LMFDB - Embedded newform 175.4.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, 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("175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 32x^{2} - 35x + 120 $ x^4 - 32x^2 - 35x + 120
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.53510$ of defining polynomial
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.53510 q^{2} +6.46622 q^{3} +12.5671 q^{4} +29.3249 q^{6} +7.00000 q^{7} +20.7124 q^{8} +14.8119 q^{9} +O(q^{10})$	\(q+4.53510 q^{2} +6.46622 q^{3} +12.5671 q^{4} +29.3249 q^{6} +7.00000 q^{7} +20.7124 q^{8} +14.8119 q^{9} -54.0684 q^{11} +81.2617 q^{12} +75.2159 q^{13} +31.7457 q^{14} -6.60441 q^{16} -71.2538 q^{17} +67.1736 q^{18} -65.5100 q^{19} +45.2635 q^{21} -245.206 q^{22} +125.688 q^{23} +133.931 q^{24} +341.111 q^{26} -78.8106 q^{27} +87.9699 q^{28} +190.405 q^{29} -193.105 q^{31} -195.650 q^{32} -349.618 q^{33} -323.143 q^{34} +186.144 q^{36} +114.673 q^{37} -297.094 q^{38} +486.362 q^{39} +216.896 q^{41} +205.275 q^{42} -413.032 q^{43} -679.484 q^{44} +570.007 q^{46} -113.555 q^{47} -42.7055 q^{48} +49.0000 q^{49} -460.743 q^{51} +945.247 q^{52} +584.366 q^{53} -357.414 q^{54} +144.986 q^{56} -423.602 q^{57} +863.504 q^{58} +203.748 q^{59} -162.539 q^{61} -875.749 q^{62} +103.684 q^{63} -834.459 q^{64} -1585.55 q^{66} +477.534 q^{67} -895.456 q^{68} +812.725 q^{69} +822.294 q^{71} +306.790 q^{72} -798.993 q^{73} +520.052 q^{74} -823.273 q^{76} -378.479 q^{77} +2205.70 q^{78} -468.087 q^{79} -909.529 q^{81} +983.643 q^{82} -310.333 q^{83} +568.832 q^{84} -1873.14 q^{86} +1231.20 q^{87} -1119.88 q^{88} +1314.90 q^{89} +526.511 q^{91} +1579.53 q^{92} -1248.66 q^{93} -514.985 q^{94} -1265.12 q^{96} -1314.66 q^{97} +222.220 q^{98} -800.858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9} + 100 q^{11} - 165 q^{12} + 44 q^{13} + 28 q^{14} + 160 q^{16} - 53 q^{17} + 433 q^{18} - 29 q^{19} - 21 q^{21} - 152 q^{22} + 295 q^{23} - 21 q^{24} + 700 q^{26} - 441 q^{27} + 252 q^{28} + 129 q^{29} + 114 q^{31} - 310 q^{32} - 865 q^{33} + 203 q^{34} + 1101 q^{36} + 403 q^{37} + 555 q^{38} + 674 q^{39} + 671 q^{41} + 7 q^{42} - 411 q^{43} + 438 q^{44} - 997 q^{46} - 8 q^{47} - 523 q^{48} + 196 q^{49} - 885 q^{51} + 74 q^{52} + 90 q^{53} - 2777 q^{54} + 189 q^{56} + 233 q^{57} + 673 q^{58} + 1018 q^{59} + 50 q^{61} - 1626 q^{62} + 427 q^{63} - 2421 q^{64} - 3841 q^{66} + 424 q^{67} - 617 q^{68} + 1080 q^{69} + 215 q^{71} + 2940 q^{72} - 1207 q^{73} + 623 q^{74} - 3257 q^{76} + 700 q^{77} + 278 q^{78} - 951 q^{79} + 28 q^{81} + 1695 q^{82} - 3035 q^{83} - 1155 q^{84} - 99 q^{86} + 2210 q^{87} + 163 q^{88} + 2819 q^{89} + 308 q^{91} + 3073 q^{92} - 852 q^{93} - 3056 q^{94} - 1345 q^{96} - 1100 q^{97} + 196 q^{98} + 2383 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9 + 100 * q^11 - 165 * q^12 + 44 * q^13 + 28 * q^14 + 160 * q^16 - 53 * q^17 + 433 * q^18 - 29 * q^19 - 21 * q^21 - 152 * q^22 + 295 * q^23 - 21 * q^24 + 700 * q^26 - 441 * q^27 + 252 * q^28 + 129 * q^29 + 114 * q^31 - 310 * q^32 - 865 * q^33 + 203 * q^34 + 1101 * q^36 + 403 * q^37 + 555 * q^38 + 674 * q^39 + 671 * q^41 + 7 * q^42 - 411 * q^43 + 438 * q^44 - 997 * q^46 - 8 * q^47 - 523 * q^48 + 196 * q^49 - 885 * q^51 + 74 * q^52 + 90 * q^53 - 2777 * q^54 + 189 * q^56 + 233 * q^57 + 673 * q^58 + 1018 * q^59 + 50 * q^61 - 1626 * q^62 + 427 * q^63 - 2421 * q^64 - 3841 * q^66 + 424 * q^67 - 617 * q^68 + 1080 * q^69 + 215 * q^71 + 2940 * q^72 - 1207 * q^73 + 623 * q^74 - 3257 * q^76 + 700 * q^77 + 278 * q^78 - 951 * q^79 + 28 * q^81 + 1695 * q^82 - 3035 * q^83 - 1155 * q^84 - 99 * q^86 + 2210 * q^87 + 163 * q^88 + 2819 * q^89 + 308 * q^91 + 3073 * q^92 - 852 * q^93 - 3056 * q^94 - 1345 * q^96 - 1100 * q^97 + 196 * q^98 + 2383 * 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 $

$2$	4.53510	1.60340	0.801700	−	0.597727i	$-0.203929\pi$
$2$	4.53510	1.60340	0.801700	+	0.597727i	$0.203929\pi$
$3$	6.46622	1.24442	0.622212	−	0.782849i	$-0.286234\pi$
$3$	6.46622	1.24442	0.622212	+	0.782849i	$0.286234\pi$
$4$	12.5671	1.57089
$5$	0	0
$5$	0	0
$6$	29.3249	1.99531
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	20.7124	0.915365
$9$	14.8119	0.548591
$10$	0	0
$11$	−54.0684	−1.48202	−0.741011	−	0.671493i	$-0.765653\pi$
$11$	−54.0684	−1.48202	−0.741011	+	0.671493i	$0.765653\pi$
$12$	81.2617	1.95485
$13$	75.2159	1.60470	0.802351	−	0.596853i	$-0.203582\pi$
$13$	75.2159	1.60470	0.802351	+	0.596853i	$0.203582\pi$
$14$	31.7457	0.606028
$15$	0	0
$16$	−6.60441	−0.103194
$17$	−71.2538	−1.01656	−0.508282	−	0.861191i	$-0.669719\pi$
$17$	−71.2538	−1.01656	−0.508282	+	0.861191i	$0.669719\pi$
$18$	67.1736	0.879610
$19$	−65.5100	−0.791002	−0.395501	−	0.918466i	$-0.629429\pi$
$19$	−65.5100	−0.791002	−0.395501	+	0.918466i	$0.629429\pi$
$20$	0	0
$21$	45.2635	0.470348
$22$	−245.206	−2.37627
$23$	125.688	1.13947	0.569733	−	0.821830i	$-0.307047\pi$
$23$	125.688	1.13947	0.569733	+	0.821830i	$0.307047\pi$
$24$	133.931	1.13910
$25$	0	0
$26$	341.111	2.57298
$27$	−78.8106	−0.561745
$28$	87.9699	0.593741
$29$	190.405	1.21922	0.609608	−	0.792703i	$-0.291327\pi$
$29$	190.405	1.21922	0.609608	+	0.792703i	$0.291327\pi$
$30$	0	0
$31$	−193.105	−1.11879	−0.559397	−	0.828900i	$-0.688967\pi$
$31$	−193.105	−1.11879	−0.559397	+	0.828900i	$0.688967\pi$
$32$	−195.650	−1.08083
$33$	−349.618	−1.84426
$34$	−323.143	−1.62996
$35$	0	0
$36$	186.144	0.861776
$37$	114.673	0.509516	0.254758	−	0.967005i	$-0.418004\pi$
$37$	114.673	0.509516	0.254758	+	0.967005i	$0.418004\pi$
$38$	−297.094	−1.26829
$39$	486.362	1.99693
$40$	0	0
$41$	216.896	0.826180	0.413090	−	0.910690i	$-0.364449\pi$
