LMFDB - Embedded newform 1175.4.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,4,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, 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("1175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1175.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:	$69.3272442567$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 12 $ x^3 - x^2 - 9*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 47)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.11903$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.60930 q^{2} -1.72833 q^{3} -5.41015 q^{4} -2.78140 q^{6} +11.3182 q^{7} -21.5810 q^{8} -24.0129 q^{9} +O(q^{10})$	\(q+1.60930 q^{2} -1.72833 q^{3} -5.41015 q^{4} -2.78140 q^{6} +11.3182 q^{7} -21.5810 q^{8} -24.0129 q^{9} -40.6469 q^{11} +9.35051 q^{12} +12.3983 q^{13} +18.2143 q^{14} +8.55095 q^{16} -59.6717 q^{17} -38.6440 q^{18} +26.4089 q^{19} -19.5615 q^{21} -65.4131 q^{22} -107.097 q^{23} +37.2990 q^{24} +19.9526 q^{26} +88.1670 q^{27} -61.2330 q^{28} +173.657 q^{29} -332.301 q^{31} +186.409 q^{32} +70.2512 q^{33} -96.0296 q^{34} +129.913 q^{36} +172.339 q^{37} +42.4998 q^{38} -21.4283 q^{39} -178.190 q^{41} -31.4804 q^{42} -63.2928 q^{43} +219.906 q^{44} -172.351 q^{46} -47.0000 q^{47} -14.7788 q^{48} -214.899 q^{49} +103.132 q^{51} -67.0767 q^{52} +402.256 q^{53} +141.887 q^{54} -244.257 q^{56} -45.6432 q^{57} +279.466 q^{58} +305.280 q^{59} -86.2464 q^{61} -534.772 q^{62} -271.782 q^{63} +231.580 q^{64} +113.055 q^{66} +681.333 q^{67} +322.833 q^{68} +185.098 q^{69} +726.348 q^{71} +518.221 q^{72} +79.8711 q^{73} +277.345 q^{74} -142.876 q^{76} -460.049 q^{77} -34.4846 q^{78} +279.707 q^{79} +495.966 q^{81} -286.761 q^{82} -556.598 q^{83} +105.831 q^{84} -101.857 q^{86} -300.135 q^{87} +877.200 q^{88} -342.069 q^{89} +140.326 q^{91} +579.410 q^{92} +574.325 q^{93} -75.6371 q^{94} -322.175 q^{96} +1637.35 q^{97} -345.837 q^{98} +976.050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 5 q^{2} + 5 q^{3} + 5 q^{4} - 8 q^{6} + 45 q^{7} + 39 q^{8} - 42 q^{9}+O(q^{10}) $ 3 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 - 8 * q^6 + 45 * q^7 + 39 * q^8 - 42 * q^9	$ 3 q + 5 q^{2} + 5 q^{3} + 5 q^{4} - 8 q^{6} + 45 q^{7} + 39 q^{8} - 42 q^{9} + 2 q^{11} - 12 q^{12} + 80 q^{13} + 162 q^{14} + 89 q^{16} + 39 q^{17} - 181 q^{18} - 24 q^{19} + 24 q^{21} + 14 q^{22} - 120 q^{23} + 192 q^{24} + 316 q^{26} - 64 q^{27} + 408 q^{28} - 184 q^{29} - 4 q^{31} + 7 q^{32} + 208 q^{33} + 218 q^{34} - 343 q^{36} + 589 q^{37} - 42 q^{38} + 60 q^{39} - 92 q^{41} + 54 q^{42} + 250 q^{43} + 466 q^{44} - 816 q^{46} - 141 q^{47} + 120 q^{48} + 30 q^{49} + 317 q^{51} + 900 q^{52} - 459 q^{53} + 106 q^{54} + 1032 q^{56} - 216 q^{57} - 684 q^{58} + 579 q^{59} + 267 q^{61} + 244 q^{62} - 1044 q^{63} - 87 q^{64} + 16 q^{66} + 540 q^{67} + 1334 q^{68} + 642 q^{69} + 749 q^{71} - 357 q^{72} + 1924 q^{73} + 950 q^{74} - 402 q^{76} + 288 q^{77} + 152 q^{78} + 805 q^{79} + 291 q^{81} + 938 q^{82} - 712 q^{83} + 372 q^{84} - 1294 q^{86} - 1216 q^{87} + 2190 q^{88} + 835 q^{89} + 2040 q^{91} - 1596 q^{92} + 1500 q^{93} - 235 q^{94} - 1432 q^{96} + 2243 q^{97} + 2989 q^{98} + 554 q^{99}+O(q^{100}) $ 3 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 - 8 * q^6 + 45 * q^7 + 39 * q^8 - 42 * q^9 + 2 * q^11 - 12 * q^12 + 80 * q^13 + 162 * q^14 + 89 * q^16 + 39 * q^17 - 181 * q^18 - 24 * q^19 + 24 * q^21 + 14 * q^22 - 120 * q^23 + 192 * q^24 + 316 * q^26 - 64 * q^27 + 408 * q^28 - 184 * q^29 - 4 * q^31 + 7 * q^32 + 208 * q^33 + 218 * q^34 - 343 * q^36 + 589 * q^37 - 42 * q^38 + 60 * q^39 - 92 * q^41 + 54 * q^42 + 250 * q^43 + 466 * q^44 - 816 * q^46 - 141 * q^47 + 120 * q^48 + 30 * q^49 + 317 * q^51 + 900 * q^52 - 459 * q^53 + 106 * q^54 + 1032 * q^56 - 216 * q^57 - 684 * q^58 + 579 * q^59 + 267 * q^61 + 244 * q^62 - 1044 * q^63 - 87 * q^64 + 16 * q^66 + 540 * q^67 + 1334 * q^68 + 642 * q^69 + 749 * q^71 - 357 * q^72 + 1924 * q^73 + 950 * q^74 - 402 * q^76 + 288 * q^77 + 152 * q^78 + 805 * q^79 + 291 * q^81 + 938 * q^82 - 712 * q^83 + 372 * q^84 - 1294 * q^86 - 1216 * q^87 + 2190 * q^88 + 835 * q^89 + 2040 * q^91 - 1596 * q^92 + 1500 * q^93 - 235 * q^94 - 1432 * q^96 + 2243 * q^97 + 2989 * q^98 + 554 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.60930	0.568974	0.284487	−	0.958680i	$-0.408177\pi$
$2$	1.60930	0.568974	0.284487	+	0.958680i	$0.408177\pi$
$3$	−1.72833	−0.332617	−0.166308	−	0.986074i	$-0.553185\pi$
$3$	−1.72833	−0.332617	−0.166308	+	0.986074i	$0.553185\pi$
$4$	−5.41015	−0.676269
$5$	0	0
$5$	0	0
$6$	−2.78140	−0.189250
$7$	11.3182	0.611124	0.305562	−	0.952172i	$-0.401156\pi$
$7$	11.3182	0.611124	0.305562	+	0.952172i	$0.401156\pi$
$8$	−21.5810	−0.953753
$9$	−24.0129	−0.889366
$10$	0	0
$11$	−40.6469	−1.11414	−0.557069	−	0.830467i	$-0.688074\pi$
$11$	−40.6469	−1.11414	−0.557069	+	0.830467i	$0.688074\pi$
$12$	9.35051	0.224938
$13$	12.3983	0.264513	0.132257	−	0.991216i	$-0.457778\pi$
$13$	12.3983	0.264513	0.132257	+	0.991216i	$0.457778\pi$
$14$	18.2143	0.347714
$15$	0	0
$16$	8.55095	0.133609
$17$	−59.6717	−0.851324	−0.425662	−	0.904882i	$-0.639959\pi$
$17$	−59.6717	−0.851324	−0.425662	+	0.904882i	$0.639959\pi$
$18$	−38.6440	−0.506026
$19$	26.4089	0.318874	0.159437	−	0.987208i	$-0.449032\pi$
$19$	26.4089	0.318874	0.159437	+	0.987208i	$0.449032\pi$
$20$	0	0
$21$	−19.5615	−0.203270
$22$	−65.4131	−0.633915
$23$	−107.097	−0.970923	−0.485461	−	0.874258i	$-0.661348\pi$
$23$	−107.097	−0.970923	−0.485461	+	0.874258i	$0.661348\pi$
$24$	37.2990	0.317234
$25$	0	0
$26$	19.9526	0.150501
$27$	88.1670	0.628435
$28$	−61.2330	−0.413284
$29$	173.657	1.11197	0.555987	−	0.831191i	$-0.312341\pi$
$29$	173.657	1.11197	0.555987	+	0.831191i	$0.312341\pi$
