LMFDB - Embedded newform 1250.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1250,2,Mod(1,1250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1250, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1250.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1250 = 2 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1250.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:	$9.98130025266$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.7625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 4x + 16 $ x^4 - x^3 - 9x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.96645$ of defining polynomial
Character	$\chi$	$=$	1250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.96645 q^{3} +1.00000 q^{4} +2.96645 q^{6} -1.83337 q^{7} -1.00000 q^{8} +5.79981 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.96645 q^{3} +1.00000 q^{4} +2.96645 q^{6} -1.83337 q^{7} -1.00000 q^{8} +5.79981 q^{9} -1.83337 q^{11} -2.96645 q^{12} +2.41785 q^{13} +1.83337 q^{14} +1.00000 q^{16} -2.78467 q^{17} -5.79981 q^{18} -1.67232 q^{19} +5.43858 q^{21} +1.83337 q^{22} +7.76626 q^{23} +2.96645 q^{24} -2.41785 q^{26} -8.30550 q^{27} -1.83337 q^{28} +7.58448 q^{29} -5.29413 q^{31} -1.00000 q^{32} +5.43858 q^{33} +2.78467 q^{34} +5.79981 q^{36} +1.31486 q^{37} +1.67232 q^{38} -7.17242 q^{39} +3.51505 q^{41} -5.43858 q^{42} +4.30550 q^{43} -1.83337 q^{44} -7.76626 q^{46} -1.83337 q^{47} -2.96645 q^{48} -3.63877 q^{49} +8.26057 q^{51} +2.41785 q^{52} +6.51738 q^{53} +8.30550 q^{54} +1.83337 q^{56} +4.96086 q^{57} -7.58448 q^{58} -9.06039 q^{59} +2.58794 q^{61} +5.29413 q^{62} -10.6332 q^{63} +1.00000 q^{64} -5.43858 q^{66} -9.50010 q^{67} -2.78467 q^{68} -23.0382 q^{69} +0.305502 q^{71} -5.79981 q^{72} -14.9480 q^{73} -1.31486 q^{74} -1.67232 q^{76} +3.36123 q^{77} +7.17242 q^{78} -3.46076 q^{79} +7.23840 q^{81} -3.51505 q^{82} +6.37261 q^{83} +5.43858 q^{84} -4.30550 q^{86} -22.4990 q^{87} +1.83337 q^{88} -3.32045 q^{89} -4.43280 q^{91} +7.76626 q^{92} +15.7047 q^{93} +1.83337 q^{94} +2.96645 q^{96} -11.0902 q^{97} +3.63877 q^{98} -10.6332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{6} - 2 q^{7} - 4 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^6 - 2 * q^7 - 4 * q^8 + 7 * q^9	$ 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{6} - 2 q^{7} - 4 q^{8} + 7 q^{9} - 2 q^{11} - q^{12} - 11 q^{13} + 2 q^{14} + 4 q^{16} - 12 q^{17} - 7 q^{18} - 5 q^{19} - 7 q^{21} + 2 q^{22} + 4 q^{23} + q^{24} + 11 q^{26} - 10 q^{27} - 2 q^{28} + 15 q^{29} - 12 q^{31} - 4 q^{32} - 7 q^{33} + 12 q^{34} + 7 q^{36} - 12 q^{37} + 5 q^{38} - 11 q^{39} + 13 q^{41} + 7 q^{42} - 6 q^{43} - 2 q^{44} - 4 q^{46} - 2 q^{47} - q^{48} - 2 q^{49} + 13 q^{51} - 11 q^{52} - 11 q^{53} + 10 q^{54} + 2 q^{56} - 15 q^{58} + 8 q^{61} + 12 q^{62} - 21 q^{63} + 4 q^{64} + 7 q^{66} - 22 q^{67} - 12 q^{68} - 31 q^{69} - 22 q^{71} - 7 q^{72} - 21 q^{73} + 12 q^{74} - 5 q^{76} + 26 q^{77} + 11 q^{78} - 10 q^{79} - 16 q^{81} - 13 q^{82} + 24 q^{83} - 7 q^{84} + 6 q^{86} - 25 q^{87} + 2 q^{88} - 5 q^{89} - 12 q^{91} + 4 q^{92} + 23 q^{93} + 2 q^{94} + q^{96} - 22 q^{97} + 2 q^{98} - 21 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^6 - 2 * q^7 - 4 * q^8 + 7 * q^9 - 2 * q^11 - q^12 - 11 * q^13 + 2 * q^14 + 4 * q^16 - 12 * q^17 - 7 * q^18 - 5 * q^19 - 7 * q^21 + 2 * q^22 + 4 * q^23 + q^24 + 11 * q^26 - 10 * q^27 - 2 * q^28 + 15 * q^29 - 12 * q^31 - 4 * q^32 - 7 * q^33 + 12 * q^34 + 7 * q^36 - 12 * q^37 + 5 * q^38 - 11 * q^39 + 13 * q^41 + 7 * q^42 - 6 * q^43 - 2 * q^44 - 4 * q^46 - 2 * q^47 - q^48 - 2 * q^49 + 13 * q^51 - 11 * q^52 - 11 * q^53 + 10 * q^54 + 2 * q^56 - 15 * q^58 + 8 * q^61 + 12 * q^62 - 21 * q^63 + 4 * q^64 + 7 * q^66 - 22 * q^67 - 12 * q^68 - 31 * q^69 - 22 * q^71 - 7 * q^72 - 21 * q^73 + 12 * q^74 - 5 * q^76 + 26 * q^77 + 11 * q^78 - 10 * q^79 - 16 * q^81 - 13 * q^82 + 24 * q^83 - 7 * q^84 + 6 * q^86 - 25 * q^87 + 2 * q^88 - 5 * q^89 - 12 * q^91 + 4 * q^92 + 23 * q^93 + 2 * q^94 + q^96 - 22 * q^97 + 2 * q^98 - 21 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.96645	−1.71268	−0.856340	−	0.516413i	$-0.827267\pi$
$3$	−2.96645	−1.71268	−0.856340	+	0.516413i	$0.827267\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.96645	1.21105
$7$	−1.83337	−0.692947	−0.346474	−	0.938060i	$-0.612621\pi$
$7$	−1.83337	−0.692947	−0.346474	+	0.938060i	$0.612621\pi$
$8$	−1.00000	−0.353553
$9$	5.79981	1.93327
$10$	0	0
$11$	−1.83337	−0.552781	−0.276390	−	0.961045i	$-0.589138\pi$
$11$	−1.83337	−0.552781	−0.276390	+	0.961045i	$0.589138\pi$
$12$	−2.96645	−0.856340
$13$	2.41785	0.670590	0.335295	−	0.942113i	$-0.391164\pi$
$13$	2.41785	0.670590	0.335295	+	0.942113i	$0.391164\pi$
$14$	1.83337	0.489988
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.78467	−0.675381	−0.337691	−	0.941257i	$-0.609646\pi$
$17$	−2.78467	−0.675381	−0.337691	+	0.941257i	$0.609646\pi$
$18$	−5.79981	−1.36703
$19$	−1.67232	−0.383657	−0.191829	−	0.981428i	$-0.561442\pi$
$19$	−1.67232	−0.383657	−0.191829	+	0.981428i	$0.561442\pi$
$20$	0	0
$21$	5.43858	1.18680
$22$	1.83337	0.390875
$23$	7.76626	1.61938	0.809689	−	0.586860i	$-0.199636\pi$
$23$	7.76626	1.61938	0.809689	+	0.586860i	$0.199636\pi$
$24$	2.96645	0.605524
$25$	0	0
$26$	−2.41785	−0.474179
$27$	−8.30550	−1.59839
$28$	−1.83337	−0.346474
$29$	7.58448	1.40840	0.704201	−	0.710000i	$-0.251305\pi$
$29$	7.58448	1.40840	0.704201	+	0.710000i	$0.251305\pi$
$30$	0	0
$31$	−5.29413	−0.950853	−0.475427	−	0.879755i	$-0.657706\pi$
$31$	−5.29413	−0.950853	−0.475427	+	0.879755i	$0.657706\pi$
$32$	−1.00000	−0.176777
$33$	5.43858	0.946736
$34$	2.78467	0.477567
$35$	0	0
$36$	5.79981	0.966636
$37$	1.31486	0.216162	0.108081	−	0.994142i	$-0.465529\pi$
$37$	1.31486	0.216162	0.108081	+	0.994142i	$0.465529\pi$
$38$	1.67232	0.271286
