LMFDB - Embedded newform 9025.2.a.ct.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.47917 q^{2} -2.48321 q^{3} +0.187941 q^{4} -3.67308 q^{6} -3.24988 q^{7} -2.68034 q^{8} +3.16631 q^{9} +O(q^{10})$	\(q+1.47917 q^{2} -2.48321 q^{3} +0.187941 q^{4} -3.67308 q^{6} -3.24988 q^{7} -2.68034 q^{8} +3.16631 q^{9} -4.18399 q^{11} -0.466696 q^{12} -1.78413 q^{13} -4.80712 q^{14} -4.34056 q^{16} +6.33226 q^{17} +4.68351 q^{18} +8.07011 q^{21} -6.18883 q^{22} +1.43368 q^{23} +6.65584 q^{24} -2.63904 q^{26} -0.412988 q^{27} -0.610785 q^{28} +0.339390 q^{29} +2.77865 q^{31} -1.05974 q^{32} +10.3897 q^{33} +9.36648 q^{34} +0.595080 q^{36} +2.70482 q^{37} +4.43037 q^{39} +7.13821 q^{41} +11.9371 q^{42} +9.89425 q^{43} -0.786344 q^{44} +2.12065 q^{46} -0.445441 q^{47} +10.7785 q^{48} +3.56169 q^{49} -15.7243 q^{51} -0.335312 q^{52} +7.23734 q^{53} -0.610879 q^{54} +8.71078 q^{56} +0.502015 q^{58} -3.14263 q^{59} -3.06562 q^{61} +4.11009 q^{62} -10.2901 q^{63} +7.11359 q^{64} +15.3681 q^{66} -8.55254 q^{67} +1.19009 q^{68} -3.56011 q^{69} -12.8928 q^{71} -8.48680 q^{72} -1.82227 q^{73} +4.00089 q^{74} +13.5974 q^{77} +6.55327 q^{78} -0.698700 q^{79} -8.47340 q^{81} +10.5586 q^{82} -0.552985 q^{83} +1.51671 q^{84} +14.6353 q^{86} -0.842775 q^{87} +11.2145 q^{88} -6.82870 q^{89} +5.79822 q^{91} +0.269446 q^{92} -6.89995 q^{93} -0.658883 q^{94} +2.63155 q^{96} +13.2006 q^{97} +5.26835 q^{98} -13.2478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

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 $

$2$	1.47917	1.04593	0.522965	−	0.852354i	$-0.324826\pi$
$2$	1.47917	1.04593	0.522965	+	0.852354i	$0.324826\pi$
$3$	−2.48321	−1.43368	−0.716840	−	0.697238i	$-0.754412\pi$
$3$	−2.48321	−1.43368	−0.716840	+	0.697238i	$0.754412\pi$
$4$	0.187941	0.0939705
$5$	0	0
$5$	0	0
$6$	−3.67308	−1.49953
$7$	−3.24988	−1.22834	−0.614169	−	0.789175i	$-0.710509\pi$
$7$	−3.24988	−1.22834	−0.614169	+	0.789175i	$0.710509\pi$
$8$	−2.68034	−0.947644
$9$	3.16631	1.05544
$10$	0	0
$11$	−4.18399	−1.26152	−0.630760	−	0.775978i	$-0.717257\pi$
$11$	−4.18399	−1.26152	−0.630760	+	0.775978i	$0.717257\pi$
$12$	−0.466696	−0.134724
$13$	−1.78413	−0.494830	−0.247415	−	0.968910i	$-0.579581\pi$
$13$	−1.78413	−0.494830	−0.247415	+	0.968910i	$0.579581\pi$
$14$	−4.80712	−1.28476
$15$	0	0
$16$	−4.34056	−1.08514
$17$	6.33226	1.53580	0.767899	−	0.640571i	$-0.221302\pi$
$17$	6.33226	1.53580	0.767899	+	0.640571i	$0.221302\pi$
$18$	4.68351	1.10391
$19$	0	0
$19$	0	0
$20$	0	0
$21$	8.07011	1.76104
$22$	−6.18883	−1.31946
$23$	1.43368	0.298942	0.149471	−	0.988766i	$-0.452243\pi$
$23$	1.43368	0.298942	0.149471	+	0.988766i	$0.452243\pi$
$24$	6.65584	1.35862
$25$	0	0
$26$	−2.63904	−0.517558
$27$	−0.412988	−0.0794796
$28$	−0.610785	−0.115428
$29$	0.339390	0.0630231	0.0315116	−	0.999503i	$-0.489968\pi$
$29$	0.339390	0.0630231	0.0315116	+	0.999503i	$0.489968\pi$
$30$	0	0
$31$	2.77865	0.499060	0.249530	−	0.968367i	$-0.419724\pi$
$31$	2.77865	0.499060	0.249530	+	0.968367i	$0.419724\pi$
$32$	−1.05974	−0.187337
$33$	10.3897	1.80862
$34$	9.36648	1.60634
$35$	0	0
$36$	0.595080	0.0991800
$37$	2.70482	0.444670	0.222335	−	0.974970i	$-0.428632\pi$
$37$	2.70482	0.444670	0.222335	+	0.974970i	$0.428632\pi$
$38$	0	0
$39$	4.43037	0.709427
$40$	0	0
$41$	7.13821	1.11480	0.557401	−	0.830244i	$-0.311799\pi$
$41$	7.13821	1.11480	0.557401	+	0.830244i	$0.311799\pi$
$42$	11.9371	1.84193
$43$	9.89425	1.50886	0.754429	−	0.656381i	$-0.227914\pi$
$43$	9.89425	1.50886	0.754429	+	0.656381i	$0.227914\pi$
$44$	−0.786344	−0.118546
$45$	0	0
$46$	2.12065	0.312673
$47$	−0.445441	−0.0649743	−0.0324871	−	0.999472i	$-0.510343\pi$
$47$	−0.445441	−0.0649743	−0.0324871	+	0.999472i	$0.510343\pi$
$48$	10.7785	1.55574
$49$	3.56169	0.508813
$50$	0	0
$51$	−15.7243	−2.20184
$52$	−0.335312	−0.0464994
$53$	7.23734	0.994125	0.497062	−	0.867715i	$-0.334412\pi$
$53$	7.23734	0.994125	0.497062	+	0.867715i	$0.334412\pi$
$54$	−0.610879	−0.0831301
$55$	0	0
$56$	8.71078	1.16403
$57$	0	0
$58$	0.502015	0.0659178
$59$	−3.14263	−0.409136	−0.204568	−	0.978852i	$-0.565579\pi$
$59$	−3.14263	−0.409136	−0.204568	+	0.978852i	$0.565579\pi$
$60$	0	0
$61$	−3.06562	−0.392512	−0.196256	−	0.980553i	$-0.562878\pi$
$61$	−3.06562	−0.392512	−0.196256	+	0.980553i	$0.562878\pi$
$62$	4.11009	0.521982
$63$	−10.2901	−1.29643
$64$	7.11359	0.889198
$65$	0	0
$66$	15.3681	1.89169
$67$	−8.55254	−1.04486	−0.522430	−	0.852682i	$-0.674974\pi$
$67$	−8.55254	−1.04486	−0.522430	+	0.852682i	$0.674974\pi$
$68$	1.19009	0.144320
$69$	−3.56011	−0.428587
$70$	0	0
$71$	−12.8928	−1.53009	−0.765046	−	0.643975i	$-0.777284\pi$
$71$	−12.8928	−1.53009	−0.765046	+	0.643975i	$0.777284\pi$
$72$	−8.48680	−1.00018
$73$	−1.82227	−0.213281	−0.106640	−	0.994298i	$-0.534009\pi$
$73$	−1.82227	−0.213281	−0.106640	+	0.994298i	$0.534009\pi$
$74$	4.00089	0.465094
$75$	0	0
$76$	0	0
$77$	13.5974	1.54957
$78$	6.55327	0.742012
$79$	−0.698700	−0.0786099	−0.0393050	−	0.999227i	$-0.512514\pi$
$79$	−0.698700	−0.0786099	−0.0393050	+	0.999227i	$0.512514\pi$
$80$	0	0
$81$	−8.47340	−0.941489
$82$	10.5586	1.16600
$83$	−0.552985	−0.0606980	−0.0303490	−	0.999539i	$-0.509662\pi$
$83$	−0.552985	−0.0606980	−0.0303490	+	0.999539i	$0.509662\pi$
