LMFDB - Embedded newform 7225.2.a.bv.1.14

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:	$0$
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			1.14
Root			$-2.19490$ 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)

$f(q)$	$=$	$q+2.19490 q^{2} +1.59866 q^{3} +2.81758 q^{4} +3.50890 q^{6} +3.21427 q^{7} +1.79451 q^{8} -0.444285 q^{9} +O(q^{10})$	\(q+2.19490 q^{2} +1.59866 q^{3} +2.81758 q^{4} +3.50890 q^{6} +3.21427 q^{7} +1.79451 q^{8} -0.444285 q^{9} -1.61532 q^{11} +4.50436 q^{12} +6.08473 q^{13} +7.05500 q^{14} -1.69639 q^{16} -0.975161 q^{18} +3.45649 q^{19} +5.13853 q^{21} -3.54545 q^{22} +6.00225 q^{23} +2.86881 q^{24} +13.3554 q^{26} -5.50624 q^{27} +9.05647 q^{28} -3.36302 q^{29} -4.00821 q^{31} -7.31244 q^{32} -2.58234 q^{33} -1.25181 q^{36} +8.05613 q^{37} +7.58665 q^{38} +9.72741 q^{39} +8.41615 q^{41} +11.2785 q^{42} -12.9241 q^{43} -4.55128 q^{44} +13.1743 q^{46} +2.53405 q^{47} -2.71196 q^{48} +3.33153 q^{49} +17.1442 q^{52} +4.83315 q^{53} -12.0856 q^{54} +5.76804 q^{56} +5.52575 q^{57} -7.38150 q^{58} +11.3408 q^{59} +5.48618 q^{61} -8.79762 q^{62} -1.42805 q^{63} -12.6573 q^{64} -5.66798 q^{66} +8.63399 q^{67} +9.59555 q^{69} +10.9876 q^{71} -0.797274 q^{72} -15.3763 q^{73} +17.6824 q^{74} +9.73895 q^{76} -5.19206 q^{77} +21.3507 q^{78} -2.08042 q^{79} -7.46976 q^{81} +18.4726 q^{82} -15.0460 q^{83} +14.4782 q^{84} -28.3671 q^{86} -5.37633 q^{87} -2.89870 q^{88} -4.63732 q^{89} +19.5579 q^{91} +16.9118 q^{92} -6.40777 q^{93} +5.56199 q^{94} -11.6901 q^{96} +8.44400 q^{97} +7.31237 q^{98} +0.717660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.19490	1.55203	0.776014	−	0.630716i	$-0.217239\pi$
$2$	2.19490	1.55203	0.776014	+	0.630716i	$0.217239\pi$
$3$	1.59866	0.922987	0.461493	−	0.887144i	$-0.347314\pi$
$3$	1.59866	0.922987	0.461493	+	0.887144i	$0.347314\pi$
$4$	2.81758	1.40879
$5$	0	0
$5$	0	0
$6$	3.50890	1.43250
$7$	3.21427	1.21488	0.607440	−	0.794366i	$-0.292197\pi$
$7$	3.21427	1.21488	0.607440	+	0.794366i	$0.292197\pi$
$8$	1.79451	0.634455
$9$	−0.444285	−0.148095
$10$	0	0
$11$	−1.61532	−0.487036	−0.243518	−	0.969896i	$-0.578301\pi$
$11$	−1.61532	−0.487036	−0.243518	+	0.969896i	$0.578301\pi$
$12$	4.50436	1.30030
$13$	6.08473	1.68760	0.843800	−	0.536658i	$-0.180314\pi$
$13$	6.08473	1.68760	0.843800	+	0.536658i	$0.180314\pi$
$14$	7.05500	1.88553
$15$	0	0
$16$	−1.69639	−0.424099
$17$	0	0
$17$	0	0
$18$	−0.975161	−0.229848
$19$	3.45649	0.792973	0.396487	−	0.918040i	$-0.370229\pi$
$19$	3.45649	0.792973	0.396487	+	0.918040i	$0.370229\pi$
$20$	0	0
$21$	5.13853	1.12132
$22$	−3.54545	−0.755893
$23$	6.00225	1.25156	0.625778	−	0.780002i	$-0.284782\pi$
$23$	6.00225	1.25156	0.625778	+	0.780002i	$0.284782\pi$
$24$	2.86881	0.585594
$25$	0	0
$26$	13.3554	2.61920
$27$	−5.50624	−1.05968
$28$	9.05647	1.71151
$29$	−3.36302	−0.624498	−0.312249	−	0.950000i	$-0.601082\pi$
$29$	−3.36302	−0.624498	−0.312249	+	0.950000i	$0.601082\pi$
$30$	0	0
$31$	−4.00821	−0.719896	−0.359948	−	0.932972i	$-0.617206\pi$
$31$	−4.00821	−0.719896	−0.359948	+	0.932972i	$0.617206\pi$
$32$	−7.31244	−1.29267
$33$	−2.58234	−0.449528
$34$	0	0
$35$	0	0
$36$	−1.25181	−0.208635
$37$	8.05613	1.32442	0.662210	−	0.749319i	$-0.269619\pi$
$37$	8.05613	1.32442	0.662210	+	0.749319i	$0.269619\pi$
$38$	7.58665	1.23072
$39$	9.72741	1.55763
$40$	0	0
$41$	8.41615	1.31438	0.657191	−	0.753724i	$-0.271745\pi$
$41$	8.41615	1.31438	0.657191	+	0.753724i	$0.271745\pi$
$42$	11.2785	1.74032
$43$	−12.9241	−1.97091	−0.985454	−	0.169942i	$-0.945642\pi$
$43$	−12.9241	−1.97091	−0.985454	+	0.169942i	$0.945642\pi$
$44$	−4.55128	−0.686132
$45$	0	0
$46$	13.1743	1.94245
$47$	2.53405	0.369630	0.184815	−	0.982773i	$-0.440831\pi$
$47$	2.53405	0.369630	0.184815	+	0.982773i	$0.440831\pi$
$48$	−2.71196	−0.391437
$49$	3.33153	0.475933
$50$	0	0
$51$	0	0
$52$	17.1442	2.37747
$53$	4.83315	0.663884	0.331942	−	0.943300i	$-0.392296\pi$
$53$	4.83315	0.663884	0.331942	+	0.943300i	$0.392296\pi$
$54$	−12.0856	−1.64465
$55$	0	0
$56$	5.76804	0.770787
$57$	5.52575	0.731904
$58$	−7.38150	−0.969238
$59$	11.3408	1.47645	0.738225	−	0.674555i	$-0.235664\pi$
$59$	11.3408	1.47645	0.738225	+	0.674555i	$0.235664\pi$
$60$	0	0
$61$	5.48618	0.702433	0.351217	−	0.936294i	$-0.385768\pi$
$61$	5.48618	0.702433	0.351217	+	0.936294i	$0.385768\pi$
$62$	−8.79762	−1.11730
$63$	−1.42805	−0.179918
$64$	−12.6573	−1.58216
$65$	0	0
$66$	−5.66798	−0.697680
$67$	8.63399	1.05481	0.527405	−	0.849614i	$-0.323165\pi$
$67$	8.63399	1.05481	0.527405	+	0.849614i	$0.323165\pi$
$68$	0	0
$69$	9.59555	1.15517
$70$	0	0
$71$	10.9876	1.30398	0.651992	−	0.758226i	$-0.273933\pi$
$71$	10.9876	1.30398	0.651992	+	0.758226i	$0.273933\pi$
$72$	−0.797274	−0.0939597
$73$	−15.3763	−1.79966	−0.899829	−	0.436242i	$-0.856309\pi$
$73$	−15.3763	−1.79966	−0.899829	+	0.436242i	$0.856309\pi$
$74$	17.6824	2.05554
$75$	0	0
$76$	9.73895	1.11713
$77$	−5.19206	−0.591690
$78$	21.3507	2.41749
$79$	−2.08042	−0.234066	−0.117033	−	0.993128i	$-0.537338\pi$
$79$	−2.08042	−0.234066	−0.117033	+	0.993128i	$0.537338\pi$
