LMFDB - Embedded newform 9025.2.a.o.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)

$f(q)$	$=$	$q-2.23607 q^{2} -2.00000 q^{3} +3.00000 q^{4} +4.47214 q^{6} +3.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23607 q^{2} -2.00000 q^{3} +3.00000 q^{4} +4.47214 q^{6} +3.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +0.763932 q^{11} -6.00000 q^{12} -4.85410 q^{13} -7.23607 q^{14} -1.00000 q^{16} +1.61803 q^{17} -2.23607 q^{18} -6.47214 q^{21} -1.70820 q^{22} -4.47214 q^{23} +4.47214 q^{24} +10.8541 q^{26} +4.00000 q^{27} +9.70820 q^{28} -4.09017 q^{29} -6.00000 q^{31} +6.70820 q^{32} -1.52786 q^{33} -3.61803 q^{34} +3.00000 q^{36} -2.14590 q^{37} +9.70820 q^{39} -7.09017 q^{41} +14.4721 q^{42} -8.47214 q^{43} +2.29180 q^{44} +10.0000 q^{46} -9.23607 q^{47} +2.00000 q^{48} +3.47214 q^{49} -3.23607 q^{51} -14.5623 q^{52} -11.0902 q^{53} -8.94427 q^{54} -7.23607 q^{56} +9.14590 q^{58} -1.23607 q^{59} +3.14590 q^{61} +13.4164 q^{62} +3.23607 q^{63} -13.0000 q^{64} +3.41641 q^{66} -8.47214 q^{67} +4.85410 q^{68} +8.94427 q^{69} +1.23607 q^{71} -2.23607 q^{72} -5.56231 q^{73} +4.79837 q^{74} +2.47214 q^{77} -21.7082 q^{78} +2.00000 q^{79} -11.0000 q^{81} +15.8541 q^{82} -3.70820 q^{83} -19.4164 q^{84} +18.9443 q^{86} +8.18034 q^{87} -1.70820 q^{88} +8.32624 q^{89} -15.7082 q^{91} -13.4164 q^{92} +12.0000 q^{93} +20.6525 q^{94} -13.4164 q^{96} -0.0901699 q^{97} -7.76393 q^{98} +0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	3.00000	1.50000
$5$	0	0
$5$	0	0
$6$	4.47214	1.82574
$7$	3.23607	1.22312	0.611559	−	0.791199i	$-0.290543\pi$
$7$	3.23607	1.22312	0.611559	+	0.791199i	$0.290543\pi$
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	0	0
$11$	0.763932	0.230334	0.115167	−	0.993346i	$-0.463260\pi$
$11$	0.763932	0.230334	0.115167	+	0.993346i	$0.463260\pi$
$12$	−6.00000	−1.73205
$13$	−4.85410	−1.34629	−0.673143	−	0.739512i	$-0.735056\pi$
$13$	−4.85410	−1.34629	−0.673143	+	0.739512i	$0.735056\pi$
$14$	−7.23607	−1.93392
$15$	0	0
$16$	−1.00000	−0.250000
$17$	1.61803	0.392431	0.196215	−	0.980561i	$-0.437135\pi$
$17$	1.61803	0.392431	0.196215	+	0.980561i	$0.437135\pi$
$18$	−2.23607	−0.527046
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−6.47214	−1.41234
$22$	−1.70820	−0.364190
$23$	−4.47214	−0.932505	−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214	−0.932505	−0.466252	+	0.884652i	$0.654396\pi$
$24$	4.47214	0.912871
$25$	0	0
$26$	10.8541	2.12866
$27$	4.00000	0.769800
$28$	9.70820	1.83468
$29$	−4.09017	−0.759525	−0.379763	−	0.925084i	$-0.623994\pi$
$29$	−4.09017	−0.759525	−0.379763	+	0.925084i	$0.623994\pi$
$30$	0	0
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	6.70820	1.18585
$33$	−1.52786	−0.265967
$34$	−3.61803	−0.620488
$35$	0	0
$36$	3.00000	0.500000
$37$	−2.14590	−0.352783	−0.176392	−	0.984320i	$-0.556443\pi$
$37$	−2.14590	−0.352783	−0.176392	+	0.984320i	$0.556443\pi$
$38$	0	0
$39$	9.70820	1.55456
$40$	0	0
$41$	−7.09017	−1.10730	−0.553649	−	0.832750i	$-0.686765\pi$
$41$	−7.09017	−1.10730	−0.553649	+	0.832750i	$0.686765\pi$
$42$	14.4721	2.23310
$43$	−8.47214	−1.29199	−0.645994	−	0.763342i	$-0.723557\pi$
$43$	−8.47214	−1.29199	−0.645994	+	0.763342i	$0.723557\pi$
$44$	2.29180	0.345501
$45$	0	0
$46$	10.0000	1.47442
$47$	−9.23607	−1.34722	−0.673609	−	0.739087i	$-0.735257\pi$
$47$	−9.23607	−1.34722	−0.673609	+	0.739087i	$0.735257\pi$
$48$	2.00000	0.288675
$49$	3.47214	0.496019
$50$	0	0
$51$	−3.23607	−0.453140
$52$	−14.5623	−2.01943
$53$	−11.0902	−1.52335	−0.761676	−	0.647958i	$-0.775623\pi$
$53$	−11.0902	−1.52335	−0.761676	+	0.647958i	$0.775623\pi$
$54$	−8.94427	−1.21716
$55$	0	0
$56$	−7.23607	−0.966960
$57$	0	0
$58$	9.14590	1.20092
$59$	−1.23607	−0.160922	−0.0804612	−	0.996758i	$-0.525639\pi$
$59$	−1.23607	−0.160922	−0.0804612	+	0.996758i	$0.525639\pi$
$60$	0	0
$61$	3.14590	0.402791	0.201395	−	0.979510i	$-0.435452\pi$
$61$	3.14590	0.402791	0.201395	+	0.979510i	$0.435452\pi$
$62$	13.4164	1.70389
$63$	3.23607	0.407706
$64$	−13.0000	−1.62500
$65$	0	0
$66$	3.41641	0.420531
$67$	−8.47214	−1.03504	−0.517518	−	0.855672i	$-0.673144\pi$
$67$	−8.47214	−1.03504	−0.517518	+	0.855672i	$0.673144\pi$
$68$	4.85410	0.588646
$69$	8.94427	1.07676
$70$	0	0
$71$	1.23607	0.146694	0.0733471	−	0.997306i	$-0.476632\pi$
$71$	1.23607	0.146694	0.0733471	+	0.997306i	$0.476632\pi$
$72$	−2.23607	−0.263523
$73$	−5.56231	−0.651019	−0.325509	−	0.945539i	$-0.605536\pi$
$73$	−5.56231	−0.651019	−0.325509	+	0.945539i	$0.605536\pi$
$74$	4.79837	0.557800
$75$	0	0
$76$	0	0
$77$	2.47214	0.281726
$78$	−21.7082	−2.45797
$79$	2.00000	0.225018	0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000	0.225018	0.112509	+	0.993651i	$0.464111\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	15.8541	1.75079
$83$	−3.70820	−0.407028	−0.203514	−	0.979072i	$-0.565236\pi$
$83$	−3.70820	−0.407028	−0.203514	+	0.979072i	$0.565236\pi$
