LMFDB - Embedded newform 3525.2.a.v.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.2379008.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} + 23x - 4 $ x^5 - 10x^3 + 23x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.176288$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.176288 q^{2} -1.00000 q^{3} -1.96892 q^{4} -0.176288 q^{6} -5.09296 q^{7} -0.699672 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.176288 q^{2} -1.00000 q^{3} -1.96892 q^{4} -0.176288 q^{6} -5.09296 q^{7} -0.699672 q^{8} +1.00000 q^{9} -0.402502 q^{11} +1.96892 q^{12} +2.39013 q^{13} -0.897826 q^{14} +3.81450 q^{16} +1.82371 q^{17} +0.176288 q^{18} +1.45475 q^{19} +5.09296 q^{21} -0.0709561 q^{22} +0.278461 q^{23} +0.699672 q^{24} +0.421351 q^{26} -1.00000 q^{27} +10.0277 q^{28} +3.56642 q^{29} -0.319037 q^{31} +2.07179 q^{32} +0.402502 q^{33} +0.321498 q^{34} -1.96892 q^{36} -3.34942 q^{37} +0.256454 q^{38} -2.39013 q^{39} +9.44970 q^{41} +0.897826 q^{42} -0.380495 q^{43} +0.792495 q^{44} +0.0490893 q^{46} -1.00000 q^{47} -3.81450 q^{48} +18.9383 q^{49} -1.82371 q^{51} -4.70599 q^{52} -0.804166 q^{53} -0.176288 q^{54} +3.56340 q^{56} -1.45475 q^{57} +0.628716 q^{58} -12.6969 q^{59} +8.38092 q^{61} -0.0562423 q^{62} -5.09296 q^{63} -7.26377 q^{64} +0.0709561 q^{66} -13.9714 q^{67} -3.59075 q^{68} -0.278461 q^{69} -13.4021 q^{71} -0.699672 q^{72} +15.5662 q^{73} -0.590461 q^{74} -2.86429 q^{76} +2.04993 q^{77} -0.421351 q^{78} +3.32150 q^{79} +1.00000 q^{81} +1.66586 q^{82} +13.7712 q^{83} -10.0277 q^{84} -0.0670765 q^{86} -3.56642 q^{87} +0.281619 q^{88} -3.33789 q^{89} -12.1729 q^{91} -0.548269 q^{92} +0.319037 q^{93} -0.176288 q^{94} -2.07179 q^{96} -5.48542 q^{97} +3.33858 q^{98} -0.402502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{3} + 10 q^{4} - 10 q^{7} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^3 + 10 * q^4 - 10 * q^7 + 5 * q^9	$ 5 q - 5 q^{3} + 10 q^{4} - 10 q^{7} + 5 q^{9} - 2 q^{11} - 10 q^{12} - 7 q^{13} - 8 q^{14} + 8 q^{16} + 10 q^{17} + 2 q^{19} + 10 q^{21} + 4 q^{22} - 3 q^{23} - 16 q^{26} - 5 q^{27} - 12 q^{28} - 2 q^{29} - 6 q^{31} + 20 q^{32} + 2 q^{33} - 20 q^{34} + 10 q^{36} - 8 q^{37} + 8 q^{38} + 7 q^{39} + 8 q^{42} - 13 q^{43} + 4 q^{44} - 12 q^{46} - 5 q^{47} - 8 q^{48} + 13 q^{49} - 10 q^{51} - 34 q^{52} + 10 q^{53} - 28 q^{56} - 2 q^{57} + 4 q^{58} - 11 q^{59} + 11 q^{61} - 16 q^{62} - 10 q^{63} - 20 q^{64} - 4 q^{66} - 24 q^{67} + 20 q^{68} + 3 q^{69} - 11 q^{71} - 17 q^{73} + 12 q^{74} - 24 q^{76} + 12 q^{77} + 16 q^{78} - 5 q^{79} + 5 q^{81} - 64 q^{82} + 12 q^{84} + 12 q^{86} + 2 q^{87} + 4 q^{88} - 3 q^{89} + 22 q^{91} - 34 q^{92} + 6 q^{93} - 20 q^{96} + 14 q^{97} + 36 q^{98} - 2 q^{99}+O(q^{100}) $ 5 * q - 5 * q^3 + 10 * q^4 - 10 * q^7 + 5 * q^9 - 2 * q^11 - 10 * q^12 - 7 * q^13 - 8 * q^14 + 8 * q^16 + 10 * q^17 + 2 * q^19 + 10 * q^21 + 4 * q^22 - 3 * q^23 - 16 * q^26 - 5 * q^27 - 12 * q^28 - 2 * q^29 - 6 * q^31 + 20 * q^32 + 2 * q^33 - 20 * q^34 + 10 * q^36 - 8 * q^37 + 8 * q^38 + 7 * q^39 + 8 * q^42 - 13 * q^43 + 4 * q^44 - 12 * q^46 - 5 * q^47 - 8 * q^48 + 13 * q^49 - 10 * q^51 - 34 * q^52 + 10 * q^53 - 28 * q^56 - 2 * q^57 + 4 * q^58 - 11 * q^59 + 11 * q^61 - 16 * q^62 - 10 * q^63 - 20 * q^64 - 4 * q^66 - 24 * q^67 + 20 * q^68 + 3 * q^69 - 11 * q^71 - 17 * q^73 + 12 * q^74 - 24 * q^76 + 12 * q^77 + 16 * q^78 - 5 * q^79 + 5 * q^81 - 64 * q^82 + 12 * q^84 + 12 * q^86 + 2 * q^87 + 4 * q^88 - 3 * q^89 + 22 * q^91 - 34 * q^92 + 6 * q^93 - 20 * q^96 + 14 * q^97 + 36 * q^98 - 2 * 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 $

$2$	0.176288	0.124654	0.0623271	−	0.998056i	$-0.480148\pi$
$2$	0.176288	0.124654	0.0623271	+	0.998056i	$0.480148\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96892	−0.984461
$5$	0	0
$5$	0	0
$6$	−0.176288	−0.0719691
$7$	−5.09296	−1.92496	−0.962480	−	0.271354i	$-0.912529\pi$
$7$	−5.09296	−1.92496	−0.962480	+	0.271354i	$0.912529\pi$
$8$	−0.699672	−0.247371
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.402502	−0.121359	−0.0606794	−	0.998157i	$-0.519327\pi$
$11$	−0.402502	−0.121359	−0.0606794	+	0.998157i	$0.519327\pi$
$12$	1.96892	0.568379
$13$	2.39013	0.662904	0.331452	−	0.943472i	$-0.392462\pi$
$13$	2.39013	0.662904	0.331452	+	0.943472i	$0.392462\pi$
$14$	−0.897826	−0.239954
$15$	0	0
$16$	3.81450	0.953625
$17$	1.82371	0.442315	0.221158	−	0.975238i	$-0.429016\pi$
$17$	1.82371	0.442315	0.221158	+	0.975238i	$0.429016\pi$
$18$	0.176288	0.0415514
$19$	1.45475	0.333742	0.166871	−	0.985979i	$-0.446634\pi$
$19$	1.45475	0.333742	0.166871	+	0.985979i	$0.446634\pi$
$20$	0	0
$21$	5.09296	1.11138
$22$	−0.0709561	−0.0151279
$23$	0.278461	0.0580632	0.0290316	−	0.999578i	$-0.490758\pi$
$23$	0.278461	0.0580632	0.0290316	+	0.999578i	$0.490758\pi$
$24$	0.699672	0.142820
$25$	0	0
$26$	0.421351	0.0826337
$27$	−1.00000	−0.192450
$28$	10.0277	1.89505
$29$	3.56642	0.662268	0.331134	−	0.943584i	$-0.392569\pi$
$29$	3.56642	0.662268	0.331134	+	0.943584i	$0.392569\pi$
$30$	0	0
$31$	−0.319037	−0.0573007	−0.0286504	−	0.999589i	$-0.509121\pi$
$31$	−0.319037	−0.0573007	−0.0286504	+	0.999589i	$0.509121\pi$
$32$	2.07179	0.366245
$33$	0.402502	0.0700666
$34$	0.321498	0.0551364
$35$	0	0
$36$	−1.96892	−0.328154
$37$	−3.34942	−0.550641	−0.275320	−	0.961353i	$-0.588784\pi$
$37$	−3.34942	−0.550641	−0.275320	+	0.961353i	$0.588784\pi$
$38$	0.256454	0.0416024
$39$	−2.39013	−0.382728
$40$	0	0
$41$	9.44970	1.47579	0.737897	−	0.674913i	$-0.235819\pi$
$41$	9.44970	1.47579	0.737897	+	0.674913i	$0.235819\pi$
$42$	0.897826	0.138538
$43$	−0.380495	−0.0580249	−0.0290124	−	0.999579i	$-0.509236\pi$