$84$	1.51671	0.165486
$85$	0	0
$86$	14.6353	1.57816
$87$	−0.842775	−0.0903550
$88$	11.2145	1.19547
$89$	−6.82870	−0.723841	−0.361920	−	0.932209i	$-0.617879\pi$
$89$	−6.82870	−0.723841	−0.361920	+	0.932209i	$0.617879\pi$
$90$	0	0
$91$	5.79822	0.607818
$92$	0.269446	0.0280917
$93$	−6.89995	−0.715492
$94$	−0.658883	−0.0679586
$95$	0	0
$96$	2.63155	0.268582
$97$	13.2006	1.34032	0.670160	−	0.742217i	$-0.266226\pi$
$97$	13.2006	1.34032	0.670160	+	0.742217i	$0.266226\pi$
$98$	5.26835	0.532183
$99$	−13.2478	−1.33146
$100$	0	0
$101$	17.2757	1.71899	0.859496	−	0.511142i	$-0.170777\pi$
$101$	17.2757	1.71899	0.859496	+	0.511142i	$0.170777\pi$
$102$	−23.2589	−2.30297
$103$	−13.8286	−1.36257	−0.681286	−	0.732017i	$-0.738579\pi$
$103$	−13.8286	−1.36257	−0.681286	+	0.732017i	$0.738579\pi$
$104$	4.78209	0.468922
$105$	0	0
$106$	10.7052	1.03979
$107$	3.26460	0.315600	0.157800	−	0.987471i	$-0.449560\pi$
$107$	3.26460	0.315600	0.157800	+	0.987471i	$0.449560\pi$
$108$	−0.0776174	−0.00746874
$109$	3.22094	0.308510	0.154255	−	0.988031i	$-0.450702\pi$
$109$	3.22094	0.308510	0.154255	+	0.988031i	$0.450702\pi$
$110$	0	0
$111$	−6.71663	−0.637514
$112$	14.1063	1.33292
$113$	−4.71007	−0.443086	−0.221543	−	0.975151i	$-0.571109\pi$
$113$	−4.71007	−0.443086	−0.221543	+	0.975151i	$0.571109\pi$
$114$	0	0
$115$	0	0
$116$	0.0637853	0.00592232
$117$	−5.64913	−0.522262
$118$	−4.64849	−0.427928
$119$	−20.5791	−1.88648
$120$	0	0
$121$	6.50577	0.591434
$122$	−4.53457	−0.410541
$123$	−17.7257	−1.59827
$124$	0.522222	0.0468969
$125$	0	0
$126$	−15.2208	−1.35598
$127$	−0.592012	−0.0525325	−0.0262663	−	0.999655i	$-0.508362\pi$
$127$	−0.592012	−0.0525325	−0.0262663	+	0.999655i	$0.508362\pi$
$128$	12.6417	1.11738
$129$	−24.5695	−2.16322
$130$	0	0
$131$	−20.5490	−1.79538	−0.897689	−	0.440629i	$-0.854755\pi$
$131$	−20.5490	−1.79538	−0.897689	+	0.440629i	$0.854755\pi$
$132$	1.95265	0.169957
$133$	0	0
$134$	−12.6507	−1.09285
$135$	0	0
$136$	−16.9726	−1.45539
$137$	8.75406	0.747910	0.373955	−	0.927447i	$-0.378001\pi$
$137$	8.75406	0.747910	0.373955	+	0.927447i	$0.378001\pi$
$138$	−5.26601	−0.448272
$139$	7.68939	0.652205	0.326103	−	0.945334i	$-0.394264\pi$
$139$	7.68939	0.652205	0.326103	+	0.945334i	$0.394264\pi$
$140$	0	0
$141$	1.10612	0.0931523
$142$	−19.0706	−1.60037
$143$	7.46480	0.624238
$144$	−13.7436	−1.14530
$145$	0	0
$146$	−2.69545	−0.223077
$147$	−8.84442	−0.729475
$148$	0.508347	0.0417859
$149$	−14.9414	−1.22404	−0.612022	−	0.790841i	$-0.709644\pi$
$149$	−14.9414	−1.22404	−0.612022	+	0.790841i	$0.709644\pi$
$150$	0	0
$151$	−13.1424	−1.06951	−0.534757	−	0.845006i	$-0.679597\pi$
$151$	−13.1424	−1.06951	−0.534757	+	0.845006i	$0.679597\pi$
$152$	0	0
$153$	20.0499	1.62094
$154$	20.1129	1.62075
$155$	0	0
$156$	0.832649	0.0666653
$157$	10.8372	0.864902	0.432451	−	0.901657i	$-0.357649\pi$
$157$	10.8372	0.864902	0.432451	+	0.901657i	$0.357649\pi$
$158$	−1.03350	−0.0822205
$159$	−17.9718	−1.42526
$160$	0	0
$161$	−4.65927	−0.367202
$162$	−12.5336	−0.984732
$163$	8.44554	0.661506	0.330753	−	0.943717i	$-0.392697\pi$
$163$	8.44554	0.661506	0.330753	+	0.943717i	$0.392697\pi$
$164$	1.34156	0.104758
$165$	0	0
$166$	−0.817959	−0.0634859
$167$	19.9012	1.54000	0.770002	−	0.638041i	$-0.220255\pi$
$167$	19.9012	1.54000	0.770002	+	0.638041i	$0.220255\pi$
$168$	−21.6307	−1.66884
$169$	−9.81686	−0.755143
$170$	0	0
$171$	0	0
$172$	1.85954	0.141788
$173$	−11.7211	−0.891135	−0.445568	−	0.895248i	$-0.646998\pi$
$173$	−11.7211	−0.891135	−0.445568	+	0.895248i	$0.646998\pi$
$174$	−1.24661	−0.0945050
$175$	0	0
$176$	18.1609	1.36893
$177$	7.80380	0.586570
$178$	−10.1008	−0.757087
$179$	−7.08378	−0.529467	−0.264733	−	0.964322i	$-0.585284\pi$
$179$	−7.08378	−0.529467	−0.264733	+	0.964322i	$0.585284\pi$
$180$	0	0
$181$	−9.28177	−0.689908	−0.344954	−	0.938620i	$-0.612106\pi$
$181$	−9.28177	−0.689908	−0.344954	+	0.938620i	$0.612106\pi$
$182$	8.57654	0.635735
$183$	7.61257	0.562737
$184$	−3.84274	−0.283291
$185$	0	0
$186$	−10.2062	−0.748355
$187$	−26.4941	−1.93744
$188$	−0.0837167	−0.00610567
$189$	1.34216	0.0976277
$190$	0	0
$191$	8.12426	0.587850	0.293925	−	0.955828i	$-0.405038\pi$
$191$	8.12426	0.587850	0.293925	+	0.955828i	$0.405038\pi$
$192$	−17.6645	−1.27483
$193$	−7.72342	−0.555944	−0.277972	−	0.960589i	$-0.589662\pi$
$193$	−7.72342	−0.555944	−0.277972	+	0.960589i	$0.589662\pi$
$194$	19.5259	1.40188
$195$	0	0
$196$	0.669388	0.0478135
$197$	3.56762	0.254183	0.127091	−	0.991891i	$-0.459436\pi$
$197$	3.56762	0.254183	0.127091	+	0.991891i	$0.459436\pi$
$198$	−19.5958	−1.39261
$199$	−8.76938	−0.621645	−0.310822	−	0.950468i	$-0.600604\pi$
$199$	−8.76938	−0.621645	−0.310822	+	0.950468i	$0.600604\pi$
$200$	0	0
$201$	21.2377	1.49799
$202$	25.5536	1.79795
$203$	−1.10298	−0.0774137
$204$	−2.95524	−0.206908
$205$	0	0
$206$	−20.4548	−1.42516
$207$	4.53946	0.315515
$208$	7.74414	0.536960
$209$	0	0
$210$	0	0
$211$	−11.8171	−0.813526	−0.406763	−	0.913534i	$-0.633343\pi$
$211$	−11.8171	−0.813526	−0.406763	+	0.913534i	$0.633343\pi$
$212$	1.36019	0.0934184
$213$	32.0155	2.19366
$214$	4.82889	0.330096
$215$	0	0
$216$	1.10695	0.0753183
$217$	−9.03026	−0.613014
$218$	4.76431	0.322680