$84$	−19.4164	−2.11850
$85$	0	0
$86$	18.9443	2.04281
$87$	8.18034	0.877024
$88$	−1.70820	−0.182095
$89$	8.32624	0.882579	0.441290	−	0.897365i	$-0.354521\pi$
$89$	8.32624	0.882579	0.441290	+	0.897365i	$0.354521\pi$
$90$	0	0
$91$	−15.7082	−1.64667
$92$	−13.4164	−1.39876
$93$	12.0000	1.24434
$94$	20.6525	2.13014
$95$	0	0
$96$	−13.4164	−1.36931
$97$	−0.0901699	−0.00915537	−0.00457769	−	0.999990i	$-0.501457\pi$
$97$	−0.0901699	−0.00915537	−0.00457769	+	0.999990i	$0.501457\pi$
$98$	−7.76393	−0.784276
$99$	0.763932	0.0767781
$100$	0	0
$101$	16.3262	1.62452	0.812261	−	0.583295i	$-0.198237\pi$
$101$	16.3262	1.62452	0.812261	+	0.583295i	$0.198237\pi$
$102$	7.23607	0.716477
$103$	5.70820	0.562446	0.281223	−	0.959642i	$-0.409260\pi$
$103$	5.70820	0.562446	0.281223	+	0.959642i	$0.409260\pi$
$104$	10.8541	1.06433
$105$	0	0
$106$	24.7984	2.40863
$107$	−5.23607	−0.506190	−0.253095	−	0.967441i	$-0.581448\pi$
$107$	−5.23607	−0.506190	−0.253095	+	0.967441i	$0.581448\pi$
$108$	12.0000	1.15470
$109$	−0.909830	−0.0871459	−0.0435730	−	0.999050i	$-0.513874\pi$
$109$	−0.909830	−0.0871459	−0.0435730	+	0.999050i	$0.513874\pi$
$110$	0	0
$111$	4.29180	0.407359
$112$	−3.23607	−0.305780
$113$	16.8541	1.58550	0.792750	−	0.609547i	$-0.208648\pi$
$113$	16.8541	1.58550	0.792750	+	0.609547i	$0.208648\pi$
$114$	0	0
$115$	0	0
$116$	−12.2705	−1.13929
$117$	−4.85410	−0.448762
$118$	2.76393	0.254441
$119$	5.23607	0.479990
$120$	0	0
$121$	−10.4164	−0.946946
$122$	−7.03444	−0.636868
$123$	14.1803	1.27860
$124$	−18.0000	−1.61645
$125$	0	0
$126$	−7.23607	−0.644640
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	15.6525	1.38350
$129$	16.9443	1.49186
$130$	0	0
$131$	8.29180	0.724458	0.362229	−	0.932089i	$-0.382016\pi$
$131$	8.29180	0.724458	0.362229	+	0.932089i	$0.382016\pi$
$132$	−4.58359	−0.398950
$133$	0	0
$134$	18.9443	1.63654
$135$	0	0
$136$	−3.61803	−0.310244
$137$	22.7984	1.94780	0.973898	−	0.226985i	$-0.0728868\pi$
$137$	22.7984	1.94780	0.973898	+	0.226985i	$0.0728868\pi$
$138$	−20.0000	−1.70251
$139$	0.291796	0.0247498	0.0123749	−	0.999923i	$-0.496061\pi$
$139$	0.291796	0.0247498	0.0123749	+	0.999923i	$0.496061\pi$
$140$	0	0
$141$	18.4721	1.55563
$142$	−2.76393	−0.231944
$143$	−3.70820	−0.310096
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	12.4377	1.02935
$147$	−6.94427	−0.572754
$148$	−6.43769	−0.529175
$149$	−4.85410	−0.397664	−0.198832	−	0.980034i	$-0.563715\pi$
$149$	−4.85410	−0.397664	−0.198832	+	0.980034i	$0.563715\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	1.61803	0.130810
$154$	−5.52786	−0.445448
$155$	0	0
$156$	29.1246	2.33184
$157$	−21.0344	−1.67873	−0.839366	−	0.543567i	$-0.817073\pi$
$157$	−21.0344	−1.67873	−0.839366	+	0.543567i	$0.817073\pi$
$158$	−4.47214	−0.355784
$159$	22.1803	1.75902
$160$	0	0
$161$	−14.4721	−1.14056
$162$	24.5967	1.93250
$163$	21.7082	1.70032	0.850159	−	0.526526i	$-0.176506\pi$
$163$	21.7082	1.70032	0.850159	+	0.526526i	$0.176506\pi$
$164$	−21.2705	−1.66095
$165$	0	0
$166$	8.29180	0.643568
$167$	9.23607	0.714708	0.357354	−	0.933969i	$-0.383679\pi$
$167$	9.23607	0.714708	0.357354	+	0.933969i	$0.383679\pi$
$168$	14.4721	1.11655
$169$	10.5623	0.812485
$170$	0	0
$171$	0	0
$172$	−25.4164	−1.93798
$173$	3.38197	0.257126	0.128563	−	0.991701i	$-0.458964\pi$
$173$	3.38197	0.257126	0.128563	+	0.991701i	$0.458964\pi$
$174$	−18.2918	−1.38670
$175$	0	0
$176$	−0.763932	−0.0575835
$177$	2.47214	0.185817
$178$	−18.6180	−1.39548
$179$	−3.05573	−0.228396	−0.114198	−	0.993458i	$-0.536430\pi$
$179$	−3.05573	−0.228396	−0.114198	+	0.993458i	$0.536430\pi$
$180$	0	0
$181$	−5.41641	−0.402598	−0.201299	−	0.979530i	$-0.564516\pi$
$181$	−5.41641	−0.402598	−0.201299	+	0.979530i	$0.564516\pi$
$182$	35.1246	2.60361
$183$	−6.29180	−0.465103
$184$	10.0000	0.737210
$185$	0	0
$186$	−26.8328	−1.96748
$187$	1.23607	0.0903902
$188$	−27.7082	−2.02083
$189$	12.9443	0.941557
$190$	0	0
$191$	−9.23607	−0.668298	−0.334149	−	0.942520i	$-0.608449\pi$
$191$	−9.23607	−0.668298	−0.334149	+	0.942520i	$0.608449\pi$
$192$	26.0000	1.87639
$193$	20.4721	1.47362	0.736808	−	0.676102i	$-0.236332\pi$
$193$	20.4721	1.47362	0.736808	+	0.676102i	$0.236332\pi$
$194$	0.201626	0.0144759
$195$	0	0
$196$	10.4164	0.744029
$197$	−5.03444	−0.358689	−0.179345	−	0.983786i	$-0.557398\pi$
$197$	−5.03444	−0.358689	−0.179345	+	0.983786i	$0.557398\pi$
$198$	−1.70820	−0.121397
$199$	4.94427	0.350490	0.175245	−	0.984525i	$-0.443928\pi$
$199$	4.94427	0.350490	0.175245	+	0.984525i	$0.443928\pi$
$200$	0	0
$201$	16.9443	1.19516
$202$	−36.5066	−2.56859
$203$	−13.2361	−0.928990
$204$	−9.70820	−0.679710
$205$	0	0
$206$	−12.7639	−0.889305
$207$	−4.47214	−0.310835
$208$	4.85410	0.336571
$209$	0	0
$210$	0	0
$211$	14.2918	0.983888	0.491944	−	0.870627i	$-0.336287\pi$
$211$	14.2918	0.983888	0.491944	+	0.870627i	$0.336287\pi$
$212$	−33.2705	−2.28503
$213$	−2.47214	−0.169388