$80$	0	0
$81$	−7.46976	−0.829973
$82$	18.4726	2.03996
$83$	−15.0460	−1.65152	−0.825759	−	0.564023i	$-0.809253\pi$
$83$	−15.0460	−1.65152	−0.825759	+	0.564023i	$0.809253\pi$
$84$	14.4782	1.57970
$85$	0	0
$86$	−28.3671	−3.05890
$87$	−5.37633	−0.576403
$88$	−2.89870	−0.309003
$89$	−4.63732	−0.491555	−0.245778	−	0.969326i	$-0.579043\pi$
$89$	−4.63732	−0.491555	−0.245778	+	0.969326i	$0.579043\pi$
$90$	0	0
$91$	19.5579	2.05023
$92$	16.9118	1.76318
$93$	−6.40777	−0.664455
$94$	5.56199	0.573676
$95$	0	0
$96$	−11.6901	−1.19312
$97$	8.44400	0.857358	0.428679	−	0.903457i	$-0.358979\pi$
$97$	8.44400	0.857358	0.428679	+	0.903457i	$0.358979\pi$
$98$	7.31237	0.738661
$99$	0.717660	0.0721276
$100$	0	0
$101$	7.80949	0.777073	0.388536	−	0.921433i	$-0.372981\pi$
$101$	7.80949	0.777073	0.388536	+	0.921433i	$0.372981\pi$
$102$	0	0
$103$	−6.08413	−0.599487	−0.299743	−	0.954020i	$-0.596901\pi$
$103$	−6.08413	−0.599487	−0.299743	+	0.954020i	$0.596901\pi$
$104$	10.9191	1.07071
$105$	0	0
$106$	10.6083	1.03037
$107$	9.94305	0.961231	0.480615	−	0.876931i	$-0.340413\pi$
$107$	9.94305	0.961231	0.480615	+	0.876931i	$0.340413\pi$
$108$	−15.5143	−1.49286
$109$	−9.16732	−0.878070	−0.439035	−	0.898470i	$-0.644680\pi$
$109$	−9.16732	−0.878070	−0.439035	+	0.898470i	$0.644680\pi$
$110$	0	0
$111$	12.8790	1.22242
$112$	−5.45267	−0.515229
$113$	5.65653	0.532121	0.266061	−	0.963956i	$-0.414278\pi$
$113$	5.65653	0.532121	0.266061	+	0.963956i	$0.414278\pi$
$114$	12.1285	1.13594
$115$	0	0
$116$	−9.47559	−0.879787
$117$	−2.70335	−0.249925
$118$	24.8920	2.29149
$119$	0	0
$120$	0	0
$121$	−8.39076	−0.762796
$122$	12.0416	1.09020
$123$	13.4546	1.21316
$124$	−11.2935	−1.01418
$125$	0	0
$126$	−3.13443	−0.279237
$127$	−7.73222	−0.686123	−0.343062	−	0.939313i	$-0.611464\pi$
$127$	−7.73222	−0.686123	−0.343062	+	0.939313i	$0.611464\pi$
$128$	−13.1566	−1.16289
$129$	−20.6613	−1.81912
$130$	0	0
$131$	−6.44599	−0.563189	−0.281595	−	0.959533i	$-0.590863\pi$
$131$	−6.44599	−0.563189	−0.281595	+	0.959533i	$0.590863\pi$
$132$	−7.27596	−0.633291
$133$	11.1101	0.963367
$134$	18.9507	1.63710
$135$	0	0
$136$	0	0
$137$	−19.8897	−1.69929	−0.849645	−	0.527355i	$-0.823184\pi$
$137$	−19.8897	−1.69929	−0.849645	+	0.527355i	$0.823184\pi$
$138$	21.0613	1.79285
$139$	6.10079	0.517463	0.258731	−	0.965949i	$-0.416696\pi$
$139$	6.10079	0.517463	0.258731	+	0.965949i	$0.416696\pi$
$140$	0	0
$141$	4.05109	0.341163
$142$	24.1166	2.02382
$143$	−9.82875	−0.821921
$144$	0.753683	0.0628069
$145$	0	0
$146$	−33.7494	−2.79312
$147$	5.32599	0.439280
$148$	22.6988	1.86583
$149$	−8.85073	−0.725080	−0.362540	−	0.931968i	$-0.618090\pi$
$149$	−8.85073	−0.725080	−0.362540	+	0.931968i	$0.618090\pi$
$150$	0	0
$151$	−16.6112	−1.35180	−0.675900	−	0.736993i	$-0.736245\pi$
$151$	−16.6112	−1.35180	−0.675900	+	0.736993i	$0.736245\pi$
$152$	6.20271	0.503106
$153$	0	0
$154$	−11.3960	−0.918320
$155$	0	0
$156$	27.4078	2.19438
$157$	−14.9337	−1.19184	−0.595920	−	0.803044i	$-0.703213\pi$
$157$	−14.9337	−1.19184	−0.595920	+	0.803044i	$0.703213\pi$
$158$	−4.56632	−0.363277
$159$	7.72657	0.612756
$160$	0	0
$161$	19.2928	1.52049
$162$	−16.3954	−1.28814
$163$	3.67013	0.287467	0.143733	−	0.989616i	$-0.454089\pi$
$163$	3.67013	0.287467	0.143733	+	0.989616i	$0.454089\pi$
$164$	23.7132	1.85169
$165$	0	0
$166$	−33.0245	−2.56320
$167$	7.70259	0.596045	0.298022	−	0.954559i	$-0.403673\pi$
$167$	7.70259	0.596045	0.298022	+	0.954559i	$0.403673\pi$
$168$	9.22114	0.711426
$169$	24.0239	1.84799
$170$	0	0
$171$	−1.53567	−0.117435
$172$	−36.4147	−2.77660
$173$	−11.5988	−0.881841	−0.440920	−	0.897546i	$-0.645348\pi$
$173$	−11.5988	−0.881841	−0.440920	+	0.897546i	$0.645348\pi$
$174$	−11.8005	−0.894594
$175$	0	0
$176$	2.74021	0.206551
$177$	18.1301	1.36274
$178$	−10.1785	−0.762907
$179$	−6.44869	−0.481998	−0.240999	−	0.970525i	$-0.577475\pi$
$179$	−6.44869	−0.481998	−0.240999	+	0.970525i	$0.577475\pi$
$180$	0	0
$181$	5.80704	0.431634	0.215817	−	0.976434i	$-0.430759\pi$
$181$	5.80704	0.431634	0.215817	+	0.976434i	$0.430759\pi$
$182$	42.9277	3.18201
$183$	8.77053	0.648337
$184$	10.7711	0.794056
$185$	0	0
$186$	−14.0644	−1.03125
$187$	0	0
$188$	7.13990	0.520731
$189$	−17.6985	−1.28738
$190$	0	0
$191$	−8.58340	−0.621073	−0.310537	−	0.950561i	$-0.600509\pi$
$191$	−8.58340	−0.621073	−0.310537	+	0.950561i	$0.600509\pi$
$192$	−20.2347	−1.46031
$193$	5.21688	0.375519	0.187760	−	0.982215i	$-0.439877\pi$
$193$	5.21688	0.375519	0.187760	+	0.982215i	$0.439877\pi$
$194$	18.5337	1.33064
$195$	0	0
$196$	9.38686	0.670490
$197$	21.2774	1.51595	0.757977	−	0.652282i	$-0.226188\pi$
$197$	21.2774	1.51595	0.757977	+	0.652282i	$0.226188\pi$
$198$	1.57519	0.111944
$199$	−0.878780	−0.0622951	−0.0311475	−	0.999515i	$-0.509916\pi$
$199$	−0.878780	−0.0622951	−0.0311475	+	0.999515i	$0.509916\pi$
$200$	0	0
$201$	13.8028	0.973576
$202$	17.1410	1.20604
$203$	−10.8097	−0.758690
$204$	0	0
$205$	0	0
$206$	−13.3540	−0.930420
$207$	−2.66671	−0.185349
$208$	−10.3221	−0.715708
$209$	−5.58332	−0.386206
$210$	0	0