$41$	216.896	0.826180	0.413090	+	0.910690i	$0.364449\pi$
$42$	205.275	0.754156
$43$	−413.032	−1.46481	−0.732405	−	0.680870i	$-0.761602\pi$
$43$	−413.032	−1.46481	−0.732405	+	0.680870i	$0.761602\pi$
$44$	−679.484	−2.32809
$45$	0	0
$46$	570.007	1.82702
$47$	−113.555	−0.352421	−0.176210	−	0.984353i	$-0.556384\pi$
$47$	−113.555	−0.352421	−0.176210	+	0.984353i	$0.556384\pi$
$48$	−42.7055	−0.128417
$49$	49.0000	0.142857
$50$	0	0
$51$	−460.743	−1.26504
$52$	945.247	2.52081
$53$	584.366	1.51451	0.757253	−	0.653122i	$-0.226541\pi$
$53$	584.366	1.51451	0.757253	+	0.653122i	$0.226541\pi$
$54$	−357.414	−0.900701
$55$	0	0
$56$	144.986	0.345976
$57$	−423.602	−0.984341
$58$	863.504	1.95489
$59$	203.748	0.449589	0.224795	−	0.974406i	$-0.427829\pi$
$59$	203.748	0.449589	0.224795	+	0.974406i	$0.427829\pi$
$60$	0	0
$61$	−162.539	−0.341163	−0.170581	−	0.985344i	$-0.554565\pi$
$61$	−162.539	−0.341163	−0.170581	+	0.985344i	$0.554565\pi$
$62$	−875.749	−1.79387
$63$	103.684	0.207348
$64$	−834.459	−1.62980
$65$	0	0
$66$	−1585.55	−2.95709
$67$	477.534	0.870747	0.435374	−	0.900250i	$-0.356616\pi$
$67$	477.534	0.870747	0.435374	+	0.900250i	$0.356616\pi$
$68$	−895.456	−1.59691
$69$	812.725	1.41798
$70$	0	0
$71$	822.294	1.37448	0.687242	−	0.726429i	$-0.258821\pi$
$71$	822.294	1.37448	0.687242	+	0.726429i	$0.258821\pi$
$72$	306.790	0.502161
$73$	−798.993	−1.28103	−0.640514	−	0.767947i	$-0.721279\pi$
$73$	−798.993	−1.28103	−0.640514	+	0.767947i	$0.721279\pi$
$74$	520.052	0.816957
$75$	0	0
$76$	−823.273	−1.24258
$77$	−378.479	−0.560152
$78$	2205.70	3.20188
$79$	−468.087	−0.666632	−0.333316	−	0.942815i	$-0.608168\pi$
$79$	−468.087	−0.666632	−0.333316	+	0.942815i	$0.608168\pi$
$80$	0	0
$81$	−909.529	−1.24764
$82$	983.643	1.32470
$83$	−310.333	−0.410403	−0.205202	−	0.978720i	$-0.565785\pi$
$83$	−310.333	−0.410403	−0.205202	+	0.978720i	$0.565785\pi$
$84$	568.832	0.738865
$85$	0	0
$86$	−1873.14	−2.34867
$87$	1231.20	1.51722
$88$	−1119.88	−1.35659
$89$	1314.90	1.56606	0.783029	−	0.621985i	$-0.213674\pi$
$89$	1314.90	1.56606	0.783029	+	0.621985i	$0.213674\pi$
$90$	0	0
$91$	526.511	0.606520
$92$	1579.53	1.78998
$93$	−1248.66	−1.39225
$94$	−514.985	−0.565071
$95$	0	0
$96$	−1265.12	−1.34501
$97$	−1314.66	−1.37612	−0.688058	−	0.725656i	$-0.741537\pi$
$97$	−1314.66	−1.37612	−0.688058	+	0.725656i	$0.741537\pi$
$98$	222.220	0.229057
$99$	−800.858	−0.813023
$100$	0	0
$101$	−401.240	−0.395296	−0.197648	−	0.980273i	$-0.563330\pi$
$101$	−401.240	−0.395296	−0.197648	+	0.980273i	$0.563330\pi$
$102$	−2089.51	−2.02836
$103$	291.844	0.279187	0.139594	−	0.990209i	$-0.455420\pi$
$103$	291.844	0.279187	0.139594	+	0.990209i	$0.455420\pi$
$104$	1557.90	1.46889
$105$	0	0
$106$	2650.16	2.42836
$107$	−21.9594	−0.0198402	−0.00992009	−	0.999951i	$-0.503158\pi$
$107$	−21.9594	−0.0198402	−0.00992009	+	0.999951i	$0.503158\pi$
$108$	−990.422	−0.882439
$109$	−17.3019	−0.0152039	−0.00760194	−	0.999971i	$-0.502420\pi$
$109$	−17.3019	−0.0152039	−0.00760194	+	0.999971i	$0.502420\pi$
$110$	0	0
$111$	741.498	0.634053
$112$	−46.2308	−0.0390036
$113$	58.8182	0.0489660	0.0244830	−	0.999700i	$-0.492206\pi$
$113$	58.8182	0.0489660	0.0244830	+	0.999700i	$0.492206\pi$
$114$	−1921.08	−1.57829
$115$	0	0
$116$	2392.84	1.91526
$117$	1114.09	0.880324
$118$	924.018	0.720871
$119$	−498.777	−0.384225
$120$	0	0
$121$	1592.39	1.19639
$122$	−737.129	−0.547020
$123$	1402.49	1.02812
$124$	−2426.77	−1.75750
$125$	0	0
$126$	470.216	0.332461
$127$	1862.03	1.30101	0.650507	−	0.759501i	$-0.274557\pi$
$127$	1862.03	1.30101	0.650507	+	0.759501i	$0.274557\pi$
$128$	−2219.15	−1.53240
$129$	−2670.75	−1.82284
$130$	0	0
$131$	775.161	0.516994	0.258497	−	0.966012i	$-0.416773\pi$
$131$	775.161	0.516994	0.258497	+	0.966012i	$0.416773\pi$
$132$	−4393.69	−2.89714
$133$	−458.570	−0.298971
$134$	2165.66	1.39616
$135$	0	0
$136$	−1475.83	−0.930528
$137$	−1027.95	−0.641051	−0.320525	−	0.947240i	$-0.603859\pi$
$137$	−1027.95	−0.641051	−0.320525	+	0.947240i	$0.603859\pi$
$138$	3685.79	2.27359
$139$	−1029.66	−0.628309	−0.314154	−	0.949372i	$-0.601721\pi$
$139$	−1029.66	−0.628309	−0.314154	+	0.949372i	$0.601721\pi$
$140$	0	0
$141$	−734.274	−0.438561
$142$	3729.18	2.20385
$143$	−4066.80	−2.37820
$144$	−97.8241	−0.0566112
$145$	0	0
$146$	−3623.51	−2.05400
$147$	316.845	0.177775
$148$	1441.11	0.800393
$149$	1414.67	0.777814	0.388907	−	0.921277i	$-0.372853\pi$
$149$	1414.67	0.777814	0.388907	+	0.921277i	$0.372853\pi$
$150$	0	0
$151$	2094.96	1.12904	0.564522	−	0.825418i	$-0.309060\pi$
$151$	2094.96	1.12904	0.564522	+	0.825418i	$0.309060\pi$
$152$	−1356.87	−0.724056
$153$	−1055.41	−0.557678
$154$	−1716.44	−0.898147
$155$	0	0
$156$	6112.17	3.13696
$157$	−709.495	−0.360662	−0.180331	−	0.983606i	$-0.557717\pi$
$157$	−709.495	−0.360662	−0.180331	+	0.983606i	$0.557717\pi$
$158$	−2122.82	−1.06888
$159$	3778.64	1.88469
$160$	0	0
$161$	879.815	0.430678
$162$	−4124.80	−2.00046
$163$	3276.23	1.57432	0.787160	−	0.616749i	$-0.211551\pi$
$163$	3276.23	1.57432	0.787160	+	0.616749i	$0.211551\pi$
$164$	2725.75	1.29784
$165$	0	0
$166$	−1407.39	−0.658040
$167$	2860.69	1.32555	0.662775	−	0.748819i	$-0.269379\pi$
$167$	2860.69	1.32555	0.662775	+	0.748819i	$0.269379\pi$
$168$	937.514	0.430540
$169$	3460.42	1.57507
$170$	0	0
$171$	−970.331	−0.433936
$172$	−5190.62	−2.30105
$173$	2803.44	1.23203	0.616015	−	0.787734i	$-0.288746\pi$
$173$	2803.44	1.23203	0.616015	+	0.787734i	$0.288746\pi$
$174$	5583.61	2.43271
$175$	0	0
$176$	357.090	0.152936
$177$	1317.48	0.559479
$178$	5963.20	2.51102
$179$	248.617	0.103813	0.0519064	−	0.998652i	$-0.483470\pi$
$179$	248.617	0.103813	0.0519064	+	0.998652i	$0.483470\pi$
$180$	0	0
