LMFDB - Embedded newform 3525.2.a.y.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
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} - 9x^{5} + 6x^{4} + 20x^{3} - 9x^{2} - 12x + 3 $ x^7 - x^6 - 9x^5 + 6x^4 + 20x^3 - 9x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.29205$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.29205 q^{2} +1.00000 q^{3} +3.25349 q^{4} +2.29205 q^{6} -4.47358 q^{7} +2.87307 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.29205 q^{2} +1.00000 q^{3} +3.25349 q^{4} +2.29205 q^{6} -4.47358 q^{7} +2.87307 q^{8} +1.00000 q^{9} -2.51991 q^{11} +3.25349 q^{12} -4.43683 q^{13} -10.2537 q^{14} +0.0782323 q^{16} -5.36761 q^{17} +2.29205 q^{18} +4.11569 q^{19} -4.47358 q^{21} -5.77577 q^{22} -2.16203 q^{23} +2.87307 q^{24} -10.1694 q^{26} +1.00000 q^{27} -14.5548 q^{28} +0.758949 q^{29} +2.74893 q^{31} -5.56683 q^{32} -2.51991 q^{33} -12.3028 q^{34} +3.25349 q^{36} +3.99860 q^{37} +9.43337 q^{38} -4.43683 q^{39} -2.29889 q^{41} -10.2537 q^{42} -11.8277 q^{43} -8.19853 q^{44} -4.95547 q^{46} +1.00000 q^{47} +0.0782323 q^{48} +13.0129 q^{49} -5.36761 q^{51} -14.4352 q^{52} -4.40100 q^{53} +2.29205 q^{54} -12.8529 q^{56} +4.11569 q^{57} +1.73955 q^{58} -6.47071 q^{59} +15.3625 q^{61} +6.30068 q^{62} -4.47358 q^{63} -12.9159 q^{64} -5.77577 q^{66} -1.66187 q^{67} -17.4635 q^{68} -2.16203 q^{69} +9.28196 q^{71} +2.87307 q^{72} -0.677803 q^{73} +9.16500 q^{74} +13.3904 q^{76} +11.2730 q^{77} -10.1694 q^{78} -11.5746 q^{79} +1.00000 q^{81} -5.26917 q^{82} -14.1094 q^{83} -14.5548 q^{84} -27.1097 q^{86} +0.758949 q^{87} -7.23989 q^{88} +7.01883 q^{89} +19.8485 q^{91} -7.03414 q^{92} +2.74893 q^{93} +2.29205 q^{94} -5.56683 q^{96} +5.26770 q^{97} +29.8263 q^{98} -2.51991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * 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 $

$2$	2.29205	1.62072	0.810362	−	0.585929i	$-0.199270\pi$
$2$	2.29205	1.62072	0.810362	+	0.585929i	$0.199270\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.25349	1.62675
$5$	0	0
$5$	0	0
$6$	2.29205	0.935726
$7$	−4.47358	−1.69085	−0.845427	−	0.534091i	$-0.820654\pi$
$7$	−4.47358	−1.69085	−0.845427	+	0.534091i	$0.820654\pi$
$8$	2.87307	1.01578
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.51991	−0.759783	−0.379891	−	0.925031i	$-0.624039\pi$
$11$	−2.51991	−0.759783	−0.379891	+	0.925031i	$0.624039\pi$
$12$	3.25349	0.939203
$13$	−4.43683	−1.23056	−0.615278	−	0.788310i	$-0.710956\pi$
$13$	−4.43683	−1.23056	−0.615278	+	0.788310i	$0.710956\pi$
$14$	−10.2537	−2.74041
$15$	0	0
$16$	0.0782323	0.0195581
$17$	−5.36761	−1.30184	−0.650919	−	0.759147i	$-0.725616\pi$
$17$	−5.36761	−1.30184	−0.650919	+	0.759147i	$0.725616\pi$
$18$	2.29205	0.540241
$19$	4.11569	0.944204	0.472102	−	0.881544i	$-0.343495\pi$
$19$	4.11569	0.944204	0.472102	+	0.881544i	$0.343495\pi$
$20$	0	0
$21$	−4.47358	−0.976215
$22$	−5.77577	−1.23140
$23$	−2.16203	−0.450814	−0.225407	−	0.974265i	$-0.572371\pi$
$23$	−2.16203	−0.450814	−0.225407	+	0.974265i	$0.572371\pi$
$24$	2.87307	0.586463
$25$	0	0
$26$	−10.1694	−1.99439
$27$	1.00000	0.192450
$28$	−14.5548	−2.75059
$29$	0.758949	0.140933	0.0704667	−	0.997514i	$-0.477551\pi$
$29$	0.758949	0.140933	0.0704667	+	0.997514i	$0.477551\pi$
$30$	0	0
$31$	2.74893	0.493722	0.246861	−	0.969051i	$-0.420601\pi$
$31$	2.74893	0.493722	0.246861	+	0.969051i	$0.420601\pi$
$32$	−5.56683	−0.984085
$33$	−2.51991	−0.438661
$34$	−12.3028	−2.10992
$35$	0	0
$36$	3.25349	0.542249
$37$	3.99860	0.657367	0.328683	−	0.944440i	$-0.393395\pi$
$37$	3.99860	0.657367	0.328683	+	0.944440i	$0.393395\pi$
$38$	9.43337	1.53029
$39$	−4.43683	−0.710461
$40$	0	0
$41$	−2.29889	−0.359026	−0.179513	−	0.983756i	$-0.557452\pi$
$41$	−2.29889	−0.359026	−0.179513	+	0.983756i	$0.557452\pi$
$42$	−10.2537	−1.58218
$43$	−11.8277	−1.80371	−0.901854	−	0.432040i	$-0.857794\pi$
$43$	−11.8277	−1.80371	−0.901854	+	0.432040i	$0.857794\pi$
$44$	−8.19853	−1.23597
$45$	0	0
$46$	−4.95547	−0.730644
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	0.0782323	0.0112919
$49$	13.0129	1.85899
$50$	0	0
$51$	−5.36761	−0.751616
$52$	−14.4352	−2.00180
$53$	−4.40100	−0.604524	−0.302262	−	0.953225i	$-0.597742\pi$
$53$	−4.40100	−0.604524	−0.302262	+	0.953225i	$0.597742\pi$
$54$	2.29205	0.311909
$55$	0	0
$56$	−12.8529	−1.71754
$57$	4.11569	0.545137
$58$	1.73955	0.228414
$59$	−6.47071	−0.842415	−0.421207	−	0.906964i	$-0.638394\pi$
$59$	−6.47071	−0.842415	−0.421207	+	0.906964i	$0.638394\pi$
$60$	0	0
$61$	15.3625	1.96697	0.983485	−	0.180992i	$-0.0579308\pi$
$61$	15.3625	1.96697	0.983485	+	0.180992i	$0.0579308\pi$
$62$	6.30068	0.800187
$63$	−4.47358	−0.563618
$64$	−12.9159	−1.61449
$65$	0	0
$66$	−5.77577	−0.710948
$67$	−1.66187	−0.203030	−0.101515	−	0.994834i	$-0.532369\pi$
$67$	−1.66187	−0.203030	−0.101515	+	0.994834i	$0.532369\pi$
$68$	−17.4635	−2.11776
$69$	−2.16203	−0.260277
$70$	0	0
$71$	9.28196	1.10157	0.550783	−	0.834649i	$-0.314329\pi$
$71$	9.28196	1.10157	0.550783	+	0.834649i	$0.314329\pi$
$72$	2.87307	0.338594
$73$	−0.677803	−0.0793308	−0.0396654	−	0.999213i	$-0.512629\pi$
$73$	−0.677803	−0.0793308	−0.0396654	+	0.999213i	$0.512629\pi$
