LMFDB - Embedded newform 1445.2.d.j.866.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(866,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1445.866");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.6
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.j.866.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.43840 q^{2} +0.109907i q^{3} +0.0689897 q^{4} +1.00000i q^{5} -0.158090i q^{6} +0.695085i q^{7} +2.77756 q^{8} +2.98792 q^{9} -1.43840i q^{10} +4.85089i q^{11} +0.00758244i q^{12} +5.63906 q^{13} -0.999809i q^{14} -0.109907 q^{15} -4.13322 q^{16} -4.29782 q^{18} +2.32272 q^{19} +0.0689897i q^{20} -0.0763945 q^{21} -6.97750i q^{22} +4.63686i q^{23} +0.305273i q^{24} -1.00000 q^{25} -8.11121 q^{26} +0.658113i q^{27} +0.0479537i q^{28} -6.50618i q^{29} +0.158090 q^{30} -6.63194i q^{31} +0.390093 q^{32} -0.533145 q^{33} -0.695085 q^{35} +0.206136 q^{36} -0.118625i q^{37} -3.34100 q^{38} +0.619770i q^{39} +2.77756i q^{40} +1.07877i q^{41} +0.109886 q^{42} +0.641108 q^{43} +0.334661i q^{44} +2.98792i q^{45} -6.66965i q^{46} +4.93703 q^{47} -0.454269i q^{48} +6.51686 q^{49} +1.43840 q^{50} +0.389037 q^{52} -11.9864 q^{53} -0.946629i q^{54} -4.85089 q^{55} +1.93064i q^{56} +0.255283i q^{57} +9.35848i q^{58} +9.91829 q^{59} -0.00758244 q^{60} +1.60292i q^{61} +9.53937i q^{62} +2.07686i q^{63} +7.70533 q^{64} +5.63906i q^{65} +0.766875 q^{66} -2.99411 q^{67} -0.509622 q^{69} +0.999809 q^{70} +4.68852i q^{71} +8.29913 q^{72} -5.49911i q^{73} +0.170630i q^{74} -0.109907i q^{75} +0.160244 q^{76} -3.37178 q^{77} -0.891477i q^{78} +14.8439i q^{79} -4.13322i q^{80} +8.89143 q^{81} -1.55170i q^{82} -5.03506 q^{83} -0.00527044 q^{84} -0.922169 q^{86} +0.715073 q^{87} +13.4736i q^{88} -2.35657 q^{89} -4.29782i q^{90} +3.91962i q^{91} +0.319896i q^{92} +0.728895 q^{93} -7.10141 q^{94} +2.32272i q^{95} +0.0428738i q^{96} +2.70080i q^{97} -9.37384 q^{98} +14.4941i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43}+ \cdots - 120 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.43840	−1.01710	−0.508551	−	0.861032i	$-0.669819\pi$
$2$	−1.43840	−1.01710	−0.508551	+	0.861032i	$0.669819\pi$
$3$	0.109907i	0.0634547i	0.999497	+	0.0317274i	$0.0101008\pi$
$3$	0.109907i	0.0634547i	−0.999497	+	0.0317274i	$0.989899\pi$
$4$	0.0689897	0.0344949
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	− 0.158090i	− 0.0645399i
$7$	0.695085i	0.262717i	0.991335	+	0.131359i	$0.0419339\pi$
$7$	0.695085i	0.262717i	−0.991335	+	0.131359i	$0.958066\pi$
$8$	2.77756	0.982016
$9$	2.98792	0.995974
$10$	− 1.43840i	− 0.454861i
$11$	4.85089i	1.46260i	0.682058	+	0.731298i	$0.261085\pi$
$11$	4.85089i	1.46260i	−0.682058	+	0.731298i	$0.738915\pi$
$12$	0.00758244i	0.00218886i
$13$	5.63906	1.56399	0.781996	−	0.623283i	$-0.214202\pi$
$13$	5.63906	1.56399	0.781996	+	0.623283i	$0.214202\pi$
$14$	− 0.999809i	− 0.267210i
$15$	−0.109907	−0.0283778
$16$	−4.13322	−1.03330
$17$	0	0
$17$	0	0
$18$	−4.29782	−1.01301
$19$	2.32272	0.532869	0.266434	−	0.963853i	$-0.414154\pi$
$19$	2.32272	0.532869	0.266434	+	0.963853i	$0.414154\pi$
$20$	0.0689897i	0.0154266i
$21$	−0.0763945	−0.0166706
$22$	− 6.97750i	− 1.48761i
$23$	4.63686i	0.966852i	0.875385	+	0.483426i	$0.160608\pi$
$23$	4.63686i	0.966852i	−0.875385	+	0.483426i	$0.839392\pi$
$24$	0.305273i	0.0623136i
$25$	−1.00000	−0.200000
$26$	−8.11121	−1.59074
$27$	0.658113i	0.126654i
$28$	0.0479537i	0.00906240i
$29$	− 6.50618i	− 1.20817i	−0.796921	−	0.604084i	$-0.793539\pi$
$29$	− 6.50618i	− 1.20817i	0.796921	−	0.604084i	$-0.206461\pi$
$30$	0.158090	0.0288631
$31$	− 6.63194i	− 1.19113i	−0.803307	−	0.595565i	$-0.796928\pi$
$31$	− 6.63194i	− 1.19113i	0.803307	−	0.595565i	$-0.203072\pi$
$32$	0.390093	0.0689593
$33$	−0.533145	−0.0928087
$34$	0	0
$35$	−0.695085	−0.117491
$36$	0.206136	0.0343560
$37$	− 0.118625i	− 0.0195018i	−0.999952	−	0.00975091i	$-0.996896\pi$
$37$	− 0.118625i	− 0.0195018i	0.999952	−	0.00975091i	$-0.00310386\pi$
$38$	−3.34100	−0.541981
$39$	0.619770i	0.0992427i
$40$	2.77756i	0.439171i
$41$	1.07877i	0.168475i	0.996446	+	0.0842375i	$0.0268454\pi$
$41$	1.07877i	0.168475i	−0.996446	+	0.0842375i	$0.973155\pi$
$42$	0.109886	0.0169557
$43$	0.641108	0.0977681	0.0488840	−	0.998804i	$-0.484434\pi$
$43$	0.641108	0.0977681	0.0488840	+	0.998804i	$0.484434\pi$
$44$	0.334661i	0.0504521i
$45$	2.98792i	0.445413i
$46$	− 6.66965i	− 0.983386i
$47$	4.93703	0.720139	0.360070	−	0.932925i	$-0.382753\pi$
$47$	4.93703	0.720139	0.360070	+	0.932925i	$0.382753\pi$
$48$	− 0.454269i	− 0.0655681i
$49$	6.51686	0.930980
$50$	1.43840	0.203420
$51$	0	0
$52$	0.389037	0.0539497
$53$	−11.9864	−1.64646	−0.823228	−	0.567711i	$-0.807829\pi$