$43$	−0.380495	−0.0580249	−0.0290124	+	0.999579i	$0.509236\pi$
$44$	0.792495	0.119473
$45$	0	0
$46$	0.0490893	0.00723782
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−3.81450	−0.550576
$49$	18.9383	2.70547
$50$	0	0
$51$	−1.82371	−0.255371
$52$	−4.70599	−0.652603
$53$	−0.804166	−0.110461	−0.0552304	−	0.998474i	$-0.517589\pi$
$53$	−0.804166	−0.110461	−0.0552304	+	0.998474i	$0.517589\pi$
$54$	−0.176288	−0.0239897
$55$	0	0
$56$	3.56340	0.476180
$57$	−1.45475	−0.192686
$58$	0.628716	0.0825544
$59$	−12.6969	−1.65300	−0.826501	−	0.562936i	$-0.809672\pi$
$59$	−12.6969	−1.65300	−0.826501	+	0.562936i	$0.809672\pi$
$60$	0	0
$61$	8.38092	1.07307	0.536534	−	0.843879i	$-0.319733\pi$
$61$	8.38092	1.07307	0.536534	+	0.843879i	$0.319733\pi$
$62$	−0.0562423	−0.00714278
$63$	−5.09296	−0.641653
$64$	−7.26377	−0.907972
$65$	0	0
$66$	0.0709561	0.00873409
$67$	−13.9714	−1.70688	−0.853438	−	0.521194i	$-0.825487\pi$
$67$	−13.9714	−1.70688	−0.853438	+	0.521194i	$0.825487\pi$
$68$	−3.59075	−0.435442
$69$	−0.278461	−0.0335228
$70$	0	0
$71$	−13.4021	−1.59054	−0.795268	−	0.606258i	$-0.792670\pi$
$71$	−13.4021	−1.59054	−0.795268	+	0.606258i	$0.792670\pi$
$72$	−0.699672	−0.0824571
$73$	15.5662	1.82188	0.910940	−	0.412539i	$-0.135358\pi$
$73$	15.5662	1.82188	0.910940	+	0.412539i	$0.135358\pi$
$74$	−0.590461	−0.0686397
$75$	0	0
$76$	−2.86429	−0.328556
$77$	2.04993	0.233611
$78$	−0.421351	−0.0477086
$79$	3.32150	0.373698	0.186849	−	0.982389i	$-0.440173\pi$
$79$	3.32150	0.373698	0.186849	+	0.982389i	$0.440173\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.66586	0.183964
$83$	13.7712	1.51159	0.755793	−	0.654811i	$-0.227252\pi$
$83$	13.7712	1.51159	0.755793	+	0.654811i	$0.227252\pi$
$84$	−10.0277	−1.09411
$85$	0	0
$86$	−0.0670765	−0.00723305
$87$	−3.56642	−0.382360
$88$	0.281619	0.0300207
$89$	−3.33789	−0.353815	−0.176908	−	0.984227i	$-0.556609\pi$
$89$	−3.33789	−0.353815	−0.176908	+	0.984227i	$0.556609\pi$
$90$	0	0
$91$	−12.1729	−1.27606
$92$	−0.548269	−0.0571610
$93$	0.319037	0.0330826
$94$	−0.176288	−0.0181827
$95$	0	0
$96$	−2.07179	−0.211452
$97$	−5.48542	−0.556960	−0.278480	−	0.960442i	$-0.589831\pi$
$97$	−5.48542	−0.556960	−0.278480	+	0.960442i	$0.589831\pi$
$98$	3.33858	0.337248
$99$	−0.402502	−0.0404529
$100$	0	0
$101$	−15.6283	−1.55507	−0.777537	−	0.628837i	$-0.783531\pi$
$101$	−15.6283	−1.55507	−0.777537	+	0.628837i	$0.783531\pi$
$102$	−0.321498	−0.0318330
$103$	3.84804	0.379159	0.189579	−	0.981865i	$-0.439288\pi$
$103$	3.84804	0.379159	0.189579	+	0.981865i	$0.439288\pi$
$104$	−1.67231	−0.163983
$105$	0	0
$106$	−0.141765	−0.0137694
$107$	−12.5664	−1.21484	−0.607421	−	0.794380i	$-0.707796\pi$
$107$	−12.5664	−1.21484	−0.607421	+	0.794380i	$0.707796\pi$
$108$	1.96892	0.189460
$109$	−5.76239	−0.551937	−0.275969	−	0.961167i	$-0.588999\pi$
$109$	−5.76239	−0.551937	−0.275969	+	0.961167i	$0.588999\pi$
$110$	0	0
$111$	3.34942	0.317913
$112$	−19.4271	−1.83569
$113$	4.36827	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$113$	4.36827	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$114$	−0.256454	−0.0240191
$115$	0	0
$116$	−7.02201	−0.651977
$117$	2.39013	0.220968
$118$	−2.23831	−0.206053
$119$	−9.28810	−0.851439
$120$	0	0
$121$	−10.8380	−0.985272
$122$	1.47745	0.133762
$123$	−9.44970	−0.852051
$124$	0.628159	0.0564104
$125$	0	0
$126$	−0.897826	−0.0799847
$127$	3.13284	0.277995	0.138997	−	0.990293i	$-0.455612\pi$
$127$	3.13284	0.277995	0.138997	+	0.990293i	$0.455612\pi$
$128$	−5.42410	−0.479427
$129$	0.380495	0.0335007
$130$	0	0
$131$	−14.7675	−1.29024	−0.645120	−	0.764082i	$-0.723192\pi$
$131$	−14.7675	−1.29024	−0.645120	+	0.764082i	$0.723192\pi$
$132$	−0.792495	−0.0689778
$133$	−7.40898	−0.642440
$134$	−2.46298	−0.212769
$135$	0	0
$136$	−1.27600	−0.109416
$137$	−6.64785	−0.567964	−0.283982	−	0.958830i	$-0.591656\pi$
$137$	−6.64785	−0.567964	−0.283982	+	0.958830i	$0.591656\pi$
$138$	−0.0490893	−0.00417876
$139$	15.7309	1.33428	0.667139	−	0.744933i	$-0.267519\pi$
$139$	15.7309	1.33428	0.667139	+	0.744933i	$0.267519\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−2.36262	−0.198267
$143$	−0.962033	−0.0804492
$144$	3.81450	0.317875
$145$	0	0
$146$	2.74412	0.227105
$147$	−18.9383	−1.56200
$148$	6.59474	0.542085
$149$	−7.26526	−0.595193	−0.297596	−	0.954692i	$-0.596185\pi$
$149$	−7.26526	−0.595193	−0.297596	+	0.954692i	$0.596185\pi$
$150$	0	0
$151$	15.0153	1.22193	0.610963	−	0.791659i	$-0.290782\pi$
$151$	15.0153	1.22193	0.610963	+	0.791659i	$0.290782\pi$
$152$	−1.01785	−0.0825583
$153$	1.82371	0.147438
$154$	0.361377	0.0291206
$155$	0	0
$156$	4.70599	0.376781
$157$	3.30117	0.263462	0.131731	−	0.991286i	$-0.457947\pi$
$157$	3.30117	0.263462	0.131731	+	0.991286i	$0.457947\pi$
$158$	0.585539	0.0465830
$159$	0.804166	0.0637745
$160$	0	0
$161$	−1.41819	−0.111769
$162$	0.176288	0.0138505
$163$	1.79080	0.140266	0.0701330	−	0.997538i	$-0.477658\pi$
$163$	1.79080	0.140266	0.0701330	+	0.997538i	$0.477658\pi$
$164$	−18.6057	−1.45286
$165$	0	0
$166$	2.42769	0.188425
$167$	9.77639	0.756520	0.378260	−	0.925699i	$-0.376523\pi$
$167$	9.77639	0.756520	0.378260	+	0.925699i	$0.376523\pi$
$168$	−3.56340	−0.274923
$169$	−7.28726	−0.560559
$170$	0	0
$171$	1.45475	0.111247
$172$	0.749165	0.0571233
$173$	5.01871	0.381565	0.190783	−	0.981632i	$-0.438897\pi$
$173$	5.01871	0.381565	0.190783	+	0.981632i	$0.438897\pi$
$174$	−0.628716	−0.0476628
$175$	0	0
$176$	−1.53534	−0.115731
$177$	12.6969	0.954361
$178$	−0.588428	−0.0441045
$179$	−21.3565	−1.59626	−0.798129	−	0.602487i	$-0.794176\pi$
$179$	−21.3565	−1.59626	−0.798129	+	0.602487i	$0.794176\pi$
$180$	0	0
$181$	−5.62345	−0.417988	−0.208994	−	0.977917i	$-0.567019\pi$