$181$	2075.56	0.852347	0.426174	−	0.904641i	$-0.359861\pi$
$181$	2075.56	0.852347	0.426174	+	0.904641i	$0.359861\pi$
$182$	2387.78	0.972494
$183$	−1051.01	−0.424551
$184$	2603.29	1.04303
$185$	0	0
$186$	−5662.78	−2.23234
$187$	3852.58	1.50657
$188$	−1427.07	−0.553614
$189$	−551.674	−0.212319
$190$	0	0
$191$	−1252.95	−0.474663	−0.237331	−	0.971429i	$-0.576273\pi$
$191$	−1252.95	−0.474663	−0.237331	+	0.971429i	$0.576273\pi$
$192$	−5395.79	−2.02817
$193$	1602.12	0.597527	0.298764	−	0.954327i	$-0.403426\pi$
$193$	1602.12	0.597527	0.298764	+	0.954327i	$0.403426\pi$
$194$	−5962.10	−2.20646
$195$	0	0
$196$	615.789	0.224413
$197$	2346.38	0.848593	0.424296	−	0.905523i	$-0.360521\pi$
$197$	2346.38	0.848593	0.424296	+	0.905523i	$0.360521\pi$
$198$	−3631.97	−1.30360
$199$	−1993.53	−0.710140	−0.355070	−	0.934840i	$-0.615543\pi$
$199$	−1993.53	−0.710140	−0.355070	+	0.934840i	$0.615543\pi$
$200$	0	0
$201$	3087.84	1.08358
$202$	−1819.67	−0.633818
$203$	1332.83	0.460820
$204$	−5790.21	−1.98723
$205$	0	0
$206$	1323.54	0.447649
$207$	1861.68	0.625101
$208$	−496.756	−0.165595
$209$	3542.02	1.17228
$210$	0	0
$211$	−5852.55	−1.90951	−0.954754	−	0.297396i	$-0.903882\pi$
$211$	−5852.55	−1.90951	−0.954754	+	0.297396i	$0.903882\pi$
$212$	7343.80	2.37912
$213$	5317.13	1.71044
$214$	−99.5883	−0.0318117
$215$	0	0
$216$	−1632.35	−0.514202
$217$	−1351.73	−0.422864
$218$	−78.4659	−0.0243779
$219$	−5166.46	−1.59414
$220$	0	0
$221$	−5359.42	−1.63128
$222$	3362.77	1.01664
$223$	−1719.58	−0.516374	−0.258187	−	0.966095i	$-0.583125\pi$
$223$	−1719.58	−0.516374	−0.258187	+	0.966095i	$0.583125\pi$
$224$	−1369.55	−0.408514
$225$	0	0
$226$	266.747	0.0785120
$227$	−5686.00	−1.66252	−0.831262	−	0.555881i	$-0.812381\pi$
$227$	−5686.00	−1.66252	−0.831262	+	0.555881i	$0.812381\pi$
$228$	−5323.46	−1.54629
$229$	−3087.40	−0.890923	−0.445461	−	0.895301i	$-0.646960\pi$
$229$	−3087.40	−0.890923	−0.445461	+	0.895301i	$0.646960\pi$
$230$	0	0
$231$	−2447.33	−0.697066
$232$	3943.73	1.11603
$233$	3997.55	1.12398	0.561991	−	0.827143i	$-0.310035\pi$
$233$	3997.55	1.12398	0.561991	+	0.827143i	$0.310035\pi$
$234$	5052.52	1.41151
$235$	0	0
$236$	2560.53	0.706255
$237$	−3026.75	−0.829573
$238$	−2262.00	−0.616067
$239$	−4499.79	−1.21786	−0.608928	−	0.793226i	$-0.708400\pi$
$239$	−4499.79	−1.21786	−0.608928	+	0.793226i	$0.708400\pi$
$240$	0	0
$241$	3633.26	0.971115	0.485557	−	0.874205i	$-0.338617\pi$
$241$	3633.26	0.971115	0.485557	+	0.874205i	$0.338617\pi$
$242$	7221.66	1.91829
$243$	−3753.32	−0.990847
$244$	−2042.64	−0.535929
$245$	0	0
$246$	6360.45	1.64849
$247$	−4927.39	−1.26932
$248$	−3999.65	−1.02411
$249$	−2006.68	−0.510715
$250$	0	0
$251$	−1211.21	−0.304585	−0.152292	−	0.988335i	$-0.548666\pi$
$251$	−1211.21	−0.304585	−0.152292	+	0.988335i	$0.548666\pi$
$252$	1303.00	0.325721
$253$	−6795.74	−1.68871
$254$	8444.50	2.08604
$255$	0	0
$256$	−3388.39	−0.827245
$257$	−6225.81	−1.51111	−0.755556	−	0.655085i	$-0.772633\pi$
$257$	−6225.81	−1.51111	−0.755556	+	0.655085i	$0.772633\pi$
$258$	−12112.1	−2.92275
$259$	802.709	0.192579
$260$	0	0
$261$	2820.27	0.668851
$262$	3515.43	0.828947
$263$	−757.377	−0.177574	−0.0887869	−	0.996051i	$-0.528299\pi$
$263$	−757.377	−0.177574	−0.0887869	+	0.996051i	$0.528299\pi$
$264$	−7241.41	−1.68817
$265$	0	0
$266$	−2079.66	−0.479369
$267$	8502.43	1.94884
$268$	6001.23	1.36785
$269$	1750.59	0.396786	0.198393	−	0.980123i	$-0.436428\pi$
$269$	1750.59	0.396786	0.198393	+	0.980123i	$0.436428\pi$
$270$	0	0
$271$	4451.86	0.997902	0.498951	−	0.866630i	$-0.333719\pi$
$271$	4451.86	0.997902	0.498951	+	0.866630i	$0.333719\pi$
$272$	470.589	0.104903
$273$	3404.53	0.754768
$274$	−4661.87	−1.02786
$275$	0	0
$276$	10213.6	2.22749
$277$	−7691.69	−1.66841	−0.834204	−	0.551456i	$-0.814072\pi$
$277$	−7691.69	−1.66841	−0.834204	+	0.551456i	$0.814072\pi$
$278$	−4669.62	−1.00743
$279$	−2860.26	−0.613760
$280$	0	0
$281$	−199.034	−0.0422540	−0.0211270	−	0.999777i	$-0.506725\pi$
$281$	−199.034	−0.0422540	−0.0211270	+	0.999777i	$0.506725\pi$
$282$	−3330.01	−0.703188
$283$	−799.307	−0.167893	−0.0839467	−	0.996470i	$-0.526753\pi$
$283$	−799.307	−0.167893	−0.0839467	+	0.996470i	$0.526753\pi$
$284$	10333.9	2.15916
$285$	0	0
$286$	−18443.3	−3.81321
$287$	1518.27	0.312267
$288$	−2897.96	−0.592931
$289$	164.110	0.0334031
$290$	0	0
$291$	−8500.86	−1.71247
$292$	−10041.0	−2.01235
$293$	3302.75	0.658528	0.329264	−	0.944238i	$-0.393199\pi$
$293$	3302.75	0.658528	0.329264	+	0.944238i	$0.393199\pi$
$294$	1436.92	0.285044
$295$	0	0
$296$	2375.14	0.466393
$297$	4261.16	0.832518
$298$	6415.67	1.24715
$299$	9453.72	1.82850
$300$	0	0
$301$	−2891.22	−0.553646
$302$	9500.87	1.81031
$303$	−2594.51	−0.491916
$304$	432.655	0.0816265
$305$	0	0
$306$	−4786.38	−0.894180
$307$	−8628.17	−1.60402	−0.802012	−	0.597308i	$-0.796237\pi$
$307$	−8628.17	−1.60402	−0.802012	+	0.597308i	$0.796237\pi$
$308$	−4756.39	−0.879937
$309$	1887.13	0.347427
$310$	0	0
$311$	−4900.60	−0.893530	−0.446765	−	0.894651i	$-0.647424\pi$
$311$	−4900.60	−0.893530	−0.446765	+	0.894651i	$0.647424\pi$
$312$	10073.7	1.82792
$313$	−9114.26	−1.64590	−0.822952	−	0.568110i	$-0.807675\pi$
$313$	−9114.26	−1.64590	−0.822952	+	0.568110i	$0.807675\pi$
$314$	−3217.63	−0.578285
$315$	0	0
$316$	−5882.51	−1.04721
$317$	−8022.82	−1.42147	−0.710736	−	0.703459i	$-0.751638\pi$
$317$	−8022.82	−1.42147	−0.710736	+	0.703459i	$0.751638\pi$
$318$	17136.5	3.02191
$319$	−10294.9	−1.80691
$320$	0	0
$321$	−141.995	−0.0246896
$322$	3990.05	0.690549
$323$	4667.84	0.804104
$324$	−11430.2	−1.95990
$325$	0	0
$326$	14858.0	2.52426
$327$	−111.878	−0.0189201
$328$	4492.42	0.756257
$329$	−794.888	−0.133202
$330$	0	0