$53$	−11.9864	−1.64646	−0.823228	+	0.567711i	$0.807829\pi$
$54$	− 0.946629i	− 0.128820i
$55$	−4.85089	−0.654093
$56$	1.93064i	0.257993i
$57$	0.255283i	0.0338130i
$58$	9.35848i	1.22883i
$59$	9.91829	1.29125	0.645626	−	0.763654i	$-0.276597\pi$
$59$	9.91829	1.29125	0.645626	+	0.763654i	$0.276597\pi$
$60$	−0.00758244	−0.000978888 0
$61$	1.60292i	0.205233i	0.994721	+	0.102617i	$0.0327215\pi$
$61$	1.60292i	0.205233i	−0.994721	+	0.102617i	$0.967278\pi$
$62$	9.53937i	1.21150i
$63$	2.07686i	0.261659i
$64$	7.70533	0.963166
$65$	5.63906i	0.699439i
$66$	0.766875	0.0943958
$67$	−2.99411	−0.365789	−0.182894	−	0.983133i	$-0.558547\pi$
$67$	−2.99411	−0.365789	−0.182894	+	0.983133i	$0.558547\pi$
$68$	0	0
$69$	−0.509622	−0.0613513
$70$	0.999809	0.119500
$71$	4.68852i	0.556425i	0.960520	+	0.278213i	$0.0897420\pi$
$71$	4.68852i	0.556425i	−0.960520	+	0.278213i	$0.910258\pi$
$72$	8.29913	0.978062
$73$	− 5.49911i	− 0.643622i	−0.946804	−	0.321811i	$-0.895708\pi$
$73$	− 5.49911i	− 0.643622i	0.946804	−	0.321811i	$-0.104292\pi$
$74$	0.170630i	0.0198353i
$75$	− 0.109907i	− 0.0126909i
$76$	0.160244	0.0183812
$77$	−3.37178	−0.384250
$78$	− 0.891477i	− 0.100940i
$79$	14.8439i	1.67007i	0.550193	+	0.835037i	$0.314554\pi$
$79$	14.8439i	1.67007i	−0.550193	+	0.835037i	$0.685446\pi$
$80$	− 4.13322i	− 0.462108i
$81$	8.89143	0.987937
$82$	− 1.55170i	− 0.171356i
$83$	−5.03506	−0.552670	−0.276335	−	0.961061i	$-0.589120\pi$
$83$	−5.03506	−0.552670	−0.276335	+	0.961061i	$0.589120\pi$
$84$	−0.00527044	−0.000575052 0
$85$	0	0
$86$	−0.922169	−0.0994400
$87$	0.715073	0.0766639
$88$	13.4736i	1.43629i
$89$	−2.35657	−0.249796	−0.124898	−	0.992170i	$-0.539860\pi$
$89$	−2.35657	−0.249796	−0.124898	+	0.992170i	$0.539860\pi$
$90$	− 4.29782i	− 0.453030i
$91$	3.91962i	0.410888i
$92$	0.319896i	0.0333514i
$93$	0.728895	0.0755829
$94$	−7.10141	−0.732454
$95$	2.32272i	0.238306i
$96$	0.0428738i	0.00437579i
$97$	2.70080i	0.274225i	0.990555	+	0.137113i	$0.0437822\pi$
$97$	2.70080i	0.274225i	−0.990555	+	0.137113i	$0.956218\pi$
$98$	−9.37384	−0.946900
$99$	14.4941i	1.45671i
$100$	−0.0689897	−0.00689897
$101$	14.3025	1.42315	0.711575	−	0.702610i	$-0.247982\pi$
$101$	14.3025	1.42315	0.711575	+	0.702610i	$0.247982\pi$
$102$	0	0
$103$	−10.8963	−1.07365	−0.536824	−	0.843694i	$-0.680376\pi$
$103$	−10.8963	−1.07365	−0.536824	+	0.843694i	$0.680376\pi$
$104$	15.6628	1.53587
$105$	− 0.0763945i	− 0.00745534i
$106$	17.2412	1.67461
$107$	16.6273i	1.60742i	0.595019	+	0.803712i	$0.297145\pi$
$107$	16.6273i	1.60742i	−0.595019	+	0.803712i	$0.702855\pi$
$108$	0.0454030i	0.00436891i
$109$	− 10.5999i	− 1.01529i	−0.861568	−	0.507643i	$-0.830517\pi$
$109$	− 10.5999i	− 1.01529i	0.861568	−	0.507643i	$-0.169483\pi$
$110$	6.97750	0.665279
$111$	0.0130377	0.00123748
$112$	− 2.87294i	− 0.271467i
$113$	− 11.5397i	− 1.08556i	−0.839875	−	0.542780i	$-0.817372\pi$
$113$	− 11.5397i	− 1.08556i	0.839875	−	0.542780i	$-0.182628\pi$
$114$	− 0.367198i	− 0.0343913i
$115$	−4.63686	−0.432389
$116$	− 0.448860i	− 0.0416756i
$117$	16.8490	1.55770
$118$	−14.2665	−1.31333
$119$	0	0
$120$	−0.305273	−0.0278675
$121$	−12.5311	−1.13919
$122$	− 2.30564i	− 0.208743i
$123$	−0.118564	−0.0106905
$124$	− 0.457535i	− 0.0410879i
$125$	− 1.00000i	− 0.0894427i
$126$	− 2.98735i	− 0.266134i
$127$	0.498539	0.0442381	0.0221191	−	0.999755i	$-0.492959\pi$
$127$	0.498539	0.0442381	0.0221191	+	0.999755i	$0.492959\pi$
$128$	−11.8635	−1.04860
$129$	0.0704621i	0.00620384i
$130$	− 8.11121i	− 0.711400i
$131$	19.5341i	1.70670i	0.521338	+	0.853350i	$0.325433\pi$
$131$	19.5341i	1.70670i	−0.521338	+	0.853350i	$0.674567\pi$
$132$	−0.0367815	−0.00320142
$133$	1.61449i	0.139994i
$134$	4.30672	0.372044
$135$	−0.658113	−0.0566414
$136$	0	0
$137$	−3.81724	−0.326129	−0.163065	−	0.986615i	$-0.552138\pi$
$137$	−3.81724	−0.326129	−0.163065	+	0.986615i	$0.552138\pi$
$138$	0.733040	0.0624005
$139$	− 13.2525i	− 1.12406i	−0.827117	−	0.562030i	$-0.810020\pi$
$139$	− 13.2525i	− 1.12406i	0.827117	−	0.562030i	$-0.189980\pi$
$140$	−0.0479537	−0.00405283
$141$	0.542613i	0.0456962i
$142$	− 6.74396i	− 0.565941i
$143$	27.3544i	2.28749i
$144$	−12.3497	−1.02914
$145$	6.50618	0.540309
$146$	7.90991i	0.654629i
$147$	0.716247i	0.0590750i
$148$	− 0.00818390i	0 0.000672712i
$149$	−17.4543	−1.42991	−0.714955	−	0.699171i	$-0.753553\pi$
$149$	−17.4543	−1.42991	−0.714955	+	0.699171i	$0.753553\pi$
$150$	0.158090i	0.0129080i
$151$	11.2715	0.917262	0.458631	−	0.888627i	$-0.348340\pi$
$151$	11.2715	0.917262	0.458631	+	0.888627i	$0.348340\pi$
$152$	6.45150	0.523286
$153$	0	0
$154$	4.84996	0.390821
$155$	6.63194	0.532690