$211$	16.8256	1.15833	0.579163	−	0.815212i	$-0.303380\pi$
$211$	16.8256	1.15833	0.579163	+	0.815212i	$0.303380\pi$
$212$	13.6178	0.935274
$213$	17.5654	1.20356
$214$	21.8240	1.49186
$215$	0	0
$216$	−9.88101	−0.672318
$217$	−12.8835	−0.874587
$218$	−20.1213	−1.36279
$219$	−24.5815	−1.66106
$220$	0	0
$221$	0	0
$222$	28.2681	1.89723
$223$	−11.3035	−0.756936	−0.378468	−	0.925614i	$-0.623549\pi$
$223$	−11.3035	−0.756936	−0.378468	+	0.925614i	$0.623549\pi$
$224$	−23.5041	−1.57044
$225$	0	0
$226$	12.4155	0.825867
$227$	26.0115	1.72644	0.863221	−	0.504827i	$-0.168444\pi$
$227$	26.0115	1.72644	0.863221	+	0.504827i	$0.168444\pi$
$228$	15.5693	1.03110
$229$	14.5122	0.958995	0.479497	−	0.877543i	$-0.340819\pi$
$229$	14.5122	0.958995	0.479497	+	0.877543i	$0.340819\pi$
$230$	0	0
$231$	−8.30034	−0.546122
$232$	−6.03498	−0.396216
$233$	−23.2433	−1.52272	−0.761358	−	0.648331i	$-0.775467\pi$
$233$	−23.2433	−1.52272	−0.761358	+	0.648331i	$0.775467\pi$
$234$	−5.93359	−0.387891
$235$	0	0
$236$	31.9537	2.08001
$237$	−3.32589	−0.216040
$238$	0	0
$239$	10.3168	0.667337	0.333669	−	0.942690i	$-0.391713\pi$
$239$	10.3168	0.667337	0.333669	+	0.942690i	$0.391713\pi$
$240$	0	0
$241$	19.2576	1.24049	0.620246	−	0.784407i	$-0.287033\pi$
$241$	19.2576	1.24049	0.620246	+	0.784407i	$0.287033\pi$
$242$	−18.4169	−1.18388
$243$	4.57712	0.293623
$244$	15.4578	0.989581
$245$	0	0
$246$	29.5314	1.88285
$247$	21.0318	1.33822
$248$	−7.19278	−0.456742
$249$	−24.0535	−1.52433
$250$	0	0
$251$	−2.47096	−0.155965	−0.0779827	−	0.996955i	$-0.524848\pi$
$251$	−2.47096	−0.155965	−0.0779827	+	0.996955i	$0.524848\pi$
$252$	−4.02365	−0.253466
$253$	−9.69552	−0.609552
$254$	−16.9714	−1.06488
$255$	0	0
$256$	−3.56278	−0.222674
$257$	−1.51132	−0.0942733	−0.0471367	−	0.998888i	$-0.515010\pi$
$257$	−1.51132	−0.0942733	−0.0471367	+	0.998888i	$0.515010\pi$
$258$	−45.3494	−2.82333
$259$	25.8946	1.60901
$260$	0	0
$261$	1.49414	0.0924850
$262$	−14.1483	−0.874085
$263$	−6.71923	−0.414325	−0.207163	−	0.978306i	$-0.566423\pi$
$263$	−6.71923	−0.414325	−0.207163	+	0.978306i	$0.566423\pi$
$264$	−4.63404	−0.285205
$265$	0	0
$266$	24.3855	1.49517
$267$	−7.41350	−0.453699
$268$	24.3270	1.48601
$269$	−10.5528	−0.643417	−0.321708	−	0.946839i	$-0.604257\pi$
$269$	−10.5528	−0.643417	−0.321708	+	0.946839i	$0.604257\pi$
$270$	0	0
$271$	−11.1632	−0.678119	−0.339059	−	0.940765i	$-0.610109\pi$
$271$	−11.1632	−0.678119	−0.339059	+	0.940765i	$0.610109\pi$
$272$	0	0
$273$	31.2665	1.89234
$274$	−43.6559	−2.63735
$275$	0	0
$276$	27.0363	1.62739
$277$	−11.3944	−0.684624	−0.342312	−	0.939586i	$-0.611210\pi$
$277$	−11.3944	−0.684624	−0.342312	+	0.939586i	$0.611210\pi$
$278$	13.3906	0.803116
$279$	1.78079	0.106613
$280$	0	0
$281$	18.2715	1.08999	0.544994	−	0.838440i	$-0.316532\pi$
$281$	18.2715	1.08999	0.544994	+	0.838440i	$0.316532\pi$
$282$	8.89173	0.529495
$283$	7.76060	0.461320	0.230660	−	0.973034i	$-0.425912\pi$
$283$	7.76060	0.461320	0.230660	+	0.973034i	$0.425912\pi$
$284$	30.9584	1.83704
$285$	0	0
$286$	−21.5731	−1.27564
$287$	27.0518	1.59682
$288$	3.24881	0.191438
$289$	0	0
$290$	0	0
$291$	13.4991	0.791330
$292$	−43.3240	−2.53534
$293$	−28.2607	−1.65101	−0.825505	−	0.564395i	$-0.809110\pi$
$293$	−28.2607	−1.65101	−0.825505	+	0.564395i	$0.809110\pi$
$294$	11.6900	0.681775
$295$	0	0
$296$	14.4568	0.840285
$297$	8.89432	0.516101
$298$	−19.4265	−1.12535
$299$	36.5220	2.11212
$300$	0	0
$301$	−41.5416	−2.39442
$302$	−36.4599	−2.09803
$303$	12.4847	0.717228
$304$	−5.86357	−0.336299
$305$	0	0
$306$	0	0
$307$	5.75236	0.328304	0.164152	−	0.986435i	$-0.447511\pi$
$307$	5.75236	0.328304	0.164152	+	0.986435i	$0.447511\pi$
$308$	−14.6291	−0.833568
$309$	−9.72645	−0.553318
$310$	0	0
$311$	−14.5217	−0.823449	−0.411725	−	0.911308i	$-0.635073\pi$
$311$	−14.5217	−0.823449	−0.411725	+	0.911308i	$0.635073\pi$
$312$	17.4559	0.988248
$313$	−21.4575	−1.21285	−0.606426	−	0.795140i	$-0.707397\pi$
$313$	−21.4575	−1.21285	−0.606426	+	0.795140i	$0.707397\pi$
$314$	−32.7780	−1.84977
$315$	0	0
$316$	−5.86176	−0.329750
$317$	−6.66525	−0.374358	−0.187179	−	0.982326i	$-0.559934\pi$
$317$	−6.66525	−0.374358	−0.187179	+	0.982326i	$0.559934\pi$
$318$	16.9590	0.951015
$319$	5.43234	0.304153
$320$	0	0
$321$	15.8956	0.887204
$322$	42.3458	2.35984
$323$	0	0
$324$	−21.0467	−1.16926
$325$	0	0
$326$	8.05556	0.446156
$327$	−14.6554	−0.810447
$328$	15.1029	0.833916
$329$	8.14513	0.449056
$330$	0	0
$331$	−3.13992	−0.172586	−0.0862929	−	0.996270i	$-0.527502\pi$
$331$	−3.13992	−0.172586	−0.0862929	+	0.996270i	$0.527502\pi$
$332$	−42.3935	−2.32664
$333$	−3.57922	−0.196140
$334$	16.9064	0.925078
$335$	0	0
$336$	−8.71697	−0.475550
$337$	−8.00568	−0.436097	−0.218048	−	0.975938i	$-0.569969\pi$
$337$	−8.00568	−0.436097	−0.218048	+	0.975938i	$0.569969\pi$
$338$	52.7300	2.86813
$339$	9.04286	0.491141
$340$	0	0
$341$	6.47452	0.350615
$342$	−3.37063	−0.182263
$343$	−11.7914	−0.636678
$344$	−23.1925	−1.25045
$345$	0	0
$346$	−25.4582	−1.36864
$347$	27.9430	1.50006	0.750029	−	0.661405i	$-0.230039\pi$
