LMFDB - Embedded newform 175.4.a.f.1.2

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:	$3$
Coefficient field:	3.3.14360.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 17x - 14 $ x^3 - 17*x - 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.861086$ 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)

$f(q)$	$=$	$q+1.86109 q^{2} -9.53636 q^{3} -4.53636 q^{4} -17.7480 q^{6} -7.00000 q^{7} -23.3312 q^{8} +63.9421 q^{9} +O(q^{10})$	\(q+1.86109 q^{2} -9.53636 q^{3} -4.53636 q^{4} -17.7480 q^{6} -7.00000 q^{7} -23.3312 q^{8} +63.9421 q^{9} -36.9807 q^{11} +43.2603 q^{12} +22.7931 q^{13} -13.0276 q^{14} -7.13061 q^{16} +135.566 q^{17} +119.002 q^{18} +6.22620 q^{19} +66.7545 q^{21} -68.8243 q^{22} +48.7397 q^{23} +222.495 q^{24} +42.4199 q^{26} -352.293 q^{27} +31.7545 q^{28} -71.1172 q^{29} +124.924 q^{31} +173.379 q^{32} +352.661 q^{33} +252.300 q^{34} -290.064 q^{36} -84.9919 q^{37} +11.5875 q^{38} -217.363 q^{39} +92.5942 q^{41} +124.236 q^{42} -299.680 q^{43} +167.758 q^{44} +90.7088 q^{46} +72.9178 q^{47} +68.0000 q^{48} +49.0000 q^{49} -1292.81 q^{51} -103.398 q^{52} -362.685 q^{53} -655.648 q^{54} +163.319 q^{56} -59.3753 q^{57} -132.355 q^{58} -375.526 q^{59} +689.610 q^{61} +232.494 q^{62} -447.595 q^{63} +379.719 q^{64} +656.333 q^{66} +972.591 q^{67} -614.976 q^{68} -464.799 q^{69} +281.900 q^{71} -1491.85 q^{72} +742.980 q^{73} -158.177 q^{74} -28.2443 q^{76} +258.865 q^{77} -404.532 q^{78} +592.843 q^{79} +1633.16 q^{81} +172.326 q^{82} +493.406 q^{83} -302.822 q^{84} -557.731 q^{86} +678.199 q^{87} +862.806 q^{88} +962.977 q^{89} -159.552 q^{91} -221.101 q^{92} -1191.32 q^{93} +135.706 q^{94} -1653.41 q^{96} -740.748 q^{97} +91.1932 q^{98} -2364.62 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9	\( 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9} - 74 q^{11} + 152 q^{12} - 44 q^{13} - 21 q^{14} - 79 q^{16} + 52 q^{17} + 411 q^{18} + 168 q^{19} + 14 q^{21} - 184 q^{22} + 124 q^{23} + 420 q^{24} - 446 q^{26} - 170 q^{27} - 91 q^{28} + 332 q^{29} + 320 q^{31} + 183 q^{32} + 106 q^{33} + 582 q^{34} + 181 q^{36} + 54 q^{37} + 460 q^{38} - 982 q^{39} + 362 q^{41} - 168 q^{42} + 16 q^{43} - 264 q^{44} - 336 q^{46} + 730 q^{47} + 204 q^{48} + 147 q^{49} - 1178 q^{51} - 1202 q^{52} - 110 q^{53} - 180 q^{54} - 105 q^{56} + 956 q^{57} - 450 q^{58} - 180 q^{59} + 1222 q^{61} - 464 q^{62} - 567 q^{63} - 391 q^{64} - 532 q^{66} - 204 q^{67} - 918 q^{68} - 716 q^{69} - 136 q^{71} - 765 q^{72} - 310 q^{73} + 502 q^{74} + 1796 q^{76} + 518 q^{77} - 3788 q^{78} - 1034 q^{79} + 2283 q^{81} + 6 q^{82} + 1660 q^{83} - 1064 q^{84} + 764 q^{86} + 1574 q^{87} + 20 q^{88} + 242 q^{89} + 308 q^{91} - 96 q^{92} - 1376 q^{93} - 1108 q^{94} - 3156 q^{96} - 100 q^{97} + 147 q^{98} - 3488 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9 - 74 * q^11 + 152 * q^12 - 44 * q^13 - 21 * q^14 - 79 * q^16 + 52 * q^17 + 411 * q^18 + 168 * q^19 + 14 * q^21 - 184 * q^22 + 124 * q^23 + 420 * q^24 - 446 * q^26 - 170 * q^27 - 91 * q^28 + 332 * q^29 + 320 * q^31 + 183 * q^32 + 106 * q^33 + 582 * q^34 + 181 * q^36 + 54 * q^37 + 460 * q^38 - 982 * q^39 + 362 * q^41 - 168 * q^42 + 16 * q^43 - 264 * q^44 - 336 * q^46 + 730 * q^47 + 204 * q^48 + 147 * q^49 - 1178 * q^51 - 1202 * q^52 - 110 * q^53 - 180 * q^54 - 105 * q^56 + 956 * q^57 - 450 * q^58 - 180 * q^59 + 1222 * q^61 - 464 * q^62 - 567 * q^63 - 391 * q^64 - 532 * q^66 - 204 * q^67 - 918 * q^68 - 716 * q^69 - 136 * q^71 - 765 * q^72 - 310 * q^73 + 502 * q^74 + 1796 * q^76 + 518 * q^77 - 3788 * q^78 - 1034 * q^79 + 2283 * q^81 + 6 * q^82 + 1660 * q^83 - 1064 * q^84 + 764 * q^86 + 1574 * q^87 + 20 * q^88 + 242 * q^89 + 308 * q^91 - 96 * q^92 - 1376 * q^93 - 1108 * q^94 - 3156 * q^96 - 100 * q^97 + 147 * q^98 - 3488 * 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 $

$2$	1.86109	0.657993	0.328997	−	0.944331i	$-0.393289\pi$
$2$	1.86109	0.657993	0.328997	+	0.944331i	$0.393289\pi$
$3$	−9.53636	−1.83527	−0.917636	−	0.397421i	$-0.869905\pi$
$3$	−9.53636	−1.83527	−0.917636	+	0.397421i	$0.869905\pi$
$4$	−4.53636	−0.567045
$5$	0	0
$5$	0	0
$6$	−17.7480	−1.20760
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−23.3312	−1.03111
$9$	63.9421	2.36823
$10$	0	0
$11$	−36.9807	−1.01365	−0.506823	−	0.862050i	$-0.669180\pi$
$11$	−36.9807	−1.01365	−0.506823	+	0.862050i	$0.669180\pi$
$12$	43.2603	1.04068
$13$	22.7931	0.486282	0.243141	−	0.969991i	$-0.421822\pi$
$13$	22.7931	0.486282	0.243141	+	0.969991i	$0.421822\pi$
$14$	−13.0276	−0.248698
$15$	0	0
$16$	−7.13061	−0.111416
$17$	135.566	1.93409	0.967047	−	0.254599i	$-0.0819436\pi$
$17$	135.566	1.93409	0.967047	+	0.254599i	$0.0819436\pi$
$18$	119.002	1.55828
$19$	6.22620	0.0751784	0.0375892	−	0.999293i	$-0.488032\pi$
$19$	6.22620	0.0751784	0.0375892	+	0.999293i	$0.488032\pi$
$20$	0	0
$21$	66.7545	0.693668
$22$	−68.8243	−0.666972
$23$	48.7397	0.441866	0.220933	−	0.975289i	$-0.429090\pi$
$23$	48.7397	0.441866	0.220933	+	0.975289i	$0.429090\pi$
$24$	222.495	1.89236
$25$	0	0
$26$	42.4199	0.319970
$27$	−352.293	−2.51107
$28$	31.7545	0.214323
$29$	−71.1172	−0.455384	−0.227692	−	0.973733i	$-0.573118\pi$
$29$	−71.1172	−0.455384	−0.227692	+	0.973733i	$0.573118\pi$
$30$	0	0
$31$	124.924	0.723773	0.361886	−	0.932222i	$-0.382133\pi$
$31$	124.924	0.723773	0.361886	+	0.932222i	$0.382133\pi$
$32$	173.379	0.957794
$33$	352.661	1.86032
$34$	252.300	1.27262
$35$	0	0
$36$	−290.064	−1.34289
$37$	−84.9919	−0.377638	−0.188819	−	0.982012i	$-0.560466\pi$
$37$	−84.9919	−0.377638	−0.188819	+	0.982012i	$0.560466\pi$
$38$	11.5875	0.0494669
$39$	−217.363	−0.892460
$40$	0	0
$41$	92.5942	0.352702	0.176351	−	0.984327i	$-0.443571\pi$
$41$	92.5942	0.352702	0.176351	+	0.984327i	$0.443571\pi$