$156$	0.0427578i	0.00342336i
$157$	−6.14541	−0.490457	−0.245229	−	0.969465i	$-0.578863\pi$
$157$	−6.14541	−0.490457	−0.245229	+	0.969465i	$0.578863\pi$
$158$	− 21.3515i	− 1.69863i
$159$	− 1.31738i	− 0.104475i
$160$	0.390093i	0.0308395i
$161$	−3.22301	−0.254009
$162$	−12.7894	−1.00483
$163$	11.2012i	0.877344i	0.898647	+	0.438672i	$0.144551\pi$
$163$	11.2012i	0.877344i	−0.898647	+	0.438672i	$0.855449\pi$
$164$	0.0744238i	0.00581152i
$165$	− 0.533145i	− 0.0415053i
$166$	7.24243	0.562121
$167$	− 5.70603i	− 0.441546i	−0.975325	−	0.220773i	$-0.929142\pi$
$167$	− 5.70603i	− 0.441546i	0.975325	−	0.220773i	$-0.0708580\pi$
$168$	−0.212190	−0.0163709
$169$	18.7989	1.44607
$170$	0	0
$171$	6.94010	0.530723
$172$	0.0442299	0.00337250
$173$	4.53754i	0.344983i	0.985011	+	0.172491i	$0.0551817\pi$
$173$	4.53754i	0.344983i	−0.985011	+	0.172491i	$0.944818\pi$
$174$	−1.02856	−0.0779750
$175$	− 0.695085i	− 0.0525435i
$176$	− 20.0498i	− 1.51131i
$177$	1.09009i	0.0819360i
$178$	3.38969	0.254068
$179$	18.3756	1.37345	0.686727	−	0.726915i	$-0.259047\pi$
$179$	18.3756	1.37345	0.686727	+	0.726915i	$0.259047\pi$
$180$	0.206136i	0.0153645i
$181$	10.7182i	0.796679i	0.917238	+	0.398339i	$0.130413\pi$
$181$	10.7182i	0.796679i	−0.917238	+	0.398339i	$0.869587\pi$
$182$	− 5.63798i	− 0.417915i
$183$	−0.176172	−0.0130230
$184$	12.8792i	0.949465i
$185$	0.118625	0.00872148
$186$	−1.04844	−0.0768754
$187$	0	0
$188$	0.340604	0.0248411
$189$	−0.457444	−0.0332742
$190$	− 3.34100i	− 0.242381i
$191$	18.5397	1.34149	0.670743	−	0.741690i	$-0.265976\pi$
$191$	18.5397	1.34149	0.670743	+	0.741690i	$0.265976\pi$
$192$	0.846868i	0.0611174i
$193$	9.88591i	0.711603i	0.934562	+	0.355802i	$0.115792\pi$
$193$	9.88591i	0.711603i	−0.934562	+	0.355802i	$0.884208\pi$
$194$	− 3.88483i	− 0.278915i
$195$	−0.619770	−0.0443827
$196$	0.449596	0.0321140
$197$	13.9534i	0.994138i	0.867711	+	0.497069i	$0.165590\pi$
$197$	13.9534i	0.994138i	−0.867711	+	0.497069i	$0.834410\pi$
$198$	− 20.8482i	− 1.48162i
$199$	− 12.7366i	− 0.902876i	−0.892303	−	0.451438i	$-0.850911\pi$
$199$	− 12.7366i	− 0.902876i	0.892303	−	0.451438i	$-0.149089\pi$
$200$	−2.77756	−0.196403
$201$	− 0.329073i	− 0.0232110i
$202$	−20.5727	−1.44749
$203$	4.52235	0.317407
$204$	0	0
$205$	−1.07877	−0.0753443
$206$	15.6733	1.09201
$207$	13.8546i	0.962959i
$208$	−23.3075	−1.61608
$209$	11.2672i	0.779372i
$210$	0.109886i	0.00758284i
$211$	− 12.8778i	− 0.886545i	−0.896387	−	0.443273i	$-0.853817\pi$
$211$	− 12.8778i	− 0.886545i	0.896387	−	0.443273i	$-0.146183\pi$
$212$	−0.826937	−0.0567943
$213$	−0.515300	−0.0353078
$214$	− 23.9167i	− 1.63491i
$215$	0.641108i	0.0437232i
$216$	1.82795i	0.124376i
$217$	4.60976	0.312931
$218$	15.2469i	1.03265i
$219$	0.604389	0.0408409
$220$	−0.334661	−0.0225629
$221$	0	0
$222$	−0.0187534	−0.00125864
$223$	−20.4208	−1.36748	−0.683738	−	0.729728i	$-0.739647\pi$
$223$	−20.4208	−1.36748	−0.683738	+	0.729728i	$0.739647\pi$
$224$	0.271147i	0.0181168i
$225$	−2.98792	−0.199195
$226$	16.5986i	1.10412i
$227$	1.22029i	0.0809935i	0.999180	+	0.0404968i	$0.0128940\pi$
$227$	1.22029i	0.0809935i	−0.999180	+	0.0404968i	$0.987106\pi$
$228$	0.0176119i	0.00116638i
$229$	−3.51944	−0.232571	−0.116286	−	0.993216i	$-0.537099\pi$
$229$	−3.51944	−0.232571	−0.116286	+	0.993216i	$0.537099\pi$
$230$	6.66965	0.439784
$231$	− 0.370581i	− 0.0243824i
$232$	− 18.0713i	− 1.18644i
$233$	29.0026i	1.90002i	0.312218	+	0.950011i	$0.398928\pi$
$233$	29.0026i	1.90002i	−0.312218	+	0.950011i	$0.601072\pi$
$234$	−24.2356	−1.58433
$235$	4.93703i	0.322056i
$236$	0.684260	0.0445415
$237$	−1.63145	−0.105974
$238$	0	0
$239$	7.87133	0.509154	0.254577	−	0.967053i	$-0.418064\pi$
$239$	7.87133	0.509154	0.254577	+	0.967053i	$0.418064\pi$
$240$	0.454269	0.0293229
$241$	− 11.6270i	− 0.748959i	−0.927235	−	0.374479i	$-0.877821\pi$
$241$	− 11.6270i	− 0.748959i	0.927235	−	0.374479i	$-0.122179\pi$
$242$	18.0247	1.15867
$243$	2.95157i	0.189343i
$244$	0.110585i	0.00707950i
$245$	6.51686i	0.416347i
$246$	0.170542	0.0108734
$247$	13.0979	0.833403
$248$	− 18.4206i	− 1.16971i
$249$	− 0.553388i	− 0.0350695i
$250$	1.43840i	0.0909723i
$251$	−7.94692	−0.501605	−0.250803	−	0.968038i	$-0.580694\pi$
$251$	−7.94692	−0.501605	−0.250803	+	0.968038i	$0.580694\pi$
$252$	0.143282i	0.00902591i
$253$	−22.4929	−1.41411
$254$	−0.717097	−0.0449947
$255$	0	0
$256$	1.65381	0.103363
$257$	7.92727	0.494489	0.247245	−	0.968953i	$-0.420475\pi$
$257$	7.92727	0.494489	0.247245	+	0.968953i	$0.420475\pi$
$258$	− 0.101353i	− 0.00630994i
$259$	0.0824544	0.00512347
$260$	0.389037i	0.0241270i
$261$	− 19.4400i	− 1.20330i
$262$	− 28.0978i	− 1.73589i
$263$	−8.53622	−0.526366	−0.263183	−	0.964746i	$-0.584772\pi$
