LMFDB - Embedded newform 1925.2.a.bc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, 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("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 13x^{5} + 10x^{4} + 47x^{3} - 25x^{2} - 35x + 20 $ x^7 - x^6 - 13x^5 + 10x^4 + 47x^3 - 25x^2 - 35*x + 20
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.633891$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.633891 q^{2} -0.425088 q^{3} -1.59818 q^{4} -0.269459 q^{6} +1.00000 q^{7} -2.28085 q^{8} -2.81930 q^{9} +O(q^{10})$	\(q+0.633891 q^{2} -0.425088 q^{3} -1.59818 q^{4} -0.269459 q^{6} +1.00000 q^{7} -2.28085 q^{8} -2.81930 q^{9} -1.00000 q^{11} +0.679368 q^{12} +4.61413 q^{13} +0.633891 q^{14} +1.75055 q^{16} -0.0874635 q^{17} -1.78713 q^{18} -2.76975 q^{19} -0.425088 q^{21} -0.633891 q^{22} -4.36257 q^{23} +0.969564 q^{24} +2.92485 q^{26} +2.47371 q^{27} -1.59818 q^{28} -0.498559 q^{29} +7.10325 q^{31} +5.67137 q^{32} +0.425088 q^{33} -0.0554423 q^{34} +4.50576 q^{36} -1.50274 q^{37} -1.75572 q^{38} -1.96141 q^{39} +6.97670 q^{41} -0.269459 q^{42} +5.66659 q^{43} +1.59818 q^{44} -2.76539 q^{46} +0.269459 q^{47} -0.744139 q^{48} +1.00000 q^{49} +0.0371797 q^{51} -7.37421 q^{52} -7.48460 q^{53} +1.56806 q^{54} -2.28085 q^{56} +1.17739 q^{57} -0.316032 q^{58} +11.7082 q^{59} +4.43160 q^{61} +4.50269 q^{62} -2.81930 q^{63} +0.0939234 q^{64} +0.269459 q^{66} +13.4088 q^{67} +0.139783 q^{68} +1.85448 q^{69} -4.40847 q^{71} +6.43041 q^{72} +5.93802 q^{73} -0.952571 q^{74} +4.42657 q^{76} -1.00000 q^{77} -1.24332 q^{78} +11.4349 q^{79} +7.40635 q^{81} +4.42246 q^{82} +2.39958 q^{83} +0.679368 q^{84} +3.59200 q^{86} +0.211931 q^{87} +2.28085 q^{88} -2.80623 q^{89} +4.61413 q^{91} +6.97219 q^{92} -3.01951 q^{93} +0.170808 q^{94} -2.41083 q^{96} +0.504324 q^{97} +0.633891 q^{98} +2.81930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 13 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q + q^2 + 13 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 13 * q^9	$ 7 q + q^{2} + 13 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 13 q^{9} - 7 q^{11} - 21 q^{12} - 3 q^{13} + q^{14} + 29 q^{16} + 14 q^{18} + 18 q^{19} - q^{22} - 7 q^{23} - 22 q^{24} + 13 q^{26} + 6 q^{27} + 13 q^{28} - 2 q^{29} + 24 q^{31} + 33 q^{32} + 33 q^{34} + 44 q^{36} + 21 q^{37} + 9 q^{38} + 10 q^{39} - 10 q^{41} - q^{42} - 2 q^{43} - 13 q^{44} + 3 q^{46} + q^{47} - 77 q^{48} + 7 q^{49} + 29 q^{51} + 9 q^{52} - 11 q^{53} - 47 q^{54} + 6 q^{56} + 7 q^{57} - 33 q^{58} + q^{59} + 28 q^{61} + 16 q^{62} + 13 q^{63} + 48 q^{64} + q^{66} - 46 q^{68} + 33 q^{69} - 10 q^{71} + 36 q^{72} - 11 q^{73} - 6 q^{74} + 20 q^{76} - 7 q^{77} - 31 q^{78} + 19 q^{79} + 27 q^{81} + 8 q^{82} - 19 q^{83} - 21 q^{84} + 55 q^{86} - 12 q^{87} - 6 q^{88} - 2 q^{89} - 3 q^{91} + 40 q^{92} + 58 q^{93} + 21 q^{94} - 23 q^{96} + 8 q^{97} + q^{98} - 13 q^{99}+O(q^{100}) $ 7 * q + q^2 + 13 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 13 * q^9 - 7 * q^11 - 21 * q^12 - 3 * q^13 + q^14 + 29 * q^16 + 14 * q^18 + 18 * q^19 - q^22 - 7 * q^23 - 22 * q^24 + 13 * q^26 + 6 * q^27 + 13 * q^28 - 2 * q^29 + 24 * q^31 + 33 * q^32 + 33 * q^34 + 44 * q^36 + 21 * q^37 + 9 * q^38 + 10 * q^39 - 10 * q^41 - q^42 - 2 * q^43 - 13 * q^44 + 3 * q^46 + q^47 - 77 * q^48 + 7 * q^49 + 29 * q^51 + 9 * q^52 - 11 * q^53 - 47 * q^54 + 6 * q^56 + 7 * q^57 - 33 * q^58 + q^59 + 28 * q^61 + 16 * q^62 + 13 * q^63 + 48 * q^64 + q^66 - 46 * q^68 + 33 * q^69 - 10 * q^71 + 36 * q^72 - 11 * q^73 - 6 * q^74 + 20 * q^76 - 7 * q^77 - 31 * q^78 + 19 * q^79 + 27 * q^81 + 8 * q^82 - 19 * q^83 - 21 * q^84 + 55 * q^86 - 12 * q^87 - 6 * q^88 - 2 * q^89 - 3 * q^91 + 40 * q^92 + 58 * q^93 + 21 * q^94 - 23 * q^96 + 8 * q^97 + q^98 - 13 * 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 $

$2$	0.633891	0.448228	0.224114	−	0.974563i	$-0.428051\pi$
$2$	0.633891	0.448228	0.224114	+	0.974563i	$0.428051\pi$
$3$	−0.425088	−0.245425	−0.122712	−	0.992442i	$-0.539159\pi$
$3$	−0.425088	−0.245425	−0.122712	+	0.992442i	$0.539159\pi$
$4$	−1.59818	−0.799091
$5$	0	0
$5$	0	0
$6$	−0.269459	−0.110006
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.28085	−0.806404
$9$	−2.81930	−0.939767
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.679368	0.196117
$13$	4.61413	1.27973	0.639864	−	0.768488i	$-0.278991\pi$
$13$	4.61413	1.27973	0.639864	+	0.768488i	$0.278991\pi$
$14$	0.633891	0.169414
$15$	0	0
$16$	1.75055	0.437638
$17$	−0.0874635	−0.0212130	−0.0106065	−	0.999944i	$-0.503376\pi$
$17$	−0.0874635	−0.0212130	−0.0106065	+	0.999944i	$0.503376\pi$
$18$	−1.78713	−0.421230
$19$	−2.76975	−0.635425	−0.317713	−	0.948187i	$-0.602915\pi$
$19$	−2.76975	−0.635425	−0.317713	+	0.948187i	$0.602915\pi$
$20$	0	0
$21$	−0.425088	−0.0927618
$22$	−0.633891	−0.135146
$23$	−4.36257	−0.909659	−0.454830	−	0.890578i	$-0.650300\pi$
$23$	−4.36257	−0.909659	−0.454830	+	0.890578i	$0.650300\pi$
$24$	0.969564	0.197911
$25$	0	0
$26$	2.92485	0.573611
$27$	2.47371	0.476067
$28$	−1.59818	−0.302028
$29$	−0.498559	−0.0925800	−0.0462900	−	0.998928i	$-0.514740\pi$
$29$	−0.498559	−0.0925800	−0.0462900	+	0.998928i	$0.514740\pi$
$30$	0	0
$31$	7.10325	1.27578	0.637891	−	0.770127i	$-0.279807\pi$
$31$	7.10325	1.27578	0.637891	+	0.770127i	$0.279807\pi$
$32$	5.67137	1.00257
$33$	0.425088	0.0739983
$34$	−0.0554423	−0.00950828
$35$	0	0
$36$	4.50576	0.750959
$37$	−1.50274	−0.247048	−0.123524	−	0.992342i	$-0.539420\pi$
$37$	−1.50274	−0.247048	−0.123524	+	0.992342i	$0.539420\pi$
$38$	−1.75572	−0.284816
$39$	−1.96141	−0.314077
$40$	0	0
$41$	6.97670	1.08958	0.544789	−	0.838573i	$-0.316610\pi$
$41$	6.97670	1.08958	0.544789	+	0.838573i	$0.316610\pi$
