LMFDB - Embedded newform 8025.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, 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("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 49 x^{9} + 71 x^{8} - 278 x^{7} - 92 x^{6} + 649 x^{5} - 127 x^{4} + \cdots - 6 $ x^12 - 3x^11 - 15x^10 + 49x^9 + 71x^8 - 278x^7 - 92x^6 + 649x^5 - 127x^4 - 529x^3 + 267x^2 + 15*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1605)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.51437$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51437 q^{2} -1.00000 q^{3} +4.32208 q^{4} +2.51437 q^{6} +0.976551 q^{7} -5.83856 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.51437 q^{2} -1.00000 q^{3} +4.32208 q^{4} +2.51437 q^{6} +0.976551 q^{7} -5.83856 q^{8} +1.00000 q^{9} +2.69409 q^{11} -4.32208 q^{12} -1.45776 q^{13} -2.45541 q^{14} +6.03618 q^{16} +6.02598 q^{17} -2.51437 q^{18} +4.87630 q^{19} -0.976551 q^{21} -6.77395 q^{22} +8.78876 q^{23} +5.83856 q^{24} +3.66536 q^{26} -1.00000 q^{27} +4.22073 q^{28} -3.21825 q^{29} -1.15455 q^{31} -3.50009 q^{32} -2.69409 q^{33} -15.1516 q^{34} +4.32208 q^{36} -11.1479 q^{37} -12.2608 q^{38} +1.45776 q^{39} -12.0741 q^{41} +2.45541 q^{42} +4.77165 q^{43} +11.6441 q^{44} -22.0982 q^{46} -8.83908 q^{47} -6.03618 q^{48} -6.04635 q^{49} -6.02598 q^{51} -6.30056 q^{52} -8.53554 q^{53} +2.51437 q^{54} -5.70166 q^{56} -4.87630 q^{57} +8.09188 q^{58} +3.95479 q^{59} -0.00540166 q^{61} +2.90298 q^{62} +0.976551 q^{63} -3.27183 q^{64} +6.77395 q^{66} +9.10553 q^{67} +26.0448 q^{68} -8.78876 q^{69} +11.2733 q^{71} -5.83856 q^{72} -13.7654 q^{73} +28.0299 q^{74} +21.0757 q^{76} +2.63092 q^{77} -3.66536 q^{78} -14.9228 q^{79} +1.00000 q^{81} +30.3587 q^{82} +3.80805 q^{83} -4.22073 q^{84} -11.9977 q^{86} +3.21825 q^{87} -15.7296 q^{88} -6.21990 q^{89} -1.42358 q^{91} +37.9857 q^{92} +1.15455 q^{93} +22.2248 q^{94} +3.50009 q^{96} -12.5906 q^{97} +15.2028 q^{98} +2.69409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9	$ 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9} + 4 q^{11} - 15 q^{12} - 13 q^{13} + 4 q^{14} + 13 q^{16} + 4 q^{17} - 3 q^{18} + 14 q^{19} + 7 q^{21} - 15 q^{22} - 11 q^{23} + 3 q^{24} - 8 q^{26} - 12 q^{27} - 16 q^{28} - 7 q^{29} + 4 q^{31} - 4 q^{32} - 4 q^{33} + q^{34} + 15 q^{36} - 24 q^{37} + 11 q^{38} + 13 q^{39} + 13 q^{41} - 4 q^{42} - 25 q^{43} + 10 q^{44} - 22 q^{46} - 19 q^{47} - 13 q^{48} + 9 q^{49} - 4 q^{51} - 20 q^{52} - 11 q^{53} + 3 q^{54} - 37 q^{56} - 14 q^{57} + 2 q^{58} + 8 q^{59} + 7 q^{61} + 11 q^{62} - 7 q^{63} - 19 q^{64} + 15 q^{66} - 33 q^{67} + 24 q^{68} + 11 q^{69} - 3 q^{72} - 34 q^{73} - 27 q^{74} - 9 q^{76} + 29 q^{77} + 8 q^{78} + 12 q^{81} - q^{82} + 24 q^{83} + 16 q^{84} - 36 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} + 30 q^{91} + 28 q^{92} - 4 q^{93} - 8 q^{94} + 4 q^{96} - 16 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9 + 4 * q^11 - 15 * q^12 - 13 * q^13 + 4 * q^14 + 13 * q^16 + 4 * q^17 - 3 * q^18 + 14 * q^19 + 7 * q^21 - 15 * q^22 - 11 * q^23 + 3 * q^24 - 8 * q^26 - 12 * q^27 - 16 * q^28 - 7 * q^29 + 4 * q^31 - 4 * q^32 - 4 * q^33 + q^34 + 15 * q^36 - 24 * q^37 + 11 * q^38 + 13 * q^39 + 13 * q^41 - 4 * q^42 - 25 * q^43 + 10 * q^44 - 22 * q^46 - 19 * q^47 - 13 * q^48 + 9 * q^49 - 4 * q^51 - 20 * q^52 - 11 * q^53 + 3 * q^54 - 37 * q^56 - 14 * q^57 + 2 * q^58 + 8 * q^59 + 7 * q^61 + 11 * q^62 - 7 * q^63 - 19 * q^64 + 15 * q^66 - 33 * q^67 + 24 * q^68 + 11 * q^69 - 3 * q^72 - 34 * q^73 - 27 * q^74 - 9 * q^76 + 29 * q^77 + 8 * q^78 + 12 * q^81 - q^82 + 24 * q^83 + 16 * q^84 - 36 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 + 30 * q^91 + 28 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^96 - 16 * q^97 + 36 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.51437	−1.77793	−0.888965	−	0.457974i	$-0.848575\pi$
$2$	−2.51437	−1.77793	−0.888965	+	0.457974i	$0.848575\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.32208	2.16104
$5$	0	0
$5$	0	0
$6$	2.51437	1.02649
$7$	0.976551	0.369102	0.184551	−	0.982823i	$-0.440917\pi$
$7$	0.976551	0.369102	0.184551	+	0.982823i	$0.440917\pi$
$8$	−5.83856	−2.06424
$9$	1.00000	0.333333
$10$	0	0
$11$	2.69409	0.812299	0.406149	−	0.913807i	$-0.366871\pi$
$11$	2.69409	0.812299	0.406149	+	0.913807i	$0.366871\pi$
$12$	−4.32208	−1.24768
$13$	−1.45776	−0.404311	−0.202155	−	0.979353i	$-0.564795\pi$
$13$	−1.45776	−0.404311	−0.202155	+	0.979353i	$0.564795\pi$
$14$	−2.45541	−0.656237
$15$	0	0
$16$	6.03618	1.50905
$17$	6.02598	1.46152	0.730758	−	0.682637i	$-0.239167\pi$
$17$	6.02598	1.46152	0.730758	+	0.682637i	$0.239167\pi$
$18$	−2.51437	−0.592644
$19$	4.87630	1.11870	0.559349	−	0.828932i	$-0.311051\pi$
$19$	4.87630	1.11870	0.559349	+	0.828932i	$0.311051\pi$
$20$	0	0
$21$	−0.976551	−0.213101
$22$	−6.77395	−1.44421
$23$	8.78876	1.83258	0.916291	−	0.400513i	$-0.131168\pi$
$23$	8.78876	1.83258	0.916291	+	0.400513i	$0.131168\pi$
$24$	5.83856	1.19179
$25$	0	0
$26$	3.66536	0.718836
$27$	−1.00000	−0.192450
$28$	4.22073	0.797642
$29$	−3.21825	−0.597614	−0.298807	−	0.954314i	$-0.596589\pi$
$29$	−3.21825	−0.597614	−0.298807	+	0.954314i	$0.596589\pi$
$30$	0	0
$31$	−1.15455	−0.207364	−0.103682	−	0.994610i	$-0.533062\pi$
$31$	−1.15455	−0.207364	−0.103682	+	0.994610i	$0.533062\pi$
$32$	−3.50009	−0.618735
$33$	−2.69409	−0.468981
$34$	−15.1516	−2.59847
$35$	0	0
$36$	4.32208	0.720346
$37$	−11.1479	−1.83270	−0.916348	−	0.400383i	$-0.868877\pi$
$37$	−11.1479	−1.83270	−0.916348	+	0.400383i	$0.868877\pi$
$38$	−12.2608	−1.98897
$39$	1.45776	0.233429
$40$	0	0