$263$	−8.53622	−0.526366	−0.263183	+	0.964746i	$0.584772\pi$
$264$	−1.48084	−0.0911396
$265$	− 11.9864i	− 0.736318i
$266$	− 2.32228i	− 0.142388i
$267$	− 0.259003i	− 0.0158507i
$268$	−0.206563	−0.0126178
$269$	− 15.9828i	− 0.974490i	−0.873265	−	0.487245i	$-0.838002\pi$
$269$	− 15.9828i	− 0.974490i	0.873265	−	0.487245i	$-0.161998\pi$
$270$	0.946629	0.0576100
$271$	−22.5289	−1.36853	−0.684266	−	0.729232i	$-0.739877\pi$
$271$	−22.5289	−1.36853	−0.684266	+	0.729232i	$0.739877\pi$
$272$	0	0
$273$	−0.430793	−0.0260728
$274$	5.49072	0.331706
$275$	− 4.85089i	− 0.292519i
$276$	−0.0351587	−0.00211630
$277$	6.90211i	0.414708i	0.978266	+	0.207354i	$0.0664851\pi$
$277$	6.90211i	0.414708i	−0.978266	+	0.207354i	$0.933515\pi$
$278$	19.0623i	1.14328i
$279$	− 19.8157i	− 1.18633i
$280$	−1.93064	−0.115378
$281$	−9.38062	−0.559601	−0.279801	−	0.960058i	$-0.590268\pi$
$281$	−9.38062	−0.559601	−0.279801	+	0.960058i	$0.590268\pi$
$282$	− 0.780493i	− 0.0464777i
$283$	− 20.5769i	− 1.22317i	−0.791179	−	0.611584i	$-0.790532\pi$
$283$	− 20.5769i	− 1.22317i	0.791179	−	0.611584i	$-0.209468\pi$
$284$	0.323460i	0.0191938i
$285$	−0.255283	−0.0151216
$286$	− 39.3465i	− 2.32661i
$287$	−0.749834	−0.0442613
$288$	1.16557	0.0686816
$289$	0	0
$290$	−9.35848	−0.549549
$291$	−0.296837	−0.0174009
$292$	− 0.379382i	− 0.0222017i
$293$	−23.4539	−1.37019	−0.685097	−	0.728452i	$-0.740240\pi$
$293$	−23.4539	−1.37019	−0.685097	+	0.728452i	$0.740240\pi$
$294$	− 1.03025i	− 0.0600853i
$295$	9.91829i	0.577465i
$296$	− 0.329488i	− 0.0191511i
$297$	−3.19243	−0.185244
$298$	25.1062	1.45436
$299$	26.1475i	1.51215i
$300$	− 0.00758244i	0 0.000437772i
$301$	0.445624i	0.0256854i
$302$	−16.2129	−0.932948
$303$	1.57194i	0.0903056i
$304$	−9.60031	−0.550616
$305$	−1.60292	−0.0917832
$306$	0	0
$307$	30.4260	1.73650	0.868251	−	0.496126i	$-0.165244\pi$
$307$	30.4260	1.73650	0.868251	+	0.496126i	$0.165244\pi$
$308$	−0.232618	−0.0132546
$309$	− 1.19758i	− 0.0681280i
$310$	−9.53937	−0.541800
$311$	1.07989i	0.0612348i	0.999531	+	0.0306174i	$0.00974734\pi$
$311$	1.07989i	0.0612348i	−0.999531	+	0.0306174i	$0.990253\pi$
$312$	1.72145i	0.0974580i
$313$	− 3.62554i	− 0.204928i	−0.994737	−	0.102464i	$-0.967327\pi$
$313$	− 3.62554i	− 0.204928i	0.994737	−	0.102464i	$-0.0326726\pi$
$314$	8.83955	0.498845
$315$	−2.07686	−0.117018
$316$	1.02408i	0.0576090i
$317$	8.79483i	0.493967i	0.969020	+	0.246984i	$0.0794394\pi$
$317$	8.79483i	0.493967i	−0.969020	+	0.246984i	$0.920561\pi$
$318$	1.89492i	0.106262i
$319$	31.5607	1.76706
$320$	7.70533i	0.430741i
$321$	−1.82746	−0.101999
$322$	4.63597	0.258353
$323$	0	0
$324$	0.613417	0.0340787
$325$	−5.63906	−0.312799
$326$	− 16.1117i	− 0.892347i
$327$	1.16500	0.0644246
$328$	2.99634i	0.165445i
$329$	3.43165i	0.189193i
$330$	0.766875i	0.0422151i
$331$	−35.1634	−1.93275	−0.966377	−	0.257128i	$-0.917224\pi$
$331$	−35.1634	−1.93275	−0.966377	+	0.257128i	$0.917224\pi$
$332$	−0.347368	−0.0190643
$333$	− 0.354442i	− 0.0194233i
$334$	8.20754i	0.449097i
$335$	− 2.99411i	− 0.163586i
$336$	0.315755	0.0172259
$337$	− 31.5152i	− 1.71674i	−0.513031	−	0.858370i	$-0.671477\pi$
$337$	− 31.5152i	− 1.71674i	0.513031	−	0.858370i	$-0.328523\pi$
$338$	−27.0404	−1.47080
$339$	1.26829	0.0688839
$340$	0	0
$341$	32.1708	1.74214
$342$	−9.98263	−0.539799
$343$	9.39536i	0.507302i
$344$	1.78072	0.0960098
$345$	− 0.509622i	− 0.0274371i
$346$	− 6.52679i	− 0.350882i
$347$	0.440312i	0.0236372i	0.999930	+	0.0118186i	$0.00376206\pi$
$347$	0.440312i	0.0236372i	−0.999930	+	0.0118186i	$0.996238\pi$
$348$	0.0493327	0.00264451
$349$	12.4222	0.664944	0.332472	−	0.943113i	$-0.392117\pi$
$349$	12.4222	0.664944	0.332472	+	0.943113i	$0.392117\pi$
$350$	0.999809i	0.0534420i
$351$	3.71114i	0.198086i
$352$	1.89229i	0.100860i
$353$	−7.38055	−0.392827	−0.196414	−	0.980521i	$-0.562929\pi$
$353$	−7.38055	−0.392827	−0.196414	+	0.980521i	$0.562929\pi$
$354$	− 1.56798i	− 0.0833372i
$355$	−4.68852	−0.248841
$356$	−0.162579	−0.00861668
$357$	0	0
$358$	−26.4314	−1.39694
$359$	7.05177	0.372178	0.186089	−	0.982533i	$-0.440419\pi$
$359$	7.05177	0.372178	0.186089	+	0.982533i	$0.440419\pi$
$360$	8.29913i	0.437403i
$361$	−13.6050	−0.716051
$362$	− 15.4171i	− 0.810303i
$363$	− 1.37725i	− 0.0722869i
$364$	0.270414i	0.0141735i
$365$	5.49911	0.287837
$366$	0.253406	0.0132457
$367$	− 16.3167i	− 0.851725i	−0.904788	−	0.425862i	$-0.859971\pi$
$367$	− 16.3167i	− 0.851725i	0.904788	−	0.425862i	$-0.140029\pi$
$368$	− 19.1652i	− 0.999053i
$369$	3.22327i	0.167797i
$370$	−0.170630	−0.00887063
$371$	− 8.33155i	− 0.432552i
$372$	0.0502862	0.00260722
$373$	−18.3821	−0.951787	−0.475893	−	0.879503i	$-0.657875\pi$
