LMFDB - Embedded newform 1175.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.106069.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 7x^{2} + 3x - 4 $ x^5 - 2x^4 - 4x^3 + 7x^2 + 3x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.69523$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24483 q^{2} -1.56903 q^{3} -0.450400 q^{4} -1.95318 q^{6} +4.85788 q^{7} -3.05033 q^{8} -0.538136 q^{9} +O(q^{10})$	\(q+1.24483 q^{2} -1.56903 q^{3} -0.450400 q^{4} -1.95318 q^{6} +4.85788 q^{7} -3.05033 q^{8} -0.538136 q^{9} -3.10161 q^{11} +0.706693 q^{12} +2.54124 q^{13} +6.04723 q^{14} -2.89634 q^{16} -0.110271 q^{17} -0.669888 q^{18} +6.42136 q^{19} -7.62217 q^{21} -3.86098 q^{22} +3.81832 q^{23} +4.78607 q^{24} +3.16341 q^{26} +5.55145 q^{27} -2.18799 q^{28} -9.12914 q^{29} +7.75002 q^{31} +2.49521 q^{32} +4.86653 q^{33} -0.137269 q^{34} +0.242377 q^{36} +3.53258 q^{37} +7.99349 q^{38} -3.98729 q^{39} -0.609541 q^{41} -9.48830 q^{42} +1.39697 q^{44} +4.75316 q^{46} +1.00000 q^{47} +4.54445 q^{48} +16.5990 q^{49} +0.173019 q^{51} -1.14457 q^{52} +3.58972 q^{53} +6.91061 q^{54} -14.8181 q^{56} -10.0753 q^{57} -11.3642 q^{58} +11.4458 q^{59} +12.9585 q^{61} +9.64745 q^{62} -2.61420 q^{63} +8.89879 q^{64} +6.05800 q^{66} +0.830083 q^{67} +0.0496662 q^{68} -5.99108 q^{69} -2.84340 q^{71} +1.64149 q^{72} +7.35401 q^{73} +4.39746 q^{74} -2.89218 q^{76} -15.0673 q^{77} -4.96349 q^{78} -15.0577 q^{79} -7.09600 q^{81} -0.758774 q^{82} +1.90546 q^{83} +3.43303 q^{84} +14.3239 q^{87} +9.46095 q^{88} -3.39912 q^{89} +12.3450 q^{91} -1.71977 q^{92} -12.1600 q^{93} +1.24483 q^{94} -3.91507 q^{96} +13.7071 q^{97} +20.6629 q^{98} +1.66909 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9	$ 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9} - q^{11} + 8 q^{12} + 11 q^{13} - 2 q^{14} + 4 q^{16} + 14 q^{17} + 6 q^{18} + 5 q^{19} - 13 q^{21} - 5 q^{22} + 6 q^{23} + 20 q^{24} - 11 q^{26} + 11 q^{27} - q^{28} - 16 q^{29} + 3 q^{31} + 3 q^{32} + 5 q^{33} + 28 q^{34} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 25 q^{39} - 24 q^{41} - 46 q^{42} + 21 q^{44} + 14 q^{46} + 5 q^{47} - 7 q^{48} + 24 q^{49} + 14 q^{51} - 15 q^{52} + 14 q^{53} + 46 q^{54} - 3 q^{56} + 3 q^{57} - 32 q^{58} + 10 q^{59} - 9 q^{61} - 13 q^{62} - 24 q^{63} + 16 q^{64} - 23 q^{66} - 4 q^{67} + 47 q^{68} - 26 q^{69} + 4 q^{71} - 5 q^{72} + 27 q^{73} + 14 q^{74} - 19 q^{76} + 33 q^{77} - q^{78} - 18 q^{79} + 9 q^{81} - 24 q^{82} - 17 q^{83} - 26 q^{84} - 18 q^{87} + 35 q^{88} + 4 q^{89} + 13 q^{91} + 6 q^{92} - 25 q^{93} + 4 q^{94} - 33 q^{96} + 30 q^{97} + 11 q^{98} - 4 q^{99}+O(q^{100}) $ 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9 - q^11 + 8 * q^12 + 11 * q^13 - 2 * q^14 + 4 * q^16 + 14 * q^17 + 6 * q^18 + 5 * q^19 - 13 * q^21 - 5 * q^22 + 6 * q^23 + 20 * q^24 - 11 * q^26 + 11 * q^27 - q^28 - 16 * q^29 + 3 * q^31 + 3 * q^32 + 5 * q^33 + 28 * q^34 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 25 * q^39 - 24 * q^41 - 46 * q^42 + 21 * q^44 + 14 * q^46 + 5 * q^47 - 7 * q^48 + 24 * q^49 + 14 * q^51 - 15 * q^52 + 14 * q^53 + 46 * q^54 - 3 * q^56 + 3 * q^57 - 32 * q^58 + 10 * q^59 - 9 * q^61 - 13 * q^62 - 24 * q^63 + 16 * q^64 - 23 * q^66 - 4 * q^67 + 47 * q^68 - 26 * q^69 + 4 * q^71 - 5 * q^72 + 27 * q^73 + 14 * q^74 - 19 * q^76 + 33 * q^77 - q^78 - 18 * q^79 + 9 * q^81 - 24 * q^82 - 17 * q^83 - 26 * q^84 - 18 * q^87 + 35 * q^88 + 4 * q^89 + 13 * q^91 + 6 * q^92 - 25 * q^93 + 4 * q^94 - 33 * q^96 + 30 * q^97 + 11 * q^98 - 4 * 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 $

$2$	1.24483	0.880227	0.440114	−	0.897942i	$-0.354938\pi$
$2$	1.24483	0.880227	0.440114	+	0.897942i	$0.354938\pi$
$3$	−1.56903	−0.905881	−0.452941	−	0.891541i	$-0.649625\pi$
$3$	−1.56903	−0.905881	−0.452941	+	0.891541i	$0.649625\pi$
$4$	−0.450400	−0.225200
$5$	0	0
$5$	0	0
$6$	−1.95318	−0.797381
$7$	4.85788	1.83611	0.918053	−	0.396459i	$-0.129761\pi$
$7$	4.85788	1.83611	0.918053	+	0.396459i	$0.129761\pi$
$8$	−3.05033	−1.07845
$9$	−0.538136	−0.179379
$10$	0	0
$11$	−3.10161	−0.935172	−0.467586	−	0.883948i	$-0.654876\pi$
$11$	−3.10161	−0.935172	−0.467586	+	0.883948i	$0.654876\pi$
$12$	0.706693	0.204005
$13$	2.54124	0.704813	0.352406	−	0.935847i	$-0.385364\pi$
$13$	2.54124	0.704813	0.352406	+	0.935847i	$0.385364\pi$
$14$	6.04723	1.61619
$15$	0	0
$16$	−2.89634	−0.724085
$17$	−0.110271	−0.0267447	−0.0133723	−	0.999911i	$-0.504257\pi$
$17$	−0.110271	−0.0267447	−0.0133723	+	0.999911i	$0.504257\pi$
$18$	−0.669888	−0.157894
$19$	6.42136	1.47316	0.736580	−	0.676350i	$-0.236439\pi$
$19$	6.42136	1.47316	0.736580	+	0.676350i	$0.236439\pi$
$20$	0	0
$21$	−7.62217	−1.66329
$22$	−3.86098	−0.823164
$23$	3.81832	0.796176	0.398088	−	0.917347i	$-0.369674\pi$
$23$	3.81832	0.796176	0.398088	+	0.917347i	$0.369674\pi$
$24$	4.78607	0.976952
$25$	0	0
$26$	3.16341	0.620395
$27$	5.55145	1.06838
$28$	−2.18799	−0.413491
$29$	−9.12914	−1.69524	−0.847619	−	0.530605i	$-0.821965\pi$
$29$	−9.12914	−1.69524	−0.847619	+	0.530605i	$0.821965\pi$
$30$	0	0
$31$	7.75002	1.39194	0.695972	−	0.718068i	$-0.254974\pi$
$31$	7.75002	1.39194	0.695972	+	0.718068i	$0.254974\pi$
$32$	2.49521	0.441095
$33$	4.86653	0.847155
$34$	−0.137269	−0.0235414
$35$	0	0
$36$	0.242377	0.0403961
$37$	3.53258	0.580753	0.290376	−	0.956913i	$-0.406219\pi$
$37$	3.53258	0.580753	0.290376	+	0.956913i	$0.406219\pi$
$38$	7.99349	1.29672
$39$	−3.98729	−0.638477
$40$	0	0
$41$	−0.609541	−0.0951943	−0.0475971	−	0.998867i	$-0.515156\pi$
$41$	−0.609541	−0.0951943	−0.0475971	+	0.998867i	$0.515156\pi$
