LMFDB - Embedded newform 1075.4.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1075.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.4270532562$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.17112$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +10.2909 q^{6} -4.58222 q^{7} -5.83236 q^{8} -20.9131 q^{9} +O(q^{10})$	\(q-4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +10.2909 q^{6} -4.58222 q^{7} -5.83236 q^{8} -20.9131 q^{9} +26.9150 q^{11} -23.1872 q^{12} +15.6529 q^{13} +19.1130 q^{14} -50.8587 q^{16} -27.2420 q^{17} +87.2309 q^{18} +38.3104 q^{19} +11.3051 q^{21} -112.266 q^{22} -82.5575 q^{23} +14.3894 q^{24} -65.2903 q^{26} +118.210 q^{27} -43.0650 q^{28} -34.2852 q^{29} +119.055 q^{31} +258.797 q^{32} -66.4040 q^{33} +113.630 q^{34} -196.547 q^{36} -378.527 q^{37} -159.797 q^{38} -38.6185 q^{39} +385.478 q^{41} -47.1551 q^{42} +43.0000 q^{43} +252.955 q^{44} +344.358 q^{46} -271.022 q^{47} +125.477 q^{48} -322.003 q^{49} +67.2108 q^{51} +147.110 q^{52} +329.363 q^{53} -493.068 q^{54} +26.7252 q^{56} -94.5184 q^{57} +143.008 q^{58} -173.956 q^{59} +54.5012 q^{61} -496.592 q^{62} +95.8283 q^{63} -672.604 q^{64} +276.979 q^{66} +906.954 q^{67} -256.028 q^{68} +203.684 q^{69} -621.376 q^{71} +121.972 q^{72} +1025.87 q^{73} +1578.88 q^{74} +360.052 q^{76} -123.331 q^{77} +161.082 q^{78} -737.945 q^{79} +273.009 q^{81} -1607.88 q^{82} -558.465 q^{83} +106.249 q^{84} -179.358 q^{86} +84.5875 q^{87} -156.978 q^{88} +1631.31 q^{89} -71.7252 q^{91} -775.898 q^{92} -293.729 q^{93} +1130.47 q^{94} -638.496 q^{96} +406.607 q^{97} +1343.12 q^{98} -562.875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.17112	−1.47471	−0.737357	−	0.675503i	$-0.763927\pi$
$2$	−4.17112	−1.47471	−0.737357	+	0.675503i	$0.763927\pi$
$3$	−2.46717	−0.474808	−0.237404	−	0.971411i	$-0.576296\pi$
$3$	−2.46717	−0.474808	−0.237404	+	0.971411i	$0.576296\pi$
$4$	9.39827	1.17478
$5$	0	0
$5$	0	0
$6$	10.2909	0.700206
$7$	−4.58222	−0.247417	−0.123708	−	0.992319i	$-0.539479\pi$
$7$	−4.58222	−0.247417	−0.123708	+	0.992319i	$0.539479\pi$
$8$	−5.83236	−0.257756
$9$	−20.9131	−0.774558
$10$	0	0
$11$	26.9150	0.737744	0.368872	−	0.929480i	$-0.379744\pi$
$11$	26.9150	0.737744	0.368872	+	0.929480i	$0.379744\pi$
$12$	−23.1872	−0.557796
$13$	15.6529	0.333949	0.166975	−	0.985961i	$-0.446600\pi$
$13$	15.6529	0.333949	0.166975	+	0.985961i	$0.446600\pi$
$14$	19.1130	0.364869
$15$	0	0
$16$	−50.8587	−0.794667
$17$	−27.2420	−0.388657	−0.194328	−	0.980937i	$-0.562253\pi$
$17$	−27.2420	−0.388657	−0.194328	+	0.980937i	$0.562253\pi$
$18$	87.2309	1.14225
$19$	38.3104	0.462580	0.231290	−	0.972885i	$-0.425705\pi$
$19$	38.3104	0.462580	0.231290	+	0.972885i	$0.425705\pi$
$20$	0	0
$21$	11.3051	0.117475
$22$	−112.266	−1.08796
$23$	−82.5575	−0.748453	−0.374227	−	0.927337i	$-0.622092\pi$
$23$	−82.5575	−0.748453	−0.374227	+	0.927337i	$0.622092\pi$
$24$	14.3894	0.122385
$25$	0	0
$26$	−65.2903	−0.492480
$27$	118.210	0.842574
$28$	−43.0650	−0.290661
$29$	−34.2852	−0.219538	−0.109769	−	0.993957i	$-0.535011\pi$
$29$	−34.2852	−0.219538	−0.109769	+	0.993957i	$0.535011\pi$
$30$	0	0
$31$	119.055	0.689770	0.344885	−	0.938645i	$-0.387918\pi$
$31$	119.055	0.689770	0.344885	+	0.938645i	$0.387918\pi$
$32$	258.797	1.42966
$33$	−66.4040	−0.350286
$34$	113.630	0.573158
$35$	0	0
$36$	−196.547	−0.909938
$37$	−378.527	−1.68188	−0.840939	−	0.541129i	$-0.817997\pi$
$37$	−378.527	−1.68188	−0.840939	+	0.541129i	$0.817997\pi$
$38$	−159.797	−0.682173
$39$	−38.6185	−0.158562
$40$	0	0
$41$	385.478	1.46833	0.734166	−	0.678970i	$-0.237573\pi$
$41$	385.478	1.46833	0.734166	+	0.678970i	$0.237573\pi$
$42$	−47.1551	−0.173243
$43$	43.0000	0.152499
$43$	43.0000	0.152499
$44$	252.955	0.866689
$45$	0	0
$46$	344.358	1.10376
$47$	−271.022	−0.841120	−0.420560	−	0.907265i	$-0.638166\pi$
$47$	−271.022	−0.841120	−0.420560	+	0.907265i	$0.638166\pi$
$48$	125.477	0.377314
$49$	−322.003	−0.938785
$50$	0	0
$51$	67.2108	0.184537
$52$	147.110	0.392318
$53$	329.363	0.853612	0.426806	−	0.904343i	$-0.359639\pi$
$53$	329.363	0.853612	0.426806	+	0.904343i	$0.359639\pi$
$54$	−493.068	−1.24256
$55$	0	0
$56$	26.7252	0.0637732
$57$	−94.5184	−0.219636
$58$	143.008	0.323756
$59$	−173.956	−0.383849	−0.191924	−	0.981410i	$-0.561473\pi$
$59$	−173.956	−0.383849	−0.191924	+	0.981410i	$0.561473\pi$
$60$	0	0
$61$	54.5012	0.114396	0.0571981	−	0.998363i	$-0.481783\pi$
$61$	54.5012	0.114396	0.0571981	+	0.998363i	$0.481783\pi$
$62$	−496.592	−1.01721
$63$	95.8283	0.191639
$64$	−672.604	−1.31368
$65$	0	0
$66$	276.979	0.516572
$67$	906.954	1.65376	0.826881	−	0.562377i	$-0.190113\pi$
$67$	906.954	1.65376	0.826881	+	0.562377i	$0.190113\pi$
$68$	−256.028	−0.456588
$69$	203.684	0.355371
$70$	0	0
$71$	−621.376	−1.03864	−0.519322	−	0.854579i	$-0.673816\pi$
$71$	−621.376	−1.03864	−0.519322	+	0.854579i	$0.673816\pi$
$72$	121.972	0.199647
$73$	1025.87	1.64477	0.822387	−	0.568928i	$-0.192642\pi$
$73$	1025.87	1.64477	0.822387	+	0.568928i	$0.192642\pi$
$74$	1578.88	2.48029
$75$	0	0
$76$	360.052	0.543431
$77$	−123.331	−0.182530
$78$	161.082	0.233833
$79$	−737.945	−1.05095	−0.525476	−	0.850808i	$-0.676113\pi$