$42$	−0.269459	−0.0415785
$43$	5.66659	0.864147	0.432074	−	0.901838i	$-0.357782\pi$
$43$	5.66659	0.864147	0.432074	+	0.901838i	$0.357782\pi$
$44$	1.59818	0.240935
$45$	0	0
$46$	−2.76539	−0.407735
$47$	0.269459	0.0393047	0.0196523	−	0.999807i	$-0.493744\pi$
$47$	0.269459	0.0393047	0.0196523	+	0.999807i	$0.493744\pi$
$48$	−0.744139	−0.107407
$49$	1.00000	0.142857
$50$	0	0
$51$	0.0371797	0.00520620
$52$	−7.37421	−1.02262
$53$	−7.48460	−1.02809	−0.514044	−	0.857764i	$-0.671853\pi$
$53$	−7.48460	−1.02809	−0.514044	+	0.857764i	$0.671853\pi$
$54$	1.56806	0.213387
$55$	0	0
$56$	−2.28085	−0.304792
$57$	1.17739	0.155949
$58$	−0.316032	−0.0414970
$59$	11.7082	1.52428	0.762142	−	0.647410i	$-0.224148\pi$
$59$	11.7082	1.52428	0.762142	+	0.647410i	$0.224148\pi$
$60$	0	0
$61$	4.43160	0.567408	0.283704	−	0.958912i	$-0.408437\pi$
$61$	4.43160	0.567408	0.283704	+	0.958912i	$0.408437\pi$
$62$	4.50269	0.571842
$63$	−2.81930	−0.355198
$64$	0.0939234	0.0117404
$65$	0	0
$66$	0.269459	0.0331682
$67$	13.4088	1.63815	0.819075	−	0.573687i	$-0.194487\pi$
$67$	13.4088	1.63815	0.819075	+	0.573687i	$0.194487\pi$
$68$	0.139783	0.0169511
$69$	1.85448	0.223253
$70$	0	0
$71$	−4.40847	−0.523189	−0.261595	−	0.965178i	$-0.584248\pi$
$71$	−4.40847	−0.523189	−0.261595	+	0.965178i	$0.584248\pi$
$72$	6.43041	0.757832
$73$	5.93802	0.694992	0.347496	−	0.937681i	$-0.387032\pi$
$73$	5.93802	0.694992	0.347496	+	0.937681i	$0.387032\pi$
$74$	−0.952571	−0.110734
$75$	0	0
$76$	4.42657	0.507763
$77$	−1.00000	−0.113961
$78$	−1.24332	−0.140778
$79$	11.4349	1.28652	0.643262	−	0.765646i	$-0.277581\pi$
$79$	11.4349	1.28652	0.643262	+	0.765646i	$0.277581\pi$
$80$	0	0
$81$	7.40635	0.822928
$82$	4.42246	0.488380
$83$	2.39958	0.263388	0.131694	−	0.991290i	$-0.457958\pi$
$83$	2.39958	0.263388	0.131694	+	0.991290i	$0.457958\pi$
$84$	0.679368	0.0741251
$85$	0	0
$86$	3.59200	0.387335
$87$	0.211931	0.0227214
$88$	2.28085	0.243140
$89$	−2.80623	−0.297459	−0.148730	−	0.988878i	$-0.547518\pi$
$89$	−2.80623	−0.297459	−0.148730	+	0.988878i	$0.547518\pi$
$90$	0	0
$91$	4.61413	0.483692
$92$	6.97219	0.726901
$93$	−3.01951	−0.313108
$94$	0.170808	0.0176175
$95$	0	0
$96$	−2.41083	−0.246054
$97$	0.504324	0.0512063	0.0256032	−	0.999672i	$-0.491849\pi$
$97$	0.504324	0.0512063	0.0256032	+	0.999672i	$0.491849\pi$
$98$	0.633891	0.0640326
$99$	2.81930	0.283350
$100$	0	0
$101$	15.9406	1.58615	0.793075	−	0.609124i	$-0.208479\pi$
$101$	15.9406	1.58615	0.793075	+	0.609124i	$0.208479\pi$
$102$	0.0235679	0.00233357
$103$	1.37151	0.135139	0.0675693	−	0.997715i	$-0.478476\pi$
$103$	1.37151	0.135139	0.0675693	+	0.997715i	$0.478476\pi$
$104$	−10.5241	−1.03198
$105$	0	0
$106$	−4.74442	−0.460819
$107$	−13.9079	−1.34452	−0.672262	−	0.740314i	$-0.734677\pi$
$107$	−13.9079	−1.34452	−0.672262	+	0.740314i	$0.734677\pi$
$108$	−3.95345	−0.380421
$109$	11.6899	1.11969	0.559845	−	0.828597i	$-0.310861\pi$
$109$	11.6899	1.11969	0.559845	+	0.828597i	$0.310861\pi$
$110$	0	0
$111$	0.638796	0.0606318
$112$	1.75055	0.165412
$113$	−7.87792	−0.741093	−0.370546	−	0.928814i	$-0.620830\pi$
$113$	−7.87792	−0.741093	−0.370546	+	0.928814i	$0.620830\pi$
$114$	0.746336	0.0699008
$115$	0	0
$116$	0.796788	0.0739799
$117$	−13.0086	−1.20265
$118$	7.42175	0.683227
$119$	−0.0874635	−0.00801777
$120$	0	0
$121$	1.00000	0.0909091
$122$	2.80915	0.254328
$123$	−2.96571	−0.267409
$124$	−11.3523	−1.01947
$125$	0	0
$126$	−1.78713	−0.159210
$127$	3.84487	0.341177	0.170589	−	0.985342i	$-0.445433\pi$
$127$	3.84487	0.341177	0.170589	+	0.985342i	$0.445433\pi$
$128$	−11.2832	−0.997303
$129$	−2.40880	−0.212083
$130$	0	0
$131$	−1.35840	−0.118684	−0.0593420	−	0.998238i	$-0.518900\pi$
$131$	−1.35840	−0.118684	−0.0593420	+	0.998238i	$0.518900\pi$
$132$	−0.679368	−0.0591314
$133$	−2.76975	−0.240168
$134$	8.49973	0.734265
$135$	0	0
$136$	0.199492	0.0171063
$137$	2.25610	0.192752	0.0963759	−	0.995345i	$-0.469275\pi$
$137$	2.25610	0.192752	0.0963759	+	0.995345i	$0.469275\pi$
$138$	1.17554	0.100068
$139$	0.275141	0.0233371	0.0116686	−	0.999932i	$-0.496286\pi$
$139$	0.275141	0.0233371	0.0116686	+	0.999932i	$0.496286\pi$
$140$	0	0
$141$	−0.114544	−0.00964634
$142$	−2.79449	−0.234508
$143$	−4.61413	−0.385853
$144$	−4.93533	−0.411278
$145$	0	0
$146$	3.76405	0.311515
$147$	−0.425088	−0.0350607
$148$	2.40165	0.197414
$149$	−3.21776	−0.263609	−0.131804	−	0.991276i	$-0.542077\pi$
$149$	−3.21776	−0.263609	−0.131804	+	0.991276i	$0.542077\pi$
$150$	0	0
$151$	12.9470	1.05361	0.526805	−	0.849986i	$-0.323390\pi$
$151$	12.9470	1.05361	0.526805	+	0.849986i	$0.323390\pi$
$152$	6.31741	0.512409
$153$	0.246586	0.0199353
$154$	−0.633891	−0.0510804
$155$	0	0
$156$	3.13469	0.250976
$157$	−19.8615	−1.58512	−0.792560	−	0.609794i	$-0.791252\pi$
$157$	−19.8615	−1.58512	−0.792560	+	0.609794i	$0.791252\pi$
$158$	7.24846	0.576656
$159$	3.18161	0.252318
$160$	0	0
$161$	−4.36257	−0.343819
$162$	4.69482	0.368860
$163$	−14.3543	−1.12431	−0.562157	−	0.827031i	$-0.690028\pi$
$163$	−14.3543	−1.12431	−0.562157	+	0.827031i	$0.690028\pi$
$164$	−11.1500	−0.870672
$165$	0	0
$166$	1.52107	0.118058
$167$	23.2790	1.80138	0.900692	−	0.434457i	$-0.143060\pi$
$167$	23.2790	1.80138	0.900692	+	0.434457i	$0.143060\pi$
$168$	0.969564	0.0748035
$169$	8.29015	0.637704
$170$	0	0
$171$	7.80877	0.597151
$172$	−9.05625	−0.690533
$173$	−10.2501	−0.779303	−0.389651	−	0.920962i	$-0.627405\pi$
$173$	−10.2501	−0.779303	−0.389651	+	0.920962i	$0.627405\pi$
$174$	0.134341	0.0101844
$175$	0	0
$176$	−1.75055	−0.131953
$177$	−4.97703	−0.374097
$178$	−1.77884	−0.133330
$179$	22.5775	1.68752	0.843761	−	0.536718i	$-0.180336\pi$
$179$	22.5775	1.68752	0.843761	+	0.536718i	$0.180336\pi$
$180$	0	0
