LMFDB - Embedded newform 7175.2.a.n.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7175,2,Mod(1,7175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7175 = 5^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7175.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:	$57.2926634503$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.45719$ of defining polynomial
Character	$\chi$	$=$	7175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +3.58059 q^{6} -1.00000 q^{7} +5.00722 q^{8} -0.876597 q^{9} +O(q^{10})$	\(q+2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +3.58059 q^{6} -1.00000 q^{7} +5.00722 q^{8} -0.876597 q^{9} -5.41988 q^{11} +5.88382 q^{12} -3.23628 q^{13} -2.45719 q^{14} +4.22813 q^{16} -2.83206 q^{17} -2.15397 q^{18} -4.32097 q^{19} -1.45719 q^{21} -13.3177 q^{22} -6.99907 q^{23} +7.29647 q^{24} -7.95216 q^{26} -5.64894 q^{27} -4.03778 q^{28} +8.06741 q^{29} +9.18123 q^{31} +0.374872 q^{32} -7.89779 q^{33} -6.95892 q^{34} -3.53951 q^{36} +0.0469023 q^{37} -10.6174 q^{38} -4.71588 q^{39} -1.00000 q^{41} -3.58059 q^{42} +6.31281 q^{43} -21.8843 q^{44} -17.1980 q^{46} -5.26448 q^{47} +6.16119 q^{48} +1.00000 q^{49} -4.12685 q^{51} -13.0674 q^{52} -6.43622 q^{53} -13.8805 q^{54} -5.00722 q^{56} -6.29647 q^{57} +19.8232 q^{58} +2.45253 q^{59} +5.28319 q^{61} +22.5600 q^{62} +0.876597 q^{63} -7.53512 q^{64} -19.4064 q^{66} +8.78423 q^{67} -11.4353 q^{68} -10.1990 q^{69} -12.1364 q^{71} -4.38931 q^{72} -2.42993 q^{73} +0.115248 q^{74} -17.4471 q^{76} +5.41988 q^{77} -11.5878 q^{78} +4.92882 q^{79} -5.60179 q^{81} -2.45719 q^{82} +1.63593 q^{83} -5.88382 q^{84} +15.5118 q^{86} +11.7558 q^{87} -27.1385 q^{88} +1.68625 q^{89} +3.23628 q^{91} -28.2607 q^{92} +13.3788 q^{93} -12.9358 q^{94} +0.546260 q^{96} -18.8278 q^{97} +2.45719 q^{98} +4.75105 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) $ 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9	$ 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} - q^{16} - 13 q^{17} - 21 q^{18} + 4 q^{21} - q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{27} - 3 q^{28} - 5 q^{29} + 17 q^{31} + 12 q^{32} - 3 q^{33} - 8 q^{34} + 15 q^{36} + 7 q^{37} + 3 q^{38} + 5 q^{39} - 5 q^{41} - 12 q^{42} - q^{43} - 47 q^{44} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 5 q^{49} + 5 q^{51} - 20 q^{52} - 5 q^{53} + 2 q^{54} - 3 q^{56} + 3 q^{57} + 27 q^{58} + 7 q^{59} + 22 q^{61} + 28 q^{62} - q^{63} - 3 q^{64} - 42 q^{66} + 3 q^{67} - 17 q^{68} - 22 q^{69} - 24 q^{71} + 12 q^{72} - 40 q^{73} - 5 q^{74} - 19 q^{76} - 2 q^{77} - 30 q^{78} - 42 q^{79} + 9 q^{81} - q^{82} + 12 q^{83} - 2 q^{84} + 16 q^{86} + 32 q^{87} - 26 q^{88} + 8 q^{89} + 5 q^{91} - 12 q^{92} + 11 q^{93} - 23 q^{94} - 17 q^{96} - 16 q^{97} + q^{98} - 45 q^{99}+O(q^{100}) $ 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - q^14 - q^16 - 13 * q^17 - 21 * q^18 + 4 * q^21 - q^22 - 2 * q^23 + 2 * q^24 - 10 * q^27 - 3 * q^28 - 5 * q^29 + 17 * q^31 + 12 * q^32 - 3 * q^33 - 8 * q^34 + 15 * q^36 + 7 * q^37 + 3 * q^38 + 5 * q^39 - 5 * q^41 - 12 * q^42 - q^43 - 47 * q^44 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 5 * q^49 + 5 * q^51 - 20 * q^52 - 5 * q^53 + 2 * q^54 - 3 * q^56 + 3 * q^57 + 27 * q^58 + 7 * q^59 + 22 * q^61 + 28 * q^62 - q^63 - 3 * q^64 - 42 * q^66 + 3 * q^67 - 17 * q^68 - 22 * q^69 - 24 * q^71 + 12 * q^72 - 40 * q^73 - 5 * q^74 - 19 * q^76 - 2 * q^77 - 30 * q^78 - 42 * q^79 + 9 * q^81 - q^82 + 12 * q^83 - 2 * q^84 + 16 * q^86 + 32 * q^87 - 26 * q^88 + 8 * q^89 + 5 * q^91 - 12 * q^92 + 11 * q^93 - 23 * q^94 - 17 * q^96 - 16 * q^97 + q^98 - 45 * 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 $

$2$	2.45719	1.73750	0.868748	−	0.495255i	$-0.164925\pi$
$2$	2.45719	1.73750	0.868748	+	0.495255i	$0.164925\pi$
$3$	1.45719	0.841309	0.420655	−	0.907221i	$-0.361800\pi$
$3$	1.45719	0.841309	0.420655	+	0.907221i	$0.361800\pi$
$4$	4.03778	2.01889
$5$	0	0
$5$	0	0
$6$	3.58059	1.46177
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	5.00722	1.77032
$9$	−0.876597	−0.292199
$10$	0	0
$11$	−5.41988	−1.63415	−0.817077	−	0.576528i	$-0.804407\pi$
$11$	−5.41988	−1.63415	−0.817077	+	0.576528i	$0.804407\pi$
$12$	5.88382	1.69851
$13$	−3.23628	−0.897584	−0.448792	−	0.893636i	$-0.648146\pi$
$13$	−3.23628	−0.897584	−0.448792	+	0.893636i	$0.648146\pi$
$14$	−2.45719	−0.656712
$15$	0	0
$16$	4.22813	1.05703
$17$	−2.83206	−0.686876	−0.343438	−	0.939175i	$-0.611592\pi$
$17$	−2.83206	−0.686876	−0.343438	+	0.939175i	$0.611592\pi$
$18$	−2.15397	−0.507694
$19$	−4.32097	−0.991298	−0.495649	−	0.868523i	$-0.665070\pi$
$19$	−4.32097	−0.991298	−0.495649	+	0.868523i	$0.665070\pi$
$20$	0	0
$21$	−1.45719	−0.317985
$22$	−13.3177	−2.83934
$23$	−6.99907	−1.45941	−0.729703	−	0.683764i	$-0.760342\pi$
$23$	−6.99907	−1.45941	−0.729703	+	0.683764i	$0.760342\pi$
$24$	7.29647	1.48939
$25$	0	0
$26$	−7.95216	−1.55955
$27$	−5.64894	−1.08714
$28$	−4.03778	−0.763069
$29$	8.06741	1.49808	0.749040	−	0.662524i	$-0.230515\pi$
$29$	8.06741	1.49808	0.749040	+	0.662524i	$0.230515\pi$
$30$	0	0
$31$	9.18123	1.64900	0.824498	−	0.565864i	$-0.191457\pi$
$31$	9.18123	1.64900	0.824498	+	0.565864i	$0.191457\pi$
$32$	0.374872	0.0662686
$33$	−7.89779	−1.37483
$34$	−6.95892	−1.19344
$35$	0	0
$36$	−3.53951	−0.589918
$37$	0.0469023	0.00771068	0.00385534	−	0.999993i	$-0.498773\pi$
$37$	0.0469023	0.00771068	0.00385534	+	0.999993i	$0.498773\pi$
$38$	−10.6174	−1.72238
$39$	−4.71588	−0.755145
$40$	0	0
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	−3.58059	−0.552498
$43$	6.31281	0.962695	0.481348	−	0.876530i	$-0.340148\pi$
