LMFDB - Embedded newform 575.4.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,4,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, 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("575.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	575.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:	$33.9260982533$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{109}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 27 $ x^2 - x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.72015$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00000 q^{2} +6.72015 q^{3} +1.00000 q^{4} +20.1605 q^{6} -26.6008 q^{7} -21.0000 q^{8} +18.1605 q^{9} +O(q^{10})$	\(q+3.00000 q^{2} +6.72015 q^{3} +1.00000 q^{4} +20.1605 q^{6} -26.6008 q^{7} -21.0000 q^{8} +18.1605 q^{9} -39.6008 q^{11} +6.72015 q^{12} +23.1605 q^{13} -79.8023 q^{14} -71.0000 q^{16} +2.95893 q^{17} +54.4814 q^{18} +32.3620 q^{19} -178.761 q^{21} -118.802 q^{22} +23.0000 q^{23} -141.123 q^{24} +69.4814 q^{26} -59.4031 q^{27} -26.6008 q^{28} -162.798 q^{29} -241.243 q^{31} -45.0000 q^{32} -266.123 q^{33} +8.87678 q^{34} +18.1605 q^{36} +180.164 q^{37} +97.0860 q^{38} +155.642 q^{39} -353.922 q^{41} -536.284 q^{42} -365.761 q^{43} -39.6008 q^{44} +69.0000 q^{46} +195.291 q^{47} -477.131 q^{48} +364.601 q^{49} +19.8844 q^{51} +23.1605 q^{52} +461.687 q^{53} -178.209 q^{54} +558.616 q^{56} +217.478 q^{57} -488.395 q^{58} -290.888 q^{59} -301.049 q^{61} -723.728 q^{62} -483.082 q^{63} +433.000 q^{64} -798.370 q^{66} +366.732 q^{67} +2.95893 q^{68} +154.564 q^{69} -8.14513 q^{71} -381.370 q^{72} -360.650 q^{73} +540.493 q^{74} +32.3620 q^{76} +1053.41 q^{77} +466.926 q^{78} +1243.87 q^{79} -889.530 q^{81} -1061.77 q^{82} +1481.70 q^{83} -178.761 q^{84} -1097.28 q^{86} -1094.03 q^{87} +831.616 q^{88} +829.628 q^{89} -616.086 q^{91} +23.0000 q^{92} -1621.19 q^{93} +585.874 q^{94} -302.407 q^{96} +390.191 q^{97} +1093.80 q^{98} -719.168 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} + 3 q^{3} + 2 q^{4} + 9 q^{6} - q^{7} - 42 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q + 6 * q^2 + 3 * q^3 + 2 * q^4 + 9 * q^6 - q^7 - 42 * q^8 + 5 * q^9	$ 2 q + 6 q^{2} + 3 q^{3} + 2 q^{4} + 9 q^{6} - q^{7} - 42 q^{8} + 5 q^{9} - 27 q^{11} + 3 q^{12} + 15 q^{13} - 3 q^{14} - 142 q^{16} + 79 q^{17} + 15 q^{18} - 71 q^{19} - 274 q^{21} - 81 q^{22} + 46 q^{23} - 63 q^{24} + 45 q^{26} + 90 q^{27} - q^{28} - 430 q^{29} - 305 q^{31} - 90 q^{32} - 313 q^{33} + 237 q^{34} + 5 q^{36} + 68 q^{37} - 213 q^{38} + 186 q^{39} - 593 q^{41} - 822 q^{42} - 648 q^{43} - 27 q^{44} + 138 q^{46} - 382 q^{47} - 213 q^{48} + 677 q^{49} - 263 q^{51} + 15 q^{52} + 464 q^{53} + 270 q^{54} + 21 q^{56} + 602 q^{57} - 1290 q^{58} - 18 q^{59} - 7 q^{61} - 915 q^{62} - 820 q^{63} + 866 q^{64} - 939 q^{66} - 60 q^{67} + 79 q^{68} + 69 q^{69} - 1029 q^{71} - 105 q^{72} - 74 q^{73} + 204 q^{74} - 71 q^{76} + 1376 q^{77} + 558 q^{78} + 692 q^{79} - 1090 q^{81} - 1779 q^{82} + 1460 q^{83} - 274 q^{84} - 1944 q^{86} - 100 q^{87} + 567 q^{88} - 220 q^{89} - 825 q^{91} + 46 q^{92} - 1384 q^{93} - 1146 q^{94} - 135 q^{96} - 1339 q^{97} + 2031 q^{98} - 885 q^{99}+O(q^{100}) $ 2 * q + 6 * q^2 + 3 * q^3 + 2 * q^4 + 9 * q^6 - q^7 - 42 * q^8 + 5 * q^9 - 27 * q^11 + 3 * q^12 + 15 * q^13 - 3 * q^14 - 142 * q^16 + 79 * q^17 + 15 * q^18 - 71 * q^19 - 274 * q^21 - 81 * q^22 + 46 * q^23 - 63 * q^24 + 45 * q^26 + 90 * q^27 - q^28 - 430 * q^29 - 305 * q^31 - 90 * q^32 - 313 * q^33 + 237 * q^34 + 5 * q^36 + 68 * q^37 - 213 * q^38 + 186 * q^39 - 593 * q^41 - 822 * q^42 - 648 * q^43 - 27 * q^44 + 138 * q^46 - 382 * q^47 - 213 * q^48 + 677 * q^49 - 263 * q^51 + 15 * q^52 + 464 * q^53 + 270 * q^54 + 21 * q^56 + 602 * q^57 - 1290 * q^58 - 18 * q^59 - 7 * q^61 - 915 * q^62 - 820 * q^63 + 866 * q^64 - 939 * q^66 - 60 * q^67 + 79 * q^68 + 69 * q^69 - 1029 * q^71 - 105 * q^72 - 74 * q^73 + 204 * q^74 - 71 * q^76 + 1376 * q^77 + 558 * q^78 + 692 * q^79 - 1090 * q^81 - 1779 * q^82 + 1460 * q^83 - 274 * q^84 - 1944 * q^86 - 100 * q^87 + 567 * q^88 - 220 * q^89 - 825 * q^91 + 46 * q^92 - 1384 * q^93 - 1146 * q^94 - 135 * q^96 - 1339 * q^97 + 2031 * q^98 - 885 * 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 $

$2$	3.00000	1.06066	0.530330	−	0.847791i	$-0.322068\pi$
$2$	3.00000	1.06066	0.530330	+	0.847791i	$0.322068\pi$
$3$	6.72015	1.29329	0.646647	−	0.762789i	$-0.276171\pi$
$3$	6.72015	1.29329	0.646647	+	0.762789i	$0.276171\pi$
$4$	1.00000	0.125000
$5$	0	0
$5$	0	0
$6$	20.1605	1.37175
$7$	−26.6008	−1.43631	−0.718153	−	0.695885i	$-0.755012\pi$
$7$	−26.6008	−1.43631	−0.718153	+	0.695885i	$0.755012\pi$
$8$	−21.0000	−0.928078
$9$	18.1605	0.672610
$10$	0	0
$11$	−39.6008	−1.08546	−0.542731	−	0.839907i	$-0.682610\pi$
$11$	−39.6008	−1.08546	−0.542731	+	0.839907i	$0.682610\pi$
$12$	6.72015	0.161662
$13$	23.1605	0.494120	0.247060	−	0.969000i	$-0.420536\pi$
$13$	23.1605	0.494120	0.247060	+	0.969000i	$0.420536\pi$
$14$	−79.8023	−1.52343
$15$	0	0
$16$	−71.0000	−1.10938
$17$	2.95893	0.0422144	0.0211072	−	0.999777i	$-0.493281\pi$
$17$	2.95893	0.0422144	0.0211072	+	0.999777i	$0.493281\pi$
$18$	54.4814	0.713410
$19$	32.3620	0.390755	0.195378	−	0.980728i	$-0.437407\pi$
$19$	32.3620	0.390755	0.195378	+	0.980728i	$0.437407\pi$
$20$	0	0
$21$	−178.761	−1.85757
$22$	−118.802	−1.15131
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−141.123	−1.20028
$25$	0	0
$26$	69.4814	0.524093
$27$	−59.4031	−0.423412
$28$	−26.6008	−0.179538
$29$	−162.798	−1.04245	−0.521223	−	0.853421i	$-0.674524\pi$
$29$	−162.798	−1.04245	−0.521223	+	0.853421i	$0.674524\pi$
$30$	0	0
$31$	−241.243	−1.39769	−0.698846	−	0.715272i	$-0.746303\pi$
$31$	−241.243	−1.39769	−0.698846	+	0.715272i	$0.746303\pi$
