LMFDB - Embedded newform 775.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} -1.23607 q^{3} -1.61803 q^{4} -0.763932 q^{6} +4.23607 q^{7} -2.23607 q^{8} -1.47214 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} -1.23607 q^{3} -1.61803 q^{4} -0.763932 q^{6} +4.23607 q^{7} -2.23607 q^{8} -1.47214 q^{9} +2.00000 q^{11} +2.00000 q^{12} -1.23607 q^{13} +2.61803 q^{14} +1.85410 q^{16} -5.23607 q^{17} -0.909830 q^{18} +2.23607 q^{19} -5.23607 q^{21} +1.23607 q^{22} +7.70820 q^{23} +2.76393 q^{24} -0.763932 q^{26} +5.52786 q^{27} -6.85410 q^{28} +7.23607 q^{29} +1.00000 q^{31} +5.61803 q^{32} -2.47214 q^{33} -3.23607 q^{34} +2.38197 q^{36} +2.00000 q^{37} +1.38197 q^{38} +1.52786 q^{39} +7.00000 q^{41} -3.23607 q^{42} +3.23607 q^{43} -3.23607 q^{44} +4.76393 q^{46} +6.47214 q^{47} -2.29180 q^{48} +10.9443 q^{49} +6.47214 q^{51} +2.00000 q^{52} +1.52786 q^{53} +3.41641 q^{54} -9.47214 q^{56} -2.76393 q^{57} +4.47214 q^{58} -2.23607 q^{59} -14.1803 q^{61} +0.618034 q^{62} -6.23607 q^{63} -0.236068 q^{64} -1.52786 q^{66} -8.00000 q^{67} +8.47214 q^{68} -9.52786 q^{69} +13.1803 q^{71} +3.29180 q^{72} +0.472136 q^{73} +1.23607 q^{74} -3.61803 q^{76} +8.47214 q^{77} +0.944272 q^{78} +1.70820 q^{79} -2.41641 q^{81} +4.32624 q^{82} -2.94427 q^{83} +8.47214 q^{84} +2.00000 q^{86} -8.94427 q^{87} -4.47214 q^{88} -1.70820 q^{89} -5.23607 q^{91} -12.4721 q^{92} -1.23607 q^{93} +4.00000 q^{94} -6.94427 q^{96} -1.94427 q^{97} +6.76393 q^{98} -2.94427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} - q^{4} - 6 q^{6} + 4 q^{7} + 6 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 - q^4 - 6 * q^6 + 4 * q^7 + 6 * q^9	$ 2 q - q^{2} + 2 q^{3} - q^{4} - 6 q^{6} + 4 q^{7} + 6 q^{9} + 4 q^{11} + 4 q^{12} + 2 q^{13} + 3 q^{14} - 3 q^{16} - 6 q^{17} - 13 q^{18} - 6 q^{21} - 2 q^{22} + 2 q^{23} + 10 q^{24} - 6 q^{26} + 20 q^{27} - 7 q^{28} + 10 q^{29} + 2 q^{31} + 9 q^{32} + 4 q^{33} - 2 q^{34} + 7 q^{36} + 4 q^{37} + 5 q^{38} + 12 q^{39} + 14 q^{41} - 2 q^{42} + 2 q^{43} - 2 q^{44} + 14 q^{46} + 4 q^{47} - 18 q^{48} + 4 q^{49} + 4 q^{51} + 4 q^{52} + 12 q^{53} - 20 q^{54} - 10 q^{56} - 10 q^{57} - 6 q^{61} - q^{62} - 8 q^{63} + 4 q^{64} - 12 q^{66} - 16 q^{67} + 8 q^{68} - 28 q^{69} + 4 q^{71} + 20 q^{72} - 8 q^{73} - 2 q^{74} - 5 q^{76} + 8 q^{77} - 16 q^{78} - 10 q^{79} + 22 q^{81} - 7 q^{82} + 12 q^{83} + 8 q^{84} + 4 q^{86} + 10 q^{89} - 6 q^{91} - 16 q^{92} + 2 q^{93} + 8 q^{94} + 4 q^{96} + 14 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 - q^4 - 6 * q^6 + 4 * q^7 + 6 * q^9 + 4 * q^11 + 4 * q^12 + 2 * q^13 + 3 * q^14 - 3 * q^16 - 6 * q^17 - 13 * q^18 - 6 * q^21 - 2 * q^22 + 2 * q^23 + 10 * q^24 - 6 * q^26 + 20 * q^27 - 7 * q^28 + 10 * q^29 + 2 * q^31 + 9 * q^32 + 4 * q^33 - 2 * q^34 + 7 * q^36 + 4 * q^37 + 5 * q^38 + 12 * q^39 + 14 * q^41 - 2 * q^42 + 2 * q^43 - 2 * q^44 + 14 * q^46 + 4 * q^47 - 18 * q^48 + 4 * q^49 + 4 * q^51 + 4 * q^52 + 12 * q^53 - 20 * q^54 - 10 * q^56 - 10 * q^57 - 6 * q^61 - q^62 - 8 * q^63 + 4 * q^64 - 12 * q^66 - 16 * q^67 + 8 * q^68 - 28 * q^69 + 4 * q^71 + 20 * q^72 - 8 * q^73 - 2 * q^74 - 5 * q^76 + 8 * q^77 - 16 * q^78 - 10 * q^79 + 22 * q^81 - 7 * q^82 + 12 * q^83 + 8 * q^84 + 4 * q^86 + 10 * q^89 - 6 * q^91 - 16 * q^92 + 2 * q^93 + 8 * q^94 + 4 * q^96 + 14 * q^97 + 18 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	−1.23607	−0.713644	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	−1.23607	−0.713644	−0.356822	+	0.934172i	$0.616140\pi$
$4$	−1.61803	−0.809017
$5$	0	0
$5$	0	0
$6$	−0.763932	−0.311874
$7$	4.23607	1.60108	0.800542	−	0.599277i	$-0.204545\pi$
$7$	4.23607	1.60108	0.800542	+	0.599277i	$0.204545\pi$
$8$	−2.23607	−0.790569
$9$	−1.47214	−0.490712
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	2.00000	0.577350
$13$	−1.23607	−0.342824	−0.171412	−	0.985199i	$-0.554833\pi$
$13$	−1.23607	−0.342824	−0.171412	+	0.985199i	$0.554833\pi$
$14$	2.61803	0.699699
$15$	0	0
$16$	1.85410	0.463525
$17$	−5.23607	−1.26993	−0.634967	−	0.772540i	$-0.718986\pi$
$17$	−5.23607	−1.26993	−0.634967	+	0.772540i	$0.718986\pi$
$18$	−0.909830	−0.214449
$19$	2.23607	0.512989	0.256495	−	0.966546i	$-0.417432\pi$
$19$	2.23607	0.512989	0.256495	+	0.966546i	$0.417432\pi$
$20$	0	0
$21$	−5.23607	−1.14260
$22$	1.23607	0.263531
$23$	7.70820	1.60727	0.803636	−	0.595121i	$-0.202896\pi$
$23$	7.70820	1.60727	0.803636	+	0.595121i	$0.202896\pi$
$24$	2.76393	0.564185
$25$	0	0
$26$	−0.763932	−0.149819
$27$	5.52786	1.06384
$28$	−6.85410	−1.29530
$29$	7.23607	1.34370	0.671852	−	0.740685i	$-0.265499\pi$
$29$	7.23607	1.34370	0.671852	+	0.740685i	$0.265499\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.61803	0.993137
$33$	−2.47214	−0.430344
$34$	−3.23607	−0.554981
$35$	0	0
$36$	2.38197	0.396994
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	1.38197	0.224184
$39$	1.52786	0.244654
$40$	0	0
$41$	7.00000	1.09322	0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000	1.09322	0.546608	+	0.837389i	$0.315919\pi$
$42$	−3.23607	−0.499336
$43$	3.23607	0.493496	0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607	0.493496	0.246748	+	0.969080i	$0.420638\pi$
$44$	−3.23607	−0.487856
$45$	0	0
$46$	4.76393	0.702403
$47$	6.47214	0.944058	0.472029	−	0.881583i	$-0.343522\pi$
$47$	6.47214	0.944058	0.472029	+	0.881583i	$0.343522\pi$
$48$	−2.29180	−0.330792
$49$	10.9443	1.56347
$50$	0	0
$51$	6.47214	0.906280
$52$	2.00000	0.277350
$53$	1.52786	0.209868	0.104934	−	0.994479i	$-0.466537\pi$
$53$	1.52786	0.209868	0.104934	+	0.994479i	$0.466537\pi$
$54$	3.41641	0.464914
$55$	0	0
$56$	−9.47214	−1.26577
$57$	−2.76393	−0.366092
$58$	4.47214	0.587220
$59$	−2.23607	−0.291111	−0.145556	−	0.989350i	$-0.546497\pi$
$59$	−2.23607	−0.291111	−0.145556	+	0.989350i	$0.546497\pi$
$60$	0	0