$331$	−1333.58	−0.221451	−0.110725	−	0.993851i	$-0.535317\pi$
$331$	−1333.58	−0.221451	−0.110725	+	0.993851i	$0.535317\pi$
$332$	−3899.99	−0.644698
$333$	1698.53	0.279515
$334$	12973.5	2.12539
$335$	0	0
$336$	−298.939	−0.0485370
$337$	−1687.33	−0.272744	−0.136372	−	0.990658i	$-0.543544\pi$
$337$	−1687.33	−0.272744	−0.136372	+	0.990658i	$0.543544\pi$
$338$	15693.4	2.52546
$339$	380.331	0.0609344
$340$	0	0
$341$	10440.9	1.65808
$342$	−4400.55	−0.695773
$343$	343.000	0.0539949
$344$	−8554.87	−1.34084
$345$	0	0
$346$	12713.9	1.97544
$347$	5955.18	0.921299	0.460649	−	0.887582i	$-0.347617\pi$
$347$	5955.18	0.921299	0.460649	+	0.887582i	$0.347617\pi$
$348$	15472.6	2.38339
$349$	6876.59	1.05471	0.527357	−	0.849644i	$-0.323183\pi$
$349$	6876.59	1.05471	0.527357	+	0.849644i	$0.323183\pi$
$350$	0	0
$351$	−5927.81	−0.901433
$352$	10578.5	1.60181
$353$	1395.95	0.210479	0.105239	−	0.994447i	$-0.466439\pi$
$353$	1395.95	0.210479	0.105239	+	0.994447i	$0.466439\pi$
$354$	5974.90	0.897069
$355$	0	0
$356$	16524.5	2.46011
$357$	−3225.20	−0.478139
$358$	1127.50	0.166453
$359$	−382.988	−0.0563046	−0.0281523	−	0.999604i	$-0.508962\pi$
$359$	−382.988	−0.0563046	−0.0281523	+	0.999604i	$0.508962\pi$
$360$	0	0
$361$	−2567.44	−0.374316
$362$	9412.85	1.36665
$363$	10296.8	1.48881
$364$	6616.73	0.952777
$365$	0	0
$366$	−4766.43	−0.680725
$367$	−10178.4	−1.44771	−0.723856	−	0.689951i	$-0.757632\pi$
$367$	−10178.4	−1.44771	−0.723856	+	0.689951i	$0.757632\pi$
$368$	−830.094	−0.117586
$369$	3212.65	0.453235
$370$	0	0
$371$	4090.56	0.572430
$372$	−15692.0	−2.18708
$373$	−2991.00	−0.415196	−0.207598	−	0.978214i	$-0.566565\pi$
$373$	−2991.00	−0.415196	−0.207598	+	0.978214i	$0.566565\pi$
$374$	17471.8	2.41563
$375$	0	0
$376$	−2352.00	−0.322594
$377$	14321.5	1.95648
$378$	−2501.90	−0.340433
$379$	7400.66	1.00302	0.501512	−	0.865150i	$-0.332777\pi$
$379$	7400.66	1.00302	0.501512	+	0.865150i	$0.332777\pi$
$380$	0	0
$381$	12040.3	1.61901
$382$	−5682.27	−0.761074
$383$	−10769.6	−1.43682	−0.718408	−	0.695622i	$-0.755129\pi$
$383$	−10769.6	−1.43682	−0.718408	+	0.695622i	$0.755129\pi$
$384$	−14349.5	−1.90695
$385$	0	0
$386$	7265.75	0.958075
$387$	−6117.81	−0.803580
$388$	−16521.5	−2.16173
$389$	−11193.3	−1.45893	−0.729466	−	0.684017i	$-0.760231\pi$
$389$	−11193.3	−1.45893	−0.729466	+	0.684017i	$0.760231\pi$
$390$	0	0
$391$	−8955.74	−1.15834
$392$	1014.91	0.130766
$393$	5012.36	0.643359
$394$	10641.1	1.36063
$395$	0	0
$396$	−10064.5	−1.27717
$397$	10371.9	1.31121	0.655605	−	0.755104i	$-0.272414\pi$
$397$	10371.9	1.31121	0.655605	+	0.755104i	$0.272414\pi$
$398$	−9040.88	−1.13864
$399$	−2965.21	−0.372046
$400$	0	0
$401$	5402.20	0.672751	0.336375	−	0.941728i	$-0.390799\pi$
$401$	5402.20	0.672751	0.336375	+	0.941728i	$0.390799\pi$
$402$	14003.7	1.73741
$403$	−14524.5	−1.79533
$404$	−5042.44	−0.620967
$405$	0	0
$406$	6044.53	0.738879
$407$	−6200.17	−0.755113
$408$	−9543.07	−1.15797
$409$	−12829.9	−1.55110	−0.775549	−	0.631288i	$-0.782527\pi$
$409$	−12829.9	−1.55110	−0.775549	+	0.631288i	$0.782527\pi$
$410$	0	0
$411$	−6646.97	−0.797739
$412$	3667.64	0.438572
$413$	1426.24	0.169929
$414$	8442.91	1.00229
$415$	0	0
$416$	−14716.0	−1.73440
$417$	−6658.02	−0.781882
$418$	16063.4	1.87964
$419$	5620.85	0.655362	0.327681	−	0.944788i	$-0.393733\pi$
$419$	5620.85	0.655362	0.327681	+	0.944788i	$0.393733\pi$
$420$	0	0
$421$	−2177.11	−0.252033	−0.126017	−	0.992028i	$-0.540219\pi$
$421$	−2177.11	−0.252033	−0.126017	+	0.992028i	$0.540219\pi$
$422$	−26541.9	−3.06171
$423$	−1681.98	−0.193335
$424$	12103.6	1.38633
$425$	0	0
$426$	24113.7	2.74252
$427$	−1137.77	−0.128947
$428$	−275.967	−0.0311668
$429$	−26296.8	−2.95949
$430$	0	0
$431$	10396.4	1.16190	0.580950	−	0.813939i	$-0.302681\pi$
$431$	10396.4	1.16190	0.580950	+	0.813939i	$0.302681\pi$
$432$	520.497	0.0579686
$433$	11875.6	1.31803	0.659015	−	0.752129i	$-0.270973\pi$
$433$	11875.6	1.31803	0.659015	+	0.752129i	$0.270973\pi$
$434$	−6130.24	−0.678021
$435$	0	0
$436$	−217.435	−0.0238836
$437$	−8233.81	−0.901320
$438$	−23430.4	−2.55605
$439$	640.369	0.0696200	0.0348100	−	0.999394i	$-0.488917\pi$
$439$	640.369	0.0696200	0.0348100	+	0.999394i	$0.488917\pi$
$440$	0	0
$441$	725.785	0.0783701
$442$	−24305.5	−2.61560
$443$	−854.852	−0.0916823	−0.0458411	−	0.998949i	$-0.514597\pi$
$443$	−854.852	−0.0916823	−0.0458411	+	0.998949i	$0.514597\pi$
$444$	9318.50	0.996028
$445$	0	0
$446$	−7798.46	−0.827954
$447$	9147.56	0.967930
$448$	−5841.21	−0.616008
$449$	3427.44	0.360247	0.180123	−	0.983644i	$-0.442350\pi$
$449$	3427.44	0.360247	0.180123	+	0.983644i	$0.442350\pi$
$450$	0	0
$451$	−11727.2	−1.22442
$452$	739.176	0.0769202
$453$	13546.5	1.40501
$454$	−25786.6	−2.66569
$455$	0	0
$456$	−8773.79	−0.901032
$457$	1709.31	0.174963	0.0874814	−	0.996166i	$-0.472118\pi$
$457$	1709.31	0.174963	0.0874814	+	0.996166i	$0.472118\pi$
$458$	−14001.7	−1.42851
$459$	5615.56	0.571050
$460$	0	0
$461$	2251.18	0.227436	0.113718	−	0.993513i	$-0.463724\pi$
$461$	2251.18	0.227436	0.113718	+	0.993513i	$0.463724\pi$
$462$	−11098.9	−1.11768
$463$	−3200.80	−0.321282	−0.160641	−	0.987013i	$-0.551356\pi$
$463$	−3200.80	−0.321282	−0.160641	+	0.987013i	$0.551356\pi$
$464$	−1257.51	−0.125816
$465$	0	0
$466$	18129.3	1.80219
$467$	5477.39	0.542748	0.271374	−	0.962474i	$-0.412522\pi$
$467$	5477.39	0.542748	0.271374	+	0.962474i	$0.412522\pi$
$468$	14000.9	1.38289
$469$	3342.74	0.329112
$470$	0	0
$471$	−4587.75	−0.448816
$472$	4220.11	0.411538
$473$	22332.0	2.17088
$474$	−13726.6	−1.33014
$475$	0	0
$476$	−6268.19	−0.603576
$477$	8655.60	0.830844
$478$	−20407.0	−1.95271
$479$	−14182.0	−1.35280	−0.676399	−	0.736535i	$-0.736461\pi$
$479$	−14182.0	−1.35280	−0.676399	+	0.736535i	$0.736461\pi$