$74$	9.16500	1.06541
$75$	0	0
$76$	13.3904	1.53598
$77$	11.2730	1.28468
$78$	−10.1694	−1.15146
$79$	−11.5746	−1.30224	−0.651120	−	0.758974i	$-0.725701\pi$
$79$	−11.5746	−1.30224	−0.651120	+	0.758974i	$0.725701\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−5.26917	−0.581882
$83$	−14.1094	−1.54871	−0.774355	−	0.632751i	$-0.781926\pi$
$83$	−14.1094	−1.54871	−0.774355	+	0.632751i	$0.781926\pi$
$84$	−14.5548	−1.58805
$85$	0	0
$86$	−27.1097	−2.92331
$87$	0.758949	0.0813679
$88$	−7.23989	−0.771775
$89$	7.01883	0.743994	0.371997	−	0.928234i	$-0.378673\pi$
$89$	7.01883	0.743994	0.371997	+	0.928234i	$0.378673\pi$
$90$	0	0
$91$	19.8485	2.08069
$92$	−7.03414	−0.733360
$93$	2.74893	0.285050
$94$	2.29205	0.236407
$95$	0	0
$96$	−5.56683	−0.568162
$97$	5.26770	0.534854	0.267427	−	0.963578i	$-0.413827\pi$
$97$	5.26770	0.534854	0.267427	+	0.963578i	$0.413827\pi$
$98$	29.8263	3.01291
$99$	−2.51991	−0.253261
$100$	0	0
$101$	−5.79856	−0.576979	−0.288489	−	0.957483i	$-0.593153\pi$
$101$	−5.79856	−0.576979	−0.288489	+	0.957483i	$0.593153\pi$
$102$	−12.3028	−1.21816
$103$	0.516870	0.0509287	0.0254644	−	0.999676i	$-0.491894\pi$
$103$	0.516870	0.0509287	0.0254644	+	0.999676i	$0.491894\pi$
$104$	−12.7473	−1.24998
$105$	0	0
$106$	−10.0873	−0.979766
$107$	9.28494	0.897609	0.448805	−	0.893630i	$-0.351850\pi$
$107$	9.28494	0.897609	0.448805	+	0.893630i	$0.351850\pi$
$108$	3.25349	0.313068
$109$	−17.0561	−1.63368	−0.816838	−	0.576867i	$-0.804275\pi$
$109$	−17.0561	−1.63368	−0.816838	+	0.576867i	$0.804275\pi$
$110$	0	0
$111$	3.99860	0.379531
$112$	−0.349979	−0.0330699
$113$	9.16418	0.862093	0.431047	−	0.902330i	$-0.358144\pi$
$113$	9.16418	0.862093	0.431047	+	0.902330i	$0.358144\pi$
$114$	9.43337	0.883516
$115$	0	0
$116$	2.46924	0.229263
$117$	−4.43683	−0.410185
$118$	−14.8312	−1.36532
$119$	24.0124	2.20122
$120$	0	0
$121$	−4.65003	−0.422730
$122$	35.2117	3.18791
$123$	−2.29889	−0.207284
$124$	8.94361	0.803160
$125$	0	0
$126$	−10.2537	−0.913469
$127$	13.2194	1.17303	0.586516	−	0.809938i	$-0.300499\pi$
$127$	13.2194	1.17303	0.586516	+	0.809938i	$0.300499\pi$
$128$	−18.4703	−1.63256
$129$	−11.8277	−1.04137
$130$	0	0
$131$	−16.5753	−1.44819	−0.724094	−	0.689702i	$-0.757742\pi$
$131$	−16.5753	−1.44819	−0.724094	+	0.689702i	$0.757742\pi$
$132$	−8.19853	−0.713590
$133$	−18.4119	−1.59651
$134$	−3.80910	−0.329056
$135$	0	0
$136$	−15.4215	−1.32239
$137$	14.3144	1.22296	0.611481	−	0.791259i	$-0.290574\pi$
$137$	14.3144	1.22296	0.611481	+	0.791259i	$0.290574\pi$
$138$	−4.95547	−0.421838
$139$	6.01812	0.510450	0.255225	−	0.966882i	$-0.417850\pi$
$139$	6.01812	0.510450	0.255225	+	0.966882i	$0.417850\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	21.2747	1.78533
$143$	11.1804	0.934955
$144$	0.0782323	0.00651936
$145$	0	0
$146$	−1.55356	−0.128573
$147$	13.0129	1.07329
$148$	13.0094	1.06937
$149$	−1.69479	−0.138842	−0.0694211	−	0.997587i	$-0.522115\pi$
$149$	−1.69479	−0.138842	−0.0694211	+	0.997587i	$0.522115\pi$
$150$	0	0
$151$	−3.73585	−0.304019	−0.152010	−	0.988379i	$-0.548574\pi$
$151$	−3.73585	−0.304019	−0.152010	+	0.988379i	$0.548574\pi$
$152$	11.8247	0.959107
$153$	−5.36761	−0.433946
$154$	25.8384	2.08212
$155$	0	0
$156$	−14.4352	−1.15574
$157$	10.7108	0.854813	0.427407	−	0.904059i	$-0.359427\pi$
$157$	10.7108	0.854813	0.427407	+	0.904059i	$0.359427\pi$
$158$	−26.5295	−2.11057
$159$	−4.40100	−0.349022
$160$	0	0
$161$	9.67200	0.762260
$162$	2.29205	0.180080
$163$	−20.4539	−1.60208	−0.801038	−	0.598613i	$-0.795719\pi$
$163$	−20.4539	−1.60208	−0.801038	+	0.598613i	$0.795719\pi$
$164$	−7.47942	−0.584045
$165$	0	0
$166$	−32.3395	−2.51003
$167$	19.2288	1.48797	0.743984	−	0.668197i	$-0.232934\pi$
$167$	19.2288	1.48797	0.743984	+	0.668197i	$0.232934\pi$
$168$	−12.8529	−0.991623
$169$	6.68546	0.514266
$170$	0	0
$171$	4.11569	0.314735
$172$	−38.4814	−2.93418
$173$	8.58785	0.652922	0.326461	−	0.945211i	$-0.394144\pi$
$173$	8.58785	0.652922	0.326461	+	0.945211i	$0.394144\pi$
$174$	1.73955	0.131875
$175$	0	0
$176$	−0.197139	−0.0148599
$177$	−6.47071	−0.486368
$178$	16.0875	1.20581
$179$	12.0431	0.900145	0.450073	−	0.892992i	$-0.351398\pi$
$179$	12.0431	0.900145	0.450073	+	0.892992i	$0.351398\pi$
$180$	0	0
$181$	−11.7352	−0.872269	−0.436134	−	0.899882i	$-0.643653\pi$
$181$	−11.7352	−0.872269	−0.436134	+	0.899882i	$0.643653\pi$
$182$	45.4938	3.37222
$183$	15.3625	1.13563
$184$	−6.21165	−0.457929
$185$	0	0
$186$	6.30068	0.461988
$187$	13.5259	0.989114
$188$	3.25349	0.237285
$189$	−4.47358	−0.325405
$190$	0	0
$191$	4.95346	0.358420	0.179210	−	0.983811i	$-0.442646\pi$
$191$	4.95346	0.358420	0.179210	+	0.983811i	$0.442646\pi$
$192$	−12.9159	−0.932125
$193$	20.9415	1.50740	0.753702	−	0.657216i	$-0.228266\pi$
$193$	20.9415	1.50740	0.753702	+	0.657216i	$0.228266\pi$
$194$	12.0738	0.866851
$195$	0	0
$196$	42.3374	3.02410
$197$	−20.8670	−1.48671	−0.743357	−	0.668895i	$-0.766767\pi$
$197$	−20.8670	−1.48671	−0.743357	+	0.668895i	$0.766767\pi$
$198$	−5.77577	−0.410466
$199$	−13.3580	−0.946924	−0.473462	−	0.880814i	$-0.656996\pi$
$199$	−13.3580	−0.946924	−0.473462	+	0.880814i	$0.656996\pi$
$200$	0	0