$42$	124.236	0.456429
$43$	−299.680	−1.06281	−0.531405	−	0.847118i	$-0.678336\pi$
$43$	−299.680	−1.06281	−0.531405	+	0.847118i	$0.678336\pi$
$44$	167.758	0.574782
$45$	0	0
$46$	90.7088	0.290745
$47$	72.9178	0.226301	0.113151	−	0.993578i	$-0.463906\pi$
$47$	72.9178	0.226301	0.113151	+	0.993578i	$0.463906\pi$
$48$	68.0000	0.204478
$49$	49.0000	0.142857
$50$	0	0
$51$	−1292.81	−3.54959
$52$	−103.398	−0.275744
$53$	−362.685	−0.939974	−0.469987	−	0.882673i	$-0.655741\pi$
$53$	−362.685	−0.939974	−0.469987	+	0.882673i	$0.655741\pi$
$54$	−655.648	−1.65227
$55$	0	0
$56$	163.319	0.389721
$57$	−59.3753	−0.137973
$58$	−132.355	−0.299640
$59$	−375.526	−0.828633	−0.414316	−	0.910133i	$-0.635979\pi$
$59$	−375.526	−0.828633	−0.414316	+	0.910133i	$0.635979\pi$
$60$	0	0
$61$	689.610	1.44747	0.723734	−	0.690079i	$-0.242424\pi$
$61$	689.610	1.44747	0.723734	+	0.690079i	$0.242424\pi$
$62$	232.494	0.476238
$63$	−447.595	−0.895105
$64$	379.719	0.741638
$65$	0	0
$66$	656.333	1.22408
$67$	972.591	1.77345	0.886723	−	0.462301i	$-0.152976\pi$
$67$	972.591	1.77345	0.886723	+	0.462301i	$0.152976\pi$
$68$	−614.976	−1.09672
$69$	−464.799	−0.810945
$70$	0	0
$71$	281.900	0.471202	0.235601	−	0.971850i	$-0.424294\pi$
$71$	281.900	0.471202	0.235601	+	0.971850i	$0.424294\pi$
$72$	−1491.85	−2.44189
$73$	742.980	1.19122	0.595612	−	0.803273i	$-0.296910\pi$
$73$	742.980	1.19122	0.595612	+	0.803273i	$0.296910\pi$
$74$	−158.177	−0.248483
$75$	0	0
$76$	−28.2443	−0.0426295
$77$	258.865	0.383122
$78$	−404.532	−0.587233
$79$	592.843	0.844304	0.422152	−	0.906525i	$-0.361275\pi$
$79$	592.843	0.844304	0.422152	+	0.906525i	$0.361275\pi$
$80$	0	0
$81$	1633.16	2.24027
$82$	172.326	0.232076
$83$	493.406	0.652510	0.326255	−	0.945282i	$-0.394213\pi$
$83$	493.406	0.652510	0.326255	+	0.945282i	$0.394213\pi$
$84$	−302.822	−0.393341
$85$	0	0
$86$	−557.731	−0.699322
$87$	678.199	0.835753
$88$	862.806	1.04518
$89$	962.977	1.14691	0.573457	−	0.819236i	$-0.305602\pi$
$89$	962.977	1.14691	0.573457	+	0.819236i	$0.305602\pi$
$90$	0	0
$91$	−159.552	−0.183797
$92$	−221.101	−0.250558
$93$	−1191.32	−1.32832
$94$	135.706	0.148905
$95$	0	0
$96$	−1653.41	−1.75781
$97$	−740.748	−0.775377	−0.387689	−	0.921790i	$-0.626726\pi$
$97$	−740.748	−0.775377	−0.387689	+	0.921790i	$0.626726\pi$
$98$	91.1932	0.0939991
$99$	−2364.62	−2.40054
$100$	0	0
$101$	613.794	0.604701	0.302351	−	0.953197i	$-0.402229\pi$
$101$	613.794	0.604701	0.302351	+	0.953197i	$0.402229\pi$
$102$	−2406.02	−2.33561
$103$	−805.493	−0.770559	−0.385280	−	0.922800i	$-0.625895\pi$
$103$	−805.493	−0.770559	−0.385280	+	0.922800i	$0.625895\pi$
$104$	−531.791	−0.501408
$105$	0	0
$106$	−674.988	−0.618497
$107$	1931.30	1.74491	0.872457	−	0.488691i	$-0.162526\pi$
$107$	1931.30	1.74491	0.872457	+	0.488691i	$0.162526\pi$
$108$	1598.13	1.42389
$109$	106.462	0.0935522	0.0467761	−	0.998905i	$-0.485105\pi$
$109$	106.462	0.0935522	0.0467761	+	0.998905i	$0.485105\pi$
$110$	0	0
$111$	810.514	0.693068
$112$	49.9142	0.0421112
$113$	−309.076	−0.257305	−0.128652	−	0.991690i	$-0.541065\pi$
$113$	−309.076	−0.257305	−0.128652	+	0.991690i	$0.541065\pi$
$114$	−110.503	−0.0907852
$115$	0	0
$116$	322.613	0.258223
$117$	1457.44	1.15163
$118$	−698.887	−0.545235
$119$	−948.962	−0.731019
$120$	0	0
$121$	36.5724	0.0274774
$122$	1283.42	0.952425
$123$	−883.012	−0.647305
$124$	−566.699	−0.410412
$125$	0	0
$126$	−833.013	−0.588973
$127$	199.470	0.139371	0.0696856	−	0.997569i	$-0.477800\pi$
$127$	199.470	0.139371	0.0696856	+	0.997569i	$0.477800\pi$
$128$	−680.345	−0.469801
$129$	2857.86	1.95055
$130$	0	0
$131$	601.722	0.401318	0.200659	−	0.979661i	$-0.435692\pi$
$131$	601.722	0.401318	0.200659	+	0.979661i	$0.435692\pi$
$132$	−1599.80	−1.05488
$133$	−43.5834	−0.0284147
$134$	1810.08	1.16692
$135$	0	0
$136$	−3162.92	−1.99425
$137$	−2092.21	−1.30474	−0.652370	−	0.757901i	$-0.726225\pi$
$137$	−2092.21	−1.30474	−0.652370	+	0.757901i	$0.726225\pi$
$138$	−865.031	−0.533597
$139$	834.466	0.509198	0.254599	−	0.967047i	$-0.418057\pi$
$139$	834.466	0.509198	0.254599	+	0.967047i	$0.418057\pi$
$140$	0	0
$141$	−695.370	−0.415324
$142$	524.639	0.310048
$143$	−842.905	−0.492918
$144$	−455.946	−0.263858
$145$	0	0
$146$	1382.75	0.783817
$147$	−467.282	−0.262182
$148$	385.554	0.214137
$149$	−244.258	−0.134298	−0.0671491	−	0.997743i	$-0.521390\pi$
$149$	−244.258	−0.134298	−0.0671491	+	0.997743i	$0.521390\pi$
$150$	0	0
$151$	−802.158	−0.432309	−0.216155	−	0.976359i	$-0.569352\pi$
$151$	−802.158	−0.432309	−0.216155	+	0.976359i	$0.569352\pi$
$152$	−145.265	−0.0775168
$153$	8668.38	4.58037
$154$	481.770	0.252092
$155$	0	0
$156$	986.037	0.506065
$157$	−3541.38	−1.80021	−0.900105	−	0.435673i	$-0.856510\pi$
$157$	−3541.38	−1.80021	−0.900105	+	0.435673i	$0.856510\pi$
$158$	1103.33	0.555546
$159$	3458.69	1.72511
$160$	0	0
$161$	−341.178	−0.167010
$162$	3039.45	1.47408
$163$	2214.57	1.06416	0.532081	−	0.846693i	$-0.321410\pi$
$163$	2214.57	1.06416	0.532081	+	0.846693i	$0.321410\pi$
$164$	−420.041	−0.199998
$165$	0	0
$166$	918.271	0.429347
$167$	2617.07	1.21266	0.606332	−	0.795212i	$-0.292640\pi$
$167$	2617.07	1.21266	0.606332	+	0.795212i	$0.292640\pi$
$168$	−1557.47	−0.715245
$169$	−1677.47	−0.763530
$170$	0	0
$171$	398.117	0.178039
$172$	1359.46	0.602661
$173$	1634.04	0.718114	0.359057	−	0.933316i	$-0.383098\pi$
$173$	1634.04	0.718114	0.359057	+	0.933316i	$0.383098\pi$
$174$	1262.19	0.549920
$175$	0	0
$176$	263.695	0.112936
$177$	3581.15	1.52077
$178$	1792.18	0.754662
$179$	969.160	0.404684	0.202342	−	0.979315i	$-0.435145\pi$
$179$	969.160	0.404684	0.202342	+	0.979315i	$0.435145\pi$
$180$	0	0
$181$	4358.20	1.78974	0.894869	−	0.446329i	$-0.147269\pi$
$181$	4358.20	1.78974	0.894869	+	0.446329i	$0.147269\pi$
$182$	−296.939	−0.120937
$183$	−6576.37	−2.65650