$181$	−13.7545	−1.02236	−0.511181	−	0.859473i	$-0.670792\pi$
$181$	−13.7545	−1.02236	−0.511181	+	0.859473i	$0.670792\pi$
$182$	2.92485	0.216804
$183$	−1.88382	−0.139256
$184$	9.95039	0.733553
$185$	0	0
$186$	−1.91404	−0.140344
$187$	0.0874635	0.00639597
$188$	−0.430645	−0.0314080
$189$	2.47371	0.179936
$190$	0	0
$191$	4.74700	0.343481	0.171741	−	0.985142i	$-0.445061\pi$
$191$	4.74700	0.343481	0.171741	+	0.985142i	$0.445061\pi$
$192$	−0.0399257	−0.00288139
$193$	15.6899	1.12938	0.564692	−	0.825301i	$-0.308995\pi$
$193$	15.6899	1.12938	0.564692	+	0.825301i	$0.308995\pi$
$194$	0.319686	0.0229521
$195$	0	0
$196$	−1.59818	−0.114156
$197$	−6.40911	−0.456630	−0.228315	−	0.973587i	$-0.573322\pi$
$197$	−6.40911	−0.456630	−0.228315	+	0.973587i	$0.573322\pi$
$198$	1.78713	0.127006
$199$	−10.4872	−0.743419	−0.371710	−	0.928349i	$-0.621228\pi$
$199$	−10.4872	−0.743419	−0.371710	+	0.928349i	$0.621228\pi$
$200$	0	0
$201$	−5.69993	−0.402042
$202$	10.1046	0.710957
$203$	−0.498559	−0.0349920
$204$	−0.0594199	−0.00416023
$205$	0	0
$206$	0.869385	0.0605729
$207$	12.2994	0.854868
$208$	8.07727	0.560058
$209$	2.76975	0.191588
$210$	0	0
$211$	−9.57881	−0.659432	−0.329716	−	0.944080i	$-0.606953\pi$
$211$	−9.57881	−0.659432	−0.329716	+	0.944080i	$0.606953\pi$
$212$	11.9618	0.821537
$213$	1.87399	0.128404
$214$	−8.81606	−0.602654
$215$	0	0
$216$	−5.64218	−0.383902
$217$	7.10325	0.482200
$218$	7.41013	0.501877
$219$	−2.52418	−0.170568
$220$	0	0
$221$	−0.403568	−0.0271469
$222$	0.404927	0.0271769
$223$	−10.0219	−0.671115	−0.335558	−	0.942020i	$-0.608925\pi$
$223$	−10.0219	−0.671115	−0.335558	+	0.942020i	$0.608925\pi$
$224$	5.67137	0.378934
$225$	0	0
$226$	−4.99374	−0.332179
$227$	−6.51139	−0.432176	−0.216088	−	0.976374i	$-0.569330\pi$
$227$	−6.51139	−0.432176	−0.216088	+	0.976374i	$0.569330\pi$
$228$	−1.88168	−0.124617
$229$	28.5066	1.88377	0.941886	−	0.335934i	$-0.109052\pi$
$229$	28.5066	1.88377	0.941886	+	0.335934i	$0.109052\pi$
$230$	0	0
$231$	0.425088	0.0279687
$232$	1.13714	0.0746569
$233$	13.7790	0.902693	0.451346	−	0.892349i	$-0.350944\pi$
$233$	13.7790	0.902693	0.451346	+	0.892349i	$0.350944\pi$
$234$	−8.24603	−0.539060
$235$	0	0
$236$	−18.7119	−1.21804
$237$	−4.86083	−0.315745
$238$	−0.0554423	−0.00359379
$239$	11.9099	0.770389	0.385195	−	0.922835i	$-0.374134\pi$
$239$	11.9099	0.770389	0.385195	+	0.922835i	$0.374134\pi$
$240$	0	0
$241$	7.72250	0.497450	0.248725	−	0.968574i	$-0.419989\pi$
$241$	7.72250	0.497450	0.248725	+	0.968574i	$0.419989\pi$
$242$	0.633891	0.0407480
$243$	−10.5695	−0.678034
$244$	−7.08250	−0.453411
$245$	0	0
$246$	−1.87994	−0.119860
$247$	−12.7800	−0.813171
$248$	−16.2015	−1.02880
$249$	−1.02003	−0.0646419
$250$	0	0
$251$	−7.54774	−0.476409	−0.238205	−	0.971215i	$-0.576559\pi$
$251$	−7.54774	−0.476409	−0.238205	+	0.971215i	$0.576559\pi$
$252$	4.50576	0.283836
$253$	4.36257	0.274273
$254$	2.43723	0.152925
$255$	0	0
$256$	−7.34016	−0.458760
$257$	−16.9146	−1.05511	−0.527553	−	0.849522i	$-0.676890\pi$
$257$	−16.9146	−1.05511	−0.527553	+	0.849522i	$0.676890\pi$
$258$	−1.52692	−0.0950617
$259$	−1.50274	−0.0933755
$260$	0	0
$261$	1.40559	0.0870036
$262$	−0.861077	−0.0531975
$263$	11.0615	0.682082	0.341041	−	0.940048i	$-0.389220\pi$
$263$	11.0615	0.682082	0.341041	+	0.940048i	$0.389220\pi$
$264$	−0.969564	−0.0596725
$265$	0	0
$266$	−1.75572	−0.107650
$267$	1.19289	0.0730039
$268$	−21.4298	−1.30903
$269$	−27.2259	−1.65999	−0.829997	−	0.557768i	$-0.811658\pi$
$269$	−27.2259	−1.65999	−0.829997	+	0.557768i	$0.811658\pi$
$270$	0	0
$271$	−14.4274	−0.876405	−0.438203	−	0.898876i	$-0.644385\pi$
$271$	−14.4274	−0.876405	−0.438203	+	0.898876i	$0.644385\pi$
$272$	−0.153109	−0.00928363
$273$	−1.96141	−0.118710
$274$	1.43012	0.0863968
$275$	0	0
$276$	−2.96379	−0.178399
$277$	−3.80344	−0.228527	−0.114263	−	0.993450i	$-0.536451\pi$
$277$	−3.80344	−0.228527	−0.114263	+	0.993450i	$0.536451\pi$
$278$	0.174409	0.0104604
$279$	−20.0262	−1.19894
$280$	0	0
$281$	−20.3505	−1.21401	−0.607005	−	0.794698i	$-0.707629\pi$
$281$	−20.3505	−1.21401	−0.607005	+	0.794698i	$0.707629\pi$
$282$	−0.0726083	−0.00432376
$283$	−4.21465	−0.250535	−0.125267	−	0.992123i	$-0.539979\pi$
$283$	−4.21465	−0.250535	−0.125267	+	0.992123i	$0.539979\pi$
$284$	7.04554	0.418076
$285$	0	0
$286$	−2.92485	−0.172950
$287$	6.97670	0.411821
$288$	−15.9893	−0.942178
$289$	−16.9924	−0.999550
$290$	0	0
$291$	−0.214382	−0.0125673
$292$	−9.49003	−0.555362
$293$	33.1882	1.93887	0.969437	−	0.245340i	$-0.0788995\pi$
$293$	33.1882	1.93887	0.969437	+	0.245340i	$0.0788995\pi$
$294$	−0.269459	−0.0157152
$295$	0	0
$296$	3.42753	0.199221
$297$	−2.47371	−0.143539
$298$	−2.03971	−0.118157
$299$	−20.1295	−1.16412
$300$	0	0
$301$	5.66659	0.326617
$302$	8.20697	0.472258
$303$	−6.77616	−0.389280
$304$	−4.84860	−0.278086
$305$	0	0
$306$	0.156309	0.00893556
$307$	−24.5918	−1.40353	−0.701765	−	0.712409i	$-0.747604\pi$
$307$	−24.5918	−1.40353	−0.701765	+	0.712409i	$0.747604\pi$
$308$	1.59818	0.0910649
$309$	−0.583011	−0.0331663
$310$	0	0
$311$	6.42367	0.364253	0.182126	−	0.983275i	$-0.441702\pi$
$311$	6.42367	0.364253	0.182126	+	0.983275i	$0.441702\pi$
$312$	4.47369	0.253273
$313$	5.05001	0.285443	0.142722	−	0.989763i	$-0.454415\pi$
$313$	5.05001	0.285443	0.142722	+	0.989763i	$0.454415\pi$
$314$	−12.5900	−0.710496
$315$	0	0
$316$	−18.2750	−1.02805
$317$	12.6498	0.710481	0.355240	−	0.934775i	$-0.384399\pi$
$317$	12.6498	0.710481	0.355240	+	0.934775i	$0.384399\pi$
$318$	2.01679	0.113096
$319$	0.498559	0.0279139
$320$	0	0
$321$	5.91206	0.329979
$322$	−2.76539	−0.154109
$323$	0.242252	0.0134793
$324$	−11.8367	−0.657595
$325$	0	0
$326$	−9.09905	−0.503950
$327$	−4.96924	−0.274800