$32$	−45.0000	−0.248592
$33$	−266.123	−1.40382
$34$	8.87678	0.0447752
$35$	0	0
$36$	18.1605	0.0840762
$37$	180.164	0.800509	0.400254	−	0.916404i	$-0.368922\pi$
$37$	180.164	0.800509	0.400254	+	0.916404i	$0.368922\pi$
$38$	97.0860	0.414459
$39$	155.642	0.639042
$40$	0	0
$41$	−353.922	−1.34813	−0.674064	−	0.738673i	$-0.735453\pi$
$41$	−353.922	−1.34813	−0.674064	+	0.738673i	$0.735453\pi$
$42$	−536.284	−1.97025
$43$	−365.761	−1.29716	−0.648582	−	0.761145i	$-0.724638\pi$
$43$	−365.761	−1.29716	−0.648582	+	0.761145i	$0.724638\pi$
$44$	−39.6008	−0.135683
$45$	0	0
$46$	69.0000	0.221163
$47$	195.291	0.606089	0.303044	−	0.952976i	$-0.401997\pi$
$47$	195.291	0.606089	0.303044	+	0.952976i	$0.401997\pi$
$48$	−477.131	−1.43475
$49$	364.601	1.06298
$50$	0	0
$51$	19.8844	0.0545957
$52$	23.1605	0.0617650
$53$	461.687	1.19656	0.598279	−	0.801288i	$-0.295852\pi$
$53$	461.687	1.19656	0.598279	+	0.801288i	$0.295852\pi$
$54$	−178.209	−0.449096
$55$	0	0
$56$	558.616	1.33300
$57$	217.478	0.505361
$58$	−488.395	−1.10568
$59$	−290.888	−0.641872	−0.320936	−	0.947101i	$-0.603997\pi$
$59$	−290.888	−0.641872	−0.320936	+	0.947101i	$0.603997\pi$
$60$	0	0
$61$	−301.049	−0.631891	−0.315945	−	0.948777i	$-0.602322\pi$
$61$	−301.049	−0.631891	−0.315945	+	0.948777i	$0.602322\pi$
$62$	−723.728	−1.48248
$63$	−483.082	−0.966073
$64$	433.000	0.845703
$65$	0	0
$66$	−798.370	−1.48898
$67$	366.732	0.668707	0.334354	−	0.942448i	$-0.391482\pi$
$67$	366.732	0.668707	0.334354	+	0.942448i	$0.391482\pi$
$68$	2.95893	0.00527680
$69$	154.564	0.269670
$70$	0	0
$71$	−8.14513	−0.0136148	−0.00680739	−	0.999977i	$-0.502167\pi$
$71$	−8.14513	−0.0136148	−0.00680739	+	0.999977i	$0.502167\pi$
$72$	−381.370	−0.624234
$73$	−360.650	−0.578231	−0.289115	−	0.957294i	$-0.593361\pi$
$73$	−360.650	−0.578231	−0.289115	+	0.957294i	$0.593361\pi$
$74$	540.493	0.849068
$75$	0	0
$76$	32.3620	0.0488444
$77$	1053.41	1.55906
$78$	466.926	0.677806
$79$	1243.87	1.77147	0.885734	−	0.464194i	$-0.153656\pi$
$79$	1243.87	1.77147	0.885734	+	0.464194i	$0.153656\pi$
$80$	0	0
$81$	−889.530	−1.22021
$82$	−1061.77	−1.42991
$83$	1481.70	1.95949	0.979747	−	0.200241i	$-0.0641727\pi$
$83$	1481.70	1.95949	0.979747	+	0.200241i	$0.0641727\pi$
$84$	−178.761	−0.232196
$85$	0	0
$86$	−1097.28	−1.37585
$87$	−1094.03	−1.34819
$88$	831.616	1.00739
$89$	829.628	0.988094	0.494047	−	0.869435i	$-0.335517\pi$
$89$	829.628	0.988094	0.494047	+	0.869435i	$0.335517\pi$
$90$	0	0
$91$	−616.086	−0.709707
$92$	23.0000	0.0260643
$93$	−1621.19	−1.80763
$94$	585.874	0.642854
$95$	0	0
$96$	−302.407	−0.321503
$97$	390.191	0.408432	0.204216	−	0.978926i	$-0.434536\pi$
$97$	390.191	0.408432	0.204216	+	0.978926i	$0.434536\pi$
$98$	1093.80	1.12746
$99$	−719.168	−0.730092
$100$	0	0
$101$	−1461.87	−1.44022	−0.720108	−	0.693862i	$-0.755908\pi$
$101$	−1461.87	−1.44022	−0.720108	+	0.693862i	$0.755908\pi$
$102$	59.6533	0.0579075
$103$	−317.534	−0.303763	−0.151881	−	0.988399i	$-0.548533\pi$
$103$	−317.534	−0.303763	−0.151881	+	0.988399i	$0.548533\pi$
$104$	−486.370	−0.458581
$105$	0	0
$106$	1385.06	1.26914
$107$	47.6199	0.0430242	0.0215121	−	0.999769i	$-0.493152\pi$
$107$	47.6199	0.0430242	0.0215121	+	0.999769i	$0.493152\pi$
$108$	−59.4031	−0.0529265
$109$	−1437.21	−1.26293	−0.631465	−	0.775404i	$-0.717546\pi$
$109$	−1437.21	−1.26293	−0.631465	+	0.775404i	$0.717546\pi$
$110$	0	0
$111$	1210.73	1.03529
$112$	1888.65	1.59340
$113$	1575.76	1.31182	0.655908	−	0.754841i	$-0.272286\pi$
$113$	1575.76	1.31182	0.655908	+	0.754841i	$0.272286\pi$
$114$	652.433	0.536017
$115$	0	0
$116$	−162.798	−0.130306
$117$	420.605	0.332350
$118$	−872.665	−0.680808
$119$	−78.7097	−0.0606329
$120$	0	0
$121$	237.221	0.178227
$122$	−903.146	−0.670221
$123$	−2378.41	−1.74353
$124$	−241.243	−0.174711
$125$	0	0
$126$	−1449.25	−1.02468
$127$	−2202.29	−1.53875	−0.769377	−	0.638795i	$-0.779433\pi$
$127$	−2202.29	−1.53875	−0.769377	+	0.638795i	$0.779433\pi$
$128$	1659.00	1.14560
$129$	−2457.97	−1.67761
$130$	0	0
$131$	2067.76	1.37909	0.689546	−	0.724242i	$-0.257810\pi$
$131$	2067.76	1.37909	0.689546	+	0.724242i	$0.257810\pi$
$132$	−266.123	−0.175478
$133$	−860.854	−0.561244
$134$	1100.19	0.709271
$135$	0	0
$136$	−62.1375	−0.0391783
$137$	−2225.67	−1.38797	−0.693984	−	0.719990i	$-0.744146\pi$
$137$	−2225.67	−1.38797	−0.693984	+	0.719990i	$0.744146\pi$
$138$	463.691	0.286029
$139$	2803.89	1.71096	0.855478	−	0.517840i	$-0.173264\pi$
$139$	2803.89	1.71096	0.855478	+	0.517840i	$0.173264\pi$
$140$	0	0
$141$	1312.39	0.783851
$142$	−24.4354	−0.0144407
$143$	−917.172	−0.536348
$144$	−1289.39	−0.746176
$145$	0	0
$146$	−1081.95	−0.613306
$147$	2450.17	1.37474
$148$	180.164	0.100064
$149$	−1322.84	−0.727324	−0.363662	−	0.931531i	$-0.618474\pi$
$149$	−1322.84	−0.727324	−0.363662	+	0.931531i	$0.618474\pi$
$150$	0	0
$151$	2052.35	1.10608	0.553039	−	0.833156i	$-0.313468\pi$
$151$	2052.35	1.10608	0.553039	+	0.833156i	$0.313468\pi$
$152$	−679.602	−0.362651
$153$	53.7355	0.0283938
$154$	3160.23	1.65363
$155$	0	0
$156$	155.642	0.0798803
$157$	381.171	0.193763	0.0968814	−	0.995296i	$-0.469113\pi$
$157$	381.171	0.193763	0.0968814	+	0.995296i	$0.469113\pi$
$158$	3731.60	1.87892
$159$	3102.61	1.54750
$160$	0	0
$161$	−611.818	−0.299491
$162$	−2668.59	−1.29422
$163$	2358.16	1.13316	0.566581	−	0.824006i	$-0.308266\pi$
$163$	2358.16	1.13316	0.566581	+	0.824006i	$0.308266\pi$
$164$	−353.922	−0.168516
$165$	0	0
$166$	4445.11	2.07836
$167$	144.267	0.0668487	0.0334244	−	0.999441i	$-0.489359\pi$
$167$	144.267	0.0668487	0.0334244	+	0.999441i	$0.489359\pi$
$168$	3753.99	1.72397
$169$	−1660.59	−0.755846
$170$	0	0
$171$	587.709	0.262826
$172$	−365.761	−0.162146
$173$	−3210.33	−1.41085	−0.705424	−	0.708786i	$-0.749243\pi$