$219$	4.52507	0.305776
$220$	0	0
$221$	−11.2976	−0.759959
$222$	−9.93503	−0.666796
$223$	−8.89760	−0.595827	−0.297914	−	0.954593i	$-0.596291\pi$
$223$	−8.89760	−0.595827	−0.297914	+	0.954593i	$0.596291\pi$
$224$	3.44402	0.230113
$225$	0	0
$226$	−6.96698	−0.463437
$227$	26.4080	1.75276	0.876380	−	0.481620i	$-0.159951\pi$
$227$	26.4080	1.75276	0.876380	+	0.481620i	$0.159951\pi$
$228$	0	0
$229$	21.7852	1.43961	0.719804	−	0.694177i	$-0.244232\pi$
$229$	21.7852	1.43961	0.719804	+	0.694177i	$0.244232\pi$
$230$	0	0
$231$	−33.7653	−2.22159
$232$	−0.909681	−0.0597235
$233$	10.0009	0.655183	0.327591	−	0.944820i	$-0.393763\pi$
$233$	10.0009	0.655183	0.327591	+	0.944820i	$0.393763\pi$
$234$	−8.35601	−0.546250
$235$	0	0
$236$	−0.590630	−0.0384467
$237$	1.73502	0.112701
$238$	−30.4399	−1.97313
$239$	17.8365	1.15374	0.576872	−	0.816834i	$-0.304273\pi$
$239$	17.8365	1.15374	0.576872	+	0.816834i	$0.304273\pi$
$240$	0	0
$241$	17.1442	1.10435	0.552177	−	0.833727i	$-0.313797\pi$
$241$	17.1442	1.10435	0.552177	+	0.833727i	$0.313797\pi$
$242$	9.62314	0.618599
$243$	22.2802	1.42927
$244$	−0.576156	−0.0368846
$245$	0	0
$246$	−26.2192	−1.67168
$247$	0	0
$248$	−7.44772	−0.472931
$249$	1.37318	0.0870215
$250$	0	0
$251$	9.69585	0.611997	0.305998	−	0.952032i	$-0.401010\pi$
$251$	9.69585	0.611997	0.305998	+	0.952032i	$0.401010\pi$
$252$	−1.93394	−0.121827
$253$	−5.99848	−0.377121
$254$	−0.875685	−0.0549454
$255$	0	0
$256$	4.47200	0.279500
$257$	10.0506	0.626942	0.313471	−	0.949598i	$-0.398508\pi$
$257$	10.0506	0.626942	0.313471	+	0.949598i	$0.398508\pi$
$258$	−36.3424	−2.26258
$259$	−8.79033	−0.546205
$260$	0	0
$261$	1.07461	0.0665170
$262$	−30.3955	−1.87784
$263$	−21.8306	−1.34613	−0.673065	−	0.739583i	$-0.735023\pi$
$263$	−21.8306	−1.34613	−0.673065	+	0.739583i	$0.735023\pi$
$264$	−27.8480	−1.71392
$265$	0	0
$266$	0	0
$267$	16.9571	1.03776
$268$	−1.60737	−0.0981860
$269$	−15.4551	−0.942312	−0.471156	−	0.882050i	$-0.656163\pi$
$269$	−15.4551	−0.942312	−0.471156	+	0.882050i	$0.656163\pi$
$270$	0	0
$271$	5.16319	0.313642	0.156821	−	0.987627i	$-0.449875\pi$
$271$	5.16319	0.313642	0.156821	+	0.987627i	$0.449875\pi$
$272$	−27.4855	−1.66656
$273$	−14.3982	−0.871416
$274$	12.9487	0.782262
$275$	0	0
$276$	−0.669091	−0.0402746
$277$	−5.57030	−0.334687	−0.167343	−	0.985899i	$-0.553519\pi$
$277$	−5.57030	−0.334687	−0.167343	+	0.985899i	$0.553519\pi$
$278$	11.3739	0.682161
$279$	8.79807	0.526726
$280$	0	0
$281$	−27.2729	−1.62697	−0.813483	−	0.581589i	$-0.802431\pi$
$281$	−27.2729	−1.62697	−0.813483	+	0.581589i	$0.802431\pi$
$282$	1.63614	0.0974308
$283$	15.0458	0.894379	0.447190	−	0.894439i	$-0.352425\pi$
$283$	15.0458	0.894379	0.447190	+	0.894439i	$0.352425\pi$
$284$	−2.42308	−0.143784
$285$	0	0
$286$	11.0417	0.652910
$287$	−23.1983	−1.36935
$288$	−3.35547	−0.197723
$289$	23.0975	1.35868
$290$	0	0
$291$	−32.7799	−1.92159
$292$	−0.342479	−0.0200421
$293$	−7.82882	−0.457364	−0.228682	−	0.973501i	$-0.573442\pi$
$293$	−7.82882	−0.457364	−0.228682	+	0.973501i	$0.573442\pi$
$294$	−13.0824	−0.762981
$295$	0	0
$296$	−7.24985	−0.421389
$297$	1.72794	0.100265
$298$	−22.1008	−1.28026
$299$	−2.55787	−0.147925
$300$	0	0
$301$	−32.1551	−1.85339
$302$	−19.4398	−1.11864
$303$	−42.8990	−2.46449
$304$	0	0
$305$	0	0
$306$	29.6572	1.69539
$307$	−15.7146	−0.896879	−0.448439	−	0.893813i	$-0.648020\pi$
$307$	−15.7146	−0.896879	−0.448439	+	0.893813i	$0.648020\pi$
$308$	2.55552	0.145614
$309$	34.3393	1.95349
$310$	0	0
$311$	17.9812	1.01962	0.509810	−	0.860287i	$-0.329716\pi$
$311$	17.9812	1.01962	0.509810	+	0.860287i	$0.329716\pi$
$312$	−11.8749	−0.672285
$313$	−21.2005	−1.19832	−0.599161	−	0.800628i	$-0.704499\pi$
$313$	−21.2005	−1.19832	−0.599161	+	0.800628i	$0.704499\pi$
$314$	16.0300	0.904627
$315$	0	0
$316$	−0.131314	−0.00738702
$317$	3.06442	0.172115	0.0860575	−	0.996290i	$-0.472573\pi$
$317$	3.06442	0.172115	0.0860575	+	0.996290i	$0.472573\pi$
$318$	−26.5833	−1.49072
$319$	−1.42000	−0.0795050
$320$	0	0
$321$	−8.10666	−0.452470
$322$	−6.89184	−0.384067
$323$	0	0
$324$	−1.59250	−0.0884722
$325$	0	0
$326$	12.4924	0.691889
$327$	−7.99825	−0.442304
$328$	−19.1328	−1.05643
$329$	1.44763	0.0798103
$330$	0	0
$331$	25.9509	1.42639	0.713195	−	0.700966i	$-0.247247\pi$
$331$	25.9509	1.42639	0.713195	+	0.700966i	$0.247247\pi$
$332$	−0.103929	−0.00570383
$333$	8.56431	0.469321
$334$	29.4373	1.61074
$335$	0	0
$336$	−35.0288	−1.91098
$337$	10.0575	0.547865	0.273933	−	0.961749i	$-0.411676\pi$
$337$	10.0575	0.547865	0.273933	+	0.961749i	$0.411676\pi$
$338$	−14.5208	−0.789828
$339$	11.6961	0.635243
$340$	0	0
$341$	−11.6258	−0.629574
$342$	0	0
$343$	11.1741	0.603343
$344$	−26.5200	−1.42986
$345$	0	0
$346$	−17.3374	−0.932065
$347$	−6.81801	−0.366010	−0.183005	−	0.983112i	$-0.558582\pi$
$347$	−6.81801	−0.366010	−0.183005	+	0.983112i	$0.558582\pi$
$348$	−0.158392	−0.00849071
$349$	31.5966	1.69133	0.845663	−	0.533718i	$-0.179205\pi$
$349$	31.5966	1.69133	0.845663	+	0.533718i	$0.179205\pi$
$350$	0	0
$351$	0.736826	0.0393289
$352$	4.43394	0.236330
$353$	6.30657	0.335665	0.167832	−	0.985816i	$-0.446323\pi$
$353$	6.30657	0.335665	0.167832	+	0.985816i	$0.446323\pi$
$354$	11.5431	0.613511
