LMFDB - Embedded newform 7225.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7225,2,Mod(1,7225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7225, 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("7225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.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:	$57.6919154604$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	7225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.17009 q^{2} +0.539189 q^{3} +2.70928 q^{4} -1.17009 q^{6} -4.87936 q^{7} -1.53919 q^{8} -2.70928 q^{9} +3.17009 q^{11} +1.46081 q^{12} -2.63090 q^{13} +10.5886 q^{14} -2.07838 q^{16} +5.87936 q^{18} -1.07838 q^{19} -2.63090 q^{21} -6.87936 q^{22} +5.21953 q^{23} -0.829914 q^{24} +5.70928 q^{26} -3.07838 q^{27} -13.2195 q^{28} -2.92162 q^{29} +4.09171 q^{31} +7.58864 q^{32} +1.70928 q^{33} -7.34017 q^{36} -5.26180 q^{37} +2.34017 q^{38} -1.41855 q^{39} +5.60197 q^{41} +5.70928 q^{42} +3.36910 q^{43} +8.58864 q^{44} -11.3268 q^{46} +6.78765 q^{47} -1.12064 q^{48} +16.8082 q^{49} -7.12783 q^{52} +3.75872 q^{53} +6.68035 q^{54} +7.51026 q^{56} -0.581449 q^{57} +6.34017 q^{58} +2.34017 q^{59} -12.2557 q^{61} -8.87936 q^{62} +13.2195 q^{63} -12.3112 q^{64} -3.70928 q^{66} -10.2062 q^{67} +2.81432 q^{69} +4.06505 q^{71} +4.17009 q^{72} -11.0784 q^{73} +11.4186 q^{74} -2.92162 q^{76} -15.4680 q^{77} +3.07838 q^{78} -6.92881 q^{79} +6.46800 q^{81} -12.1568 q^{82} +8.23287 q^{83} -7.12783 q^{84} -7.31124 q^{86} -1.57531 q^{87} -4.87936 q^{88} +7.15449 q^{89} +12.8371 q^{91} +14.1412 q^{92} +2.20620 q^{93} -14.7298 q^{94} +4.09171 q^{96} +8.18342 q^{97} -36.4752 q^{98} -8.58864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + q^{4} + 2 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} + 4 q^{11} + 6 q^{12} - 4 q^{13} + 12 q^{14} - 3 q^{16} + 5 q^{18} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 10 q^{26} - 6 q^{27} - 16 q^{28}+ \cdots - 6 q^{99}+O(q^{100}) $ 3 * q - q^2 + q^4 + 2 * q^6 - 2 * q^7 - 3 * q^8 - q^9 + 4 * q^11 + 6 * q^12 - 4 * q^13 + 12 * q^14 - 3 * q^16 + 5 * q^18 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 10 * q^26 - 6 * q^27 - 16 * q^28 - 12 * q^29 + 10 * q^31 + 3 * q^32 - 2 * q^33 - 11 * q^36 - 8 * q^37 - 4 * q^38 + 10 * q^39 - 2 * q^41 + 10 * q^42 + 14 * q^43 + 6 * q^44 - 22 * q^46 + 10 * q^47 - 16 * q^48 + 7 * q^49 - 14 * q^53 - 2 * q^54 + 6 * q^56 - 16 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^61 - 14 * q^62 + 16 * q^63 - 11 * q^64 - 4 * q^66 - 6 * q^67 + 8 * q^71 + 7 * q^72 - 30 * q^73 + 20 * q^74 - 12 * q^76 - 14 * q^77 + 6 * q^78 + 10 * q^79 - 13 * q^81 - 30 * q^82 + 2 * q^83 + 4 * q^86 + 16 * q^87 - 2 * q^88 + 2 * q^89 + 10 * q^91 + 22 * q^92 - 18 * q^93 - 4 * q^94 + 10 * q^96 + 20 * q^97 - 43 * q^98 - 6 * q^99

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 $

$2$	−2.17009	−1.53448	−0.767241	−	0.641358i	$-0.778371\pi$
$2$	−2.17009	−1.53448	−0.767241	+	0.641358i	$0.778371\pi$
$3$	0.539189	0.311301	0.155650	−	0.987812i	$-0.450253\pi$
$3$	0.539189	0.311301	0.155650	+	0.987812i	$0.450253\pi$
$4$	2.70928	1.35464
$5$	0	0
$5$	0	0
$6$	−1.17009	−0.477686
$7$	−4.87936	−1.84423	−0.922113	−	0.386921i	$-0.873538\pi$
$7$	−4.87936	−1.84423	−0.922113	+	0.386921i	$0.873538\pi$
$8$	−1.53919	−0.544185
$9$	−2.70928	−0.903092
$10$	0	0
$11$	3.17009	0.955817	0.477909	−	0.878410i	$-0.341395\pi$
$11$	3.17009	0.955817	0.477909	+	0.878410i	$0.341395\pi$
$12$	1.46081	0.421700
$13$	−2.63090	−0.729680	−0.364840	−	0.931070i	$-0.618876\pi$
$13$	−2.63090	−0.729680	−0.364840	+	0.931070i	$0.618876\pi$
$14$	10.5886	2.82993
$15$	0	0
$16$	−2.07838	−0.519594
$17$	0	0
$17$	0	0
$18$	5.87936	1.38578
$19$	−1.07838	−0.247397	−0.123698	−	0.992320i	$-0.539476\pi$
$19$	−1.07838	−0.247397	−0.123698	+	0.992320i	$0.539476\pi$
$20$	0	0
$21$	−2.63090	−0.574109
$22$	−6.87936	−1.46668
$23$	5.21953	1.08835	0.544174	−	0.838972i	$-0.316843\pi$
$23$	5.21953	1.08835	0.544174	+	0.838972i	$0.316843\pi$
$24$	−0.829914	−0.169405
$25$	0	0
$26$	5.70928	1.11968
$27$	−3.07838	−0.592434
$28$	−13.2195	−2.49826
$29$	−2.92162	−0.542532	−0.271266	−	0.962504i	$-0.587442\pi$
$29$	−2.92162	−0.542532	−0.271266	+	0.962504i	$0.587442\pi$
$30$	0	0
$31$	4.09171	0.734893	0.367446	−	0.930045i	$-0.380232\pi$
$31$	4.09171	0.734893	0.367446	+	0.930045i	$0.380232\pi$
$32$	7.58864	1.34149
$33$	1.70928	0.297547
$34$	0	0
$35$	0	0
$36$	−7.34017	−1.22336
$37$	−5.26180	−0.865034	−0.432517	−	0.901626i	$-0.642374\pi$
$37$	−5.26180	−0.865034	−0.432517	+	0.901626i	$0.642374\pi$
$38$	2.34017	0.379626
$39$	−1.41855	−0.227150
$40$	0	0
$41$	5.60197	0.874880	0.437440	−	0.899247i	$-0.355885\pi$
$41$	5.60197	0.874880	0.437440	+	0.899247i	$0.355885\pi$
$42$	5.70928	0.880960
$43$	3.36910	0.513783	0.256892	−	0.966440i	$-0.417302\pi$
$43$	3.36910	0.513783	0.256892	+	0.966440i	$0.417302\pi$
$44$	8.58864	1.29479
$45$	0	0
$46$	−11.3268	−1.67005
$47$	6.78765	0.990081	0.495040	−	0.868870i	$-0.335153\pi$
$47$	6.78765	0.990081	0.495040	+	0.868870i	$0.335153\pi$
$48$	−1.12064	−0.161750
$49$	16.8082	2.40117
$50$	0	0
$51$	0	0
$52$	−7.12783	−0.988452
$53$	3.75872	0.516300	0.258150	−	0.966105i	$-0.416887\pi$
$53$	3.75872	0.516300	0.258150	+	0.966105i	$0.416887\pi$
$54$	6.68035	0.909080
$55$	0	0
$56$	7.51026	1.00360
$57$	−0.581449	−0.0770148
$58$	6.34017	0.832505
$59$	2.34017	0.304665	0.152332	−	0.988329i	$-0.451322\pi$