$61$	−14.1803	−1.81561	−0.907803	−	0.419396i	$-0.862242\pi$
$61$	−14.1803	−1.81561	−0.907803	+	0.419396i	$0.862242\pi$
$62$	0.618034	0.0784904
$63$	−6.23607	−0.785671
$64$	−0.236068	−0.0295085
$65$	0	0
$66$	−1.52786	−0.188067
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	8.47214	1.02740
$69$	−9.52786	−1.14702
$70$	0	0
$71$	13.1803	1.56422	0.782109	−	0.623141i	$-0.214144\pi$
$71$	13.1803	1.56422	0.782109	+	0.623141i	$0.214144\pi$
$72$	3.29180	0.387942
$73$	0.472136	0.0552593	0.0276297	−	0.999618i	$-0.491204\pi$
$73$	0.472136	0.0552593	0.0276297	+	0.999618i	$0.491204\pi$
$74$	1.23607	0.143690
$75$	0	0
$76$	−3.61803	−0.415017
$77$	8.47214	0.965489
$78$	0.944272	0.106918
$79$	1.70820	0.192188	0.0960940	−	0.995372i	$-0.469365\pi$
$79$	1.70820	0.192188	0.0960940	+	0.995372i	$0.469365\pi$
$80$	0	0
$81$	−2.41641	−0.268490
$82$	4.32624	0.477753
$83$	−2.94427	−0.323176	−0.161588	−	0.986858i	$-0.551662\pi$
$83$	−2.94427	−0.323176	−0.161588	+	0.986858i	$0.551662\pi$
$84$	8.47214	0.924386
$85$	0	0
$86$	2.00000	0.215666
$87$	−8.94427	−0.958927
$88$	−4.47214	−0.476731
$89$	−1.70820	−0.181069	−0.0905346	−	0.995893i	$-0.528858\pi$
$89$	−1.70820	−0.181069	−0.0905346	+	0.995893i	$0.528858\pi$
$90$	0	0
$91$	−5.23607	−0.548889
$92$	−12.4721	−1.30031
$93$	−1.23607	−0.128174
$94$	4.00000	0.412568
$95$	0	0
$96$	−6.94427	−0.708747
$97$	−1.94427	−0.197411	−0.0987055	−	0.995117i	$-0.531470\pi$
$97$	−1.94427	−0.197411	−0.0987055	+	0.995117i	$0.531470\pi$
$98$	6.76393	0.683260
$99$	−2.94427	−0.295910
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	4.00000	0.396059
$103$	−1.76393	−0.173805	−0.0869027	−	0.996217i	$-0.527697\pi$
$103$	−1.76393	−0.173805	−0.0869027	+	0.996217i	$0.527697\pi$
$104$	2.76393	0.271026
$105$	0	0
$106$	0.944272	0.0917158
$107$	−10.2361	−0.989558	−0.494779	−	0.869019i	$-0.664751\pi$
$107$	−10.2361	−0.989558	−0.494779	+	0.869019i	$0.664751\pi$
$108$	−8.94427	−0.860663
$109$	3.94427	0.377793	0.188896	−	0.981997i	$-0.439509\pi$
$109$	3.94427	0.377793	0.188896	+	0.981997i	$0.439509\pi$
$110$	0	0
$111$	−2.47214	−0.234645
$112$	7.85410	0.742143
$113$	5.47214	0.514775	0.257388	−	0.966308i	$-0.417138\pi$
$113$	5.47214	0.514775	0.257388	+	0.966308i	$0.417138\pi$
$114$	−1.70820	−0.159988
$115$	0	0
$116$	−11.7082	−1.08708
$117$	1.81966	0.168228
$118$	−1.38197	−0.127220
$119$	−22.1803	−2.03327
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−8.76393	−0.793449
$123$	−8.65248	−0.780167
$124$	−1.61803	−0.145304
$125$	0	0
$126$	−3.85410	−0.343351
$127$	−3.52786	−0.313047	−0.156524	−	0.987674i	$-0.550029\pi$
$127$	−3.52786	−0.313047	−0.156524	+	0.987674i	$0.550029\pi$
$128$	−11.3820	−1.00603
$129$	−4.00000	−0.352180
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	4.00000	0.348155
$133$	9.47214	0.821338
$134$	−4.94427	−0.427120
$135$	0	0
$136$	11.7082	1.00397
$137$	−19.7082	−1.68379	−0.841893	−	0.539645i	$-0.818559\pi$
$137$	−19.7082	−1.68379	−0.841893	+	0.539645i	$0.818559\pi$
$138$	−5.88854	−0.501266
$139$	−13.4164	−1.13796	−0.568982	−	0.822350i	$-0.692663\pi$
$139$	−13.4164	−1.13796	−0.568982	+	0.822350i	$0.692663\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	8.14590	0.683589
$143$	−2.47214	−0.206730
$144$	−2.72949	−0.227458
$145$	0	0
$146$	0.291796	0.0241492
$147$	−13.5279	−1.11576
$148$	−3.23607	−0.266003
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	8.18034	0.665707	0.332853	−	0.942979i	$-0.391989\pi$
$151$	8.18034	0.665707	0.332853	+	0.942979i	$0.391989\pi$
$152$	−5.00000	−0.405554
$153$	7.70820	0.623171
$154$	5.23607	0.421934
$155$	0	0
$156$	−2.47214	−0.197929
$157$	14.8885	1.18824	0.594118	−	0.804378i	$-0.297501\pi$
$157$	14.8885	1.18824	0.594118	+	0.804378i	$0.297501\pi$
$158$	1.05573	0.0839892
$159$	−1.88854	−0.149771
$160$	0	0
$161$	32.6525	2.57338
$162$	−1.49342	−0.117334
$163$	2.70820	0.212123	0.106061	−	0.994360i	$-0.466176\pi$
$163$	2.70820	0.212123	0.106061	+	0.994360i	$0.466176\pi$
$164$	−11.3262	−0.884431
$165$	0	0
$166$	−1.81966	−0.141233
$167$	−2.47214	−0.191300	−0.0956498	−	0.995415i	$-0.530493\pi$
$167$	−2.47214	−0.191300	−0.0956498	+	0.995415i	$0.530493\pi$
$168$	11.7082	0.903308
$169$	−11.4721	−0.882472
$170$	0	0
$171$	−3.29180	−0.251730
$172$	−5.23607	−0.399246
$173$	14.9443	1.13619	0.568096	−	0.822962i	$-0.307680\pi$
$173$	14.9443	1.13619	0.568096	+	0.822962i	$0.307680\pi$
$174$	−5.52786	−0.419066
$175$	0	0
$176$	3.70820	0.279516
$177$	2.76393	0.207750
$178$	−1.05573	−0.0791302
$179$	−11.7082	−0.875112	−0.437556	−	0.899191i	$-0.644156\pi$
$179$	−11.7082	−0.875112	−0.437556	+	0.899191i	$0.644156\pi$
$180$	0	0
$181$	18.1803	1.35133	0.675667	−	0.737207i	$-0.263856\pi$
$181$	18.1803	1.35133	0.675667	+	0.737207i	$0.263856\pi$
$182$	−3.23607	−0.239873
$183$	17.5279	1.29570
$184$	−17.2361	−1.27066
$185$	0	0
$186$	−0.763932	−0.0560142
$187$	−10.4721	−0.765798
$188$	−10.4721	−0.763759
$189$	23.4164	1.70329
$190$	0	0
$191$	3.18034	0.230121	0.115061	−	0.993358i	$-0.463294\pi$
$191$	3.18034	0.230121	0.115061	+	0.993358i	$0.463294\pi$
$192$	0.291796	0.0210586
$193$	5.47214	0.393893	0.196946	−	0.980414i	$-0.436897\pi$
$193$	5.47214	0.393893	0.196946	+	0.980414i	$0.436897\pi$
$194$	−1.20163	−0.0862717
$195$	0	0
$196$	−17.7082	−1.26487
$197$	15.4164	1.09837	0.549187	−	0.835700i	$-0.314938\pi$
$197$	15.4164	1.09837	0.549187	+	0.835700i	$0.314938\pi$
$198$	−1.81966	−0.129318
$199$	−1.05573	−0.0748386	−0.0374193	−	0.999300i	$-0.511914\pi$
$199$	−1.05573	−0.0748386	−0.0374193	+	0.999300i	$0.511914\pi$
$200$	0	0
$201$	9.88854	0.697484
$202$	−1.85410	−0.130454
$203$	30.6525	2.15138
$204$	−10.4721	−0.733196
$205$	0	0
$206$	−1.09017	−0.0759557
$207$	−11.3475	−0.788707
$208$	−2.29180	−0.158907
$209$	4.47214	0.309344
$210$	0	0
$211$	0.819660	0.0564277	0.0282139	−	0.999602i	$-0.491018\pi$
