LMFDB - Embedded newform 7225.2.a.bu.1.4

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 21 x^{13} - 2 x^{12} + 171 x^{11} + 30 x^{10} - 678 x^{9} - 153 x^{8} + 1350 x^{7} + 301 x^{6} + \cdots + 3 $ x^15 - 21x^13 - 2x^12 + 171x^11 + 30x^10 - 678x^9 - 153x^8 + 1350x^7 + 301x^6 - 1284x^5 - 183x^4 + 555x^3 + 18x^2 - 81*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.71131$ 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)

$f(q)$	$=$	$q-1.71131 q^{2} +0.109608 q^{3} +0.928572 q^{4} -0.187572 q^{6} +4.34210 q^{7} +1.83354 q^{8} -2.98799 q^{9} +O(q^{10})$	\(q-1.71131 q^{2} +0.109608 q^{3} +0.928572 q^{4} -0.187572 q^{6} +4.34210 q^{7} +1.83354 q^{8} -2.98799 q^{9} -5.20553 q^{11} +0.101779 q^{12} +4.88189 q^{13} -7.43066 q^{14} -4.99490 q^{16} +5.11336 q^{18} -1.64053 q^{19} +0.475927 q^{21} +8.90825 q^{22} -8.39280 q^{23} +0.200970 q^{24} -8.35442 q^{26} -0.656330 q^{27} +4.03195 q^{28} +0.485258 q^{29} +6.30076 q^{31} +4.88072 q^{32} -0.570566 q^{33} -2.77456 q^{36} -0.930097 q^{37} +2.80745 q^{38} +0.535093 q^{39} +5.44822 q^{41} -0.814458 q^{42} +7.53358 q^{43} -4.83371 q^{44} +14.3627 q^{46} +4.88962 q^{47} -0.547479 q^{48} +11.8538 q^{49} +4.53319 q^{52} -3.10894 q^{53} +1.12318 q^{54} +7.96142 q^{56} -0.179815 q^{57} -0.830425 q^{58} -7.94104 q^{59} -14.1498 q^{61} -10.7825 q^{62} -12.9741 q^{63} +1.63738 q^{64} +0.976414 q^{66} +11.5894 q^{67} -0.919916 q^{69} +0.201195 q^{71} -5.47860 q^{72} -5.37389 q^{73} +1.59168 q^{74} -1.52335 q^{76} -22.6029 q^{77} -0.915709 q^{78} -6.62508 q^{79} +8.89202 q^{81} -9.32358 q^{82} -10.5231 q^{83} +0.441933 q^{84} -12.8923 q^{86} +0.0531880 q^{87} -9.54455 q^{88} -13.0569 q^{89} +21.1977 q^{91} -7.79333 q^{92} +0.690612 q^{93} -8.36764 q^{94} +0.534965 q^{96} +1.17959 q^{97} -20.2855 q^{98} +15.5540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 9 q^{3} + 12 q^{4} + 9 q^{6} - 12 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 15 * q - 9 * q^3 + 12 * q^4 + 9 * q^6 - 12 * q^7 - 6 * q^8 + 12 * q^9	$ 15 q - 9 q^{3} + 12 q^{4} + 9 q^{6} - 12 q^{7} - 6 q^{8} + 12 q^{9} + 6 q^{11} - 24 q^{12} + 6 q^{16} - 12 q^{18} + 6 q^{19} + 30 q^{21} - 12 q^{22} - 36 q^{23} + 18 q^{24} + 36 q^{26} - 36 q^{27} - 24 q^{28} - 18 q^{29} - 12 q^{32} - 12 q^{33} - 9 q^{36} - 12 q^{37} + 6 q^{38} + 9 q^{39} - 18 q^{41} - 36 q^{42} + 3 q^{43} - 12 q^{44} + 21 q^{46} + 3 q^{47} + 12 q^{48} + 15 q^{49} + 27 q^{52} + 21 q^{54} - 6 q^{56} - 39 q^{57} - 18 q^{58} - 12 q^{59} - 15 q^{61} - 54 q^{62} - 60 q^{63} - 36 q^{64} + 18 q^{66} + 24 q^{67} + 42 q^{69} + 6 q^{71} - 66 q^{72} + 9 q^{73} - 36 q^{74} - 18 q^{76} - 30 q^{77} - 30 q^{78} - 9 q^{79} + 51 q^{81} + 36 q^{82} - 15 q^{83} + 9 q^{84} - 36 q^{86} + 51 q^{87} - 30 q^{88} - 24 q^{89} + 27 q^{91} - 15 q^{92} + 42 q^{93} - 57 q^{94} + 42 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) $ 15 * q - 9 * q^3 + 12 * q^4 + 9 * q^6 - 12 * q^7 - 6 * q^8 + 12 * q^9 + 6 * q^11 - 24 * q^12 + 6 * q^16 - 12 * q^18 + 6 * q^19 + 30 * q^21 - 12 * q^22 - 36 * q^23 + 18 * q^24 + 36 * q^26 - 36 * q^27 - 24 * q^28 - 18 * q^29 - 12 * q^32 - 12 * q^33 - 9 * q^36 - 12 * q^37 + 6 * q^38 + 9 * q^39 - 18 * q^41 - 36 * q^42 + 3 * q^43 - 12 * q^44 + 21 * q^46 + 3 * q^47 + 12 * q^48 + 15 * q^49 + 27 * q^52 + 21 * q^54 - 6 * q^56 - 39 * q^57 - 18 * q^58 - 12 * q^59 - 15 * q^61 - 54 * q^62 - 60 * q^63 - 36 * q^64 + 18 * q^66 + 24 * q^67 + 42 * q^69 + 6 * q^71 - 66 * q^72 + 9 * q^73 - 36 * q^74 - 18 * q^76 - 30 * q^77 - 30 * q^78 - 9 * q^79 + 51 * q^81 + 36 * q^82 - 15 * q^83 + 9 * q^84 - 36 * q^86 + 51 * q^87 - 30 * q^88 - 24 * q^89 + 27 * q^91 - 15 * q^92 + 42 * q^93 - 57 * q^94 + 42 * q^96 - 48 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.71131	−1.21008	−0.605038	−	0.796196i	$-0.706842\pi$
$2$	−1.71131	−1.21008	−0.605038	+	0.796196i	$0.706842\pi$
$3$	0.109608	0.0632820	0.0316410	−	0.999499i	$-0.489927\pi$
$3$	0.109608	0.0632820	0.0316410	+	0.999499i	$0.489927\pi$
$4$	0.928572	0.464286
$5$	0	0
$5$	0	0
$6$	−0.187572	−0.0765761
$7$	4.34210	1.64116	0.820579	−	0.571533i	$-0.193651\pi$
$7$	4.34210	1.64116	0.820579	+	0.571533i	$0.193651\pi$
$8$	1.83354	0.648255
$9$	−2.98799	−0.995995
$10$	0	0
$11$	−5.20553	−1.56953	−0.784763	−	0.619796i	$-0.787215\pi$
$11$	−5.20553	−1.56953	−0.784763	+	0.619796i	$0.787215\pi$
$12$	0.101779	0.0293810
$13$	4.88189	1.35399	0.676997	−	0.735986i	$-0.263281\pi$
$13$	4.88189	1.35399	0.676997	+	0.735986i	$0.263281\pi$
$14$	−7.43066	−1.98593
$15$	0	0
$16$	−4.99490	−1.24872
$17$	0	0
$17$	0	0
$18$	5.11336	1.20523
$19$	−1.64053	−0.376364	−0.188182	−	0.982134i	$-0.560259\pi$
$19$	−1.64053	−0.376364	−0.188182	+	0.982134i	$0.560259\pi$
$20$	0	0
$21$	0.475927	0.103856
$22$	8.90825	1.89925
$23$	−8.39280	−1.75002	−0.875010	−	0.484105i	$-0.839145\pi$
$23$	−8.39280	−1.75002	−0.875010	+	0.484105i	$0.839145\pi$
$24$	0.200970	0.0410229
$25$	0	0
$26$	−8.35442	−1.63844
$27$	−0.656330	−0.126311
$28$	4.03195	0.761967
$29$	0.485258	0.0901101	0.0450551	−	0.998985i	$-0.485654\pi$
$29$	0.485258	0.0901101	0.0450551	+	0.998985i	$0.485654\pi$
$30$	0	0
$31$	6.30076	1.13165	0.565825	−	0.824525i	$-0.308558\pi$
$31$	6.30076	1.13165	0.565825	+	0.824525i	$0.308558\pi$
$32$	4.88072	0.862798
$33$	−0.570566	−0.0993228
$34$	0	0
$35$	0	0
$36$	−2.77456	−0.462427
$37$	−0.930097	−0.152907	−0.0764535	−	0.997073i	$-0.524360\pi$
$37$	−0.930097	−0.152907	−0.0764535	+	0.997073i	$0.524360\pi$
$38$	2.80745	0.455429
$39$	0.535093	0.0856835
$40$	0	0
$41$	5.44822	0.850869	0.425434	−	0.904989i	$-0.360121\pi$