$42$	−9.48830	−1.46408
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	1.39697	0.210601
$45$	0	0
$46$	4.75316	0.700815
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	4.54445	0.655935
$49$	16.5990	2.37128
$50$	0	0
$51$	0.173019	0.0242275
$52$	−1.14457	−0.158724
$53$	3.58972	0.493085	0.246543	−	0.969132i	$-0.420705\pi$
$53$	3.58972	0.493085	0.246543	+	0.969132i	$0.420705\pi$
$54$	6.91061	0.940415
$55$	0	0
$56$	−14.8181	−1.98016
$57$	−10.0753	−1.33451
$58$	−11.3642	−1.49220
$59$	11.4458	1.49011	0.745057	−	0.667001i	$-0.232422\pi$
$59$	11.4458	1.49011	0.745057	+	0.667001i	$0.232422\pi$
$60$	0	0
$61$	12.9585	1.65917	0.829585	−	0.558380i	$-0.188577\pi$
$61$	12.9585	1.65917	0.829585	+	0.558380i	$0.188577\pi$
$62$	9.64745	1.22523
$63$	−2.61420	−0.329358
$64$	8.89879	1.11235
$65$	0	0
$66$	6.05800	0.745689
$67$	0.830083	0.101411	0.0507054	−	0.998714i	$-0.483853\pi$
$67$	0.830083	0.101411	0.0507054	+	0.998714i	$0.483853\pi$
$68$	0.0496662	0.00602291
$69$	−5.99108	−0.721241
$70$	0	0
$71$	−2.84340	−0.337449	−0.168725	−	0.985663i	$-0.553965\pi$
$71$	−2.84340	−0.337449	−0.168725	+	0.985663i	$0.553965\pi$
$72$	1.64149	0.193452
$73$	7.35401	0.860722	0.430361	−	0.902657i	$-0.358386\pi$
$73$	7.35401	0.860722	0.430361	+	0.902657i	$0.358386\pi$
$74$	4.39746	0.511194
$75$	0	0
$76$	−2.89218	−0.331756
$77$	−15.0673	−1.71707
$78$	−4.96349	−0.562005
$79$	−15.0577	−1.69413	−0.847064	−	0.531491i	$-0.821632\pi$
$79$	−15.0577	−1.69413	−0.847064	+	0.531491i	$0.821632\pi$
$80$	0	0
$81$	−7.09600	−0.788445
$82$	−0.758774	−0.0837926
$83$	1.90546	0.209151	0.104576	−	0.994517i	$-0.466652\pi$
$83$	1.90546	0.209151	0.104576	+	0.994517i	$0.466652\pi$
$84$	3.43303	0.374574
$85$	0	0
$86$	0	0
$87$	14.3239	1.53569
$88$	9.46095	1.00854
$89$	−3.39912	−0.360306	−0.180153	−	0.983639i	$-0.557659\pi$
$89$	−3.39912	−0.360306	−0.180153	+	0.983639i	$0.557659\pi$
$90$	0	0
$91$	12.3450	1.29411
$92$	−1.71977	−0.179299
$93$	−12.1600	−1.26094
$94$	1.24483	0.128394
$95$	0	0
$96$	−3.91507	−0.399580
$97$	13.7071	1.39174	0.695872	−	0.718165i	$-0.255018\pi$
$97$	13.7071	1.39174	0.695872	+	0.718165i	$0.255018\pi$
$98$	20.6629	2.08727
$99$	1.66909	0.167750
$100$	0	0
$101$	−5.75963	−0.573105	−0.286552	−	0.958065i	$-0.592509\pi$
$101$	−5.75963	−0.573105	−0.286552	+	0.958065i	$0.592509\pi$
$102$	0.215379	0.0213257
$103$	−12.6477	−1.24622	−0.623108	−	0.782135i	$-0.714130\pi$
$103$	−12.6477	−1.24622	−0.623108	+	0.782135i	$0.714130\pi$
$104$	−7.75162	−0.760108
$105$	0	0
$106$	4.46858	0.434027
$107$	−6.92123	−0.669100	−0.334550	−	0.942378i	$-0.608584\pi$
$107$	−6.92123	−0.669100	−0.334550	+	0.942378i	$0.608584\pi$
$108$	−2.50038	−0.240599
$109$	4.04448	0.387391	0.193695	−	0.981062i	$-0.437953\pi$
$109$	4.04448	0.387391	0.193695	+	0.981062i	$0.437953\pi$
$110$	0	0
$111$	−5.54274	−0.526093
$112$	−14.0701	−1.32950
$113$	10.1881	0.958416	0.479208	−	0.877701i	$-0.340924\pi$
$113$	10.1881	0.958416	0.479208	+	0.877701i	$0.340924\pi$
$114$	−12.5420	−1.17467
$115$	0	0
$116$	4.11177	0.381768
$117$	−1.36753	−0.126428
$118$	14.2480	1.31164
$119$	−0.535684	−0.0491060
$120$	0	0
$121$	−1.37999	−0.125454
$122$	16.1312	1.46045
$123$	0.956390	0.0862348
$124$	−3.49061	−0.313466
$125$	0	0
$126$	−3.25423	−0.289910
$127$	13.9039	1.23377	0.616884	−	0.787054i	$-0.288395\pi$
$127$	13.9039	1.23377	0.616884	+	0.787054i	$0.288395\pi$
$128$	6.08705	0.538024
$129$	0	0
$130$	0	0
$131$	−16.2681	−1.42135	−0.710674	−	0.703522i	$-0.751610\pi$
$131$	−16.2681	−1.42135	−0.710674	+	0.703522i	$0.751610\pi$
$132$	−2.19189	−0.190779
$133$	31.1942	2.70488
$134$	1.03331	0.0892645
$135$	0	0
$136$	0.336363	0.0288429
$137$	−3.90394	−0.333536	−0.166768	−	0.985996i	$-0.553333\pi$
$137$	−3.90394	−0.333536	−0.166768	+	0.985996i	$0.553333\pi$
$138$	−7.45787	−0.634856
$139$	−8.49207	−0.720288	−0.360144	−	0.932897i	$-0.617272\pi$
$139$	−8.49207	−0.720288	−0.360144	+	0.932897i	$0.617272\pi$
$140$	0	0
$141$	−1.56903	−0.132136
$142$	−3.53955	−0.297032
$143$	−7.88194	−0.659121
$144$	1.55862	0.129885
$145$	0	0
$146$	9.15448	0.757630
$147$	−26.0443	−2.14810
$148$	−1.59108	−0.130786
$149$	−19.9523	−1.63456	−0.817279	−	0.576242i	$-0.804519\pi$
$149$	−19.9523	−1.63456	−0.817279	+	0.576242i	$0.804519\pi$
$150$	0	0
$151$	8.34284	0.678931	0.339465	−	0.940619i	$-0.389754\pi$
$151$	8.34284	0.678931	0.339465	+	0.940619i	$0.389754\pi$
$152$	−19.5873	−1.58874
$153$	0.0593409	0.00479743
$154$	−18.7562	−1.51142
$155$	0	0
$156$	1.79588	0.143785
$157$	−5.20231	−0.415190	−0.207595	−	0.978215i	$-0.566564\pi$
$157$	−5.20231	−0.415190	−0.207595	+	0.978215i	$0.566564\pi$
$158$	−18.7443	−1.49122
$159$	−5.63238	−0.446677
$160$	0	0
$161$	18.5490	1.46186
$162$	−8.83331	−0.694010
$163$	−22.4553	−1.75884	−0.879418	−	0.476051i	$-0.842068\pi$
$163$	−22.4553	−1.75884	−0.879418	+	0.476051i	$0.842068\pi$
$164$	0.274537	0.0214378
$165$	0	0
$166$	2.37197	0.184101
$167$	4.48966	0.347420	0.173710	−	0.984797i	$-0.444424\pi$
$167$	4.48966	0.347420	0.173710	+	0.984797i	$0.444424\pi$
$168$	23.2501	1.79379
$169$	−6.54211	−0.503239
$170$	0	0
$171$	−3.45556	−0.264254
$172$	0	0
$173$	0.632735	0.0481060	0.0240530	−	0.999711i	$-0.492343\pi$
$173$	0.632735	0.0481060	0.0240530	+	0.999711i	$0.492343\pi$
$174$	17.8308	1.35175
$175$	0	0
$176$	8.98333	0.677144
$177$	−17.9588	−1.34987
$178$	−4.23132	−0.317151
$179$	−4.42786	−0.330954	−0.165477	−	0.986214i	$-0.552916\pi$
$179$	−4.42786	−0.330954	−0.165477	+	0.986214i	$0.552916\pi$
$180$	0	0
$181$	−18.7339	−1.39248	−0.696241	−	0.717808i	$-0.745146\pi$
$181$	−18.7339	−1.39248	−0.696241	+	0.717808i	$0.745146\pi$