$373$	−18.3821	−0.951787	−0.475893	+	0.879503i	$0.657875\pi$
$374$	0	0
$375$	0.109907	0.00567556
$376$	13.7129	0.707189
$377$	− 36.6887i	− 1.88957i
$378$	0.657987	0.0338432
$379$	− 16.4955i	− 0.847315i	−0.905822	−	0.423657i	$-0.860746\pi$
$379$	− 16.4955i	− 0.847315i	0.905822	−	0.423657i	$-0.139254\pi$
$380$	0.160244i	0.00822033i
$381$	0.0547928i	0.00280712i
$382$	−26.6675	−1.36443
$383$	36.3426	1.85702	0.928510	−	0.371307i	$-0.121090\pi$
$383$	36.3426	1.85702	0.928510	+	0.371307i	$0.121090\pi$
$384$	− 1.30388i	− 0.0665384i
$385$	− 3.37178i	− 0.171842i
$386$	− 14.2199i	− 0.723772i
$387$	1.91558	0.0973744
$388$	0.186328i	0.00945935i
$389$	−6.36837	−0.322889	−0.161445	−	0.986882i	$-0.551615\pi$
$389$	−6.36837	−0.322889	−0.161445	+	0.986882i	$0.551615\pi$
$390$	0.891477	0.0451417
$391$	0	0
$392$	18.1010	0.914237
$393$	−2.14693	−0.108298
$394$	− 20.0705i	− 1.01114i
$395$	−14.8439	−0.746880
$396$	0.999941i	0.0502489i
$397$	− 33.3778i	− 1.67518i	−0.546298	−	0.837591i	$-0.683963\pi$
$397$	− 33.3778i	− 1.67518i	0.546298	−	0.837591i	$-0.316037\pi$
$398$	18.3203i	0.918316i
$399$	−0.177443	−0.00888327
$400$	4.13322	0.206661
$401$	− 11.7500i	− 0.586769i	−0.955995	−	0.293384i	$-0.905218\pi$
$401$	− 11.7500i	− 0.586769i	0.955995	−	0.293384i	$-0.0947816\pi$
$402$	0.473338i	0.0236080i
$403$	− 37.3979i	− 1.86292i
$404$	0.986724	0.0490914
$405$	8.89143i	0.441819i
$406$	−6.50494	−0.322835
$407$	0.575436	0.0285233
$408$	0	0
$409$	12.6834	0.627154	0.313577	−	0.949563i	$-0.398473\pi$
$409$	12.6834	0.627154	0.313577	+	0.949563i	$0.398473\pi$
$410$	1.55170	0.0766328
$411$	− 0.419541i	− 0.0206944i
$412$	−0.751735	−0.0370353
$413$	6.89405i	0.339234i
$414$	− 19.9284i	− 0.979427i
$415$	− 5.03506i	− 0.247162i
$416$	2.19975	0.107852
$417$	1.45654	0.0713269
$418$	− 16.2068i	− 0.792700i
$419$	− 35.0224i	− 1.71095i	−0.517840	−	0.855477i	$-0.673264\pi$
$419$	− 35.0224i	− 1.71095i	0.517840	−	0.855477i	$-0.326736\pi$
$420$	− 0.00527044i	0 0.000257171i
$421$	−10.0231	−0.488497	−0.244248	−	0.969713i	$-0.578541\pi$
$421$	−10.0231	−0.488497	−0.244248	+	0.969713i	$0.578541\pi$
$422$	18.5234i	0.901706i
$423$	14.7514	0.717240
$424$	−33.2929	−1.61685
$425$	0	0
$426$	0.741207	0.0359116
$427$	−1.11417	−0.0539184
$428$	1.14711i	0.0554479i
$429$	−3.00643	−0.145152
$430$	− 0.922169i	− 0.0444709i
$431$	23.7461i	1.14381i	0.820320	+	0.571905i	$0.193795\pi$
$431$	23.7461i	1.14381i	−0.820320	+	0.571905i	$0.806205\pi$
$432$	− 2.72013i	− 0.130872i
$433$	32.2917	1.55184	0.775919	−	0.630832i	$-0.217286\pi$
$433$	32.2917	1.55184	0.775919	+	0.630832i	$0.217286\pi$
$434$	−6.63067	−0.318282
$435$	0.715073i	0.0342851i
$436$	− 0.731283i	− 0.0350221i
$437$	10.7701i	0.515205i
$438$	−0.869353	−0.0415393
$439$	− 21.3269i	− 1.01788i	−0.860803	−	0.508939i	$-0.830038\pi$
$439$	− 21.3269i	− 1.01788i	0.860803	−	0.508939i	$-0.169962\pi$
$440$	−13.4736	−0.642330
$441$	19.4719	0.927231
$442$	0	0
$443$	−13.8187	−0.656546	−0.328273	−	0.944583i	$-0.606467\pi$
$443$	−13.8187	−0.656546	−0.328273	+	0.944583i	$0.606467\pi$
$444$	0.000899466 0	4.26868e−5 0
$445$	− 2.35657i	− 0.111712i
$446$	29.3732	1.39086
$447$	− 1.91834i	− 0.0907345i
$448$	5.35586i	0.253040i
$449$	6.61380i	0.312125i	0.987747	+	0.156062i	$0.0498801\pi$
$449$	6.61380i	0.312125i	−0.987747	+	0.156062i	$0.950120\pi$
$450$	4.29782	0.202601
$451$	−5.23297	−0.246411
$452$	− 0.796118i	− 0.0374462i
$453$	1.23881i	0.0582046i
$454$	− 1.75526i	− 0.0823786i
$455$	−3.91962	−0.183755
$456$	0.709063i	0.0332049i
$457$	−5.01039	−0.234376	−0.117188	−	0.993110i	$-0.537388\pi$
$457$	−5.01039	−0.234376	−0.117188	+	0.993110i	$0.537388\pi$
$458$	5.06236	0.236548
$459$	0	0
$460$	−0.319896	−0.0149152
$461$	−16.3822	−0.762994	−0.381497	−	0.924370i	$-0.624591\pi$
$461$	−16.3822	−0.762994	−0.381497	+	0.924370i	$0.624591\pi$
$462$	0.533043i	0.0247994i
$463$	−27.3768	−1.27231	−0.636153	−	0.771563i	$-0.719475\pi$
$463$	−27.3768	−1.27231	−0.636153	+	0.771563i	$0.719475\pi$
$464$	26.8915i	1.24841i
$465$	0.728895i	0.0338017i
$466$	− 41.7172i	− 1.93251i
$467$	0.646341	0.0299091	0.0149545	−	0.999888i	$-0.495240\pi$
$467$	0.646341	0.0299091	0.0149545	+	0.999888i	$0.495240\pi$
$468$	1.16241	0.0537325
$469$	− 2.08116i	− 0.0960991i
$470$	− 7.10141i	− 0.327564i
$471$	− 0.675423i	− 0.0311218i
$472$	27.5487	1.26803
$473$	3.10994i	0.142995i
$474$	2.34668	0.107786
$475$	−2.32272	−0.106574
$476$	0	0
$477$	−35.8144	−1.63983
$478$	−11.3221	−0.517861
$479$	13.5649i	0.619795i	0.950770	+	0.309898i	$0.100295\pi$
$479$	13.5649i	0.619795i	−0.950770	+	0.309898i	$0.899705\pi$
$480$	−0.0428738	−0.00195691
$481$	− 0.668933i	− 0.0305007i