$480$	0	0
$481$	8625.20	0.817620
$482$	16477.2	1.55709
$483$	5689.07	0.535946
$484$	20011.8	1.87940
$485$	0	0
$486$	−17021.7	−1.58872
$487$	−5320.83	−0.495092	−0.247546	−	0.968876i	$-0.579624\pi$
$487$	−5320.83	−0.495092	−0.247546	+	0.968876i	$0.579624\pi$
$488$	−3366.56	−0.312289
$489$	21184.8	1.95912
$490$	0	0
$491$	−6574.80	−0.604311	−0.302155	−	0.953259i	$-0.597706\pi$
$491$	−6574.80	−0.604311	−0.302155	+	0.953259i	$0.597706\pi$
$492$	17625.3	1.61506
$493$	−13567.1	−1.23941
$494$	−22346.2	−2.03523
$495$	0	0
$496$	1275.34	0.115453
$497$	5756.06	0.519506
$498$	−9100.49	−0.818881
$499$	−1507.68	−0.135256	−0.0676282	−	0.997711i	$-0.521543\pi$
$499$	−1507.68	−0.135256	−0.0676282	+	0.997711i	$0.521543\pi$
$500$	0	0
$501$	18497.8	1.64955
$502$	−5492.95	−0.488371
$503$	−8782.24	−0.778491	−0.389245	−	0.921134i	$-0.627264\pi$
$503$	−8782.24	−0.778491	−0.389245	+	0.921134i	$0.627264\pi$
$504$	2147.53	0.189799
$505$	0	0
$506$	−30819.4	−2.70768
$507$	22375.9	1.96005
$508$	23400.4	2.04375
$509$	12696.6	1.10563	0.552815	−	0.833304i	$-0.313553\pi$
$509$	12696.6	1.10563	0.552815	+	0.833304i	$0.313553\pi$
$510$	0	0
$511$	−5592.95	−0.484183
$512$	2386.50	0.205995
$513$	5162.88	0.444341
$514$	−28234.7	−2.42291
$515$	0	0
$516$	−33563.7	−2.86349
$517$	6139.76	0.522295
$518$	3640.36	0.308781
$519$	18127.6	1.53317
$520$	0	0
$521$	−10434.7	−0.877455	−0.438727	−	0.898620i	$-0.644571\pi$
$521$	−10434.7	−0.877455	−0.438727	+	0.898620i	$0.644571\pi$
$522$	12790.2	1.07243
$523$	−8403.03	−0.702560	−0.351280	−	0.936270i	$-0.614254\pi$
$523$	−8403.03	−0.702560	−0.351280	+	0.936270i	$0.614254\pi$
$524$	9741.55	0.812140
$525$	0	0
$526$	−3434.78	−0.284722
$527$	13759.4	1.13733
$528$	2309.02	0.190317
$529$	3630.43	0.298384
$530$	0	0
$531$	3017.91	0.246640
$532$	−5762.91	−0.469650
$533$	16314.0	1.32577
$534$	38559.4	3.12477
$535$	0	0
$536$	9890.85	0.797052
$537$	1607.61	0.129187
$538$	7939.11	0.636207
$539$	−2649.35	−0.211717
$540$	0	0
$541$	8349.66	0.663549	0.331775	−	0.943359i	$-0.392353\pi$
$541$	8349.66	0.663549	0.331775	+	0.943359i	$0.392353\pi$
$542$	20189.6	1.60004
$543$	13421.0	1.06068
$544$	13940.8	1.09873
$545$	0	0
$546$	15439.9	1.21020
$547$	12185.7	0.952509	0.476254	−	0.879308i	$-0.341994\pi$
$547$	12185.7	0.952509	0.476254	+	0.879308i	$0.341994\pi$
$548$	−12918.4	−1.00702
$549$	−2407.51	−0.187159
$550$	0	0
$551$	−12473.4	−0.964402
$552$	16833.4	1.29797
$553$	−3276.61	−0.251963
$554$	−34882.6	−2.67512
$555$	0	0
$556$	−12939.9	−0.987004
$557$	−540.209	−0.0410940	−0.0205470	−	0.999789i	$-0.506541\pi$
$557$	−540.209	−0.0410940	−0.0205470	+	0.999789i	$0.506541\pi$
$558$	−12971.5	−0.984103
$559$	−31066.6	−2.35058
$560$	0	0
$561$	24911.6	1.87481
$562$	−902.639	−0.0677501
$563$	−1949.26	−0.145917	−0.0729587	−	0.997335i	$-0.523244\pi$
$563$	−1949.26	−0.145917	−0.0729587	+	0.997335i	$0.523244\pi$
$564$	−9227.71	−0.688930
$565$	0	0
$566$	−3624.94	−0.269200
$567$	−6366.70	−0.471563
$568$	17031.6	1.25815
$569$	9487.28	0.698994	0.349497	−	0.936938i	$-0.386353\pi$
$569$	9487.28	0.698994	0.349497	+	0.936938i	$0.386353\pi$
$570$	0	0
$571$	−20172.3	−1.47843	−0.739215	−	0.673470i	$-0.764803\pi$
$571$	−20172.3	−1.47843	−0.739215	+	0.673470i	$0.764803\pi$
$572$	−51108.0	−3.73590
$573$	−8101.87	−0.590681
$574$	6885.50	0.500689
$575$	0	0
$576$	−12360.0	−0.894094
$577$	12937.3	0.933423	0.466712	−	0.884410i	$-0.345439\pi$
$577$	12937.3	0.933423	0.466712	+	0.884410i	$0.345439\pi$
$578$	744.254	0.0535586
$579$	10359.6	0.743577
$580$	0	0
$581$	−2172.33	−0.155118
$582$	−38552.2	−2.74578
$583$	−31595.7	−2.24453
$584$	−16549.0	−1.17261
$585$	0	0
$586$	14978.3	1.05588
$587$	−6489.43	−0.456299	−0.228149	−	0.973626i	$-0.573267\pi$
$587$	−6489.43	−0.456299	−0.228149	+	0.973626i	$0.573267\pi$
$588$	3981.82	0.279265
$589$	12650.3	0.884968
$590$	0	0
$591$	15172.2	1.05601
$592$	−757.345	−0.0525789
$593$	−16803.6	−1.16364	−0.581821	−	0.813317i	$-0.697660\pi$
$593$	−16803.6	−1.16364	−0.581821	+	0.813317i	$0.697660\pi$
$594$	19324.8	1.33486
$595$	0	0
$596$	17778.3	1.22186
$597$	−12890.6	−0.883716
$598$	42873.5	2.93182
$599$	19139.6	1.30554	0.652772	−	0.757554i	$-0.273606\pi$
$599$	19139.6	1.30554	0.652772	+	0.757554i	$0.273606\pi$
$600$	0	0
$601$	14304.0	0.970838	0.485419	−	0.874282i	$-0.338667\pi$
$601$	14304.0	0.970838	0.485419	+	0.874282i	$0.338667\pi$
$602$	−13112.0	−0.887715
$603$	7073.21	0.477684
$604$	26327.7	1.77361
$605$	0	0
$606$	−11766.3	−0.788738
$607$	−2018.10	−0.134946	−0.0674730	−	0.997721i	$-0.521494\pi$
$607$	−2018.10	−0.134946	−0.0674730	+	0.997721i	$0.521494\pi$
$608$	12817.1	0.854935
$609$	8618.39	0.573456
$610$	0	0
$611$	−8541.17	−0.565530
$612$	−13263.4	−0.876050
$613$	21479.4	1.41524	0.707621	−	0.706592i	$-0.249768\pi$
$613$	21479.4	1.41524	0.707621	+	0.706592i	$0.249768\pi$
$614$	−39129.6	−2.57189
$615$	0	0
$616$	−7839.19	−0.512743
$617$	−5856.83	−0.382151	−0.191075	−	0.981575i	$-0.561197\pi$
$617$	−5856.83	−0.382151	−0.191075	+	0.981575i	$0.561197\pi$
$618$	8558.31	0.557065
$619$	−17619.3	−1.14407	−0.572035	−	0.820229i	$-0.693846\pi$
$619$	−17619.3	−1.14407	−0.572035	+	0.820229i	$0.693846\pi$
$620$	0	0
$621$	−9905.53	−0.640089
$622$	−22224.7	−1.43269
$623$	9204.30	0.591914
$624$	−3212.13	−0.206071
$625$	0	0
$626$	−41334.1	−2.63904
$627$	22903.5	1.45882
$628$	−8916.31	−0.566560
$629$	−8170.87	−0.517955
$630$	0	0
$631$	26395.7	1.66529	0.832643	−	0.553810i	$-0.186827\pi$
$631$	26395.7	1.66529	0.832643	+	0.553810i	$0.186827\pi$
$632$	−9695.19	−0.610212
$633$	−37843.9	−2.37624
$634$	−36384.3	−2.27919
$635$	0	0
$636$	47486.6	2.96064
$637$	3685.58	0.229243
$638$	−46688.3	−2.89719
$639$	12179.8	0.754029