$182$	15.3674	1.13911
$183$	−20.3324	−1.50301
$184$	−11.6471	−0.858639
$185$	0	0
$186$	−15.1372	−1.10991
$187$	0.342019	0.0250109
$188$	−0.450400	−0.0328488
$189$	26.9683	1.96165
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	−13.9625	−1.00766
$193$	−10.6190	−0.764370	−0.382185	−	0.924086i	$-0.624828\pi$
$193$	−10.6190	−0.764370	−0.382185	+	0.924086i	$0.624828\pi$
$194$	17.0630	1.22505
$195$	0	0
$196$	−7.47619	−0.534013
$197$	12.2032	0.869444	0.434722	−	0.900565i	$-0.356847\pi$
$197$	12.2032	0.869444	0.434722	+	0.900565i	$0.356847\pi$
$198$	2.07773	0.147658
$199$	5.80940	0.411817	0.205909	−	0.978571i	$-0.433985\pi$
$199$	5.80940	0.411817	0.205909	+	0.978571i	$0.433985\pi$
$200$	0	0
$201$	−1.30243	−0.0918662
$202$	−7.16976	−0.504462
$203$	−44.3483	−3.11264
$204$	−0.0779278	−0.00545604
$205$	0	0
$206$	−15.7443	−1.09695
$207$	−2.05478	−0.142817
$208$	−7.36029	−0.510344
$209$	−19.9166	−1.37766
$210$	0	0
$211$	−20.3098	−1.39818	−0.699091	−	0.715032i	$-0.746412\pi$
$211$	−20.3098	−1.39818	−0.699091	+	0.715032i	$0.746412\pi$
$212$	−1.61681	−0.111043
$213$	4.46139	0.305689
$214$	−8.61575	−0.588960
$215$	0	0
$216$	−16.9338	−1.15220
$217$	37.6487	2.55576
$218$	5.03469	0.340992
$219$	−11.5387	−0.779712
$220$	0	0
$221$	−0.280225	−0.0188500
$222$	−6.89976	−0.463082
$223$	−23.3963	−1.56674	−0.783368	−	0.621559i	$-0.786500\pi$
$223$	−23.3963	−1.56674	−0.783368	+	0.621559i	$0.786500\pi$
$224$	12.1214	0.809898
$225$	0	0
$226$	12.6824	0.843624
$227$	−18.9841	−1.26002	−0.630011	−	0.776586i	$-0.716950\pi$
$227$	−18.9841	−1.26002	−0.630011	+	0.776586i	$0.716950\pi$
$228$	4.53793	0.300532
$229$	4.34042	0.286823	0.143412	−	0.989663i	$-0.454193\pi$
$229$	4.34042	0.286823	0.143412	+	0.989663i	$0.454193\pi$
$230$	0	0
$231$	23.6410	1.55547
$232$	27.8469	1.82824
$233$	23.2989	1.52636	0.763181	−	0.646184i	$-0.223636\pi$
$233$	23.2989	1.52636	0.763181	+	0.646184i	$0.223636\pi$
$234$	−1.70234	−0.111286
$235$	0	0
$236$	−5.15518	−0.335574
$237$	23.6261	1.53468
$238$	−0.666835	−0.0432245
$239$	1.76092	0.113905	0.0569523	−	0.998377i	$-0.481862\pi$
$239$	1.76092	0.113905	0.0569523	+	0.998377i	$0.481862\pi$
$240$	0	0
$241$	23.7960	1.53284	0.766418	−	0.642343i	$-0.222037\pi$
$241$	23.7960	1.53284	0.766418	+	0.642343i	$0.222037\pi$
$242$	−1.71785	−0.110428
$243$	−5.52050	−0.354140
$244$	−5.83653	−0.373646
$245$	0	0
$246$	1.19054	0.0759062
$247$	16.3182	1.03830
$248$	−23.6401	−1.50115
$249$	−2.98973	−0.189466
$250$	0	0
$251$	19.2783	1.21683	0.608417	−	0.793617i	$-0.291805\pi$
$251$	19.2783	1.21683	0.608417	+	0.793617i	$0.291805\pi$
$252$	1.17744	0.0741715
$253$	−11.8430	−0.744561
$254$	17.3079	1.08600
$255$	0	0
$256$	−10.2202	−0.638765
$257$	27.5575	1.71899	0.859495	−	0.511144i	$-0.170778\pi$
$257$	27.5575	1.71899	0.859495	+	0.511144i	$0.170778\pi$
$258$	0	0
$259$	17.1608	1.06632
$260$	0	0
$261$	4.91272	0.304090
$262$	−20.2510	−1.25111
$263$	25.3194	1.56126	0.780630	−	0.624993i	$-0.214898\pi$
$263$	25.3194	1.56126	0.780630	+	0.624993i	$0.214898\pi$
$264$	−14.8445	−0.913618
$265$	0	0
$266$	38.8314	2.38091
$267$	5.33332	0.326394
$268$	−0.373870	−0.0228377
$269$	−10.2978	−0.627866	−0.313933	−	0.949445i	$-0.601647\pi$
$269$	−10.2978	−0.627866	−0.313933	+	0.949445i	$0.601647\pi$
$270$	0	0
$271$	−8.13401	−0.494106	−0.247053	−	0.969002i	$-0.579462\pi$
$271$	−8.13401	−0.494106	−0.247053	+	0.969002i	$0.579462\pi$
$272$	0.319383	0.0193654
$273$	−19.3697	−1.17231
$274$	−4.85974	−0.293588
$275$	0	0
$276$	2.69838	0.162424
$277$	−0.354867	−0.0213219	−0.0106609	−	0.999943i	$-0.503394\pi$
$277$	−0.354867	−0.0213219	−0.0106609	+	0.999943i	$0.503394\pi$
$278$	−10.5712	−0.634017
$279$	−4.17057	−0.249685
$280$	0	0
$281$	12.1090	0.722362	0.361181	−	0.932496i	$-0.382374\pi$
$281$	12.1090	0.722362	0.361181	+	0.932496i	$0.382374\pi$
$282$	−1.95318	−0.116310
$283$	−5.63259	−0.334823	−0.167411	−	0.985887i	$-0.553541\pi$
$283$	−5.63259	−0.334823	−0.167411	+	0.985887i	$0.553541\pi$
$284$	1.28067	0.0759937
$285$	0	0
$286$	−9.81167	−0.580176
$287$	−2.96108	−0.174787
$288$	−1.34276	−0.0791231
$289$	−16.9878	−0.999285
$290$	0	0
$291$	−21.5069	−1.26076
$292$	−3.31225	−0.193835
$293$	20.9861	1.22602	0.613011	−	0.790075i	$-0.289958\pi$
$293$	20.9861	1.22602	0.613011	+	0.790075i	$0.289958\pi$
$294$	−32.4207	−1.89082
$295$	0	0
$296$	−10.7755	−0.626315
$297$	−17.2185	−0.999116
$298$	−24.8372	−1.43878
$299$	9.70327	0.561155
$300$	0	0
$301$	0	0
$302$	10.3854	0.597613
$303$	9.03705	0.519165
$304$	−18.5984	−1.06669
$305$	0	0
$306$	0.0738693	0.00422282
$307$	−2.54835	−0.145442	−0.0727210	−	0.997352i	$-0.523168\pi$
$307$	−2.54835	−0.145442	−0.0727210	+	0.997352i	$0.523168\pi$
$308$	6.78630	0.386685
$309$	19.8447	1.12892
$310$	0	0
$311$	24.0153	1.36178	0.680892	−	0.732384i	$-0.261592\pi$
$311$	24.0153	1.36178	0.680892	+	0.732384i	$0.261592\pi$
$312$	12.1625	0.688568
$313$	−12.4235	−0.702220	−0.351110	−	0.936334i	$-0.614196\pi$
$313$	−12.4235	−0.702220	−0.351110	+	0.936334i	$0.614196\pi$
$314$	−6.47599	−0.365461
$315$	0	0
$316$	6.78201	0.381518
$317$	−6.82298	−0.383217	−0.191608	−	0.981471i	$-0.561370\pi$
$317$	−6.82298	−0.383217	−0.191608	+	0.981471i	$0.561370\pi$
$318$	−7.01135	−0.393177
$319$	28.3151	1.58534
$320$	0	0
$321$	10.8596	0.606126
$322$	23.0903	1.28677
$323$	−0.708090	−0.0393992
$324$	3.19604	0.177558
$325$	0	0
$326$	−27.9530	−1.54817
$327$	−6.34592	−0.350930
$328$	1.85930	0.102663
$329$	4.85788	0.267823
$330$	0	0
$331$	16.6190	0.913463	0.456732	−	0.889605i	$-0.349020\pi$
$331$	16.6190	0.913463	0.456732	+	0.889605i	$0.349020\pi$
$332$	−0.858220	−0.0471009