$355$	0	0
$356$	−1.28339	−0.0680197
$357$	51.1020	2.70461
$358$	−10.4781	−0.553785
$359$	4.17666	0.220436	0.110218	−	0.993907i	$-0.464845\pi$
$359$	4.17666	0.220436	0.110218	+	0.993907i	$0.464845\pi$
$360$	0	0
$361$	0	0
$362$	−13.7293	−0.721596
$363$	−16.1552	−0.847927
$364$	1.08972	0.0571170
$365$	0	0
$366$	11.2603	0.588584
$367$	16.5710	0.864998	0.432499	−	0.901634i	$-0.357632\pi$
$367$	16.5710	0.864998	0.432499	+	0.901634i	$0.357632\pi$
$368$	−6.22295	−0.324394
$369$	22.6018	1.17660
$370$	0	0
$371$	−23.5204	−1.22112
$372$	−1.29678	−0.0672352
$373$	−37.0004	−1.91581	−0.957905	−	0.287085i	$-0.907314\pi$
$373$	−37.0004	−1.91581	−0.957905	+	0.287085i	$0.907314\pi$
$374$	−39.1893	−2.02643
$375$	0	0
$376$	1.19393	0.0615725
$377$	−0.605517	−0.0311857
$378$	1.98528	0.102112
$379$	−31.5147	−1.61880	−0.809400	−	0.587257i	$-0.800208\pi$
$379$	−31.5147	−1.61880	−0.809400	+	0.587257i	$0.800208\pi$
$380$	0	0
$381$	1.47009	0.0753148
$382$	12.0171	0.614851
$383$	−3.09813	−0.158307	−0.0791536	−	0.996862i	$-0.525222\pi$
$383$	−3.09813	−0.158307	−0.0791536	+	0.996862i	$0.525222\pi$
$384$	−31.3919	−1.60196
$385$	0	0
$386$	−11.4243	−0.581479
$387$	31.3283	1.59251
$388$	2.48094	0.125951
$389$	26.0318	1.31986	0.659931	−	0.751326i	$-0.270585\pi$
$389$	26.0318	1.31986	0.659931	+	0.751326i	$0.270585\pi$
$390$	0	0
$391$	9.07840	0.459115
$392$	−9.54655	−0.482174
$393$	51.0275	2.57400
$394$	5.27712	0.265857
$395$	0	0
$396$	−2.48981	−0.125118
$397$	−12.6607	−0.635423	−0.317712	−	0.948187i	$-0.602914\pi$
$397$	−12.6607	−0.635423	−0.317712	+	0.948187i	$0.602914\pi$
$398$	−12.9714	−0.650197
$399$	0	0
$400$	0	0
$401$	9.22180	0.460515	0.230257	−	0.973130i	$-0.426043\pi$
$401$	9.22180	0.460515	0.230257	+	0.973130i	$0.426043\pi$
$402$	31.4142	1.56680
$403$	−4.95748	−0.246950
$404$	3.24681	0.161535
$405$	0	0
$406$	−1.63149	−0.0809693
$407$	−11.3169	−0.560960
$408$	42.1465	2.08656
$409$	−34.4572	−1.70380	−0.851899	−	0.523706i	$-0.824549\pi$
$409$	−34.4572	−1.70380	−0.851899	+	0.523706i	$0.824549\pi$
$410$	0	0
$411$	−21.7381	−1.07226
$412$	−2.59896	−0.128042
$413$	10.2132	0.502557
$414$	6.71464	0.330006
$415$	0	0
$416$	1.89072	0.0927001
$417$	−19.0943	−0.935053
$418$	0	0
$419$	−7.86047	−0.384009	−0.192005	−	0.981394i	$-0.561499\pi$
$419$	−7.86047	−0.384009	−0.192005	+	0.981394i	$0.561499\pi$
$420$	0	0
$421$	−10.4922	−0.511360	−0.255680	−	0.966761i	$-0.582299\pi$
$421$	−10.4922	−0.511360	−0.255680	+	0.966761i	$0.582299\pi$
$422$	−17.4796	−0.850892
$423$	−1.41041	−0.0685763
$424$	−19.3985	−0.942076
$425$	0	0
$426$	47.3563	2.29442
$427$	9.96288	0.482138
$428$	0.613552	0.0296571
$429$	−18.5366	−0.894957
$430$	0	0
$431$	−29.8923	−1.43986	−0.719931	−	0.694046i	$-0.755827\pi$
$431$	−29.8923	−1.43986	−0.719931	+	0.694046i	$0.755827\pi$
$432$	1.79260	0.0862465
$433$	6.79977	0.326776	0.163388	−	0.986562i	$-0.447758\pi$
$433$	6.79977	0.326776	0.163388	+	0.986562i	$0.447758\pi$
$434$	−13.3573	−0.641170
$435$	0	0
$436$	0.605347	0.0289908
$437$	0	0
$438$	6.69335	0.319820
$439$	−7.96606	−0.380199	−0.190100	−	0.981765i	$-0.560881\pi$
$439$	−7.96606	−0.380199	−0.190100	+	0.981765i	$0.560881\pi$
$440$	0	0
$441$	11.2774	0.537021
$442$	−16.7111	−0.794864
$443$	21.7893	1.03524	0.517621	−	0.855610i	$-0.326818\pi$
$443$	21.7893	1.03524	0.517621	+	0.855610i	$0.326818\pi$
$444$	−1.26233	−0.0599076
$445$	0	0
$446$	−13.1611	−0.623194
$447$	37.1025	1.75489
$448$	−23.1183	−1.09224
$449$	−18.7837	−0.886458	−0.443229	−	0.896409i	$-0.646167\pi$
$449$	−18.7837	−0.886458	−0.443229	+	0.896409i	$0.646167\pi$
$450$	0	0
$451$	−29.8662	−1.40634
$452$	−0.885215	−0.0416370
$453$	32.6353	1.53334
$454$	39.0619	1.83327
$455$	0	0
$456$	0	0
$457$	−28.2368	−1.32086	−0.660431	−	0.750887i	$-0.729627\pi$
$457$	−28.2368	−1.32086	−0.660431	+	0.750887i	$0.729627\pi$
$458$	32.2240	1.50573
$459$	−2.61515	−0.122065
$460$	0	0
$461$	−0.196008	−0.00912900	−0.00456450	−	0.999990i	$-0.501453\pi$
$461$	−0.196008	−0.00912900	−0.00456450	+	0.999990i	$0.501453\pi$
$462$	−49.9445	−2.32363
$463$	−13.9641	−0.648967	−0.324484	−	0.945891i	$-0.605191\pi$
$463$	−13.9641	−0.648967	−0.324484	+	0.945891i	$0.605191\pi$
$464$	−1.47314	−0.0683889
$465$	0	0
$466$	14.7931	0.685275
$467$	32.1025	1.48553	0.742763	−	0.669555i	$-0.233515\pi$
$467$	32.1025	1.48553	0.742763	+	0.669555i	$0.233515\pi$
$468$	−1.06170	−0.0490772
$469$	27.7947	1.28344
$470$	0	0
$471$	−26.9110	−1.23999
$472$	8.42333	0.387715
$473$	−41.3974	−1.90346
$474$	2.56638	0.117878
$475$	0	0
$476$	−3.86765	−0.177273
$477$	22.9157	1.04924
$478$	26.3831	1.20674
$479$	−1.98226	−0.0905717	−0.0452858	−	0.998974i	$-0.514420\pi$
$479$	−1.98226	−0.0905717	−0.0452858	+	0.998974i	$0.514420\pi$
$480$	0	0
$481$	−4.82576	−0.220036
$482$	25.3591	1.15508
$483$	11.5699	0.526450
$484$	1.22270	0.0555774
$485$	0	0
$486$	32.9561	1.49492
$487$	8.58916	0.389212	0.194606	−	0.980881i	$-0.437657\pi$
$487$	8.58916	0.389212	0.194606	+	0.980881i	$0.437657\pi$
$488$	8.21691	0.371962
$489$	−20.9720	−0.948387
$490$	0	0
$491$	25.9002	1.16886	0.584430	−	0.811444i	$-0.301318\pi$
$491$	25.9002	1.16886	0.584430	+	0.811444i	$0.301318\pi$
$492$	−3.33138	−0.150190
$493$	2.14910	0.0967908
$494$	0	0