$41$	5.44822	0.850869	0.425434	+	0.904989i	$0.360121\pi$
$42$	−0.814458	−0.125674
$43$	7.53358	1.14886	0.574430	−	0.818554i	$-0.305224\pi$
$43$	7.53358	1.14886	0.574430	+	0.818554i	$0.305224\pi$
$44$	−4.83371	−0.728709
$45$	0	0
$46$	14.3627	2.11766
$47$	4.88962	0.713224	0.356612	−	0.934253i	$-0.383932\pi$
$47$	4.88962	0.713224	0.356612	+	0.934253i	$0.383932\pi$
$48$	−0.547479	−0.0790218
$49$	11.8538	1.69340
$50$	0	0
$51$	0	0
$52$	4.53319	0.628641
$53$	−3.10894	−0.427046	−0.213523	−	0.976938i	$-0.568494\pi$
$53$	−3.10894	−0.427046	−0.213523	+	0.976938i	$0.568494\pi$
$54$	1.12318	0.152846
$55$	0	0
$56$	7.96142	1.06389
$57$	−0.179815	−0.0238171
$58$	−0.830425	−0.109040
$59$	−7.94104	−1.03384	−0.516918	−	0.856035i	$-0.672921\pi$
$59$	−7.94104	−1.03384	−0.516918	+	0.856035i	$0.672921\pi$
$60$	0	0
$61$	−14.1498	−1.81169	−0.905845	−	0.423608i	$-0.860763\pi$
$61$	−14.1498	−1.81169	−0.905845	+	0.423608i	$0.860763\pi$
$62$	−10.7825	−1.36938
$63$	−12.9741	−1.63459
$64$	1.63738	0.204673
$65$	0	0
$66$	0.976414	0.120188
$67$	11.5894	1.41588	0.707938	−	0.706275i	$-0.249626\pi$
$67$	11.5894	1.41588	0.707938	+	0.706275i	$0.249626\pi$
$68$	0	0
$69$	−0.919916	−0.110745
$70$	0	0
$71$	0.201195	0.0238775	0.0119387	−	0.999929i	$-0.496200\pi$
$71$	0.201195	0.0238775	0.0119387	+	0.999929i	$0.496200\pi$
$72$	−5.47860	−0.645659
$73$	−5.37389	−0.628967	−0.314483	−	0.949263i	$-0.601831\pi$
$73$	−5.37389	−0.628967	−0.314483	+	0.949263i	$0.601831\pi$
$74$	1.59168	0.185029
$75$	0	0
$76$	−1.52335	−0.174740
$77$	−22.6029	−2.57584
$78$	−0.915709	−0.103684
$79$	−6.62508	−0.745380	−0.372690	−	0.927956i	$-0.621564\pi$
$79$	−6.62508	−0.745380	−0.372690	+	0.927956i	$0.621564\pi$
$80$	0	0
$81$	8.89202	0.988002
$82$	−9.32358	−1.02962
$83$	−10.5231	−1.15507	−0.577533	−	0.816367i	$-0.695984\pi$
$83$	−10.5231	−1.15507	−0.577533	+	0.816367i	$0.695984\pi$
$84$	0.441933	0.0482188
$85$	0	0
$86$	−12.8923	−1.39021
$87$	0.0531880	0.00570235
$88$	−9.54455	−1.01745
$89$	−13.0569	−1.38403	−0.692016	−	0.721882i	$-0.743277\pi$
$89$	−13.0569	−1.38403	−0.692016	+	0.721882i	$0.743277\pi$
$90$	0	0
$91$	21.1977	2.22212
$92$	−7.79333	−0.812510
$93$	0.690612	0.0716132
$94$	−8.36764	−0.863056
$95$	0	0
$96$	0.534965	0.0545996
$97$	1.17959	0.119769	0.0598846	−	0.998205i	$-0.480927\pi$
$97$	1.17959	0.119769	0.0598846	+	0.998205i	$0.480927\pi$
$98$	−20.2855	−2.04915
$99$	15.5540	1.56324
$100$	0	0
$101$	−3.46756	−0.345035	−0.172518	−	0.985006i	$-0.555190\pi$
$101$	−3.46756	−0.345035	−0.172518	+	0.985006i	$0.555190\pi$
$102$	0	0
$103$	−12.5490	−1.23649	−0.618244	−	0.785986i	$-0.712156\pi$
$103$	−12.5490	−1.23649	−0.618244	+	0.785986i	$0.712156\pi$
$104$	8.95116	0.877733
$105$	0	0
$106$	5.32035	0.516758
$107$	−4.36167	−0.421659	−0.210829	−	0.977523i	$-0.567616\pi$
$107$	−4.36167	−0.421659	−0.210829	+	0.977523i	$0.567616\pi$
$108$	−0.609450	−0.0586443
$109$	4.02991	0.385995	0.192998	−	0.981199i	$-0.438179\pi$
$109$	4.02991	0.385995	0.192998	+	0.981199i	$0.438179\pi$
$110$	0	0
$111$	−0.101946	−0.00967627
$112$	−21.6883	−2.04935
$113$	9.65991	0.908728	0.454364	−	0.890816i	$-0.349867\pi$
$113$	9.65991	0.908728	0.454364	+	0.890816i	$0.349867\pi$
$114$	0.307718	0.0288205
$115$	0	0
$116$	0.450597	0.0418369
$117$	−14.5870	−1.34857
$118$	13.5896	1.25102
$119$	0	0
$120$	0	0
$121$	16.0975	1.46341
$122$	24.2146	2.19229
$123$	0.597167	0.0538447
$124$	5.85071	0.525410
$125$	0	0
$126$	22.2027	1.97798
$127$	−12.0444	−1.06877	−0.534385	−	0.845241i	$-0.679457\pi$
$127$	−12.0444	−1.06877	−0.534385	+	0.845241i	$0.679457\pi$
$128$	−12.5635	−1.11047
$129$	0.825739	0.0727022
$130$	0	0
$131$	−1.82113	−0.159112	−0.0795562	−	0.996830i	$-0.525350\pi$
$131$	−1.82113	−0.159112	−0.0795562	+	0.996830i	$0.525350\pi$
$132$	−0.529812	−0.0461142
$133$	−7.12334	−0.617672
$134$	−19.8331	−1.71332
$135$	0	0
$136$	0	0
$137$	14.8662	1.27010	0.635052	−	0.772470i	$-0.280979\pi$
$137$	14.8662	1.27010	0.635052	+	0.772470i	$0.280979\pi$
$138$	1.57426	0.134010
$139$	16.3516	1.38693	0.693463	−	0.720493i	$-0.256084\pi$
$139$	16.3516	1.38693	0.693463	+	0.720493i	$0.256084\pi$
$140$	0	0
$141$	0.535940	0.0451343
$142$	−0.344307	−0.0288936
$143$	−25.4128	−2.12513
$144$	14.9247	1.24372
$145$	0	0
$146$	9.19639	0.761098
$147$	1.29927	0.107162
$148$	−0.863663	−0.0709926
$149$	−2.23082	−0.182756	−0.0913779	−	0.995816i	$-0.529127\pi$
$149$	−2.23082	−0.182756	−0.0913779	+	0.995816i	$0.529127\pi$
$150$	0	0
$151$	−4.11034	−0.334495	−0.167247	−	0.985915i	$-0.553488\pi$
$151$	−4.11034	−0.334495	−0.167247	+	0.985915i	$0.553488\pi$
$152$	−3.00798	−0.243980
$153$	0	0
$154$	38.6805	3.11696
$155$	0	0
$156$	0.496873	0.0397817
$157$	2.58687	0.206454	0.103227	−	0.994658i	$-0.467083\pi$
$157$	2.58687	0.206454	0.103227	+	0.994658i	$0.467083\pi$
$158$	11.3375	0.901967
$159$	−0.340764	−0.0270243
$160$	0	0
$161$	−36.4424	−2.87206
$162$	−15.2170	−1.19556
$163$	4.78278	0.374616	0.187308	−	0.982301i	$-0.440024\pi$
$163$	4.78278	0.374616	0.187308	+	0.982301i	$0.440024\pi$
$164$	5.05907	0.395047
$165$	0	0
$166$	18.0083	1.39772
$167$	−1.16937	−0.0904888	−0.0452444	−	0.998976i	$-0.514407\pi$
$167$	−1.16937	−0.0904888	−0.0452444	+	0.998976i	$0.514407\pi$
$168$	0.872633	0.0673251
$169$	10.8329	0.833299
$170$	0	0
$171$	4.90188	0.374856
$172$	6.99548	0.533400
$173$	−1.81101	−0.137688	−0.0688441	−	0.997627i	$-0.521931\pi$
$173$	−1.81101	−0.137688	−0.0688441	+	0.997627i	$0.521931\pi$
$174$	−0.0910210	−0.00690029
$175$	0	0
$176$	26.0011	1.95990
$177$	−0.870400	−0.0654232
$178$	22.3444	1.67479
$179$	−18.3075	−1.36837	−0.684183	−	0.729310i	$-0.739841\pi$