$333$	−1.90101	−0.104175
$334$	5.58886	0.305809
$335$	0	0
$336$	22.0764	1.20437
$337$	−18.8148	−1.02491	−0.512455	−	0.858714i	$-0.671264\pi$
$337$	−18.8148	−1.02491	−0.512455	+	0.858714i	$0.671264\pi$
$338$	−8.14381	−0.442965
$339$	−15.9855	−0.868211
$340$	0	0
$341$	−24.0376	−1.30171
$342$	−4.30159	−0.232603
$343$	46.6306	2.51782
$344$	0	0
$345$	0	0
$346$	0.787647	0.0423442
$347$	21.1569	1.13576	0.567880	−	0.823111i	$-0.307764\pi$
$347$	21.1569	1.13576	0.567880	+	0.823111i	$0.307764\pi$
$348$	−6.45150	−0.345837
$349$	−5.05955	−0.270831	−0.135416	−	0.990789i	$-0.543237\pi$
$349$	−5.05955	−0.270831	−0.135416	+	0.990789i	$0.543237\pi$
$350$	0	0
$351$	14.1076	0.753006
$352$	−7.73919	−0.412500
$353$	12.0847	0.643202	0.321601	−	0.946875i	$-0.395779\pi$
$353$	12.0847	0.643202	0.321601	+	0.946875i	$0.395779\pi$
$354$	−22.3556	−1.18819
$355$	0	0
$356$	1.53096	0.0811409
$357$	0.840505	0.0444843
$358$	−5.51194	−0.291315
$359$	26.2394	1.38486	0.692430	−	0.721485i	$-0.256540\pi$
$359$	26.2394	1.38486	0.692430	+	0.721485i	$0.256540\pi$
$360$	0	0
$361$	22.2338	1.17020
$362$	−23.3206	−1.22570
$363$	2.16525	0.113646
$364$	−5.56020	−0.291434
$365$	0	0
$366$	−25.3103	−1.32299
$367$	−2.09583	−0.109401	−0.0547007	−	0.998503i	$-0.517420\pi$
$367$	−2.09583	−0.109401	−0.0547007	+	0.998503i	$0.517420\pi$
$368$	−11.0592	−0.576499
$369$	0.328016	0.0170758
$370$	0	0
$371$	17.4384	0.905357
$372$	5.47689	0.283963
$373$	−6.81058	−0.352639	−0.176319	−	0.984333i	$-0.556419\pi$
$373$	−6.81058	−0.352639	−0.176319	+	0.984333i	$0.556419\pi$
$374$	0.425755	0.0220152
$375$	0	0
$376$	−3.05033	−0.157309
$377$	−23.1993	−1.19483
$378$	33.5709	1.72670
$379$	−30.2644	−1.55458	−0.777290	−	0.629143i	$-0.783406\pi$
$379$	−30.2644	−1.55458	−0.777290	+	0.629143i	$0.783406\pi$
$380$	0	0
$381$	−21.8156	−1.11765
$382$	14.9379	0.764292
$383$	−4.17024	−0.213089	−0.106545	−	0.994308i	$-0.533979\pi$
$383$	−4.17024	−0.213089	−0.106545	+	0.994308i	$0.533979\pi$
$384$	−9.55078	−0.487386
$385$	0	0
$386$	−13.2188	−0.672819
$387$	0	0
$388$	−6.17368	−0.313421
$389$	−3.30863	−0.167754	−0.0838772	−	0.996476i	$-0.526730\pi$
$389$	−3.30863	−0.167754	−0.0838772	+	0.996476i	$0.526730\pi$
$390$	0	0
$391$	−0.421051	−0.0212935
$392$	−50.6323	−2.55732
$393$	25.5251	1.28757
$394$	15.1909	0.765308
$395$	0	0
$396$	−0.751759	−0.0377773
$397$	21.0437	1.05615	0.528077	−	0.849196i	$-0.322913\pi$
$397$	21.0437	1.05615	0.528077	+	0.849196i	$0.322913\pi$
$398$	7.23171	0.362493
$399$	−48.9447	−2.45030
$400$	0	0
$401$	22.1154	1.10439	0.552195	−	0.833715i	$-0.313790\pi$
$401$	22.1154	1.10439	0.552195	+	0.833715i	$0.313790\pi$
$402$	−1.62130	−0.0808631
$403$	19.6947	0.981061
$404$	2.59414	0.129063
$405$	0	0
$406$	−55.2060	−2.73983
$407$	−10.9567	−0.543104
$408$	−0.527765	−0.0261283
$409$	11.6135	0.574251	0.287125	−	0.957893i	$-0.407300\pi$
$409$	11.6135	0.574251	0.287125	+	0.957893i	$0.407300\pi$
$410$	0	0
$411$	6.12541	0.302144
$412$	5.69654	0.280648
$413$	55.6022	2.73601
$414$	−2.55785	−0.125711
$415$	0	0
$416$	6.34093	0.310890
$417$	13.3243	0.652496
$418$	−24.7927	−1.21265
$419$	29.8371	1.45764	0.728818	−	0.684707i	$-0.240070\pi$
$419$	29.8371	1.45764	0.728818	+	0.684707i	$0.240070\pi$
$420$	0	0
$421$	−10.3642	−0.505118	−0.252559	−	0.967581i	$-0.581272\pi$
$421$	−10.3642	−0.505118	−0.252559	+	0.967581i	$0.581272\pi$
$422$	−25.2822	−1.23072
$423$	−0.538136	−0.0261651
$424$	−10.9498	−0.531770
$425$	0	0
$426$	5.55366	0.269076
$427$	62.9510	3.04641
$428$	3.11732	0.150682
$429$	12.3670	0.597086
$430$	0	0
$431$	11.5824	0.557904	0.278952	−	0.960305i	$-0.410013\pi$
$431$	11.5824	0.557904	0.278952	+	0.960305i	$0.410013\pi$
$432$	−16.0789	−0.773596
$433$	−22.0994	−1.06203	−0.531016	−	0.847362i	$-0.678190\pi$
$433$	−22.0994	−1.06203	−0.531016	+	0.847362i	$0.678190\pi$
$434$	46.8661	2.24965
$435$	0	0
$436$	−1.82164	−0.0872405
$437$	24.5188	1.17289
$438$	−14.3637	−0.686323
$439$	8.21917	0.392279	0.196140	−	0.980576i	$-0.437159\pi$
$439$	8.21917	0.392279	0.196140	+	0.980576i	$0.437159\pi$
$440$	0	0
$441$	−8.93251	−0.425358
$442$	−0.348833	−0.0165923
$443$	−29.9823	−1.42450	−0.712251	−	0.701925i	$-0.752324\pi$
$443$	−29.9823	−1.42450	−0.712251	+	0.701925i	$0.752324\pi$
$444$	2.49645	0.118476
$445$	0	0
$446$	−29.1245	−1.37908
$447$	31.3059	1.48072
$448$	43.2292	2.04239
$449$	14.0361	0.662407	0.331203	−	0.943559i	$-0.392545\pi$
$449$	14.0361	0.662407	0.331203	+	0.943559i	$0.392545\pi$
$450$	0	0
$451$	1.89056	0.0890230
$452$	−4.58872	−0.215835
$453$	−13.0902	−0.615031
$454$	−23.6320	−1.10911
$455$	0	0
$456$	30.7330	1.43921
$457$	−8.11147	−0.379439	−0.189719	−	0.981838i	$-0.560758\pi$
$457$	−8.11147	−0.379439	−0.189719	+	0.981838i	$0.560758\pi$
$458$	5.40309	0.252470
$459$	−0.612165	−0.0285734
$460$	0	0
$461$	2.79983	0.130401	0.0652004	−	0.997872i	$-0.479231\pi$
$461$	2.79983	0.130401	0.0652004	+	0.997872i	$0.479231\pi$
$462$	29.4290	1.36916
$463$	6.04607	0.280985	0.140492	−	0.990082i	$-0.455131\pi$
$463$	6.04607	0.280985	0.140492	+	0.990082i	$0.455131\pi$
$464$	26.4411	1.22750
$465$	0	0
$466$	29.0032	1.34355
$467$	−39.1834	−1.81319	−0.906595	−	0.422002i	$-0.861327\pi$
$467$	−39.1834	−1.81319	−0.906595	+	0.422002i	$0.861327\pi$
$468$	0.615937	0.0284717
$469$	4.03244	0.186201
$470$	0	0
$471$	8.16260	0.376113
$472$	−34.9134	−1.60702
$473$	0	0
$474$	29.4104	1.35087
$475$	0	0
$476$	0.241272	0.0110587
$477$	−1.93176	−0.0884490
$478$	2.19205	0.100262
$479$	−28.2663	−1.29152	−0.645761	−	0.763539i	$-0.723460\pi$
$479$	−28.2663	−1.29152	−0.645761	+	0.763539i	$0.723460\pi$
$480$	0	0