$79$	−737.945	−1.05095	−0.525476	+	0.850808i	$0.676113\pi$
$80$	0	0
$81$	273.009	0.374497
$82$	−1607.88	−2.16537
$83$	−558.465	−0.738548	−0.369274	−	0.929321i	$-0.620394\pi$
$83$	−558.465	−0.738548	−0.369274	+	0.929321i	$0.620394\pi$
$84$	106.249	0.138008
$85$	0	0
$86$	−179.358	−0.224892
$87$	84.5875	0.104238
$88$	−156.978	−0.190158
$89$	1631.31	1.94291	0.971453	−	0.237231i	$-0.0762398\pi$
$89$	1631.31	1.94291	0.971453	+	0.237231i	$0.0762398\pi$
$90$	0	0
$91$	−71.7252	−0.0826247
$92$	−775.898	−0.879271
$93$	−293.729	−0.327508
$94$	1130.47	1.24041
$95$	0	0
$96$	−638.496	−0.678815
$97$	406.607	0.425616	0.212808	−	0.977094i	$-0.431739\pi$
$97$	406.607	0.425616	0.212808	+	0.977094i	$0.431739\pi$
$98$	1343.12	1.38444
$99$	−562.875	−0.571425
$100$	0	0
$101$	1000.43	0.985606	0.492803	−	0.870141i	$-0.335972\pi$
$101$	1000.43	0.985606	0.492803	+	0.870141i	$0.335972\pi$
$102$	−280.345	−0.272140
$103$	1659.81	1.58783	0.793913	−	0.608031i	$-0.208040\pi$
$103$	1659.81	1.58783	0.793913	+	0.608031i	$0.208040\pi$
$104$	−91.2935	−0.0860775
$105$	0	0
$106$	−1373.81	−1.25883
$107$	151.590	0.136961	0.0684803	−	0.997652i	$-0.478185\pi$
$107$	151.590	0.136961	0.0684803	+	0.997652i	$0.478185\pi$
$108$	1110.97	0.989842
$109$	1092.76	0.960254	0.480127	−	0.877199i	$-0.340591\pi$
$109$	1092.76	0.960254	0.480127	+	0.877199i	$0.340591\pi$
$110$	0	0
$111$	933.892	0.798569
$112$	233.046	0.196614
$113$	970.442	0.807889	0.403945	−	0.914783i	$-0.367639\pi$
$113$	970.442	0.807889	0.403945	+	0.914783i	$0.367639\pi$
$114$	394.248	0.323901
$115$	0	0
$116$	−322.222	−0.257910
$117$	−327.351	−0.258663
$118$	725.590	0.566068
$119$	124.829	0.0961602
$120$	0	0
$121$	−606.582	−0.455734
$122$	−227.331	−0.168702
$123$	−951.042	−0.697175
$124$	1118.91	0.810331
$125$	0	0
$126$	−399.712	−0.282612
$127$	−2115.78	−1.47831	−0.739155	−	0.673535i	$-0.764775\pi$
$127$	−2115.78	−1.47831	−0.739155	+	0.673535i	$0.764775\pi$
$128$	735.139	0.507638
$129$	−106.088	−0.0724075
$130$	0	0
$131$	−1695.44	−1.13077	−0.565386	−	0.824826i	$-0.691273\pi$
$131$	−1695.44	−1.13077	−0.565386	+	0.824826i	$0.691273\pi$
$132$	−624.083	−0.411511
$133$	−175.547	−0.114450
$134$	−3783.02	−2.43883
$135$	0	0
$136$	158.885	0.100179
$137$	−1613.51	−1.00622	−0.503108	−	0.864224i	$-0.667810\pi$
$137$	−1613.51	−1.00622	−0.503108	+	0.864224i	$0.667810\pi$
$138$	−849.590	−0.524071
$139$	2072.45	1.26463	0.632313	−	0.774713i	$-0.282106\pi$
$139$	2072.45	1.26463	0.632313	+	0.774713i	$0.282106\pi$
$140$	0	0
$141$	668.658	0.399370
$142$	2591.84	1.53170
$143$	421.299	0.246369
$144$	1063.61	0.615515
$145$	0	0
$146$	−4279.01	−2.42557
$147$	794.438	0.445742
$148$	−3557.50	−1.97584
$149$	−811.396	−0.446122	−0.223061	−	0.974805i	$-0.571605\pi$
$149$	−811.396	−0.446122	−0.223061	+	0.974805i	$0.571605\pi$
$150$	0	0
$151$	−944.326	−0.508928	−0.254464	−	0.967082i	$-0.581899\pi$
$151$	−944.326	−0.508928	−0.254464	+	0.967082i	$0.581899\pi$
$152$	−223.440	−0.119233
$153$	569.714	0.301037
$154$	514.427	0.269180
$155$	0	0
$156$	−362.947	−0.186276
$157$	−2138.58	−1.08712	−0.543558	−	0.839372i	$-0.682923\pi$
$157$	−2138.58	−1.08712	−0.543558	+	0.839372i	$0.682923\pi$
$158$	3078.06	1.54986
$159$	−812.595	−0.405302
$160$	0	0
$161$	378.297	0.185180
$162$	−1138.75	−0.552277
$163$	2184.57	1.04975	0.524873	−	0.851180i	$-0.324113\pi$
$163$	2184.57	1.04975	0.524873	+	0.851180i	$0.324113\pi$
$164$	3622.83	1.72497
$165$	0	0
$166$	2329.43	1.08915
$167$	−3334.42	−1.54506	−0.772531	−	0.634978i	$-0.781009\pi$
$167$	−3334.42	−1.54506	−0.772531	+	0.634978i	$0.781009\pi$
$168$	−65.9356	−0.0302800
$169$	−1951.99	−0.888478
$170$	0	0
$171$	−801.188	−0.358295
$172$	404.126	0.179153
$173$	−1169.82	−0.514105	−0.257052	−	0.966397i	$-0.582751\pi$
$173$	−1169.82	−0.514105	−0.257052	+	0.966397i	$0.582751\pi$
$174$	−352.825	−0.153722
$175$	0	0
$176$	−1368.86	−0.586260
$177$	429.178	0.182254
$178$	−6804.40	−2.86523
$179$	206.597	0.0862669	0.0431334	−	0.999069i	$-0.486266\pi$
$179$	206.597	0.0862669	0.0431334	+	0.999069i	$0.486266\pi$
$180$	0	0
$181$	652.242	0.267849	0.133925	−	0.990992i	$-0.457242\pi$
$181$	652.242	0.267849	0.133925	+	0.990992i	$0.457242\pi$
$182$	299.175	0.121848
$183$	−134.464	−0.0543162
$184$	481.505	0.192919
$185$	0	0
$186$	1225.18	0.482981
$187$	−733.220	−0.286729
$188$	−2547.14	−0.988134
$189$	−541.664	−0.208467
$190$	0	0
$191$	−1128.21	−0.427404	−0.213702	−	0.976899i	$-0.568552\pi$
$191$	−1128.21	−0.427404	−0.213702	+	0.976899i	$0.568552\pi$
$192$	1659.43	0.623745
$193$	−355.606	−0.132627	−0.0663136	−	0.997799i	$-0.521124\pi$
$193$	−355.606	−0.132627	−0.0663136	+	0.997799i	$0.521124\pi$
$194$	−1696.01	−0.627662
$195$	0	0
$196$	−3026.27	−1.10287
$197$	−4347.00	−1.57214	−0.786068	−	0.618140i	$-0.787886\pi$
$197$	−4347.00	−1.57214	−0.786068	+	0.618140i	$0.787886\pi$
$198$	2347.82	0.842689
$199$	430.375	0.153309	0.0766545	−	0.997058i	$-0.475576\pi$
$199$	430.375	0.153309	0.0766545	+	0.997058i	$0.475576\pi$
$200$	0	0
$201$	−2237.61	−0.785219
$202$	−4172.91	−1.45349
$203$	157.102	0.0543174
$204$	631.665	0.216791
$205$	0	0
$206$	−6923.28	−2.34159
$207$	1726.53	0.579720
$208$	−796.087	−0.265378