$59$	2.34017	0.304665	0.152332	+	0.988329i	$0.451322\pi$
$60$	0	0
$61$	−12.2557	−1.56918	−0.784588	−	0.620018i	$-0.787125\pi$
$61$	−12.2557	−1.56918	−0.784588	+	0.620018i	$0.787125\pi$
$62$	−8.87936	−1.12768
$63$	13.2195	1.66550
$64$	−12.3112	−1.53891
$65$	0	0
$66$	−3.70928	−0.456580
$67$	−10.2062	−1.24689	−0.623443	−	0.781869i	$-0.714267\pi$
$67$	−10.2062	−1.24689	−0.623443	+	0.781869i	$0.714267\pi$
$68$	0	0
$69$	2.81432	0.338804
$70$	0	0
$71$	4.06505	0.482432	0.241216	−	0.970471i	$-0.422454\pi$
$71$	4.06505	0.482432	0.241216	+	0.970471i	$0.422454\pi$
$72$	4.17009	0.491449
$73$	−11.0784	−1.29663	−0.648313	−	0.761374i	$-0.724525\pi$
$73$	−11.0784	−1.29663	−0.648313	+	0.761374i	$0.724525\pi$
$74$	11.4186	1.32738
$75$	0	0
$76$	−2.92162	−0.335133
$77$	−15.4680	−1.76274
$78$	3.07838	0.348558
$79$	−6.92881	−0.779552	−0.389776	−	0.920910i	$-0.627448\pi$
$79$	−6.92881	−0.779552	−0.389776	+	0.920910i	$0.627448\pi$
$80$	0	0
$81$	6.46800	0.718667
$82$	−12.1568	−1.34249
$83$	8.23287	0.903674	0.451837	−	0.892100i	$-0.350769\pi$
$83$	8.23287	0.903674	0.451837	+	0.892100i	$0.350769\pi$
$84$	−7.12783	−0.777710
$85$	0	0
$86$	−7.31124	−0.788392
$87$	−1.57531	−0.168891
$88$	−4.87936	−0.520142
$89$	7.15449	0.758374	0.379187	−	0.925320i	$-0.376204\pi$
$89$	7.15449	0.758374	0.379187	+	0.925320i	$0.376204\pi$
$90$	0	0
$91$	12.8371	1.34569
$92$	14.1412	1.47432
$93$	2.20620	0.228773
$94$	−14.7298	−1.51926
$95$	0	0
$96$	4.09171	0.417608
$97$	8.18342	0.830900	0.415450	−	0.909616i	$-0.363624\pi$
$97$	8.18342	0.830900	0.415450	+	0.909616i	$0.363624\pi$
$98$	−36.4752	−3.68455
$99$	−8.58864	−0.863191
$100$	0	0
$101$	−2.47414	−0.246186	−0.123093	−	0.992395i	$-0.539281\pi$
$101$	−2.47414	−0.246186	−0.123093	+	0.992395i	$0.539281\pi$
$102$	0	0
$103$	19.6514	1.93631	0.968156	−	0.250348i	$-0.0805452\pi$
$103$	19.6514	1.93631	0.968156	+	0.250348i	$0.0805452\pi$
$104$	4.04945	0.397081
$105$	0	0
$106$	−8.15676	−0.792254
$107$	12.6381	1.22177	0.610885	−	0.791719i	$-0.290814\pi$
$107$	12.6381	1.22177	0.610885	+	0.791719i	$0.290814\pi$
$108$	−8.34017	−0.802534
$109$	8.15676	0.781275	0.390638	−	0.920544i	$-0.372255\pi$
$109$	8.15676	0.781275	0.390638	+	0.920544i	$0.372255\pi$
$110$	0	0
$111$	−2.83710	−0.269286
$112$	10.1412	0.958249
$113$	17.0205	1.60116	0.800578	−	0.599229i	$-0.204526\pi$
$113$	17.0205	1.60116	0.800578	+	0.599229i	$0.204526\pi$
$114$	1.26180	0.118178
$115$	0	0
$116$	−7.91548	−0.734934
$117$	7.12783	0.658968
$118$	−5.07838	−0.467503
$119$	0	0
$120$	0	0
$121$	−0.950552	−0.0864138
$122$	26.5958	2.40787
$123$	3.02052	0.272351
$124$	11.0856	0.995513
$125$	0	0
$126$	−28.6875	−2.55569
$127$	−8.04945	−0.714273	−0.357137	−	0.934052i	$-0.616247\pi$
$127$	−8.04945	−0.714273	−0.357137	+	0.934052i	$0.616247\pi$
$128$	11.5392	1.01993
$129$	1.81658	0.159941
$130$	0	0
$131$	11.6937	1.02168	0.510841	−	0.859675i	$-0.329334\pi$
$131$	11.6937	1.02168	0.510841	+	0.859675i	$0.329334\pi$
$132$	4.63090	0.403068
$133$	5.26180	0.456256
$134$	22.1483	1.91333
$135$	0	0
$136$	0	0
$137$	−1.95055	−0.166647	−0.0833234	−	0.996523i	$-0.526553\pi$
$137$	−1.95055	−0.166647	−0.0833234	+	0.996523i	$0.526553\pi$
$138$	−6.10731	−0.519889
$139$	−2.00719	−0.170247	−0.0851237	−	0.996370i	$-0.527129\pi$
$139$	−2.00719	−0.170247	−0.0851237	+	0.996370i	$0.527129\pi$
$140$	0	0
$141$	3.65983	0.308213
$142$	−8.82150	−0.740284
$143$	−8.34017	−0.697440
$144$	5.63090	0.469241
$145$	0	0
$146$	24.0410	1.98965
$147$	9.06278	0.747485
$148$	−14.2557	−1.17181
$149$	−14.2823	−1.17005	−0.585026	−	0.811014i	$-0.698916\pi$
$149$	−14.2823	−1.17005	−0.585026	+	0.811014i	$0.698916\pi$
$150$	0	0
$151$	−12.8638	−1.04684	−0.523419	−	0.852075i	$-0.675344\pi$
$151$	−12.8638	−1.04684	−0.523419	+	0.852075i	$0.675344\pi$
$152$	1.65983	0.134630
$153$	0	0
$154$	33.5669	2.70490
$155$	0	0
$156$	−3.84324	−0.307706
$157$	−3.75872	−0.299979	−0.149989	−	0.988688i	$-0.547924\pi$
$157$	−3.75872	−0.299979	−0.149989	+	0.988688i	$0.547924\pi$
$158$	15.0361	1.19621
$159$	2.02666	0.160725
$160$	0	0
$161$	−25.4680	−2.00716
$162$	−14.0361	−1.10278
$163$	−8.69594	−0.681119	−0.340559	−	0.940223i	$-0.610616\pi$
$163$	−8.69594	−0.681119	−0.340559	+	0.940223i	$0.610616\pi$
$164$	15.1773	1.18515
$165$	0	0
$166$	−17.8660	−1.38667
$167$	−1.37629	−0.106501	−0.0532503	−	0.998581i	$-0.516958\pi$
$167$	−1.37629	−0.106501	−0.0532503	+	0.998581i	$0.516958\pi$
$168$	4.04945	0.312422
$169$	−6.07838	−0.467568
$170$	0	0
$171$	2.92162	0.223422
$172$	9.12783	0.695990
$173$	17.3607	1.31991	0.659954	−	0.751306i	$-0.270576\pi$
$173$	17.3607	1.31991	0.659954	+	0.751306i	$0.270576\pi$
$174$	3.41855	0.259160
$175$	0	0
$176$	−6.58864	−0.496637
$177$	1.26180	0.0948423
$178$	−15.5259	−1.16371
$179$	−6.83710	−0.511029	−0.255514	−	0.966805i	$-0.582245\pi$
$179$	−6.83710	−0.511029	−0.255514	+	0.966805i	$0.582245\pi$
$180$	0	0
$181$	−15.0205	−1.11647	−0.558233	−	0.829684i	$-0.688521\pi$
$181$	−15.0205	−1.11647	−0.558233	+	0.829684i	$0.688521\pi$
$182$	−27.8576	−2.06494
$183$	−6.60811	−0.488486
$184$	−8.03385	−0.592263
$185$	0	0
$186$	−4.78765	−0.351048
$187$	0	0
$188$	18.3896	1.34120
$189$	15.0205	1.09258
$190$	0	0
$191$	−24.2823	−1.75701	−0.878503	−	0.477736i	$-0.841457\pi$
$191$	−24.2823	−1.75701	−0.878503	+	0.477736i	$0.841457\pi$
$192$	−6.63809	−0.479063
$193$	−11.8576	−0.853530	−0.426765	−	0.904363i	$-0.640347\pi$
$193$	−11.8576	−0.853530	−0.426765	+	0.904363i	$0.640347\pi$