$184$	−1137.16	−0.455611
$185$	0	0
$186$	−2217.14	−0.874026
$187$	−5013.33	−1.96049
$188$	−330.781	−0.128323
$189$	2466.05	0.949095
$190$	0	0
$191$	2909.97	1.10240	0.551199	−	0.834374i	$-0.314170\pi$
$191$	2909.97	1.10240	0.551199	+	0.834374i	$0.314170\pi$
$192$	−3621.13	−1.36111
$193$	3719.25	1.38714	0.693568	−	0.720391i	$-0.256038\pi$
$193$	3719.25	1.38714	0.693568	+	0.720391i	$0.256038\pi$
$194$	−1378.60	−0.510193
$195$	0	0
$196$	−222.282	−0.0810064
$197$	1550.03	0.560582	0.280291	−	0.959915i	$-0.409569\pi$
$197$	1550.03	0.560582	0.280291	+	0.959915i	$0.409569\pi$
$198$	−4400.77	−1.57954
$199$	−3605.14	−1.28423	−0.642115	−	0.766608i	$-0.721943\pi$
$199$	−3605.14	−1.28423	−0.642115	+	0.766608i	$0.721943\pi$
$200$	0	0
$201$	−9274.97	−3.25476
$202$	1142.32	0.397889
$203$	497.820	0.172119
$204$	5864.63	2.01278
$205$	0	0
$206$	−1499.09	−0.507023
$207$	3116.52	1.04644
$208$	−162.529	−0.0541795
$209$	−230.249	−0.0762042
$210$	0	0
$211$	−3305.27	−1.07841	−0.539204	−	0.842175i	$-0.681275\pi$
$211$	−3305.27	−1.07841	−0.539204	+	0.842175i	$0.681275\pi$
$212$	1645.27	0.533007
$213$	−2688.29	−0.864784
$214$	3594.31	1.14814
$215$	0	0
$216$	8219.44	2.58918
$217$	−874.466	−0.273560
$218$	198.135	0.0615567
$219$	−7085.33	−2.18622
$220$	0	0
$221$	3089.97	0.940515
$222$	1508.44	0.456034
$223$	−3451.37	−1.03642	−0.518209	−	0.855254i	$-0.673401\pi$
$223$	−3451.37	−1.03642	−0.518209	+	0.855254i	$0.673401\pi$
$224$	−1213.65	−0.362012
$225$	0	0
$226$	−575.218	−0.169305
$227$	−2047.24	−0.598591	−0.299296	−	0.954160i	$-0.596752\pi$
$227$	−2047.24	−0.598591	−0.299296	+	0.954160i	$0.596752\pi$
$228$	269.348	0.0782367
$229$	−1387.42	−0.400362	−0.200181	−	0.979759i	$-0.564153\pi$
$229$	−1387.42	−0.400362	−0.200181	+	0.979759i	$0.564153\pi$
$230$	0	0
$231$	−2468.63	−0.703133
$232$	1659.25	0.469549
$233$	374.993	0.105436	0.0527181	−	0.998609i	$-0.483212\pi$
$233$	374.993	0.105436	0.0527181	+	0.998609i	$0.483212\pi$
$234$	2712.42	0.757762
$235$	0	0
$236$	1703.52	0.469872
$237$	−5653.56	−1.54953
$238$	−1766.10	−0.481005
$239$	−5560.93	−1.50505	−0.752525	−	0.658564i	$-0.771164\pi$
$239$	−5560.93	−1.50505	−0.752525	+	0.658564i	$0.771164\pi$
$240$	0	0
$241$	4706.19	1.25789	0.628947	−	0.777448i	$-0.283486\pi$
$241$	4706.19	1.25789	0.628947	+	0.777448i	$0.283486\pi$
$242$	68.0644	0.0180799
$243$	−6062.45	−1.60044
$244$	−3128.32	−0.820779
$245$	0	0
$246$	−1643.36	−0.425922
$247$	141.914	0.0365579
$248$	−2914.63	−0.746286
$249$	−4705.29	−1.19753
$250$	0	0
$251$	589.085	0.148138	0.0740692	−	0.997253i	$-0.476401\pi$
$251$	589.085	0.148138	0.0740692	+	0.997253i	$0.476401\pi$
$252$	2030.45	0.507565
$253$	−1802.43	−0.447896
$254$	371.232	0.0917053
$255$	0	0
$256$	−4303.93	−1.05076
$257$	4666.16	1.13256	0.566278	−	0.824214i	$-0.308383\pi$
$257$	4666.16	1.13256	0.566278	+	0.824214i	$0.308383\pi$
$258$	5318.72	1.28345
$259$	594.944	0.142734
$260$	0	0
$261$	−4547.38	−1.07845
$262$	1119.86	0.264065
$263$	4471.96	1.04849	0.524246	−	0.851567i	$-0.324347\pi$
$263$	4471.96	1.04849	0.524246	+	0.851567i	$0.324347\pi$
$264$	−8228.02	−1.91818
$265$	0	0
$266$	−81.1125	−0.0186967
$267$	−9183.29	−2.10490
$268$	−4412.02	−1.00562
$269$	−4257.13	−0.964913	−0.482457	−	0.875920i	$-0.660255\pi$
$269$	−4257.13	−0.964913	−0.482457	+	0.875920i	$0.660255\pi$
$270$	0	0
$271$	−3868.69	−0.867182	−0.433591	−	0.901110i	$-0.642754\pi$
$271$	−3868.69	−0.867182	−0.433591	+	0.901110i	$0.642754\pi$
$272$	−966.668	−0.215488
$273$	1521.54	0.337318
$274$	−3893.78	−0.858510
$275$	0	0
$276$	2108.49	0.459842
$277$	−8207.30	−1.78025	−0.890124	−	0.455718i	$-0.849382\pi$
$277$	−8207.30	−1.78025	−0.890124	+	0.455718i	$0.849382\pi$
$278$	1553.01	0.335049
$279$	7987.88	1.71406
$280$	0	0
$281$	6471.27	1.37382	0.686910	−	0.726743i	$-0.258967\pi$
$281$	6471.27	1.37382	0.686910	+	0.726743i	$0.258967\pi$
$282$	−1294.14	−0.273281
$283$	−1470.80	−0.308940	−0.154470	−	0.987997i	$-0.549367\pi$
$283$	−1470.80	−0.308940	−0.154470	+	0.987997i	$0.549367\pi$
$284$	−1278.80	−0.267192
$285$	0	0
$286$	−1568.72	−0.324337
$287$	−648.160	−0.133309
$288$	11086.2	2.26827
$289$	13465.1	2.74072
$290$	0	0
$291$	7064.04	1.42303
$292$	−3370.42	−0.675477
$293$	5489.18	1.09448	0.547238	−	0.836977i	$-0.315679\pi$
$293$	5489.18	1.09448	0.547238	+	0.836977i	$0.315679\pi$
$294$	−869.651	−0.172514
$295$	0	0
$296$	1982.97	0.389384
$297$	13028.0	2.54533
$298$	−454.586	−0.0883673
$299$	1110.93	0.214872
$300$	0	0
$301$	2097.76	0.401705
$302$	−1492.89	−0.284457
$303$	−5853.36	−1.10979
$304$	−44.3966	−0.00837605
$305$	0	0
$306$	16132.6	3.01385
$307$	−1035.35	−0.192477	−0.0962383	−	0.995358i	$-0.530681\pi$
$307$	−1035.35	−0.192477	−0.0962383	+	0.995358i	$0.530681\pi$
$308$	−1174.30	−0.217247
$309$	7681.47	1.41419
$310$	0	0
$311$	2544.04	0.463856	0.231928	−	0.972733i	$-0.425497\pi$
$311$	2544.04	0.463856	0.231928	+	0.972733i	$0.425497\pi$
$312$	5071.35	0.920220
$313$	−2599.72	−0.469473	−0.234737	−	0.972059i	$-0.575423\pi$
$313$	−2599.72	−0.469473	−0.234737	+	0.972059i	$0.575423\pi$
$314$	−6590.82	−1.18453
$315$	0	0
$316$	−2689.35	−0.478758
$317$	2725.13	0.482835	0.241417	−	0.970421i	$-0.422388\pi$
$317$	2725.13	0.482835	0.241417	+	0.970421i	$0.422388\pi$
$318$	6436.93	1.13511
$319$	2629.96	0.461598
$320$	0	0
$321$	−18417.6	−3.20239
$322$	−634.961	−0.109891
$323$	844.061	0.145402
$324$	−7408.58	−1.27033
$325$	0	0
$326$	4121.50	0.700212
$327$	−1015.26	−0.171694
$328$	−2160.34	−0.363673
$329$	−510.425	−0.0855338
$330$	0	0
$331$	−5178.12	−0.859865	−0.429933	−	0.902861i	$-0.641463\pi$
$331$	−5178.12	−0.859865	−0.429933	+	0.902861i	$0.641463\pi$
$332$	−2238.26	−0.370002
$333$	−5434.56	−0.894331
$334$	4870.59	0.797924
$335$	0	0
$336$	−476.000	−0.0772855
$337$	3656.07	0.590975	0.295488	−	0.955347i	$-0.404518\pi$