$39$	−7.17242	−1.14851
$40$	0	0
$41$	3.51505	0.548958	0.274479	−	0.961593i	$-0.411495\pi$
$41$	3.51505	0.548958	0.274479	+	0.961593i	$0.411495\pi$
$42$	−5.43858	−0.839192
$43$	4.30550	0.656583	0.328291	−	0.944576i	$-0.393527\pi$
$43$	4.30550	0.656583	0.328291	+	0.944576i	$0.393527\pi$
$44$	−1.83337	−0.276390
$45$	0	0
$46$	−7.76626	−1.14507
$47$	−1.83337	−0.267424	−0.133712	−	0.991020i	$-0.542690\pi$
$47$	−1.83337	−0.267424	−0.133712	+	0.991020i	$0.542690\pi$
$48$	−2.96645	−0.428170
$49$	−3.63877	−0.519824
$50$	0	0
$51$	8.26057	1.15671
$52$	2.41785	0.335295
$53$	6.51738	0.895231	0.447615	−	0.894226i	$-0.352273\pi$
$53$	6.51738	0.895231	0.447615	+	0.894226i	$0.352273\pi$
$54$	8.30550	1.13024
$55$	0	0
$56$	1.83337	0.244994
$57$	4.96086	0.657082
$58$	−7.58448	−0.995891
$59$	−9.06039	−1.17956	−0.589781	−	0.807563i	$-0.700786\pi$
$59$	−9.06039	−1.17956	−0.589781	+	0.807563i	$0.700786\pi$
$60$	0	0
$61$	2.58794	0.331351	0.165676	−	0.986180i	$-0.447019\pi$
$61$	2.58794	0.331351	0.165676	+	0.986180i	$0.447019\pi$
$62$	5.29413	0.672355
$63$	−10.6332	−1.33965
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.43858	−0.669443
$67$	−9.50010	−1.16062	−0.580311	−	0.814395i	$-0.697069\pi$
$67$	−9.50010	−1.16062	−0.580311	+	0.814395i	$0.697069\pi$
$68$	−2.78467	−0.337691
$69$	−23.0382	−2.77347
$70$	0	0
$71$	0.305502	0.0362564	0.0181282	−	0.999836i	$-0.494229\pi$
$71$	0.305502	0.0362564	0.0181282	+	0.999836i	$0.494229\pi$
$72$	−5.79981	−0.683515
$73$	−14.9480	−1.74954	−0.874768	−	0.484542i	$-0.838986\pi$
$73$	−14.9480	−1.74954	−0.874768	+	0.484542i	$0.838986\pi$
$74$	−1.31486	−0.152850
$75$	0	0
$76$	−1.67232	−0.191829
$77$	3.36123	0.383048
$78$	7.17242	0.812117
$79$	−3.46076	−0.389366	−0.194683	−	0.980866i	$-0.562368\pi$
$79$	−3.46076	−0.389366	−0.194683	+	0.980866i	$0.562368\pi$
$80$	0	0
$81$	7.23840	0.804266
$82$	−3.51505	−0.388172
$83$	6.37261	0.699484	0.349742	−	0.936846i	$-0.386269\pi$
$83$	6.37261	0.699484	0.349742	+	0.936846i	$0.386269\pi$
$84$	5.43858	0.593398
$85$	0	0
$86$	−4.30550	−0.464274
$87$	−22.4990	−2.41214
$88$	1.83337	0.195437
$89$	−3.32045	−0.351967	−0.175984	−	0.984393i	$-0.556311\pi$
$89$	−3.32045	−0.351967	−0.175984	+	0.984393i	$0.556311\pi$
$90$	0	0
$91$	−4.43280	−0.464684
$92$	7.76626	0.809689
$93$	15.7047	1.62851
$94$	1.83337	0.189097
$95$	0	0
$96$	2.96645	0.302762
$97$	−11.0902	−1.12604	−0.563018	−	0.826445i	$-0.690360\pi$
$97$	−11.0902	−1.12604	−0.563018	+	0.826445i	$0.690360\pi$
$98$	3.63877	0.367571
$99$	−10.6332	−1.06867
$100$	0	0
$101$	−13.1807	−1.31152	−0.655762	−	0.754968i	$-0.727653\pi$
$101$	−13.1807	−1.31152	−0.655762	+	0.754968i	$0.727653\pi$
$102$	−8.26057	−0.817919
$103$	2.63318	0.259455	0.129727	−	0.991550i	$-0.458590\pi$
$103$	2.63318	0.259455	0.129727	+	0.991550i	$0.458590\pi$
$104$	−2.41785	−0.237089
$105$	0	0
$106$	−6.51738	−0.633024
$107$	−18.8045	−1.81790	−0.908949	−	0.416908i	$-0.863114\pi$
$107$	−18.8045	−1.81790	−0.908949	+	0.416908i	$0.863114\pi$
$108$	−8.30550	−0.799197
$109$	10.3093	0.987449	0.493725	−	0.869618i	$-0.335635\pi$
$109$	10.3093	0.987449	0.493725	+	0.869618i	$0.335635\pi$
$110$	0	0
$111$	−3.90047	−0.370216
$112$	−1.83337	−0.173237
$113$	−6.05662	−0.569759	−0.284879	−	0.958563i	$-0.591954\pi$
$113$	−6.05662	−0.569759	−0.284879	+	0.958563i	$0.591954\pi$
$114$	−4.96086	−0.464627
$115$	0	0
$116$	7.58448	0.704201
$117$	14.0231	1.29643
$118$	9.06039	0.834076
$119$	5.10532	0.468003
$120$	0	0
$121$	−7.63877	−0.694434
$122$	−2.58794	−0.234301
$123$	−10.4272	−0.940190
$124$	−5.29413	−0.475427
$125$	0	0
$126$	10.6332	0.947279
$127$	−0.333269	−0.0295728	−0.0147864	−	0.999891i	$-0.504707\pi$
$127$	−0.333269	−0.0295728	−0.0147864	+	0.999891i	$0.504707\pi$
$128$	−1.00000	−0.0883883
$129$	−12.7720	−1.12452
$130$	0	0
$131$	−5.17801	−0.452405	−0.226202	−	0.974080i	$-0.572631\pi$
$131$	−5.17801	−0.452405	−0.226202	+	0.974080i	$0.572631\pi$
$132$	5.43858	0.473368
$133$	3.06598	0.265854
$134$	9.50010	0.820683
$135$	0	0
$136$	2.78467	0.238783
$137$	19.5232	1.66798	0.833988	−	0.551782i	$-0.186052\pi$
$137$	19.5232	1.66798	0.833988	+	0.551782i	$0.186052\pi$
$138$	23.0382	1.96114
$139$	−7.95507	−0.674740	−0.337370	−	0.941372i	$-0.609537\pi$
$139$	−7.95507	−0.674740	−0.337370	+	0.941372i	$0.609537\pi$
$140$	0	0
$141$	5.43858	0.458011
$142$	−0.305502	−0.0256371
$143$	−4.43280	−0.370689
$144$	5.79981	0.483318
$145$	0	0
$146$	14.9480	1.23711
$147$	10.7942	0.890292
$148$	1.31486	0.108081
$149$	−1.67955	−0.137594	−0.0687969	−	0.997631i	$-0.521916\pi$
$149$	−1.67955	−0.137594	−0.0687969	+	0.997631i	$0.521916\pi$
$150$	0	0
$151$	−21.2664	−1.73063	−0.865316	−	0.501227i	$-0.832882\pi$
$151$	−21.2664	−1.73063	−0.865316	+	0.501227i	$0.832882\pi$
$152$	1.67232	0.135643
$153$	−16.1506	−1.30570
$154$	−3.36123	−0.270856
$155$	0	0
$156$	−7.17242	−0.574253
$157$	−10.4514	−0.834113	−0.417056	−	0.908881i	$-0.636938\pi$
$157$	−10.4514	−0.834113	−0.417056	+	0.908881i	$0.636938\pi$
$158$	3.46076	0.275323
$159$	−19.3335	−1.53324
$160$	0	0
$161$	−14.2384	−1.12214
$162$	−7.23840	−0.568702
$163$	−10.4106	−0.815423	−0.407711	−	0.913111i	$-0.633673\pi$
$163$	−10.4106	−0.815423	−0.407711	+	0.913111i	$0.633673\pi$
$164$	3.51505	0.274479
$165$	0	0
$166$	−6.37261	−0.494610
$167$	−2.12171	−0.164183	−0.0820913	−	0.996625i	$-0.526160\pi$
$167$	−2.12171	−0.164183	−0.0820913	+	0.996625i	$0.526160\pi$
$168$	−5.43858	−0.419596
$169$	−7.15401	−0.550309
$170$	0	0
$171$	−9.69916	−0.741713
$172$	4.30550	0.328291
$173$	18.1147	1.37723	0.688617	−	0.725126i	$-0.258218\pi$
$173$	18.1147	1.37723	0.688617	+	0.725126i	$0.258218\pi$
$174$	22.4990	1.70564
$175$	0	0
$176$	−1.83337	−0.138195
$177$	26.8772	2.02021
$178$	3.32045	0.248878
$179$	10.5605	0.789328	0.394664	−	0.918826i	$-0.370861\pi$
$179$	10.5605	0.789328	0.394664	+	0.918826i	$0.370861\pi$