$41$	−12.0741	−1.88565	−0.942827	−	0.333282i	$-0.891844\pi$
$41$	−12.0741	−1.88565	−0.942827	+	0.333282i	$0.891844\pi$
$42$	2.45541	0.378879
$43$	4.77165	0.727670	0.363835	−	0.931463i	$-0.381467\pi$
$43$	4.77165	0.727670	0.363835	+	0.931463i	$0.381467\pi$
$44$	11.6441	1.75541
$45$	0	0
$46$	−22.0982	−3.25820
$47$	−8.83908	−1.28931	−0.644656	−	0.764473i	$-0.722999\pi$
$47$	−8.83908	−1.28931	−0.644656	+	0.764473i	$0.722999\pi$
$48$	−6.03618	−0.871248
$49$	−6.04635	−0.863764
$50$	0	0
$51$	−6.02598	−0.843806
$52$	−6.30056	−0.873730
$53$	−8.53554	−1.17245	−0.586224	−	0.810149i	$-0.699386\pi$
$53$	−8.53554	−1.17245	−0.586224	+	0.810149i	$0.699386\pi$
$54$	2.51437	0.342163
$55$	0	0
$56$	−5.70166	−0.761916
$57$	−4.87630	−0.645881
$58$	8.09188	1.06252
$59$	3.95479	0.514870	0.257435	−	0.966296i	$-0.417123\pi$
$59$	3.95479	0.514870	0.257435	+	0.966296i	$0.417123\pi$
$60$	0	0
$61$	−0.00540166	−0.000691612 0	−0.000345806	−	1.00000i	$-0.500110\pi$
$61$	−0.00540166	−0.000691612 0	−0.000345806		1.00000i	$0.500110\pi$
$62$	2.90298	0.368679
$63$	0.976551	0.123034
$64$	−3.27183	−0.408979
$65$	0	0
$66$	6.77395	0.833816
$67$	9.10553	1.11242	0.556208	−	0.831043i	$-0.312256\pi$
$67$	9.10553	1.11242	0.556208	+	0.831043i	$0.312256\pi$
$68$	26.0448	3.15839
$69$	−8.78876	−1.05804
$70$	0	0
$71$	11.2733	1.33789	0.668947	−	0.743310i	$-0.266745\pi$
$71$	11.2733	1.33789	0.668947	+	0.743310i	$0.266745\pi$
$72$	−5.83856	−0.688081
$73$	−13.7654	−1.61112	−0.805559	−	0.592516i	$-0.798135\pi$
$73$	−13.7654	−1.61112	−0.805559	+	0.592516i	$0.798135\pi$
$74$	28.0299	3.25841
$75$	0	0
$76$	21.0757	2.41755
$77$	2.63092	0.299821
$78$	−3.66536	−0.415020
$79$	−14.9228	−1.67895	−0.839474	−	0.543399i	$-0.817137\pi$
$79$	−14.9228	−1.67895	−0.839474	+	0.543399i	$0.817137\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	30.3587	3.35256
$83$	3.80805	0.417988	0.208994	−	0.977917i	$-0.432981\pi$
$83$	3.80805	0.417988	0.208994	+	0.977917i	$0.432981\pi$
$84$	−4.22073	−0.460519
$85$	0	0
$86$	−11.9977	−1.29375
$87$	3.21825	0.345033
$88$	−15.7296	−1.67678
$89$	−6.21990	−0.659308	−0.329654	−	0.944102i	$-0.606932\pi$
$89$	−6.21990	−0.659308	−0.329654	+	0.944102i	$0.606932\pi$
$90$	0	0
$91$	−1.42358	−0.149232
$92$	37.9857	3.96028
$93$	1.15455	0.119722
$94$	22.2248	2.29231
$95$	0	0
$96$	3.50009	0.357227
$97$	−12.5906	−1.27838	−0.639188	−	0.769050i	$-0.720730\pi$
$97$	−12.5906	−1.27838	−0.639188	+	0.769050i	$0.720730\pi$
$98$	15.2028	1.53571
$99$	2.69409	0.270766
$100$	0	0
$101$	1.21143	0.120542	0.0602709	−	0.998182i	$-0.480804\pi$
$101$	1.21143	0.120542	0.0602709	+	0.998182i	$0.480804\pi$
$102$	15.1516	1.50023
$103$	0.0306327	0.00301833	0.00150917	−	0.999999i	$-0.499520\pi$
$103$	0.0306327	0.00301833	0.00150917	+	0.999999i	$0.499520\pi$
$104$	8.51124	0.834596
$105$	0	0
$106$	21.4615	2.08453
$107$	−1.00000	−0.0966736
$107$	−1.00000	−0.0966736
$108$	−4.32208	−0.415892
$109$	−16.8921	−1.61797	−0.808987	−	0.587827i	$-0.799984\pi$
$109$	−16.8921	−1.61797	−0.808987	+	0.587827i	$0.799984\pi$
$110$	0	0
$111$	11.1479	1.05811
$112$	5.89464	0.556991
$113$	−15.4323	−1.45175	−0.725876	−	0.687826i	$-0.758565\pi$
$113$	−15.4323	−1.45175	−0.725876	+	0.687826i	$0.758565\pi$
$114$	12.2608	1.14833
$115$	0	0
$116$	−13.9095	−1.29147
$117$	−1.45776	−0.134770
$118$	−9.94382	−0.915402
$119$	5.88468	0.539448
$120$	0	0
$121$	−3.74187	−0.340170
$122$	0.0135818	0.00122964
$123$	12.0741	1.08868
$124$	−4.99007	−0.448122
$125$	0	0
$126$	−2.45541	−0.218746
$127$	−8.08010	−0.716993	−0.358497	−	0.933531i	$-0.616711\pi$
$127$	−8.08010	−0.716993	−0.358497	+	0.933531i	$0.616711\pi$
$128$	15.2268	1.34587
$129$	−4.77165	−0.420121
$130$	0	0
$131$	−15.9140	−1.39041	−0.695205	−	0.718811i	$-0.744687\pi$
$131$	−15.9140	−1.39041	−0.695205	+	0.718811i	$0.744687\pi$
$132$	−11.6441	−1.01349
$133$	4.76195	0.412914
$134$	−22.8947	−1.97780
$135$	0	0
$136$	−35.1831	−3.01693
$137$	17.4470	1.49060	0.745299	−	0.666730i	$-0.232307\pi$
$137$	17.4470	1.49060	0.745299	+	0.666730i	$0.232307\pi$
$138$	22.0982	1.88113
$139$	−3.92616	−0.333012	−0.166506	−	0.986040i	$-0.553249\pi$
$139$	−3.92616	−0.333012	−0.166506	+	0.986040i	$0.553249\pi$
$140$	0	0
$141$	8.83908	0.744385
$142$	−28.3453	−2.37868
$143$	−3.92735	−0.328421
$144$	6.03618	0.503015
$145$	0	0
$146$	34.6113	2.86446
$147$	6.04635	0.498694
$148$	−48.1819	−3.96052
$149$	−18.3721	−1.50511	−0.752553	−	0.658532i	$-0.771178\pi$
$149$	−18.3721	−1.50511	−0.752553	+	0.658532i	$0.771178\pi$
$150$	0	0
$151$	−11.4866	−0.934766	−0.467383	−	0.884055i	$-0.654803\pi$
$151$	−11.4866	−0.934766	−0.467383	+	0.884055i	$0.654803\pi$
$152$	−28.4706	−2.30927
$153$	6.02598	0.487172
$154$	−6.61511	−0.533061
$155$	0	0
$156$	6.30056	0.504448
$157$	−4.01035	−0.320061	−0.160030	−	0.987112i	$-0.551159\pi$
$157$	−4.01035	−0.320061	−0.160030	+	0.987112i	$0.551159\pi$
$158$	37.5216	2.98505
$159$	8.53554	0.676913
$160$	0	0
$161$	8.58267	0.676409
$162$	−2.51437	−0.197548
$163$	−23.8007	−1.86421	−0.932107	−	0.362183i	$-0.882031\pi$
$163$	−23.8007	−1.86421	−0.932107	+	0.362183i	$0.882031\pi$
$164$	−52.1851	−4.07497
$165$	0	0
$166$	−9.57487	−0.743154
$167$	16.1634	1.25076	0.625381	−	0.780320i	$-0.284944\pi$
$167$	16.1634	1.25076	0.625381	+	0.780320i	$0.284944\pi$
$168$	5.70166	0.439892
$169$	−10.8749	−0.836533
$170$	0	0
$171$	4.87630	0.372900
$172$	20.6234	1.57252
$173$	−4.38020	−0.333020	−0.166510	−	0.986040i	$-0.553250\pi$
$173$	−4.38020	−0.333020	−0.166510	+	0.986040i	$0.553250\pi$
$174$	−8.09188	−0.613444
$175$	0	0
$176$	16.2620	1.22580
$177$	−3.95479	−0.297260
$178$	15.6392	1.17220
$179$	−7.76722	−0.580550	−0.290275	−	0.956943i	$-0.593747\pi$