$194$	−17.7587	−1.27500
$195$	0	0
$196$	45.5380	3.25271
$197$	−18.2557	−1.30066	−0.650331	−	0.759651i	$-0.725370\pi$
$197$	−18.2557	−1.30066	−0.650331	+	0.759651i	$0.725370\pi$
$198$	18.6381	1.32455
$199$	3.72487	0.264049	0.132025	−	0.991246i	$-0.457852\pi$
$199$	3.72487	0.264049	0.132025	+	0.991246i	$0.457852\pi$
$200$	0	0
$201$	−5.50307	−0.388157
$202$	5.36910	0.377769
$203$	14.2557	1.00055
$204$	0	0
$205$	0	0
$206$	−42.6453	−2.97124
$207$	−14.1412	−0.982878
$208$	5.46800	0.379138
$209$	−3.41855	−0.236466
$210$	0	0
$211$	22.2485	1.53165	0.765824	−	0.643051i	$-0.222332\pi$
$211$	22.2485	1.53165	0.765824	+	0.643051i	$0.222332\pi$
$212$	10.1834	0.699400
$213$	2.19183	0.150182
$214$	−27.4257	−1.87478
$215$	0	0
$216$	4.73820	0.322394
$217$	−19.9649	−1.35531
$218$	−17.7009	−1.19885
$219$	−5.97334	−0.403641
$220$	0	0
$221$	0	0
$222$	6.15676	0.413214
$223$	−2.19183	−0.146776	−0.0733878	−	0.997303i	$-0.523381\pi$
$223$	−2.19183	−0.146776	−0.0733878	+	0.997303i	$0.523381\pi$
$224$	−37.0277	−2.47402
$225$	0	0
$226$	−36.9360	−2.45695
$227$	9.55971	0.634500	0.317250	−	0.948342i	$-0.397241\pi$
$227$	9.55971	0.634500	0.317250	+	0.948342i	$0.397241\pi$
$228$	−1.57531	−0.104327
$229$	−7.36910	−0.486964	−0.243482	−	0.969905i	$-0.578290\pi$
$229$	−7.36910	−0.486964	−0.243482	+	0.969905i	$0.578290\pi$
$230$	0	0
$231$	−8.34017	−0.548743
$232$	4.49693	0.295238
$233$	−9.44521	−0.618776	−0.309388	−	0.950936i	$-0.600124\pi$
$233$	−9.44521	−0.618776	−0.309388	+	0.950936i	$0.600124\pi$
$234$	−15.4680	−1.01117
$235$	0	0
$236$	6.34017	0.412710
$237$	−3.73594	−0.242675
$238$	0	0
$239$	6.25565	0.404644	0.202322	−	0.979319i	$-0.435151\pi$
$239$	6.25565	0.404644	0.202322	+	0.979319i	$0.435151\pi$
$240$	0	0
$241$	−2.49693	−0.160841	−0.0804207	−	0.996761i	$-0.525626\pi$
$241$	−2.49693	−0.160841	−0.0804207	+	0.996761i	$0.525626\pi$
$242$	2.06278	0.132600
$243$	12.7226	0.816156
$244$	−33.2039	−2.12566
$245$	0	0
$246$	−6.55479	−0.417918
$247$	2.83710	0.180520
$248$	−6.29791	−0.399918
$249$	4.43907	0.281315
$250$	0	0
$251$	−11.8166	−0.745856	−0.372928	−	0.927860i	$-0.621646\pi$
$251$	−11.8166	−0.745856	−0.372928	+	0.927860i	$0.621646\pi$
$252$	35.8154	2.25616
$253$	16.5464	1.04026
$254$	17.4680	1.09604
$255$	0	0
$256$	−0.418551	−0.0261594
$257$	14.9444	0.932207	0.466103	−	0.884730i	$-0.345658\pi$
$257$	14.9444	0.932207	0.466103	+	0.884730i	$0.345658\pi$
$258$	−3.94214	−0.245427
$259$	25.6742	1.59532
$260$	0	0
$261$	7.91548	0.489956
$262$	−25.3763	−1.56775
$263$	−12.9444	−0.798186	−0.399093	−	0.916910i	$-0.630675\pi$
$263$	−12.9444	−0.798186	−0.399093	+	0.916910i	$0.630675\pi$
$264$	−2.63090	−0.161921
$265$	0	0
$266$	−11.4186	−0.700116
$267$	3.85762	0.236083
$268$	−27.6514	−1.68908
$269$	−7.47641	−0.455845	−0.227922	−	0.973679i	$-0.573193\pi$
$269$	−7.47641	−0.455845	−0.227922	+	0.973679i	$0.573193\pi$
$270$	0	0
$271$	−2.15676	−0.131014	−0.0655068	−	0.997852i	$-0.520866\pi$
$271$	−2.15676	−0.131014	−0.0655068	+	0.997852i	$0.520866\pi$
$272$	0	0
$273$	6.92162	0.418916
$274$	4.23287	0.255717
$275$	0	0
$276$	7.62475	0.458956
$277$	−12.1568	−0.730429	−0.365214	−	0.930923i	$-0.619004\pi$
$277$	−12.1568	−0.730429	−0.365214	+	0.930923i	$0.619004\pi$
$278$	4.35577	0.261242
$279$	−11.0856	−0.663675
$280$	0	0
$281$	−13.1194	−0.782639	−0.391319	−	0.920255i	$-0.627981\pi$
$281$	−13.1194	−0.782639	−0.391319	+	0.920255i	$0.627981\pi$
$282$	−7.94214	−0.472948
$283$	−13.9577	−0.829701	−0.414851	−	0.909889i	$-0.636166\pi$
$283$	−13.9577	−0.829701	−0.414851	+	0.909889i	$0.636166\pi$
$284$	11.0133	0.653521
$285$	0	0
$286$	18.0989	1.07021
$287$	−27.3340	−1.61348
$288$	−20.5597	−1.21149
$289$	0	0
$290$	0	0
$291$	4.41241	0.258660
$292$	−30.0144	−1.75646
$293$	−4.73820	−0.276809	−0.138404	−	0.990376i	$-0.544197\pi$
$293$	−4.73820	−0.276809	−0.138404	+	0.990376i	$0.544197\pi$
$294$	−19.6670	−1.14700
$295$	0	0
$296$	8.09890	0.470739
$297$	−9.75872	−0.566259
$298$	30.9939	1.79543
$299$	−13.7321	−0.794146
$300$	0	0
$301$	−16.4391	−0.947532
$302$	27.9155	1.60636
$303$	−1.33403	−0.0766380
$304$	2.24128	0.128546
$305$	0	0
$306$	0	0
$307$	21.5936	1.23241	0.616205	−	0.787586i	$-0.288669\pi$
$307$	21.5936	1.23241	0.616205	+	0.787586i	$0.288669\pi$
$308$	−41.9071	−2.38788
$309$	10.5958	0.602775
$310$	0	0
$311$	24.2628	1.37582	0.687910	−	0.725796i	$-0.258528\pi$
$311$	24.2628	1.37582	0.687910	+	0.725796i	$0.258528\pi$
$312$	2.18342	0.123612
$313$	4.07223	0.230176	0.115088	−	0.993355i	$-0.463285\pi$
$313$	4.07223	0.230176	0.115088	+	0.993355i	$0.463285\pi$
$314$	8.15676	0.460312
$315$	0	0
$316$	−18.7721	−1.05601
$317$	8.05786	0.452574	0.226287	−	0.974061i	$-0.427341\pi$
$317$	8.05786	0.452574	0.226287	+	0.974061i	$0.427341\pi$
$318$	−4.39803	−0.246629
$319$	−9.26180	−0.518561
$320$	0	0
$321$	6.81432	0.380338
$322$	55.2678	3.07995
$323$	0	0
$324$	17.5236	0.973533
$325$	0	0
$326$	18.8710	1.04517
$327$	4.39803	0.243212
$328$	−8.62249	−0.476097
$329$	−33.1194	−1.82593
$330$	0	0
$331$	10.0722	0.553620	0.276810	−	0.960925i	$-0.410723\pi$
$331$	10.0722	0.553620	0.276810	+	0.960925i	$0.410723\pi$
$332$	22.3051	1.22415
$333$	14.2557	0.781205
$334$	2.98667	0.163423
$335$	0	0
$336$	5.46800	0.298304
$337$	11.2351	0.612017	0.306008	−	0.952029i	$-0.401006\pi$
$337$	11.2351	0.612017	0.306008	+	0.952029i	$0.401006\pi$
$338$	13.1906	0.717474
$339$	9.17727	0.498441
$340$	0	0
$341$	12.9711	0.702423
$342$	−6.34017	−0.342837