$180$	0	0
$181$	18.1561	1.34954	0.674768	−	0.738030i	$-0.264244\pi$
$181$	18.1561	1.34954	0.674768	+	0.738030i	$0.264244\pi$
$182$	4.43280	0.328581
$183$	−7.67698	−0.567499
$184$	−7.76626	−0.572536
$185$	0	0
$186$	−15.7047	−1.15153
$187$	5.10532	0.373338
$188$	−1.83337	−0.133712
$189$	15.2270	1.10760
$190$	0	0
$191$	−21.9051	−1.58500	−0.792500	−	0.609872i	$-0.791221\pi$
$191$	−21.9051	−1.58500	−0.792500	+	0.609872i	$0.791221\pi$
$192$	−2.96645	−0.214085
$193$	−27.4248	−1.97408	−0.987041	−	0.160465i	$-0.948700\pi$
$193$	−27.4248	−1.97408	−0.987041	+	0.160465i	$0.948700\pi$
$194$	11.0902	0.796228
$195$	0	0
$196$	−3.63877	−0.259912
$197$	1.12372	0.0800619	0.0400309	−	0.999198i	$-0.487254\pi$
$197$	1.12372	0.0800619	0.0400309	+	0.999198i	$0.487254\pi$
$198$	10.6332	0.755667
$199$	25.4992	1.80759	0.903794	−	0.427968i	$-0.140770\pi$
$199$	25.4992	1.80759	0.903794	+	0.427968i	$0.140770\pi$
$200$	0	0
$201$	28.1815	1.98777
$202$	13.1807	0.927388
$203$	−13.9051	−0.975949
$204$	8.26057	0.578356
$205$	0	0
$206$	−2.63318	−0.183462
$207$	45.0429	3.13070
$208$	2.41785	0.167648
$209$	3.06598	0.212078
$210$	0	0
$211$	21.3044	1.46665	0.733327	−	0.679876i	$-0.237967\pi$
$211$	21.3044	1.46665	0.733327	+	0.679876i	$0.237967\pi$
$212$	6.51738	0.447615
$213$	−0.906255	−0.0620956
$214$	18.8045	1.28545
$215$	0	0
$216$	8.30550	0.565118
$217$	9.70607	0.658891
$218$	−10.3093	−0.698232
$219$	44.3426	2.99639
$220$	0	0
$221$	−6.73290	−0.452904
$222$	3.90047	0.261782
$223$	−3.24511	−0.217309	−0.108654	−	0.994080i	$-0.534654\pi$
$223$	−3.24511	−0.217309	−0.108654	+	0.994080i	$0.534654\pi$
$224$	1.83337	0.122497
$225$	0	0
$226$	6.05662	0.402880
$227$	−16.3773	−1.08700	−0.543499	−	0.839410i	$-0.682901\pi$
$227$	−16.3773	−1.08700	−0.543499	+	0.839410i	$0.682901\pi$
$228$	4.96086	0.328541
$229$	−5.08998	−0.336355	−0.168178	−	0.985757i	$-0.553788\pi$
$229$	−5.08998	−0.336355	−0.168178	+	0.985757i	$0.553788\pi$
$230$	0	0
$231$	−9.97091	−0.656038
$232$	−7.58448	−0.497946
$233$	1.66296	0.108944	0.0544721	−	0.998515i	$-0.482652\pi$
$233$	1.66296	0.108944	0.0544721	+	0.998515i	$0.482652\pi$
$234$	−14.0231	−0.916716
$235$	0	0
$236$	−9.06039	−0.589781
$237$	10.2662	0.666859
$238$	−5.10532	−0.330928
$239$	12.7998	0.827951	0.413976	−	0.910288i	$-0.364140\pi$
$239$	12.7998	0.827951	0.413976	+	0.910288i	$0.364140\pi$
$240$	0	0
$241$	0.395477	0.0254749	0.0127375	−	0.999919i	$-0.495945\pi$
$241$	0.395477	0.0254749	0.0127375	+	0.999919i	$0.495945\pi$
$242$	7.63877	0.491039
$243$	3.44417	0.220944
$244$	2.58794	0.165676
$245$	0	0
$246$	10.4272	0.664815
$247$	−4.04342	−0.257277
$248$	5.29413	0.336177
$249$	−18.9040	−1.19799
$250$	0	0
$251$	9.36589	0.591170	0.295585	−	0.955316i	$-0.404485\pi$
$251$	9.36589	0.591170	0.295585	+	0.955316i	$0.404485\pi$
$252$	−10.6332	−0.669827
$253$	−14.2384	−0.895160
$254$	0.333269	0.0209111
$255$	0	0
$256$	1.00000	0.0625000
$257$	4.97926	0.310598	0.155299	−	0.987868i	$-0.450366\pi$
$257$	4.97926	0.310598	0.155299	+	0.987868i	$0.450366\pi$
$258$	12.7720	0.795153
$259$	−2.41062	−0.149789
$260$	0	0
$261$	43.9886	2.72282
$262$	5.17801	0.319899
$263$	19.8112	1.22161	0.610805	−	0.791781i	$-0.290846\pi$
$263$	19.8112	1.22161	0.610805	+	0.791781i	$0.290846\pi$
$264$	−5.43858	−0.334722
$265$	0	0
$266$	−3.06598	−0.187987
$267$	9.84995	0.602807
$268$	−9.50010	−0.580311
$269$	14.7939	0.902001	0.451000	−	0.892524i	$-0.351067\pi$
$269$	14.7939	0.902001	0.451000	+	0.892524i	$0.351067\pi$
$270$	0	0
$271$	−12.5564	−0.762747	−0.381374	−	0.924421i	$-0.624549\pi$
$271$	−12.5564	−0.762747	−0.381374	+	0.924421i	$0.624549\pi$
$272$	−2.78467	−0.168845
$273$	13.1497	0.795854
$274$	−19.5232	−1.17944
$275$	0	0
$276$	−23.0382	−1.38674
$277$	6.33183	0.380443	0.190221	−	0.981741i	$-0.439079\pi$
$277$	6.33183	0.380443	0.190221	+	0.981741i	$0.439079\pi$
$278$	7.95507	0.477114
$279$	−30.7049	−1.83826
$280$	0	0
$281$	−20.0892	−1.19842	−0.599212	−	0.800591i	$-0.704519\pi$
$281$	−20.0892	−1.19842	−0.599212	+	0.800591i	$0.704519\pi$
$282$	−5.43858	−0.323863
$283$	−1.81678	−0.107996	−0.0539982	−	0.998541i	$-0.517197\pi$
$283$	−1.81678	−0.107996	−0.0539982	+	0.998541i	$0.517197\pi$
$284$	0.305502	0.0181282
$285$	0	0
$286$	4.43280	0.262117
$287$	−6.44437	−0.380399
$288$	−5.79981	−0.341757
$289$	−9.24562	−0.543860
$290$	0	0
$291$	32.8984	1.92854
$292$	−14.9480	−0.874768
$293$	6.85931	0.400725	0.200363	−	0.979722i	$-0.435788\pi$
$293$	6.85931	0.400725	0.200363	+	0.979722i	$0.435788\pi$
$294$	−10.7942	−0.629532
$295$	0	0
$296$	−1.31486	−0.0764248
$297$	15.2270	0.883561
$298$	1.67955	0.0972936
$299$	18.7776	1.08594
$300$	0	0
$301$	−7.89356	−0.454977
$302$	21.2664	1.22374
$303$	39.0997	2.24622
$304$	−1.67232	−0.0959143
$305$	0	0
$306$	16.1506	0.923266
$307$	2.89526	0.165241	0.0826206	−	0.996581i	$-0.473671\pi$
$307$	2.89526	0.165241	0.0826206	+	0.996581i	$0.473671\pi$
$308$	3.36123	0.191524
$309$	−7.81119	−0.444363
$310$	0	0
$311$	−20.6490	−1.17090	−0.585449	−	0.810709i	$-0.699082\pi$
$311$	−20.6490	−1.17090	−0.585449	+	0.810709i	$0.699082\pi$
$312$	7.17242	0.406058
$313$	−16.4272	−0.928521	−0.464260	−	0.885699i	$-0.653680\pi$
$313$	−16.4272	−0.928521	−0.464260	+	0.885699i	$0.653680\pi$
$314$	10.4514	0.589807
$315$	0	0
$316$	−3.46076	−0.194683
$317$	−16.5059	−0.927063	−0.463531	−	0.886081i	$-0.653418\pi$
$317$	−16.5059	−0.927063	−0.463531	+	0.886081i	$0.653418\pi$
$318$	19.3335	1.08417
$319$	−13.9051	−0.778538
$320$	0	0
$321$	55.7825	3.11348
$322$	14.2384	0.793475
$323$	4.65686	0.259115
$324$	7.23840	0.402133
$325$	0	0
$326$	10.4106	0.576591
$327$	−30.5819	−1.69118
$328$	−3.51505	−0.194086
$329$	3.36123	0.185311
$330$	0	0
$331$	27.4710	1.50994	0.754972	−	0.655757i	$-0.227651\pi$
$331$	27.4710	1.50994	0.754972	+	0.655757i	$0.227651\pi$