$482$	16.7242i	0.761767i
$483$	− 0.354231i	− 0.0161181i
$484$	−0.864516	−0.0392962
$485$	−2.70080	−0.122637
$486$	− 4.24553i	− 0.192581i
$487$	29.0339i	1.31565i	0.753170	+	0.657826i	$0.228524\pi$
$487$	29.0339i	1.31565i	−0.753170	+	0.657826i	$0.771476\pi$
$488$	4.45222i	0.201543i
$489$	−1.23108	−0.0556716
$490$	− 9.37384i	− 0.423467i
$491$	−13.1298	−0.592541	−0.296271	−	0.955104i	$-0.595743\pi$
$491$	−13.1298	−0.592541	−0.296271	+	0.955104i	$0.595743\pi$
$492$	−0.00817968	−0.000368768 0
$493$	0	0
$494$	−18.8401	−0.847655
$495$	−14.4941	−0.651460
$496$	27.4113i	1.23080i
$497$	−3.25892	−0.146183
$498$	0.795992i	0.0356692i
$499$	11.3410i	0.507691i	0.967245	+	0.253846i	$0.0816955\pi$
$499$	11.3410i	0.507691i	−0.967245	+	0.253846i	$0.918305\pi$
$500$	− 0.0689897i	− 0.00308531i
$501$	0.627131	0.0280182
$502$	11.4308	0.510183
$503$	20.5436i	0.915995i	0.888953	+	0.457998i	$0.151433\pi$
$503$	20.5436i	0.915995i	−0.888953	+	0.457998i	$0.848567\pi$
$504$	5.76860i	0.256954i
$505$	14.3025i	0.636452i
$506$	32.3537	1.43830
$507$	2.06613i	0.0917601i
$508$	0.0343940	0.00152599
$509$	8.40900	0.372722	0.186361	−	0.982481i	$-0.440331\pi$
$509$	8.40900	0.372722	0.186361	+	0.982481i	$0.440331\pi$
$510$	0	0
$511$	3.82235	0.169091
$512$	21.3482	0.943467
$513$	1.52861i	0.0674899i
$514$	−11.4026	−0.502946
$515$	− 10.8963i	− 0.480150i
$516$	0.00486116i	0 0.000214001i
$517$	23.9489i	1.05327i
$518$	−0.118602	−0.00521108
$519$	−0.498706	−0.0218908
$520$	15.6628i	0.686860i
$521$	21.3561i	0.935627i	0.883827	+	0.467813i	$0.154958\pi$
$521$	21.3561i	0.935627i	−0.883827	+	0.467813i	$0.845042\pi$
$522$	27.9624i	1.22388i
$523$	−24.4644	−1.06975	−0.534877	−	0.844930i	$-0.679642\pi$
$523$	−24.4644	−1.06975	−0.534877	+	0.844930i	$0.679642\pi$
$524$	1.34765i	0.0588724i
$525$	0.0763945	0.00333413
$526$	12.2785	0.535367
$527$	0	0
$528$	2.20361	0.0958996
$529$	1.49953	0.0651969
$530$	17.2412i	0.748909i
$531$	29.6351	1.28605
$532$	0.111383i	0.00482907i
$533$	6.08323i	0.263494i
$534$	0.372550i	0.0161218i
$535$	−16.6273	−0.718862
$536$	−8.31633	−0.359211
$537$	2.01960i	0.0871521i
$538$	22.9897i	0.991155i
$539$	31.6125i	1.36165i
$540$	−0.0454030	−0.00195384
$541$	1.92406i	0.0827219i	0.999144	+	0.0413610i	$0.0131694\pi$
$541$	1.92406i	0.0827219i	−0.999144	+	0.0413610i	$0.986831\pi$
$542$	32.4055	1.39194
$543$	−1.17800	−0.0505530
$544$	0	0
$545$	10.5999	0.454049
$546$	0.619652	0.0265186
$547$	− 14.7222i	− 0.629475i	−0.949179	−	0.314737i	$-0.898084\pi$
$547$	− 14.7222i	− 0.629475i	0.949179	−	0.314737i	$-0.101916\pi$
$548$	−0.263350	−0.0112498
$549$	4.78941i	0.204407i
$550$	6.97750i	0.297522i
$551$	− 15.1120i	− 0.643794i
$552$	−1.41551	−0.0602480
$553$	−10.3178	−0.438757
$554$	− 9.92798i	− 0.421800i
$555$	0.0130377i	0 0.000553419i
$556$	− 0.914285i	− 0.0387743i
$557$	−24.3617	−1.03224	−0.516119	−	0.856517i	$-0.672624\pi$
$557$	−24.3617	−1.03224	−0.516119	+	0.856517i	$0.672624\pi$
$558$	28.5029i	1.20662i
$559$	3.61524	0.152909
$560$	2.87294	0.121404
$561$	0	0
$562$	13.4931	0.569171
$563$	30.7200	1.29470	0.647348	−	0.762195i	$-0.275878\pi$
$563$	30.7200	1.29470	0.647348	+	0.762195i	$0.275878\pi$
$564$	0.0374347i	0.00157628i
$565$	11.5397	0.485477
$566$	29.5978i	1.24409i
$567$	6.18030i	0.259548i
$568$	13.0227i	0.546419i
$569$	−5.35732	−0.224590	−0.112295	−	0.993675i	$-0.535820\pi$
$569$	−5.35732	−0.224590	−0.112295	+	0.993675i	$0.535820\pi$
$570$	0.367198	0.0153802
$571$	36.0360i	1.50806i	0.656839	+	0.754031i	$0.271893\pi$
$571$	36.0360i	1.50806i	−0.656839	+	0.754031i	$0.728107\pi$
$572$	1.88717i	0.0789067i
$573$	2.03764i	0.0851235i
$574$	1.07856	0.0450182
$575$	− 4.63686i	− 0.193370i
$576$	23.0229	0.959288
$577$	−39.5472	−1.64637	−0.823186	−	0.567772i	$-0.807806\pi$
$577$	−39.5472	−1.64637	−0.823186	+	0.567772i	$0.807806\pi$
$578$	0	0
$579$	−1.08653	−0.0451546
$580$	0.448860	0.0186379
$581$	− 3.49979i	− 0.145196i
$582$	0.426969	0.0176984
$583$	− 58.1446i	− 2.40810i
$584$	− 15.2741i	− 0.632048i
$585$	16.8490i	0.696622i
$586$	33.7361	1.39363
$587$	−17.9282	−0.739975	−0.369988	−	0.929037i	$-0.620638\pi$
$587$	−17.9282	−0.739975	−0.369988	+	0.929037i	$0.620638\pi$
$588$	0.0494137i	0.00203778i
$589$	− 15.4041i	− 0.634716i
$590$	− 14.2665i	− 0.587341i
$591$	−1.53357	−0.0630827
$592$	0.490303i	0.0201513i
$593$	15.2975	0.628192	0.314096	−	0.949391i	$-0.398299\pi$
$593$	15.2975	0.628192	0.314096	+	0.949391i	$0.398299\pi$
$594$	4.59199	0.188412
$595$	0	0
$596$	−1.20416	−0.0493245
$597$	1.39984	0.0572917
$598$	− 37.6105i	− 1.53801i
$599$	34.6498	1.41575	0.707877	−	0.706336i	$-0.249653\pi$
$599$	34.6498	1.41575	0.707877	+	0.706336i	$0.249653\pi$