$43$	6.31281	0.962695	0.481348	+	0.876530i	$0.340148\pi$
$44$	−21.8843	−3.29918
$45$	0	0
$46$	−17.1980	−2.53571
$47$	−5.26448	−0.767903	−0.383952	−	0.923353i	$-0.625437\pi$
$47$	−5.26448	−0.767903	−0.383952	+	0.923353i	$0.625437\pi$
$48$	6.16119	0.889291
$49$	1.00000	0.142857
$50$	0	0
$51$	−4.12685	−0.577875
$52$	−13.0674	−1.81212
$53$	−6.43622	−0.884082	−0.442041	−	0.896995i	$-0.645745\pi$
$53$	−6.43622	−0.884082	−0.442041	+	0.896995i	$0.645745\pi$
$54$	−13.8805	−1.88890
$55$	0	0
$56$	−5.00722	−0.669118
$57$	−6.29647	−0.833988
$58$	19.8232	2.60291
$59$	2.45253	0.319292	0.159646	−	0.987174i	$-0.448965\pi$
$59$	2.45253	0.319292	0.159646	+	0.987174i	$0.448965\pi$
$60$	0	0
$61$	5.28319	0.676443	0.338221	−	0.941067i	$-0.390175\pi$
$61$	5.28319	0.676443	0.338221	+	0.941067i	$0.390175\pi$
$62$	22.5600	2.86513
$63$	0.876597	0.110441
$64$	−7.53512	−0.941891
$65$	0	0
$66$	−19.4064	−2.38876
$67$	8.78423	1.07316	0.536582	−	0.843848i	$-0.319715\pi$
$67$	8.78423	1.07316	0.536582	+	0.843848i	$0.319715\pi$
$68$	−11.4353	−1.38673
$69$	−10.1990	−1.22781
$70$	0	0
$71$	−12.1364	−1.44033	−0.720165	−	0.693802i	$-0.755934\pi$
$71$	−12.1364	−1.44033	−0.720165	+	0.693802i	$0.755934\pi$
$72$	−4.38931	−0.517286
$73$	−2.42993	−0.284402	−0.142201	−	0.989838i	$-0.545418\pi$
$73$	−2.42993	−0.284402	−0.142201	+	0.989838i	$0.545418\pi$
$74$	0.115248	0.0133973
$75$	0	0
$76$	−17.4471	−2.00132
$77$	5.41988	0.617652
$78$	−11.5878	−1.31206
$79$	4.92882	0.554536	0.277268	−	0.960793i	$-0.410571\pi$
$79$	4.92882	0.554536	0.277268	+	0.960793i	$0.410571\pi$
$80$	0	0
$81$	−5.60179	−0.622421
$82$	−2.45719	−0.271351
$83$	1.63593	0.179567	0.0897833	−	0.995961i	$-0.471383\pi$
$83$	1.63593	0.179567	0.0897833	+	0.995961i	$0.471383\pi$
$84$	−5.88382	−0.641977
$85$	0	0
$86$	15.5118	1.67268
$87$	11.7558	1.26035
$88$	−27.1385	−2.89298
$89$	1.68625	0.178742	0.0893712	−	0.995998i	$-0.471514\pi$
$89$	1.68625	0.178742	0.0893712	+	0.995998i	$0.471514\pi$
$90$	0	0
$91$	3.23628	0.339255
$92$	−28.2607	−2.94638
$93$	13.3788	1.38732
$94$	−12.9358	−1.33423
$95$	0	0
$96$	0.546260	0.0557524
$97$	−18.8278	−1.91168	−0.955838	−	0.293894i	$-0.905049\pi$
$97$	−18.8278	−1.91168	−0.955838	+	0.293894i	$0.905049\pi$
$98$	2.45719	0.248214
$99$	4.75105	0.477498
$100$	0	0
$101$	7.44903	0.741207	0.370603	−	0.928791i	$-0.379151\pi$
$101$	7.44903	0.741207	0.370603	+	0.928791i	$0.379151\pi$
$102$	−10.1405	−1.00406
$103$	−3.68672	−0.363264	−0.181632	−	0.983367i	$-0.558138\pi$
$103$	−3.68672	−0.363264	−0.181632	+	0.983367i	$0.558138\pi$
$104$	−16.2048	−1.58901
$105$	0	0
$106$	−15.8150	−1.53609
$107$	8.58781	0.830215	0.415108	−	0.909772i	$-0.363744\pi$
$107$	8.58781	0.830215	0.415108	+	0.909772i	$0.363744\pi$
$108$	−22.8092	−2.19482
$109$	−2.91912	−0.279601	−0.139800	−	0.990180i	$-0.544646\pi$
$109$	−2.91912	−0.279601	−0.139800	+	0.990180i	$0.544646\pi$
$110$	0	0
$111$	0.0683455	0.00648707
$112$	−4.22813	−0.399521
$113$	7.03990	0.662258	0.331129	−	0.943585i	$-0.392570\pi$
$113$	7.03990	0.662258	0.331129	+	0.943585i	$0.392570\pi$
$114$	−15.4716	−1.44905
$115$	0	0
$116$	32.5745	3.02446
$117$	2.83692	0.262273
$118$	6.02633	0.554768
$119$	2.83206	0.259615
$120$	0	0
$121$	18.3751	1.67046
$122$	12.9818	1.17532
$123$	−1.45719	−0.131390
$124$	37.0718	3.32915
$125$	0	0
$126$	2.15397	0.191890
$127$	−19.1099	−1.69573	−0.847863	−	0.530216i	$-0.822111\pi$
$127$	−19.1099	−1.69573	−0.847863	+	0.530216i	$0.822111\pi$
$128$	−19.2650	−1.70280
$129$	9.19897	0.809924
$130$	0	0
$131$	9.99440	0.873215	0.436608	−	0.899652i	$-0.356180\pi$
$131$	9.99440	0.873215	0.436608	+	0.899652i	$0.356180\pi$
$132$	−31.8896	−2.77563
$133$	4.32097	0.374676
$134$	21.5845	1.86462
$135$	0	0
$136$	−14.1808	−1.21599
$137$	−4.66385	−0.398459	−0.199230	−	0.979953i	$-0.563844\pi$
$137$	−4.66385	−0.398459	−0.199230	+	0.979953i	$0.563844\pi$
$138$	−25.0608	−2.13332
$139$	−10.3954	−0.881725	−0.440862	−	0.897575i	$-0.645327\pi$
$139$	−10.3954	−0.881725	−0.440862	+	0.897575i	$0.645327\pi$
$140$	0	0
$141$	−7.67135	−0.646044
$142$	−29.8215	−2.50257
$143$	17.5403	1.46679
$144$	−3.70636	−0.308864
$145$	0	0
$146$	−5.97080	−0.494147
$147$	1.45719	0.120187
$148$	0.189381	0.0155670
$149$	6.23050	0.510422	0.255211	−	0.966885i	$-0.417855\pi$
$149$	6.23050	0.510422	0.255211	+	0.966885i	$0.417855\pi$
$150$	0	0
$151$	−21.1548	−1.72156	−0.860778	−	0.508981i	$-0.830022\pi$
$151$	−21.1548	−1.72156	−0.860778	+	0.508981i	$0.830022\pi$
$152$	−21.6360	−1.75492
$153$	2.48258	0.200704
$154$	13.3177	1.07317
$155$	0	0
$156$	−19.0417	−1.52456
$157$	−20.4912	−1.63538	−0.817688	−	0.575662i	$-0.804745\pi$
$157$	−20.4912	−1.63538	−0.817688	+	0.575662i	$0.804745\pi$
$158$	12.1111	0.963504
$159$	−9.37879	−0.743787
$160$	0	0
$161$	6.99907	0.551604
$162$	−13.7647	−1.08145
$163$	1.63497	0.128060	0.0640302	−	0.997948i	$-0.479605\pi$
$163$	1.63497	0.128060	0.0640302	+	0.997948i	$0.479605\pi$
$164$	−4.03778	−0.315298
$165$	0	0
$166$	4.01979	0.311996
$167$	19.8243	1.53405	0.767026	−	0.641616i	$-0.221736\pi$
$167$	19.8243	1.53405	0.767026	+	0.641616i	$0.221736\pi$
$168$	−7.29647	−0.562935
$169$	−2.52647	−0.194344
$170$	0	0
$171$	3.78775	0.289656
$172$	25.4898	1.94358
$173$	9.31394	0.708126	0.354063	−	0.935222i	$-0.384800\pi$
$173$	9.31394	0.708126	0.354063	+	0.935222i	$0.384800\pi$
$174$	28.8861	2.18985
$175$	0	0
$176$	−22.9159	−1.72735
$177$	3.57380	0.268623
$178$	4.14344	0.310564
$179$	−17.3459	−1.29649	−0.648245	−	0.761432i	$-0.724497\pi$
$179$	−17.3459	−1.29649	−0.648245	+	0.761432i	$0.724497\pi$
$180$	0	0
$181$	10.1355	0.753364	0.376682	−	0.926343i	$-0.377065\pi$