$337$	3656.07	0.590975	0.295488	+	0.955347i	$0.404518\pi$
$338$	−3121.93	−0.502398
$339$	2947.46	0.472225
$340$	0	0
$341$	−4619.77	−0.733649
$342$	740.929	0.117149
$343$	−343.000	−0.0539949
$344$	6991.92	1.09587
$345$	0	0
$346$	3041.09	0.472514
$347$	1673.15	0.258846	0.129423	−	0.991589i	$-0.458688\pi$
$347$	1673.15	0.258846	0.129423	+	0.991589i	$0.458688\pi$
$348$	−3076.55	−0.473910
$349$	777.313	0.119222	0.0596112	−	0.998222i	$-0.481014\pi$
$349$	777.313	0.119222	0.0596112	+	0.998222i	$0.481014\pi$
$350$	0	0
$351$	−8029.85	−1.22109
$352$	−6411.69	−0.970864
$353$	−4422.92	−0.666879	−0.333439	−	0.942772i	$-0.608209\pi$
$353$	−4422.92	−0.666879	−0.333439	+	0.942772i	$0.608209\pi$
$354$	6664.83	1.00065
$355$	0	0
$356$	−4368.41	−0.650351
$357$	9049.64	1.34162
$358$	1803.69	0.266279
$359$	−962.163	−0.141451	−0.0707256	−	0.997496i	$-0.522531\pi$
$359$	−962.163	−0.141451	−0.0707256	+	0.997496i	$0.522531\pi$
$360$	0	0
$361$	−6820.23	−0.994348
$362$	8110.99	1.17764
$363$	−348.767	−0.0504285
$364$	723.783	0.104221
$365$	0	0
$366$	−12239.2	−1.74796
$367$	7282.68	1.03584	0.517919	−	0.855430i	$-0.326707\pi$
$367$	7282.68	1.03584	0.517919	+	0.855430i	$0.326707\pi$
$368$	−347.543	−0.0492308
$369$	5920.67	0.835279
$370$	0	0
$371$	2538.79	0.355277
$372$	5404.24	0.753217
$373$	1149.24	0.159532	0.0797658	−	0.996814i	$-0.474583\pi$
$373$	1149.24	0.159532	0.0797658	+	0.996814i	$0.474583\pi$
$374$	−9330.23	−1.28999
$375$	0	0
$376$	−1701.26	−0.233340
$377$	−1620.98	−0.221445
$378$	4589.54	0.624498
$379$	−10452.6	−1.41666	−0.708332	−	0.705879i	$-0.750552\pi$
$379$	−10452.6	−1.41666	−0.708332	+	0.705879i	$0.750552\pi$
$380$	0	0
$381$	−1902.22	−0.255784
$382$	5415.71	0.725371
$383$	13469.3	1.79699	0.898496	−	0.438982i	$-0.144661\pi$
$383$	13469.3	1.79699	0.898496	+	0.438982i	$0.144661\pi$
$384$	6488.01	0.862214
$385$	0	0
$386$	6921.84	0.912727
$387$	−19162.2	−2.51698
$388$	3360.30	0.439674
$389$	10635.5	1.38622	0.693110	−	0.720832i	$-0.256240\pi$
$389$	10635.5	1.38622	0.693110	+	0.720832i	$0.256240\pi$
$390$	0	0
$391$	6607.44	0.854611
$392$	−1143.23	−0.147301
$393$	−5738.23	−0.736528
$394$	2884.73	0.368860
$395$	0	0
$396$	10726.8	1.36121
$397$	−1031.93	−0.130456	−0.0652282	−	0.997870i	$-0.520778\pi$
$397$	−1031.93	−0.130456	−0.0652282	+	0.997870i	$0.520778\pi$
$398$	−6709.48	−0.845015
$399$	415.627	0.0521488
$400$	0	0
$401$	−6468.95	−0.805596	−0.402798	−	0.915289i	$-0.631962\pi$
$401$	−6468.95	−0.805596	−0.402798	+	0.915289i	$0.631962\pi$
$402$	−17261.5	−2.14161
$403$	2847.40	0.351958
$404$	−2784.39	−0.342893
$405$	0	0
$406$	926.487	0.113253
$407$	3143.06	0.382791
$408$	30162.8	3.66000
$409$	−8652.18	−1.04602	−0.523011	−	0.852326i	$-0.675191\pi$
$409$	−8652.18	−1.04602	−0.523011	+	0.852326i	$0.675191\pi$
$410$	0	0
$411$	19952.0	2.39455
$412$	3654.01	0.436942
$413$	2628.68	0.313194
$414$	5800.11	0.688550
$415$	0	0
$416$	3951.85	0.465758
$417$	−7957.77	−0.934517
$418$	−428.514	−0.0501419
$419$	7303.41	0.851539	0.425770	−	0.904832i	$-0.360003\pi$
$419$	7303.41	0.851539	0.425770	+	0.904832i	$0.360003\pi$
$420$	0	0
$421$	−11599.8	−1.34285	−0.671425	−	0.741072i	$-0.734317\pi$
$421$	−11599.8	−1.34285	−0.671425	+	0.741072i	$0.734317\pi$
$422$	−6151.39	−0.709585
$423$	4662.52	0.535933
$424$	8461.89	0.969212
$425$	0	0
$426$	−5003.15	−0.569022
$427$	−4827.27	−0.547092
$428$	−8761.06	−0.989444
$429$	8038.24	0.904638
$430$	0	0
$431$	−1506.87	−0.168407	−0.0842034	−	0.996449i	$-0.526835\pi$
$431$	−1506.87	−0.168407	−0.0842034	+	0.996449i	$0.526835\pi$
$432$	2512.06	0.279772
$433$	−2112.02	−0.234405	−0.117203	−	0.993108i	$-0.537393\pi$
$433$	−2112.02	−0.234405	−0.117203	+	0.993108i	$0.537393\pi$
$434$	−1627.46	−0.180001
$435$	0	0
$436$	−482.949	−0.0530483
$437$	303.463	0.0332188
$438$	−13186.4	−1.43852
$439$	−3492.88	−0.379740	−0.189870	−	0.981809i	$-0.560807\pi$
$439$	−3492.88	−0.379740	−0.189870	+	0.981809i	$0.560807\pi$
$440$	0	0
$441$	3133.16	0.338318
$442$	5750.70	0.618853
$443$	−974.674	−0.104533	−0.0522666	−	0.998633i	$-0.516645\pi$
$443$	−974.674	−0.104533	−0.0522666	+	0.998633i	$0.516645\pi$
$444$	−3676.78	−0.393000
$445$	0	0
$446$	−6423.30	−0.681956
$447$	2329.34	0.246474
$448$	−2658.03	−0.280313
$449$	6113.63	0.642584	0.321292	−	0.946980i	$-0.395883\pi$
$449$	6113.63	0.642584	0.321292	+	0.946980i	$0.395883\pi$
$450$	0	0
$451$	−3424.20	−0.357515
$452$	1402.08	0.145903
$453$	7649.66	0.793405
$454$	−3810.09	−0.393869
$455$	0	0
$456$	1385.30	0.142264
$457$	1553.51	0.159015	0.0795077	−	0.996834i	$-0.474665\pi$
$457$	1553.51	0.159015	0.0795077	+	0.996834i	$0.474665\pi$
$458$	−2582.10	−0.263436
$459$	−47759.0	−4.85664
$460$	0	0
$461$	9419.28	0.951626	0.475813	−	0.879546i	$-0.342154\pi$
$461$	9419.28	0.951626	0.475813	+	0.879546i	$0.342154\pi$
$462$	−4594.33	−0.462657
$463$	11458.4	1.15014	0.575070	−	0.818104i	$-0.304975\pi$
$463$	11458.4	1.15014	0.575070	+	0.818104i	$0.304975\pi$
$464$	507.109	0.0507369
$465$	0	0
$466$	697.895	0.0693763
$467$	−2121.08	−0.210175	−0.105087	−	0.994463i	$-0.533512\pi$
$467$	−2121.08	−0.210175	−0.105087	+	0.994463i	$0.533512\pi$
$468$	−6611.46	−0.653023
$469$	−6808.14	−0.670300
$470$	0	0
$471$	33771.9	3.30388
$472$	8761.49	0.854407
$473$	11082.4	1.07731
$474$	−10521.8	−1.01958
$475$	0	0
$476$	4304.83	0.414520
$477$	−23190.8	−2.22607
$478$	−10349.4	−0.990313
$479$	17261.2	1.64653	0.823263	−	0.567660i	$-0.192151\pi$
$479$	17261.2	1.64653	0.823263	+	0.567660i	$0.192151\pi$
$480$	0	0
$481$	−1937.23	−0.183638
$482$	8758.63	0.827686
$483$	3253.59	0.306508
$484$	−165.905	−0.0155809
$485$	0	0
$486$	−11282.7	−1.05308
$487$	18516.8	1.72295	0.861473	−	0.507804i	$-0.169543\pi$
$487$	18516.8	1.72295	0.861473	+	0.507804i	$0.169543\pi$
$488$	−16089.5	−1.49249