$328$	−15.9128	−0.878639
$329$	0.269459	0.0148558
$330$	0	0
$331$	31.6097	1.73743	0.868714	−	0.495314i	$-0.164947\pi$
$331$	31.6097	1.73743	0.868714	+	0.495314i	$0.164947\pi$
$332$	−3.83496	−0.210471
$333$	4.23667	0.232168
$334$	14.7564	0.807432
$335$	0	0
$336$	−0.744139	−0.0405961
$337$	−15.8472	−0.863251	−0.431625	−	0.902053i	$-0.642060\pi$
$337$	−15.8472	−0.863251	−0.431625	+	0.902053i	$0.642060\pi$
$338$	5.25505	0.285837
$339$	3.34881	0.181882
$340$	0	0
$341$	−7.10325	−0.384663
$342$	4.94991	0.267660
$343$	1.00000	0.0539949
$344$	−12.9247	−0.696852
$345$	0	0
$346$	−6.49746	−0.349306
$347$	8.60284	0.461825	0.230912	−	0.972975i	$-0.425829\pi$
$347$	8.60284	0.461825	0.230912	+	0.972975i	$0.425829\pi$
$348$	−0.338705	−0.0181565
$349$	31.7291	1.69842	0.849209	−	0.528057i	$-0.177079\pi$
$349$	31.7291	1.69842	0.849209	+	0.528057i	$0.177079\pi$
$350$	0	0
$351$	11.4140	0.609236
$352$	−5.67137	−0.302285
$353$	−17.4824	−0.930494	−0.465247	−	0.885181i	$-0.654035\pi$
$353$	−17.4824	−0.930494	−0.465247	+	0.885181i	$0.654035\pi$
$354$	−3.15490	−0.167681
$355$	0	0
$356$	4.48486	0.237697
$357$	0.0371797	0.00196776
$358$	14.3117	0.756396
$359$	−29.4116	−1.55229	−0.776143	−	0.630557i	$-0.782826\pi$
$359$	−29.4116	−1.55229	−0.776143	+	0.630557i	$0.782826\pi$
$360$	0	0
$361$	−11.3285	−0.596235
$362$	−8.71884	−0.458252
$363$	−0.425088	−0.0223113
$364$	−7.37421	−0.386514
$365$	0	0
$366$	−1.19414	−0.0624185
$367$	−29.0423	−1.51600	−0.757999	−	0.652256i	$-0.773823\pi$
$367$	−29.0423	−1.51600	−0.757999	+	0.652256i	$0.773823\pi$
$368$	−7.63691	−0.398102
$369$	−19.6694	−1.02395
$370$	0	0
$371$	−7.48460	−0.388581
$372$	4.82572	0.250202
$373$	22.5467	1.16743	0.583713	−	0.811960i	$-0.301599\pi$
$373$	22.5467	1.16743	0.583713	+	0.811960i	$0.301599\pi$
$374$	0.0554423	0.00286685
$375$	0	0
$376$	−0.614598	−0.0316955
$377$	−2.30041	−0.118477
$378$	1.56806	0.0806526
$379$	23.7421	1.21955	0.609775	−	0.792574i	$-0.291260\pi$
$379$	23.7421	1.21955	0.609775	+	0.792574i	$0.291260\pi$
$380$	0	0
$381$	−1.63441	−0.0837333
$382$	3.00908	0.153958
$383$	4.69277	0.239790	0.119895	−	0.992787i	$-0.461744\pi$
$383$	4.69277	0.239790	0.119895	+	0.992787i	$0.461744\pi$
$384$	4.79635	0.244763
$385$	0	0
$386$	9.94569	0.506222
$387$	−15.9758	−0.812097
$388$	−0.806001	−0.0409185
$389$	13.3329	0.676007	0.338003	−	0.941145i	$-0.390248\pi$
$389$	13.3329	0.676007	0.338003	+	0.941145i	$0.390248\pi$
$390$	0	0
$391$	0.381566	0.0192966
$392$	−2.28085	−0.115201
$393$	0.577439	0.0291280
$394$	−4.06268	−0.204675
$395$	0	0
$396$	−4.50576	−0.226423
$397$	−18.4351	−0.925229	−0.462614	−	0.886560i	$-0.653089\pi$
$397$	−18.4351	−0.925229	−0.462614	+	0.886560i	$0.653089\pi$
$398$	−6.64775	−0.333222
$399$	1.17739	0.0589432
$400$	0	0
$401$	−24.8247	−1.23968	−0.619842	−	0.784726i	$-0.712803\pi$
$401$	−24.8247	−1.23968	−0.619842	+	0.784726i	$0.712803\pi$
$402$	−3.61313	−0.180207
$403$	32.7753	1.63265
$404$	−25.4760	−1.26748
$405$	0	0
$406$	−0.316032	−0.0156844
$407$	1.50274	0.0744879
$408$	−0.0848015	−0.00419830
$409$	−22.1055	−1.09305	−0.546524	−	0.837443i	$-0.684049\pi$
$409$	−22.1055	−1.09305	−0.546524	+	0.837443i	$0.684049\pi$
$410$	0	0
$411$	−0.959042	−0.0473060
$412$	−2.19192	−0.107988
$413$	11.7082	0.576125
$414$	7.79648	0.383176
$415$	0	0
$416$	26.1684	1.28301
$417$	−0.116959	−0.00572751
$418$	1.75572	0.0858751
$419$	29.4106	1.43680	0.718401	−	0.695629i	$-0.244874\pi$
$419$	29.4106	1.43680	0.718401	+	0.695629i	$0.244874\pi$
$420$	0	0
$421$	−22.9317	−1.11762	−0.558812	−	0.829295i	$-0.688743\pi$
$421$	−22.9317	−1.11762	−0.558812	+	0.829295i	$0.688743\pi$
$422$	−6.07192	−0.295576
$423$	−0.759687	−0.0369372
$424$	17.0713	0.829055
$425$	0	0
$426$	1.18790	0.0575541
$427$	4.43160	0.214460
$428$	22.2273	1.07440
$429$	1.96141	0.0946977
$430$	0	0
$431$	31.0474	1.49550	0.747750	−	0.663981i	$-0.231134\pi$
$431$	31.0474	1.49550	0.747750	+	0.663981i	$0.231134\pi$
$432$	4.33037	0.208345
$433$	27.3772	1.31566	0.657832	−	0.753165i	$-0.271474\pi$
$433$	27.3772	1.31566	0.657832	+	0.753165i	$0.271474\pi$
$434$	4.50269	0.216136
$435$	0	0
$436$	−18.6826	−0.894735
$437$	12.0833	0.578020
$438$	−1.60005	−0.0764535
$439$	5.43727	0.259507	0.129753	−	0.991546i	$-0.458581\pi$
$439$	5.43727	0.259507	0.129753	+	0.991546i	$0.458581\pi$
$440$	0	0
$441$	−2.81930	−0.134252
$442$	−0.255818	−0.0121680
$443$	10.3375	0.491148	0.245574	−	0.969378i	$-0.421024\pi$
$443$	10.3375	0.491148	0.245574	+	0.969378i	$0.421024\pi$
$444$	−1.02091	−0.0484503
$445$	0	0
$446$	−6.35278	−0.300813
$447$	1.36783	0.0646961
$448$	0.0939234	0.00443747
$449$	17.5398	0.827754	0.413877	−	0.910333i	$-0.364174\pi$
$449$	17.5398	0.827754	0.413877	+	0.910333i	$0.364174\pi$
$450$	0	0
$451$	−6.97670	−0.328520
$452$	12.5904	0.592201
$453$	−5.50360	−0.258582
$454$	−4.12751	−0.193714
$455$	0	0
$456$	−2.68545	−0.125758
$457$	−1.34919	−0.0631124	−0.0315562	−	0.999502i	$-0.510046\pi$
$457$	−1.34919	−0.0631124	−0.0315562	+	0.999502i	$0.510046\pi$
$458$	18.0701	0.844360
$459$	−0.216360	−0.0100988
$460$	0	0
$461$	−30.5881	−1.42463	−0.712316	−	0.701859i	$-0.752354\pi$
$461$	−30.5881	−1.42463	−0.712316	+	0.701859i	$0.752354\pi$
$462$	0.269459	0.0125364
$463$	40.4250	1.87871	0.939354	−	0.342949i	$-0.111426\pi$
$463$	40.4250	1.87871	0.939354	+	0.342949i	$0.111426\pi$
$464$	−0.872753	−0.0405165
$465$	0	0
$466$	8.73438	0.404613
$467$	−26.3158	−1.21775	−0.608875	−	0.793266i	$-0.708379\pi$
$467$	−26.3158	−1.21775	−0.608875	+	0.793266i	$0.708379\pi$
$468$	20.7901	0.961024
$469$	13.4088	0.619162
$470$	0	0
$471$	8.44288	0.389027
$472$	−26.7048	−1.22919
$473$	−5.66659	−0.260550
$474$	−3.08123	−0.141526
$475$	0	0
$476$	0.139783	0.00640693
$477$	21.1013	0.966163