$173$	−3210.33	−1.41085	−0.705424	+	0.708786i	$0.749243\pi$
$174$	−3282.09	−1.42997
$175$	0	0
$176$	2811.65	1.20418
$177$	−1954.81	−0.830129
$178$	2488.88	1.04803
$179$	−4070.43	−1.69965	−0.849827	−	0.527062i	$-0.823294\pi$
$179$	−4070.43	−1.69965	−0.849827	+	0.527062i	$0.823294\pi$
$180$	0	0
$181$	−4123.13	−1.69320	−0.846602	−	0.532226i	$-0.821356\pi$
$181$	−4123.13	−1.69320	−0.846602	+	0.532226i	$0.821356\pi$
$182$	−1848.26	−0.752758
$183$	−2023.09	−0.817221
$184$	−483.000	−0.193518
$185$	0	0
$186$	−4863.56	−1.91728
$187$	−117.176	−0.0458221
$188$	195.291	0.0757611
$189$	1580.17	0.608149
$190$	0	0
$191$	−1827.02	−0.692140	−0.346070	−	0.938209i	$-0.612484\pi$
$191$	−1827.02	−0.692140	−0.346070	+	0.938209i	$0.612484\pi$
$192$	2909.83	1.09374
$193$	−2358.93	−0.879792	−0.439896	−	0.898049i	$-0.644985\pi$
$193$	−2358.93	−0.879792	−0.439896	+	0.898049i	$0.644985\pi$
$194$	1170.57	0.433208
$195$	0	0
$196$	364.601	0.132872
$197$	−1236.21	−0.447089	−0.223545	−	0.974694i	$-0.571763\pi$
$197$	−1236.21	−0.447089	−0.223545	+	0.974694i	$0.571763\pi$
$198$	−2157.50	−0.774380
$199$	−30.6572	−0.0109207	−0.00546037	−	0.999985i	$-0.501738\pi$
$199$	−30.6572	−0.0109207	−0.00546037	+	0.999985i	$0.501738\pi$
$200$	0	0
$201$	2464.49	0.864835
$202$	−4385.62	−1.52758
$203$	4330.56	1.49727
$204$	19.8844	0.00682446
$205$	0	0
$206$	−952.602	−0.322189
$207$	417.691	0.140249
$208$	−1644.39	−0.548164
$209$	−1281.56	−0.424150
$210$	0	0
$211$	−416.808	−0.135992	−0.0679959	−	0.997686i	$-0.521660\pi$
$211$	−416.808	−0.135992	−0.0679959	+	0.997686i	$0.521660\pi$
$212$	461.687	0.149570
$213$	−54.7366	−0.0176079
$214$	142.860	0.0456341
$215$	0	0
$216$	1247.46	0.392959
$217$	6417.24	2.00751
$218$	−4311.62	−1.33954
$219$	−2423.62	−0.747822
$220$	0	0
$221$	68.5301	0.0208590
$222$	3632.19	1.09809
$223$	2604.60	0.782139	0.391069	−	0.920361i	$-0.372105\pi$
$223$	2604.60	0.782139	0.391069	+	0.920361i	$0.372105\pi$
$224$	1197.03	0.357055
$225$	0	0
$226$	4727.28	1.39139
$227$	−5092.32	−1.48894	−0.744470	−	0.667656i	$-0.767298\pi$
$227$	−5092.32	−1.48894	−0.744470	+	0.667656i	$0.767298\pi$
$228$	217.478	0.0631702
$229$	809.702	0.233653	0.116827	−	0.993152i	$-0.462728\pi$
$229$	809.702	0.233653	0.116827	+	0.993152i	$0.462728\pi$
$230$	0	0
$231$	7079.08	2.01632
$232$	3418.77	0.967470
$233$	−6122.68	−1.72150	−0.860752	−	0.509025i	$-0.830006\pi$
$233$	−6122.68	−1.72150	−0.860752	+	0.509025i	$0.830006\pi$
$234$	1261.81	0.352510
$235$	0	0
$236$	−290.888	−0.0802340
$237$	8358.97	2.29103
$238$	−236.129	−0.0643108
$239$	−4503.21	−1.21878	−0.609390	−	0.792871i	$-0.708586\pi$
$239$	−4503.21	−1.21878	−0.609390	+	0.792871i	$0.708586\pi$
$240$	0	0
$241$	−7119.43	−1.90292	−0.951459	−	0.307776i	$-0.900415\pi$
$241$	−7119.43	−1.90292	−0.951459	+	0.307776i	$0.900415\pi$
$242$	711.662	0.189039
$243$	−4373.90	−1.15467
$244$	−301.049	−0.0789864
$245$	0	0
$246$	−7135.22	−1.84929
$247$	749.519	0.193080
$248$	5066.09	1.29717
$249$	9957.26	2.53420
$250$	0	0
$251$	−451.556	−0.113554	−0.0567768	−	0.998387i	$-0.518082\pi$
$251$	−451.556	−0.113554	−0.0567768	+	0.998387i	$0.518082\pi$
$252$	−483.082	−0.120759
$253$	−910.818	−0.226334
$254$	−6606.88	−1.63210
$255$	0	0
$256$	1513.00	0.369385
$257$	2413.83	0.585878	0.292939	−	0.956131i	$-0.405367\pi$
$257$	2413.83	0.585878	0.292939	+	0.956131i	$0.405367\pi$
$258$	−7373.91	−1.77938
$259$	−4792.51	−1.14978
$260$	0	0
$261$	−2956.50	−0.701159
$262$	6203.28	1.46275
$263$	−1214.24	−0.284689	−0.142345	−	0.989817i	$-0.545464\pi$
$263$	−1214.24	−0.284689	−0.142345	+	0.989817i	$0.545464\pi$
$264$	5588.59	1.30286
$265$	0	0
$266$	−2582.56	−0.595289
$267$	5575.22	1.27790
$268$	366.732	0.0835884
$269$	5286.97	1.19833	0.599167	−	0.800624i	$-0.295498\pi$
$269$	5286.97	1.19833	0.599167	+	0.800624i	$0.295498\pi$
$270$	0	0
$271$	4648.30	1.04193	0.520967	−	0.853577i	$-0.325572\pi$
$271$	4648.30	1.04193	0.520967	+	0.853577i	$0.325572\pi$
$272$	−210.084	−0.0468316
$273$	−4140.19	−0.917860
$274$	−6677.01	−1.47216
$275$	0	0
$276$	154.564	0.0337088
$277$	46.5805	0.0101038	0.00505190	−	0.999987i	$-0.498392\pi$
$277$	46.5805	0.0101038	0.00505190	+	0.999987i	$0.498392\pi$
$278$	8411.67	1.81474
$279$	−4381.08	−0.940101
$280$	0	0
$281$	7012.40	1.48870	0.744350	−	0.667790i	$-0.232759\pi$
$281$	7012.40	1.48870	0.744350	+	0.667790i	$0.232759\pi$
$282$	3937.16	0.831399
$283$	7210.00	1.51445	0.757227	−	0.653152i	$-0.226554\pi$
$283$	7210.00	1.51445	0.757227	+	0.653152i	$0.226554\pi$
$284$	−8.14513	−0.00170185
$285$	0	0
$286$	−2751.52	−0.568883
$287$	9414.59	1.93633
$288$	−817.221	−0.167206
$289$	−4904.24	−0.998218
$290$	0	0
$291$	2622.14	0.528223
$292$	−360.650	−0.0722788
$293$	392.296	0.0782190	0.0391095	−	0.999235i	$-0.487548\pi$
$293$	392.296	0.0782190	0.0391095	+	0.999235i	$0.487548\pi$
$294$	7350.52	1.45813
$295$	0	0
$296$	−3783.45	−0.742934
$297$	2352.41	0.459598
$298$	−3968.52	−0.771443
$299$	532.691	0.103031
$300$	0	0
$301$	9729.53	1.86313
$302$	6157.04	1.17317
$303$	−9824.02	−1.86262
$304$	−2297.70	−0.433494
$305$	0	0
$306$	161.206	0.0301162
$307$	−5640.01	−1.04851	−0.524255	−	0.851562i	$-0.675656\pi$
$307$	−5640.01	−1.04851	−0.524255	+	0.851562i	$0.675656\pi$
$308$	1053.41	0.194882
$309$	−2133.88	−0.392854
$310$	0	0
$311$	5270.57	0.960985	0.480493	−	0.876999i	$-0.340458\pi$
$311$	5270.57	0.960985	0.480493	+	0.876999i	$0.340458\pi$
$312$	−3268.48	−0.593081
$313$	−2219.57	−0.400823	−0.200411	−	0.979712i	$-0.564228\pi$
$313$	−2219.57	−0.400823	−0.200411	+	0.979712i	$0.564228\pi$
$314$	1143.51	0.205516
$315$	0	0
$316$	1243.87	0.221433
$317$	7556.36	1.33882	0.669412	−	0.742891i	$-0.266546\pi$
$317$	7556.36	1.33882	0.669412	+	0.742891i	$0.266546\pi$
$318$	9307.82	1.64137
$319$	6446.94	1.13153
$320$	0	0