$181$	−5.62345	−0.417988	−0.208994	+	0.977917i	$0.567019\pi$
$182$	−2.14592	−0.159067
$183$	−8.38092	−0.619536
$184$	−0.194832	−0.0143632
$185$	0	0
$186$	0.0562423	0.00412388
$187$	−0.734047	−0.0536789
$188$	1.96892	0.143598
$189$	5.09296	0.370459
$190$	0	0
$191$	−0.271840	−0.0196697	−0.00983484	−	0.999952i	$-0.503131\pi$
$191$	−0.271840	−0.0196697	−0.00983484	+	0.999952i	$0.503131\pi$
$192$	7.26377	0.524218
$193$	−15.7817	−1.13599	−0.567995	−	0.823032i	$-0.692281\pi$
$193$	−15.7817	−1.13599	−0.567995	+	0.823032i	$0.692281\pi$
$194$	−0.967011	−0.0694274
$195$	0	0
$196$	−37.2880	−2.66343
$197$	11.6617	0.830862	0.415431	−	0.909625i	$-0.363631\pi$
$197$	11.6617	0.830862	0.415431	+	0.909625i	$0.363631\pi$
$198$	−0.0709561	−0.00504263
$199$	1.88383	0.133541	0.0667707	−	0.997768i	$-0.478730\pi$
$199$	1.88383	0.133541	0.0667707	+	0.997768i	$0.478730\pi$
$200$	0	0
$201$	13.9714	0.985465
$202$	−2.75508	−0.193847
$203$	−18.1637	−1.27484
$204$	3.59075	0.251403
$205$	0	0
$206$	0.678362	0.0472637
$207$	0.278461	0.0193544
$208$	9.11717	0.632162
$209$	−0.585539	−0.0405026
$210$	0	0
$211$	−7.22882	−0.497652	−0.248826	−	0.968548i	$-0.580045\pi$
$211$	−7.22882	−0.497652	−0.248826	+	0.968548i	$0.580045\pi$
$212$	1.58334	0.108744
$213$	13.4021	0.918296
$214$	−2.21530	−0.151435
$215$	0	0
$216$	0.699672	0.0476066
$217$	1.62484	0.110302
$218$	−1.01584	−0.0688013
$219$	−15.5662	−1.05186
$220$	0	0
$221$	4.35892	0.293212
$222$	0.590461	0.0396291
$223$	−3.17038	−0.212304	−0.106152	−	0.994350i	$-0.533853\pi$
$223$	−3.17038	−0.212304	−0.106152	+	0.994350i	$0.533853\pi$
$224$	−10.5516	−0.705006
$225$	0	0
$226$	0.770071	0.0512244
$227$	13.4208	0.890770	0.445385	−	0.895339i	$-0.353067\pi$
$227$	13.4208	0.890770	0.445385	+	0.895339i	$0.353067\pi$
$228$	2.86429	0.189692
$229$	−19.6378	−1.29770	−0.648851	−	0.760915i	$-0.724750\pi$
$229$	−19.6378	−1.29770	−0.648851	+	0.760915i	$0.724750\pi$
$230$	0	0
$231$	−2.04993	−0.134875
$232$	−2.49532	−0.163826
$233$	−23.4656	−1.53728	−0.768641	−	0.639680i	$-0.779067\pi$
$233$	−23.4656	−1.53728	−0.768641	+	0.639680i	$0.779067\pi$
$234$	0.421351	0.0275446
$235$	0	0
$236$	24.9993	1.62732
$237$	−3.32150	−0.215754
$238$	−1.63738	−0.106135
$239$	14.2569	0.922201	0.461101	−	0.887348i	$-0.347455\pi$
$239$	14.2569	0.922201	0.461101	+	0.887348i	$0.347455\pi$
$240$	0	0
$241$	−29.0806	−1.87325	−0.936624	−	0.350338i	$-0.886067\pi$
$241$	−29.0806	−1.87325	−0.936624	+	0.350338i	$0.886067\pi$
$242$	−1.91060	−0.122818
$243$	−1.00000	−0.0641500
$244$	−16.5014	−1.05639
$245$	0	0
$246$	−1.66586	−0.106212
$247$	3.47704	0.221239
$248$	0.223221	0.0141746
$249$	−13.7712	−0.872714
$250$	0	0
$251$	23.5643	1.48736	0.743681	−	0.668534i	$-0.233078\pi$
$251$	23.5643	1.48736	0.743681	+	0.668534i	$0.233078\pi$
$252$	10.0277	0.631683
$253$	−0.112081	−0.00704648
$254$	0.552281	0.0346532
$255$	0	0
$256$	13.5713	0.848209
$257$	2.23072	0.139148	0.0695741	−	0.997577i	$-0.477836\pi$
$257$	2.23072	0.139148	0.0695741	+	0.997577i	$0.477836\pi$
$258$	0.0670765	0.00417600
$259$	17.0585	1.05996
$260$	0	0
$261$	3.56642	0.220756
$262$	−2.60332	−0.160834
$263$	26.2077	1.61604	0.808018	−	0.589158i	$-0.200541\pi$
$263$	26.2077	1.61604	0.808018	+	0.589158i	$0.200541\pi$
$264$	−0.281619	−0.0173325
$265$	0	0
$266$	−1.30611	−0.0800829
$267$	3.33789	0.204275
$268$	27.5086	1.68035
$269$	−6.80986	−0.415205	−0.207602	−	0.978213i	$-0.566566\pi$
$269$	−6.80986	−0.415205	−0.207602	+	0.978213i	$0.566566\pi$
$270$	0	0
$271$	−9.77120	−0.593558	−0.296779	−	0.954946i	$-0.595912\pi$
$271$	−9.77120	−0.593558	−0.296779	+	0.954946i	$0.595912\pi$
$272$	6.95655	0.421803
$273$	12.1729	0.736735
$274$	−1.17193	−0.0707991
$275$	0	0
$276$	0.548269	0.0330019
$277$	25.5549	1.53545	0.767723	−	0.640782i	$-0.221390\pi$
$277$	25.5549	1.53545	0.767723	+	0.640782i	$0.221390\pi$
$278$	2.77316	0.166323
$279$	−0.319037	−0.0191002
$280$	0	0
$281$	24.9850	1.49048	0.745241	−	0.666795i	$-0.232334\pi$
$281$	24.9850	1.49048	0.745241	+	0.666795i	$0.232334\pi$
$282$	0.176288	0.0104978
$283$	−11.2572	−0.669168	−0.334584	−	0.942366i	$-0.608596\pi$
$283$	−11.2572	−0.669168	−0.334584	+	0.942366i	$0.608596\pi$
$284$	26.3877	1.56582
$285$	0	0
$286$	−0.169594	−0.0100283
$287$	−48.1270	−2.84084
$288$	2.07179	0.122082
$289$	−13.6741	−0.804357
$290$	0	0
$291$	5.48542	0.321561
$292$	−30.6485	−1.79357
$293$	12.5186	0.731346	0.365673	−	0.930743i	$-0.380839\pi$
$293$	12.5186	0.731346	0.365673	+	0.930743i	$0.380839\pi$
$294$	−3.33858	−0.194710
$295$	0	0
$296$	2.34349	0.136213
$297$	0.402502	0.0233555
$298$	−1.28077	−0.0741933
$299$	0.665560	0.0384903
$300$	0	0
$301$	1.93785	0.111696
$302$	2.64701	0.152318
$303$	15.6283	0.897823
$304$	5.54914	0.318265
$305$	0	0
$306$	0.321498	0.0183788
$307$	−15.1198	−0.862934	−0.431467	−	0.902129i	$-0.642004\pi$
$307$	−15.1198	−0.862934	−0.431467	+	0.902129i	$0.642004\pi$
$308$	−4.03615	−0.229981
$309$	−3.84804	−0.218907
$310$	0	0
$311$	18.3219	1.03894	0.519471	−	0.854488i	$-0.326129\pi$
$311$	18.3219	1.03894	0.519471	+	0.854488i	$0.326129\pi$
$312$	1.67231	0.0946759
$313$	−28.3232	−1.60092	−0.800461	−	0.599384i	$-0.795412\pi$
$313$	−28.3232	−1.60092	−0.800461	+	0.599384i	$0.795412\pi$
$314$	0.581955	0.0328416
$315$	0	0
$316$	−6.53977	−0.367891
$317$	13.6912	0.768976	0.384488	−	0.923130i	$-0.374378\pi$
$317$	13.6912	0.768976	0.384488	+	0.923130i	$0.374378\pi$
$318$	0.141765	0.00794976
$319$	−1.43549	−0.0803720
$320$	0	0
$321$	12.5664	0.701389
$322$	−0.250010	−0.0139325
$323$	2.65304	0.147619
$324$	−1.96892	−0.109385
$325$	0	0
$326$	0.315695	0.0174847
$327$	5.76239	0.318661
$328$	−6.61169	−0.365069
$329$	5.09296	0.280784
$330$	0	0