$332$	6.37261	0.349742
$333$	7.62595	0.417900
$334$	2.12171	0.116095
$335$	0	0
$336$	5.43858	0.296699
$337$	2.74521	0.149541	0.0747706	−	0.997201i	$-0.476178\pi$
$337$	2.74521	0.149541	0.0747706	+	0.997201i	$0.476178\pi$
$338$	7.15401	0.389127
$339$	17.9666	0.975814
$340$	0	0
$341$	9.70607	0.525613
$342$	9.69916	0.524470
$343$	19.5048	1.05316
$344$	−4.30550	−0.232137
$345$	0	0
$346$	−18.1147	−0.973851
$347$	21.3391	1.14554	0.572770	−	0.819716i	$-0.305869\pi$
$347$	21.3391	1.14554	0.572770	+	0.819716i	$0.305869\pi$
$348$	−22.4990	−1.20607
$349$	−16.7650	−0.897411	−0.448705	−	0.893680i	$-0.648115\pi$
$349$	−16.7650	−0.897411	−0.448705	+	0.893680i	$0.648115\pi$
$350$	0	0
$351$	−20.0814	−1.07187
$352$	1.83337	0.0977187
$353$	−2.98862	−0.159068	−0.0795342	−	0.996832i	$-0.525343\pi$
$353$	−2.98862	−0.159068	−0.0795342	+	0.996832i	$0.525343\pi$
$354$	−26.8772	−1.42851
$355$	0	0
$356$	−3.32045	−0.175984
$357$	−15.1447	−0.801540
$358$	−10.5605	−0.558139
$359$	6.70494	0.353873	0.176937	−	0.984222i	$-0.443381\pi$
$359$	6.70494	0.353873	0.176937	+	0.984222i	$0.443381\pi$
$360$	0	0
$361$	−16.2033	−0.852807
$362$	−18.1561	−0.954266
$363$	22.6600	1.18934
$364$	−4.43280	−0.232342
$365$	0	0
$366$	7.67698	0.401282
$367$	−4.01659	−0.209664	−0.104832	−	0.994490i	$-0.533430\pi$
$367$	−4.01659	−0.209664	−0.104832	+	0.994490i	$0.533430\pi$
$368$	7.76626	0.404844
$369$	20.3866	1.06129
$370$	0	0
$371$	−11.9487	−0.620348
$372$	15.7047	0.814253
$373$	−26.5832	−1.37643	−0.688214	−	0.725508i	$-0.741605\pi$
$373$	−26.5832	−1.37643	−0.688214	+	0.725508i	$0.741605\pi$
$374$	−5.10532	−0.263990
$375$	0	0
$376$	1.83337	0.0945486
$377$	18.3381	0.944461
$378$	−15.2270	−0.783193
$379$	−15.6278	−0.802745	−0.401373	−	0.915915i	$-0.631467\pi$
$379$	−15.6278	−0.802745	−0.401373	+	0.915915i	$0.631467\pi$
$380$	0	0
$381$	0.988624	0.0506487
$382$	21.9051	1.12076
$383$	−13.4455	−0.687033	−0.343516	−	0.939147i	$-0.611618\pi$
$383$	−13.4455	−0.687033	−0.343516	+	0.939147i	$0.611618\pi$
$384$	2.96645	0.151381
$385$	0	0
$386$	27.4248	1.39589
$387$	24.9711	1.26935
$388$	−11.0902	−0.563018
$389$	−25.1116	−1.27321	−0.636605	−	0.771190i	$-0.719662\pi$
$389$	−25.1116	−1.27321	−0.636605	+	0.771190i	$0.719662\pi$
$390$	0	0
$391$	−21.6265	−1.09370
$392$	3.63877	0.183786
$393$	15.3603	0.774825
$394$	−1.12372	−0.0566123
$395$	0	0
$396$	−10.6332	−0.534337
$397$	−3.51819	−0.176573	−0.0882864	−	0.996095i	$-0.528139\pi$
$397$	−3.51819	−0.176573	−0.0882864	+	0.996095i	$0.528139\pi$
$398$	−25.4992	−1.27816
$399$	−9.09507	−0.455323
$400$	0	0
$401$	29.8696	1.49161	0.745807	−	0.666162i	$-0.232064\pi$
$401$	29.8696	1.49161	0.745807	+	0.666162i	$0.232064\pi$
$402$	−28.1815	−1.40557
$403$	−12.8004	−0.637633
$404$	−13.1807	−0.655762
$405$	0	0
$406$	13.9051	0.690100
$407$	−2.41062	−0.119490
$408$	−8.26057	−0.408959
$409$	−38.7628	−1.91670	−0.958348	−	0.285604i	$-0.907806\pi$
$409$	−38.7628	−1.91670	−0.958348	+	0.285604i	$0.907806\pi$
$410$	0	0
$411$	−57.9144	−2.85671
$412$	2.63318	0.129727
$413$	16.6110	0.817374
$414$	−45.0429	−2.21374
$415$	0	0
$416$	−2.41785	−0.118545
$417$	23.5983	1.15561
$418$	−3.06598	−0.149962
$419$	−18.9103	−0.923830	−0.461915	−	0.886924i	$-0.652838\pi$
$419$	−18.9103	−0.923830	−0.461915	+	0.886924i	$0.652838\pi$
$420$	0	0
$421$	−22.0532	−1.07481	−0.537403	−	0.843326i	$-0.680594\pi$
$421$	−22.0532	−1.07481	−0.537403	+	0.843326i	$0.680594\pi$
$422$	−21.3044	−1.03708
$423$	−10.6332	−0.517003
$424$	−6.51738	−0.316512
$425$	0	0
$426$	0.906255	0.0439082
$427$	−4.74464	−0.229609
$428$	−18.8045	−0.908949
$429$	13.1497	0.634872
$430$	0	0
$431$	−9.20578	−0.443427	−0.221713	−	0.975112i	$-0.571165\pi$
$431$	−9.20578	−0.443427	−0.221713	+	0.975112i	$0.571165\pi$
$432$	−8.30550	−0.399599
$433$	−34.7972	−1.67225	−0.836125	−	0.548540i	$-0.815184\pi$
$433$	−34.7972	−1.67225	−0.836125	+	0.548540i	$0.815184\pi$
$434$	−9.70607	−0.465906
$435$	0	0
$436$	10.3093	0.493725
$437$	−12.9877	−0.621286
$438$	−44.3426	−2.11877
$439$	−8.34985	−0.398517	−0.199258	−	0.979947i	$-0.563853\pi$
$439$	−8.34985	−0.398517	−0.199258	+	0.979947i	$0.563853\pi$
$440$	0	0
$441$	−21.1042	−1.00496
$442$	6.73290	0.320252
$443$	1.19887	0.0569599	0.0284799	−	0.999594i	$-0.490933\pi$
$443$	1.19887	0.0569599	0.0284799	+	0.999594i	$0.490933\pi$
$444$	−3.90047	−0.185108
$445$	0	0
$446$	3.24511	0.153661
$447$	4.98229	0.235654
$448$	−1.83337	−0.0866184
$449$	32.7953	1.54771	0.773853	−	0.633365i	$-0.218327\pi$
$449$	32.7953	1.54771	0.773853	+	0.633365i	$0.218327\pi$
$450$	0	0
$451$	−6.44437	−0.303453
$452$	−6.05662	−0.284879
$453$	63.0855	2.96402
$454$	16.3773	0.768623
$455$	0	0
$456$	−4.96086	−0.232313
$457$	−19.7884	−0.925664	−0.462832	−	0.886446i	$-0.653167\pi$
$457$	−19.7884	−0.925664	−0.462832	+	0.886446i	$0.653167\pi$
$458$	5.08998	0.237839
$459$	23.1281	1.07953
$460$	0	0
$461$	9.39976	0.437790	0.218895	−	0.975748i	$-0.429755\pi$
$461$	9.39976	0.437790	0.218895	+	0.975748i	$0.429755\pi$
$462$	9.97091	0.463889
$463$	−17.7329	−0.824118	−0.412059	−	0.911157i	$-0.635190\pi$
$463$	−17.7329	−0.824118	−0.412059	+	0.911157i	$0.635190\pi$
$464$	7.58448	0.352101
$465$	0	0
$466$	−1.66296	−0.0770352
$467$	−21.8608	−1.01160	−0.505798	−	0.862652i	$-0.668802\pi$
$467$	−21.8608	−1.01160	−0.505798	+	0.862652i	$0.668802\pi$
$468$	14.0231	0.648216
$469$	17.4172	0.804249
$470$	0	0
$471$	31.0035	1.42857
$472$	9.06039	0.417038
$473$	−7.89356	−0.362946
$474$	−10.2662	−0.471541
$475$	0	0
$476$	5.10532	0.234002
$477$	37.7996	1.73072
$478$	−12.7998	−0.585450
$479$	−6.11052	−0.279197	−0.139598	−	0.990208i	$-0.544581\pi$
$479$	−6.11052	−0.279197	−0.139598	+	0.990208i	$0.544581\pi$
$480$	0	0
$481$	3.17914	0.144956
$482$	−0.395477	−0.0180135
$483$	42.2375	1.92187
$484$	−7.63877	−0.347217
$485$	0	0
$486$	−3.44417	−0.156231