$179$	−18.3075	−1.36837	−0.684183	+	0.729310i	$0.739841\pi$
$180$	0	0
$181$	−4.61305	−0.342885	−0.171443	−	0.985194i	$-0.554843\pi$
$181$	−4.61305	−0.342885	−0.171443	+	0.985194i	$0.554843\pi$
$182$	−36.2757	−2.68893
$183$	−1.55092	−0.114648
$184$	−15.3886	−1.13446
$185$	0	0
$186$	−1.18185	−0.0866574
$187$	0	0
$188$	4.54036	0.331140
$189$	−2.84985	−0.207296
$190$	0	0
$191$	11.6370	0.842026	0.421013	−	0.907055i	$-0.361675\pi$
$191$	11.6370	0.842026	0.421013	+	0.907055i	$0.361675\pi$
$192$	0.179470	0.0129521
$193$	−7.61788	−0.548347	−0.274174	−	0.961680i	$-0.588404\pi$
$193$	−7.61788	−0.548347	−0.274174	+	0.961680i	$0.588404\pi$
$194$	−2.01864	−0.144930
$195$	0	0
$196$	11.0071	0.786223
$197$	5.91667	0.421545	0.210773	−	0.977535i	$-0.432402\pi$
$197$	5.91667	0.421545	0.210773	+	0.977535i	$0.432402\pi$
$198$	−26.6177	−1.89164
$199$	−21.8358	−1.54790	−0.773949	−	0.633248i	$-0.781721\pi$
$199$	−21.8358	−1.54790	−0.773949	+	0.633248i	$0.781721\pi$
$200$	0	0
$201$	1.27029	0.0895995
$202$	5.93407	0.417519
$203$	2.10704	0.147885
$204$	0	0
$205$	0	0
$206$	21.4752	1.49625
$207$	25.0776	1.74301
$208$	−24.3846	−1.69077
$209$	8.53983	0.590712
$210$	0	0
$211$	2.27702	0.156757	0.0783784	−	0.996924i	$-0.475026\pi$
$211$	2.27702	0.156757	0.0783784	+	0.996924i	$0.475026\pi$
$212$	−2.88688	−0.198272
$213$	0.0220525	0.00151101
$214$	7.46416	0.510240
$215$	0	0
$216$	−1.20341	−0.0818815
$217$	27.3585	1.85722
$218$	−6.89641	−0.467084
$219$	−0.589020	−0.0398023
$220$	0	0
$221$	0	0
$222$	0.174461	0.0117090
$223$	−15.9071	−1.06522	−0.532608	−	0.846362i	$-0.678788\pi$
$223$	−15.9071	−1.06522	−0.532608	+	0.846362i	$0.678788\pi$
$224$	21.1926	1.41599
$225$	0	0
$226$	−16.5311	−1.09963
$227$	−12.0149	−0.797456	−0.398728	−	0.917069i	$-0.630548\pi$
$227$	−12.0149	−0.797456	−0.398728	+	0.917069i	$0.630548\pi$
$228$	−0.166971	−0.0110579
$229$	−23.5914	−1.55897	−0.779483	−	0.626423i	$-0.784518\pi$
$229$	−23.5914	−1.55897	−0.779483	+	0.626423i	$0.784518\pi$
$230$	0	0
$231$	−2.47745	−0.163004
$232$	0.889741	0.0584143
$233$	−12.9704	−0.849717	−0.424859	−	0.905260i	$-0.639676\pi$
$233$	−12.9704	−0.849717	−0.424859	+	0.905260i	$0.639676\pi$
$234$	24.9629	1.63188
$235$	0	0
$236$	−7.37383	−0.479996
$237$	−0.726160	−0.0471691
$238$	0	0
$239$	−26.2648	−1.69893	−0.849465	−	0.527646i	$-0.823075\pi$
$239$	−26.2648	−1.69893	−0.849465	+	0.527646i	$0.823075\pi$
$240$	0	0
$241$	22.5879	1.45501	0.727506	−	0.686101i	$-0.240679\pi$
$241$	22.5879	1.45501	0.727506	+	0.686101i	$0.240679\pi$
$242$	−27.5478	−1.77084
$243$	2.94362	0.188833
$244$	−13.1391	−0.841143
$245$	0	0
$246$	−1.02194	−0.0651563
$247$	−8.00890	−0.509594
$248$	11.5527	0.733598
$249$	−1.15342	−0.0730949
$250$	0	0
$251$	28.9971	1.83028	0.915141	−	0.403133i	$-0.132079\pi$
$251$	28.9971	1.83028	0.915141	+	0.403133i	$0.132079\pi$
$252$	−12.0474	−0.758916
$253$	43.6890	2.74670
$254$	20.6117	1.29329
$255$	0	0
$256$	18.2253	1.13908
$257$	21.6041	1.34762	0.673812	−	0.738902i	$-0.264656\pi$
$257$	21.6041	1.34762	0.673812	+	0.738902i	$0.264656\pi$
$258$	−1.41309	−0.0879753
$259$	−4.03857	−0.250945
$260$	0	0
$261$	−1.44994	−0.0897493
$262$	3.11651	0.192538
$263$	−10.2248	−0.630489	−0.315245	−	0.949010i	$-0.602087\pi$
$263$	−10.2248	−0.630489	−0.315245	+	0.949010i	$0.602087\pi$
$264$	−1.04616	−0.0643865
$265$	0	0
$266$	12.1902	0.747431
$267$	−1.43114	−0.0875844
$268$	10.7616	0.657372
$269$	−30.5487	−1.86259	−0.931294	−	0.364269i	$-0.881319\pi$
$269$	−30.5487	−1.86259	−0.931294	+	0.364269i	$0.881319\pi$
$270$	0	0
$271$	−10.7654	−0.653953	−0.326976	−	0.945033i	$-0.606030\pi$
$271$	−10.7654	−0.653953	−0.326976	+	0.945033i	$0.606030\pi$
$272$	0	0
$273$	2.32343	0.140620
$274$	−25.4406	−1.53692
$275$	0	0
$276$	−0.854209	−0.0514173
$277$	22.9465	1.37872	0.689361	−	0.724418i	$-0.257891\pi$
$277$	22.9465	1.37872	0.689361	+	0.724418i	$0.257891\pi$
$278$	−27.9826	−1.67829
$279$	−18.8266	−1.12712
$280$	0	0
$281$	21.3918	1.27612	0.638062	−	0.769985i	$-0.279736\pi$
$281$	21.3918	1.27612	0.638062	+	0.769985i	$0.279736\pi$
$282$	−0.917158	−0.0546160
$283$	−15.5072	−0.921807	−0.460904	−	0.887450i	$-0.652475\pi$
$283$	−15.5072	−0.921807	−0.460904	+	0.887450i	$0.652475\pi$
$284$	0.186824	0.0110860
$285$	0	0
$286$	43.4892	2.57157
$287$	23.6567	1.39641
$288$	−14.5835	−0.859343
$289$	0	0
$290$	0	0
$291$	0.129292	0.00757924
$292$	−4.99005	−0.292021
$293$	11.1577	0.651842	0.325921	−	0.945397i	$-0.394326\pi$
$293$	11.1577	0.651842	0.325921	+	0.945397i	$0.394326\pi$
$294$	−2.22345	−0.129674
$295$	0	0
$296$	−1.70537	−0.0991227
$297$	3.41654	0.198248
$298$	3.81762	0.221149
$299$	−40.9728	−2.36952
$300$	0	0
$301$	32.7115	1.88546
$302$	7.03406	0.404764
$303$	−0.380072	−0.0218345
$304$	8.19428	0.469974
$305$	0	0
$306$	0	0
$307$	32.7577	1.86958	0.934790	−	0.355201i	$-0.115588\pi$
$307$	32.7577	1.86958	0.934790	+	0.355201i	$0.115588\pi$
$308$	−20.9884	−1.19593
$309$	−1.37547	−0.0782475
$310$	0	0
$311$	−19.1267	−1.08458	−0.542289	−	0.840192i	$-0.682442\pi$
$311$	−19.1267	−1.08458	−0.542289	+	0.840192i	$0.682442\pi$
$312$	0.981116	0.0555447
$313$	−9.62567	−0.544075	−0.272037	−	0.962287i	$-0.587697\pi$
$313$	−9.62567	−0.544075	−0.272037	+	0.962287i	$0.587697\pi$
$314$	−4.42692	−0.249826
$315$	0	0
$316$	−6.15187	−0.346069
$317$	7.48875	0.420610	0.210305	−	0.977636i	$-0.432554\pi$
$317$	7.48875	0.420610	0.210305	+	0.977636i	$0.432554\pi$
$318$	0.583152	0.0327015
$319$	−2.52602	−0.141430
$320$	0	0
$321$	−0.478073	−0.0266834
$322$	62.3641	3.47541
$323$	0	0
$324$	8.25688	0.458716
$325$	0	0
$326$	−8.18480	−0.453314