$347$	27.9430	1.50006	0.750029	+	0.661405i	$0.230039\pi$
$348$	−15.1483	−0.812032
$349$	−3.27207	−0.175150	−0.0875749	−	0.996158i	$-0.527912\pi$
$349$	−3.27207	−0.175150	−0.0875749	+	0.996158i	$0.527912\pi$
$350$	0	0
$351$	−33.5040	−1.78831
$352$	11.8119	0.629576
$353$	−11.3112	−0.602033	−0.301017	−	0.953619i	$-0.597326\pi$
$353$	−11.3112	−0.602033	−0.301017	+	0.953619i	$0.597326\pi$
$354$	39.7938	2.11502
$355$	0	0
$356$	−13.0660	−0.692499
$357$	0	0
$358$	−14.1542	−0.748075
$359$	1.36170	0.0718680	0.0359340	−	0.999354i	$-0.488559\pi$
$359$	1.36170	0.0718680	0.0359340	+	0.999354i	$0.488559\pi$
$360$	0	0
$361$	−7.05267	−0.371193
$362$	12.7459	0.669908
$363$	−13.4140	−0.704051
$364$	55.1061	2.88835
$365$	0	0
$366$	19.2504	1.00624
$367$	−14.7675	−0.770858	−0.385429	−	0.922738i	$-0.625946\pi$
$367$	−14.7675	−0.770858	−0.385429	+	0.922738i	$0.625946\pi$
$368$	−10.1822	−0.530783
$369$	−3.73917	−0.194653
$370$	0	0
$371$	15.5350	0.806540
$372$	−18.0544	−0.936078
$373$	−18.0123	−0.932642	−0.466321	−	0.884616i	$-0.654421\pi$
$373$	−18.0123	−0.932642	−0.466321	+	0.884616i	$0.654421\pi$
$374$	0	0
$375$	0	0
$376$	4.54739	0.234513
$377$	−20.4631	−1.05390
$378$	−38.8465	−1.99805
$379$	−34.5340	−1.77389	−0.886947	−	0.461871i	$-0.847178\pi$
$379$	−34.5340	−1.77389	−0.886947	+	0.461871i	$0.847178\pi$
$380$	0	0
$381$	−12.3612	−0.633283
$382$	−18.8397	−0.963923
$383$	−8.39329	−0.428877	−0.214438	−	0.976738i	$-0.568792\pi$
$383$	−8.39329	−0.428877	−0.214438	+	0.976738i	$0.568792\pi$
$384$	−21.0329	−1.07333
$385$	0	0
$386$	11.4505	0.582817
$387$	5.74199	0.291882
$388$	23.7917	1.20784
$389$	25.2291	1.27916	0.639582	−	0.768723i	$-0.279107\pi$
$389$	25.2291	1.27916	0.639582	+	0.768723i	$0.279107\pi$
$390$	0	0
$391$	0	0
$392$	5.97847	0.301958
$393$	−10.3050	−0.519816
$394$	46.7018	2.35280
$395$	0	0
$396$	2.02207	0.101613
$397$	−30.9877	−1.55523	−0.777614	−	0.628741i	$-0.783570\pi$
$397$	−30.9877	−1.55523	−0.777614	+	0.628741i	$0.783570\pi$
$398$	−1.92883	−0.0966837
$399$	17.7613	0.889176
$400$	0	0
$401$	−13.3609	−0.667211	−0.333605	−	0.942713i	$-0.608265\pi$
$401$	−13.3609	−0.667211	−0.333605	+	0.942713i	$0.608265\pi$
$402$	30.2958	1.51102
$403$	−24.3889	−1.21490
$404$	22.0039	1.09473
$405$	0	0
$406$	−23.7261	−1.17751
$407$	−13.0132	−0.645040
$408$	0	0
$409$	27.7796	1.37361	0.686805	−	0.726841i	$-0.259012\pi$
$409$	27.7796	1.37361	0.686805	+	0.726841i	$0.259012\pi$
$410$	0	0
$411$	−31.7969	−1.56842
$412$	−17.1425	−0.844552
$413$	36.4525	1.79371
$414$	−5.85316	−0.287667
$415$	0	0
$416$	−44.4942	−2.18151
$417$	9.75310	0.477611
$418$	−12.2548	−0.599403
$419$	−14.7612	−0.721131	−0.360566	−	0.932734i	$-0.617416\pi$
$419$	−14.7612	−0.721131	−0.360566	+	0.932734i	$0.617416\pi$
$420$	0	0
$421$	22.7500	1.10877	0.554384	−	0.832261i	$-0.312954\pi$
$421$	22.7500	1.10877	0.554384	+	0.832261i	$0.312954\pi$
$422$	36.9306	1.79775
$423$	−1.12584	−0.0547403
$424$	8.67314	0.421205
$425$	0	0
$426$	38.5543	1.86796
$427$	17.6341	0.853372
$428$	28.0154	1.35417
$429$	−15.7128	−0.758623
$430$	0	0
$431$	−3.94022	−0.189794	−0.0948968	−	0.995487i	$-0.530252\pi$
$431$	−3.94022	−0.189794	−0.0948968	+	0.995487i	$0.530252\pi$
$432$	9.34076	0.449407
$433$	−9.63689	−0.463119	−0.231560	−	0.972821i	$-0.574383\pi$
$433$	−9.63689	−0.463119	−0.231560	+	0.972821i	$0.574383\pi$
$434$	−28.2779	−1.35738
$435$	0	0
$436$	−25.8297	−1.23702
$437$	20.7467	0.992450
$438$	−53.9538	−2.57801
$439$	−20.5628	−0.981409	−0.490705	−	0.871326i	$-0.663261\pi$
$439$	−20.5628	−0.981409	−0.490705	+	0.871326i	$0.663261\pi$
$440$	0	0
$441$	−1.48015	−0.0704833
$442$	0	0
$443$	29.8971	1.42046	0.710228	−	0.703972i	$-0.248592\pi$
$443$	29.8971	1.42046	0.710228	+	0.703972i	$0.248592\pi$
$444$	36.2877	1.72214
$445$	0	0
$446$	−24.8100	−1.17479
$447$	−14.1493	−0.669240
$448$	−40.6839	−1.92213
$449$	−33.6358	−1.58737	−0.793686	−	0.608328i	$-0.791841\pi$
$449$	−33.6358	−1.58737	−0.793686	+	0.608328i	$0.791841\pi$
$450$	0	0
$451$	−13.5947	−0.640151
$452$	15.9377	0.749648
$453$	−26.5557	−1.24769
$454$	57.0925	2.67949
$455$	0	0
$456$	9.91603	0.464361
$457$	8.72654	0.408210	0.204105	−	0.978949i	$-0.434572\pi$
$457$	8.72654	0.408210	0.204105	+	0.978949i	$0.434572\pi$
$458$	31.8529	1.48839
$459$	0	0
$460$	0	0
$461$	−18.5071	−0.861961	−0.430981	−	0.902361i	$-0.641832\pi$
$461$	−18.5071	−0.861961	−0.430981	+	0.902361i	$0.641832\pi$
$462$	−18.2184	−0.847597
$463$	34.3834	1.59793	0.798967	−	0.601375i	$-0.205380\pi$
$463$	34.3834	1.59793	0.798967	+	0.601375i	$0.205380\pi$
$464$	5.70501	0.264849
$465$	0	0
$466$	−51.0166	−2.36330
$467$	−17.9940	−0.832662	−0.416331	−	0.909213i	$-0.636684\pi$
$467$	−17.9940	−0.832662	−0.416331	+	0.909213i	$0.636684\pi$
$468$	−7.61692	−0.352092
$469$	27.7520	1.28147
$470$	0	0
$471$	−23.8739	−1.10005
$472$	20.3512	0.936741
$473$	20.8765	0.959903
$474$	−7.29999	−0.335300
$475$	0	0
$476$	0	0
$477$	−2.14730	−0.0983179
$478$	22.6443	1.03573
$479$	18.3559	0.838701	0.419351	−	0.907824i	$-0.362258\pi$
$479$	18.3559	0.838701	0.419351	+	0.907824i	$0.362258\pi$
$480$	0	0