$179$	−7.76722	−0.580550	−0.290275	+	0.956943i	$0.593747\pi$
$180$	0	0
$181$	14.0029	1.04082	0.520412	−	0.853915i	$-0.325778\pi$
$181$	14.0029	1.04082	0.520412	+	0.853915i	$0.325778\pi$
$182$	3.57941	0.265324
$183$	0.00540166	0.000399302 0
$184$	−51.3137	−3.78290
$185$	0	0
$186$	−2.90298	−0.212857
$187$	16.2345	1.18719
$188$	−38.2032	−2.78625
$189$	−0.976551	−0.0710336
$190$	0	0
$191$	15.6093	1.12945	0.564725	−	0.825279i	$-0.308982\pi$
$191$	15.6093	1.12945	0.564725	+	0.825279i	$0.308982\pi$
$192$	3.27183	0.236124
$193$	−14.9061	−1.07296	−0.536482	−	0.843912i	$-0.680247\pi$
$193$	−14.9061	−1.07296	−0.536482	+	0.843912i	$0.680247\pi$
$194$	31.6574	2.27287
$195$	0	0
$196$	−26.1328	−1.86663
$197$	17.9891	1.28167	0.640834	−	0.767680i	$-0.278589\pi$
$197$	17.9891	1.28167	0.640834	+	0.767680i	$0.278589\pi$
$198$	−6.77395	−0.481404
$199$	4.61422	0.327093	0.163547	−	0.986536i	$-0.447707\pi$
$199$	4.61422	0.327093	0.163547	+	0.986536i	$0.447707\pi$
$200$	0	0
$201$	−9.10553	−0.642254
$202$	−3.04599	−0.214315
$203$	−3.14278	−0.220580
$204$	−26.0448	−1.82350
$205$	0	0
$206$	−0.0770222	−0.00536639
$207$	8.78876	0.610861
$208$	−8.79932	−0.610123
$209$	13.1372	0.908718
$210$	0	0
$211$	6.62645	0.456184	0.228092	−	0.973640i	$-0.426751\pi$
$211$	6.62645	0.456184	0.228092	+	0.973640i	$0.426751\pi$
$212$	−36.8913	−2.53370
$213$	−11.2733	−0.772433
$214$	2.51437	0.171879
$215$	0	0
$216$	5.83856	0.397264
$217$	−1.12748	−0.0765384
$218$	42.4732	2.87665
$219$	13.7654	0.930179
$220$	0	0
$221$	−8.78445	−0.590906
$222$	−28.0299	−1.88124
$223$	−12.7619	−0.854601	−0.427300	−	0.904110i	$-0.640535\pi$
$223$	−12.7619	−0.854601	−0.427300	+	0.904110i	$0.640535\pi$
$224$	−3.41802	−0.228376
$225$	0	0
$226$	38.8026	2.58111
$227$	−11.2560	−0.747084	−0.373542	−	0.927613i	$-0.621857\pi$
$227$	−11.2560	−0.747084	−0.373542	+	0.927613i	$0.621857\pi$
$228$	−21.0757	−1.39577
$229$	−18.8479	−1.24550	−0.622751	−	0.782420i	$-0.713985\pi$
$229$	−18.8479	−1.24550	−0.622751	+	0.782420i	$0.713985\pi$
$230$	0	0
$231$	−2.63092	−0.173102
$232$	18.7900	1.23362
$233$	−12.7808	−0.837297	−0.418648	−	0.908148i	$-0.637496\pi$
$233$	−12.7808	−0.837297	−0.418648	+	0.908148i	$0.637496\pi$
$234$	3.66536	0.239612
$235$	0	0
$236$	17.0929	1.11265
$237$	14.9228	0.969342
$238$	−14.7963	−0.959101
$239$	16.6112	1.07449	0.537243	−	0.843427i	$-0.319466\pi$
$239$	16.6112	1.07449	0.537243	+	0.843427i	$0.319466\pi$
$240$	0	0
$241$	16.3588	1.05376	0.526881	−	0.849939i	$-0.323361\pi$
$241$	16.3588	1.05376	0.526881	+	0.849939i	$0.323361\pi$
$242$	9.40847	0.604799
$243$	−1.00000	−0.0641500
$244$	−0.0233464	−0.00149460
$245$	0	0
$246$	−30.3587	−1.93560
$247$	−7.10848	−0.452302
$248$	6.74094	0.428050
$249$	−3.80805	−0.241326
$250$	0	0
$251$	−2.06314	−0.130224	−0.0651121	−	0.997878i	$-0.520741\pi$
$251$	−2.06314	−0.130224	−0.0651121	+	0.997878i	$0.520741\pi$
$252$	4.22073	0.265881
$253$	23.6777	1.48860
$254$	20.3164	1.27476
$255$	0	0
$256$	−31.7422	−1.98389
$257$	2.58658	0.161346	0.0806732	−	0.996741i	$-0.474293\pi$
$257$	2.58658	0.161346	0.0806732	+	0.996741i	$0.474293\pi$
$258$	11.9977	0.746945
$259$	−10.8864	−0.676451
$260$	0	0
$261$	−3.21825	−0.199205
$262$	40.0137	2.47205
$263$	−2.06530	−0.127352	−0.0636759	−	0.997971i	$-0.520282\pi$
$263$	−2.06530	−0.127352	−0.0636759	+	0.997971i	$0.520282\pi$
$264$	15.7296	0.968091
$265$	0	0
$266$	−11.9733	−0.734132
$267$	6.21990	0.380652
$268$	39.3548	2.40397
$269$	−3.64899	−0.222483	−0.111242	−	0.993793i	$-0.535483\pi$
$269$	−3.64899	−0.222483	−0.111242	+	0.993793i	$0.535483\pi$
$270$	0	0
$271$	22.6648	1.37679	0.688395	−	0.725336i	$-0.258315\pi$
$271$	22.6648	1.37679	0.688395	+	0.725336i	$0.258315\pi$
$272$	36.3739	2.20549
$273$	1.42358	0.0861590
$274$	−43.8683	−2.65018
$275$	0	0
$276$	−37.9857	−2.28647
$277$	10.2715	0.617152	0.308576	−	0.951200i	$-0.400148\pi$
$277$	10.2715	0.617152	0.308576	+	0.951200i	$0.400148\pi$
$278$	9.87182	0.592073
$279$	−1.15455	−0.0691214
$280$	0	0
$281$	29.6371	1.76800	0.884001	−	0.467485i	$-0.154840\pi$
$281$	29.6371	1.76800	0.884001	+	0.467485i	$0.154840\pi$
$282$	−22.2248	−1.32346
$283$	−20.6666	−1.22850	−0.614251	−	0.789111i	$-0.710542\pi$
$283$	−20.6666	−1.22850	−0.614251	+	0.789111i	$0.710542\pi$
$284$	48.7240	2.89124
$285$	0	0
$286$	9.87481	0.583910
$287$	−11.7910	−0.695998
$288$	−3.50009	−0.206245
$289$	19.3125	1.13603
$290$	0	0
$291$	12.5906	0.738071
$292$	−59.4951	−3.48169
$293$	2.15468	0.125878	0.0629389	−	0.998017i	$-0.479953\pi$
$293$	2.15468	0.125878	0.0629389	+	0.998017i	$0.479953\pi$
$294$	−15.2028	−0.886644
$295$	0	0
$296$	65.0875	3.78313
$297$	−2.69409	−0.156327
$298$	46.1944	2.67597
$299$	−12.8119	−0.740932
$300$	0	0
$301$	4.65976	0.268584
$302$	28.8816	1.66195
$303$	−1.21143	−0.0695949
$304$	29.4342	1.68817
$305$	0	0
$306$	−15.1516	−0.866158
$307$	14.1161	0.805648	0.402824	−	0.915277i	$-0.368029\pi$
$307$	14.1161	0.805648	0.402824	+	0.915277i	$0.368029\pi$
$308$	11.3710	0.647924
$309$	−0.0306327	−0.00174264
$310$	0	0
$311$	12.1397	0.688378	0.344189	−	0.938900i	$-0.388154\pi$
$311$	12.1397	0.688378	0.344189	+	0.938900i	$0.388154\pi$
$312$	−8.51124	−0.481854
$313$	−24.3123	−1.37421	−0.687105	−	0.726558i	$-0.741119\pi$
$313$	−24.3123	−1.37421	−0.687105	+	0.726558i	$0.741119\pi$
$314$	10.0835	0.569046
$315$	0	0
$316$	−64.4976	−3.62827
$317$	−6.55173	−0.367982	−0.183991	−	0.982928i	$-0.558902\pi$
$317$	−6.55173	−0.367982	−0.183991	+	0.982928i	$0.558902\pi$
$318$	−21.4615	−1.20350
$319$	−8.67026	−0.485441
$320$	0	0
$321$	1.00000	0.0558146
$322$	−21.5800	−1.20261
$323$	29.3845	1.63500
$324$	4.32208	0.240115
$325$	0	0