$214$	11.7082	0.800356
$215$	0	0
$216$	−8.94427	−0.608581
$217$	−19.4164	−1.31807
$218$	2.03444	0.137790
$219$	11.1246	0.751732
$220$	0	0
$221$	−7.85410	−0.528324
$222$	−9.59675	−0.644092
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	21.7082	1.45044
$225$	0	0
$226$	−37.6869	−2.50690
$227$	−22.4721	−1.49153	−0.745764	−	0.666210i	$-0.767915\pi$
$227$	−22.4721	−1.49153	−0.745764	+	0.666210i	$0.767915\pi$
$228$	0	0
$229$	−20.9787	−1.38631	−0.693156	−	0.720787i	$-0.743780\pi$
$229$	−20.9787	−1.38631	−0.693156	+	0.720787i	$0.743780\pi$
$230$	0	0
$231$	−4.94427	−0.325309
$232$	9.14590	0.600458
$233$	4.09017	0.267956	0.133978	−	0.990984i	$-0.457225\pi$
$233$	4.09017	0.267956	0.133978	+	0.990984i	$0.457225\pi$
$234$	10.8541	0.709555
$235$	0	0
$236$	−3.70820	−0.241384
$237$	−4.00000	−0.259828
$238$	−11.7082	−0.758930
$239$	18.9443	1.22540	0.612702	−	0.790314i	$-0.290083\pi$
$239$	18.9443	1.22540	0.612702	+	0.790314i	$0.290083\pi$
$240$	0	0
$241$	−18.9443	−1.22031	−0.610154	−	0.792283i	$-0.708892\pi$
$241$	−18.9443	−1.22031	−0.610154	+	0.792283i	$0.708892\pi$
$242$	23.2918	1.49725
$243$	10.0000	0.641500
$244$	9.43769	0.604186
$245$	0	0
$246$	−31.7082	−2.02164
$247$	0	0
$248$	13.4164	0.851943
$249$	7.41641	0.469996
$250$	0	0
$251$	8.76393	0.553174	0.276587	−	0.960989i	$-0.410797\pi$
$251$	8.76393	0.553174	0.276587	+	0.960989i	$0.410797\pi$
$252$	9.70820	0.611559
$253$	−3.41641	−0.214788
$254$	−26.8328	−1.68364
$255$	0	0
$256$	−9.00000	−0.562500
$257$	23.0902	1.44033	0.720163	−	0.693805i	$-0.244067\pi$
$257$	23.0902	1.44033	0.720163	+	0.693805i	$0.244067\pi$
$258$	−37.8885	−2.35884
$259$	−6.94427	−0.431496
$260$	0	0
$261$	−4.09017	−0.253175
$262$	−18.5410	−1.14547
$263$	−30.1803	−1.86100	−0.930500	−	0.366293i	$-0.880627\pi$
$263$	−30.1803	−1.86100	−0.930500	+	0.366293i	$0.880627\pi$
$264$	3.41641	0.210265
$265$	0	0
$266$	0	0
$267$	−16.6525	−1.01911
$268$	−25.4164	−1.55255
$269$	25.7984	1.57295	0.786477	−	0.617619i	$-0.211903\pi$
$269$	25.7984	1.57295	0.786477	+	0.617619i	$0.211903\pi$
$270$	0	0
$271$	−16.6525	−1.01157	−0.505783	−	0.862661i	$-0.668796\pi$
$271$	−16.6525	−1.01157	−0.505783	+	0.862661i	$0.668796\pi$
$272$	−1.61803	−0.0981077
$273$	31.4164	1.90141
$274$	−50.9787	−3.07974
$275$	0	0
$276$	26.8328	1.61515
$277$	12.6180	0.758144	0.379072	−	0.925367i	$-0.376243\pi$
$277$	12.6180	0.758144	0.379072	+	0.925367i	$0.376243\pi$
$278$	−0.652476	−0.0391329
$279$	−6.00000	−0.359211
$280$	0	0
$281$	−7.90983	−0.471861	−0.235930	−	0.971770i	$-0.575814\pi$
$281$	−7.90983	−0.471861	−0.235930	+	0.971770i	$0.575814\pi$
$282$	−41.3050	−2.45967
$283$	4.58359	0.272466	0.136233	−	0.990677i	$-0.456500\pi$
$283$	4.58359	0.272466	0.136233	+	0.990677i	$0.456500\pi$
$284$	3.70820	0.220041
$285$	0	0
$286$	8.29180	0.490304
$287$	−22.9443	−1.35436
$288$	6.70820	0.395285
$289$	−14.3820	−0.845998
$290$	0	0
$291$	0.180340	0.0105717
$292$	−16.6869	−0.976528
$293$	1.41641	0.0827474	0.0413737	−	0.999144i	$-0.486827\pi$
$293$	1.41641	0.0827474	0.0413737	+	0.999144i	$0.486827\pi$
$294$	15.5279	0.905603
$295$	0	0
$296$	4.79837	0.278900
$297$	3.05573	0.177311
$298$	10.8541	0.628761
$299$	21.7082	1.25542
$300$	0	0
$301$	−27.4164	−1.58026
$302$	0	0
$303$	−32.6525	−1.87584
$304$	0	0
$305$	0	0
$306$	−3.61803	−0.206829
$307$	−24.4721	−1.39670	−0.698349	−	0.715757i	$-0.746082\pi$
$307$	−24.4721	−1.39670	−0.698349	+	0.715757i	$0.746082\pi$
$308$	7.41641	0.422589
$309$	−11.4164	−0.649457
$310$	0	0
$311$	19.2361	1.09078	0.545389	−	0.838183i	$-0.316382\pi$
$311$	19.2361	1.09078	0.545389	+	0.838183i	$0.316382\pi$
$312$	−21.7082	−1.22899
$313$	−20.9787	−1.18579	−0.592894	−	0.805281i	$-0.702015\pi$
$313$	−20.9787	−1.18579	−0.592894	+	0.805281i	$0.702015\pi$
$314$	47.0344	2.65431
$315$	0	0
$316$	6.00000	0.337526
$317$	−12.6180	−0.708699	−0.354350	−	0.935113i	$-0.615298\pi$
$317$	−12.6180	−0.708699	−0.354350	+	0.935113i	$0.615298\pi$
$318$	−49.5967	−2.78125
$319$	−3.12461	−0.174945
$320$	0	0
$321$	10.4721	0.584498
$322$	32.3607	1.80339
$323$	0	0
$324$	−33.0000	−1.83333
$325$	0	0
$326$	−48.5410	−2.68844
$327$	1.81966	0.100627
$328$	15.8541	0.875396
$329$	−29.8885	−1.64781
$330$	0	0
$331$	−28.1803	−1.54893	−0.774466	−	0.632616i	$-0.781981\pi$
$331$	−28.1803	−1.54893	−0.774466	+	0.632616i	$0.781981\pi$
$332$	−11.1246	−0.610542
$333$	−2.14590	−0.117594
$334$	−20.6525	−1.13005
$335$	0	0
$336$	6.47214	0.353084
$337$	32.9787	1.79647	0.898233	−	0.439521i	$-0.144852\pi$
$337$	32.9787	1.79647	0.898233	+	0.439521i	$0.144852\pi$
$338$	−23.6180	−1.28465
$339$	−33.7082	−1.83078
$340$	0	0
$341$	−4.58359	−0.248215
$342$	0	0
$343$	−11.4164	−0.616428
$344$	18.9443	1.02141
$345$	0	0
$346$	−7.56231	−0.406552
$347$	23.5967	1.26674	0.633370	−	0.773849i	$-0.281671\pi$
$347$	23.5967	1.26674	0.633370	+	0.773849i	$0.281671\pi$
$348$	24.5410	1.31554
$349$	−8.85410	−0.473949	−0.236975	−	0.971516i	$-0.576156\pi$