$481$	49.0193	2.23509
$482$	42.2685	1.92528
$483$	30.8427	1.40339
$484$	−23.6416	−1.07462
$485$	0	0
$486$	10.0463	0.455711
$487$	15.3303	0.694680	0.347340	−	0.937739i	$-0.387085\pi$
$487$	15.3303	0.694680	0.347340	+	0.937739i	$0.387085\pi$
$488$	9.84500	0.445662
$489$	5.86729	0.265328
$490$	0	0
$491$	−11.3499	−0.512215	−0.256108	−	0.966648i	$-0.582440\pi$
$491$	−11.3499	−0.512215	−0.256108	+	0.966648i	$0.582440\pi$
$492$	37.9093	1.70908
$493$	0	0
$494$	46.1627	2.07696
$495$	0	0
$496$	6.79951	0.305307
$497$	35.3170	1.58418
$498$	−52.7950	−2.36580
$499$	12.3325	0.552079	0.276039	−	0.961146i	$-0.410978\pi$
$499$	12.3325	0.552079	0.276039	+	0.961146i	$0.410978\pi$
$500$	0	0
$501$	12.3138	0.550141
$502$	−5.42350	−0.242063
$503$	−5.99716	−0.267400	−0.133700	−	0.991022i	$-0.542686\pi$
$503$	−5.99716	−0.267400	−0.133700	+	0.991022i	$0.542686\pi$
$504$	−2.56265	−0.114150
$505$	0	0
$506$	−21.2807	−0.946042
$507$	38.4060	1.70567
$508$	−21.7862	−0.966605
$509$	−44.2640	−1.96197	−0.980984	−	0.194090i	$-0.937825\pi$
$509$	−44.2640	−1.96197	−0.980984	+	0.194090i	$0.937825\pi$
$510$	0	0
$511$	−49.4235	−2.18637
$512$	18.4932	0.817290
$513$	−19.0323	−0.840295
$514$	−3.31719	−0.146315
$515$	0	0
$516$	−58.2148	−2.56276
$517$	−4.09329	−0.180023
$518$	56.8360	2.49723
$519$	−18.5425	−0.813927
$520$	0	0
$521$	−23.8047	−1.04290	−0.521451	−	0.853281i	$-0.674609\pi$
$521$	−23.8047	−1.04290	−0.521451	+	0.853281i	$0.674609\pi$
$522$	3.27949	0.143539
$523$	−21.4247	−0.936835	−0.468417	−	0.883507i	$-0.655176\pi$
$523$	−21.4247	−0.936835	−0.468417	+	0.883507i	$0.655176\pi$
$524$	−18.1621	−0.793416
$525$	0	0
$526$	−14.7480	−0.643045
$527$	0	0
$528$	4.38067	0.190644
$529$	13.0270	0.566390
$530$	0	0
$531$	−5.03856	−0.218655
$532$	31.3036	1.35718
$533$	51.2099	2.21815
$534$	−16.2719	−0.704154
$535$	0	0
$536$	15.4938	0.669230
$537$	−10.3093	−0.444878
$538$	−23.1624	−0.998601
$539$	−5.38147	−0.231796
$540$	0	0
$541$	−28.2278	−1.21361	−0.606804	−	0.794852i	$-0.707549\pi$
$541$	−28.2278	−1.21361	−0.606804	+	0.794852i	$0.707549\pi$
$542$	−24.5022	−1.05246
$543$	9.28349	0.398393
$544$	0	0
$545$	0	0
$546$	68.6269	2.93696
$547$	−13.1508	−0.562288	−0.281144	−	0.959666i	$-0.590714\pi$
$547$	−13.1508	−0.562288	−0.281144	+	0.959666i	$0.590714\pi$
$548$	−56.0408	−2.39395
$549$	−2.43743	−0.104027
$550$	0	0
$551$	−11.6243	−0.495210
$552$	17.2193	0.732903
$553$	−6.68704	−0.284362
$554$	−25.0096	−1.06256
$555$	0	0
$556$	17.1895	0.728997
$557$	36.2078	1.53417	0.767087	−	0.641543i	$-0.221705\pi$
$557$	36.2078	1.53417	0.767087	+	0.641543i	$0.221705\pi$
$558$	3.90865	0.165466
$559$	−78.6396	−3.32610
$560$	0	0
$561$	0	0
$562$	40.1042	1.69169
$563$	−24.6156	−1.03743	−0.518713	−	0.854948i	$-0.673589\pi$
$563$	−24.6156	−1.03743	−0.518713	+	0.854948i	$0.673589\pi$
$564$	11.4143	0.480628
$565$	0	0
$566$	17.0337	0.715981
$567$	−24.0098	−1.00832
$568$	19.7173	0.827320
$569$	35.2638	1.47834	0.739168	−	0.673522i	$-0.235219\pi$
$569$	35.2638	1.47834	0.739168	+	0.673522i	$0.235219\pi$
$570$	0	0
$571$	31.4427	1.31584	0.657918	−	0.753090i	$-0.271438\pi$
$571$	31.4427	1.31584	0.657918	+	0.753090i	$0.271438\pi$
$572$	−27.6933	−1.15792
$573$	−13.7219	−0.573242
$574$	59.3759	2.47830
$575$	0	0
$576$	5.62344	0.234310
$577$	32.1350	1.33780	0.668899	−	0.743353i	$-0.266766\pi$
$577$	32.1350	1.33780	0.668899	+	0.743353i	$0.266766\pi$
$578$	0	0
$579$	8.34002	0.346600
$580$	0	0
$581$	−48.3620	−2.00640
$582$	29.6291	1.22817
$583$	−7.80706	−0.323335
$584$	−27.5929	−1.14180
$585$	0	0
$586$	−62.0295	−2.56241
$587$	−28.8260	−1.18977	−0.594887	−	0.803809i	$-0.702803\pi$
$587$	−28.8260	−1.18977	−0.594887	+	0.803809i	$0.702803\pi$
$588$	15.0064	0.618854
$589$	−13.8543	−0.570858
$590$	0	0
$591$	34.0154	1.39921
$592$	−13.6664	−0.561684
$593$	10.9292	0.448810	0.224405	−	0.974496i	$-0.427956\pi$
$593$	10.9292	0.448810	0.224405	+	0.974496i	$0.427956\pi$
$594$	19.5221	0.801003
$595$	0	0
$596$	−24.9377	−1.02149
$597$	−1.40487	−0.0574975
$598$	80.1622	3.27807
$599$	−22.8746	−0.934632	−0.467316	−	0.884090i	$-0.654779\pi$
$599$	−22.8746	−0.934632	−0.467316	+	0.884090i	$0.654779\pi$
$600$	0	0
$601$	−0.323365	−0.0131903	−0.00659516	−	0.999978i	$-0.502099\pi$
$601$	−0.323365	−0.0131903	−0.00659516	+	0.999978i	$0.502099\pi$
$602$	−91.1796	−3.71620
$603$	−3.83595	−0.156212
$604$	−46.8034	−1.90440
$605$	0	0
$606$	27.4027	1.11316
$607$	−41.6507	−1.69055	−0.845275	−	0.534331i	$-0.820564\pi$
$607$	−41.6507	−1.69055	−0.845275	+	0.534331i	$0.820564\pi$
$608$	−25.2754	−1.02505
$609$	−17.2810	−0.700261
$610$	0	0
$611$	15.4190	0.623787
$612$	0	0
$613$	−3.73065	−0.150680	−0.0753398	−	0.997158i	$-0.524004\pi$
$613$	−3.73065	−0.150680	−0.0753398	+	0.997158i	$0.524004\pi$
$614$	12.6258	0.509538
$615$	0	0
$616$	−9.31721	−0.375401
$617$	10.3785	0.417821	0.208910	−	0.977935i	$-0.433008\pi$
$617$	10.3785	0.417821	0.208910	+	0.977935i	$0.433008\pi$
$618$	−21.3486	−0.858766
$619$	−15.4298	−0.620177	−0.310089	−	0.950708i	$-0.600359\pi$
$619$	−15.4298	−0.620177	−0.310089	+	0.950708i	$0.600359\pi$