$30$	0	0
$31$	−332.301	−1.92526	−0.962629	−	0.270823i	$-0.912704\pi$
$31$	−332.301	−1.92526	−0.962629	+	0.270823i	$0.912704\pi$
$32$	186.409	1.02977
$33$	70.2512	0.370581
$34$	−96.0296	−0.484381
$35$	0	0
$36$	129.913	0.601451
$37$	172.339	0.765739	0.382869	−	0.923802i	$-0.374936\pi$
$37$	172.339	0.765739	0.382869	+	0.923802i	$0.374936\pi$
$38$	42.4998	0.181431
$39$	−21.4283	−0.0879815
$40$	0	0
$41$	−178.190	−0.678746	−0.339373	−	0.940652i	$-0.610215\pi$
$41$	−178.190	−0.678746	−0.339373	+	0.940652i	$0.610215\pi$
$42$	−31.4804	−0.115655
$43$	−63.2928	−0.224467	−0.112233	−	0.993682i	$-0.535800\pi$
$43$	−63.2928	−0.224467	−0.112233	+	0.993682i	$0.535800\pi$
$44$	219.906	0.753456
$45$	0	0
$46$	−172.351	−0.552429
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	−14.7788	−0.0444404
$49$	−214.899	−0.626527
$50$	0	0
$51$	103.132	0.283165
$52$	−67.0767	−0.178882
$53$	402.256	1.04253	0.521266	−	0.853395i	$-0.325460\pi$
$53$	402.256	1.04253	0.521266	+	0.853395i	$0.325460\pi$
$54$	141.887	0.357563
$55$	0	0
$56$	−244.257	−0.582861
$57$	−45.6432	−0.106063
$58$	279.466	0.632684
$59$	305.280	0.673628	0.336814	−	0.941571i	$-0.390651\pi$
$59$	305.280	0.673628	0.336814	+	0.941571i	$0.390651\pi$
$60$	0	0
$61$	−86.2464	−0.181028	−0.0905141	−	0.995895i	$-0.528851\pi$
$61$	−86.2464	−0.181028	−0.0905141	+	0.995895i	$0.528851\pi$
$62$	−534.772	−1.09542
$63$	−271.782	−0.543513
$64$	231.580	0.452305
$65$	0	0
$66$	113.055	0.210851
$67$	681.333	1.24236	0.621179	−	0.783668i	$-0.286654\pi$
$67$	681.333	1.24236	0.621179	+	0.783668i	$0.286654\pi$
$68$	322.833	0.575724
$69$	185.098	0.322945
$70$	0	0
$71$	726.348	1.21411	0.607054	−	0.794661i	$-0.292351\pi$
$71$	726.348	1.21411	0.607054	+	0.794661i	$0.292351\pi$
$72$	518.221	0.848236
$73$	79.8711	0.128058	0.0640288	−	0.997948i	$-0.479605\pi$
$73$	79.8711	0.128058	0.0640288	+	0.997948i	$0.479605\pi$
$74$	277.345	0.435685
$75$	0	0
$76$	−142.876	−0.215645
$77$	−460.049	−0.680876
$78$	−34.4846	−0.0500591
$79$	279.707	0.398348	0.199174	−	0.979964i	$-0.436174\pi$
$79$	279.707	0.398348	0.199174	+	0.979964i	$0.436174\pi$
$80$	0	0
$81$	495.966	0.680338
$82$	−286.761	−0.386189
$83$	−556.598	−0.736080	−0.368040	−	0.929810i	$-0.619971\pi$
$83$	−556.598	−0.736080	−0.368040	+	0.929810i	$0.619971\pi$
$84$	105.831	0.137465
$85$	0	0
$86$	−101.857	−0.127716
$87$	−300.135	−0.369861
$88$	877.200	1.06261
$89$	−342.069	−0.407408	−0.203704	−	0.979033i	$-0.565298\pi$
$89$	−342.069	−0.407408	−0.203704	+	0.979033i	$0.565298\pi$
$90$	0	0
$91$	140.326	0.161650
$92$	579.410	0.656605
$93$	574.325	0.640373
$94$	−75.6371	−0.0829933
$95$	0	0
$96$	−322.175	−0.342520
$97$	1637.35	1.71390	0.856949	−	0.515402i	$-0.172357\pi$
$97$	1637.35	1.71390	0.856949	+	0.515402i	$0.172357\pi$
$98$	−345.837	−0.356478
$99$	976.050	0.990876
$100$	0	0
$101$	−1453.29	−1.43176	−0.715879	−	0.698224i	$-0.753974\pi$
$101$	−1453.29	−1.43176	−0.715879	+	0.698224i	$0.753974\pi$
$102$	165.971	0.161113
$103$	−1363.10	−1.30398	−0.651992	−	0.758226i	$-0.726067\pi$
$103$	−1363.10	−1.30398	−0.651992	+	0.758226i	$0.726067\pi$
$104$	−267.567	−0.252280
$105$	0	0
$106$	647.351	0.593173
$107$	−274.746	−0.248231	−0.124116	−	0.992268i	$-0.539609\pi$
$107$	−274.746	−0.248231	−0.124116	+	0.992268i	$0.539609\pi$
$108$	−476.997	−0.424991
$109$	1448.56	1.27291	0.636454	−	0.771315i	$-0.280401\pi$
$109$	1448.56	1.27291	0.636454	+	0.771315i	$0.280401\pi$
$110$	0	0
$111$	−297.858	−0.254698
$112$	96.7811	0.0816514
$113$	1591.30	1.32475	0.662376	−	0.749171i	$-0.269548\pi$
$113$	1591.30	1.32475	0.662376	+	0.749171i	$0.269548\pi$
$114$	−73.4536	−0.0603470
$115$	0	0
$116$	−939.509	−0.751993
$117$	−297.719	−0.235249
$118$	491.287	0.383277
$119$	−675.374	−0.520264
$120$	0	0
$121$	321.172	0.241301
$122$	−138.796	−0.103000
$123$	307.970	0.225762
$124$	1797.80	1.30199
$125$	0	0
$126$	−437.379	−0.309245
$127$	−747.668	−0.522400	−0.261200	−	0.965285i	$-0.584118\pi$
$127$	−747.668	−0.522400	−0.261200	+	0.965285i	$0.584118\pi$
$128$	−1118.59	−0.772423
$129$	109.391	0.0746614
$130$	0	0
$131$	−624.528	−0.416529	−0.208264	−	0.978073i	$-0.566781\pi$
$131$	−624.528	−0.416529	−0.208264	+	0.978073i	$0.566781\pi$
$132$	−380.070	−0.250612
$133$	298.900	0.194872
$134$	1096.47	0.706869
$135$	0	0
$136$	1287.77	0.811953
$137$	336.418	0.209796	0.104898	−	0.994483i	$-0.466548\pi$
$137$	336.418	0.209796	0.104898	+	0.994483i	$0.466548\pi$
$138$	297.879	0.183747
$139$	1940.28	1.18397	0.591987	−	0.805948i	$-0.298344\pi$
$139$	1940.28	1.18397	0.591987	+	0.805948i	$0.298344\pi$
$140$	0	0
$141$	81.2314	0.0485171
$142$	1168.91	0.690795
$143$	−503.953	−0.294704
$144$	−205.333	−0.118827
$145$	0	0
$146$	128.537	0.0728614
$147$	371.416	0.208394
$148$	−932.380	−0.517845
$149$	2810.71	1.54538	0.772692	−	0.634781i	$-0.218910\pi$
$149$	2810.71	1.54538	0.772692	+	0.634781i	$0.218910\pi$
$150$	0	0
$151$	1710.82	0.922014	0.461007	−	0.887396i	$-0.347488\pi$
$151$	1710.82	0.922014	0.461007	+	0.887396i	$0.347488\pi$
$152$	−569.929	−0.304127
$153$	1432.89	0.757138
$154$	−740.357	−0.387401
$155$	0	0
$156$	115.930	0.0594991
$157$	1378.36	0.700669	0.350334	−	0.936625i	$-0.386068\pi$
$157$	1378.36	0.700669	0.350334	+	0.936625i	$0.386068\pi$
$158$	450.133	0.226650
$159$	−695.231	−0.346763
$160$	0	0
$161$	−1212.14	−0.593354
$162$	798.159	0.387095
$163$	3255.46	1.56434	0.782170	−	0.623066i	$-0.214113\pi$
$163$	3255.46	1.56434	0.782170	+	0.623066i	$0.214113\pi$
$164$	964.034	0.459015
$165$	0	0
$166$	−895.734	−0.418810
$167$	2337.08	1.08293	0.541463	−	0.840725i	$-0.317871\pi$
$167$	2337.08	1.08293	0.541463	+	0.840725i	$0.317871\pi$
$168$	422.156	0.193869
$169$	−2043.28	−0.930033
$170$	0	0
$171$	−634.153	−0.283596
$172$	342.424	0.151800
$173$	3269.43	1.43682	0.718412	−	0.695618i	$-0.244870\pi$