$489$	−21118.9	−1.95303
$490$	0	0
$491$	7914.77	0.727472	0.363736	−	0.931502i	$-0.381501\pi$
$491$	7914.77	0.727472	0.363736	+	0.931502i	$0.381501\pi$
$492$	4005.66	0.367051
$493$	−9641.07	−0.880755
$494$	264.115	0.0240549
$495$	0	0
$496$	−890.782	−0.0806397
$497$	−1973.30	−0.178097
$498$	−8756.96	−0.787969
$499$	2388.91	0.214314	0.107157	−	0.994242i	$-0.465825\pi$
$499$	2388.91	0.214314	0.107157	+	0.994242i	$0.465825\pi$
$500$	0	0
$501$	−24957.3	−2.22557
$502$	1096.34	0.0974740
$503$	−18073.0	−1.60206	−0.801030	−	0.598624i	$-0.795715\pi$
$503$	−18073.0	−1.60206	−0.801030	+	0.598624i	$0.795715\pi$
$504$	10442.9	0.922948
$505$	0	0
$506$	−3354.47	−0.294713
$507$	15997.0	1.40129
$508$	−904.869	−0.0790296
$509$	18671.7	1.62595	0.812975	−	0.582299i	$-0.197847\pi$
$509$	18671.7	1.62595	0.812975	+	0.582299i	$0.197847\pi$
$510$	0	0
$511$	−5200.86	−0.450240
$512$	−2567.23	−0.221595
$513$	−2193.45	−0.188778
$514$	8684.12	0.745214
$515$	0	0
$516$	−12964.3	−1.10605
$517$	−2696.55	−0.229389
$518$	1107.24	0.0939178
$519$	−15582.8	−1.31793
$520$	0	0
$521$	−3526.04	−0.296504	−0.148252	−	0.988950i	$-0.547365\pi$
$521$	−3526.04	−0.296504	−0.148252	+	0.988950i	$0.547365\pi$
$522$	−8463.07	−0.709614
$523$	10966.3	0.916865	0.458433	−	0.888729i	$-0.348411\pi$
$523$	10966.3	0.916865	0.458433	+	0.888729i	$0.348411\pi$
$524$	−2729.62	−0.227565
$525$	0	0
$526$	8322.71	0.689900
$527$	16935.4	1.39984
$528$	−2514.69	−0.207268
$529$	−9791.44	−0.804754
$530$	0	0
$531$	−24011.9	−1.96239
$532$	197.710	0.0161124
$533$	2110.51	0.171513
$534$	−17090.9	−1.38501
$535$	0	0
$536$	−22691.8	−1.82861
$537$	−9242.26	−0.742705
$538$	−7922.88	−0.634907
$539$	−1812.05	−0.144807
$540$	0	0
$541$	11349.8	0.901971	0.450985	−	0.892531i	$-0.351073\pi$
$541$	11349.8	0.901971	0.450985	+	0.892531i	$0.351073\pi$
$542$	−7199.97	−0.570600
$543$	−41561.4	−3.28466
$544$	23504.3	1.85246
$545$	0	0
$546$	2831.72	0.221953
$547$	−11206.1	−0.875940	−0.437970	−	0.898989i	$-0.644302\pi$
$547$	−11206.1	−0.875940	−0.437970	+	0.898989i	$0.644302\pi$
$548$	9491.00	0.739845
$549$	44095.1	3.42793
$550$	0	0
$551$	−442.790	−0.0342350
$552$	10844.3	0.836170
$553$	−4149.90	−0.319117
$554$	−15274.5	−1.17139
$555$	0	0
$556$	−3785.44	−0.288738
$557$	−12631.0	−0.960847	−0.480424	−	0.877037i	$-0.659517\pi$
$557$	−12631.0	−0.960847	−0.480424	+	0.877037i	$0.659517\pi$
$558$	14866.1	1.12784
$559$	−6830.65	−0.516826
$560$	0	0
$561$	47808.9	3.59803
$562$	12043.6	0.903964
$563$	−7000.69	−0.524057	−0.262028	−	0.965060i	$-0.584391\pi$
$563$	−7000.69	−0.524057	−0.262028	+	0.965060i	$0.584391\pi$
$564$	3154.45	0.235508
$565$	0	0
$566$	−2737.29	−0.203281
$567$	−11432.1	−0.846742
$568$	−6577.07	−0.485858
$569$	−8659.25	−0.637987	−0.318994	−	0.947757i	$-0.603345\pi$
$569$	−8659.25	−0.637987	−0.318994	+	0.947757i	$0.603345\pi$
$570$	0	0
$571$	25631.9	1.87857	0.939283	−	0.343145i	$-0.111492\pi$
$571$	25631.9	1.87857	0.939283	+	0.343145i	$0.111492\pi$
$572$	3823.72	0.279506
$573$	−27750.5	−2.02320
$574$	−1206.28	−0.0877164
$575$	0	0
$576$	24280.0	1.75637
$577$	−2546.85	−0.183755	−0.0918775	−	0.995770i	$-0.529287\pi$
$577$	−2546.85	−0.183755	−0.0918775	+	0.995770i	$0.529287\pi$
$578$	25059.8	1.80337
$579$	−35468.1	−2.54577
$580$	0	0
$581$	−3453.84	−0.246626
$582$	13146.8	0.936344
$583$	13412.3	0.952800
$584$	−17334.7	−1.22828
$585$	0	0
$586$	10215.8	0.720158
$587$	−17798.8	−1.25150	−0.625752	−	0.780022i	$-0.715208\pi$
$587$	−17798.8	−1.25150	−0.625752	+	0.780022i	$0.715208\pi$
$588$	2119.76	0.148669
$589$	777.800	0.0544121
$590$	0	0
$591$	−14781.6	−1.02882
$592$	606.044	0.0420748
$593$	−3191.29	−0.220996	−0.110498	−	0.993876i	$-0.535245\pi$
$593$	−3191.29	−0.220996	−0.110498	+	0.993876i	$0.535245\pi$
$594$	24246.3	1.67481
$595$	0	0
$596$	1108.04	0.0761531
$597$	34379.9	2.35691
$598$	2067.53	0.141384
$599$	20511.7	1.39914	0.699571	−	0.714563i	$-0.253374\pi$
$599$	20511.7	1.39914	0.699571	+	0.714563i	$0.253374\pi$
$600$	0	0
$601$	22802.2	1.54762	0.773810	−	0.633418i	$-0.218349\pi$
$601$	22802.2	1.54762	0.773810	+	0.633418i	$0.218349\pi$
$602$	3904.12	0.264319
$603$	62189.5	4.19992
$604$	3638.87	0.245139
$605$	0	0
$606$	−10893.6	−0.730236
$607$	−3130.15	−0.209306	−0.104653	−	0.994509i	$-0.533373\pi$
$607$	−3130.15	−0.209306	−0.104653	+	0.994509i	$0.533373\pi$
$608$	1079.49	0.0720054
$609$	−4747.39	−0.315885
$610$	0	0
$611$	1662.02	0.110046
$612$	−39322.9	−2.59727
$613$	12736.1	0.839162	0.419581	−	0.907718i	$-0.362177\pi$
$613$	12736.1	0.839162	0.419581	+	0.907718i	$0.362177\pi$
$614$	−1926.87	−0.126648
$615$	0	0
$616$	−6039.64	−0.395039
$617$	16662.4	1.08720	0.543600	−	0.839345i	$-0.317061\pi$
$617$	16662.4	1.08720	0.543600	+	0.839345i	$0.317061\pi$
$618$	14295.9	0.930526
$619$	−9967.73	−0.647232	−0.323616	−	0.946188i	$-0.604899\pi$
$619$	−9967.73	−0.647232	−0.323616	+	0.946188i	$0.604899\pi$
$620$	0	0
$621$	−17170.7	−1.10956
$622$	4734.68	0.305215
$623$	−6740.84	−0.433493
$624$	1549.93	0.0994341
$625$	0	0
$626$	−4838.31	−0.308910
$627$	2195.74	0.139856
$628$	16065.0	1.02080
$629$	−11522.0	−0.730386
$630$	0	0
$631$	−6243.76	−0.393914	−0.196957	−	0.980412i	$-0.563106\pi$
$631$	−6243.76	−0.393914	−0.196957	+	0.980412i	$0.563106\pi$
$632$	−13831.8	−0.870566
$633$	31520.2	1.97917
$634$	5071.70	0.317702
$635$	0	0
$636$	−15689.9	−0.978214
$637$	1116.86	0.0694689
$638$	4894.59	0.303728
$639$	18025.3	1.11591
$640$	0	0
$641$	−25915.9	−1.59690	−0.798452	−	0.602059i	$-0.794347\pi$
$641$	−25915.9	−1.59690	−0.798452	+	0.602059i	$0.794347\pi$
$642$	−34276.7	−2.10715
$643$	−11833.7	−0.725778	−0.362889	−	0.931832i	$-0.618210\pi$
$643$	−11833.7	−0.725778	−0.362889	+	0.931832i	$0.618210\pi$
$644$	1547.70	0.0947020
$645$	0	0
$646$	1570.87	0.0956735