$209$	1031.13	0.341265
$210$	0	0
$211$	103.702	0.0338347	0.0169174	−	0.999857i	$-0.494615\pi$
$211$	103.702	0.0338347	0.0169174	+	0.999857i	$0.494615\pi$
$212$	3095.44	1.00281
$213$	1533.04	0.493156
$214$	−632.302	−0.201978
$215$	0	0
$216$	−689.442	−0.217179
$217$	−545.535	−0.170661
$218$	−4558.05	−1.41610
$219$	−2530.99	−0.780951
$220$	0	0
$221$	−426.418	−0.129792
$222$	−3895.38	−1.17766
$223$	−4447.94	−1.33568	−0.667839	−	0.744306i	$-0.732781\pi$
$223$	−4447.94	−1.33568	−0.667839	+	0.744306i	$0.732781\pi$
$224$	−1185.86	−0.353723
$225$	0	0
$226$	−4047.83	−1.19141
$227$	−509.808	−0.149062	−0.0745311	−	0.997219i	$-0.523746\pi$
$227$	−509.808	−0.149062	−0.0745311	+	0.997219i	$0.523746\pi$
$228$	−888.310	−0.258025
$229$	−4754.86	−1.37210	−0.686049	−	0.727556i	$-0.740656\pi$
$229$	−4754.86	−1.37210	−0.686049	+	0.727556i	$0.740656\pi$
$230$	0	0
$231$	304.278	0.0866667
$232$	199.964	0.0565873
$233$	−893.223	−0.251146	−0.125573	−	0.992084i	$-0.540077\pi$
$233$	−893.223	−0.251146	−0.125573	+	0.992084i	$0.540077\pi$
$234$	1365.42	0.381454
$235$	0	0
$236$	−1634.88	−0.450939
$237$	1820.64	0.499000
$238$	−520.677	−0.141809
$239$	−3883.75	−1.05112	−0.525562	−	0.850755i	$-0.676145\pi$
$239$	−3883.75	−1.05112	−0.525562	+	0.850755i	$0.676145\pi$
$240$	0	0
$241$	−3118.83	−0.833616	−0.416808	−	0.908995i	$-0.636851\pi$
$241$	−3118.83	−0.833616	−0.416808	+	0.908995i	$0.636851\pi$
$242$	2530.13	0.672078
$243$	−3865.22	−1.02039
$244$	512.217	0.134391
$245$	0	0
$246$	3966.91	1.02813
$247$	599.670	0.154478
$248$	−694.370	−0.177793
$249$	1377.83	0.350668
$250$	0	0
$251$	5196.19	1.30669	0.653347	−	0.757058i	$-0.273364\pi$
$251$	5196.19	1.30669	0.653347	+	0.757058i	$0.273364\pi$
$252$	900.620	0.225134
$253$	−2222.04	−0.552167
$254$	8825.19	2.18009
$255$	0	0
$256$	2314.47	0.565057
$257$	2441.32	0.592550	0.296275	−	0.955103i	$-0.404256\pi$
$257$	2441.32	0.592550	0.296275	+	0.955103i	$0.404256\pi$
$258$	442.508	0.106780
$259$	1734.50	0.416125
$260$	0	0
$261$	717.008	0.170045
$262$	7071.89	1.66757
$263$	−5831.01	−1.36713	−0.683566	−	0.729889i	$-0.739572\pi$
$263$	−5831.01	−1.36713	−0.683566	+	0.729889i	$0.739572\pi$
$264$	387.292	0.0902885
$265$	0	0
$266$	732.227	0.168781
$267$	−4024.73	−0.922507
$268$	8523.80	1.94281
$269$	−2605.41	−0.590538	−0.295269	−	0.955414i	$-0.595409\pi$
$269$	−2605.41	−0.590538	−0.295269	+	0.955414i	$0.595409\pi$
$270$	0	0
$271$	1793.84	0.402097	0.201049	−	0.979581i	$-0.435565\pi$
$271$	1793.84	0.402097	0.201049	+	0.979581i	$0.435565\pi$
$272$	1385.49	0.308853
$273$	176.958	0.0392308
$274$	6730.16	1.48388
$275$	0	0
$276$	1914.27	0.417485
$277$	825.071	0.178967	0.0894833	−	0.995988i	$-0.471478\pi$
$277$	825.071	0.178967	0.0894833	+	0.995988i	$0.471478\pi$
$278$	−8644.45	−1.86496
$279$	−2489.80	−0.534267
$280$	0	0
$281$	−5114.69	−1.08582	−0.542912	−	0.839789i	$-0.682678\pi$
$281$	−5114.69	−1.08582	−0.542912	+	0.839789i	$0.682678\pi$
$282$	−2789.06	−0.588957
$283$	3703.40	0.777895	0.388947	−	0.921260i	$-0.372839\pi$
$283$	3703.40	0.777895	0.388947	+	0.921260i	$0.372839\pi$
$284$	−5839.86	−1.22018
$285$	0	0
$286$	−1757.29	−0.363324
$287$	−1766.35	−0.363290
$288$	−5412.23	−1.10736
$289$	−4170.87	−0.848946
$290$	0	0
$291$	−1003.17	−0.202085
$292$	9641.37	1.93225
$293$	−749.193	−0.149380	−0.0746899	−	0.997207i	$-0.523797\pi$
$293$	−749.193	−0.149380	−0.0746899	+	0.997207i	$0.523797\pi$
$294$	−3313.70	−0.657343
$295$	0	0
$296$	2207.71	0.433515
$297$	3181.62	0.621603
$298$	3384.43	0.657902
$299$	−1292.27	−0.249946
$300$	0	0
$301$	−197.036	−0.0377307
$302$	3938.90	0.750524
$303$	−2468.23	−0.467973
$304$	−1948.42	−0.367597
$305$	0	0
$306$	−2376.35	−0.443944
$307$	4761.00	0.885097	0.442548	−	0.896745i	$-0.354075\pi$
$307$	4761.00	0.885097	0.442548	+	0.896745i	$0.354075\pi$
$308$	−1159.09	−0.214433
$309$	−4095.04	−0.753912
$310$	0	0
$311$	−5995.99	−1.09325	−0.546626	−	0.837377i	$-0.684088\pi$
$311$	−5995.99	−1.09325	−0.546626	+	0.837377i	$0.684088\pi$
$312$	225.237	0.0408703
$313$	−398.261	−0.0719203	−0.0359602	−	0.999353i	$-0.511449\pi$
$313$	−398.261	−0.0719203	−0.0359602	+	0.999353i	$0.511449\pi$
$314$	8920.27	1.60318
$315$	0	0
$316$	−6935.40	−1.23464
$317$	−4657.19	−0.825154	−0.412577	−	0.910923i	$-0.635371\pi$
$317$	−4657.19	−0.825154	−0.412577	+	0.910923i	$0.635371\pi$
$318$	3389.43	0.597704
$319$	−922.786	−0.161963
$320$	0	0
$321$	−374.000	−0.0650300
$322$	−1577.92	−0.273088
$323$	−1043.65	−0.179785
$324$	2565.81	0.439954
$325$	0	0
$326$	−9112.11	−1.54808
$327$	−2696.03	−0.455936
$328$	−2248.25	−0.378472
$329$	1241.88	0.208107
$330$	0	0
$331$	10013.6	1.66282	0.831412	−	0.555656i	$-0.187533\pi$
$331$	10013.6	1.66282	0.831412	+	0.555656i	$0.187533\pi$
$332$	−5248.60	−0.867634
$333$	7916.16	1.30271
$334$	13908.3	2.27852
$335$	0	0
$336$	−574.964	−0.0933538
$337$	3872.11	0.625897	0.312949	−	0.949770i	$-0.398683\pi$
$337$	3872.11	0.625897	0.312949	+	0.949770i	$0.398683\pi$
$338$	8141.97	1.31025
$339$	−2394.25	−0.383592
$340$	0	0
$341$	3204.36	0.508874
$342$	3341.85	0.528382
$343$	3047.19	0.479688
$344$	−250.791	−0.0393075
$345$	0	0
$346$	4879.48	0.758158
$347$	−10290.8	−1.59204	−0.796022	−	0.605267i	$-0.793066\pi$