$173$	3269.43	1.43682	0.718412	+	0.695618i	$0.244870\pi$
$174$	−483.008	−0.210441
$175$	0	0
$176$	−347.570	−0.148858
$177$	−527.624	−0.224060
$178$	−550.492	−0.231804
$179$	−2203.96	−0.920290	−0.460145	−	0.887844i	$-0.652203\pi$
$179$	−2203.96	−0.920290	−0.460145	+	0.887844i	$0.652203\pi$
$180$	0	0
$181$	1522.63	0.625282	0.312641	−	0.949871i	$-0.398786\pi$
$181$	1522.63	0.625282	0.312641	+	0.949871i	$0.398786\pi$
$182$	225.827	0.0919748
$183$	149.062	0.0602130
$184$	2311.25	0.926020
$185$	0	0
$186$	924.261	0.364356
$187$	2425.47	0.948491
$188$	254.277	0.0986440
$189$	997.889	0.384052
$190$	0	0
$191$	−2019.27	−0.764968	−0.382484	−	0.923962i	$-0.624931\pi$
$191$	−2019.27	−0.764968	−0.382484	+	0.923962i	$0.624931\pi$
$192$	−400.246	−0.150444
$193$	4447.95	1.65891	0.829456	−	0.558571i	$-0.188650\pi$
$193$	4447.95	1.65891	0.829456	+	0.558571i	$0.188650\pi$
$194$	2634.99	0.975163
$195$	0	0
$196$	1162.64	0.423701
$197$	−1790.04	−0.647388	−0.323694	−	0.946162i	$-0.604925\pi$
$197$	−1790.04	−0.647388	−0.323694	+	0.946162i	$0.604925\pi$
$198$	1570.76	0.563782
$199$	3481.42	1.24016	0.620079	−	0.784540i	$-0.287101\pi$
$199$	3481.42	1.24016	0.620079	+	0.784540i	$0.287101\pi$
$200$	0	0
$201$	−1177.57	−0.413229
$202$	−2338.78	−0.814633
$203$	1965.48	0.679554
$204$	−557.961	−0.191495
$205$	0	0
$206$	−2193.64	−0.741933
$207$	2571.70	0.863506
$208$	106.017	0.0353412
$209$	−1073.44	−0.355270
$210$	0	0
$211$	5216.72	1.70206	0.851028	−	0.525120i	$-0.175979\pi$
$211$	5216.72	1.70206	0.851028	+	0.525120i	$0.175979\pi$
$212$	−2176.27	−0.705031
$213$	−1255.37	−0.403833
$214$	−442.150	−0.141237
$215$	0	0
$216$	−1902.73	−0.599372
$217$	−3761.04	−1.17657
$218$	2331.17	0.724251
$219$	−138.043	−0.0425941
$220$	0	0
$221$	−739.827	−0.225186
$222$	−479.343	−0.144916
$223$	−5075.44	−1.52411	−0.762055	−	0.647512i	$-0.775810\pi$
$223$	−5075.44	−1.52411	−0.762055	+	0.647512i	$0.775810\pi$
$224$	2109.81	0.629319
$225$	0	0
$226$	2560.88	0.753749
$227$	−1752.66	−0.512460	−0.256230	−	0.966616i	$-0.582480\pi$
$227$	−1752.66	−0.512460	−0.256230	+	0.966616i	$0.582480\pi$
$228$	246.936	0.0717270
$229$	−4676.77	−1.34956	−0.674781	−	0.738018i	$-0.735762\pi$
$229$	−4676.77	−1.34956	−0.674781	+	0.738018i	$0.735762\pi$
$230$	0	0
$231$	795.115	0.226471
$232$	−3747.68	−1.06055
$233$	−4261.89	−1.19831	−0.599154	−	0.800634i	$-0.704496\pi$
$233$	−4261.89	−1.19831	−0.599154	+	0.800634i	$0.704496\pi$
$234$	−479.119	−0.133850
$235$	0	0
$236$	−1651.61	−0.455554
$237$	−483.426	−0.132497
$238$	−1086.88	−0.296017
$239$	−3227.38	−0.873479	−0.436740	−	0.899588i	$-0.643867\pi$
$239$	−3227.38	−0.873479	−0.436740	+	0.899588i	$0.643867\pi$
$240$	0	0
$241$	−1310.37	−0.350242	−0.175121	−	0.984547i	$-0.556032\pi$
$241$	−1310.37	−0.350242	−0.175121	+	0.984547i	$0.556032\pi$
$242$	516.863	0.137294
$243$	−3237.70	−0.854727
$244$	466.606	0.122424
$245$	0	0
$246$	495.617	0.128453
$247$	327.425	0.0843464
$248$	7171.38	1.83622
$249$	961.984	0.244832
$250$	0	0
$251$	4906.61	1.23387	0.616937	−	0.787013i	$-0.288373\pi$
$251$	4906.61	1.23387	0.616937	+	0.787013i	$0.288373\pi$
$252$	1470.38	0.367561
$253$	4353.15	1.08174
$254$	−1203.22	−0.297232
$255$	0	0
$256$	−3652.79	−0.891793
$257$	−2103.21	−0.510485	−0.255243	−	0.966877i	$-0.582155\pi$
$257$	−2103.21	−0.510485	−0.255243	+	0.966877i	$0.582155\pi$
$258$	176.043	0.0424804
$259$	1950.56	0.467962
$260$	0	0
$261$	−4170.00	−0.988951
$262$	−1005.05	−0.236994
$263$	6993.90	1.63978	0.819890	−	0.572521i	$-0.194035\pi$
$263$	6993.90	1.63978	0.819890	+	0.572521i	$0.194035\pi$
$264$	−1516.09	−0.353442
$265$	0	0
$266$	481.020	0.110877
$267$	591.208	0.135511
$268$	−3686.11	−0.840168
$269$	6466.63	1.46571	0.732857	−	0.680382i	$-0.238186\pi$
$269$	6466.63	1.46571	0.732857	+	0.680382i	$0.238186\pi$
$270$	0	0
$271$	−8154.65	−1.82790	−0.913948	−	0.405831i	$-0.866982\pi$
$271$	−8154.65	−1.82790	−0.913948	+	0.405831i	$0.866982\pi$
$272$	−510.249	−0.113744
$273$	−242.530	−0.0537676
$274$	541.397	0.119369
$275$	0	0
$276$	−1001.41	−0.218398
$277$	−3722.71	−0.807495	−0.403748	−	0.914870i	$-0.632293\pi$
$277$	−3722.71	−0.807495	−0.403748	+	0.914870i	$0.632293\pi$
$278$	3122.49	0.673650
$279$	7979.50	1.71226
$280$	0	0
$281$	−6046.33	−1.28361	−0.641804	−	0.766869i	$-0.721814\pi$
$281$	−6046.33	−1.28361	−0.641804	+	0.766869i	$0.721814\pi$
$282$	130.726	0.0276050
$283$	−268.000	−0.0562931	−0.0281466	−	0.999604i	$-0.508961\pi$
$283$	−268.000	−0.0562931	−0.0281466	+	0.999604i	$0.508961\pi$
$284$	−3929.65	−0.821063
$285$	0	0
$286$	−811.011	−0.167679
$287$	−2016.78	−0.414798
$288$	−4476.21	−0.915845
$289$	−1352.29	−0.275248
$290$	0	0
$291$	−2829.88	−0.570071
$292$	−432.115	−0.0866014
$293$	−2731.03	−0.544535	−0.272267	−	0.962222i	$-0.587774\pi$
$293$	−2731.03	−0.544535	−0.272267	+	0.962222i	$0.587774\pi$
$294$	597.719	0.118570
$295$	0	0
$296$	−3719.24	−0.730326
$297$	−3583.72	−0.700163
$298$	4523.28	0.879283
$299$	−1327.82	−0.256822
$300$	0	0
$301$	−716.360	−0.137177
$302$	2753.22	0.524602
$303$	2511.76	0.476227
$304$	225.821	0.0426043
$305$	0	0
$306$	2305.95	0.430792
$307$	7009.57	1.30312	0.651559	−	0.758598i	$-0.274115\pi$
$307$	7009.57	1.30312	0.651559	+	0.758598i	$0.274115\pi$
$308$	2488.93	0.460455
$309$	2355.89	0.433727
$310$	0	0
$311$	−867.418	−0.158157	−0.0790784	−	0.996868i	$-0.525198\pi$
$311$	−867.418	−0.158157	−0.0790784	+	0.996868i	$0.525198\pi$
$312$	462.444	0.0839126
$313$	−5724.10	−1.03369	−0.516845	−	0.856079i	$-0.672894\pi$
$313$	−5724.10	−1.03369	−0.516845	+	0.856079i	$0.672894\pi$
$314$	2218.19	0.398662
$315$	0	0
$316$	−1513.26	−0.269391
$317$	−5821.24	−1.03140	−0.515700	−	0.856769i	$-0.672468\pi$
$317$	−5821.24	−1.03140	−0.515700	+	0.856769i	$0.672468\pi$
$318$	−1118.84	−0.197299
$319$	−7058.61	−1.23889
$320$	0	0
$321$	474.852	0.0825659