$349$	−8.85410	−0.473949	−0.236975	+	0.971516i	$0.576156\pi$
$350$	0	0
$351$	−19.4164	−1.03637
$352$	5.12461	0.273143
$353$	7.50658	0.399535	0.199767	−	0.979843i	$-0.435981\pi$
$353$	7.50658	0.399535	0.199767	+	0.979843i	$0.435981\pi$
$354$	−5.52786	−0.293803
$355$	0	0
$356$	24.9787	1.32387
$357$	−10.4721	−0.554244
$358$	6.83282	0.361126
$359$	8.29180	0.437624	0.218812	−	0.975767i	$-0.429782\pi$
$359$	8.29180	0.437624	0.218812	+	0.975767i	$0.429782\pi$
$360$	0	0
$361$	0	0
$362$	12.1115	0.636564
$363$	20.8328	1.09344
$364$	−47.1246	−2.47000
$365$	0	0
$366$	14.0689	0.735392
$367$	−4.58359	−0.239262	−0.119631	−	0.992818i	$-0.538171\pi$
$367$	−4.58359	−0.239262	−0.119631	+	0.992818i	$0.538171\pi$
$368$	4.47214	0.233126
$369$	−7.09017	−0.369100
$370$	0	0
$371$	−35.8885	−1.86324
$372$	36.0000	1.86651
$373$	18.5623	0.961120	0.480560	−	0.876962i	$-0.340433\pi$
$373$	18.5623	0.961120	0.480560	+	0.876962i	$0.340433\pi$
$374$	−2.76393	−0.142920
$375$	0	0
$376$	20.6525	1.06507
$377$	19.8541	1.02254
$378$	−28.9443	−1.48873
$379$	−13.8885	−0.713407	−0.356703	−	0.934218i	$-0.616099\pi$
$379$	−13.8885	−0.713407	−0.356703	+	0.934218i	$0.616099\pi$
$380$	0	0
$381$	−24.0000	−1.22956
$382$	20.6525	1.05667
$383$	24.7639	1.26538	0.632689	−	0.774406i	$-0.281951\pi$
$383$	24.7639	1.26538	0.632689	+	0.774406i	$0.281951\pi$
$384$	−31.3050	−1.59752
$385$	0	0
$386$	−45.7771	−2.32999
$387$	−8.47214	−0.430663
$388$	−0.270510	−0.0137331
$389$	19.1459	0.970736	0.485368	−	0.874310i	$-0.338686\pi$
$389$	19.1459	0.970736	0.485368	+	0.874310i	$0.338686\pi$
$390$	0	0
$391$	−7.23607	−0.365944
$392$	−7.76393	−0.392138
$393$	−16.5836	−0.836532
$394$	11.2574	0.567137
$395$	0	0
$396$	2.29180	0.115167
$397$	25.4164	1.27561	0.637806	−	0.770197i	$-0.279842\pi$
$397$	25.4164	1.27561	0.637806	+	0.770197i	$0.279842\pi$
$398$	−11.0557	−0.554174
$399$	0	0
$400$	0	0
$401$	1.41641	0.0707320	0.0353660	−	0.999374i	$-0.488740\pi$
$401$	1.41641	0.0707320	0.0353660	+	0.999374i	$0.488740\pi$
$402$	−37.8885	−1.88971
$403$	29.1246	1.45080
$404$	48.9787	2.43678
$405$	0	0
$406$	29.5967	1.46886
$407$	−1.63932	−0.0812581
$408$	7.23607	0.358239
$409$	13.2705	0.656184	0.328092	−	0.944646i	$-0.393594\pi$
$409$	13.2705	0.656184	0.328092	+	0.944646i	$0.393594\pi$
$410$	0	0
$411$	−45.5967	−2.24912
$412$	17.1246	0.843669
$413$	−4.00000	−0.196827
$414$	10.0000	0.491473
$415$	0	0
$416$	−32.5623	−1.59650
$417$	−0.583592	−0.0285786
$418$	0	0
$419$	31.4164	1.53479	0.767396	−	0.641173i	$-0.221552\pi$
$419$	31.4164	1.53479	0.767396	+	0.641173i	$0.221552\pi$
$420$	0	0
$421$	−2.79837	−0.136384	−0.0681922	−	0.997672i	$-0.521723\pi$
$421$	−2.79837	−0.136384	−0.0681922	+	0.997672i	$0.521723\pi$
$422$	−31.9574	−1.55566
$423$	−9.23607	−0.449073
$424$	24.7984	1.20432
$425$	0	0
$426$	5.52786	0.267826
$427$	10.1803	0.492661
$428$	−15.7082	−0.759285
$429$	7.41641	0.358068
$430$	0	0
$431$	−23.2361	−1.11924	−0.559621	−	0.828749i	$-0.689053\pi$
$431$	−23.2361	−1.11924	−0.559621	+	0.828749i	$0.689053\pi$
$432$	−4.00000	−0.192450
$433$	29.5623	1.42067	0.710337	−	0.703862i	$-0.248543\pi$
$433$	29.5623	1.42067	0.710337	+	0.703862i	$0.248543\pi$
$434$	43.4164	2.08405
$435$	0	0
$436$	−2.72949	−0.130719
$437$	0	0
$438$	−24.8754	−1.18859
$439$	10.0000	0.477274	0.238637	−	0.971109i	$-0.423299\pi$
$439$	10.0000	0.477274	0.238637	+	0.971109i	$0.423299\pi$
$440$	0	0
$441$	3.47214	0.165340
$442$	17.5623	0.835354
$443$	−25.4164	−1.20757	−0.603785	−	0.797147i	$-0.706341\pi$
$443$	−25.4164	−1.20757	−0.603785	+	0.797147i	$0.706341\pi$
$444$	12.8754	0.611039
$445$	0	0
$446$	−22.3607	−1.05881
$447$	9.70820	0.459182
$448$	−42.0689	−1.98757
$449$	20.4508	0.965135	0.482568	−	0.875859i	$-0.339704\pi$
$449$	20.4508	0.965135	0.482568	+	0.875859i	$0.339704\pi$
$450$	0	0
$451$	−5.41641	−0.255049
$452$	50.5623	2.37825
$453$	0	0
$454$	50.2492	2.35831
$455$	0	0
$456$	0	0
$457$	−11.0902	−0.518776	−0.259388	−	0.965773i	$-0.583521\pi$
$457$	−11.0902	−0.518776	−0.259388	+	0.965773i	$0.583521\pi$
$458$	46.9098	2.19195
$459$	6.47214	0.302093
$460$	0	0
$461$	8.47214	0.394587	0.197293	−	0.980344i	$-0.436785\pi$
$461$	8.47214	0.394587	0.197293	+	0.980344i	$0.436785\pi$
$462$	11.0557	0.514359
$463$	−12.2918	−0.571248	−0.285624	−	0.958342i	$-0.592201\pi$
$463$	−12.2918	−0.571248	−0.285624	+	0.958342i	$0.592201\pi$
$464$	4.09017	0.189881
$465$	0	0
$466$	−9.14590	−0.423676
$467$	−25.8885	−1.19798	−0.598989	−	0.800757i	$-0.704431\pi$
$467$	−25.8885	−1.19798	−0.598989	+	0.800757i	$0.704431\pi$
$468$	−14.5623	−0.673143
$469$	−27.4164	−1.26597
$470$	0	0
$471$	42.0689	1.93843
$472$	2.76393	0.127220
$473$	−6.47214	−0.297589
$474$	8.94427	0.410824
$475$	0	0
$476$	15.7082	0.719984
$477$	−11.0902	−0.507784
$478$	−42.3607	−1.93753
$479$	26.9443	1.23112	0.615558	−	0.788092i	$-0.288931\pi$
$479$	26.9443	1.23112	0.615558	+	0.788092i	$0.288931\pi$
