LMFDB - Embedded newform 4025.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
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} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 $ x^12 - 2x^11 - 14x^10 + 26x^9 + 71x^8 - 120x^7 - 162x^6 + 244x^5 + 170x^4 - 210x^3 - 81x^2 + 58*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.53413$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53413 q^{2} -2.66039 q^{3} +0.353561 q^{4} +4.08139 q^{6} +1.00000 q^{7} +2.52585 q^{8} +4.07768 q^{9} +O(q^{10})$	\(q-1.53413 q^{2} -2.66039 q^{3} +0.353561 q^{4} +4.08139 q^{6} +1.00000 q^{7} +2.52585 q^{8} +4.07768 q^{9} -5.84745 q^{11} -0.940610 q^{12} -0.0444244 q^{13} -1.53413 q^{14} -4.58212 q^{16} +7.20179 q^{17} -6.25569 q^{18} -2.29291 q^{19} -2.66039 q^{21} +8.97076 q^{22} -1.00000 q^{23} -6.71976 q^{24} +0.0681529 q^{26} -2.86704 q^{27} +0.353561 q^{28} +7.92658 q^{29} -6.44342 q^{31} +1.97786 q^{32} +15.5565 q^{33} -11.0485 q^{34} +1.44171 q^{36} -0.590146 q^{37} +3.51762 q^{38} +0.118186 q^{39} -11.0590 q^{41} +4.08139 q^{42} +3.01294 q^{43} -2.06743 q^{44} +1.53413 q^{46} -9.08931 q^{47} +12.1902 q^{48} +1.00000 q^{49} -19.1596 q^{51} -0.0157067 q^{52} -5.31834 q^{53} +4.39842 q^{54} +2.52585 q^{56} +6.10003 q^{57} -12.1604 q^{58} -3.75523 q^{59} +12.6040 q^{61} +9.88506 q^{62} +4.07768 q^{63} +6.12993 q^{64} -23.8657 q^{66} +1.58900 q^{67} +2.54627 q^{68} +2.66039 q^{69} -2.44237 q^{71} +10.2996 q^{72} +1.09091 q^{73} +0.905362 q^{74} -0.810682 q^{76} -5.84745 q^{77} -0.181313 q^{78} +0.301216 q^{79} -4.60558 q^{81} +16.9659 q^{82} +12.3450 q^{83} -0.940610 q^{84} -4.62224 q^{86} -21.0878 q^{87} -14.7698 q^{88} +6.18893 q^{89} -0.0444244 q^{91} -0.353561 q^{92} +17.1420 q^{93} +13.9442 q^{94} -5.26188 q^{96} +15.4115 q^{97} -1.53413 q^{98} -23.8440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.53413	−1.08480	−0.542398	−	0.840122i	$-0.682483\pi$
$2$	−1.53413	−1.08480	−0.542398	+	0.840122i	$0.682483\pi$
$3$	−2.66039	−1.53598	−0.767989	−	0.640464i	$-0.778742\pi$
$3$	−2.66039	−1.53598	−0.767989	+	0.640464i	$0.778742\pi$
$4$	0.353561	0.176780
$5$	0	0
$5$	0	0
$6$	4.08139	1.66622
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.52585	0.893025
$9$	4.07768	1.35923
$10$	0	0
$11$	−5.84745	−1.76307	−0.881536	−	0.472117i	$-0.843490\pi$
$11$	−5.84745	−1.76307	−0.881536	+	0.472117i	$0.843490\pi$
$12$	−0.940610	−0.271531
$13$	−0.0444244	−0.0123211	−0.00616055	−	0.999981i	$-0.501961\pi$
$13$	−0.0444244	−0.0123211	−0.00616055	+	0.999981i	$0.501961\pi$
$14$	−1.53413	−0.410014
$15$	0	0
$16$	−4.58212	−1.14553
$17$	7.20179	1.74669	0.873345	−	0.487103i	$-0.161946\pi$
$17$	7.20179	1.74669	0.873345	+	0.487103i	$0.161946\pi$
$18$	−6.25569	−1.47448
$19$	−2.29291	−0.526029	−0.263015	−	0.964792i	$-0.584717\pi$
$19$	−2.29291	−0.526029	−0.263015	+	0.964792i	$0.584717\pi$
$20$	0	0
$21$	−2.66039	−0.580545
$22$	8.97076	1.91257
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−6.71976	−1.37167
$25$	0	0
$26$	0.0681529	0.0133659
$27$	−2.86704	−0.551762
$28$	0.353561	0.0668167
$29$	7.92658	1.47193	0.735965	−	0.677020i	$-0.236729\pi$
$29$	7.92658	1.47193	0.735965	+	0.677020i	$0.236729\pi$
$30$	0	0
$31$	−6.44342	−1.15727	−0.578636	−	0.815586i	$-0.696415\pi$
$31$	−6.44342	−1.15727	−0.578636	+	0.815586i	$0.696415\pi$
$32$	1.97786	0.349640
$33$	15.5565	2.70804
$34$	−11.0485	−1.89480
$35$	0	0
$36$	1.44171	0.240285
$37$	−0.590146	−0.0970195	−0.0485097	−	0.998823i	$-0.515447\pi$
$37$	−0.590146	−0.0970195	−0.0485097	+	0.998823i	$0.515447\pi$
$38$	3.51762	0.570634
$39$	0.118186	0.0189249
$40$	0	0
$41$	−11.0590	−1.72712	−0.863561	−	0.504244i	$-0.831771\pi$
$41$	−11.0590	−1.72712	−0.863561	+	0.504244i	$0.831771\pi$
$42$	4.08139	0.629772
$43$	3.01294	0.459468	0.229734	−	0.973253i	$-0.426214\pi$
$43$	3.01294	0.459468	0.229734	+	0.973253i	$0.426214\pi$
$44$	−2.06743	−0.311677
$45$	0	0
$46$	1.53413	0.226195
$47$	−9.08931	−1.32581	−0.662906	−	0.748703i	$-0.730677\pi$
$47$	−9.08931	−1.32581	−0.662906	+	0.748703i	$0.730677\pi$
$48$	12.1902	1.75951
$49$	1.00000	0.142857
$50$	0	0
$51$	−19.1596	−2.68287
$52$	−0.0157067	−0.00217813
$53$	−5.31834	−0.730530	−0.365265	−	0.930904i	$-0.619022\pi$
$53$	−5.31834	−0.730530	−0.365265	+	0.930904i	$0.619022\pi$
$54$	4.39842	0.598549
$55$	0	0
$56$	2.52585	0.337532
$57$	6.10003	0.807969
$58$	−12.1604	−1.59674
$59$	−3.75523	−0.488890	−0.244445	−	0.969663i	$-0.578606\pi$
$59$	−3.75523	−0.488890	−0.244445	+	0.969663i	$0.578606\pi$
$60$	0	0
$61$	12.6040	1.61377	0.806886	−	0.590707i	$-0.201151\pi$
$61$	12.6040	1.61377	0.806886	+	0.590707i	$0.201151\pi$
$62$	9.88506	1.25540
$63$	4.07768	0.513739
$64$	6.12993	0.766242
$65$	0	0
$66$	−23.8657	−2.93767
$67$	1.58900	0.194127	0.0970637	−	0.995278i	$-0.469055\pi$
$67$	1.58900	0.194127	0.0970637	+	0.995278i	$0.469055\pi$
$68$	2.54627	0.308781
$69$	2.66039	0.320273
$70$	0	0
$71$	−2.44237	−0.289856	−0.144928	−	0.989442i	$-0.546295\pi$
$71$	−2.44237	−0.289856	−0.144928	+	0.989442i	$0.546295\pi$
$72$	10.2996	1.21382
$73$	1.09091	0.127682	0.0638408	−	0.997960i	$-0.479665\pi$
$73$	1.09091	0.127682	0.0638408	+	0.997960i	$0.479665\pi$
$74$	0.905362	0.105246
$75$	0	0
