LMFDB - Embedded newform 9025.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, 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("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 361)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{2} +2.00000 q^{3} +3.00000 q^{4} -4.47214 q^{6} -1.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23607 q^{2} +2.00000 q^{3} +3.00000 q^{4} -4.47214 q^{6} -1.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +5.23607 q^{11} +6.00000 q^{12} -1.85410 q^{13} +2.76393 q^{14} -1.00000 q^{16} -0.618034 q^{17} -2.23607 q^{18} -2.47214 q^{21} -11.7082 q^{22} +4.47214 q^{23} -4.47214 q^{24} +4.14590 q^{26} -4.00000 q^{27} -3.70820 q^{28} -7.09017 q^{29} +6.00000 q^{31} +6.70820 q^{32} +10.4721 q^{33} +1.38197 q^{34} +3.00000 q^{36} +8.85410 q^{37} -3.70820 q^{39} -4.09017 q^{41} +5.52786 q^{42} +0.472136 q^{43} +15.7082 q^{44} -10.0000 q^{46} -4.76393 q^{47} -2.00000 q^{48} -5.47214 q^{49} -1.23607 q^{51} -5.56231 q^{52} -0.0901699 q^{53} +8.94427 q^{54} +2.76393 q^{56} +15.8541 q^{58} -3.23607 q^{59} +9.85410 q^{61} -13.4164 q^{62} -1.23607 q^{63} -13.0000 q^{64} -23.4164 q^{66} -0.472136 q^{67} -1.85410 q^{68} +8.94427 q^{69} +3.23607 q^{71} -2.23607 q^{72} +14.5623 q^{73} -19.7984 q^{74} -6.47214 q^{77} +8.29180 q^{78} -2.00000 q^{79} -11.0000 q^{81} +9.14590 q^{82} +9.70820 q^{83} -7.41641 q^{84} -1.05573 q^{86} -14.1803 q^{87} -11.7082 q^{88} +7.32624 q^{89} +2.29180 q^{91} +13.4164 q^{92} +12.0000 q^{93} +10.6525 q^{94} +13.4164 q^{96} -11.0902 q^{97} +12.2361 q^{98} +5.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} + 6 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 + 2 * q^9	$ 2 q + 4 q^{3} + 6 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{11} + 12 q^{12} + 3 q^{13} + 10 q^{14} - 2 q^{16} + q^{17} + 4 q^{21} - 10 q^{22} + 15 q^{26} - 8 q^{27} + 6 q^{28} - 3 q^{29} + 12 q^{31} + 12 q^{33} + 5 q^{34} + 6 q^{36} + 11 q^{37} + 6 q^{39} + 3 q^{41} + 20 q^{42} - 8 q^{43} + 18 q^{44} - 20 q^{46} - 14 q^{47} - 4 q^{48} - 2 q^{49} + 2 q^{51} + 9 q^{52} + 11 q^{53} + 10 q^{56} + 25 q^{58} - 2 q^{59} + 13 q^{61} + 2 q^{63} - 26 q^{64} - 20 q^{66} + 8 q^{67} + 3 q^{68} + 2 q^{71} + 9 q^{73} - 15 q^{74} - 4 q^{77} + 30 q^{78} - 4 q^{79} - 22 q^{81} + 25 q^{82} + 6 q^{83} + 12 q^{84} - 20 q^{86} - 6 q^{87} - 10 q^{88} - q^{89} + 18 q^{91} + 24 q^{93} - 10 q^{94} - 11 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^11 + 12 * q^12 + 3 * q^13 + 10 * q^14 - 2 * q^16 + q^17 + 4 * q^21 - 10 * q^22 + 15 * q^26 - 8 * q^27 + 6 * q^28 - 3 * q^29 + 12 * q^31 + 12 * q^33 + 5 * q^34 + 6 * q^36 + 11 * q^37 + 6 * q^39 + 3 * q^41 + 20 * q^42 - 8 * q^43 + 18 * q^44 - 20 * q^46 - 14 * q^47 - 4 * q^48 - 2 * q^49 + 2 * q^51 + 9 * q^52 + 11 * q^53 + 10 * q^56 + 25 * q^58 - 2 * q^59 + 13 * q^61 + 2 * q^63 - 26 * q^64 - 20 * q^66 + 8 * q^67 + 3 * q^68 + 2 * q^71 + 9 * q^73 - 15 * q^74 - 4 * q^77 + 30 * q^78 - 4 * q^79 - 22 * q^81 + 25 * q^82 + 6 * q^83 + 12 * q^84 - 20 * q^86 - 6 * q^87 - 10 * q^88 - q^89 + 18 * q^91 + 24 * q^93 - 10 * q^94 - 11 * q^97 + 20 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.23607	−1.58114	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−2.23607	−1.58114	−0.790569	+	0.612372i	$0.790215\pi$
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	3.00000	1.50000
$5$	0	0
$5$	0	0
$6$	−4.47214	−1.82574
$7$	−1.23607	−0.467190	−0.233595	−	0.972334i	$-0.575049\pi$
$7$	−1.23607	−0.467190	−0.233595	+	0.972334i	$0.575049\pi$
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	0	0
$11$	5.23607	1.57873	0.789367	−	0.613922i	$-0.210409\pi$
$11$	5.23607	1.57873	0.789367	+	0.613922i	$0.210409\pi$
$12$	6.00000	1.73205
$13$	−1.85410	−0.514235	−0.257118	−	0.966380i	$-0.582773\pi$
$13$	−1.85410	−0.514235	−0.257118	+	0.966380i	$0.582773\pi$
$14$	2.76393	0.738692
$15$	0	0
$16$	−1.00000	−0.250000
$17$	−0.618034	−0.149895	−0.0749476	−	0.997187i	$-0.523879\pi$
$17$	−0.618034	−0.149895	−0.0749476	+	0.997187i	$0.523879\pi$
$18$	−2.23607	−0.527046
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−2.47214	−0.539464
$22$	−11.7082	−2.49620
$23$	4.47214	0.932505	0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214	0.932505	0.466252	+	0.884652i	$0.345604\pi$
$24$	−4.47214	−0.912871
$25$	0	0
$26$	4.14590	0.813077
$27$	−4.00000	−0.769800
$28$	−3.70820	−0.700785
$29$	−7.09017	−1.31661	−0.658306	−	0.752751i	$-0.728727\pi$
$29$	−7.09017	−1.31661	−0.658306	+	0.752751i	$0.728727\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	6.70820	1.18585
$33$	10.4721	1.82296
$34$	1.38197	0.237005
$35$	0	0
$36$	3.00000	0.500000
$37$	8.85410	1.45561	0.727803	−	0.685787i	$-0.240542\pi$
$37$	8.85410	1.45561	0.727803	+	0.685787i	$0.240542\pi$
$38$	0	0
$39$	−3.70820	−0.593788
$40$	0	0
$41$	−4.09017	−0.638777	−0.319389	−	0.947624i	$-0.603478\pi$
$41$	−4.09017	−0.638777	−0.319389	+	0.947624i	$0.603478\pi$
$42$	5.52786	0.852968
$43$	0.472136	0.0720001	0.0360000	−	0.999352i	$-0.488538\pi$
$43$	0.472136	0.0720001	0.0360000	+	0.999352i	$0.488538\pi$
$44$	15.7082	2.36810
$45$	0	0
$46$	−10.0000	−1.47442
$47$	−4.76393	−0.694891	−0.347445	−	0.937700i	$-0.612951\pi$
$47$	−4.76393	−0.694891	−0.347445	+	0.937700i	$0.612951\pi$
$48$	−2.00000	−0.288675
$49$	−5.47214	−0.781734
$50$	0	0
$51$	−1.23607	−0.173084
$52$	−5.56231	−0.771353
$53$	−0.0901699	−0.0123858	−0.00619290	−	0.999981i	$-0.501971\pi$
$53$	−0.0901699	−0.0123858	−0.00619290	+	0.999981i	$0.501971\pi$