$211$	0.819660	0.0564277	0.0282139	+	0.999602i	$0.491018\pi$
$212$	−2.47214	−0.169787
$213$	−16.2918	−1.11630
$214$	−6.32624	−0.432453
$215$	0	0
$216$	−12.3607	−0.841038
$217$	4.23607	0.287563
$218$	2.43769	0.165101
$219$	−0.583592	−0.0394355
$220$	0	0
$221$	6.47214	0.435363
$222$	−1.52786	−0.102544
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	23.7984	1.59010
$225$	0	0
$226$	3.38197	0.224965
$227$	−2.47214	−0.164081	−0.0820407	−	0.996629i	$-0.526144\pi$
$227$	−2.47214	−0.164081	−0.0820407	+	0.996629i	$0.526144\pi$
$228$	4.47214	0.296174
$229$	13.4164	0.886581	0.443291	−	0.896378i	$-0.353811\pi$
$229$	13.4164	0.886581	0.443291	+	0.896378i	$0.353811\pi$
$230$	0	0
$231$	−10.4721	−0.689016
$232$	−16.1803	−1.06229
$233$	−0.0557281	−0.00365087	−0.00182543	−	0.999998i	$-0.500581\pi$
$233$	−0.0557281	−0.00365087	−0.00182543	+	0.999998i	$0.500581\pi$
$234$	1.12461	0.0735182
$235$	0	0
$236$	3.61803	0.235514
$237$	−2.11146	−0.137154
$238$	−13.7082	−0.888571
$239$	1.70820	0.110495	0.0552473	−	0.998473i	$-0.482405\pi$
$239$	1.70820	0.110495	0.0552473	+	0.998473i	$0.482405\pi$
$240$	0	0
$241$	−30.3607	−1.95570	−0.977852	−	0.209299i	$-0.932882\pi$
$241$	−30.3607	−1.95570	−0.977852	+	0.209299i	$0.932882\pi$
$242$	−4.32624	−0.278101
$243$	−13.5967	−0.872232
$244$	22.9443	1.46886
$245$	0	0
$246$	−5.34752	−0.340946
$247$	−2.76393	−0.175865
$248$	−2.23607	−0.141990
$249$	3.63932	0.230633
$250$	0	0
$251$	−24.1803	−1.52625	−0.763125	−	0.646251i	$-0.776336\pi$
$251$	−24.1803	−1.52625	−0.763125	+	0.646251i	$0.776336\pi$
$252$	10.0902	0.635621
$253$	15.4164	0.969221
$254$	−2.18034	−0.136807
$255$	0	0
$256$	−6.56231	−0.410144
$257$	15.9443	0.994576	0.497288	−	0.867585i	$-0.334329\pi$
$257$	15.9443	0.994576	0.497288	+	0.867585i	$0.334329\pi$
$258$	−2.47214	−0.153908
$259$	8.47214	0.526433
$260$	0	0
$261$	−10.6525	−0.659372
$262$	7.41641	0.458187
$263$	18.7639	1.15703	0.578517	−	0.815670i	$-0.303632\pi$
$263$	18.7639	1.15703	0.578517	+	0.815670i	$0.303632\pi$
$264$	5.52786	0.340217
$265$	0	0
$266$	5.85410	0.358938
$267$	2.11146	0.129219
$268$	12.9443	0.790697
$269$	−28.9443	−1.76476	−0.882382	−	0.470534i	$-0.844061\pi$
$269$	−28.9443	−1.76476	−0.882382	+	0.470534i	$0.844061\pi$
$270$	0	0
$271$	8.18034	0.496920	0.248460	−	0.968642i	$-0.420076\pi$
$271$	8.18034	0.496920	0.248460	+	0.968642i	$0.420076\pi$
$272$	−9.70820	−0.588646
$273$	6.47214	0.391711
$274$	−12.1803	−0.735841
$275$	0	0
$276$	15.4164	0.927959
$277$	−18.6525	−1.12072	−0.560359	−	0.828250i	$-0.689337\pi$
$277$	−18.6525	−1.12072	−0.560359	+	0.828250i	$0.689337\pi$
$278$	−8.29180	−0.497309
$279$	−1.47214	−0.0881345
$280$	0	0
$281$	17.0000	1.01413	0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000	1.01413	0.507067	+	0.861906i	$0.330729\pi$
$282$	−4.94427	−0.294427
$283$	−21.8885	−1.30114	−0.650569	−	0.759447i	$-0.725470\pi$
$283$	−21.8885	−1.30114	−0.650569	+	0.759447i	$0.725470\pi$
$284$	−21.3262	−1.26548
$285$	0	0
$286$	−1.52786	−0.0903445
$287$	29.6525	1.75033
$288$	−8.27051	−0.487344
$289$	10.4164	0.612730
$290$	0	0
$291$	2.40325	0.140881
$292$	−0.763932	−0.0447057
$293$	−8.47214	−0.494947	−0.247474	−	0.968895i	$-0.579600\pi$
$293$	−8.47214	−0.494947	−0.247474	+	0.968895i	$0.579600\pi$
$294$	−8.36068	−0.487605
$295$	0	0
$296$	−4.47214	−0.259938
$297$	11.0557	0.641518
$298$	6.18034	0.358017
$299$	−9.52786	−0.551011
$300$	0	0
$301$	13.7082	0.790128
$302$	5.05573	0.290924
$303$	3.70820	0.213031
$304$	4.14590	0.237784
$305$	0	0
$306$	4.76393	0.272336
$307$	15.2918	0.872749	0.436374	−	0.899765i	$-0.356262\pi$
$307$	15.2918	0.872749	0.436374	+	0.899765i	$0.356262\pi$
$308$	−13.7082	−0.781097
$309$	2.18034	0.124035
$310$	0	0
$311$	−6.81966	−0.386707	−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966	−0.386707	−0.193354	+	0.981129i	$0.561936\pi$
$312$	−3.41641	−0.193416
$313$	−21.2361	−1.20033	−0.600167	−	0.799875i	$-0.704899\pi$
$313$	−21.2361	−1.20033	−0.600167	+	0.799875i	$0.704899\pi$
$314$	9.20163	0.519278
$315$	0	0
$316$	−2.76393	−0.155483
$317$	−21.9443	−1.23251	−0.616257	−	0.787545i	$-0.711352\pi$
$317$	−21.9443	−1.23251	−0.616257	+	0.787545i	$0.711352\pi$
$318$	−1.16718	−0.0654524
$319$	14.4721	0.810284
$320$	0	0
$321$	12.6525	0.706192
$322$	20.1803	1.12461
$323$	−11.7082	−0.651462
$324$	3.90983	0.217213
$325$	0	0
$326$	1.67376	0.0927011
$327$	−4.87539	−0.269610
$328$	−15.6525	−0.864263
$329$	27.4164	1.51152
$330$	0	0
$331$	2.00000	0.109930	0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000	0.109930	0.0549650	+	0.998488i	$0.482495\pi$
$332$	4.76393	0.261455
$333$	−2.94427	−0.161345
$334$	−1.52786	−0.0836010
$335$	0	0
$336$	−9.70820	−0.529626
$337$	19.2361	1.04786	0.523928	−	0.851763i	$-0.324466\pi$
$337$	19.2361	1.04786	0.523928	+	0.851763i	$0.324466\pi$
$338$	−7.09017	−0.385654
$339$	−6.76393	−0.367366
$340$	0	0
$341$	2.00000	0.108306
$342$	−2.03444	−0.110010
$343$	16.7082	0.902158
$344$	−7.23607	−0.390143
$345$	0	0
$346$	9.23607	0.496534
$347$	−1.81966	−0.0976845	−0.0488422	−	0.998807i	$-0.515553\pi$
$347$	−1.81966	−0.0976845	−0.0488422	+	0.998807i	$0.515553\pi$
$348$	14.4721	0.775788
$349$	27.8885	1.49284	0.746420	−	0.665475i	$-0.231771\pi$
$349$	27.8885	1.49284	0.746420	+	0.665475i	$0.231771\pi$
$350$	0	0
$351$	−6.83282	−0.364709
$352$	11.2361	0.598884
$353$	19.4164	1.03343	0.516716	−	0.856157i	$-0.327154\pi$
$353$	19.4164	1.03343	0.516716	+	0.856157i	$0.327154\pi$
$354$	1.70820	0.0907900
$355$	0	0
$356$	2.76393	0.146488
$357$	27.4164	1.45103
$358$	−7.23607	−0.382438
$359$	17.7639	0.937544	0.468772	−	0.883319i	$-0.344697\pi$
$359$	17.7639	0.937544	0.468772	+	0.883319i	$0.344697\pi$
$360$	0	0
$361$	−14.0000	−0.736842
$362$	11.2361	0.590555
$363$	8.65248	0.454137
$364$	8.47214	0.444061
$365$	0	0
$366$	10.8328	0.566240