$76$	−0.810682	−0.0929916
$77$	−5.84745	−0.666379
$78$	−0.181313	−0.0205297
$79$	0.301216	0.0338894	0.0169447	−	0.999856i	$-0.494606\pi$
$79$	0.301216	0.0338894	0.0169447	+	0.999856i	$0.494606\pi$
$80$	0	0
$81$	−4.60558	−0.511731
$82$	16.9659	1.87357
$83$	12.3450	1.35504	0.677519	−	0.735505i	$-0.263055\pi$
$83$	12.3450	1.35504	0.677519	+	0.735505i	$0.263055\pi$
$84$	−0.940610	−0.102629
$85$	0	0
$86$	−4.62224	−0.498429
$87$	−21.0878	−2.26085
$88$	−14.7698	−1.57447
$89$	6.18893	0.656025	0.328012	−	0.944673i	$-0.393621\pi$
$89$	6.18893	0.656025	0.328012	+	0.944673i	$0.393621\pi$
$90$	0	0
$91$	−0.0444244	−0.00465694
$92$	−0.353561	−0.0368613
$93$	17.1420	1.77754
$94$	13.9442	1.43823
$95$	0	0
$96$	−5.26188	−0.537039
$97$	15.4115	1.56480	0.782400	−	0.622777i	$-0.213996\pi$
$97$	15.4115	1.56480	0.782400	+	0.622777i	$0.213996\pi$
$98$	−1.53413	−0.154971
$99$	−23.8440	−2.39641
$100$	0	0
$101$	16.6168	1.65343	0.826716	−	0.562620i	$-0.190206\pi$
$101$	16.6168	1.65343	0.826716	+	0.562620i	$0.190206\pi$
$102$	29.3933	2.91037
$103$	−10.2458	−1.00955	−0.504776	−	0.863250i	$-0.668425\pi$
$103$	−10.2458	−1.00955	−0.504776	+	0.863250i	$0.668425\pi$
$104$	−0.112210	−0.0110030
$105$	0	0
$106$	8.15904	0.792476
$107$	14.8612	1.43668	0.718342	−	0.695690i	$-0.244901\pi$
$107$	14.8612	1.43668	0.718342	+	0.695690i	$0.244901\pi$
$108$	−1.01367	−0.0975408
$109$	−6.48526	−0.621175	−0.310588	−	0.950545i	$-0.600526\pi$
$109$	−6.48526	−0.621175	−0.310588	+	0.950545i	$0.600526\pi$
$110$	0	0
$111$	1.57002	0.149020
$112$	−4.58212	−0.432969
$113$	6.08765	0.572678	0.286339	−	0.958128i	$-0.407562\pi$
$113$	6.08765	0.572678	0.286339	+	0.958128i	$0.407562\pi$
$114$	−9.35825	−0.876480
$115$	0	0
$116$	2.80253	0.260208
$117$	−0.181148	−0.0167472
$118$	5.76103	0.530345
$119$	7.20179	0.660187
$120$	0	0
$121$	23.1926	2.10842
$122$	−19.3361	−1.75061
$123$	29.4212	2.65282
$124$	−2.27814	−0.204583
$125$	0	0
$126$	−6.25569	−0.557302
$127$	−3.41982	−0.303460	−0.151730	−	0.988422i	$-0.548484\pi$
$127$	−3.41982	−0.303460	−0.151730	+	0.988422i	$0.548484\pi$
$128$	−13.3598	−1.18085
$129$	−8.01558	−0.705733
$130$	0	0
$131$	12.2790	1.07282	0.536412	−	0.843956i	$-0.319779\pi$
$131$	12.2790	1.07282	0.536412	+	0.843956i	$0.319779\pi$
$132$	5.50017	0.478728
$133$	−2.29291	−0.198820
$134$	−2.43774	−0.210588
$135$	0	0
$136$	18.1907	1.55984
$137$	−1.21300	−0.103634	−0.0518168	−	0.998657i	$-0.516501\pi$
$137$	−1.21300	−0.103634	−0.0518168	+	0.998657i	$0.516501\pi$
$138$	−4.08139	−0.347431
$139$	7.53216	0.638870	0.319435	−	0.947608i	$-0.396507\pi$
$139$	7.53216	0.638870	0.319435	+	0.947608i	$0.396507\pi$
$140$	0	0
$141$	24.1811	2.03642
$142$	3.74692	0.314435
$143$	0.259769	0.0217230
$144$	−18.6844	−1.55703
$145$	0	0
$146$	−1.67360	−0.138508
$147$	−2.66039	−0.219425
$148$	−0.208653	−0.0171511
$149$	−2.24652	−0.184042	−0.0920210	−	0.995757i	$-0.529333\pi$
$149$	−2.24652	−0.184042	−0.0920210	+	0.995757i	$0.529333\pi$
$150$	0	0
$151$	−13.9643	−1.13640	−0.568198	−	0.822892i	$-0.692359\pi$
$151$	−13.9643	−1.13640	−0.568198	+	0.822892i	$0.692359\pi$
$152$	−5.79155	−0.469757
$153$	29.3666	2.37414
$154$	8.97076	0.722884
$155$	0	0
$156$	0.0417860	0.00334556
$157$	0.0899912	0.00718208	0.00359104	−	0.999994i	$-0.498857\pi$
$157$	0.0899912	0.00718208	0.00359104	+	0.999994i	$0.498857\pi$
$158$	−0.462104	−0.0367631
$159$	14.1489	1.12208
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	7.06557	0.555124
$163$	7.53351	0.590070	0.295035	−	0.955486i	$-0.404669\pi$
$163$	7.53351	0.590070	0.295035	+	0.955486i	$0.404669\pi$
$164$	−3.91002	−0.305321
$165$	0	0
$166$	−18.9388	−1.46994
$167$	−7.56740	−0.585583	−0.292792	−	0.956176i	$-0.594584\pi$
$167$	−7.56740	−0.585583	−0.292792	+	0.956176i	$0.594584\pi$
$168$	−6.71976	−0.518441
$169$	−12.9980	−0.999848
$170$	0	0
$171$	−9.34973	−0.714992
$172$	1.06526	0.0812250
$173$	−6.89548	−0.524254	−0.262127	−	0.965033i	$-0.584424\pi$
$173$	−6.89548	−0.524254	−0.262127	+	0.965033i	$0.584424\pi$
$174$	32.3515	2.45256
$175$	0	0
$176$	26.7937	2.01965
$177$	9.99039	0.750924
$178$	−9.49463	−0.711653
$179$	22.7833	1.70290	0.851451	−	0.524434i	$-0.175723\pi$
$179$	22.7833	1.70290	0.851451	+	0.524434i	$0.175723\pi$
$180$	0	0
$181$	−9.93003	−0.738093	−0.369047	−	0.929411i	$-0.620316\pi$
$181$	−9.93003	−0.738093	−0.369047	+	0.929411i	$0.620316\pi$
$182$	0.0681529	0.00505183
$183$	−33.5315	−2.47872
$184$	−2.52585	−0.186208
$185$	0	0
$186$	−26.2981	−1.92827
$187$	−42.1121	−3.07954
$188$	−3.21362	−0.234378
$189$	−2.86704	−0.208547
$190$	0	0
$191$	−6.39126	−0.462455	−0.231228	−	0.972900i	$-0.574274\pi$
$191$	−6.39126	−0.462455	−0.231228	+	0.972900i	$0.574274\pi$
$192$	−16.3080	−1.17693
$193$	−7.98914	−0.575071	−0.287535	−	0.957770i	$-0.592836\pi$
$193$	−7.98914	−0.575071	−0.287535	+	0.957770i	$0.592836\pi$
$194$	−23.6433	−1.69749
$195$	0	0
$196$	0.353561	0.0252543
$197$	18.2321	1.29898	0.649492	−	0.760369i	$-0.274982\pi$
$197$	18.2321	1.29898	0.649492	+	0.760369i	$0.274982\pi$
$198$	36.5798	2.59962
$199$	−12.7332	−0.902632	−0.451316	−	0.892364i	$-0.649045\pi$
$199$	−12.7332	−0.902632	−0.451316	+	0.892364i	$0.649045\pi$
$200$	0	0
$201$	−4.22736	−0.298175
$202$	−25.4923	−1.79363