$620$	0	0
$621$	−33.0498	−1.32624
$622$	−31.8736	−1.27802
$623$	−14.9056	−0.597180
$624$	−16.5015	−0.660590
$625$	0	0
$626$	−47.0971	−1.88238
$627$	−8.92584	−0.356464
$628$	−42.0770	−1.67905
$629$	0	0
$630$	0	0
$631$	−23.2927	−0.927270	−0.463635	−	0.886026i	$-0.653455\pi$
$631$	−23.2927	−0.927270	−0.463635	+	0.886026i	$0.653455\pi$
$632$	−3.73334	−0.148504
$633$	26.8985	1.06912
$634$	−14.6295	−0.581013
$635$	0	0
$636$	21.7702	0.863246
$637$	20.2715	0.803184
$638$	11.9234	0.472054
$639$	−4.88161	−0.193114
$640$	0	0
$641$	28.1094	1.11026	0.555128	−	0.831765i	$-0.312669\pi$
$641$	28.1094	1.11026	0.555128	+	0.831765i	$0.312669\pi$
$642$	34.8891	1.37696
$643$	−23.4590	−0.925132	−0.462566	−	0.886585i	$-0.653071\pi$
$643$	−23.4590	−0.925132	−0.462566	+	0.886585i	$0.653071\pi$
$644$	54.3592	2.14205
$645$	0	0
$646$	0	0
$647$	9.62573	0.378427	0.189213	−	0.981936i	$-0.439406\pi$
$647$	9.62573	0.378427	0.189213	+	0.981936i	$0.439406\pi$
$648$	−13.4046	−0.526581
$649$	−18.3190	−0.719084
$650$	0	0
$651$	−20.5963	−0.807232
$652$	10.3409	0.404980
$653$	14.2875	0.559112	0.279556	−	0.960129i	$-0.409813\pi$
$653$	14.2875	0.559112	0.279556	+	0.960129i	$0.409813\pi$
$654$	−32.1672	−1.25784
$655$	0	0
$656$	−14.2771	−0.557427
$657$	6.83146	0.266520
$658$	17.8777	0.696947
$659$	−22.6678	−0.883010	−0.441505	−	0.897259i	$-0.645555\pi$
$659$	−22.6678	−0.883010	−0.441505	+	0.897259i	$0.645555\pi$
$660$	0	0
$661$	27.7821	1.08060	0.540299	−	0.841473i	$-0.318311\pi$
$661$	27.7821	1.08060	0.540299	+	0.841473i	$0.318311\pi$
$662$	−6.89182	−0.267858
$663$	0	0
$664$	−27.0003	−1.04781
$665$	0	0
$666$	−7.85602	−0.304415
$667$	−20.1857	−0.781593
$668$	21.7027	0.839702
$669$	−18.0704	−0.698642
$670$	0	0
$671$	−8.86191	−0.342110
$672$	−37.5751	−1.44949
$673$	−9.28927	−0.358075	−0.179038	−	0.983842i	$-0.557298\pi$
$673$	−9.28927	−0.358075	−0.179038	+	0.983842i	$0.557298\pi$
$674$	−17.5717	−0.676835
$675$	0	0
$676$	67.6893	2.60343
$677$	40.1934	1.54476	0.772379	−	0.635162i	$-0.219067\pi$
$677$	40.1934	1.54476	0.772379	+	0.635162i	$0.219067\pi$
$678$	19.8482	0.762265
$679$	27.1413	1.04159
$680$	0	0
$681$	41.5835	1.59348
$682$	14.2109	0.544164
$683$	13.1207	0.502051	0.251026	−	0.967980i	$-0.419232\pi$
$683$	13.1207	0.502051	0.251026	+	0.967980i	$0.419232\pi$
$684$	−4.32687	−0.165442
$685$	0	0
$686$	−25.8810	−0.988143
$687$	23.2001	0.885140
$688$	21.9244	0.835859
$689$	29.4084	1.12037
$690$	0	0
$691$	16.8912	0.642570	0.321285	−	0.946982i	$-0.395885\pi$
$691$	16.8912	0.642570	0.321285	+	0.946982i	$0.395885\pi$
$692$	−32.6806	−1.24233
$693$	2.30675	0.0876263
$694$	61.3320	2.32813
$695$	0	0
$696$	−9.64788	−0.365702
$697$	0	0
$698$	−7.18186	−0.271837
$699$	−37.1581	−1.40545
$700$	0	0
$701$	9.31870	0.351962	0.175981	−	0.984394i	$-0.443690\pi$
$701$	9.31870	0.351962	0.175981	+	0.984394i	$0.443690\pi$
$702$	−73.5378	−2.77551
$703$	27.8459	1.05023
$704$	20.4455	0.770568
$705$	0	0
$706$	−24.8269	−0.934372
$707$	25.1018	0.944050
$708$	51.0831	1.91982
$709$	−0.873218	−0.0327944	−0.0163972	−	0.999866i	$-0.505220\pi$
$709$	−0.873218	−0.0327944	−0.0163972	+	0.999866i	$0.505220\pi$
$710$	0	0
$711$	0.924300	0.0346640
$712$	−8.32173	−0.311870
$713$	−24.0583	−0.900989
$714$	0	0
$715$	0	0
$716$	−18.1697	−0.679035
$717$	16.4930	0.615944
$718$	2.98880	0.111541
$719$	0.851141	0.0317422	0.0158711	−	0.999874i	$-0.494948\pi$
$719$	0.851141	0.0317422	0.0158711	+	0.999874i	$0.494948\pi$
$720$	0	0
$721$	−19.5560	−0.728304
$722$	−15.4799	−0.576102
$723$	30.7864	1.14496
$724$	16.3618	0.608082
$725$	0	0
$726$	−29.4423	−1.09271
$727$	7.37846	0.273652	0.136826	−	0.990595i	$-0.456310\pi$
$727$	7.37846	0.273652	0.136826	+	0.990595i	$0.456310\pi$
$728$	35.0970	1.30078
$729$	29.7265	1.10098
$730$	0	0
$731$	0	0
$732$	24.7117	0.913371
$733$	−45.8453	−1.69333	−0.846667	−	0.532124i	$-0.821394\pi$
$733$	−45.8453	−1.69333	−0.846667	+	0.532124i	$0.821394\pi$
$734$	−32.4132	−1.19639
$735$	0	0
$736$	−43.8910	−1.61785
$737$	−13.9466	−0.513730
$738$	−8.20710	−0.302107
$739$	−28.9573	−1.06521	−0.532607	−	0.846363i	$-0.678787\pi$
$739$	−28.9573	−1.06521	−0.532607	+	0.846363i	$0.678787\pi$
$740$	0	0
$741$	33.6227	1.23516
$742$	34.0979	1.25177
$743$	48.6257	1.78391	0.891953	−	0.452129i	$-0.149335\pi$
$743$	48.6257	1.78391	0.891953	+	0.452129i	$0.149335\pi$
$744$	−11.4988	−0.421567
$745$	0	0
$746$	−39.5352	−1.44749
$747$	6.68473	0.244581
$748$	0	0
$749$	31.9596	1.16778
$750$	0	0
$751$	−2.55693	−0.0933036	−0.0466518	−	0.998911i	$-0.514855\pi$
$751$	−2.55693	−0.0933036	−0.0466518	+	0.998911i	$0.514855\pi$
$752$	−4.29875	−0.156759
$753$	−3.95022	−0.143954
$754$	−44.9144	−1.63568
$755$	0	0
$756$	−49.8671	−1.81365
$757$	−35.3746	−1.28571	−0.642855	−	0.765988i	$-0.722250\pi$
$757$	−35.3746	−1.28571	−0.642855	+	0.765988i	$0.722250\pi$
$758$	−75.7987	−2.75313
$759$	−15.4998	−0.562609
$760$	0	0
$761$	54.2877	1.96793	0.983963	−	0.178370i	$-0.0570824\pi$
$761$	54.2877	1.96793	0.983963	+	0.178370i	$0.0570824\pi$
$762$	−27.1316	−0.982873
$763$	−29.4662	−1.06675
$764$	−24.1844	−0.874962