$201$	−1.66187	−0.117219
$202$	−13.2906	−0.935123
$203$	−3.39522	−0.238298
$204$	−17.4635	−1.22269
$205$	0	0
$206$	1.18469	0.0825414
$207$	−2.16203	−0.150271
$208$	−0.347104	−0.0240673
$209$	−10.3712	−0.717390
$210$	0	0
$211$	26.8648	1.84945	0.924723	−	0.380640i	$-0.124296\pi$
$211$	26.8648	1.84945	0.924723	+	0.380640i	$0.124296\pi$
$212$	−14.3186	−0.983407
$213$	9.28196	0.635989
$214$	21.2816	1.45478
$215$	0	0
$216$	2.87307	0.195488
$217$	−12.2975	−0.834812
$218$	−39.0934	−2.64774
$219$	−0.677803	−0.0458017
$220$	0	0
$221$	23.8152	1.60198
$222$	9.16500	0.615115
$223$	−9.88334	−0.661838	−0.330919	−	0.943659i	$-0.607359\pi$
$223$	−9.88334	−0.661838	−0.330919	+	0.943659i	$0.607359\pi$
$224$	24.9036	1.66394
$225$	0	0
$226$	21.0048	1.39722
$227$	−15.6296	−1.03738	−0.518688	−	0.854964i	$-0.673579\pi$
$227$	−15.6296	−1.03738	−0.518688	+	0.854964i	$0.673579\pi$
$228$	13.3904	0.886799
$229$	−8.42747	−0.556903	−0.278451	−	0.960450i	$-0.589821\pi$
$229$	−8.42747	−0.556903	−0.278451	+	0.960450i	$0.589821\pi$
$230$	0	0
$231$	11.2730	0.741712
$232$	2.18051	0.143158
$233$	−23.6282	−1.54794	−0.773968	−	0.633225i	$-0.781731\pi$
$233$	−23.6282	−1.54794	−0.773968	+	0.633225i	$0.781731\pi$
$234$	−10.1694	−0.664797
$235$	0	0
$236$	−21.0524	−1.37040
$237$	−11.5746	−0.751849
$238$	55.0377	3.56757
$239$	16.7691	1.08470	0.542351	−	0.840152i	$-0.317534\pi$
$239$	16.7691	1.08470	0.542351	+	0.840152i	$0.317534\pi$
$240$	0	0
$241$	−12.1497	−0.782631	−0.391316	−	0.920257i	$-0.627980\pi$
$241$	−12.1497	−0.782631	−0.391316	+	0.920257i	$0.627980\pi$
$242$	−10.6581	−0.685128
$243$	1.00000	0.0641500
$244$	49.9819	3.19976
$245$	0	0
$246$	−5.26917	−0.335950
$247$	−18.2606	−1.16190
$248$	7.89786	0.501514
$249$	−14.1094	−0.894148
$250$	0	0
$251$	−19.9545	−1.25952	−0.629758	−	0.776791i	$-0.716846\pi$
$251$	−19.9545	−1.25952	−0.629758	+	0.776791i	$0.716846\pi$
$252$	−14.5548	−0.916864
$253$	5.44812	0.342520
$254$	30.2995	1.90116
$255$	0	0
$256$	−16.5029	−1.03143
$257$	−12.3779	−0.772110	−0.386055	−	0.922476i	$-0.626163\pi$
$257$	−12.3779	−0.772110	−0.386055	+	0.922476i	$0.626163\pi$
$258$	−27.1097	−1.68778
$259$	−17.8881	−1.11151
$260$	0	0
$261$	0.758949	0.0469778
$262$	−37.9913	−2.34711
$263$	20.4980	1.26396	0.631980	−	0.774984i	$-0.282242\pi$
$263$	20.4980	1.26396	0.631980	+	0.774984i	$0.282242\pi$
$264$	−7.23989	−0.445584
$265$	0	0
$266$	−42.2009	−2.58750
$267$	7.01883	0.429545
$268$	−5.40689	−0.330279
$269$	−10.9866	−0.669866	−0.334933	−	0.942242i	$-0.608714\pi$
$269$	−10.9866	−0.669866	−0.334933	+	0.942242i	$0.608714\pi$
$270$	0	0
$271$	−16.7847	−1.01960	−0.509800	−	0.860293i	$-0.670281\pi$
$271$	−16.7847	−1.01960	−0.509800	+	0.860293i	$0.670281\pi$
$272$	−0.419921	−0.0254614
$273$	19.8485	1.20129
$274$	32.8093	1.98208
$275$	0	0
$276$	−7.03414	−0.423405
$277$	−19.8154	−1.19059	−0.595297	−	0.803506i	$-0.702965\pi$
$277$	−19.8154	−1.19059	−0.595297	+	0.803506i	$0.702965\pi$
$278$	13.7938	0.827299
$279$	2.74893	0.164574
$280$	0	0
$281$	−22.5638	−1.34604	−0.673020	−	0.739624i	$-0.735003\pi$
$281$	−22.5638	−1.34604	−0.673020	+	0.739624i	$0.735003\pi$
$282$	2.29205	0.136490
$283$	−8.29887	−0.493317	−0.246658	−	0.969102i	$-0.579333\pi$
$283$	−8.29887	−0.493317	−0.246658	+	0.969102i	$0.579333\pi$
$284$	30.1988	1.79197
$285$	0	0
$286$	25.6261	1.51530
$287$	10.2843	0.607061
$288$	−5.56683	−0.328028
$289$	11.8113	0.694781
$290$	0	0
$291$	5.26770	0.308798
$292$	−2.20523	−0.129051
$293$	−0.923291	−0.0539392	−0.0269696	−	0.999636i	$-0.508586\pi$
$293$	−0.923291	−0.0539392	−0.0269696	+	0.999636i	$0.508586\pi$
$294$	29.8263	1.73950
$295$	0	0
$296$	11.4883	0.667742
$297$	−2.51991	−0.146220
$298$	−3.88453	−0.225025
$299$	9.59254	0.554751
$300$	0	0
$301$	52.9122	3.04981
$302$	−8.56276	−0.492731
$303$	−5.79856	−0.333119
$304$	0.321980	0.0184668
$305$	0	0
$306$	−12.3028	−0.703306
$307$	18.7467	1.06993	0.534966	−	0.844873i	$-0.320324\pi$
$307$	18.7467	1.06993	0.534966	+	0.844873i	$0.320324\pi$
$308$	36.6768	2.08985
$309$	0.516870	0.0294037
$310$	0	0
$311$	−2.98503	−0.169266	−0.0846329	−	0.996412i	$-0.526972\pi$
$311$	−2.98503	−0.169266	−0.0846329	+	0.996412i	$0.526972\pi$
$312$	−12.7473	−0.721675
$313$	−13.2791	−0.750580	−0.375290	−	0.926907i	$-0.622457\pi$
$313$	−13.2791	−0.750580	−0.375290	+	0.926907i	$0.622457\pi$
$314$	24.5496	1.38542
$315$	0	0
$316$	−37.6578	−2.11842
$317$	−25.6179	−1.43885	−0.719423	−	0.694572i	$-0.755594\pi$
$317$	−25.6179	−1.43885	−0.719423	+	0.694572i	$0.755594\pi$
$318$	−10.0873	−0.565668
$319$	−1.91249	−0.107079
$320$	0	0
$321$	9.28494	0.518235
$322$	22.1687	1.23541
$323$	−22.0914	−1.22920
$324$	3.25349	0.180750
$325$	0	0
$326$	−46.8815	−2.59652
$327$	−17.0561	−0.943204
$328$	−6.60487	−0.364693
$329$	−4.47358	−0.246636
$330$	0	0
$331$	26.4817	1.45557	0.727783	−	0.685808i	$-0.240551\pi$
$331$	26.4817	1.45557	0.727783	+	0.685808i	$0.240551\pi$
$332$	−45.9049	−2.51936
$333$	3.99860	0.219122
$334$	44.0733	2.41159
$335$	0	0
$336$	−0.349979	−0.0190929
$337$	1.41864	0.0772784	0.0386392	−	0.999253i	$-0.487698\pi$
$337$	1.41864	0.0772784	0.0386392	+	0.999253i	$0.487698\pi$
$338$	15.3234	0.833484
$339$	9.16418	0.497730