$480$	0	0
$481$	10.4164	0.474947
$482$	42.3607	1.92948
$483$	28.9443	1.31701
$484$	−31.2492	−1.42042
$485$	0	0
$486$	−22.3607	−1.01430
$487$	−20.7639	−0.940904	−0.470452	−	0.882426i	$-0.655909\pi$
$487$	−20.7639	−0.940904	−0.470452	+	0.882426i	$0.655909\pi$
$488$	−7.03444	−0.318434
$489$	−43.4164	−1.96336
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	42.5410	1.91790
$493$	−6.61803	−0.298061
$494$	0	0
$495$	0	0
$496$	6.00000	0.269408
$497$	4.00000	0.179425
$498$	−16.5836	−0.743129
$499$	−2.76393	−0.123731	−0.0618653	−	0.998085i	$-0.519705\pi$
$499$	−2.76393	−0.123731	−0.0618653	+	0.998085i	$0.519705\pi$
$500$	0	0
$501$	−18.4721	−0.825274
$502$	−19.5967	−0.874646
$503$	−34.3607	−1.53207	−0.766033	−	0.642801i	$-0.777772\pi$
$503$	−34.3607	−1.53207	−0.766033	+	0.642801i	$0.777772\pi$
$504$	−7.23607	−0.322320
$505$	0	0
$506$	7.63932	0.339609
$507$	−21.1246	−0.938177
$508$	36.0000	1.59724
$509$	11.9098	0.527894	0.263947	−	0.964537i	$-0.414976\pi$
$509$	11.9098	0.527894	0.263947	+	0.964537i	$0.414976\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	−11.1803	−0.494106
$513$	0	0
$514$	−51.6312	−2.27735
$515$	0	0
$516$	50.8328	2.23779
$517$	−7.05573	−0.310311
$518$	15.5279	0.682255
$519$	−6.76393	−0.296904
$520$	0	0
$521$	2.56231	0.112257	0.0561283	−	0.998424i	$-0.482124\pi$
$521$	2.56231	0.112257	0.0561283	+	0.998424i	$0.482124\pi$
$522$	9.14590	0.400305
$523$	−15.4164	−0.674112	−0.337056	−	0.941485i	$-0.609431\pi$
$523$	−15.4164	−0.674112	−0.337056	+	0.941485i	$0.609431\pi$
$524$	24.8754	1.08669
$525$	0	0
$526$	67.4853	2.94250
$527$	−9.70820	−0.422896
$528$	1.52786	0.0664917
$529$	−3.00000	−0.130435
$530$	0	0
$531$	−1.23607	−0.0536408
$532$	0	0
$533$	34.4164	1.49074
$534$	37.2361	1.61136
$535$	0	0
$536$	18.9443	0.818268
$537$	6.11146	0.263729
$538$	−57.6869	−2.48706
$539$	2.65248	0.114250
$540$	0	0
$541$	19.1459	0.823146	0.411573	−	0.911377i	$-0.364979\pi$
$541$	19.1459	0.823146	0.411573	+	0.911377i	$0.364979\pi$
$542$	37.2361	1.59943
$543$	10.8328	0.464881
$544$	10.8541	0.465366
$545$	0	0
$546$	−70.2492	−3.00639
$547$	9.23607	0.394906	0.197453	−	0.980312i	$-0.436733\pi$
$547$	9.23607	0.394906	0.197453	+	0.980312i	$0.436733\pi$
$548$	68.3951	2.92169
$549$	3.14590	0.134264
$550$	0	0
$551$	0	0
$552$	−20.0000	−0.851257
$553$	6.47214	0.275223
$554$	−28.2148	−1.19873
$555$	0	0
$556$	0.875388	0.0371247
$557$	19.5279	0.827422	0.413711	−	0.910408i	$-0.364232\pi$
$557$	19.5279	0.827422	0.413711	+	0.910408i	$0.364232\pi$
$558$	13.4164	0.567962
$559$	41.1246	1.73939
$560$	0	0
$561$	−2.47214	−0.104374
$562$	17.6869	0.746078
$563$	−34.6525	−1.46043	−0.730214	−	0.683219i	$-0.760580\pi$
$563$	−34.6525	−1.46043	−0.730214	+	0.683219i	$0.760580\pi$
$564$	55.4164	2.33345
$565$	0	0
$566$	−10.2492	−0.430807
$567$	−35.5967	−1.49492
$568$	−2.76393	−0.115972
$569$	−24.6180	−1.03204	−0.516021	−	0.856576i	$-0.672587\pi$
$569$	−24.6180	−1.03204	−0.516021	+	0.856576i	$0.672587\pi$
$570$	0	0
$571$	−2.29180	−0.0959087	−0.0479543	−	0.998850i	$-0.515270\pi$
$571$	−2.29180	−0.0959087	−0.0479543	+	0.998850i	$0.515270\pi$
$572$	−11.1246	−0.465143
$573$	18.4721	0.771685
$574$	51.3050	2.14143
$575$	0	0
$576$	−13.0000	−0.541667
$577$	−2.38197	−0.0991625	−0.0495813	−	0.998770i	$-0.515789\pi$
$577$	−2.38197	−0.0991625	−0.0495813	+	0.998770i	$0.515789\pi$
$578$	32.1591	1.33764
$579$	−40.9443	−1.70159
$580$	0	0
$581$	−12.0000	−0.497844
$582$	−0.403252	−0.0167153
$583$	−8.47214	−0.350880
$584$	12.4377	0.514675
$585$	0	0
$586$	−3.16718	−0.130835
$587$	7.23607	0.298664	0.149332	−	0.988787i	$-0.452288\pi$
$587$	7.23607	0.298664	0.149332	+	0.988787i	$0.452288\pi$
$588$	−20.8328	−0.859131
$589$	0	0
$590$	0	0
$591$	10.0689	0.414179
$592$	2.14590	0.0881959
$593$	−22.1459	−0.909423	−0.454712	−	0.890639i	$-0.650258\pi$
$593$	−22.1459	−0.909423	−0.454712	+	0.890639i	$0.650258\pi$
$594$	−6.83282	−0.280354
$595$	0	0
$596$	−14.5623	−0.596495
$597$	−9.88854	−0.404711
$598$	−48.5410	−1.98499
$599$	17.0557	0.696878	0.348439	−	0.937331i	$-0.386712\pi$
$599$	17.0557	0.696878	0.348439	+	0.937331i	$0.386712\pi$
$600$	0	0
$601$	−6.00000	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$602$	61.3050	2.49860
$603$	−8.47214	−0.345012
$604$	0	0
$605$	0	0
$606$	73.0132	2.96596
$607$	8.58359	0.348397	0.174199	−	0.984711i	$-0.444267\pi$
$607$	8.58359	0.348397	0.174199	+	0.984711i	$0.444267\pi$
$608$	0	0
$609$	26.4721	1.07271
$610$	0	0
$611$	44.8328	1.81374
$612$	4.85410	0.196215
$613$	−13.2705	−0.535991	−0.267995	−	0.963420i	$-0.586361\pi$
$613$	−13.2705	−0.535991	−0.267995	+	0.963420i	$0.586361\pi$
$614$	54.7214	2.20837
$615$	0	0
$616$	−5.52786	−0.222724
$617$	38.3607	1.54434	0.772171	−	0.635414i	$-0.219171\pi$
$617$	38.3607	1.54434	0.772171	+	0.635414i	$0.219171\pi$
$618$	25.5279	1.02688
$619$	−0.875388	−0.0351848	−0.0175924	−	0.999845i	$-0.505600\pi$