$322$	−1950.70	−0.337603
$323$	−1575.86	−0.271465
$324$	−2683.25	−0.460092
$325$	0	0
$326$	5239.01	0.890068
$327$	−2503.59	−0.423390
$328$	3845.51	0.647356
$329$	−531.954	−0.0891416
$330$	0	0
$331$	−2300.44	−0.382005	−0.191002	−	0.981590i	$-0.561174\pi$
$331$	−2300.44	−0.382005	−0.191002	+	0.981590i	$0.561174\pi$
$332$	3011.28	0.497788
$333$	−4138.35	−0.681022
$334$	3761.06	0.616156
$335$	0	0
$336$	−167.269	−0.0271586
$337$	6399.32	1.03440	0.517201	−	0.855864i	$-0.326974\pi$
$337$	6399.32	1.03440	0.517201	+	0.855864i	$0.326974\pi$
$338$	−3288.26	−0.529164
$339$	−2750.29	−0.440635
$340$	0	0
$341$	13507.0	2.14500
$342$	−1020.54	−0.161359
$343$	−6314.40	−0.994010
$344$	1365.92	0.214086
$345$	0	0
$346$	5261.50	0.817515
$347$	9188.96	1.42158	0.710791	−	0.703403i	$-0.248337\pi$
$347$	9188.96	1.42158	0.710791	+	0.703403i	$0.248337\pi$
$348$	1623.78	0.250125
$349$	6327.24	0.970457	0.485229	−	0.874387i	$-0.338736\pi$
$349$	6327.24	0.970457	0.485229	+	0.874387i	$0.338736\pi$
$350$	0	0
$351$	1093.12	0.166229
$352$	−7576.94	−1.14731
$353$	−8212.76	−1.23830	−0.619152	−	0.785271i	$-0.712523\pi$
$353$	−8212.76	−1.23830	−0.619152	+	0.785271i	$0.712523\pi$
$354$	−849.105	−0.127484
$355$	0	0
$356$	1850.65	0.275517
$357$	1167.27	0.173049
$358$	−3546.84	−0.523621
$359$	−5614.24	−0.825371	−0.412685	−	0.910874i	$-0.635409\pi$
$359$	−5614.24	−0.825371	−0.412685	+	0.910874i	$0.635409\pi$
$360$	0	0
$361$	−6161.57	−0.898319
$362$	2450.37	0.355769
$363$	−555.091	−0.0802609
$364$	−759.186	−0.109319
$365$	0	0
$366$	239.886	0.0342596
$367$	3282.91	0.466938	0.233469	−	0.972364i	$-0.424992\pi$
$367$	3282.91	0.466938	0.233469	+	0.972364i	$0.424992\pi$
$368$	−915.778	−0.129724
$369$	4278.85	0.603654
$370$	0	0
$371$	4552.81	0.637116
$372$	−3107.18	−0.433065
$373$	9749.67	1.35340	0.676701	−	0.736258i	$-0.263409\pi$
$373$	9749.67	1.35340	0.676701	+	0.736258i	$0.263409\pi$
$374$	3903.31	0.539667
$375$	0	0
$376$	1014.31	0.139119
$377$	2153.05	0.294131
$378$	1605.90	0.218515
$379$	−7875.26	−1.06735	−0.533674	−	0.845690i	$-0.679189\pi$
$379$	−7875.26	−1.06735	−0.533674	+	0.845690i	$0.679189\pi$
$380$	0	0
$381$	1292.21	0.173759
$382$	−3249.61	−0.435247
$383$	1599.65	0.213416	0.106708	−	0.994290i	$-0.465969\pi$
$383$	1599.65	0.213416	0.106708	+	0.994290i	$0.465969\pi$
$384$	1933.29	0.256921
$385$	0	0
$386$	7158.08	0.943878
$387$	1519.84	0.199633
$388$	−8858.33	−1.15906
$389$	−5101.31	−0.664901	−0.332451	−	0.943121i	$-0.607876\pi$
$389$	−5101.31	−0.664901	−0.332451	+	0.943121i	$0.607876\pi$
$390$	0	0
$391$	6390.64	0.826569
$392$	4637.73	0.597552
$393$	1079.39	0.138544
$394$	−2880.72	−0.368347
$395$	0	0
$396$	−5280.58	−0.670098
$397$	8835.01	1.11692	0.558459	−	0.829532i	$-0.311393\pi$
$397$	8835.01	1.11692	0.558459	+	0.829532i	$0.311393\pi$
$398$	5602.65	0.705617
$399$	−516.597	−0.0648176
$400$	0	0
$401$	−15444.1	−1.92330	−0.961649	−	0.274284i	$-0.911559\pi$
$401$	−15444.1	−1.92330	−0.961649	+	0.274284i	$0.911559\pi$
$402$	−1895.06	−0.235117
$403$	−4119.97	−0.509256
$404$	7862.51	0.968253
$405$	0	0
$406$	3163.04	0.386648
$407$	−7005.05	−0.853138
$408$	−2225.69	−0.270069
$409$	−13309.7	−1.60910	−0.804552	−	0.593882i	$-0.797595\pi$
$409$	−13309.7	−1.60910	−0.804552	+	0.593882i	$0.797595\pi$
$410$	0	0
$411$	−581.440	−0.0697818
$412$	7374.59	0.881844
$413$	3455.21	0.411671
$414$	4138.64	0.491312
$415$	0	0
$416$	2311.15	0.272388
$417$	−3353.44	−0.393809
$418$	−1727.49	−0.202139
$419$	−2074.44	−0.241869	−0.120934	−	0.992661i	$-0.538589\pi$
$419$	−2074.44	−0.241869	−0.120934	+	0.992661i	$0.538589\pi$
$420$	0	0
$421$	14903.2	1.72526	0.862631	−	0.505833i	$-0.168815\pi$
$421$	14903.2	1.72526	0.862631	+	0.505833i	$0.168815\pi$
$422$	8395.27	0.968426
$423$	1128.61	0.129727
$424$	−8681.08	−0.994317
$425$	0	0
$426$	−2020.26	−0.229770
$427$	−976.152	−0.110631
$428$	1486.42	0.167871
$429$	870.995	0.0980234
$430$	0	0
$431$	7434.74	0.830902	0.415451	−	0.909616i	$-0.363624\pi$
$431$	7434.74	0.830902	0.415451	+	0.909616i	$0.363624\pi$
$432$	753.911	0.0839642
$433$	−4385.47	−0.486725	−0.243363	−	0.969935i	$-0.578251\pi$
$433$	−4385.47	−0.486725	−0.243363	+	0.969935i	$0.578251\pi$
$434$	−6052.65	−0.669438
$435$	0	0
$436$	−7836.93	−0.860828
$437$	−2828.30	−0.309602
$438$	−222.153	−0.0242349
$439$	−10300.7	−1.11988	−0.559939	−	0.828534i	$-0.689175\pi$
$439$	−10300.7	−1.11988	−0.559939	+	0.828534i	$0.689175\pi$
$440$	0	0
$441$	5160.34	0.557212
$442$	−1190.60	−0.128125
$443$	−5700.48	−0.611372	−0.305686	−	0.952132i	$-0.598886\pi$
$443$	−5700.48	−0.611372	−0.305686	+	0.952132i	$0.598886\pi$
$444$	1611.46	0.172244
$445$	0	0
$446$	−8167.91	−0.867179
$447$	−4857.83	−0.514021
$448$	2621.07	0.276415
$449$	−8946.30	−0.940317	−0.470158	−	0.882582i	$-0.655803\pi$
$449$	−8946.30	−0.940317	−0.470158	+	0.882582i	$0.655803\pi$
$450$	0	0
$451$	7242.87	0.756216
$452$	−8609.18	−0.895889
$453$	−2956.85	−0.306677
$454$	−2820.56	−0.291576
$455$	0	0
$456$	985.024	0.101158
$457$	16498.3	1.68875	0.844374	−	0.535755i	$-0.179973\pi$
$457$	16498.3	1.68875	0.844374	+	0.535755i	$0.179973\pi$
$458$	−7526.33	−0.767865
$459$	−5261.07	−0.535001
$460$	0	0
$461$	9016.08	0.910891	0.455445	−	0.890264i	$-0.349480\pi$
$461$	9016.08	0.910891	0.455445	+	0.890264i	$0.349480\pi$
$462$	1279.58	0.128856
$463$	−3241.41	−0.325359	−0.162679	−	0.986679i	$-0.552014\pi$
$463$	−3241.41	−0.325359	−0.162679	+	0.986679i	$0.552014\pi$
$464$	1484.93	0.148569
$465$	0	0
$466$	−6858.67	−0.681806
$467$	−12186.1	−1.20751	−0.603755	−	0.797170i	$-0.706329\pi$
$467$	−12186.1	−1.20751	−0.603755	+	0.797170i	$0.706329\pi$
$468$	1610.70	0.159092
$469$	7711.44	0.759235
$470$	0	0
$471$	−2382.25	−0.233054
$472$	−6588.24	−0.642475
$473$	2572.66	0.250087
$474$	−777.977	−0.0753875
$475$	0	0
$476$	3653.88	0.351839