$331$	1.80543	0.0992355	0.0496177	−	0.998768i	$-0.484200\pi$
$331$	1.80543	0.0992355	0.0496177	+	0.998768i	$0.484200\pi$
$332$	−27.1144	−1.48810
$333$	−3.34942	−0.183547
$334$	1.72346	0.0943033
$335$	0	0
$336$	19.4271	1.05984
$337$	19.5730	1.06621	0.533106	−	0.846049i	$-0.321025\pi$
$337$	19.5730	1.06621	0.533106	+	0.846049i	$0.321025\pi$
$338$	−1.28465	−0.0698760
$339$	−4.36827	−0.237252
$340$	0	0
$341$	0.128413	0.00695395
$342$	0.256454	0.0138675
$343$	−60.8012	−3.28296
$344$	0.266221	0.0143537
$345$	0	0
$346$	0.884736	0.0475637
$347$	−6.84734	−0.367585	−0.183792	−	0.982965i	$-0.558837\pi$
$347$	−6.84734	−0.367585	−0.183792	+	0.982965i	$0.558837\pi$
$348$	7.02201	0.376419
$349$	−13.8191	−0.739719	−0.369859	−	0.929088i	$-0.620594\pi$
$349$	−13.8191	−0.739719	−0.369859	+	0.929088i	$0.620594\pi$
$350$	0	0
$351$	−2.39013	−0.127576
$352$	−0.833900	−0.0444470
$353$	−24.5930	−1.30896	−0.654478	−	0.756081i	$-0.727111\pi$
$353$	−24.5930	−1.30896	−0.654478	+	0.756081i	$0.727111\pi$
$354$	2.23831	0.118965
$355$	0	0
$356$	6.57204	0.348317
$357$	9.28810	0.491578
$358$	−3.76488	−0.198980
$359$	5.24365	0.276749	0.138375	−	0.990380i	$-0.455812\pi$
$359$	5.24365	0.276749	0.138375	+	0.990380i	$0.455812\pi$
$360$	0	0
$361$	−16.8837	−0.888616
$362$	−0.991345	−0.0521039
$363$	10.8380	0.568847
$364$	23.9674	1.25623
$365$	0	0
$366$	−1.47745	−0.0772277
$367$	−2.04234	−0.106609	−0.0533046	−	0.998578i	$-0.516975\pi$
$367$	−2.04234	−0.106609	−0.0533046	+	0.998578i	$0.516975\pi$
$368$	1.06219	0.0553705
$369$	9.44970	0.491932
$370$	0	0
$371$	4.09559	0.212632
$372$	−0.628159	−0.0325685
$373$	−12.0321	−0.622997	−0.311499	−	0.950247i	$-0.600831\pi$
$373$	−12.0321	−0.622997	−0.311499	+	0.950247i	$0.600831\pi$
$374$	−0.129403	−0.00669129
$375$	0	0
$376$	0.699672	0.0360828
$377$	8.52422	0.439020
$378$	0.897826	0.0461792
$379$	−17.4061	−0.894092	−0.447046	−	0.894511i	$-0.647524\pi$
$379$	−17.4061	−0.894092	−0.447046	+	0.894511i	$0.647524\pi$
$380$	0	0
$381$	−3.13284	−0.160500
$382$	−0.0479221	−0.00245191
$383$	−30.6912	−1.56825	−0.784123	−	0.620606i	$-0.786887\pi$
$383$	−30.6912	−1.56825	−0.784123	+	0.620606i	$0.786887\pi$
$384$	5.42410	0.276797
$385$	0	0
$386$	−2.78211	−0.141606
$387$	−0.380495	−0.0193416
$388$	10.8004	0.548305
$389$	3.93742	0.199635	0.0998175	−	0.995006i	$-0.468174\pi$
$389$	3.93742	0.199635	0.0998175	+	0.995006i	$0.468174\pi$
$390$	0	0
$391$	0.507833	0.0256822
$392$	−13.2506	−0.669255
$393$	14.7675	0.744920
$394$	2.05581	0.103570
$395$	0	0
$396$	0.792495	0.0398244
$397$	−1.87105	−0.0939053	−0.0469526	−	0.998897i	$-0.514951\pi$
$397$	−1.87105	−0.0939053	−0.0469526	+	0.998897i	$0.514951\pi$
$398$	0.332097	0.0166465
$399$	7.40898	0.370913
$400$	0	0
$401$	15.1426	0.756186	0.378093	−	0.925768i	$-0.376580\pi$
$401$	15.1426	0.756186	0.378093	+	0.925768i	$0.376580\pi$
$402$	2.46298	0.122842
$403$	−0.762541	−0.0379849
$404$	30.7709	1.53091
$405$	0	0
$406$	−3.20203	−0.158914
$407$	1.34815	0.0668251
$408$	1.27600	0.0631714
$409$	5.43752	0.268868	0.134434	−	0.990923i	$-0.457078\pi$
$409$	5.43752	0.268868	0.134434	+	0.990923i	$0.457078\pi$
$410$	0	0
$411$	6.64785	0.327914
$412$	−7.57649	−0.373267
$413$	64.6651	3.18196
$414$	0.0490893	0.00241261
$415$	0	0
$416$	4.95186	0.242785
$417$	−15.7309	−0.770346
$418$	−0.103223	−0.00504882
$419$	−25.2764	−1.23483	−0.617417	−	0.786636i	$-0.711821\pi$
$419$	−25.2764	−1.23483	−0.617417	+	0.786636i	$0.711821\pi$
$420$	0	0
$421$	−1.00443	−0.0489529	−0.0244764	−	0.999700i	$-0.507792\pi$
$421$	−1.00443	−0.0489529	−0.0244764	+	0.999700i	$0.507792\pi$
$422$	−1.27435	−0.0620344
$423$	−1.00000	−0.0486217
$424$	0.562653	0.0273248
$425$	0	0
$426$	2.36262	0.114469
$427$	−42.6837	−2.06561
$428$	24.7423	1.19596
$429$	0.962033	0.0464474
$430$	0	0
$431$	−3.24494	−0.156303	−0.0781517	−	0.996941i	$-0.524902\pi$
$431$	−3.24494	−0.156303	−0.0781517	+	0.996941i	$0.524902\pi$
$432$	−3.81450	−0.183525
$433$	−4.39159	−0.211046	−0.105523	−	0.994417i	$-0.533652\pi$
$433$	−4.39159	−0.211046	−0.105523	+	0.994417i	$0.533652\pi$
$434$	0.286440	0.0137496
$435$	0	0
$436$	11.3457	0.543361
$437$	0.405091	0.0193781
$438$	−2.74412	−0.131119
$439$	−9.69742	−0.462832	−0.231416	−	0.972855i	$-0.574336\pi$
$439$	−9.69742	−0.462832	−0.231416	+	0.972855i	$0.574336\pi$
$440$	0	0
$441$	18.9383	0.901823
$442$	0.768423	0.0365501
$443$	−20.4377	−0.971026	−0.485513	−	0.874229i	$-0.661367\pi$
$443$	−20.4377	−0.971026	−0.485513	+	0.874229i	$0.661367\pi$
$444$	−6.59474	−0.312973
$445$	0	0
$446$	−0.558899	−0.0264646
$447$	7.26526	0.343635
$448$	36.9941	1.74781
$449$	−41.1088	−1.94004	−0.970022	−	0.243015i	$-0.921863\pi$
$449$	−41.1088	−1.94004	−0.970022	+	0.243015i	$0.921863\pi$
$450$	0	0
$451$	−3.80352	−0.179101
$452$	−8.60078	−0.404547
$453$	−15.0153	−0.705479
$454$	2.36592	0.111038
$455$	0	0
$456$	1.01785	0.0476651
$457$	−31.2091	−1.45990	−0.729950	−	0.683501i	$-0.760457\pi$
$457$	−31.2091	−1.45990	−0.729950	+	0.683501i	$0.760457\pi$
$458$	−3.46190	−0.161764
$459$	−1.82371	−0.0851236
$460$	0	0
$461$	0.341618	0.0159107	0.00795537	−	0.999968i	$-0.497468\pi$
$461$	0.341618	0.0159107	0.00795537	+	0.999968i	$0.497468\pi$
$462$	−0.361377	−0.0168128
$463$	10.4938	0.487688	0.243844	−	0.969814i	$-0.421592\pi$
$463$	10.4938	0.487688	0.243844	+	0.969814i	$0.421592\pi$
$464$	13.6041	0.631555
$465$	0	0
$466$	−4.13670	−0.191629
$467$	14.1932	0.656785	0.328393	−	0.944541i	$-0.393493\pi$
$467$	14.1932	0.656785	0.328393	+	0.944541i	$0.393493\pi$
$468$	−4.70599	−0.217534
$469$	71.1557	3.28567
$470$	0	0
$471$	−3.30117	−0.152110
$472$	8.88369	0.408905
$473$	0.153150	0.00704183
$474$	−0.585539	−0.0268947
$475$	0	0
$476$	18.2876	0.838209