$495$	0	0
$496$	−12.0609	−0.541550
$497$	41.9000	1.87947
$498$	2.03116	0.0910185
$499$	−21.2038	−0.949214	−0.474607	−	0.880198i	$-0.657410\pi$
$499$	−21.2038	−0.949214	−0.474607	+	0.880198i	$0.657410\pi$
$500$	0	0
$501$	−49.4189	−2.20787
$502$	14.3418	0.640106
$503$	−25.5162	−1.13771	−0.568855	−	0.822438i	$-0.692614\pi$
$503$	−25.5162	−1.13771	−0.568855	+	0.822438i	$0.692614\pi$
$504$	27.5810	1.22856
$505$	0	0
$506$	−8.87277	−0.394443
$507$	24.3773	1.08263
$508$	−0.111263	−0.00493651
$509$	17.0407	0.755314	0.377657	−	0.925946i	$-0.376730\pi$
$509$	17.0407	0.755314	0.377657	+	0.925946i	$0.376730\pi$
$510$	0	0
$511$	5.92215	0.261981
$512$	−18.6685	−0.825039
$513$	0	0
$514$	14.8666	0.655738
$515$	0	0
$516$	−4.61761	−0.203279
$517$	1.86372	0.0819664
$518$	−13.0024	−0.571292
$519$	29.1058	1.27760
$520$	0	0
$521$	−21.7817	−0.954274	−0.477137	−	0.878829i	$-0.658325\pi$
$521$	−21.7817	−0.954274	−0.477137	+	0.878829i	$0.658325\pi$
$522$	1.58954	0.0695721
$523$	−17.4855	−0.764589	−0.382294	−	0.924041i	$-0.624866\pi$
$523$	−17.4855	−0.764589	−0.382294	+	0.924041i	$0.624866\pi$
$524$	−3.86201	−0.168713
$525$	0	0
$526$	−32.2911	−1.40796
$527$	17.5951	0.766455
$528$	−45.0972	−1.96260
$529$	−20.9446	−0.910634
$530$	0	0
$531$	−9.95056	−0.431817
$532$	0	0
$533$	−12.7355	−0.551637
$534$	25.0824	1.08542
$535$	0	0
$536$	22.9237	0.990154
$537$	17.5905	0.759086
$538$	−22.8607	−0.985593
$539$	−14.9021	−0.641878
$540$	0	0
$541$	14.8091	0.636691	0.318346	−	0.947975i	$-0.396873\pi$
$541$	14.8091	0.636691	0.318346	+	0.947975i	$0.396873\pi$
$542$	7.63724	0.328047
$543$	23.0485	0.989108
$544$	−6.71054	−0.287712
$545$	0	0
$546$	−21.2973	−0.911441
$547$	−26.5735	−1.13620	−0.568100	−	0.822959i	$-0.692321\pi$
$547$	−26.5735	−1.13620	−0.568100	+	0.822959i	$0.692321\pi$
$548$	1.64525	0.0702815
$549$	−9.70671	−0.414272
$550$	0	0
$551$	0	0
$552$	9.54231	0.406148
$553$	2.27069	0.0965595
$554$	−8.23942	−0.350059
$555$	0	0
$556$	1.44515	0.0612881
$557$	16.0752	0.681129	0.340565	−	0.940221i	$-0.389382\pi$
$557$	16.0752	0.681129	0.340565	+	0.940221i	$0.389382\pi$
$558$	13.0138	0.550919
$559$	−17.6527	−0.746628
$560$	0	0
$561$	65.7903	2.77767
$562$	−40.3413	−1.70169
$563$	−2.03145	−0.0856155	−0.0428078	−	0.999083i	$-0.513630\pi$
$563$	−2.03145	−0.0856155	−0.0428078	+	0.999083i	$0.513630\pi$
$564$	0.207886	0.00875357
$565$	0	0
$566$	22.2553	0.935459
$567$	27.5375	1.15647
$568$	34.5571	1.44998
$569$	12.8224	0.537543	0.268772	−	0.963204i	$-0.413382\pi$
$569$	12.8224	0.537543	0.268772	+	0.963204i	$0.413382\pi$
$570$	0	0
$571$	12.9168	0.540551	0.270276	−	0.962783i	$-0.412885\pi$
$571$	12.9168	0.540551	0.270276	+	0.962783i	$0.412885\pi$
$572$	1.40294	0.0586600
$573$	−20.1742	−0.842789
$574$	−34.3142	−1.43225
$575$	0	0
$576$	22.5238	0.938493
$577$	8.11359	0.337773	0.168887	−	0.985635i	$-0.445983\pi$
$577$	8.11359	0.337773	0.168887	+	0.985635i	$0.445983\pi$
$578$	34.1651	1.42108
$579$	19.1789	0.797046
$580$	0	0
$581$	1.79713	0.0745577
$582$	−48.4869	−2.00985
$583$	−30.2809	−1.25411
$584$	4.88431	0.202114
$585$	0	0
$586$	−11.5801	−0.478371
$587$	−32.5617	−1.34396	−0.671982	−	0.740568i	$-0.734557\pi$
$587$	−32.5617	−1.34396	−0.671982	+	0.740568i	$0.734557\pi$
$588$	−1.66223	−0.0685492
$589$	0	0
$590$	0	0
$591$	−8.85914	−0.364416
$592$	−11.7404	−0.482529
$593$	−11.4752	−0.471231	−0.235616	−	0.971846i	$-0.575711\pi$
$593$	−11.4752	−0.471231	−0.235616	+	0.971846i	$0.575711\pi$
$594$	2.55591	0.104870
$595$	0	0
$596$	−2.80809	−0.115024
$597$	21.7762	0.891239
$598$	−3.78352	−0.154720
$599$	−33.2099	−1.35692	−0.678460	−	0.734637i	$-0.737352\pi$
$599$	−33.2099	−1.35692	−0.678460	+	0.734637i	$0.737352\pi$
$600$	0	0
$601$	−27.3180	−1.11433	−0.557163	−	0.830403i	$-0.688110\pi$
$601$	−27.3180	−1.11433	−0.557163	+	0.830403i	$0.688110\pi$
$602$	−47.5628	−1.93851
$603$	−27.0800	−1.10278
$604$	−2.47000	−0.100503
$605$	0	0
$606$	−63.4549	−2.57768
$607$	−25.7405	−1.04478	−0.522388	−	0.852708i	$-0.674959\pi$
$607$	−25.7405	−1.04478	−0.522388	+	0.852708i	$0.674959\pi$
$608$	0	0
$609$	2.73892	0.110986
$610$	0	0
$611$	0.794727	0.0321512
$612$	3.76820	0.152320
$613$	40.6039	1.63997	0.819987	−	0.572382i	$-0.193980\pi$
$613$	40.6039	1.63997	0.819987	+	0.572382i	$0.193980\pi$
$614$	−23.2445	−0.938073
$615$	0	0
$616$	−36.4458	−1.46844
$617$	14.2113	0.572125	0.286063	−	0.958211i	$-0.407653\pi$
$617$	14.2113	0.572125	0.286063	+	0.958211i	$0.407653\pi$
$618$	50.7936	2.04322
$619$	−29.5635	−1.18826	−0.594129	−	0.804370i	$-0.702503\pi$
$619$	−29.5635	−1.18826	−0.594129	+	0.804370i	$0.702503\pi$
$620$	0	0
$621$	−0.592091	−0.0237598
$622$	26.5973	1.06645
$623$	22.1924	0.889121
$624$	−19.2303	−0.769828
$625$	0	0
$626$	−31.3591	−1.25336
$627$	0	0
$628$	2.03675	0.0812753
$629$	17.1276	0.682923
$630$	0	0
$631$	−1.70763	−0.0679798	−0.0339899	−	0.999422i	$-0.510821\pi$
$631$	−1.70763	−0.0679798	−0.0339899	+	0.999422i	$0.510821\pi$
$632$	1.87276	0.0744942
$633$	29.3444	1.16634
$634$	4.53280	0.180020
$635$	0	0
$636$	−3.37764	−0.133932
$637$	−6.35454	−0.251776
$638$	−2.10043	−0.0831567
$639$	−40.8226	−1.61492
$640$	0	0
$641$	−2.76200	−0.109092	−0.0545462	−	0.998511i	$-0.517371\pi$