$54$	8.94427	1.21716
$55$	0	0
$56$	2.76393	0.369346
$57$	0	0
$58$	15.8541	2.08175
$59$	−3.23607	−0.421300	−0.210650	−	0.977562i	$-0.567558\pi$
$59$	−3.23607	−0.421300	−0.210650	+	0.977562i	$0.567558\pi$
$60$	0	0
$61$	9.85410	1.26169	0.630844	−	0.775909i	$-0.282709\pi$
$61$	9.85410	1.26169	0.630844	+	0.775909i	$0.282709\pi$
$62$	−13.4164	−1.70389
$63$	−1.23607	−0.155730
$64$	−13.0000	−1.62500
$65$	0	0
$66$	−23.4164	−2.88236
$67$	−0.472136	−0.0576806	−0.0288403	−	0.999584i	$-0.509181\pi$
$67$	−0.472136	−0.0576806	−0.0288403	+	0.999584i	$0.509181\pi$
$68$	−1.85410	−0.224843
$69$	8.94427	1.07676
$70$	0	0
$71$	3.23607	0.384051	0.192025	−	0.981390i	$-0.438494\pi$
$71$	3.23607	0.384051	0.192025	+	0.981390i	$0.438494\pi$
$72$	−2.23607	−0.263523
$73$	14.5623	1.70439	0.852194	−	0.523225i	$-0.175271\pi$
$73$	14.5623	1.70439	0.852194	+	0.523225i	$0.175271\pi$
$74$	−19.7984	−2.30151
$75$	0	0
$76$	0	0
$77$	−6.47214	−0.737568
$78$	8.29180	0.938861
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	9.14590	1.01000
$83$	9.70820	1.06561	0.532807	−	0.846237i	$-0.321137\pi$
$83$	9.70820	1.06561	0.532807	+	0.846237i	$0.321137\pi$
$84$	−7.41641	−0.809196
$85$	0	0
$86$	−1.05573	−0.113842
$87$	−14.1803	−1.52029
$88$	−11.7082	−1.24810
$89$	7.32624	0.776580	0.388290	−	0.921537i	$-0.373066\pi$
$89$	7.32624	0.776580	0.388290	+	0.921537i	$0.373066\pi$
$90$	0	0
$91$	2.29180	0.240246
$92$	13.4164	1.39876
$93$	12.0000	1.24434
$94$	10.6525	1.09872
$95$	0	0
$96$	13.4164	1.36931
$97$	−11.0902	−1.12604	−0.563018	−	0.826445i	$-0.690360\pi$
$97$	−11.0902	−1.12604	−0.563018	+	0.826445i	$0.690360\pi$
$98$	12.2361	1.23603
$99$	5.23607	0.526245
$100$	0	0
$101$	0.673762	0.0670418	0.0335209	−	0.999438i	$-0.489328\pi$
$101$	0.673762	0.0670418	0.0335209	+	0.999438i	$0.489328\pi$
$102$	2.76393	0.273670
$103$	7.70820	0.759512	0.379756	−	0.925087i	$-0.376008\pi$
$103$	7.70820	0.759512	0.379756	+	0.925087i	$0.376008\pi$
$104$	4.14590	0.406539
$105$	0	0
$106$	0.201626	0.0195837
$107$	0.763932	0.0738521	0.0369260	−	0.999318i	$-0.488243\pi$
$107$	0.763932	0.0738521	0.0369260	+	0.999318i	$0.488243\pi$
$108$	−12.0000	−1.15470
$109$	12.0902	1.15803	0.579014	−	0.815318i	$-0.303438\pi$
$109$	12.0902	1.15803	0.579014	+	0.815318i	$0.303438\pi$
$110$	0	0
$111$	17.7082	1.68079
$112$	1.23607	0.116797
$113$	−10.1459	−0.954446	−0.477223	−	0.878782i	$-0.658357\pi$
$113$	−10.1459	−0.954446	−0.477223	+	0.878782i	$0.658357\pi$
$114$	0	0
$115$	0	0
$116$	−21.2705	−1.97492
$117$	−1.85410	−0.171412
$118$	7.23607	0.666134
$119$	0.763932	0.0700295
$120$	0	0
$121$	16.4164	1.49240
$122$	−22.0344	−1.99490
$123$	−8.18034	−0.737596
$124$	18.0000	1.61645
$125$	0	0
$126$	2.76393	0.246231
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	15.6525	1.38350
$129$	0.944272	0.0831385
$130$	0	0
$131$	21.7082	1.89665	0.948327	−	0.317294i	$-0.102774\pi$
$131$	21.7082	1.89665	0.948327	+	0.317294i	$0.102774\pi$
$132$	31.4164	2.73445
$133$	0	0
$134$	1.05573	0.0912010
$135$	0	0
$136$	1.38197	0.118503
$137$	−1.79837	−0.153645	−0.0768227	−	0.997045i	$-0.524478\pi$
$137$	−1.79837	−0.153645	−0.0768227	+	0.997045i	$0.524478\pi$
$138$	−20.0000	−1.70251
$139$	13.7082	1.16271	0.581357	−	0.813648i	$-0.302522\pi$
$139$	13.7082	1.16271	0.581357	+	0.813648i	$0.302522\pi$
$140$	0	0
$141$	−9.52786	−0.802391
$142$	−7.23607	−0.607237
$143$	−9.70820	−0.811841
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−32.5623	−2.69488
$147$	−10.9443	−0.902668
$148$	26.5623	2.18341
$149$	1.85410	0.151894	0.0759470	−	0.997112i	$-0.475802\pi$
$149$	1.85410	0.151894	0.0759470	+	0.997112i	$0.475802\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	−0.618034	−0.0499651
$154$	14.4721	1.16620
$155$	0	0
$156$	−11.1246	−0.890682
$157$	8.03444	0.641218	0.320609	−	0.947212i	$-0.396112\pi$
$157$	8.03444	0.641218	0.320609	+	0.947212i	$0.396112\pi$
$158$	4.47214	0.355784
$159$	−0.180340	−0.0143019
$160$	0	0
$161$	−5.52786	−0.435657
$162$	24.5967	1.93250
$163$	8.29180	0.649464	0.324732	−	0.945806i	$-0.394726\pi$
$163$	8.29180	0.649464	0.324732	+	0.945806i	$0.394726\pi$
$164$	−12.2705	−0.958166
$165$	0	0
$166$	−21.7082	−1.68488
$167$	−4.76393	−0.368644	−0.184322	−	0.982866i	$-0.559009\pi$
$167$	−4.76393	−0.368644	−0.184322	+	0.982866i	$0.559009\pi$
$168$	5.52786	0.426484
$169$	−9.56231	−0.735562
$170$	0	0
$171$	0	0
$172$	1.41641	0.108000
$173$	−5.61803	−0.427131	−0.213566	−	0.976929i	$-0.568508\pi$
$173$	−5.61803	−0.427131	−0.213566	+	0.976929i	$0.568508\pi$
$174$	31.7082	2.40379
$175$	0	0
$176$	−5.23607	−0.394683
$177$	−6.47214	−0.486476
$178$	−16.3820	−1.22788
$179$	20.9443	1.56545	0.782724	−	0.622369i	$-0.213830\pi$
$179$	20.9443	1.56545	0.782724	+	0.622369i	$0.213830\pi$
$180$	0	0
$181$	−21.4164	−1.59187	−0.795935	−	0.605383i	$-0.793020\pi$
$181$	−21.4164	−1.59187	−0.795935	+	0.605383i	$0.793020\pi$
$182$	−5.12461	−0.379861
$183$	19.7082	1.45687
$184$	−10.0000	−0.737210
$185$	0	0
$186$	−26.8328	−1.96748
$187$	−3.23607	−0.236645
$188$	−14.2918	−1.04234
$189$	4.94427	0.359643
$190$	0	0
$191$	−4.76393	−0.344706	−0.172353	−	0.985035i	$-0.555137\pi$
$191$	−4.76393	−0.344706	−0.172353	+	0.985035i	$0.555137\pi$
$192$	−26.0000	−1.87639
$193$	−11.5279	−0.829794	−0.414897	−	0.909868i	$-0.636182\pi$
$193$	−11.5279	−0.829794	−0.414897	+	0.909868i	$0.636182\pi$
$194$	24.7984	1.78042
$195$	0	0
$196$	−16.4164	−1.17260
$197$	24.0344	1.71238	0.856192	−	0.516659i	$-0.172824\pi$