$477$	−0.804166	−0.0368202
$478$	2.51331	0.114956
$479$	31.9200	1.45846	0.729231	−	0.684267i	$-0.239878\pi$
$479$	31.9200	1.45846	0.729231	+	0.684267i	$0.239878\pi$
$480$	0	0
$481$	−8.00555	−0.365022
$482$	−5.12655	−0.233508
$483$	1.41819	0.0645300
$484$	21.3392	0.969962
$485$	0	0
$486$	−0.176288	−0.00799657
$487$	−43.7623	−1.98306	−0.991529	−	0.129884i	$-0.958540\pi$
$487$	−43.7623	−1.98306	−0.991529	+	0.129884i	$0.958540\pi$
$488$	−5.86390	−0.265446
$489$	−1.79080	−0.0809826
$490$	0	0
$491$	−32.9741	−1.48810	−0.744050	−	0.668124i	$-0.767097\pi$
$491$	−32.9741	−1.48810	−0.744050	+	0.668124i	$0.767097\pi$
$492$	18.6057	0.838811
$493$	6.50413	0.292931
$494$	0.612960	0.0275784
$495$	0	0
$496$	−1.21697	−0.0546434
$497$	68.2564	3.06172
$498$	−2.42769	−0.108787
$499$	−21.9039	−0.980552	−0.490276	−	0.871567i	$-0.663104\pi$
$499$	−21.9039	−0.980552	−0.490276	+	0.871567i	$0.663104\pi$
$500$	0	0
$501$	−9.77639	−0.436777
$502$	4.15409	0.185406
$503$	−33.6205	−1.49906	−0.749532	−	0.661968i	$-0.769721\pi$
$503$	−33.6205	−1.49906	−0.749532	+	0.661968i	$0.769721\pi$
$504$	3.56340	0.158727
$505$	0	0
$506$	−0.0197585	−0.000878373 0
$507$	7.28726	0.323639
$508$	−6.16832	−0.273675
$509$	38.3899	1.70160	0.850801	−	0.525488i	$-0.176117\pi$
$509$	38.3899	1.70160	0.850801	+	0.525488i	$0.176117\pi$
$510$	0	0
$511$	−79.2778	−3.50705
$512$	13.2407	0.585160
$513$	−1.45475	−0.0642287
$514$	0.393247	0.0173454
$515$	0	0
$516$	−0.749165	−0.0329801
$517$	0.402502	0.0177020
$518$	3.00720	0.132129
$519$	−5.01871	−0.220297
$520$	0	0
$521$	15.7496	0.690002	0.345001	−	0.938602i	$-0.387879\pi$
$521$	15.7496	0.690002	0.345001	+	0.938602i	$0.387879\pi$
$522$	0.628716	0.0275181
$523$	9.13066	0.399256	0.199628	−	0.979872i	$-0.436027\pi$
$523$	9.13066	0.399256	0.199628	+	0.979872i	$0.436027\pi$
$524$	29.0760	1.27019
$525$	0	0
$526$	4.62009	0.201446
$527$	−0.581832	−0.0253450
$528$	1.53534	0.0668173
$529$	−22.9225	−0.996629
$530$	0	0
$531$	−12.6969	−0.551000
$532$	14.5877	0.632458
$533$	22.5860	0.978310
$534$	0.588428	0.0254638
$535$	0	0
$536$	9.77538	0.422232
$537$	21.3565	0.921600
$538$	−1.20049	−0.0517570
$539$	−7.62269	−0.328332
$540$	0	0
$541$	12.8401	0.552040	0.276020	−	0.961152i	$-0.410984\pi$
$541$	12.8401	0.552040	0.276020	+	0.961152i	$0.410984\pi$
$542$	−1.72254	−0.0739895
$543$	5.62345	0.241325
$544$	3.77836	0.161996
$545$	0	0
$546$	2.14592	0.0918371
$547$	38.7129	1.65525	0.827623	−	0.561285i	$-0.189693\pi$
$547$	38.7129	1.65525	0.827623	+	0.561285i	$0.189693\pi$
$548$	13.0891	0.559139
$549$	8.38092	0.357689
$550$	0	0
$551$	5.18825	0.221027
$552$	0.194832	0.00829258
$553$	−16.9163	−0.719353
$554$	4.50501	0.191400
$555$	0	0
$556$	−30.9729	−1.31355
$557$	−15.3475	−0.650296	−0.325148	−	0.945663i	$-0.605414\pi$
$557$	−15.3475	−0.650296	−0.325148	+	0.945663i	$0.605414\pi$
$558$	−0.0562423	−0.00238093
$559$	−0.909433	−0.0384649
$560$	0	0
$561$	0.734047	0.0309915
$562$	4.40455	0.185795
$563$	−0.0765749	−0.00322725	−0.00161362	−	0.999999i	$-0.500514\pi$
$563$	−0.0765749	−0.00322725	−0.00161362	+	0.999999i	$0.500514\pi$
$564$	−1.96892	−0.0829066
$565$	0	0
$566$	−1.98450	−0.0834146
$567$	−5.09296	−0.213884
$568$	9.37707	0.393453
$569$	−29.5517	−1.23887	−0.619435	−	0.785048i	$-0.712638\pi$
$569$	−29.5517	−1.23887	−0.619435	+	0.785048i	$0.712638\pi$
$570$	0	0
$571$	10.3620	0.433634	0.216817	−	0.976212i	$-0.430432\pi$
$571$	10.3620	0.433634	0.216817	+	0.976212i	$0.430432\pi$
$572$	1.89417	0.0791992
$573$	0.271840	0.0113563
$574$	−8.48419	−0.354123
$575$	0	0
$576$	−7.26377	−0.302657
$577$	26.9097	1.12027	0.560133	−	0.828402i	$-0.310750\pi$
$577$	26.9097	1.12027	0.560133	+	0.828402i	$0.310750\pi$
$578$	−2.41057	−0.100266
$579$	15.7817	0.655864
$580$	0	0
$581$	−70.1362	−2.90974
$582$	0.967011	0.0400839
$583$	0.323678	0.0134054
$584$	−10.8912	−0.450681
$585$	0	0
$586$	2.20688	0.0911653
$587$	31.7512	1.31051	0.655255	−	0.755407i	$-0.272561\pi$
$587$	31.7512	1.31051	0.655255	+	0.755407i	$0.272561\pi$
$588$	37.2880	1.53773
$589$	−0.464119	−0.0191237
$590$	0	0
$591$	−11.6617	−0.479698
$592$	−12.7764	−0.525105
$593$	15.2826	0.627582	0.313791	−	0.949492i	$-0.398401\pi$
$593$	15.2826	0.627582	0.313791	+	0.949492i	$0.398401\pi$
$594$	0.0709561	0.00291136
$595$	0	0
$596$	14.3047	0.585944
$597$	−1.88383	−0.0771002
$598$	0.117330	0.00479798
$599$	42.1221	1.72106	0.860531	−	0.509398i	$-0.170132\pi$
$599$	42.1221	1.72106	0.860531	+	0.509398i	$0.170132\pi$
$600$	0	0
$601$	13.5893	0.554318	0.277159	−	0.960824i	$-0.410607\pi$
$601$	13.5893	0.554318	0.277159	+	0.960824i	$0.410607\pi$
$602$	0.341618	0.0139233
$603$	−13.9714	−0.568959
$604$	−29.5639	−1.20294
$605$	0	0
$606$	2.75508	0.111917
$607$	−37.1145	−1.50643	−0.753215	−	0.657774i	$-0.771498\pi$
$607$	−37.1145	−1.50643	−0.753215	+	0.657774i	$0.771498\pi$
$608$	3.01394	0.122231
$609$	18.1637	0.736028
$610$	0	0
$611$	−2.39013	−0.0966944
$612$	−3.59075	−0.145147
$613$	17.9504	0.725008	0.362504	−	0.931982i	$-0.381922\pi$
$613$	17.9504	0.725008	0.362504	+	0.931982i	$0.381922\pi$
$614$	−2.66544	−0.107568
$615$	0	0
$616$	−1.43428	−0.0577886
$617$	−20.9569	−0.843691	−0.421846	−	0.906668i	$-0.638618\pi$
$617$	−20.9569	−0.843691	−0.421846	+	0.906668i	$0.638618\pi$
$618$	−0.678362	−0.0272877
$619$	−21.3910	−0.859776	−0.429888	−	0.902882i	$-0.641447\pi$
$619$	−21.3910	−0.859776	−0.429888	+	0.902882i	$0.641447\pi$
$620$	0	0
$621$	−0.278461	−0.0111743
$622$	3.22993	0.129508
$623$	16.9997	0.681080
$624$	−9.11717	−0.364979
$625$	0	0
$626$	−4.99303	−0.199562
$627$	0.585539	0.0233842
$628$	−6.49974	−0.259368
$629$	−6.10837	−0.243557
$630$	0	0
$631$	29.8119	1.18679	0.593397	−	0.804910i	$-0.297787\pi$