$487$	−5.06189	−0.229376	−0.114688	−	0.993402i	$-0.536587\pi$
$487$	−5.06189	−0.229376	−0.114688	+	0.993402i	$0.536587\pi$
$488$	−2.58794	−0.117150
$489$	30.8826	1.39656
$490$	0	0
$491$	2.38228	0.107511	0.0537554	−	0.998554i	$-0.482881\pi$
$491$	2.38228	0.107511	0.0537554	+	0.998554i	$0.482881\pi$
$492$	−10.4272	−0.470095
$493$	−21.1203	−0.951209
$494$	4.04342	0.181922
$495$	0	0
$496$	−5.29413	−0.237713
$497$	−0.560096	−0.0251237
$498$	18.9040	0.847109
$499$	−0.0503313	−0.00225314	−0.00112657	−	0.999999i	$-0.500359\pi$
$499$	−0.0503313	−0.00225314	−0.00112657	+	0.999999i	$0.500359\pi$
$500$	0	0
$501$	6.29393	0.281192
$502$	−9.36589	−0.418020
$503$	5.41082	0.241256	0.120628	−	0.992698i	$-0.461509\pi$
$503$	5.41082	0.241256	0.120628	+	0.992698i	$0.461509\pi$
$504$	10.6332	0.473639
$505$	0	0
$506$	14.2384	0.632974
$507$	21.2220	0.942502
$508$	−0.333269	−0.0147864
$509$	18.9463	0.839779	0.419890	−	0.907575i	$-0.362069\pi$
$509$	18.9463	0.839779	0.419890	+	0.907575i	$0.362069\pi$
$510$	0	0
$511$	27.4052	1.21234
$512$	−1.00000	−0.0441942
$513$	13.8895	0.613235
$514$	−4.97926	−0.219626
$515$	0	0
$516$	−12.7720	−0.562258
$517$	3.36123	0.147827
$518$	2.41062	0.105917
$519$	−53.7362	−2.35876
$520$	0	0
$521$	38.4191	1.68317	0.841585	−	0.540125i	$-0.181623\pi$
$521$	38.4191	1.68317	0.841585	+	0.540125i	$0.181623\pi$
$522$	−43.9886	−1.92533
$523$	12.2666	0.536379	0.268189	−	0.963366i	$-0.413575\pi$
$523$	12.2666	0.536379	0.268189	+	0.963366i	$0.413575\pi$
$524$	−5.17801	−0.226202
$525$	0	0
$526$	−19.8112	−0.863809
$527$	14.7424	0.642188
$528$	5.43858	0.236684
$529$	37.3148	1.62238
$530$	0	0
$531$	−52.5486	−2.28041
$532$	3.06598	0.132927
$533$	8.49885	0.368126
$534$	−9.84995	−0.426249
$535$	0	0
$536$	9.50010	0.410342
$537$	−31.3271	−1.35187
$538$	−14.7939	−0.637811
$539$	6.67120	0.287349
$540$	0	0
$541$	42.0273	1.80690	0.903448	−	0.428697i	$-0.141027\pi$
$541$	42.0273	1.80690	0.903448	+	0.428697i	$0.141027\pi$
$542$	12.5564	0.539344
$543$	−53.8593	−2.31132
$544$	2.78467	0.119392
$545$	0	0
$546$	−13.1497	−0.562754
$547$	−19.3715	−0.828265	−0.414132	−	0.910217i	$-0.635915\pi$
$547$	−19.3715	−0.828265	−0.414132	+	0.910217i	$0.635915\pi$
$548$	19.5232	0.833988
$549$	15.0096	0.640592
$550$	0	0
$551$	−12.6837	−0.540344
$552$	23.0382	0.980571
$553$	6.34484	0.269810
$554$	−6.33183	−0.269014
$555$	0	0
$556$	−7.95507	−0.337370
$557$	−8.54685	−0.362142	−0.181071	−	0.983470i	$-0.557956\pi$
$557$	−8.54685	−0.362142	−0.181071	+	0.983470i	$0.557956\pi$
$558$	30.7049	1.29984
$559$	10.4100	0.440298
$560$	0	0
$561$	−15.1447	−0.639408
$562$	20.0892	0.847413
$563$	23.4598	0.988714	0.494357	−	0.869259i	$-0.335404\pi$
$563$	23.4598	0.988714	0.494357	+	0.869259i	$0.335404\pi$
$564$	5.43858	0.229006
$565$	0	0
$566$	1.81678	0.0763650
$567$	−13.2706	−0.557314
$568$	−0.305502	−0.0128186
$569$	−7.10054	−0.297670	−0.148835	−	0.988862i	$-0.547552\pi$
$569$	−7.10054	−0.297670	−0.148835	+	0.988862i	$0.547552\pi$
$570$	0	0
$571$	−11.9620	−0.500593	−0.250297	−	0.968169i	$-0.580528\pi$
$571$	−11.9620	−0.500593	−0.250297	+	0.968169i	$0.580528\pi$
$572$	−4.43280	−0.185345
$573$	64.9804	2.71460
$574$	6.44437	0.268983
$575$	0	0
$576$	5.79981	0.241659
$577$	−41.5696	−1.73057	−0.865283	−	0.501284i	$-0.832861\pi$
$577$	−41.5696	−1.73057	−0.865283	+	0.501284i	$0.832861\pi$
$578$	9.24562	0.384567
$579$	81.3544	3.38097
$580$	0	0
$581$	−11.6833	−0.484706
$582$	−32.8984	−1.36368
$583$	−11.9487	−0.494866
$584$	14.9480	0.618554
$585$	0	0
$586$	−6.85931	−0.283356
$587$	−19.1275	−0.789476	−0.394738	−	0.918794i	$-0.629165\pi$
$587$	−19.1275	−0.789476	−0.394738	+	0.918794i	$0.629165\pi$
$588$	10.7942	0.445146
$589$	8.85348	0.364801
$590$	0	0
$591$	−3.33346	−0.137120
$592$	1.31486	0.0540405
$593$	−0.538428	−0.0221106	−0.0110553	−	0.999939i	$-0.503519\pi$
$593$	−0.538428	−0.0221106	−0.0110553	+	0.999939i	$0.503519\pi$
$594$	−15.2270	−0.624772
$595$	0	0
$596$	−1.67955	−0.0687969
$597$	−75.6419	−3.09582
$598$	−18.7776	−0.767875
$599$	−38.4209	−1.56983	−0.784917	−	0.619601i	$-0.787295\pi$
$599$	−38.4209	−1.56983	−0.784917	+	0.619601i	$0.787295\pi$
$600$	0	0
$601$	19.6034	0.799639	0.399820	−	0.916594i	$-0.369073\pi$
$601$	19.6034	0.799639	0.399820	+	0.916594i	$0.369073\pi$
$602$	7.89356	0.321717
$603$	−55.0988	−2.24380
$604$	−21.2664	−0.865316
$605$	0	0
$606$	−39.0997	−1.58832
$607$	32.4415	1.31676	0.658381	−	0.752685i	$-0.271242\pi$
$607$	32.4415	1.31676	0.658381	+	0.752685i	$0.271242\pi$
$608$	1.67232	0.0678216
$609$	41.2488	1.67149
$610$	0	0
$611$	−4.43280	−0.179332
$612$	−16.1506	−0.652848
$613$	23.4703	0.947957	0.473979	−	0.880536i	$-0.342817\pi$
$613$	23.4703	0.947957	0.473979	+	0.880536i	$0.342817\pi$
$614$	−2.89526	−0.116843
$615$	0	0
$616$	−3.36123	−0.135428
$617$	−17.4133	−0.701032	−0.350516	−	0.936557i	$-0.613994\pi$
$617$	−17.4133	−0.701032	−0.350516	+	0.936557i	$0.613994\pi$
$618$	7.81119	0.314212
$619$	12.5832	0.505763	0.252881	−	0.967497i	$-0.418622\pi$
$619$	12.5832	0.505763	0.252881	+	0.967497i	$0.418622\pi$
$620$	0	0
$621$	−64.5027	−2.58840
$622$	20.6490	0.827950
$623$	6.08760	0.243895
$624$	−7.17242	−0.287127
$625$	0	0
$626$	16.4272	0.656563
$627$	−9.09507	−0.363222
$628$	−10.4514	−0.417056
$629$	−3.66145	−0.145992
$630$	0	0
$631$	41.7362	1.66149	0.830747	−	0.556650i	$-0.187914\pi$
$631$	41.7362	1.66149	0.830747	+	0.556650i	$0.187914\pi$
$632$	3.46076	0.137662
$633$	−63.1983	−2.51191
$634$	16.5059	0.655532
$635$	0	0
$636$	−19.3335	−0.766622
$637$	−8.79799	−0.348589
$638$	13.9051	0.550509
$639$	1.77185	0.0700934
$640$	0	0
$641$	−14.3981	−0.568692	−0.284346	−	0.958722i	$-0.591776\pi$
$641$	−14.3981	−0.568692	−0.284346	+	0.958722i	$0.591776\pi$
$642$	−55.7825	−2.20156
$643$	−30.1666	−1.18966	−0.594828	−	0.803853i	$-0.702780\pi$
$643$	−30.1666	−1.18966	−0.594828	+	0.803853i	$0.702780\pi$