$340$	0	0
$341$	−6.92706	−0.375121
$342$	9.43337	0.510098
$343$	−26.8993	−1.45242
$344$	−33.9818	−1.83218
$345$	0	0
$346$	19.6838	1.05821
$347$	32.5780	1.74888	0.874440	−	0.485134i	$-0.161229\pi$
$347$	32.5780	1.74888	0.874440	+	0.485134i	$0.161229\pi$
$348$	2.46924	0.132365
$349$	10.8562	0.581117	0.290559	−	0.956857i	$-0.406159\pi$
$349$	10.8562	0.581117	0.290559	+	0.956857i	$0.406159\pi$
$350$	0	0
$351$	−4.43683	−0.236820
$352$	14.0279	0.747691
$353$	−4.54465	−0.241887	−0.120944	−	0.992659i	$-0.538592\pi$
$353$	−4.54465	−0.241887	−0.120944	+	0.992659i	$0.538592\pi$
$354$	−14.8312	−0.788269
$355$	0	0
$356$	22.8357	1.21029
$357$	24.0124	1.27087
$358$	27.6034	1.45889
$359$	−24.0203	−1.26774	−0.633872	−	0.773438i	$-0.718535\pi$
$359$	−24.0203	−1.26774	−0.633872	+	0.773438i	$0.718535\pi$
$360$	0	0
$361$	−2.06109	−0.108478
$362$	−26.8976	−1.41371
$363$	−4.65003	−0.244063
$364$	64.5770	3.38475
$365$	0	0
$366$	35.2117	1.84054
$367$	−1.42767	−0.0745237	−0.0372619	−	0.999306i	$-0.511864\pi$
$367$	−1.42767	−0.0745237	−0.0372619	+	0.999306i	$0.511864\pi$
$368$	−0.169140	−0.00881705
$369$	−2.29889	−0.119675
$370$	0	0
$371$	19.6882	1.02216
$372$	8.94361	0.463705
$373$	11.7375	0.607743	0.303872	−	0.952713i	$-0.401721\pi$
$373$	11.7375	0.607743	0.303872	+	0.952713i	$0.401721\pi$
$374$	31.0021	1.60308
$375$	0	0
$376$	2.87307	0.148167
$377$	−3.36733	−0.173426
$378$	−10.2537	−0.527392
$379$	19.6411	1.00890	0.504448	−	0.863442i	$-0.331696\pi$
$379$	19.6411	1.00890	0.504448	+	0.863442i	$0.331696\pi$
$380$	0	0
$381$	13.2194	0.677250
$382$	11.3536	0.580900
$383$	−21.5577	−1.10155	−0.550773	−	0.834655i	$-0.685667\pi$
$383$	−21.5577	−1.10155	−0.550773	+	0.834655i	$0.685667\pi$
$384$	−18.4703	−0.942556
$385$	0	0
$386$	47.9990	2.44309
$387$	−11.8277	−0.601236
$388$	17.1384	0.870072
$389$	32.5347	1.64957	0.824787	−	0.565444i	$-0.191295\pi$
$389$	32.5347	1.64957	0.824787	+	0.565444i	$0.191295\pi$
$390$	0	0
$391$	11.6049	0.586886
$392$	37.3870	1.88833
$393$	−16.5753	−0.836111
$394$	−47.8282	−2.40955
$395$	0	0
$396$	−8.19853	−0.411991
$397$	27.4262	1.37648	0.688241	−	0.725482i	$-0.258383\pi$
$397$	27.4262	1.37648	0.688241	+	0.725482i	$0.258383\pi$
$398$	−30.6172	−1.53470
$399$	−18.4119	−0.921746
$400$	0	0
$401$	−7.93408	−0.396209	−0.198105	−	0.980181i	$-0.563479\pi$
$401$	−7.93408	−0.396209	−0.198105	+	0.980181i	$0.563479\pi$
$402$	−3.80910	−0.189980
$403$	−12.1965	−0.607552
$404$	−18.8656	−0.938598
$405$	0	0
$406$	−7.78201	−0.386215
$407$	−10.0761	−0.499456
$408$	−15.4215	−0.763479
$409$	19.8086	0.979472	0.489736	−	0.871871i	$-0.337093\pi$
$409$	19.8086	0.979472	0.489736	+	0.871871i	$0.337093\pi$
$410$	0	0
$411$	14.3144	0.706078
$412$	1.68163	0.0828481
$413$	28.9472	1.42440
$414$	−4.95547	−0.243548
$415$	0	0
$416$	24.6991	1.21097
$417$	6.01812	0.294708
$418$	−23.7713	−1.16269
$419$	−29.3779	−1.43521	−0.717603	−	0.696453i	$-0.754761\pi$
$419$	−29.3779	−1.43521	−0.717603	+	0.696453i	$0.754761\pi$
$420$	0	0
$421$	7.65604	0.373132	0.186566	−	0.982442i	$-0.440264\pi$
$421$	7.65604	0.373132	0.186566	+	0.982442i	$0.440264\pi$
$422$	61.5754	2.99744
$423$	1.00000	0.0486217
$424$	−12.6444	−0.614065
$425$	0	0
$426$	21.2747	1.03076
$427$	−68.7255	−3.32586
$428$	30.2085	1.46018
$429$	11.1804	0.539796
$430$	0	0
$431$	−11.2584	−0.542299	−0.271149	−	0.962537i	$-0.587404\pi$
$431$	−11.2584	−0.542299	−0.271149	+	0.962537i	$0.587404\pi$
$432$	0.0782323	0.00376396
$433$	16.2161	0.779295	0.389647	−	0.920964i	$-0.372597\pi$
$433$	16.2161	0.779295	0.389647	+	0.920964i	$0.372597\pi$
$434$	−28.1866	−1.35300
$435$	0	0
$436$	−55.4919	−2.65758
$437$	−8.89823	−0.425660
$438$	−1.55356	−0.0742319
$439$	−23.9918	−1.14507	−0.572534	−	0.819881i	$-0.694040\pi$
$439$	−23.9918	−1.14507	−0.572534	+	0.819881i	$0.694040\pi$
$440$	0	0
$441$	13.0129	0.619663
$442$	54.5856	2.59637
$443$	−8.61153	−0.409146	−0.204573	−	0.978851i	$-0.565581\pi$
$443$	−8.61153	−0.409146	−0.204573	+	0.978851i	$0.565581\pi$
$444$	13.0094	0.617400
$445$	0	0
$446$	−22.6531	−1.07266
$447$	−1.69479	−0.0801606
$448$	57.7804	2.72986
$449$	36.5902	1.72680	0.863400	−	0.504520i	$-0.168330\pi$
$449$	36.5902	1.72680	0.863400	+	0.504520i	$0.168330\pi$
$450$	0	0
$451$	5.79300	0.272782
$452$	29.8156	1.40241
$453$	−3.73585	−0.175526
$454$	−35.8239	−1.68130
$455$	0	0
$456$	11.8247	0.553741
$457$	−21.8037	−1.01994	−0.509968	−	0.860193i	$-0.670343\pi$
$457$	−21.8037	−1.01994	−0.509968	+	0.860193i	$0.670343\pi$
$458$	−19.3162	−0.902586
$459$	−5.36761	−0.250539
$460$	0	0
$461$	25.8149	1.20232	0.601159	−	0.799129i	$-0.294706\pi$
$461$	25.8149	1.20232	0.601159	+	0.799129i	$0.294706\pi$
$462$	25.8384	1.20211
$463$	−4.37473	−0.203311	−0.101655	−	0.994820i	$-0.532414\pi$
$463$	−4.37473	−0.203311	−0.101655	+	0.994820i	$0.532414\pi$
$464$	0.0593744	0.00275639
$465$	0	0
$466$	−54.1571	−2.50878
$467$	−2.05522	−0.0951044	−0.0475522	−	0.998869i	$-0.515142\pi$
$467$	−2.05522	−0.0951044	−0.0475522	+	0.998869i	$0.515142\pi$
$468$	−14.4352	−0.667267
$469$	7.43452	0.343294
$470$	0	0
$471$	10.7108	0.493527
$472$	−18.5908	−0.855711
$473$	29.8048	1.37043
$474$	−26.5295	−1.21854
$475$	0	0