$181$	10.1355	0.753364	0.376682	+	0.926343i	$0.377065\pi$
$182$	7.95216	0.589454
$183$	7.69861	0.569097
$184$	−35.0459	−2.58362
$185$	0	0
$186$	32.8742	2.41046
$187$	15.3494	1.12246
$188$	−21.2568	−1.55031
$189$	5.64894	0.410900
$190$	0	0
$191$	18.1959	1.31661	0.658306	−	0.752750i	$-0.271273\pi$
$191$	18.1959	1.31661	0.658306	+	0.752750i	$0.271273\pi$
$192$	−10.9801	−0.792421
$193$	−1.29950	−0.0935398	−0.0467699	−	0.998906i	$-0.514893\pi$
$193$	−1.29950	−0.0935398	−0.0467699	+	0.998906i	$0.514893\pi$
$194$	−46.2635	−3.32153
$195$	0	0
$196$	4.03778	0.288413
$197$	−5.64679	−0.402317	−0.201159	−	0.979559i	$-0.564471\pi$
$197$	−5.64679	−0.402317	−0.201159	+	0.979559i	$0.564471\pi$
$198$	11.6742	0.829651
$199$	−11.5069	−0.815699	−0.407850	−	0.913049i	$-0.633721\pi$
$199$	−11.5069	−0.815699	−0.407850	+	0.913049i	$0.633721\pi$
$200$	0	0
$201$	12.8003	0.902863
$202$	18.3037	1.28784
$203$	−8.06741	−0.566221
$204$	−16.6633	−1.16667
$205$	0	0
$206$	−9.05898	−0.631169
$207$	6.13536	0.426437
$208$	−13.6834	−0.948775
$209$	23.4191	1.61993
$210$	0	0
$211$	−9.92599	−0.683333	−0.341667	−	0.939821i	$-0.610991\pi$
$211$	−9.92599	−0.683333	−0.341667	+	0.939821i	$0.610991\pi$
$212$	−25.9880	−1.78487
$213$	−17.6851	−1.21176
$214$	21.1019	1.44250
$215$	0	0
$216$	−28.2855	−1.92458
$217$	−9.18123	−0.623262
$218$	−7.17282	−0.485805
$219$	−3.54087	−0.239270
$220$	0	0
$221$	9.16536	0.616529
$222$	0.167938	0.0112713
$223$	11.8232	0.791738	0.395869	−	0.918307i	$-0.370443\pi$
$223$	11.8232	0.791738	0.395869	+	0.918307i	$0.370443\pi$
$224$	−0.374872	−0.0250472
$225$	0	0
$226$	17.2984	1.15067
$227$	−1.60275	−0.106378	−0.0531892	−	0.998584i	$-0.516939\pi$
$227$	−1.60275	−0.106378	−0.0531892	+	0.998584i	$0.516939\pi$
$228$	−25.4238	−1.68373
$229$	−9.93349	−0.656423	−0.328212	−	0.944604i	$-0.606446\pi$
$229$	−9.93349	−0.656423	−0.328212	+	0.944604i	$0.606446\pi$
$230$	0	0
$231$	7.89779	0.519636
$232$	40.3953	2.65208
$233$	7.91248	0.518364	0.259182	−	0.965829i	$-0.416547\pi$
$233$	7.91248	0.518364	0.259182	+	0.965829i	$0.416547\pi$
$234$	6.97084	0.455698
$235$	0	0
$236$	9.90278	0.644616
$237$	7.18223	0.466536
$238$	6.95892	0.451079
$239$	27.1893	1.75873	0.879365	−	0.476148i	$-0.157967\pi$
$239$	27.1893	1.75873	0.879365	+	0.476148i	$0.157967\pi$
$240$	0	0
$241$	19.4014	1.24975	0.624877	−	0.780723i	$-0.285149\pi$
$241$	19.4014	1.24975	0.624877	+	0.780723i	$0.285149\pi$
$242$	45.1510	2.90242
$243$	8.78395	0.563490
$244$	21.3324	1.36566
$245$	0	0
$246$	−3.58059	−0.228290
$247$	13.9839	0.889773
$248$	45.9724	2.91925
$249$	2.38386	0.151071
$250$	0	0
$251$	27.4697	1.73387	0.866935	−	0.498421i	$-0.166087\pi$
$251$	27.4697	1.73387	0.866935	+	0.498421i	$0.166087\pi$
$252$	3.53951	0.222968
$253$	37.9341	2.38489
$254$	−46.9566	−2.94632
$255$	0	0
$256$	−32.2675	−2.01672
$257$	−21.6328	−1.34942	−0.674710	−	0.738083i	$-0.735731\pi$
$257$	−21.6328	−1.34942	−0.674710	+	0.738083i	$0.735731\pi$
$258$	22.6036	1.40724
$259$	−0.0469023	−0.00291436
$260$	0	0
$261$	−7.07187	−0.437738
$262$	24.5581	1.51721
$263$	9.84482	0.607058	0.303529	−	0.952822i	$-0.401835\pi$
$263$	9.84482	0.607058	0.303529	+	0.952822i	$0.401835\pi$
$264$	−39.5460	−2.43389
$265$	0	0
$266$	10.6174	0.650997
$267$	2.45719	0.150378
$268$	35.4688	2.16660
$269$	−26.0627	−1.58907	−0.794535	−	0.607219i	$-0.792285\pi$
$269$	−26.0627	−1.58907	−0.794535	+	0.607219i	$0.792285\pi$
$270$	0	0
$271$	25.4506	1.54602	0.773008	−	0.634396i	$-0.218751\pi$
$271$	25.4506	1.54602	0.773008	+	0.634396i	$0.218751\pi$
$272$	−11.9743	−0.726050
$273$	4.71588	0.285418
$274$	−11.4600	−0.692321
$275$	0	0
$276$	−41.1812	−2.47882
$277$	−29.3678	−1.76454	−0.882270	−	0.470743i	$-0.843986\pi$
$277$	−29.3678	−1.76454	−0.882270	+	0.470743i	$0.843986\pi$
$278$	−25.5434	−1.53199
$279$	−8.04823	−0.481835
$280$	0	0
$281$	24.2120	1.44437	0.722184	−	0.691701i	$-0.243139\pi$
$281$	24.2120	1.44437	0.722184	+	0.691701i	$0.243139\pi$
$282$	−18.8500	−1.12250
$283$	−8.91251	−0.529794	−0.264897	−	0.964277i	$-0.585338\pi$
$283$	−8.91251	−0.529794	−0.264897	+	0.964277i	$0.585338\pi$
$284$	−49.0043	−2.90787
$285$	0	0
$286$	43.0997	2.54854
$287$	1.00000	0.0590281
$288$	−0.328612	−0.0193636
$289$	−8.97942	−0.528201
$290$	0	0
$291$	−27.4357	−1.60831
$292$	−9.81153	−0.574176
$293$	8.79238	0.513656	0.256828	−	0.966457i	$-0.417323\pi$
$293$	8.79238	0.513656	0.256828	+	0.966457i	$0.417323\pi$
$294$	3.58059	0.208824
$295$	0	0
$296$	0.234850	0.0136504
$297$	30.6166	1.77655
$298$	15.3095	0.886856
$299$	22.6510	1.30994
$300$	0	0
$301$	−6.31281	−0.363865
$302$	−51.9814	−2.99120
$303$	10.8547	0.623584
$304$	−18.2696	−1.04783
$305$	0	0
$306$	6.10016	0.348723
$307$	−25.4509	−1.45256	−0.726281	−	0.687398i	$-0.758753\pi$
$307$	−25.4509	−1.45256	−0.726281	+	0.687398i	$0.758753\pi$
$308$	21.8843	1.24697
$309$	−5.37226	−0.305617
$310$	0	0
$311$	−8.20774	−0.465418	−0.232709	−	0.972546i	$-0.574759\pi$
$311$	−8.20774	−0.465418	−0.232709	+	0.972546i	$0.574759\pi$
$312$	−23.6135	−1.33685
$313$	−7.84025	−0.443157	−0.221578	−	0.975143i	$-0.571121\pi$
$313$	−7.84025	−0.443157	−0.221578	+	0.975143i	$0.571121\pi$
$314$	−50.3508	−2.84146
$315$	0	0
$316$	19.9015	1.11955
$317$	−32.4359	−1.82178	−0.910891	−	0.412647i	$-0.864604\pi$
$317$	−32.4359	−1.82178	−0.910891	+	0.412647i	$0.864604\pi$
$318$	−23.0455	−1.29233
$319$	−43.7244	−2.44810
$320$	0	0
$321$	12.5141	0.698468
$322$	17.1980	0.958409
$323$	12.2373	0.680899
$324$	−22.6188	−1.25660
$325$	0	0
$326$	4.01742	0.222504
$327$	−4.25371	−0.235230
$328$	−5.00722	−0.276478
$329$	5.26448	0.290240
$330$	0	0