$203$	7.92658	0.556337
$204$	−6.77407	−0.474280
$205$	0	0
$206$	15.7185	1.09516
$207$	−4.07768	−0.283418
$208$	0.203558	0.0141142
$209$	13.4077	0.927427
$210$	0	0
$211$	−4.75457	−0.327318	−0.163659	−	0.986517i	$-0.552330\pi$
$211$	−4.75457	−0.327318	−0.163659	+	0.986517i	$0.552330\pi$
$212$	−1.88036	−0.129143
$213$	6.49766	0.445213
$214$	−22.7990	−1.55851
$215$	0	0
$216$	−7.24173	−0.492737
$217$	−6.44342	−0.437408
$218$	9.94925	0.673848
$219$	−2.90225	−0.196116
$220$	0	0
$221$	−0.319935	−0.0215211
$222$	−2.40862	−0.161656
$223$	26.5866	1.78037	0.890184	−	0.455602i	$-0.150576\pi$
$223$	26.5866	1.78037	0.890184	+	0.455602i	$0.150576\pi$
$224$	1.97786	0.132151
$225$	0	0
$226$	−9.33926	−0.621238
$227$	−3.76751	−0.250059	−0.125029	−	0.992153i	$-0.539902\pi$
$227$	−3.76751	−0.250059	−0.125029	+	0.992153i	$0.539902\pi$
$228$	2.15673	0.142833
$229$	−13.5176	−0.893270	−0.446635	−	0.894716i	$-0.647378\pi$
$229$	−13.5176	−0.893270	−0.446635	+	0.894716i	$0.647378\pi$
$230$	0	0
$231$	15.5565	1.02354
$232$	20.0214	1.31447
$233$	−6.81789	−0.446655	−0.223327	−	0.974743i	$-0.571692\pi$
$233$	−6.81789	−0.446655	−0.223327	+	0.974743i	$0.571692\pi$
$234$	0.277905	0.0181672
$235$	0	0
$236$	−1.32770	−0.0864262
$237$	−0.801351	−0.0520533
$238$	−11.0485	−0.716167
$239$	7.35354	0.475661	0.237831	−	0.971307i	$-0.423564\pi$
$239$	7.35354	0.475661	0.237831	+	0.971307i	$0.423564\pi$
$240$	0	0
$241$	−19.8543	−1.27892	−0.639462	−	0.768822i	$-0.720843\pi$
$241$	−19.8543	−1.27892	−0.639462	+	0.768822i	$0.720843\pi$
$242$	−35.5806	−2.28721
$243$	20.8538	1.33777
$244$	4.45627	0.285283
$245$	0	0
$246$	−45.1360	−2.87777
$247$	0.101861	0.00648126
$248$	−16.2751	−1.03347
$249$	−32.8425	−2.08131
$250$	0	0
$251$	−13.7478	−0.867755	−0.433878	−	0.900972i	$-0.642855\pi$
$251$	−13.7478	−0.867755	−0.433878	+	0.900972i	$0.642855\pi$
$252$	1.44171	0.0908190
$253$	5.84745	0.367626
$254$	5.24646	0.329192
$255$	0	0
$256$	8.23591	0.514744
$257$	1.04042	0.0648997	0.0324499	−	0.999473i	$-0.489669\pi$
$257$	1.04042	0.0648997	0.0324499	+	0.999473i	$0.489669\pi$
$258$	12.2970	0.765575
$259$	−0.590146	−0.0366699
$260$	0	0
$261$	32.3220	2.00068
$262$	−18.8376	−1.16379
$263$	−12.7175	−0.784192	−0.392096	−	0.919924i	$-0.628250\pi$
$263$	−12.7175	−0.784192	−0.392096	+	0.919924i	$0.628250\pi$
$264$	39.2934	2.41834
$265$	0	0
$266$	3.51762	0.215679
$267$	−16.4650	−1.00764
$268$	0.561809	0.0343179
$269$	−18.4312	−1.12377	−0.561885	−	0.827216i	$-0.689924\pi$
$269$	−18.4312	−1.12377	−0.561885	+	0.827216i	$0.689924\pi$
$270$	0	0
$271$	−22.2816	−1.35351	−0.676755	−	0.736209i	$-0.736614\pi$
$271$	−22.2816	−1.35351	−0.676755	+	0.736209i	$0.736614\pi$
$272$	−32.9994	−2.00088
$273$	0.118186	0.00715295
$274$	1.86090	0.112421
$275$	0	0
$276$	0.940610	0.0566181
$277$	−22.6500	−1.36091	−0.680453	−	0.732791i	$-0.738217\pi$
$277$	−22.6500	−1.36091	−0.680453	+	0.732791i	$0.738217\pi$
$278$	−11.5553	−0.693043
$279$	−26.2742	−1.57299
$280$	0	0
$281$	18.7126	1.11630	0.558151	−	0.829739i	$-0.311511\pi$
$281$	18.7126	1.11630	0.558151	+	0.829739i	$0.311511\pi$
$282$	−37.0970	−2.20909
$283$	5.98802	0.355951	0.177975	−	0.984035i	$-0.443045\pi$
$283$	5.98802	0.355951	0.177975	+	0.984035i	$0.443045\pi$
$284$	−0.863527	−0.0512409
$285$	0	0
$286$	−0.398520	−0.0235650
$287$	−11.0590	−0.652791
$288$	8.06508	0.475239
$289$	34.8657	2.05092
$290$	0	0
$291$	−41.0006	−2.40350
$292$	0.385704	0.0225716
$293$	−23.5579	−1.37627	−0.688133	−	0.725585i	$-0.741569\pi$
$293$	−23.5579	−1.37627	−0.688133	+	0.725585i	$0.741569\pi$
$294$	4.08139	0.238031
$295$	0	0
$296$	−1.49062	−0.0866408
$297$	16.7649	0.972796
$298$	3.44646	0.199648
$299$	0.0444244	0.00256913
$300$	0	0
$301$	3.01294	0.173663
$302$	21.4230	1.23276
$303$	−44.2071	−2.53963
$304$	10.5064	0.602582
$305$	0	0
$306$	−45.0522	−2.57546
$307$	30.5545	1.74384	0.871918	−	0.489653i	$-0.162876\pi$
$307$	30.5545	1.74384	0.871918	+	0.489653i	$0.162876\pi$
$308$	−2.06743	−0.117803
$309$	27.2579	1.55065
$310$	0	0
$311$	12.8768	0.730176	0.365088	−	0.930973i	$-0.381039\pi$
$311$	12.8768	0.730176	0.365088	+	0.930973i	$0.381039\pi$
$312$	0.298521	0.0169004
$313$	−25.9654	−1.46765	−0.733824	−	0.679339i	$-0.762267\pi$
$313$	−25.9654	−1.46765	−0.733824	+	0.679339i	$0.762267\pi$
$314$	−0.138058	−0.00779109
$315$	0	0
$316$	0.106498	0.00599098
$317$	−5.00852	−0.281307	−0.140653	−	0.990059i	$-0.544920\pi$
$317$	−5.00852	−0.281307	−0.140653	+	0.990059i	$0.544920\pi$
$318$	−21.7062	−1.21722
$319$	−46.3503	−2.59512
$320$	0	0
$321$	−39.5365	−2.20671
$322$	1.53413	0.0854938
$323$	−16.5130	−0.918809
$324$	−1.62835	−0.0904641
$325$	0	0
$326$	−11.5574	−0.640105
$327$	17.2533	0.954111
$328$	−27.9334	−1.54236
$329$	−9.08931	−0.501110
$330$	0	0
$331$	−29.6122	−1.62763	−0.813816	−	0.581123i	$-0.802614\pi$
$331$	−29.6122	−1.62763	−0.813816	+	0.581123i	$0.802614\pi$
$332$	4.36470	0.239544
$333$	−2.40643	−0.131871
$334$	11.6094	0.635238
$335$	0	0
$336$	12.1902	0.665031
$337$	−18.2156	−0.992269	−0.496135	−	0.868246i	$-0.665248\pi$
$337$	−18.2156	−0.992269	−0.496135	+	0.868246i	$0.665248\pi$
$338$	19.9407	1.08463
$339$	−16.1955	−0.879620
$340$	0	0
$341$	37.6776	2.04035
$342$	14.3437	0.775620