$640$	0	0
$641$	3209.30	0.197753	0.0988764	−	0.995100i	$-0.468475\pi$
$641$	3209.30	0.197753	0.0988764	+	0.995100i	$0.468475\pi$
$642$	−643.959	−0.0395873
$643$	−1762.48	−0.108096	−0.0540478	−	0.998538i	$-0.517212\pi$
$643$	−1762.48	−0.108096	−0.0540478	+	0.998538i	$0.517212\pi$
$644$	11056.7	0.676548
$645$	0	0
$646$	21169.1	1.28930
$647$	−24372.7	−1.48098	−0.740488	−	0.672070i	$-0.765405\pi$
$647$	−24372.7	−1.48098	−0.740488	+	0.672070i	$0.765405\pi$
$648$	−18838.5	−1.14205
$649$	−11016.3	−0.666301
$650$	0	0
$651$	−8740.60	−0.526223
$652$	41172.8	2.47308
$653$	6389.97	0.382938	0.191469	−	0.981499i	$-0.438675\pi$
$653$	6389.97	0.382938	0.191469	+	0.981499i	$0.438675\pi$
$654$	−507.377	−0.0303364
$655$	0	0
$656$	−1432.47	−0.0852567
$657$	−11834.6	−0.702760
$658$	−3604.90	−0.213577
$659$	−6111.68	−0.361270	−0.180635	−	0.983550i	$-0.557815\pi$
$659$	−6111.68	−0.361270	−0.180635	+	0.983550i	$0.557815\pi$
$660$	0	0
$661$	16391.1	0.964510	0.482255	−	0.876031i	$-0.339818\pi$
$661$	16391.1	0.964510	0.482255	+	0.876031i	$0.339818\pi$
$662$	−6047.92	−0.355074
$663$	−34655.2	−2.03001
$664$	−6427.72	−0.375669
$665$	0	0
$666$	7702.98	0.448175
$667$	23931.6	1.38926
$668$	35950.6	2.08229
$669$	−11119.2	−0.642588
$670$	0	0
$671$	8788.20	0.505611
$672$	−8855.83	−0.508365
$673$	−13055.9	−0.747799	−0.373900	−	0.927469i	$-0.621980\pi$
$673$	−13055.9	−0.747799	−0.373900	+	0.927469i	$0.621980\pi$
$674$	−7652.20	−0.437317
$675$	0	0
$676$	43487.6	2.47426
$677$	−3154.53	−0.179082	−0.0895410	−	0.995983i	$-0.528540\pi$
$677$	−3154.53	−0.179082	−0.0895410	+	0.995983i	$0.528540\pi$
$678$	1724.84	0.0977022
$679$	−9202.60	−0.520123
$680$	0	0
$681$	−36766.9	−2.06888
$682$	47350.4	2.65856
$683$	17282.7	0.968233	0.484117	−	0.875004i	$-0.339141\pi$
$683$	17282.7	0.968233	0.484117	+	0.875004i	$0.339141\pi$
$684$	−12194.3	−0.681666
$685$	0	0
$686$	1555.54	0.0865754
$687$	−19963.8	−1.10869
$688$	2727.83	0.151159
$689$	43953.6	2.43033
$690$	0	0
$691$	26838.3	1.47753	0.738766	−	0.673961i	$-0.235409\pi$
$691$	26838.3	1.47753	0.738766	+	0.673961i	$0.235409\pi$
$692$	35231.1	1.93538
$693$	−5606.01	−0.307294
$694$	27007.3	1.47721
$695$	0	0
$696$	25501.0	1.38881
$697$	−15454.6	−0.839866
$698$	31186.0	1.69113
$699$	25849.0	1.39871
$700$	0	0
$701$	−8374.52	−0.451214	−0.225607	−	0.974218i	$-0.572437\pi$
$701$	−8374.52	−0.451214	−0.225607	+	0.974218i	$0.572437\pi$
$702$	−26883.2	−1.44536
$703$	−7512.21	−0.403028
$704$	45117.9	2.41540
$705$	0	0
$706$	6330.79	0.337482
$707$	−2808.68	−0.149408
$708$	16556.9	0.878881
$709$	11929.4	0.631902	0.315951	−	0.948775i	$-0.397676\pi$
$709$	11929.4	0.631902	0.315951	+	0.948775i	$0.397676\pi$
$710$	0	0
$711$	−6933.28	−0.365708
$712$	27234.7	1.43352
$713$	−24270.9	−1.27483
$714$	−14626.6	−0.766648
$715$	0	0
$716$	3124.40	0.163078
$717$	−29096.6	−1.51553
$718$	−1736.89	−0.0902788
$719$	−23392.3	−1.21333	−0.606666	−	0.794957i	$-0.707493\pi$
$719$	−23392.3	−1.21333	−0.606666	+	0.794957i	$0.707493\pi$
$720$	0	0
$721$	2042.91	0.105523
$722$	−11643.6	−0.600179
$723$	23493.4	1.20848
$724$	26083.8	1.33894
$725$	0	0
$726$	46696.8	2.38717
$727$	10659.8	0.543810	0.271905	−	0.962324i	$-0.412346\pi$
$727$	10659.8	0.543810	0.271905	+	0.962324i	$0.412346\pi$
$728$	10905.3	0.555188
$729$	287.476	0.0146053
$730$	0	0
$731$	29430.1	1.48907
$732$	−13208.2	−0.666923
$733$	23919.1	1.20528	0.602642	−	0.798011i	$-0.294115\pi$
$733$	23919.1	1.20528	0.602642	+	0.798011i	$0.294115\pi$
$734$	−46160.2	−2.32126
$735$	0	0
$736$	−24590.9	−1.23157
$737$	−25819.5	−1.29047
$738$	14569.7	0.726717
$739$	34535.1	1.71907	0.859536	−	0.511074i	$-0.170752\pi$
$739$	34535.1	1.71907	0.859536	+	0.511074i	$0.170752\pi$
$740$	0	0
$741$	−31861.6	−1.57957
$742$	18551.1	0.917833
$743$	17526.8	0.865403	0.432702	−	0.901537i	$-0.357560\pi$
$743$	17526.8	0.865403	0.432702	+	0.901537i	$0.357560\pi$
$744$	−25862.6	−1.27442
$745$	0	0
$746$	−13564.5	−0.665725
$747$	−4596.63	−0.225143
$748$	48415.9	2.36666
$749$	−153.716	−0.00749889
$750$	0	0
$751$	18534.3	0.900565	0.450283	−	0.892886i	$-0.351323\pi$
$751$	18534.3	0.900565	0.450283	+	0.892886i	$0.351323\pi$
$752$	749.966	0.0363676
$753$	−7831.94	−0.379033
$754$	64949.2	3.13702
$755$	0	0
$756$	−6932.96	−0.333531
$757$	−9309.64	−0.446981	−0.223491	−	0.974706i	$-0.571745\pi$
$757$	−9309.64	−0.446981	−0.223491	+	0.974706i	$0.571745\pi$
$758$	33562.7	1.60825
$759$	−43942.7	−2.10148
$760$	0	0
$761$	−2968.41	−0.141399	−0.0706996	−	0.997498i	$-0.522523\pi$
$761$	−2968.41	−0.141399	−0.0706996	+	0.997498i	$0.522523\pi$
$762$	54604.0	2.59592
$763$	−121.113	−0.00574653
$764$	−15746.0	−0.745643
$765$	0	0
$766$	−48841.1	−2.30379
$767$	15325.1	0.721457
$768$	−21910.1	−1.02944
$769$	−34932.9	−1.63812	−0.819060	−	0.573708i	$-0.805505\pi$
$769$	−34932.9	−1.63812	−0.819060	+	0.573708i	$0.805505\pi$
$770$	0	0
$771$	−40257.5	−1.88046
$772$	20134.0	0.938650
$773$	−13595.4	−0.632591	−0.316295	−	0.948661i	$-0.602439\pi$
$773$	−13595.4	−0.632591	−0.316295	+	0.948661i	$0.602439\pi$
$774$	−27744.9	−1.28846
$775$	0	0
$776$	−27229.7	−1.25965
$777$	5190.49	0.239650
$778$	−50762.9	−2.33925
$779$	−14208.8	−0.653510
$780$	0	0
$781$	−44460.1	−2.03701
$782$	−40615.2	−1.85728
$783$	−15005.9	−0.684888
$784$	−323.616	−0.0147420
$785$	0	0
$786$	22731.6	1.03156
$787$	−14228.1	−0.644444	−0.322222	−	0.946664i	$-0.604430\pi$
$787$	−14228.1	−0.644444	−0.322222	+	0.946664i	$0.604430\pi$
$788$	29487.3	1.33305
$789$	−4897.36	−0.220977
$790$	0	0
$791$	411.728	0.0185074
$792$	−16587.7	−0.744213
$793$	−12225.5	−0.547465
$794$	47037.5	2.10239
$795$	0	0
$796$	−25053.0	−1.11555
$797$	11442.3	0.508539	0.254270	−	0.967133i	$-0.418165\pi$