$331$	13.8576	0.761685	0.380843	−	0.924640i	$-0.375634\pi$
$331$	13.8576	0.761685	0.380843	+	0.924640i	$0.375634\pi$
$332$	6.60553	0.362526
$333$	−0.0411144	−0.00225305
$334$	48.7121	2.66541
$335$	0	0
$336$	−6.16119	−0.336120
$337$	−18.6080	−1.01364	−0.506822	−	0.862050i	$-0.669180\pi$
$337$	−18.6080	−1.01364	−0.506822	+	0.862050i	$0.669180\pi$
$338$	−6.20802	−0.337672
$339$	10.2585	0.557164
$340$	0	0
$341$	−49.7611	−2.69472
$342$	9.30722	0.503277
$343$	−1.00000	−0.0539949
$344$	31.6097	1.70428
$345$	0	0
$346$	22.8861	1.23037
$347$	−23.3306	−1.25245	−0.626225	−	0.779642i	$-0.715401\pi$
$347$	−23.3306	−1.25245	−0.626225	+	0.779642i	$0.715401\pi$
$348$	47.4672	2.54451
$349$	−5.59571	−0.299531	−0.149766	−	0.988722i	$-0.547852\pi$
$349$	−5.59571	−0.299531	−0.149766	+	0.988722i	$0.547852\pi$
$350$	0	0
$351$	18.2816	0.975798
$352$	−2.03176	−0.108293
$353$	19.4280	1.03405	0.517023	−	0.855971i	$-0.327040\pi$
$353$	19.4280	1.03405	0.517023	+	0.855971i	$0.327040\pi$
$354$	8.78150	0.466732
$355$	0	0
$356$	6.80872	0.360862
$357$	4.12685	0.218416
$358$	−42.6221	−2.25265
$359$	14.3127	0.755398	0.377699	−	0.925929i	$-0.376715\pi$
$359$	14.3127	0.755398	0.377699	+	0.925929i	$0.376715\pi$
$360$	0	0
$361$	−0.329226	−0.0173277
$362$	24.9048	1.30897
$363$	26.7760	1.40537
$364$	13.0674	0.684918
$365$	0	0
$366$	18.9169	0.988804
$367$	21.2458	1.10902	0.554512	−	0.832176i	$-0.312905\pi$
$367$	21.2458	1.10902	0.554512	+	0.832176i	$0.312905\pi$
$368$	−29.5929	−1.54264
$369$	0.876597	0.0456338
$370$	0	0
$371$	6.43622	0.334152
$372$	54.0207	2.80084
$373$	−28.2272	−1.46155	−0.730774	−	0.682620i	$-0.760840\pi$
$373$	−28.2272	−1.46155	−0.730774	+	0.682620i	$0.760840\pi$
$374$	37.7165	1.95027
$375$	0	0
$376$	−26.3604	−1.35943
$377$	−26.1084	−1.34465
$378$	13.8805	0.713937
$379$	−8.57635	−0.440538	−0.220269	−	0.975439i	$-0.570693\pi$
$379$	−8.57635	−0.440538	−0.220269	+	0.975439i	$0.570693\pi$
$380$	0	0
$381$	−27.8467	−1.42663
$382$	44.7109	2.28761
$383$	−2.63393	−0.134588	−0.0672938	−	0.997733i	$-0.521436\pi$
$383$	−2.63393	−0.134588	−0.0672938	+	0.997733i	$0.521436\pi$
$384$	−28.0727	−1.43258
$385$	0	0
$386$	−3.19311	−0.162525
$387$	−5.53379	−0.281298
$388$	−76.0227	−3.85947
$389$	−13.2656	−0.672595	−0.336298	−	0.941756i	$-0.609175\pi$
$389$	−13.2656	−0.672595	−0.336298	+	0.941756i	$0.609175\pi$
$390$	0	0
$391$	19.8218	1.00243
$392$	5.00722	0.252903
$393$	14.5637	0.734644
$394$	−13.8752	−0.699025
$395$	0	0
$396$	19.1837	0.964017
$397$	−2.28602	−0.114732	−0.0573661	−	0.998353i	$-0.518270\pi$
$397$	−2.28602	−0.114732	−0.0573661	+	0.998353i	$0.518270\pi$
$398$	−28.2745	−1.41727
$399$	6.29647	0.315218
$400$	0	0
$401$	2.79191	0.139421	0.0697107	−	0.997567i	$-0.477792\pi$
$401$	2.79191	0.139421	0.0697107	+	0.997567i	$0.477792\pi$
$402$	31.4527	1.56872
$403$	−29.7130	−1.48011
$404$	30.0776	1.49642
$405$	0	0
$406$	−19.8232	−0.983807
$407$	−0.254204	−0.0126004
$408$	−20.6641	−1.02302
$409$	−10.8769	−0.537826	−0.268913	−	0.963164i	$-0.586664\pi$
$409$	−10.8769	−0.537826	−0.268913	+	0.963164i	$0.586664\pi$
$410$	0	0
$411$	−6.79611	−0.335227
$412$	−14.8862	−0.733390
$413$	−2.45253	−0.120681
$414$	15.0757	0.740932
$415$	0	0
$416$	−1.21319	−0.0594816
$417$	−15.1480	−0.741803
$418$	57.5452	2.81463
$419$	−24.9047	−1.21668	−0.608338	−	0.793678i	$-0.708164\pi$
$419$	−24.9047	−1.21668	−0.608338	+	0.793678i	$0.708164\pi$
$420$	0	0
$421$	−7.16405	−0.349155	−0.174577	−	0.984643i	$-0.555856\pi$
$421$	−7.16405	−0.349155	−0.174577	+	0.984643i	$0.555856\pi$
$422$	−24.3900	−1.18729
$423$	4.61483	0.224380
$424$	−32.2276	−1.56511
$425$	0	0
$426$	−43.4557	−2.10543
$427$	−5.28319	−0.255671
$428$	34.6757	1.67611
$429$	25.5595	1.23402
$430$	0	0
$431$	−14.6538	−0.705850	−0.352925	−	0.935652i	$-0.614813\pi$
$431$	−14.6538	−0.705850	−0.352925	+	0.935652i	$0.614813\pi$
$432$	−23.8844	−1.14914
$433$	29.4173	1.41370	0.706851	−	0.707362i	$-0.250115\pi$
$433$	29.4173	1.41370	0.706851	+	0.707362i	$0.250115\pi$
$434$	−22.5600	−1.08292
$435$	0	0
$436$	−11.7868	−0.564483
$437$	30.2427	1.44671
$438$	−8.70059	−0.415730
$439$	26.5607	1.26767	0.633837	−	0.773466i	$-0.281479\pi$
$439$	26.5607	1.26767	0.633837	+	0.773466i	$0.281479\pi$
$440$	0	0
$441$	−0.876597	−0.0417427
$442$	22.5210	1.07122
$443$	12.2373	0.581409	0.290705	−	0.956813i	$-0.406110\pi$
$443$	12.2373	0.581409	0.290705	+	0.956813i	$0.406110\pi$
$444$	0.275964	0.0130967
$445$	0	0
$446$	29.0518	1.37564
$447$	9.07902	0.429423
$448$	7.53512	0.356001
$449$	−23.4334	−1.10589	−0.552944	−	0.833218i	$-0.686496\pi$
$449$	−23.4334	−1.10589	−0.552944	+	0.833218i	$0.686496\pi$
$450$	0	0
$451$	5.41988	0.255212
$452$	28.4256	1.33703
$453$	−30.8266	−1.44836
$454$	−3.93826	−0.184832
$455$	0	0
$456$	−31.5278	−1.47643
$457$	8.25626	0.386212	0.193106	−	0.981178i	$-0.438144\pi$
$457$	8.25626	0.386212	0.193106	+	0.981178i	$0.438144\pi$
$458$	−24.4085	−1.14053
$459$	15.9981	0.746729
$460$	0	0
$461$	−8.79238	−0.409502	−0.204751	−	0.978814i	$-0.565638\pi$
$461$	−8.79238	−0.409502	−0.204751	+	0.978814i	$0.565638\pi$
$462$	19.4064	0.902866
$463$	−36.8884	−1.71435	−0.857175	−	0.515025i	$-0.827783\pi$
$463$	−36.8884	−1.71435	−0.857175	+	0.515025i	$0.827783\pi$
$464$	34.1100	1.58352
$465$	0	0
$466$	19.4425	0.900655
$467$	21.8803	1.01250	0.506250	−	0.862387i	$-0.331031\pi$
$467$	21.8803	1.01250	0.506250	+	0.862387i	$0.331031\pi$
$468$	11.4549	0.529501
$469$	−8.78423	−0.405618
$470$	0	0
$471$	−29.8596	−1.37586
$472$	12.2803	0.565249
$473$	−34.2147	−1.57319
$474$	17.6481	0.810605
$475$	0	0
$476$	11.4353	0.524134
$477$	5.64197	0.258328
