14} +13.3393 q^{16} -84.9913 q^{17} +41.8875 q^{18} -142.827 q^{19} -78.1335 q^{21} +11.7096 q^{22} +157.199 q^{23} +79.0448 q^{24} +184.399 q^{26} +27.0000 q^{27} -355.800 q^{28} -100.233 q^{29} -173.361 q^{31} -148.703 q^{32} +7.54780 q^{33} -395.563 q^{34} +122.951 q^{36} -59.3956 q^{37} -664.741 q^{38} +118.860 q^{39} -355.427 q^{41} -363.646 q^{42} +109.742 q^{43} +34.3707 q^{44} +731.630 q^{46} -58.1116 q^{47} +40.0178 q^{48} +335.317 q^{49} -254.974 q^{51} +541.260 q^{52} -390.876 q^{53} +125.662 q^{54} -686.228 q^{56} -428.481 q^{57} -466.501 q^{58} +412.549 q^{59} +358.635 q^{61} -806.851 q^{62} -234.401 q^{63} -798.802 q^{64} +35.1287 q^{66} +351.010 q^{67} -1161.09 q^{68} +471.597 q^{69} +170.828 q^{71} +237.134 q^{72} -932.891 q^{73} -276.437 q^{74} -1951.19 q^{76} -65.5263 q^{77} +553.196 q^{78} -1313.26 q^{79} +81.0000 q^{81} -1654.21 q^{82} -653.900 q^{83} -1067.40 q^{84} +510.757 q^{86} -300.699 q^{87} +66.2905 q^{88} +1059.65 q^{89} -1031.89 q^{91} +2147.53 q^{92} -520.083 q^{93} -270.461 q^{94} -446.109 q^{96} +641.500 q^{97} +1560.62 q^{98} +22.6434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9}+O(q^{10}) $ 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9	$ 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9} - 33 q^{11} + 150 q^{12} - 188 q^{13} - 287 q^{14} + 82 q^{16} - 146 q^{17} - 184 q^{19} - 81 q^{21} - 277 q^{22} - 164 q^{23} + 63 q^{24} + 103 q^{26} + 378 q^{27} + 224 q^{28} + 252 q^{29} - 889 q^{31} - 422 q^{32} - 99 q^{33} - 230 q^{34} + 450 q^{36} - 642 q^{37} - 1833 q^{38} - 564 q^{39} - 164 q^{41} - 861 q^{42} - 696 q^{43} - 6 q^{44} - 419 q^{46} + 92 q^{47} + 246 q^{48} + 81 q^{49} - 438 q^{51} - 1956 q^{52} - 949 q^{53} - 2380 q^{56} - 552 q^{57} - 1041 q^{58} - 81 q^{59} - 496 q^{61} - 1454 q^{62} - 243 q^{63} - 3903 q^{64} - 831 q^{66} - 1926 q^{67} - 685 q^{68} - 492 q^{69} + 2498 q^{71} + 189 q^{72} + 1026 q^{73} - 707 q^{74} - 5704 q^{76} - 5434 q^{77} + 309 q^{78} - 695 q^{79} + 1134 q^{81} + 886 q^{82} - 5315 q^{83} + 672 q^{84} + 3997 q^{86} + 756 q^{87} - 2969 q^{88} - 1424 q^{89} - 1194 q^{91} - 1607 q^{92} - 2667 q^{93} - 629 q^{94} - 1266 q^{96} - 291 q^{97} + 1018 q^{98} - 297 q^{99}+O(q^{100}) $ 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9 - 33 * q^11 + 150 * q^12 - 188 * q^13 - 287 * q^14 + 82 * q^16 - 146 * q^17 - 184 * q^19 - 81 * q^21 - 277 * q^22 - 164 * q^23 + 63 * q^24 + 103 * q^26 + 378 * q^27 + 224 * q^28 + 252 * q^29 - 889 * q^31 - 422 * q^32 - 99 * q^33 - 230 * q^34 + 450 * q^36 - 642 * q^37 - 1833 * q^38 - 564 * q^39 - 164 * q^41 - 861 * q^42 - 696 * q^43 - 6 * q^44 - 419 * q^46 + 92 * q^47 + 246 * q^48 + 81 * q^49 - 438 * q^51 - 1956 * q^52 - 949 * q^53 - 2380 * q^56 - 552 * q^57 - 1041 * q^58 - 81 * q^59 - 496 * q^61 - 1454 * q^62 - 243 * q^63 - 3903 * q^64 - 831 * q^66 - 1926 * q^67 - 685 * q^68 - 492 * q^69 + 2498 * q^71 + 189 * q^72 + 1026 * q^73 - 707 * q^74 - 5704 * q^76 - 5434 * q^77 + 309 * q^78 - 695 * q^79 + 1134 * q^81 + 886 * q^82 - 5315 * q^83 + 672 * q^84 + 3997 * q^86 + 756 * q^87 - 2969 * q^88 - 1424 * q^89 - 1194 * q^91 - 1607 * q^92 - 2667 * q^93 - 629 * q^94 - 1266 * q^96 - 291 * q^97 + 1018 * q^98 - 297 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.65416	1.64549	0.822747	−	0.568407i	$-0.192440\pi$
$2$	4.65416	1.64549	0.822747	+	0.568407i	$0.192440\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	13.6612	1.70765
$5$	0	0
$5$	0	0
$6$	13.9625	0.950027
$7$	−26.0445	−1.40627	−0.703136	−	0.711056i	$-0.748217\pi$
$7$	−26.0445	−1.40627	−0.703136	+	0.711056i	$0.748217\pi$
$8$	26.3483	1.16444
$9$	9.00000	0.333333
$10$	0	0
$11$	2.51593	0.0689621	0.0344810	−	0.999405i	$-0.489022\pi$
$11$	2.51593	0.0689621	0.0344810	+	0.999405i	$0.489022\pi$
$12$	40.9837	0.985914
$13$	39.6201	0.845281	0.422640	−	0.906298i	$-0.361103\pi$
$13$	39.6201	0.845281	0.422640	+	0.906298i	$0.361103\pi$
$14$	−121.215	−2.31401
$15$	0	0
$16$	13.3393	0.208426
$17$	−84.9913	−1.21255	−0.606277	−	0.795253i	$-0.707338\pi$
$17$	−84.9913	−1.21255	−0.606277	+	0.795253i	$0.707338\pi$
$18$	41.8875	0.548498
$19$	−142.827	−1.72457	−0.862284	−	0.506425i	$-0.830967\pi$
$19$	−142.827	−1.72457	−0.862284	+	0.506425i	$0.830967\pi$
$20$	0	0
$21$	−78.1335	−0.811911
$22$	11.7096	0.113477
$23$	157.199	1.42514	0.712571	−	0.701600i	$-0.247531\pi$
$23$	157.199	1.42514	0.712571	+	0.701600i	$0.247531\pi$
$24$	79.0448	0.672289
$25$	0	0
$26$	184.399	1.39090
$27$	27.0000	0.192450
$28$	−355.800	−2.40142
$29$	−100.233	−0.641821	−0.320911	−	0.947109i	$-0.603989\pi$
$29$	−100.233	−0.641821	−0.320911	+	0.947109i	$0.603989\pi$
$30$	0	0
$31$	−173.361	−1.00441	−0.502203	−	0.864750i	$-0.667477\pi$
$31$	−173.361	−1.00441	−0.502203	+	0.864750i	$0.667477\pi$
$32$	−148.703	−0.821476
$33$	7.54780	0.0398153
$34$	−395.563	−1.99525
$35$	0	0
$36$	122.951	0.569218
$37$	−59.3956	−0.263907	−0.131954	−	0.991256i	$-0.542125\pi$
$37$	−59.3956	−0.263907	−0.131954	+	0.991256i	$0.542125\pi$
$38$	−664.741	−2.83777
$39$	118.860	0.488023
$40$	0	0
$41$	−355.427	−1.35386	−0.676930	−	0.736047i	$-0.736690\pi$
$41$	−355.427	−1.35386	−0.676930	+	0.736047i	$0.736690\pi$
$42$	−363.646	−1.33600
$43$	109.742	0.389198	0.194599	−	0.980883i	$-0.437659\pi$
$43$	109.742	0.389198	0.194599	+	0.980883i	$0.437659\pi$
$44$	34.3707	0.117763
$45$	0	0
$46$	731.630	2.34506
$47$	−58.1116	−0.180350	−0.0901750	−	0.995926i	$-0.528743\pi$
$47$	−58.1116	−0.180350	−0.0901750	+	0.995926i	$0.528743\pi$
$48$	40.0178	0.120335
$49$	335.317	0.977600
$50$	0	0
$51$	−254.974	−0.700069
$52$	541.260	1.44345