$477$	−9659.33	−0.927192
$478$	−5193.82	−0.496987
$479$	−9110.87	−0.869074	−0.434537	−	0.900654i	$-0.643088\pi$
$479$	−9110.87	−0.869074	−0.434537	+	0.900654i	$0.643088\pi$
$480$	0	0
$481$	2136.71	0.202548
$482$	−2108.78	−0.199279
$483$	2094.97	0.197360
$484$	−1737.59	−0.163185
$485$	0	0
$486$	−5210.43	−0.486317
$487$	−535.218	−0.0498009	−0.0249004	−	0.999690i	$-0.507927\pi$
$487$	−535.218	−0.0498009	−0.0249004	+	0.999690i	$0.507927\pi$
$488$	1861.28	0.172656
$489$	−5626.50	−0.520325
$490$	0	0
$491$	10810.8	0.993658	0.496829	−	0.867848i	$-0.334498\pi$
$491$	10810.8	0.993658	0.496829	+	0.867848i	$0.334498\pi$
$492$	−1666.17	−0.152676
$493$	−10362.4	−0.946649
$494$	526.925	0.0479909
$495$	0	0
$496$	−2841.49	−0.257231
$497$	8220.93	0.741970
$498$	1548.12	0.139303
$499$	16736.4	1.50146	0.750728	−	0.660612i	$-0.229703\pi$
$499$	16736.4	1.50146	0.750728	+	0.660612i	$0.229703\pi$
$500$	0	0
$501$	−4039.24	−0.360199
$502$	7896.21	0.702042
$503$	−6612.65	−0.586170	−0.293085	−	0.956086i	$-0.594682\pi$
$503$	−6612.65	−0.586170	−0.293085	+	0.956086i	$0.594682\pi$
$504$	5865.32	0.518377
$505$	0	0
$506$	7005.53	0.615482
$507$	3531.46	0.309345
$508$	4045.00	0.353283
$509$	14953.5	1.30216	0.651081	−	0.759008i	$-0.274316\pi$
$509$	14953.5	1.30216	0.651081	+	0.759008i	$0.274316\pi$
$510$	0	0
$511$	903.995	0.0782591
$512$	3070.27	0.265016
$513$	2328.39	0.200392
$514$	−3384.70	−0.290453
$515$	0	0
$516$	−591.820	−0.0504912
$517$	1910.41	0.162514
$518$	3139.04	0.266258
$519$	−5650.65	−0.477911
$520$	0	0
$521$	822.169	0.0691361	0.0345680	−	0.999402i	$-0.488994\pi$
$521$	822.169	0.0691361	0.0345680	+	0.999402i	$0.488994\pi$
$522$	−6710.78	−0.562687
$523$	−97.2265	−0.00812890	−0.00406445	−	0.999992i	$-0.501294\pi$
$523$	−97.2265	−0.00812890	−0.00406445	+	0.999992i	$0.501294\pi$
$524$	3378.79	0.281685
$525$	0	0
$526$	11255.3	0.932992
$527$	19828.9	1.63902
$528$	600.714	0.0495127
$529$	−697.284	−0.0573095
$530$	0	0
$531$	−7330.65	−0.599102
$532$	−1617.10	−0.131786
$533$	−2209.25	−0.179537
$534$	951.431	0.0771020
$535$	0	0
$536$	−14703.8	−1.18490
$537$	3809.17	0.306104
$538$	10406.7	0.833953
$539$	8734.98	0.698037
$540$	0	0
$541$	−3856.31	−0.306462	−0.153231	−	0.988190i	$-0.548968\pi$
$541$	−3856.31	−0.306462	−0.153231	+	0.988190i	$0.548968\pi$
$542$	−13123.3	−1.04003
$543$	−2631.60	−0.207979
$544$	−11123.3	−0.876670
$545$	0	0
$546$	−390.303	−0.0305923
$547$	4147.40	0.324186	0.162093	−	0.986775i	$-0.448175\pi$
$547$	4147.40	0.324186	0.162093	+	0.986775i	$0.448175\pi$
$548$	−1820.07	−0.141879
$549$	2071.03	0.161000
$550$	0	0
$551$	4586.07	0.354580
$552$	−3994.60	−0.308010
$553$	3165.78	0.243440
$554$	−5990.96	−0.459443
$555$	0	0
$556$	−10497.2	−0.800684
$557$	−85.2280	−0.00648335	−0.00324168	−	0.999995i	$-0.501032\pi$
$557$	−85.2280	−0.00648335	−0.00324168	+	0.999995i	$0.501032\pi$
$558$	12841.4	0.974231
$559$	−784.724	−0.0593744
$560$	0	0
$561$	−4192.00	−0.315484
$562$	−9730.37	−0.730340
$563$	−12824.3	−0.960003	−0.480001	−	0.877268i	$-0.659364\pi$
$563$	−12824.3	−0.960003	−0.480001	+	0.877268i	$0.659364\pi$
$564$	−439.474	−0.0328106
$565$	0	0
$566$	−431.293	−0.0320293
$567$	5613.44	0.415771
$568$	−15675.3	−1.15796
$569$	−12096.8	−0.891253	−0.445626	−	0.895219i	$-0.647019\pi$
$569$	−12096.8	−0.891253	−0.445626	+	0.895219i	$0.647019\pi$
$570$	0	0
$571$	5688.49	0.416910	0.208455	−	0.978032i	$-0.433156\pi$
$571$	5688.49	0.416910	0.208455	+	0.978032i	$0.433156\pi$
$572$	2726.46	0.199299
$573$	3489.95	0.254441
$574$	−3245.61	−0.236009
$575$	0	0
$576$	−5560.91	−0.402265
$577$	9878.78	0.712754	0.356377	−	0.934342i	$-0.384012\pi$
$577$	9878.78	0.712754	0.356377	+	0.934342i	$0.384012\pi$
$578$	−2176.25	−0.156609
$579$	−7687.51	−0.551782
$580$	0	0
$581$	−6299.68	−0.449836
$582$	−4554.13	−0.324355
$583$	−16350.5	−1.16152
$584$	−1723.70	−0.122135
$585$	0	0
$586$	−4395.05	−0.309826
$587$	17342.9	1.21945	0.609726	−	0.792613i	$-0.291280\pi$
$587$	17342.9	1.21945	0.609726	+	0.792613i	$0.291280\pi$
$588$	−2009.41	−0.140930
$589$	−8775.69	−0.613915
$590$	0	0
$591$	3093.78	0.215332
$592$	1473.66	0.102309
$593$	−698.313	−0.0483580	−0.0241790	−	0.999708i	$-0.507697\pi$
$593$	−698.313	−0.0483580	−0.0241790	+	0.999708i	$0.507697\pi$
$594$	−5767.28	−0.398374
$595$	0	0
$596$	−15206.4	−1.04510
$597$	−6017.03	−0.412497
$598$	−2136.86	−0.146125
$599$	9549.46	0.651386	0.325693	−	0.945476i	$-0.394402\pi$
$599$	9549.46	0.651386	0.325693	+	0.945476i	$0.394402\pi$
$600$	0	0
$601$	27369.5	1.85761	0.928805	−	0.370568i	$-0.120837\pi$
$601$	27369.5	1.85761	0.928805	+	0.370568i	$0.120837\pi$
$602$	−1152.84	−0.0780501
$603$	−16360.8	−1.10491
$604$	−9255.77	−0.623530
$605$	0	0
$606$	4042.17	0.270960
$607$	−18179.8	−1.21564	−0.607821	−	0.794074i	$-0.707956\pi$
$607$	−18179.8	−1.21564	−0.607821	+	0.794074i	$0.707956\pi$
$608$	4922.84	0.328368
$609$	−3396.99	−0.226031
$610$	0	0
$611$	−582.720	−0.0385832
$612$	−7752.14	−0.512029
$613$	3148.69	0.207462	0.103731	−	0.994605i	$-0.466922\pi$
$613$	3148.69	0.207462	0.103731	+	0.994605i	$0.466922\pi$
$614$	11280.5	0.741440
$615$	0	0
$616$	9928.30	0.649387
$617$	24002.0	1.56610	0.783050	−	0.621959i	$-0.213663\pi$
$617$	24002.0	1.56610	0.783050	+	0.621959i	$0.213663\pi$
$618$	3791.33	0.246779
$619$	17997.2	1.16861	0.584304	−	0.811535i	$-0.301367\pi$
$619$	17997.2	1.16861	0.584304	+	0.811535i	$0.301367\pi$
$620$	0	0
$621$	−9442.40	−0.610162
$622$	−1395.94	−0.0899871
$623$	−3871.60	−0.248977
$624$	−183.232	−0.0117551
$625$	0	0
$626$	−9211.80	−0.588143
$627$	1855.25	0.118169
$628$	−7457.13	−0.473840
$629$	−10283.7	−0.651892
$630$	0	0
$631$	5508.64	0.347536	0.173768	−	0.984787i	$-0.444406\pi$
$631$	5508.64	0.347536	0.173768	+	0.984787i	$0.444406\pi$
$632$	−6036.35	−0.379926
$633$	−9016.20	−0.566133