$631$	29.8119	1.18679	0.593397	+	0.804910i	$0.297787\pi$
$632$	−2.32396	−0.0924421
$633$	7.22882	0.287320
$634$	2.41359	0.0958560
$635$	0	0
$636$	−1.58334	−0.0627836
$637$	45.2650	1.79346
$638$	−0.253059	−0.0100187
$639$	−13.4021	−0.530179
$640$	0	0
$641$	16.4335	0.649083	0.324542	−	0.945871i	$-0.394790\pi$
$641$	16.4335	0.649083	0.324542	+	0.945871i	$0.394790\pi$
$642$	2.21530	0.0874311
$643$	−34.9799	−1.37947	−0.689736	−	0.724061i	$-0.742273\pi$
$643$	−34.9799	−1.37947	−0.689736	+	0.724061i	$0.742273\pi$
$644$	2.79231	0.110033
$645$	0	0
$646$	0.467699	0.0184014
$647$	−18.3488	−0.721365	−0.360683	−	0.932689i	$-0.617456\pi$
$647$	−18.3488	−0.721365	−0.360683	+	0.932689i	$0.617456\pi$
$648$	−0.699672	−0.0274857
$649$	5.11054	0.200606
$650$	0	0
$651$	−1.62484	−0.0636826
$652$	−3.52594	−0.138086
$653$	−16.7156	−0.654134	−0.327067	−	0.945001i	$-0.606060\pi$
$653$	−16.7156	−0.654134	−0.327067	+	0.945001i	$0.606060\pi$
$654$	1.01584	0.0397224
$655$	0	0
$656$	36.0459	1.40736
$657$	15.5662	0.607293
$658$	0.897826	0.0350009
$659$	23.9795	0.934108	0.467054	−	0.884229i	$-0.345315\pi$
$659$	23.9795	0.934108	0.467054	+	0.884229i	$0.345315\pi$
$660$	0	0
$661$	−21.5821	−0.839447	−0.419723	−	0.907652i	$-0.637873\pi$
$661$	−21.5821	−0.839447	−0.419723	+	0.907652i	$0.637873\pi$
$662$	0.318275	0.0123701
$663$	−4.35892	−0.169286
$664$	−9.63532	−0.373923
$665$	0	0
$666$	−0.590461	−0.0228799
$667$	0.993110	0.0384534
$668$	−19.2490	−0.744764
$669$	3.17038	0.122574
$670$	0	0
$671$	−3.37334	−0.130226
$672$	10.5516	0.407036
$673$	33.3365	1.28503	0.642514	−	0.766274i	$-0.277891\pi$
$673$	33.3365	1.28503	0.642514	+	0.766274i	$0.277891\pi$
$674$	3.45048	0.132908
$675$	0	0
$676$	14.3481	0.551848
$677$	36.0993	1.38741	0.693703	−	0.720261i	$-0.255978\pi$
$677$	36.0993	1.38741	0.693703	+	0.720261i	$0.255978\pi$
$678$	−0.770071	−0.0295744
$679$	27.9370	1.07212
$680$	0	0
$681$	−13.4208	−0.514286
$682$	0.0226376	0.000866839 0
$683$	−19.2797	−0.737716	−0.368858	−	0.929486i	$-0.620251\pi$
$683$	−19.2797	−0.737716	−0.368858	+	0.929486i	$0.620251\pi$
$684$	−2.86429	−0.109519
$685$	0	0
$686$	−10.7185	−0.409234
$687$	19.6378	0.749229
$688$	−1.45140	−0.0553340
$689$	−1.92206	−0.0732248
$690$	0	0
$691$	45.2884	1.72285	0.861426	−	0.507883i	$-0.169572\pi$
$691$	45.2884	1.72285	0.861426	+	0.507883i	$0.169572\pi$
$692$	−9.88145	−0.375636
$693$	2.04993	0.0778703
$694$	−1.20710	−0.0458210
$695$	0	0
$696$	2.49532	0.0945850
$697$	17.2335	0.652767
$698$	−2.43613	−0.0922090
$699$	23.4656	0.887551
$700$	0	0
$701$	13.9551	0.527078	0.263539	−	0.964649i	$-0.415110\pi$
$701$	13.9551	0.527078	0.263539	+	0.964649i	$0.415110\pi$
$702$	−0.421351	−0.0159029
$703$	−4.87256	−0.183772
$704$	2.92368	0.110190
$705$	0	0
$706$	−4.33545	−0.163167
$707$	79.5944	2.99346
$708$	−24.9993	−0.939531
$709$	−11.0571	−0.415259	−0.207629	−	0.978208i	$-0.566575\pi$
$709$	−11.0571	−0.415259	−0.207629	+	0.978208i	$0.566575\pi$
$710$	0	0
$711$	3.32150	0.124566
$712$	2.33543	0.0875238
$713$	−0.0888394	−0.00332706
$714$	1.63738	0.0612773
$715$	0	0
$716$	42.0492	1.57145
$717$	−14.2569	−0.532433
$718$	0.924391	0.0344980
$719$	−15.6303	−0.582912	−0.291456	−	0.956584i	$-0.594140\pi$
$719$	−15.6303	−0.582912	−0.291456	+	0.956584i	$0.594140\pi$
$720$	0	0
$721$	−19.5979	−0.729865
$722$	−2.97639	−0.110770
$723$	29.0806	1.08152
$724$	11.0721	0.411493
$725$	0	0
$726$	1.91060	0.0709092
$727$	48.1649	1.78634	0.893169	−	0.449721i	$-0.148476\pi$
$727$	48.1649	1.78634	0.893169	+	0.449721i	$0.148476\pi$
$728$	8.51701	0.315661
$729$	1.00000	0.0370370
$730$	0	0
$731$	−0.693913	−0.0256653
$732$	16.5014	0.609909
$733$	−7.66290	−0.283036	−0.141518	−	0.989936i	$-0.545198\pi$
$733$	−7.66290	−0.283036	−0.141518	+	0.989936i	$0.545198\pi$
$734$	−0.360039	−0.0132893
$735$	0	0
$736$	0.576914	0.0212653
$737$	5.62351	0.207145
$738$	1.66586	0.0613213
$739$	−10.9949	−0.404455	−0.202228	−	0.979339i	$-0.564818\pi$
$739$	−10.9949	−0.404455	−0.202228	+	0.979339i	$0.564818\pi$
$740$	0	0
$741$	−3.47704	−0.127732
$742$	0.722002	0.0265055
$743$	−26.4289	−0.969582	−0.484791	−	0.874630i	$-0.661104\pi$
$743$	−26.4289	−0.969582	−0.484791	+	0.874630i	$0.661104\pi$
$744$	−0.223221	−0.00818369
$745$	0	0
$746$	−2.12111	−0.0776592
$747$	13.7712	0.503862
$748$	1.44528	0.0528448
$749$	64.0003	2.33852
$750$	0	0
$751$	38.1435	1.39188	0.695938	−	0.718102i	$-0.254989\pi$
$751$	38.1435	1.39188	0.695938	+	0.718102i	$0.254989\pi$
$752$	−3.81450	−0.139101
$753$	−23.5643	−0.858729
$754$	1.50271	0.0547256
$755$	0	0
$756$	−10.0277	−0.364702
$757$	−46.2891	−1.68241	−0.841203	−	0.540719i	$-0.818152\pi$
$757$	−46.2891	−1.68241	−0.841203	+	0.540719i	$0.818152\pi$
$758$	−3.06848	−0.111452
$759$	0.112081	0.00406829
$760$	0	0
$761$	12.4421	0.451026	0.225513	−	0.974240i	$-0.427594\pi$
$761$	12.4421	0.451026	0.225513	+	0.974240i	$0.427594\pi$
$762$	−0.552281	−0.0200070
$763$	29.3477	1.06246
$764$	0.535232	0.0193640
$765$	0	0
$766$	−5.41047	−0.195488
$767$	−30.3474	−1.09578
$768$	−13.5713	−0.489714
$769$	11.4449	0.412712	0.206356	−	0.978477i	$-0.433839\pi$
$769$	11.4449	0.412712	0.206356	+	0.978477i	$0.433839\pi$
$770$	0	0
$771$	−2.23072	−0.0803372
$772$	31.0729	1.11834
$773$	−22.7442	−0.818052	−0.409026	−	0.912523i	$-0.634131\pi$
$773$	−22.7442	−0.818052	−0.409026	+	0.912523i	$0.634131\pi$
$774$	−0.0670765	−0.00241102
$775$	0	0
$776$	3.83799	0.137776
$777$	−17.0585	−0.611969
$778$	0.694118	0.0248853
$779$	13.7469	0.492535
$780$	0	0
$781$	5.39437	0.193026
$782$	0.0895247	0.00320140
$783$	−3.56642	−0.127453
$784$	72.2401	2.58000
$785$	0	0
$786$	2.60332	0.0928574
$787$	3.55763	0.126816	0.0634079	−	0.997988i	$-0.479803\pi$