$53$	−390.876	−1.01304	−0.506518	−	0.862229i	$-0.669068\pi$
$53$	−390.876	−1.01304	−0.506518	+	0.862229i	$0.669068\pi$
$54$	125.662	0.316676
$55$	0	0
$56$	−686.228	−1.63752
$57$	−428.481	−0.995680
$58$	−466.501	−1.05611
$59$	412.549	0.910327	0.455163	−	0.890408i	$-0.349581\pi$
$59$	412.549	0.910327	0.455163	+	0.890408i	$0.349581\pi$
$60$	0	0
$61$	358.635	0.752763	0.376381	−	0.926465i	$-0.377168\pi$
$61$	358.635	0.752763	0.376381	+	0.926465i	$0.377168\pi$
$62$	−806.851	−1.65274
$63$	−234.401	−0.468757
$64$	−798.802	−1.56016
$65$	0	0
$66$	35.1287	0.0655158
$67$	351.010	0.640041	0.320020	−	0.947411i	$-0.396310\pi$
$67$	351.010	0.640041	0.320020	+	0.947411i	$0.396310\pi$
$68$	−1161.09	−2.07062
$69$	471.597	0.822806
$70$	0	0
$71$	170.828	0.285543	0.142771	−	0.989756i	$-0.454399\pi$
$71$	170.828	0.285543	0.142771	+	0.989756i	$0.454399\pi$
$72$	237.134	0.388146
$73$	−932.891	−1.49571	−0.747853	−	0.663864i	$-0.768915\pi$
$73$	−932.891	−1.49571	−0.747853	+	0.663864i	$0.768915\pi$
$74$	−276.437	−0.434258
$75$	0	0
$76$	−1951.19	−2.94496
$77$	−65.5263	−0.0969794
$78$	553.196	0.803039
$79$	−1313.26	−1.87029	−0.935147	−	0.354261i	$-0.884733\pi$
$79$	−1313.26	−1.87029	−0.935147	+	0.354261i	$0.884733\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1654.21	−2.22777
$83$	−653.900	−0.864757	−0.432378	−	0.901692i	$-0.642326\pi$
$83$	−653.900	−0.864757	−0.432378	+	0.901692i	$0.642326\pi$
$84$	−1067.40	−1.38646
$85$	0	0
$86$	510.757	0.640423
$87$	−300.699	−0.370556
$88$	66.2905	0.0803021
$89$	1059.65	1.26205	0.631025	−	0.775763i	$-0.282635\pi$
$89$	1059.65	1.26205	0.631025	+	0.775763i	$0.282635\pi$
$90$	0	0
$91$	−1031.89	−1.18869
$92$	2147.53	2.43365
$93$	−520.083	−0.579894
$94$	−270.461	−0.296765
$95$	0	0
$96$	−446.109	−0.474279
$97$	641.500	0.671489	0.335745	−	0.941953i	$-0.391012\pi$
$97$	641.500	0.671489	0.335745	+	0.941953i	$0.391012\pi$
$98$	1560.62	1.60864
$99$	22.6434	0.0229874
$100$	0	0
$101$	864.030	0.851229	0.425615	−	0.904904i	$-0.360058\pi$
$101$	864.030	0.851229	0.425615	+	0.904904i	$0.360058\pi$
$102$	−1186.69	−1.15196
$103$	1832.11	1.75265	0.876324	−	0.481722i	$-0.159988\pi$
$103$	1832.11	1.75265	0.876324	+	0.481722i	$0.159988\pi$
$104$	1043.92	0.984278
$105$	0	0
$106$	−1819.20	−1.66695
$107$	−1037.99	−0.937816	−0.468908	−	0.883247i	$-0.655352\pi$
$107$	−1037.99	−0.937816	−0.468908	+	0.883247i	$0.655352\pi$
$108$	368.853	0.328638
$109$	1557.03	1.36823	0.684113	−	0.729376i	$-0.260189\pi$
$109$	1557.03	1.36823	0.684113	+	0.729376i	$0.260189\pi$
$110$	0	0
$111$	−178.187	−0.152367
$112$	−347.415	−0.293104
$113$	−975.199	−0.811850	−0.405925	−	0.913906i	$-0.633051\pi$
$113$	−975.199	−0.811850	−0.405925	+	0.913906i	$0.633051\pi$
$114$	−1994.22	−1.63839
$115$	0	0
$116$	−1369.31	−1.09601
$117$	356.581	0.281760
$118$	1920.07	1.49794
$119$	2213.56	1.70518
$120$	0	0
$121$	−1324.67	−0.995244
$122$	1669.15	1.23867
$123$	−1066.28	−0.781652
$124$	−2368.33	−1.71518
$125$	0	0
$126$	−1090.94	−0.771338
$127$	−1028.89	−0.718894	−0.359447	−	0.933166i	$-0.617035\pi$
$127$	−1028.89	−0.718894	−0.359447	+	0.933166i	$0.617035\pi$
$128$	−2528.13	−1.74576
$129$	329.226	0.224704
$130$	0	0
$131$	−2669.90	−1.78069	−0.890346	−	0.455285i	$-0.849537\pi$
$131$	−2669.90	−1.78069	−0.890346	+	0.455285i	$0.849537\pi$
$132$	103.112	0.0679907
$133$	3719.86	2.42521
$134$	1633.66	1.05318
$135$	0	0
$136$	−2239.37	−1.41195
$137$	−1219.42	−0.760454	−0.380227	−	0.924893i	$-0.624154\pi$
$137$	−1219.42	−0.760454	−0.380227	+	0.924893i	$0.624154\pi$
$138$	2194.89	1.35392
$139$	875.292	0.534110	0.267055	−	0.963681i	$-0.413949\pi$
$139$	875.292	0.534110	0.267055	+	0.963681i	$0.413949\pi$
$140$	0	0
$141$	−174.335	−0.104125
$142$	795.061	0.469859
$143$	99.6816	0.0582923
$144$	120.053	0.0694753
$145$	0	0
$146$	−4341.82	−2.46118
$147$	1005.95	0.564417
$148$	−811.416	−0.450662
$149$	−819.633	−0.450650	−0.225325	−	0.974284i	$-0.572344\pi$
$149$	−819.633	−0.450650	−0.225325	+	0.974284i	$0.572344\pi$
$150$	0	0
$151$	567.457	0.305821	0.152911	−	0.988240i	$-0.451135\pi$
$151$	567.457	0.305821	0.152911	+	0.988240i	$0.451135\pi$
$152$	−3763.25	−2.00815
$153$	−764.922	−0.404185
$154$	−304.970	−0.159579
$155$	0	0
$156$	1623.78	0.833374
$157$	−1643.63	−0.835516	−0.417758	−	0.908558i	$-0.637184\pi$
$157$	−1643.63	−0.835516	−0.417758	+	0.908558i	$0.637184\pi$
$158$	−6112.12	−3.07756
$159$	−1172.63	−0.584877
$160$	0	0
$161$	−4094.17	−2.00414
$162$	376.987	0.182833
$163$	−1280.29	−0.615217	−0.307608	−	0.951513i	$-0.599529\pi$
$163$	−1280.29	−0.615217	−0.307608	+	0.951513i	$0.599529\pi$
$164$	−4855.56	−2.31192
$165$	0	0
$166$	−3043.36	−1.42295
$167$	−1576.61	−0.730547	−0.365274	−	0.930900i	$-0.619025\pi$
$167$	−1576.61	−0.730547	−0.365274	+	0.930900i	$0.619025\pi$
$168$	−2058.68	−0.945422
$169$	−627.245	−0.285501
$170$	0	0
$171$	−1285.44	−0.574856
$172$	1499.21	0.664615
$173$	2221.62	0.976337	0.488169	−	0.872749i	$-0.337665\pi$
$173$	2221.62	0.976337	0.488169	+	0.872749i	$0.337665\pi$
$174$	−1399.50	−0.609747
$175$	0	0
$176$	33.5607	0.0143735
$177$	1237.65	0.525577
$178$	4931.77	2.07670
$179$	3015.07	1.25898	0.629489	−	0.777010i	$-0.283264\pi$
$179$	3015.07	1.25898	0.629489	+	0.777010i	$0.283264\pi$
$180$	0	0
$181$	2472.66	1.01542	0.507710	−	0.861528i	$-0.330492\pi$
$181$	2472.66	1.01542	0.507710	+	0.861528i	$0.330492\pi$
$182$	−4802.57	−1.95599
$183$	1075.91	0.434608
$184$	4141.92	1.65949
$185$	0	0
$186$	−2420.55	−0.954212
$187$	−213.833	−0.0836203
$188$	−793.876	−0.307975
$189$	−703.202	−0.270637
$190$	0	0
$191$	−640.945	−0.242812	−0.121406	−	0.992603i	$-0.538740\pi$
$191$	−640.945	−0.242812	−0.121406	+	0.992603i	$0.538740\pi$