$197$	24.0344	1.71238	0.856192	+	0.516659i	$0.172824\pi$
$198$	−11.7082	−0.832066
$199$	−12.9443	−0.917595	−0.458798	−	0.888541i	$-0.651720\pi$
$199$	−12.9443	−0.917595	−0.458798	+	0.888541i	$0.651720\pi$
$200$	0	0
$201$	−0.944272	−0.0666038
$202$	−1.50658	−0.106002
$203$	8.76393	0.615107
$204$	−3.70820	−0.259626
$205$	0	0
$206$	−17.2361	−1.20089
$207$	4.47214	0.310835
$208$	1.85410	0.128559
$209$	0	0
$210$	0	0
$211$	−27.7082	−1.90751	−0.953756	−	0.300583i	$-0.902819\pi$
$211$	−27.7082	−1.90751	−0.953756	+	0.300583i	$0.902819\pi$
$212$	−0.270510	−0.0185787
$213$	6.47214	0.443463
$214$	−1.70820	−0.116770
$215$	0	0
$216$	8.94427	0.608581
$217$	−7.41641	−0.503459
$218$	−27.0344	−1.83100
$219$	29.1246	1.96806
$220$	0	0
$221$	1.14590	0.0770814
$222$	−39.5967	−2.65756
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	−8.29180	−0.554019
$225$	0	0
$226$	22.6869	1.50911
$227$	13.5279	0.897876	0.448938	−	0.893563i	$-0.351802\pi$
$227$	13.5279	0.897876	0.448938	+	0.893563i	$0.351802\pi$
$228$	0	0
$229$	25.9787	1.71672	0.858361	−	0.513046i	$-0.171483\pi$
$229$	25.9787	1.71672	0.858361	+	0.513046i	$0.171483\pi$
$230$	0	0
$231$	−12.9443	−0.851671
$232$	15.8541	1.04087
$233$	−7.09017	−0.464492	−0.232246	−	0.972657i	$-0.574608\pi$
$233$	−7.09017	−0.464492	−0.232246	+	0.972657i	$0.574608\pi$
$234$	4.14590	0.271026
$235$	0	0
$236$	−9.70820	−0.631950
$237$	−4.00000	−0.259828
$238$	−1.70820	−0.110726
$239$	1.05573	0.0682894	0.0341447	−	0.999417i	$-0.489129\pi$
$239$	1.05573	0.0682894	0.0341447	+	0.999417i	$0.489129\pi$
$240$	0	0
$241$	1.05573	0.0680054	0.0340027	−	0.999422i	$-0.489175\pi$
$241$	1.05573	0.0680054	0.0340027	+	0.999422i	$0.489175\pi$
$242$	−36.7082	−2.35969
$243$	−10.0000	−0.641500
$244$	29.5623	1.89253
$245$	0	0
$246$	18.2918	1.16624
$247$	0	0
$248$	−13.4164	−0.851943
$249$	19.4164	1.23046
$250$	0	0
$251$	13.2361	0.835453	0.417727	−	0.908573i	$-0.362827\pi$
$251$	13.2361	0.835453	0.417727	+	0.908573i	$0.362827\pi$
$252$	−3.70820	−0.233595
$253$	23.4164	1.47218
$254$	26.8328	1.68364
$255$	0	0
$256$	−9.00000	−0.562500
$257$	−11.9098	−0.742915	−0.371457	−	0.928450i	$-0.621142\pi$
$257$	−11.9098	−0.742915	−0.371457	+	0.928450i	$0.621142\pi$
$258$	−2.11146	−0.131454
$259$	−10.9443	−0.680044
$260$	0	0
$261$	−7.09017	−0.438871
$262$	−48.5410	−2.99887
$263$	−7.81966	−0.482181	−0.241090	−	0.970503i	$-0.577505\pi$
$263$	−7.81966	−0.482181	−0.241090	+	0.970503i	$0.577505\pi$
$264$	−23.4164	−1.44118
$265$	0	0
$266$	0	0
$267$	14.6525	0.896717
$268$	−1.41641	−0.0865209
$269$	−1.20163	−0.0732644	−0.0366322	−	0.999329i	$-0.511663\pi$
$269$	−1.20163	−0.0732644	−0.0366322	+	0.999329i	$0.511663\pi$
$270$	0	0
$271$	14.6525	0.890075	0.445037	−	0.895512i	$-0.353190\pi$
$271$	14.6525	0.890075	0.445037	+	0.895512i	$0.353190\pi$
$272$	0.618034	0.0374738
$273$	4.58359	0.277412
$274$	4.02129	0.242935
$275$	0	0
$276$	26.8328	1.61515
$277$	10.3820	0.623792	0.311896	−	0.950116i	$-0.399036\pi$
$277$	10.3820	0.623792	0.311896	+	0.950116i	$0.399036\pi$
$278$	−30.6525	−1.83841
$279$	6.00000	0.359211
$280$	0	0
$281$	19.0902	1.13882	0.569412	−	0.822052i	$-0.307171\pi$
$281$	19.0902	1.13882	0.569412	+	0.822052i	$0.307171\pi$
$282$	21.3050	1.26869
$283$	31.4164	1.86751	0.933756	−	0.357911i	$-0.116511\pi$
$283$	31.4164	1.86751	0.933756	+	0.357911i	$0.116511\pi$
$284$	9.70820	0.576076
$285$	0	0
$286$	21.7082	1.28363
$287$	5.05573	0.298430
$288$	6.70820	0.395285
$289$	−16.6180	−0.977531
$290$	0	0
$291$	−22.1803	−1.30023
$292$	43.6869	2.55658
$293$	25.4164	1.48484	0.742421	−	0.669933i	$-0.233677\pi$
$293$	25.4164	1.48484	0.742421	+	0.669933i	$0.233677\pi$
$294$	24.4721	1.42724
$295$	0	0
$296$	−19.7984	−1.15076
$297$	−20.9443	−1.21531
$298$	−4.14590	−0.240165
$299$	−8.29180	−0.479527
$300$	0	0
$301$	−0.583592	−0.0336377
$302$	0	0
$303$	1.34752	0.0774132
$304$	0	0
$305$	0	0
$306$	1.38197	0.0790017
$307$	15.5279	0.886222	0.443111	−	0.896467i	$-0.353875\pi$
$307$	15.5279	0.886222	0.443111	+	0.896467i	$0.353875\pi$
$308$	−19.4164	−1.10635
$309$	15.4164	0.877009
$310$	0	0
$311$	14.7639	0.837186	0.418593	−	0.908174i	$-0.362523\pi$
$311$	14.7639	0.837186	0.418593	+	0.908174i	$0.362523\pi$
$312$	8.29180	0.469431
$313$	25.9787	1.46840	0.734202	−	0.678931i	$-0.237557\pi$
$313$	25.9787	1.46840	0.734202	+	0.678931i	$0.237557\pi$
$314$	−17.9656	−1.01386
$315$	0	0
$316$	−6.00000	−0.337526
$317$	10.3820	0.583109	0.291555	−	0.956554i	$-0.405827\pi$
$317$	10.3820	0.583109	0.291555	+	0.956554i	$0.405827\pi$
$318$	0.403252	0.0226133
$319$	−37.1246	−2.07858
$320$	0	0
$321$	1.52786	0.0852771
$322$	12.3607	0.688834
$323$	0	0
$324$	−33.0000	−1.83333
$325$	0	0
$326$	−18.5410	−1.02689
$327$	24.1803	1.33718
$328$	9.14590	0.504998
$329$	5.88854	0.324646
$330$	0	0
$331$	5.81966	0.319877	0.159939	−	0.987127i	$-0.448870\pi$
$331$	5.81966	0.319877	0.159939	+	0.987127i	$0.448870\pi$
$332$	29.1246	1.59842
$333$	8.85410	0.485202
$334$	10.6525	0.582878
$335$	0	0
$336$	2.47214	0.134866
$337$	13.9787	0.761469	0.380735	−	0.924684i	$-0.375671\pi$
$337$	13.9787	0.761469	0.380735	+	0.924684i	$0.375671\pi$
$338$	21.3820	1.16303
$339$	−20.2918	−1.10210
$340$	0	0
$341$	31.4164	1.70129
$342$	0	0
$343$	15.4164	0.832408
$344$	−1.05573	−0.0569210
$345$	0	0
$346$	12.5623	0.675354
$347$	−25.5967	−1.37411	−0.687053	−	0.726608i	$-0.741096\pi$
$347$	−25.5967	−1.37411	−0.687053	+	0.726608i	$0.741096\pi$
$348$	−42.5410	−2.28044
$349$	−2.14590	−0.114867	−0.0574336	−	0.998349i	$-0.518292\pi$