$476$	78.1243	3.58082
$477$	−4.40100	−0.201508
$478$	38.4356	1.75800
$479$	9.28770	0.424366	0.212183	−	0.977230i	$-0.431943\pi$
$479$	9.28770	0.424366	0.212183	+	0.977230i	$0.431943\pi$
$480$	0	0
$481$	−17.7411	−0.808926
$482$	−27.8477	−1.26843
$483$	9.67200	0.440091
$484$	−15.1288	−0.687674
$485$	0	0
$486$	2.29205	0.103970
$487$	−18.8405	−0.853744	−0.426872	−	0.904312i	$-0.640384\pi$
$487$	−18.8405	−0.853744	−0.426872	+	0.904312i	$0.640384\pi$
$488$	44.1376	1.99801
$489$	−20.4539	−0.924959
$490$	0	0
$491$	−39.0071	−1.76037	−0.880183	−	0.474634i	$-0.842580\pi$
$491$	−39.0071	−1.76037	−0.880183	+	0.474634i	$0.842580\pi$
$492$	−7.47942	−0.337198
$493$	−4.07375	−0.183472
$494$	−41.8543	−1.88311
$495$	0	0
$496$	0.215055	0.00965625
$497$	−41.5236	−1.86259
$498$	−32.3395	−1.44917
$499$	20.9038	0.935780	0.467890	−	0.883787i	$-0.345014\pi$
$499$	20.9038	0.935780	0.467890	+	0.883787i	$0.345014\pi$
$500$	0	0
$501$	19.2288	0.859079
$502$	−45.7367	−2.04133
$503$	−32.7888	−1.46198	−0.730991	−	0.682387i	$-0.760942\pi$
$503$	−32.7888	−1.46198	−0.730991	+	0.682387i	$0.760942\pi$
$504$	−12.8529	−0.572514
$505$	0	0
$506$	12.4874	0.555131
$507$	6.68546	0.296912
$508$	43.0092	1.90823
$509$	−27.6184	−1.22417	−0.612083	−	0.790794i	$-0.709668\pi$
$509$	−27.6184	−1.22417	−0.612083	+	0.790794i	$0.709668\pi$
$510$	0	0
$511$	3.03220	0.134137
$512$	−0.885040	−0.0391136
$513$	4.11569	0.181712
$514$	−28.3707	−1.25138
$515$	0	0
$516$	−38.4814	−1.69405
$517$	−2.51991	−0.110826
$518$	−41.0004	−1.80145
$519$	8.58785	0.376965
$520$	0	0
$521$	4.15734	0.182136	0.0910682	−	0.995845i	$-0.470972\pi$
$521$	4.15734	0.182136	0.0910682	+	0.995845i	$0.470972\pi$
$522$	1.73955	0.0761380
$523$	−28.2019	−1.23318	−0.616592	−	0.787283i	$-0.711487\pi$
$523$	−28.2019	−1.23318	−0.616592	+	0.787283i	$0.711487\pi$
$524$	−53.9275	−2.35583
$525$	0	0
$526$	46.9824	2.04853
$527$	−14.7552	−0.642746
$528$	−0.197139	−0.00857937
$529$	−18.3256	−0.796767
$530$	0	0
$531$	−6.47071	−0.280805
$532$	−59.9029	−2.59712
$533$	10.1998	0.441802
$534$	16.0875	0.696174
$535$	0	0
$536$	−4.77468	−0.206235
$537$	12.0431	0.519699
$538$	−25.1819	−1.08567
$539$	−32.7914	−1.41243
$540$	0	0
$541$	−38.8793	−1.67155	−0.835777	−	0.549069i	$-0.814982\pi$
$541$	−38.8793	−1.67155	−0.835777	+	0.549069i	$0.814982\pi$
$542$	−38.4715	−1.65249
$543$	−11.7352	−0.503605
$544$	29.8806	1.28112
$545$	0	0
$546$	45.4938	1.94695
$547$	−42.3359	−1.81015	−0.905076	−	0.425250i	$-0.860186\pi$
$547$	−42.3359	−1.81015	−0.905076	+	0.425250i	$0.860186\pi$
$548$	46.5718	1.98945
$549$	15.3625	0.655656
$550$	0	0
$551$	3.12360	0.133070
$552$	−6.21165	−0.264385
$553$	51.7798	2.20190
$554$	−45.4179	−1.92962
$555$	0	0
$556$	19.5799	0.830373
$557$	25.0119	1.05979	0.529895	−	0.848063i	$-0.322231\pi$
$557$	25.0119	1.05979	0.529895	+	0.848063i	$0.322231\pi$
$558$	6.30068	0.266729
$559$	52.4775	2.21956
$560$	0	0
$561$	13.5259	0.571065
$562$	−51.7173	−2.18156
$563$	−39.3426	−1.65809	−0.829046	−	0.559180i	$-0.811116\pi$
$563$	−39.3426	−1.65809	−0.829046	+	0.559180i	$0.811116\pi$
$564$	3.25349	0.136997
$565$	0	0
$566$	−19.0214	−0.799531
$567$	−4.47358	−0.187873
$568$	26.6677	1.11895
$569$	−24.5245	−1.02812	−0.514061	−	0.857754i	$-0.671859\pi$
$569$	−24.5245	−1.02812	−0.514061	+	0.857754i	$0.671859\pi$
$570$	0	0
$571$	33.7686	1.41317	0.706585	−	0.707628i	$-0.250235\pi$
$571$	33.7686	1.41317	0.706585	+	0.707628i	$0.250235\pi$
$572$	36.3755	1.52093
$573$	4.95346	0.206934
$574$	23.5720	0.983878
$575$	0	0
$576$	−12.9159	−0.538163
$577$	31.0149	1.29117	0.645584	−	0.763690i	$-0.276614\pi$
$577$	31.0149	1.29117	0.645584	+	0.763690i	$0.276614\pi$
$578$	27.0720	1.12605
$579$	20.9415	0.870300
$580$	0	0
$581$	63.1196	2.61864
$582$	12.0738	0.500477
$583$	11.0901	0.459307
$584$	−1.94737	−0.0805829
$585$	0	0
$586$	−2.11623	−0.0874206
$587$	17.2515	0.712046	0.356023	−	0.934477i	$-0.384132\pi$
$587$	17.2515	0.712046	0.356023	+	0.934477i	$0.384132\pi$
$588$	42.3374	1.74597
$589$	11.3137	0.466174
$590$	0	0
$591$	−20.8670	−0.858354
$592$	0.312820	0.0128568
$593$	−5.06182	−0.207864	−0.103932	−	0.994584i	$-0.533142\pi$
$593$	−5.06182	−0.207864	−0.103932	+	0.994584i	$0.533142\pi$
$594$	−5.77577	−0.236983
$595$	0	0
$596$	−5.51398	−0.225861
$597$	−13.3580	−0.546707
$598$	21.9866	0.899098
$599$	20.7547	0.848014	0.424007	−	0.905659i	$-0.360623\pi$
$599$	20.7547	0.848014	0.424007	+	0.905659i	$0.360623\pi$
$600$	0	0
$601$	−23.5587	−0.960980	−0.480490	−	0.877000i	$-0.659541\pi$
$601$	−23.5587	−0.960980	−0.480490	+	0.877000i	$0.659541\pi$
$602$	121.277	4.94290
$603$	−1.66187	−0.0676767
$604$	−12.1546	−0.494562
$605$	0	0
$606$	−13.2906	−0.539894
$607$	22.9475	0.931411	0.465705	−	0.884940i	$-0.345801\pi$
$607$	22.9475	0.931411	0.465705	+	0.884940i	$0.345801\pi$
$608$	−22.9113	−0.929177
$609$	−3.39522	−0.137581
$610$	0	0
$611$	−4.43683	−0.179495
$612$	−17.4635	−0.705920
$613$	−12.0113	−0.485130	−0.242565	−	0.970135i	$-0.577989\pi$
$613$	−12.0113	−0.485130	−0.242565	+	0.970135i	$0.577989\pi$
$614$	42.9685	1.73407
$615$	0	0
$616$	32.3882	1.30496
$617$	8.03611	0.323522	0.161761	−	0.986830i	$-0.448283\pi$
$617$	8.03611	0.323522	0.161761	+	0.986830i	$0.448283\pi$