$326$	59.8438	3.31444
$327$	16.8921	0.934138
$328$	70.4953	3.89245
$329$	−8.63181	−0.475887
$330$	0	0
$331$	−3.02973	−0.166529	−0.0832645	−	0.996527i	$-0.526535\pi$
$331$	−3.02973	−0.166529	−0.0832645	+	0.996527i	$0.526535\pi$
$332$	16.4587	0.903288
$333$	−11.1479	−0.610899
$334$	−40.6408	−2.22377
$335$	0	0
$336$	−5.89464	−0.321579
$337$	−12.4975	−0.680781	−0.340390	−	0.940284i	$-0.610559\pi$
$337$	−12.4975	−0.680781	−0.340390	+	0.940284i	$0.610559\pi$
$338$	27.3436	1.48730
$339$	15.4323	0.838169
$340$	0	0
$341$	−3.11047	−0.168442
$342$	−12.2608	−0.662990
$343$	−12.7404	−0.687918
$344$	−27.8596	−1.50209
$345$	0	0
$346$	11.0135	0.592087
$347$	−18.0254	−0.967653	−0.483827	−	0.875164i	$-0.660753\pi$
$347$	−18.0254	−0.967653	−0.483827	+	0.875164i	$0.660753\pi$
$348$	13.9095	0.745628
$349$	−5.16225	−0.276329	−0.138164	−	0.990409i	$-0.544120\pi$
$349$	−5.16225	−0.276329	−0.138164	+	0.990409i	$0.544120\pi$
$350$	0	0
$351$	1.45776	0.0778096
$352$	−9.42957	−0.502598
$353$	25.3115	1.34719	0.673597	−	0.739099i	$-0.264748\pi$
$353$	25.3115	1.34719	0.673597	+	0.739099i	$0.264748\pi$
$354$	9.94382	0.528508
$355$	0	0
$356$	−26.8829	−1.42479
$357$	−5.88468	−0.311450
$358$	19.5297	1.03218
$359$	−20.4904	−1.08144	−0.540722	−	0.841202i	$-0.681849\pi$
$359$	−20.4904	−1.08144	−0.540722	+	0.841202i	$0.681849\pi$
$360$	0	0
$361$	4.77826	0.251487
$362$	−35.2084	−1.85051
$363$	3.74187	0.196397
$364$	−6.15282	−0.322495
$365$	0	0
$366$	−0.0135818	−0.000709932 0
$367$	−37.0550	−1.93426	−0.967129	−	0.254288i	$-0.918159\pi$
$367$	−37.0550	−1.93426	−0.967129	+	0.254288i	$0.918159\pi$
$368$	53.0505	2.76545
$369$	−12.0741	−0.628551
$370$	0	0
$371$	−8.33539	−0.432752
$372$	4.99007	0.258723
$373$	31.2054	1.61575	0.807877	−	0.589351i	$-0.200616\pi$
$373$	31.2054	1.61575	0.807877	+	0.589351i	$0.200616\pi$
$374$	−40.8197	−2.11074
$375$	0	0
$376$	51.6075	2.66146
$377$	4.69144	0.241622
$378$	2.45541	0.126293
$379$	6.80447	0.349522	0.174761	−	0.984611i	$-0.444085\pi$
$379$	6.80447	0.349522	0.174761	+	0.984611i	$0.444085\pi$
$380$	0	0
$381$	8.08010	0.413956
$382$	−39.2477	−2.00809
$383$	10.7422	0.548903	0.274451	−	0.961601i	$-0.411504\pi$
$383$	10.7422	0.548903	0.274451	+	0.961601i	$0.411504\pi$
$384$	−15.2268	−0.777039
$385$	0	0
$386$	37.4795	1.90766
$387$	4.77165	0.242557
$388$	−54.4173	−2.76262
$389$	−22.1285	−1.12196	−0.560980	−	0.827829i	$-0.689575\pi$
$389$	−22.1285	−1.12196	−0.560980	+	0.827829i	$0.689575\pi$
$390$	0	0
$391$	52.9609	2.67835
$392$	35.3020	1.78302
$393$	15.9140	0.802754
$394$	−45.2312	−2.27872
$395$	0	0
$396$	11.6441	0.585136
$397$	18.6371	0.935370	0.467685	−	0.883895i	$-0.345088\pi$
$397$	18.6371	0.935370	0.467685	+	0.883895i	$0.345088\pi$
$398$	−11.6019	−0.581549
$399$	−4.76195	−0.238396
$400$	0	0
$401$	−17.8804	−0.892904	−0.446452	−	0.894808i	$-0.647313\pi$
$401$	−17.8804	−0.892904	−0.446452	+	0.894808i	$0.647313\pi$
$402$	22.8947	1.14188
$403$	1.68307	0.0838395
$404$	5.23589	0.260496
$405$	0	0
$406$	7.90213	0.392176
$407$	−30.0333	−1.48870
$408$	35.1831	1.74182
$409$	28.0562	1.38729	0.693645	−	0.720317i	$-0.256004\pi$
$409$	28.0562	1.38729	0.693645	+	0.720317i	$0.256004\pi$
$410$	0	0
$411$	−17.4470	−0.860598
$412$	0.132397	0.00652273
$413$	3.86205	0.190039
$414$	−22.0982	−1.08607
$415$	0	0
$416$	5.10230	0.250161
$417$	3.92616	0.192265
$418$	−33.0318	−1.61564
$419$	32.6393	1.59453	0.797267	−	0.603627i	$-0.206279\pi$
$419$	32.6393	1.59453	0.797267	+	0.603627i	$0.206279\pi$
$420$	0	0
$421$	−2.55539	−0.124542	−0.0622711	−	0.998059i	$-0.519834\pi$
$421$	−2.55539	−0.124542	−0.0622711	+	0.998059i	$0.519834\pi$
$422$	−16.6614	−0.811063
$423$	−8.83908	−0.429771
$424$	49.8353	2.42022
$425$	0	0
$426$	28.3453	1.37333
$427$	−0.00527500	−0.000255275 0
$428$	−4.32208	−0.208915
$429$	3.92735	0.189614
$430$	0	0
$431$	−20.8380	−1.00373	−0.501867	−	0.864945i	$-0.667353\pi$
$431$	−20.8380	−1.00373	−0.501867	+	0.864945i	$0.667353\pi$
$432$	−6.03618	−0.290416
$433$	−2.79578	−0.134357	−0.0671784	−	0.997741i	$-0.521400\pi$
$433$	−2.79578	−0.134357	−0.0671784	+	0.997741i	$0.521400\pi$
$434$	2.83491	0.136080
$435$	0	0
$436$	−73.0091	−3.49650
$437$	42.8566	2.05011
$438$	−34.6113	−1.65379
$439$	−6.60921	−0.315441	−0.157720	−	0.987484i	$-0.550414\pi$
$439$	−6.60921	−0.315441	−0.157720	+	0.987484i	$0.550414\pi$
$440$	0	0
$441$	−6.04635	−0.287921
$442$	22.0874	1.05059
$443$	3.65894	0.173841	0.0869207	−	0.996215i	$-0.472297\pi$
$443$	3.65894	0.173841	0.0869207	+	0.996215i	$0.472297\pi$
$444$	48.1819	2.28661
$445$	0	0
$446$	32.0882	1.51942
$447$	18.3721	0.868973
$448$	−3.19511	−0.150955
$449$	3.11536	0.147023	0.0735115	−	0.997294i	$-0.476579\pi$
$449$	3.11536	0.147023	0.0735115	+	0.997294i	$0.476579\pi$
$450$	0	0
$451$	−32.5287	−1.53172
$452$	−66.6997	−3.13729
$453$	11.4866	0.539687
$454$	28.3017	1.32826
$455$	0	0
$456$	28.4706	1.33326
$457$	29.9081	1.39904	0.699522	−	0.714611i	$-0.253396\pi$
$457$	29.9081	1.39904	0.699522	+	0.714611i	$0.253396\pi$
$458$	47.3906	2.21442
$459$	−6.02598	−0.281269
$460$	0	0
$461$	−10.3722	−0.483079	−0.241540	−	0.970391i	$-0.577652\pi$
$461$	−10.3722	−0.483079	−0.241540	+	0.970391i	$0.577652\pi$
$462$	6.61511	0.307763
$463$	12.9774	0.603111	0.301556	−	0.953449i	$-0.402494\pi$
$463$	12.9774	0.603111	0.301556	+	0.953449i	$0.402494\pi$
$464$	−19.4259	−0.901827
$465$	0	0
$466$	32.1357	1.48866
$467$	−38.0421	−1.76038	−0.880188	−	0.474625i	$-0.842584\pi$
$467$	−38.0421	−1.76038	−0.880188	+	0.474625i	$0.842584\pi$
$468$	−6.30056	−0.291243
$469$	8.89201	0.410595
$470$	0	0
$471$	4.01035	0.184787
$472$	−23.0903	−1.06282
$473$	12.8553	0.591086