$321$	320.013	0.0556430
$322$	−1835.45	−0.317658
$323$	95.7568	0.0164955
$324$	−889.530	−0.152526
$325$	0	0
$326$	7074.48	1.20190
$327$	−9658.25	−1.63334
$328$	7432.36	1.25117
$329$	−5194.90	−0.870529
$330$	0	0
$331$	5161.93	0.857177	0.428588	−	0.903500i	$-0.359011\pi$
$331$	5161.93	0.857177	0.428588	+	0.903500i	$0.359011\pi$
$332$	1481.70	0.244937
$333$	3271.87	0.538430
$334$	432.802	0.0709038
$335$	0	0
$336$	12692.0	2.06074
$337$	−5589.58	−0.903513	−0.451756	−	0.892141i	$-0.649202\pi$
$337$	−5589.58	−0.903513	−0.451756	+	0.892141i	$0.649202\pi$
$338$	−4981.78	−0.801695
$339$	10589.4	1.69656
$340$	0	0
$341$	9553.39	1.51714
$342$	1763.13	0.278769
$343$	−574.597	−0.0904528
$344$	7680.99	1.20387
$345$	0	0
$346$	−9630.98	−1.49643
$347$	−9794.09	−1.51520	−0.757600	−	0.652719i	$-0.773628\pi$
$347$	−9794.09	−1.51520	−0.757600	+	0.652719i	$0.773628\pi$
$348$	−1094.03	−0.168524
$349$	8022.81	1.23052	0.615260	−	0.788325i	$-0.289051\pi$
$349$	8022.81	1.23052	0.615260	+	0.788325i	$0.289051\pi$
$350$	0	0
$351$	−1375.80	−0.209216
$352$	1782.03	0.269837
$353$	−4388.90	−0.661749	−0.330875	−	0.943675i	$-0.607344\pi$
$353$	−4388.90	−0.661749	−0.330875	+	0.943675i	$0.607344\pi$
$354$	−5864.44	−0.880485
$355$	0	0
$356$	829.628	0.123512
$357$	−528.941	−0.0784161
$358$	−12211.3	−1.80276
$359$	−4538.82	−0.667270	−0.333635	−	0.942702i	$-0.608275\pi$
$359$	−4538.82	−0.667270	−0.333635	+	0.942702i	$0.608275\pi$
$360$	0	0
$361$	−5811.70	−0.847310
$362$	−12369.4	−1.79591
$363$	1594.16	0.230500
$364$	−616.086	−0.0887134
$365$	0	0
$366$	−6069.28	−0.866793
$367$	−9270.56	−1.31858	−0.659290	−	0.751888i	$-0.729143\pi$
$367$	−9270.56	−1.31858	−0.659290	+	0.751888i	$0.729143\pi$
$368$	−1633.00	−0.231321
$369$	−6427.38	−0.906764
$370$	0	0
$371$	−12281.2	−1.71862
$372$	−1621.19	−0.225953
$373$	8132.28	1.12888	0.564442	−	0.825473i	$-0.309091\pi$
$373$	8132.28	1.12888	0.564442	+	0.825473i	$0.309091\pi$
$374$	−351.527	−0.0486017
$375$	0	0
$376$	−4101.12	−0.562497
$377$	−3770.49	−0.515093
$378$	4740.50	0.645040
$379$	−7678.93	−1.04074	−0.520370	−	0.853941i	$-0.674206\pi$
$379$	−7678.93	−1.04074	−0.520370	+	0.853941i	$0.674206\pi$
$380$	0	0
$381$	−14799.7	−1.99006
$382$	−5481.07	−0.734125
$383$	8597.37	1.14701	0.573505	−	0.819202i	$-0.305583\pi$
$383$	8597.37	1.14701	0.573505	+	0.819202i	$0.305583\pi$
$384$	11148.7	1.48159
$385$	0	0
$386$	−7076.80	−0.933160
$387$	−6642.39	−0.872485
$388$	390.191	0.0510540
$389$	−833.374	−0.108621	−0.0543107	−	0.998524i	$-0.517296\pi$
$389$	−833.374	−0.108621	−0.0543107	+	0.998524i	$0.517296\pi$
$390$	0	0
$391$	68.0553	0.00880232
$392$	−7656.62	−0.986524
$393$	13895.7	1.78357
$394$	−3708.64	−0.474210
$395$	0	0
$396$	−719.168	−0.0912615
$397$	295.817	0.0373970	0.0186985	−	0.999825i	$-0.494048\pi$
$397$	295.817	0.0373970	0.0186985	+	0.999825i	$0.494048\pi$
$398$	−91.9715	−0.0115832
$399$	−5785.07	−0.725854
$400$	0	0
$401$	5080.23	0.632655	0.316327	−	0.948650i	$-0.397550\pi$
$401$	5080.23	0.632655	0.316327	+	0.948650i	$0.397550\pi$
$402$	7393.48	0.917297
$403$	−5587.29	−0.690627
$404$	−1461.87	−0.180027
$405$	0	0
$406$	12991.7	1.58810
$407$	−7134.64	−0.868922
$408$	−417.573	−0.0506690
$409$	−6043.43	−0.730632	−0.365316	−	0.930884i	$-0.619039\pi$
$409$	−6043.43	−0.730632	−0.365316	+	0.930884i	$0.619039\pi$
$410$	0	0
$411$	−14956.8	−1.79505
$412$	−317.534	−0.0379703
$413$	7737.85	0.921924
$414$	1253.07	0.148756
$415$	0	0
$416$	−1042.22	−0.122834
$417$	18842.6	2.21277
$418$	−3844.68	−0.449879
$419$	−9872.50	−1.15108	−0.575541	−	0.817773i	$-0.695208\pi$
$419$	−9872.50	−1.15108	−0.575541	+	0.817773i	$0.695208\pi$
$420$	0	0
$421$	4088.28	0.473279	0.236639	−	0.971598i	$-0.423954\pi$
$421$	4088.28	0.473279	0.236639	+	0.971598i	$0.423954\pi$
$422$	−1250.42	−0.144241
$423$	3546.58	0.407661
$424$	−9695.42	−1.11050
$425$	0	0
$426$	−164.210	−0.0186760
$427$	8008.13	0.907589
$428$	47.6199	0.00537803
$429$	−6163.54	−0.693656
$430$	0	0
$431$	5325.61	0.595187	0.297593	−	0.954693i	$-0.403816\pi$
$431$	5325.61	0.595187	0.297593	+	0.954693i	$0.403816\pi$
$432$	4217.62	0.469723
$433$	−2448.60	−0.271760	−0.135880	−	0.990725i	$-0.543386\pi$
$433$	−2448.60	−0.271760	−0.135880	+	0.990725i	$0.543386\pi$
$434$	19251.7	2.12929
$435$	0	0
$436$	−1437.21	−0.157866
$437$	744.326	0.0814781
$438$	−7270.86	−0.793185
$439$	3960.18	0.430544	0.215272	−	0.976554i	$-0.430936\pi$
$439$	3960.18	0.430544	0.215272	+	0.976554i	$0.430936\pi$
$440$	0	0
$441$	6621.32	0.714968
$442$	205.590	0.0221243
$443$	6174.42	0.662202	0.331101	−	0.943595i	$-0.392580\pi$
$443$	6174.42	0.662202	0.331101	+	0.943595i	$0.392580\pi$
$444$	1210.73	0.129412
$445$	0	0
$446$	7813.80	0.829583
$447$	−8889.68	−0.940644
$448$	−11518.1	−1.21469
$449$	−6003.87	−0.631048	−0.315524	−	0.948918i	$-0.602180\pi$
$449$	−6003.87	−0.631048	−0.315524	+	0.948918i	$0.602180\pi$
$450$	0	0
$451$	14015.6	1.46334
$452$	1575.76	0.163977
$453$	13792.1	1.43048
$454$	−15277.0	−1.57926
$455$	0	0
$456$	−4567.03	−0.469015
$457$	−6044.87	−0.618746	−0.309373	−	0.950941i	$-0.600119\pi$
$457$	−6044.87	−0.618746	−0.309373	+	0.950941i	$0.600119\pi$
$458$	2429.11	0.247827
$459$	−175.769	−0.0178741
$460$	0	0
$461$	−4620.62	−0.466819	−0.233410	−	0.972378i	$-0.574988\pi$
$461$	−4620.62	−0.466819	−0.233410	+	0.972378i	$0.574988\pi$
$462$	21237.2	2.13863
$463$	10322.9	1.03616	0.518082	−	0.855331i	$-0.326646\pi$
$463$	10322.9	1.03616	0.518082	+	0.855331i	$0.326646\pi$
$464$	11558.7	1.15646
$465$	0	0
$466$	−18368.0	−1.82593
$467$	−16496.0	−1.63456	−0.817282	−	0.576238i	$-0.804520\pi$
$467$	−16496.0	−1.63456	−0.817282	+	0.576238i	$0.804520\pi$
$468$	420.605	0.0415437
$469$	−9755.34	−0.960469
$470$	0	0
$471$	2561.53	0.250592
$472$	6108.65	0.595707
$473$	14484.4	1.40802