$634$	−9368.13	−0.586839
$635$	0	0
$636$	3761.30	0.234505
$637$	−2664.38	−0.165725
$638$	−11359.4	−0.704896
$639$	−17441.7	−1.07979
$640$	0	0
$641$	11605.9	0.715142	0.357571	−	0.933886i	$-0.383605\pi$
$641$	11605.9	0.715142	0.357571	+	0.933886i	$0.383605\pi$
$642$	764.179	0.0469778
$643$	−7998.88	−0.490583	−0.245292	−	0.969449i	$-0.578884\pi$
$643$	−7998.88	−0.490583	−0.245292	+	0.969449i	$0.578884\pi$
$644$	6557.86	0.401267
$645$	0	0
$646$	−2536.03	−0.154457
$647$	5421.64	0.329438	0.164719	−	0.986341i	$-0.447328\pi$
$647$	5421.64	0.329438	0.164719	+	0.986341i	$0.447328\pi$
$648$	−10703.4	−0.648875
$649$	−12408.7	−0.750514
$650$	0	0
$651$	6500.31	0.391348
$652$	−17612.5	−1.05791
$653$	21419.1	1.28361	0.641804	−	0.766869i	$-0.278186\pi$
$653$	21419.1	1.28361	0.641804	+	0.766869i	$0.278186\pi$
$654$	−4029.02	−0.240898
$655$	0	0
$656$	−1523.69	−0.0906862
$657$	−1917.94	−0.113890
$658$	−856.074	−0.0507192
$659$	−11435.7	−0.675982	−0.337991	−	0.941149i	$-0.609747\pi$
$659$	−11435.7	−0.675982	−0.337991	+	0.941149i	$0.609747\pi$
$660$	0	0
$661$	27123.2	1.59602	0.798011	−	0.602643i	$-0.205886\pi$
$661$	27123.2	1.59602	0.798011	+	0.602643i	$0.205886\pi$
$662$	−3702.10	−0.217351
$663$	1278.66	0.0749007
$664$	12011.9	0.702038
$665$	0	0
$666$	−6659.86	−0.387484
$667$	−18598.1	−1.07964
$668$	−12644.0	−0.732349
$669$	8772.02	0.506945
$670$	0	0
$671$	3505.65	0.201690
$672$	−3646.44	−0.209322
$673$	11097.2	0.635612	0.317806	−	0.948156i	$-0.397054\pi$
$673$	11097.2	0.635612	0.317806	+	0.948156i	$0.397054\pi$
$674$	10298.4	0.588547
$675$	0	0
$676$	11054.5	0.628952
$677$	1647.83	0.0935468	0.0467734	−	0.998906i	$-0.485106\pi$
$677$	1647.83	0.0935468	0.0467734	+	0.998906i	$0.485106\pi$
$678$	−4426.04	−0.250710
$679$	18531.9	1.04740
$680$	0	0
$681$	3029.18	0.170453
$682$	21736.8	1.22045
$683$	−9256.41	−0.518575	−0.259287	−	0.965800i	$-0.583488\pi$
$683$	−9256.41	−0.518575	−0.259287	+	0.965800i	$0.583488\pi$
$684$	3430.86	0.191787
$685$	0	0
$686$	−10161.8	−0.565566
$687$	8082.99	0.448887
$688$	−541.214	−0.0299907
$689$	4987.29	0.275763
$690$	0	0
$691$	−2404.88	−0.132397	−0.0661983	−	0.997806i	$-0.521087\pi$
$691$	−2404.88	−0.132397	−0.0661983	+	0.997806i	$0.521087\pi$
$692$	−17688.1	−0.971679
$693$	11047.1	0.605548
$694$	14787.8	0.808843
$695$	0	0
$696$	6477.21	0.352756
$697$	10632.9	0.577833
$698$	10182.4	0.552165
$699$	7365.94	0.398577
$700$	0	0
$701$	1158.57	0.0624232	0.0312116	−	0.999513i	$-0.490063\pi$
$701$	1158.57	0.0624232	0.0312116	+	0.999513i	$0.490063\pi$
$702$	1759.16	0.0945801
$703$	4551.28	0.244174
$704$	−9413.02	−0.503930
$705$	0	0
$706$	−13216.8	−0.704562
$707$	−16448.6	−0.874982
$708$	2854.52	0.151525
$709$	−26868.0	−1.42320	−0.711600	−	0.702585i	$-0.752029\pi$
$709$	−26868.0	−1.42320	−0.711600	+	0.702585i	$0.752029\pi$
$710$	0	0
$711$	−6716.58	−0.354278
$712$	7382.19	0.388566
$713$	35588.4	1.86928
$714$	1878.49	0.0984601
$715$	0	0
$716$	11923.8	0.622363
$717$	5577.96	0.290534
$718$	−9035.00	−0.469614
$719$	12313.1	0.638666	0.319333	−	0.947643i	$-0.396541\pi$
$719$	12313.1	0.638666	0.319333	+	0.947643i	$0.396541\pi$
$720$	0	0
$721$	−15427.8	−0.796896
$722$	−9915.82	−0.511120
$723$	2264.75	0.116496
$724$	−8237.65	−0.422859
$725$	0	0
$726$	−893.308	−0.0456663
$727$	−4104.02	−0.209367	−0.104683	−	0.994506i	$-0.533383\pi$
$727$	−4104.02	−0.209367	−0.104683	+	0.994506i	$0.533383\pi$
$728$	−3028.37	−0.154174
$729$	−7795.29	−0.396042
$730$	0	0
$731$	3776.79	0.191094
$732$	−806.448	−0.0407202
$733$	−36113.9	−1.81978	−0.909888	−	0.414854i	$-0.863833\pi$
$733$	−36113.9	−1.81978	−0.909888	+	0.414854i	$0.863833\pi$
$734$	5283.18	0.265675
$735$	0	0
$736$	−19963.8	−0.999829
$737$	−27694.1	−1.38416
$738$	6885.96	0.343463
$739$	−4185.77	−0.208357	−0.104179	−	0.994559i	$-0.533221\pi$
$739$	−4185.77	−0.208357	−0.104179	+	0.994559i	$0.533221\pi$
$740$	0	0
$741$	−565.898	−0.0280550
$742$	7326.84	0.362502
$743$	24708.4	1.22001	0.610003	−	0.792399i	$-0.291168\pi$
$743$	24708.4	1.22001	0.610003	+	0.792399i	$0.291168\pi$
$744$	−12394.5	−0.610758
$745$	0	0
$746$	15690.2	0.770050
$747$	13365.5	0.654644
$748$	−13122.2	−0.641435
$749$	−3109.63	−0.151700
$750$	0	0
$751$	24154.5	1.17365	0.586824	−	0.809714i	$-0.300378\pi$
$751$	24154.5	1.17365	0.586824	+	0.809714i	$0.300378\pi$
$752$	−401.894	−0.0194888
$753$	−8480.22	−0.410407
$754$	3464.90	0.167353
$755$	0	0
$756$	−5398.73	−0.259722
$757$	29215.5	1.40272	0.701358	−	0.712809i	$-0.252577\pi$
$757$	29215.5	1.40272	0.701358	+	0.712809i	$0.252577\pi$
$758$	−12673.7	−0.607293
$759$	−7523.67	−0.359805
$760$	0	0
$761$	29582.7	1.40916	0.704581	−	0.709624i	$-0.251135\pi$
$761$	29582.7	1.40916	0.704581	+	0.709624i	$0.251135\pi$
$762$	2079.56	0.0988643
$763$	16395.1	0.777905
$764$	10924.5	0.517324
$765$	0	0
$766$	2574.32	0.121428
$767$	3784.95	0.178183
$768$	6313.21	0.296625
$769$	−30737.1	−1.44136	−0.720682	−	0.693265i	$-0.756171\pi$
$769$	−30737.1	−1.44136	−0.720682	+	0.693265i	$0.756171\pi$
$770$	0	0
$771$	3635.04	0.169796
$772$	−24064.1	−1.12187
$773$	13581.6	0.631947	0.315973	−	0.948768i	$-0.397669\pi$
$773$	13581.6	0.631947	0.315973	+	0.948768i	$0.397669\pi$
$774$	2445.89	0.113586
$775$	0	0
$776$	−35335.7	−1.63463
$777$	−3371.21	−0.155652
$778$	−8209.54	−0.378311
$779$	−4705.79	−0.216435
$780$	0	0
$781$	−29523.8	−1.35268
$782$	10284.5	0.470296
$783$	15310.8	0.698803
$784$	−1837.59	−0.0837094
$785$	0	0
$786$	1737.06	0.0788281
$787$	37723.8	1.70865	0.854325	−	0.519739i	$-0.173971\pi$
$787$	37723.8	1.70865	0.854325	+	0.519739i	$0.173971\pi$
$788$	9684.41	0.437808
$789$	−12087.7	−0.545418
$790$	0	0
$791$	18010.6	0.809588
$792$	−21064.1	−0.945051
$793$	−1069.31	−0.0478843
$794$	14218.2	0.635497
$795$	0	0
$796$	−18835.0	−0.838680
$797$	6349.61	0.282202	0.141101	−	0.989995i	$-0.454936\pi$