$474$	−37.5216	−1.72342
$475$	0	0
$476$	25.4340	1.16577
$477$	−8.53554	−0.390816
$478$	−41.7667	−1.91036
$479$	−12.7781	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$479$	−12.7781	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$480$	0	0
$481$	16.2509	0.740978
$482$	−41.1321	−1.87351
$483$	−8.58267	−0.390525
$484$	−16.1727	−0.735121
$485$	0	0
$486$	2.51437	0.114054
$487$	1.33859	0.0606575	0.0303288	−	0.999540i	$-0.490345\pi$
$487$	1.33859	0.0606575	0.0303288	+	0.999540i	$0.490345\pi$
$488$	0.0315379	0.00142766
$489$	23.8007	1.07630
$490$	0	0
$491$	28.9425	1.30615	0.653077	−	0.757291i	$-0.273478\pi$
$491$	28.9425	1.30615	0.653077	+	0.757291i	$0.273478\pi$
$492$	52.1851	2.35268
$493$	−19.3931	−0.873422
$494$	17.8734	0.804161
$495$	0	0
$496$	−6.96910	−0.312922
$497$	11.0089	0.493819
$498$	9.57487	0.429060
$499$	43.9231	1.96627	0.983134	−	0.182889i	$-0.0585449\pi$
$499$	43.9231	1.96627	0.983134	+	0.182889i	$0.0585449\pi$
$500$	0	0
$501$	−16.1634	−0.722128
$502$	5.18750	0.231530
$503$	21.2223	0.946256	0.473128	−	0.880994i	$-0.343125\pi$
$503$	21.2223	0.946256	0.473128	+	0.880994i	$0.343125\pi$
$504$	−5.70166	−0.253972
$505$	0	0
$506$	−59.5346	−2.64664
$507$	10.8749	0.482973
$508$	−34.9228	−1.54945
$509$	−7.26637	−0.322076	−0.161038	−	0.986948i	$-0.551484\pi$
$509$	−7.26637	−0.322076	−0.161038	+	0.986948i	$0.551484\pi$
$510$	0	0
$511$	−13.4426	−0.594666
$512$	49.3581	2.18134
$513$	−4.87630	−0.215294
$514$	−6.50363	−0.286863
$515$	0	0
$516$	−20.6234	−0.907896
$517$	−23.8133	−1.04731
$518$	27.3726	1.20268
$519$	4.38020	0.192269
$520$	0	0
$521$	7.69893	0.337296	0.168648	−	0.985676i	$-0.446060\pi$
$521$	7.69893	0.337296	0.168648	+	0.985676i	$0.446060\pi$
$522$	8.09188	0.354172
$523$	−22.5811	−0.987401	−0.493700	−	0.869632i	$-0.664356\pi$
$523$	−22.5811	−0.987401	−0.493700	+	0.869632i	$0.664356\pi$
$524$	−68.7814	−3.00473
$525$	0	0
$526$	5.19293	0.226423
$527$	−6.95732	−0.303066
$528$	−16.2620	−0.707714
$529$	54.2422	2.35836
$530$	0	0
$531$	3.95479	0.171623
$532$	20.5815	0.892322
$533$	17.6011	0.762390
$534$	−15.6392	−0.676772
$535$	0	0
$536$	−53.1632	−2.29630
$537$	7.76722	0.335180
$538$	9.17493	0.395559
$539$	−16.2894	−0.701635
$540$	0	0
$541$	2.84269	0.122217	0.0611085	−	0.998131i	$-0.480536\pi$
$541$	2.84269	0.122217	0.0611085	+	0.998131i	$0.480536\pi$
$542$	−56.9879	−2.44784
$543$	−14.0029	−0.600920
$544$	−21.0915	−0.904290
$545$	0	0
$546$	−3.57941	−0.153185
$547$	12.6520	0.540961	0.270480	−	0.962726i	$-0.412818\pi$
$547$	12.6520	0.540961	0.270480	+	0.962726i	$0.412818\pi$
$548$	75.4073	3.22124
$549$	−0.00540166	−0.000230537 0
$550$	0	0
$551$	−15.6931	−0.668550
$552$	51.3137	2.18406
$553$	−14.5729	−0.619703
$554$	−25.8263	−1.09725
$555$	0	0
$556$	−16.9691	−0.719652
$557$	−32.0008	−1.35592	−0.677958	−	0.735101i	$-0.737135\pi$
$557$	−32.0008	−1.35592	−0.677958	+	0.735101i	$0.737135\pi$
$558$	2.90298	0.122893
$559$	−6.95594	−0.294205
$560$	0	0
$561$	−16.2345	−0.685423
$562$	−74.5188	−3.14338
$563$	−37.3763	−1.57522	−0.787611	−	0.616173i	$-0.788682\pi$
$563$	−37.3763	−1.57522	−0.787611	+	0.616173i	$0.788682\pi$
$564$	38.2032	1.60864
$565$	0	0
$566$	51.9635	2.18419
$567$	0.976551	0.0410113
$568$	−65.8198	−2.76174
$569$	−0.704935	−0.0295524	−0.0147762	−	0.999891i	$-0.504704\pi$
$569$	−0.704935	−0.0295524	−0.0147762	+	0.999891i	$0.504704\pi$
$570$	0	0
$571$	21.5905	0.903536	0.451768	−	0.892136i	$-0.350794\pi$
$571$	21.5905	0.903536	0.451768	+	0.892136i	$0.350794\pi$
$572$	−16.9743	−0.709730
$573$	−15.6093	−0.652089
$574$	29.6469	1.23744
$575$	0	0
$576$	−3.27183	−0.136326
$577$	20.3061	0.845355	0.422677	−	0.906280i	$-0.361090\pi$
$577$	20.3061	0.845355	0.422677	+	0.906280i	$0.361090\pi$
$578$	−48.5588	−2.01978
$579$	14.9061	0.619476
$580$	0	0
$581$	3.71876	0.154280
$582$	−31.6574	−1.31224
$583$	−22.9955	−0.952378
$584$	80.3701	3.32574
$585$	0	0
$586$	−5.41768	−0.223802
$587$	−9.86589	−0.407209	−0.203605	−	0.979053i	$-0.565266\pi$
$587$	−9.86589	−0.407209	−0.203605	+	0.979053i	$0.565266\pi$
$588$	26.1328	1.07770
$589$	−5.62995	−0.231978
$590$	0	0
$591$	−17.9891	−0.739971
$592$	−67.2905	−2.76562
$593$	−17.2430	−0.708085	−0.354043	−	0.935229i	$-0.615193\pi$
$593$	−17.2430	−0.708085	−0.354043	+	0.935229i	$0.615193\pi$
$594$	6.77395	0.277939
$595$	0	0
$596$	−79.4058	−3.25259
$597$	−4.61422	−0.188847
$598$	32.2140	1.31733
$599$	−30.8674	−1.26121	−0.630604	−	0.776104i	$-0.717193\pi$
$599$	−30.8674	−1.26121	−0.630604	+	0.776104i	$0.717193\pi$
$600$	0	0
$601$	11.3006	0.460962	0.230481	−	0.973077i	$-0.425970\pi$
$601$	11.3006	0.460962	0.230481	+	0.973077i	$0.425970\pi$
$602$	−11.7164	−0.477524
$603$	9.10553	0.370806
$604$	−49.6459	−2.02006
$605$	0	0
$606$	3.04599	0.123735
$607$	−0.761698	−0.0309164	−0.0154582	−	0.999881i	$-0.504921\pi$
$607$	−0.761698	−0.0309164	−0.0154582	+	0.999881i	$0.504921\pi$
$608$	−17.0675	−0.692178
$609$	3.14278	0.127352
$610$	0	0
$611$	12.8853	0.521283
$612$	26.0448	1.05280
$613$	12.4197	0.501626	0.250813	−	0.968036i	$-0.419302\pi$
$613$	12.4197	0.501626	0.250813	+	0.968036i	$0.419302\pi$
$614$	−35.4931	−1.43239
$615$	0	0
$616$	−15.3608	−0.618904
$617$	−8.96284	−0.360830	−0.180415	−	0.983591i	$-0.557744\pi$
$617$	−8.96284	−0.360830	−0.180415	+	0.983591i	$0.557744\pi$
$618$	0.0770222	0.00309829
$619$	37.3621	1.50171	0.750856	−	0.660466i	$-0.229641\pi$
$619$	37.3621	1.50171	0.750856	+	0.660466i	$0.229641\pi$
$620$	0	0
$621$	−8.78876	−0.352681
$622$	−30.5237	−1.22389
$623$	−6.07405	−0.243352
$624$	8.79932	0.352255
$625$	0	0
$626$	61.1301	2.44325
$627$	−13.1372	−0.524649
$628$	−17.3330	−0.691663