$327$	0.441709	0.0244266
$328$	9.98954	0.551580
$329$	21.2312	1.17051
$330$	0	0
$331$	12.6115	0.693189	0.346594	−	0.938015i	$-0.387338\pi$
$331$	12.6115	0.693189	0.346594	+	0.938015i	$0.387338\pi$
$332$	−9.77151	−0.536281
$333$	2.77912	0.152295
$334$	2.00116	0.109498
$335$	0	0
$336$	−2.37721	−0.129687
$337$	−31.7383	−1.72889	−0.864447	−	0.502724i	$-0.832331\pi$
$337$	−31.7383	−1.72889	−0.864447	+	0.502724i	$0.832331\pi$
$338$	−18.5384	−1.00836
$339$	1.05880	0.0575062
$340$	0	0
$341$	−32.7988	−1.77615
$342$	−8.38863	−0.453605
$343$	21.0757	1.13798
$344$	13.8131	0.744754
$345$	0	0
$346$	3.09919	0.166613
$347$	3.79210	0.203571	0.101785	−	0.994806i	$-0.467544\pi$
$347$	3.79210	0.203571	0.101785	+	0.994806i	$0.467544\pi$
$348$	0.0493889	0.00264752
$349$	16.8636	0.902689	0.451344	−	0.892350i	$-0.350945\pi$
$349$	16.8636	0.902689	0.451344	+	0.892350i	$0.350945\pi$
$350$	0	0
$351$	−3.20413	−0.171024
$352$	−25.4067	−1.35418
$353$	−24.7095	−1.31516	−0.657578	−	0.753387i	$-0.728419\pi$
$353$	−24.7095	−1.31516	−0.657578	+	0.753387i	$0.728419\pi$
$354$	1.48952	0.0791672
$355$	0	0
$356$	−12.1243	−0.642587
$357$	0	0
$358$	31.3298	1.65583
$359$	16.5864	0.875395	0.437697	−	0.899122i	$-0.355794\pi$
$359$	16.5864	0.875395	0.437697	+	0.899122i	$0.355794\pi$
$360$	0	0
$361$	−16.3087	−0.858350
$362$	7.89435	0.414918
$363$	1.76441	0.0926075
$364$	19.6836	1.03170
$365$	0	0
$366$	2.65411	0.138732
$367$	−23.5105	−1.22724	−0.613619	−	0.789602i	$-0.710287\pi$
$367$	−23.5105	−1.22724	−0.613619	+	0.789602i	$0.710287\pi$
$368$	41.9212	2.18529
$369$	−16.2792	−0.847461
$370$	0	0
$371$	−13.4993	−0.700850
$372$	0.641284	0.0332490
$373$	6.07680	0.314645	0.157322	−	0.987547i	$-0.449714\pi$
$373$	6.07680	0.314645	0.157322	+	0.987547i	$0.449714\pi$
$374$	0	0
$375$	0	0
$376$	8.96532	0.462351
$377$	2.36898	0.122009
$378$	4.87696	0.250844
$379$	−0.531157	−0.0272837	−0.0136419	−	0.999907i	$-0.504342\pi$
$379$	−0.531157	−0.0272837	−0.0136419	+	0.999907i	$0.504342\pi$
$380$	0	0
$381$	−1.32016	−0.0676340
$382$	−19.9145	−1.01892
$383$	4.35039	0.222294	0.111147	−	0.993804i	$-0.464547\pi$
$383$	4.35039	0.222294	0.111147	+	0.993804i	$0.464547\pi$
$384$	−1.37706	−0.0702727
$385$	0	0
$386$	13.0365	0.663542
$387$	−22.5102	−1.14426
$388$	1.09533	0.0556072
$389$	6.47149	0.328118	0.164059	−	0.986451i	$-0.447541\pi$
$389$	6.47149	0.328118	0.164059	+	0.986451i	$0.447541\pi$
$390$	0	0
$391$	0	0
$392$	21.7344	1.09776
$393$	−0.199609	−0.0100690
$394$	−10.1252	−0.510102
$395$	0	0
$396$	14.4431	0.725791
$397$	−23.8954	−1.19928	−0.599639	−	0.800271i	$-0.704689\pi$
$397$	−23.8954	−1.19928	−0.599639	+	0.800271i	$0.704689\pi$
$398$	37.3677	1.87307
$399$	−0.780773	−0.0390876
$400$	0	0
$401$	18.5433	0.926007	0.463003	−	0.886357i	$-0.346772\pi$
$401$	18.5433	0.926007	0.463003	+	0.886357i	$0.346772\pi$
$402$	−2.17386	−0.108422
$403$	30.7597	1.53225
$404$	−3.21988	−0.160195
$405$	0	0
$406$	−3.60579	−0.178952
$407$	4.84164	0.239991
$408$	0	0
$409$	10.7079	0.529469	0.264735	−	0.964321i	$-0.414716\pi$
$409$	10.7079	0.529469	0.264735	+	0.964321i	$0.414716\pi$
$410$	0	0
$411$	1.62945	0.0803747
$412$	−11.6526	−0.574085
$413$	−34.4808	−1.69669
$414$	−42.9154	−2.10918
$415$	0	0
$416$	23.8272	1.16822
$417$	1.79226	0.0877675
$418$	−14.6143	−0.714807
$419$	−10.3145	−0.503895	−0.251947	−	0.967741i	$-0.581071\pi$
$419$	−10.3145	−0.503895	−0.251947	+	0.967741i	$0.581071\pi$
$420$	0	0
$421$	−28.0974	−1.36939	−0.684693	−	0.728832i	$-0.740064\pi$
$421$	−28.0974	−1.36939	−0.684693	+	0.728832i	$0.740064\pi$
$422$	−3.89669	−0.189688
$423$	−14.6101	−0.710368
$424$	−5.70037	−0.276835
$425$	0	0
$426$	−0.0377387	−0.00182844
$427$	−61.4396	−2.97327
$428$	−4.05013	−0.195770
$429$	−2.78544	−0.134482
$430$	0	0
$431$	17.0458	0.821066	0.410533	−	0.911846i	$-0.365343\pi$
$431$	17.0458	0.821066	0.410533	+	0.911846i	$0.365343\pi$
$432$	3.27830	0.157727
$433$	−0.719105	−0.0345580	−0.0172790	−	0.999851i	$-0.505500\pi$
$433$	−0.719105	−0.0345580	−0.0172790	+	0.999851i	$0.505500\pi$
$434$	−46.8188	−2.24738
$435$	0	0
$436$	3.74206	0.179212
$437$	13.7686	0.658644
$438$	1.00799	0.0481639
$439$	11.8427	0.565222	0.282611	−	0.959235i	$-0.408799\pi$
$439$	11.8427	0.565222	0.282611	+	0.959235i	$0.408799\pi$
$440$	0	0
$441$	−35.4190	−1.68662
$442$	0	0
$443$	−2.37057	−0.112629	−0.0563147	−	0.998413i	$-0.517935\pi$
$443$	−2.37057	−0.112629	−0.0563147	+	0.998413i	$0.517935\pi$
$444$	−0.0946641	−0.00449256
$445$	0	0
$446$	27.2219	1.28899
$447$	−0.244515	−0.0115652
$448$	7.10967	0.335900
$449$	−14.1762	−0.669016	−0.334508	−	0.942393i	$-0.608570\pi$
$449$	−14.1762	−0.669016	−0.334508	+	0.942393i	$0.608570\pi$
$450$	0	0
$451$	−28.3608	−1.33546
$452$	8.96993	0.421910
$453$	−0.450525	−0.0211675
$454$	20.5612	0.964984
$455$	0	0
$456$	−0.329698	−0.0154395
$457$	−24.3340	−1.13830	−0.569149	−	0.822235i	$-0.692727\pi$
$457$	−24.3340	−1.13830	−0.569149	+	0.822235i	$0.692727\pi$
$458$	40.3722	1.88647
$459$	0	0
$460$	0	0
$461$	−36.8238	−1.71506	−0.857528	−	0.514437i	$-0.828001\pi$
$461$	−36.8238	−1.71506	−0.857528	+	0.514437i	$0.828001\pi$
$462$	4.23968	0.197248
$463$	−25.0303	−1.16326	−0.581628	−	0.813455i	$-0.697584\pi$
$463$	−25.0303	−1.16326	−0.581628	+	0.813455i	$0.697584\pi$
$464$	−2.42381	−0.112523
$465$	0	0
$466$	22.1963	1.02822
$467$	14.2892	0.661224	0.330612	−	0.943767i	$-0.392745\pi$
$467$	14.2892	0.661224	0.330612	+	0.943767i	$0.392745\pi$
$468$	−13.5451	−0.626123
$469$	50.3225	2.32368
$470$	0	0
$471$	0.283541	0.0130649
$472$	−14.5602	−0.670189
$473$	−39.2163	−1.80317
$474$	1.24268	0.0570783
$475$	0	0