$641$	−2.76200	−0.109092	−0.0545462	+	0.998511i	$0.517371\pi$
$642$	−11.9911	−0.473252
$643$	21.6971	0.855648	0.427824	−	0.903862i	$-0.359280\pi$
$643$	21.6971	0.855648	0.427824	+	0.903862i	$0.359280\pi$
$644$	−0.875668	−0.0345061
$645$	0	0
$646$	0	0
$647$	−28.0268	−1.10185	−0.550923	−	0.834556i	$-0.685724\pi$
$647$	−28.0268	−1.10185	−0.550923	+	0.834556i	$0.685724\pi$
$648$	22.7116	0.892196
$649$	13.1487	0.516133
$650$	0	0
$651$	22.4240	0.878866
$652$	1.58726	0.0621620
$653$	7.59308	0.297140	0.148570	−	0.988902i	$-0.452533\pi$
$653$	7.59308	0.297140	0.148570	+	0.988902i	$0.452533\pi$
$654$	−11.8308	−0.462620
$655$	0	0
$656$	−30.9838	−1.20972
$657$	−5.76988	−0.225104
$658$	2.14129	0.0834761
$659$	−7.18394	−0.279847	−0.139923	−	0.990162i	$-0.544686\pi$
$659$	−7.18394	−0.279847	−0.139923	+	0.990162i	$0.544686\pi$
$660$	0	0
$661$	28.8678	1.12283	0.561413	−	0.827536i	$-0.310258\pi$
$661$	28.8678	1.12283	0.561413	+	0.827536i	$0.310258\pi$
$662$	38.3857	1.49190
$663$	28.0543	1.08954
$664$	1.48219	0.0575201
$665$	0	0
$666$	12.6681	0.490877
$667$	0.486575	0.0188403
$668$	3.74026	0.144715
$669$	22.0946	0.854226
$670$	0	0
$671$	12.8265	0.495162
$672$	−8.55222	−0.329909
$673$	23.3191	0.898885	0.449442	−	0.893309i	$-0.351623\pi$
$673$	23.3191	0.898885	0.449442	+	0.893309i	$0.351623\pi$
$674$	14.8767	0.573029
$675$	0	0
$676$	−1.84499	−0.0709612
$677$	−17.5099	−0.672958	−0.336479	−	0.941691i	$-0.609236\pi$
$677$	−17.5099	−0.672958	−0.336479	+	0.941691i	$0.609236\pi$
$678$	17.3005	0.664420
$679$	−42.9004	−1.64636
$680$	0	0
$681$	−65.5765	−2.51290
$682$	−17.1966	−0.658491
$683$	22.0114	0.842243	0.421122	−	0.907004i	$-0.361637\pi$
$683$	22.0114	0.842243	0.421122	+	0.907004i	$0.361637\pi$
$684$	0	0
$685$	0	0
$686$	16.5283	0.631055
$687$	−54.0972	−2.06394
$688$	−42.9466	−1.63732
$689$	−12.9124	−0.491923
$690$	0	0
$691$	−2.65623	−0.101048	−0.0505238	−	0.998723i	$-0.516089\pi$
$691$	−2.65623	−0.101048	−0.0505238	+	0.998723i	$0.516089\pi$
$692$	−2.20287	−0.0837404
$693$	43.0538	1.63548
$694$	−10.0850	−0.382821
$695$	0	0
$696$	2.25893	0.0856244
$697$	45.2010	1.71211
$698$	46.7367	1.76901
$699$	−24.8344	−0.939322
$700$	0	0
$701$	−7.36728	−0.278258	−0.139129	−	0.990274i	$-0.544430\pi$
$701$	−7.36728	−0.278258	−0.139129	+	0.990274i	$0.544430\pi$
$702$	1.08989	0.0411352
$703$	0	0
$704$	−29.7632	−1.12174
$705$	0	0
$706$	9.32848	0.351082
$707$	−56.1438	−2.11150
$708$	1.46666	0.0551203
$709$	−5.99178	−0.225026	−0.112513	−	0.993650i	$-0.535890\pi$
$709$	−5.99178	−0.225026	−0.112513	+	0.993650i	$0.535890\pi$
$710$	0	0
$711$	−2.21230	−0.0829679
$712$	18.3032	0.685943
$713$	3.98368	0.149190
$714$	75.5885	2.82883
$715$	0	0
$716$	−1.33133	−0.0497543
$717$	−44.2916	−1.65410
$718$	6.17798	0.230560
$719$	13.5815	0.506504	0.253252	−	0.967400i	$-0.418500\pi$
$719$	13.5815	0.506504	0.253252	+	0.967400i	$0.418500\pi$
$720$	0	0
$721$	44.9412	1.67370
$722$	0	0
$723$	−42.5725	−1.58329
$724$	−1.74443	−0.0648311
$725$	0	0
$726$	−23.8962	−0.886872
$727$	−41.2448	−1.52968	−0.764842	−	0.644218i	$-0.777183\pi$
$727$	−41.2448	−1.52968	−0.764842	+	0.644218i	$0.777183\pi$
$728$	−15.5412	−0.575995
$729$	−29.9060	−1.10763
$730$	0	0
$731$	62.6529	2.31730
$732$	1.43071	0.0528807
$733$	−0.123848	−0.00457443	−0.00228722	−	0.999997i	$-0.500728\pi$
$733$	−0.123848	−0.00457443	−0.00228722	+	0.999997i	$0.500728\pi$
$734$	24.5113	0.904728
$735$	0	0
$736$	−1.51932	−0.0560030
$737$	35.7837	1.31811
$738$	33.4319	1.23065
$739$	−36.5134	−1.34317	−0.671584	−	0.740928i	$-0.734386\pi$
$739$	−36.5134	−1.34317	−0.671584	+	0.740928i	$0.734386\pi$
$740$	0	0
$741$	0	0
$742$	−34.7907	−1.27721
$743$	−9.06197	−0.332451	−0.166226	−	0.986088i	$-0.553158\pi$
$743$	−9.06197	−0.332451	−0.166226	+	0.986088i	$0.553158\pi$
$744$	18.4942	0.678032
$745$	0	0
$746$	−54.7299	−2.00380
$747$	−1.75092	−0.0640630
$748$	−4.97933	−0.182062
$749$	−10.6095	−0.387664
$750$	0	0
$751$	4.08610	0.149104	0.0745519	−	0.997217i	$-0.476247\pi$
$751$	4.08610	0.149104	0.0745519	+	0.997217i	$0.476247\pi$
$752$	1.93346	0.0705062
$753$	−24.0768	−0.877407
$754$	−0.895663	−0.0326181
$755$	0	0
$756$	0.252247	0.00917413
$757$	−34.4597	−1.25246	−0.626230	−	0.779638i	$-0.715403\pi$
$757$	−34.4597	−1.25246	−0.626230	+	0.779638i	$0.715403\pi$
$758$	−46.6155	−1.69315
$759$	14.8955	0.540671
$760$	0	0
$761$	20.5813	0.746072	0.373036	−	0.927817i	$-0.378317\pi$
$761$	20.5813	0.746072	0.373036	+	0.927817i	$0.378317\pi$
$762$	2.17451	0.0787741
$763$	−10.4676	−0.378954
$764$	1.52688	0.0552406
$765$	0	0
$766$	−4.58266	−0.165578
$767$	5.60688	0.202453
$768$	−11.1049	−0.400714
$769$	−30.3550	−1.09463	−0.547315	−	0.836927i	$-0.684350\pi$
$769$	−30.3550	−1.09463	−0.547315	+	0.836927i	$0.684350\pi$
$770$	0	0
$771$	−24.9578	−0.898834
$772$	−1.45155	−0.0522424
$773$	−19.5225	−0.702176	−0.351088	−	0.936343i	$-0.614188\pi$
$773$	−19.5225	−0.702176	−0.351088	+	0.936343i	$0.614188\pi$
$774$	46.3398	1.66565
$775$	0	0
$776$	−35.3822	−1.27015
$777$	21.8282	0.783083
$778$	38.5054	1.38048
$779$	0	0
$780$	0	0
$781$	53.9433	1.93024
$782$	13.4285	0.480202
$783$	−0.140164	−0.00500905
$784$	−15.4597	−0.552134
$785$	0	0
$786$	75.4783	2.69222
$787$	35.2236	1.25559	0.627793	−	0.778380i	$-0.283958\pi$