$618$	1.18469	0.0476553
$619$	−48.6273	−1.95450	−0.977248	−	0.212101i	$-0.931970\pi$
$619$	−48.6273	−1.95450	−0.977248	+	0.212101i	$0.931970\pi$
$620$	0	0
$621$	−2.16203	−0.0867591
$622$	−6.84185	−0.274333
$623$	−31.3993	−1.25799
$624$	−0.347104	−0.0138953
$625$	0	0
$626$	−30.4364	−1.21648
$627$	−10.3712	−0.414185
$628$	34.8475	1.39056
$629$	−21.4630	−0.855784
$630$	0	0
$631$	24.2417	0.965048	0.482524	−	0.875883i	$-0.339720\pi$
$631$	24.2417	0.965048	0.482524	+	0.875883i	$0.339720\pi$
$632$	−33.2545	−1.32279
$633$	26.8648	1.06778
$634$	−58.7175	−2.33197
$635$	0	0
$636$	−14.3186	−0.567770
$637$	−57.7361	−2.28759
$638$	−4.38352	−0.173545
$639$	9.28196	0.367189
$640$	0	0
$641$	15.5211	0.613049	0.306524	−	0.951863i	$-0.400834\pi$
$641$	15.5211	0.613049	0.306524	+	0.951863i	$0.400834\pi$
$642$	21.2816	0.839916
$643$	−42.6644	−1.68252	−0.841260	−	0.540631i	$-0.818186\pi$
$643$	−42.6644	−1.68252	−0.841260	+	0.540631i	$0.818186\pi$
$644$	31.4678	1.24000
$645$	0	0
$646$	−50.6347	−1.99219
$647$	−37.3211	−1.46724	−0.733622	−	0.679558i	$-0.762171\pi$
$647$	−37.3211	−1.46724	−0.733622	+	0.679558i	$0.762171\pi$
$648$	2.87307	0.112865
$649$	16.3056	0.640052
$650$	0	0
$651$	−12.2975	−0.481979
$652$	−66.5468	−2.60617
$653$	20.6551	0.808295	0.404147	−	0.914694i	$-0.367568\pi$
$653$	20.6551	0.808295	0.404147	+	0.914694i	$0.367568\pi$
$654$	−39.0934	−1.52867
$655$	0	0
$656$	−0.179847	−0.00702186
$657$	−0.677803	−0.0264436
$658$	−10.2537	−0.399730
$659$	−16.7207	−0.651347	−0.325673	−	0.945482i	$-0.605591\pi$
$659$	−16.7207	−0.651347	−0.325673	+	0.945482i	$0.605591\pi$
$660$	0	0
$661$	8.50849	0.330942	0.165471	−	0.986215i	$-0.447086\pi$
$661$	8.50849	0.330942	0.165471	+	0.986215i	$0.447086\pi$
$662$	60.6974	2.35907
$663$	23.8152	0.924905
$664$	−40.5374	−1.57315
$665$	0	0
$666$	9.16500	0.355137
$667$	−1.64087	−0.0635347
$668$	62.5607	2.42055
$669$	−9.88334	−0.382112
$670$	0	0
$671$	−38.7122	−1.49447
$672$	24.9036	0.960679
$673$	27.8511	1.07358	0.536790	−	0.843716i	$-0.319637\pi$
$673$	27.8511	1.07358	0.536790	+	0.843716i	$0.319637\pi$
$674$	3.25160	0.125247
$675$	0	0
$676$	21.7511	0.836581
$677$	−46.3945	−1.78309	−0.891543	−	0.452936i	$-0.850377\pi$
$677$	−46.3945	−1.78309	−0.891543	+	0.452936i	$0.850377\pi$
$678$	21.0048	0.806683
$679$	−23.5655	−0.904361
$680$	0	0
$681$	−15.6296	−0.598929
$682$	−15.8772	−0.607968
$683$	−18.6375	−0.713144	−0.356572	−	0.934268i	$-0.616055\pi$
$683$	−18.6375	−0.713144	−0.356572	+	0.934268i	$0.616055\pi$
$684$	13.3904	0.511994
$685$	0	0
$686$	−61.6544	−2.35398
$687$	−8.42747	−0.321528
$688$	−0.925309	−0.0352771
$689$	19.5265	0.743900
$690$	0	0
$691$	8.21715	0.312595	0.156298	−	0.987710i	$-0.450044\pi$
$691$	8.21715	0.312595	0.156298	+	0.987710i	$0.450044\pi$
$692$	27.9405	1.06214
$693$	11.2730	0.428227
$694$	74.6704	2.83445
$695$	0	0
$696$	2.18051	0.0826522
$697$	12.3395	0.467394
$698$	24.8829	0.941831
$699$	−23.6282	−0.893701
$700$	0	0
$701$	21.1453	0.798649	0.399324	−	0.916810i	$-0.369245\pi$
$701$	21.1453	0.798649	0.399324	+	0.916810i	$0.369245\pi$
$702$	−10.1694	−0.383821
$703$	16.4570	0.620688
$704$	32.5470	1.22666
$705$	0	0
$706$	−10.4166	−0.392033
$707$	25.9403	0.975587
$708$	−21.0524	−0.791198
$709$	−0.759089	−0.0285082	−0.0142541	−	0.999898i	$-0.504537\pi$
$709$	−0.759089	−0.0285082	−0.0142541	+	0.999898i	$0.504537\pi$
$710$	0	0
$711$	−11.5746	−0.434080
$712$	20.1656	0.755737
$713$	−5.94325	−0.222577
$714$	55.0377	2.05974
$715$	0	0
$716$	39.1822	1.46431
$717$	16.7691	0.626253
$718$	−55.0558	−2.05466
$719$	33.9886	1.26756	0.633781	−	0.773513i	$-0.281502\pi$
$719$	33.9886	1.26756	0.633781	+	0.773513i	$0.281502\pi$
$720$	0	0
$721$	−2.31226	−0.0861130
$722$	−4.72412	−0.175814
$723$	−12.1497	−0.451852
$724$	−38.1803	−1.41896
$725$	0	0
$726$	−10.6581	−0.395559
$727$	44.7501	1.65969	0.829845	−	0.557993i	$-0.188429\pi$
$727$	44.7501	1.65969	0.829845	+	0.557993i	$0.188429\pi$
$728$	57.0262	2.11353
$729$	1.00000	0.0370370
$730$	0	0
$731$	63.4866	2.34814
$732$	49.9819	1.84738
$733$	27.5828	1.01879	0.509397	−	0.860531i	$-0.329868\pi$
$733$	27.5828	1.01879	0.509397	+	0.860531i	$0.329868\pi$
$734$	−3.27229	−0.120782
$735$	0	0
$736$	12.0356	0.443639
$737$	4.18778	0.154259
$738$	−5.26917	−0.193961
$739$	−22.7905	−0.838361	−0.419181	−	0.907903i	$-0.637683\pi$
$739$	−22.7905	−0.838361	−0.419181	+	0.907903i	$0.637683\pi$
$740$	0	0
$741$	−18.2606	−0.670821
$742$	45.1264	1.65664
$743$	−15.3218	−0.562103	−0.281051	−	0.959693i	$-0.590683\pi$
$743$	−15.3218	−0.562103	−0.281051	+	0.959693i	$0.590683\pi$
$744$	7.89786	0.289549
$745$	0	0
$746$	26.9029	0.984984
$747$	−14.1094	−0.516237
$748$	44.0065	1.60904
$749$	−41.5369	−1.51773
$750$	0	0
$751$	−44.4665	−1.62261	−0.811303	−	0.584626i	$-0.801241\pi$
$751$	−44.4665	−1.62261	−0.811303	+	0.584626i	$0.801241\pi$
$752$	0.0782323	0.00285284
$753$	−19.9545	−0.727182
$754$	−7.71809	−0.281076
$755$	0	0
$756$	−14.5548	−0.529352
$757$	23.4659	0.852882	0.426441	−	0.904515i	$-0.359767\pi$
$757$	23.4659	0.852882	0.426441	+	0.904515i	$0.359767\pi$
$758$	45.0184	1.63514
$759$	5.44812	0.197754
$760$	0	0