$647$	−7268.54	−0.441662	−0.220831	−	0.975312i	$-0.570877\pi$
$647$	−7268.54	−0.441662	−0.220831	+	0.975312i	$0.570877\pi$
$648$	−38103.6	−2.30995
$649$	13887.2	0.839940
$650$	0	0
$651$	8339.22	0.502058
$652$	−10046.1	−0.603427
$653$	30455.8	1.82515	0.912577	−	0.408904i	$-0.134089\pi$
$653$	30455.8	1.82515	0.912577	+	0.408904i	$0.134089\pi$
$654$	−1889.48	−0.112973
$655$	0	0
$656$	−660.253	−0.0392966
$657$	47507.7	2.82109
$658$	−949.945	−0.0562807
$659$	16170.2	0.955843	0.477922	−	0.878403i	$-0.341390\pi$
$659$	16170.2	0.955843	0.477922	+	0.878403i	$0.341390\pi$
$660$	0	0
$661$	10331.9	0.607962	0.303981	−	0.952678i	$-0.401684\pi$
$661$	10331.9	0.607962	0.303981	+	0.952678i	$0.401684\pi$
$662$	−9636.93	−0.565786
$663$	−29467.0	−1.72610
$664$	−11511.8	−0.672806
$665$	0	0
$666$	−10114.2	−0.588464
$667$	−3466.23	−0.201219
$668$	−11872.0	−0.687634
$669$	32913.5	1.90211
$670$	0	0
$671$	−25502.3	−1.46722
$672$	11573.8	0.664391
$673$	−18387.1	−1.05315	−0.526576	−	0.850128i	$-0.676525\pi$
$673$	−18387.1	−1.05315	−0.526576	+	0.850128i	$0.676525\pi$
$674$	6804.25	0.388858
$675$	0	0
$676$	7609.63	0.432955
$677$	1795.92	0.101954	0.0509770	−	0.998700i	$-0.483766\pi$
$677$	1795.92	0.101954	0.0509770	+	0.998700i	$0.483766\pi$
$678$	5485.48	0.310721
$679$	5185.24	0.293065
$680$	0	0
$681$	19523.2	1.09858
$682$	−8597.78	−0.482736
$683$	5203.86	0.291537	0.145769	−	0.989319i	$-0.453434\pi$
$683$	5203.86	0.291537	0.145769	+	0.989319i	$0.453434\pi$
$684$	−1806.00	−0.100956
$685$	0	0
$686$	−638.353	−0.0355283
$687$	13230.9	0.734774
$688$	2136.90	0.118414
$689$	−8266.71	−0.457092
$690$	0	0
$691$	−8903.56	−0.490170	−0.245085	−	0.969502i	$-0.578816\pi$
$691$	−8903.56	−0.490170	−0.245085	+	0.969502i	$0.578816\pi$
$692$	−7412.58	−0.407202
$693$	16552.4	0.907320
$694$	3113.88	0.170319
$695$	0	0
$696$	−15823.2	−0.861750
$697$	12552.6	0.682159
$698$	1446.65	0.0784476
$699$	−3576.07	−0.193504
$700$	0	0
$701$	−8343.11	−0.449522	−0.224761	−	0.974414i	$-0.572160\pi$
$701$	−8343.11	−0.449522	−0.224761	+	0.974414i	$0.572160\pi$
$702$	−14944.2	−0.803468
$703$	−529.177	−0.0283902
$704$	−14042.3	−0.751758
$705$	0	0
$706$	−8231.43	−0.438802
$707$	−4296.56	−0.228556
$708$	−16245.4	−0.862343
$709$	−28590.0	−1.51441	−0.757206	−	0.653176i	$-0.773436\pi$
$709$	−28590.0	−1.51441	−0.757206	+	0.653176i	$0.773436\pi$
$710$	0	0
$711$	37907.6	1.99950
$712$	−22467.4	−1.18259
$713$	6088.74	0.319811
$714$	16842.2	0.882776
$715$	0	0
$716$	−4396.46	−0.229474
$717$	53031.0	2.76218
$718$	−1790.67	−0.0930740
$719$	26730.4	1.38647	0.693237	−	0.720710i	$-0.256184\pi$
$719$	26730.4	1.38647	0.693237	+	0.720710i	$0.256184\pi$
$720$	0	0
$721$	5638.45	0.291244
$722$	−12693.0	−0.654275
$723$	−44879.9	−2.30858
$724$	−19770.4	−1.01486
$725$	0	0
$726$	−649.086	−0.0331816
$727$	8903.62	0.454219	0.227109	−	0.973869i	$-0.427073\pi$
$727$	8903.62	0.454219	0.227109	+	0.973869i	$0.427073\pi$
$728$	3722.54	0.189514
$729$	13718.4	0.696969
$730$	0	0
$731$	−40626.5	−2.05557
$732$	29832.8	1.50635
$733$	6022.56	0.303477	0.151738	−	0.988421i	$-0.451513\pi$
$733$	6022.56	0.303477	0.151738	+	0.988421i	$0.451513\pi$
$734$	13553.7	0.681575
$735$	0	0
$736$	8450.45	0.423217
$737$	−35967.1	−1.79765
$738$	11018.9	0.549608
$739$	14078.5	0.700795	0.350398	−	0.936601i	$-0.386046\pi$
$739$	14078.5	0.700795	0.350398	+	0.936601i	$0.386046\pi$
$740$	0	0
$741$	−1353.35	−0.0670937
$742$	4724.92	0.233770
$743$	−31431.4	−1.55196	−0.775980	−	0.630757i	$-0.782744\pi$
$743$	−31431.4	−1.55196	−0.775980	+	0.630757i	$0.782744\pi$
$744$	27794.9	1.36964
$745$	0	0
$746$	2138.83	0.104971
$747$	31549.4	1.54529
$748$	22742.2	1.11168
$749$	−13519.1	−0.659515
$750$	0	0
$751$	−2463.12	−0.119681	−0.0598405	−	0.998208i	$-0.519059\pi$
$751$	−2463.12	−0.119681	−0.0598405	+	0.998208i	$0.519059\pi$
$752$	−519.948	−0.0252135
$753$	−5617.73	−0.271874
$754$	−3016.79	−0.145709
$755$	0	0
$756$	−11186.9	−0.538179
$757$	−37987.2	−1.82387	−0.911935	−	0.410335i	$-0.865412\pi$
$757$	−37987.2	−1.82387	−0.911935	+	0.410335i	$0.865412\pi$
$758$	−19453.3	−0.932156
$759$	17188.6	0.822011
$760$	0	0
$761$	18691.9	0.890384	0.445192	−	0.895435i	$-0.353135\pi$
$761$	18691.9	0.890384	0.445192	+	0.895435i	$0.353135\pi$
$762$	−3540.20	−0.168304
$763$	−745.232	−0.0353594
$764$	−13200.7	−0.625109
$765$	0	0
$766$	25067.5	1.18241
$767$	−8559.40	−0.402949
$768$	41043.8	1.92844
$769$	−27250.5	−1.27786	−0.638932	−	0.769263i	$-0.720624\pi$
$769$	−27250.5	−1.27786	−0.638932	+	0.769263i	$0.720624\pi$
$770$	0	0
$771$	−44498.1	−2.07855
$772$	−16871.8	−0.786568
$773$	1092.67	0.0508417	0.0254209	−	0.999677i	$-0.491907\pi$
$773$	1092.67	0.0508417	0.0254209	+	0.999677i	$0.491907\pi$
$774$	−35662.5	−1.65615
$775$	0	0
$776$	17282.6	0.799495
$777$	−5673.59	−0.261955
$778$	19793.5	0.912124
$779$	576.511	0.0265156
$780$	0	0
$781$	−10424.8	−0.477631
$782$	12297.0	0.562328
$783$	25054.1	1.14350
$784$	−349.400	−0.0159165
$785$	0	0
$786$	−10679.3	−0.484631
$787$	12639.1	0.572474	0.286237	−	0.958159i	$-0.407596\pi$
$787$	12639.1	0.572474	0.286237	+	0.958159i	$0.407596\pi$
$788$	−7031.47	−0.317875
$789$	−42646.3	−1.92427
$790$	0	0
$791$	2163.53	0.0972521
$792$	55169.6	2.47521
$793$	15718.4	0.703878
$794$	−1920.51	−0.0858394
$795$	0	0
$796$	16354.2	0.728216
$797$	−8666.66	−0.385180	−0.192590	−	0.981279i	$-0.561689\pi$
$797$	−8666.66	−0.385180	−0.192590	+	0.981279i	$0.561689\pi$
$798$	773.518	0.0343136
$799$	9885.18	0.437688
$800$	0	0
$801$	61574.8	2.71615
$802$	−12039.3	−0.530077
$803$	−27475.9	−1.20748
$804$	42074.6	1.84559
$805$	0	0
$806$	5299.25	0.231586
$807$	40597.5	1.77088
$808$	−14320.6	−0.623511
$809$	3555.20	0.154504	0.0772522	−	0.997012i	$-0.475385\pi$
$809$	3555.20	0.154504	0.0772522	+	0.997012i	$0.475385\pi$
$810$	0	0