$797$	6349.61	0.282202	0.141101	+	0.989995i	$0.454936\pi$
$798$	−831.361	−0.0368795
$799$	2804.57	0.124178
$800$	0	0
$801$	8214.07	0.362334
$802$	−24854.2	−1.09431
$803$	−3246.51	−0.142674
$804$	6370.81	0.279454
$805$	0	0
$806$	−6630.27	−0.289753
$807$	−11176.4	−0.487521
$808$	31363.4	1.36554
$809$	32315.3	1.40438	0.702191	−	0.711988i	$-0.252205\pi$
$809$	32315.3	1.40438	0.702191	+	0.711988i	$0.252205\pi$
$810$	0	0
$811$	−27000.2	−1.16906	−0.584528	−	0.811373i	$-0.698720\pi$
$811$	−27000.2	−1.16906	−0.584528	+	0.811373i	$0.698720\pi$
$812$	−10633.5	−0.459561
$813$	14093.9	0.607989
$814$	−11273.2	−0.485413
$815$	0	0
$816$	881.877	0.0378332
$817$	−1671.49	−0.0715766
$818$	−21419.4	−0.915538
$819$	−3369.64	−0.143766
$820$	0	0
$821$	−8734.23	−0.371287	−0.185644	−	0.982617i	$-0.559437\pi$
$821$	−8734.23	−0.371287	−0.185644	+	0.982617i	$0.559437\pi$
$822$	−935.712	−0.0397040
$823$	−37165.8	−1.57414	−0.787070	−	0.616864i	$-0.788403\pi$
$823$	−37165.8	−1.57414	−0.787070	+	0.616864i	$0.788403\pi$
$824$	29417.1	1.24368
$825$	0	0
$826$	5560.48	0.234230
$827$	−44504.9	−1.87133	−0.935664	−	0.352892i	$-0.885198\pi$
$827$	−44504.9	−1.87133	−0.935664	+	0.352892i	$0.885198\pi$
$828$	−13913.3	−0.583962
$829$	8435.36	0.353404	0.176702	−	0.984264i	$-0.443457\pi$
$829$	8435.36	0.353404	0.176702	+	0.984264i	$0.443457\pi$
$830$	0	0
$831$	6434.07	0.268586
$832$	2871.20	0.119641
$833$	12823.4	0.533378
$834$	−5396.69	−0.224067
$835$	0	0
$836$	5807.47	0.240258
$837$	−29298.0	−1.20990
$838$	−3338.40	−0.137617
$839$	−15830.0	−0.651384	−0.325692	−	0.945476i	$-0.605597\pi$
$839$	−15830.0	−0.651384	−0.325692	+	0.945476i	$0.605597\pi$
$840$	0	0
$841$	5767.62	0.236484
$842$	23983.7	0.981629
$843$	10450.0	0.426950
$844$	−28223.3	−1.15105
$845$	0	0
$846$	1816.27	0.0738115
$847$	3635.08	0.147465
$848$	3439.67	0.139291
$849$	463.192	0.0187240
$850$	0	0
$851$	−18456.9	−0.743473
$852$	6791.73	0.273099
$853$	25517.9	1.02429	0.512144	−	0.858900i	$-0.328852\pi$
$853$	25517.9	1.02429	0.512144	+	0.858900i	$0.328852\pi$
$854$	−1570.92	−0.0629460
$855$	0	0
$856$	5929.29	0.236751
$857$	−1353.59	−0.0539530	−0.0269765	−	0.999636i	$-0.508588\pi$
$857$	−1353.59	−0.0539530	−0.0269765	+	0.999636i	$0.508588\pi$
$858$	1401.69	0.0557728
$859$	44829.9	1.78065	0.890325	−	0.455326i	$-0.150477\pi$
$859$	44829.9	1.78065	0.890325	+	0.455326i	$0.150477\pi$
$860$	0	0
$861$	3485.66	0.137969
$862$	11964.7	0.472761
$863$	22467.5	0.886216	0.443108	−	0.896468i	$-0.353876\pi$
$863$	22467.5	0.886216	0.443108	+	0.896468i	$0.353876\pi$
$864$	16435.1	0.647145
$865$	0	0
$866$	−7057.53	−0.276934
$867$	2337.21	0.0915521
$868$	20347.8	0.795679
$869$	−11369.2	−0.443815
$870$	0	0
$871$	8447.37	0.328620
$872$	−31261.3	−1.21404
$873$	−39317.6	−1.52428
$874$	−4551.59	−0.176155
$875$	0	0
$876$	746.836	0.0288051
$877$	−408.941	−0.0157457	−0.00787283	−	0.999969i	$-0.502506\pi$
$877$	−408.941	−0.0157457	−0.00787283	+	0.999969i	$0.502506\pi$
$878$	−16576.9	−0.637181
$879$	4720.12	0.181121
$880$	0	0
$881$	−20458.5	−0.782366	−0.391183	−	0.920313i	$-0.627934\pi$
$881$	−20458.5	−0.782366	−0.391183	+	0.920313i	$0.627934\pi$
$882$	8304.54	0.317039
$883$	−3746.69	−0.142793	−0.0713965	−	0.997448i	$-0.522746\pi$
$883$	−3746.69	−0.142793	−0.0713965	+	0.997448i	$0.522746\pi$
$884$	4002.58	0.152286
$885$	0	0
$886$	−9173.78	−0.347855
$887$	−5289.38	−0.200225	−0.100113	−	0.994976i	$-0.531920\pi$
$887$	−5289.38	−0.200225	−0.100113	+	0.994976i	$0.531920\pi$
$888$	6428.06	0.242919
$889$	−8462.24	−0.319251
$890$	0	0
$891$	−20159.5	−0.757990
$892$	27458.9	1.03071
$893$	−1241.22	−0.0465126
$894$	−7817.70	−0.292464
$895$	0	0
$896$	−12660.4	−0.472046
$897$	2294.90	0.0854232
$898$	−14397.3	−0.535015
$899$	−57706.3	−2.14084
$900$	0	0
$901$	−24003.3	−0.887531
$902$	11656.0	0.430267
$903$	1238.10	0.0456274
$904$	−34341.8	−1.26349
$905$	0	0
$906$	−4758.46	−0.174491
$907$	10720.8	0.392480	0.196240	−	0.980556i	$-0.437127\pi$
$907$	10720.8	0.392480	0.196240	+	0.980556i	$0.437127\pi$
$908$	9482.18	0.346561
$909$	34897.6	1.27336
$910$	0	0
$911$	3405.66	0.123858	0.0619290	−	0.998081i	$-0.480275\pi$
$911$	3405.66	0.123858	0.0619290	+	0.998081i	$0.480275\pi$
$912$	−390.292	−0.0141709
$913$	22624.0	0.820094
$914$	26550.7	0.960853
$915$	0	0
$916$	25302.0	0.912666
$917$	−7068.52	−0.254551
$918$	−8466.64	−0.304402
$919$	3184.34	0.114300	0.0571500	−	0.998366i	$-0.481799\pi$
$919$	3184.34	0.114300	0.0571500	+	0.998366i	$0.481799\pi$
$920$	0	0
$921$	−12114.8	−0.433439
$922$	14509.6	0.518273
$923$	9005.48	0.321147
$924$	−4301.69	−0.153155
$925$	0	0
$926$	−5216.40	−0.185121
$927$	32732.0	1.15972
$928$	32371.1	1.14508
$929$	24847.1	0.877510	0.438755	−	0.898607i	$-0.355420\pi$
$929$	24847.1	0.877510	0.438755	+	0.898607i	$0.355420\pi$
$930$	0	0
$931$	−5675.24	−0.199783
$932$	23057.5	0.810379
$933$	1499.18	0.0526056
$934$	−19611.2	−0.687041
$935$	0	0
$936$	6425.06	0.224369
$937$	−16072.8	−0.560381	−0.280191	−	0.959944i	$-0.590398\pi$
$937$	−16072.8	−0.560381	−0.280191	+	0.959944i	$0.590398\pi$
$938$	12410.0	0.431985
$939$	9893.12	0.343823
$940$	0	0
$941$	49359.1	1.70995	0.854974	−	0.518672i	$-0.173573\pi$
$941$	49359.1	1.70995	0.854974	+	0.518672i	$0.173573\pi$
$942$	−3833.76	−0.132602
$943$	19083.6	0.659010
$944$	2610.43	0.0900025
$945$	0	0
$946$	4140.18	0.142293
$947$	−19624.5	−0.673400	−0.336700	−	0.941612i	$-0.609311\pi$
$947$	−19624.5	−0.673400	−0.336700	+	0.941612i	$0.609311\pi$
$948$	2615.41	0.0896038
$949$	990.266	0.0338729
$950$	0	0
$951$	10061.0	0.343061
$952$	14575.2	0.496204
$953$	−39172.6	−1.33151	−0.665753	−	0.746172i	$-0.731890\pi$
$953$	−39172.6	−1.33151	−0.665753	+	0.746172i	$0.731890\pi$
$954$	−15544.8	−0.527548
$955$	0	0
$956$	17460.6	0.590707
$957$	12199.6	0.412076
$958$	−14662.1	−0.494480