$478$	7.54960	0.345310
$479$	3.35349	0.153225	0.0766123	−	0.997061i	$-0.475590\pi$
$479$	3.35349	0.153225	0.0766123	+	0.997061i	$0.475590\pi$
$480$	0	0
$481$	−6.93382	−0.316155
$482$	4.89522	0.222971
$483$	1.85448	0.0843816
$484$	−1.59818	−0.0726447
$485$	0	0
$486$	−6.69991	−0.303914
$487$	13.7963	0.625169	0.312585	−	0.949890i	$-0.398805\pi$
$487$	13.7963	0.625169	0.312585	+	0.949890i	$0.398805\pi$
$488$	−10.1078	−0.457560
$489$	6.10183	0.275934
$490$	0	0
$491$	−37.0100	−1.67024	−0.835119	−	0.550070i	$-0.814601\pi$
$491$	−37.0100	−1.67024	−0.835119	+	0.550070i	$0.814601\pi$
$492$	4.73975	0.213684
$493$	0.0436057	0.00196390
$494$	−8.10112	−0.364487
$495$	0	0
$496$	12.4346	0.558331
$497$	−4.40847	−0.197747
$498$	−0.646589	−0.0289743
$499$	−17.0397	−0.762803	−0.381401	−	0.924410i	$-0.624558\pi$
$499$	−17.0397	−0.762803	−0.381401	+	0.924410i	$0.624558\pi$
$500$	0	0
$501$	−9.89563	−0.442104
$502$	−4.78444	−0.213540
$503$	7.14111	0.318406	0.159203	−	0.987246i	$-0.449108\pi$
$503$	7.14111	0.318406	0.159203	+	0.987246i	$0.449108\pi$
$504$	6.43041	0.286433
$505$	0	0
$506$	2.76539	0.122937
$507$	−3.52404	−0.156508
$508$	−6.14480	−0.272632
$509$	−19.5536	−0.866697	−0.433348	−	0.901226i	$-0.642668\pi$
$509$	−19.5536	−0.866697	−0.433348	+	0.901226i	$0.642668\pi$
$510$	0	0
$511$	5.93802	0.262682
$512$	17.9135	0.791674
$513$	−6.85158	−0.302505
$514$	−10.7220	−0.472928
$515$	0	0
$516$	3.84970	0.169474
$517$	−0.269459	−0.0118508
$518$	−0.952571	−0.0418536
$519$	4.35721	0.191260
$520$	0	0
$521$	19.9867	0.875635	0.437818	−	0.899064i	$-0.355752\pi$
$521$	19.9867	0.875635	0.437818	+	0.899064i	$0.355752\pi$
$522$	0.890989	0.0389975
$523$	−20.3762	−0.890990	−0.445495	−	0.895284i	$-0.646972\pi$
$523$	−20.3762	−0.890990	−0.445495	+	0.895284i	$0.646972\pi$
$524$	2.17097	0.0948393
$525$	0	0
$526$	7.01179	0.305729
$527$	−0.621275	−0.0270632
$528$	0.744139	0.0323845
$529$	−3.96796	−0.172520
$530$	0	0
$531$	−33.0091	−1.43247
$532$	4.42657	0.191916
$533$	32.1914	1.39436
$534$	0.756164	0.0327224
$535$	0	0
$536$	−30.5836	−1.32101
$537$	−9.59743	−0.414160
$538$	−17.2583	−0.744057
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	37.7722	1.62395	0.811977	−	0.583689i	$-0.198391\pi$
$541$	37.7722	1.62395	0.811977	+	0.583689i	$0.198391\pi$
$542$	−9.14543	−0.392830
$543$	5.84687	0.250913
$544$	−0.496038	−0.0212674
$545$	0	0
$546$	−1.24332	−0.0532092
$547$	−17.2831	−0.738972	−0.369486	−	0.929236i	$-0.620466\pi$
$547$	−17.2831	−0.738972	−0.369486	+	0.929236i	$0.620466\pi$
$548$	−3.60566	−0.154026
$549$	−12.4940	−0.533231
$550$	0	0
$551$	1.38089	0.0588277
$552$	−4.22979	−0.180032
$553$	11.4349	0.486260
$554$	−2.41097	−0.102432
$555$	0	0
$556$	−0.439725	−0.0186485
$557$	6.79002	0.287703	0.143851	−	0.989599i	$-0.454051\pi$
$557$	6.79002	0.287703	0.143851	+	0.989599i	$0.454051\pi$
$558$	−12.6944	−0.537398
$559$	26.1464	1.10587
$560$	0	0
$561$	−0.0371797	−0.00156973
$562$	−12.9000	−0.544154
$563$	4.49862	0.189594	0.0947972	−	0.995497i	$-0.469780\pi$
$563$	4.49862	0.189594	0.0947972	+	0.995497i	$0.469780\pi$
$564$	0.183062	0.00770831
$565$	0	0
$566$	−2.67163	−0.112297
$567$	7.40635	0.311038
$568$	10.0551	0.421902
$569$	27.7691	1.16414	0.582070	−	0.813139i	$-0.302243\pi$
$569$	27.7691	1.16414	0.582070	+	0.813139i	$0.302243\pi$
$570$	0	0
$571$	−17.7674	−0.743542	−0.371771	−	0.928325i	$-0.621249\pi$
$571$	−17.7674	−0.743542	−0.371771	+	0.928325i	$0.621249\pi$
$572$	7.37421	0.308331
$573$	−2.01789	−0.0842987
$574$	4.42246	0.184590
$575$	0	0
$576$	−0.264798	−0.0110333
$577$	−44.9562	−1.87155	−0.935776	−	0.352595i	$-0.885299\pi$
$577$	−44.9562	−1.87155	−0.935776	+	0.352595i	$0.885299\pi$
$578$	−10.7713	−0.448027
$579$	−6.66959	−0.277179
$580$	0	0
$581$	2.39958	0.0995512
$582$	−0.135895	−0.00563302
$583$	7.48460	0.309980
$584$	−13.5438	−0.560444
$585$	0	0
$586$	21.0377	0.869059
$587$	17.9592	0.741255	0.370627	−	0.928782i	$-0.379143\pi$
$587$	17.9592	0.741255	0.370627	+	0.928782i	$0.379143\pi$
$588$	0.679368	0.0280167
$589$	−19.6743	−0.810664
$590$	0	0
$591$	2.72444	0.112068
$592$	−2.63062	−0.108118
$593$	33.4098	1.37198	0.685988	−	0.727613i	$-0.259370\pi$
$593$	33.4098	1.37198	0.685988	+	0.727613i	$0.259370\pi$
$594$	−1.56806	−0.0643385
$595$	0	0
$596$	5.14256	0.210648
$597$	4.45799	0.182453
$598$	−12.7599	−0.521790
$599$	−20.7221	−0.846681	−0.423341	−	0.905971i	$-0.639143\pi$
$599$	−20.7221	−0.846681	−0.423341	+	0.905971i	$0.639143\pi$
$600$	0	0
$601$	−28.3592	−1.15680	−0.578398	−	0.815755i	$-0.696322\pi$
$601$	−28.3592	−1.15680	−0.578398	+	0.815755i	$0.696322\pi$
$602$	3.59200	0.146399
$603$	−37.8035	−1.53948
$604$	−20.6916	−0.841930
$605$	0	0
$606$	−4.29535	−0.174487
$607$	46.1211	1.87200	0.935998	−	0.352004i	$-0.114500\pi$
$607$	46.1211	1.87200	0.935998	+	0.352004i	$0.114500\pi$
$608$	−15.7083	−0.637055
$609$	0.211931	0.00858789
$610$	0	0
$611$	1.24332	0.0502993
$612$	−0.394089	−0.0159301
$613$	0.542682	0.0219187	0.0109594	−	0.999940i	$-0.496511\pi$
$613$	0.542682	0.0219187	0.0109594	+	0.999940i	$0.496511\pi$
$614$	−15.5885	−0.629102
$615$	0	0
$616$	2.28085	0.0918983
$617$	19.0924	0.768630	0.384315	−	0.923202i	$-0.374438\pi$
$617$	19.0924	0.768630	0.384315	+	0.923202i	$0.374438\pi$
$618$	−0.369565	−0.0148661
$619$	32.9718	1.32525	0.662624	−	0.748952i	$-0.269443\pi$
$619$	32.9718	1.32525	0.662624	+	0.748952i	$0.269443\pi$
$620$	0	0
$621$	−10.7918	−0.433058
$622$	4.07190	0.163268
$623$	−2.80623	−0.112429
$624$	−3.43355	−0.137452
$625$	0	0
$626$	3.20115	0.127944
$627$	−1.17739	−0.0470204
$628$	31.7423	1.26665
$629$	0.131435	0.00524064
$630$	0	0
$631$	29.5879	1.17787	0.588937	−	0.808179i	$-0.299546\pi$