$619$	−0.875388	−0.0351848	−0.0175924	+	0.999845i	$0.505600\pi$
$620$	0	0
$621$	−17.8885	−0.717843
$622$	−43.0132	−1.72467
$623$	26.9443	1.07950
$624$	−9.70820	−0.388639
$625$	0	0
$626$	46.9098	1.87489
$627$	0	0
$628$	−63.1033	−2.51810
$629$	−3.47214	−0.138443
$630$	0	0
$631$	18.3607	0.730927	0.365464	−	0.930826i	$-0.380910\pi$
$631$	18.3607	0.730927	0.365464	+	0.930826i	$0.380910\pi$
$632$	−4.47214	−0.177892
$633$	−28.5836	−1.13610
$634$	28.2148	1.12055
$635$	0	0
$636$	66.5410	2.63852
$637$	−16.8541	−0.667784
$638$	6.98684	0.276612
$639$	1.23607	0.0488981
$640$	0	0
$641$	33.6180	1.32783	0.663916	−	0.747807i	$-0.268893\pi$
$641$	33.6180	1.32783	0.663916	+	0.747807i	$0.268893\pi$
$642$	−23.4164	−0.924172
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	−43.4164	−1.71085
$645$	0	0
$646$	0	0
$647$	7.59675	0.298659	0.149329	−	0.988787i	$-0.452288\pi$
$647$	7.59675	0.298659	0.149329	+	0.988787i	$0.452288\pi$
$648$	24.5967	0.966252
$649$	−0.944272	−0.0370659
$650$	0	0
$651$	38.8328	1.52198
$652$	65.1246	2.55048
$653$	−19.7426	−0.772589	−0.386295	−	0.922375i	$-0.626245\pi$
$653$	−19.7426	−0.772589	−0.386295	+	0.922375i	$0.626245\pi$
$654$	−4.06888	−0.159106
$655$	0	0
$656$	7.09017	0.276825
$657$	−5.56231	−0.217006
$658$	66.8328	2.60541
$659$	21.7082	0.845632	0.422816	−	0.906216i	$-0.361042\pi$
$659$	21.7082	0.845632	0.422816	+	0.906216i	$0.361042\pi$
$660$	0	0
$661$	15.8885	0.617993	0.308996	−	0.951063i	$-0.400007\pi$
$661$	15.8885	0.617993	0.308996	+	0.951063i	$0.400007\pi$
$662$	63.0132	2.44908
$663$	15.7082	0.610056
$664$	8.29180	0.321784
$665$	0	0
$666$	4.79837	0.185933
$667$	18.2918	0.708261
$668$	27.7082	1.07206
$669$	−20.0000	−0.773245
$670$	0	0
$671$	2.40325	0.0927765
$672$	−43.4164	−1.67482
$673$	−25.8541	−0.996602	−0.498301	−	0.867004i	$-0.666043\pi$
$673$	−25.8541	−0.996602	−0.498301	+	0.867004i	$0.666043\pi$
$674$	−73.7426	−2.84046
$675$	0	0
$676$	31.6869	1.21873
$677$	46.3394	1.78097	0.890484	−	0.455015i	$-0.150366\pi$
$677$	46.3394	1.78097	0.890484	+	0.455015i	$0.150366\pi$
$678$	75.3738	2.89471
$679$	−0.291796	−0.0111981
$680$	0	0
$681$	44.9443	1.72227
$682$	10.2492	0.392463
$683$	39.0132	1.49280	0.746398	−	0.665499i	$-0.231781\pi$
$683$	39.0132	1.49280	0.746398	+	0.665499i	$0.231781\pi$
$684$	0	0
$685$	0	0
$686$	25.5279	0.974658
$687$	41.9574	1.60078
$688$	8.47214	0.322997
$689$	53.8328	2.05087
$690$	0	0
$691$	−46.5410	−1.77050	−0.885252	−	0.465112i	$-0.846014\pi$
$691$	−46.5410	−1.77050	−0.885252	+	0.465112i	$0.846014\pi$
$692$	10.1459	0.385689
$693$	2.47214	0.0939087
$694$	−52.7639	−2.00289
$695$	0	0
$696$	−18.2918	−0.693349
$697$	−11.4721	−0.434538
$698$	19.7984	0.749380
$699$	−8.18034	−0.309409
$700$	0	0
$701$	1.85410	0.0700285	0.0350142	−	0.999387i	$-0.488852\pi$
$701$	1.85410	0.0700285	0.0350142	+	0.999387i	$0.488852\pi$
$702$	43.4164	1.63865
$703$	0	0
$704$	−9.93112	−0.374293
$705$	0	0
$706$	−16.7852	−0.631720
$707$	52.8328	1.98698
$708$	7.41641	0.278726
$709$	−26.1591	−0.982424	−0.491212	−	0.871040i	$-0.663446\pi$
$709$	−26.1591	−0.982424	−0.491212	+	0.871040i	$0.663446\pi$
$710$	0	0
$711$	2.00000	0.0750059
$712$	−18.6180	−0.697740
$713$	26.8328	1.00490
$714$	23.4164	0.876337
$715$	0	0
$716$	−9.16718	−0.342594
$717$	−37.8885	−1.41497
$718$	−18.5410	−0.691945
$719$	−31.3050	−1.16748	−0.583739	−	0.811941i	$-0.698411\pi$
$719$	−31.3050	−1.16748	−0.583739	+	0.811941i	$0.698411\pi$
$720$	0	0
$721$	18.4721	0.687938
$722$	0	0
$723$	37.8885	1.40909
$724$	−16.2492	−0.603898
$725$	0	0
$726$	−46.5836	−1.72888
$727$	−11.1246	−0.412589	−0.206295	−	0.978490i	$-0.566140\pi$
$727$	−11.1246	−0.412589	−0.206295	+	0.978490i	$0.566140\pi$
$728$	35.1246	1.30180
$729$	13.0000	0.481481
$730$	0	0
$731$	−13.7082	−0.507016
$732$	−18.8754	−0.697654
$733$	−3.72949	−0.137752	−0.0688759	−	0.997625i	$-0.521941\pi$
$733$	−3.72949	−0.137752	−0.0688759	+	0.997625i	$0.521941\pi$
$734$	10.2492	0.378306
$735$	0	0
$736$	−30.0000	−1.10581
$737$	−6.47214	−0.238404
$738$	15.8541	0.583598
$739$	37.7082	1.38712	0.693559	−	0.720399i	$-0.256042\pi$
$739$	37.7082	1.38712	0.693559	+	0.720399i	$0.256042\pi$
$740$	0	0
$741$	0	0
$742$	80.2492	2.94604
$743$	19.4164	0.712319	0.356159	−	0.934425i	$-0.384086\pi$
$743$	19.4164	0.712319	0.356159	+	0.934425i	$0.384086\pi$
$744$	−26.8328	−0.983739
$745$	0	0
$746$	−41.5066	−1.51966
$747$	−3.70820	−0.135676
$748$	3.70820	0.135585
$749$	−16.9443	−0.619130
$750$	0	0
$751$	−5.41641	−0.197648	−0.0988238	−	0.995105i	$-0.531508\pi$
$751$	−5.41641	−0.197648	−0.0988238	+	0.995105i	$0.531508\pi$
$752$	9.23607	0.336805
$753$	−17.5279	−0.638751
$754$	−44.3951	−1.61677
$755$	0	0
$756$	38.8328	1.41234
$757$	−31.5066	−1.14513	−0.572563	−	0.819861i	$-0.694051\pi$
$757$	−31.5066	−1.14513	−0.572563	+	0.819861i	$0.694051\pi$
$758$	31.0557	1.12799
$759$	6.83282	0.248015
$760$	0	0
$761$	15.8885	0.575959	0.287980	−	0.957637i	$-0.407016\pi$