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	14.2918	0.745011
$369$	−10.3050	−0.536454
$370$	0	0
$371$	6.47214	0.336017
$372$	2.00000	0.103695
$373$	−19.0000	−0.983783	−0.491891	−	0.870657i	$-0.663694\pi$
$373$	−19.0000	−0.983783	−0.491891	+	0.870657i	$0.663694\pi$
$374$	−6.47214	−0.334666
$375$	0	0
$376$	−14.4721	−0.746343
$377$	−8.94427	−0.460653
$378$	14.4721	0.744366
$379$	−37.8885	−1.94620	−0.973102	−	0.230375i	$-0.926005\pi$
$379$	−37.8885	−1.94620	−0.973102	+	0.230375i	$0.926005\pi$
$380$	0	0
$381$	4.36068	0.223404
$382$	1.96556	0.100567
$383$	−11.8885	−0.607476	−0.303738	−	0.952756i	$-0.598235\pi$
$383$	−11.8885	−0.607476	−0.303738	+	0.952756i	$0.598235\pi$
$384$	14.0689	0.717950
$385$	0	0
$386$	3.38197	0.172138
$387$	−4.76393	−0.242164
$388$	3.14590	0.159709
$389$	17.8885	0.906985	0.453493	−	0.891260i	$-0.350178\pi$
$389$	17.8885	0.906985	0.453493	+	0.891260i	$0.350178\pi$
$390$	0	0
$391$	−40.3607	−2.04113
$392$	−24.4721	−1.23603
$393$	−14.8328	−0.748217
$394$	9.52786	0.480007
$395$	0	0
$396$	4.76393	0.239397
$397$	7.00000	0.351320	0.175660	−	0.984451i	$-0.443794\pi$
$397$	7.00000	0.351320	0.175660	+	0.984451i	$0.443794\pi$
$398$	−0.652476	−0.0327057
$399$	−11.7082	−0.586143
$400$	0	0
$401$	15.8197	0.789996	0.394998	−	0.918682i	$-0.370745\pi$
$401$	15.8197	0.789996	0.394998	+	0.918682i	$0.370745\pi$
$402$	6.11146	0.304812
$403$	−1.23607	−0.0615729
$404$	4.85410	0.241501
$405$	0	0
$406$	18.9443	0.940188
$407$	4.00000	0.198273
$408$	−14.4721	−0.716477
$409$	−26.1803	−1.29453	−0.647267	−	0.762263i	$-0.724088\pi$
$409$	−26.1803	−1.29453	−0.647267	+	0.762263i	$0.724088\pi$
$410$	0	0
$411$	24.3607	1.20162
$412$	2.85410	0.140612
$413$	−9.47214	−0.466093
$414$	−7.01316	−0.344678
$415$	0	0
$416$	−6.94427	−0.340471
$417$	16.5836	0.812102
$418$	2.76393	0.135188
$419$	30.1246	1.47168	0.735842	−	0.677153i	$-0.236787\pi$
$419$	30.1246	1.47168	0.735842	+	0.677153i	$0.236787\pi$
$420$	0	0
$421$	−15.3607	−0.748634	−0.374317	−	0.927301i	$-0.622123\pi$
$421$	−15.3607	−0.748634	−0.374317	+	0.927301i	$0.622123\pi$
$422$	0.506578	0.0246598
$423$	−9.52786	−0.463261
$424$	−3.41641	−0.165915
$425$	0	0
$426$	−10.0689	−0.487839
$427$	−60.0689	−2.90694
$428$	16.5623	0.800569
$429$	3.05573	0.147532
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	10.2492	0.493116
$433$	12.1803	0.585350	0.292675	−	0.956212i	$-0.405455\pi$
$433$	12.1803	0.585350	0.292675	+	0.956212i	$0.405455\pi$
$434$	2.61803	0.125670
$435$	0	0
$436$	−6.38197	−0.305641
$437$	17.2361	0.824513
$438$	−0.360680	−0.0172339
$439$	21.1803	1.01088	0.505441	−	0.862861i	$-0.331330\pi$
$439$	21.1803	1.01088	0.505441	+	0.862861i	$0.331330\pi$
$440$	0	0
$441$	−16.1115	−0.767212
$442$	4.00000	0.190261
$443$	−17.2918	−0.821558	−0.410779	−	0.911735i	$-0.634743\pi$
$443$	−17.2918	−0.821558	−0.410779	+	0.911735i	$0.634743\pi$
$444$	4.00000	0.189832
$445$	0	0
$446$	−2.47214	−0.117059
$447$	−12.3607	−0.584640
$448$	−1.00000	−0.0472456
$449$	31.3050	1.47737	0.738686	−	0.674050i	$-0.235447\pi$
$449$	31.3050	1.47737	0.738686	+	0.674050i	$0.235447\pi$
$450$	0	0
$451$	14.0000	0.659234
$452$	−8.85410	−0.416462
$453$	−10.1115	−0.475078
$454$	−1.52786	−0.0717062
$455$	0	0
$456$	6.18034	0.289421
$457$	20.9443	0.979732	0.489866	−	0.871798i	$-0.337046\pi$
$457$	20.9443	0.979732	0.489866	+	0.871798i	$0.337046\pi$
$458$	8.29180	0.387450
$459$	−28.9443	−1.35100
$460$	0	0
$461$	−10.3607	−0.482545	−0.241272	−	0.970457i	$-0.577565\pi$
$461$	−10.3607	−0.482545	−0.241272	+	0.970457i	$0.577565\pi$
$462$	−6.47214	−0.301111
$463$	29.4164	1.36710	0.683548	−	0.729905i	$-0.260436\pi$
$463$	29.4164	1.36710	0.683548	+	0.729905i	$0.260436\pi$
$464$	13.4164	0.622841
$465$	0	0
$466$	−0.0344419	−0.00159549
$467$	8.70820	0.402968	0.201484	−	0.979492i	$-0.435424\pi$
$467$	8.70820	0.402968	0.201484	+	0.979492i	$0.435424\pi$
$468$	−2.94427	−0.136099
$469$	−33.8885	−1.56483
$470$	0	0
$471$	−18.4033	−0.847977
$472$	5.00000	0.230144
$473$	6.47214	0.297589
$474$	−1.30495	−0.0599384
$475$	0	0
$476$	35.8885	1.64495
$477$	−2.24922	−0.102985
$478$	1.05573	0.0482879
$479$	36.7082	1.67724	0.838620	−	0.544716i	$-0.183363\pi$
$479$	36.7082	1.67724	0.838620	+	0.544716i	$0.183363\pi$
$480$	0	0
$481$	−2.47214	−0.112720
$482$	−18.7639	−0.854674
$483$	−40.3607	−1.83647
$484$	11.3262	0.514829
$485$	0	0
$486$	−8.40325	−0.381179
$487$	14.7639	0.669018	0.334509	−	0.942393i	$-0.391430\pi$
$487$	14.7639	0.669018	0.334509	+	0.942393i	$0.391430\pi$
$488$	31.7082	1.43536
$489$	−3.34752	−0.151380
$490$	0	0
$491$	−40.3607	−1.82145	−0.910726	−	0.413011i	$-0.864477\pi$
$491$	−40.3607	−1.82145	−0.910726	+	0.413011i	$0.864477\pi$
$492$	14.0000	0.631169
$493$	−37.8885	−1.70641
$494$	−1.70820	−0.0768557
$495$	0	0
$496$	1.85410	0.0832516
$497$	55.8328	2.50444
$498$	2.24922	0.100790
$499$	−33.4164	−1.49592	−0.747962	−	0.663742i	$-0.768967\pi$
$499$	−33.4164	−1.49592	−0.747962	+	0.663742i	$0.768967\pi$
$500$	0	0
$501$	3.05573	0.136520
$502$	−14.9443	−0.666995
$503$	1.65248	0.0736803	0.0368401	−	0.999321i	$-0.488271\pi$
$503$	1.65248	0.0736803	0.0368401	+	0.999321i	$0.488271\pi$
$504$	13.9443	0.621127
$505$	0	0
$506$	9.52786	0.423565
$507$	14.1803	0.629771
$508$	5.70820	0.253261
$509$	−19.5967	−0.868611	−0.434305	−	0.900766i	$-0.643006\pi$
$509$	−19.5967	−0.868611	−0.434305	+	0.900766i	$0.643006\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	18.7082	0.826794
$513$	12.3607	0.545737
$514$	9.85410	0.434646
$515$	0	0
$516$	6.47214	0.284920
$517$	12.9443	0.569288
$518$	5.23607	0.230060
$519$	−18.4721	−0.810837
$520$	0	0
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	−6.58359	−0.288156
$523$	4.29180	0.187667	0.0938336	−	0.995588i	$-0.470088\pi$
$523$	4.29180	0.187667	0.0938336	+	0.995588i	$0.470088\pi$