$631$	29.5879	1.17787	0.588937	+	0.808179i	$0.299546\pi$
$632$	−26.0813	−1.03746
$633$	4.07184	0.161841
$634$	8.01856	0.318458
$635$	0	0
$636$	−5.08480	−0.201625
$637$	4.61413	0.182818
$638$	0.316032	0.0125118
$639$	12.4288	0.491676
$640$	0	0
$641$	−13.8383	−0.546579	−0.273290	−	0.961932i	$-0.588112\pi$
$641$	−13.8383	−0.546579	−0.273290	+	0.961932i	$0.588112\pi$
$642$	3.74760	0.147906
$643$	9.95758	0.392689	0.196344	−	0.980535i	$-0.437093\pi$
$643$	9.95758	0.392689	0.196344	+	0.980535i	$0.437093\pi$
$644$	6.97219	0.274743
$645$	0	0
$646$	0.153562	0.00604180
$647$	−28.3400	−1.11416	−0.557080	−	0.830459i	$-0.688079\pi$
$647$	−28.3400	−1.11416	−0.557080	+	0.830459i	$0.688079\pi$
$648$	−16.8928	−0.663613
$649$	−11.7082	−0.459589
$650$	0	0
$651$	−3.01951	−0.118344
$652$	22.9408	0.898430
$653$	−44.6604	−1.74770	−0.873848	−	0.486199i	$-0.838383\pi$
$653$	−44.6604	−1.74770	−0.873848	+	0.486199i	$0.838383\pi$
$654$	−3.14996	−0.123173
$655$	0	0
$656$	12.2131	0.476840
$657$	−16.7410	−0.653131
$658$	0.170808	0.00665878
$659$	−1.54774	−0.0602913	−0.0301456	−	0.999546i	$-0.509597\pi$
$659$	−1.54774	−0.0602913	−0.0301456	+	0.999546i	$0.509597\pi$
$660$	0	0
$661$	31.8659	1.23944	0.619721	−	0.784822i	$-0.287246\pi$
$661$	31.8659	1.23944	0.619721	+	0.784822i	$0.287246\pi$
$662$	20.0371	0.778765
$663$	0.171552	0.00666252
$664$	−5.47309	−0.212397
$665$	0	0
$666$	2.68558	0.104064
$667$	2.17500	0.0842163
$668$	−37.2041	−1.43947
$669$	4.26019	0.164708
$670$	0	0
$671$	−4.43160	−0.171080
$672$	−2.41083	−0.0929998
$673$	−26.5399	−1.02304	−0.511519	−	0.859272i	$-0.670917\pi$
$673$	−26.5399	−1.02304	−0.511519	+	0.859272i	$0.670917\pi$
$674$	−10.0454	−0.386934
$675$	0	0
$676$	−13.2492	−0.509584
$677$	16.5717	0.636904	0.318452	−	0.947939i	$-0.396837\pi$
$677$	16.5717	0.636904	0.318452	+	0.947939i	$0.396837\pi$
$678$	2.12278	0.0815249
$679$	0.504324	0.0193542
$680$	0	0
$681$	2.76791	0.106067
$682$	−4.50269	−0.172417
$683$	−3.06152	−0.117146	−0.0585730	−	0.998283i	$-0.518655\pi$
$683$	−3.06152	−0.117146	−0.0585730	+	0.998283i	$0.518655\pi$
$684$	−12.4798	−0.477178
$685$	0	0
$686$	0.633891	0.0242021
$687$	−12.1178	−0.462324
$688$	9.91967	0.378184
$689$	−34.5349	−1.31567
$690$	0	0
$691$	29.7730	1.13262	0.566309	−	0.824193i	$-0.308371\pi$
$691$	29.7730	1.13262	0.566309	+	0.824193i	$0.308371\pi$
$692$	16.3816	0.622734
$693$	2.81930	0.107096
$694$	5.45326	0.207003
$695$	0	0
$696$	−0.483385	−0.0183226
$697$	−0.610207	−0.0231132
$698$	20.1128	0.761279
$699$	−5.85729	−0.221543
$700$	0	0
$701$	2.55517	0.0965076	0.0482538	−	0.998835i	$-0.484634\pi$
$701$	2.55517	0.0965076	0.0482538	+	0.998835i	$0.484634\pi$
$702$	7.23525	0.273077
$703$	4.16221	0.156981
$704$	−0.0939234	−0.00353987
$705$	0	0
$706$	−11.0819	−0.417074
$707$	15.9406	0.599508
$708$	7.95421	0.298937
$709$	−6.53595	−0.245463	−0.122731	−	0.992440i	$-0.539165\pi$
$709$	−6.53595	−0.245463	−0.122731	+	0.992440i	$0.539165\pi$
$710$	0	0
$711$	−32.2383	−1.20903
$712$	6.40060	0.239872
$713$	−30.9885	−1.16053
$714$	0.0235679	0.000882005 0
$715$	0	0
$716$	−36.0830	−1.34848
$717$	−5.06277	−0.189073
$718$	−18.6437	−0.695778
$719$	27.4125	1.02231	0.511157	−	0.859487i	$-0.329217\pi$
$719$	27.4125	1.02231	0.511157	+	0.859487i	$0.329217\pi$
$720$	0	0
$721$	1.37151	0.0510776
$722$	−7.18101	−0.267249
$723$	−3.28274	−0.122086
$724$	21.9822	0.816961
$725$	0	0
$726$	−0.269459	−0.0100006
$727$	30.1724	1.11903	0.559516	−	0.828819i	$-0.310987\pi$
$727$	30.1724	1.11903	0.559516	+	0.828819i	$0.310987\pi$
$728$	−10.5241	−0.390051
$729$	−17.7261	−0.656522
$730$	0	0
$731$	−0.495620	−0.0183312
$732$	3.01069	0.111278
$733$	14.4616	0.534152	0.267076	−	0.963675i	$-0.413942\pi$
$733$	14.4616	0.534152	0.267076	+	0.963675i	$0.413942\pi$
$734$	−18.4097	−0.679513
$735$	0	0
$736$	−24.7418	−0.911993
$737$	−13.4088	−0.493921
$738$	−12.4683	−0.458963
$739$	32.9543	1.21224	0.606121	−	0.795372i	$-0.292725\pi$
$739$	32.9543	1.21224	0.606121	+	0.795372i	$0.292725\pi$
$740$	0	0
$741$	5.43262	0.199572
$742$	−4.74442	−0.174173
$743$	3.76396	0.138086	0.0690432	−	0.997614i	$-0.478005\pi$
$743$	3.76396	0.138086	0.0690432	+	0.997614i	$0.478005\pi$
$744$	6.88706	0.252492
$745$	0	0
$746$	14.2922	0.523274
$747$	−6.76513	−0.247523
$748$	−0.139783	−0.00511096
$749$	−13.9079	−0.508182
$750$	0	0
$751$	45.9444	1.67653	0.838267	−	0.545260i	$-0.183569\pi$
$751$	45.9444	1.67653	0.838267	+	0.545260i	$0.183569\pi$
$752$	0.471703	0.0172012
$753$	3.20845	0.116923
$754$	−1.45821	−0.0531049
$755$	0	0
$756$	−3.95345	−0.143785
$757$	40.3467	1.46643	0.733213	−	0.679999i	$-0.238020\pi$
$757$	40.3467	1.46643	0.733213	+	0.679999i	$0.238020\pi$
$758$	15.0499	0.546637
$759$	−1.85448	−0.0673133
$760$	0	0
$761$	−13.6871	−0.496157	−0.248079	−	0.968740i	$-0.579799\pi$
$761$	−13.6871	−0.496157	−0.248079	+	0.968740i	$0.579799\pi$
$762$	−1.03604	−0.0375316
$763$	11.6899	0.423203
$764$	−7.58658	−0.274473
$765$	0	0
$766$	2.97471	0.107480
$767$	54.0233	1.95067
$768$	3.12022	0.112591
$769$	38.5474	1.39006	0.695028	−	0.718983i	$-0.255392\pi$
$769$	38.5474	1.39006	0.695028	+	0.718983i	$0.255392\pi$
$770$	0	0
$771$	7.19021	0.258949
$772$	−25.0753	−0.902482
$773$	5.51659	0.198418	0.0992090	−	0.995067i	$-0.468369\pi$
$773$	5.51659	0.198418	0.0992090	+	0.995067i	$0.468369\pi$
$774$	−10.1269	−0.364005
$775$	0	0
$776$	−1.15029	−0.0412930
$777$	0.638796	0.0229167
$778$	8.45163	0.303006
$779$	−19.3237	−0.692345
$780$	0	0
$781$	4.40847	0.157748
$782$	0.241871	0.00864930
$783$	−1.23329	−0.0440743
$784$	1.75055	0.0625197
$785$	0	0
$786$	0.366034	0.0130560
$787$	−29.7792	−1.06151	−0.530756	−	0.847524i	$-0.678092\pi$
$787$	−29.7792	−1.06151	−0.530756	+	0.847524i	$0.678092\pi$
$788$	10.2429	0.364889