$343$	1.00000	0.0539949
$344$	7.61024	0.410316
$345$	0	0
$346$	10.5786	0.568708
$347$	5.01092	0.269000	0.134500	−	0.990914i	$-0.457057\pi$
$347$	5.01092	0.269000	0.134500	+	0.990914i	$0.457057\pi$
$348$	−7.45582	−0.399674
$349$	−4.42081	−0.236641	−0.118320	−	0.992975i	$-0.537751\pi$
$349$	−4.42081	−0.236641	−0.118320	+	0.992975i	$0.537751\pi$
$350$	0	0
$351$	0.127366	0.00679832
$352$	−11.5654	−0.616440
$353$	10.7456	0.571931	0.285965	−	0.958240i	$-0.407686\pi$
$353$	10.7456	0.571931	0.285965	+	0.958240i	$0.407686\pi$
$354$	−15.3266	−0.814598
$355$	0	0
$356$	2.18816	0.115972
$357$	−19.1596	−1.01403
$358$	−34.9526	−1.84730
$359$	−11.5145	−0.607711	−0.303855	−	0.952718i	$-0.598274\pi$
$359$	−11.5145	−0.607711	−0.303855	+	0.952718i	$0.598274\pi$
$360$	0	0
$361$	−13.7426	−0.723293
$362$	15.2340	0.800680
$363$	−61.7015	−3.23849
$364$	−0.0157067	−0.000823256 0
$365$	0	0
$366$	51.4417	2.68890
$367$	3.15274	0.164572	0.0822859	−	0.996609i	$-0.473778\pi$
$367$	3.15274	0.164572	0.0822859	+	0.996609i	$0.473778\pi$
$368$	4.58212	0.238859
$369$	−45.0949	−2.34755
$370$	0	0
$371$	−5.31834	−0.276114
$372$	6.06075	0.314235
$373$	9.25639	0.479278	0.239639	−	0.970862i	$-0.422971\pi$
$373$	9.25639	0.479278	0.239639	+	0.970862i	$0.422971\pi$
$374$	64.6055	3.34067
$375$	0	0
$376$	−22.9583	−1.18398
$377$	−0.352134	−0.0181358
$378$	4.39842	0.226230
$379$	−36.5965	−1.87984	−0.939919	−	0.341397i	$-0.889100\pi$
$379$	−36.5965	−1.87984	−0.939919	+	0.341397i	$0.889100\pi$
$380$	0	0
$381$	9.09806	0.466108
$382$	9.80504	0.501669
$383$	18.3797	0.939156	0.469578	−	0.882891i	$-0.344406\pi$
$383$	18.3797	0.939156	0.469578	+	0.882891i	$0.344406\pi$
$384$	35.5424	1.81377
$385$	0	0
$386$	12.2564	0.623834
$387$	12.2858	0.624521
$388$	5.44890	0.276626
$389$	−1.84084	−0.0933344	−0.0466672	−	0.998910i	$-0.514860\pi$
$389$	−1.84084	−0.0933344	−0.0466672	+	0.998910i	$0.514860\pi$
$390$	0	0
$391$	−7.20179	−0.364210
$392$	2.52585	0.127575
$393$	−32.6670	−1.64783
$394$	−27.9704	−1.40913
$395$	0	0
$396$	−8.43031	−0.423639
$397$	30.9012	1.55089	0.775443	−	0.631418i	$-0.217527\pi$
$397$	30.9012	1.55089	0.775443	+	0.631418i	$0.217527\pi$
$398$	19.5344	0.979171
$399$	6.10003	0.305383
$400$	0	0
$401$	−9.04586	−0.451728	−0.225864	−	0.974159i	$-0.572521\pi$
$401$	−9.04586	−0.451728	−0.225864	+	0.974159i	$0.572521\pi$
$402$	6.48533	0.323459
$403$	0.286245	0.0142589
$404$	5.87504	0.292294
$405$	0	0
$406$	−12.1604	−0.603512
$407$	3.45085	0.171052
$408$	−48.3943	−2.39587
$409$	9.73025	0.481130	0.240565	−	0.970633i	$-0.422667\pi$
$409$	9.73025	0.481130	0.240565	+	0.970633i	$0.422667\pi$
$410$	0	0
$411$	3.22705	0.159179
$412$	−3.62253	−0.178469
$413$	−3.75523	−0.184783
$414$	6.25569	0.307451
$415$	0	0
$416$	−0.0878653	−0.00430795
$417$	−20.0385	−0.981289
$418$	−20.5691	−1.00607
$419$	−6.99729	−0.341840	−0.170920	−	0.985285i	$-0.554674\pi$
$419$	−6.99729	−0.341840	−0.170920	+	0.985285i	$0.554674\pi$
$420$	0	0
$421$	−16.5420	−0.806209	−0.403104	−	0.915154i	$-0.632069\pi$
$421$	−16.5420	−0.806209	−0.403104	+	0.915154i	$0.632069\pi$
$422$	7.29413	0.355073
$423$	−37.0633	−1.80208
$424$	−13.4334	−0.652381
$425$	0	0
$426$	−9.96828	−0.482965
$427$	12.6040	0.609948
$428$	5.25433	0.253978
$429$	−0.691088	−0.0333660
$430$	0	0
$431$	4.03469	0.194344	0.0971721	−	0.995268i	$-0.469020\pi$
$431$	4.03469	0.194344	0.0971721	+	0.995268i	$0.469020\pi$
$432$	13.1371	0.632060
$433$	−10.8719	−0.522468	−0.261234	−	0.965276i	$-0.584129\pi$
$433$	−10.8719	−0.522468	−0.261234	+	0.965276i	$0.584129\pi$
$434$	9.88506	0.474498
$435$	0	0
$436$	−2.29293	−0.109812
$437$	2.29291	0.109685
$438$	4.45244	0.212746
$439$	22.5326	1.07542	0.537711	−	0.843129i	$-0.319289\pi$
$439$	22.5326	1.07542	0.537711	+	0.843129i	$0.319289\pi$
$440$	0	0
$441$	4.07768	0.194175
$442$	0.490822	0.0233460
$443$	40.8033	1.93862	0.969312	−	0.245834i	$-0.0790620\pi$
$443$	40.8033	1.93862	0.969312	+	0.245834i	$0.0790620\pi$
$444$	0.555098	0.0263438
$445$	0	0
$446$	−40.7873	−1.93133
$447$	5.97662	0.282684
$448$	6.12993	0.289612
$449$	38.8789	1.83481	0.917404	−	0.397957i	$-0.130281\pi$
$449$	38.8789	1.83481	0.917404	+	0.397957i	$0.130281\pi$
$450$	0	0
$451$	64.6668	3.04504
$452$	2.15236	0.101238
$453$	37.1504	1.74548
$454$	5.77986	0.271262
$455$	0	0
$456$	15.4078	0.721536
$457$	−23.5917	−1.10357	−0.551787	−	0.833985i	$-0.686054\pi$
$457$	−23.5917	−1.10357	−0.551787	+	0.833985i	$0.686054\pi$
$458$	20.7378	0.969015
$459$	−20.6478	−0.963757
$460$	0	0
$461$	13.4335	0.625659	0.312829	−	0.949809i	$-0.398723\pi$
$461$	13.4335	0.625659	0.312829	+	0.949809i	$0.398723\pi$
$462$	−23.8657	−1.11033
$463$	−35.0951	−1.63101	−0.815505	−	0.578750i	$-0.803541\pi$
$463$	−35.0951	−1.63101	−0.815505	+	0.578750i	$0.803541\pi$
$464$	−36.3205	−1.68614
$465$	0	0
$466$	10.4595	0.484529
$467$	29.4556	1.36304	0.681521	−	0.731798i	$-0.261319\pi$
$467$	29.4556	1.36304	0.681521	+	0.731798i	$0.261319\pi$
$468$	−0.0640469	−0.00296057
$469$	1.58900	0.0733733
$470$	0	0
$471$	−0.239412	−0.0110315
$472$	−9.48518	−0.436591
$473$	−17.6180	−0.810076
$474$	1.22938	0.0564672
$475$	0	0
$476$	2.54627	0.116708
$477$	−21.6865	−0.992955
$478$	−11.2813	−0.515995