$343$	−47.8576	−2.58407
$344$	−5.18568	−0.279593
$345$	0	0
$346$	−37.6742	−2.02538
$347$	−8.74927	−0.469685	−0.234843	−	0.972033i	$-0.575457\pi$
$347$	−8.74927	−0.469685	−0.234843	+	0.972033i	$0.575457\pi$
$348$	−4.26794	−0.228786
$349$	26.9093	1.44042	0.720212	−	0.693754i	$-0.244045\pi$
$349$	26.9093	1.44042	0.720212	+	0.693754i	$0.244045\pi$
$350$	0	0
$351$	8.09890	0.432287
$352$	24.0566	1.28222
$353$	−18.3135	−0.974730	−0.487365	−	0.873198i	$-0.662042\pi$
$353$	−18.3135	−0.974730	−0.487365	+	0.873198i	$0.662042\pi$
$354$	−2.73820	−0.145534
$355$	0	0
$356$	19.3835	1.02732
$357$	0	0
$358$	14.8371	0.784165
$359$	9.57531	0.505365	0.252683	−	0.967549i	$-0.418687\pi$
$359$	9.57531	0.505365	0.252683	+	0.967549i	$0.418687\pi$
$360$	0	0
$361$	−17.8371	−0.938795
$362$	32.5958	1.71320
$363$	−0.512527	−0.0269007
$364$	34.7792	1.82293
$365$	0	0
$366$	14.3402	0.749573
$367$	12.1145	0.632371	0.316186	−	0.948697i	$-0.397598\pi$
$367$	12.1145	0.632371	0.316186	+	0.948697i	$0.397598\pi$
$368$	−10.8482	−0.565500
$369$	−15.1773	−0.790097
$370$	0	0
$371$	−18.3402	−0.952174
$372$	5.97721	0.309904
$373$	−30.4619	−1.57726	−0.788628	−	0.614871i	$-0.789208\pi$
$373$	−30.4619	−1.57726	−0.788628	+	0.614871i	$0.789208\pi$
$374$	0	0
$375$	0	0
$376$	−10.4475	−0.538788
$377$	7.68649	0.395874
$378$	−32.5958	−1.67655
$379$	−0.986669	−0.0506818	−0.0253409	−	0.999679i	$-0.508067\pi$
$379$	−0.986669	−0.0506818	−0.0253409	+	0.999679i	$0.508067\pi$
$380$	0	0
$381$	−4.34017	−0.222354
$382$	52.6947	2.69610
$383$	−24.9588	−1.27533	−0.637667	−	0.770312i	$-0.720100\pi$
$383$	−24.9588	−1.27533	−0.637667	+	0.770312i	$0.720100\pi$
$384$	6.22180	0.317505
$385$	0	0
$386$	25.7321	1.30973
$387$	−9.12783	−0.463993
$388$	22.1711	1.12557
$389$	−33.8082	−1.71414	−0.857071	−	0.515198i	$-0.827718\pi$
$389$	−33.8082	−1.71414	−0.857071	+	0.515198i	$0.827718\pi$
$390$	0	0
$391$	0	0
$392$	−25.8710	−1.30668
$393$	6.30510	0.318050
$394$	39.6163	1.99584
$395$	0	0
$396$	−23.2690	−1.16931
$397$	28.5236	1.43156	0.715779	−	0.698327i	$-0.246072\pi$
$397$	28.5236	1.43156	0.715779	+	0.698327i	$0.246072\pi$
$398$	−8.08330	−0.405179
$399$	2.83710	0.142033
$400$	0	0
$401$	33.0928	1.65257	0.826287	−	0.563250i	$-0.190449\pi$
$401$	33.0928	1.65257	0.826287	+	0.563250i	$0.190449\pi$
$402$	11.9421	0.595620
$403$	−10.7649	−0.536236
$404$	−6.70313	−0.333493
$405$	0	0
$406$	−30.9360	−1.53533
$407$	−16.6803	−0.826814
$408$	0	0
$409$	−30.1978	−1.49318	−0.746592	−	0.665282i	$-0.768311\pi$
$409$	−30.1978	−1.49318	−0.746592	+	0.665282i	$0.768311\pi$
$410$	0	0
$411$	−1.05172	−0.0518773
$412$	53.2411	2.62300
$413$	−11.4186	−0.561870
$414$	30.6875	1.50821
$415$	0	0
$416$	−19.9649	−0.978861
$417$	−1.08225	−0.0529982
$418$	7.41855	0.362853
$419$	−18.1639	−0.887367	−0.443683	−	0.896184i	$-0.646329\pi$
$419$	−18.1639	−0.887367	−0.443683	+	0.896184i	$0.646329\pi$
$420$	0	0
$421$	0.760991	0.0370884	0.0185442	−	0.999828i	$-0.494097\pi$
$421$	0.760991	0.0370884	0.0185442	+	0.999828i	$0.494097\pi$
$422$	−48.2811	−2.35029
$423$	−18.3896	−0.894134
$424$	−5.78539	−0.280963
$425$	0	0
$426$	−4.75646	−0.230451
$427$	59.7998	2.89391
$428$	34.2401	1.65506
$429$	−4.49693	−0.217114
$430$	0	0
$431$	−6.34736	−0.305742	−0.152871	−	0.988246i	$-0.548852\pi$
$431$	−6.34736	−0.305742	−0.152871	+	0.988246i	$0.548852\pi$
$432$	6.39803	0.307825
$433$	3.62475	0.174195	0.0870973	−	0.996200i	$-0.472241\pi$
$433$	3.62475	0.174195	0.0870973	+	0.996200i	$0.472241\pi$
$434$	43.3256	2.07970
$435$	0	0
$436$	22.0989	1.05835
$437$	−5.62863	−0.269254
$438$	12.9627	0.619380
$439$	−6.40522	−0.305704	−0.152852	−	0.988249i	$-0.548846\pi$
$439$	−6.40522	−0.305704	−0.152852	+	0.988249i	$0.548846\pi$
$440$	0	0
$441$	−45.5380	−2.16847
$442$	0	0
$443$	−27.4824	−1.30573	−0.652864	−	0.757476i	$-0.726432\pi$
$443$	−27.4824	−1.30573	−0.652864	+	0.757476i	$0.726432\pi$
$444$	−7.68649	−0.364785
$445$	0	0
$446$	4.75646	0.225225
$447$	−7.70086	−0.364238
$448$	60.0710	2.83809
$449$	28.7526	1.35692	0.678459	−	0.734638i	$-0.262648\pi$
$449$	28.7526	1.35692	0.678459	+	0.734638i	$0.262648\pi$
$450$	0	0
$451$	17.7587	0.836226
$452$	46.1133	2.16899
$453$	−6.93600	−0.325882
$454$	−20.7454	−0.973630
$455$	0	0
$456$	0.894960	0.0419104
$457$	−31.4101	−1.46930	−0.734652	−	0.678444i	$-0.762655\pi$
$457$	−31.4101	−1.46930	−0.734652	+	0.678444i	$0.762655\pi$
$458$	15.9916	0.747238
$459$	0	0
$460$	0	0
$461$	7.75872	0.361360	0.180680	−	0.983542i	$-0.442170\pi$
$461$	7.75872	0.361360	0.180680	+	0.983542i	$0.442170\pi$
$462$	18.0989	0.842037
$463$	−24.2329	−1.12620	−0.563098	−	0.826390i	$-0.690391\pi$
$463$	−24.2329	−1.12620	−0.563098	+	0.826390i	$0.690391\pi$
$464$	6.07223	0.281896
$465$	0	0
$466$	20.4969	0.949502
$467$	−12.3174	−0.569981	−0.284990	−	0.958530i	$-0.591990\pi$
$467$	−12.3174	−0.569981	−0.284990	+	0.958530i	$0.591990\pi$
$468$	19.3112	0.892663
$469$	49.7998	2.29954
$470$	0	0
$471$	−2.02666	−0.0933837
$472$	−3.60197	−0.165794
$473$	10.6803	0.491083
$474$	8.10731	0.372381
$475$	0	0
$476$	0	0
$477$	−10.1834	−0.466267
$478$	−13.5753	−0.620920
$479$	2.14957	0.0982162	0.0491081	−	0.998793i	$-0.484362\pi$
$479$	2.14957	0.0982162	0.0491081	+	0.998793i	$0.484362\pi$
$480$	0	0
$481$	13.8432	0.631198
$482$	5.41855	0.246808
$483$	−13.7321	−0.624830
$484$	−2.57531	−0.117059
$485$	0	0
$486$	−27.6092	−1.25238
$487$	−40.0833	−1.81635	−0.908174	−	0.418593i	$-0.862523\pi$