$629$	−67.1768	−2.67851
$630$	0	0
$631$	−18.9228	−0.753303	−0.376652	−	0.926355i	$-0.622925\pi$
$631$	−18.9228	−0.753303	−0.376652	+	0.926355i	$0.622925\pi$
$632$	87.1279	3.46576
$633$	−6.62645	−0.263378
$634$	16.4735	0.654246
$635$	0	0
$636$	36.8913	1.46283
$637$	8.81414	0.349229
$638$	21.8003	0.863081
$639$	11.2733	0.445965
$640$	0	0
$641$	−22.1470	−0.874753	−0.437376	−	0.899278i	$-0.644092\pi$
$641$	−22.1470	−0.874753	−0.437376	+	0.899278i	$0.644092\pi$
$642$	−2.51437	−0.0992344
$643$	5.40013	0.212960	0.106480	−	0.994315i	$-0.466042\pi$
$643$	5.40013	0.212960	0.106480	+	0.994315i	$0.466042\pi$
$644$	37.0949	1.46175
$645$	0	0
$646$	−73.8836	−2.90691
$647$	−30.7191	−1.20769	−0.603846	−	0.797101i	$-0.706366\pi$
$647$	−30.7191	−1.20769	−0.603846	+	0.797101i	$0.706366\pi$
$648$	−5.83856	−0.229360
$649$	10.6546	0.418228
$650$	0	0
$651$	1.12748	0.0441895
$652$	−102.868	−4.02864
$653$	−1.61474	−0.0631898	−0.0315949	−	0.999501i	$-0.510059\pi$
$653$	−1.61474	−0.0631898	−0.0315949	+	0.999501i	$0.510059\pi$
$654$	−42.4732	−1.66083
$655$	0	0
$656$	−72.8814	−2.84554
$657$	−13.7654	−0.537039
$658$	21.7036	0.846095
$659$	−14.7948	−0.576323	−0.288161	−	0.957582i	$-0.593044\pi$
$659$	−14.7948	−0.576323	−0.288161	+	0.957582i	$0.593044\pi$
$660$	0	0
$661$	43.2258	1.68129	0.840644	−	0.541588i	$-0.182177\pi$
$661$	43.2258	1.68129	0.840644	+	0.541588i	$0.182177\pi$
$662$	7.61788	0.296077
$663$	8.78445	0.341160
$664$	−22.2336	−0.862830
$665$	0	0
$666$	28.0299	1.08614
$667$	−28.2844	−1.09518
$668$	69.8595	2.70294
$669$	12.7619	0.493404
$670$	0	0
$671$	−0.0145526	−0.000561795 0
$672$	3.41802	0.131853
$673$	1.04646	0.0403382	0.0201691	−	0.999797i	$-0.493580\pi$
$673$	1.04646	0.0403382	0.0201691	+	0.999797i	$0.493580\pi$
$674$	31.4233	1.21038
$675$	0	0
$676$	−47.0023	−1.80778
$677$	7.90024	0.303631	0.151815	−	0.988409i	$-0.451488\pi$
$677$	7.90024	0.303631	0.151815	+	0.988409i	$0.451488\pi$
$678$	−38.8026	−1.49021
$679$	−12.2953	−0.471851
$680$	0	0
$681$	11.2560	0.431329
$682$	7.82089	0.299478
$683$	22.1213	0.846449	0.423225	−	0.906025i	$-0.360898\pi$
$683$	22.1213	0.846449	0.423225	+	0.906025i	$0.360898\pi$
$684$	21.0757	0.805850
$685$	0	0
$686$	32.0342	1.22307
$687$	18.8479	0.719091
$688$	28.8026	1.09809
$689$	12.4428	0.474033
$690$	0	0
$691$	42.0379	1.59920	0.799598	−	0.600535i	$-0.205046\pi$
$691$	42.0379	1.59920	0.799598	+	0.600535i	$0.205046\pi$
$692$	−18.9315	−0.719669
$693$	2.63092	0.0999403
$694$	45.3226	1.72042
$695$	0	0
$696$	−18.7900	−0.712231
$697$	−72.7582	−2.75591
$698$	12.9798	0.491294
$699$	12.7808	0.483413
$700$	0	0
$701$	2.86167	0.108084	0.0540418	−	0.998539i	$-0.482790\pi$
$701$	2.86167	0.108084	0.0540418	+	0.998539i	$0.482790\pi$
$702$	−3.66536	−0.138340
$703$	−54.3602	−2.05023
$704$	−8.81460	−0.332213
$705$	0	0
$706$	−63.6425	−2.39522
$707$	1.18302	0.0444922
$708$	−17.0929	−0.642390
$709$	3.46286	0.130050	0.0650252	−	0.997884i	$-0.479287\pi$
$709$	3.46286	0.130050	0.0650252	+	0.997884i	$0.479287\pi$
$710$	0	0
$711$	−14.9228	−0.559650
$712$	36.3153	1.36097
$713$	−10.1471	−0.380012
$714$	14.7963	0.553737
$715$	0	0
$716$	−33.5705	−1.25459
$717$	−16.6112	−0.620355
$718$	51.5206	1.92273
$719$	−14.6835	−0.547603	−0.273801	−	0.961786i	$-0.588281\pi$
$719$	−14.6835	−0.547603	−0.273801	+	0.961786i	$0.588281\pi$
$720$	0	0
$721$	0.0299144	0.00111407
$722$	−12.0143	−0.447127
$723$	−16.3588	−0.608389
$724$	60.5214	2.24926
$725$	0	0
$726$	−9.40847	−0.349181
$727$	23.6132	0.875764	0.437882	−	0.899033i	$-0.355729\pi$
$727$	23.6132	0.875764	0.437882	+	0.899033i	$0.355729\pi$
$728$	8.31166	0.308051
$729$	1.00000	0.0370370
$730$	0	0
$731$	28.7539	1.06350
$732$	0.0233464	0.000862907 0
$733$	−22.2462	−0.821681	−0.410841	−	0.911707i	$-0.634765\pi$
$733$	−22.2462	−0.821681	−0.410841	+	0.911707i	$0.634765\pi$
$734$	93.1702	3.43898
$735$	0	0
$736$	−30.7614	−1.13388
$737$	24.5311	0.903615
$738$	30.3587	1.11752
$739$	−43.6292	−1.60493	−0.802463	−	0.596702i	$-0.796477\pi$
$739$	−43.6292	−1.60493	−0.802463	+	0.596702i	$0.796477\pi$
$740$	0	0
$741$	7.10848	0.261137
$742$	20.9583	0.769403
$743$	49.3025	1.80873	0.904367	−	0.426755i	$-0.140343\pi$
$743$	49.3025	1.80873	0.904367	+	0.426755i	$0.140343\pi$
$744$	−6.74094	−0.247135
$745$	0	0
$746$	−78.4621	−2.87270
$747$	3.80805	0.139329
$748$	70.1669	2.56556
$749$	−0.976551	−0.0356824
$750$	0	0
$751$	−6.53666	−0.238526	−0.119263	−	0.992863i	$-0.538053\pi$
$751$	−6.53666	−0.238526	−0.119263	+	0.992863i	$0.538053\pi$
$752$	−53.3543	−1.94563
$753$	2.06314	0.0751850
$754$	−11.7960	−0.429586
$755$	0	0
$756$	−4.22073	−0.153506
$757$	−20.1262	−0.731498	−0.365749	−	0.930714i	$-0.619187\pi$
$757$	−20.1262	−0.731498	−0.365749	+	0.930714i	$0.619187\pi$
$758$	−17.1090	−0.621426
$759$	−23.6777	−0.859446
$760$	0	0
$761$	−2.57302	−0.0932720	−0.0466360	−	0.998912i	$-0.514850\pi$
$761$	−2.57302	−0.0932720	−0.0466360	+	0.998912i	$0.514850\pi$
$762$	−20.3164	−0.735985
$763$	−16.4960	−0.597197
$764$	67.4646	2.44079
$765$	0	0
$766$	−27.0100	−0.975911
$767$	−5.76514	−0.208167
$768$	31.7422	1.14540
$769$	−28.1270	−1.01428	−0.507142	−	0.861862i	$-0.669298\pi$
$769$	−28.1270	−1.01428	−0.507142	+	0.861862i	$0.669298\pi$
$770$	0	0
$771$	−2.58658	−0.0931534
$772$	−64.4253	−2.31872
$773$	48.5607	1.74661	0.873304	−	0.487175i	$-0.161973\pi$
$773$	48.5607	1.74661	0.873304	+	0.487175i	$0.161973\pi$
$774$	−11.9977	−0.431249
$775$	0	0
$776$	73.5108	2.63888
$777$	10.8864	0.390549
$778$	55.6393	1.99477
$779$	−58.8768	−2.10948
$780$	0	0
$781$	30.3713	1.08677
$782$	−133.163	−4.76192
$783$	3.21825	0.115011
$784$	−36.4969	−1.30346
$785$	0	0
$786$	−40.0137	−1.42724