$524$	−19.4164	−0.848210
$525$	0	0
$526$	11.5967	0.505642
$527$	−5.23607	−0.228087
$528$	−4.58359	−0.199475
$529$	36.4164	1.58332
$530$	0	0
$531$	3.29180	0.142852
$532$	−15.3262	−0.664477
$533$	−8.65248	−0.374780
$534$	1.30495	0.0564708
$535$	0	0
$536$	17.8885	0.772667
$537$	14.4721	0.624519
$538$	−17.8885	−0.771230
$539$	21.8885	0.942806
$540$	0	0
$541$	19.3607	0.832381	0.416190	−	0.909278i	$-0.363365\pi$
$541$	19.3607	0.832381	0.416190	+	0.909278i	$0.363365\pi$
$542$	5.05573	0.217162
$543$	−22.4721	−0.964372
$544$	−29.4164	−1.26122
$545$	0	0
$546$	4.00000	0.171184
$547$	−28.1246	−1.20252	−0.601261	−	0.799053i	$-0.705335\pi$
$547$	−28.1246	−1.20252	−0.601261	+	0.799053i	$0.705335\pi$
$548$	31.8885	1.36221
$549$	20.8754	0.890940
$550$	0	0
$551$	16.1803	0.689306
$552$	21.3050	0.906799
$553$	7.23607	0.307709
$554$	−11.5279	−0.489772
$555$	0	0
$556$	21.7082	0.920633
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	−0.909830	−0.0385162
$559$	−4.00000	−0.169182
$560$	0	0
$561$	12.9443	0.546508
$562$	10.5066	0.443193
$563$	39.5410	1.66646	0.833228	−	0.552930i	$-0.186490\pi$
$563$	39.5410	1.66646	0.833228	+	0.552930i	$0.186490\pi$
$564$	12.9443	0.545052
$565$	0	0
$566$	−13.5279	−0.568619
$567$	−10.2361	−0.429874
$568$	−29.4721	−1.23662
$569$	14.4721	0.606704	0.303352	−	0.952879i	$-0.401894\pi$
$569$	14.4721	0.606704	0.303352	+	0.952879i	$0.401894\pi$
$570$	0	0
$571$	5.81966	0.243545	0.121773	−	0.992558i	$-0.461142\pi$
$571$	5.81966	0.243545	0.121773	+	0.992558i	$0.461142\pi$
$572$	4.00000	0.167248
$573$	−3.93112	−0.164225
$574$	18.3262	0.764922
$575$	0	0
$576$	0.347524	0.0144802
$577$	−24.8328	−1.03380	−0.516902	−	0.856045i	$-0.672915\pi$
$577$	−24.8328	−1.03380	−0.516902	+	0.856045i	$0.672915\pi$
$578$	6.43769	0.267773
$579$	−6.76393	−0.281099
$580$	0	0
$581$	−12.4721	−0.517431
$582$	1.48529	0.0615673
$583$	3.05573	0.126555
$584$	−1.05573	−0.0436863
$585$	0	0
$586$	−5.23607	−0.216300
$587$	−2.47214	−0.102036	−0.0510180	−	0.998698i	$-0.516247\pi$
$587$	−2.47214	−0.102036	−0.0510180	+	0.998698i	$0.516247\pi$
$588$	21.8885	0.902668
$589$	2.23607	0.0921356
$590$	0	0
$591$	−19.0557	−0.783848
$592$	3.70820	0.152406
$593$	15.4721	0.635364	0.317682	−	0.948197i	$-0.397095\pi$
$593$	15.4721	0.635364	0.317682	+	0.948197i	$0.397095\pi$
$594$	6.83282	0.280354
$595$	0	0
$596$	−16.1803	−0.662773
$597$	1.30495	0.0534081
$598$	−5.88854	−0.240800
$599$	34.5967	1.41358	0.706792	−	0.707421i	$-0.250141\pi$
$599$	34.5967	1.41358	0.706792	+	0.707421i	$0.250141\pi$
$600$	0	0
$601$	−36.5410	−1.49054	−0.745270	−	0.666763i	$-0.767679\pi$
$601$	−36.5410	−1.49054	−0.745270	+	0.666763i	$0.767679\pi$
$602$	8.47214	0.345298
$603$	11.7771	0.479600
$604$	−13.2361	−0.538568
$605$	0	0
$606$	2.29180	0.0930979
$607$	−13.5279	−0.549079	−0.274540	−	0.961576i	$-0.588525\pi$
$607$	−13.5279	−0.549079	−0.274540	+	0.961576i	$0.588525\pi$
$608$	12.5623	0.509469
$609$	−37.8885	−1.53532
$610$	0	0
$611$	−8.00000	−0.323645
$612$	−12.4721	−0.504156
$613$	8.11146	0.327619	0.163809	−	0.986492i	$-0.447622\pi$
$613$	8.11146	0.327619	0.163809	+	0.986492i	$0.447622\pi$
$614$	9.45085	0.381405
$615$	0	0
$616$	−18.9443	−0.763286
$617$	−23.5279	−0.947196	−0.473598	−	0.880741i	$-0.657045\pi$
$617$	−23.5279	−0.947196	−0.473598	+	0.880741i	$0.657045\pi$
$618$	1.34752	0.0542054
$619$	−16.1803	−0.650343	−0.325171	−	0.945655i	$-0.605422\pi$
$619$	−16.1803	−0.650343	−0.325171	+	0.945655i	$0.605422\pi$
$620$	0	0
$621$	42.6099	1.70988
$622$	−4.21478	−0.168997
$623$	−7.23607	−0.289907
$624$	2.83282	0.113403
$625$	0	0
$626$	−13.1246	−0.524565
$627$	−5.52786	−0.220762
$628$	−24.0902	−0.961302
$629$	−10.4721	−0.417551
$630$	0	0
$631$	−10.3607	−0.412452	−0.206226	−	0.978504i	$-0.566118\pi$
$631$	−10.3607	−0.412452	−0.206226	+	0.978504i	$0.566118\pi$
$632$	−3.81966	−0.151938
$633$	−1.01316	−0.0402693
$634$	−13.5623	−0.538628
$635$	0	0
$636$	3.05573	0.121168
$637$	−13.5279	−0.535993
$638$	8.94427	0.354107
$639$	−19.4033	−0.767581
$640$	0	0
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	7.81966	0.308617
$643$	−28.4721	−1.12283	−0.561416	−	0.827534i	$-0.689743\pi$
$643$	−28.4721	−1.12283	−0.561416	+	0.827534i	$0.689743\pi$
$644$	−52.8328	−2.08190
$645$	0	0
$646$	−7.23607	−0.284699
$647$	−16.9443	−0.666148	−0.333074	−	0.942901i	$-0.608086\pi$
$647$	−16.9443	−0.666148	−0.333074	+	0.942901i	$0.608086\pi$
$648$	5.40325	0.212260
$649$	−4.47214	−0.175547
$650$	0	0
$651$	−5.23607	−0.205218
$652$	−4.38197	−0.171611
$653$	−15.3050	−0.598929	−0.299465	−	0.954107i	$-0.596808\pi$
$653$	−15.3050	−0.598929	−0.299465	+	0.954107i	$0.596808\pi$
$654$	−3.01316	−0.117824
$655$	0	0
$656$	12.9787	0.506734
$657$	−0.695048	−0.0271164
$658$	16.9443	0.660556
$659$	−5.65248	−0.220189	−0.110095	−	0.993921i	$-0.535115\pi$
$659$	−5.65248	−0.220189	−0.110095	+	0.993921i	$0.535115\pi$
$660$	0	0
$661$	−45.3607	−1.76433	−0.882163	−	0.470944i	$-0.843913\pi$
$661$	−45.3607	−1.76433	−0.882163	+	0.470944i	$0.843913\pi$
$662$	1.23607	0.0480411
$663$	−8.00000	−0.310694
$664$	6.58359	0.255493
$665$	0	0
$666$	−1.81966	−0.0705104
$667$	55.7771	2.15970
$668$	4.00000	0.154765
$669$	4.94427	0.191157
$670$	0	0
$671$	−28.3607	−1.09485
$672$	−29.4164	−1.13476
$673$	−47.0132	−1.81222	−0.906112	−	0.423038i	$-0.860964\pi$
$673$	−47.0132	−1.81222	−0.906112	+	0.423038i	$0.860964\pi$
$674$	11.8885	0.457930
$675$	0	0
$676$	18.5623	0.713935
$677$	−42.7214	−1.64192	−0.820958	−	0.570989i	$-0.806560\pi$
$677$	−42.7214	−1.64192	−0.820958	+	0.570989i	$0.806560\pi$
$678$	−4.18034	−0.160545
$679$	−8.23607	−0.316071
$680$	0	0
$681$	3.05573	0.117096
$682$	1.23607	0.0473315
$683$	17.1803	0.657387	0.328694	−	0.944437i	$-0.393392\pi$
$683$	17.1803	0.657387	0.328694	+	0.944437i	$0.393392\pi$
$684$	5.32624	0.203654
$685$	0	0