$481$	8.97713	0.409322
$482$	29.6220	1.34924
$483$	−29.1039	−1.32427
$484$	0.621548	0.0282522
$485$	0	0
$486$	−6.87207	−0.311724
$487$	−13.2797	−0.601759	−0.300879	−	0.953662i	$-0.597280\pi$
$487$	−13.2797	−0.601759	−0.300879	+	0.953662i	$0.597280\pi$
$488$	−39.5278	−1.78934
$489$	35.2331	1.59330
$490$	0	0
$491$	−37.1491	−1.67651	−0.838257	−	0.545276i	$-0.816425\pi$
$491$	−37.1491	−1.67651	−0.838257	+	0.545276i	$0.816425\pi$
$492$	−0.430758	−0.0194201
$493$	1.00668	0.0453386
$494$	20.3134	0.913942
$495$	0	0
$496$	−22.4467	−1.00789
$497$	−13.8129	−0.619592
$498$	−3.72170	−0.166773
$499$	−27.2013	−1.21770	−0.608848	−	0.793287i	$-0.708368\pi$
$499$	−27.2013	−1.21770	−0.608848	+	0.793287i	$0.708368\pi$
$500$	0	0
$501$	−7.04442	−0.314722
$502$	23.9982	1.07109
$503$	10.7491	0.479277	0.239639	−	0.970862i	$-0.422971\pi$
$503$	10.7491	0.479277	0.239639	+	0.970862i	$0.422971\pi$
$504$	7.97417	0.355198
$505$	0	0
$506$	−14.7425	−0.655383
$507$	10.2648	0.455875
$508$	−6.26230	−0.277845
$509$	12.1374	0.537981	0.268991	−	0.963143i	$-0.413310\pi$
$509$	12.1374	0.537981	0.268991	+	0.963143i	$0.413310\pi$
$510$	0	0
$511$	35.7249	1.58038
$512$	−24.8966	−1.10028
$513$	35.6478	1.57389
$514$	34.3044	1.51310
$515$	0	0
$516$	0	0
$517$	−3.10161	−0.136409
$518$	21.3623	0.938607
$519$	−0.992782	−0.0435783
$520$	0	0
$521$	6.51071	0.285240	0.142620	−	0.989778i	$-0.454447\pi$
$521$	6.51071	0.285240	0.142620	+	0.989778i	$0.454447\pi$
$522$	6.11550	0.267668
$523$	41.7274	1.82461	0.912305	−	0.409511i	$-0.134301\pi$
$523$	41.7274	1.82461	0.912305	+	0.409511i	$0.134301\pi$
$524$	7.32714	0.320088
$525$	0	0
$526$	31.5183	1.37426
$527$	−0.854604	−0.0372271
$528$	−14.0951	−0.613412
$529$	−8.42040	−0.366104
$530$	0	0
$531$	−6.15939	−0.267295
$532$	−14.0499	−0.609139
$533$	−1.54899	−0.0670941
$534$	6.63908	0.287301
$535$	0	0
$536$	−2.53203	−0.109367
$537$	6.94747	0.299805
$538$	−12.8190	−0.552665
$539$	−51.4836	−2.21756
$540$	0	0
$541$	6.04913	0.260072	0.130036	−	0.991509i	$-0.458491\pi$
$541$	6.04913	0.260072	0.130036	+	0.991509i	$0.458491\pi$
$542$	−10.1255	−0.434925
$543$	29.3942	1.26142
$544$	−0.275150	−0.0117970
$545$	0	0
$546$	−24.1120	−1.03190
$547$	−8.06888	−0.345001	−0.172500	−	0.985009i	$-0.555185\pi$
$547$	−8.06888	−0.345001	−0.172500	+	0.985009i	$0.555185\pi$
$548$	1.75834	0.0751124
$549$	−6.97346	−0.297620
$550$	0	0
$551$	−58.6215	−2.49736
$552$	18.2748	0.777825
$553$	−73.1486	−3.11060
$554$	−0.441748	−0.0187681
$555$	0	0
$556$	3.82483	0.162209
$557$	−27.3348	−1.15821	−0.579106	−	0.815252i	$-0.696598\pi$
$557$	−27.3348	−1.15821	−0.579106	+	0.815252i	$0.696598\pi$
$558$	−5.19164	−0.219780
$559$	0	0
$560$	0	0
$561$	−0.536638	−0.0226569
$562$	15.0736	0.635843
$563$	4.97350	0.209608	0.104804	−	0.994493i	$-0.466578\pi$
$563$	4.97350	0.209608	0.104804	+	0.994493i	$0.466578\pi$
$564$	0.706693	0.0297571
$565$	0	0
$566$	−7.01161	−0.294720
$567$	−34.4715	−1.44767
$568$	8.67330	0.363924
$569$	−24.5774	−1.03034	−0.515169	−	0.857089i	$-0.672271\pi$
$569$	−24.5774	−1.03034	−0.515169	+	0.857089i	$0.672271\pi$
$570$	0	0
$571$	−4.41342	−0.184696	−0.0923480	−	0.995727i	$-0.529437\pi$
$571$	−4.41342	−0.184696	−0.0923480	+	0.995727i	$0.529437\pi$
$572$	3.55003	0.148434
$573$	−18.8284	−0.786567
$574$	−3.68603	−0.153852
$575$	0	0
$576$	−4.78876	−0.199532
$577$	−5.33798	−0.222223	−0.111112	−	0.993808i	$-0.535441\pi$
$577$	−5.33798	−0.222223	−0.111112	+	0.993808i	$0.535441\pi$
$578$	−21.1470	−0.879598
$579$	16.6615	0.692429
$580$	0	0
$581$	9.25649	0.384024
$582$	−26.7724	−1.10975
$583$	−11.1339	−0.461120
$584$	−22.4321	−0.928249
$585$	0	0
$586$	26.1241	1.07918
$587$	−26.5476	−1.09574	−0.547869	−	0.836564i	$-0.684561\pi$
$587$	−26.5476	−1.09574	−0.547869	+	0.836564i	$0.684561\pi$
$588$	11.7304	0.483753
$589$	49.7656	2.05056
$590$	0	0
$591$	−19.1473	−0.787613
$592$	−10.2316	−0.420514
$593$	−31.9007	−1.31000	−0.655001	−	0.755628i	$-0.727332\pi$
$593$	−31.9007	−1.31000	−0.655001	+	0.755628i	$0.727332\pi$
$594$	−21.4340	−0.879449
$595$	0	0
$596$	8.98654	0.368103
$597$	−9.11514	−0.373058
$598$	12.0789	0.493944
$599$	−28.6029	−1.16868	−0.584342	−	0.811507i	$-0.698647\pi$
$599$	−28.6029	−1.16868	−0.584342	+	0.811507i	$0.698647\pi$
$600$	0	0
$601$	−9.88280	−0.403128	−0.201564	−	0.979475i	$-0.564602\pi$
$601$	−9.88280	−0.403128	−0.201564	+	0.979475i	$0.564602\pi$
$602$	0	0
$603$	−0.446698	−0.0181909
$604$	−3.75762	−0.152895
$605$	0	0
$606$	11.2496	0.456983
$607$	−24.4825	−0.993712	−0.496856	−	0.867833i	$-0.665512\pi$
$607$	−24.4825	−0.993712	−0.496856	+	0.867833i	$0.665512\pi$
$608$	16.0226	0.649804
$609$	69.5839	2.81968
$610$	0	0
$611$	2.54124	0.102807
$612$	−0.0267272	−0.00108038
$613$	11.3629	0.458943	0.229472	−	0.973315i	$-0.426300\pi$
$613$	11.3629	0.458943	0.229472	+	0.973315i	$0.426300\pi$
$614$	−3.17226	−0.128022
$615$	0	0
$616$	45.9601	1.85179
$617$	12.3388	0.496743	0.248371	−	0.968665i	$-0.420105\pi$
$617$	12.3388	0.496743	0.248371	+	0.968665i	$0.420105\pi$
$618$	24.7032	0.993710
$619$	−39.9109	−1.60415	−0.802077	−	0.597221i	$-0.796271\pi$
$619$	−39.9109	−1.60415	−0.802077	+	0.597221i	$0.796271\pi$
$620$	0	0
$621$	21.1972	0.850616
$622$	29.8950	1.19868
$623$	−16.5125	−0.661559
$624$	11.5485	0.462311
$625$	0	0
$626$	−15.4652	−0.618113
$627$	31.2497	1.24799
$628$	2.34312	0.0935008
$629$	−0.389542	−0.0155320
$630$	0	0
$631$	17.2020	0.684799	0.342400	−	0.939554i	$-0.388760\pi$
$631$	17.2020	0.684799	0.342400	+	0.939554i	$0.388760\pi$
$632$	45.9311	1.82704
$633$	31.8667	1.26659
$634$	−8.49345	−0.337318
$635$	0	0
$636$	2.53683	0.100592