$347$	−10290.8	−1.59204	−0.796022	+	0.605267i	$0.793066\pi$
$348$	794.976	0.122457
$349$	700.572	0.107452	0.0537260	−	0.998556i	$-0.482890\pi$
$349$	700.572	0.107452	0.0537260	+	0.998556i	$0.482890\pi$
$350$	0	0
$351$	1850.33	0.281377
$352$	6965.52	1.05473
$353$	−3608.33	−0.544057	−0.272028	−	0.962289i	$-0.587694\pi$
$353$	−3608.33	−0.544057	−0.272028	+	0.962289i	$0.587694\pi$
$354$	−1790.16	−0.268773
$355$	0	0
$356$	15331.5	2.28250
$357$	−307.975	−0.0456576
$358$	−861.741	−0.127219
$359$	−12085.9	−1.77680	−0.888399	−	0.459072i	$-0.848182\pi$
$359$	−12085.9	−1.77680	−0.888399	+	0.459072i	$0.848182\pi$
$360$	0	0
$361$	−5391.31	−0.786020
$362$	−2720.58	−0.395001
$363$	1496.54	0.216386
$364$	−674.093	−0.0970661
$365$	0	0
$366$	560.866	0.0801009
$367$	−968.974	−0.137820	−0.0689101	−	0.997623i	$-0.521952\pi$
$367$	−968.974	−0.137820	−0.0689101	+	0.997623i	$0.521952\pi$
$368$	4198.77	0.594771
$369$	−8061.53	−1.13731
$370$	0	0
$371$	−1509.21	−0.211198
$372$	−2760.54	−0.384751
$373$	−13006.0	−1.80543	−0.902713	−	0.430243i	$-0.858428\pi$
$373$	−13006.0	−1.80543	−0.902713	+	0.430243i	$0.858428\pi$
$374$	3058.35	0.422844
$375$	0	0
$376$	1580.70	0.216804
$377$	−536.664	−0.0733146
$378$	2259.35	0.307429
$379$	1901.08	0.257657	0.128828	−	0.991667i	$-0.458878\pi$
$379$	1901.08	0.257657	0.128828	+	0.991667i	$0.458878\pi$
$380$	0	0
$381$	5220.00	0.701913
$382$	4705.89	0.630299
$383$	9501.65	1.26765	0.633827	−	0.773475i	$-0.281483\pi$
$383$	9501.65	1.26765	0.633827	+	0.773475i	$0.281483\pi$
$384$	−1813.71	−0.241031
$385$	0	0
$386$	1483.27	0.195587
$387$	−899.262	−0.118119
$388$	3821.40	0.500006
$389$	4640.26	0.604808	0.302404	−	0.953180i	$-0.402211\pi$
$389$	4640.26	0.604808	0.302404	+	0.953180i	$0.402211\pi$
$390$	0	0
$391$	2249.03	0.290891
$392$	1878.04	0.241978
$393$	4182.94	0.536899
$394$	18131.9	2.31845
$395$	0	0
$396$	−5290.05	−0.671301
$397$	−4633.90	−0.585815	−0.292908	−	0.956141i	$-0.594623\pi$
$397$	−4633.90	−0.585815	−0.292908	+	0.956141i	$0.594623\pi$
$398$	−1795.15	−0.226087
$399$	433.104	0.0543417
$400$	0	0
$401$	−11801.3	−1.46965	−0.734823	−	0.678258i	$-0.762735\pi$
$401$	−11801.3	−1.46965	−0.734823	+	0.678258i	$0.762735\pi$
$402$	9333.35	1.15797
$403$	1863.56	0.230348
$404$	9402.29	1.15787
$405$	0	0
$406$	−655.293	−0.0801026
$407$	−10188.1	−1.24080
$408$	−391.998	−0.0475656
$409$	5588.72	0.675658	0.337829	−	0.941207i	$-0.390307\pi$
$409$	5588.72	0.675658	0.337829	+	0.941207i	$0.390307\pi$
$410$	0	0
$411$	3980.81	0.477759
$412$	15599.4	1.86535
$413$	797.103	0.0949706
$414$	−7201.57	−0.854922
$415$	0	0
$416$	4050.93	0.477435
$417$	−5113.09	−0.600454
$418$	−4300.95	−0.503269
$419$	−6908.94	−0.805547	−0.402773	−	0.915300i	$-0.631954\pi$
$419$	−6908.94	−0.805547	−0.402773	+	0.915300i	$0.631954\pi$
$420$	0	0
$421$	16499.6	1.91007	0.955036	−	0.296491i	$-0.0958165\pi$
$421$	16499.6	1.91007	0.955036	+	0.296491i	$0.0958165\pi$
$422$	−432.553	−0.0498966
$423$	5667.90	0.651496
$424$	−1920.96	−0.220024
$425$	0	0
$426$	−6394.51	−0.727265
$427$	−249.737	−0.0283035
$428$	1424.69	0.160899
$429$	−1039.42	−0.116978
$430$	0	0
$431$	−7101.67	−0.793679	−0.396839	−	0.917888i	$-0.629893\pi$
$431$	−7101.67	−0.793679	−0.396839	+	0.917888i	$0.629893\pi$
$432$	−6011.99	−0.669565
$433$	8935.72	0.991739	0.495870	−	0.868397i	$-0.334849\pi$
$433$	8935.72	0.991739	0.495870	+	0.868397i	$0.334849\pi$
$434$	2275.50	0.251676
$435$	0	0
$436$	10270.1	1.12809
$437$	−3162.81	−0.346219
$438$	10557.1	1.15168
$439$	17789.3	1.93403	0.967015	−	0.254720i	$-0.0819833\pi$
$439$	17789.3	1.93403	0.967015	+	0.254720i	$0.0819833\pi$
$440$	0	0
$441$	6734.07	0.727143
$442$	1778.64	0.191406
$443$	−2744.62	−0.294359	−0.147180	−	0.989110i	$-0.547020\pi$
$443$	−2744.62	−0.294359	−0.147180	+	0.989110i	$0.547020\pi$
$444$	8776.97	0.938146
$445$	0	0
$446$	18552.9	1.96974
$447$	2001.85	0.211822
$448$	3082.02	0.325026
$449$	−12051.9	−1.26673	−0.633366	−	0.773853i	$-0.718327\pi$
$449$	−12051.9	−1.26673	−0.633366	+	0.773853i	$0.718327\pi$
$450$	0	0
$451$	10375.2	1.08325
$452$	9120.47	0.949095
$453$	2329.81	0.241643
$454$	2126.47	0.219824
$455$	0	0
$456$	551.265	0.0566126
$457$	−130.425	−0.0133502	−0.00667509	−	0.999978i	$-0.502125\pi$
$457$	−130.425	−0.0133502	−0.00667509	+	0.999978i	$0.502125\pi$
$458$	19833.1	2.02345
$459$	−3220.28	−0.327472
$460$	0	0
$461$	−981.122	−0.0991223	−0.0495612	−	0.998771i	$-0.515782\pi$
$461$	−981.122	−0.0991223	−0.0495612	+	0.998771i	$0.515782\pi$
$462$	−1269.18	−0.127809
$463$	−6359.89	−0.638378	−0.319189	−	0.947691i	$-0.603411\pi$
$463$	−6359.89	−0.638378	−0.319189	+	0.947691i	$0.603411\pi$
$464$	1743.70	0.174460
$465$	0	0
$466$	3725.75	0.370369
$467$	14159.9	1.40309	0.701546	−	0.712624i	$-0.252494\pi$
$467$	14159.9	1.40309	0.701546	+	0.712624i	$0.252494\pi$
$468$	−3076.53	−0.303873
$469$	−4155.86	−0.409168
$470$	0	0
$471$	5276.24	0.516170
$472$	1014.57	0.0989395
$473$	1157.35	0.112505
$474$	−7594.10	−0.735883
$475$	0	0
$476$	1173.18	0.112967
$477$	−6887.98	−0.661172
$478$	16199.6	1.55011
$479$	−20583.3	−1.96342	−0.981709	−	0.190390i	$-0.939025\pi$
$479$	−20583.3	−1.96342	−0.981709	+	0.190390i	$0.939025\pi$