$644$	−14.2384	−0.561071
$645$	0	0
$646$	−4.65686	−0.183222
$647$	10.6878	0.420180	0.210090	−	0.977682i	$-0.432624\pi$
$647$	10.6878	0.420180	0.210090	+	0.977682i	$0.432624\pi$
$648$	−7.23840	−0.284351
$649$	16.6110	0.652039
$650$	0	0
$651$	−28.7925	−1.12847
$652$	−10.4106	−0.407711
$653$	−10.1658	−0.397819	−0.198910	−	0.980018i	$-0.563740\pi$
$653$	−10.1658	−0.397819	−0.198910	+	0.980018i	$0.563740\pi$
$654$	30.5819	1.19585
$655$	0	0
$656$	3.51505	0.137240
$657$	−86.6959	−3.38233
$658$	−3.36123	−0.131034
$659$	31.1202	1.21227	0.606136	−	0.795361i	$-0.292719\pi$
$659$	31.1202	1.21227	0.606136	+	0.795361i	$0.292719\pi$
$660$	0	0
$661$	41.4641	1.61277	0.806383	−	0.591393i	$-0.201422\pi$
$661$	41.4641	1.61277	0.806383	+	0.591393i	$0.201422\pi$
$662$	−27.4710	−1.06769
$663$	19.9728	0.775680
$664$	−6.37261	−0.247305
$665$	0	0
$666$	−7.62595	−0.295500
$667$	58.9031	2.28074
$668$	−2.12171	−0.0820913
$669$	9.62646	0.372181
$670$	0	0
$671$	−4.74464	−0.183165
$672$	−5.43858	−0.209798
$673$	−2.14497	−0.0826824	−0.0413412	−	0.999145i	$-0.513163\pi$
$673$	−2.14497	−0.0826824	−0.0413412	+	0.999145i	$0.513163\pi$
$674$	−2.74521	−0.105742
$675$	0	0
$676$	−7.15401	−0.275154
$677$	−41.5482	−1.59683	−0.798413	−	0.602110i	$-0.794327\pi$
$677$	−41.5482	−1.59683	−0.798413	+	0.602110i	$0.794327\pi$
$678$	−17.9666	−0.690005
$679$	20.3323	0.780283
$680$	0	0
$681$	48.5823	1.86168
$682$	−9.70607	−0.371665
$683$	28.8309	1.10318	0.551592	−	0.834114i	$-0.314020\pi$
$683$	28.8309	1.10318	0.551592	+	0.834114i	$0.314020\pi$
$684$	−9.69916	−0.370857
$685$	0	0
$686$	−19.5048	−0.744695
$687$	15.0991	0.576068
$688$	4.30550	0.164146
$689$	15.7580	0.600333
$690$	0	0
$691$	−49.2045	−1.87183	−0.935914	−	0.352230i	$-0.885424\pi$
$691$	−49.2045	−1.87183	−0.935914	+	0.352230i	$0.885424\pi$
$692$	18.1147	0.688617
$693$	19.4945	0.740535
$694$	−21.3391	−0.810019
$695$	0	0
$696$	22.4990	0.852821
$697$	−9.78824	−0.370756
$698$	16.7650	0.634565
$699$	−4.93309	−0.186587
$700$	0	0
$701$	−24.9783	−0.943419	−0.471709	−	0.881754i	$-0.656363\pi$
$701$	−24.9783	−0.943419	−0.471709	+	0.881754i	$0.656363\pi$
$702$	20.0814	0.757925
$703$	−2.19887	−0.0829321
$704$	−1.83337	−0.0690976
$705$	0	0
$706$	2.98862	0.112478
$707$	24.1650	0.908817
$708$	26.8772	1.01011
$709$	9.79239	0.367761	0.183881	−	0.982949i	$-0.441134\pi$
$709$	9.79239	0.367761	0.183881	+	0.982949i	$0.441134\pi$
$710$	0	0
$711$	−20.0718	−0.752750
$712$	3.32045	0.124439
$713$	−41.1156	−1.53979
$714$	15.1447	0.566774
$715$	0	0
$716$	10.5605	0.394664
$717$	−37.9700	−1.41801
$718$	−6.70494	−0.250226
$719$	−8.58417	−0.320135	−0.160068	−	0.987106i	$-0.551171\pi$
$719$	−8.58417	−0.320135	−0.160068	+	0.987106i	$0.551171\pi$
$720$	0	0
$721$	−4.82758	−0.179788
$722$	16.2033	0.603026
$723$	−1.17316	−0.0436304
$724$	18.1561	0.674768
$725$	0	0
$726$	−22.6600	−0.840992
$727$	24.0162	0.890713	0.445356	−	0.895353i	$-0.353077\pi$
$727$	24.0162	0.890713	0.445356	+	0.895353i	$0.353077\pi$
$728$	4.43280	0.164290
$729$	−31.9322	−1.18267
$730$	0	0
$731$	−11.9894	−0.443444
$732$	−7.67698	−0.283749
$733$	19.0091	0.702118	0.351059	−	0.936353i	$-0.385822\pi$
$733$	19.0091	0.702118	0.351059	+	0.936353i	$0.385822\pi$
$734$	4.01659	0.148255
$735$	0	0
$736$	−7.76626	−0.286268
$737$	17.4172	0.641569
$738$	−20.3866	−0.750442
$739$	−20.7920	−0.764845	−0.382423	−	0.923988i	$-0.624910\pi$
$739$	−20.7920	−0.764845	−0.382423	+	0.923988i	$0.624910\pi$
$740$	0	0
$741$	11.9946	0.440633
$742$	11.9487	0.438652
$743$	−6.53365	−0.239696	−0.119848	−	0.992792i	$-0.538241\pi$
$743$	−6.53365	−0.239696	−0.119848	+	0.992792i	$0.538241\pi$
$744$	−15.7047	−0.575764
$745$	0	0
$746$	26.5832	0.973281
$747$	36.9599	1.35229
$748$	5.10532	0.186669
$749$	34.4755	1.25971
$750$	0	0
$751$	27.9879	1.02129	0.510646	−	0.859791i	$-0.329406\pi$
$751$	27.9879	1.02129	0.510646	+	0.859791i	$0.329406\pi$
$752$	−1.83337	−0.0668560
$753$	−27.7834	−1.01248
$754$	−18.3381	−0.667835
$755$	0	0
$756$	15.2270	0.553801
$757$	−4.48558	−0.163031	−0.0815156	−	0.996672i	$-0.525976\pi$
$757$	−4.48558	−0.163031	−0.0815156	+	0.996672i	$0.525976\pi$
$758$	15.6278	0.567627
$759$	42.2375	1.53312
$760$	0	0
$761$	0.449070	0.0162788	0.00813939	−	0.999967i	$-0.497409\pi$
$761$	0.449070	0.0162788	0.00813939	+	0.999967i	$0.497409\pi$
$762$	−0.988624	−0.0358141
$763$	−18.9007	−0.684250
$764$	−21.9051	−0.792500
$765$	0	0
$766$	13.4455	0.485805
$767$	−21.9066	−0.791003
$768$	−2.96645	−0.107042
$769$	20.9864	0.756788	0.378394	−	0.925645i	$-0.376476\pi$
$769$	20.9864	0.756788	0.378394	+	0.925645i	$0.376476\pi$
$770$	0	0
$771$	−14.7707	−0.531955
$772$	−27.4248	−0.987041
$773$	−35.0412	−1.26035	−0.630173	−	0.776455i	$-0.717016\pi$
$773$	−35.0412	−1.26035	−0.630173	+	0.776455i	$0.717016\pi$
$774$	−24.9711	−0.897568
$775$	0	0
$776$	11.0902	0.398114
$777$	7.15099	0.256540
$778$	25.1116	0.900295
$779$	−5.87829	−0.210612
$780$	0	0
$781$	−0.560096	−0.0200418
$782$	21.6265	0.773361
$783$	−62.9929	−2.25118
$784$	−3.63877	−0.129956
$785$	0	0
$786$	−15.3603	−0.547884
$787$	−39.1993	−1.39730	−0.698651	−	0.715462i	$-0.746216\pi$
$787$	−39.1993	−1.39730	−0.698651	+	0.715462i	$0.746216\pi$
$788$	1.12372	0.0400309
$789$	−58.7689	−2.09223
$790$	0	0
$791$	11.1040	0.394813
$792$	10.6332	0.377834
$793$	6.25724	0.222201
$794$	3.51819	0.124856
$795$	0	0
$796$	25.4992	0.903794
$797$	8.63368	0.305821	0.152910	−	0.988240i	$-0.451135\pi$
$797$	8.63368	0.305821	0.152910	+	0.988240i	$0.451135\pi$
$798$	9.09507	0.321962
$799$	5.10532	0.180613
$800$	0	0
$801$	−19.2580	−0.680448
$802$	−29.8696	−1.05473
$803$	27.4052	0.967109
$804$	28.1815	0.993886
$805$	0	0
$806$	12.8004	0.450874
$807$	−43.8854	−1.54484
$808$	13.1807	0.463694
$809$	−45.8972	−1.61366	−0.806829	−	0.590785i	$-0.798818\pi$