$686$	10.3262	0.394258
$687$	−16.5836	−0.632704
$688$	6.00000	0.228748
$689$	−1.88854	−0.0719478
$690$	0	0
$691$	−19.1803	−0.729655	−0.364827	−	0.931075i	$-0.618872\pi$
$691$	−19.1803	−0.729655	−0.364827	+	0.931075i	$0.618872\pi$
$692$	−24.1803	−0.919199
$693$	−12.4721	−0.473777
$694$	−1.12461	−0.0426897
$695$	0	0
$696$	20.0000	0.758098
$697$	−36.6525	−1.38831
$698$	17.2361	0.652395
$699$	0.0688837	0.00260542
$700$	0	0
$701$	7.00000	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$701$	7.00000	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$702$	−4.22291	−0.159384
$703$	4.47214	0.168670
$704$	−0.472136	−0.0177943
$705$	0	0
$706$	12.0000	0.451626
$707$	−12.7082	−0.477941
$708$	−4.47214	−0.168073
$709$	34.4721	1.29463	0.647314	−	0.762223i	$-0.275892\pi$
$709$	34.4721	1.29463	0.647314	+	0.762223i	$0.275892\pi$
$710$	0	0
$711$	−2.51471	−0.0943089
$712$	3.81966	0.143148
$713$	7.70820	0.288675
$714$	16.9443	0.634123
$715$	0	0
$716$	18.9443	0.707981
$717$	−2.11146	−0.0788538
$718$	10.9787	0.409722
$719$	−36.1803	−1.34930	−0.674649	−	0.738138i	$-0.735705\pi$
$719$	−36.1803	−1.34930	−0.674649	+	0.738138i	$0.735705\pi$
$720$	0	0
$721$	−7.47214	−0.278277
$722$	−8.65248	−0.322012
$723$	37.5279	1.39568
$724$	−29.4164	−1.09325
$725$	0	0
$726$	5.34752	0.198465
$727$	39.7639	1.47476	0.737381	−	0.675477i	$-0.236062\pi$
$727$	39.7639	1.47476	0.737381	+	0.675477i	$0.236062\pi$
$728$	11.7082	0.433935
$729$	24.0557	0.890953
$730$	0	0
$731$	−16.9443	−0.626707
$732$	−28.3607	−1.04824
$733$	5.47214	0.202118	0.101059	−	0.994880i	$-0.467777\pi$
$733$	5.47214	0.202118	0.101059	+	0.994880i	$0.467777\pi$
$734$	−11.1246	−0.410617
$735$	0	0
$736$	43.3050	1.59624
$737$	−16.0000	−0.589368
$738$	−6.36881	−0.234439
$739$	−16.1803	−0.595203	−0.297602	−	0.954690i	$-0.596187\pi$
$739$	−16.1803	−0.595203	−0.297602	+	0.954690i	$0.596187\pi$
$740$	0	0
$741$	3.41641	0.125505
$742$	4.00000	0.146845
$743$	−27.8197	−1.02060	−0.510302	−	0.859995i	$-0.670466\pi$
$743$	−27.8197	−1.02060	−0.510302	+	0.859995i	$0.670466\pi$
$744$	2.76393	0.101331
$745$	0	0
$746$	−11.7426	−0.429929
$747$	4.33437	0.158586
$748$	16.9443	0.619544
$749$	−43.3607	−1.58436
$750$	0	0
$751$	45.5410	1.66182	0.830908	−	0.556410i	$-0.187822\pi$
$751$	45.5410	1.66182	0.830908	+	0.556410i	$0.187822\pi$
$752$	12.0000	0.437595
$753$	29.8885	1.08920
$754$	−5.52786	−0.201313
$755$	0	0
$756$	−37.8885	−1.37799
$757$	22.6525	0.823318	0.411659	−	0.911338i	$-0.364949\pi$
$757$	22.6525	0.823318	0.411659	+	0.911338i	$0.364949\pi$
$758$	−23.4164	−0.850522
$759$	−19.0557	−0.691679
$760$	0	0
$761$	2.00000	0.0724999	0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000	0.0724999	0.0362500	+	0.999343i	$0.488459\pi$
$762$	2.69505	0.0976313
$763$	16.7082	0.604878
$764$	−5.14590	−0.186172
$765$	0	0
$766$	−7.34752	−0.265477
$767$	2.76393	0.0997998
$768$	8.11146	0.292697
$769$	−2.63932	−0.0951763	−0.0475882	−	0.998867i	$-0.515154\pi$
$769$	−2.63932	−0.0951763	−0.0475882	+	0.998867i	$0.515154\pi$
$770$	0	0
$771$	−19.7082	−0.709774
$772$	−8.85410	−0.318666
$773$	−29.1246	−1.04754	−0.523770	−	0.851860i	$-0.675475\pi$
$773$	−29.1246	−1.04754	−0.523770	+	0.851860i	$0.675475\pi$
$774$	−2.94427	−0.105830
$775$	0	0
$776$	4.34752	0.156067
$777$	−10.4721	−0.375686
$778$	11.0557	0.396367
$779$	15.6525	0.560808
$780$	0	0
$781$	26.3607	0.943259
$782$	−24.9443	−0.892005
$783$	40.0000	1.42948
$784$	20.2918	0.724707
$785$	0	0
$786$	−9.16718	−0.326983
$787$	−38.6525	−1.37781	−0.688906	−	0.724851i	$-0.741909\pi$
$787$	−38.6525	−1.37781	−0.688906	+	0.724851i	$0.741909\pi$
$788$	−24.9443	−0.888603
$789$	−23.1935	−0.825710
$790$	0	0
$791$	23.1803	0.824198
$792$	6.58359	0.233938
$793$	17.5279	0.622433
$794$	4.32624	0.153532
$795$	0	0
$796$	1.70820	0.0605457
$797$	28.5836	1.01248	0.506241	−	0.862392i	$-0.331034\pi$
$797$	28.5836	1.01248	0.506241	+	0.862392i	$0.331034\pi$
$798$	−7.23607	−0.256154
$799$	−33.8885	−1.19889
$800$	0	0
$801$	2.51471	0.0888529
$802$	9.77709	0.345241
$803$	0.944272	0.0333226
$804$	−16.0000	−0.564276
$805$	0	0
$806$	−0.763932	−0.0269084
$807$	35.7771	1.25941
$808$	6.70820	0.235994
$809$	−3.41641	−0.120115	−0.0600573	−	0.998195i	$-0.519128\pi$
$809$	−3.41641	−0.120115	−0.0600573	+	0.998195i	$0.519128\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	−49.5967	−1.74050
$813$	−10.1115	−0.354624
$814$	2.47214	0.0866483
$815$	0	0
$816$	12.0000	0.420084
$817$	7.23607	0.253158
$818$	−16.1803	−0.565732
$819$	7.70820	0.269346
$820$	0	0
$821$	−36.5410	−1.27529	−0.637645	−	0.770330i	$-0.720091\pi$
$821$	−36.5410	−1.27529	−0.637645	+	0.770330i	$0.720091\pi$
$822$	15.0557	0.525129
$823$	27.7082	0.965847	0.482924	−	0.875662i	$-0.339575\pi$
$823$	27.7082	0.965847	0.482924	+	0.875662i	$0.339575\pi$
$824$	3.94427	0.137405
$825$	0	0
$826$	−5.85410	−0.203690
$827$	−48.6525	−1.69181	−0.845906	−	0.533332i	$-0.820940\pi$
$827$	−48.6525	−1.69181	−0.845906	+	0.533332i	$0.820940\pi$
$828$	18.3607	0.638078
$829$	−36.8328	−1.27926	−0.639628	−	0.768684i	$-0.720912\pi$
$829$	−36.8328	−1.27926	−0.639628	+	0.768684i	$0.720912\pi$
$830$	0	0
$831$	23.0557	0.799794
$832$	0.291796	0.0101162
$833$	−57.3050	−1.98550
$834$	10.2492	0.354902
$835$	0	0
$836$	−7.23607	−0.250265
$837$	5.52786	0.191071
$838$	18.6180	0.643149
$839$	11.0557	0.381686	0.190843	−	0.981621i	$-0.438878\pi$
$839$	11.0557	0.381686	0.190843	+	0.981621i	$0.438878\pi$
$840$	0	0
$841$	23.3607	0.805541
$842$	−9.49342	−0.327165
$843$	−21.0132	−0.723732
$844$	−1.32624	−0.0456510
$845$	0	0
$846$	−5.88854	−0.202452
$847$	−29.6525	−1.01887
$848$	2.83282	0.0972793
$849$	27.0557	0.928550
$850$	0	0
$851$	15.4164	0.528468
$852$	26.3607	0.903102
$853$	−37.4164	−1.28111	−0.640557	−	0.767911i	$-0.721296\pi$
$853$	−37.4164	−1.28111	−0.640557	+	0.767911i	$0.721296\pi$