$480$	0	0
$481$	−5925.06	−0.561662
$482$	13009.0	1.22935
$483$	−933.324	−0.0879248
$484$	−5700.82	−0.535389
$485$	0	0
$486$	16122.3	1.50478
$487$	17672.3	1.64437	0.822186	−	0.569218i	$-0.192754\pi$
$487$	17672.3	1.64437	0.822186	+	0.569218i	$0.192754\pi$
$488$	−317.871	−0.0294863
$489$	−5389.71	−0.498428
$490$	0	0
$491$	−3484.50	−0.320271	−0.160136	−	0.987095i	$-0.551193\pi$
$491$	−3484.50	−0.320271	−0.160136	+	0.987095i	$0.551193\pi$
$492$	−8938.15	−0.819030
$493$	933.998	0.0853249
$494$	−2501.30	−0.227811
$495$	0	0
$496$	−6054.97	−0.548137
$497$	2847.28	0.256978
$498$	−5747.09	−0.517135
$499$	1393.45	0.125009	0.0625046	−	0.998045i	$-0.480091\pi$
$499$	1393.45	0.125009	0.0625046	+	0.998045i	$0.480091\pi$
$500$	0	0
$501$	8226.59	0.733607
$502$	−21673.9	−1.92700
$503$	−3191.15	−0.282875	−0.141438	−	0.989947i	$-0.545172\pi$
$503$	−3191.15	−0.282875	−0.141438	+	0.989947i	$0.545172\pi$
$504$	−558.905	−0.0493960
$505$	0	0
$506$	9268.39	0.814289
$507$	4815.89	0.421856
$508$	−19884.7	−1.73670
$509$	10831.8	0.943247	0.471624	−	0.881800i	$-0.343668\pi$
$509$	10831.8	0.943247	0.471624	+	0.881800i	$0.343668\pi$
$510$	0	0
$511$	−4700.75	−0.406945
$512$	−15535.1	−1.34094
$513$	4528.67	0.389757
$514$	−10183.0	−0.873842
$515$	0	0
$516$	−997.048	−0.0850631
$517$	−7294.56	−0.620531
$518$	−7234.80	−0.613666
$519$	2886.16	0.244101
$520$	0	0
$521$	14277.5	1.20059	0.600296	−	0.799778i	$-0.295049\pi$
$521$	14277.5	1.20059	0.600296	+	0.799778i	$0.295049\pi$
$522$	−2990.73	−0.250768
$523$	−4181.28	−0.349588	−0.174794	−	0.984605i	$-0.555926\pi$
$523$	−4181.28	−0.349588	−0.174794	+	0.984605i	$0.555926\pi$
$524$	−15934.2	−1.32841
$525$	0	0
$526$	24321.9	2.01613
$527$	−3243.29	−0.268084
$528$	3377.22	0.278361
$529$	−5351.26	−0.439817
$530$	0	0
$531$	3637.94	0.297313
$532$	−1649.84	−0.134454
$533$	6033.87	0.490348
$534$	16787.6	1.36043
$535$	0	0
$536$	−5289.68	−0.426267
$537$	−509.710	−0.0409602
$538$	10867.5	0.870875
$539$	−8666.72	−0.692583
$540$	0	0
$541$	5123.26	0.407146	0.203573	−	0.979060i	$-0.434745\pi$
$541$	5123.26	0.407146	0.203573	+	0.979060i	$0.434745\pi$
$542$	−7482.35	−0.592979
$543$	−1609.19	−0.127177
$544$	−7050.15	−0.555648
$545$	0	0
$546$	−738.116	−0.0578543
$547$	15435.6	1.20654	0.603271	−	0.797537i	$-0.293864\pi$
$547$	15435.6	1.20654	0.603271	+	0.797537i	$0.293864\pi$
$548$	−15164.2	−1.18209
$549$	−1139.79	−0.0886064
$550$	0	0
$551$	−1313.48	−0.101554
$552$	−1187.96	−0.0915992
$553$	3381.43	0.260023
$554$	−3441.47	−0.263925
$555$	0	0
$556$	19477.5	1.48566
$557$	978.643	0.0744460	0.0372230	−	0.999307i	$-0.488149\pi$
$557$	978.643	0.0744460	0.0372230	+	0.999307i	$0.488149\pi$
$558$	10385.3	0.787891
$559$	673.076	0.0509268
$560$	0	0
$561$	1808.98	0.136141
$562$	21334.0	1.60128
$563$	24362.4	1.82371	0.911857	−	0.410507i	$-0.134648\pi$
$563$	24362.4	1.82371	0.911857	+	0.410507i	$0.134648\pi$
$564$	6284.23	0.469174
$565$	0	0
$566$	−15447.3	−1.14717
$567$	−1250.99	−0.0926569
$568$	3624.09	0.267717
$569$	−12733.1	−0.938135	−0.469067	−	0.883162i	$-0.655410\pi$
$569$	−12733.1	−0.938135	−0.469067	+	0.883162i	$0.655410\pi$
$570$	0	0
$571$	−6363.95	−0.466415	−0.233208	−	0.972427i	$-0.574922\pi$
$571$	−6363.95	−0.466415	−0.233208	+	0.972427i	$0.574922\pi$
$572$	3959.48	0.289430
$573$	2783.48	0.202935
$574$	7367.65	0.535749
$575$	0	0
$576$	14066.2	1.01752
$577$	11981.3	0.864449	0.432225	−	0.901766i	$-0.357729\pi$
$577$	11981.3	0.864449	0.432225	+	0.901766i	$0.357729\pi$
$578$	17397.2	1.25195
$579$	877.340	0.0629724
$580$	0	0
$581$	2559.01	0.182729
$582$	4184.35	0.298018
$583$	8864.80	0.629747
$584$	−5983.22	−0.423951
$585$	0	0
$586$	3124.97	0.220293
$587$	−17927.4	−1.26055	−0.630276	−	0.776371i	$-0.717058\pi$
$587$	−17927.4	−1.26055	−0.630276	+	0.776371i	$0.717058\pi$
$588$	7466.34	0.523651
$589$	4561.04	0.319074
$590$	0	0
$591$	10724.8	0.746462
$592$	19251.4	1.33653
$593$	−19927.7	−1.37999	−0.689993	−	0.723816i	$-0.742387\pi$
$593$	−19927.7	−1.37999	−0.689993	+	0.723816i	$0.742387\pi$
$594$	−13270.9	−0.916688
$595$	0	0
$596$	−7625.72	−0.524097
$597$	−1061.81	−0.0727923
$598$	5390.20	0.368598
$599$	−4155.72	−0.283469	−0.141735	−	0.989905i	$-0.545268\pi$
$599$	−4155.72	−0.283469	−0.141735	+	0.989905i	$0.545268\pi$
$600$	0	0
$601$	−4104.20	−0.278559	−0.139279	−	0.990253i	$-0.544479\pi$
$601$	−4104.20	−0.278559	−0.139279	+	0.990253i	$0.544479\pi$
$602$	821.860	0.0556420
$603$	−18967.2	−1.28093
$604$	−8875.03	−0.597880
$605$	0	0
$606$	10295.3	0.690127
$607$	−5870.16	−0.392525	−0.196262	−	0.980551i	$-0.562880\pi$
$607$	−5870.16	−0.392525	−0.196262	+	0.980551i	$0.562880\pi$
$608$	9914.61	0.661333
$609$	−387.599	−0.0257903
$610$	0	0
$611$	−4242.29	−0.280891
$612$	5354.33	0.353653
$613$	−29802.4	−1.96363	−0.981817	−	0.189830i	$-0.939206\pi$
$613$	−29802.4	−1.96363	−0.981817	+	0.189830i	$0.939206\pi$
$614$	−19858.7	−1.30527
$615$	0	0
$616$	719.308	0.0470483
$617$	−27394.8	−1.78748	−0.893738	−	0.448588i	$-0.851927\pi$
$617$	−27394.8	−1.78748	−0.893738	+	0.448588i	$0.851927\pi$
$618$	17080.9	1.11181
$619$	−25129.8	−1.63174	−0.815872	−	0.578232i	$-0.803743\pi$