$349$	−2.14590	−0.114867	−0.0574336	+	0.998349i	$0.518292\pi$
$350$	0	0
$351$	7.41641	0.395859
$352$	35.1246	1.87215
$353$	−30.5066	−1.62370	−0.811851	−	0.583865i	$-0.801540\pi$
$353$	−30.5066	−1.62370	−0.811851	+	0.583865i	$0.801540\pi$
$354$	14.4721	0.769185
$355$	0	0
$356$	21.9787	1.16487
$357$	1.52786	0.0808631
$358$	−46.8328	−2.47519
$359$	21.7082	1.14572	0.572858	−	0.819655i	$-0.305835\pi$
$359$	21.7082	1.14572	0.572858	+	0.819655i	$0.305835\pi$
$360$	0	0
$361$	0	0
$362$	47.8885	2.51697
$363$	32.8328	1.72328
$364$	6.87539	0.360368
$365$	0	0
$366$	−44.0689	−2.30352
$367$	−31.4164	−1.63992	−0.819962	−	0.572419i	$-0.806005\pi$
$367$	−31.4164	−1.63992	−0.819962	+	0.572419i	$0.806005\pi$
$368$	−4.47214	−0.233126
$369$	−4.09017	−0.212926
$370$	0	0
$371$	0.111456	0.00578652
$372$	36.0000	1.86651
$373$	1.56231	0.0808931	0.0404466	−	0.999182i	$-0.487122\pi$
$373$	1.56231	0.0808931	0.0404466	+	0.999182i	$0.487122\pi$
$374$	7.23607	0.374168
$375$	0	0
$376$	10.6525	0.549359
$377$	13.1459	0.677048
$378$	−11.0557	−0.568645
$379$	−21.8885	−1.12434	−0.562169	−	0.827022i	$-0.690033\pi$
$379$	−21.8885	−1.12434	−0.562169	+	0.827022i	$0.690033\pi$
$380$	0	0
$381$	−24.0000	−1.22956
$382$	10.6525	0.545028
$383$	−29.2361	−1.49389	−0.746947	−	0.664884i	$-0.768481\pi$
$383$	−29.2361	−1.49389	−0.746947	+	0.664884i	$0.768481\pi$
$384$	31.3050	1.59752
$385$	0	0
$386$	25.7771	1.31202
$387$	0.472136	0.0240000
$388$	−33.2705	−1.68905
$389$	25.8541	1.31086	0.655428	−	0.755258i	$-0.272488\pi$
$389$	25.8541	1.31086	0.655428	+	0.755258i	$0.272488\pi$
$390$	0	0
$391$	−2.76393	−0.139778
$392$	12.2361	0.618015
$393$	43.4164	2.19007
$394$	−53.7426	−2.70752
$395$	0	0
$396$	15.7082	0.789367
$397$	−1.41641	−0.0710875	−0.0355437	−	0.999368i	$-0.511316\pi$
$397$	−1.41641	−0.0710875	−0.0355437	+	0.999368i	$0.511316\pi$
$398$	28.9443	1.45085
$399$	0	0
$400$	0	0
$401$	25.4164	1.26923	0.634617	−	0.772826i	$-0.281158\pi$
$401$	25.4164	1.26923	0.634617	+	0.772826i	$0.281158\pi$
$402$	2.11146	0.105310
$403$	−11.1246	−0.554156
$404$	2.02129	0.100563
$405$	0	0
$406$	−19.5967	−0.972570
$407$	46.3607	2.29801
$408$	2.76393	0.136835
$409$	20.2705	1.00231	0.501156	−	0.865357i	$-0.332908\pi$
$409$	20.2705	1.00231	0.501156	+	0.865357i	$0.332908\pi$
$410$	0	0
$411$	−3.59675	−0.177414
$412$	23.1246	1.13927
$413$	4.00000	0.196827
$414$	−10.0000	−0.491473
$415$	0	0
$416$	−12.4377	−0.609808
$417$	27.4164	1.34259
$418$	0	0
$419$	4.58359	0.223923	0.111962	−	0.993713i	$-0.464287\pi$
$419$	4.58359	0.223923	0.111962	+	0.993713i	$0.464287\pi$
$420$	0	0
$421$	−21.7984	−1.06239	−0.531194	−	0.847250i	$-0.678256\pi$
$421$	−21.7984	−1.06239	−0.531194	+	0.847250i	$0.678256\pi$
$422$	61.9574	3.01604
$423$	−4.76393	−0.231630
$424$	0.201626	0.00979183
$425$	0	0
$426$	−14.4721	−0.701177
$427$	−12.1803	−0.589448
$428$	2.29180	0.110778
$429$	−19.4164	−0.937433
$430$	0	0
$431$	18.7639	0.903827	0.451913	−	0.892062i	$-0.350742\pi$
$431$	18.7639	0.903827	0.451913	+	0.892062i	$0.350742\pi$
$432$	4.00000	0.192450
$433$	−9.43769	−0.453547	−0.226773	−	0.973948i	$-0.572818\pi$
$433$	−9.43769	−0.453547	−0.226773	+	0.973948i	$0.572818\pi$
$434$	16.5836	0.796038
$435$	0	0
$436$	36.2705	1.73704
$437$	0	0
$438$	−65.1246	−3.11177
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	0	0
$441$	−5.47214	−0.260578
$442$	−2.56231	−0.121876
$443$	1.41641	0.0672956	0.0336478	−	0.999434i	$-0.489288\pi$
$443$	1.41641	0.0672956	0.0336478	+	0.999434i	$0.489288\pi$
$444$	53.1246	2.52118
$445$	0	0
$446$	22.3607	1.05881
$447$	3.70820	0.175392
$448$	16.0689	0.759183
$449$	35.4508	1.67303	0.836515	−	0.547945i	$-0.184590\pi$
$449$	35.4508	1.67303	0.836515	+	0.547945i	$0.184590\pi$
$450$	0	0
$451$	−21.4164	−1.00846
$452$	−30.4377	−1.43167
$453$	0	0
$454$	−30.2492	−1.41967
$455$	0	0
$456$	0	0
$457$	0.0901699	0.00421797	0.00210899	−	0.999998i	$-0.499329\pi$
$457$	0.0901699	0.00421797	0.00210899	+	0.999998i	$0.499329\pi$
$458$	−58.0902	−2.71438
$459$	2.47214	0.115389
$460$	0	0
$461$	−0.472136	−0.0219896	−0.0109948	−	0.999940i	$-0.503500\pi$
$461$	−0.472136	−0.0219896	−0.0109948	+	0.999940i	$0.503500\pi$
$462$	28.9443	1.34661
$463$	−25.7082	−1.19476	−0.597381	−	0.801958i	$-0.703792\pi$
$463$	−25.7082	−1.19476	−0.597381	+	0.801958i	$0.703792\pi$
$464$	7.09017	0.329153
$465$	0	0
$466$	15.8541	0.734427
$467$	9.88854	0.457587	0.228794	−	0.973475i	$-0.426522\pi$
$467$	9.88854	0.457587	0.228794	+	0.973475i	$0.426522\pi$
$468$	−5.56231	−0.257118
$469$	0.583592	0.0269478
$470$	0	0
$471$	16.0689	0.740415
$472$	7.23607	0.333067
$473$	2.47214	0.113669
$474$	8.94427	0.410824
$475$	0	0
$476$	2.29180	0.105044
$477$	−0.0901699	−0.00412860
$478$	−2.36068	−0.107975
$479$	9.05573	0.413767	0.206883	−	0.978366i	$-0.433668\pi$
$479$	9.05573	0.413767	0.206883	+	0.978366i	$0.433668\pi$
$480$	0	0
$481$	−16.4164	−0.748524
$482$	−2.36068	−0.107526
$483$	−11.0557	−0.503053
$484$	49.2492	2.23860
$485$	0	0
$486$	22.3607	1.01430
$487$	25.2361	1.14356	0.571778	−	0.820409i	$-0.306254\pi$
$487$	25.2361	1.14356	0.571778	+	0.820409i	$0.306254\pi$
$488$	−22.0344	−0.997452
$489$	16.5836	0.749936
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	−24.5410	−1.10639
$493$	4.38197	0.197354
$494$	0	0
$495$	0	0
$496$	−6.00000	−0.269408
$497$	−4.00000	−0.179425
$498$	−43.4164	−1.94554
$499$	−7.23607	−0.323931	−0.161965	−	0.986796i	$-0.551783\pi$
$499$	−7.23607	−0.323931	−0.161965	+	0.986796i	$0.551783\pi$
$500$	0	0
$501$	−9.52786	−0.425674