$600$	− 0.305273i	− 0.0124627i
$601$	− 16.0361i	− 0.654126i	−0.945003	−	0.327063i	$-0.893941\pi$
$601$	− 16.0361i	− 0.654126i	0.945003	−	0.327063i	$-0.106059\pi$
$602$	− 0.640985i	− 0.0261246i
$603$	−8.94617	−0.364316
$604$	0.777618	0.0316408
$605$	− 12.5311i	− 0.509461i
$606$	− 2.26108i	− 0.0918499i
$607$	− 36.5119i	− 1.48197i	−0.671521	−	0.740986i	$-0.734359\pi$
$607$	− 36.5119i	− 1.48197i	0.671521	−	0.740986i	$-0.265641\pi$
$608$	0.906076	0.0367462
$609$	0.497037i	0.0201409i
$610$	2.30564	0.0933528
$611$	27.8402	1.12629
$612$	0	0
$613$	33.2758	1.34400	0.671998	−	0.740553i	$-0.265436\pi$
$613$	33.2758	1.34400	0.671998	+	0.740553i	$0.265436\pi$
$614$	−43.7647	−1.76620
$615$	− 0.118564i	− 0.00478095i
$616$	−9.36532	−0.377339
$617$	31.7084i	1.27653i	0.769815	+	0.638267i	$0.220348\pi$
$617$	31.7084i	1.27653i	−0.769815	+	0.638267i	$0.779652\pi$
$618$	1.72260i	0.0692931i
$619$	40.8302i	1.64110i	0.571572	+	0.820552i	$0.306334\pi$
$619$	40.8302i	1.64110i	−0.571572	+	0.820552i	$0.693666\pi$
$620$	0.457535	0.0183751
$621$	−3.05158	−0.122456
$622$	− 1.55331i	− 0.0622820i
$623$	− 1.63802i	− 0.0656258i
$624$	− 2.56165i	− 0.102548i
$625$	1.00000	0.0400000
$626$	5.21497i	0.208432i
$627$	−1.23835	−0.0494548
$628$	−0.423970	−0.0169183
$629$	0	0
$630$	2.98735	0.119019
$631$	15.8001	0.628992	0.314496	−	0.949259i	$-0.398165\pi$
$631$	15.8001	0.628992	0.314496	+	0.949259i	$0.398165\pi$
$632$	41.2300i	1.64004i
$633$	1.41536	0.0562555
$634$	− 12.6505i	− 0.502415i
$635$	0.498539i	0.0197839i
$636$	− 0.0908860i	− 0.00360386i
$637$	36.7489	1.45605
$638$	−45.3969	−1.79728
$639$	14.0089i	0.554185i
$640$	− 11.8635i	− 0.468947i
$641$	− 24.9339i	− 0.984831i	−0.870360	−	0.492415i	$-0.836114\pi$
$641$	− 24.9339i	− 0.984831i	0.870360	−	0.492415i	$-0.163886\pi$
$642$	2.62861	0.103743
$643$	24.0161i	0.947103i	0.880766	+	0.473552i	$0.157028\pi$
$643$	24.0161i	0.947103i	−0.880766	+	0.473552i	$0.842972\pi$
$644$	−0.222355	−0.00876200
$645$	−0.0704621	−0.00277444
$646$	0	0
$647$	−23.8307	−0.936882	−0.468441	−	0.883495i	$-0.655184\pi$
$647$	−23.8307	−0.936882	−0.468441	+	0.883495i	$0.655184\pi$
$648$	24.6965	0.970170
$649$	48.1125i	1.88858i
$650$	8.11121	0.318148
$651$	0.506644i	0.0198569i
$652$	0.772766i	0.0302638i
$653$	− 16.5191i	− 0.646441i	−0.946324	−	0.323221i	$-0.895234\pi$
$653$	− 16.5191i	− 0.646441i	0.946324	−	0.323221i	$-0.104766\pi$
$654$	−1.67573	−0.0655264
$655$	−19.5341	−0.763260
$656$	− 4.45878i	− 0.174086i
$657$	− 16.4309i	− 0.641031i
$658$	− 4.93608i	− 0.192428i
$659$	10.2510	0.399324	0.199662	−	0.979865i	$-0.436016\pi$
$659$	10.2510	0.399324	0.199662	+	0.979865i	$0.436016\pi$
$660$	− 0.0367815i	− 0.00143172i
$661$	21.3416	0.830090	0.415045	−	0.909801i	$-0.363766\pi$
$661$	21.3416	0.830090	0.415045	+	0.909801i	$0.363766\pi$
$662$	50.5790	1.96581
$663$	0	0
$664$	−13.9852	−0.542731
$665$	−1.61449	−0.0626071
$666$	0.509829i	0.0197555i
$667$	30.1683	1.16812
$668$	− 0.393657i	− 0.0152311i
$669$	− 2.24438i	− 0.0867728i
$670$	4.30672i	0.166383i
$671$	−7.77560	−0.300174
$672$	−0.0298009	−0.00114960
$673$	− 27.5159i	− 1.06066i	−0.847791	−	0.530331i	$-0.822068\pi$
$673$	− 27.5159i	− 1.06066i	0.847791	−	0.530331i	$-0.177932\pi$
$674$	45.3314i	1.74610i
$675$	− 0.658113i	− 0.0253308i
$676$	1.29693	0.0498821
$677$	17.0437i	0.655042i	0.944844	+	0.327521i	$0.106213\pi$
$677$	17.0437i	0.655042i	−0.944844	+	0.327521i	$0.893787\pi$
$678$	−1.82430	−0.0700619
$679$	−1.87729	−0.0720437
$680$	0	0
$681$	−0.134118	−0.00513942
$682$	−46.2744	−1.77194
$683$	3.12281i	0.119491i	0.998214	+	0.0597456i	$0.0190289\pi$
$683$	3.12281i	0.119491i	−0.998214	+	0.0597456i	$0.980971\pi$
$684$	0.478796	0.0183072
$685$	− 3.81724i	− 0.145849i
$686$	− 13.5143i	− 0.515977i
$687$	− 0.386810i	− 0.0147577i
$688$	−2.64984	−0.101024
$689$	−67.5919	−2.57505
$690$	0.733040i	0.0279064i
$691$	36.1278i	1.37437i	0.726484	+	0.687184i	$0.241153\pi$
$691$	36.1278i	1.37437i	−0.726484	+	0.687184i	$0.758847\pi$
$692$	0.313044i	0.0119001i
$693$	−10.0746	−0.382702
$694$	− 0.633344i	− 0.0240414i
$695$	13.2525	0.502695
$696$	1.98616	0.0752852
$697$	0	0
$698$	−17.8680	−0.676315
$699$	−3.18758	−0.120565
$700$	− 0.0479537i	− 0.00181248i
$701$	−18.1677	−0.686185	−0.343093	−	0.939302i	$-0.611474\pi$
$701$	−18.1677	−0.686185	−0.343093	+	0.939302i	$0.611474\pi$
$702$	− 5.33809i	− 0.201473i
$703$	− 0.275533i	− 0.0103919i
$704$	37.3777i	1.40872i
$705$	−0.542613	−0.0204360
$706$	10.6162	0.399545
$707$	9.94144i	0.373886i
$708$	0.0752048i	0.00282637i
$709$	− 11.6045i	− 0.435817i	−0.975969	−	0.217909i	$-0.930077\pi$
$709$	− 11.6045i	− 0.435817i	0.975969	−	0.217909i	$-0.0699235\pi$