$619$	−25129.8	−1.63174	−0.815872	+	0.578232i	$0.803743\pi$
$620$	0	0
$621$	−9759.11	−0.630627
$622$	25010.0	1.61223
$623$	−7475.03	−0.480708
$624$	1964.08	0.126004
$625$	0	0
$626$	1661.20	0.106062
$627$	−2543.96	−0.162035
$628$	−20098.9	−1.27713
$629$	10311.9	0.653673
$630$	0	0
$631$	−1190.63	−0.0751160	−0.0375580	−	0.999294i	$-0.511958\pi$
$631$	−1190.63	−0.0751160	−0.0375580	+	0.999294i	$0.511958\pi$
$632$	4303.96	0.270890
$633$	−255.850	−0.0160650
$634$	19425.7	1.21687
$635$	0	0
$636$	−7636.98	−0.476142
$637$	−5040.29	−0.313507
$638$	3849.06	0.238849
$639$	12994.9	0.804490
$640$	0	0
$641$	28828.0	1.77635	0.888174	−	0.459508i	$-0.151974\pi$
$641$	28828.0	1.77635	0.888174	+	0.459508i	$0.151974\pi$
$642$	1560.00	0.0959007
$643$	−16853.2	−1.03363	−0.516816	−	0.856096i	$-0.672883\pi$
$643$	−16853.2	−1.03363	−0.516816	+	0.856096i	$0.672883\pi$
$644$	3555.34	0.217546
$645$	0	0
$646$	4353.21	0.265131
$647$	20234.3	1.22951	0.614754	−	0.788719i	$-0.289255\pi$
$647$	20234.3	1.22951	0.614754	+	0.788719i	$0.289255\pi$
$648$	−1592.28	−0.0965291
$649$	−4682.02	−0.283182
$650$	0	0
$651$	1345.93	0.0810310
$652$	20531.2	1.23323
$653$	−24965.3	−1.49612	−0.748062	−	0.663629i	$-0.769015\pi$
$653$	−24965.3	−1.49612	−0.748062	+	0.663629i	$0.769015\pi$
$654$	11245.5	0.672375
$655$	0	0
$656$	−19604.9	−1.16683
$657$	−21454.0	−1.27397
$658$	−5180.05	−0.306899
$659$	9033.00	0.533954	0.266977	−	0.963703i	$-0.413975\pi$
$659$	9033.00	0.533954	0.266977	+	0.963703i	$0.413975\pi$
$660$	0	0
$661$	−19710.5	−1.15983	−0.579915	−	0.814677i	$-0.696914\pi$
$661$	−19710.5	−1.15983	−0.579915	+	0.814677i	$0.696914\pi$
$662$	−41767.8	−2.45219
$663$	1052.05	0.0616261
$664$	3257.17	0.190365
$665$	0	0
$666$	−33019.3	−1.92113
$667$	2830.50	0.164314
$668$	−31337.8	−1.81511
$669$	10973.8	0.634190
$670$	0	0
$671$	1466.90	0.0843951
$672$	2925.73	0.167950
$673$	−19293.1	−1.10504	−0.552521	−	0.833499i	$-0.686334\pi$
$673$	−19293.1	−1.10504	−0.552521	+	0.833499i	$0.686334\pi$
$674$	−16151.1	−0.923020
$675$	0	0
$676$	−18345.3	−1.04377
$677$	16029.1	0.909968	0.454984	−	0.890500i	$-0.349645\pi$
$677$	16029.1	0.909968	0.454984	+	0.890500i	$0.349645\pi$
$678$	9986.70	0.565689
$679$	−1863.16	−0.105304
$680$	0	0
$681$	1257.78	0.0707759
$682$	−13365.8	−0.750443
$683$	4293.48	0.240535	0.120267	−	0.992742i	$-0.461625\pi$
$683$	4293.48	0.240535	0.120267	+	0.992742i	$0.461625\pi$
$684$	−7529.78	−0.420919
$685$	0	0
$686$	−12710.2	−0.707403
$687$	11731.1	0.651482
$688$	−2186.92	−0.121186
$689$	5155.49	0.285063
$690$	0	0
$691$	−19631.7	−1.08079	−0.540393	−	0.841413i	$-0.681724\pi$
$691$	−19631.7	−1.08079	−0.540393	+	0.841413i	$0.681724\pi$
$692$	−10994.3	−0.603962
$693$	2579.22	0.141380
$694$	42924.2	2.34781
$695$	0	0
$696$	−493.345	−0.0268681
$697$	−10501.2	−0.570677
$698$	−2922.17	−0.158461
$699$	2203.74	0.119246
$700$	0	0
$701$	−13399.7	−0.721967	−0.360983	−	0.932572i	$-0.617559\pi$
$701$	−13399.7	−0.721967	−0.360983	+	0.932572i	$0.617559\pi$
$702$	−7717.95	−0.414951
$703$	−14501.5	−0.778003
$704$	−18103.1	−0.969158
$705$	0	0
$706$	15050.8	0.802329
$707$	−4584.18	−0.243855
$708$	4033.53	0.214109
$709$	−510.833	−0.0270589	−0.0135294	−	0.999908i	$-0.504307\pi$
$709$	−510.833	−0.0270589	−0.0135294	+	0.999908i	$0.504307\pi$
$710$	0	0
$711$	15432.7	0.814023
$712$	−9514.40	−0.500796
$713$	−9828.87	−0.516261
$714$	1284.60	0.0673319
$715$	0	0
$716$	1941.65	0.101345
$717$	9581.88	0.499082
$718$	50411.9	2.62027
$719$	−29685.4	−1.53975	−0.769875	−	0.638195i	$-0.779681\pi$
$719$	−29685.4	−1.53975	−0.769875	+	0.638195i	$0.779681\pi$
$720$	0	0
$721$	−7605.63	−0.392855
$722$	22487.8	1.15916
$723$	7694.69	0.395807
$724$	6129.94	0.314665
$725$	0	0
$726$	−6242.26	−0.319108
$727$	10575.9	0.539529	0.269765	−	0.962926i	$-0.413054\pi$
$727$	10575.9	0.539529	0.269765	+	0.962926i	$0.413054\pi$
$728$	418.327	0.0212970
$729$	2164.94	0.109990
$730$	0	0
$731$	−1171.41	−0.0592696
$732$	−1263.73	−0.0638098
$733$	4428.93	0.223173	0.111587	−	0.993755i	$-0.464407\pi$
$733$	4428.93	0.223173	0.111587	+	0.993755i	$0.464407\pi$
$734$	4041.71	0.203246
$735$	0	0
$736$	−21365.6	−1.07004
$737$	24410.7	1.22005
$738$	33625.6	1.67720
$739$	20131.6	1.00210	0.501052	−	0.865417i	$-0.332947\pi$
$739$	20131.6	1.00210	0.501052	+	0.865417i	$0.332947\pi$
$740$	0	0
$741$	−1479.49	−0.0733474
$742$	6295.11	0.311457
$743$	7362.63	0.363538	0.181769	−	0.983341i	$-0.441818\pi$
$743$	7362.63	0.363538	0.181769	+	0.983341i	$0.441818\pi$
$744$	1713.13	0.0844173
$745$	0	0
$746$	54249.5	2.66249
$747$	11679.2	0.572048
$748$	−6891.00	−0.336845
$749$	−694.621	−0.0338864
$750$	0	0
$751$	−7494.93	−0.364173	−0.182087	−	0.983283i	$-0.558285\pi$
$751$	−7494.93	−0.364173	−0.182087	+	0.983283i	$0.558285\pi$
$752$	13783.8	0.668410
$753$	−12819.9	−0.620429
$754$	2238.49	0.108118
$755$	0	0
$756$	−5090.70	−0.244903
$757$	−26060.4	−1.25123	−0.625615	−	0.780132i	$-0.715152\pi$
$757$	−26060.4	−1.25123	−0.625615	+	0.780132i	$0.715152\pi$
$758$	−7929.64	−0.379971
$759$	5482.15	0.262173
$760$	0	0
$761$	−23064.0	−1.09865	−0.549323	−	0.835610i	$-0.685114\pi$
$761$	−23064.0	−1.09865	−0.549323	+	0.835610i	$0.685114\pi$
$762$	−21773.3	−1.03512