$959$	3807.64	0.128212
$960$	0	0
$961$	80632.9	2.70662
$962$	3438.61	0.115244
$963$	6597.46	0.220768
$964$	7089.30	0.236858
$965$	0	0
$966$	3371.44	0.112292
$967$	50809.7	1.68969	0.844845	−	0.535010i	$-0.179692\pi$
$967$	50809.7	1.68969	0.844845	+	0.535010i	$0.179692\pi$
$968$	−6931.21	−0.230142
$969$	2723.60	0.0902939
$970$	0	0
$971$	−49995.3	−1.65235	−0.826173	−	0.563417i	$-0.809486\pi$
$971$	−49995.3	−1.65235	−0.826173	+	0.563417i	$0.809486\pi$
$972$	17516.4	0.578025
$973$	21960.4	0.723555
$974$	−861.326	−0.0283354
$975$	0	0
$976$	−737.488	−0.0241869
$977$	6507.03	0.213079	0.106540	−	0.994308i	$-0.466023\pi$
$977$	6507.03	0.213079	0.106540	+	0.994308i	$0.466023\pi$
$978$	−9054.73	−0.296052
$979$	13904.1	0.453908
$980$	0	0
$981$	−34784.1	−1.13208
$982$	17397.9	0.565365
$983$	37044.4	1.20197	0.600983	−	0.799262i	$-0.294776\pi$
$983$	37044.4	1.20197	0.600983	+	0.799262i	$0.294776\pi$
$984$	−6646.30	−0.215321
$985$	0	0
$986$	−16676.2	−0.538618
$987$	919.391	0.0296500
$988$	−1771.42	−0.0570408
$989$	6778.46	0.217940
$990$	0	0
$991$	−17372.8	−0.556877	−0.278439	−	0.960454i	$-0.589817\pi$
$991$	−17372.8	−0.556877	−0.278439	+	0.960454i	$0.589817\pi$
$992$	−61943.8	−1.98258
$993$	3975.91	0.127061
$994$	13230.0	0.422162
$995$	0	0
$996$	−5204.48	−0.165573
$997$	45015.4	1.42994	0.714971	−	0.699154i	$-0.246440\pi$
$997$	45015.4	1.42994	0.714971	+	0.699154i	$0.246440\pi$
$998$	26934.0	0.854289
$999$	15194.6	0.481217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.4.a.a.1.2		3
5.4	even	2		47.4.a.a.1.2	✓	3
15.14	odd	2		423.4.a.b.1.2		3
20.19	odd	2		752.4.a.c.1.1		3
35.34	odd	2		2303.4.a.a.1.2		3
235.234	odd	2		2209.4.a.a.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.4.a.a.1.2	✓	3	5.4	even	2
423.4.a.b.1.2		3	15.14	odd	2
752.4.a.c.1.1		3	20.19	odd	2
1175.4.a.a.1.2		3	1.1	even	1	trivial
2209.4.a.a.1.2		3	235.234	odd	2
2303.4.a.a.1.2		3	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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q+1.60930 q^{2} -1.72833 q^{3} -5.41015 q^{4} -2.78140 q^{6} +11.3182 q^{7} -21.5810 q^{8} -24.0129 q^{9} +O(q^{10})\)	\(q+1.60930 q^{2} -1.72833 q^{3} -5.41015 q^{4} -2.78140 q^{6} +11.3182 q^{7} -21.5810 q^{8} -24.0129 q^{9} -40.6469 q^{11} +9.35051 q^{12} +12.3983 q^{13} +18.2143 q^{14} +8.55095 q^{16} -59.6717 q^{17} -38.6440 q^{18} +26.4089 q^{19} -19.5615 q^{21} -65.4131 q^{22} -107.097 q^{23} +37.2990 q^{24} +19.9526 q^{26} +88.1670 q^{27} -61.2330 q^{28} +173.657 q^{29} -332.301 q^{31} +186.409 q^{32} +70.2512 q^{33} -96.0296 q^{34} +129.913 q^{36} +172.339 q^{37} +42.4998 q^{38} -21.4283 q^{39} -178.190 q^{41} -31.4804 q^{42} -63.2928 q^{43} +219.906 q^{44} -172.351 q^{46} -47.0000 q^{47} -14.7788 q^{48} -214.899 q^{49} +103.132 q^{51} -67.0767 q^{52} +402.256 q^{53} +141.887 q^{54} -244.257 q^{56} -45.6432 q^{57} +279.466 q^{58} +305.280 q^{59} -86.2464 q^{61} -534.772 q^{62} -271.782 q^{63} +231.580 q^{64} +113.055 q^{66} +681.333 q^{67} +322.833 q^{68} +185.098 q^{69} +726.348 q^{71} +518.221 q^{72} +79.8711 q^{73} +277.345 q^{74} -142.876 q^{76} -460.049 q^{77} -34.4846 q^{78} +279.707 q^{79} +495.966 q^{81} -286.761 q^{82} -556.598 q^{83} +105.831 q^{84} -101.857 q^{86} -300.135 q^{87} +877.200 q^{88} -342.069 q^{89} +140.326 q^{91} +579.410 q^{92} +574.325 q^{93} -75.6371 q^{94} -322.175 q^{96} +1637.35 q^{97} -345.837 q^{98} +976.050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 5 q^{2} + 5 q^{3} + 5 q^{4} - 8 q^{6} + 45 q^{7} + 39 q^{8} - 42 q^{9}+O(q^{10}) \) 3 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 - 8 * q^6 + 45 * q^7 + 39 * q^8 - 42 * q^9	\( 3 q + 5 q^{2} + 5 q^{3} + 5 q^{4} - 8 q^{6} + 45 q^{7} + 39 q^{8} - 42 q^{9} + 2 q^{11} - 12 q^{12} + 80 q^{13} + 162 q^{14} + 89 q^{16} + 39 q^{17} - 181 q^{18} - 24 q^{19} + 24 q^{21} + 14 q^{22} - 120 q^{23} + 192 q^{24} + 316 q^{26} - 64 q^{27} + 408 q^{28} - 184 q^{29} - 4 q^{31} + 7 q^{32} + 208 q^{33} + 218 q^{34} - 343 q^{36} + 589 q^{37} - 42 q^{38} + 60 q^{39} - 92 q^{41} + 54 q^{42} + 250 q^{43} + 466 q^{44} - 816 q^{46} - 141 q^{47} + 120 q^{48} + 30 q^{49} + 317 q^{51} + 900 q^{52} - 459 q^{53} + 106 q^{54} + 1032 q^{56} - 216 q^{57} - 684 q^{58} + 579 q^{59} + 267 q^{61} + 244 q^{62} - 1044 q^{63} - 87 q^{64} + 16 q^{66} + 540 q^{67} + 1334 q^{68} + 642 q^{69} + 749 q^{71} - 357 q^{72} + 1924 q^{73} + 950 q^{74} - 402 q^{76} + 288 q^{77} + 152 q^{78} + 805 q^{79} + 291 q^{81} + 938 q^{82} - 712 q^{83} + 372 q^{84} - 1294 q^{86} - 1216 q^{87} + 2190 q^{88} + 835 q^{89} + 2040 q^{91} - 1596 q^{92} + 1500 q^{93} - 235 q^{94} - 1432 q^{96} + 2243 q^{97} + 2989 q^{98} + 554 q^{99}+O(q^{100}) \) 3 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 - 8 * q^6 + 45 * q^7 + 39 * q^8 - 42 * q^9 + 2 * q^11 - 12 * q^12 + 80 * q^13 + 162 * q^14 + 89 * q^16 + 39 * q^17 - 181 * q^18 - 24 * q^19 + 24 * q^21 + 14 * q^22 - 120 * q^23 + 192 * q^24 + 316 * q^26 - 64 * q^27 + 408 * q^28 - 184 * q^29 - 4 * q^31 + 7 * q^32 + 208 * q^33 + 218 * q^34 - 343 * q^36 + 589 * q^37 - 42 * q^38 + 60 * q^39 - 92 * q^41 + 54 * q^42 + 250 * q^43 + 466 * q^44 - 816 * q^46 - 141 * q^47 + 120 * q^48 + 30 * q^49 + 317 * q^51 + 900 * q^52 - 459 * q^53 + 106 * q^54 + 1032 * q^56 - 216 * q^57 - 684 * q^58 + 579 * q^59 + 267 * q^61 + 244 * q^62 - 1044 * q^63 - 87 * q^64 + 16 * q^66 + 540 * q^67 + 1334 * q^68 + 642 * q^69 + 749 * q^71 - 357 * q^72 + 1924 * q^73 + 950 * q^74 - 402 * q^76 + 288 * q^77 + 152 * q^78 + 805 * q^79 + 291 * q^81 + 938 * q^82 - 712 * q^83 + 372 * q^84 - 1294 * q^86 - 1216 * q^87 + 2190 * q^88 + 835 * q^89 + 2040 * q^91 - 1596 * q^92 + 1500 * q^93 - 235 * q^94 - 1432 * q^96 + 2243 * q^97 + 2989 * q^98 + 554 * q^99

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