$797$	11442.3	0.508539	0.254270	+	0.967133i	$0.418165\pi$
$798$	−13447.5	−0.596538
$799$	8091.26	0.358258
$800$	0	0
$801$	19476.2	0.859125
$802$	24499.5	1.07869
$803$	43200.3	1.89851
$804$	38805.2	1.70218
$805$	0	0
$806$	−65870.2	−2.87863
$807$	11319.7	0.493770
$808$	−8310.63	−0.361840
$809$	22732.9	0.987944	0.493972	−	0.869478i	$-0.335545\pi$
$809$	22732.9	0.987944	0.493972	+	0.869478i	$0.335545\pi$
$810$	0	0
$811$	−29768.2	−1.28890	−0.644452	−	0.764644i	$-0.722915\pi$
$811$	−29768.2	−1.28890	−0.644452	+	0.764644i	$0.722915\pi$
$812$	16749.9	0.723898
$813$	28786.7	1.24181
$814$	−28118.4	−1.21075
$815$	0	0
$816$	3042.93	0.130544
$817$	27057.7	1.15867
$818$	−58185.0	−2.48703
$819$	7798.65	0.332731
$820$	0	0
$821$	6408.35	0.272416	0.136208	−	0.990680i	$-0.456509\pi$
$821$	6408.35	0.272416	0.136208	+	0.990680i	$0.456509\pi$
$822$	−30144.6	−1.27909
$823$	−20876.0	−0.884194	−0.442097	−	0.896967i	$-0.645765\pi$
$823$	−20876.0	−0.884194	−0.442097	+	0.896967i	$0.645765\pi$
$824$	6044.78	0.255558
$825$	0	0
$826$	6468.13	0.272464
$827$	−41650.1	−1.75129	−0.875645	−	0.482955i	$-0.839563\pi$
$827$	−41650.1	−1.75129	−0.875645	+	0.482955i	$0.839563\pi$
$828$	23396.0	0.981964
$829$	17194.7	0.720380	0.360190	−	0.932879i	$-0.382712\pi$
$829$	17194.7	0.720380	0.360190	+	0.932879i	$0.382712\pi$
$830$	0	0
$831$	−49736.1	−2.07621
$832$	−62764.5	−2.61535
$833$	−3491.44	−0.145223
$834$	−30194.8	−1.25367
$835$	0	0
$836$	44513.0	1.84153
$837$	15218.7	0.628477
$838$	25491.1	1.05081
$839$	40583.7	1.66997	0.834985	−	0.550273i	$-0.185476\pi$
$839$	40583.7	1.66997	0.834985	+	0.550273i	$0.185476\pi$
$840$	0	0
$841$	11865.0	0.486489
$842$	−9873.42	−0.404110
$843$	−1287.00	−0.0525819
$844$	−73549.7	−2.99963
$845$	0	0
$846$	−7627.93	−0.309993
$847$	11146.8	0.452192
$848$	−3859.39	−0.156288
$849$	−5168.49	−0.208931
$850$	0	0
$851$	14413.0	0.580576
$852$	66821.0	2.68691
$853$	23020.1	0.924023	0.462012	−	0.886874i	$-0.347128\pi$
$853$	23020.1	0.924023	0.462012	+	0.886874i	$0.347128\pi$
$854$	−5159.90	−0.206754
$855$	0	0
$856$	−454.832	−0.0181610
$857$	−18075.5	−0.720476	−0.360238	−	0.932861i	$-0.617304\pi$
$857$	−18075.5	−0.720476	−0.360238	+	0.932861i	$0.617304\pi$
$858$	−119259.	−4.74525
$859$	20308.2	0.806643	0.403321	−	0.915058i	$-0.367856\pi$
$859$	20308.2	0.806643	0.403321	+	0.915058i	$0.367856\pi$
$860$	0	0
$861$	9817.46	0.388592
$862$	47148.9	1.86299
$863$	−31023.5	−1.22370	−0.611849	−	0.790975i	$-0.709574\pi$
$863$	−31023.5	−1.22370	−0.611849	+	0.790975i	$0.709574\pi$
$864$	15419.3	0.607148
$865$	0	0
$866$	53857.2	2.11333
$867$	1061.17	0.0415677
$868$	−16987.4	−0.664274
$869$	25308.7	0.987963
$870$	0	0
$871$	35918.1	1.39729
$872$	−358.363	−0.0139171
$873$	−19472.6	−0.754924
$874$	−37341.2	−1.44518
$875$	0	0
$876$	−64927.5	−2.50422
$877$	−28344.1	−1.09135	−0.545674	−	0.837997i	$-0.683726\pi$
$877$	−28344.1	−1.09135	−0.545674	+	0.837997i	$0.683726\pi$
$878$	2904.14	0.111629
$879$	21356.3	0.819488
$880$	0	0
$881$	41264.5	1.57802	0.789010	−	0.614380i	$-0.210594\pi$
$881$	41264.5	1.57802	0.789010	+	0.614380i	$0.210594\pi$
$882$	3291.51	0.125659
$883$	−7995.59	−0.304726	−0.152363	−	0.988325i	$-0.548688\pi$
$883$	−7995.59	−0.304726	−0.152363	+	0.988325i	$0.548688\pi$
$884$	−67352.5	−2.56257
$885$	0	0
$886$	−3876.84	−0.147003
$887$	24438.3	0.925093	0.462547	−	0.886595i	$-0.346936\pi$
$887$	24438.3	0.925093	0.462547	+	0.886595i	$0.346936\pi$
$888$	15358.2	0.580390
$889$	13034.2	0.491737
$890$	0	0
$891$	49176.8	1.84903
$892$	−21610.1	−0.811167
$893$	7439.02	0.278765
$894$	41485.1	1.55198
$895$	0	0
$896$	−15534.1	−0.579192
$897$	61129.8	2.27543
$898$	15543.8	0.577620
$899$	−36768.0	−1.36405
$900$	0	0
$901$	−41638.3	−1.53959
$902$	−53184.0	−1.96323
$903$	−18695.3	−0.688970
$904$	1218.26	0.0448218
$905$	0	0
$906$	61434.7	2.25279
$907$	17241.6	0.631201	0.315601	−	0.948892i	$-0.397794\pi$
$907$	17241.6	0.631201	0.315601	+	0.948892i	$0.397794\pi$
$908$	−71456.6	−2.61164
$909$	−5943.15	−0.216856
$910$	0	0
$911$	17407.8	0.633092	0.316546	−	0.948577i	$-0.397477\pi$
$911$	17407.8	0.633092	0.316546	+	0.948577i	$0.397477\pi$
$912$	2797.64	0.101578
$913$	16779.2	0.608226
$914$	7751.87	0.280535
$915$	0	0
$916$	−38799.8	−1.39954
$917$	5426.13	0.195405
$918$	25467.1	0.915621
$919$	7704.64	0.276553	0.138277	−	0.990394i	$-0.455844\pi$
$919$	7704.64	0.276553	0.138277	+	0.990394i	$0.455844\pi$
$920$	0	0
$921$	−55791.6	−1.99609
$922$	10209.3	0.364671
$923$	61849.5	2.20564
$924$	−30755.9	−1.09501
$925$	0	0
$926$	−14515.9	−0.515144
$927$	4322.78	0.153159
$928$	−37252.8	−1.31776
$929$	−48184.3	−1.70170	−0.850849	−	0.525411i	$-0.823912\pi$
$929$	−48184.3	−1.70170	−0.850849	+	0.525411i	$0.823912\pi$
$930$	0	0
$931$	−3209.99	−0.113000
$932$	50237.7	1.76565
$933$	−31688.4	−1.11193
$934$	24840.5	0.870242
$935$	0	0
$936$	23075.5	0.805818
$937$	23371.6	0.814853	0.407427	−	0.913238i	$-0.366426\pi$
$937$	23371.6	0.814853	0.407427	+	0.913238i	$0.366426\pi$
$938$	15159.7	0.527697
$939$	−58934.7	−2.04820
$940$	0	0
$941$	18048.6	0.625258	0.312629	−	0.949875i	$-0.398790\pi$
$941$	18048.6	0.625258	0.312629	+	0.949875i	$0.398790\pi$
$942$	−20805.9	−0.719631
$943$	27261.1	0.941405
$944$	−1345.64	−0.0463948
$945$	0	0
$946$	101278.	3.48079
$947$	10346.2	0.355022	0.177511	−	0.984119i	$-0.443195\pi$
$947$	10346.2	0.355022	0.177511	+	0.984119i	$0.443195\pi$
$948$	−38037.6	−1.30317
$949$	−60096.9	−2.05567
$950$	0	0
$951$	−51877.3	−1.76891
$952$	−10330.8	−0.351706
$953$	8691.77	0.295440	0.147720	−	0.989029i	$-0.452807\pi$
$953$	8691.77	0.295440	0.147720	+	0.989029i	$0.452807\pi$
$954$	39254.0	1.33217
$955$	0	0
$956$	−56549.5	−1.91312
$957$	−66568.9	−2.24856