$479$	27.6443	1.26310	0.631550	−	0.775335i	$-0.282419\pi$
$479$	27.6443	1.26310	0.631550	+	0.775335i	$0.282419\pi$
$480$	0	0
$481$	0.0262169	0.00119539
$482$	30.4590	1.38737
$483$	2.66039	0.121052
$484$	8.20001	0.372728
$485$	0	0
$486$	−31.9924	−1.45121
$487$	−10.5707	−0.479004	−0.239502	−	0.970896i	$-0.576984\pi$
$487$	−10.5707	−0.479004	−0.239502	+	0.970896i	$0.576984\pi$
$488$	31.8358	1.44114
$489$	−20.0421	−0.906334
$490$	0	0
$491$	−11.7758	−0.531434	−0.265717	−	0.964051i	$-0.585609\pi$
$491$	−11.7758	−0.531434	−0.265717	+	0.964051i	$0.585609\pi$
$492$	10.4022	0.468967
$493$	57.0856	2.57100
$494$	−0.156268	−0.00703084
$495$	0	0
$496$	29.5245	1.32569
$497$	−2.44237	−0.109555
$498$	50.3847	2.25779
$499$	19.8327	0.887831	0.443916	−	0.896069i	$-0.353589\pi$
$499$	19.8327	0.887831	0.443916	+	0.896069i	$0.353589\pi$
$500$	0	0
$501$	20.1322	0.899442
$502$	21.0910	0.941337
$503$	−39.7040	−1.77032	−0.885158	−	0.465291i	$-0.845950\pi$
$503$	−39.7040	−1.77032	−0.885158	+	0.465291i	$0.845950\pi$
$504$	10.2996	0.458782
$505$	0	0
$506$	−8.97076	−0.398799
$507$	34.5798	1.53574
$508$	−1.20912	−0.0536458
$509$	−35.5293	−1.57481	−0.787404	−	0.616437i	$-0.788576\pi$
$509$	−35.5293	−1.57481	−0.787404	+	0.616437i	$0.788576\pi$
$510$	0	0
$511$	1.09091	0.0482591
$512$	14.0847	0.622463
$513$	6.57386	0.290243
$514$	−1.59614	−0.0704029
$515$	0	0
$516$	−2.83400	−0.124760
$517$	53.1492	2.33750
$518$	0.905362	0.0397793
$519$	18.3447	0.805241
$520$	0	0
$521$	−13.0961	−0.573753	−0.286876	−	0.957968i	$-0.592617\pi$
$521$	−13.0961	−0.573753	−0.286876	+	0.957968i	$0.592617\pi$
$522$	−49.5863	−2.17033
$523$	−15.4915	−0.677395	−0.338698	−	0.940895i	$-0.609986\pi$
$523$	−15.4915	−0.677395	−0.338698	+	0.940895i	$0.609986\pi$
$524$	4.34138	0.189654
$525$	0	0
$526$	19.5102	0.850687
$527$	−46.4041	−2.02140
$528$	−71.2817	−3.10214
$529$	1.00000	0.0434783
$530$	0	0
$531$	−15.3126	−0.664512
$532$	−0.810682	−0.0351475
$533$	0.491288	0.0212801
$534$	25.2594	1.09308
$535$	0	0
$536$	4.01359	0.173361
$537$	−60.6124	−2.61562
$538$	28.2759	1.21906
$539$	−5.84745	−0.251867
$540$	0	0
$541$	−30.6655	−1.31841	−0.659205	−	0.751963i	$-0.729107\pi$
$541$	−30.6655	−1.31841	−0.659205	+	0.751963i	$0.729107\pi$
$542$	34.1829	1.46828
$543$	26.4178	1.13369
$544$	14.2441	0.610712
$545$	0	0
$546$	−0.181313	−0.00775949
$547$	−13.4001	−0.572946	−0.286473	−	0.958088i	$-0.592483\pi$
$547$	−13.4001	−0.572946	−0.286473	+	0.958088i	$0.592483\pi$
$548$	−0.428869	−0.0183204
$549$	51.3949	2.19348
$550$	0	0
$551$	−18.1749	−0.774278
$552$	6.71976	0.286012
$553$	0.301216	0.0128090
$554$	34.7481	1.47630
$555$	0	0
$556$	2.66308	0.112940
$557$	−29.5160	−1.25063	−0.625316	−	0.780371i	$-0.715030\pi$
$557$	−29.5160	−1.25063	−0.625316	+	0.780371i	$0.715030\pi$
$558$	40.3081	1.70638
$559$	−0.133848	−0.00566116
$560$	0	0
$561$	112.035	4.73010
$562$	−28.7077	−1.21096
$563$	16.7153	0.704464	0.352232	−	0.935913i	$-0.385423\pi$
$563$	16.7153	0.704464	0.352232	+	0.935913i	$0.385423\pi$
$564$	8.54949	0.359999
$565$	0	0
$566$	−9.18641	−0.386134
$567$	−4.60558	−0.193416
$568$	−6.16908	−0.258849
$569$	−0.879898	−0.0368872	−0.0184436	−	0.999830i	$-0.505871\pi$
$569$	−0.879898	−0.0368872	−0.0184436	+	0.999830i	$0.505871\pi$
$570$	0	0
$571$	−27.4017	−1.14672	−0.573362	−	0.819302i	$-0.694361\pi$
$571$	−27.4017	−1.14672	−0.573362	+	0.819302i	$0.694361\pi$
$572$	0.0918442	0.00384020
$573$	17.0032	0.710321
$574$	16.9659	0.708144
$575$	0	0
$576$	24.9959	1.04150
$577$	6.85040	0.285186	0.142593	−	0.989781i	$-0.454456\pi$
$577$	6.85040	0.285186	0.142593	+	0.989781i	$0.454456\pi$
$578$	−53.4886	−2.22483
$579$	21.2542	0.883295
$580$	0	0
$581$	12.3450	0.512156
$582$	62.9003	2.60730
$583$	31.0987	1.28798
$584$	2.75548	0.114023
$585$	0	0
$586$	36.1409	1.49297
$587$	−7.19749	−0.297072	−0.148536	−	0.988907i	$-0.547456\pi$
$587$	−7.19749	−0.297072	−0.148536	+	0.988907i	$0.547456\pi$
$588$	−0.940610	−0.0387901
$589$	14.7742	0.608759
$590$	0	0
$591$	−48.5045	−1.99521
$592$	2.70412	0.111139
$593$	−5.50071	−0.225887	−0.112944	−	0.993601i	$-0.536028\pi$
$593$	−5.50071	−0.225887	−0.112944	+	0.993601i	$0.536028\pi$
$594$	−25.7195	−1.05528
$595$	0	0
$596$	−0.794281	−0.0325350
$597$	33.8753	1.38642
$598$	−0.0681529	−0.00278698
$599$	−21.3379	−0.871845	−0.435922	−	0.899984i	$-0.643578\pi$
$599$	−21.3379	−0.871845	−0.435922	+	0.899984i	$0.643578\pi$
$600$	0	0
$601$	−3.76359	−0.153520	−0.0767599	−	0.997050i	$-0.524458\pi$
$601$	−3.76359	−0.153520	−0.0767599	+	0.997050i	$0.524458\pi$
$602$	−4.62224	−0.188388
$603$	6.47943	0.263863
$604$	−4.93722	−0.200893
$605$	0	0
$606$	67.8196	2.75498
$607$	−27.7160	−1.12496	−0.562479	−	0.826812i	$-0.690152\pi$
$607$	−27.7160	−1.12496	−0.562479	+	0.826812i	$0.690152\pi$
$608$	−4.53505	−0.183921
$609$	−21.0878	−0.854521
$610$	0	0
$611$	0.403787	0.0163355
$612$	10.3829	0.419702
$613$	−23.4433	−0.946866	−0.473433	−	0.880830i	$-0.656985\pi$
$613$	−23.4433	−0.946866	−0.473433	+	0.880830i	$0.656985\pi$
$614$	−46.8746	−1.89170
$615$	0	0
$616$	−14.7698	−0.595092
$617$	−19.6379	−0.790594	−0.395297	−	0.918553i	$-0.629358\pi$
$617$	−19.6379	−0.790594	−0.395297	+	0.918553i	$0.629358\pi$
$618$	−41.8172	−1.68214