$787$	21.9772	0.783403	0.391702	−	0.920092i	$-0.371887\pi$
$787$	21.9772	0.783403	0.391702	+	0.920092i	$0.371887\pi$
$788$	77.7501	2.76973
$789$	2.06530	0.0735266
$790$	0	0
$791$	−15.0705	−0.535844
$792$	−15.7296	−0.558928
$793$	0.00787434	0.000279626 0
$794$	−46.8607	−1.66302
$795$	0	0
$796$	19.9430	0.706860
$797$	5.95542	0.210952	0.105476	−	0.994422i	$-0.466363\pi$
$797$	5.95542	0.210952	0.105476	+	0.994422i	$0.466363\pi$
$798$	11.9733	0.423851
$799$	−53.2642	−1.88435
$800$	0	0
$801$	−6.21990	−0.219769
$802$	44.9580	1.58752
$803$	−37.0852	−1.30871
$804$	−39.3548	−1.38794
$805$	0	0
$806$	−4.23186	−0.149061
$807$	3.64899	0.128451
$808$	−7.07302	−0.248828
$809$	−30.7320	−1.08048	−0.540240	−	0.841511i	$-0.681667\pi$
$809$	−30.7320	−1.08048	−0.540240	+	0.841511i	$0.681667\pi$
$810$	0	0
$811$	−3.54073	−0.124332	−0.0621659	−	0.998066i	$-0.519801\pi$
$811$	−3.54073	−0.124332	−0.0621659	+	0.998066i	$0.519801\pi$
$812$	−13.5834	−0.476682
$813$	−22.6648	−0.794891
$814$	75.5150	2.64680
$815$	0	0
$816$	−36.3739	−1.27334
$817$	23.2680	0.814044
$818$	−70.5438	−2.46651
$819$	−1.42358	−0.0497439
$820$	0	0
$821$	−0.869512	−0.0303462	−0.0151731	−	0.999885i	$-0.504830\pi$
$821$	−0.869512	−0.0303462	−0.0151731	+	0.999885i	$0.504830\pi$
$822$	43.8683	1.53008
$823$	−41.4076	−1.44338	−0.721689	−	0.692218i	$-0.756634\pi$
$823$	−41.4076	−1.44338	−0.721689	+	0.692218i	$0.756634\pi$
$824$	−0.178851	−0.00623058
$825$	0	0
$826$	−9.71064	−0.337876
$827$	−37.2927	−1.29679	−0.648397	−	0.761302i	$-0.724560\pi$
$827$	−37.2927	−1.29679	−0.648397	+	0.761302i	$0.724560\pi$
$828$	37.9857	1.32009
$829$	−9.06114	−0.314707	−0.157353	−	0.987542i	$-0.550296\pi$
$829$	−9.06114	−0.314707	−0.157353	+	0.987542i	$0.550296\pi$
$830$	0	0
$831$	−10.2715	−0.356313
$832$	4.76955	0.165354
$833$	−36.4352	−1.26240
$834$	−9.87182	−0.341833
$835$	0	0
$836$	56.7799	1.96377
$837$	1.15455	0.0399072
$838$	−82.0673	−2.83497
$839$	25.9540	0.896030	0.448015	−	0.894026i	$-0.352131\pi$
$839$	25.9540	0.896030	0.448015	+	0.894026i	$0.352131\pi$
$840$	0	0
$841$	−18.6429	−0.642858
$842$	6.42521	0.221427
$843$	−29.6371	−1.02076
$844$	28.6400	0.985831
$845$	0	0
$846$	22.2248	0.764103
$847$	−3.65413	−0.125557
$848$	−51.5221	−1.76928
$849$	20.6666	0.709276
$850$	0	0
$851$	−97.9758	−3.35857
$852$	−48.7240	−1.66926
$853$	−6.47702	−0.221769	−0.110885	−	0.993833i	$-0.535368\pi$
$853$	−6.47702	−0.221769	−0.110885	+	0.993833i	$0.535368\pi$
$854$	0.0132633	0.000453861 0
$855$	0	0
$856$	5.83856	0.199558
$857$	−6.09104	−0.208066	−0.104033	−	0.994574i	$-0.533175\pi$
$857$	−6.09104	−0.208066	−0.104033	+	0.994574i	$0.533175\pi$
$858$	−9.87481	−0.337121
$859$	−14.1619	−0.483196	−0.241598	−	0.970376i	$-0.577672\pi$
$859$	−14.1619	−0.483196	−0.241598	+	0.970376i	$0.577672\pi$
$860$	0	0
$861$	11.7910	0.401835
$862$	52.3946	1.78457
$863$	−56.2099	−1.91341	−0.956704	−	0.291061i	$-0.905992\pi$
$863$	−56.2099	−1.91341	−0.956704	+	0.291061i	$0.905992\pi$
$864$	3.50009	0.119076
$865$	0	0
$866$	7.02965	0.238877
$867$	−19.3125	−0.655886
$868$	−4.87306	−0.165402
$869$	−40.2034	−1.36381
$870$	0	0
$871$	−13.2737	−0.449762
$872$	98.6259	3.33989
$873$	−12.5906	−0.426126
$874$	−107.757	−3.64495
$875$	0	0
$876$	59.4951	2.01015
$877$	−22.4069	−0.756626	−0.378313	−	0.925678i	$-0.623496\pi$
$877$	−22.4069	−0.756626	−0.378313	+	0.925678i	$0.623496\pi$
$878$	16.6180	0.560831
$879$	−2.15468	−0.0726756
$880$	0	0
$881$	37.1206	1.25062	0.625312	−	0.780375i	$-0.284972\pi$
$881$	37.1206	1.25062	0.625312	+	0.780375i	$0.284972\pi$
$882$	15.2028	0.511904
$883$	47.6484	1.60350	0.801748	−	0.597662i	$-0.203904\pi$
$883$	47.6484	1.60350	0.801748	+	0.597662i	$0.203904\pi$
$884$	−37.9671	−1.27697
$885$	0	0
$886$	−9.19994	−0.309078
$887$	49.6033	1.66552	0.832759	−	0.553636i	$-0.186760\pi$
$887$	49.6033	1.66552	0.832759	+	0.553636i	$0.186760\pi$
$888$	−65.0875	−2.18419
$889$	−7.89063	−0.264643
$890$	0	0
$891$	2.69409	0.0902554
$892$	−55.1579	−1.84682
$893$	−43.1020	−1.44235
$894$	−46.1944	−1.54497
$895$	0	0
$896$	14.8697	0.496763
$897$	12.8119	0.427778
$898$	−7.83318	−0.261397
$899$	3.71564	0.123924
$900$	0	0
$901$	−51.4351	−1.71355
$902$	81.7892	2.72328
$903$	−4.65976	−0.155067
$904$	90.1027	2.99677
$905$	0	0
$906$	−28.8816	−0.959527
$907$	40.0327	1.32926	0.664632	−	0.747171i	$-0.268589\pi$
$907$	40.0327	1.32926	0.664632	+	0.747171i	$0.268589\pi$
$908$	−48.6491	−1.61448
$909$	1.21143	0.0401806
$910$	0	0
$911$	18.4802	0.612275	0.306137	−	0.951987i	$-0.400963\pi$
$911$	18.4802	0.612275	0.306137	+	0.951987i	$0.400963\pi$
$912$	−29.4342	−0.974664
$913$	10.2592	0.339531
$914$	−75.2002	−2.48740
$915$	0	0
$916$	−81.4619	−2.69158
$917$	−15.5408	−0.513203
$918$	15.1516	0.500076
$919$	9.12599	0.301039	0.150519	−	0.988607i	$-0.451905\pi$
$919$	9.12599	0.301039	0.150519	+	0.988607i	$0.451905\pi$
$920$	0	0
$921$	−14.1161	−0.465141
$922$	26.0795	0.858882
$923$	−16.4338	−0.540925
$924$	−11.3710	−0.374079
$925$	0	0
$926$	−32.6301	−1.07229
$927$	0.0306327	0.00100611
$928$	11.2642	0.369764
$929$	−9.08371	−0.298027	−0.149013	−	0.988835i	$-0.547610\pi$
$929$	−9.08371	−0.298027	−0.149013	+	0.988835i	$0.547610\pi$
$930$	0	0
$931$	−29.4838	−0.966292
$932$	−55.2395	−1.80943
$933$	−12.1397	−0.397435
$934$	95.6519	3.12983
$935$	0	0
$936$	8.51124	0.278199
$937$	−27.0821	−0.884732	−0.442366	−	0.896835i	$-0.645861\pi$
$937$	−27.0821	−0.884732	−0.442366	+	0.896835i	$0.645861\pi$
$938$	−22.3578	−0.730009
$939$	24.3123	0.793401
$940$	0	0
$941$	6.44710	0.210170	0.105085	−	0.994463i	$-0.466489\pi$
$941$	6.44710	0.210170	0.105085	+	0.994463i	$0.466489\pi$