$958$	−64316.6	−2.16908
$959$	−7195.67	−0.242294
$960$	0	0
$961$	7498.41	0.251701
$962$	39116.2	1.31097
$963$	−325.262	−0.0108841
$964$	45659.6	1.52552
$965$	0	0
$966$	25800.5	0.859335
$967$	8971.58	0.298352	0.149176	−	0.988811i	$-0.452338\pi$
$967$	8971.58	0.298352	0.149176	+	0.988811i	$0.452338\pi$
$968$	32982.2	1.09513
$969$	30183.3	1.00065
$970$	0	0
$971$	29275.1	0.967541	0.483771	−	0.875195i	$-0.339267\pi$
$971$	29275.1	0.967541	0.483771	+	0.875195i	$0.339267\pi$
$972$	−47168.5	−1.55651
$973$	−7207.64	−0.237478
$974$	−24130.5	−0.793831
$975$	0	0
$976$	1073.47	0.0352059
$977$	−16477.5	−0.539572	−0.269786	−	0.962920i	$-0.586953\pi$
$977$	−16477.5	−0.539572	−0.269786	+	0.962920i	$0.586953\pi$
$978$	96075.2	3.14125
$979$	−71094.6	−2.32093
$980$	0	0
$981$	−256.275	−0.00834071
$982$	−29817.4	−0.968952
$983$	45912.9	1.48972	0.744859	−	0.667222i	$-0.232517\pi$
$983$	45912.9	1.48972	0.744859	+	0.667222i	$0.232517\pi$
$984$	29048.9	0.941104
$985$	0	0
$986$	−61528.0	−1.98727
$987$	−5139.92	−0.165760
$988$	−61923.2	−1.99397
$989$	−51913.1	−1.66910
$990$	0	0
$991$	46124.8	1.47851	0.739255	−	0.673426i	$-0.235178\pi$
$991$	46124.8	1.47851	0.739255	+	0.673426i	$0.235178\pi$
$992$	37781.0	1.20922
$993$	−8623.22	−0.275579
$994$	26104.3	0.832975
$995$	0	0
$996$	−25218.2	−0.802278
$997$	−30984.5	−0.984240	−0.492120	−	0.870527i	$-0.663778\pi$
$997$	−30984.5	−0.984240	−0.492120	+	0.870527i	$0.663778\pi$
$998$	−6837.47	−0.216870
$999$	−9037.42	−0.286218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.a.h.1.3	yes	4
3.2	odd	2		1575.4.a.bg.1.2		4
5.2	odd	4		175.4.b.f.99.6		8
5.3	odd	4		175.4.b.f.99.3		8
5.4	even	2		175.4.a.g.1.2	✓	4
7.6	odd	2		1225.4.a.bd.1.3		4
15.14	odd	2		1575.4.a.bl.1.3		4
35.34	odd	2		1225.4.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.a.g.1.2	✓	4	5.4	even	2
175.4.a.h.1.3	yes	4	1.1	even	1	trivial
175.4.b.f.99.3		8	5.3	odd	4
175.4.b.f.99.6		8	5.2	odd	4
1225.4.a.z.1.2		4	35.34	odd	2
1225.4.a.bd.1.3		4	7.6	odd	2
1575.4.a.bg.1.2		4	3.2	odd	2
1575.4.a.bl.1.3		4	15.14	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q+4.53510 q^{2} +6.46622 q^{3} +12.5671 q^{4} +29.3249 q^{6} +7.00000 q^{7} +20.7124 q^{8} +14.8119 q^{9} +O(q^{10})\)	\(q+4.53510 q^{2} +6.46622 q^{3} +12.5671 q^{4} +29.3249 q^{6} +7.00000 q^{7} +20.7124 q^{8} +14.8119 q^{9} -54.0684 q^{11} +81.2617 q^{12} +75.2159 q^{13} +31.7457 q^{14} -6.60441 q^{16} -71.2538 q^{17} +67.1736 q^{18} -65.5100 q^{19} +45.2635 q^{21} -245.206 q^{22} +125.688 q^{23} +133.931 q^{24} +341.111 q^{26} -78.8106 q^{27} +87.9699 q^{28} +190.405 q^{29} -193.105 q^{31} -195.650 q^{32} -349.618 q^{33} -323.143 q^{34} +186.144 q^{36} +114.673 q^{37} -297.094 q^{38} +486.362 q^{39} +216.896 q^{41} +205.275 q^{42} -413.032 q^{43} -679.484 q^{44} +570.007 q^{46} -113.555 q^{47} -42.7055 q^{48} +49.0000 q^{49} -460.743 q^{51} +945.247 q^{52} +584.366 q^{53} -357.414 q^{54} +144.986 q^{56} -423.602 q^{57} +863.504 q^{58} +203.748 q^{59} -162.539 q^{61} -875.749 q^{62} +103.684 q^{63} -834.459 q^{64} -1585.55 q^{66} +477.534 q^{67} -895.456 q^{68} +812.725 q^{69} +822.294 q^{71} +306.790 q^{72} -798.993 q^{73} +520.052 q^{74} -823.273 q^{76} -378.479 q^{77} +2205.70 q^{78} -468.087 q^{79} -909.529 q^{81} +983.643 q^{82} -310.333 q^{83} +568.832 q^{84} -1873.14 q^{86} +1231.20 q^{87} -1119.88 q^{88} +1314.90 q^{89} +526.511 q^{91} +1579.53 q^{92} -1248.66 q^{93} -514.985 q^{94} -1265.12 q^{96} -1314.66 q^{97} +222.220 q^{98} -800.858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 36 q^{4} + q^{6} + 28 q^{7} + 27 q^{8} + 61 q^{9} + 100 q^{11} - 165 q^{12} + 44 q^{13} + 28 q^{14} + 160 q^{16} - 53 q^{17} + 433 q^{18} - 29 q^{19} - 21 q^{21} - 152 q^{22} + 295 q^{23} - 21 q^{24} + 700 q^{26} - 441 q^{27} + 252 q^{28} + 129 q^{29} + 114 q^{31} - 310 q^{32} - 865 q^{33} + 203 q^{34} + 1101 q^{36} + 403 q^{37} + 555 q^{38} + 674 q^{39} + 671 q^{41} + 7 q^{42} - 411 q^{43} + 438 q^{44} - 997 q^{46} - 8 q^{47} - 523 q^{48} + 196 q^{49} - 885 q^{51} + 74 q^{52} + 90 q^{53} - 2777 q^{54} + 189 q^{56} + 233 q^{57} + 673 q^{58} + 1018 q^{59} + 50 q^{61} - 1626 q^{62} + 427 q^{63} - 2421 q^{64} - 3841 q^{66} + 424 q^{67} - 617 q^{68} + 1080 q^{69} + 215 q^{71} + 2940 q^{72} - 1207 q^{73} + 623 q^{74} - 3257 q^{76} + 700 q^{77} + 278 q^{78} - 951 q^{79} + 28 q^{81} + 1695 q^{82} - 3035 q^{83} - 1155 q^{84} - 99 q^{86} + 2210 q^{87} + 163 q^{88} + 2819 q^{89} + 308 q^{91} + 3073 q^{92} - 852 q^{93} - 3056 q^{94} - 1345 q^{96} - 1100 q^{97} + 196 q^{98} + 2383 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 36 * q^4 + q^6 + 28 * q^7 + 27 * q^8 + 61 * q^9 + 100 * q^11 - 165 * q^12 + 44 * q^13 + 28 * q^14 + 160 * q^16 - 53 * q^17 + 433 * q^18 - 29 * q^19 - 21 * q^21 - 152 * q^22 + 295 * q^23 - 21 * q^24 + 700 * q^26 - 441 * q^27 + 252 * q^28 + 129 * q^29 + 114 * q^31 - 310 * q^32 - 865 * q^33 + 203 * q^34 + 1101 * q^36 + 403 * q^37 + 555 * q^38 + 674 * q^39 + 671 * q^41 + 7 * q^42 - 411 * q^43 + 438 * q^44 - 997 * q^46 - 8 * q^47 - 523 * q^48 + 196 * q^49 - 885 * q^51 + 74 * q^52 + 90 * q^53 - 2777 * q^54 + 189 * q^56 + 233 * q^57 + 673 * q^58 + 1018 * q^59 + 50 * q^61 - 1626 * q^62 + 427 * q^63 - 2421 * q^64 - 3841 * q^66 + 424 * q^67 - 617 * q^68 + 1080 * q^69 + 215 * q^71 + 2940 * q^72 - 1207 * q^73 + 623 * q^74 - 3257 * q^76 + 700 * q^77 + 278 * q^78 - 951 * q^79 + 28 * q^81 + 1695 * q^82 - 3035 * q^83 - 1155 * q^84 - 99 * q^86 + 2210 * q^87 + 163 * q^88 + 2819 * q^89 + 308 * q^91 + 3073 * q^92 - 852 * q^93 - 3056 * q^94 - 1345 * q^96 - 1100 * q^97 + 196 * q^98 + 2383 * q^99

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