$192$	−2396.41	−0.900759
$193$	−658.953	−0.245764	−0.122882	−	0.992421i	$-0.539214\pi$
$193$	−658.953	−0.245764	−0.122882	+	0.992421i	$0.539214\pi$
$194$	2985.65	1.10493
$195$	0	0
$196$	4580.84	1.66940
$197$	2802.27	1.01347	0.506734	−	0.862102i	$-0.330853\pi$
$197$	2802.27	1.01347	0.506734	+	0.862102i	$0.330853\pi$
$198$	105.386	0.0378256
$199$	−2715.89	−0.967459	−0.483729	−	0.875218i	$-0.660718\pi$
$199$	−2715.89	−0.967459	−0.483729	+	0.875218i	$0.660718\pi$
$200$	0	0
$201$	1053.03	0.369528
$202$	4021.33	1.40069
$203$	2610.52	0.902575
$204$	−3483.26	−1.19547
$205$	0	0
$206$	8526.92	2.88397
$207$	1414.79	0.475047
$208$	528.503	0.176178
$209$	−359.344	−0.118930
$210$	0	0
$211$	−1733.25	−0.565507	−0.282753	−	0.959193i	$-0.591248\pi$
$211$	−1733.25	−0.565507	−0.282753	+	0.959193i	$0.591248\pi$
$212$	−5339.84	−1.72991
$213$	512.484	0.164858
$214$	−4830.97	−1.54317
$215$	0	0
$216$	711.403	0.224096
$217$	4515.11	1.41247
$218$	7246.68	2.25141
$219$	−2798.67	−0.863547
$220$	0	0
$221$	−3367.37	−1.02495
$222$	−829.310	−0.250719
$223$	4377.14	1.31442	0.657208	−	0.753709i	$-0.271737\pi$
$223$	4377.14	1.31442	0.657208	+	0.753709i	$0.271737\pi$
$224$	3872.90	1.15522
$225$	0	0
$226$	−4538.74	−1.33589
$227$	−2248.73	−0.657503	−0.328752	−	0.944416i	$-0.606628\pi$
$227$	−2248.73	−0.657503	−0.328752	+	0.944416i	$0.606628\pi$
$228$	−5853.58	−1.70028
$229$	2245.32	0.647926	0.323963	−	0.946070i	$-0.394985\pi$
$229$	2245.32	0.647926	0.323963	+	0.946070i	$0.394985\pi$
$230$	0	0
$231$	−196.579	−0.0559911
$232$	−2640.97	−0.747362
$233$	708.378	0.199173	0.0995866	−	0.995029i	$-0.468248\pi$
$233$	708.378	0.199173	0.0995866	+	0.995029i	$0.468248\pi$
$234$	1659.59	0.463635
$235$	0	0
$236$	5635.92	1.55452
$237$	−3939.78	−1.07981
$238$	10302.3	2.80587
$239$	5452.75	1.47577	0.737885	−	0.674927i	$-0.235825\pi$
$239$	5452.75	1.47577	0.737885	+	0.674927i	$0.235825\pi$
$240$	0	0
$241$	5720.73	1.52906	0.764532	−	0.644585i	$-0.222970\pi$
$241$	5720.73	1.52906	0.764532	+	0.644585i	$0.222970\pi$
$242$	−6165.23	−1.63767
$243$	243.000	0.0641500
$244$	4899.39	1.28546
$245$	0	0
$246$	−4962.64	−1.28620
$247$	−5658.83	−1.45774
$248$	−4567.76	−1.16957
$249$	−1961.70	−0.499268
$250$	0	0
$251$	2045.23	0.514319	0.257159	−	0.966369i	$-0.417213\pi$
$251$	2045.23	0.514319	0.257159	+	0.966369i	$0.417213\pi$
$252$	−3202.20	−0.800475
$253$	395.502	0.0982807
$254$	−4788.64	−1.18294
$255$	0	0
$256$	−5375.91	−1.31248
$257$	407.547	0.0989186	0.0494593	−	0.998776i	$-0.484250\pi$
$257$	407.547	0.0989186	0.0494593	+	0.998776i	$0.484250\pi$
$258$	1532.27	0.369748
$259$	1546.93	0.371125
$260$	0	0
$261$	−902.098	−0.213940
$262$	−12426.2	−2.93012
$263$	−887.485	−0.208079	−0.104039	−	0.994573i	$-0.533177\pi$
$263$	−887.485	−0.208079	−0.104039	+	0.994573i	$0.533177\pi$
$264$	198.871	0.0463625
$265$	0	0
$266$	17312.8	3.99067
$267$	3178.94	0.728645
$268$	4795.23	1.09297
$269$	6033.48	1.36754	0.683769	−	0.729699i	$-0.260340\pi$
$269$	6033.48	1.36754	0.683769	+	0.729699i	$0.260340\pi$
$270$	0	0
$271$	6534.92	1.46483	0.732413	−	0.680860i	$-0.238394\pi$
$271$	6534.92	1.46483	0.732413	+	0.680860i	$0.238394\pi$
$272$	−1133.72	−0.252728
$273$	−3095.66	−0.686293
$274$	−5675.39	−1.25132
$275$	0	0
$276$	6442.59	1.40507
$277$	−5506.53	−1.19442	−0.597212	−	0.802084i	$-0.703725\pi$
$277$	−5506.53	−1.19442	−0.597212	+	0.802084i	$0.703725\pi$
$278$	4073.75	0.878875
$279$	−1560.25	−0.334802
$280$	0	0
$281$	−7519.12	−1.59627	−0.798137	−	0.602476i	$-0.794181\pi$
$281$	−7519.12	−1.59627	−0.798137	+	0.602476i	$0.794181\pi$
$282$	−811.382	−0.171337
$283$	4480.16	0.941052	0.470526	−	0.882386i	$-0.344064\pi$
$283$	4480.16	0.941052	0.470526	+	0.882386i	$0.344064\pi$
$284$	2333.72	0.487608
$285$	0	0
$286$	463.934	0.0959197
$287$	9256.91	1.90390
$288$	−1338.33	−0.273825
$289$	2310.53	0.470289
$290$	0	0
$291$	1924.50	0.387685
$292$	−12744.4	−2.55415
$293$	−6672.17	−1.33035	−0.665174	−	0.746688i	$-0.731643\pi$
$293$	−6672.17	−1.33035	−0.665174	+	0.746688i	$0.731643\pi$
$294$	4681.85	0.928746
$295$	0	0
$296$	−1564.97	−0.307304
$297$	67.9302	0.0132718
$298$	−3814.70	−0.741543
$299$	6228.25	1.20464
$300$	0	0
$301$	−2858.18	−0.547318
$302$	2641.04	0.503227
$303$	2592.09	0.491458
$304$	−1905.21	−0.359445
$305$	0	0
$306$	−3560.07	−0.665084
$307$	5433.28	1.01008	0.505039	−	0.863097i	$-0.331478\pi$
$307$	5433.28	1.01008	0.505039	+	0.863097i	$0.331478\pi$
$308$	−895.169	−0.165607
$309$	5496.32	1.01189
$310$	0	0
$311$	513.012	0.0935377	0.0467689	−	0.998906i	$-0.485108\pi$
$311$	513.012	0.0935377	0.0467689	+	0.998906i	$0.485108\pi$
$312$	3131.76	0.568273
$313$	−996.467	−0.179948	−0.0899739	−	0.995944i	$-0.528678\pi$
$313$	−996.467	−0.179948	−0.0899739	+	0.995944i	$0.528678\pi$
$314$	−7649.72	−1.37484
$315$	0	0
$316$	−17940.7	−3.19381
$317$	4280.57	0.758425	0.379213	−	0.925310i	$-0.376195\pi$
$317$	4280.57	0.758425	0.379213	+	0.925310i	$0.376195\pi$
$318$	−5457.60	−0.962411
$319$	−252.180	−0.0442613
$320$	0	0
$321$	−3113.97	−0.541448
$322$	−19054.9	−3.29780
$323$	12139.1	2.09113
$324$	1106.56	0.189739
$325$	0	0
$326$	−5958.70	−1.01234
$327$	4671.10	0.789946
$328$	−9364.87	−1.57649
$329$	1513.49	0.253621
$330$	0	0
$331$	−2972.75	−0.493647	−0.246823	−	0.969060i	$-0.579387\pi$
$331$	−2972.75	−0.493647	−0.246823	+	0.969060i	$0.579387\pi$
$332$	−8933.07	−1.47670
$333$	−534.560	−0.0879691
$334$	−7337.78	−1.20211
$335$	0	0
$336$	−1042.24	−0.169223
$337$	1542.78	0.249379	0.124690	−	0.992196i	$-0.460206\pi$
$337$	1542.78	0.249379	0.124690	+	0.992196i	$0.460206\pi$
$338$	−2919.30	−0.469790