$809$	−45.8972	−1.61366	−0.806829	+	0.590785i	$0.798818\pi$
$810$	0	0
$811$	39.3940	1.38331	0.691656	−	0.722227i	$-0.256881\pi$
$811$	39.3940	1.38331	0.691656	+	0.722227i	$0.256881\pi$
$812$	−13.9051	−0.487974
$813$	37.2479	1.30634
$814$	2.41062	0.0844923
$815$	0	0
$816$	8.26057	0.289178
$817$	−7.20019	−0.251903
$818$	38.7628	1.35531
$819$	−25.7094	−0.898359
$820$	0	0
$821$	27.2766	0.951960	0.475980	−	0.879456i	$-0.342093\pi$
$821$	27.2766	0.951960	0.475980	+	0.879456i	$0.342093\pi$
$822$	57.9144	2.02000
$823$	−6.13887	−0.213987	−0.106994	−	0.994260i	$-0.534122\pi$
$823$	−6.13887	−0.213987	−0.106994	+	0.994260i	$0.534122\pi$
$824$	−2.63318	−0.0917311
$825$	0	0
$826$	−16.6110	−0.577971
$827$	−44.0654	−1.53231	−0.766153	−	0.642659i	$-0.777831\pi$
$827$	−44.0654	−1.53231	−0.766153	+	0.642659i	$0.777831\pi$
$828$	45.0429	1.56535
$829$	4.69997	0.163237	0.0816183	−	0.996664i	$-0.473991\pi$
$829$	4.69997	0.163237	0.0816183	+	0.996664i	$0.473991\pi$
$830$	0	0
$831$	−18.7830	−0.651576
$832$	2.41785	0.0838238
$833$	10.1328	0.351080
$834$	−23.5983	−0.817143
$835$	0	0
$836$	3.06598	0.106039
$837$	43.9704	1.51984
$838$	18.9103	0.653247
$839$	−46.1940	−1.59480	−0.797398	−	0.603454i	$-0.793791\pi$
$839$	−46.1940	−1.59480	−0.797398	+	0.603454i	$0.793791\pi$
$840$	0	0
$841$	28.5244	0.983599
$842$	22.0532	0.760002
$843$	59.5937	2.05252
$844$	21.3044	0.733327
$845$	0	0
$846$	10.6332	0.365576
$847$	14.0047	0.481206
$848$	6.51738	0.223808
$849$	5.38938	0.184963
$850$	0	0
$851$	10.2116	0.350048
$852$	−0.906255	−0.0310478
$853$	−12.6427	−0.432879	−0.216439	−	0.976296i	$-0.569444\pi$
$853$	−12.6427	−0.432879	−0.216439	+	0.976296i	$0.569444\pi$
$854$	4.74464	0.162358
$855$	0	0
$856$	18.8045	0.642724
$857$	19.4162	0.663245	0.331623	−	0.943412i	$-0.392404\pi$
$857$	19.4162	0.663245	0.331623	+	0.943412i	$0.392404\pi$
$858$	−13.1497	−0.448922
$859$	9.33905	0.318644	0.159322	−	0.987227i	$-0.449069\pi$
$859$	9.33905	0.318644	0.159322	+	0.987227i	$0.449069\pi$
$860$	0	0
$861$	19.1169	0.651502
$862$	9.20578	0.313550
$863$	16.3445	0.556372	0.278186	−	0.960527i	$-0.410267\pi$
$863$	16.3445	0.556372	0.278186	+	0.960527i	$0.410267\pi$
$864$	8.30550	0.282559
$865$	0	0
$866$	34.7972	1.18246
$867$	27.4267	0.931458
$868$	9.70607	0.329445
$869$	6.34484	0.215234
$870$	0	0
$871$	−22.9698	−0.778302
$872$	−10.3093	−0.349116
$873$	−64.3209	−2.17693
$874$	12.9877	0.439315
$875$	0	0
$876$	44.3426	1.49820
$877$	35.5051	1.19892	0.599461	−	0.800404i	$-0.295382\pi$
$877$	35.5051	1.19892	0.599461	+	0.800404i	$0.295382\pi$
$878$	8.34985	0.281794
$879$	−20.3478	−0.686314
$880$	0	0
$881$	−31.5665	−1.06350	−0.531750	−	0.846901i	$-0.678466\pi$
$881$	−31.5665	−1.06350	−0.531750	+	0.846901i	$0.678466\pi$
$882$	21.1042	0.710615
$883$	−34.9303	−1.17550	−0.587748	−	0.809044i	$-0.699986\pi$
$883$	−34.9303	−1.17550	−0.587748	+	0.809044i	$0.699986\pi$
$884$	−6.73290	−0.226452
$885$	0	0
$886$	−1.19887	−0.0402767
$887$	42.9323	1.44153	0.720764	−	0.693181i	$-0.243791\pi$
$887$	42.9323	1.44153	0.720764	+	0.693181i	$0.243791\pi$
$888$	3.90047	0.130891
$889$	0.611003	0.0204924
$890$	0	0
$891$	−13.2706	−0.444583
$892$	−3.24511	−0.108654
$893$	3.06598	0.102599
$894$	−4.98229	−0.166633
$895$	0	0
$896$	1.83337	0.0612484
$897$	−55.7029	−1.85987
$898$	−32.7953	−1.09439
$899$	−40.1532	−1.33918
$900$	0	0
$901$	−18.1487	−0.604622
$902$	6.44437	0.214574
$903$	23.4158	0.779230
$904$	6.05662	0.201440
$905$	0	0
$906$	−63.0855	−2.09588
$907$	39.8259	1.32240	0.661199	−	0.750211i	$-0.270048\pi$
$907$	39.8259	1.32240	0.661199	+	0.750211i	$0.270048\pi$
$908$	−16.3773	−0.543499
$909$	−76.4453	−2.53553
$910$	0	0
$911$	−1.68984	−0.0559869	−0.0279934	−	0.999608i	$-0.508912\pi$
$911$	−1.68984	−0.0559869	−0.0279934	+	0.999608i	$0.508912\pi$
$912$	4.96086	0.164270
$913$	−11.6833	−0.386661
$914$	19.7884	0.654543
$915$	0	0
$916$	−5.08998	−0.168178
$917$	9.49319	0.313493
$918$	−23.1281	−0.763340
$919$	−29.9144	−0.986787	−0.493393	−	0.869806i	$-0.664244\pi$
$919$	−29.9144	−0.986787	−0.493393	+	0.869806i	$0.664244\pi$
$920$	0	0
$921$	−8.58864	−0.283005
$922$	−9.39976	−0.309564
$923$	0.738656	0.0243132
$924$	−9.97091	−0.328019
$925$	0	0
$926$	17.7329	0.582739
$927$	15.2719	0.501597
$928$	−7.58448	−0.248973
$929$	−15.9037	−0.521783	−0.260892	−	0.965368i	$-0.584017\pi$
$929$	−15.9037	−0.521783	−0.260892	+	0.965368i	$0.584017\pi$
$930$	0	0
$931$	6.08520	0.199434
$932$	1.66296	0.0544721
$933$	61.2542	2.00537
$934$	21.8608	0.715306
$935$	0	0
$936$	−14.0231	−0.458358
$937$	−46.2671	−1.51148	−0.755739	−	0.654872i	$-0.772722\pi$
$937$	−46.2671	−1.51148	−0.755739	+	0.654872i	$0.772722\pi$
$938$	−17.4172	−0.568690
$939$	48.7305	1.59026
$940$	0	0
$941$	−11.6709	−0.380460	−0.190230	−	0.981740i	$-0.560923\pi$
$941$	−11.6709	−0.380460	−0.190230	+	0.981740i	$0.560923\pi$
$942$	−31.0035	−1.01015
$943$	27.2988	0.888971
$944$	−9.06039	−0.294890
$945$	0	0
$946$	7.89356	0.256642
$947$	2.93363	0.0953303	0.0476651	−	0.998863i	$-0.484822\pi$
$947$	2.93363	0.0953303	0.0476651	+	0.998863i	$0.484822\pi$
$948$	10.2662	0.333430
$949$	−36.1421	−1.17322
$950$	0	0
$951$	48.9638	1.58776
$952$	−5.10532	−0.165464
$953$	9.93705	0.321893	0.160946	−	0.986963i	$-0.448545\pi$
$953$	9.93705	0.321893	0.160946	+	0.986963i	$0.448545\pi$
$954$	−37.7996	−1.22381
$955$	0	0
$956$	12.7998	0.413976
$957$	41.2488	1.33339
$958$	6.11052	0.197422
$959$	−35.7931	−1.15582
$960$	0	0
$961$	−2.97223	−0.0958785
$962$	−3.17914	−0.102499
$963$	−109.062	−3.51449
$964$	0.395477	0.0127375
$965$	0	0
$966$	−42.2375	−1.35897
$967$	−45.3875	−1.45956	−0.729782	−	0.683680i	$-0.760379\pi$
$967$	−45.3875	−1.45956	−0.729782	+	0.683680i	$0.760379\pi$
$968$	7.63877	0.245519
$969$	−13.8143	−0.443781
$970$	0	0
$971$	−4.68277	−0.150277	−0.0751386	−	0.997173i	$-0.523940\pi$