$811$	21940.0	0.949961	0.474981	−	0.879996i	$-0.342455\pi$
$811$	21940.0	0.949961	0.474981	+	0.879996i	$0.342455\pi$
$812$	−2258.29	−0.0975991
$813$	36893.2	1.59152
$814$	5849.51	0.251874
$815$	0	0
$816$	9218.49	0.395480
$817$	−1865.87	−0.0799003
$818$	−16102.5	−0.688275
$819$	−10202.1	−0.435274
$820$	0	0
$821$	−29572.7	−1.25712	−0.628560	−	0.777761i	$-0.716355\pi$
$821$	−29572.7	−1.25712	−0.628560	+	0.777761i	$0.716355\pi$
$822$	37132.5	1.57560
$823$	19314.7	0.818067	0.409034	−	0.912519i	$-0.365866\pi$
$823$	19314.7	0.818067	0.409034	+	0.912519i	$0.365866\pi$
$824$	18793.2	0.794528
$825$	0	0
$826$	4892.21	0.206079
$827$	−21107.8	−0.887535	−0.443768	−	0.896142i	$-0.646358\pi$
$827$	−21107.8	−0.887535	−0.443768	+	0.896142i	$0.646358\pi$
$828$	−14137.6	−0.593378
$829$	10799.8	0.452463	0.226231	−	0.974074i	$-0.427359\pi$
$829$	10799.8	0.452463	0.226231	+	0.974074i	$0.427359\pi$
$830$	0	0
$831$	78267.7	3.26724
$832$	8654.96	0.360645
$833$	6642.73	0.276299
$834$	−14810.1	−0.614906
$835$	0	0
$836$	1044.49	0.0432112
$837$	−44009.8	−1.81744
$838$	13592.3	0.560307
$839$	−11829.3	−0.486761	−0.243381	−	0.969931i	$-0.578256\pi$
$839$	−11829.3	−0.486761	−0.243381	+	0.969931i	$0.578256\pi$
$840$	0	0
$841$	−19331.3	−0.792626
$842$	−21588.2	−0.883587
$843$	−61712.3	−2.52133
$844$	14993.9	0.611506
$845$	0	0
$846$	8677.35	0.352640
$847$	−256.007	−0.0103855
$848$	2586.16	0.104728
$849$	14026.1	0.566989
$850$	0	0
$851$	−4142.48	−0.166865
$852$	12195.1	0.490371
$853$	3426.91	0.137556	0.0687779	−	0.997632i	$-0.478090\pi$
$853$	3426.91	0.137556	0.0687779	+	0.997632i	$0.478090\pi$
$854$	−8983.97	−0.359983
$855$	0	0
$856$	−45059.6	−1.79919
$857$	−7308.16	−0.291298	−0.145649	−	0.989336i	$-0.546527\pi$
$857$	−7308.16	−0.291298	−0.145649	+	0.989336i	$0.546527\pi$
$858$	14959.9	0.595246
$859$	−22539.8	−0.895282	−0.447641	−	0.894213i	$-0.647736\pi$
$859$	−22539.8	−0.895282	−0.447641	+	0.894213i	$0.647736\pi$
$860$	0	0
$861$	6181.08	0.244658
$862$	−2804.41	−0.110811
$863$	−1690.95	−0.0666983	−0.0333491	−	0.999444i	$-0.510617\pi$
$863$	−1690.95	−0.0666983	−0.0333491	+	0.999444i	$0.510617\pi$
$864$	−61080.3	−2.40509
$865$	0	0
$866$	−3930.66	−0.154237
$867$	−128408.	−5.02996
$868$	3966.89	0.155121
$869$	−21923.7	−0.855825
$870$	0	0
$871$	22168.4	0.862395
$872$	−2483.89	−0.0964621
$873$	−47365.0	−1.83627
$874$	564.771	0.0218577
$875$	0	0
$876$	32141.6	1.23968
$877$	−33021.5	−1.27145	−0.635723	−	0.771917i	$-0.719298\pi$
$877$	−33021.5	−1.27145	−0.635723	+	0.771917i	$0.719298\pi$
$878$	−6500.54	−0.249866
$879$	−52346.8	−2.00866
$880$	0	0
$881$	−29413.5	−1.12482	−0.562410	−	0.826859i	$-0.690126\pi$
$881$	−29413.5	−1.12482	−0.562410	+	0.826859i	$0.690126\pi$
$882$	5831.09	0.222611
$883$	−22413.5	−0.854218	−0.427109	−	0.904200i	$-0.640468\pi$
$883$	−22413.5	−0.854218	−0.427109	+	0.904200i	$0.640468\pi$
$884$	−14017.2	−0.533314
$885$	0	0
$886$	−1813.95	−0.0687821
$887$	49069.5	1.85749	0.928744	−	0.370723i	$-0.120890\pi$
$887$	49069.5	1.85749	0.928744	+	0.370723i	$0.120890\pi$
$888$	−18910.3	−0.714626
$889$	−1396.29	−0.0526773
$890$	0	0
$891$	−60395.3	−2.27084
$892$	15656.7	0.587695
$893$	454.001	0.0170130
$894$	4335.10	0.162178
$895$	0	0
$896$	4762.41	0.177568
$897$	−10594.2	−0.394348
$898$	11378.0	0.422816
$899$	−8884.22	−0.329594
$900$	0	0
$901$	−49167.8	−1.81800
$902$	−6372.73	−0.235243
$903$	−20005.0	−0.737237
$904$	7211.13	0.265308
$905$	0	0
$906$	14236.7	0.522055
$907$	42854.4	1.56886	0.784431	−	0.620216i	$-0.212955\pi$
$907$	42854.4	1.56886	0.784431	+	0.620216i	$0.212955\pi$
$908$	9287.02	0.339428
$909$	39247.3	1.43207
$910$	0	0
$911$	−48846.7	−1.77647	−0.888234	−	0.459391i	$-0.848068\pi$
$911$	−48846.7	−1.77647	−0.888234	+	0.459391i	$0.848068\pi$
$912$	423.382	0.0153723
$913$	−18246.5	−0.661414
$914$	2891.21	0.104631
$915$	0	0
$916$	6293.81	0.227023
$917$	−4212.05	−0.151684
$918$	−88883.6	−3.19564
$919$	−22400.9	−0.804067	−0.402033	−	0.915625i	$-0.631696\pi$
$919$	−22400.9	−0.804067	−0.402033	+	0.915625i	$0.631696\pi$
$920$	0	0
$921$	9873.43	0.353247
$922$	17530.1	0.626164
$923$	6425.36	0.229137
$924$	11198.6	0.398708
$925$	0	0
$926$	21325.0	0.756785
$927$	−51504.9	−1.82486
$928$	−12330.2	−0.436164
$929$	2298.05	0.0811587	0.0405794	−	0.999176i	$-0.487080\pi$
$929$	2298.05	0.0811587	0.0405794	+	0.999176i	$0.487080\pi$
$930$	0	0
$931$	305.084	0.0107398
$932$	−1701.10	−0.0597870
$933$	−24260.9	−0.851303
$934$	−3947.51	−0.138294
$935$	0	0
$936$	−34003.9	−1.18745
$937$	47163.3	1.64435	0.822176	−	0.569233i	$-0.192760\pi$
$937$	47163.3	1.64435	0.822176	+	0.569233i	$0.192760\pi$
$938$	−12670.5	−0.441053
$939$	24791.9	0.861611
$940$	0	0
$941$	40457.0	1.40155	0.700776	−	0.713382i	$-0.252837\pi$
$941$	40457.0	1.40155	0.700776	+	0.713382i	$0.252837\pi$
$942$	62852.4	2.17393
$943$	4513.01	0.155847
$944$	2677.73	0.0923227
$945$	0	0
$946$	20625.3	0.708865
$947$	6363.14	0.218347	0.109173	−	0.994023i	$-0.465180\pi$
$947$	6363.14	0.218347	0.109173	+	0.994023i	$0.465180\pi$
$948$	25646.6	0.878652
$949$	16934.8	0.579270
$950$	0	0
$951$	−25987.8	−0.886133
$952$	22140.5	0.753757
$953$	48268.8	1.64069	0.820346	−	0.571867i	$-0.193781\pi$
$953$	48268.8	1.64069	0.820346	+	0.571867i	$0.193781\pi$
$954$	−43160.2	−1.46474
$955$	0	0
$956$	25226.4	0.853430
$957$	−25080.3	−0.847158
$958$	32124.7	1.08340
$959$	14645.4	0.493145
$960$	0	0
$961$	−14185.1	−0.476153
$962$	−3605.35	−0.120833
$963$	123491.	4.13235
$964$	−21349.0	−0.713282
$965$	0	0
$966$	6055.22	0.201681
$967$	26795.3	0.891084	0.445542	−	0.895261i	$-0.353011\pi$
$967$	26795.3	0.891084	0.445542	+	0.895261i	$0.353011\pi$
$968$	−853.280	−0.0283321
$969$	−8049.27	−0.266852
$970$	0	0
$971$	21583.8	0.713345	0.356672	−	0.934230i	$-0.383911\pi$
$971$	21583.8	0.713345	0.356672	+	0.934230i	$0.383911\pi$