$339$	−2925.60	−0.468722
$340$	0	0
$341$	−436.165	−0.0692659
$342$	−5982.67	−0.945922
$343$	200.108	0.0315009
$344$	2891.51	0.453197
$345$	0	0
$346$	10339.8	1.60656
$347$	−5624.32	−0.870114	−0.435057	−	0.900403i	$-0.643272\pi$
$347$	−5624.32	−0.870114	−0.435057	+	0.900403i	$0.643272\pi$
$348$	−4107.92	−0.632780
$349$	3546.44	0.543945	0.271972	−	0.962305i	$-0.412324\pi$
$349$	3546.44	0.543945	0.271972	+	0.962305i	$0.412324\pi$
$350$	0	0
$351$	1069.74	0.162674
$352$	−374.127	−0.0566506
$353$	−1916.05	−0.288898	−0.144449	−	0.989512i	$-0.546141\pi$
$353$	−1916.05	−0.288898	−0.144449	+	0.989512i	$0.546141\pi$
$354$	5760.21	0.864835
$355$	0	0
$356$	14476.1	2.15514
$357$	6640.67	0.984487
$358$	14032.6	2.07164
$359$	2633.09	0.387101	0.193550	−	0.981090i	$-0.438000\pi$
$359$	2633.09	0.387101	0.193550	+	0.981090i	$0.438000\pi$
$360$	0	0
$361$	13540.6	1.97413
$362$	11508.1	1.67087
$363$	−3974.01	−0.574605
$364$	−14096.8	−2.02988
$365$	0	0
$366$	5007.44	0.715145
$367$	−6802.59	−0.967554	−0.483777	−	0.875191i	$-0.660735\pi$
$367$	−6802.59	−0.967554	−0.483777	+	0.875191i	$0.660735\pi$
$368$	2096.92	0.297037
$369$	−3198.84	−0.451287
$370$	0	0
$371$	10180.2	1.42460
$372$	−7104.98	−0.990258
$373$	−6705.12	−0.930772	−0.465386	−	0.885108i	$-0.654084\pi$
$373$	−6705.12	−0.930772	−0.465386	+	0.885108i	$0.654084\pi$
$374$	−995.212	−0.137597
$375$	0	0
$376$	−1531.14	−0.210007
$377$	−3971.25	−0.542519
$378$	−3272.82	−0.445332
$379$	3890.69	0.527312	0.263656	−	0.964617i	$-0.415072\pi$
$379$	3890.69	0.527312	0.263656	+	0.964617i	$0.415072\pi$
$380$	0	0
$381$	−3086.68	−0.415054
$382$	−2983.06	−0.399547
$383$	−5642.19	−0.752748	−0.376374	−	0.926468i	$-0.622829\pi$
$383$	−5642.19	−0.752748	−0.376374	+	0.926468i	$0.622829\pi$
$384$	−7584.39	−1.00791
$385$	0	0
$386$	−3066.87	−0.404403
$387$	987.679	0.129733
$388$	8763.68	1.14667
$389$	−4678.95	−0.609852	−0.304926	−	0.952376i	$-0.598632\pi$
$389$	−4678.95	−0.609852	−0.304926	+	0.952376i	$0.598632\pi$
$390$	0	0
$391$	−13360.6	−1.72806
$392$	8835.01	1.13836
$393$	−8009.71	−1.02808
$394$	13042.2	1.66766
$395$	0	0
$396$	309.337	0.0392544
$397$	8379.25	1.05930	0.529650	−	0.848216i	$-0.322323\pi$
$397$	8379.25	1.05930	0.529650	+	0.848216i	$0.322323\pi$
$398$	−12640.2	−1.59195
$399$	11159.6	1.40020
$400$	0	0
$401$	6042.30	0.752464	0.376232	−	0.926525i	$-0.377220\pi$
$401$	6042.30	0.752464	0.376232	+	0.926525i	$0.377220\pi$
$402$	4900.98	0.608056
$403$	−6868.59	−0.849005
$404$	11803.7	1.45360
$405$	0	0
$406$	12149.8	1.48518
$407$	−149.435	−0.0181996
$408$	−6718.12	−0.815188
$409$	6539.69	0.790628	0.395314	−	0.918546i	$-0.370636\pi$
$409$	6539.69	0.790628	0.395314	+	0.918546i	$0.370636\pi$
$410$	0	0
$411$	−3658.27	−0.439049
$412$	25028.8	2.99292
$413$	−10744.6	−1.28017
$414$	6584.67	0.781688
$415$	0	0
$416$	−5891.63	−0.694377
$417$	2625.88	0.308368
$418$	−1672.44	−0.195698
$419$	13109.1	1.52846	0.764228	−	0.644946i	$-0.223120\pi$
$419$	13109.1	1.52846	0.764228	+	0.644946i	$0.223120\pi$
$420$	0	0
$421$	3413.16	0.395124	0.197562	−	0.980290i	$-0.436698\pi$
$421$	3413.16	0.395124	0.197562	+	0.980290i	$0.436698\pi$
$422$	−8066.83	−0.930538
$423$	−523.004	−0.0601167
$424$	−10298.9	−1.17962
$425$	0	0
$426$	2385.18	0.271273
$427$	−9340.48	−1.05859
$428$	−14180.2	−1.60146
$429$	299.045	0.0336551
$430$	0	0
$431$	−1511.82	−0.168960	−0.0844801	−	0.996425i	$-0.526923\pi$
$431$	−1511.82	−0.168960	−0.0844801	+	0.996425i	$0.526923\pi$
$432$	360.160	0.0401116
$433$	−8624.67	−0.957218	−0.478609	−	0.878028i	$-0.658859\pi$
$433$	−8624.67	−0.957218	−0.478609	+	0.878028i	$0.658859\pi$
$434$	21014.0	2.32421
$435$	0	0
$436$	21271.0	2.33646
$437$	−22452.3	−2.45775
$438$	−13025.5	−1.42096
$439$	−3528.80	−0.383645	−0.191823	−	0.981430i	$-0.561440\pi$
$439$	−3528.80	−0.383645	−0.191823	+	0.981430i	$0.561440\pi$
$440$	0	0
$441$	3017.85	0.325867
$442$	−15672.3	−1.68655
$443$	−9589.40	−1.02846	−0.514228	−	0.857653i	$-0.671922\pi$
$443$	−9589.40	−1.02846	−0.514228	+	0.857653i	$0.671922\pi$
$444$	−2434.25	−0.260190
$445$	0	0
$446$	20371.9	2.16286
$447$	−2458.90	−0.260183
$448$	20804.4	2.19401
$449$	−9820.81	−1.03223	−0.516117	−	0.856518i	$-0.672623\pi$
$449$	−9820.81	−1.03223	−0.516117	+	0.856518i	$0.672623\pi$
$450$	0	0
$451$	−894.230	−0.0933650
$452$	−13322.4	−1.38636
$453$	1702.37	0.176566
$454$	−10465.9	−1.08192
$455$	0	0
$456$	−11289.7	−1.15941
$457$	1597.23	0.163491	0.0817455	−	0.996653i	$-0.473951\pi$
$457$	1597.23	0.163491	0.0817455	+	0.996653i	$0.473951\pi$
$458$	10450.1	1.06616
$459$	−2294.77	−0.233356
$460$	0	0
$461$	−3903.07	−0.394325	−0.197163	−	0.980371i	$-0.563173\pi$
$461$	−3903.07	−0.394325	−0.197163	+	0.980371i	$0.563173\pi$
$462$	−914.910	−0.0921330
$463$	−15661.9	−1.57208	−0.786039	−	0.618177i	$-0.787871\pi$
$463$	−15661.9	−1.57208	−0.786039	+	0.618177i	$0.787871\pi$
$464$	−1337.04	−0.133772
$465$	0	0
$466$	3296.90	0.327739
$467$	−6397.32	−0.633903	−0.316951	−	0.948442i	$-0.602659\pi$
$467$	−6397.32	−0.633903	−0.316951	+	0.948442i	$0.602659\pi$
$468$	4871.34	0.481149
$469$	−9141.89	−0.900071
$470$	0	0
$471$	−4930.89	−0.482385
$472$	10869.9	1.06002
$473$	276.104	0.0268399
$474$	−18336.4	−1.77683
$475$	0	0
$476$	30239.9	2.91186
$477$	−3517.88	−0.337679
$478$	25378.0	2.42837
$479$	−10285.8	−0.981153	−0.490576	−	0.871398i	$-0.663214\pi$
$479$	−10285.8	−0.981153	−0.490576	+	0.871398i	$0.663214\pi$
$480$	0	0
$481$	−2353.26	−0.223076
$482$	26625.2	2.51607
$483$	−12282.5	−1.15709
$484$	−18096.6	−1.69953
$485$	0	0
$486$	1130.96	0.105559
$487$	2083.46	0.193861	0.0969306	−	0.995291i	$-0.469098\pi$
$487$	2083.46	0.193861	0.0969306	+	0.995291i	$0.469098\pi$