$478$	66.8093	3.05579
$479$	34.3678	1.57030	0.785152	−	0.619303i	$-0.212585\pi$
$479$	34.3678	1.57030	0.785152	+	0.619303i	$0.212585\pi$
$480$	0	0
$481$	−0.151789	−0.00692098
$482$	47.6729	2.17144
$483$	10.1990	0.464069
$484$	74.1945	3.37248
$485$	0	0
$486$	21.5838	0.979062
$487$	−15.9585	−0.723146	−0.361573	−	0.932344i	$-0.617760\pi$
$487$	−15.9585	−0.723146	−0.361573	+	0.932344i	$0.617760\pi$
$488$	26.4541	1.19752
$489$	2.38246	0.107738
$490$	0	0
$491$	−1.69863	−0.0766581	−0.0383290	−	0.999265i	$-0.512204\pi$
$491$	−1.69863	−0.0766581	−0.0383290	+	0.999265i	$0.512204\pi$
$492$	−5.88382	−0.265263
$493$	−22.8474	−1.02900
$494$	34.3611	1.54598
$495$	0	0
$496$	38.8194	1.74304
$497$	12.1364	0.544394
$498$	5.85760	0.262485
$499$	−23.0520	−1.03195	−0.515975	−	0.856604i	$-0.672570\pi$
$499$	−23.0520	−1.03195	−0.515975	+	0.856604i	$0.672570\pi$
$500$	0	0
$501$	28.8878	1.29061
$502$	67.4982	3.01259
$503$	−34.6937	−1.54692	−0.773458	−	0.633848i	$-0.781474\pi$
$503$	−34.6937	−1.54692	−0.773458	+	0.633848i	$0.781474\pi$
$504$	4.38931	0.195516
$505$	0	0
$506$	93.2112	4.14374
$507$	−3.68155	−0.163503
$508$	−77.1615	−3.42349
$509$	−7.41125	−0.328498	−0.164249	−	0.986419i	$-0.552520\pi$
$509$	−7.41125	−0.328498	−0.164249	+	0.986419i	$0.552520\pi$
$510$	0	0
$511$	2.42993	0.107494
$512$	−40.7573	−1.80124
$513$	24.4089	1.07768
$514$	−53.1560	−2.34461
$515$	0	0
$516$	37.1434	1.63515
$517$	28.5328	1.25487
$518$	−0.115248	−0.00506370
$519$	13.5722	0.595753
$520$	0	0
$521$	−24.2278	−1.06144	−0.530719	−	0.847548i	$-0.678078\pi$
$521$	−24.2278	−1.06144	−0.530719	+	0.847548i	$0.678078\pi$
$522$	−17.3769	−0.760567
$523$	43.3265	1.89454	0.947268	−	0.320442i	$-0.103831\pi$
$523$	43.3265	1.89454	0.947268	+	0.320442i	$0.103831\pi$
$524$	40.3552	1.76293
$525$	0	0
$526$	24.1906	1.05476
$527$	−26.0018	−1.13266
$528$	−33.3929	−1.45324
$529$	25.9869	1.12987
$530$	0	0
$531$	−2.14988	−0.0932968
$532$	17.4471	0.756429
$533$	3.23628	0.140179
$534$	6.03778	0.261280
$535$	0	0
$536$	43.9846	1.89984
$537$	−25.2762	−1.09075
$538$	−64.0410	−2.76100
$539$	−5.41988	−0.233451
$540$	0	0
$541$	−12.7180	−0.546788	−0.273394	−	0.961902i	$-0.588146\pi$
$541$	−12.7180	−0.546788	−0.273394	+	0.961902i	$0.588146\pi$
$542$	62.5370	2.68620
$543$	14.7693	0.633812
$544$	−1.06166	−0.0455183
$545$	0	0
$546$	11.5878	0.495913
$547$	4.71489	0.201594	0.100797	−	0.994907i	$-0.467861\pi$
$547$	4.71489	0.201594	0.100797	+	0.994907i	$0.467861\pi$
$548$	−18.8316	−0.804446
$549$	−4.63122	−0.197656
$550$	0	0
$551$	−34.8590	−1.48504
$552$	−51.0685	−2.17362
$553$	−4.92882	−0.209595
$554$	−72.1623	−3.06588
$555$	0	0
$556$	−41.9743	−1.78011
$557$	11.0756	0.469288	0.234644	−	0.972081i	$-0.424608\pi$
$557$	11.0756	0.469288	0.234644	+	0.972081i	$0.424608\pi$
$558$	−19.7760	−0.837187
$559$	−20.4301	−0.864099
$560$	0	0
$561$	22.3670	0.944337
$562$	59.4935	2.50958
$563$	−24.9735	−1.05251	−0.526255	−	0.850327i	$-0.676404\pi$
$563$	−24.9735	−1.05251	−0.526255	+	0.850327i	$0.676404\pi$
$564$	−30.9752	−1.30429
$565$	0	0
$566$	−21.8997	−0.920515
$567$	5.60179	0.235253
$568$	−60.7698	−2.54985
$569$	3.14116	0.131684	0.0658422	−	0.997830i	$-0.479027\pi$
$569$	3.14116	0.131684	0.0658422	+	0.997830i	$0.479027\pi$
$570$	0	0
$571$	7.13418	0.298556	0.149278	−	0.988795i	$-0.452305\pi$
$571$	7.13418	0.298556	0.149278	+	0.988795i	$0.452305\pi$
$572$	70.8238	2.96129
$573$	26.5150	1.10768
$574$	2.45719	0.102561
$575$	0	0
$576$	6.60527	0.275219
$577$	−4.41995	−0.184005	−0.0920024	−	0.995759i	$-0.529327\pi$
$577$	−4.41995	−0.184005	−0.0920024	+	0.995759i	$0.529327\pi$
$578$	−22.0642	−0.917748
$579$	−1.89361	−0.0786959
$580$	0	0
$581$	−1.63593	−0.0678698
$582$	−67.4148	−2.79443
$583$	34.8835	1.44473
$584$	−12.1672	−0.503482
$585$	0	0
$586$	21.6046	0.892476
$587$	−29.7123	−1.22636	−0.613178	−	0.789944i	$-0.710109\pi$
$587$	−29.7123	−1.22636	−0.613178	+	0.789944i	$0.710109\pi$
$588$	5.88382	0.242645
$589$	−39.6718	−1.63465
$590$	0	0
$591$	−8.22845	−0.338473
$592$	0.198309	0.00815044
$593$	14.3020	0.587315	0.293657	−	0.955911i	$-0.405128\pi$
$593$	14.3020	0.587315	0.293657	+	0.955911i	$0.405128\pi$
$594$	75.2307	3.08675
$595$	0	0
$596$	25.1574	1.03049
$597$	−16.7677	−0.686255
$598$	55.6577	2.27601
$599$	38.6159	1.57780	0.788902	−	0.614518i	$-0.210650\pi$
$599$	38.6159	1.57780	0.788902	+	0.614518i	$0.210650\pi$
$600$	0	0
$601$	2.04839	0.0835557	0.0417779	−	0.999127i	$-0.486698\pi$
$601$	2.04839	0.0835557	0.0417779	+	0.999127i	$0.486698\pi$
$602$	−15.5118	−0.632213
$603$	−7.70022	−0.313577
$604$	−85.4186	−3.47563
$605$	0	0
$606$	26.6720	1.08347
$607$	−5.79770	−0.235321	−0.117661	−	0.993054i	$-0.537540\pi$
$607$	−5.79770	−0.235321	−0.117661	+	0.993054i	$0.537540\pi$
$608$	−1.61981	−0.0656920
$609$	−11.7558	−0.476367
$610$	0	0
$611$	17.0373	0.689257
$612$	10.0241	0.405201
$613$	−45.3061	−1.82989	−0.914947	−	0.403573i	$-0.867768\pi$
$613$	−45.3061	−1.82989	−0.914947	+	0.403573i	$0.867768\pi$
$614$	−62.5378	−2.52382
$615$	0	0
$616$	27.1385	1.09344
$617$	22.8349	0.919300	0.459650	−	0.888100i	$-0.347975\pi$
$617$	22.8349	0.919300	0.459650	+	0.888100i	$0.347975\pi$
$618$	−13.2007	−0.531008
$619$	15.2514	0.613007	0.306503	−	0.951870i	$-0.400841\pi$
$619$	15.2514	0.613007	0.306503	+	0.951870i	$0.400841\pi$
$620$	0	0
$621$	39.5373	1.58658
$622$	−20.1680	−0.808662
$623$	−1.68625	−0.0675583
$624$	−19.9393	−0.798213
$625$	0	0
$626$	−19.2650	−0.769983
$627$	34.1261	1.36287
$628$	−82.7390	−3.30165
$629$	−0.132830	−0.00529628
$630$	0	0
$631$	−40.2426	−1.60203	−0.801016	−	0.598643i	$-0.795707\pi$
$631$	−40.2426	−1.60203	−0.801016	+	0.598643i	$0.795707\pi$