$474$	25076.9	2.43000
$475$	0	0
$476$	−78.7097	−0.00757911
$477$	8384.44	0.804816
$478$	−13509.6	−1.29271
$479$	3767.40	0.359367	0.179684	−	0.983724i	$-0.442493\pi$
$479$	3767.40	0.359367	0.179684	+	0.983724i	$0.442493\pi$
$480$	0	0
$481$	4172.69	0.395547
$482$	−21358.3	−2.01835
$483$	−4111.51	−0.387329
$484$	237.221	0.0222784
$485$	0	0
$486$	−13121.7	−1.22472
$487$	2901.21	0.269951	0.134976	−	0.990849i	$-0.456904\pi$
$487$	2901.21	0.269951	0.134976	+	0.990849i	$0.456904\pi$
$488$	6322.02	0.586444
$489$	15847.2	1.46551
$490$	0	0
$491$	−13508.0	−1.24157	−0.620783	−	0.783982i	$-0.713185\pi$
$491$	−13508.0	−1.24157	−0.620783	+	0.783982i	$0.713185\pi$
$492$	−2378.41	−0.217941
$493$	−481.709	−0.0440062
$494$	2248.56	0.204792
$495$	0	0
$496$	17128.2	1.55056
$497$	216.667	0.0195550
$498$	29871.8	2.68793
$499$	−7470.55	−0.670196	−0.335098	−	0.942183i	$-0.608769\pi$
$499$	−7470.55	−0.670196	−0.335098	+	0.942183i	$0.608769\pi$
$500$	0	0
$501$	969.498	0.0864551
$502$	−1354.67	−0.120442
$503$	−6962.88	−0.617215	−0.308608	−	0.951189i	$-0.599863\pi$
$503$	−6962.88	−0.617215	−0.308608	+	0.951189i	$0.599863\pi$
$504$	10144.7	0.896591
$505$	0	0
$506$	−2732.45	−0.240064
$507$	−11159.4	−0.977531
$508$	−2202.29	−0.192344
$509$	12963.8	1.12890	0.564451	−	0.825467i	$-0.309088\pi$
$509$	12963.8	1.12890	0.564451	+	0.825467i	$0.309088\pi$
$510$	0	0
$511$	9593.55	0.830516
$512$	−8733.00	−0.753804
$513$	−1922.40	−0.165450
$514$	7241.49	0.621417
$515$	0	0
$516$	−2457.97	−0.209702
$517$	−7733.69	−0.657886
$518$	−14377.5	−1.21952
$519$	−21573.9	−1.82464
$520$	0	0
$521$	−2256.37	−0.189738	−0.0948688	−	0.995490i	$-0.530243\pi$
$521$	−2256.37	−0.189738	−0.0948688	+	0.995490i	$0.530243\pi$
$522$	−8869.49	−0.743691
$523$	−20058.2	−1.67703	−0.838514	−	0.544880i	$-0.816575\pi$
$523$	−20058.2	−1.67703	−0.838514	+	0.544880i	$0.816575\pi$
$524$	2067.76	0.172387
$525$	0	0
$526$	−3642.72	−0.301959
$527$	−713.819	−0.0590028
$528$	18894.7	1.55736
$529$	529.000	0.0434783
$530$	0	0
$531$	−5282.66	−0.431729
$532$	−860.854	−0.0701555
$533$	−8196.99	−0.666137
$534$	16725.7	1.35541
$535$	0	0
$536$	−7701.36	−0.620612
$537$	−27353.9	−2.19815
$538$	15860.9	1.27103
$539$	−14438.5	−1.15382
$540$	0	0
$541$	3300.93	0.262325	0.131163	−	0.991361i	$-0.458129\pi$
$541$	3300.93	0.262325	0.131163	+	0.991361i	$0.458129\pi$
$542$	13944.9	1.10514
$543$	−27708.1	−2.18981
$544$	−133.152	−0.0104942
$545$	0	0
$546$	−12420.6	−0.973538
$547$	18198.7	1.42252	0.711260	−	0.702929i	$-0.248125\pi$
$547$	18198.7	1.42252	0.711260	+	0.702929i	$0.248125\pi$
$548$	−2225.67	−0.173496
$549$	−5467.18	−0.425016
$550$	0	0
$551$	−5268.48	−0.407341
$552$	−3245.83	−0.250275
$553$	−33087.8	−2.54437
$554$	139.742	0.0107167
$555$	0	0
$556$	2803.89	0.213869
$557$	−5899.11	−0.448749	−0.224375	−	0.974503i	$-0.572034\pi$
$557$	−5899.11	−0.448749	−0.224375	+	0.974503i	$0.572034\pi$
$558$	−13143.2	−0.997128
$559$	−8471.20	−0.640954
$560$	0	0
$561$	−787.439	−0.0592615
$562$	21037.2	1.57900
$563$	18106.3	1.35540	0.677698	−	0.735340i	$-0.262977\pi$
$563$	18106.3	1.35540	0.677698	+	0.735340i	$0.262977\pi$
$564$	1312.39	0.0979814
$565$	0	0
$566$	21630.0	1.60632
$567$	23662.2	1.75259
$568$	171.048	0.0126356
$569$	5985.76	0.441012	0.220506	−	0.975386i	$-0.429229\pi$
$569$	5985.76	0.441012	0.220506	+	0.975386i	$0.429229\pi$
$570$	0	0
$571$	−24457.6	−1.79250	−0.896252	−	0.443546i	$-0.853720\pi$
$571$	−24457.6	−1.79250	−0.896252	+	0.443546i	$0.853720\pi$
$572$	−917.172	−0.0670435
$573$	−12277.9	−0.895140
$574$	28243.8	2.05378
$575$	0	0
$576$	7863.48	0.568828
$577$	−8812.01	−0.635787	−0.317893	−	0.948126i	$-0.602975\pi$
$577$	−8812.01	−0.635787	−0.317893	+	0.948126i	$0.602975\pi$
$578$	−14712.7	−1.05877
$579$	−15852.4	−1.13783
$580$	0	0
$581$	−39414.4	−2.81443
$582$	7866.43	0.560265
$583$	−18283.1	−1.29882
$584$	7573.64	0.536643
$585$	0	0
$586$	1176.89	0.0829638
$587$	−21952.3	−1.54356	−0.771779	−	0.635891i	$-0.780633\pi$
$587$	−21952.3	−1.54356	−0.771779	+	0.635891i	$0.780633\pi$
$588$	2450.17	0.171843
$589$	−7807.09	−0.546156
$590$	0	0
$591$	−8307.55	−0.578218
$592$	−12791.7	−0.888064
$593$	−916.597	−0.0634741	−0.0317370	−	0.999496i	$-0.510104\pi$
$593$	−916.597	−0.0634741	−0.0317370	+	0.999496i	$0.510104\pi$
$594$	7057.22	0.487477
$595$	0	0
$596$	−1322.84	−0.0909155
$597$	−206.021	−0.0141237
$598$	1598.07	0.109281
$599$	−7327.24	−0.499804	−0.249902	−	0.968271i	$-0.580398\pi$
$599$	−7327.24	−0.499804	−0.249902	+	0.968271i	$0.580398\pi$
$600$	0	0
$601$	4378.57	0.297181	0.148590	−	0.988899i	$-0.452526\pi$
$601$	4378.57	0.297181	0.148590	+	0.988899i	$0.452526\pi$
$602$	29188.6	1.97614
$603$	6660.02	0.449779
$604$	2052.35	0.138260
$605$	0	0
$606$	−29472.1	−1.97561
$607$	13150.8	0.879367	0.439683	−	0.898153i	$-0.355091\pi$
$607$	13150.8	0.879367	0.439683	+	0.898153i	$0.355091\pi$
$608$	−1456.29	−0.0971387
$609$	29102.1	1.93641
$610$	0	0
$611$	4523.04	0.299480
$612$	53.7355	0.00354923
$613$	−23672.8	−1.55976	−0.779881	−	0.625928i	$-0.784721\pi$
$613$	−23672.8	−1.55976	−0.779881	+	0.625928i	$0.784721\pi$
$614$	−16920.0	−1.11211
$615$	0	0
$616$	−22121.6	−1.44692
$617$	−5581.73	−0.364201	−0.182101	−	0.983280i	$-0.558290\pi$
$617$	−5581.73	−0.364201	−0.182101	+	0.983280i	$0.558290\pi$
$618$	−6401.63	−0.416685
$619$	24249.7	1.57460	0.787301	−	0.616568i	$-0.211478\pi$
$619$	24249.7	1.57460	0.787301	+	0.616568i	$0.211478\pi$
$620$	0	0
$621$	−1366.27	−0.0882875
$622$	15811.7	1.01928
$623$	−22068.7	−1.41921
$624$	−11050.6	−0.708937
$625$	0	0
$626$	−6658.71	−0.425137
$627$	−8612.28	−0.548551
$628$	381.171	0.0242203
$629$	533.093	0.0337930
$630$	0	0
$631$	15717.9	0.991633	0.495816	−	0.868427i	$-0.334869\pi$
$631$	15717.9	0.991633	0.495816	+	0.868427i	$0.334869\pi$