$488$	9449.41	0.876546
$489$	−3840.88	−0.355196
$490$	0	0
$491$	17704.5	1.62727	0.813636	−	0.581374i	$-0.197485\pi$
$491$	17704.5	1.62727	0.813636	+	0.581374i	$0.197485\pi$
$492$	−14566.7	−1.33479
$493$	8518.94	0.778243
$494$	−26337.1	−2.39871
$495$	0	0
$496$	−2312.51	−0.209344
$497$	−4449.13	−0.401551
$498$	−9130.07	−0.821542
$499$	5018.92	0.450256	0.225128	−	0.974329i	$-0.427720\pi$
$499$	5018.92	0.450256	0.225128	+	0.974329i	$0.427720\pi$
$500$	0	0
$501$	−4729.82	−0.421782
$502$	9518.85	0.846309
$503$	−10061.9	−0.891924	−0.445962	−	0.895052i	$-0.647138\pi$
$503$	−10061.9	−0.891924	−0.445962	+	0.895052i	$0.647138\pi$
$504$	−6176.05	−0.545839
$505$	0	0
$506$	1840.73	0.161720
$507$	−1881.73	−0.164834
$508$	−14055.9	−1.22762
$509$	−5317.01	−0.463011	−0.231505	−	0.972834i	$-0.574365\pi$
$509$	−5317.01	−0.463011	−0.231505	+	0.972834i	$0.574365\pi$
$510$	0	0
$511$	24296.7	2.10337
$512$	−4795.32	−0.413916
$513$	−3856.33	−0.331893
$514$	1896.79	0.162770
$515$	0	0
$516$	4497.63	0.383716
$517$	−146.205	−0.0124373
$518$	7199.66	0.610685
$519$	6664.85	0.563689
$520$	0	0
$521$	−6274.02	−0.527582	−0.263791	−	0.964580i	$-0.584973\pi$
$521$	−6274.02	−0.527582	−0.263791	+	0.964580i	$0.584973\pi$
$522$	−4198.51	−0.352038
$523$	14059.6	1.17549	0.587746	−	0.809045i	$-0.300015\pi$
$523$	14059.6	1.17549	0.587746	+	0.809045i	$0.300015\pi$
$524$	−36474.1	−3.04080
$525$	0	0
$526$	−4130.50	−0.342392
$527$	14734.2	1.21790
$528$	100.682	0.00829853
$529$	12544.5	1.03103
$530$	0	0
$531$	3712.94	0.303442
$532$	50817.9	4.14142
$533$	−14082.0	−1.14439
$534$	14795.3	1.19898
$535$	0	0
$536$	9248.51	0.745289
$537$	9045.21	0.726871
$538$	28080.8	2.25028
$539$	843.635	0.0674173
$540$	0	0
$541$	−20130.6	−1.59978	−0.799891	−	0.600145i	$-0.795110\pi$
$541$	−20130.6	−1.59978	−0.799891	+	0.600145i	$0.795110\pi$
$542$	30414.6	2.41036
$543$	7417.97	0.586253
$544$	12638.5	0.996084
$545$	0	0
$546$	−14407.7	−1.12929
$547$	−13220.8	−1.03342	−0.516711	−	0.856160i	$-0.672844\pi$
$547$	−13220.8	−1.03342	−0.516711	+	0.856160i	$0.672844\pi$
$548$	−16658.8	−1.29859
$549$	3227.72	0.250921
$550$	0	0
$551$	14316.0	1.10686
$552$	12425.8	0.958108
$553$	34203.2	2.63014
$554$	−25628.3	−1.96542
$555$	0	0
$556$	11957.6	0.912074
$557$	−14165.4	−1.07757	−0.538786	−	0.842442i	$-0.681117\pi$
$557$	−14165.4	−1.07757	−0.538786	+	0.842442i	$0.681117\pi$
$558$	−7261.66	−0.550915
$559$	4348.00	0.328981
$560$	0	0
$561$	−641.498	−0.0482782
$562$	−34995.2	−2.62666
$563$	11266.9	0.843413	0.421707	−	0.906732i	$-0.361431\pi$
$563$	11266.9	0.843413	0.421707	+	0.906732i	$0.361431\pi$
$564$	−2381.63	−0.177810
$565$	0	0
$566$	20851.4	1.54850
$567$	−2109.61	−0.156252
$568$	4501.02	0.332497
$569$	−7401.52	−0.545322	−0.272661	−	0.962110i	$-0.587904\pi$
$569$	−7401.52	−0.545322	−0.272661	+	0.962110i	$0.587904\pi$
$570$	0	0
$571$	−13070.2	−0.957919	−0.478959	−	0.877837i	$-0.658986\pi$
$571$	−13070.2	−0.957919	−0.478959	+	0.877837i	$0.658986\pi$
$572$	1361.77	0.0995430
$573$	−1922.84	−0.140188
$574$	43083.2	3.13285
$575$	0	0
$576$	−7189.22	−0.520053
$577$	8216.81	0.592843	0.296421	−	0.955057i	$-0.404207\pi$
$577$	8216.81	0.592843	0.296421	+	0.955057i	$0.404207\pi$
$578$	10753.6	0.773857
$579$	−1976.86	−0.141892
$580$	0	0
$581$	17030.5	1.21608
$582$	8956.94	0.637933
$583$	−983.417	−0.0698610
$584$	−24580.0	−1.74166
$585$	0	0
$586$	−31053.3	−2.18908
$587$	19965.0	1.40382	0.701911	−	0.712265i	$-0.252331\pi$
$587$	19965.0	1.40382	0.701911	+	0.712265i	$0.252331\pi$
$588$	13742.5	0.963829
$589$	24760.7	1.73217
$590$	0	0
$591$	8406.80	0.585126
$592$	−792.293	−0.0550051
$593$	−14429.9	−0.999267	−0.499634	−	0.866237i	$-0.666532\pi$
$593$	−14429.9	−0.999267	−0.499634	+	0.866237i	$0.666532\pi$
$594$	316.158	0.0218386
$595$	0	0
$596$	−11197.2	−0.769555
$597$	−8147.67	−0.558563
$598$	28987.3	1.98224
$599$	−7838.61	−0.534686	−0.267343	−	0.963601i	$-0.586146\pi$
$599$	−7838.61	−0.534686	−0.267343	+	0.963601i	$0.586146\pi$
$600$	0	0
$601$	−25163.3	−1.70787	−0.853937	−	0.520376i	$-0.825792\pi$
$601$	−25163.3	−1.70787	−0.853937	+	0.520376i	$0.825792\pi$
$602$	−13302.4	−0.900609
$603$	3159.09	0.213347
$604$	7752.16	0.522237
$605$	0	0
$606$	12064.0	0.808691
$607$	−563.698	−0.0376932	−0.0188466	−	0.999822i	$-0.505999\pi$
$607$	−563.698	−0.0376932	−0.0188466	+	0.999822i	$0.505999\pi$
$608$	21238.8	1.41669
$609$	7831.56	0.521102
$610$	0	0
$611$	−2302.39	−0.152446
$612$	−10449.8	−0.690208
$613$	−6736.20	−0.443838	−0.221919	−	0.975065i	$-0.571232\pi$
$613$	−6736.20	−0.443838	−0.221919	+	0.975065i	$0.571232\pi$
$614$	25287.4	1.66208
$615$	0	0
$616$	−1726.50	−0.112927
$617$	−10198.6	−0.665448	−0.332724	−	0.943024i	$-0.607968\pi$
$617$	−10198.6	−0.665448	−0.332724	+	0.943024i	$0.607968\pi$
$618$	25580.8	1.66506
$619$	7579.25	0.492142	0.246071	−	0.969252i	$-0.420860\pi$
$619$	7579.25	0.492142	0.246071	+	0.969252i	$0.420860\pi$
$620$	0	0
$621$	4244.37	0.274269
$622$	2387.64	0.153916
$623$	−27598.0	−1.77478
$624$	1585.51	0.101717
$625$	0	0
$626$	−4637.72	−0.296103
$627$	−1078.03	−0.0686641
$628$	−22454.0	−1.42677
$629$	5048.11	0.320002
$630$	0	0
$631$	4575.59	0.288671	0.144335	−	0.989529i	$-0.453896\pi$
$631$	4575.59	0.288671	0.144335	+	0.989529i	$0.453896\pi$
$632$	−34602.1	−2.17784
$633$	−5199.75	−0.326495
$634$	19922.5	1.24799
$635$	0	0
$636$	−16019.5	−0.998766
$637$	13285.3	0.826346
$638$	−1173.69	−0.0728317
$639$	1537.45	0.0951809
$640$	0	0
$641$	−17713.6	−1.09149	−0.545745	−	0.837951i	$-0.683753\pi$
$641$	−17713.6	−1.09149	−0.545745	+	0.837951i	$0.683753\pi$
$642$	−14492.9	−0.890950