$637$	42.1820	1.67131
$638$	35.2474	1.39546
$639$	1.53014	0.0605312
$640$	0	0
$641$	−24.4710	−0.966547	−0.483274	−	0.875469i	$-0.660552\pi$
$641$	−24.4710	−0.966547	−0.483274	+	0.875469i	$0.660552\pi$
$642$	13.5184	0.533528
$643$	30.7952	1.21444	0.607222	−	0.794532i	$-0.292284\pi$
$643$	30.7952	1.21444	0.607222	+	0.794532i	$0.292284\pi$
$644$	−8.35446	−0.329212
$645$	0	0
$646$	−0.881451	−0.0346802
$647$	−18.9055	−0.743251	−0.371625	−	0.928383i	$-0.621199\pi$
$647$	−18.9055	−0.743251	−0.371625	+	0.928383i	$0.621199\pi$
$648$	21.6451	0.850302
$649$	−35.5004	−1.39351
$650$	0	0
$651$	−59.0720	−2.31521
$652$	10.1139	0.396090
$653$	26.8183	1.04948	0.524740	−	0.851262i	$-0.324162\pi$
$653$	26.8183	1.04948	0.524740	+	0.851262i	$0.324162\pi$
$654$	−7.89959	−0.308898
$655$	0	0
$656$	1.76544	0.0689287
$657$	−3.95746	−0.154395
$658$	6.04723	0.235745
$659$	−6.68518	−0.260418	−0.130209	−	0.991487i	$-0.541565\pi$
$659$	−6.68518	−0.260418	−0.130209	+	0.991487i	$0.541565\pi$
$660$	0	0
$661$	−6.11541	−0.237862	−0.118931	−	0.992903i	$-0.537947\pi$
$661$	−6.11541	−0.237862	−0.118931	+	0.992903i	$0.537947\pi$
$662$	20.6878	0.804055
$663$	0.439683	0.0170759
$664$	−5.81228	−0.225560
$665$	0	0
$666$	−2.36643	−0.0916974
$667$	−34.8580	−1.34971
$668$	−2.02214	−0.0782391
$669$	36.7096	1.41928
$670$	0	0
$671$	−40.1924	−1.55161
$672$	−19.0189	−0.733671
$673$	37.1941	1.43373	0.716863	−	0.697214i	$-0.245577\pi$
$673$	37.1941	1.43373	0.716863	+	0.697214i	$0.245577\pi$
$674$	−23.4213	−0.902153
$675$	0	0
$676$	2.94657	0.113330
$677$	−3.75841	−0.144447	−0.0722237	−	0.997388i	$-0.523010\pi$
$677$	−3.75841	−0.144447	−0.0722237	+	0.997388i	$0.523010\pi$
$678$	−19.8992	−0.764223
$679$	66.5874	2.55539
$680$	0	0
$681$	29.7867	1.14143
$682$	−29.9227	−1.14580
$683$	−15.9014	−0.608450	−0.304225	−	0.952600i	$-0.598398\pi$
$683$	−15.9014	−0.608450	−0.304225	+	0.952600i	$0.598398\pi$
$684$	1.55639	0.0595100
$685$	0	0
$686$	58.0472	2.21625
$687$	−6.81027	−0.259828
$688$	0	0
$689$	9.12232	0.347533
$690$	0	0
$691$	−46.6018	−1.77282	−0.886409	−	0.462903i	$-0.846808\pi$
$691$	−46.6018	−1.77282	−0.886409	+	0.462903i	$0.846808\pi$
$692$	−0.284984	−0.0108335
$693$	8.10824	0.308007
$694$	26.3367	0.999727
$695$	0	0
$696$	−43.6927	−1.65617
$697$	0.0672148	0.00254594
$698$	−6.29828	−0.238393
$699$	−36.5568	−1.38270
$700$	0	0
$701$	6.35690	0.240097	0.120048	−	0.992768i	$-0.461695\pi$
$701$	6.35690	0.240097	0.120048	+	0.992768i	$0.461695\pi$
$702$	17.5615	0.662816
$703$	22.6840	0.855542
$704$	−27.6006	−1.04024
$705$	0	0
$706$	15.0434	0.566164
$707$	−27.9796	−1.05228
$708$	8.08865	0.303990
$709$	30.4636	1.14408	0.572042	−	0.820224i	$-0.306151\pi$
$709$	30.4636	1.14408	0.572042	+	0.820224i	$0.306151\pi$
$710$	0	0
$711$	8.10311	0.303890
$712$	10.3684	0.388573
$713$	29.5921	1.10823
$714$	1.04629	0.0391563
$715$	0	0
$716$	1.99431	0.0745309
$717$	−2.76294	−0.103184
$718$	32.6635	1.21899
$719$	7.75891	0.289358	0.144679	−	0.989479i	$-0.453785\pi$
$719$	7.75891	0.289358	0.144679	+	0.989479i	$0.453785\pi$
$720$	0	0
$721$	−61.4411	−2.28819
$722$	27.6773	1.03004
$723$	−37.3367	−1.38857
$724$	8.43777	0.313587
$725$	0	0
$726$	2.69536	0.100034
$727$	−20.6269	−0.765008	−0.382504	−	0.923954i	$-0.624938\pi$
$727$	−20.6269	−0.765008	−0.382504	+	0.923954i	$0.624938\pi$
$728$	−37.6564	−1.39564
$729$	29.9498	1.10925
$730$	0	0
$731$	0	0
$732$	9.15771	0.338479
$733$	−1.17490	−0.0433959	−0.0216979	−	0.999765i	$-0.506907\pi$
$733$	−1.17490	−0.0433959	−0.0216979	+	0.999765i	$0.506907\pi$
$734$	−2.60895	−0.0962981
$735$	0	0
$736$	9.52753	0.351189
$737$	−2.57460	−0.0948365
$738$	0.408324	0.0150306
$739$	−13.9115	−0.511741	−0.255871	−	0.966711i	$-0.582362\pi$
$739$	−13.9115	−0.511741	−0.255871	+	0.966711i	$0.582362\pi$
$740$	0	0
$741$	−25.6038	−0.940578
$742$	21.7078	0.796920
$743$	−1.16399	−0.0427026	−0.0213513	−	0.999772i	$-0.506797\pi$
$743$	−1.16399	−0.0427026	−0.0213513	+	0.999772i	$0.506797\pi$
$744$	37.0921	1.35986
$745$	0	0
$746$	−8.47801	−0.310402
$747$	−1.02540	−0.0375173
$748$	−0.154045	−0.00563245
$749$	−33.6225	−1.22854
$750$	0	0
$751$	26.9968	0.985128	0.492564	−	0.870276i	$-0.336060\pi$
$751$	26.9968	0.985128	0.492564	+	0.870276i	$0.336060\pi$
$752$	−2.89634	−0.105619
$753$	−30.2483	−1.10231
$754$	−28.8792	−1.05172
$755$	0	0
$756$	−12.1465	−0.441765
$757$	−1.54929	−0.0563100	−0.0281550	−	0.999604i	$-0.508963\pi$
$757$	−1.54929	−0.0563100	−0.0281550	+	0.999604i	$0.508963\pi$
$758$	−37.6741	−1.36838
$759$	18.5820	0.674484
$760$	0	0
$761$	−50.3544	−1.82535	−0.912674	−	0.408689i	$-0.865986\pi$
$761$	−50.3544	−1.82535	−0.912674	+	0.408689i	$0.865986\pi$
$762$	−27.1567	−0.983783
$763$	19.6476	0.711290
$764$	−5.40480	−0.195539
$765$	0	0
$766$	−5.19124	−0.187567
$767$	29.0865	1.05025
$768$	16.0359	0.578646
$769$	18.3924	0.663246	0.331623	−	0.943412i	$-0.392404\pi$
$769$	18.3924	0.663246	0.331623	+	0.943412i	$0.392404\pi$
$770$	0	0
$771$	−43.2386	−1.55720
$772$	4.78279	0.172136
$773$	30.3766	1.09257	0.546285	−	0.837600i	$-0.316042\pi$
$773$	30.3766	1.09257	0.546285	+	0.837600i	$0.316042\pi$
$774$	0	0
$775$	0	0
$776$	−41.8112	−1.50093
$777$	−26.9259	−0.965962
$778$	−4.11868	−0.147662
$779$	−3.91408	−0.140236
$780$	0	0
$781$	8.81913	0.315573
$782$	−0.524137	−0.0187431
$783$	−50.6800	−1.81115
$784$	−48.0763	−1.71701
$785$	0	0
$786$	31.7744	1.13336
$787$	22.9335	0.817492	0.408746	−	0.912648i	$-0.365966\pi$
$787$	22.9335	0.817492	0.408746	+	0.912648i	$0.365966\pi$
$788$	−5.49634	−0.195799
$789$	−39.7270	−1.41432
$790$	0	0
$791$	49.4925	1.75975
$792$	−5.09128	−0.180911