$632$	24.6797	0.981706
$633$	−14.4640	−0.574894
$634$	−79.7012	−3.16534
$635$	0	0
$636$	−37.8695	−1.50162
$637$	−3.23628	−0.128226
$638$	−107.439	−4.25355
$639$	10.6388	0.420863
$640$	0	0
$641$	8.41075	0.332205	0.166102	−	0.986109i	$-0.446882\pi$
$641$	8.41075	0.332205	0.166102	+	0.986109i	$0.446882\pi$
$642$	30.7495	1.21358
$643$	23.9146	0.943101	0.471550	−	0.881839i	$-0.343695\pi$
$643$	23.9146	0.943101	0.471550	+	0.881839i	$0.343695\pi$
$644$	28.2607	1.11363
$645$	0	0
$646$	30.0693	1.18306
$647$	−10.9669	−0.431152	−0.215576	−	0.976487i	$-0.569163\pi$
$647$	−10.9669	−0.431152	−0.215576	+	0.976487i	$0.569163\pi$
$648$	−28.0494	−1.10188
$649$	−13.2924	−0.521772
$650$	0	0
$651$	−13.3788	−0.524356
$652$	6.60164	0.258540
$653$	−29.3523	−1.14865	−0.574323	−	0.818629i	$-0.694735\pi$
$653$	−29.3523	−1.14865	−0.574323	+	0.818629i	$0.694735\pi$
$654$	−10.4522	−0.408712
$655$	0	0
$656$	−4.22813	−0.165081
$657$	2.13007	0.0831019
$658$	12.9358	0.504291
$659$	−12.7905	−0.498245	−0.249123	−	0.968472i	$-0.580142\pi$
$659$	−12.7905	−0.498245	−0.249123	+	0.968472i	$0.580142\pi$
$660$	0	0
$661$	15.1159	0.587942	0.293971	−	0.955814i	$-0.405023\pi$
$661$	15.1159	0.587942	0.293971	+	0.955814i	$0.405023\pi$
$662$	34.0509	1.32342
$663$	13.3557	0.518691
$664$	8.19146	0.317890
$665$	0	0
$666$	−0.101026	−0.00391467
$667$	−56.4643	−2.18631
$668$	80.0463	3.09708
$669$	17.2286	0.666096
$670$	0	0
$671$	−28.6342	−1.10541
$672$	−0.546260	−0.0210724
$673$	−10.3101	−0.397425	−0.198713	−	0.980058i	$-0.563676\pi$
$673$	−10.3101	−0.397425	−0.198713	+	0.980058i	$0.563676\pi$
$674$	−45.7235	−1.76120
$675$	0	0
$676$	−10.2013	−0.392359
$677$	1.97105	0.0757535	0.0378768	−	0.999282i	$-0.487941\pi$
$677$	1.97105	0.0757535	0.0378768	+	0.999282i	$0.487941\pi$
$678$	25.2070	0.968070
$679$	18.8278	0.722546
$680$	0	0
$681$	−2.33551	−0.0894970
$682$	−122.273	−4.68206
$683$	9.53970	0.365026	0.182513	−	0.983203i	$-0.441577\pi$
$683$	9.53970	0.365026	0.182513	+	0.983203i	$0.441577\pi$
$684$	15.2941	0.584785
$685$	0	0
$686$	−2.45719	−0.0938160
$687$	−14.4750	−0.552255
$688$	26.6914	1.01760
$689$	20.8294	0.793538
$690$	0	0
$691$	16.3915	0.623562	0.311781	−	0.950154i	$-0.399075\pi$
$691$	16.3915	0.623562	0.311781	+	0.950154i	$0.399075\pi$
$692$	37.6077	1.42963
$693$	−4.75105	−0.180477
$694$	−57.3276	−2.17613
$695$	0	0
$696$	58.8637	2.23122
$697$	2.83206	0.107272
$698$	−13.7497	−0.520434
$699$	11.5300	0.436104
$700$	0	0
$701$	12.1383	0.458457	0.229229	−	0.973373i	$-0.426380\pi$
$701$	12.1383	0.458457	0.229229	+	0.973373i	$0.426380\pi$
$702$	44.9213	1.69544
$703$	−0.202663	−0.00764359
$704$	40.8394	1.53919
$705$	0	0
$706$	47.7382	1.79665
$707$	−7.44903	−0.280150
$708$	14.4302	0.542321
$709$	−29.6150	−1.11222	−0.556108	−	0.831110i	$-0.687706\pi$
$709$	−29.6150	−1.11222	−0.556108	+	0.831110i	$0.687706\pi$
$710$	0	0
$711$	−4.32059	−0.162035
$712$	8.44344	0.316431
$713$	−64.2600	−2.40656
$714$	10.1405	0.379497
$715$	0	0
$716$	−70.0388	−2.61747
$717$	39.6200	1.47964
$718$	35.1691	1.31250
$719$	42.0273	1.56735	0.783676	−	0.621169i	$-0.213342\pi$
$719$	42.0273	1.56735	0.783676	+	0.621169i	$0.213342\pi$
$720$	0	0
$721$	3.68672	0.137301
$722$	−0.808971	−0.0301068
$723$	28.2715	1.05143
$724$	40.9249	1.52096
$725$	0	0
$726$	65.7936	2.44183
$727$	41.0718	1.52327	0.761635	−	0.648007i	$-0.224397\pi$
$727$	41.0718	1.52327	0.761635	+	0.648007i	$0.224397\pi$
$728$	16.2048	0.600589
$729$	29.6052	1.09649
$730$	0	0
$731$	−17.8783	−0.661252
$732$	31.0853	1.14895
$733$	−9.51418	−0.351414	−0.175707	−	0.984442i	$-0.556221\pi$
$733$	−9.51418	−0.351414	−0.175707	+	0.984442i	$0.556221\pi$
$734$	52.2051	1.92693
$735$	0	0
$736$	−2.62375	−0.0967128
$737$	−47.6094	−1.75372
$738$	2.15397	0.0792886
$739$	−45.4606	−1.67230	−0.836148	−	0.548504i	$-0.815197\pi$
$739$	−45.4606	−1.67230	−0.836148	+	0.548504i	$0.815197\pi$
$740$	0	0
$741$	20.3772	0.748574
$742$	15.8150	0.580587
$743$	51.1920	1.87805	0.939027	−	0.343845i	$-0.111729\pi$
$743$	51.1920	1.87805	0.939027	+	0.343845i	$0.111729\pi$
$744$	66.9906	2.45599
$745$	0	0
$746$	−69.3595	−2.53943
$747$	−1.43405	−0.0524692
$748$	61.9777	2.26613
$749$	−8.58781	−0.313792
$750$	0	0
$751$	−32.2359	−1.17631	−0.588153	−	0.808750i	$-0.700145\pi$
$751$	−32.2359	−1.17631	−0.588153	+	0.808750i	$0.700145\pi$
$752$	−22.2589	−0.811698
$753$	40.0285	1.45872
$754$	−64.1534	−2.33633
$755$	0	0
$756$	22.8092	0.829562
$757$	26.3465	0.957581	0.478790	−	0.877929i	$-0.341075\pi$
$757$	26.3465	0.957581	0.478790	+	0.877929i	$0.341075\pi$
$758$	−21.0737	−0.765432
$759$	55.2772	2.00643
$760$	0	0
$761$	−30.0811	−1.09044	−0.545219	−	0.838293i	$-0.683554\pi$
$761$	−30.0811	−1.09044	−0.545219	+	0.838293i	$0.683554\pi$
$762$	−68.4246	−2.47876
$763$	2.91912	0.105679
$764$	73.4713	2.65810
$765$	0	0
$766$	−6.47207	−0.233845
$767$	−7.93707	−0.286591
$768$	−47.0198	−1.69668
$769$	−0.608700	−0.0219503	−0.0109751	−	0.999940i	$-0.503494\pi$
$769$	−0.608700	−0.0219503	−0.0109751	+	0.999940i	$0.503494\pi$
$770$	0	0
$771$	−31.5232	−1.13528
$772$	−5.24708	−0.188847
$773$	8.67944	0.312178	0.156089	−	0.987743i	$-0.450111\pi$
$773$	8.67944	0.312178	0.156089	+	0.987743i	$0.450111\pi$
$774$	−13.5976	−0.488755
$775$	0	0
$776$	−94.2751	−3.38428
$777$	−0.0683455	−0.00245188
$778$	−32.5962	−1.16863
$779$	4.32097	0.154815
$780$	0	0
$781$	65.7780	2.35372
$782$	48.7059	1.74172
$783$	−45.5723	−1.62862
$784$	4.22813	0.151005
$785$	0	0
$786$	35.7859	1.27644
$787$	−34.2640	−1.22138	−0.610689	−	0.791870i	$-0.709108\pi$
$787$	−34.2640	−1.22138	−0.610689	+	0.791870i	$0.709108\pi$