$502$	−29.5967	−1.32097
$503$	10.3607	0.461960	0.230980	−	0.972959i	$-0.425807\pi$
$503$	10.3607	0.461960	0.230980	+	0.972959i	$0.425807\pi$
$504$	2.76393	0.123115
$505$	0	0
$506$	−52.3607	−2.32772
$507$	−19.1246	−0.849354
$508$	−36.0000	−1.59724
$509$	−23.0902	−1.02345	−0.511727	−	0.859148i	$-0.670994\pi$
$509$	−23.0902	−1.02345	−0.511727	+	0.859148i	$0.670994\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	−11.1803	−0.494106
$513$	0	0
$514$	26.6312	1.17465
$515$	0	0
$516$	2.83282	0.124708
$517$	−24.9443	−1.09705
$518$	24.4721	1.07524
$519$	−11.2361	−0.493209
$520$	0	0
$521$	17.5623	0.769419	0.384709	−	0.923038i	$-0.374302\pi$
$521$	17.5623	0.769419	0.384709	+	0.923038i	$0.374302\pi$
$522$	15.8541	0.693915
$523$	−11.4164	−0.499205	−0.249602	−	0.968348i	$-0.580300\pi$
$523$	−11.4164	−0.499205	−0.249602	+	0.968348i	$0.580300\pi$
$524$	65.1246	2.84498
$525$	0	0
$526$	17.4853	0.762395
$527$	−3.70820	−0.161532
$528$	−10.4721	−0.455741
$529$	−3.00000	−0.130435
$530$	0	0
$531$	−3.23607	−0.140433
$532$	0	0
$533$	7.58359	0.328482
$534$	−32.7639	−1.41783
$535$	0	0
$536$	1.05573	0.0456005
$537$	41.8885	1.80762
$538$	2.68692	0.115841
$539$	−28.6525	−1.23415
$540$	0	0
$541$	25.8541	1.11155	0.555777	−	0.831331i	$-0.312421\pi$
$541$	25.8541	1.11155	0.555777	+	0.831331i	$0.312421\pi$
$542$	−32.7639	−1.40733
$543$	−42.8328	−1.83813
$544$	−4.14590	−0.177754
$545$	0	0
$546$	−10.2492	−0.438626
$547$	−4.76393	−0.203691	−0.101846	−	0.994800i	$-0.532475\pi$
$547$	−4.76393	−0.203691	−0.101846	+	0.994800i	$0.532475\pi$
$548$	−5.39512	−0.230468
$549$	9.85410	0.420563
$550$	0	0
$551$	0	0
$552$	−20.0000	−0.851257
$553$	2.47214	0.105126
$554$	−23.2148	−0.986302
$555$	0	0
$556$	41.1246	1.74407
$557$	28.4721	1.20640	0.603202	−	0.797589i	$-0.293891\pi$
$557$	28.4721	1.20640	0.603202	+	0.797589i	$0.293891\pi$
$558$	−13.4164	−0.567962
$559$	−0.875388	−0.0370250
$560$	0	0
$561$	−6.47214	−0.273254
$562$	−42.6869	−1.80064
$563$	3.34752	0.141081	0.0705407	−	0.997509i	$-0.477528\pi$
$563$	3.34752	0.141081	0.0705407	+	0.997509i	$0.477528\pi$
$564$	−28.5836	−1.20359
$565$	0	0
$566$	−70.2492	−2.95280
$567$	13.5967	0.571010
$568$	−7.23607	−0.303619
$569$	22.3820	0.938301	0.469150	−	0.883118i	$-0.344560\pi$
$569$	22.3820	0.938301	0.469150	+	0.883118i	$0.344560\pi$
$570$	0	0
$571$	−15.7082	−0.657368	−0.328684	−	0.944440i	$-0.606605\pi$
$571$	−15.7082	−0.657368	−0.328684	+	0.944440i	$0.606605\pi$
$572$	−29.1246	−1.21776
$573$	−9.52786	−0.398032
$574$	−11.3050	−0.471860
$575$	0	0
$576$	−13.0000	−0.541667
$577$	−4.61803	−0.192251	−0.0961256	−	0.995369i	$-0.530645\pi$
$577$	−4.61803	−0.192251	−0.0961256	+	0.995369i	$0.530645\pi$
$578$	37.1591	1.54561
$579$	−23.0557	−0.958163
$580$	0	0
$581$	−12.0000	−0.497844
$582$	49.5967	2.05585
$583$	−0.472136	−0.0195539
$584$	−32.5623	−1.34744
$585$	0	0
$586$	−56.8328	−2.34774
$587$	2.76393	0.114080	0.0570398	−	0.998372i	$-0.481834\pi$
$587$	2.76393	0.114080	0.0570398	+	0.998372i	$0.481834\pi$
$588$	−32.8328	−1.35400
$589$	0	0
$590$	0	0
$591$	48.0689	1.97729
$592$	−8.85410	−0.363901
$593$	−28.8541	−1.18490	−0.592448	−	0.805609i	$-0.701838\pi$
$593$	−28.8541	−1.18490	−0.592448	+	0.805609i	$0.701838\pi$
$594$	46.8328	1.92157
$595$	0	0
$596$	5.56231	0.227841
$597$	−25.8885	−1.05955
$598$	18.5410	0.758199
$599$	−34.9443	−1.42778	−0.713892	−	0.700256i	$-0.753069\pi$
$599$	−34.9443	−1.42778	−0.713892	+	0.700256i	$0.753069\pi$
$600$	0	0
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	1.30495	0.0531859
$603$	−0.472136	−0.0192269
$604$	0	0
$605$	0	0
$606$	−3.01316	−0.122401
$607$	−35.4164	−1.43751	−0.718754	−	0.695265i	$-0.755287\pi$
$607$	−35.4164	−1.43751	−0.718754	+	0.695265i	$0.755287\pi$
$608$	0	0
$609$	17.5279	0.710265
$610$	0	0
$611$	8.83282	0.357337
$612$	−1.85410	−0.0749476
$613$	20.2705	0.818718	0.409359	−	0.912373i	$-0.365752\pi$
$613$	20.2705	0.818718	0.409359	+	0.912373i	$0.365752\pi$
$614$	−34.7214	−1.40124
$615$	0	0
$616$	14.4721	0.583099
$617$	−6.36068	−0.256071	−0.128036	−	0.991770i	$-0.540867\pi$
$617$	−6.36068	−0.256071	−0.128036	+	0.991770i	$0.540867\pi$
$618$	−34.4721	−1.38667
$619$	−41.1246	−1.65294	−0.826469	−	0.562982i	$-0.809654\pi$
$619$	−41.1246	−1.65294	−0.826469	+	0.562982i	$0.809654\pi$
$620$	0	0
$621$	−17.8885	−0.717843
$622$	−33.0132	−1.32371
$623$	−9.05573	−0.362810
$624$	3.70820	0.148447
$625$	0	0
$626$	−58.0902	−2.32175
$627$	0	0
$628$	24.1033	0.961827
$629$	−5.47214	−0.218188
$630$	0	0
$631$	−26.3607	−1.04940	−0.524701	−	0.851287i	$-0.675823\pi$
$631$	−26.3607	−1.04940	−0.524701	+	0.851287i	$0.675823\pi$
$632$	4.47214	0.177892
$633$	−55.4164	−2.20260
$634$	−23.2148	−0.921977
$635$	0	0
$636$	−0.541020	−0.0214528
$637$	10.1459	0.401995
$638$	83.0132	3.28652
$639$	3.23607	0.128017
$640$	0	0
$641$	−31.3820	−1.23951	−0.619757	−	0.784794i	$-0.712769\pi$
$641$	−31.3820	−1.23951	−0.619757	+	0.784794i	$0.712769\pi$
$642$	−3.41641	−0.134835
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	−16.5836	−0.653485
$645$	0	0
$646$	0	0
$647$	−41.5967	−1.63534	−0.817668	−	0.575689i	$-0.804734\pi$
$647$	−41.5967	−1.63534	−0.817668	+	0.575689i	$0.804734\pi$
$648$	24.5967	0.966252
$649$	−16.9443	−0.665121
$650$	0	0
$651$	−14.8328	−0.581344
$652$	24.8754	0.974195
$653$	22.7426	0.889989	0.444994	−	0.895533i	$-0.353206\pi$
$653$	22.7426	0.889989	0.444994	+	0.895533i	$0.353206\pi$
$654$	−54.0689	−2.11426
$655$	0	0
$656$	4.09017	0.159694
$657$	14.5623	0.568130
$658$	−13.1672	−0.513310