$643$	−13212.2	−0.810323	−0.405162	−	0.914245i	$-0.632785\pi$
$643$	−13212.2	−0.810323	−0.405162	+	0.914245i	$0.632785\pi$
$644$	−55931.4	−3.42237
$645$	0	0
$646$	56497.2	3.44095
$647$	4215.72	0.256163	0.128081	−	0.991764i	$-0.459118\pi$
$647$	4215.72	0.256163	0.128081	+	0.991764i	$0.459118\pi$
$648$	2134.21	0.129382
$649$	1037.95	0.0627780
$650$	0	0
$651$	13545.3	0.815488
$652$	−17490.4	−1.05058
$653$	26191.1	1.56958	0.784792	−	0.619759i	$-0.212770\pi$
$653$	26191.1	1.56958	0.784792	+	0.619759i	$0.212770\pi$
$654$	21740.1	1.29985
$655$	0	0
$656$	−4741.13	−0.282180
$657$	−8396.02	−0.498569
$658$	7044.02	0.417332
$659$	−12868.3	−0.760665	−0.380332	−	0.924850i	$-0.624190\pi$
$659$	−12868.3	−0.760665	−0.380332	+	0.924850i	$0.624190\pi$
$660$	0	0
$661$	−21599.8	−1.27101	−0.635503	−	0.772099i	$-0.719207\pi$
$661$	−21599.8	−1.27101	−0.635503	+	0.772099i	$0.719207\pi$
$662$	−13835.7	−0.812293
$663$	−10102.1	−0.591755
$664$	−17229.1	−1.00696
$665$	0	0
$666$	−2487.93	−0.144753
$667$	−15756.5	−0.914686
$668$	−21538.4	−1.24752
$669$	13131.4	0.758878
$670$	0	0
$671$	902.302	0.0519121
$672$	11618.7	0.666965
$673$	10572.3	0.605546	0.302773	−	0.953063i	$-0.402088\pi$
$673$	10572.3	0.605546	0.302773	+	0.953063i	$0.402088\pi$
$674$	7180.37	0.410352
$675$	0	0
$676$	−8568.93	−0.487536
$677$	−15661.0	−0.889070	−0.444535	−	0.895762i	$-0.646631\pi$
$677$	−15661.0	−0.889070	−0.444535	+	0.895762i	$0.646631\pi$
$678$	−13616.2	−0.771279
$679$	−16707.6	−0.944296
$680$	0	0
$681$	−6746.18	−0.379610
$682$	−2029.98	−0.113977
$683$	23697.9	1.32763	0.663817	−	0.747895i	$-0.268935\pi$
$683$	23697.9	1.32763	0.663817	+	0.747895i	$0.268935\pi$
$684$	−17560.7	−0.981655
$685$	0	0
$686$	931.335	0.0518346
$687$	6735.97	0.374080
$688$	1463.88	0.0811189
$689$	−15486.5	−0.856300
$690$	0	0
$691$	4426.30	0.243682	0.121841	−	0.992550i	$-0.461120\pi$
$691$	4426.30	0.243682	0.121841	+	0.992550i	$0.461120\pi$
$692$	30350.0	1.66725
$693$	−589.736	−0.0323265
$694$	−26176.5	−1.43177
$695$	0	0
$696$	−7922.90	−0.431490
$697$	30208.2	1.64163
$698$	16505.7	0.895059
$699$	2125.13	0.114993
$700$	0	0
$701$	5192.49	0.279768	0.139884	−	0.990168i	$-0.455327\pi$
$701$	5192.49	0.279768	0.139884	+	0.990168i	$0.455327\pi$
$702$	4978.76	0.267680
$703$	8483.30	0.455126
$704$	−2009.73	−0.107592
$705$	0	0
$706$	−8917.59	−0.475379
$707$	−22503.2	−1.19706
$708$	16907.8	0.897504
$709$	−1120.17	−0.0593356	−0.0296678	−	0.999560i	$-0.509445\pi$
$709$	−1120.17	−0.0593356	−0.0296678	+	0.999560i	$0.509445\pi$
$710$	0	0
$711$	−11819.3	−0.623431
$712$	27919.9	1.46958
$713$	−27252.2	−1.43142
$714$	30906.8	1.61997
$715$	0	0
$716$	41189.5	2.14990
$717$	16358.2	0.852036
$718$	12254.8	0.636973
$719$	22785.4	1.18185	0.590927	−	0.806725i	$-0.298762\pi$
$719$	22785.4	1.18185	0.590927	+	0.806725i	$0.298762\pi$
$720$	0	0
$721$	−47716.3	−2.46470
$722$	63020.1	3.24843
$723$	17162.2	0.882806
$724$	33779.5	1.73399
$725$	0	0
$726$	−18495.7	−0.945509
$727$	32028.6	1.63394	0.816970	−	0.576680i	$-0.195652\pi$
$727$	32028.6	1.63394	0.816970	+	0.576680i	$0.195652\pi$
$728$	−27188.4	−1.38416
$729$	729.000	0.0370370
$730$	0	0
$731$	−9327.13	−0.471924
$732$	14698.2	0.742159
$733$	21723.1	1.09463	0.547313	−	0.836928i	$-0.315651\pi$
$733$	21723.1	1.09463	0.547313	+	0.836928i	$0.315651\pi$
$734$	−31660.4	−1.59211
$735$	0	0
$736$	−23376.0	−1.17072
$737$	883.119	0.0441385
$738$	−14887.9	−0.742590
$739$	30000.0	1.49332	0.746662	−	0.665203i	$-0.231655\pi$
$739$	30000.0	1.49332	0.746662	+	0.665203i	$0.231655\pi$
$740$	0	0
$741$	−16976.5	−0.841629
$742$	47380.2	2.34418
$743$	−5551.03	−0.274088	−0.137044	−	0.990565i	$-0.543760\pi$
$743$	−5551.03	−0.274088	−0.137044	+	0.990565i	$0.543760\pi$
$744$	−13703.3	−0.675251
$745$	0	0
$746$	−31206.7	−1.53158
$747$	−5885.10	−0.288252
$748$	−2921.21	−0.142794
$749$	27033.9	1.31882
$750$	0	0
$751$	5337.87	0.259363	0.129682	−	0.991556i	$-0.458604\pi$
$751$	5337.87	0.259363	0.129682	+	0.991556i	$0.458604\pi$
$752$	−775.166	−0.0375896
$753$	6135.70	0.296942
$754$	−18482.8	−0.892712
$755$	0	0
$756$	−9606.60	−0.462154
$757$	−17462.2	−0.838409	−0.419205	−	0.907892i	$-0.637691\pi$
$757$	−17462.2	−0.838409	−0.419205	+	0.907892i	$0.637691\pi$
$758$	18107.9	0.867690
$759$	1186.51	0.0567424
$760$	0	0
$761$	13611.2	0.648367	0.324183	−	0.945994i	$-0.394911\pi$
$761$	13611.2	0.648367	0.324183	+	0.945994i	$0.394911\pi$
$762$	−14365.9	−0.682969
$763$	−40552.2	−1.92410
$764$	−8756.10	−0.414639
$765$	0	0
$766$	−26259.7	−1.23864
$767$	16345.2	0.769481
$768$	−16127.7	−0.757759
$769$	−23956.9	−1.12342	−0.561709	−	0.827335i	$-0.689856\pi$
$769$	−23956.9	−1.12342	−0.561709	+	0.827335i	$0.689856\pi$
$770$	0	0
$771$	1222.64	0.0571107
$772$	−9002.10	−0.419680
$773$	−35279.7	−1.64156	−0.820779	−	0.571246i	$-0.806460\pi$
$773$	−35279.7	−1.64156	−0.820779	+	0.571246i	$0.806460\pi$
$774$	4596.82	0.213474
$775$	0	0
$776$	16902.4	0.781909
$777$	4640.79	0.214269
$778$	−21776.6	−1.00351
$779$	50764.5	2.33482
$780$	0	0
$781$	429.792	0.0196916
$782$	−62182.2	−2.84352
$783$	−2706.29	−0.123519
$784$	4472.88	0.203757
$785$	0	0
$786$	−37278.5	−1.69170
$787$	−3904.96	−0.176870	−0.0884351	−	0.996082i	$-0.528187\pi$
$787$	−3904.96	−0.176870	−0.0884351	+	0.996082i	$0.528187\pi$
$788$	38282.4	1.73065
$789$	−2662.46	−0.120134
$790$	0	0
$791$	25398.6	1.14168
$792$	596.614	0.0267674
$793$	14209.2	0.636296
$794$	38998.4	1.74307
$795$	0	0
$796$	−37102.4	−1.65208
$797$	6743.01	0.299686	0.149843	−	0.988710i	$-0.452123\pi$
$797$	6743.01	0.299686	0.149843	+	0.988710i	$0.452123\pi$
$798$	51938.5	2.30402
$799$	4938.98	0.218684
$800$	0	0