$787$	3.55763	0.126816	0.0634079	+	0.997988i	$0.479803\pi$
$788$	−22.9610	−0.817952
$789$	−26.2077	−0.933018
$790$	0	0
$791$	−22.2474	−0.791027
$792$	0.281619	0.0100069
$793$	20.0315	0.711340
$794$	−0.329843	−0.0117057
$795$	0	0
$796$	−3.70912	−0.131466
$797$	36.6644	1.29872	0.649360	−	0.760481i	$-0.275037\pi$
$797$	36.6644	1.29872	0.649360	+	0.760481i	$0.275037\pi$
$798$	1.30611	0.0462359
$799$	−1.82371	−0.0645183
$800$	0	0
$801$	−3.33789	−0.117938
$802$	2.66946	0.0942618
$803$	−6.26540	−0.221101
$804$	−27.5086	−0.970153
$805$	0	0
$806$	−0.134427	−0.00473497
$807$	6.80986	0.239718
$808$	10.9347	0.384681
$809$	−37.8986	−1.33245	−0.666223	−	0.745753i	$-0.732090\pi$
$809$	−37.8986	−1.33245	−0.666223	+	0.745753i	$0.732090\pi$
$810$	0	0
$811$	−13.3691	−0.469453	−0.234726	−	0.972062i	$-0.575419\pi$
$811$	−13.3691	−0.469453	−0.234726	+	0.972062i	$0.575419\pi$
$812$	35.7628	1.25503
$813$	9.77120	0.342691
$814$	0.237661	0.00833003
$815$	0	0
$816$	−6.95655	−0.243528
$817$	−0.553524	−0.0193654
$818$	0.958568	0.0335155
$819$	−12.1729	−0.425354
$820$	0	0
$821$	−34.7118	−1.21145	−0.605725	−	0.795674i	$-0.707117\pi$
$821$	−34.7118	−1.21145	−0.605725	+	0.795674i	$0.707117\pi$
$822$	1.17193	0.0408759
$823$	8.20056	0.285854	0.142927	−	0.989733i	$-0.454349\pi$
$823$	8.20056	0.285854	0.142927	+	0.989733i	$0.454349\pi$
$824$	−2.69237	−0.0937930
$825$	0	0
$826$	11.3996	0.396645
$827$	−34.1996	−1.18924	−0.594619	−	0.804007i	$-0.702697\pi$
$827$	−34.1996	−1.18924	−0.594619	+	0.804007i	$0.702697\pi$
$828$	−0.548269	−0.0190537
$829$	15.1529	0.526283	0.263142	−	0.964757i	$-0.415241\pi$
$829$	15.1529	0.526283	0.263142	+	0.964757i	$0.415241\pi$
$830$	0	0
$831$	−25.5549	−0.886490
$832$	−17.3614	−0.601898
$833$	34.5380	1.19667
$834$	−2.77316	−0.0960268
$835$	0	0
$836$	1.15288	0.0398732
$837$	0.319037	0.0110275
$838$	−4.45592	−0.153927
$839$	−30.7668	−1.06219	−0.531093	−	0.847313i	$-0.678219\pi$
$839$	−30.7668	−1.06219	−0.531093	+	0.847313i	$0.678219\pi$
$840$	0	0
$841$	−16.2806	−0.561401
$842$	−0.177068	−0.00610218
$843$	−24.9850	−0.860531
$844$	14.2330	0.489919
$845$	0	0
$846$	−0.176288	−0.00606089
$847$	55.1975	1.89661
$848$	−3.06749	−0.105338
$849$	11.2572	0.386344
$850$	0	0
$851$	−0.932683	−0.0319720
$852$	−26.3877	−0.904027
$853$	−43.9899	−1.50619	−0.753093	−	0.657914i	$-0.771439\pi$
$853$	−43.9899	−1.50619	−0.753093	+	0.657914i	$0.771439\pi$
$854$	−7.52461	−0.257487
$855$	0	0
$856$	8.79237	0.300517
$857$	27.0633	0.924465	0.462233	−	0.886759i	$-0.347049\pi$
$857$	27.0633	0.924465	0.462233	+	0.886759i	$0.347049\pi$
$858$	0.169594	0.00578986
$859$	−0.642573	−0.0219243	−0.0109622	−	0.999940i	$-0.503489\pi$
$859$	−0.642573	−0.0219243	−0.0109622	+	0.999940i	$0.503489\pi$
$860$	0	0
$861$	48.1270	1.64016
$862$	−0.572043	−0.0194839
$863$	30.9904	1.05493	0.527463	−	0.849578i	$-0.323143\pi$
$863$	30.9904	1.05493	0.527463	+	0.849578i	$0.323143\pi$
$864$	−2.07179	−0.0704838
$865$	0	0
$866$	−0.774183	−0.0263078
$867$	13.6741	0.464396
$868$	−3.19919	−0.108588
$869$	−1.33691	−0.0453515
$870$	0	0
$871$	−33.3935	−1.13149
$872$	4.03179	0.136534
$873$	−5.48542	−0.185653
$874$	0.0714126	0.00241557
$875$	0	0
$876$	30.6485	1.03552
$877$	15.4070	0.520258	0.260129	−	0.965574i	$-0.416235\pi$
$877$	15.4070	0.520258	0.260129	+	0.965574i	$0.416235\pi$
$878$	−1.70953	−0.0576940
$879$	−12.5186	−0.422243
$880$	0	0
$881$	−32.2397	−1.08618	−0.543091	−	0.839674i	$-0.682746\pi$
$881$	−32.2397	−1.08618	−0.543091	+	0.839674i	$0.682746\pi$
$882$	3.33858	0.112416
$883$	1.60882	0.0541410	0.0270705	−	0.999634i	$-0.491382\pi$
$883$	1.60882	0.0541410	0.0270705	+	0.999634i	$0.491382\pi$
$884$	−8.58237	−0.288656
$885$	0	0
$886$	−3.60292	−0.121042
$887$	−29.6644	−0.996034	−0.498017	−	0.867167i	$-0.665938\pi$
$887$	−29.6644	−0.996034	−0.498017	+	0.867167i	$0.665938\pi$
$888$	−2.34349	−0.0786425
$889$	−15.9554	−0.535129
$890$	0	0
$891$	−0.402502	−0.0134843
$892$	6.24223	0.209005
$893$	−1.45475	−0.0486813
$894$	1.28077	0.0428355
$895$	0	0
$896$	27.6247	0.922878
$897$	−0.665560	−0.0222224
$898$	−7.24697	−0.241835
$899$	−1.13782	−0.0379484
$900$	0	0
$901$	−1.46657	−0.0488585
$902$	−0.670513	−0.0223257
$903$	−1.93785	−0.0644875
$904$	−3.05635	−0.101653
$905$	0	0
$906$	−2.64701	−0.0879410
$907$	−29.5994	−0.982833	−0.491416	−	0.870925i	$-0.663521\pi$
$907$	−29.5994	−0.982833	−0.491416	+	0.870925i	$0.663521\pi$
$908$	−26.4245	−0.876929
$909$	−15.6283	−0.518358
$910$	0	0
$911$	−45.7000	−1.51411	−0.757054	−	0.653352i	$-0.773362\pi$
$911$	−45.7000	−1.51411	−0.757054	+	0.653352i	$0.773362\pi$
$912$	−5.54914	−0.183750
$913$	−5.54293	−0.183444
$914$	−5.50178	−0.181983
$915$	0	0
$916$	38.6653	1.27754
$917$	75.2102	2.48366
$918$	−0.321498	−0.0106110
$919$	−28.7413	−0.948089	−0.474044	−	0.880501i	$-0.657206\pi$
$919$	−28.7413	−0.948089	−0.474044	+	0.880501i	$0.657206\pi$
$920$	0	0
$921$	15.1198	0.498215
$922$	0.0602230	0.00198334
$923$	−32.0328	−1.05437
$924$	4.03615	0.132779
$925$	0	0
$926$	1.84993	0.0607923
$927$	3.84804	0.126386
$928$	7.38889	0.242552
$929$	−10.2204	−0.335322	−0.167661	−	0.985845i	$-0.553621\pi$
$929$	−10.2204	−0.335322	−0.167661	+	0.985845i	$0.553621\pi$
$930$	0	0
$931$	27.5504	0.902929
$932$	46.2020	1.51340
$933$	−18.3219	−0.599833
$934$	2.50209	0.0818710
$935$	0	0
$936$	−1.67231	−0.0546611
$937$	−24.1988	−0.790539	−0.395270	−	0.918565i	$-0.629349\pi$
$937$	−24.1988	−0.790539	−0.395270	+	0.918565i	$0.629349\pi$
$938$	12.5439	0.409572
$939$	28.3232	0.924293
$940$	0	0
$941$	−48.3975	−1.57771	−0.788857	−	0.614577i	$-0.789327\pi$
$941$	−48.3975	−1.57771	−0.788857	+	0.614577i	$0.789327\pi$
$942$	−0.581955	−0.0189611
$943$	2.63138	0.0856894