$789$	−4.70212	−0.167400
$790$	0	0
$791$	−7.87792	−0.280107
$792$	−6.43041	−0.228495
$793$	20.4479	0.726128
$794$	−11.6858	−0.414714
$795$	0	0
$796$	16.7605	0.594060
$797$	−17.9922	−0.637315	−0.318658	−	0.947870i	$-0.603232\pi$
$797$	−17.9922	−0.637315	−0.318658	+	0.947870i	$0.603232\pi$
$798$	0.746336	0.0264200
$799$	−0.0235679	−0.000833771 0
$800$	0	0
$801$	7.91160	0.279543
$802$	−15.7361	−0.555662
$803$	−5.93802	−0.209548
$804$	9.10953	0.321268
$805$	0	0
$806$	20.7760	0.731802
$807$	11.5734	0.407404
$808$	−36.3582	−1.27908
$809$	10.4613	0.367801	0.183901	−	0.982945i	$-0.441128\pi$
$809$	10.4613	0.367801	0.183901	+	0.982945i	$0.441128\pi$
$810$	0	0
$811$	43.7701	1.53698	0.768489	−	0.639863i	$-0.221009\pi$
$811$	43.7701	1.53698	0.768489	+	0.639863i	$0.221009\pi$
$812$	0.796788	0.0279618
$813$	6.13293	0.215091
$814$	0.952571	0.0333876
$815$	0	0
$816$	0.0650850	0.00227843
$817$	−15.6951	−0.549101
$818$	−14.0125	−0.489936
$819$	−13.0086	−0.454557
$820$	0	0
$821$	−11.8371	−0.413119	−0.206559	−	0.978434i	$-0.566227\pi$
$821$	−11.8371	−0.413119	−0.206559	+	0.978434i	$0.566227\pi$
$822$	−0.607928	−0.0212039
$823$	−46.7082	−1.62815	−0.814073	−	0.580762i	$-0.802755\pi$
$823$	−46.7082	−1.62815	−0.814073	+	0.580762i	$0.802755\pi$
$824$	−3.12821	−0.108976
$825$	0	0
$826$	7.42175	0.258236
$827$	40.2990	1.40133	0.700666	−	0.713489i	$-0.252886\pi$
$827$	40.2990	1.40133	0.700666	+	0.713489i	$0.252886\pi$
$828$	−19.6567	−0.683117
$829$	7.42077	0.257734	0.128867	−	0.991662i	$-0.458866\pi$
$829$	7.42077	0.257734	0.128867	+	0.991662i	$0.458866\pi$
$830$	0	0
$831$	1.61680	0.0560861
$832$	0.433374	0.0150246
$833$	−0.0874635	−0.00303043
$834$	−0.0741392	−0.00256723
$835$	0	0
$836$	−4.42657	−0.153096
$837$	17.5714	0.607357
$838$	18.6431	0.644016
$839$	23.6372	0.816046	0.408023	−	0.912972i	$-0.366218\pi$
$839$	23.6372	0.816046	0.408023	+	0.912972i	$0.366218\pi$
$840$	0	0
$841$	−28.7514	−0.991429
$842$	−14.5362	−0.500951
$843$	8.65076	0.297948
$844$	15.3087	0.526947
$845$	0	0
$846$	−0.481558	−0.0165563
$847$	1.00000	0.0343604
$848$	−13.1022	−0.449931
$849$	1.79160	0.0614874
$850$	0	0
$851$	6.55580	0.224730
$852$	−2.99498	−0.102606
$853$	−31.5024	−1.07862	−0.539311	−	0.842106i	$-0.681315\pi$
$853$	−31.5024	−1.07862	−0.539311	+	0.842106i	$0.681315\pi$
$854$	2.80915	0.0961271
$855$	0	0
$856$	31.7218	1.08423
$857$	30.8943	1.05533	0.527665	−	0.849452i	$-0.323068\pi$
$857$	30.8943	1.05533	0.527665	+	0.849452i	$0.323068\pi$
$858$	1.24332	0.0424462
$859$	35.8938	1.22468	0.612340	−	0.790594i	$-0.290228\pi$
$859$	35.8938	1.22468	0.612340	+	0.790594i	$0.290228\pi$
$860$	0	0
$861$	−2.96571	−0.101071
$862$	19.6806	0.670325
$863$	−16.3679	−0.557170	−0.278585	−	0.960412i	$-0.589865\pi$
$863$	−16.3679	−0.557170	−0.278585	+	0.960412i	$0.589865\pi$
$864$	14.0293	0.477288
$865$	0	0
$866$	17.3542	0.589718
$867$	7.22324	0.245314
$868$	−11.3523	−0.385322
$869$	−11.4349	−0.387901
$870$	0	0
$871$	61.8700	2.09639
$872$	−26.6630	−0.902923
$873$	−1.42184	−0.0481220
$874$	7.65946	0.259085
$875$	0	0
$876$	4.03410	0.136300
$877$	−19.6026	−0.661932	−0.330966	−	0.943643i	$-0.607375\pi$
$877$	−19.6026	−0.661932	−0.330966	+	0.943643i	$0.607375\pi$
$878$	3.44664	0.116318
$879$	−14.1079	−0.475848
$880$	0	0
$881$	19.6500	0.662025	0.331012	−	0.943626i	$-0.392610\pi$
$881$	19.6500	0.662025	0.331012	+	0.943626i	$0.392610\pi$
$882$	−1.78713	−0.0601757
$883$	35.2229	1.18534	0.592672	−	0.805444i	$-0.298073\pi$
$883$	35.2229	1.18534	0.592672	+	0.805444i	$0.298073\pi$
$884$	0.644975	0.0216928
$885$	0	0
$886$	6.55283	0.220147
$887$	−38.4382	−1.29063	−0.645314	−	0.763918i	$-0.723273\pi$
$887$	−38.4382	−1.29063	−0.645314	+	0.763918i	$0.723273\pi$
$888$	−1.45700	−0.0488937
$889$	3.84487	0.128953
$890$	0	0
$891$	−7.40635	−0.248122
$892$	16.0168	0.536282
$893$	−0.746336	−0.0249752
$894$	0.867055	0.0289986
$895$	0	0
$896$	−11.2832	−0.376945
$897$	8.55679	0.285703
$898$	11.1183	0.371023
$899$	−3.54139	−0.118112
$900$	0	0
$901$	0.654629	0.0218089
$902$	−4.42246	−0.147252
$903$	−2.40880	−0.0801599
$904$	17.9684	0.597620
$905$	0	0
$906$	−3.48868	−0.115904
$907$	−40.3084	−1.33842	−0.669209	−	0.743075i	$-0.733367\pi$
$907$	−40.3084	−1.33842	−0.669209	+	0.743075i	$0.733367\pi$
$908$	10.4064	0.345348
$909$	−44.9414	−1.49061
$910$	0	0
$911$	18.7318	0.620612	0.310306	−	0.950637i	$-0.399568\pi$
$911$	18.7318	0.620612	0.310306	+	0.950637i	$0.399568\pi$
$912$	2.06108	0.0682492
$913$	−2.39958	−0.0794144
$914$	−0.855238	−0.0282888
$915$	0	0
$916$	−45.5588	−1.50531
$917$	−1.35840	−0.0448583
$918$	−0.137148	−0.00452657
$919$	21.0980	0.695958	0.347979	−	0.937502i	$-0.386868\pi$
$919$	21.0980	0.695958	0.347979	+	0.937502i	$0.386868\pi$
$920$	0	0
$921$	10.4537	0.344461
$922$	−19.3895	−0.638561
$923$	−20.3412	−0.669540
$924$	−0.679368	−0.0223496
$925$	0	0
$926$	25.6250	0.842090
$927$	−3.86669	−0.126999
$928$	−2.82751	−0.0928176
$929$	42.6410	1.39901	0.699503	−	0.714629i	$-0.253405\pi$
$929$	42.6410	1.39901	0.699503	+	0.714629i	$0.253405\pi$
$930$	0	0
$931$	−2.76975	−0.0907750
$932$	−22.0214	−0.721334
$933$	−2.73062	−0.0893966
$934$	−16.6814	−0.545831
$935$	0	0
$936$	29.6707	0.969818
$937$	5.15757	0.168491	0.0842453	−	0.996445i	$-0.473152\pi$
$937$	5.15757	0.168491	0.0842453	+	0.996445i	$0.473152\pi$
$938$	8.49973	0.277526
$939$	−2.14670	−0.0700548
$940$	0	0
$941$	−53.5224	−1.74478	−0.872390	−	0.488810i	$-0.837431\pi$
$941$	−53.5224	−1.74478	−0.872390	+	0.488810i	$0.837431\pi$
$942$	5.35186	0.174373
$943$	−30.4364	−0.991144
$944$	20.4959	0.667084
$945$	0	0
$946$	−3.59200	−0.116786
$947$	16.2031	0.526530	0.263265	−	0.964724i	$-0.415201\pi$
$947$	16.2031	0.526530	0.263265	+	0.964724i	$0.415201\pi$