$801$	9536.83	0.420683
$802$	28121.8	1.23818
$803$	−2347.09	−0.103147
$804$	14385.7	0.631025
$805$	0	0
$806$	−31967.5	−1.39703
$807$	18100.4	0.789548
$808$	22765.7	0.991205
$809$	13083.1	0.568577	0.284288	−	0.958739i	$-0.408243\pi$
$809$	13083.1	0.568577	0.284288	+	0.958739i	$0.408243\pi$
$810$	0	0
$811$	7501.06	0.324782	0.162391	−	0.986727i	$-0.448079\pi$
$811$	7501.06	0.324782	0.162391	+	0.986727i	$0.448079\pi$
$812$	35662.9	1.54128
$813$	19604.8	0.845718
$814$	−695.496	−0.0299473
$815$	0	0
$816$	−3401.17	−0.145913
$817$	−15674.1	−0.671198
$818$	30436.8	1.30097
$819$	−9286.98	−0.396231
$820$	0	0
$821$	−23440.2	−0.996431	−0.498215	−	0.867053i	$-0.666011\pi$
$821$	−23440.2	−0.996431	−0.498215	+	0.867053i	$0.666011\pi$
$822$	−17026.2	−0.722452
$823$	−6213.94	−0.263189	−0.131594	−	0.991304i	$-0.542010\pi$
$823$	−6213.94	−0.263189	−0.131594	+	0.991304i	$0.542010\pi$
$824$	48272.8	2.04085
$825$	0	0
$826$	−50007.3	−2.10651
$827$	−589.434	−0.0247843	−0.0123922	−	0.999923i	$-0.503945\pi$
$827$	−589.434	−0.0247843	−0.0123922	+	0.999923i	$0.503945\pi$
$828$	19327.8	0.811216
$829$	39666.0	1.66183	0.830916	−	0.556398i	$-0.187817\pi$
$829$	39666.0	1.66183	0.830916	+	0.556398i	$0.187817\pi$
$830$	0	0
$831$	−16519.6	−0.689601
$832$	−31648.6	−1.31877
$833$	−28499.0	−1.18539
$834$	12221.2	0.507419
$835$	0	0
$836$	−4909.07	−0.203091
$837$	−4680.75	−0.193298
$838$	61012.0	2.51507
$839$	−6048.43	−0.248885	−0.124443	−	0.992227i	$-0.539714\pi$
$839$	−6048.43	−0.248885	−0.124443	+	0.992227i	$0.539714\pi$
$840$	0	0
$841$	−14342.3	−0.588066
$842$	15885.4	0.650174
$843$	−22557.4	−0.921610
$844$	−23678.3	−0.965689
$845$	0	0
$846$	−2434.15	−0.0989216
$847$	34500.4	1.39958
$848$	−5213.99	−0.211143
$849$	13440.5	0.543317
$850$	0	0
$851$	−9336.93	−0.376105
$852$	7001.16	0.281521
$853$	−31051.4	−1.24640	−0.623200	−	0.782063i	$-0.714168\pi$
$853$	−31051.4	−1.24640	−0.623200	+	0.782063i	$0.714168\pi$
$854$	−43472.1	−1.74190
$855$	0	0
$856$	−27349.2	−1.09203
$857$	10170.1	0.405371	0.202685	−	0.979244i	$-0.435033\pi$
$857$	10170.1	0.405371	0.202685	+	0.979244i	$0.435033\pi$
$858$	1391.80	0.0553792
$859$	−41323.5	−1.64137	−0.820687	−	0.571378i	$-0.806409\pi$
$859$	−41323.5	−1.64137	−0.820687	+	0.571378i	$0.806409\pi$
$860$	0	0
$861$	27770.7	1.09921
$862$	−7036.26	−0.278023
$863$	30910.9	1.21926	0.609628	−	0.792688i	$-0.291319\pi$
$863$	30910.9	1.21926	0.609628	+	0.792688i	$0.291319\pi$
$864$	−4014.98	−0.158093
$865$	0	0
$866$	−40140.6	−1.57510
$867$	6931.58	0.271521
$868$	61681.9	2.41200
$869$	−3304.07	−0.128979
$870$	0	0
$871$	13907.1	0.541014
$872$	41025.1	1.59322
$873$	5773.50	0.223830
$874$	−104497.	−4.04422
$875$	0	0
$876$	−38233.3	−1.47464
$877$	−10750.3	−0.413923	−0.206961	−	0.978349i	$-0.566357\pi$
$877$	−10750.3	−0.413923	−0.206961	+	0.978349i	$0.566357\pi$
$878$	−16423.6	−0.631286
$879$	−20016.5	−0.768077
$880$	0	0
$881$	−20982.9	−0.802419	−0.401209	−	0.915986i	$-0.631410\pi$
$881$	−20982.9	−0.802419	−0.401209	+	0.915986i	$0.631410\pi$
$882$	14045.6	0.536212
$883$	−30286.5	−1.15427	−0.577136	−	0.816648i	$-0.695830\pi$
$883$	−30286.5	−1.15427	−0.577136	+	0.816648i	$0.695830\pi$
$884$	−46002.4	−1.75026
$885$	0	0
$886$	−44630.6	−1.69232
$887$	18397.5	0.696423	0.348212	−	0.937416i	$-0.386789\pi$
$887$	18397.5	0.696423	0.348212	+	0.937416i	$0.386789\pi$
$888$	−4694.91	−0.177422
$889$	26797.0	1.01096
$890$	0	0
$891$	203.791	0.00766245
$892$	59797.0	2.24457
$893$	8299.91	0.311026
$894$	−11444.1	−0.428130
$895$	0	0
$896$	65843.9	2.45501
$897$	18684.7	0.695502
$898$	−45707.6	−1.69853
$899$	17376.5	0.644649
$900$	0	0
$901$	33221.1	1.22836
$902$	−4161.89	−0.153632
$903$	−8574.54	−0.315994
$904$	−25694.8	−0.945350
$905$	0	0
$906$	7923.12	0.290539
$907$	−22143.3	−0.810648	−0.405324	−	0.914173i	$-0.632841\pi$
$907$	−22143.3	−0.810648	−0.405324	+	0.914173i	$0.632841\pi$
$908$	−30720.4	−1.12279
$909$	7776.27	0.283743
$910$	0	0
$911$	42399.1	1.54198	0.770991	−	0.636846i	$-0.219761\pi$
$911$	42399.1	1.54198	0.770991	+	0.636846i	$0.219761\pi$
$912$	−5715.63	−0.207526
$913$	−1645.17	−0.0596354
$914$	7433.78	0.269024
$915$	0	0
$916$	30673.9	1.10643
$917$	69536.3	2.50414
$918$	−10680.2	−0.383986
$919$	11557.8	0.414859	0.207429	−	0.978250i	$-0.433490\pi$
$919$	11557.8	0.414859	0.207429	+	0.978250i	$0.433490\pi$
$920$	0	0
$921$	16299.9	0.583169
$922$	−18165.5	−0.648860
$923$	6768.22	0.241364
$924$	−2685.51	−0.0956133
$925$	0	0
$926$	−72893.2	−2.58685
$927$	16489.0	0.584216
$928$	14905.0	0.527240
$929$	−16273.9	−0.574735	−0.287367	−	0.957820i	$-0.592780\pi$
$929$	−16273.9	−0.574735	−0.287367	+	0.957820i	$0.592780\pi$
$930$	0	0
$931$	−47892.3	−1.68594
$932$	9677.31	0.340119
$933$	1539.04	0.0540040
$934$	−29774.2	−1.04308
$935$	0	0
$936$	9395.29	0.328093
$937$	−39685.9	−1.38365	−0.691825	−	0.722065i	$-0.743193\pi$
$937$	−39685.9	−1.38365	−0.691825	+	0.722065i	$0.743193\pi$
$938$	−42547.8	−1.48106
$939$	−2989.40	−0.103893
$940$	0	0
$941$	−21618.8	−0.748940	−0.374470	−	0.927239i	$-0.622175\pi$
$941$	−21618.8	−0.748940	−0.374470	+	0.927239i	$0.622175\pi$
$942$	−22949.2	−0.793762
$943$	−55872.7	−1.92944
$944$	5503.10	0.189736
$945$	0	0
$946$	1285.03	0.0441649
$947$	3083.65	0.105813	0.0529066	−	0.998599i	$-0.483151\pi$
$947$	3083.65	0.105813	0.0529066	+	0.998599i	$0.483151\pi$
$948$	−53822.2	−1.84395
$949$	−36961.2	−1.26429
$950$	0	0
$951$	12841.7	0.437877
$952$	58323.4	1.98558
$953$	35749.5	1.21515	0.607576	−	0.794261i	$-0.292142\pi$
$953$	35749.5	1.21515	0.607576	+	0.794261i	$0.292142\pi$
$954$	−16372.8	−0.555649
$955$	0	0
$956$	74491.2	2.52010
$957$	−756.539	−0.0255543