$944$	−48.4325	−1.57634
$945$	0	0
$946$	0.0269984	0.000877794 0
$947$	−33.8367	−1.09954	−0.549772	−	0.835315i	$-0.685286\pi$
$947$	−33.8367	−1.09954	−0.549772	+	0.835315i	$0.685286\pi$
$948$	6.53977	0.212402
$949$	37.2052	1.20773
$950$	0	0
$951$	−13.6912	−0.443968
$952$	6.49862	0.210622
$953$	23.8805	0.773567	0.386783	−	0.922171i	$-0.373586\pi$
$953$	23.8805	0.773567	0.386783	+	0.922171i	$0.373586\pi$
$954$	−0.141765	−0.00458980
$955$	0	0
$956$	−28.0707	−0.907871
$957$	1.43549	0.0464028
$958$	5.62710	0.181803
$959$	33.8573	1.09331
$960$	0	0
$961$	−30.8982	−0.996717
$962$	−1.41128	−0.0455015
$963$	−12.5664	−0.404947
$964$	57.2575	1.84414
$965$	0	0
$966$	0.250010	0.00804394
$967$	10.1477	0.326328	0.163164	−	0.986599i	$-0.447830\pi$
$967$	10.1477	0.326328	0.163164	+	0.986599i	$0.447830\pi$
$968$	7.58304	0.243728
$969$	−2.65304	−0.0852280
$970$	0	0
$971$	−24.6950	−0.792502	−0.396251	−	0.918142i	$-0.629689\pi$
$971$	−24.6950	−0.792502	−0.396251	+	0.918142i	$0.629689\pi$
$972$	1.96892	0.0631532
$973$	−80.1169	−2.56843
$974$	−7.71475	−0.247197
$975$	0	0
$976$	31.9690	1.02330
$977$	12.3435	0.394904	0.197452	−	0.980313i	$-0.436733\pi$
$977$	12.3435	0.394904	0.197452	+	0.980313i	$0.436733\pi$
$978$	−0.315695	−0.0100948
$979$	1.34350	0.0429386
$980$	0	0
$981$	−5.76239	−0.183979
$982$	−5.81292	−0.185498
$983$	−10.2725	−0.327643	−0.163822	−	0.986490i	$-0.552382\pi$
$983$	−10.2725	−0.327643	−0.163822	+	0.986490i	$0.552382\pi$
$984$	6.61169	0.210773
$985$	0	0
$986$	1.14660	0.0365151
$987$	−5.09296	−0.162111
$988$	−6.84603	−0.217801
$989$	−0.105953	−0.00336911
$990$	0	0
$991$	28.0570	0.891261	0.445631	−	0.895217i	$-0.352979\pi$
$991$	28.0570	0.891261	0.445631	+	0.895217i	$0.352979\pi$
$992$	−0.660979	−0.0209861
$993$	−1.80543	−0.0572936
$994$	12.0328	0.381656
$995$	0	0
$996$	27.1144	0.859153
$997$	−39.3765	−1.24707	−0.623533	−	0.781797i	$-0.714303\pi$
$997$	−39.3765	−1.24707	−0.623533	+	0.781797i	$0.714303\pi$
$998$	−3.86138	−0.122230
$999$	3.34942	0.105971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.v.1.3		5
5.4	even	2		705.2.a.l.1.3	✓	5
15.14	odd	2		2115.2.a.q.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.a.l.1.3	✓	5	5.4	even	2
2115.2.a.q.1.3		5	15.14	odd	2
3525.2.a.v.1.3		5	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.176288 q^{2} -1.00000 q^{3} -1.96892 q^{4} -0.176288 q^{6} -5.09296 q^{7} -0.699672 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.176288 q^{2} -1.00000 q^{3} -1.96892 q^{4} -0.176288 q^{6} -5.09296 q^{7} -0.699672 q^{8} +1.00000 q^{9} -0.402502 q^{11} +1.96892 q^{12} +2.39013 q^{13} -0.897826 q^{14} +3.81450 q^{16} +1.82371 q^{17} +0.176288 q^{18} +1.45475 q^{19} +5.09296 q^{21} -0.0709561 q^{22} +0.278461 q^{23} +0.699672 q^{24} +0.421351 q^{26} -1.00000 q^{27} +10.0277 q^{28} +3.56642 q^{29} -0.319037 q^{31} +2.07179 q^{32} +0.402502 q^{33} +0.321498 q^{34} -1.96892 q^{36} -3.34942 q^{37} +0.256454 q^{38} -2.39013 q^{39} +9.44970 q^{41} +0.897826 q^{42} -0.380495 q^{43} +0.792495 q^{44} +0.0490893 q^{46} -1.00000 q^{47} -3.81450 q^{48} +18.9383 q^{49} -1.82371 q^{51} -4.70599 q^{52} -0.804166 q^{53} -0.176288 q^{54} +3.56340 q^{56} -1.45475 q^{57} +0.628716 q^{58} -12.6969 q^{59} +8.38092 q^{61} -0.0562423 q^{62} -5.09296 q^{63} -7.26377 q^{64} +0.0709561 q^{66} -13.9714 q^{67} -3.59075 q^{68} -0.278461 q^{69} -13.4021 q^{71} -0.699672 q^{72} +15.5662 q^{73} -0.590461 q^{74} -2.86429 q^{76} +2.04993 q^{77} -0.421351 q^{78} +3.32150 q^{79} +1.00000 q^{81} +1.66586 q^{82} +13.7712 q^{83} -10.0277 q^{84} -0.0670765 q^{86} -3.56642 q^{87} +0.281619 q^{88} -3.33789 q^{89} -12.1729 q^{91} -0.548269 q^{92} +0.319037 q^{93} -0.176288 q^{94} -2.07179 q^{96} -5.48542 q^{97} +3.33858 q^{98} -0.402502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{3} + 10 q^{4} - 10 q^{7} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^3 + 10 * q^4 - 10 * q^7 + 5 * q^9	\( 5 q - 5 q^{3} + 10 q^{4} - 10 q^{7} + 5 q^{9} - 2 q^{11} - 10 q^{12} - 7 q^{13} - 8 q^{14} + 8 q^{16} + 10 q^{17} + 2 q^{19} + 10 q^{21} + 4 q^{22} - 3 q^{23} - 16 q^{26} - 5 q^{27} - 12 q^{28} - 2 q^{29} - 6 q^{31} + 20 q^{32} + 2 q^{33} - 20 q^{34} + 10 q^{36} - 8 q^{37} + 8 q^{38} + 7 q^{39} + 8 q^{42} - 13 q^{43} + 4 q^{44} - 12 q^{46} - 5 q^{47} - 8 q^{48} + 13 q^{49} - 10 q^{51} - 34 q^{52} + 10 q^{53} - 28 q^{56} - 2 q^{57} + 4 q^{58} - 11 q^{59} + 11 q^{61} - 16 q^{62} - 10 q^{63} - 20 q^{64} - 4 q^{66} - 24 q^{67} + 20 q^{68} + 3 q^{69} - 11 q^{71} - 17 q^{73} + 12 q^{74} - 24 q^{76} + 12 q^{77} + 16 q^{78} - 5 q^{79} + 5 q^{81} - 64 q^{82} + 12 q^{84} + 12 q^{86} + 2 q^{87} + 4 q^{88} - 3 q^{89} + 22 q^{91} - 34 q^{92} + 6 q^{93} - 20 q^{96} + 14 q^{97} + 36 q^{98} - 2 q^{99}+O(q^{100}) \) 5 * q - 5 * q^3 + 10 * q^4 - 10 * q^7 + 5 * q^9 - 2 * q^11 - 10 * q^12 - 7 * q^13 - 8 * q^14 + 8 * q^16 + 10 * q^17 + 2 * q^19 + 10 * q^21 + 4 * q^22 - 3 * q^23 - 16 * q^26 - 5 * q^27 - 12 * q^28 - 2 * q^29 - 6 * q^31 + 20 * q^32 + 2 * q^33 - 20 * q^34 + 10 * q^36 - 8 * q^37 + 8 * q^38 + 7 * q^39 + 8 * q^42 - 13 * q^43 + 4 * q^44 - 12 * q^46 - 5 * q^47 - 8 * q^48 + 13 * q^49 - 10 * q^51 - 34 * q^52 + 10 * q^53 - 28 * q^56 - 2 * q^57 + 4 * q^58 - 11 * q^59 + 11 * q^61 - 16 * q^62 - 10 * q^63 - 20 * q^64 - 4 * q^66 - 24 * q^67 + 20 * q^68 + 3 * q^69 - 11 * q^71 - 17 * q^73 + 12 * q^74 - 24 * q^76 + 12 * q^77 + 16 * q^78 - 5 * q^79 + 5 * q^81 - 64 * q^82 + 12 * q^84 + 12 * q^86 + 2 * q^87 + 4 * q^88 - 3 * q^89 + 22 * q^91 - 34 * q^92 + 6 * q^93 - 20 * q^96 + 14 * q^97 + 36 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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