$948$	7.76849	0.252309
$949$	27.3987	0.889401
$950$	0	0
$951$	−5.37726	−0.174370
$952$	0.199492	0.00646556
$953$	−35.2173	−1.14080	−0.570401	−	0.821366i	$-0.693212\pi$
$953$	−35.2173	−1.14080	−0.570401	+	0.821366i	$0.693212\pi$
$954$	13.3759	0.433062
$955$	0	0
$956$	−19.0342	−0.615611
$957$	−0.211931	−0.00685077
$958$	2.12574	0.0686797
$959$	2.25610	0.0728533
$960$	0	0
$961$	19.4562	0.627619
$962$	−4.39528	−0.141710
$963$	39.2104	1.26354
$964$	−12.3420	−0.397508
$965$	0	0
$966$	1.17554	0.0378223
$967$	50.4619	1.62275	0.811373	−	0.584529i	$-0.198721\pi$
$967$	50.4619	1.62275	0.811373	+	0.584529i	$0.198721\pi$
$968$	−2.28085	−0.0733094
$969$	−0.102979	−0.00330815
$970$	0	0
$971$	37.8328	1.21411	0.607057	−	0.794659i	$-0.292350\pi$
$971$	37.8328	1.21411	0.607057	+	0.794659i	$0.292350\pi$
$972$	16.8920	0.541811
$973$	0.275141	0.00882061
$974$	8.74534	0.280219
$975$	0	0
$976$	7.75774	0.248319
$977$	19.6920	0.630002	0.315001	−	0.949091i	$-0.397995\pi$
$977$	19.6920	0.630002	0.315001	+	0.949091i	$0.397995\pi$
$978$	3.86790	0.123682
$979$	2.80623	0.0896874
$980$	0	0
$981$	−32.9574	−1.05225
$982$	−23.4603	−0.748648
$983$	−61.7486	−1.96947	−0.984736	−	0.174052i	$-0.944314\pi$
$983$	−61.7486	−1.96947	−0.984736	+	0.174052i	$0.944314\pi$
$984$	6.76435	0.215640
$985$	0	0
$986$	0.0276413	0.000880277 0
$987$	−0.114544	−0.00364597
$988$	20.4248	0.649798
$989$	−24.7209	−0.786080
$990$	0	0
$991$	27.0205	0.858336	0.429168	−	0.903225i	$-0.358807\pi$
$991$	27.0205	0.858336	0.429168	+	0.903225i	$0.358807\pi$
$992$	40.2852	1.27905
$993$	−13.4369	−0.426408
$994$	−2.79449	−0.0886358
$995$	0	0
$996$	1.63020	0.0516547
$997$	−49.4068	−1.56473	−0.782364	−	0.622821i	$-0.785986\pi$
$997$	−49.4068	−1.56473	−0.782364	+	0.622821i	$0.785986\pi$
$998$	−10.8013	−0.341910
$999$	−3.71734	−0.117612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.bc.1.4	yes	7
5.2	odd	4		1925.2.b.q.1849.8		14
5.3	odd	4		1925.2.b.q.1849.7		14
5.4	even	2		1925.2.a.ba.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1925.2.a.ba.1.4	✓	7	5.4	even	2
1925.2.a.bc.1.4	yes	7	1.1	even	1	trivial
1925.2.b.q.1849.7		14	5.3	odd	4
1925.2.b.q.1849.8		14	5.2	odd	4

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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q+0.633891 q^{2} -0.425088 q^{3} -1.59818 q^{4} -0.269459 q^{6} +1.00000 q^{7} -2.28085 q^{8} -2.81930 q^{9} +O(q^{10})\)	\(q+0.633891 q^{2} -0.425088 q^{3} -1.59818 q^{4} -0.269459 q^{6} +1.00000 q^{7} -2.28085 q^{8} -2.81930 q^{9} -1.00000 q^{11} +0.679368 q^{12} +4.61413 q^{13} +0.633891 q^{14} +1.75055 q^{16} -0.0874635 q^{17} -1.78713 q^{18} -2.76975 q^{19} -0.425088 q^{21} -0.633891 q^{22} -4.36257 q^{23} +0.969564 q^{24} +2.92485 q^{26} +2.47371 q^{27} -1.59818 q^{28} -0.498559 q^{29} +7.10325 q^{31} +5.67137 q^{32} +0.425088 q^{33} -0.0554423 q^{34} +4.50576 q^{36} -1.50274 q^{37} -1.75572 q^{38} -1.96141 q^{39} +6.97670 q^{41} -0.269459 q^{42} +5.66659 q^{43} +1.59818 q^{44} -2.76539 q^{46} +0.269459 q^{47} -0.744139 q^{48} +1.00000 q^{49} +0.0371797 q^{51} -7.37421 q^{52} -7.48460 q^{53} +1.56806 q^{54} -2.28085 q^{56} +1.17739 q^{57} -0.316032 q^{58} +11.7082 q^{59} +4.43160 q^{61} +4.50269 q^{62} -2.81930 q^{63} +0.0939234 q^{64} +0.269459 q^{66} +13.4088 q^{67} +0.139783 q^{68} +1.85448 q^{69} -4.40847 q^{71} +6.43041 q^{72} +5.93802 q^{73} -0.952571 q^{74} +4.42657 q^{76} -1.00000 q^{77} -1.24332 q^{78} +11.4349 q^{79} +7.40635 q^{81} +4.42246 q^{82} +2.39958 q^{83} +0.679368 q^{84} +3.59200 q^{86} +0.211931 q^{87} +2.28085 q^{88} -2.80623 q^{89} +4.61413 q^{91} +6.97219 q^{92} -3.01951 q^{93} +0.170808 q^{94} -2.41083 q^{96} +0.504324 q^{97} +0.633891 q^{98} +2.81930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 13 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q + q^2 + 13 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} + 13 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 13 q^{9} - 7 q^{11} - 21 q^{12} - 3 q^{13} + q^{14} + 29 q^{16} + 14 q^{18} + 18 q^{19} - q^{22} - 7 q^{23} - 22 q^{24} + 13 q^{26} + 6 q^{27} + 13 q^{28} - 2 q^{29} + 24 q^{31} + 33 q^{32} + 33 q^{34} + 44 q^{36} + 21 q^{37} + 9 q^{38} + 10 q^{39} - 10 q^{41} - q^{42} - 2 q^{43} - 13 q^{44} + 3 q^{46} + q^{47} - 77 q^{48} + 7 q^{49} + 29 q^{51} + 9 q^{52} - 11 q^{53} - 47 q^{54} + 6 q^{56} + 7 q^{57} - 33 q^{58} + q^{59} + 28 q^{61} + 16 q^{62} + 13 q^{63} + 48 q^{64} + q^{66} - 46 q^{68} + 33 q^{69} - 10 q^{71} + 36 q^{72} - 11 q^{73} - 6 q^{74} + 20 q^{76} - 7 q^{77} - 31 q^{78} + 19 q^{79} + 27 q^{81} + 8 q^{82} - 19 q^{83} - 21 q^{84} + 55 q^{86} - 12 q^{87} - 6 q^{88} - 2 q^{89} - 3 q^{91} + 40 q^{92} + 58 q^{93} + 21 q^{94} - 23 q^{96} + 8 q^{97} + q^{98} - 13 q^{99}+O(q^{100}) \) 7 * q + q^2 + 13 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 13 * q^9 - 7 * q^11 - 21 * q^12 - 3 * q^13 + q^14 + 29 * q^16 + 14 * q^18 + 18 * q^19 - q^22 - 7 * q^23 - 22 * q^24 + 13 * q^26 + 6 * q^27 + 13 * q^28 - 2 * q^29 + 24 * q^31 + 33 * q^32 + 33 * q^34 + 44 * q^36 + 21 * q^37 + 9 * q^38 + 10 * q^39 - 10 * q^41 - q^42 - 2 * q^43 - 13 * q^44 + 3 * q^46 + q^47 - 77 * q^48 + 7 * q^49 + 29 * q^51 + 9 * q^52 - 11 * q^53 - 47 * q^54 + 6 * q^56 + 7 * q^57 - 33 * q^58 + q^59 + 28 * q^61 + 16 * q^62 + 13 * q^63 + 48 * q^64 + q^66 - 46 * q^68 + 33 * q^69 - 10 * q^71 + 36 * q^72 - 11 * q^73 - 6 * q^74 + 20 * q^76 - 7 * q^77 - 31 * q^78 + 19 * q^79 + 27 * q^81 + 8 * q^82 - 19 * q^83 - 21 * q^84 + 55 * q^86 - 12 * q^87 - 6 * q^88 - 2 * q^89 - 3 * q^91 + 40 * q^92 + 58 * q^93 + 21 * q^94 - 23 * q^96 + 8 * q^97 + q^98 - 13 * q^99

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