$476$	0	0
$477$	9.28947	0.425336
$478$	44.9472	2.05584
$479$	−32.6409	−1.49140	−0.745701	−	0.666281i	$-0.767885\pi$
$479$	−32.6409	−1.49140	−0.745701	+	0.666281i	$0.767885\pi$
$480$	0	0
$481$	−4.54063	−0.207035
$482$	−38.6548	−1.76068
$483$	−3.99436	−0.181750
$484$	14.9477	0.679441
$485$	0	0
$486$	−5.03744	−0.228503
$487$	−21.4885	−0.973739	−0.486869	−	0.873475i	$-0.661861\pi$
$487$	−21.4885	−0.973739	−0.486869	+	0.873475i	$0.661861\pi$
$488$	−25.9442	−1.17444
$489$	0.524229	0.0237065
$490$	0	0
$491$	15.9151	0.718240	0.359120	−	0.933291i	$-0.383077\pi$
$491$	15.9151	0.718240	0.359120	+	0.933291i	$0.383077\pi$
$492$	0.554513	0.0249994
$493$	0	0
$494$	13.7057	0.616648
$495$	0	0
$496$	−31.4717	−1.41312
$497$	0.873608	0.0391867
$498$	1.97385	0.0884505
$499$	−11.1698	−0.500031	−0.250015	−	0.968242i	$-0.580436\pi$
$499$	−11.1698	−0.500031	−0.250015	+	0.968242i	$0.580436\pi$
$500$	0	0
$501$	−0.128172	−0.00572631
$502$	−49.6230	−2.21478
$503$	−24.0544	−1.07253	−0.536266	−	0.844049i	$-0.680166\pi$
$503$	−24.0544	−1.07253	−0.536266	+	0.844049i	$0.680166\pi$
$504$	−23.7886	−1.05963
$505$	0	0
$506$	−74.7652	−3.32372
$507$	1.18737	0.0527329
$508$	−11.1841	−0.496215
$509$	8.62627	0.382353	0.191176	−	0.981556i	$-0.438770\pi$
$509$	8.62627	0.382353	0.191176	+	0.981556i	$0.438770\pi$
$510$	0	0
$511$	−23.3340	−1.03223
$512$	−6.06200	−0.267905
$513$	1.07673	0.0475387
$514$	−36.9712	−1.63073
$515$	0	0
$516$	0.766758	0.0337547
$517$	−25.4530	−1.11942
$518$	6.91124	0.303662
$519$	−0.198500	−0.00871319
$520$	0	0
$521$	3.15348	0.138157	0.0690783	−	0.997611i	$-0.477994\pi$
$521$	3.15348	0.138157	0.0690783	+	0.997611i	$0.477994\pi$
$522$	2.48130	0.108604
$523$	14.8175	0.647923	0.323962	−	0.946070i	$-0.394985\pi$
$523$	14.8175	0.647923	0.323962	+	0.946070i	$0.394985\pi$
$524$	−1.69105	−0.0738737
$525$	0	0
$526$	17.4978	0.762940
$527$	0	0
$528$	2.84992	0.124027
$529$	47.4391	2.06257
$530$	0	0
$531$	23.7277	1.02970
$532$	−6.61454	−0.286777
$533$	26.5976	1.15207
$534$	2.44912	0.105984
$535$	0	0
$536$	21.2497	0.917848
$537$	−2.00664	−0.0865930
$538$	52.2782	2.25387
$539$	−61.7053	−2.65784
$540$	0	0
$541$	−25.4124	−1.09256	−0.546282	−	0.837602i	$-0.683957\pi$
$541$	−25.4124	−1.09256	−0.546282	+	0.837602i	$0.683957\pi$
$542$	18.4229	0.791333
$543$	−0.505626	−0.0216985
$544$	0	0
$545$	0	0
$546$	−3.97610	−0.170161
$547$	13.1706	0.563133	0.281566	−	0.959542i	$-0.409146\pi$
$547$	13.1706	0.563133	0.281566	+	0.959542i	$0.409146\pi$
$548$	13.8043	0.589692
$549$	42.2793	1.80444
$550$	0	0
$551$	−0.796080	−0.0339142
$552$	−1.68670	−0.0717909
$553$	−28.7667	−1.22329
$554$	−39.2685	−1.66836
$555$	0	0
$556$	15.1837	0.643930
$557$	−27.4786	−1.16431	−0.582154	−	0.813079i	$-0.697790\pi$
$557$	−27.4786	−1.16431	−0.582154	+	0.813079i	$0.697790\pi$
$558$	32.2181	1.36390
$559$	36.7781	1.55555
$560$	0	0
$561$	0	0
$562$	−36.6079	−1.54421
$563$	4.57643	0.192874	0.0964368	−	0.995339i	$-0.469255\pi$
$563$	4.57643	0.192874	0.0964368	+	0.995339i	$0.469255\pi$
$564$	0.497659	0.0209552
$565$	0	0
$566$	26.5376	1.11546
$567$	38.6100	1.62147
$568$	0.368900	0.0154787
$569$	26.9526	1.12991	0.564956	−	0.825121i	$-0.308893\pi$
$569$	26.9526	1.12991	0.564956	+	0.825121i	$0.308893\pi$
$570$	0	0
$571$	30.6171	1.28128	0.640642	−	0.767840i	$-0.278668\pi$
$571$	30.6171	1.28128	0.640642	+	0.767840i	$0.278668\pi$
$572$	−23.5976	−0.986667
$573$	1.27551	0.0532851
$574$	−40.4839	−1.68976
$575$	0	0
$576$	−4.89247	−0.203853
$577$	−28.7634	−1.19744	−0.598718	−	0.800960i	$-0.704323\pi$
$577$	−28.7634	−1.19744	−0.598718	+	0.800960i	$0.704323\pi$
$578$	0	0
$579$	−0.834979	−0.0347005
$580$	0	0
$581$	−45.6925	−1.89565
$582$	−0.221259	−0.00917146
$583$	16.1837	0.670259
$584$	−9.85326	−0.407731
$585$	0	0
$586$	−19.0943	−0.788779
$587$	11.2016	0.462339	0.231170	−	0.972913i	$-0.425745\pi$
$587$	11.2016	0.462339	0.231170	+	0.972913i	$0.425745\pi$
$588$	1.20647	0.0497538
$589$	−10.3366	−0.425912
$590$	0	0
$591$	0.648512	0.0266762
$592$	4.64574	0.190939
$593$	5.70078	0.234103	0.117051	−	0.993126i	$-0.462656\pi$
$593$	5.70078	0.234103	0.117051	+	0.993126i	$0.462656\pi$
$594$	−5.84675	−0.239895
$595$	0	0
$596$	−2.07148	−0.0848510
$597$	−2.39337	−0.0979541
$598$	70.1170	2.86730
$599$	8.28563	0.338542	0.169271	−	0.985570i	$-0.445859\pi$
$599$	8.28563	0.338542	0.169271	+	0.985570i	$0.445859\pi$
$600$	0	0
$601$	−42.9633	−1.75251	−0.876254	−	0.481849i	$-0.839965\pi$
$601$	−42.9633	−1.75251	−0.876254	+	0.481849i	$0.839965\pi$
$602$	−55.9795	−2.28155
$603$	−34.6291	−1.41021
$604$	−3.81675	−0.155301
$605$	0	0
$606$	0.650419	0.0264215
$607$	−18.1339	−0.736032	−0.368016	−	0.929820i	$-0.619963\pi$
$607$	−18.1339	−0.736032	−0.368016	+	0.929820i	$0.619963\pi$
$608$	−8.00697	−0.324726
$609$	0.230948	0.00935847
$610$	0	0
$611$	23.8706	0.965701
$612$	0	0
$613$	17.0246	0.687616	0.343808	−	0.939040i	$-0.388283\pi$
$613$	17.0246	0.687616	0.343808	+	0.939040i	$0.388283\pi$
$614$	−56.0585	−2.26234
$615$	0	0
$616$	−41.4434	−1.66980
$617$	7.40951	0.298296	0.149148	−	0.988815i	$-0.452347\pi$
$617$	7.40951	0.298296	0.149148	+	0.988815i	$0.452347\pi$
$618$	2.35384	0.0946855
$619$	−22.0128	−0.884769	−0.442385	−	0.896825i	$-0.645867\pi$
$619$	−22.0128	−0.884769	−0.442385	+	0.896825i	$0.645867\pi$
$620$	0	0
$621$	5.50844	0.221046
$622$	32.7317	1.31242
$623$	−56.6945	−2.27142
$624$	−2.67274	−0.106995
$625$	0	0
$626$	16.4725	0.658372
$627$	0.936031	0.0373815
$628$	2.40209	0.0958540
$629$	0	0
$630$	0	0
$631$	−32.5360	−1.29524	−0.647619	−	0.761965i	$-0.724235\pi$
$631$	−32.5360	−1.29524	−0.647619	+	0.761965i	$0.724235\pi$