$972$	27501.4	0.907519
$973$	−5841.26	−0.192459
$974$	34461.3	1.13369
$975$	0	0
$976$	−4917.34	−0.161271
$977$	−51106.3	−1.67353	−0.836763	−	0.547565i	$-0.815555\pi$
$977$	−51106.3	−1.67353	−0.836763	+	0.547565i	$0.815555\pi$
$978$	−39304.1	−1.28508
$979$	−35611.6	−1.16256
$980$	0	0
$981$	6807.39	0.221553
$982$	14730.1	0.478672
$983$	41585.7	1.34932	0.674658	−	0.738131i	$-0.264291\pi$
$983$	41585.7	1.34932	0.674658	+	0.738131i	$0.264291\pi$
$984$	20601.8	0.667439
$985$	0	0
$986$	−17942.9	−0.579531
$987$	4867.59	0.156978
$988$	−643.775	−0.0207300
$989$	−14606.3	−0.469620
$990$	0	0
$991$	−29082.5	−0.932227	−0.466114	−	0.884725i	$-0.654346\pi$
$991$	−29082.5	−0.932227	−0.466114	+	0.884725i	$0.654346\pi$
$992$	21659.2	0.693226
$993$	49380.4	1.57809
$994$	−3672.48	−0.117187
$995$	0	0
$996$	21344.9	0.679055
$997$	−34503.0	−1.09601	−0.548004	−	0.836476i	$-0.684612\pi$
$997$	−34503.0	−1.09601	−0.548004	+	0.836476i	$0.684612\pi$
$998$	4445.98	0.141017
$999$	29942.1	0.948274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.a.f.1.2		3
3.2	odd	2		1575.4.a.ba.1.2		3
5.2	odd	4		175.4.b.e.99.4		6
5.3	odd	4		175.4.b.e.99.3		6
5.4	even	2		35.4.a.c.1.2	✓	3
7.6	odd	2		1225.4.a.y.1.2		3
15.14	odd	2		315.4.a.p.1.2		3
20.19	odd	2		560.4.a.u.1.1		3
35.4	even	6		245.4.e.m.226.2		6
35.9	even	6		245.4.e.m.116.2		6
35.19	odd	6		245.4.e.n.116.2		6
35.24	odd	6		245.4.e.n.226.2		6
35.34	odd	2		245.4.a.l.1.2		3
40.19	odd	2		2240.4.a.bv.1.3		3
40.29	even	2		2240.4.a.bt.1.1		3
105.104	even	2		2205.4.a.bm.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.2	✓	3	5.4	even	2
175.4.a.f.1.2		3	1.1	even	1	trivial
175.4.b.e.99.3		6	5.3	odd	4
175.4.b.e.99.4		6	5.2	odd	4
245.4.a.l.1.2		3	35.34	odd	2
245.4.e.m.116.2		6	35.9	even	6
245.4.e.m.226.2		6	35.4	even	6
245.4.e.n.116.2		6	35.19	odd	6
245.4.e.n.226.2		6	35.24	odd	6
315.4.a.p.1.2		3	15.14	odd	2
560.4.a.u.1.1		3	20.19	odd	2
1225.4.a.y.1.2		3	7.6	odd	2
1575.4.a.ba.1.2		3	3.2	odd	2
2205.4.a.bm.1.2		3	105.104	even	2
2240.4.a.bt.1.1		3	40.29	even	2
2240.4.a.bv.1.3		3	40.19	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)

\(f(q)\)	\(=\)	\(q+1.86109 q^{2} -9.53636 q^{3} -4.53636 q^{4} -17.7480 q^{6} -7.00000 q^{7} -23.3312 q^{8} +63.9421 q^{9} +O(q^{10})\)	\(q+1.86109 q^{2} -9.53636 q^{3} -4.53636 q^{4} -17.7480 q^{6} -7.00000 q^{7} -23.3312 q^{8} +63.9421 q^{9} -36.9807 q^{11} +43.2603 q^{12} +22.7931 q^{13} -13.0276 q^{14} -7.13061 q^{16} +135.566 q^{17} +119.002 q^{18} +6.22620 q^{19} +66.7545 q^{21} -68.8243 q^{22} +48.7397 q^{23} +222.495 q^{24} +42.4199 q^{26} -352.293 q^{27} +31.7545 q^{28} -71.1172 q^{29} +124.924 q^{31} +173.379 q^{32} +352.661 q^{33} +252.300 q^{34} -290.064 q^{36} -84.9919 q^{37} +11.5875 q^{38} -217.363 q^{39} +92.5942 q^{41} +124.236 q^{42} -299.680 q^{43} +167.758 q^{44} +90.7088 q^{46} +72.9178 q^{47} +68.0000 q^{48} +49.0000 q^{49} -1292.81 q^{51} -103.398 q^{52} -362.685 q^{53} -655.648 q^{54} +163.319 q^{56} -59.3753 q^{57} -132.355 q^{58} -375.526 q^{59} +689.610 q^{61} +232.494 q^{62} -447.595 q^{63} +379.719 q^{64} +656.333 q^{66} +972.591 q^{67} -614.976 q^{68} -464.799 q^{69} +281.900 q^{71} -1491.85 q^{72} +742.980 q^{73} -158.177 q^{74} -28.2443 q^{76} +258.865 q^{77} -404.532 q^{78} +592.843 q^{79} +1633.16 q^{81} +172.326 q^{82} +493.406 q^{83} -302.822 q^{84} -557.731 q^{86} +678.199 q^{87} +862.806 q^{88} +962.977 q^{89} -159.552 q^{91} -221.101 q^{92} -1191.32 q^{93} +135.706 q^{94} -1653.41 q^{96} -740.748 q^{97} +91.1932 q^{98} -2364.62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9	\( 3 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 24 q^{6} - 21 q^{7} + 15 q^{8} + 81 q^{9} - 74 q^{11} + 152 q^{12} - 44 q^{13} - 21 q^{14} - 79 q^{16} + 52 q^{17} + 411 q^{18} + 168 q^{19} + 14 q^{21} - 184 q^{22} + 124 q^{23} + 420 q^{24} - 446 q^{26} - 170 q^{27} - 91 q^{28} + 332 q^{29} + 320 q^{31} + 183 q^{32} + 106 q^{33} + 582 q^{34} + 181 q^{36} + 54 q^{37} + 460 q^{38} - 982 q^{39} + 362 q^{41} - 168 q^{42} + 16 q^{43} - 264 q^{44} - 336 q^{46} + 730 q^{47} + 204 q^{48} + 147 q^{49} - 1178 q^{51} - 1202 q^{52} - 110 q^{53} - 180 q^{54} - 105 q^{56} + 956 q^{57} - 450 q^{58} - 180 q^{59} + 1222 q^{61} - 464 q^{62} - 567 q^{63} - 391 q^{64} - 532 q^{66} - 204 q^{67} - 918 q^{68} - 716 q^{69} - 136 q^{71} - 765 q^{72} - 310 q^{73} + 502 q^{74} + 1796 q^{76} + 518 q^{77} - 3788 q^{78} - 1034 q^{79} + 2283 q^{81} + 6 q^{82} + 1660 q^{83} - 1064 q^{84} + 764 q^{86} + 1574 q^{87} + 20 q^{88} + 242 q^{89} + 308 q^{91} - 96 q^{92} - 1376 q^{93} - 1108 q^{94} - 3156 q^{96} - 100 q^{97} + 147 q^{98} - 3488 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 24 * q^6 - 21 * q^7 + 15 * q^8 + 81 * q^9 - 74 * q^11 + 152 * q^12 - 44 * q^13 - 21 * q^14 - 79 * q^16 + 52 * q^17 + 411 * q^18 + 168 * q^19 + 14 * q^21 - 184 * q^22 + 124 * q^23 + 420 * q^24 - 446 * q^26 - 170 * q^27 - 91 * q^28 + 332 * q^29 + 320 * q^31 + 183 * q^32 + 106 * q^33 + 582 * q^34 + 181 * q^36 + 54 * q^37 + 460 * q^38 - 982 * q^39 + 362 * q^41 - 168 * q^42 + 16 * q^43 - 264 * q^44 - 336 * q^46 + 730 * q^47 + 204 * q^48 + 147 * q^49 - 1178 * q^51 - 1202 * q^52 - 110 * q^53 - 180 * q^54 - 105 * q^56 + 956 * q^57 - 450 * q^58 - 180 * q^59 + 1222 * q^61 - 464 * q^62 - 567 * q^63 - 391 * q^64 - 532 * q^66 - 204 * q^67 - 918 * q^68 - 716 * q^69 - 136 * q^71 - 765 * q^72 - 310 * q^73 + 502 * q^74 + 1796 * q^76 + 518 * q^77 - 3788 * q^78 - 1034 * q^79 + 2283 * q^81 + 6 * q^82 + 1660 * q^83 - 1064 * q^84 + 764 * q^86 + 1574 * q^87 + 20 * q^88 + 242 * q^89 + 308 * q^91 - 96 * q^92 - 1376 * q^93 - 1108 * q^94 - 3156 * q^96 - 100 * q^97 + 147 * q^98 - 3488 * q^99

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