$958$	−47872.0	−1.61448
$959$	31759.3	1.06941
$960$	0	0
$961$	263.073	0.00883061
$962$	−10952.5	−0.367070
$963$	−9341.91	−0.312605
$964$	78152.2	2.61111
$965$	0	0
$966$	−57164.8	−1.90398
$967$	−23629.2	−0.785796	−0.392898	−	0.919582i	$-0.628527\pi$
$967$	−23629.2	−0.785796	−0.392898	+	0.919582i	$0.628527\pi$
$968$	−34902.7	−1.15890
$969$	36417.2	1.20732
$970$	0	0
$971$	15734.9	0.520039	0.260019	−	0.965603i	$-0.416271\pi$
$971$	15734.9	0.520039	0.260019	+	0.965603i	$0.416271\pi$
$972$	3319.68	0.109546
$973$	−22796.5	−0.751104
$974$	9696.74	0.318997
$975$	0	0
$976$	4783.93	0.156895
$977$	−4163.71	−0.136345	−0.0681724	−	0.997674i	$-0.521717\pi$
$977$	−4163.71	−0.136345	−0.0681724	+	0.997674i	$0.521717\pi$
$978$	−17876.1	−0.584473
$979$	2666.00	0.0870335
$980$	0	0
$981$	14013.3	0.456076
$982$	82399.4	2.67767
$983$	−40241.6	−1.30571	−0.652853	−	0.757485i	$-0.726428\pi$
$983$	−40241.6	−1.30571	−0.652853	+	0.757485i	$0.726428\pi$
$984$	−28094.6	−0.910186
$985$	0	0
$986$	39648.5	1.28060
$987$	4540.47	0.146428
$988$	−77306.5	−2.48932
$989$	17251.3	0.554662
$990$	0	0
$991$	52220.5	1.67390	0.836952	−	0.547276i	$-0.184335\pi$
$991$	52220.5	1.67390	0.836952	+	0.547276i	$0.184335\pi$
$992$	25779.3	0.825095
$993$	−8918.25	−0.285007
$994$	−20707.0	−0.660750
$995$	0	0
$996$	−26799.2	−0.852576
$997$	−57238.6	−1.81822	−0.909109	−	0.416558i	$-0.863236\pi$
$997$	−57238.6	−1.81822	−0.909109	+	0.416558i	$0.863236\pi$
$998$	23358.9	0.740894
$999$	−1603.68	−0.0507890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.g.1.13		14
5.4	even	2		1875.4.a.f.1.2		14
25.6	even	5		75.4.g.b.61.1	yes	28
25.21	even	5		75.4.g.b.16.1	✓	28
75.56	odd	10		225.4.h.a.136.7		28
75.71	odd	10		225.4.h.a.91.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.1	✓	28	25.21	even	5
75.4.g.b.61.1	yes	28	25.6	even	5
225.4.h.a.91.7		28	75.71	odd	10
225.4.h.a.136.7		28	75.56	odd	10
1875.4.a.f.1.2		14	5.4	even	2
1875.4.a.g.1.13		14	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+4.65416 q^{2} +3.00000 q^{3} +13.6612 q^{4} +13.9625 q^{6} -26.0445 q^{7} +26.3483 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.65416 q^{2} +3.00000 q^{3} +13.6612 q^{4} +13.9625 q^{6} -26.0445 q^{7} +26.3483 q^{8} +9.00000 q^{9} +2.51593 q^{11} +40.9837 q^{12} +39.6201 q^{13} -121.215 q^{14} +13.3393 q^{16} -84.9913 q^{17} +41.8875 q^{18} -142.827 q^{19} -78.1335 q^{21} +11.7096 q^{22} +157.199 q^{23} +79.0448 q^{24} +184.399 q^{26} +27.0000 q^{27} -355.800 q^{28} -100.233 q^{29} -173.361 q^{31} -148.703 q^{32} +7.54780 q^{33} -395.563 q^{34} +122.951 q^{36} -59.3956 q^{37} -664.741 q^{38} +118.860 q^{39} -355.427 q^{41} -363.646 q^{42} +109.742 q^{43} +34.3707 q^{44} +731.630 q^{46} -58.1116 q^{47} +40.0178 q^{48} +335.317 q^{49} -254.974 q^{51} +541.260 q^{52} -390.876 q^{53} +125.662 q^{54} -686.228 q^{56} -428.481 q^{57} -466.501 q^{58} +412.549 q^{59} +358.635 q^{61} -806.851 q^{62} -234.401 q^{63} -798.802 q^{64} +35.1287 q^{66} +351.010 q^{67} -1161.09 q^{68} +471.597 q^{69} +170.828 q^{71} +237.134 q^{72} -932.891 q^{73} -276.437 q^{74} -1951.19 q^{76} -65.5263 q^{77} +553.196 q^{78} -1313.26 q^{79} +81.0000 q^{81} -1654.21 q^{82} -653.900 q^{83} -1067.40 q^{84} +510.757 q^{86} -300.699 q^{87} +66.2905 q^{88} +1059.65 q^{89} -1031.89 q^{91} +2147.53 q^{92} -520.083 q^{93} -270.461 q^{94} -446.109 q^{96} +641.500 q^{97} +1560.62 q^{98} +22.6434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9}+O(q^{10}) \) 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9	\( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9} - 33 q^{11} + 150 q^{12} - 188 q^{13} - 287 q^{14} + 82 q^{16} - 146 q^{17} - 184 q^{19} - 81 q^{21} - 277 q^{22} - 164 q^{23} + 63 q^{24} + 103 q^{26} + 378 q^{27} + 224 q^{28} + 252 q^{29} - 889 q^{31} - 422 q^{32} - 99 q^{33} - 230 q^{34} + 450 q^{36} - 642 q^{37} - 1833 q^{38} - 564 q^{39} - 164 q^{41} - 861 q^{42} - 696 q^{43} - 6 q^{44} - 419 q^{46} + 92 q^{47} + 246 q^{48} + 81 q^{49} - 438 q^{51} - 1956 q^{52} - 949 q^{53} - 2380 q^{56} - 552 q^{57} - 1041 q^{58} - 81 q^{59} - 496 q^{61} - 1454 q^{62} - 243 q^{63} - 3903 q^{64} - 831 q^{66} - 1926 q^{67} - 685 q^{68} - 492 q^{69} + 2498 q^{71} + 189 q^{72} + 1026 q^{73} - 707 q^{74} - 5704 q^{76} - 5434 q^{77} + 309 q^{78} - 695 q^{79} + 1134 q^{81} + 886 q^{82} - 5315 q^{83} + 672 q^{84} + 3997 q^{86} + 756 q^{87} - 2969 q^{88} - 1424 q^{89} - 1194 q^{91} - 1607 q^{92} - 2667 q^{93} - 629 q^{94} - 1266 q^{96} - 291 q^{97} + 1018 q^{98} - 297 q^{99}+O(q^{100}) \) 14 * q + 42 * q^3 + 50 * q^4 - 27 * q^7 + 21 * q^8 + 126 * q^9 - 33 * q^11 + 150 * q^12 - 188 * q^13 - 287 * q^14 + 82 * q^16 - 146 * q^17 - 184 * q^19 - 81 * q^21 - 277 * q^22 - 164 * q^23 + 63 * q^24 + 103 * q^26 + 378 * q^27 + 224 * q^28 + 252 * q^29 - 889 * q^31 - 422 * q^32 - 99 * q^33 - 230 * q^34 + 450 * q^36 - 642 * q^37 - 1833 * q^38 - 564 * q^39 - 164 * q^41 - 861 * q^42 - 696 * q^43 - 6 * q^44 - 419 * q^46 + 92 * q^47 + 246 * q^48 + 81 * q^49 - 438 * q^51 - 1956 * q^52 - 949 * q^53 - 2380 * q^56 - 552 * q^57 - 1041 * q^58 - 81 * q^59 - 496 * q^61 - 1454 * q^62 - 243 * q^63 - 3903 * q^64 - 831 * q^66 - 1926 * q^67 - 685 * q^68 - 492 * q^69 + 2498 * q^71 + 189 * q^72 + 1026 * q^73 - 707 * q^74 - 5704 * q^76 - 5434 * q^77 + 309 * q^78 - 695 * q^79 + 1134 * q^81 + 886 * q^82 - 5315 * q^83 + 672 * q^84 + 3997 * q^86 + 756 * q^87 - 2969 * q^88 - 1424 * q^89 - 1194 * q^91 - 1607 * q^92 - 2667 * q^93 - 629 * q^94 - 1266 * q^96 - 291 * q^97 + 1018 * q^98 - 297 * q^99

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