$632$	−12.1474	−0.483196
$633$	0.249579	0.00991989
$634$	−12.8156	−0.508971
$635$	0	0
$636$	−0.316424	−0.0125470
$637$	57.8690	2.29285
$638$	4.32280	0.171141
$639$	−0.601168	−0.0237818
$640$	0	0
$641$	−3.52036	−0.139046	−0.0695229	−	0.997580i	$-0.522148\pi$
$641$	−3.52036	−0.139046	−0.0695229	+	0.997580i	$0.522148\pi$
$642$	0.818130	0.0322890
$643$	−21.1594	−0.834445	−0.417223	−	0.908804i	$-0.636996\pi$
$643$	−21.1594	−0.834445	−0.417223	+	0.908804i	$0.636996\pi$
$644$	−33.8394	−1.33346
$645$	0	0
$646$	0	0
$647$	−9.06885	−0.356533	−0.178267	−	0.983982i	$-0.557049\pi$
$647$	−9.06885	−0.356533	−0.178267	+	0.983982i	$0.557049\pi$
$648$	16.3039	0.640477
$649$	41.3373	1.62263
$650$	0	0
$651$	2.99871	0.117529
$652$	4.44116	0.173929
$653$	−15.2290	−0.595958	−0.297979	−	0.954572i	$-0.596313\pi$
$653$	−15.2290	−0.595958	−0.297979	+	0.954572i	$0.596313\pi$
$654$	−0.755900	−0.0295580
$655$	0	0
$656$	−27.2133	−1.06250
$657$	16.0571	0.626448
$658$	−36.3331	−1.41641
$659$	−4.19934	−0.163583	−0.0817916	−	0.996649i	$-0.526064\pi$
$659$	−4.19934	−0.163583	−0.0817916	+	0.996649i	$0.526064\pi$
$660$	0	0
$661$	46.7564	1.81861	0.909306	−	0.416127i	$-0.136613\pi$
$661$	46.7564	1.81861	0.909306	+	0.416127i	$0.136613\pi$
$662$	−21.5821	−0.838812
$663$	0	0
$664$	−19.2946	−0.748777
$665$	0	0
$666$	−4.75592	−0.184288
$667$	−4.07267	−0.157695
$668$	−1.08585	−0.0420127
$669$	−1.74354	−0.0674090
$670$	0	0
$671$	73.6569	2.84349
$672$	2.32287	0.0896066
$673$	10.3268	0.398068	0.199034	−	0.979993i	$-0.436220\pi$
$673$	10.3268	0.398068	0.199034	+	0.979993i	$0.436220\pi$
$674$	54.3139	2.09209
$675$	0	0
$676$	10.0591	0.386889
$677$	−32.2638	−1.24000	−0.619999	−	0.784602i	$-0.712867\pi$
$677$	−32.2638	−1.24000	−0.619999	+	0.784602i	$0.712867\pi$
$678$	−1.81193	−0.0695869
$679$	5.12189	0.196560
$680$	0	0
$681$	−1.31692	−0.0504647
$682$	56.1288	2.14928
$683$	−20.7965	−0.795755	−0.397877	−	0.917439i	$-0.630253\pi$
$683$	−20.7965	−0.795755	−0.397877	+	0.917439i	$0.630253\pi$
$684$	4.55175	0.174041
$685$	0	0
$686$	−36.0670	−1.37704
$687$	−2.58580	−0.0986546
$688$	−37.6295	−1.43461
$689$	−15.1775	−0.578217
$690$	0	0
$691$	−19.7441	−0.751102	−0.375551	−	0.926802i	$-0.622547\pi$
$691$	−19.7441	−0.751102	−0.375551	+	0.926802i	$0.622547\pi$
$692$	−1.68165	−0.0639267
$693$	67.5372	2.56552
$694$	−6.48946	−0.246336
$695$	0	0
$696$	0.0975224	0.00369658
$697$	0	0
$698$	−28.8588	−1.09232
$699$	−1.42165	−0.0537718
$700$	0	0
$701$	−9.51246	−0.359281	−0.179640	−	0.983732i	$-0.557493\pi$
$701$	−9.51246	−0.359281	−0.179640	+	0.983732i	$0.557493\pi$
$702$	5.48325	0.206952
$703$	1.52585	0.0575486
$704$	−8.52343	−0.321239
$705$	0	0
$706$	42.2856	1.59144
$707$	−15.0565	−0.566258
$708$	−0.808229	−0.0303751
$709$	26.5052	0.995425	0.497713	−	0.867342i	$-0.334173\pi$
$709$	26.5052	0.995425	0.497713	+	0.867342i	$0.334173\pi$
$710$	0	0
$711$	19.7956	0.742395
$712$	−23.9404	−0.897205
$713$	−52.8811	−1.98041
$714$	0	0
$715$	0	0
$716$	−16.9998	−0.635314
$717$	−2.87883	−0.107512
$718$	−28.3844	−1.05929
$719$	−24.3830	−0.909331	−0.454666	−	0.890662i	$-0.650241\pi$
$719$	−24.3830	−0.909331	−0.454666	+	0.890662i	$0.650241\pi$
$720$	0	0
$721$	−54.4889	−2.02927
$722$	27.9091	1.03867
$723$	2.47580	0.0920761
$724$	−4.28355	−0.159197
$725$	0	0
$726$	−3.01945	−0.112062
$727$	0.0836850	0.00310371	0.00155185	−	0.999999i	$-0.499506\pi$
$727$	0.0836850	0.00310371	0.00155185	+	0.999999i	$0.499506\pi$
$728$	38.8668	1.44050
$729$	−26.3534	−0.976052
$730$	0	0
$731$	0	0
$732$	−1.44014	−0.0532293
$733$	3.01445	0.111341	0.0556706	−	0.998449i	$-0.482270\pi$
$733$	3.01445	0.111341	0.0556706	+	0.998449i	$0.482270\pi$
$734$	40.2337	1.48505
$735$	0	0
$736$	−40.9629	−1.50991
$737$	−60.3292	−2.22225
$738$	27.8587	1.02549
$739$	21.4747	0.789958	0.394979	−	0.918690i	$-0.370752\pi$
$739$	21.4747	0.789958	0.394979	+	0.918690i	$0.370752\pi$
$740$	0	0
$741$	−0.877837	−0.0322481
$742$	23.1015	0.848082
$743$	−1.29230	−0.0474101	−0.0237050	−	0.999719i	$-0.507546\pi$
$743$	−1.29230	−0.0474101	−0.0237050	+	0.999719i	$0.507546\pi$
$744$	1.26627	0.0464236
$745$	0	0
$746$	−10.3993	−0.380744
$747$	31.4430	1.15044
$748$	0	0
$749$	−18.9388	−0.692009
$750$	0	0
$751$	−29.3569	−1.07125	−0.535623	−	0.844457i	$-0.679923\pi$
$751$	−29.3569	−1.07125	−0.535623	+	0.844457i	$0.679923\pi$
$752$	−24.4231	−0.890620
$753$	3.17831	0.115824
$754$	−4.05405	−0.147640
$755$	0	0
$756$	−2.64629	−0.0962446
$757$	1.20743	0.0438848	0.0219424	−	0.999759i	$-0.493015\pi$
$757$	1.20743	0.0438848	0.0219424	+	0.999759i	$0.493015\pi$
$758$	0.908973	0.0330154
$759$	4.78865	0.173817
$760$	0	0
$761$	−7.48319	−0.271265	−0.135633	−	0.990759i	$-0.543307\pi$
$761$	−7.48319	−0.271265	−0.135633	+	0.990759i	$0.543307\pi$
$762$	2.25920	0.0818423
$763$	17.4983	0.633479
$764$	10.8058	0.390941
$765$	0	0
$766$	−7.44485	−0.268993
$767$	−38.7673	−1.39981
$768$	1.99763	0.0720832
$769$	−43.3632	−1.56372	−0.781859	−	0.623456i	$-0.785728\pi$
$769$	−43.3632	−1.56372	−0.781859	+	0.623456i	$0.785728\pi$
$770$	0	0
$771$	2.36797	0.0852805
$772$	−7.07376	−0.254590
$773$	35.7762	1.28678	0.643390	−	0.765539i	$-0.277528\pi$
$773$	35.7762	1.28678	0.643390	+	0.765539i	$0.277528\pi$
$774$	38.5219	1.38464
$775$	0	0
$776$	2.16283	0.0776409
$777$	−0.442659	−0.0158803
$778$	−11.0747	−0.397047
$779$	−8.93797	−0.320236
$780$	0	0
$781$	−1.04733	−0.0374763
$782$	0	0
$783$	−0.318489	−0.0113819
$784$	−59.2086	−2.11459
$785$	0	0
$786$	0.341593	0.0121842
$787$	−29.8797	−1.06510	−0.532549	−	0.846399i	$-0.678766\pi$