$487$	−40.0833	−1.81635	−0.908174	+	0.418593i	$0.862523\pi$
$488$	18.8638	0.853922
$489$	−4.68876	−0.212033
$490$	0	0
$491$	2.25565	0.101796	0.0508981	−	0.998704i	$-0.483792\pi$
$491$	2.25565	0.101796	0.0508981	+	0.998704i	$0.483792\pi$
$492$	8.18342	0.368937
$493$	0	0
$494$	−6.15676	−0.277006
$495$	0	0
$496$	−8.50412	−0.381846
$497$	−19.8348	−0.889714
$498$	−9.63317	−0.431672
$499$	42.5452	1.90458	0.952291	−	0.305190i	$-0.0987201\pi$
$499$	42.5452	1.90458	0.952291	+	0.305190i	$0.0987201\pi$
$500$	0	0
$501$	−0.742080	−0.0331537
$502$	25.6430	1.14450
$503$	−9.55971	−0.426246	−0.213123	−	0.977025i	$-0.568364\pi$
$503$	−9.55971	−0.426246	−0.213123	+	0.977025i	$0.568364\pi$
$504$	−20.3474	−0.906343
$505$	0	0
$506$	−35.9071	−1.59626
$507$	−3.27739	−0.145554
$508$	−21.8082	−0.967581
$509$	28.3545	1.25679	0.628397	−	0.777893i	$-0.283712\pi$
$509$	28.3545	1.25679	0.628397	+	0.777893i	$0.283712\pi$
$510$	0	0
$511$	54.0554	2.39127
$512$	−22.1701	−0.979789
$513$	3.31965	0.146566
$514$	−32.4307	−1.43046
$515$	0	0
$516$	4.92162	0.216662
$517$	21.5174	0.946336
$518$	−55.7152	−2.44799
$519$	9.36069	0.410889
$520$	0	0
$521$	−15.1050	−0.661764	−0.330882	−	0.943672i	$-0.607346\pi$
$521$	−15.1050	−0.661764	−0.330882	+	0.943672i	$0.607346\pi$
$522$	−17.1773	−0.751829
$523$	10.8865	0.476036	0.238018	−	0.971261i	$-0.423502\pi$
$523$	10.8865	0.476036	0.238018	+	0.971261i	$0.423502\pi$
$524$	31.6814	1.38401
$525$	0	0
$526$	28.0905	1.22480
$527$	0	0
$528$	−3.55252	−0.154604
$529$	4.24354	0.184502
$530$	0	0
$531$	−6.34017	−0.275140
$532$	14.2557	0.618061
$533$	−14.7382	−0.638383
$534$	−8.37137	−0.362265
$535$	0	0
$536$	15.7093	0.678537
$537$	−3.68649	−0.159084
$538$	16.2245	0.699486
$539$	53.2834	2.29508
$540$	0	0
$541$	6.86830	0.295291	0.147646	−	0.989040i	$-0.452830\pi$
$541$	6.86830	0.295291	0.147646	+	0.989040i	$0.452830\pi$
$542$	4.68035	0.201038
$543$	−8.09890	−0.347557
$544$	0	0
$545$	0	0
$546$	−15.0205	−0.642819
$547$	5.89988	0.252261	0.126130	−	0.992014i	$-0.459744\pi$
$547$	5.89988	0.252261	0.126130	+	0.992014i	$0.459744\pi$
$548$	−5.28458	−0.225746
$549$	33.2039	1.41711
$550$	0	0
$551$	3.15061	0.134221
$552$	−4.33176	−0.184372
$553$	33.8082	1.43767
$554$	26.3812	1.12083
$555$	0	0
$556$	−5.43802	−0.230624
$557$	17.7359	0.751496	0.375748	−	0.926722i	$-0.377386\pi$
$557$	17.7359	0.751496	0.375748	+	0.926722i	$0.377386\pi$
$558$	24.0566	1.01840
$559$	−8.86376	−0.374897
$560$	0	0
$561$	0	0
$562$	28.4703	1.20095
$563$	−38.8020	−1.63531	−0.817655	−	0.575708i	$-0.804726\pi$
$563$	−38.8020	−1.63531	−0.817655	+	0.575708i	$0.804726\pi$
$564$	9.91548	0.417517
$565$	0	0
$566$	30.2895	1.27316
$567$	−31.5597	−1.32538
$568$	−6.25687	−0.262533
$569$	−12.1568	−0.509638	−0.254819	−	0.966989i	$-0.582016\pi$
$569$	−12.1568	−0.509638	−0.254819	+	0.966989i	$0.582016\pi$
$570$	0	0
$571$	15.4569	0.646853	0.323426	−	0.946253i	$-0.395165\pi$
$571$	15.4569	0.646853	0.323426	+	0.946253i	$0.395165\pi$
$572$	−22.5958	−0.944779
$573$	−13.0928	−0.546958
$574$	59.3172	2.47585
$575$	0	0
$576$	33.3545	1.38977
$577$	2.36296	0.0983713	0.0491856	−	0.998790i	$-0.484337\pi$
$577$	2.36296	0.0983713	0.0491856	+	0.998790i	$0.484337\pi$
$578$	0	0
$579$	−6.39350	−0.265705
$580$	0	0
$581$	−40.1711	−1.66658
$582$	−9.57531	−0.396909
$583$	11.9155	0.493489
$584$	17.0517	0.705605
$585$	0	0
$586$	10.2823	0.424758
$587$	−3.65142	−0.150710	−0.0753550	−	0.997157i	$-0.524009\pi$
$587$	−3.65142	−0.150710	−0.0753550	+	0.997157i	$0.524009\pi$
$588$	24.5536	1.01257
$589$	−4.41241	−0.181810
$590$	0	0
$591$	−9.84324	−0.404897
$592$	10.9360	0.449467
$593$	−1.38735	−0.0569718	−0.0284859	−	0.999594i	$-0.509069\pi$
$593$	−1.38735	−0.0569718	−0.0284859	+	0.999594i	$0.509069\pi$
$594$	21.1773	0.868914
$595$	0	0
$596$	−38.6947	−1.58500
$597$	2.00841	0.0821988
$598$	29.7998	1.21860
$599$	−0.451356	−0.0184419	−0.00922095	−	0.999957i	$-0.502935\pi$
$599$	−0.451356	−0.0184419	−0.00922095	+	0.999957i	$0.502935\pi$
$600$	0	0
$601$	−22.1301	−0.902705	−0.451353	−	0.892346i	$-0.649058\pi$
$601$	−22.1301	−0.902705	−0.451353	+	0.892346i	$0.649058\pi$
$602$	35.6742	1.45397
$603$	27.6514	1.12605
$604$	−34.8515	−1.41809
$605$	0	0
$606$	2.89496	0.117600
$607$	−10.2667	−0.416713	−0.208357	−	0.978053i	$-0.566811\pi$
$607$	−10.2667	−0.416713	−0.208357	+	0.978053i	$0.566811\pi$
$608$	−8.18342	−0.331881
$609$	7.68649	0.311472
$610$	0	0
$611$	−17.8576	−0.722442
$612$	0	0
$613$	9.05172	0.365595	0.182798	−	0.983151i	$-0.441485\pi$
$613$	9.05172	0.365595	0.182798	+	0.983151i	$0.441485\pi$
$614$	−46.8599	−1.89111
$615$	0	0
$616$	23.8082	0.959259
$617$	−17.8166	−0.717269	−0.358634	−	0.933478i	$-0.616757\pi$
$617$	−17.8166	−0.717269	−0.358634	+	0.933478i	$0.616757\pi$
$618$	−22.9939	−0.924949
$619$	−38.3884	−1.54296	−0.771480	−	0.636254i	$-0.780483\pi$
$619$	−38.3884	−1.54296	−0.771480	+	0.636254i	$0.780483\pi$
$620$	0	0
$621$	−16.0677	−0.644775
$622$	−52.6525	−2.11117
$623$	−34.9093	−1.39861
$624$	2.94828	0.118026
$625$	0	0
$626$	−8.83710	−0.353202
$627$	−1.84324	−0.0736121
$628$	−10.1834	−0.406363
$629$	0	0
$630$	0	0
$631$	27.4863	1.09421	0.547105	−	0.837064i	$-0.315730\pi$
$631$	27.4863	1.09421	0.547105	+	0.837064i	$0.315730\pi$
$632$	10.6647	0.424221
$633$	11.9961	0.476803
$634$	−17.4863	−0.694468
$635$	0	0
$636$	5.49079	0.217724
$637$	−44.2206	−1.75208
$638$	20.0989	0.795723
$639$	−11.0133	−0.435681
$640$	0	0
$641$	9.79976	0.387067	0.193534	−	0.981094i	$-0.438005\pi$