$763$	−5007.28	−0.237583
$764$	−10603.2	−0.502108
$765$	0	0
$766$	−39632.6	−1.86943
$767$	−2722.91	−0.128186
$768$	−5710.21	−0.268293
$769$	19455.7	0.912341	0.456171	−	0.889892i	$-0.349221\pi$
$769$	19455.7	0.912341	0.456171	+	0.889892i	$0.349221\pi$
$770$	0	0
$771$	−6023.16	−0.281347
$772$	−3342.08	−0.155808
$773$	14025.4	0.652599	0.326300	−	0.945266i	$-0.394198\pi$
$773$	14025.4	0.652599	0.326300	+	0.945266i	$0.394198\pi$
$774$	3750.93	0.174192
$775$	0	0
$776$	−2371.48	−0.109705
$777$	−4279.30	−0.197579
$778$	−19355.1	−0.891920
$779$	14767.8	0.679220
$780$	0	0
$781$	−16724.3	−0.766253
$782$	−9381.00	−0.428982
$783$	−4052.85	−0.184977
$784$	16376.7	0.746021
$785$	0	0
$786$	−17447.6	−0.791774
$787$	41219.6	1.86699	0.933495	−	0.358589i	$-0.116742\pi$
$787$	41219.6	1.86699	0.933495	+	0.358589i	$0.116742\pi$
$788$	−40854.3	−1.84692
$789$	14386.1	0.649124
$790$	0	0
$791$	−4446.78	−0.199885
$792$	3282.89	0.147288
$793$	853.104	0.0382025
$794$	19328.6	0.863910
$795$	0	0
$796$	4044.78	0.180105
$797$	−10289.5	−0.457305	−0.228653	−	0.973508i	$-0.573432\pi$
$797$	−10289.5	−0.457305	−0.228653	+	0.973508i	$0.573432\pi$
$798$	−1806.53	−0.0801385
$799$	7383.19	0.326907
$800$	0	0
$801$	−34115.7	−1.50489
$802$	49224.6	2.16731
$803$	27611.2	1.21342
$804$	−21029.7	−0.922462
$805$	0	0
$806$	−7773.12	−0.339698
$807$	6428.00	0.280392
$808$	−5834.85	−0.254046
$809$	−20063.0	−0.871912	−0.435956	−	0.899968i	$-0.643590\pi$
$809$	−20063.0	−0.871912	−0.435956	+	0.899968i	$0.643590\pi$
$810$	0	0
$811$	26523.6	1.14842	0.574210	−	0.818708i	$-0.305309\pi$
$811$	26523.6	1.14842	0.574210	+	0.818708i	$0.305309\pi$
$812$	1476.49	0.0638112
$813$	−4425.73	−0.190919
$814$	42495.7	1.82982
$815$	0	0
$816$	−3418.25	−0.146646
$817$	1647.35	0.0705427
$818$	−23311.2	−0.996403
$819$	1499.99	0.0639976
$820$	0	0
$821$	−9204.45	−0.391276	−0.195638	−	0.980676i	$-0.562678\pi$
$821$	−9204.45	−0.391276	−0.195638	+	0.980676i	$0.562678\pi$
$822$	−16604.5	−0.704558
$823$	−15569.2	−0.659427	−0.329713	−	0.944081i	$-0.606952\pi$
$823$	−15569.2	−0.659427	−0.329713	+	0.944081i	$0.606952\pi$
$824$	−9680.62	−0.409272
$825$	0	0
$826$	−3324.82	−0.140055
$827$	11786.2	0.495582	0.247791	−	0.968814i	$-0.420295\pi$
$827$	11786.2	0.495582	0.247791	+	0.968814i	$0.420295\pi$
$828$	16226.4	0.681046
$829$	−33661.5	−1.41027	−0.705133	−	0.709075i	$-0.749113\pi$
$829$	−33661.5	−1.41027	−0.705133	+	0.709075i	$0.749113\pi$
$830$	0	0
$831$	−2035.59	−0.0849747
$832$	−10528.2	−0.438702
$833$	8772.02	0.364865
$834$	21327.3	0.885498
$835$	0	0
$836$	9690.79	0.400913
$837$	14073.4	0.581182
$838$	28818.1	1.18795
$839$	−2686.31	−0.110538	−0.0552691	−	0.998471i	$-0.517602\pi$
$839$	−2686.31	−0.110538	−0.0552691	+	0.998471i	$0.517602\pi$
$840$	0	0
$841$	−23213.5	−0.951803
$842$	−68821.8	−2.81681
$843$	12618.8	0.515558
$844$	974.618	0.0397485
$845$	0	0
$846$	−23641.5	−0.960771
$847$	2779.49	0.112756
$848$	−16750.9	−0.678337
$849$	−9136.93	−0.369350
$850$	0	0
$851$	31250.3	1.25881
$852$	14407.9	0.579352
$853$	−7920.78	−0.317940	−0.158970	−	0.987283i	$-0.550817\pi$
$853$	−7920.78	−0.317940	−0.158970	+	0.987283i	$0.550817\pi$
$854$	1041.68	0.0417396
$855$	0	0
$856$	−884.129	−0.0353025
$857$	−36678.1	−1.46196	−0.730980	−	0.682398i	$-0.760937\pi$
$857$	−36678.1	−1.46196	−0.730980	+	0.682398i	$0.760937\pi$
$858$	4335.54	0.172509
$859$	31205.9	1.23950	0.619750	−	0.784799i	$-0.287234\pi$
$859$	31205.9	1.23950	0.619750	+	0.784799i	$0.287234\pi$
$860$	0	0
$861$	4357.88	0.172493
$862$	29622.0	1.17045
$863$	−38340.4	−1.51231	−0.756155	−	0.654392i	$-0.772924\pi$
$863$	−38340.4	−1.51231	−0.756155	+	0.654392i	$0.772924\pi$
$864$	30592.3	1.20460
$865$	0	0
$866$	−37272.0	−1.46253
$867$	10290.3	0.403086
$868$	−5127.09	−0.200489
$869$	−19861.8	−0.775334
$870$	0	0
$871$	14196.5	0.552273
$872$	−6373.38	−0.247511
$873$	−8503.40	−0.329664
$874$	13192.5	0.510575
$875$	0	0
$876$	−23786.9	−0.917449
$877$	38409.6	1.47890	0.739452	−	0.673210i	$-0.235085\pi$
$877$	38409.6	1.47890	0.739452	+	0.673210i	$0.235085\pi$
$878$	−74201.5	−2.85214
$879$	1848.39	0.0709267
$880$	0	0
$881$	41203.4	1.57568	0.787842	−	0.615877i	$-0.211198\pi$
$881$	41203.4	1.57568	0.787842	+	0.615877i	$0.211198\pi$
$882$	−28088.6	−1.07233
$883$	−30194.6	−1.15077	−0.575384	−	0.817883i	$-0.695148\pi$
$883$	−30194.6	−1.15077	−0.575384	+	0.817883i	$0.695148\pi$
$884$	−4007.59	−0.152477
$885$	0	0
$886$	11448.2	0.434096
$887$	13570.8	0.513712	0.256856	−	0.966450i	$-0.417313\pi$
$887$	13570.8	0.513712	0.256856	+	0.966450i	$0.417313\pi$
$888$	−5446.80	−0.205836
$889$	9694.99	0.365759
$890$	0	0
$891$	7348.03	0.276283
$892$	−41803.0	−1.56913
$893$	−10383.0	−0.389085
$894$	−8349.98	−0.312377
$895$	0	0
$896$	−3368.57	−0.125598
$897$	3188.25	0.118676
$898$	50269.8	1.86807
$899$	−4081.82	−0.151431
$900$	0	0
$901$	−8972.51	−0.331762
$902$	−43276.1	−1.59749
$903$	486.121	0.0179148
$904$	−5659.96	−0.208239
$905$	0	0
$906$	−9717.94	−0.356354
$907$	−21966.6	−0.804176	−0.402088	−	0.915601i	$-0.631715\pi$
$907$	−21966.6	−0.804176	−0.402088	+	0.915601i	$0.631715\pi$
$908$	−4791.31	−0.175116
$909$	−20922.0	−0.763409
$910$	0	0