$765$	0	0
$766$	−18.4224	−0.665629
$767$	69.0058	2.49165
$768$	−5.69568	−0.205525
$769$	3.64949	0.131604	0.0658020	−	0.997833i	$-0.479039\pi$
$769$	3.64949	0.131604	0.0658020	+	0.997833i	$0.479039\pi$
$770$	0	0
$771$	−2.41608	−0.0870130
$772$	14.6990	0.529028
$773$	16.1429	0.580620	0.290310	−	0.956933i	$-0.406242\pi$
$773$	16.1429	0.580620	0.290310	+	0.956933i	$0.406242\pi$
$774$	12.6031	0.453008
$775$	0	0
$776$	15.1528	0.543955
$777$	41.3966	1.48510
$778$	55.3753	1.98530
$779$	29.0903	1.04227
$780$	0	0
$781$	−17.7484	−0.635087
$782$	0	0
$783$	18.5176	0.661766
$784$	−5.65159	−0.201843
$785$	0	0
$786$	−22.6183	−0.806769
$787$	22.1167	0.788374	0.394187	−	0.919030i	$-0.371026\pi$
$787$	22.1167	0.788374	0.394187	+	0.919030i	$0.371026\pi$
$788$	59.9509	2.13566
$789$	−10.7418	−0.382417
$790$	0	0
$791$	18.1816	0.646463
$792$	1.28785	0.0457617
$793$	33.3819	1.18543
$794$	−68.0149	−2.41376
$795$	0	0
$796$	−2.47603	−0.0877607
$797$	48.6425	1.72301	0.861504	−	0.507751i	$-0.169523\pi$
$797$	48.6425	1.72301	0.861504	+	0.507751i	$0.169523\pi$
$798$	38.9842	1.38003
$799$	0	0
$800$	0	0
$801$	2.06029	0.0727969
$802$	−29.3258	−1.03553
$803$	24.8376	0.876498
$804$	38.8906	1.37157
$805$	0	0
$806$	−53.5311	−1.88555
$807$	−16.8704	−0.593866
$808$	14.0142	0.493018
$809$	−5.32728	−0.187297	−0.0936486	−	0.995605i	$-0.529853\pi$
$809$	−5.32728	−0.187297	−0.0936486	+	0.995605i	$0.529853\pi$
$810$	0	0
$811$	−16.9694	−0.595876	−0.297938	−	0.954585i	$-0.596299\pi$
$811$	−16.9694	−0.595876	−0.297938	+	0.954585i	$0.596299\pi$
$812$	−30.4571	−1.06884
$813$	−17.8462	−0.625895
$814$	−28.5626	−1.00112
$815$	0	0
$816$	0	0
$817$	−44.6721	−1.56288
$818$	60.9733	2.13188
$819$	−8.68930	−0.303629
$820$	0	0
$821$	−17.7129	−0.618185	−0.309093	−	0.951032i	$-0.600025\pi$
$821$	−17.7129	−0.618185	−0.309093	+	0.951032i	$0.600025\pi$
$822$	−69.7909	−2.43424
$823$	4.77776	0.166542	0.0832710	−	0.996527i	$-0.473463\pi$
$823$	4.77776	0.166542	0.0832710	+	0.996527i	$0.473463\pi$
$824$	−10.9180	−0.380348
$825$	0	0
$826$	80.0095	2.78389
$827$	23.2808	0.809554	0.404777	−	0.914415i	$-0.367349\pi$
$827$	23.2808	0.809554	0.404777	+	0.914415i	$0.367349\pi$
$828$	−7.51367	−0.261118
$829$	6.20920	0.215654	0.107827	−	0.994170i	$-0.465611\pi$
$829$	6.20920	0.215654	0.107827	+	0.994170i	$0.465611\pi$
$830$	0	0
$831$	−18.2158	−0.631899
$832$	−77.0160	−2.67005
$833$	0	0
$834$	21.4071	0.741266
$835$	0	0
$836$	−15.7315	−0.544084
$837$	22.0702	0.762857
$838$	−32.3993	−1.11922
$839$	−9.49799	−0.327907	−0.163954	−	0.986468i	$-0.552425\pi$
$839$	−9.49799	−0.327907	−0.163954	+	0.986468i	$0.552425\pi$
$840$	0	0
$841$	−17.6901	−0.610003
$842$	49.9340	1.72084
$843$	29.2100	1.00605
$844$	47.4076	1.63184
$845$	0	0
$846$	−2.47111	−0.0849585
$847$	−26.9702	−0.926706
$848$	−8.19893	−0.281552
$849$	12.4066	0.425792
$850$	0	0
$851$	48.3549	1.65758
$852$	49.4919	1.69557
$853$	5.96698	0.204305	0.102153	−	0.994769i	$-0.467427\pi$
$853$	5.96698	0.204305	0.102153	+	0.994769i	$0.467427\pi$
$854$	38.7050	1.32446
$855$	0	0
$856$	17.8429	0.609858
$857$	3.61817	0.123594	0.0617972	−	0.998089i	$-0.480317\pi$
$857$	3.61817	0.123594	0.0617972	+	0.998089i	$0.480317\pi$
$858$	−34.4881	−1.17740
$859$	5.52108	0.188377	0.0941885	−	0.995554i	$-0.469974\pi$
$859$	5.52108	0.188377	0.0941885	+	0.995554i	$0.469974\pi$
$860$	0	0
$861$	43.2466	1.47384
$862$	−8.64838	−0.294565
$863$	47.8129	1.62757	0.813785	−	0.581166i	$-0.197403\pi$
$863$	47.8129	1.62757	0.813785	+	0.581166i	$0.197403\pi$
$864$	40.2640	1.36981
$865$	0	0
$866$	−21.1520	−0.718774
$867$	0	0
$868$	−36.3002	−1.23211
$869$	3.36054	0.113998
$870$	0	0
$871$	52.5355	1.78010
$872$	−16.4509	−0.557096
$873$	−3.75154	−0.126970
$874$	45.5369	1.54031
$875$	0	0
$876$	−69.2603	−2.34009
$877$	6.66240	0.224973	0.112487	−	0.993653i	$-0.464118\pi$
$877$	6.66240	0.224973	0.112487	+	0.993653i	$0.464118\pi$
$878$	−45.1333	−1.52317
$879$	−45.1793	−1.52386
$880$	0	0
$881$	−24.8417	−0.836940	−0.418470	−	0.908231i	$-0.637433\pi$
$881$	−24.8417	−0.836940	−0.418470	+	0.908231i	$0.637433\pi$
$882$	−3.24878	−0.109392
$883$	32.0845	1.07973	0.539864	−	0.841752i	$-0.318476\pi$
$883$	32.0845	1.07973	0.539864	+	0.841752i	$0.318476\pi$
$884$	0	0
$885$	0	0
$886$	65.6212	2.20459
$887$	44.6294	1.49851	0.749254	−	0.662282i	$-0.230412\pi$
$887$	44.6294	1.49851	0.749254	+	0.662282i	$0.230412\pi$
$888$	23.1115	0.775572
$889$	−24.8534	−0.833557
$890$	0	0
$891$	12.0660	0.404227
$892$	−31.8484	−1.06636
$893$	8.75893	0.293106
$894$	−31.0563	−1.03868
$895$	0	0
$896$	−42.2887	−1.41277
$897$	58.3863	1.94946
$898$	−73.8272	−2.46365
$899$	13.4797	0.449573
$900$	0	0
$901$	0	0
$902$	−29.8391	−0.993532
$903$	−66.4109	−2.21002
$904$	10.1507	0.337607
$905$	0	0
$906$	−58.2870	−1.93646
$907$	−13.7992	−0.458196	−0.229098	−	0.973403i	$-0.573578\pi$
$907$	−13.7992	−0.458196	−0.229098	+	0.973403i	$0.573578\pi$
$908$	73.2894	2.43220
$909$	−3.46964	−0.115081
$910$	0	0
$911$	48.7114	1.61388	0.806940	−	0.590633i	$-0.201122\pi$
$911$	48.7114	1.61388	0.806940	+	0.590633i	$0.201122\pi$