$641$	9.79976	0.387067	0.193534	+	0.981094i	$0.438005\pi$
$642$	−14.7877	−0.583622
$643$	−16.9372	−0.667939	−0.333969	−	0.942584i	$-0.608388\pi$
$643$	−16.9372	−0.667939	−0.333969	+	0.942584i	$0.608388\pi$
$644$	−68.9998	−2.71897
$645$	0	0
$646$	0	0
$647$	2.98545	0.117370	0.0586850	−	0.998277i	$-0.481309\pi$
$647$	2.98545	0.117370	0.0586850	+	0.998277i	$0.481309\pi$
$648$	−9.95547	−0.391088
$649$	7.41855	0.291204
$650$	0	0
$651$	−10.7649	−0.421908
$652$	−23.5597	−0.922669
$653$	40.1978	1.57306	0.786531	−	0.617551i	$-0.211875\pi$
$653$	40.1978	1.57306	0.786531	+	0.617551i	$0.211875\pi$
$654$	−9.54411	−0.373204
$655$	0	0
$656$	−11.6430	−0.454583
$657$	30.0144	1.17097
$658$	71.8720	2.80186
$659$	43.9832	1.71334	0.856671	−	0.515864i	$-0.172529\pi$
$659$	43.9832	1.71334	0.856671	+	0.515864i	$0.172529\pi$
$660$	0	0
$661$	−26.1133	−1.01569	−0.507844	−	0.861449i	$-0.669557\pi$
$661$	−26.1133	−1.01569	−0.507844	+	0.861449i	$0.669557\pi$
$662$	−21.8576	−0.849521
$663$	0	0
$664$	−12.6719	−0.491766
$665$	0	0
$666$	−30.9360	−1.19875
$667$	−15.2495	−0.590463
$668$	−3.72875	−0.144270
$669$	−1.18181	−0.0456914
$670$	0	0
$671$	−38.8515	−1.49984
$672$	−19.9649	−0.770164
$673$	−13.3340	−0.513989	−0.256995	−	0.966413i	$-0.582732\pi$
$673$	−13.3340	−0.513989	−0.256995	+	0.966413i	$0.582732\pi$
$674$	−24.3812	−0.939129
$675$	0	0
$676$	−16.4680	−0.633385
$677$	26.5113	1.01891	0.509456	−	0.860497i	$-0.329847\pi$
$677$	26.5113	1.01891	0.509456	+	0.860497i	$0.329847\pi$
$678$	−19.9155	−0.764849
$679$	−39.9299	−1.53237
$680$	0	0
$681$	5.15449	0.197520
$682$	−28.1483	−1.07786
$683$	−5.71646	−0.218734	−0.109367	−	0.994001i	$-0.534882\pi$
$683$	−5.71646	−0.218734	−0.109367	+	0.994001i	$0.534882\pi$
$684$	7.91548	0.302656
$685$	0	0
$686$	103.855	3.96521
$687$	−3.97334	−0.151592
$688$	−7.00227	−0.266959
$689$	−9.88882	−0.376734
$690$	0	0
$691$	43.8504	1.66815	0.834075	−	0.551652i	$-0.186002\pi$
$691$	43.8504	1.66815	0.834075	+	0.551652i	$0.186002\pi$
$692$	47.0349	1.78800
$693$	41.9071	1.59192
$694$	18.9867	0.720724
$695$	0	0
$696$	2.42469	0.0919078
$697$	0	0
$698$	−58.3956	−2.21031
$699$	−5.09275	−0.192626
$700$	0	0
$701$	0.0806452	0.00304593	0.00152296	−	0.999999i	$-0.499515\pi$
$701$	0.0806452	0.00304593	0.00152296	+	0.999999i	$0.499515\pi$
$702$	−17.5753	−0.663337
$703$	5.67420	0.214007
$704$	−39.0277	−1.47091
$705$	0	0
$706$	39.7419	1.49571
$707$	12.0722	0.454023
$708$	3.41855	0.128477
$709$	−10.8227	−0.406456	−0.203228	−	0.979131i	$-0.565143\pi$
$709$	−10.8227	−0.406456	−0.203228	+	0.979131i	$0.565143\pi$
$710$	0	0
$711$	18.7721	0.704007
$712$	−11.0121	−0.412696
$713$	21.3568	0.799819
$714$	0	0
$715$	0	0
$716$	−18.5236	−0.692259
$717$	3.37298	0.125966
$718$	−20.7792	−0.775474
$719$	−43.7659	−1.63219	−0.816097	−	0.577916i	$-0.803866\pi$
$719$	−43.7659	−1.63219	−0.816097	+	0.577916i	$0.803866\pi$
$720$	0	0
$721$	−95.8864	−3.57100
$722$	38.7081	1.44056
$723$	−1.34632	−0.0500700
$724$	−40.6947	−1.51241
$725$	0	0
$726$	1.11223	0.0412786
$727$	3.59809	0.133446	0.0667229	−	0.997772i	$-0.478746\pi$
$727$	3.59809	0.133446	0.0667229	+	0.997772i	$0.478746\pi$
$728$	−19.7587	−0.732307
$729$	−12.5441	−0.464597
$730$	0	0
$731$	0	0
$732$	−17.9032	−0.661721
$733$	−39.8264	−1.47102	−0.735511	−	0.677513i	$-0.763058\pi$
$733$	−39.8264	−1.47102	−0.735511	+	0.677513i	$0.763058\pi$
$734$	−26.2895	−0.970363
$735$	0	0
$736$	39.6092	1.46001
$737$	−32.3545	−1.19180
$738$	32.9360	1.21239
$739$	−13.7587	−0.506123	−0.253061	−	0.967450i	$-0.581437\pi$
$739$	−13.7587	−0.506123	−0.253061	+	0.967450i	$0.581437\pi$
$740$	0	0
$741$	1.52973	0.0561962
$742$	39.7998	1.46110
$743$	9.34963	0.343005	0.171502	−	0.985184i	$-0.445138\pi$
$743$	9.34963	0.343005	0.171502	+	0.985184i	$0.445138\pi$
$744$	−3.39576	−0.124495
$745$	0	0
$746$	66.1049	2.42027
$747$	−22.3051	−0.816101
$748$	0	0
$749$	−61.6658	−2.25322
$750$	0	0
$751$	53.7392	1.96097	0.980487	−	0.196586i	$-0.0629856\pi$
$751$	53.7392	1.96097	0.980487	+	0.196586i	$0.0629856\pi$
$752$	−14.1073	−0.514441
$753$	−6.37137	−0.232186
$754$	−16.6803	−0.607462
$755$	0	0
$756$	40.6947	1.48005
$757$	−41.5136	−1.50884	−0.754418	−	0.656394i	$-0.772081\pi$
$757$	−41.5136	−1.50884	−0.754418	+	0.656394i	$0.772081\pi$
$758$	2.14116	0.0777703
$759$	8.92162	0.323834
$760$	0	0
$761$	−18.0372	−0.653847	−0.326923	−	0.945051i	$-0.606012\pi$
$761$	−18.0372	−0.653847	−0.326923	+	0.945051i	$0.606012\pi$
$762$	9.41855	0.341198
$763$	−39.7998	−1.44085
$764$	−65.7875	−2.38011
$765$	0	0
$766$	54.1627	1.95698
$767$	−6.15676	−0.222308
$768$	−0.225678	−0.00814345
$769$	−23.0843	−0.832443	−0.416221	−	0.909263i	$-0.636646\pi$
$769$	−23.0843	−0.832443	−0.416221	+	0.909263i	$0.636646\pi$
$770$	0	0
$771$	8.05786	0.290197
$772$	−32.1256	−1.15622
$773$	−27.4101	−0.985874	−0.492937	−	0.870065i	$-0.664077\pi$
$773$	−27.4101	−0.985874	−0.492937	+	0.870065i	$0.664077\pi$
$774$	19.8082	0.711990
$775$	0	0
$776$	−12.5958	−0.452164
$777$	13.8432	0.496624
$778$	73.3667	2.63032
$779$	−6.04104	−0.216443
$780$	0	0
$781$	12.8865	0.461117
$782$	0	0
$783$	8.99386	0.321414
$784$	−34.9337	−1.24763
$785$	0	0
$786$	−13.6826	−0.488043
$787$	−30.6069	−1.09102	−0.545509	−	0.838105i	$-0.683664\pi$
$787$	−30.6069	−1.09102	−0.545509	+	0.838105i	$0.683664\pi$
$788$	−49.4596	−1.76192
$789$	−6.97948	−0.248476
$790$	0	0
$791$	−83.0493	−2.95289
$792$	13.2195	0.469736
$793$	32.2434	1.14500