$788$	−22.8005	−0.812235
$789$	14.3458	0.510723
$790$	0	0
$791$	−7.03990	−0.250310
$792$	23.7895	0.845325
$793$	−17.0979	−0.607164
$794$	−5.61719	−0.199347
$795$	0	0
$796$	−46.4622	−1.64681
$797$	−13.1568	−0.466036	−0.233018	−	0.972472i	$-0.574860\pi$
$797$	−13.1568	−0.466036	−0.233018	+	0.972472i	$0.574860\pi$
$798$	15.4716	0.547690
$799$	14.9093	0.527454
$800$	0	0
$801$	−1.47816	−0.0522283
$802$	6.86026	0.242244
$803$	13.1699	0.464756
$804$	51.6848	1.82278
$805$	0	0
$806$	−73.0106	−2.57169
$807$	−37.9783	−1.33690
$808$	37.2990	1.31217
$809$	−2.04798	−0.0720033	−0.0360017	−	0.999352i	$-0.511462\pi$
$809$	−2.04798	−0.0720033	−0.0360017	+	0.999352i	$0.511462\pi$
$810$	0	0
$811$	5.48050	0.192446	0.0962232	−	0.995360i	$-0.469324\pi$
$811$	5.48050	0.192446	0.0962232	+	0.995360i	$0.469324\pi$
$812$	−32.5745	−1.14314
$813$	37.0864	1.30068
$814$	−0.624629	−0.0218932
$815$	0	0
$816$	−17.4489	−0.610832
$817$	−27.2775	−0.954318
$818$	−26.7265	−0.934471
$819$	−2.83692	−0.0991299
$820$	0	0
$821$	−1.55848	−0.0543913	−0.0271957	−	0.999630i	$-0.508658\pi$
$821$	−1.55848	−0.0543913	−0.0271957	+	0.999630i	$0.508658\pi$
$822$	−16.6993	−0.582456
$823$	−39.3703	−1.37236	−0.686182	−	0.727430i	$-0.740714\pi$
$823$	−39.3703	−1.37236	−0.686182	+	0.727430i	$0.740714\pi$
$824$	−18.4602	−0.643093
$825$	0	0
$826$	−6.02633	−0.209683
$827$	26.3888	0.917628	0.458814	−	0.888532i	$-0.348274\pi$
$827$	26.3888	0.917628	0.458814	+	0.888532i	$0.348274\pi$
$828$	24.7733	0.860930
$829$	45.0610	1.56503	0.782517	−	0.622629i	$-0.213935\pi$
$829$	45.0610	1.56503	0.782517	+	0.622629i	$0.213935\pi$
$830$	0	0
$831$	−42.7945	−1.48452
$832$	24.3858	0.845425
$833$	−2.83206	−0.0981251
$834$	−37.2216	−1.28888
$835$	0	0
$836$	94.5613	3.27047
$837$	−51.8642	−1.79269
$838$	−61.1957	−2.11397
$839$	−42.0761	−1.45263	−0.726314	−	0.687363i	$-0.758768\pi$
$839$	−42.0761	−1.45263	−0.726314	+	0.687363i	$0.758768\pi$
$840$	0	0
$841$	36.0831	1.24425
$842$	−17.6034	−0.606655
$843$	35.2815	1.21516
$844$	−40.0790	−1.37958
$845$	0	0
$846$	11.3395	0.389860
$847$	−18.3751	−0.631375
$848$	−27.2131	−0.934503
$849$	−12.9872	−0.445720
$850$	0	0
$851$	−0.328272	−0.0112530
$852$	−71.4086	−2.44642
$853$	20.2803	0.694384	0.347192	−	0.937794i	$-0.387135\pi$
$853$	20.2803	0.694384	0.347192	+	0.937794i	$0.387135\pi$
$854$	−12.9818	−0.444228
$855$	0	0
$856$	43.0011	1.46975
$857$	49.2604	1.68270	0.841351	−	0.540490i	$-0.181761\pi$
$857$	49.2604	1.68270	0.841351	+	0.540490i	$0.181761\pi$
$858$	62.8045	2.14411
$859$	−12.7326	−0.434430	−0.217215	−	0.976124i	$-0.569697\pi$
$859$	−12.7326	−0.434430	−0.217215	+	0.976124i	$0.569697\pi$
$860$	0	0
$861$	1.45719	0.0496609
$862$	−36.0072	−1.22641
$863$	14.7535	0.502216	0.251108	−	0.967959i	$-0.419205\pi$
$863$	14.7535	0.502216	0.251108	+	0.967959i	$0.419205\pi$
$864$	−2.11763	−0.0720432
$865$	0	0
$866$	72.2838	2.45630
$867$	−13.0847	−0.444381
$868$	−37.0718	−1.25830
$869$	−26.7136	−0.906197
$870$	0	0
$871$	−28.4282	−0.963254
$872$	−14.6167	−0.494982
$873$	16.5044	0.558590
$874$	74.3122	2.51365
$875$	0	0
$876$	−14.2973	−0.483060
$877$	20.7432	0.700450	0.350225	−	0.936666i	$-0.386105\pi$
$877$	20.7432	0.700450	0.350225	+	0.936666i	$0.386105\pi$
$878$	65.2648	2.20258
$879$	12.8122	0.432144
$880$	0	0
$881$	−19.5041	−0.657110	−0.328555	−	0.944485i	$-0.606562\pi$
$881$	−19.5041	−0.657110	−0.328555	+	0.944485i	$0.606562\pi$
$882$	−2.15397	−0.0725278
$883$	−27.7626	−0.934286	−0.467143	−	0.884182i	$-0.654717\pi$
$883$	−27.7626	−0.934286	−0.467143	+	0.884182i	$0.654717\pi$
$884$	37.0077	1.24470
$885$	0	0
$886$	30.0693	1.01020
$887$	−35.3228	−1.18602	−0.593012	−	0.805194i	$-0.702061\pi$
$887$	−35.3228	−1.18602	−0.593012	+	0.805194i	$0.702061\pi$
$888$	0.342221	0.0114842
$889$	19.1099	0.640924
$890$	0	0
$891$	30.3610	1.01713
$892$	47.7394	1.59843
$893$	22.7476	0.761221
$894$	22.3089	0.746120
$895$	0	0
$896$	19.2650	0.643598
$897$	33.0068	1.10206
$898$	−57.5802	−1.92148
$899$	74.0687	2.47033
$900$	0	0
$901$	18.2278	0.607255
$902$	13.3177	0.443430
$903$	−9.19897	−0.306123
$904$	35.2503	1.17241
$905$	0	0
$906$	−75.7469	−2.51652
$907$	−10.5803	−0.351312	−0.175656	−	0.984452i	$-0.556205\pi$
$907$	−10.5803	−0.351312	−0.175656	+	0.984452i	$0.556205\pi$
$908$	−6.47156	−0.214766
$909$	−6.52980	−0.216580
$910$	0	0
$911$	−18.0853	−0.599192	−0.299596	−	0.954066i	$-0.596852\pi$
$911$	−18.0853	−0.599192	−0.299596	+	0.954066i	$0.596852\pi$
$912$	−26.6223	−0.881552
$913$	−8.86654	−0.293440
$914$	20.2872	0.671041
$915$	0	0
$916$	−40.1093	−1.32525
$917$	−9.99440	−0.330044
$918$	39.3105	1.29744
$919$	9.90775	0.326826	0.163413	−	0.986558i	$-0.447750\pi$
$919$	9.90775	0.326826	0.163413	+	0.986558i	$0.447750\pi$
$920$	0	0
$921$	−37.0869	−1.22205
$922$	−21.6046	−0.711508
$923$	39.2770	1.29282
$924$	31.8896	1.04909
$925$	0	0
$926$	−90.6419	−2.97868
$927$	3.23177	0.106145
$928$	3.02425	0.0992757
$929$	−15.2665	−0.500878	−0.250439	−	0.968132i	$-0.580575\pi$
$929$	−15.2665	−0.500878	−0.250439	+	0.968132i	$0.580575\pi$
$930$	0	0
$931$	−4.32097	−0.141614
$932$	31.9489	1.04652
$933$	−11.9602	−0.391561
$934$	53.7641	1.75921
$935$	0	0
$936$	14.2051	0.464307
$937$	−21.2126	−0.692985	−0.346492	−	0.938053i	$-0.612627\pi$
$937$	−21.2126	−0.692985	−0.346492	+	0.938053i	$0.612627\pi$
$938$	−21.5845	−0.704759
$939$	−11.4247	−0.372832
$940$	0	0
$941$	−34.1282	−1.11255	−0.556274	−	0.830999i	$-0.687770\pi$
$941$	−34.1282	−1.11255	−0.556274	+	0.830999i	$0.687770\pi$
$942$	−73.3707	−2.39055
$943$	6.99907	0.227921
$944$	10.3696	0.337502
$945$	0	0
$946$	−84.0720	−2.73342