$854$	−37.1246	−1.27038
$855$	0	0
$856$	22.8885	0.782314
$857$	−51.6656	−1.76486	−0.882432	−	0.470440i	$-0.844095\pi$
$857$	−51.6656	−1.76486	−0.882432	+	0.470440i	$0.844095\pi$
$858$	1.88854	0.0644738
$859$	37.8885	1.29274	0.646370	−	0.763024i	$-0.276286\pi$
$859$	37.8885	1.29274	0.646370	+	0.763024i	$0.276286\pi$
$860$	0	0
$861$	−36.6525	−1.24911
$862$	7.41641	0.252604
$863$	32.1803	1.09543	0.547716	−	0.836664i	$-0.315498\pi$
$863$	32.1803	1.09543	0.547716	+	0.836664i	$0.315498\pi$
$864$	31.0557	1.05654
$865$	0	0
$866$	7.52786	0.255807
$867$	−12.8754	−0.437271
$868$	−6.85410	−0.232643
$869$	3.41641	0.115894
$870$	0	0
$871$	9.88854	0.335061
$872$	−8.81966	−0.298671
$873$	2.86223	0.0968719
$874$	10.6525	0.360325
$875$	0	0
$876$	0.944272	0.0319040
$877$	35.9443	1.21375	0.606876	−	0.794797i	$-0.292422\pi$
$877$	35.9443	1.21375	0.606876	+	0.794797i	$0.292422\pi$
$878$	13.0902	0.441772
$879$	10.4721	0.353216
$880$	0	0
$881$	24.3607	0.820732	0.410366	−	0.911921i	$-0.365401\pi$
$881$	24.3607	0.820732	0.410366	+	0.911921i	$0.365401\pi$
$882$	−9.95743	−0.335284
$883$	−39.7771	−1.33861	−0.669303	−	0.742990i	$-0.733407\pi$
$883$	−39.7771	−1.33861	−0.669303	+	0.742990i	$0.733407\pi$
$884$	−10.4721	−0.352216
$885$	0	0
$886$	−10.6869	−0.359034
$887$	31.0689	1.04319	0.521596	−	0.853193i	$-0.325337\pi$
$887$	31.0689	1.04319	0.521596	+	0.853193i	$0.325337\pi$
$888$	5.52786	0.185503
$889$	−14.9443	−0.501215
$890$	0	0
$891$	−4.83282	−0.161905
$892$	6.47214	0.216703
$893$	14.4721	0.484292
$894$	−7.63932	−0.255497
$895$	0	0
$896$	−48.2148	−1.61074
$897$	11.7771	0.393226
$898$	19.3475	0.645635
$899$	7.23607	0.241336
$900$	0	0
$901$	−8.00000	−0.266519
$902$	8.65248	0.288096
$903$	−16.9443	−0.563870
$904$	−12.2361	−0.406966
$905$	0	0
$906$	−6.24922	−0.207617
$907$	19.7639	0.656251	0.328125	−	0.944634i	$-0.393583\pi$
$907$	19.7639	0.656251	0.328125	+	0.944634i	$0.393583\pi$
$908$	4.00000	0.132745
$909$	4.41641	0.146483
$910$	0	0
$911$	−4.18034	−0.138501	−0.0692504	−	0.997599i	$-0.522061\pi$
$911$	−4.18034	−0.138501	−0.0692504	+	0.997599i	$0.522061\pi$
$912$	−5.12461	−0.169693
$913$	−5.88854	−0.194882
$914$	12.9443	0.428158
$915$	0	0
$916$	−21.7082	−0.717259
$917$	50.8328	1.67865
$918$	−17.8885	−0.590410
$919$	−5.52786	−0.182347	−0.0911737	−	0.995835i	$-0.529062\pi$
$919$	−5.52786	−0.182347	−0.0911737	+	0.995835i	$0.529062\pi$
$920$	0	0
$921$	−18.9017	−0.622832
$922$	−6.40325	−0.210880
$923$	−16.2918	−0.536251
$924$	16.9443	0.557426
$925$	0	0
$926$	18.1803	0.597443
$927$	2.59675	0.0852884
$928$	40.6525	1.33448
$929$	−20.0000	−0.656179	−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000	−0.656179	−0.328089	+	0.944647i	$0.606405\pi$
$930$	0	0
$931$	24.4721	0.802042
$932$	0.0901699	0.00295361
$933$	8.42956	0.275972
$934$	5.38197	0.176103
$935$	0	0
$936$	−4.06888	−0.132996
$937$	−26.9443	−0.880231	−0.440115	−	0.897941i	$-0.645063\pi$
$937$	−26.9443	−0.880231	−0.440115	+	0.897941i	$0.645063\pi$
$938$	−20.9443	−0.683855
$939$	26.2492	0.856611
$940$	0	0
$941$	−38.0000	−1.23876	−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000	−1.23876	−0.619382	+	0.785090i	$0.712617\pi$
$942$	−11.3738	−0.370580
$943$	53.9574	1.75710
$944$	−4.14590	−0.134937
$945$	0	0
$946$	4.00000	0.130051
$947$	30.9443	1.00555	0.502777	−	0.864416i	$-0.332312\pi$
$947$	30.9443	1.00555	0.502777	+	0.864416i	$0.332312\pi$
$948$	3.41641	0.110960
$949$	−0.583592	−0.0189442
$950$	0	0
$951$	27.1246	0.879576
$952$	49.5967	1.60744
$953$	−32.2918	−1.04603	−0.523017	−	0.852322i	$-0.675194\pi$
$953$	−32.2918	−1.04603	−0.523017	+	0.852322i	$0.675194\pi$
$954$	−1.39010	−0.0450060
$955$	0	0
$956$	−2.76393	−0.0893920
$957$	−17.8885	−0.578254
$958$	22.6869	0.732981
$959$	−83.4853	−2.69588
$960$	0	0
$961$	1.00000	0.0322581
$962$	−1.52786	−0.0492603
$963$	15.0689	0.485588
$964$	49.1246	1.58220
$965$	0	0
$966$	−24.9443	−0.802569
$967$	−15.6393	−0.502927	−0.251463	−	0.967867i	$-0.580912\pi$
$967$	−15.6393	−0.502927	−0.251463	+	0.967867i	$0.580912\pi$
$968$	15.6525	0.503090
$969$	14.4721	0.464912
$970$	0	0
$971$	−28.0000	−0.898563	−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000	−0.898563	−0.449281	+	0.893390i	$0.648320\pi$
$972$	22.0000	0.705650
$973$	−56.8328	−1.82198
$974$	9.12461	0.292371
$975$	0	0
$976$	−26.2918	−0.841580
$977$	−33.2492	−1.06374	−0.531868	−	0.846827i	$-0.678510\pi$
$977$	−33.2492	−1.06374	−0.531868	+	0.846827i	$0.678510\pi$
$978$	−2.06888	−0.0661556
$979$	−3.41641	−0.109189
$980$	0	0
$981$	−5.80650	−0.185387
$982$	−24.9443	−0.796004
$983$	−48.4721	−1.54602	−0.773011	−	0.634393i	$-0.781250\pi$
$983$	−48.4721	−1.54602	−0.773011	+	0.634393i	$0.781250\pi$
$984$	19.3475	0.616777
$985$	0	0
$986$	−23.4164	−0.745730
$987$	−33.8885	−1.07868
$988$	4.47214	0.142278
$989$	24.9443	0.793182
$990$	0	0
$991$	50.5410	1.60549	0.802744	−	0.596324i	$-0.203372\pi$
$991$	50.5410	1.60549	0.802744	+	0.596324i	$0.203372\pi$
$992$	5.61803	0.178373
$993$	−2.47214	−0.0784509
$994$	34.5066	1.09448
$995$	0	0
$996$	−5.88854	−0.186586
$997$	−15.3607	−0.486478	−0.243239	−	0.969966i	$-0.578210\pi$
$997$	−15.3607	−0.486478	−0.243239	+	0.969966i	$0.578210\pi$
$998$	−20.6525	−0.653743
$999$	11.0557	0.349788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.d.1.2		2
3.2	odd	2		6975.2.a.y.1.1		2
5.2	odd	4		775.2.b.d.249.3		4
5.3	odd	4		775.2.b.d.249.2		4
5.4	even	2		31.2.a.a.1.1	✓	2
15.14	odd	2		279.2.a.a.1.2		2
20.19	odd	2		496.2.a.i.1.1		2
35.34	odd	2		1519.2.a.a.1.1		2
40.19	odd	2		1984.2.a.n.1.2		2
40.29	even	2		1984.2.a.r.1.1		2
55.54	odd	2		3751.2.a.b.1.2		2
60.59	even	2		4464.2.a.bf.1.2		2
65.64	even	2		5239.2.a.f.1.2		2
85.84	even	2		8959.2.a.b.1.1		2
155.4	even	10		961.2.d.d.388.1		4
155.9	even	30		961.2.g.h.732.1		8
155.14	even	30		961.2.g.h.816.1		8