$787$	−29.8797	−1.06510	−0.532549	+	0.846399i	$0.678766\pi$
$788$	5.49405	0.195718
$789$	−1.12072	−0.0398986
$790$	0	0
$791$	41.9443	1.49137
$792$	28.5190	1.01338
$793$	−69.0776	−2.45302
$794$	40.8924	1.45122
$795$	0	0
$796$	−20.2761	−0.718667
$797$	5.40524	0.191463	0.0957317	−	0.995407i	$-0.469481\pi$
$797$	5.40524	0.191463	0.0957317	+	0.995407i	$0.469481\pi$
$798$	1.33614	0.0472990
$799$	0	0
$800$	0	0
$801$	39.0139	1.37849
$802$	−31.7332	−1.12054
$803$	27.9740	0.987179
$804$	1.17956	0.0415998
$805$	0	0
$806$	−52.6392	−1.85414
$807$	−3.34837	−0.117868
$808$	−6.35792	−0.223671
$809$	30.2974	1.06520	0.532600	−	0.846367i	$-0.321215\pi$
$809$	30.2974	1.06520	0.532600	+	0.846367i	$0.321215\pi$
$810$	0	0
$811$	−44.5944	−1.56592	−0.782961	−	0.622071i	$-0.786292\pi$
$811$	−44.5944	−1.56592	−0.782961	+	0.622071i	$0.786292\pi$
$812$	1.95654	0.0686610
$813$	−1.17997	−0.0413835
$814$	−8.28554	−0.290408
$815$	0	0
$816$	0	0
$817$	−12.3591	−0.432389
$818$	−18.3244	−0.640698
$819$	−63.3383	−2.21322
$820$	0	0
$821$	−13.5220	−0.471921	−0.235961	−	0.971763i	$-0.575824\pi$
$821$	−13.5220	−0.471921	−0.235961	+	0.971763i	$0.575824\pi$
$822$	−2.78849	−0.0972596
$823$	−12.8097	−0.446518	−0.223259	−	0.974759i	$-0.571670\pi$
$823$	−12.8097	−0.446518	−0.223259	+	0.974759i	$0.571670\pi$
$824$	−23.0091	−0.801560
$825$	0	0
$826$	59.0072	2.05312
$827$	32.6667	1.13593	0.567965	−	0.823052i	$-0.307731\pi$
$827$	32.6667	1.13593	0.567965	+	0.823052i	$0.307731\pi$
$828$	23.2863	0.809257
$829$	−21.7442	−0.755207	−0.377603	−	0.925967i	$-0.623252\pi$
$829$	−21.7442	−0.755207	−0.377603	+	0.925967i	$0.623252\pi$
$830$	0	0
$831$	2.51511	0.0872484
$832$	7.99352	0.277126
$833$	0	0
$834$	−3.06711	−0.106205
$835$	0	0
$836$	7.92985	0.274259
$837$	−4.13538	−0.142940
$838$	17.6512	0.609751
$839$	26.6031	0.918441	0.459221	−	0.888322i	$-0.348129\pi$
$839$	26.6031	0.918441	0.459221	+	0.888322i	$0.348129\pi$
$840$	0	0
$841$	−28.7645	−0.991880
$842$	48.0834	1.65706
$843$	2.34470	0.0807558
$844$	2.11438	0.0727800
$845$	0	0
$846$	25.0024	0.859600
$847$	69.8969	2.40169
$848$	15.5288	0.533263
$849$	−1.69971	−0.0583339
$850$	0	0
$851$	7.80612	0.267590
$852$	0.0204774	0.000701543 0
$853$	14.5178	0.497079	0.248539	−	0.968622i	$-0.420049\pi$
$853$	14.5178	0.497079	0.248539	+	0.968622i	$0.420049\pi$
$854$	105.142	3.59789
$855$	0	0
$856$	−7.99731	−0.273342
$857$	54.4262	1.85916	0.929582	−	0.368615i	$-0.120168\pi$
$857$	54.4262	1.85916	0.929582	+	0.368615i	$0.120168\pi$
$858$	4.76675	0.162734
$859$	32.4771	1.10811	0.554053	−	0.832482i	$-0.313081\pi$
$859$	32.4771	1.10811	0.554053	+	0.832482i	$0.313081\pi$
$860$	0	0
$861$	2.59296	0.0883677
$862$	−29.1706	−0.993553
$863$	50.6141	1.72292	0.861462	−	0.507823i	$-0.169549\pi$
$863$	50.6141	1.72292	0.861462	+	0.507823i	$0.169549\pi$
$864$	−3.20336	−0.108981
$865$	0	0
$866$	1.23061	0.0418178
$867$	0	0
$868$	25.4044	0.862281
$869$	34.4870	1.16989
$870$	0	0
$871$	56.5784	1.91709
$872$	7.38900	0.250223
$873$	−3.52460	−0.119290
$874$	−23.5624	−0.797010
$875$	0	0
$876$	−0.546948	−0.0184797
$877$	−8.66586	−0.292625	−0.146313	−	0.989238i	$-0.546741\pi$
$877$	−8.66586	−0.292625	−0.146313	+	0.989238i	$0.546741\pi$
$878$	−20.2665	−0.683963
$879$	1.22297	0.0412499
$880$	0	0
$881$	−3.98342	−0.134205	−0.0671024	−	0.997746i	$-0.521375\pi$
$881$	−3.98342	−0.134205	−0.0671024	+	0.997746i	$0.521375\pi$
$882$	60.6128	2.04094
$883$	−16.9182	−0.569341	−0.284671	−	0.958625i	$-0.591884\pi$
$883$	−16.9182	−0.569341	−0.284671	+	0.958625i	$0.591884\pi$
$884$	0	0
$885$	0	0
$886$	4.05678	0.136290
$887$	−31.6739	−1.06350	−0.531752	−	0.846900i	$-0.678466\pi$
$887$	−31.6739	−1.06350	−0.531752	+	0.846900i	$0.678466\pi$
$888$	−0.186922	−0.00627269
$889$	−52.2981	−1.75402
$890$	0	0
$891$	−46.2876	−1.55069
$892$	−14.7709	−0.494565
$893$	−8.02157	−0.268432
$894$	0.418440	0.0139947
$895$	0	0
$896$	−54.5520	−1.82245
$897$	−4.49093	−0.149948
$898$	24.2598	0.809561
$899$	3.05749	0.101973
$900$	0	0
$901$	0	0
$902$	48.5341	1.61601
$903$	3.58544	0.119316
$904$	17.7118	0.589087
$905$	0	0
$906$	0.770987	0.0256143
$907$	−30.6815	−1.01876	−0.509381	−	0.860541i	$-0.670126\pi$
$907$	−30.6815	−1.01876	−0.509381	+	0.860541i	$0.670126\pi$
$908$	−11.1567	−0.370248
$909$	10.3610	0.343654
$910$	0	0
$911$	47.2836	1.56658	0.783288	−	0.621659i	$-0.213541\pi$
$911$	47.2836	1.56658	0.783288	+	0.621659i	$0.213541\pi$
$912$	0.898157	0.0297409
$913$	54.7785	1.81290
$914$	41.6430	1.37743
$915$	0	0
$916$	−21.9064	−0.723807
$917$	−7.90750	−0.261129
$918$	0	0
$919$	44.6124	1.47163	0.735813	−	0.677184i	$-0.236800\pi$
$919$	44.6124	1.47163	0.735813	+	0.677184i	$0.236800\pi$
$920$	0	0
$921$	3.59050	0.118311
$922$	63.0169	2.07535
$923$	0.982213	0.0323299
$924$	−2.30049	−0.0756807
$925$	0	0
$926$	42.8345	1.40763
$927$	37.4962	1.23154
$928$	2.36841	0.0777468
$929$	−8.94983	−0.293634	−0.146817	−	0.989164i	$-0.546903\pi$
$929$	−8.94983	−0.293634	−0.146817	+	0.989164i	$0.546903\pi$
$930$	0	0
$931$	−19.4465	−0.637334
$932$	−12.0439	−0.394512
$933$	−2.09644	−0.0686343
$934$	−24.4532	−0.800132
$935$	0	0
$936$	−26.7459	−0.874218
$937$	−4.68402	−0.153020	−0.0765102	−	0.997069i	$-0.524378\pi$
$937$	−4.68402	−0.153020	−0.0765102	+	0.997069i	$0.524378\pi$
$938$	−86.1172	−2.81183
$939$	−1.05505	−0.0344302
$940$	0	0
$941$	−47.5249	−1.54927	−0.774634	−	0.632409i	$-0.782066\pi$
$941$	−47.5249	−1.54927	−0.774634	+	0.632409i	$0.782066\pi$
$942$	−0.485225	−0.0158095
$943$	−45.7258	−1.48904
$944$	39.6647	1.29098
$945$	0	0
$946$	67.1111	2.18197
$947$	−19.1409	−0.621997	−0.310998	−	0.950410i	$-0.600663\pi$