$911$	27091.0	0.985252	0.492626	−	0.870241i	$-0.336037\pi$
$911$	27091.0	0.985252	0.492626	+	0.870241i	$0.336037\pi$
$912$	4807.08	0.174538
$913$	−15031.1	−0.544859
$914$	544.020	0.0196877
$915$	0	0
$916$	−44687.5	−1.61192
$917$	7768.88	0.279772
$918$	13432.2	0.482928
$919$	−24533.7	−0.880622	−0.440311	−	0.897845i	$-0.645132\pi$
$919$	−24533.7	−0.880622	−0.440311	+	0.897845i	$0.645132\pi$
$920$	0	0
$921$	−11746.2	−0.420251
$922$	4092.38	0.146177
$923$	−9726.35	−0.346855
$924$	2859.69	0.101815
$925$	0	0
$926$	26527.9	0.941426
$927$	−34711.8	−1.22986
$928$	−8872.89	−0.313865
$929$	9220.40	0.325631	0.162816	−	0.986657i	$-0.447942\pi$
$929$	9220.40	0.325631	0.162816	+	0.986657i	$0.447942\pi$
$930$	0	0
$931$	−12336.1	−0.434263
$932$	−8394.76	−0.295042
$933$	14793.1	0.519084
$934$	−59062.9	−2.06916
$935$	0	0
$936$	1909.23	0.0666720
$937$	−22526.6	−0.785392	−0.392696	−	0.919668i	$-0.628458\pi$
$937$	−22526.6	−0.785392	−0.392696	+	0.919668i	$0.628458\pi$
$938$	17334.6	0.603407
$939$	982.580	0.0341483
$940$	0	0
$941$	−776.782	−0.0269100	−0.0134550	−	0.999909i	$-0.504283\pi$
$941$	−776.782	−0.0269100	−0.0134550	+	0.999909i	$0.504283\pi$
$942$	−22007.8	−0.761204
$943$	−31824.1	−1.09898
$944$	8847.15	0.305032
$945$	0	0
$946$	−4827.43	−0.165913
$947$	45677.6	1.56739	0.783697	−	0.621143i	$-0.213331\pi$
$947$	45677.6	1.56739	0.783697	+	0.621143i	$0.213331\pi$
$948$	17110.8	0.586217
$949$	16057.8	0.549271
$950$	0	0
$951$	11490.1	0.391790
$952$	−728.048	−0.0247859
$953$	41584.5	1.41349	0.706743	−	0.707470i	$-0.250164\pi$
$953$	41584.5	1.41349	0.706743	+	0.707470i	$0.250164\pi$
$954$	28730.6	0.975040
$955$	0	0
$956$	−36500.5	−1.23484
$957$	2276.67	0.0769012
$958$	85855.7	2.89548
$959$	7393.47	0.248955
$960$	0	0
$961$	−15617.0	−0.524217
$962$	24714.2	0.828292
$963$	−3170.22	−0.106084
$964$	−29311.6	−0.979318
$965$	0	0
$966$	3893.01	0.129664
$967$	−5961.61	−0.198255	−0.0991274	−	0.995075i	$-0.531605\pi$
$967$	−5961.61	−0.198255	−0.0991274	+	0.995075i	$0.531605\pi$
$968$	3537.80	0.117468
$969$	2574.87	0.0853631
$970$	0	0
$971$	−25246.9	−0.834410	−0.417205	−	0.908812i	$-0.636990\pi$
$971$	−25246.9	−0.834410	−0.417205	+	0.908812i	$0.636990\pi$
$972$	−36326.4	−1.19874
$973$	−9496.43	−0.312890
$974$	−73713.5	−2.42498
$975$	0	0
$976$	−2771.86	−0.0909068
$977$	−44505.1	−1.45736	−0.728682	−	0.684852i	$-0.759867\pi$
$977$	−44505.1	−1.45736	−0.728682	+	0.684852i	$0.759867\pi$
$978$	22481.1	0.735039
$979$	43906.8	1.43337
$980$	0	0
$981$	−22853.0	−0.743772
$982$	14534.3	0.472308
$983$	−14970.7	−0.485750	−0.242875	−	0.970058i	$-0.578090\pi$
$983$	−14970.7	−0.485750	−0.242875	+	0.970058i	$0.578090\pi$
$984$	5546.82	0.179701
$985$	0	0
$986$	−3895.82	−0.125830
$987$	−3063.94	−0.0988109
$988$	5635.86	0.181478
$989$	−3549.97	−0.114138
$990$	0	0
$991$	−10815.1	−0.346674	−0.173337	−	0.984863i	$-0.555455\pi$
$991$	−10815.1	−0.346674	−0.173337	+	0.984863i	$0.555455\pi$
$992$	30811.0	0.986139
$993$	−24705.2	−0.789522
$994$	−11876.4	−0.378969
$995$	0	0
$996$	12949.2	0.411959
$997$	39556.1	1.25652	0.628262	−	0.778002i	$-0.283767\pi$
$997$	39556.1	1.25652	0.628262	+	0.778002i	$0.283767\pi$
$998$	−5812.27	−0.184353
$999$	−44745.6	−1.41711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.4.a.b.1.2		6
5.4	even	2		43.4.a.b.1.5	✓	6
15.14	odd	2		387.4.a.h.1.2		6
20.19	odd	2		688.4.a.i.1.3		6
35.34	odd	2		2107.4.a.c.1.5		6
215.214	odd	2		1849.4.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.5	✓	6	5.4	even	2
387.4.a.h.1.2		6	15.14	odd	2
688.4.a.i.1.3		6	20.19	odd	2
1075.4.a.b.1.2		6	1.1	even	1	trivial
1849.4.a.c.1.2		6	215.214	odd	2
2107.4.a.c.1.5		6	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +10.2909 q^{6} -4.58222 q^{7} -5.83236 q^{8} -20.9131 q^{9} +O(q^{10})\)	\(q-4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +10.2909 q^{6} -4.58222 q^{7} -5.83236 q^{8} -20.9131 q^{9} +26.9150 q^{11} -23.1872 q^{12} +15.6529 q^{13} +19.1130 q^{14} -50.8587 q^{16} -27.2420 q^{17} +87.2309 q^{18} +38.3104 q^{19} +11.3051 q^{21} -112.266 q^{22} -82.5575 q^{23} +14.3894 q^{24} -65.2903 q^{26} +118.210 q^{27} -43.0650 q^{28} -34.2852 q^{29} +119.055 q^{31} +258.797 q^{32} -66.4040 q^{33} +113.630 q^{34} -196.547 q^{36} -378.527 q^{37} -159.797 q^{38} -38.6185 q^{39} +385.478 q^{41} -47.1551 q^{42} +43.0000 q^{43} +252.955 q^{44} +344.358 q^{46} -271.022 q^{47} +125.477 q^{48} -322.003 q^{49} +67.2108 q^{51} +147.110 q^{52} +329.363 q^{53} -493.068 q^{54} +26.7252 q^{56} -94.5184 q^{57} +143.008 q^{58} -173.956 q^{59} +54.5012 q^{61} -496.592 q^{62} +95.8283 q^{63} -672.604 q^{64} +276.979 q^{66} +906.954 q^{67} -256.028 q^{68} +203.684 q^{69} -621.376 q^{71} +121.972 q^{72} +1025.87 q^{73} +1578.88 q^{74} +360.052 q^{76} -123.331 q^{77} +161.082 q^{78} -737.945 q^{79} +273.009 q^{81} -1607.88 q^{82} -558.465 q^{83} +106.249 q^{84} -179.358 q^{86} +84.5875 q^{87} -156.978 q^{88} +1631.31 q^{89} -71.7252 q^{91} -775.898 q^{92} -293.729 q^{93} +1130.47 q^{94} -638.496 q^{96} +406.607 q^{97} +1343.12 q^{98} -562.875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * q^99

Introduction

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