$761$	15.8885	0.575959	0.287980	+	0.957637i	$0.407016\pi$
$762$	53.6656	1.94410
$763$	−2.94427	−0.106590
$764$	−27.7082	−1.00245
$765$	0	0
$766$	−55.3738	−2.00074
$767$	6.00000	0.216647
$768$	18.0000	0.649519
$769$	−37.8541	−1.36505	−0.682527	−	0.730860i	$-0.739119\pi$
$769$	−37.8541	−1.36505	−0.682527	+	0.730860i	$0.739119\pi$
$770$	0	0
$771$	−46.1803	−1.66314
$772$	61.4164	2.21042
$773$	−32.6312	−1.17366	−0.586831	−	0.809709i	$-0.699625\pi$
$773$	−32.6312	−1.17366	−0.586831	+	0.809709i	$0.699625\pi$
$774$	18.9443	0.680938
$775$	0	0
$776$	0.201626	0.00723796
$777$	13.8885	0.498249
$778$	−42.8115	−1.53487
$779$	0	0
$780$	0	0
$781$	0.944272	0.0337887
$782$	16.1803	0.578608
$783$	−16.3607	−0.584683
$784$	−3.47214	−0.124005
$785$	0	0
$786$	37.0820	1.32267
$787$	−1.23607	−0.0440611	−0.0220305	−	0.999757i	$-0.507013\pi$
$787$	−1.23607	−0.0440611	−0.0220305	+	0.999757i	$0.507013\pi$
$788$	−15.1033	−0.538034
$789$	60.3607	2.14890
$790$	0	0
$791$	54.5410	1.93926
$792$	−1.70820	−0.0606984
$793$	−15.2705	−0.542272
$794$	−56.8328	−2.01692
$795$	0	0
$796$	14.8328	0.525735
$797$	19.5066	0.690958	0.345479	−	0.938426i	$-0.387716\pi$
$797$	19.5066	0.690958	0.345479	+	0.938426i	$0.387716\pi$
$798$	0	0
$799$	−14.9443	−0.528690
$800$	0	0
$801$	8.32624	0.294193
$802$	−3.16718	−0.111837
$803$	−4.24922	−0.149952
$804$	50.8328	1.79274
$805$	0	0
$806$	−65.1246	−2.29392
$807$	−51.5967	−1.81629
$808$	−36.5066	−1.28430
$809$	28.0344	0.985638	0.492819	−	0.870132i	$-0.335966\pi$
$809$	28.0344	0.985638	0.492819	+	0.870132i	$0.335966\pi$
$810$	0	0
$811$	26.0000	0.912983	0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000	0.912983	0.456492	+	0.889728i	$0.349106\pi$
$812$	−39.7082	−1.39348
$813$	33.3050	1.16806
$814$	3.66563	0.128480
$815$	0	0
$816$	3.23607	0.113285
$817$	0	0
$818$	−29.6738	−1.03752
$819$	−15.7082	−0.548889
$820$	0	0
$821$	−10.7426	−0.374921	−0.187460	−	0.982272i	$-0.560026\pi$
$821$	−10.7426	−0.374921	−0.187460	+	0.982272i	$0.560026\pi$
$822$	101.957	3.55617
$823$	44.6525	1.55649	0.778244	−	0.627962i	$-0.216111\pi$
$823$	44.6525	1.55649	0.778244	+	0.627962i	$0.216111\pi$
$824$	−12.7639	−0.444653
$825$	0	0
$826$	8.94427	0.311211
$827$	−44.8328	−1.55899	−0.779495	−	0.626409i	$-0.784524\pi$
$827$	−44.8328	−1.55899	−0.779495	+	0.626409i	$0.784524\pi$
$828$	−13.4164	−0.466252
$829$	16.9787	0.589695	0.294848	−	0.955544i	$-0.404731\pi$
$829$	16.9787	0.589695	0.294848	+	0.955544i	$0.404731\pi$
$830$	0	0
$831$	−25.2361	−0.875429
$832$	63.1033	2.18771
$833$	5.61803	0.194653
$834$	1.30495	0.0451868
$835$	0	0
$836$	0	0
$837$	−24.0000	−0.829561
$838$	−70.2492	−2.42672
$839$	−23.1246	−0.798350	−0.399175	−	0.916875i	$-0.630703\pi$
$839$	−23.1246	−0.798350	−0.399175	+	0.916875i	$0.630703\pi$
$840$	0	0
$841$	−12.2705	−0.423121
$842$	6.25735	0.215643
$843$	15.8197	0.544858
$844$	42.8754	1.47583
$845$	0	0
$846$	20.6525	0.710047
$847$	−33.7082	−1.15823
$848$	11.0902	0.380838
$849$	−9.16718	−0.314617
$850$	0	0
$851$	9.59675	0.328972
$852$	−7.41641	−0.254082
$853$	−9.61803	−0.329315	−0.164658	−	0.986351i	$-0.552652\pi$
$853$	−9.61803	−0.329315	−0.164658	+	0.986351i	$0.552652\pi$
$854$	−22.7639	−0.778966
$855$	0	0
$856$	11.7082	0.400178
$857$	−31.1459	−1.06392	−0.531962	−	0.846768i	$-0.678545\pi$
$857$	−31.1459	−1.06392	−0.531962	+	0.846768i	$0.678545\pi$
$858$	−16.5836	−0.566155
$859$	49.4164	1.68607	0.843033	−	0.537862i	$-0.180768\pi$
$859$	49.4164	1.68607	0.843033	+	0.537862i	$0.180768\pi$
$860$	0	0
$861$	45.8885	1.56388
$862$	51.9574	1.76968
$863$	16.9443	0.576790	0.288395	−	0.957512i	$-0.406878\pi$
$863$	16.9443	0.576790	0.288395	+	0.957512i	$0.406878\pi$
$864$	26.8328	0.912871
$865$	0	0
$866$	−66.1033	−2.24628
$867$	28.7639	0.976874
$868$	−58.2492	−1.97711
$869$	1.52786	0.0518292
$870$	0	0
$871$	41.1246	1.39345
$872$	2.03444	0.0688949
$873$	−0.0901699	−0.00305179
$874$	0	0
$875$	0	0
$876$	33.3738	1.12760
$877$	10.5623	0.356664	0.178332	−	0.983970i	$-0.442930\pi$
$877$	10.5623	0.356664	0.178332	+	0.983970i	$0.442930\pi$
$878$	−22.3607	−0.754636
$879$	−2.83282	−0.0955485
$880$	0	0
$881$	−12.3262	−0.415282	−0.207641	−	0.978205i	$-0.566579\pi$
$881$	−12.3262	−0.415282	−0.207641	+	0.978205i	$0.566579\pi$
$882$	−7.76393	−0.261425
$883$	15.8885	0.534692	0.267346	−	0.963601i	$-0.413853\pi$
$883$	15.8885	0.534692	0.267346	+	0.963601i	$0.413853\pi$
$884$	−23.5623	−0.792486
$885$	0	0
$886$	56.8328	1.90934
$887$	35.4853	1.19148	0.595740	−	0.803178i	$-0.296859\pi$
$887$	35.4853	1.19148	0.595740	+	0.803178i	$0.296859\pi$
$888$	−9.59675	−0.322046
$889$	38.8328	1.30241
$890$	0	0
$891$	−8.40325	−0.281520
$892$	30.0000	1.00447
$893$	0	0
$894$	−21.7082	−0.726031
$895$	0	0
$896$	50.6525	1.69218
$897$	−43.4164	−1.44963
$898$	−45.7295	−1.52601
$899$	24.5410	0.818489
$900$	0	0
$901$	−17.9443	−0.597810
$902$	12.1115	0.403267
$903$	54.8328	1.82472
$904$	−37.6869	−1.25345