$942$	−10.0835	−0.328539
$943$	−106.116	−3.45562
$944$	23.8718	0.776962
$945$	0	0
$946$	−32.3229	−1.05091
$947$	29.8809	0.970998	0.485499	−	0.874237i	$-0.338638\pi$
$947$	29.8809	0.970998	0.485499	+	0.874237i	$0.338638\pi$
$948$	64.4976	2.09478
$949$	20.0667	0.651392
$950$	0	0
$951$	6.55173	0.212454
$952$	−34.3581	−1.11355
$953$	−26.7779	−0.867421	−0.433710	−	0.901052i	$-0.642796\pi$
$953$	−26.7779	−0.867421	−0.433710	+	0.901052i	$0.642796\pi$
$954$	21.4615	0.694843
$955$	0	0
$956$	71.7947	2.32201
$957$	8.67026	0.280270
$958$	32.1290	1.03804
$959$	17.0379	0.550182
$960$	0	0
$961$	−29.6670	−0.957000
$962$	−40.8609	−1.31741
$963$	−1.00000	−0.0322245
$964$	70.7039	2.27722
$965$	0	0
$966$	21.5800	0.694326
$967$	−9.56573	−0.307613	−0.153807	−	0.988101i	$-0.549153\pi$
$967$	−9.56573	−0.307613	−0.153807	+	0.988101i	$0.549153\pi$
$968$	21.8472	0.702195
$969$	−29.3845	−0.943965
$970$	0	0
$971$	7.16591	0.229965	0.114982	−	0.993368i	$-0.463319\pi$
$971$	7.16591	0.229965	0.114982	+	0.993368i	$0.463319\pi$
$972$	−4.32208	−0.138631
$973$	−3.83409	−0.122915
$974$	−3.36573	−0.107845
$975$	0	0
$976$	−0.0326054	−0.00104367
$977$	20.8084	0.665719	0.332859	−	0.942976i	$-0.391987\pi$
$977$	20.8084	0.665719	0.332859	+	0.942976i	$0.391987\pi$
$978$	−59.8438	−1.91359
$979$	−16.7570	−0.535555
$980$	0	0
$981$	−16.8921	−0.539325
$982$	−72.7722	−2.32225
$983$	30.0586	0.958720	0.479360	−	0.877618i	$-0.340869\pi$
$983$	30.0586	0.958720	0.479360	+	0.877618i	$0.340869\pi$
$984$	−70.4953	−2.24731
$985$	0	0
$986$	48.7615	1.55288
$987$	8.63181	0.274754
$988$	−30.7234	−0.977441
$989$	41.9369	1.33352
$990$	0	0
$991$	6.42169	0.203992	0.101996	−	0.994785i	$-0.467477\pi$
$991$	6.42169	0.203992	0.101996	+	0.994785i	$0.467477\pi$
$992$	4.04105	0.128303
$993$	3.02973	0.0961456
$994$	−27.6806	−0.877975
$995$	0	0
$996$	−16.4587	−0.521514
$997$	30.6461	0.970570	0.485285	−	0.874356i	$-0.338716\pi$
$997$	30.6461	0.970570	0.485285	+	0.874356i	$0.338716\pi$
$998$	−110.439	−3.49589
$999$	11.1479	0.352702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.bf.1.1		12
5.4	even	2		1605.2.a.n.1.12	✓	12
15.14	odd	2		4815.2.a.u.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1605.2.a.n.1.12	✓	12	5.4	even	2
4815.2.a.u.1.1		12	15.14	odd	2
8025.2.a.bf.1.1		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51437 q^{2} -1.00000 q^{3} +4.32208 q^{4} +2.51437 q^{6} +0.976551 q^{7} -5.83856 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.51437 q^{2} -1.00000 q^{3} +4.32208 q^{4} +2.51437 q^{6} +0.976551 q^{7} -5.83856 q^{8} +1.00000 q^{9} +2.69409 q^{11} -4.32208 q^{12} -1.45776 q^{13} -2.45541 q^{14} +6.03618 q^{16} +6.02598 q^{17} -2.51437 q^{18} +4.87630 q^{19} -0.976551 q^{21} -6.77395 q^{22} +8.78876 q^{23} +5.83856 q^{24} +3.66536 q^{26} -1.00000 q^{27} +4.22073 q^{28} -3.21825 q^{29} -1.15455 q^{31} -3.50009 q^{32} -2.69409 q^{33} -15.1516 q^{34} +4.32208 q^{36} -11.1479 q^{37} -12.2608 q^{38} +1.45776 q^{39} -12.0741 q^{41} +2.45541 q^{42} +4.77165 q^{43} +11.6441 q^{44} -22.0982 q^{46} -8.83908 q^{47} -6.03618 q^{48} -6.04635 q^{49} -6.02598 q^{51} -6.30056 q^{52} -8.53554 q^{53} +2.51437 q^{54} -5.70166 q^{56} -4.87630 q^{57} +8.09188 q^{58} +3.95479 q^{59} -0.00540166 q^{61} +2.90298 q^{62} +0.976551 q^{63} -3.27183 q^{64} +6.77395 q^{66} +9.10553 q^{67} +26.0448 q^{68} -8.78876 q^{69} +11.2733 q^{71} -5.83856 q^{72} -13.7654 q^{73} +28.0299 q^{74} +21.0757 q^{76} +2.63092 q^{77} -3.66536 q^{78} -14.9228 q^{79} +1.00000 q^{81} +30.3587 q^{82} +3.80805 q^{83} -4.22073 q^{84} -11.9977 q^{86} +3.21825 q^{87} -15.7296 q^{88} -6.21990 q^{89} -1.42358 q^{91} +37.9857 q^{92} +1.15455 q^{93} +22.2248 q^{94} +3.50009 q^{96} -12.5906 q^{97} +15.2028 q^{98} +2.69409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9	\( 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9} + 4 q^{11} - 15 q^{12} - 13 q^{13} + 4 q^{14} + 13 q^{16} + 4 q^{17} - 3 q^{18} + 14 q^{19} + 7 q^{21} - 15 q^{22} - 11 q^{23} + 3 q^{24} - 8 q^{26} - 12 q^{27} - 16 q^{28} - 7 q^{29} + 4 q^{31} - 4 q^{32} - 4 q^{33} + q^{34} + 15 q^{36} - 24 q^{37} + 11 q^{38} + 13 q^{39} + 13 q^{41} - 4 q^{42} - 25 q^{43} + 10 q^{44} - 22 q^{46} - 19 q^{47} - 13 q^{48} + 9 q^{49} - 4 q^{51} - 20 q^{52} - 11 q^{53} + 3 q^{54} - 37 q^{56} - 14 q^{57} + 2 q^{58} + 8 q^{59} + 7 q^{61} + 11 q^{62} - 7 q^{63} - 19 q^{64} + 15 q^{66} - 33 q^{67} + 24 q^{68} + 11 q^{69} - 3 q^{72} - 34 q^{73} - 27 q^{74} - 9 q^{76} + 29 q^{77} + 8 q^{78} + 12 q^{81} - q^{82} + 24 q^{83} + 16 q^{84} - 36 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} + 30 q^{91} + 28 q^{92} - 4 q^{93} - 8 q^{94} + 4 q^{96} - 16 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9 + 4 * q^11 - 15 * q^12 - 13 * q^13 + 4 * q^14 + 13 * q^16 + 4 * q^17 - 3 * q^18 + 14 * q^19 + 7 * q^21 - 15 * q^22 - 11 * q^23 + 3 * q^24 - 8 * q^26 - 12 * q^27 - 16 * q^28 - 7 * q^29 + 4 * q^31 - 4 * q^32 - 4 * q^33 + q^34 + 15 * q^36 - 24 * q^37 + 11 * q^38 + 13 * q^39 + 13 * q^41 - 4 * q^42 - 25 * q^43 + 10 * q^44 - 22 * q^46 - 19 * q^47 - 13 * q^48 + 9 * q^49 - 4 * q^51 - 20 * q^52 - 11 * q^53 + 3 * q^54 - 37 * q^56 - 14 * q^57 + 2 * q^58 + 8 * q^59 + 7 * q^61 + 11 * q^62 - 7 * q^63 - 19 * q^64 + 15 * q^66 - 33 * q^67 + 24 * q^68 + 11 * q^69 - 3 * q^72 - 34 * q^73 - 27 * q^74 - 9 * q^76 + 29 * q^77 + 8 * q^78 + 12 * q^81 - q^82 + 24 * q^83 + 16 * q^84 - 36 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 + 30 * q^91 + 28 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^96 - 16 * q^97 + 36 * q^98 + 4 * q^99

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