$793$	32.9307	1.16940
$794$	26.1959	0.929656
$795$	0	0
$796$	−2.61656	−0.0927414
$797$	40.0287	1.41789	0.708945	−	0.705264i	$-0.249171\pi$
$797$	40.0287	1.41789	0.708945	+	0.705264i	$0.249171\pi$
$798$	−60.9277	−2.15682
$799$	−0.110271	−0.00390111
$800$	0	0
$801$	1.82919	0.0646311
$802$	27.5299	0.972115
$803$	−22.8093	−0.804923
$804$	0.586614	0.0206883
$805$	0	0
$806$	24.5165	0.863556
$807$	16.1575	0.568772
$808$	17.5688	0.618068
$809$	41.8088	1.46992	0.734960	−	0.678110i	$-0.237201\pi$
$809$	41.8088	1.46992	0.734960	+	0.678110i	$0.237201\pi$
$810$	0	0
$811$	−7.75781	−0.272414	−0.136207	−	0.990680i	$-0.543491\pi$
$811$	−7.75781	−0.272414	−0.136207	+	0.990680i	$0.543491\pi$
$812$	19.9745	0.700966
$813$	12.7625	0.447601
$814$	−13.6392	−0.478055
$815$	0	0
$816$	−0.501122	−0.0175428
$817$	0	0
$818$	14.4568	0.505471
$819$	−6.64330	−0.232136
$820$	0	0
$821$	30.0752	1.04963	0.524816	−	0.851215i	$-0.324134\pi$
$821$	30.0752	1.04963	0.524816	+	0.851215i	$0.324134\pi$
$822$	7.62509	0.265956
$823$	39.4512	1.37518	0.687592	−	0.726097i	$-0.258668\pi$
$823$	39.4512	1.37518	0.687592	+	0.726097i	$0.258668\pi$
$824$	38.5797	1.34399
$825$	0	0
$826$	69.2152	2.40831
$827$	7.35646	0.255809	0.127905	−	0.991786i	$-0.459175\pi$
$827$	7.35646	0.255809	0.127905	+	0.991786i	$0.459175\pi$
$828$	0.925473	0.0321624
$829$	29.5367	1.02585	0.512926	−	0.858433i	$-0.328561\pi$
$829$	29.5367	1.02585	0.512926	+	0.858433i	$0.328561\pi$
$830$	0	0
$831$	0.556797	0.0193151
$832$	22.6139	0.783998
$833$	−1.83039	−0.0634192
$834$	16.5865	0.574345
$835$	0	0
$836$	8.97043	0.310249
$837$	43.0239	1.48712
$838$	37.1421	1.28305
$839$	−25.7611	−0.889373	−0.444687	−	0.895686i	$-0.646685\pi$
$839$	−25.7611	−0.889373	−0.444687	+	0.895686i	$0.646685\pi$
$840$	0	0
$841$	54.3412	1.87384
$842$	−12.9016	−0.444619
$843$	−18.9994	−0.654374
$844$	9.14753	0.314871
$845$	0	0
$846$	−0.669888	−0.0230312
$847$	−6.70382	−0.230346
$848$	−10.3970	−0.357036
$849$	8.83772	0.303310
$850$	0	0
$851$	13.4885	0.462381
$852$	−2.00941	−0.0688412
$853$	14.5052	0.496647	0.248324	−	0.968677i	$-0.420120\pi$
$853$	14.5052	0.496647	0.248324	+	0.968677i	$0.420120\pi$
$854$	78.3632	2.68153
$855$	0	0
$856$	21.1120	0.721594
$857$	6.74146	0.230284	0.115142	−	0.993349i	$-0.463268\pi$
$857$	6.74146	0.230284	0.115142	+	0.993349i	$0.463268\pi$
$858$	15.3948	0.525571
$859$	−14.5534	−0.496555	−0.248278	−	0.968689i	$-0.579865\pi$
$859$	−14.5534	−0.496555	−0.248278	+	0.968689i	$0.579865\pi$
$860$	0	0
$861$	4.64602	0.158336
$862$	14.4181	0.491082
$863$	−51.1956	−1.74272	−0.871359	−	0.490646i	$-0.836761\pi$
$863$	−51.1956	−1.74272	−0.871359	+	0.490646i	$0.836761\pi$
$864$	13.8521	0.471256
$865$	0	0
$866$	−27.5100	−0.934829
$867$	26.6545	0.905234
$868$	−16.9570	−0.575557
$869$	46.7033	1.58430
$870$	0	0
$871$	2.10944	0.0714756
$872$	−12.3370	−0.417783
$873$	−7.37628	−0.249649
$874$	30.5217	1.03241
$875$	0	0
$876$	5.19703	0.175591
$877$	−20.2978	−0.685409	−0.342704	−	0.939443i	$-0.611343\pi$
$877$	−20.2978	−0.685409	−0.342704	+	0.939443i	$0.611343\pi$
$878$	10.2315	0.345295
$879$	−32.9279	−1.11063
$880$	0	0
$881$	17.1953	0.579325	0.289662	−	0.957129i	$-0.406457\pi$
$881$	17.1953	0.579325	0.289662	+	0.957129i	$0.406457\pi$
$882$	−11.1194	−0.374411
$883$	−7.82841	−0.263447	−0.131724	−	0.991286i	$-0.542051\pi$
$883$	−7.82841	−0.263447	−0.131724	+	0.991286i	$0.542051\pi$
$884$	0.126214	0.00424502
$885$	0	0
$886$	−37.3228	−1.25389
$887$	−25.7483	−0.864542	−0.432271	−	0.901744i	$-0.642288\pi$
$887$	−25.7483	−0.864542	−0.432271	+	0.901744i	$0.642288\pi$
$888$	16.9072	0.567368
$889$	67.5432	2.26533
$890$	0	0
$891$	22.0091	0.737331
$892$	10.5377	0.352829
$893$	6.42136	0.214882
$894$	38.9705	1.30337
$895$	0	0
$896$	29.5701	0.987869
$897$	−15.2248	−0.508340
$898$	17.4726	0.583068
$899$	−70.7510	−2.35968
$900$	0	0
$901$	−0.395842	−0.0131874
$902$	2.35343	0.0783605
$903$	0	0
$904$	−31.0771	−1.03361
$905$	0	0
$906$	−16.2950	−0.541367
$907$	−45.6749	−1.51661	−0.758305	−	0.651900i	$-0.773972\pi$
$907$	−45.6749	−1.51661	−0.758305	+	0.651900i	$0.773972\pi$
$908$	8.55047	0.283757
$909$	3.09947	0.102803
$910$	0	0
$911$	46.2056	1.53086	0.765431	−	0.643518i	$-0.222526\pi$
$911$	46.2056	1.53086	0.765431	+	0.643518i	$0.222526\pi$
$912$	29.1815	0.966297
$913$	−5.91000	−0.195592
$914$	−10.0974	−0.333992
$915$	0	0
$916$	−1.95493	−0.0645927
$917$	−79.0283	−2.60974
$918$	−0.762041	−0.0251511
$919$	−23.5394	−0.776493	−0.388246	−	0.921556i	$-0.626919\pi$
$919$	−23.5394	−0.776493	−0.388246	+	0.921556i	$0.626919\pi$
$920$	0	0
$921$	3.99844	0.131753
$922$	3.48530	0.114782
$923$	−7.22575	−0.237839
$924$	−10.6479	−0.350291
$925$	0	0
$926$	7.52633	0.247330
$927$	6.80620	0.223545
$928$	−22.7792	−0.747762
$929$	17.5447	0.575622	0.287811	−	0.957687i	$-0.407073\pi$
$929$	17.5447	0.575622	0.287811	+	0.957687i	$0.407073\pi$
$930$	0	0
$931$	106.588	3.49328
$932$	−10.4938	−0.343737
$933$	−37.6808	−1.23361
$934$	−48.7766	−1.59602
$935$	0	0
$936$	4.17142	0.136347
$937$	−23.4849	−0.767219	−0.383609	−	0.923495i	$-0.625319\pi$
$937$	−23.4849	−0.767219	−0.383609	+	0.923495i	$0.625319\pi$
$938$	5.01970	0.163899
$939$	19.4929	0.636128
$940$	0	0
$941$	−37.2218	−1.21340	−0.606699	−	0.794932i	$-0.707507\pi$
$941$	−37.2218	−1.21340	−0.606699	+	0.794932i	$0.707507\pi$
$942$	10.1610	0.331065
$943$	−2.32742	−0.0757914
$944$	−33.1509	−1.07897
$945$	0	0
$946$	0	0
$947$	46.9286	1.52497	0.762487	−	0.647003i	$-0.223978\pi$
$947$	46.9286	1.52497	0.762487	+	0.647003i	$0.223978\pi$
$948$	−10.6412	−0.345610
$949$	18.6883	0.606647
$950$	0	0
$951$	10.7055	0.347149