$632$	−26121.2	−1.64406
$633$	−2801.02	−0.175877
$634$	22669.1	1.42004
$635$	0	0
$636$	3102.61	0.193438
$637$	8444.32	0.525237
$638$	19340.8	1.20017
$639$	−147.919	−0.00915743
$640$	0	0
$641$	−17043.9	−1.05022	−0.525111	−	0.851034i	$-0.675976\pi$
$641$	−17043.9	−1.05022	−0.525111	+	0.851034i	$0.675976\pi$
$642$	960.040	0.0590183
$643$	6648.00	0.407732	0.203866	−	0.978999i	$-0.434649\pi$
$643$	6648.00	0.407732	0.203866	+	0.978999i	$0.434649\pi$
$644$	−611.818	−0.0374363
$645$	0	0
$646$	287.270	0.0174961
$647$	1899.44	0.115417	0.0577085	−	0.998333i	$-0.481621\pi$
$647$	1899.44	0.115417	0.0577085	+	0.998333i	$0.481621\pi$
$648$	18680.1	1.13245
$649$	11519.4	0.696727
$650$	0	0
$651$	43124.8	2.59631
$652$	2358.16	0.141645
$653$	−14942.8	−0.895492	−0.447746	−	0.894161i	$-0.647773\pi$
$653$	−14942.8	−0.895492	−0.447746	+	0.894161i	$0.647773\pi$
$654$	−28974.7	−1.73242
$655$	0	0
$656$	25128.4	1.49558
$657$	−6549.56	−0.388923
$658$	−15584.7	−0.923336
$659$	13828.4	0.817419	0.408710	−	0.912664i	$-0.365979\pi$
$659$	13828.4	0.817419	0.408710	+	0.912664i	$0.365979\pi$
$660$	0	0
$661$	−17897.0	−1.05312	−0.526559	−	0.850138i	$-0.676518\pi$
$661$	−17897.0	−1.05312	−0.526559	+	0.850138i	$0.676518\pi$
$662$	15485.8	0.909173
$663$	460.533	0.0269768
$664$	−31115.7	−1.81856
$665$	0	0
$666$	9815.60	0.571091
$667$	−3744.36	−0.217365
$668$	144.267	0.00835609
$669$	17503.3	1.01154
$670$	0	0
$671$	11921.8	0.685893
$672$	8044.26	0.461777
$673$	13486.7	0.772475	0.386238	−	0.922399i	$-0.373774\pi$
$673$	13486.7	0.772475	0.386238	+	0.922399i	$0.373774\pi$
$674$	−16768.7	−0.958320
$675$	0	0
$676$	−1660.59	−0.0944807
$677$	11202.2	0.635949	0.317974	−	0.948099i	$-0.396997\pi$
$677$	11202.2	0.635949	0.317974	+	0.948099i	$0.396997\pi$
$678$	31768.1	1.79948
$679$	−10379.4	−0.586633
$680$	0	0
$681$	−34221.2	−1.92564
$682$	28660.2	1.60917
$683$	12993.0	0.727909	0.363955	−	0.931417i	$-0.381426\pi$
$683$	12993.0	0.727909	0.363955	+	0.931417i	$0.381426\pi$
$684$	587.709	0.0328532
$685$	0	0
$686$	−1723.79	−0.0959397
$687$	5441.32	0.302183
$688$	25969.0	1.43904
$689$	10692.9	0.591243
$690$	0	0
$691$	−19132.4	−1.05330	−0.526650	−	0.850082i	$-0.676552\pi$
$691$	−19132.4	−1.05330	−0.526650	+	0.850082i	$0.676552\pi$
$692$	−3210.33	−0.176356
$693$	19130.4	1.04864
$694$	−29382.3	−1.60711
$695$	0	0
$696$	22974.6	1.25122
$697$	−1047.23	−0.0569105
$698$	24068.4	1.30516
$699$	−41145.4	−2.22641
$700$	0	0
$701$	21743.7	1.17154	0.585768	−	0.810479i	$-0.300793\pi$
$701$	21743.7	1.17154	0.585768	+	0.810479i	$0.300793\pi$
$702$	−4127.41	−0.221907
$703$	5830.48	0.312803
$704$	−17147.1	−0.917978
$705$	0	0
$706$	−13166.7	−0.701891
$707$	38887.0	2.06859
$708$	−1954.81	−0.103766
$709$	−4085.34	−0.216401	−0.108200	−	0.994129i	$-0.534509\pi$
$709$	−4085.34	−0.216401	−0.108200	+	0.994129i	$0.534509\pi$
$710$	0	0
$711$	22589.2	1.19151
$712$	−17422.2	−0.917028
$713$	−5548.58	−0.291439
$714$	−1586.82	−0.0831728
$715$	0	0
$716$	−4070.43	−0.212457
$717$	−30262.3	−1.57624
$718$	−13616.5	−0.707746
$719$	34076.1	1.76749	0.883744	−	0.467971i	$-0.155015\pi$
$719$	34076.1	1.76749	0.883744	+	0.467971i	$0.155015\pi$
$720$	0	0
$721$	8446.65	0.436296
$722$	−17435.1	−0.898708
$723$	−47843.7	−2.46103
$724$	−4123.13	−0.211651
$725$	0	0
$726$	4782.48	0.244483
$727$	880.475	0.0449175	0.0224587	−	0.999748i	$-0.492851\pi$
$727$	880.475	0.0449175	0.0224587	+	0.999748i	$0.492851\pi$
$728$	12937.8	0.658663
$729$	−5375.94	−0.273126
$730$	0	0
$731$	−1082.26	−0.0547590
$732$	−2023.09	−0.102153
$733$	14731.6	0.742324	0.371162	−	0.928568i	$-0.378959\pi$
$733$	14731.6	0.742324	0.371162	+	0.928568i	$0.378959\pi$
$734$	−27811.7	−1.39857
$735$	0	0
$736$	−1035.00	−0.0518351
$737$	−14522.9	−0.725856
$738$	−19282.1	−0.961769
$739$	6380.78	0.317619	0.158810	−	0.987309i	$-0.449234\pi$
$739$	6380.78	0.317619	0.158810	+	0.987309i	$0.449234\pi$
$740$	0	0
$741$	5036.88	0.249709
$742$	−36843.7	−1.82288
$743$	11649.5	0.575208	0.287604	−	0.957749i	$-0.407141\pi$
$743$	11649.5	0.575208	0.287604	+	0.957749i	$0.407141\pi$
$744$	34044.9	1.67762
$745$	0	0
$746$	24396.9	1.19736
$747$	26908.4	1.31797
$748$	−117.176	−0.00572777
$749$	−1266.73	−0.0617960
$750$	0	0
$751$	14143.0	0.687199	0.343600	−	0.939116i	$-0.388354\pi$
$751$	14143.0	0.687199	0.343600	+	0.939116i	$0.388354\pi$
$752$	−13865.7	−0.672380
$753$	−3034.52	−0.146858
$754$	−11311.5	−0.546338
$755$	0	0
$756$	1580.17	0.0760187
$757$	30054.3	1.44299	0.721495	−	0.692420i	$-0.243455\pi$
$757$	30054.3	1.44299	0.721495	+	0.692420i	$0.243455\pi$
$758$	−23036.8	−1.10387
$759$	−6120.83	−0.292717
$760$	0	0
$761$	29327.5	1.39701	0.698503	−	0.715607i	$-0.253850\pi$
$761$	29327.5	1.39701	0.698503	+	0.715607i	$0.253850\pi$
$762$	−44399.2	−2.11078
$763$	38230.8	1.81395
$764$	−1827.02	−0.0865175
$765$	0	0
$766$	25792.1	1.21659
$767$	−6737.11	−0.317161
$768$	10167.6	0.477723
$769$	−16343.8	−0.766413	−0.383207	−	0.923663i	$-0.625180\pi$
$769$	−16343.8	−0.766413	−0.383207	+	0.923663i	$0.625180\pi$
$770$	0	0
$771$	16221.3	0.757712
$772$	−2358.93	−0.109974
$773$	32875.3	1.52968	0.764839	−	0.644221i	$-0.222818\pi$
$773$	32875.3	1.52968	0.764839	+	0.644221i	$0.222818\pi$
$774$	−19927.2	−0.925410
$775$	0	0
$776$	−8194.01	−0.379057
$777$	−32206.4	−1.48700
$778$	−2500.12	−0.115210
$779$	−11453.6	−0.526788
$780$	0	0
$781$	322.554	0.0147783
$782$	204.166	0.00933627
$783$	9670.73	0.441384
$784$	−25886.7	−1.17924
$785$	0	0
$786$	41687.0	1.89176
$787$	15927.1	0.721397	0.360699	−	0.932682i	$-0.382538\pi$
$787$	15927.1	0.721397	0.360699	+	0.932682i	$0.382538\pi$
$788$	−1236.21	−0.0558862
$789$	−8159.88	−0.368187
$790$	0	0
$791$	−41916.5	−1.88417
$792$	15102.5	0.677582
$793$	−6972.43	−0.312230
$794$	887.450	0.0396655
$795$	0	0