$659$	−8.29180	−0.323003	−0.161501	−	0.986873i	$-0.551634\pi$
$659$	−8.29180	−0.323003	−0.161501	+	0.986873i	$0.551634\pi$
$660$	0	0
$661$	19.8885	0.773575	0.386787	−	0.922169i	$-0.373585\pi$
$661$	19.8885	0.773575	0.386787	+	0.922169i	$0.373585\pi$
$662$	−13.0132	−0.505771
$663$	2.29180	0.0890060
$664$	−21.7082	−0.842442
$665$	0	0
$666$	−19.7984	−0.767171
$667$	−31.7082	−1.22775
$668$	−14.2918	−0.552966
$669$	−20.0000	−0.773245
$670$	0	0
$671$	51.5967	1.99187
$672$	−16.5836	−0.639726
$673$	19.1459	0.738020	0.369010	−	0.929425i	$-0.379697\pi$
$673$	19.1459	0.738020	0.369010	+	0.929425i	$0.379697\pi$
$674$	−31.2574	−1.20399
$675$	0	0
$676$	−28.6869	−1.10334
$677$	45.3394	1.74253	0.871267	−	0.490809i	$-0.163299\pi$
$677$	45.3394	1.74253	0.871267	+	0.490809i	$0.163299\pi$
$678$	45.3738	1.74257
$679$	13.7082	0.526073
$680$	0	0
$681$	27.0557	1.03678
$682$	−70.2492	−2.68998
$683$	37.0132	1.41627	0.708135	−	0.706078i	$-0.249537\pi$
$683$	37.0132	1.41627	0.708135	+	0.706078i	$0.249537\pi$
$684$	0	0
$685$	0	0
$686$	−34.4721	−1.31615
$687$	51.9574	1.98230
$688$	−0.472136	−0.0180000
$689$	0.167184	0.00636921
$690$	0	0
$691$	20.5410	0.781417	0.390709	−	0.920514i	$-0.372230\pi$
$691$	20.5410	0.781417	0.390709	+	0.920514i	$0.372230\pi$
$692$	−16.8541	−0.640697
$693$	−6.47214	−0.245856
$694$	57.2361	2.17265
$695$	0	0
$696$	31.7082	1.20190
$697$	2.52786	0.0957497
$698$	4.79837	0.181621
$699$	−14.1803	−0.536350
$700$	0	0
$701$	−4.85410	−0.183337	−0.0916685	−	0.995790i	$-0.529220\pi$
$701$	−4.85410	−0.183337	−0.0916685	+	0.995790i	$0.529220\pi$
$702$	−16.5836	−0.625907
$703$	0	0
$704$	−68.0689	−2.56544
$705$	0	0
$706$	68.2148	2.56730
$707$	−0.832816	−0.0313213
$708$	−19.4164	−0.729713
$709$	43.1591	1.62087	0.810436	−	0.585827i	$-0.199230\pi$
$709$	43.1591	1.62087	0.810436	+	0.585827i	$0.199230\pi$
$710$	0	0
$711$	−2.00000	−0.0750059
$712$	−16.3820	−0.613940
$713$	26.8328	1.00490
$714$	−3.41641	−0.127856
$715$	0	0
$716$	62.8328	2.34817
$717$	2.11146	0.0788538
$718$	−48.5410	−1.81153
$719$	31.3050	1.16748	0.583739	−	0.811941i	$-0.301589\pi$
$719$	31.3050	1.16748	0.583739	+	0.811941i	$0.301589\pi$
$720$	0	0
$721$	−9.52786	−0.354836
$722$	0	0
$723$	2.11146	0.0785259
$724$	−64.2492	−2.38780
$725$	0	0
$726$	−73.4164	−2.72474
$727$	29.1246	1.08017	0.540086	−	0.841610i	$-0.318392\pi$
$727$	29.1246	1.08017	0.540086	+	0.841610i	$0.318392\pi$
$728$	−5.12461	−0.189931
$729$	13.0000	0.481481
$730$	0	0
$731$	−0.291796	−0.0107925
$732$	59.1246	2.18531
$733$	−37.2705	−1.37662	−0.688309	−	0.725418i	$-0.741647\pi$
$733$	−37.2705	−1.37662	−0.688309	+	0.725418i	$0.741647\pi$
$734$	70.2492	2.59295
$735$	0	0
$736$	30.0000	1.10581
$737$	−2.47214	−0.0910623
$738$	9.14590	0.336665
$739$	24.2918	0.893588	0.446794	−	0.894637i	$-0.352566\pi$
$739$	24.2918	0.893588	0.446794	+	0.894637i	$0.352566\pi$
$740$	0	0
$741$	0	0
$742$	−0.249224	−0.00914929
$743$	7.41641	0.272082	0.136041	−	0.990703i	$-0.456562\pi$
$743$	7.41641	0.272082	0.136041	+	0.990703i	$0.456562\pi$
$744$	−26.8328	−0.983739
$745$	0	0
$746$	−3.49342	−0.127903
$747$	9.70820	0.355205
$748$	−9.70820	−0.354967
$749$	−0.944272	−0.0345029
$750$	0	0
$751$	−21.4164	−0.781496	−0.390748	−	0.920498i	$-0.627784\pi$
$751$	−21.4164	−0.781496	−0.390748	+	0.920498i	$0.627784\pi$
$752$	4.76393	0.173723
$753$	26.4721	0.964698
$754$	−29.3951	−1.07051
$755$	0	0
$756$	14.8328	0.539464
$757$	6.50658	0.236486	0.118243	−	0.992985i	$-0.462274\pi$
$757$	6.50658	0.236486	0.118243	+	0.992985i	$0.462274\pi$
$758$	48.9443	1.77774
$759$	46.8328	1.69992
$760$	0	0
$761$	−19.8885	−0.720959	−0.360480	−	0.932767i	$-0.617387\pi$
$761$	−19.8885	−0.720959	−0.360480	+	0.932767i	$0.617387\pi$
$762$	53.6656	1.94410
$763$	−14.9443	−0.541019
$764$	−14.2918	−0.517059
$765$	0	0
$766$	65.3738	2.36205
$767$	6.00000	0.216647
$768$	−18.0000	−0.649519
$769$	−31.1459	−1.12315	−0.561575	−	0.827426i	$-0.689804\pi$
$769$	−31.1459	−1.12315	−0.561575	+	0.827426i	$0.689804\pi$
$770$	0	0
$771$	−23.8197	−0.857844
$772$	−34.5836	−1.24469
$773$	−45.6312	−1.64124	−0.820620	−	0.571474i	$-0.806372\pi$
$773$	−45.6312	−1.64124	−0.820620	+	0.571474i	$0.806372\pi$
$774$	−1.05573	−0.0379474
$775$	0	0
$776$	24.7984	0.890210
$777$	−21.8885	−0.785247
$778$	−57.8115	−2.07264
$779$	0	0
$780$	0	0
$781$	16.9443	0.606314
$782$	6.18034	0.221009
$783$	28.3607	1.01353
$784$	5.47214	0.195433
$785$	0	0
$786$	−97.0820	−3.46280
$787$	−3.23607	−0.115353	−0.0576767	−	0.998335i	$-0.518369\pi$
$787$	−3.23607	−0.115353	−0.0576767	+	0.998335i	$0.518369\pi$
$788$	72.1033	2.56857
$789$	−15.6393	−0.556775
$790$	0	0
$791$	12.5410	0.445907
$792$	−11.7082	−0.416033
$793$	−18.2705	−0.648805
$794$	3.16718	0.112399
$795$	0	0
$796$	−38.8328	−1.37639
$797$	18.5066	0.655537	0.327768	−	0.944758i	$-0.393703\pi$
$797$	18.5066	0.655537	0.327768	+	0.944758i	$0.393703\pi$
$798$	0	0
$799$	2.94427	0.104161
$800$	0	0
$801$	7.32624	0.258860
$802$	−56.8328	−2.00684
$803$	76.2492	2.69078
$804$	−2.83282	−0.0999057
$805$	0	0
$806$	24.8754	0.876198
$807$	−2.40325	−0.0845985
$808$	−1.50658	−0.0530012
$809$	−1.03444	−0.0363690	−0.0181845	−	0.999835i	$-0.505789\pi$
$809$	−1.03444	−0.0363690	−0.0181845	+	0.999835i	$0.505789\pi$
$810$	0	0
$811$	−26.0000	−0.912983	−0.456492	−	0.889728i	$-0.650894\pi$
$811$	−26.0000	−0.912983	−0.456492	+	0.889728i	$0.650894\pi$
$812$	26.2918	0.922661
$813$	29.3050	1.02777
$814$	−103.666	−3.63348
$815$	0	0
$816$	1.23607	0.0432710
$817$	0	0