$761$	−24.5851	−0.891210	−0.445605	−	0.895230i	$-0.647011\pi$
$761$	−24.5851	−0.891210	−0.445605	+	0.895230i	$0.647011\pi$
$762$	30.2995	1.09764
$763$	76.3017	2.76231
$764$	16.1161	0.583059
$765$	0	0
$766$	−49.4113	−1.78530
$767$	28.7094	1.03664
$768$	−16.5029	−0.595498
$769$	26.5119	0.956043	0.478021	−	0.878348i	$-0.341354\pi$
$769$	26.5119	0.956043	0.478021	+	0.878348i	$0.341354\pi$
$770$	0	0
$771$	−12.3779	−0.445778
$772$	68.1331	2.45217
$773$	−4.64391	−0.167030	−0.0835149	−	0.996507i	$-0.526615\pi$
$773$	−4.64391	−0.167030	−0.0835149	+	0.996507i	$0.526615\pi$
$774$	−27.1097	−0.974438
$775$	0	0
$776$	15.1345	0.543296
$777$	−17.8881	−0.641731
$778$	74.5711	2.67350
$779$	−9.46152	−0.338994
$780$	0	0
$781$	−23.3897	−0.836951
$782$	26.5991	0.951180
$783$	0.758949	0.0271226
$784$	1.01803	0.0363582
$785$	0	0
$786$	−37.9913	−1.35511
$787$	24.5868	0.876425	0.438212	−	0.898871i	$-0.355612\pi$
$787$	24.5868	0.876425	0.438212	+	0.898871i	$0.355612\pi$
$788$	−67.8907	−2.41851
$789$	20.4980	0.729748
$790$	0	0
$791$	−40.9967	−1.45767
$792$	−7.23989	−0.257258
$793$	−68.1609	−2.42046
$794$	62.8623	2.23090
$795$	0	0
$796$	−43.4602	−1.54040
$797$	10.1081	0.358049	0.179024	−	0.983845i	$-0.442706\pi$
$797$	10.1081	0.358049	0.179024	+	0.983845i	$0.442706\pi$
$798$	−42.2009	−1.49390
$799$	−5.36761	−0.189893
$800$	0	0
$801$	7.01883	0.247998
$802$	−18.1853	−0.642146
$803$	1.70801	0.0602742
$804$	−5.40689	−0.190686
$805$	0	0
$806$	−27.9550	−0.984674
$807$	−10.9866	−0.386747
$808$	−16.6597	−0.586085
$809$	1.89899	0.0667650	0.0333825	−	0.999443i	$-0.489372\pi$
$809$	1.89899	0.0667650	0.0333825	+	0.999443i	$0.489372\pi$
$810$	0	0
$811$	18.7302	0.657706	0.328853	−	0.944381i	$-0.393338\pi$
$811$	18.7302	0.657706	0.328853	+	0.944381i	$0.393338\pi$
$812$	−11.0463	−0.387650
$813$	−16.7847	−0.588667
$814$	−23.0950	−0.809480
$815$	0	0
$816$	−0.419921	−0.0147002
$817$	−48.6792	−1.70307
$818$	45.4023	1.58745
$819$	19.8485	0.693563
$820$	0	0
$821$	54.9789	1.91878	0.959388	−	0.282088i	$-0.0910272\pi$
$821$	54.9789	1.91878	0.959388	+	0.282088i	$0.0910272\pi$
$822$	32.8093	1.14436
$823$	26.2390	0.914635	0.457317	−	0.889304i	$-0.348810\pi$
$823$	26.2390	0.914635	0.457317	+	0.889304i	$0.348810\pi$
$824$	1.48500	0.0517325
$825$	0	0
$826$	66.3485	2.30856
$827$	−14.6165	−0.508265	−0.254132	−	0.967169i	$-0.581790\pi$
$827$	−14.6165	−0.508265	−0.254132	+	0.967169i	$0.581790\pi$
$828$	−7.03414	−0.244453
$829$	24.4569	0.849422	0.424711	−	0.905329i	$-0.360376\pi$
$829$	24.4569	0.849422	0.424711	+	0.905329i	$0.360376\pi$
$830$	0	0
$831$	−19.8154	−0.687389
$832$	57.3057	1.98672
$833$	−69.8483	−2.42010
$834$	13.7938	0.477641
$835$	0	0
$836$	−33.7426	−1.16701
$837$	2.74893	0.0950168
$838$	−67.3357	−2.32607
$839$	−4.17121	−0.144006	−0.0720030	−	0.997404i	$-0.522939\pi$
$839$	−4.17121	−0.144006	−0.0720030	+	0.997404i	$0.522939\pi$
$840$	0	0
$841$	−28.4240	−0.980138
$842$	17.5480	0.604745
$843$	−22.5638	−0.777137
$844$	87.4043	3.00858
$845$	0	0
$846$	2.29205	0.0788023
$847$	20.8023	0.714775
$848$	−0.344301	−0.0118233
$849$	−8.29887	−0.284817
$850$	0	0
$851$	−8.64509	−0.296350
$852$	30.1988	1.03459
$853$	−2.26212	−0.0774537	−0.0387268	−	0.999250i	$-0.512330\pi$
$853$	−2.26212	−0.0774537	−0.0387268	+	0.999250i	$0.512330\pi$
$854$	−157.522	−5.39030
$855$	0	0
$856$	26.6763	0.911777
$857$	23.6090	0.806467	0.403234	−	0.915097i	$-0.367886\pi$
$857$	23.6090	0.806467	0.403234	+	0.915097i	$0.367886\pi$
$858$	25.6261	0.874861
$859$	−40.3434	−1.37650	−0.688250	−	0.725474i	$-0.741621\pi$
$859$	−40.3434	−1.37650	−0.688250	+	0.725474i	$0.741621\pi$
$860$	0	0
$861$	10.2843	0.350487
$862$	−25.8049	−0.878917
$863$	30.7957	1.04830	0.524149	−	0.851627i	$-0.324384\pi$
$863$	30.7957	1.04830	0.524149	+	0.851627i	$0.324384\pi$
$864$	−5.56683	−0.189387
$865$	0	0
$866$	37.1681	1.26302
$867$	11.8113	0.401132
$868$	−40.0100	−1.35803
$869$	29.1669	0.989421
$870$	0	0
$871$	7.37345	0.249840
$872$	−49.0033	−1.65946
$873$	5.26770	0.178285
$874$	−20.3952	−0.689878
$875$	0	0
$876$	−2.20523	−0.0745077
$877$	50.2363	1.69636	0.848179	−	0.529710i	$-0.177699\pi$
$877$	50.2363	1.69636	0.848179	+	0.529710i	$0.177699\pi$
$878$	−54.9905	−1.85584
$879$	−0.923291	−0.0311418
$880$	0	0
$881$	11.1589	0.375952	0.187976	−	0.982174i	$-0.439807\pi$
$881$	11.1589	0.375952	0.187976	+	0.982174i	$0.439807\pi$
$882$	29.8263	1.00430
$883$	10.2779	0.345880	0.172940	−	0.984932i	$-0.444673\pi$
$883$	10.2779	0.345880	0.172940	+	0.984932i	$0.444673\pi$
$884$	77.4826	2.60602
$885$	0	0
$886$	−19.7381	−0.663113
$887$	18.1293	0.608721	0.304361	−	0.952557i	$-0.401557\pi$
$887$	18.1293	0.608721	0.304361	+	0.952557i	$0.401557\pi$
$888$	11.4883	0.385521
$889$	−59.1380	−1.98343
$890$	0	0
$891$	−2.51991	−0.0844203
$892$	−32.1554	−1.07664
$893$	4.11569	0.137726
$894$	−3.88453	−0.129918
$895$	0	0
$896$	82.6282	2.76041
$897$	9.59254	0.320286
$898$	83.8667	2.79867
$899$	2.08630	0.0695819
$900$	0	0
$901$	23.6229	0.786992
$902$	13.2779	0.442104
$903$	52.9122	1.76081
$904$	26.3293	0.875700
$905$	0	0
$906$	−8.56276	−0.284479
$907$	−48.6936	−1.61685	−0.808423	−	0.588602i	$-0.799678\pi$
$907$	−48.6936	−1.61685	−0.808423	+	0.588602i	$0.799678\pi$