$796$	−30.6572	−0.00136509
$797$	21390.5	0.950676	0.475338	−	0.879803i	$-0.342326\pi$
$797$	21390.5	0.950676	0.475338	+	0.879803i	$0.342326\pi$
$798$	−17355.2	−0.769884
$799$	577.853	0.0255857
$800$	0	0
$801$	15066.4	0.664601
$802$	15240.7	0.671032
$803$	14282.0	0.627647
$804$	2464.49	0.108104
$805$	0	0
$806$	−16761.9	−0.732521
$807$	35529.2	1.54980
$808$	30699.4	1.33663
$809$	23294.4	1.01234	0.506172	−	0.862432i	$-0.331060\pi$
$809$	23294.4	1.01234	0.506172	+	0.862432i	$0.331060\pi$
$810$	0	0
$811$	−33524.8	−1.45156	−0.725779	−	0.687928i	$-0.758521\pi$
$811$	−33524.8	−1.45156	−0.725779	+	0.687928i	$0.758521\pi$
$812$	4330.56	0.187159
$813$	31237.3	1.34753
$814$	−21403.9	−0.921631
$815$	0	0
$816$	−1411.80	−0.0605671
$817$	−11836.8	−0.506874
$818$	−18130.3	−0.774952
$819$	−11188.4	−0.477356
$820$	0	0
$821$	−12493.6	−0.531095	−0.265548	−	0.964098i	$-0.585553\pi$
$821$	−12493.6	−0.531095	−0.265548	+	0.964098i	$0.585553\pi$
$822$	−44870.5	−1.90394
$823$	−6236.39	−0.264140	−0.132070	−	0.991240i	$-0.542162\pi$
$823$	−6236.39	−0.264140	−0.132070	+	0.991240i	$0.542162\pi$
$824$	6668.21	0.281915
$825$	0	0
$826$	23213.6	0.977848
$827$	31346.5	1.31805	0.659023	−	0.752122i	$-0.270970\pi$
$827$	31346.5	1.31805	0.659023	+	0.752122i	$0.270970\pi$
$828$	417.691	0.0175311
$829$	1452.79	0.0608657	0.0304328	−	0.999537i	$-0.490311\pi$
$829$	1452.79	0.0608657	0.0304328	+	0.999537i	$0.490311\pi$
$830$	0	0
$831$	313.028	0.0130672
$832$	10028.5	0.417879
$833$	1078.83	0.0448729
$834$	56527.7	2.34700
$835$	0	0
$836$	−1281.56	−0.0530187
$837$	14330.6	0.591800
$838$	−29617.5	−1.22091
$839$	18327.7	0.754161	0.377081	−	0.926180i	$-0.376928\pi$
$839$	18327.7	0.754161	0.377081	+	0.926180i	$0.376928\pi$
$840$	0	0
$841$	2114.34	0.0866924
$842$	12264.8	0.501988
$843$	47124.4	1.92533
$844$	−416.808	−0.0169990
$845$	0	0
$846$	10639.7	0.432390
$847$	−6310.25	−0.255989
$848$	−32779.8	−1.32743
$849$	48452.3	1.95863
$850$	0	0
$851$	4143.78	0.166918
$852$	−54.7366	−0.00220099
$853$	−48657.4	−1.95311	−0.976553	−	0.215279i	$-0.930934\pi$
$853$	−48657.4	−1.95311	−0.976553	+	0.215279i	$0.930934\pi$
$854$	24024.4	0.962643
$855$	0	0
$856$	−1000.02	−0.0399298
$857$	2116.61	0.0843666	0.0421833	−	0.999110i	$-0.486569\pi$
$857$	2116.61	0.0843666	0.0421833	+	0.999110i	$0.486569\pi$
$858$	−18490.6	−0.735733
$859$	16391.3	0.651063	0.325531	−	0.945531i	$-0.394457\pi$
$859$	16391.3	0.651063	0.325531	+	0.945531i	$0.394457\pi$
$860$	0	0
$861$	63267.5	2.50424
$862$	15976.8	0.631291
$863$	33241.8	1.31120	0.655600	−	0.755109i	$-0.272416\pi$
$863$	33241.8	1.31120	0.655600	+	0.755109i	$0.272416\pi$
$864$	2673.14	0.105257
$865$	0	0
$866$	−7345.79	−0.288245
$867$	−32957.3	−1.29099
$868$	6417.24	0.250939
$869$	−49258.1	−1.92286
$870$	0	0
$871$	8493.67	0.330422
$872$	30181.3	1.17210
$873$	7086.05	0.274715
$874$	2232.98	0.0864206
$875$	0	0
$876$	−2423.62	−0.0934778
$877$	−14732.4	−0.567249	−0.283625	−	0.958935i	$-0.591537\pi$
$877$	−14732.4	−0.567249	−0.283625	+	0.958935i	$0.591537\pi$
$878$	11880.5	0.456661
$879$	2636.29	0.101160
$880$	0	0
$881$	−604.107	−0.0231020	−0.0115510	−	0.999933i	$-0.503677\pi$
$881$	−604.107	−0.0231020	−0.0115510	+	0.999933i	$0.503677\pi$
$882$	19864.0	0.758338
$883$	−40030.5	−1.52563	−0.762816	−	0.646616i	$-0.776184\pi$
$883$	−40030.5	−1.52563	−0.762816	+	0.646616i	$0.776184\pi$
$884$	68.5301	0.00260737
$885$	0	0
$886$	18523.3	0.702371
$887$	35364.3	1.33869	0.669344	−	0.742953i	$-0.266575\pi$
$887$	35364.3	1.33869	0.669344	+	0.742953i	$0.266575\pi$
$888$	−25425.4	−0.960833
$889$	58582.7	2.21012
$890$	0	0
$891$	35226.1	1.32449
$892$	2604.60	0.0977673
$893$	6320.02	0.236832
$894$	−26669.1	−0.997703
$895$	0	0
$896$	−44130.7	−1.64543
$897$	3579.76	0.133249
$898$	−18011.6	−0.669327
$899$	39273.9	1.45702
$900$	0	0
$901$	1366.10	0.0505120
$902$	42046.7	1.55211
$903$	65383.9	2.40957
$904$	−33091.0	−1.21747
$905$	0	0
$906$	41376.3	1.51726
$907$	−46960.3	−1.71918	−0.859588	−	0.510988i	$-0.829280\pi$
$907$	−46960.3	−1.71918	−0.859588	+	0.510988i	$0.829280\pi$
$908$	−5092.32	−0.186117
$909$	−26548.3	−0.968704
$910$	0	0
$911$	−23027.3	−0.837461	−0.418731	−	0.908110i	$-0.637525\pi$
$911$	−23027.3	−0.837461	−0.418731	+	0.908110i	$0.637525\pi$
$912$	−15440.9	−0.560635
$913$	−58676.5	−2.12696
$914$	−18134.6	−0.656280
$915$	0	0
$916$	809.702	0.0292067
$917$	−55004.0	−1.98080
$918$	−527.308	−0.0189583
$919$	−20203.7	−0.725198	−0.362599	−	0.931945i	$-0.618111\pi$
$919$	−20203.7	−0.725198	−0.362599	+	0.931945i	$0.618111\pi$
$920$	0	0
$921$	−37901.7	−1.35603
$922$	−13861.9	−0.495137
$923$	−188.645	−0.00672733
$924$	7079.08	0.252040
$925$	0	0
$926$	30968.6	1.09902
$927$	−5766.56	−0.204314
$928$	7325.93	0.259144
$929$	28382.1	1.00235	0.501177	−	0.865345i	$-0.332901\pi$
$929$	28382.1	1.00235	0.501177	+	0.865345i	$0.332901\pi$
$930$	0	0
$931$	11799.2	0.415363
$932$	−6122.68	−0.215188
$933$	35419.0	1.24284
$934$	−49487.9	−1.73372
$935$	0	0
$936$	−8832.70	−0.308446
$937$	−855.936	−0.0298423	−0.0149211	−	0.999889i	$-0.504750\pi$
$937$	−855.936	−0.0298423	−0.0149211	+	0.999889i	$0.504750\pi$
$938$	−29266.0	−1.01873
$939$	−14915.8	−0.518381
$940$	0	0
$941$	−15957.0	−0.552797	−0.276399	−	0.961043i	$-0.589141\pi$
$941$	−15957.0	−0.552797	−0.276399	+	0.961043i	$0.589141\pi$
$942$	7684.58	0.265793
$943$	−8140.20	−0.281104
$944$	20653.1	0.712076
$945$	0	0
$946$	43453.3	1.49343
$947$	51719.6	1.77472	0.887361	−	0.461074i	$-0.152536\pi$
$947$	51719.6	1.77472	0.887361	+	0.461074i	$0.152536\pi$
$948$	8358.97	0.286378
$949$	−8352.81	−0.285715
$950$	0	0
$951$	50779.9	1.73149
$952$	1652.90	0.0562720
$953$	25040.6	0.851147	0.425574	−	0.904924i	$-0.360072\pi$
$953$	25040.6	0.851147	0.425574	+	0.904924i	$0.360072\pi$
$954$	25153.3	0.853636