$619$	20.6941	0.831766	0.415883	−	0.909418i	$-0.363473\pi$
$619$	20.6941	0.831766	0.415883	+	0.909418i	$0.363473\pi$
$620$	0	0
$621$	2.86704	0.115050
$622$	−19.7547	−0.792091
$623$	6.18893	0.247954
$624$	−0.541543	−0.0216791
$625$	0	0
$626$	39.8343	1.59210
$627$	−35.6696	−1.42451
$628$	0.0318174	0.00126965
$629$	−4.25011	−0.169463
$630$	0	0
$631$	−12.1580	−0.484002	−0.242001	−	0.970276i	$-0.577804\pi$
$631$	−12.1580	−0.484002	−0.242001	+	0.970276i	$0.577804\pi$
$632$	0.760827	0.0302641
$633$	12.6490	0.502753
$634$	7.68373	0.305160
$635$	0	0
$636$	5.00248	0.198361
$637$	−0.0444244	−0.00176016
$638$	71.1075	2.81517
$639$	−9.95921	−0.393980
$640$	0	0
$641$	0.520035	0.0205402	0.0102701	−	0.999947i	$-0.496731\pi$
$641$	0.520035	0.0205402	0.0102701	+	0.999947i	$0.496731\pi$
$642$	60.6542	2.39383
$643$	−4.35842	−0.171879	−0.0859396	−	0.996300i	$-0.527389\pi$
$643$	−4.35842	−0.171879	−0.0859396	+	0.996300i	$0.527389\pi$
$644$	−0.353561	−0.0139323
$645$	0	0
$646$	25.3332	0.996720
$647$	25.7828	1.01363	0.506814	−	0.862056i	$-0.330823\pi$
$647$	25.7828	1.01363	0.506814	+	0.862056i	$0.330823\pi$
$648$	−11.6330	−0.456989
$649$	21.9585	0.861948
$650$	0	0
$651$	17.1420	0.671849
$652$	2.66355	0.104313
$653$	5.42222	0.212188	0.106094	−	0.994356i	$-0.466166\pi$
$653$	5.42222	0.212188	0.106094	+	0.994356i	$0.466166\pi$
$654$	−26.4689	−1.03502
$655$	0	0
$656$	50.6735	1.97847
$657$	4.44838	0.173548
$658$	13.9442	0.543601
$659$	−0.588596	−0.0229284	−0.0114642	−	0.999934i	$-0.503649\pi$
$659$	−0.588596	−0.0229284	−0.0114642	+	0.999934i	$0.503649\pi$
$660$	0	0
$661$	−10.2075	−0.397025	−0.198512	−	0.980098i	$-0.563611\pi$
$661$	−10.2075	−0.397025	−0.198512	+	0.980098i	$0.563611\pi$
$662$	45.4290	1.76565
$663$	0.851151	0.0330560
$664$	31.1816	1.21008
$665$	0	0
$666$	3.69178	0.143053
$667$	−7.92658	−0.306919
$668$	−2.67554	−0.103520
$669$	−70.7306	−2.73460
$670$	0	0
$671$	−73.7010	−2.84520
$672$	−5.26188	−0.202982
$673$	−10.5029	−0.404858	−0.202429	−	0.979297i	$-0.564883\pi$
$673$	−10.5029	−0.404858	−0.202429	+	0.979297i	$0.564883\pi$
$674$	27.9452	1.07641
$675$	0	0
$676$	−4.59559	−0.176754
$677$	45.6656	1.75507	0.877536	−	0.479512i	$-0.159186\pi$
$677$	45.6656	1.75507	0.877536	+	0.479512i	$0.159186\pi$
$678$	24.8461	0.954208
$679$	15.4115	0.591438
$680$	0	0
$681$	10.0231	0.384084
$682$	−57.8024	−2.21337
$683$	−44.5094	−1.70310	−0.851552	−	0.524271i	$-0.824338\pi$
$683$	−44.5094	−1.70310	−0.851552	+	0.524271i	$0.824338\pi$
$684$	−3.30570	−0.126397
$685$	0	0
$686$	−1.53413	−0.0585734
$687$	35.9622	1.37204
$688$	−13.8056	−0.526334
$689$	0.236264	0.00900094
$690$	0	0
$691$	48.7437	1.85430	0.927148	−	0.374694i	$-0.122252\pi$
$691$	48.7437	1.85430	0.927148	+	0.374694i	$0.122252\pi$
$692$	−2.43797	−0.0926778
$693$	−23.8440	−0.905759
$694$	−7.68741	−0.291810
$695$	0	0
$696$	−53.2647	−2.01899
$697$	−79.6444	−3.01675
$698$	6.78211	0.256707
$699$	18.1383	0.686052
$700$	0	0
$701$	−21.8750	−0.826207	−0.413103	−	0.910684i	$-0.635555\pi$
$701$	−21.8750	−0.826207	−0.413103	+	0.910684i	$0.635555\pi$
$702$	−0.195397	−0.00737478
$703$	1.35315	0.0510351
$704$	−35.8445	−1.35094
$705$	0	0
$706$	−16.4852	−0.620428
$707$	16.6168	0.624938
$708$	3.53221	0.132749
$709$	−24.7697	−0.930246	−0.465123	−	0.885246i	$-0.653990\pi$
$709$	−24.7697	−0.930246	−0.465123	+	0.885246i	$0.653990\pi$
$710$	0	0
$711$	1.22826	0.0460633
$712$	15.6323	0.585846
$713$	6.44342	0.241308
$714$	29.3933	1.10002
$715$	0	0
$716$	8.05528	0.301040
$717$	−19.5633	−0.730605
$718$	17.6647	0.659242
$719$	−34.4980	−1.28656	−0.643278	−	0.765632i	$-0.722426\pi$
$719$	−34.4980	−1.28656	−0.643278	+	0.765632i	$0.722426\pi$
$720$	0	0
$721$	−10.2458	−0.381575
$722$	21.0829	0.784625
$723$	52.8201	1.96440
$724$	−3.51087	−0.130480
$725$	0	0
$726$	94.6582	3.51310
$727$	−8.46738	−0.314038	−0.157019	−	0.987596i	$-0.550188\pi$
$727$	−8.46738	−0.314038	−0.157019	+	0.987596i	$0.550188\pi$
$728$	−0.112210	−0.00415876
$729$	−41.6624	−1.54305
$730$	0	0
$731$	21.6985	0.802548
$732$	−11.8554	−0.438189
$733$	−8.25993	−0.305087	−0.152544	−	0.988297i	$-0.548746\pi$
$733$	−8.25993	−0.305087	−0.152544	+	0.988297i	$0.548746\pi$
$734$	−4.83672	−0.178527
$735$	0	0
$736$	−1.97786	−0.0729049
$737$	−9.29160	−0.342261
$738$	69.1816	2.54661
$739$	10.5936	0.389690	0.194845	−	0.980834i	$-0.437580\pi$
$739$	10.5936	0.389690	0.194845	+	0.980834i	$0.437580\pi$
$740$	0	0
$741$	−0.270990	−0.00995506
$742$	8.15904	0.299528
$743$	−22.9817	−0.843117	−0.421559	−	0.906801i	$-0.638517\pi$
$743$	−22.9817	−0.843117	−0.421559	+	0.906801i	$0.638517\pi$
$744$	43.2982	1.58739
$745$	0	0
$746$	−14.2005	−0.519918
$747$	50.3388	1.84180
$748$	−14.8892	−0.544402
$749$	14.8612	0.543015
$750$	0	0
$751$	−43.2485	−1.57816	−0.789080	−	0.614291i	$-0.789442\pi$
$751$	−43.2485	−1.57816	−0.789080	+	0.614291i	$0.789442\pi$
$752$	41.6483	1.51876
$753$	36.5746	1.33285
$754$	0.540219	0.0196736
$755$	0	0
$756$	−1.01367	−0.0368669
$757$	2.26509	0.0823263	0.0411631	−	0.999152i	$-0.486894\pi$
$757$	2.26509	0.0823263	0.0411631	+	0.999152i	$0.486894\pi$
$758$	56.1439	2.03924
$759$	−15.5565	−0.564665
$760$	0	0
$761$	−41.6486	−1.50976	−0.754880	−	0.655863i	$-0.772305\pi$