$787$	35.2236	1.25559	0.627793	+	0.778380i	$0.283958\pi$
$788$	0.670503	0.0238857
$789$	54.2098	1.92992
$790$	0	0
$791$	15.3071	0.544259
$792$	35.5087	1.26175
$793$	5.46948	0.194227
$794$	−18.7273	−0.664608
$795$	0	0
$796$	−1.64813	−0.0584163
$797$	−28.7940	−1.01994	−0.509969	−	0.860193i	$-0.670343\pi$
$797$	−28.7940	−1.01994	−0.509969	+	0.860193i	$0.670343\pi$
$798$	0	0
$799$	−2.82065	−0.0997874
$800$	0	0
$801$	−21.6218	−0.763969
$802$	13.6406	0.481666
$803$	7.62436	0.269058
$804$	3.99144	0.140767
$805$	0	0
$806$	−7.33295	−0.258292
$807$	38.3781	1.35097
$808$	−46.3047	−1.62899
$809$	−48.0068	−1.68783	−0.843915	−	0.536478i	$-0.819755\pi$
$809$	−48.0068	−1.68783	−0.843915	+	0.536478i	$0.819755\pi$
$810$	0	0
$811$	9.62886	0.338115	0.169057	−	0.985606i	$-0.445928\pi$
$811$	9.62886	0.338115	0.169057	+	0.985606i	$0.445928\pi$
$812$	−0.207294	−0.00727461
$813$	−12.8213	−0.449662
$814$	−16.7397	−0.586725
$815$	0	0
$816$	68.2523	2.38931
$817$	0	0
$818$	−50.9680	−1.78205
$819$	18.3590	0.641514
$820$	0	0
$821$	−25.7257	−0.897834	−0.448917	−	0.893573i	$-0.648190\pi$
$821$	−25.7257	−0.897834	−0.448917	+	0.893573i	$0.648190\pi$
$822$	−32.1544	−1.12151
$823$	−13.4584	−0.469132	−0.234566	−	0.972100i	$-0.575367\pi$
$823$	−13.4584	−0.469132	−0.234566	+	0.972100i	$0.575367\pi$
$824$	37.0654	1.29123
$825$	0	0
$826$	15.1070	0.525640
$827$	−0.172408	−0.00599520	−0.00299760	−	0.999996i	$-0.500954\pi$
$827$	−0.172408	−0.00599520	−0.00299760	+	0.999996i	$0.500954\pi$
$828$	0.853152	0.0296491
$829$	42.3791	1.47189	0.735943	−	0.677044i	$-0.236739\pi$
$829$	42.3791	1.47189	0.735943	+	0.677044i	$0.236739\pi$
$830$	0	0
$831$	13.8322	0.479834
$832$	−12.6916	−0.440002
$833$	22.5536	0.781435
$834$	−28.2437	−0.978001
$835$	0	0
$836$	0	0
$837$	−1.14755	−0.0396651
$838$	−11.6270	−0.401647
$839$	−45.1399	−1.55840	−0.779200	−	0.626775i	$-0.784375\pi$
$839$	−45.1399	−1.55840	−0.779200	+	0.626775i	$0.784375\pi$
$840$	0	0
$841$	−28.8848	−0.996028
$842$	−15.5198	−0.534847
$843$	67.7243	2.33255
$844$	−2.22093	−0.0764475
$845$	0	0
$846$	−2.08623	−0.0717260
$847$	−21.1430	−0.726481
$848$	−31.4141	−1.07876
$849$	−37.3618	−1.28225
$850$	0	0
$851$	3.87784	0.132931
$852$	6.01702	0.206140
$853$	−46.3405	−1.58667	−0.793333	−	0.608787i	$-0.791656\pi$
$853$	−46.3405	−1.58667	−0.793333	+	0.608787i	$0.791656\pi$
$854$	14.7368	0.504283
$855$	0	0
$856$	−8.75023	−0.299077
$857$	−21.8934	−0.747863	−0.373931	−	0.927456i	$-0.621990\pi$
$857$	−21.8934	−0.747863	−0.373931	+	0.927456i	$0.621990\pi$
$858$	−27.4188	−0.936063
$859$	33.4020	1.13966	0.569830	−	0.821762i	$-0.307009\pi$
$859$	33.4020	1.13966	0.569830	+	0.821762i	$0.307009\pi$
$860$	0	0
$861$	57.6062	1.96321
$862$	−44.2158	−1.50600
$863$	27.1254	0.923359	0.461680	−	0.887047i	$-0.347247\pi$
$863$	27.1254	0.923359	0.461680	+	0.887047i	$0.347247\pi$
$864$	0.437660	0.0148895
$865$	0	0
$866$	10.0580	0.341785
$867$	−57.3558	−1.94791
$868$	−1.69716	−0.0576052
$869$	2.92335	0.0991680
$870$	0	0
$871$	15.2589	0.517027
$872$	−8.63321	−0.292358
$873$	41.7973	1.41462
$874$	0	0
$875$	0	0
$876$	0.850447	0.0287339
$877$	49.0823	1.65739	0.828695	−	0.559700i	$-0.189084\pi$
$877$	49.0823	1.65739	0.828695	+	0.559700i	$0.189084\pi$
$878$	−11.7832	−0.397662
$879$	19.4406	0.655714
$880$	0	0
$881$	37.9778	1.27951	0.639753	−	0.768581i	$-0.279037\pi$
$881$	37.9778	1.27951	0.639753	+	0.768581i	$0.279037\pi$
$882$	16.6812	0.561686
$883$	33.2100	1.11761	0.558803	−	0.829300i	$-0.311261\pi$
$883$	33.2100	1.11761	0.558803	+	0.829300i	$0.311261\pi$
$884$	−2.12328	−0.0714137
$885$	0	0
$886$	32.2301	1.08279
$887$	−26.2525	−0.881474	−0.440737	−	0.897636i	$-0.645283\pi$
$887$	−26.2525	−0.881474	−0.440737	+	0.897636i	$0.645283\pi$
$888$	18.0029	0.604136
$889$	1.92396	0.0645277
$890$	0	0
$891$	35.4526	1.18771
$892$	−1.67222	−0.0559902
$893$	0	0
$894$	54.8808	1.83549
$895$	0	0
$896$	−41.0839	−1.37252
$897$	6.35172	0.212078
$898$	−27.7843	−0.927173
$899$	0.943045	0.0314523
$900$	0	0
$901$	45.8287	1.52677
$902$	−44.1772	−1.47094
$903$	79.8477	2.65716
$904$	12.6246	0.419888
$905$	0	0
$906$	48.2731	1.60377
$907$	−7.92760	−0.263231	−0.131616	−	0.991301i	$-0.542017\pi$
$907$	−7.92760	−0.263231	−0.131616	+	0.991301i	$0.542017\pi$
$908$	4.96315	0.164708
$909$	54.7002	1.81429
$910$	0	0
$911$	0.619746	0.0205331	0.0102665	−	0.999947i	$-0.496732\pi$
$911$	0.619746	0.0205331	0.0102665	+	0.999947i	$0.496732\pi$
$912$	0	0
$913$	2.31369	0.0765718
$914$	−41.7670	−1.38153
$915$	0	0
$916$	4.09434	0.135281
$917$	66.7818	2.20533
$918$	−3.86824	−0.127671
$919$	−35.0574	−1.15644	−0.578219	−	0.815882i	$-0.696252\pi$
$919$	−35.0574	−1.15644	−0.578219	+	0.815882i	$0.696252\pi$
$920$	0	0
$921$	39.0226	1.28584
$922$	−0.289929	−0.00954830
$923$	23.0025	0.757135
$924$	−6.34588	−0.208764
$925$	0	0
$926$	−20.6553	−0.678775
$927$	−43.7857	−1.43811
$928$	−0.359665	−0.0118066
$929$	12.0434	0.395132	0.197566	−	0.980290i	$-0.436696\pi$
$929$	12.0434	0.395132	0.197566	+	0.980290i	$0.436696\pi$
$930$	0	0
$931$	0	0
$932$	1.87959	0.0615679
$933$	−44.6511	−1.46181
$934$	47.4850	1.55376
$935$	0	0
$936$	15.1416	0.494918
$937$	14.9304	0.487757	0.243878	−	0.969806i	$-0.421580\pi$