$947$	18.3584	0.596567	0.298284	−	0.954477i	$-0.403586\pi$
$947$	18.3584	0.596567	0.298284	+	0.954477i	$0.403586\pi$
$948$	29.0003	0.941886
$949$	7.86394	0.255274
$950$	0	0
$951$	−47.2653	−1.53268
$952$	14.1808	0.459601
$953$	16.0790	0.520849	0.260424	−	0.965494i	$-0.416138\pi$
$953$	16.0790	0.520849	0.260424	+	0.965494i	$0.416138\pi$
$954$	13.8634	0.448844
$955$	0	0
$956$	109.785	3.55069
$957$	−63.7147	−2.05960
$958$	84.4482	2.72840
$959$	4.66385	0.150603
$960$	0	0
$961$	53.2949	1.71919
$962$	−0.372974	−0.0120252
$963$	−7.52805	−0.242588
$964$	78.3386	2.52312
$965$	0	0
$966$	25.0608	0.806318
$967$	−38.0340	−1.22309	−0.611546	−	0.791209i	$-0.709452\pi$
$967$	−38.0340	−1.22309	−0.611546	+	0.791209i	$0.709452\pi$
$968$	92.0080	2.95725
$969$	17.8320	0.572847
$970$	0	0
$971$	60.7488	1.94952	0.974761	−	0.223250i	$-0.0716667\pi$
$971$	60.7488	1.94952	0.974761	+	0.223250i	$0.0716667\pi$
$972$	35.4677	1.13763
$973$	10.3954	0.333261
$974$	−39.2129	−1.25646
$975$	0	0
$976$	22.3380	0.715021
$977$	4.23580	0.135515	0.0677576	−	0.997702i	$-0.478416\pi$
$977$	4.23580	0.135515	0.0677576	+	0.997702i	$0.478416\pi$
$978$	5.85415	0.187195
$979$	−9.13928	−0.292093
$980$	0	0
$981$	2.55889	0.0816990
$982$	−4.17386	−0.133193
$983$	7.21490	0.230120	0.115060	−	0.993359i	$-0.463294\pi$
$983$	7.21490	0.230120	0.115060	+	0.993359i	$0.463294\pi$
$984$	−7.29647	−0.232603
$985$	0	0
$986$	−56.1404	−1.78788
$987$	7.67135	0.244182
$988$	56.4639	1.79636
$989$	−44.1838	−1.40496
$990$	0	0
$991$	−20.9196	−0.664533	−0.332267	−	0.943186i	$-0.607813\pi$
$991$	−20.9196	−0.664533	−0.332267	+	0.943186i	$0.607813\pi$
$992$	3.44178	0.109277
$993$	20.1932	0.640813
$994$	29.8215	0.945882
$995$	0	0
$996$	9.62551	0.304996
$997$	18.4455	0.584175	0.292088	−	0.956392i	$-0.405650\pi$
$997$	18.4455	0.584175	0.292088	+	0.956392i	$0.405650\pi$
$998$	−56.6432	−1.79301
$999$	−0.264948	−0.00838258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7175.2.a.n.1.5		5
5.4	even	2		287.2.a.e.1.1	✓	5
15.14	odd	2		2583.2.a.r.1.5		5
20.19	odd	2		4592.2.a.bb.1.5		5
35.34	odd	2		2009.2.a.n.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.1	✓	5	5.4	even	2
2009.2.a.n.1.1		5	35.34	odd	2
2583.2.a.r.1.5		5	15.14	odd	2
4592.2.a.bb.1.5		5	20.19	odd	2
7175.2.a.n.1.5		5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7175 = 5^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7175.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +3.58059 q^{6} -1.00000 q^{7} +5.00722 q^{8} -0.876597 q^{9} +O(q^{10})\)	\(q+2.45719 q^{2} +1.45719 q^{3} +4.03778 q^{4} +3.58059 q^{6} -1.00000 q^{7} +5.00722 q^{8} -0.876597 q^{9} -5.41988 q^{11} +5.88382 q^{12} -3.23628 q^{13} -2.45719 q^{14} +4.22813 q^{16} -2.83206 q^{17} -2.15397 q^{18} -4.32097 q^{19} -1.45719 q^{21} -13.3177 q^{22} -6.99907 q^{23} +7.29647 q^{24} -7.95216 q^{26} -5.64894 q^{27} -4.03778 q^{28} +8.06741 q^{29} +9.18123 q^{31} +0.374872 q^{32} -7.89779 q^{33} -6.95892 q^{34} -3.53951 q^{36} +0.0469023 q^{37} -10.6174 q^{38} -4.71588 q^{39} -1.00000 q^{41} -3.58059 q^{42} +6.31281 q^{43} -21.8843 q^{44} -17.1980 q^{46} -5.26448 q^{47} +6.16119 q^{48} +1.00000 q^{49} -4.12685 q^{51} -13.0674 q^{52} -6.43622 q^{53} -13.8805 q^{54} -5.00722 q^{56} -6.29647 q^{57} +19.8232 q^{58} +2.45253 q^{59} +5.28319 q^{61} +22.5600 q^{62} +0.876597 q^{63} -7.53512 q^{64} -19.4064 q^{66} +8.78423 q^{67} -11.4353 q^{68} -10.1990 q^{69} -12.1364 q^{71} -4.38931 q^{72} -2.42993 q^{73} +0.115248 q^{74} -17.4471 q^{76} +5.41988 q^{77} -11.5878 q^{78} +4.92882 q^{79} -5.60179 q^{81} -2.45719 q^{82} +1.63593 q^{83} -5.88382 q^{84} +15.5118 q^{86} +11.7558 q^{87} -27.1385 q^{88} +1.68625 q^{89} +3.23628 q^{91} -28.2607 q^{92} +13.3788 q^{93} -12.9358 q^{94} +0.546260 q^{96} -18.8278 q^{97} +2.45719 q^{98} +4.75105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9	\( 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} - q^{16} - 13 q^{17} - 21 q^{18} + 4 q^{21} - q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{27} - 3 q^{28} - 5 q^{29} + 17 q^{31} + 12 q^{32} - 3 q^{33} - 8 q^{34} + 15 q^{36} + 7 q^{37} + 3 q^{38} + 5 q^{39} - 5 q^{41} - 12 q^{42} - q^{43} - 47 q^{44} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 5 q^{49} + 5 q^{51} - 20 q^{52} - 5 q^{53} + 2 q^{54} - 3 q^{56} + 3 q^{57} + 27 q^{58} + 7 q^{59} + 22 q^{61} + 28 q^{62} - q^{63} - 3 q^{64} - 42 q^{66} + 3 q^{67} - 17 q^{68} - 22 q^{69} - 24 q^{71} + 12 q^{72} - 40 q^{73} - 5 q^{74} - 19 q^{76} - 2 q^{77} - 30 q^{78} - 42 q^{79} + 9 q^{81} - q^{82} + 12 q^{83} - 2 q^{84} + 16 q^{86} + 32 q^{87} - 26 q^{88} + 8 q^{89} + 5 q^{91} - 12 q^{92} + 11 q^{93} - 23 q^{94} - 17 q^{96} - 16 q^{97} + q^{98} - 45 q^{99}+O(q^{100}) \) 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - q^14 - q^16 - 13 * q^17 - 21 * q^18 + 4 * q^21 - q^22 - 2 * q^23 + 2 * q^24 - 10 * q^27 - 3 * q^28 - 5 * q^29 + 17 * q^31 + 12 * q^32 - 3 * q^33 - 8 * q^34 + 15 * q^36 + 7 * q^37 + 3 * q^38 + 5 * q^39 - 5 * q^41 - 12 * q^42 - q^43 - 47 * q^44 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 5 * q^49 + 5 * q^51 - 20 * q^52 - 5 * q^53 + 2 * q^54 - 3 * q^56 + 3 * q^57 + 27 * q^58 + 7 * q^59 + 22 * q^61 + 28 * q^62 - q^63 - 3 * q^64 - 42 * q^66 + 3 * q^67 - 17 * q^68 - 22 * q^69 - 24 * q^71 + 12 * q^72 - 40 * q^73 - 5 * q^74 - 19 * q^76 - 2 * q^77 - 30 * q^78 - 42 * q^79 + 9 * q^81 - q^82 + 12 * q^83 - 2 * q^84 + 16 * q^86 + 32 * q^87 - 26 * q^88 + 8 * q^89 + 5 * q^91 - 12 * q^92 + 11 * q^93 - 23 * q^94 - 17 * q^96 - 16 * q^97 + q^98 - 45 * q^99

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