$761$	−41.6486	−1.50976	−0.754880	+	0.655863i	$0.772305\pi$
$762$	−13.9576	−0.505631
$763$	−6.48526	−0.234782
$764$	−2.25970	−0.0817531
$765$	0	0
$766$	−28.1968	−1.01879
$767$	0.166824	0.00602366
$768$	−21.9107	−0.790635
$769$	−1.75425	−0.0632600	−0.0316300	−	0.999500i	$-0.510070\pi$
$769$	−1.75425	−0.0632600	−0.0316300	+	0.999500i	$0.510070\pi$
$770$	0	0
$771$	−2.76793	−0.0996845
$772$	−2.82465	−0.101661
$773$	−51.5019	−1.85239	−0.926197	−	0.377040i	$-0.876942\pi$
$773$	−51.5019	−1.85239	−0.926197	+	0.377040i	$0.876942\pi$
$774$	−18.8480	−0.677477
$775$	0	0
$776$	38.9272	1.39740
$777$	1.57002	0.0563241
$778$	2.82410	0.101249
$779$	25.3572	0.908516
$780$	0	0
$781$	14.2816	0.511038
$782$	11.0485	0.395093
$783$	−22.7258	−0.812155
$784$	−4.58212	−0.163647
$785$	0	0
$786$	50.1155	1.78756
$787$	16.3938	0.584377	0.292189	−	0.956361i	$-0.405617\pi$
$787$	16.3938	0.584377	0.292189	+	0.956361i	$0.405617\pi$
$788$	6.44616	0.229635
$789$	33.8334	1.20450
$790$	0	0
$791$	6.08765	0.216452
$792$	−60.2265	−2.14006
$793$	−0.559923	−0.0198834
$794$	−47.4065	−1.68239
$795$	0	0
$796$	−4.50196	−0.159568
$797$	9.76893	0.346033	0.173017	−	0.984919i	$-0.444649\pi$
$797$	9.76893	0.346033	0.173017	+	0.984919i	$0.444649\pi$
$798$	−9.35825	−0.331278
$799$	−65.4592	−2.31578
$800$	0	0
$801$	25.2364	0.891686
$802$	13.8775	0.490033
$803$	−6.37905	−0.225112
$804$	−1.49463	−0.0527116
$805$	0	0
$806$	−0.439138	−0.0154680
$807$	49.0341	1.72608
$808$	41.9716	1.47655
$809$	18.1414	0.637819	0.318910	−	0.947785i	$-0.396683\pi$
$809$	18.1414	0.637819	0.318910	+	0.947785i	$0.396683\pi$
$810$	0	0
$811$	−23.7279	−0.833199	−0.416600	−	0.909090i	$-0.636778\pi$
$811$	−23.7279	−0.833199	−0.416600	+	0.909090i	$0.636778\pi$
$812$	2.80253	0.0983495
$813$	59.2777	2.07896
$814$	−5.29406	−0.185557
$815$	0	0
$816$	87.7913	3.07331
$817$	−6.90838	−0.241694
$818$	−14.9275	−0.521927
$819$	−0.181148	−0.00632983
$820$	0	0
$821$	0.744129	0.0259703	0.0129851	−	0.999916i	$-0.495867\pi$
$821$	0.744129	0.0259703	0.0129851	+	0.999916i	$0.495867\pi$
$822$	−4.95073	−0.172676
$823$	−8.11920	−0.283018	−0.141509	−	0.989937i	$-0.545195\pi$
$823$	−8.11920	−0.283018	−0.141509	+	0.989937i	$0.545195\pi$
$824$	−25.8795	−0.901554
$825$	0	0
$826$	5.76103	0.200452
$827$	−37.5943	−1.30728	−0.653641	−	0.756805i	$-0.726759\pi$
$827$	−37.5943	−1.30728	−0.653641	+	0.756805i	$0.726759\pi$
$828$	−1.44171	−0.0501028
$829$	3.27714	0.113820	0.0569099	−	0.998379i	$-0.481875\pi$
$829$	3.27714	0.113820	0.0569099	+	0.998379i	$0.481875\pi$
$830$	0	0
$831$	60.2578	2.09032
$832$	−0.272318	−0.00944094
$833$	7.20179	0.249527
$834$	30.7417	1.06450
$835$	0	0
$836$	4.74042	0.163951
$837$	18.4736	0.638539
$838$	10.7348	0.370827
$839$	24.4843	0.845291	0.422645	−	0.906295i	$-0.361102\pi$
$839$	24.4843	0.845291	0.422645	+	0.906295i	$0.361102\pi$
$840$	0	0
$841$	33.8307	1.16658
$842$	25.3776	0.874572
$843$	−49.7829	−1.71461
$844$	−1.68103	−0.0578634
$845$	0	0
$846$	56.8599	1.95488
$847$	23.1926	0.796909
$848$	24.3693	0.836844
$849$	−15.9305	−0.546732
$850$	0	0
$851$	0.590146	0.0202300
$852$	2.29732	0.0787049
$853$	−51.6274	−1.76769	−0.883844	−	0.467782i	$-0.845053\pi$
$853$	−51.6274	−1.76769	−0.883844	+	0.467782i	$0.845053\pi$
$854$	−19.3361	−0.661669
$855$	0	0
$856$	37.5372	1.28299
$857$	12.7598	0.435867	0.217933	−	0.975964i	$-0.430068\pi$
$857$	12.7598	0.435867	0.217933	+	0.975964i	$0.430068\pi$
$858$	1.06022	0.0361953
$859$	−34.0681	−1.16239	−0.581194	−	0.813765i	$-0.697414\pi$
$859$	−34.0681	−1.16239	−0.581194	+	0.813765i	$0.697414\pi$
$860$	0	0
$861$	29.4212	1.00267
$862$	−6.18975	−0.210824
$863$	0.0669072	0.00227755	0.00113877	−	0.999999i	$-0.499638\pi$
$863$	0.0669072	0.00227755	0.00113877	+	0.999999i	$0.499638\pi$
$864$	−5.67061	−0.192918
$865$	0	0
$866$	16.6789	0.566771
$867$	−92.7564	−3.15017
$868$	−2.27814	−0.0773252
$869$	−1.76134	−0.0597495
$870$	0	0
$871$	−0.0705904	−0.00239186
$872$	−16.3808	−0.554725
$873$	62.8431	2.12692
$874$	−3.51762	−0.118985
$875$	0	0
$876$	−1.02612	−0.0346695
$877$	14.1049	0.476289	0.238145	−	0.971230i	$-0.423461\pi$
$877$	14.1049	0.476289	0.238145	+	0.971230i	$0.423461\pi$
$878$	−34.5680	−1.16661
$879$	62.6731	2.11391
$880$	0	0
$881$	0.314739	0.0106038	0.00530191	−	0.999986i	$-0.498312\pi$
$881$	0.314739	0.0106038	0.00530191	+	0.999986i	$0.498312\pi$
$882$	−6.25569	−0.210640
$883$	29.6381	0.997400	0.498700	−	0.866775i	$-0.333811\pi$
$883$	29.6381	0.997400	0.498700	+	0.866775i	$0.333811\pi$
$884$	−0.113116	−0.00380452
$885$	0	0
$886$	−62.5977	−2.10301
$887$	12.9347	0.434305	0.217153	−	0.976138i	$-0.430323\pi$
$887$	12.9347	0.434305	0.217153	+	0.976138i	$0.430323\pi$
$888$	3.96564	0.133078
$889$	−3.41982	−0.114697
$890$	0	0
$891$	26.9309	0.902219
$892$	9.39997	0.314734
$893$	20.8409	0.697415
$894$	−9.16892	−0.306655
$895$	0	0
$896$	−13.3598	−0.446321
$897$	−0.118186	−0.00394612
$898$	−59.6453	−1.99039
$899$	−51.0743	−1.70342
$900$	0	0
$901$	−38.3015	−1.27601
$902$	−99.2074	−3.30325
$903$	−8.01558	−0.266742
$904$	15.3765	0.511416
$905$	0	0
$906$	−56.9936	−1.89349
$907$	39.6205	1.31558	0.657789	−	0.753203i	$-0.271492\pi$
$907$	39.6205	1.31558	0.657789	+	0.753203i	$0.271492\pi$