$908$	−50.8509	−1.68755
$909$	−5.79856	−0.192326
$910$	0	0
$911$	39.4262	1.30625	0.653124	−	0.757251i	$-0.273458\pi$
$911$	39.4262	1.30625	0.653124	+	0.757251i	$0.273458\pi$
$912$	0.321980	0.0106618
$913$	35.5545	1.17668
$914$	−49.9753	−1.65303
$915$	0	0
$916$	−27.4187	−0.905940
$917$	74.1507	2.44867
$918$	−12.3028	−0.406054
$919$	1.51929	0.0501166	0.0250583	−	0.999686i	$-0.492023\pi$
$919$	1.51929	0.0501166	0.0250583	+	0.999686i	$0.492023\pi$
$920$	0	0
$921$	18.7467	0.617726
$922$	59.1690	1.94863
$923$	−41.1825	−1.35554
$924$	36.6768	1.20658
$925$	0	0
$926$	−10.0271	−0.329511
$927$	0.516870	0.0169762
$928$	−4.22494	−0.138690
$929$	−59.1261	−1.93987	−0.969933	−	0.243373i	$-0.921746\pi$
$929$	−59.1261	−1.93987	−0.969933	+	0.243373i	$0.921746\pi$
$930$	0	0
$931$	53.5571	1.75526
$932$	−76.8743	−2.51810
$933$	−2.98503	−0.0977256
$934$	−4.71068	−0.154138
$935$	0	0
$936$	−12.7473	−0.416659
$937$	29.6529	0.968719	0.484359	−	0.874869i	$-0.339053\pi$
$937$	29.6529	0.968719	0.484359	+	0.874869i	$0.339053\pi$
$938$	17.0403	0.556385
$939$	−13.2791	−0.433348
$940$	0	0
$941$	−27.4224	−0.893945	−0.446972	−	0.894548i	$-0.647498\pi$
$941$	−27.4224	−0.893945	−0.446972	+	0.894548i	$0.647498\pi$
$942$	24.5496	0.799871
$943$	4.97026	0.161854
$944$	−0.506219	−0.0164760
$945$	0	0
$946$	68.3141	2.22108
$947$	−28.2224	−0.917105	−0.458552	−	0.888667i	$-0.651632\pi$
$947$	−28.2224	−0.917105	−0.458552	+	0.888667i	$0.651632\pi$
$948$	−37.6578	−1.22307
$949$	3.00730	0.0976210
$950$	0	0
$951$	−25.6179	−0.830718
$952$	68.9894	2.23596
$953$	10.2799	0.332997	0.166499	−	0.986042i	$-0.446754\pi$
$953$	10.2799	0.332997	0.166499	+	0.986042i	$0.446754\pi$
$954$	−10.0873	−0.326589
$955$	0	0
$956$	54.5581	1.76454
$957$	−1.91249	−0.0618219
$958$	21.2879	0.687780
$959$	−64.0366	−2.06785
$960$	0	0
$961$	−23.4434	−0.756239
$962$	−40.6636	−1.31105
$963$	9.28494	0.299203
$964$	−39.5290	−1.27314
$965$	0	0
$966$	22.1687	0.713266
$967$	0.779593	0.0250700	0.0125350	−	0.999921i	$-0.496010\pi$
$967$	0.779593	0.0250700	0.0125350	+	0.999921i	$0.496010\pi$
$968$	−13.3599	−0.429402
$969$	−22.0914	−0.709679
$970$	0	0
$971$	−29.1688	−0.936073	−0.468036	−	0.883709i	$-0.655038\pi$
$971$	−29.1688	−0.936073	−0.468036	+	0.883709i	$0.655038\pi$
$972$	3.25349	0.104356
$973$	−26.9225	−0.863096
$974$	−43.1833	−1.38368
$975$	0	0
$976$	1.20185	0.0384702
$977$	−5.94053	−0.190054	−0.0950272	−	0.995475i	$-0.530294\pi$
$977$	−5.94053	−0.190054	−0.0950272	+	0.995475i	$0.530294\pi$
$978$	−46.8815	−1.49910
$979$	−17.6868	−0.565274
$980$	0	0
$981$	−17.0561	−0.544559
$982$	−89.4063	−2.85307
$983$	−25.1295	−0.801505	−0.400753	−	0.916186i	$-0.631251\pi$
$983$	−25.1295	−0.801505	−0.400753	+	0.916186i	$0.631251\pi$
$984$	−6.60487	−0.210555
$985$	0	0
$986$	−9.33723	−0.297358
$987$	−4.47358	−0.142396
$988$	−59.4108	−1.89011
$989$	25.5718	0.813137
$990$	0	0
$991$	40.6058	1.28989	0.644943	−	0.764231i	$-0.276881\pi$
$991$	40.6058	1.28989	0.644943	+	0.764231i	$0.276881\pi$
$992$	−15.3028	−0.485864
$993$	26.4817	0.840371
$994$	−95.1741	−3.01874
$995$	0	0
$996$	−45.9049	−1.45455
$997$	14.7609	0.467481	0.233741	−	0.972299i	$-0.424903\pi$
$997$	14.7609	0.467481	0.233741	+	0.972299i	$0.424903\pi$
$998$	47.9124	1.51664
$999$	3.99860	0.126510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.y.1.7	✓	7
5.4	even	2		3525.2.a.bb.1.1	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.y.1.7	✓	7	1.1	even	1	trivial
3525.2.a.bb.1.1	yes	7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+2.29205 q^{2} +1.00000 q^{3} +3.25349 q^{4} +2.29205 q^{6} -4.47358 q^{7} +2.87307 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.29205 q^{2} +1.00000 q^{3} +3.25349 q^{4} +2.29205 q^{6} -4.47358 q^{7} +2.87307 q^{8} +1.00000 q^{9} -2.51991 q^{11} +3.25349 q^{12} -4.43683 q^{13} -10.2537 q^{14} +0.0782323 q^{16} -5.36761 q^{17} +2.29205 q^{18} +4.11569 q^{19} -4.47358 q^{21} -5.77577 q^{22} -2.16203 q^{23} +2.87307 q^{24} -10.1694 q^{26} +1.00000 q^{27} -14.5548 q^{28} +0.758949 q^{29} +2.74893 q^{31} -5.56683 q^{32} -2.51991 q^{33} -12.3028 q^{34} +3.25349 q^{36} +3.99860 q^{37} +9.43337 q^{38} -4.43683 q^{39} -2.29889 q^{41} -10.2537 q^{42} -11.8277 q^{43} -8.19853 q^{44} -4.95547 q^{46} +1.00000 q^{47} +0.0782323 q^{48} +13.0129 q^{49} -5.36761 q^{51} -14.4352 q^{52} -4.40100 q^{53} +2.29205 q^{54} -12.8529 q^{56} +4.11569 q^{57} +1.73955 q^{58} -6.47071 q^{59} +15.3625 q^{61} +6.30068 q^{62} -4.47358 q^{63} -12.9159 q^{64} -5.77577 q^{66} -1.66187 q^{67} -17.4635 q^{68} -2.16203 q^{69} +9.28196 q^{71} +2.87307 q^{72} -0.677803 q^{73} +9.16500 q^{74} +13.3904 q^{76} +11.2730 q^{77} -10.1694 q^{78} -11.5746 q^{79} +1.00000 q^{81} -5.26917 q^{82} -14.1094 q^{83} -14.5548 q^{84} -27.1097 q^{86} +0.758949 q^{87} -7.23989 q^{88} +7.01883 q^{89} +19.8485 q^{91} -7.03414 q^{92} +2.74893 q^{93} +2.29205 q^{94} -5.56683 q^{96} +5.26770 q^{97} +29.8263 q^{98} -2.51991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * q^99

Introduction

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Database

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