155.19	even	30		961.2.g.a.547.1		8
155.24	odd	30		961.2.g.e.235.1		8
155.29	odd	10		961.2.d.a.531.1		4
155.34	odd	30		961.2.g.d.846.1		8
155.39	even	10		961.2.d.d.374.1		4
155.44	odd	30		961.2.g.d.448.1		8
155.49	even	30		961.2.g.a.448.1		8
155.54	odd	10		961.2.d.g.374.1		4
155.59	even	30		961.2.g.a.846.1		8
155.64	even	10		961.2.d.c.531.1		4
155.69	even	30		961.2.g.h.235.1		8
155.74	odd	30		961.2.g.d.547.1		8
155.79	odd	30		961.2.g.e.816.1		8
155.84	odd	30		961.2.g.e.732.1		8
155.89	odd	10		961.2.d.g.388.1		4
155.99	odd	6		961.2.c.c.439.1		4
155.104	odd	30		961.2.g.e.338.1		8
155.109	even	10		961.2.d.c.628.1		4
155.114	odd	30		961.2.g.d.844.1		8
155.119	odd	6		961.2.c.c.521.1		4
155.129	even	6		961.2.c.e.521.1		4
155.134	even	30		961.2.g.a.844.1		8
155.139	odd	10		961.2.d.a.628.1		4
155.144	even	30		961.2.g.h.338.1		8
155.149	even	6		961.2.c.e.439.1		4
155.154	odd	2		961.2.a.f.1.1		2
465.464	even	2		8649.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.1	✓	2	5.4	even	2
279.2.a.a.1.2		2	15.14	odd	2
496.2.a.i.1.1		2	20.19	odd	2
775.2.a.d.1.2		2	1.1	even	1	trivial
775.2.b.d.249.2		4	5.3	odd	4
775.2.b.d.249.3		4	5.2	odd	4
961.2.a.f.1.1		2	155.154	odd	2
961.2.c.c.439.1		4	155.99	odd	6
961.2.c.c.521.1		4	155.119	odd	6
961.2.c.e.439.1		4	155.149	even	6
961.2.c.e.521.1		4	155.129	even	6
961.2.d.a.531.1		4	155.29	odd	10
961.2.d.a.628.1		4	155.139	odd	10
961.2.d.c.531.1		4	155.64	even	10
961.2.d.c.628.1		4	155.109	even	10
961.2.d.d.374.1		4	155.39	even	10
961.2.d.d.388.1		4	155.4	even	10
961.2.d.g.374.1		4	155.54	odd	10
961.2.d.g.388.1		4	155.89	odd	10
961.2.g.a.448.1		8	155.49	even	30
961.2.g.a.547.1		8	155.19	even	30
961.2.g.a.844.1		8	155.134	even	30
961.2.g.a.846.1		8	155.59	even	30
961.2.g.d.448.1		8	155.44	odd	30
961.2.g.d.547.1		8	155.74	odd	30
961.2.g.d.844.1		8	155.114	odd	30
961.2.g.d.846.1		8	155.34	odd	30
961.2.g.e.235.1		8	155.24	odd	30
961.2.g.e.338.1		8	155.104	odd	30
961.2.g.e.732.1		8	155.84	odd	30
961.2.g.e.816.1		8	155.79	odd	30
961.2.g.h.235.1		8	155.69	even	30
961.2.g.h.338.1		8	155.144	even	30
961.2.g.h.732.1		8	155.9	even	30
961.2.g.h.816.1		8	155.14	even	30
1519.2.a.a.1.1		2	35.34	odd	2
1984.2.a.n.1.2		2	40.19	odd	2
1984.2.a.r.1.1		2	40.29	even	2
3751.2.a.b.1.2		2	55.54	odd	2
4464.2.a.bf.1.2		2	60.59	even	2
5239.2.a.f.1.2		2	65.64	even	2
6975.2.a.y.1.1		2	3.2	odd	2
8649.2.a.c.1.2		2	465.464	even	2
8959.2.a.b.1.1		2	85.84	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} -1.23607 q^{3} -1.61803 q^{4} -0.763932 q^{6} +4.23607 q^{7} -2.23607 q^{8} -1.47214 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} -1.23607 q^{3} -1.61803 q^{4} -0.763932 q^{6} +4.23607 q^{7} -2.23607 q^{8} -1.47214 q^{9} +2.00000 q^{11} +2.00000 q^{12} -1.23607 q^{13} +2.61803 q^{14} +1.85410 q^{16} -5.23607 q^{17} -0.909830 q^{18} +2.23607 q^{19} -5.23607 q^{21} +1.23607 q^{22} +7.70820 q^{23} +2.76393 q^{24} -0.763932 q^{26} +5.52786 q^{27} -6.85410 q^{28} +7.23607 q^{29} +1.00000 q^{31} +5.61803 q^{32} -2.47214 q^{33} -3.23607 q^{34} +2.38197 q^{36} +2.00000 q^{37} +1.38197 q^{38} +1.52786 q^{39} +7.00000 q^{41} -3.23607 q^{42} +3.23607 q^{43} -3.23607 q^{44} +4.76393 q^{46} +6.47214 q^{47} -2.29180 q^{48} +10.9443 q^{49} +6.47214 q^{51} +2.00000 q^{52} +1.52786 q^{53} +3.41641 q^{54} -9.47214 q^{56} -2.76393 q^{57} +4.47214 q^{58} -2.23607 q^{59} -14.1803 q^{61} +0.618034 q^{62} -6.23607 q^{63} -0.236068 q^{64} -1.52786 q^{66} -8.00000 q^{67} +8.47214 q^{68} -9.52786 q^{69} +13.1803 q^{71} +3.29180 q^{72} +0.472136 q^{73} +1.23607 q^{74} -3.61803 q^{76} +8.47214 q^{77} +0.944272 q^{78} +1.70820 q^{79} -2.41641 q^{81} +4.32624 q^{82} -2.94427 q^{83} +8.47214 q^{84} +2.00000 q^{86} -8.94427 q^{87} -4.47214 q^{88} -1.70820 q^{89} -5.23607 q^{91} -12.4721 q^{92} -1.23607 q^{93} +4.00000 q^{94} -6.94427 q^{96} -1.94427 q^{97} +6.76393 q^{98} -2.94427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} - q^{4} - 6 q^{6} + 4 q^{7} + 6 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 - q^4 - 6 * q^6 + 4 * q^7 + 6 * q^9	\( 2 q - q^{2} + 2 q^{3} - q^{4} - 6 q^{6} + 4 q^{7} + 6 q^{9} + 4 q^{11} + 4 q^{12} + 2 q^{13} + 3 q^{14} - 3 q^{16} - 6 q^{17} - 13 q^{18} - 6 q^{21} - 2 q^{22} + 2 q^{23} + 10 q^{24} - 6 q^{26} + 20 q^{27} - 7 q^{28} + 10 q^{29} + 2 q^{31} + 9 q^{32} + 4 q^{33} - 2 q^{34} + 7 q^{36} + 4 q^{37} + 5 q^{38} + 12 q^{39} + 14 q^{41} - 2 q^{42} + 2 q^{43} - 2 q^{44} + 14 q^{46} + 4 q^{47} - 18 q^{48} + 4 q^{49} + 4 q^{51} + 4 q^{52} + 12 q^{53} - 20 q^{54} - 10 q^{56} - 10 q^{57} - 6 q^{61} - q^{62} - 8 q^{63} + 4 q^{64} - 12 q^{66} - 16 q^{67} + 8 q^{68} - 28 q^{69} + 4 q^{71} + 20 q^{72} - 8 q^{73} - 2 q^{74} - 5 q^{76} + 8 q^{77} - 16 q^{78} - 10 q^{79} + 22 q^{81} - 7 q^{82} + 12 q^{83} + 8 q^{84} + 4 q^{86} + 10 q^{89} - 6 q^{91} - 16 q^{92} + 2 q^{93} + 8 q^{94} + 4 q^{96} + 14 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 - q^4 - 6 * q^6 + 4 * q^7 + 6 * q^9 + 4 * q^11 + 4 * q^12 + 2 * q^13 + 3 * q^14 - 3 * q^16 - 6 * q^17 - 13 * q^18 - 6 * q^21 - 2 * q^22 + 2 * q^23 + 10 * q^24 - 6 * q^26 + 20 * q^27 - 7 * q^28 + 10 * q^29 + 2 * q^31 + 9 * q^32 + 4 * q^33 - 2 * q^34 + 7 * q^36 + 4 * q^37 + 5 * q^38 + 12 * q^39 + 14 * q^41 - 2 * q^42 + 2 * q^43 - 2 * q^44 + 14 * q^46 + 4 * q^47 - 18 * q^48 + 4 * q^49 + 4 * q^51 + 4 * q^52 + 12 * q^53 - 20 * q^54 - 10 * q^56 - 10 * q^57 - 6 * q^61 - q^62 - 8 * q^63 + 4 * q^64 - 12 * q^66 - 16 * q^67 + 8 * q^68 - 28 * q^69 + 4 * q^71 + 20 * q^72 - 8 * q^73 - 2 * q^74 - 5 * q^76 + 8 * q^77 - 16 * q^78 - 10 * q^79 + 22 * q^81 - 7 * q^82 + 12 * q^83 + 8 * q^84 + 4 * q^86 + 10 * q^89 - 6 * q^91 - 16 * q^92 + 2 * q^93 + 8 * q^94 + 4 * q^96 + 14 * q^97 + 18 * q^98 + 12 * q^99

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