$952$	1.63401	0.0529586
$953$	−8.19621	−0.265501	−0.132751	−	0.991149i	$-0.542381\pi$
$953$	−8.19621	−0.265501	−0.132751	+	0.991149i	$0.542381\pi$
$954$	−2.40471	−0.0778552
$955$	0	0
$956$	−0.793120	−0.0256513
$957$	−44.4273	−1.43613
$958$	−35.1868	−1.13683
$959$	−18.9649	−0.612407
$960$	0	0
$961$	29.0628	0.937511
$962$	11.1750	0.360296
$963$	3.72456	0.120022
$964$	−10.7177	−0.345195
$965$	0	0
$966$	−36.2294	−1.16566
$967$	−31.2216	−1.00402	−0.502009	−	0.864862i	$-0.667406\pi$
$967$	−31.2216	−1.00402	−0.502009	+	0.864862i	$0.667406\pi$
$968$	4.20942	0.135296
$969$	1.11102	0.0356910
$970$	0	0
$971$	−32.6950	−1.04923	−0.524616	−	0.851339i	$-0.675791\pi$
$971$	−32.6950	−1.04923	−0.524616	+	0.851339i	$0.675791\pi$
$972$	2.48643	0.0797524
$973$	−41.2535	−1.32252
$974$	−16.5309	−0.529685
$975$	0	0
$976$	−37.5323	−1.20138
$977$	−24.0746	−0.770216	−0.385108	−	0.922872i	$-0.625836\pi$
$977$	−24.0746	−0.770216	−0.385108	+	0.922872i	$0.625836\pi$
$978$	43.8592	1.40246
$979$	10.5427	0.336948
$980$	0	0
$981$	−2.17648	−0.0694897
$982$	−46.2442	−1.47571
$983$	42.1060	1.34297	0.671486	−	0.741017i	$-0.265656\pi$
$983$	42.1060	1.34297	0.671486	+	0.741017i	$0.265656\pi$
$984$	−2.91730	−0.0930003
$985$	0	0
$986$	1.25315	0.0399083
$987$	−7.62217	−0.242616
$988$	−7.34972	−0.233826
$989$	0	0
$990$	0	0
$991$	−34.4287	−1.09366	−0.546832	−	0.837242i	$-0.684166\pi$
$991$	−34.4287	−1.09366	−0.546832	+	0.837242i	$0.684166\pi$
$992$	19.3380	0.613981
$993$	−26.0758	−0.827490
$994$	−17.1947	−0.545382
$995$	0	0
$996$	1.34657	0.0426679
$997$	14.9817	0.474477	0.237238	−	0.971451i	$-0.423758\pi$
$997$	14.9817	0.474477	0.237238	+	0.971451i	$0.423758\pi$
$998$	−33.8609	−1.07185
$999$	19.6110	0.620463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.g.1.3		5
5.2	odd	4		1175.2.c.f.424.7		10
5.3	odd	4		1175.2.c.f.424.4		10
5.4	even	2		235.2.a.d.1.3	✓	5
15.14	odd	2		2115.2.a.r.1.3		5
20.19	odd	2		3760.2.a.bg.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.a.d.1.3	✓	5	5.4	even	2
1175.2.a.g.1.3		5	1.1	even	1	trivial
1175.2.c.f.424.4		10	5.3	odd	4
1175.2.c.f.424.7		10	5.2	odd	4
2115.2.a.r.1.3		5	15.14	odd	2
3760.2.a.bg.1.1		5	20.19	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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q+1.24483 q^{2} -1.56903 q^{3} -0.450400 q^{4} -1.95318 q^{6} +4.85788 q^{7} -3.05033 q^{8} -0.538136 q^{9} +O(q^{10})\)	\(q+1.24483 q^{2} -1.56903 q^{3} -0.450400 q^{4} -1.95318 q^{6} +4.85788 q^{7} -3.05033 q^{8} -0.538136 q^{9} -3.10161 q^{11} +0.706693 q^{12} +2.54124 q^{13} +6.04723 q^{14} -2.89634 q^{16} -0.110271 q^{17} -0.669888 q^{18} +6.42136 q^{19} -7.62217 q^{21} -3.86098 q^{22} +3.81832 q^{23} +4.78607 q^{24} +3.16341 q^{26} +5.55145 q^{27} -2.18799 q^{28} -9.12914 q^{29} +7.75002 q^{31} +2.49521 q^{32} +4.86653 q^{33} -0.137269 q^{34} +0.242377 q^{36} +3.53258 q^{37} +7.99349 q^{38} -3.98729 q^{39} -0.609541 q^{41} -9.48830 q^{42} +1.39697 q^{44} +4.75316 q^{46} +1.00000 q^{47} +4.54445 q^{48} +16.5990 q^{49} +0.173019 q^{51} -1.14457 q^{52} +3.58972 q^{53} +6.91061 q^{54} -14.8181 q^{56} -10.0753 q^{57} -11.3642 q^{58} +11.4458 q^{59} +12.9585 q^{61} +9.64745 q^{62} -2.61420 q^{63} +8.89879 q^{64} +6.05800 q^{66} +0.830083 q^{67} +0.0496662 q^{68} -5.99108 q^{69} -2.84340 q^{71} +1.64149 q^{72} +7.35401 q^{73} +4.39746 q^{74} -2.89218 q^{76} -15.0673 q^{77} -4.96349 q^{78} -15.0577 q^{79} -7.09600 q^{81} -0.758774 q^{82} +1.90546 q^{83} +3.43303 q^{84} +14.3239 q^{87} +9.46095 q^{88} -3.39912 q^{89} +12.3450 q^{91} -1.71977 q^{92} -12.1600 q^{93} +1.24483 q^{94} -3.91507 q^{96} +13.7071 q^{97} +20.6629 q^{98} +1.66909 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9	\( 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9} - q^{11} + 8 q^{12} + 11 q^{13} - 2 q^{14} + 4 q^{16} + 14 q^{17} + 6 q^{18} + 5 q^{19} - 13 q^{21} - 5 q^{22} + 6 q^{23} + 20 q^{24} - 11 q^{26} + 11 q^{27} - q^{28} - 16 q^{29} + 3 q^{31} + 3 q^{32} + 5 q^{33} + 28 q^{34} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 25 q^{39} - 24 q^{41} - 46 q^{42} + 21 q^{44} + 14 q^{46} + 5 q^{47} - 7 q^{48} + 24 q^{49} + 14 q^{51} - 15 q^{52} + 14 q^{53} + 46 q^{54} - 3 q^{56} + 3 q^{57} - 32 q^{58} + 10 q^{59} - 9 q^{61} - 13 q^{62} - 24 q^{63} + 16 q^{64} - 23 q^{66} - 4 q^{67} + 47 q^{68} - 26 q^{69} + 4 q^{71} - 5 q^{72} + 27 q^{73} + 14 q^{74} - 19 q^{76} + 33 q^{77} - q^{78} - 18 q^{79} + 9 q^{81} - 24 q^{82} - 17 q^{83} - 26 q^{84} - 18 q^{87} + 35 q^{88} + 4 q^{89} + 13 q^{91} + 6 q^{92} - 25 q^{93} + 4 q^{94} - 33 q^{96} + 30 q^{97} + 11 q^{98} - 4 q^{99}+O(q^{100}) \) 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9 - q^11 + 8 * q^12 + 11 * q^13 - 2 * q^14 + 4 * q^16 + 14 * q^17 + 6 * q^18 + 5 * q^19 - 13 * q^21 - 5 * q^22 + 6 * q^23 + 20 * q^24 - 11 * q^26 + 11 * q^27 - q^28 - 16 * q^29 + 3 * q^31 + 3 * q^32 + 5 * q^33 + 28 * q^34 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 25 * q^39 - 24 * q^41 - 46 * q^42 + 21 * q^44 + 14 * q^46 + 5 * q^47 - 7 * q^48 + 24 * q^49 + 14 * q^51 - 15 * q^52 + 14 * q^53 + 46 * q^54 - 3 * q^56 + 3 * q^57 - 32 * q^58 + 10 * q^59 - 9 * q^61 - 13 * q^62 - 24 * q^63 + 16 * q^64 - 23 * q^66 - 4 * q^67 + 47 * q^68 - 26 * q^69 + 4 * q^71 - 5 * q^72 + 27 * q^73 + 14 * q^74 - 19 * q^76 + 33 * q^77 - q^78 - 18 * q^79 + 9 * q^81 - 24 * q^82 - 17 * q^83 - 26 * q^84 - 18 * q^87 + 35 * q^88 + 4 * q^89 + 13 * q^91 + 6 * q^92 - 25 * q^93 + 4 * q^94 - 33 * q^96 + 30 * q^97 + 11 * q^98 - 4 * q^99

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