$912$	−9.37386	−0.310400
$913$	24.3041	0.804348
$914$	19.1539	0.633554
$915$	0	0
$916$	40.8894	1.35102
$917$	−20.7192	−0.684207
$918$	0	0
$919$	−43.6154	−1.43874	−0.719370	−	0.694628i	$-0.755569\pi$
$919$	−43.6154	−1.43874	−0.719370	+	0.694628i	$0.755569\pi$
$920$	0	0
$921$	9.19606	0.303021
$922$	−40.6212	−1.33779
$923$	66.8563	2.20060
$924$	−23.3869	−0.769372
$925$	0	0
$926$	75.4682	2.48004
$927$	2.70309	0.0887810
$928$	24.5919	0.807268
$929$	17.5780	0.576717	0.288358	−	0.957523i	$-0.406891\pi$
$929$	17.5780	0.576717	0.288358	+	0.957523i	$0.406891\pi$
$930$	0	0
$931$	11.5154	0.377402
$932$	−65.4898	−2.14519
$933$	−23.2152	−0.760033
$934$	−39.4950	−1.29231
$935$	0	0
$936$	−4.85119	−0.158566
$937$	−22.1447	−0.723436	−0.361718	−	0.932288i	$-0.617810\pi$
$937$	−22.1447	−0.723436	−0.361718	+	0.932288i	$0.617810\pi$
$938$	60.9128	1.98887
$939$	−34.3033	−1.11945
$940$	0	0
$941$	−42.7957	−1.39510	−0.697550	−	0.716536i	$-0.745727\pi$
$941$	−42.7957	−1.39510	−0.697550	+	0.716536i	$0.745727\pi$
$942$	−52.4009	−1.70731
$943$	50.5158	1.64502
$944$	−19.2385	−0.626160
$945$	0	0
$946$	45.8218	1.48980
$947$	9.90461	0.321856	0.160928	−	0.986966i	$-0.448551\pi$
$947$	9.90461	0.321856	0.160928	+	0.986966i	$0.448551\pi$
$948$	−9.37096	−0.304355
$949$	−93.5605	−3.03710
$950$	0	0
$951$	−10.6555	−0.345527
$952$	0	0
$953$	−32.3327	−1.04736	−0.523680	−	0.851915i	$-0.675441\pi$
$953$	−32.3327	−1.04736	−0.523680	+	0.851915i	$0.675441\pi$
$954$	−4.71310	−0.152592
$955$	0	0
$956$	29.0684	0.940139
$957$	8.68447	0.280729
$958$	40.2893	1.30169
$959$	−63.9308	−2.06443
$960$	0	0
$961$	−14.9342	−0.481750
$962$	107.592	3.46892
$963$	−4.41755	−0.142353
$964$	54.2599	1.74759
$965$	0	0
$966$	67.6966	2.17810
$967$	−15.1062	−0.485781	−0.242891	−	0.970054i	$-0.578096\pi$
$967$	−15.1062	−0.485781	−0.242891	+	0.970054i	$0.578096\pi$
$968$	−15.0573	−0.483960
$969$	0	0
$970$	0	0
$971$	−40.2430	−1.29146	−0.645730	−	0.763565i	$-0.723447\pi$
$971$	−40.2430	−1.29146	−0.645730	+	0.763565i	$0.723447\pi$
$972$	12.8964	0.413653
$973$	19.6096	0.628655
$974$	33.6484	1.07816
$975$	0	0
$976$	−9.30672	−0.297901
$977$	−0.942962	−0.0301680	−0.0150840	−	0.999886i	$-0.504802\pi$
$977$	−0.942962	−0.0301680	−0.0150840	+	0.999886i	$0.504802\pi$
$978$	12.8781	0.411796
$979$	7.49074	0.239405
$980$	0	0
$981$	4.07290	0.130038
$982$	−24.9119	−0.794972
$983$	48.2639	1.53938	0.769689	−	0.638419i	$-0.220411\pi$
$983$	48.2639	1.53938	0.769689	+	0.638419i	$0.220411\pi$
$984$	24.1444	0.769694
$985$	0	0
$986$	0	0
$987$	13.0213	0.414472
$988$	59.2588	1.88527
$989$	−77.5737	−2.46670
$990$	0	0
$991$	−25.1122	−0.797715	−0.398858	−	0.917013i	$-0.630593\pi$
$991$	−25.1122	−0.797715	−0.398858	+	0.917013i	$0.630593\pi$
$992$	29.3098	0.930587
$993$	−5.01967	−0.159294
$994$	77.5173	2.45870
$995$	0	0
$996$	−67.7727	−2.14746
$997$	20.0022	0.633475	0.316737	−	0.948513i	$-0.397413\pi$
$997$	20.0022	0.633475	0.316737	+	0.948513i	$0.397413\pi$
$998$	27.0686	0.856842
$999$	−44.3590	−1.40346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bv.1.14	yes	15
5.4	even	2		7225.2.a.bt.1.2	✓	15
17.16	even	2		7225.2.a.bu.1.14	yes	15
85.84	even	2		7225.2.a.bw.1.2	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7225.2.a.bt.1.2	✓	15	5.4	even	2
7225.2.a.bu.1.14	yes	15	17.16	even	2
7225.2.a.bv.1.14	yes	15	1.1	even	1	trivial
7225.2.a.bw.1.2	yes	15	85.84	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)

\(f(q)\)	\(=\)	\(q+2.19490 q^{2} +1.59866 q^{3} +2.81758 q^{4} +3.50890 q^{6} +3.21427 q^{7} +1.79451 q^{8} -0.444285 q^{9} +O(q^{10})\)	\(q+2.19490 q^{2} +1.59866 q^{3} +2.81758 q^{4} +3.50890 q^{6} +3.21427 q^{7} +1.79451 q^{8} -0.444285 q^{9} -1.61532 q^{11} +4.50436 q^{12} +6.08473 q^{13} +7.05500 q^{14} -1.69639 q^{16} -0.975161 q^{18} +3.45649 q^{19} +5.13853 q^{21} -3.54545 q^{22} +6.00225 q^{23} +2.86881 q^{24} +13.3554 q^{26} -5.50624 q^{27} +9.05647 q^{28} -3.36302 q^{29} -4.00821 q^{31} -7.31244 q^{32} -2.58234 q^{33} -1.25181 q^{36} +8.05613 q^{37} +7.58665 q^{38} +9.72741 q^{39} +8.41615 q^{41} +11.2785 q^{42} -12.9241 q^{43} -4.55128 q^{44} +13.1743 q^{46} +2.53405 q^{47} -2.71196 q^{48} +3.33153 q^{49} +17.1442 q^{52} +4.83315 q^{53} -12.0856 q^{54} +5.76804 q^{56} +5.52575 q^{57} -7.38150 q^{58} +11.3408 q^{59} +5.48618 q^{61} -8.79762 q^{62} -1.42805 q^{63} -12.6573 q^{64} -5.66798 q^{66} +8.63399 q^{67} +9.59555 q^{69} +10.9876 q^{71} -0.797274 q^{72} -15.3763 q^{73} +17.6824 q^{74} +9.73895 q^{76} -5.19206 q^{77} +21.3507 q^{78} -2.08042 q^{79} -7.46976 q^{81} +18.4726 q^{82} -15.0460 q^{83} +14.4782 q^{84} -28.3671 q^{86} -5.37633 q^{87} -2.89870 q^{88} -4.63732 q^{89} +19.5579 q^{91} +16.9118 q^{92} -6.40777 q^{93} +5.56199 q^{94} -11.6901 q^{96} +8.44400 q^{97} +7.31237 q^{98} +0.717660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 9 q^{3} + 12 q^{4} - 9 q^{6} + 12 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 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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