$818$	−45.3262	−1.58479
$819$	2.29180	0.0800818
$820$	0	0
$821$	31.7426	1.10783	0.553913	−	0.832575i	$-0.313134\pi$
$821$	31.7426	1.10783	0.553913	+	0.832575i	$0.313134\pi$
$822$	8.04257	0.280517
$823$	13.3475	0.465265	0.232633	−	0.972565i	$-0.425266\pi$
$823$	13.3475	0.465265	0.232633	+	0.972565i	$0.425266\pi$
$824$	−17.2361	−0.600447
$825$	0	0
$826$	−8.94427	−0.311211
$827$	−8.83282	−0.307147	−0.153574	−	0.988137i	$-0.549078\pi$
$827$	−8.83282	−0.307147	−0.153574	+	0.988137i	$0.549078\pi$
$828$	13.4164	0.466252
$829$	29.9787	1.04120	0.520602	−	0.853800i	$-0.325708\pi$
$829$	29.9787	1.04120	0.520602	+	0.853800i	$0.325708\pi$
$830$	0	0
$831$	20.7639	0.720293
$832$	24.1033	0.835632
$833$	3.38197	0.117178
$834$	−61.3050	−2.12282
$835$	0	0
$836$	0	0
$837$	−24.0000	−0.829561
$838$	−10.2492	−0.354054
$839$	−17.1246	−0.591207	−0.295604	−	0.955311i	$-0.595521\pi$
$839$	−17.1246	−0.591207	−0.295604	+	0.955311i	$0.595521\pi$
$840$	0	0
$841$	21.2705	0.733466
$842$	48.7426	1.67978
$843$	38.1803	1.31500
$844$	−83.1246	−2.86127
$845$	0	0
$846$	10.6525	0.366240
$847$	−20.2918	−0.697234
$848$	0.0901699	0.00309645
$849$	62.8328	2.15642
$850$	0	0
$851$	39.5967	1.35736
$852$	19.4164	0.665195
$853$	−7.38197	−0.252754	−0.126377	−	0.991982i	$-0.540335\pi$
$853$	−7.38197	−0.252754	−0.126377	+	0.991982i	$0.540335\pi$
$854$	27.2361	0.931999
$855$	0	0
$856$	−1.70820	−0.0583852
$857$	37.8541	1.29307	0.646536	−	0.762884i	$-0.276217\pi$
$857$	37.8541	1.29307	0.646536	+	0.762884i	$0.276217\pi$
$858$	43.4164	1.48221
$859$	22.5836	0.770542	0.385271	−	0.922803i	$-0.374108\pi$
$859$	22.5836	0.770542	0.385271	+	0.922803i	$0.374108\pi$
$860$	0	0
$861$	10.1115	0.344598
$862$	−41.9574	−1.42908
$863$	0.944272	0.0321434	0.0160717	−	0.999871i	$-0.494884\pi$
$863$	0.944272	0.0321434	0.0160717	+	0.999871i	$0.494884\pi$
$864$	−26.8328	−0.912871
$865$	0	0
$866$	21.1033	0.717120
$867$	−33.2361	−1.12876
$868$	−22.2492	−0.755188
$869$	−10.4721	−0.355243
$870$	0	0
$871$	0.875388	0.0296614
$872$	−27.0344	−0.915502
$873$	−11.0902	−0.375345
$874$	0	0
$875$	0	0
$876$	87.3738	2.95209
$877$	9.56231	0.322896	0.161448	−	0.986881i	$-0.448384\pi$
$877$	9.56231	0.322896	0.161448	+	0.986881i	$0.448384\pi$
$878$	22.3607	0.754636
$879$	50.8328	1.71455
$880$	0	0
$881$	3.32624	0.112064	0.0560319	−	0.998429i	$-0.482155\pi$
$881$	3.32624	0.112064	0.0560319	+	0.998429i	$0.482155\pi$
$882$	12.2361	0.412010
$883$	−19.8885	−0.669303	−0.334651	−	0.942342i	$-0.608619\pi$
$883$	−19.8885	−0.669303	−0.334651	+	0.942342i	$0.608619\pi$
$884$	3.43769	0.115622
$885$	0	0
$886$	−3.16718	−0.106404
$887$	49.4853	1.66155	0.830777	−	0.556606i	$-0.187897\pi$
$887$	49.4853	1.66155	0.830777	+	0.556606i	$0.187897\pi$
$888$	−39.5967	−1.32878
$889$	14.8328	0.497477
$890$	0	0
$891$	−57.5967	−1.92956
$892$	−30.0000	−1.00447
$893$	0	0
$894$	−8.29180	−0.277319
$895$	0	0
$896$	−19.3475	−0.646355
$897$	−16.5836	−0.553710
$898$	−79.2705	−2.64529
$899$	−42.5410	−1.41882
$900$	0	0
$901$	0.0557281	0.00185657
$902$	47.8885	1.59451
$903$	−1.16718	−0.0388415
$904$	22.6869	0.754556
$905$	0	0
$906$	0	0
$907$	25.4164	0.843938	0.421969	−	0.906610i	$-0.361339\pi$
$907$	25.4164	0.843938	0.421969	+	0.906610i	$0.361339\pi$
$908$	40.5836	1.34681
$909$	0.673762	0.0223473
$910$	0	0
$911$	−32.8328	−1.08780	−0.543900	−	0.839150i	$-0.683053\pi$
$911$	−32.8328	−1.08780	−0.543900	+	0.839150i	$0.683053\pi$
$912$	0	0
$913$	50.8328	1.68232
$914$	−0.201626	−0.00666920
$915$	0	0
$916$	77.9361	2.57508
$917$	−26.8328	−0.886098
$918$	−5.52786	−0.182447
$919$	−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
$921$	31.0557	1.02332
$922$	1.05573	0.0347686
$923$	−6.00000	−0.197492
$924$	−38.8328	−1.27751
$925$	0	0
$926$	57.4853	1.88908
$927$	7.70820	0.253171
$928$	−47.5623	−1.56131
$929$	30.8673	1.01272	0.506361	−	0.862322i	$-0.330990\pi$
$929$	30.8673	1.01272	0.506361	+	0.862322i	$0.330990\pi$
$930$	0	0
$931$	0	0
$932$	−21.2705	−0.696739
$933$	29.5279	0.966699
$934$	−22.1115	−0.723509
$935$	0	0
$936$	4.14590	0.135513
$937$	23.3050	0.761340	0.380670	−	0.924711i	$-0.375693\pi$
$937$	23.3050	0.761340	0.380670	+	0.924711i	$0.375693\pi$
$938$	−1.30495	−0.0426082
$939$	51.9574	1.69557
$940$	0	0
$941$	27.5279	0.897383	0.448691	−	0.893687i	$-0.351890\pi$
$941$	27.5279	0.897383	0.448691	+	0.893687i	$0.351890\pi$
$942$	−35.9311	−1.17070
$943$	−18.2918	−0.595663
$944$	3.23607	0.105325
$945$	0	0
$946$	−5.52786	−0.179726
$947$	−13.5967	−0.441835	−0.220917	−	0.975293i	$-0.570905\pi$
$947$	−13.5967	−0.441835	−0.220917	+	0.975293i	$0.570905\pi$
$948$	−12.0000	−0.389742
$949$	−27.0000	−0.876457
$950$	0	0
$951$	20.7639	0.673317
$952$	−1.70820	−0.0553632
$953$	51.7426	1.67611	0.838054	−	0.545587i	$-0.183693\pi$
$953$	51.7426	1.67611	0.838054	+	0.545587i	$0.183693\pi$
$954$	0.201626	0.00652789
$955$	0	0
$956$	3.16718	0.102434
$957$	−74.2492	−2.40014
$958$	−20.2492	−0.654223
$959$	2.22291	0.0717816
$960$	0	0
$961$	5.00000	0.161290
$962$	36.7082	1.18352
$963$	0.763932	0.0246174
$964$	3.16718	0.102008
$965$	0	0
$966$	24.7214	0.795397
$967$	−51.9574	−1.67084	−0.835419	−	0.549613i	$-0.814775\pi$
$967$	−51.9574	−1.67084	−0.835419	+	0.549613i	$0.814775\pi$
$968$	−36.7082	−1.17985
$969$	0	0
$970$	0	0
$971$	−0.652476	−0.0209389	−0.0104695	−	0.999945i	$-0.503333\pi$
$971$	−0.652476	−0.0209389	−0.0104695	+	0.999945i	$0.503333\pi$
$972$	−30.0000	−0.962250
$973$	−16.9443	−0.543208
$974$	−56.4296	−1.80812
$975$	0	0
$976$	−9.85410	−0.315422