$937$	14.9304	0.487757	0.243878	+	0.969806i	$0.421580\pi$
$938$	41.1131	1.34239
$939$	52.6452	1.71801
$940$	0	0
$941$	−19.4198	−0.633068	−0.316534	−	0.948581i	$-0.602519\pi$
$941$	−19.4198	−0.633068	−0.316534	+	0.948581i	$0.602519\pi$
$942$	−39.8059	−1.29695
$943$	10.2339	0.333261
$944$	13.6408	0.443970
$945$	0	0
$946$	−61.2338	−1.99088
$947$	16.7369	0.543878	0.271939	−	0.962315i	$-0.412335\pi$
$947$	16.7369	0.543878	0.271939	+	0.962315i	$0.412335\pi$
$948$	0.326081	0.0105906
$949$	3.25117	0.105538
$950$	0	0
$951$	−7.60959	−0.246758
$952$	55.1589	1.78771
$953$	53.1772	1.72258	0.861290	−	0.508114i	$-0.169657\pi$
$953$	53.1772	1.72258	0.861290	+	0.508114i	$0.169657\pi$
$954$	33.8962	1.09743
$955$	0	0
$956$	3.35220	0.108418
$957$	3.52616	0.113985
$958$	−2.93209	−0.0947317
$959$	−28.4496	−0.918686
$960$	0	0
$961$	−23.2791	−0.750939
$962$	−7.13812	−0.230142
$963$	10.3367	0.333096
$964$	3.22209	0.103777
$965$	0	0
$966$	17.1139	0.550630
$967$	30.0281	0.965637	0.482819	−	0.875720i	$-0.339613\pi$
$967$	30.0281	0.965637	0.482819	+	0.875720i	$0.339613\pi$
$968$	−17.4377	−0.560469
$969$	0	0
$970$	0	0
$971$	−24.1413	−0.774732	−0.387366	−	0.921926i	$-0.626615\pi$
$971$	−24.1413	−0.774732	−0.387366	+	0.921926i	$0.626615\pi$
$972$	4.18736	0.134310
$973$	−24.9896	−0.801128
$974$	12.7048	0.407089
$975$	0	0
$976$	13.3065	0.425931
$977$	9.57680	0.306389	0.153195	−	0.988196i	$-0.451044\pi$
$977$	9.57680	0.306389	0.153195	+	0.988196i	$0.451044\pi$
$978$	−31.0211	−0.991947
$979$	28.5712	0.913140
$980$	0	0
$981$	10.1985	0.325613
$982$	38.3108	1.22255
$983$	−31.1715	−0.994216	−0.497108	−	0.867689i	$-0.665605\pi$
$983$	−31.1715	−0.994216	−0.497108	+	0.867689i	$0.665605\pi$
$984$	47.5108	1.51459
$985$	0	0
$986$	3.17889	0.101236
$987$	−3.59476	−0.114422
$988$	0	0
$989$	14.1851	0.451061
$990$	0	0
$991$	48.6643	1.54587	0.772937	−	0.634483i	$-0.218787\pi$
$991$	48.6643	1.54587	0.772937	+	0.634483i	$0.218787\pi$
$992$	−2.94464	−0.0934925
$993$	−64.4414	−2.04499
$994$	61.9771	1.96580
$995$	0	0
$996$	0.258076	0.00817746
$997$	31.8954	1.01014	0.505068	−	0.863080i	$-0.331467\pi$
$997$	31.8954	1.01014	0.505068	+	0.863080i	$0.331467\pi$
$998$	−31.3641	−0.992812
$999$	−1.11706	−0.0353422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.ct.1.18		24
5.2	odd	4		1805.2.b.l.1084.18		24
5.3	odd	4		1805.2.b.l.1084.7		24
5.4	even	2	inner	9025.2.a.ct.1.7		24
19.3	odd	18		475.2.l.f.351.2		48
19.13	odd	18		475.2.l.f.226.2		48
19.18	odd	2		9025.2.a.cu.1.7		24
95.3	even	36		95.2.p.a.9.2	✓	48
95.13	even	36		95.2.p.a.74.7	yes	48
95.18	even	4		1805.2.b.k.1084.18		24
95.22	even	36		95.2.p.a.9.7	yes	48
95.32	even	36		95.2.p.a.74.2	yes	48
95.37	even	4		1805.2.b.k.1084.7		24
95.79	odd	18		475.2.l.f.351.7		48
95.89	odd	18		475.2.l.f.226.7		48
95.94	odd	2		9025.2.a.cu.1.18		24
285.32	odd	36		855.2.da.b.739.7		48
285.98	odd	36		855.2.da.b.199.7		48
285.203	odd	36		855.2.da.b.739.2		48
285.212	odd	36		855.2.da.b.199.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.2	✓	48	95.3	even	36
95.2.p.a.9.7	yes	48	95.22	even	36
95.2.p.a.74.2	yes	48	95.32	even	36
95.2.p.a.74.7	yes	48	95.13	even	36
475.2.l.f.226.2		48	19.13	odd	18
475.2.l.f.226.7		48	95.89	odd	18
475.2.l.f.351.2		48	19.3	odd	18
475.2.l.f.351.7		48	95.79	odd	18
855.2.da.b.199.2		48	285.212	odd	36
855.2.da.b.199.7		48	285.98	odd	36
855.2.da.b.739.2		48	285.203	odd	36
855.2.da.b.739.7		48	285.32	odd	36
1805.2.b.k.1084.7		24	95.37	even	4
1805.2.b.k.1084.18		24	95.18	even	4
1805.2.b.l.1084.7		24	5.3	odd	4
1805.2.b.l.1084.18		24	5.2	odd	4
9025.2.a.ct.1.7		24	5.4	even	2	inner
9025.2.a.ct.1.18		24	1.1	even	1	trivial
9025.2.a.cu.1.7		24	19.18	odd	2
9025.2.a.cu.1.18		24	95.94	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.47917 q^{2} -2.48321 q^{3} +0.187941 q^{4} -3.67308 q^{6} -3.24988 q^{7} -2.68034 q^{8} +3.16631 q^{9} +O(q^{10})\)	\(q+1.47917 q^{2} -2.48321 q^{3} +0.187941 q^{4} -3.67308 q^{6} -3.24988 q^{7} -2.68034 q^{8} +3.16631 q^{9} -4.18399 q^{11} -0.466696 q^{12} -1.78413 q^{13} -4.80712 q^{14} -4.34056 q^{16} +6.33226 q^{17} +4.68351 q^{18} +8.07011 q^{21} -6.18883 q^{22} +1.43368 q^{23} +6.65584 q^{24} -2.63904 q^{26} -0.412988 q^{27} -0.610785 q^{28} +0.339390 q^{29} +2.77865 q^{31} -1.05974 q^{32} +10.3897 q^{33} +9.36648 q^{34} +0.595080 q^{36} +2.70482 q^{37} +4.43037 q^{39} +7.13821 q^{41} +11.9371 q^{42} +9.89425 q^{43} -0.786344 q^{44} +2.12065 q^{46} -0.445441 q^{47} +10.7785 q^{48} +3.56169 q^{49} -15.7243 q^{51} -0.335312 q^{52} +7.23734 q^{53} -0.610879 q^{54} +8.71078 q^{56} +0.502015 q^{58} -3.14263 q^{59} -3.06562 q^{61} +4.11009 q^{62} -10.2901 q^{63} +7.11359 q^{64} +15.3681 q^{66} -8.55254 q^{67} +1.19009 q^{68} -3.56011 q^{69} -12.8928 q^{71} -8.48680 q^{72} -1.82227 q^{73} +4.00089 q^{74} +13.5974 q^{77} +6.55327 q^{78} -0.698700 q^{79} -8.47340 q^{81} +10.5586 q^{82} -0.552985 q^{83} +1.51671 q^{84} +14.6353 q^{86} -0.842775 q^{87} +11.2145 q^{88} -6.82870 q^{89} +5.79822 q^{91} +0.269446 q^{92} -6.89995 q^{93} -0.658883 q^{94} +2.63155 q^{96} +13.2006 q^{97} +5.26835 q^{98} -13.2478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

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