$971$	−4.68277	−0.150277	−0.0751386	+	0.997173i	$0.523940\pi$
$972$	3.44417	0.110472
$973$	14.5846	0.467559
$974$	5.06189	0.162194
$975$	0	0
$976$	2.58794	0.0828379
$977$	−3.20804	−0.102634	−0.0513171	−	0.998682i	$-0.516342\pi$
$977$	−3.20804	−0.102634	−0.0513171	+	0.998682i	$0.516342\pi$
$978$	−30.8826	−0.987516
$979$	6.08760	0.194561
$980$	0	0
$981$	59.7919	1.90901
$982$	−2.38228	−0.0760216
$983$	−19.5715	−0.624233	−0.312117	−	0.950044i	$-0.601038\pi$
$983$	−19.5715	−0.624233	−0.312117	+	0.950044i	$0.601038\pi$
$984$	10.4272	0.332407
$985$	0	0
$986$	21.1203	0.672606
$987$	−9.97091	−0.317378
$988$	−4.04342	−0.128638
$989$	33.4377	1.06326
$990$	0	0
$991$	45.2280	1.43671	0.718357	−	0.695674i	$-0.244894\pi$
$991$	45.2280	1.43671	0.718357	+	0.695674i	$0.244894\pi$
$992$	5.29413	0.168089
$993$	−81.4913	−2.58605
$994$	0.560096	0.0177652
$995$	0	0
$996$	−18.9040	−0.598996
$997$	58.0714	1.83914	0.919570	−	0.392926i	$-0.128537\pi$
$997$	58.0714	1.83914	0.919570	+	0.392926i	$0.128537\pi$
$998$	0.0503313	0.00159321
$999$	−10.9206	−0.345512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.2.a.f.1.1		4
4.3	odd	2		10000.2.a.x.1.4		4
5.2	odd	4		1250.2.b.e.1249.4		8
5.3	odd	4		1250.2.b.e.1249.5		8
5.4	even	2		1250.2.a.l.1.4		4
20.19	odd	2		10000.2.a.t.1.1		4
25.2	odd	20		250.2.e.c.149.2		16
25.9	even	10		50.2.d.b.31.1	yes	8
25.11	even	5		250.2.d.d.101.2		8
25.12	odd	20		250.2.e.c.99.3		16
25.13	odd	20		250.2.e.c.99.2		16
25.14	even	10		50.2.d.b.21.1	✓	8
25.16	even	5		250.2.d.d.151.2		8
25.23	odd	20		250.2.e.c.149.3		16
75.14	odd	10		450.2.h.e.271.1		8
75.59	odd	10		450.2.h.e.181.1		8
100.39	odd	10		400.2.u.d.321.2		8
100.59	odd	10		400.2.u.d.81.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.21.1	✓	8	25.14	even	10
50.2.d.b.31.1	yes	8	25.9	even	10
250.2.d.d.101.2		8	25.11	even	5
250.2.d.d.151.2		8	25.16	even	5
250.2.e.c.99.2		16	25.13	odd	20
250.2.e.c.99.3		16	25.12	odd	20
250.2.e.c.149.2		16	25.2	odd	20
250.2.e.c.149.3		16	25.23	odd	20
400.2.u.d.81.2		8	100.59	odd	10
400.2.u.d.321.2		8	100.39	odd	10
450.2.h.e.181.1		8	75.59	odd	10
450.2.h.e.271.1		8	75.14	odd	10
1250.2.a.f.1.1		4	1.1	even	1	trivial
1250.2.a.l.1.4		4	5.4	even	2
1250.2.b.e.1249.4		8	5.2	odd	4
1250.2.b.e.1249.5		8	5.3	odd	4
10000.2.a.t.1.1		4	20.19	odd	2
10000.2.a.x.1.4		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1250.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.96645 q^{3} +1.00000 q^{4} +2.96645 q^{6} -1.83337 q^{7} -1.00000 q^{8} +5.79981 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.96645 q^{3} +1.00000 q^{4} +2.96645 q^{6} -1.83337 q^{7} -1.00000 q^{8} +5.79981 q^{9} -1.83337 q^{11} -2.96645 q^{12} +2.41785 q^{13} +1.83337 q^{14} +1.00000 q^{16} -2.78467 q^{17} -5.79981 q^{18} -1.67232 q^{19} +5.43858 q^{21} +1.83337 q^{22} +7.76626 q^{23} +2.96645 q^{24} -2.41785 q^{26} -8.30550 q^{27} -1.83337 q^{28} +7.58448 q^{29} -5.29413 q^{31} -1.00000 q^{32} +5.43858 q^{33} +2.78467 q^{34} +5.79981 q^{36} +1.31486 q^{37} +1.67232 q^{38} -7.17242 q^{39} +3.51505 q^{41} -5.43858 q^{42} +4.30550 q^{43} -1.83337 q^{44} -7.76626 q^{46} -1.83337 q^{47} -2.96645 q^{48} -3.63877 q^{49} +8.26057 q^{51} +2.41785 q^{52} +6.51738 q^{53} +8.30550 q^{54} +1.83337 q^{56} +4.96086 q^{57} -7.58448 q^{58} -9.06039 q^{59} +2.58794 q^{61} +5.29413 q^{62} -10.6332 q^{63} +1.00000 q^{64} -5.43858 q^{66} -9.50010 q^{67} -2.78467 q^{68} -23.0382 q^{69} +0.305502 q^{71} -5.79981 q^{72} -14.9480 q^{73} -1.31486 q^{74} -1.67232 q^{76} +3.36123 q^{77} +7.17242 q^{78} -3.46076 q^{79} +7.23840 q^{81} -3.51505 q^{82} +6.37261 q^{83} +5.43858 q^{84} -4.30550 q^{86} -22.4990 q^{87} +1.83337 q^{88} -3.32045 q^{89} -4.43280 q^{91} +7.76626 q^{92} +15.7047 q^{93} +1.83337 q^{94} +2.96645 q^{96} -11.0902 q^{97} +3.63877 q^{98} -10.6332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{6} - 2 q^{7} - 4 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^6 - 2 * q^7 - 4 * q^8 + 7 * q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{6} - 2 q^{7} - 4 q^{8} + 7 q^{9} - 2 q^{11} - q^{12} - 11 q^{13} + 2 q^{14} + 4 q^{16} - 12 q^{17} - 7 q^{18} - 5 q^{19} - 7 q^{21} + 2 q^{22} + 4 q^{23} + q^{24} + 11 q^{26} - 10 q^{27} - 2 q^{28} + 15 q^{29} - 12 q^{31} - 4 q^{32} - 7 q^{33} + 12 q^{34} + 7 q^{36} - 12 q^{37} + 5 q^{38} - 11 q^{39} + 13 q^{41} + 7 q^{42} - 6 q^{43} - 2 q^{44} - 4 q^{46} - 2 q^{47} - q^{48} - 2 q^{49} + 13 q^{51} - 11 q^{52} - 11 q^{53} + 10 q^{54} + 2 q^{56} - 15 q^{58} + 8 q^{61} + 12 q^{62} - 21 q^{63} + 4 q^{64} + 7 q^{66} - 22 q^{67} - 12 q^{68} - 31 q^{69} - 22 q^{71} - 7 q^{72} - 21 q^{73} + 12 q^{74} - 5 q^{76} + 26 q^{77} + 11 q^{78} - 10 q^{79} - 16 q^{81} - 13 q^{82} + 24 q^{83} - 7 q^{84} + 6 q^{86} - 25 q^{87} + 2 q^{88} - 5 q^{89} - 12 q^{91} + 4 q^{92} + 23 q^{93} + 2 q^{94} + q^{96} - 22 q^{97} + 2 q^{98} - 21 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^6 - 2 * q^7 - 4 * q^8 + 7 * q^9 - 2 * q^11 - q^12 - 11 * q^13 + 2 * q^14 + 4 * q^16 - 12 * q^17 - 7 * q^18 - 5 * q^19 - 7 * q^21 + 2 * q^22 + 4 * q^23 + q^24 + 11 * q^26 - 10 * q^27 - 2 * q^28 + 15 * q^29 - 12 * q^31 - 4 * q^32 - 7 * q^33 + 12 * q^34 + 7 * q^36 - 12 * q^37 + 5 * q^38 - 11 * q^39 + 13 * q^41 + 7 * q^42 - 6 * q^43 - 2 * q^44 - 4 * q^46 - 2 * q^47 - q^48 - 2 * q^49 + 13 * q^51 - 11 * q^52 - 11 * q^53 + 10 * q^54 + 2 * q^56 - 15 * q^58 + 8 * q^61 + 12 * q^62 - 21 * q^63 + 4 * q^64 + 7 * q^66 - 22 * q^67 - 12 * q^68 - 31 * q^69 - 22 * q^71 - 7 * q^72 - 21 * q^73 + 12 * q^74 - 5 * q^76 + 26 * q^77 + 11 * q^78 - 10 * q^79 - 16 * q^81 - 13 * q^82 + 24 * q^83 - 7 * q^84 + 6 * q^86 - 25 * q^87 + 2 * q^88 - 5 * q^89 - 12 * q^91 + 4 * q^92 + 23 * q^93 + 2 * q^94 + q^96 - 22 * q^97 + 2 * q^98 - 21 * q^99

Introduction

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