$977$	27.5066	0.880013	0.440007	−	0.897994i	$-0.354976\pi$
$977$	27.5066	0.880013	0.440007	+	0.897994i	$0.354976\pi$
$978$	−37.0820	−1.18575
$979$	38.3607	1.22601
$980$	0	0
$981$	12.0902	0.386009
$982$	−26.8328	−0.856270
$983$	37.9574	1.21065	0.605327	−	0.795977i	$-0.293042\pi$
$983$	37.9574	1.21065	0.605327	+	0.795977i	$0.293042\pi$
$984$	18.2918	0.583121
$985$	0	0
$986$	−9.79837	−0.312044
$987$	11.7771	0.374869
$988$	0	0
$989$	2.11146	0.0671404
$990$	0	0
$991$	51.1246	1.62403	0.812013	−	0.583639i	$-0.198372\pi$
$991$	51.1246	1.62403	0.812013	+	0.583639i	$0.198372\pi$
$992$	40.2492	1.27791
$993$	11.6393	0.369363
$994$	8.94427	0.283695
$995$	0	0
$996$	58.2492	1.84570
$997$	−0.0901699	−0.00285571	−0.00142786	−	0.999999i	$-0.500455\pi$
$997$	−0.0901699	−0.00285571	−0.00142786	+	0.999999i	$0.500455\pi$
$998$	16.1803	0.512180
$999$	−35.4164	−1.12053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.r.1.1		2
5.4	even	2		361.2.a.d.1.2	✓	2
15.14	odd	2		3249.2.a.n.1.1		2
19.18	odd	2		9025.2.a.o.1.2		2
20.19	odd	2		5776.2.a.bh.1.2		2
95.4	even	18		361.2.e.l.54.2		12
95.9	even	18		361.2.e.l.62.1		12
95.14	odd	18		361.2.e.k.234.1		12
95.24	even	18		361.2.e.l.234.2		12
95.29	odd	18		361.2.e.k.62.2		12
95.34	odd	18		361.2.e.k.54.1		12
95.44	even	18		361.2.e.l.245.2		12
95.49	even	6		361.2.c.f.292.1		4
95.54	even	18		361.2.e.l.28.2		12
95.59	odd	18		361.2.e.k.99.2		12
95.64	even	6		361.2.c.f.68.1		4
95.69	odd	6		361.2.c.e.68.2		4
95.74	even	18		361.2.e.l.99.1		12
95.79	odd	18		361.2.e.k.28.1		12
95.84	odd	6		361.2.c.e.292.2		4
95.89	odd	18		361.2.e.k.245.1		12
95.94	odd	2		361.2.a.e.1.1	yes	2
285.284	even	2		3249.2.a.m.1.2		2
380.379	even	2		5776.2.a.r.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.d.1.2	✓	2	5.4	even	2
361.2.a.e.1.1	yes	2	95.94	odd	2
361.2.c.e.68.2		4	95.69	odd	6
361.2.c.e.292.2		4	95.84	odd	6
361.2.c.f.68.1		4	95.64	even	6
361.2.c.f.292.1		4	95.49	even	6
361.2.e.k.28.1		12	95.79	odd	18
361.2.e.k.54.1		12	95.34	odd	18
361.2.e.k.62.2		12	95.29	odd	18
361.2.e.k.99.2		12	95.59	odd	18
361.2.e.k.234.1		12	95.14	odd	18
361.2.e.k.245.1		12	95.89	odd	18
361.2.e.l.28.2		12	95.54	even	18
361.2.e.l.54.2		12	95.4	even	18
361.2.e.l.62.1		12	95.9	even	18
361.2.e.l.99.1		12	95.74	even	18
361.2.e.l.234.2		12	95.24	even	18
361.2.e.l.245.2		12	95.44	even	18
3249.2.a.m.1.2		2	285.284	even	2
3249.2.a.n.1.1		2	15.14	odd	2
5776.2.a.r.1.2		2	380.379	even	2
5776.2.a.bh.1.2		2	20.19	odd	2
9025.2.a.o.1.2		2	19.18	odd	2
9025.2.a.r.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} +2.00000 q^{3} +3.00000 q^{4} -4.47214 q^{6} -1.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} +2.00000 q^{3} +3.00000 q^{4} -4.47214 q^{6} -1.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +5.23607 q^{11} +6.00000 q^{12} -1.85410 q^{13} +2.76393 q^{14} -1.00000 q^{16} -0.618034 q^{17} -2.23607 q^{18} -2.47214 q^{21} -11.7082 q^{22} +4.47214 q^{23} -4.47214 q^{24} +4.14590 q^{26} -4.00000 q^{27} -3.70820 q^{28} -7.09017 q^{29} +6.00000 q^{31} +6.70820 q^{32} +10.4721 q^{33} +1.38197 q^{34} +3.00000 q^{36} +8.85410 q^{37} -3.70820 q^{39} -4.09017 q^{41} +5.52786 q^{42} +0.472136 q^{43} +15.7082 q^{44} -10.0000 q^{46} -4.76393 q^{47} -2.00000 q^{48} -5.47214 q^{49} -1.23607 q^{51} -5.56231 q^{52} -0.0901699 q^{53} +8.94427 q^{54} +2.76393 q^{56} +15.8541 q^{58} -3.23607 q^{59} +9.85410 q^{61} -13.4164 q^{62} -1.23607 q^{63} -13.0000 q^{64} -23.4164 q^{66} -0.472136 q^{67} -1.85410 q^{68} +8.94427 q^{69} +3.23607 q^{71} -2.23607 q^{72} +14.5623 q^{73} -19.7984 q^{74} -6.47214 q^{77} +8.29180 q^{78} -2.00000 q^{79} -11.0000 q^{81} +9.14590 q^{82} +9.70820 q^{83} -7.41641 q^{84} -1.05573 q^{86} -14.1803 q^{87} -11.7082 q^{88} +7.32624 q^{89} +2.29180 q^{91} +13.4164 q^{92} +12.0000 q^{93} +10.6525 q^{94} +13.4164 q^{96} -11.0902 q^{97} +12.2361 q^{98} +5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} + 6 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 + 2 * q^9	\( 2 q + 4 q^{3} + 6 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{11} + 12 q^{12} + 3 q^{13} + 10 q^{14} - 2 q^{16} + q^{17} + 4 q^{21} - 10 q^{22} + 15 q^{26} - 8 q^{27} + 6 q^{28} - 3 q^{29} + 12 q^{31} + 12 q^{33} + 5 q^{34} + 6 q^{36} + 11 q^{37} + 6 q^{39} + 3 q^{41} + 20 q^{42} - 8 q^{43} + 18 q^{44} - 20 q^{46} - 14 q^{47} - 4 q^{48} - 2 q^{49} + 2 q^{51} + 9 q^{52} + 11 q^{53} + 10 q^{56} + 25 q^{58} - 2 q^{59} + 13 q^{61} + 2 q^{63} - 26 q^{64} - 20 q^{66} + 8 q^{67} + 3 q^{68} + 2 q^{71} + 9 q^{73} - 15 q^{74} - 4 q^{77} + 30 q^{78} - 4 q^{79} - 22 q^{81} + 25 q^{82} + 6 q^{83} + 12 q^{84} - 20 q^{86} - 6 q^{87} - 10 q^{88} - q^{89} + 18 q^{91} + 24 q^{93} - 10 q^{94} - 11 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^11 + 12 * q^12 + 3 * q^13 + 10 * q^14 - 2 * q^16 + q^17 + 4 * q^21 - 10 * q^22 + 15 * q^26 - 8 * q^27 + 6 * q^28 - 3 * q^29 + 12 * q^31 + 12 * q^33 + 5 * q^34 + 6 * q^36 + 11 * q^37 + 6 * q^39 + 3 * q^41 + 20 * q^42 - 8 * q^43 + 18 * q^44 - 20 * q^46 - 14 * q^47 - 4 * q^48 - 2 * q^49 + 2 * q^51 + 9 * q^52 + 11 * q^53 + 10 * q^56 + 25 * q^58 - 2 * q^59 + 13 * q^61 + 2 * q^63 - 26 * q^64 - 20 * q^66 + 8 * q^67 + 3 * q^68 + 2 * q^71 + 9 * q^73 - 15 * q^74 - 4 * q^77 + 30 * q^78 - 4 * q^79 - 22 * q^81 + 25 * q^82 + 6 * q^83 + 12 * q^84 - 20 * q^86 - 6 * q^87 - 10 * q^88 - q^89 + 18 * q^91 + 24 * q^93 - 10 * q^94 - 11 * q^97 + 20 * q^98 + 6 * q^99

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