$947$	−19.1409	−0.621997	−0.310998	+	0.950410i	$0.600663\pi$
$948$	−0.674292	−0.0219000
$949$	−26.2348	−0.851617
$950$	0	0
$951$	0.820825	0.0266171
$952$	0	0
$953$	−41.5915	−1.34728	−0.673640	−	0.739060i	$-0.735270\pi$
$953$	−41.5915	−1.34728	−0.673640	+	0.739060i	$0.735270\pi$
$954$	−15.8971	−0.514689
$955$	0	0
$956$	−24.3888	−0.788789
$957$	−0.276872	−0.00894999
$958$	55.8586	1.80471
$959$	64.5504	2.08444
$960$	0	0
$961$	8.69961	0.280633
$962$	7.77042	0.250528
$963$	13.0326	0.419970
$964$	20.9745	0.675542
$965$	0	0
$966$	6.83558	0.219931
$967$	−46.3577	−1.49076	−0.745381	−	0.666638i	$-0.767733\pi$
$967$	−46.3577	−1.49076	−0.745381	+	0.666638i	$0.767733\pi$
$968$	29.5154	0.948662
$969$	0	0
$970$	0	0
$971$	−18.5657	−0.595802	−0.297901	−	0.954597i	$-0.596287\pi$
$971$	−18.5657	−0.595802	−0.297901	+	0.954597i	$0.596287\pi$
$972$	2.73337	0.0876728
$973$	71.0003	2.27616
$974$	36.7735	1.17830
$975$	0	0
$976$	70.6766	2.26230
$977$	−46.3204	−1.48192	−0.740961	−	0.671548i	$-0.765629\pi$
$977$	−46.3204	−1.48192	−0.740961	+	0.671548i	$0.765629\pi$
$978$	−0.897118	−0.0286867
$979$	67.9682	2.17227
$980$	0	0
$981$	−12.0413	−0.384449
$982$	−27.2357	−0.869125
$983$	−36.3105	−1.15813	−0.579063	−	0.815283i	$-0.696581\pi$
$983$	−36.3105	−1.15813	−0.579063	+	0.815283i	$0.696581\pi$
$984$	1.09493	0.0349051
$985$	0	0
$986$	0	0
$987$	2.32710	0.0740725
$988$	−7.43684	−0.236597
$989$	−63.2279	−2.01053
$990$	0	0
$991$	−8.15237	−0.258968	−0.129484	−	0.991581i	$-0.541332\pi$
$991$	−8.15237	−0.258968	−0.129484	+	0.991581i	$0.541332\pi$
$992$	30.7523	0.976386
$993$	1.38231	0.0438664
$994$	−1.49501	−0.0474189
$995$	0	0
$996$	−1.07103	−0.0339370
$997$	−21.6186	−0.684668	−0.342334	−	0.939578i	$-0.611217\pi$
$997$	−21.6186	−0.684668	−0.342334	+	0.939578i	$0.611217\pi$
$998$	19.1150	0.605075
$999$	0.610450	0.0193138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bu.1.4	yes	15
5.4	even	2		7225.2.a.bw.1.12	yes	15
17.16	even	2		7225.2.a.bv.1.4	yes	15
85.84	even	2		7225.2.a.bt.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7225.2.a.bt.1.12	✓	15	85.84	even	2
7225.2.a.bu.1.4	yes	15	1.1	even	1	trivial
7225.2.a.bv.1.4	yes	15	17.16	even	2
7225.2.a.bw.1.12	yes	15	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71131 q^{2} +0.109608 q^{3} +0.928572 q^{4} -0.187572 q^{6} +4.34210 q^{7} +1.83354 q^{8} -2.98799 q^{9} +O(q^{10})\)	\(q-1.71131 q^{2} +0.109608 q^{3} +0.928572 q^{4} -0.187572 q^{6} +4.34210 q^{7} +1.83354 q^{8} -2.98799 q^{9} -5.20553 q^{11} +0.101779 q^{12} +4.88189 q^{13} -7.43066 q^{14} -4.99490 q^{16} +5.11336 q^{18} -1.64053 q^{19} +0.475927 q^{21} +8.90825 q^{22} -8.39280 q^{23} +0.200970 q^{24} -8.35442 q^{26} -0.656330 q^{27} +4.03195 q^{28} +0.485258 q^{29} +6.30076 q^{31} +4.88072 q^{32} -0.570566 q^{33} -2.77456 q^{36} -0.930097 q^{37} +2.80745 q^{38} +0.535093 q^{39} +5.44822 q^{41} -0.814458 q^{42} +7.53358 q^{43} -4.83371 q^{44} +14.3627 q^{46} +4.88962 q^{47} -0.547479 q^{48} +11.8538 q^{49} +4.53319 q^{52} -3.10894 q^{53} +1.12318 q^{54} +7.96142 q^{56} -0.179815 q^{57} -0.830425 q^{58} -7.94104 q^{59} -14.1498 q^{61} -10.7825 q^{62} -12.9741 q^{63} +1.63738 q^{64} +0.976414 q^{66} +11.5894 q^{67} -0.919916 q^{69} +0.201195 q^{71} -5.47860 q^{72} -5.37389 q^{73} +1.59168 q^{74} -1.52335 q^{76} -22.6029 q^{77} -0.915709 q^{78} -6.62508 q^{79} +8.89202 q^{81} -9.32358 q^{82} -10.5231 q^{83} +0.441933 q^{84} -12.8923 q^{86} +0.0531880 q^{87} -9.54455 q^{88} -13.0569 q^{89} +21.1977 q^{91} -7.79333 q^{92} +0.690612 q^{93} -8.36764 q^{94} +0.534965 q^{96} +1.17959 q^{97} -20.2855 q^{98} +15.5540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 9 q^{3} + 12 q^{4} + 9 q^{6} - 12 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 15 * q - 9 * q^3 + 12 * q^4 + 9 * q^6 - 12 * q^7 - 6 * q^8 + 12 * q^9	\( 15 q - 9 q^{3} + 12 q^{4} + 9 q^{6} - 12 q^{7} - 6 q^{8} + 12 q^{9} + 6 q^{11} - 24 q^{12} + 6 q^{16} - 12 q^{18} + 6 q^{19} + 30 q^{21} - 12 q^{22} - 36 q^{23} + 18 q^{24} + 36 q^{26} - 36 q^{27} - 24 q^{28} - 18 q^{29} - 12 q^{32} - 12 q^{33} - 9 q^{36} - 12 q^{37} + 6 q^{38} + 9 q^{39} - 18 q^{41} - 36 q^{42} + 3 q^{43} - 12 q^{44} + 21 q^{46} + 3 q^{47} + 12 q^{48} + 15 q^{49} + 27 q^{52} + 21 q^{54} - 6 q^{56} - 39 q^{57} - 18 q^{58} - 12 q^{59} - 15 q^{61} - 54 q^{62} - 60 q^{63} - 36 q^{64} + 18 q^{66} + 24 q^{67} + 42 q^{69} + 6 q^{71} - 66 q^{72} + 9 q^{73} - 36 q^{74} - 18 q^{76} - 30 q^{77} - 30 q^{78} - 9 q^{79} + 51 q^{81} + 36 q^{82} - 15 q^{83} + 9 q^{84} - 36 q^{86} + 51 q^{87} - 30 q^{88} - 24 q^{89} + 27 q^{91} - 15 q^{92} + 42 q^{93} - 57 q^{94} + 42 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) \) 15 * q - 9 * q^3 + 12 * q^4 + 9 * q^6 - 12 * q^7 - 6 * q^8 + 12 * q^9 + 6 * q^11 - 24 * q^12 + 6 * q^16 - 12 * q^18 + 6 * q^19 + 30 * q^21 - 12 * q^22 - 36 * q^23 + 18 * q^24 + 36 * q^26 - 36 * q^27 - 24 * q^28 - 18 * q^29 - 12 * q^32 - 12 * q^33 - 9 * q^36 - 12 * q^37 + 6 * q^38 + 9 * q^39 - 18 * q^41 - 36 * q^42 + 3 * q^43 - 12 * q^44 + 21 * q^46 + 3 * q^47 + 12 * q^48 + 15 * q^49 + 27 * q^52 + 21 * q^54 - 6 * q^56 - 39 * q^57 - 18 * q^58 - 12 * q^59 - 15 * q^61 - 54 * q^62 - 60 * q^63 - 36 * q^64 + 18 * q^66 + 24 * q^67 + 42 * q^69 + 6 * q^71 - 66 * q^72 + 9 * q^73 - 36 * q^74 - 18 * q^76 - 30 * q^77 - 30 * q^78 - 9 * q^79 + 51 * q^81 + 36 * q^82 - 15 * q^83 + 9 * q^84 - 36 * q^86 + 51 * q^87 - 30 * q^88 - 24 * q^89 + 27 * q^91 - 15 * q^92 + 42 * q^93 - 57 * q^94 + 42 * q^96 - 48 * q^97 + 12 * q^99

Introduction

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