$908$	−1.33204	−0.0442055
$909$	67.7579	2.24739
$910$	0	0
$911$	−31.9218	−1.05762	−0.528809	−	0.848741i	$-0.677361\pi$
$911$	−31.9218	−1.05762	−0.528809	+	0.848741i	$0.677361\pi$
$912$	−27.9510	−0.925551
$913$	−72.1866	−2.38903
$914$	36.1928	1.19715
$915$	0	0
$916$	−4.77930	−0.157913
$917$	12.2790	0.405489
$918$	31.6765	1.04548
$919$	8.96185	0.295624	0.147812	−	0.989015i	$-0.452777\pi$
$919$	8.96185	0.295624	0.147812	+	0.989015i	$0.452777\pi$
$920$	0	0
$921$	−81.2868	−2.67849
$922$	−20.6087	−0.678712
$923$	0.108501	0.00357135
$924$	5.50017	0.180942
$925$	0	0
$926$	53.8406	1.76931
$927$	−41.7792	−1.37221
$928$	15.6777	0.514645
$929$	−22.5482	−0.739782	−0.369891	−	0.929075i	$-0.620605\pi$
$929$	−22.5482	−0.739782	−0.369891	+	0.929075i	$0.620605\pi$
$930$	0	0
$931$	−2.29291	−0.0751470
$932$	−2.41054	−0.0789599
$933$	−34.2573	−1.12153
$934$	−45.1888	−1.47862
$935$	0	0
$936$	−0.457554	−0.0149556
$937$	−15.5669	−0.508547	−0.254274	−	0.967132i	$-0.581836\pi$
$937$	−15.5669	−0.508547	−0.254274	+	0.967132i	$0.581836\pi$
$938$	−2.43774	−0.0795950
$939$	69.0780	2.25428
$940$	0	0
$941$	−22.7677	−0.742207	−0.371103	−	0.928592i	$-0.621020\pi$
$941$	−22.7677	−0.742207	−0.371103	+	0.928592i	$0.621020\pi$
$942$	0.367289	0.0119669
$943$	11.0590	0.360130
$944$	17.2069	0.560038
$945$	0	0
$946$	27.0283	0.878766
$947$	−31.4177	−1.02094	−0.510469	−	0.859896i	$-0.670528\pi$
$947$	−31.4177	−1.02094	−0.510469	+	0.859896i	$0.670528\pi$
$948$	−0.283326	−0.00920201
$949$	−0.0484631	−0.00157318
$950$	0	0
$951$	13.3246	0.432080
$952$	18.1907	0.589563
$953$	−26.8729	−0.870499	−0.435249	−	0.900310i	$-0.643340\pi$
$953$	−26.8729	−0.870499	−0.435249	+	0.900310i	$0.643340\pi$
$954$	33.2699	1.07715
$955$	0	0
$956$	2.59993	0.0840876
$957$	123.310	3.98604
$958$	−42.4100	−1.37021
$959$	−1.21300	−0.0391698
$960$	0	0
$961$	10.5177	0.339280
$962$	−0.0402202	−0.00129675
$963$	60.5990	1.95278
$964$	−7.01969	−0.226089
$965$	0	0
$966$	−4.08139	−0.131317
$967$	17.7697	0.571436	0.285718	−	0.958314i	$-0.407768\pi$
$967$	17.7697	0.571436	0.285718	+	0.958314i	$0.407768\pi$
$968$	58.5813	1.88287
$969$	43.9311	1.41127
$970$	0	0
$971$	53.7925	1.72628	0.863141	−	0.504962i	$-0.168494\pi$
$971$	53.7925	1.72628	0.863141	+	0.504962i	$0.168494\pi$
$972$	7.37308	0.236492
$973$	7.53216	0.241470
$974$	16.2168	0.519621
$975$	0	0
$976$	−57.7528	−1.84862
$977$	57.8020	1.84925	0.924625	−	0.380878i	$-0.124378\pi$
$977$	57.8020	1.84925	0.924625	+	0.380878i	$0.124378\pi$
$978$	30.7472	0.983187
$979$	−36.1894	−1.15662
$980$	0	0
$981$	−26.4448	−0.844317
$982$	18.0656	0.576497
$983$	11.4133	0.364027	0.182014	−	0.983296i	$-0.441739\pi$
$983$	11.4133	0.364027	0.182014	+	0.983296i	$0.441739\pi$
$984$	74.3137	2.36903
$985$	0	0
$986$	−87.5768	−2.78901
$987$	24.1811	0.769693
$988$	0.0360141	0.00114576
$989$	−3.01294	−0.0958058
$990$	0	0
$991$	−22.8328	−0.725307	−0.362654	−	0.931924i	$-0.618129\pi$
$991$	−22.8328	−0.725307	−0.362654	+	0.931924i	$0.618129\pi$
$992$	−12.7442	−0.404629
$993$	78.7799	2.50001
$994$	3.74692	0.118845
$995$	0	0
$996$	−11.6118	−0.367934
$997$	−4.70495	−0.149007	−0.0745037	−	0.997221i	$-0.523737\pi$
$997$	−4.70495	−0.149007	−0.0745037	+	0.997221i	$0.523737\pi$
$998$	−30.4259	−0.963115
$999$	1.69197	0.0535317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.x.1.3		12
5.2	odd	4		805.2.c.b.484.6	✓	24
5.3	odd	4		805.2.c.b.484.19	yes	24
5.4	even	2		4025.2.a.y.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.b.484.6	✓	24	5.2	odd	4
805.2.c.b.484.19	yes	24	5.3	odd	4
4025.2.a.x.1.3		12	1.1	even	1	trivial
4025.2.a.y.1.10		12	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53413 q^{2} -2.66039 q^{3} +0.353561 q^{4} +4.08139 q^{6} +1.00000 q^{7} +2.52585 q^{8} +4.07768 q^{9} +O(q^{10})\)	\(q-1.53413 q^{2} -2.66039 q^{3} +0.353561 q^{4} +4.08139 q^{6} +1.00000 q^{7} +2.52585 q^{8} +4.07768 q^{9} -5.84745 q^{11} -0.940610 q^{12} -0.0444244 q^{13} -1.53413 q^{14} -4.58212 q^{16} +7.20179 q^{17} -6.25569 q^{18} -2.29291 q^{19} -2.66039 q^{21} +8.97076 q^{22} -1.00000 q^{23} -6.71976 q^{24} +0.0681529 q^{26} -2.86704 q^{27} +0.353561 q^{28} +7.92658 q^{29} -6.44342 q^{31} +1.97786 q^{32} +15.5565 q^{33} -11.0485 q^{34} +1.44171 q^{36} -0.590146 q^{37} +3.51762 q^{38} +0.118186 q^{39} -11.0590 q^{41} +4.08139 q^{42} +3.01294 q^{43} -2.06743 q^{44} +1.53413 q^{46} -9.08931 q^{47} +12.1902 q^{48} +1.00000 q^{49} -19.1596 q^{51} -0.0157067 q^{52} -5.31834 q^{53} +4.39842 q^{54} +2.52585 q^{56} +6.10003 q^{57} -12.1604 q^{58} -3.75523 q^{59} +12.6040 q^{61} +9.88506 q^{62} +4.07768 q^{63} +6.12993 q^{64} -23.8657 q^{66} +1.58900 q^{67} +2.54627 q^{68} +2.66039 q^{69} -2.44237 q^{71} +10.2996 q^{72} +1.09091 q^{73} +0.905362 q^{74} -0.810682 q^{76} -5.84745 q^{77} -0.181313 q^{78} +0.301216 q^{79} -4.60558 q^{81} +16.9659 q^{82} +12.3450 q^{83} -0.940610 q^{84} -4.62224 q^{86} -21.0878 q^{87} -14.7698 q^{88} +6.18893 q^{89} -0.0444244 q^{91} -0.353561 q^{92} +17.1420 q^{93} +13.9442 q^{94} -5.26188 q^{96} +15.4115 q^{97} -1.53413 q^{98} -23.8440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * q^99

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