$955$	0	0
$956$	−4503.21	−0.152347
$957$	43324.5	1.46341
$958$	11302.2	0.381167
$959$	59204.5	1.99355
$960$	0	0
$961$	28407.0	0.953543
$962$	12518.1	0.419541
$963$	864.800	0.0289385
$964$	−7119.43	−0.237865
$965$	0	0
$966$	−12334.5	−0.410825
$967$	35852.9	1.19230	0.596148	−	0.802874i	$-0.296697\pi$
$967$	35852.9	1.19230	0.596148	+	0.802874i	$0.296697\pi$
$968$	−4981.63	−0.165409
$969$	643.500	0.0213335
$970$	0	0
$971$	−19740.9	−0.652437	−0.326218	−	0.945294i	$-0.605775\pi$
$971$	−19740.9	−0.652437	−0.326218	+	0.945294i	$0.605775\pi$
$972$	−4373.90	−0.144334
$973$	−74585.6	−2.45746
$974$	8703.62	0.286327
$975$	0	0
$976$	21374.5	0.701004
$977$	28263.7	0.925524	0.462762	−	0.886483i	$-0.346859\pi$
$977$	28263.7	0.925524	0.462762	+	0.886483i	$0.346859\pi$
$978$	47541.6	1.55441
$979$	−32853.9	−1.07254
$980$	0	0
$981$	−26100.3	−0.849459
$982$	−40524.1	−1.31688
$983$	24050.0	0.780340	0.390170	−	0.920743i	$-0.372416\pi$
$983$	24050.0	0.780340	0.390170	+	0.920743i	$0.372416\pi$
$984$	49946.6	1.61813
$985$	0	0
$986$	−1445.13	−0.0466757
$987$	−34910.5	−1.12585
$988$	749.519	0.0241350
$989$	−8412.51	−0.270477
$990$	0	0
$991$	−52738.0	−1.69049	−0.845246	−	0.534378i	$-0.820546\pi$
$991$	−52738.0	−1.69049	−0.845246	+	0.534378i	$0.820546\pi$
$992$	10855.9	0.347455
$993$	34689.0	1.10858
$994$	650.000	0.0207412
$995$	0	0
$996$	9957.26	0.316775
$997$	−6903.86	−0.219305	−0.109653	−	0.993970i	$-0.534974\pi$
$997$	−6903.86	−0.219305	−0.109653	+	0.993970i	$0.534974\pi$
$998$	−22411.7	−0.710850
$999$	−10702.3	−0.338945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.4.a.h.1.2		2
5.2	odd	4		575.4.b.f.24.3		4
5.3	odd	4		575.4.b.f.24.2		4
5.4	even	2		115.4.a.c.1.1	✓	2
15.14	odd	2		1035.4.a.g.1.2		2
20.19	odd	2		1840.4.a.h.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.a.c.1.1	✓	2	5.4	even	2
575.4.a.h.1.2		2	1.1	even	1	trivial
575.4.b.f.24.2		4	5.3	odd	4
575.4.b.f.24.3		4	5.2	odd	4
1035.4.a.g.1.2		2	15.14	odd	2
1840.4.a.h.1.2		2	20.19	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q+3.00000 q^{2} +6.72015 q^{3} +1.00000 q^{4} +20.1605 q^{6} -26.6008 q^{7} -21.0000 q^{8} +18.1605 q^{9} +O(q^{10})\)	\(q+3.00000 q^{2} +6.72015 q^{3} +1.00000 q^{4} +20.1605 q^{6} -26.6008 q^{7} -21.0000 q^{8} +18.1605 q^{9} -39.6008 q^{11} +6.72015 q^{12} +23.1605 q^{13} -79.8023 q^{14} -71.0000 q^{16} +2.95893 q^{17} +54.4814 q^{18} +32.3620 q^{19} -178.761 q^{21} -118.802 q^{22} +23.0000 q^{23} -141.123 q^{24} +69.4814 q^{26} -59.4031 q^{27} -26.6008 q^{28} -162.798 q^{29} -241.243 q^{31} -45.0000 q^{32} -266.123 q^{33} +8.87678 q^{34} +18.1605 q^{36} +180.164 q^{37} +97.0860 q^{38} +155.642 q^{39} -353.922 q^{41} -536.284 q^{42} -365.761 q^{43} -39.6008 q^{44} +69.0000 q^{46} +195.291 q^{47} -477.131 q^{48} +364.601 q^{49} +19.8844 q^{51} +23.1605 q^{52} +461.687 q^{53} -178.209 q^{54} +558.616 q^{56} +217.478 q^{57} -488.395 q^{58} -290.888 q^{59} -301.049 q^{61} -723.728 q^{62} -483.082 q^{63} +433.000 q^{64} -798.370 q^{66} +366.732 q^{67} +2.95893 q^{68} +154.564 q^{69} -8.14513 q^{71} -381.370 q^{72} -360.650 q^{73} +540.493 q^{74} +32.3620 q^{76} +1053.41 q^{77} +466.926 q^{78} +1243.87 q^{79} -889.530 q^{81} -1061.77 q^{82} +1481.70 q^{83} -178.761 q^{84} -1097.28 q^{86} -1094.03 q^{87} +831.616 q^{88} +829.628 q^{89} -616.086 q^{91} +23.0000 q^{92} -1621.19 q^{93} +585.874 q^{94} -302.407 q^{96} +390.191 q^{97} +1093.80 q^{98} -719.168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} + 3 q^{3} + 2 q^{4} + 9 q^{6} - q^{7} - 42 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q + 6 * q^2 + 3 * q^3 + 2 * q^4 + 9 * q^6 - q^7 - 42 * q^8 + 5 * q^9	\( 2 q + 6 q^{2} + 3 q^{3} + 2 q^{4} + 9 q^{6} - q^{7} - 42 q^{8} + 5 q^{9} - 27 q^{11} + 3 q^{12} + 15 q^{13} - 3 q^{14} - 142 q^{16} + 79 q^{17} + 15 q^{18} - 71 q^{19} - 274 q^{21} - 81 q^{22} + 46 q^{23} - 63 q^{24} + 45 q^{26} + 90 q^{27} - q^{28} - 430 q^{29} - 305 q^{31} - 90 q^{32} - 313 q^{33} + 237 q^{34} + 5 q^{36} + 68 q^{37} - 213 q^{38} + 186 q^{39} - 593 q^{41} - 822 q^{42} - 648 q^{43} - 27 q^{44} + 138 q^{46} - 382 q^{47} - 213 q^{48} + 677 q^{49} - 263 q^{51} + 15 q^{52} + 464 q^{53} + 270 q^{54} + 21 q^{56} + 602 q^{57} - 1290 q^{58} - 18 q^{59} - 7 q^{61} - 915 q^{62} - 820 q^{63} + 866 q^{64} - 939 q^{66} - 60 q^{67} + 79 q^{68} + 69 q^{69} - 1029 q^{71} - 105 q^{72} - 74 q^{73} + 204 q^{74} - 71 q^{76} + 1376 q^{77} + 558 q^{78} + 692 q^{79} - 1090 q^{81} - 1779 q^{82} + 1460 q^{83} - 274 q^{84} - 1944 q^{86} - 100 q^{87} + 567 q^{88} - 220 q^{89} - 825 q^{91} + 46 q^{92} - 1384 q^{93} - 1146 q^{94} - 135 q^{96} - 1339 q^{97} + 2031 q^{98} - 885 q^{99}+O(q^{100}) \) 2 * q + 6 * q^2 + 3 * q^3 + 2 * q^4 + 9 * q^6 - q^7 - 42 * q^8 + 5 * q^9 - 27 * q^11 + 3 * q^12 + 15 * q^13 - 3 * q^14 - 142 * q^16 + 79 * q^17 + 15 * q^18 - 71 * q^19 - 274 * q^21 - 81 * q^22 + 46 * q^23 - 63 * q^24 + 45 * q^26 + 90 * q^27 - q^28 - 430 * q^29 - 305 * q^31 - 90 * q^32 - 313 * q^33 + 237 * q^34 + 5 * q^36 + 68 * q^37 - 213 * q^38 + 186 * q^39 - 593 * q^41 - 822 * q^42 - 648 * q^43 - 27 * q^44 + 138 * q^46 - 382 * q^47 - 213 * q^48 + 677 * q^49 - 263 * q^51 + 15 * q^52 + 464 * q^53 + 270 * q^54 + 21 * q^56 + 602 * q^57 - 1290 * q^58 - 18 * q^59 - 7 * q^61 - 915 * q^62 - 820 * q^63 + 866 * q^64 - 939 * q^66 - 60 * q^67 + 79 * q^68 + 69 * q^69 - 1029 * q^71 - 105 * q^72 - 74 * q^73 + 204 * q^74 - 71 * q^76 + 1376 * q^77 + 558 * q^78 + 692 * q^79 - 1090 * q^81 - 1779 * q^82 + 1460 * q^83 - 274 * q^84 - 1944 * q^86 - 100 * q^87 + 567 * q^88 - 220 * q^89 - 825 * q^91 + 46 * q^92 - 1384 * q^93 - 1146 * q^94 - 135 * q^96 - 1339 * q^97 + 2031 * q^98 - 885 * q^99

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