$794$	−61.8987	−2.19670
$795$	0	0
$796$	10.0917	0.357691
$797$	22.9770	0.813888	0.406944	−	0.913453i	$-0.366594\pi$
$797$	22.9770	0.813888	0.406944	+	0.913453i	$0.366594\pi$
$798$	−6.15676	−0.217947
$799$	0	0
$800$	0	0
$801$	−19.3835	−0.684882
$802$	−71.8141	−2.53585
$803$	−35.1194	−1.23934
$804$	−14.9093	−0.525812
$805$	0	0
$806$	23.3607	0.822845
$807$	−4.03120	−0.141905
$808$	3.80817	0.133971
$809$	−42.7670	−1.50361	−0.751803	−	0.659388i	$-0.770816\pi$
$809$	−42.7670	−1.50361	−0.751803	+	0.659388i	$0.770816\pi$
$810$	0	0
$811$	9.41136	0.330478	0.165239	−	0.986254i	$-0.447161\pi$
$811$	9.41136	0.330478	0.165239	+	0.986254i	$0.447161\pi$
$812$	38.6225	1.35538
$813$	−1.16290	−0.0407846
$814$	36.1978	1.26873
$815$	0	0
$816$	0	0
$817$	−3.63317	−0.127108
$818$	65.5318	2.29127
$819$	−34.7792	−1.21529
$820$	0	0
$821$	−32.6681	−1.14012	−0.570062	−	0.821602i	$-0.693081\pi$
$821$	−32.6681	−1.14012	−0.570062	+	0.821602i	$0.693081\pi$
$822$	2.28231	0.0796048
$823$	−15.9265	−0.555164	−0.277582	−	0.960702i	$-0.589533\pi$
$823$	−15.9265	−0.555164	−0.277582	+	0.960702i	$0.589533\pi$
$824$	−30.2472	−1.05371
$825$	0	0
$826$	24.7792	0.862180
$827$	−6.01560	−0.209183	−0.104591	−	0.994515i	$-0.533353\pi$
$827$	−6.01560	−0.209183	−0.104591	+	0.994515i	$0.533353\pi$
$828$	−38.3123	−1.33144
$829$	11.0472	0.383684	0.191842	−	0.981426i	$-0.438554\pi$
$829$	11.0472	0.383684	0.191842	+	0.981426i	$0.438554\pi$
$830$	0	0
$831$	−6.55479	−0.227383
$832$	32.3896	1.12291
$833$	0	0
$834$	2.34858	0.0813248
$835$	0	0
$836$	−9.26180	−0.320326
$837$	−12.5958	−0.435375
$838$	39.4173	1.36165
$839$	35.9805	1.24219	0.621093	−	0.783737i	$-0.286689\pi$
$839$	35.9805	1.24219	0.621093	+	0.783737i	$0.286689\pi$
$840$	0	0
$841$	−20.4641	−0.705659
$842$	−1.65142	−0.0569116
$843$	−7.07384	−0.243636
$844$	60.2772	2.07483
$845$	0	0
$846$	39.9071	1.37203
$847$	4.63809	0.159367
$848$	−7.81205	−0.268267
$849$	−7.52586	−0.258287
$850$	0	0
$851$	−27.4641	−0.941458
$852$	5.93827	0.203442
$853$	28.7792	0.985382	0.492691	−	0.870204i	$-0.336013\pi$
$853$	28.7792	0.985382	0.492691	+	0.870204i	$0.336013\pi$
$854$	−129.771	−4.44066
$855$	0	0
$856$	−19.4524	−0.664869
$857$	−17.0661	−0.582967	−0.291483	−	0.956576i	$-0.594149\pi$
$857$	−17.0661	−0.582967	−0.291483	+	0.956576i	$0.594149\pi$
$858$	9.75872	0.333157
$859$	18.9360	0.646088	0.323044	−	0.946384i	$-0.395294\pi$
$859$	18.9360	0.646088	0.323044	+	0.946384i	$0.395294\pi$
$860$	0	0
$861$	−14.7382	−0.502277
$862$	13.7743	0.469155
$863$	−30.8332	−1.04958	−0.524788	−	0.851233i	$-0.675855\pi$
$863$	−30.8332	−1.04958	−0.524788	+	0.851233i	$0.675855\pi$
$864$	−23.3607	−0.794747
$865$	0	0
$866$	−7.86603	−0.267299
$867$	0	0
$868$	−54.0905	−1.83595
$869$	−21.9649	−0.745109
$870$	0	0
$871$	26.8515	0.909828
$872$	−12.5548	−0.425159
$873$	−22.1711	−0.750379
$874$	12.2146	0.413165
$875$	0	0
$876$	−16.1834	−0.546787
$877$	4.30898	0.145504	0.0727519	−	0.997350i	$-0.476822\pi$
$877$	4.30898	0.145504	0.0727519	+	0.997350i	$0.476822\pi$
$878$	13.8999	0.469098
$879$	−2.55479	−0.0861708
$880$	0	0
$881$	−12.2245	−0.411852	−0.205926	−	0.978568i	$-0.566021\pi$
$881$	−12.2245	−0.411852	−0.205926	+	0.978568i	$0.566021\pi$
$882$	98.8213	3.32749
$883$	28.2329	0.950112	0.475056	−	0.879956i	$-0.342428\pi$
$883$	28.2329	0.950112	0.475056	+	0.879956i	$0.342428\pi$
$884$	0	0
$885$	0	0
$886$	59.6391	2.00362
$887$	−5.17396	−0.173725	−0.0868623	−	0.996220i	$-0.527684\pi$
$887$	−5.17396	−0.173725	−0.0868623	+	0.996220i	$0.527684\pi$
$888$	4.36683	0.146541
$889$	39.2762	1.31728
$890$	0	0
$891$	20.5041	0.686914
$892$	−5.93827	−0.198828
$893$	−7.31965	−0.244943
$894$	16.7115	0.558918
$895$	0	0
$896$	−56.3039	−1.88098
$897$	−7.40417	−0.247218
$898$	−62.3956	−2.08217
$899$	−11.9544	−0.398702
$900$	0	0
$901$	0	0
$902$	−38.5380	−1.28317
$903$	−8.86376	−0.294968
$904$	−26.1978	−0.871326
$905$	0	0
$906$	15.0517	0.500060
$907$	−6.32457	−0.210004	−0.105002	−	0.994472i	$-0.533485\pi$
$907$	−6.32457	−0.210004	−0.105002	+	0.994472i	$0.533485\pi$
$908$	25.8999	0.859518
$909$	6.70313	0.222329
$910$	0	0
$911$	−27.6526	−0.916173	−0.458086	−	0.888908i	$-0.651465\pi$
$911$	−27.6526	−0.916173	−0.458086	+	0.888908i	$0.651465\pi$
$912$	1.20847	0.0400165
$913$	26.0989	0.863747
$914$	68.1627	2.25462
$915$	0	0
$916$	−19.9649	−0.659660
$917$	−57.0577	−1.88421
$918$	0	0
$919$	−47.5318	−1.56793	−0.783965	−	0.620805i	$-0.786806\pi$
$919$	−47.5318	−1.56793	−0.783965	+	0.620805i	$0.786806\pi$
$920$	0	0
$921$	11.6430	0.383650
$922$	−16.8371	−0.554500
$923$	−10.6947	−0.352021
$924$	−22.5958	−0.743348
$925$	0	0
$926$	52.5874	1.72813
$927$	−53.2411	−1.74867
$928$	−22.1711	−0.727803
$929$	43.7875	1.43662	0.718310	−	0.695723i	$-0.244916\pi$
$929$	43.7875	1.43662	0.718310	+	0.695723i	$0.244916\pi$
$930$	0	0
$931$	−18.1256	−0.594041
$932$	−25.5897	−0.838218
$933$	13.0823	0.428294
$934$	26.7298	0.874626
$935$	0	0
$936$	−10.9711	−0.358601
$937$	14.2367	0.465094	0.232547	−	0.972585i	$-0.425294\pi$
$937$	14.2367	0.465094	0.232547	+	0.972585i	$0.425294\pi$
$938$	−108.070	−3.52860
$939$	2.19570	0.0716541
$940$	0	0
$941$	−35.2183	−1.14808	−0.574042	−	0.818826i	$-0.694625\pi$
$941$	−35.2183	−1.14808	−0.574042	+	0.818826i	$0.694625\pi$
$942$	4.39803	0.143296
$943$	29.2397	0.952175
$944$	−4.86376	−0.158302
$945$	0	0
$946$	−23.1773	−0.753558
$947$	−49.1227	−1.59627	−0.798137	−	0.602476i	$-0.794181\pi$
$947$	−49.1227	−1.59627	−0.798137	+	0.602476i	$0.794181\pi$