$905$	0	0
$906$	0	0
$907$	1.41641	0.0470311	0.0235155	−	0.999723i	$-0.492514\pi$
$907$	1.41641	0.0470311	0.0235155	+	0.999723i	$0.492514\pi$
$908$	−67.4164	−2.23729
$909$	16.3262	0.541507
$910$	0	0
$911$	−20.8328	−0.690222	−0.345111	−	0.938562i	$-0.612159\pi$
$911$	−20.8328	−0.690222	−0.345111	+	0.938562i	$0.612159\pi$
$912$	0	0
$913$	−2.83282	−0.0937525
$914$	24.7984	0.820257
$915$	0	0
$916$	−62.9361	−2.07947
$917$	26.8328	0.886098
$918$	−14.4721	−0.477652
$919$	−14.4721	−0.477392	−0.238696	−	0.971094i	$-0.576720\pi$
$919$	−14.4721	−0.477392	−0.238696	+	0.971094i	$0.576720\pi$
$920$	0	0
$921$	48.9443	1.61277
$922$	−18.9443	−0.623896
$923$	−6.00000	−0.197492
$924$	−14.8328	−0.487964
$925$	0	0
$926$	27.4853	0.903223
$927$	5.70820	0.187482
$928$	−27.4377	−0.900686
$929$	−51.8673	−1.70171	−0.850855	−	0.525401i	$-0.823915\pi$
$929$	−51.8673	−1.70171	−0.850855	+	0.525401i	$0.823915\pi$
$930$	0	0
$931$	0	0
$932$	12.2705	0.401934
$933$	−38.4721	−1.25952
$934$	57.8885	1.89417
$935$	0	0
$936$	10.8541	0.354777
$937$	−39.3050	−1.28404	−0.642018	−	0.766689i	$-0.721903\pi$
$937$	−39.3050	−1.28404	−0.642018	+	0.766689i	$0.721903\pi$
$938$	61.3050	2.00168
$939$	41.9574	1.36923
$940$	0	0
$941$	−36.4721	−1.18896	−0.594479	−	0.804111i	$-0.702642\pi$
$941$	−36.4721	−1.18896	−0.594479	+	0.804111i	$0.702642\pi$
$942$	−94.0689	−3.06493
$943$	31.7082	1.03256
$944$	1.23607	0.0402306
$945$	0	0
$946$	14.4721	0.470530
$947$	35.5967	1.15674	0.578369	−	0.815775i	$-0.303689\pi$
$947$	35.5967	1.15674	0.578369	+	0.815775i	$0.303689\pi$
$948$	−12.0000	−0.389742
$949$	27.0000	0.876457
$950$	0	0
$951$	25.2361	0.818336
$952$	−11.7082	−0.379465
$953$	−9.25735	−0.299875	−0.149938	−	0.988695i	$-0.547907\pi$
$953$	−9.25735	−0.299875	−0.149938	+	0.988695i	$0.547907\pi$
$954$	24.7984	0.802877
$955$	0	0
$956$	56.8328	1.83810
$957$	6.24922	0.202009
$958$	−60.2492	−1.94656
$959$	73.7771	2.38239
$960$	0	0
$961$	5.00000	0.161290
$962$	−23.2918	−0.750958
$963$	−5.23607	−0.168730
$964$	−56.8328	−1.83046
$965$	0	0
$966$	−64.7214	−2.08238
$967$	41.9574	1.34926	0.674630	−	0.738156i	$-0.264303\pi$
$967$	41.9574	1.34926	0.674630	+	0.738156i	$0.264303\pi$
$968$	23.2918	0.748627
$969$	0	0
$970$	0	0
$971$	−30.6525	−0.983685	−0.491842	−	0.870684i	$-0.663676\pi$
$971$	−30.6525	−0.983685	−0.491842	+	0.870684i	$0.663676\pi$
$972$	30.0000	0.962250
$973$	0.944272	0.0302720
$974$	46.4296	1.48770
$975$	0	0
$976$	−3.14590	−0.100698
$977$	10.5066	0.336135	0.168068	−	0.985775i	$-0.446247\pi$
$977$	10.5066	0.336135	0.168068	+	0.985775i	$0.446247\pi$
$978$	97.0820	3.10434
$979$	6.36068	0.203288
$980$	0	0
$981$	−0.909830	−0.0290486
$982$	−26.8328	−0.856270
$983$	55.9574	1.78476	0.892382	−	0.451280i	$-0.149032\pi$
$983$	55.9574	1.78476	0.892382	+	0.451280i	$0.149032\pi$
$984$	−31.7082	−1.01082
$985$	0	0
$986$	14.7984	0.471276
$987$	59.7771	1.90273
$988$	0	0
$989$	37.8885	1.20479
$990$	0	0
$991$	−10.8754	−0.345468	−0.172734	−	0.984969i	$-0.555260\pi$
$991$	−10.8754	−0.345468	−0.172734	+	0.984969i	$0.555260\pi$
$992$	−40.2492	−1.27791
$993$	56.3607	1.78855
$994$	−8.94427	−0.283695
$995$	0	0
$996$	22.2492	0.704994
$997$	11.0902	0.351229	0.175615	−	0.984459i	$-0.443809\pi$
$997$	11.0902	0.351229	0.175615	+	0.984459i	$0.443809\pi$
$998$	6.18034	0.195635
$999$	−8.58359	−0.271573

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} -2.00000 q^{3} +3.00000 q^{4} +4.47214 q^{6} +3.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} -2.00000 q^{3} +3.00000 q^{4} +4.47214 q^{6} +3.23607 q^{7} -2.23607 q^{8} +1.00000 q^{9} +0.763932 q^{11} -6.00000 q^{12} -4.85410 q^{13} -7.23607 q^{14} -1.00000 q^{16} +1.61803 q^{17} -2.23607 q^{18} -6.47214 q^{21} -1.70820 q^{22} -4.47214 q^{23} +4.47214 q^{24} +10.8541 q^{26} +4.00000 q^{27} +9.70820 q^{28} -4.09017 q^{29} -6.00000 q^{31} +6.70820 q^{32} -1.52786 q^{33} -3.61803 q^{34} +3.00000 q^{36} -2.14590 q^{37} +9.70820 q^{39} -7.09017 q^{41} +14.4721 q^{42} -8.47214 q^{43} +2.29180 q^{44} +10.0000 q^{46} -9.23607 q^{47} +2.00000 q^{48} +3.47214 q^{49} -3.23607 q^{51} -14.5623 q^{52} -11.0902 q^{53} -8.94427 q^{54} -7.23607 q^{56} +9.14590 q^{58} -1.23607 q^{59} +3.14590 q^{61} +13.4164 q^{62} +3.23607 q^{63} -13.0000 q^{64} +3.41641 q^{66} -8.47214 q^{67} +4.85410 q^{68} +8.94427 q^{69} +1.23607 q^{71} -2.23607 q^{72} -5.56231 q^{73} +4.79837 q^{74} +2.47214 q^{77} -21.7082 q^{78} +2.00000 q^{79} -11.0000 q^{81} +15.8541 q^{82} -3.70820 q^{83} -19.4164 q^{84} +18.9443 q^{86} +8.18034 q^{87} -1.70820 q^{88} +8.32624 q^{89} -15.7082 q^{91} -13.4164 q^{92} +12.0000 q^{93} +20.6525 q^{94} -13.4164 q^{96} -0.0901699 q^{97} -7.76393 q^{98} +0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} + 6 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 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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