$948$	−10.1217	−0.328737
$949$	29.1461	0.946122
$950$	0	0
$951$	4.34471	0.140887
$952$	0	0
$953$	17.0556	0.552485	0.276242	−	0.961088i	$-0.410911\pi$
$953$	17.0556	0.552485	0.276242	+	0.961088i	$0.410911\pi$
$954$	22.0989	0.715478
$955$	0	0
$956$	16.9483	0.548147
$957$	−4.99386	−0.161428
$958$	−4.66475	−0.150711
$959$	9.51745	0.307334
$960$	0	0
$961$	−14.2579	−0.459933
$962$	−30.0410	−0.968562
$963$	−34.2401	−1.10337
$964$	−6.76487	−0.217882
$965$	0	0
$966$	29.7998	0.958792
$967$	−25.1955	−0.810233	−0.405117	−	0.914265i	$-0.632769\pi$
$967$	−25.1955	−0.810233	−0.405117	+	0.914265i	$0.632769\pi$
$968$	1.46308	0.0470251
$969$	0	0
$970$	0	0
$971$	−1.67420	−0.0537277	−0.0268639	−	0.999639i	$-0.508552\pi$
$971$	−1.67420	−0.0537277	−0.0268639	+	0.999639i	$0.508552\pi$
$972$	34.4690	1.10560
$973$	9.79380	0.313975
$974$	86.9842	2.78715
$975$	0	0
$976$	25.4719	0.815335
$977$	−39.9109	−1.27686	−0.638432	−	0.769678i	$-0.720417\pi$
$977$	−39.9109	−1.27686	−0.638432	+	0.769678i	$0.720417\pi$
$978$	10.1750	0.325361
$979$	22.6803	0.724867
$980$	0	0
$981$	−22.0989	−0.705563
$982$	−4.89496	−0.156204
$983$	5.46081	0.174173	0.0870864	−	0.996201i	$-0.472244\pi$
$983$	5.46081	0.174173	0.0870864	+	0.996201i	$0.472244\pi$
$984$	−4.64915	−0.148209
$985$	0	0
$986$	0	0
$987$	−17.8576	−0.568414
$988$	7.68649	0.244540
$989$	17.5851	0.559175
$990$	0	0
$991$	−42.0749	−1.33655	−0.668276	−	0.743913i	$-0.732968\pi$
$991$	−42.0749	−1.33655	−0.668276	+	0.743913i	$0.732968\pi$
$992$	31.0505	0.985854
$993$	5.43084	0.172342
$994$	43.0433	1.36525
$995$	0	0
$996$	12.0267	0.381079
$997$	−54.6681	−1.73135	−0.865677	−	0.500602i	$-0.833112\pi$
$997$	−54.6681	−1.73135	−0.865677	+	0.500602i	$0.833112\pi$
$998$	−92.3267	−2.92255
$999$	16.1978	0.512476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.r.1.1		3
5.4	even	2		1445.2.a.k.1.3		3
17.4	even	4		425.2.d.c.101.5		6
17.13	even	4		425.2.d.c.101.6		6
17.16	even	2		7225.2.a.q.1.1		3
85.4	even	4		85.2.d.a.16.2	yes	6
85.13	odd	4		425.2.c.b.424.1		6
85.38	odd	4		425.2.c.a.424.1		6
85.47	odd	4		425.2.c.a.424.6		6
85.64	even	4		85.2.d.a.16.1	✓	6
85.72	odd	4		425.2.c.b.424.6		6
85.84	even	2		1445.2.a.j.1.3		3
255.89	odd	4		765.2.g.b.271.6		6
255.149	odd	4		765.2.g.b.271.5		6
340.259	odd	4		1360.2.c.f.1121.3		6
340.319	odd	4		1360.2.c.f.1121.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.1	✓	6	85.64	even	4
85.2.d.a.16.2	yes	6	85.4	even	4
425.2.c.a.424.1		6	85.38	odd	4
425.2.c.a.424.6		6	85.47	odd	4
425.2.c.b.424.1		6	85.13	odd	4
425.2.c.b.424.6		6	85.72	odd	4
425.2.d.c.101.5		6	17.4	even	4
425.2.d.c.101.6		6	17.13	even	4
765.2.g.b.271.5		6	255.149	odd	4
765.2.g.b.271.6		6	255.89	odd	4
1360.2.c.f.1121.3		6	340.259	odd	4
1360.2.c.f.1121.4		6	340.319	odd	4
1445.2.a.j.1.3		3	85.84	even	2
1445.2.a.k.1.3		3	5.4	even	2
7225.2.a.q.1.1		3	17.16	even	2
7225.2.a.r.1.1		3	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:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17009 q^{2} +0.539189 q^{3} +2.70928 q^{4} -1.17009 q^{6} -4.87936 q^{7} -1.53919 q^{8} -2.70928 q^{9} +3.17009 q^{11} +1.46081 q^{12} -2.63090 q^{13} +10.5886 q^{14} -2.07838 q^{16} +5.87936 q^{18} -1.07838 q^{19} -2.63090 q^{21} -6.87936 q^{22} +5.21953 q^{23} -0.829914 q^{24} +5.70928 q^{26} -3.07838 q^{27} -13.2195 q^{28} -2.92162 q^{29} +4.09171 q^{31} +7.58864 q^{32} +1.70928 q^{33} -7.34017 q^{36} -5.26180 q^{37} +2.34017 q^{38} -1.41855 q^{39} +5.60197 q^{41} +5.70928 q^{42} +3.36910 q^{43} +8.58864 q^{44} -11.3268 q^{46} +6.78765 q^{47} -1.12064 q^{48} +16.8082 q^{49} -7.12783 q^{52} +3.75872 q^{53} +6.68035 q^{54} +7.51026 q^{56} -0.581449 q^{57} +6.34017 q^{58} +2.34017 q^{59} -12.2557 q^{61} -8.87936 q^{62} +13.2195 q^{63} -12.3112 q^{64} -3.70928 q^{66} -10.2062 q^{67} +2.81432 q^{69} +4.06505 q^{71} +4.17009 q^{72} -11.0784 q^{73} +11.4186 q^{74} -2.92162 q^{76} -15.4680 q^{77} +3.07838 q^{78} -6.92881 q^{79} +6.46800 q^{81} -12.1568 q^{82} +8.23287 q^{83} -7.12783 q^{84} -7.31124 q^{86} -1.57531 q^{87} -4.87936 q^{88} +7.15449 q^{89} +12.8371 q^{91} +14.1412 q^{92} +2.20620 q^{93} -14.7298 q^{94} +4.09171 q^{96} +8.18342 q^{97} -36.4752 q^{98} -8.58864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + q^{4} + 2 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} + 4 q^{11} + 6 q^{12} - 4 q^{13} + 12 q^{14} - 3 q^{16} + 5 q^{18} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 10 q^{26} - 6 q^{27} - 16 q^{28}+ \cdots - 6 q^{99}+O(q^{100}) \) 3 * q - q^2 + q^4 + 2 * q^6 - 2 * q^7 - 3 * q^8 - q^9 + 4 * q^11 + 6 * q^12 - 4 * q^13 + 12 * q^14 - 3 * q^16 + 5 * q^18 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 10 * q^26 - 6 * q^27 - 16 * q^28 - 12 * q^29 + 10 * q^31 + 3 * q^32 - 2 * q^33 - 11 * q^36 - 8 * q^37 - 4 * q^38 + 10 * q^39 - 2 * q^41 + 10 * q^42 + 14 * q^43 + 6 * q^44 - 22 * q^46 + 10 * q^47 - 16 * q^48 + 7 * q^49 - 14 * q^53 - 2 * q^54 + 6 * q^56 - 16 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^61 - 14 * q^62 + 16 * q^63 - 11 * q^64 - 4 * q^66 - 6 * q^67 + 8 * q^71 + 7 * q^72 - 30 * q^73 + 20 * q^74 - 12 * q^76 - 14 * q^77 + 6 * q^78 + 10 * q^79 - 13 * q^81 - 30 * q^82 + 2 * q^83 + 4 * q^86 + 16 * q^87 - 2 * q^88 + 2 * q^89 + 10 * q^91 + 22 * q^92 - 18 * q^93 - 4 * q^94 + 10 * q^96 + 20 * q^97 - 43 * q^98 - 6 * q^99

Introduction

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