$710$	6.74396	0.253096
$711$	44.3525i	1.66335i
$712$	−6.54553	−0.245304
$713$	30.7514	1.15165
$714$	0	0
$715$	−27.3544	−1.02300
$716$	1.26772	0.0473771
$717$	0.865112i	0.0323082i
$718$	−10.1433	−0.378543
$719$	− 25.7861i	− 0.961658i	−0.876814	−	0.480829i	$-0.840336\pi$
$719$	− 25.7861i	− 0.961658i	0.876814	−	0.480829i	$-0.159664\pi$
$720$	− 12.3497i	− 0.460247i
$721$	− 7.57388i	− 0.282066i
$722$	19.5694	0.728296
$723$	1.27788	0.0475249
$724$	0.739447i	0.0274813i
$725$	6.50618i	0.241634i
$726$	1.98104i	0.0735231i
$727$	17.7430	0.658051	0.329025	−	0.944321i	$-0.393280\pi$
$727$	17.7430	0.658051	0.329025	+	0.944321i	$0.393280\pi$
$728$	10.8870i	0.403499i
$729$	26.3499	0.975922
$730$	−7.90991	−0.292759
$731$	0	0
$732$	−0.0121541	−0.000449227 0
$733$	26.8221	0.990695	0.495348	−	0.868695i	$-0.335041\pi$
$733$	26.8221	0.990695	0.495348	+	0.868695i	$0.335041\pi$
$734$	23.4699i	0.866290i
$735$	−0.716247	−0.0264192
$736$	1.80880i	0.0666734i
$737$	− 14.5241i	− 0.535002i
$738$	− 4.63634i	− 0.170666i
$739$	−0.451458	−0.0166071	−0.00830357	−	0.999966i	$-0.502643\pi$
$739$	−0.451458	−0.0166071	−0.00830357	+	0.999966i	$0.502643\pi$
$740$	0.00818390	0.000300846 0
$741$	1.43955i	0.0528833i
$742$	11.9841i	0.439950i
$743$	− 20.6466i	− 0.757450i	−0.925509	−	0.378725i	$-0.876363\pi$
$743$	− 20.6466i	− 0.757450i	0.925509	−	0.378725i	$-0.123637\pi$
$744$	2.02455	0.0742236
$745$	− 17.4543i	− 0.639475i
$746$	26.4407	0.968063
$747$	−15.0444	−0.550445
$748$	0	0
$749$	−11.5574	−0.422298
$750$	−0.158090	−0.00577262
$751$	− 26.7059i	− 0.974514i	−0.873259	−	0.487257i	$-0.837998\pi$
$751$	− 26.7059i	− 0.974514i	0.873259	−	0.487257i	$-0.162002\pi$
$752$	−20.4058	−0.744123
$753$	− 0.873420i	− 0.0318292i
$754$	52.7730i	1.92188i
$755$	11.2715i	0.410212i
$756$	−0.0315589	−0.00114779
$757$	−19.3283	−0.702499	−0.351250	−	0.936282i	$-0.614243\pi$
$757$	−19.3283	−0.702499	−0.351250	+	0.936282i	$0.614243\pi$
$758$	23.7270i	0.861805i
$759$	− 2.47212i	− 0.0897322i
$760$	6.45150i	0.234020i
$761$	−9.52382	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$761$	−9.52382	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$762$	− 0.0788138i	− 0.00285512i
$763$	7.36782	0.266733
$764$	1.27905	0.0462743
$765$	0	0
$766$	−52.2751	−1.88878
$767$	55.9298	2.01951
$768$	0.181764i	0.00655886i
$769$	21.8393	0.787544	0.393772	−	0.919208i	$-0.371170\pi$
$769$	21.8393	0.787544	0.393772	+	0.919208i	$0.371170\pi$
$770$	4.84996i	0.174780i
$771$	0.871260i	0.0313777i
$772$	0.682026i	0.0245466i
$773$	18.2320	0.655760	0.327880	−	0.944719i	$-0.393666\pi$
$773$	18.2320	0.655760	0.327880	+	0.944719i	$0.393666\pi$
$774$	−2.75537	−0.0990396
$775$	6.63194i	0.238226i
$776$	7.50165i	0.269294i
$777$	0.00906229i	0 0.000325108i
$778$	9.16025	0.328411
$779$	2.50567i	0.0897751i
$780$	−0.0427578	−0.00153097
$781$	−22.7435	−0.813826
$782$	0	0
$783$	4.28180	0.153019
$784$	−26.9356	−0.961986
$785$	− 6.14541i	− 0.219339i
$786$	3.08814	0.110150
$787$	10.0983i	0.359967i	0.983670	+	0.179983i	$0.0576044\pi$
$787$	10.0983i	0.359967i	−0.983670	+	0.179983i	$0.942396\pi$
$788$	0.962641i	0.0342927i
$789$	− 0.938188i	− 0.0334004i
$790$	21.3515	0.759653
$791$	8.02104	0.285195
$792$	40.2581i	1.43051i
$793$	9.03898i	0.320984i
$794$	48.0105i	1.70383i
$795$	1.31738	0.0467228
$796$	− 0.878696i	− 0.0311446i
$797$	30.2149	1.07027	0.535133	−	0.844768i	$-0.320262\pi$
$797$	30.2149	1.07027	0.535133	+	0.844768i	$0.320262\pi$
$798$	0.255234	0.00903518
$799$	0	0
$800$	−0.390093	−0.0137919
$801$	−7.04125	−0.248790
$802$	16.9012i	0.596803i
$803$	26.6756	0.941360
$804$	− 0.0227027i	0 0.000800661i
$805$	− 3.22301i	− 0.113596i
$806$	53.7930i	1.89478i
$807$	1.75662	0.0618360
$808$	39.7260	1.39756
$809$	25.8073i	0.907337i	0.891170	+	0.453669i	$0.149885\pi$
$809$	25.8073i	0.907337i	−0.891170	+	0.453669i	$0.850115\pi$
$810$	− 12.7894i	− 0.449374i
$811$	47.1759i	1.65657i	0.560308	+	0.828284i	$0.310683\pi$
$811$	47.1759i	1.65657i	−0.560308	+	0.828284i	$0.689317\pi$
$812$	0.311995	0.0109489
$813$	− 2.47608i	− 0.0868399i
$814$	−0.827706	−0.0290111
$815$	−11.2012	−0.392360
$816$	0	0
$817$	1.48911	0.0520975
$818$	−18.2438	−0.637880
$819$	11.7115i	0.409233i
$820$	−0.0744238	−0.00259899
$821$	− 34.8152i	− 1.21506i	−0.794297	−	0.607530i	$-0.792161\pi$
$821$	− 34.8152i	− 1.21506i	0.794297	−	0.607530i	$-0.207839\pi$
$822$	0.603467i	0.0210483i
$823$	− 11.9291i	− 0.415823i	−0.978148	−	0.207912i	$-0.933333\pi$
$823$	− 11.9291i	− 0.415823i	0.978148	−	0.207912i	$-0.0666666\pi$
$824$	−30.2652	−1.05434
$825$	0.533145	0.0185617
$826$	− 9.91639i	− 0.345035i
$827$	7.58265i	0.263674i	0.991271	+	0.131837i	$0.0420876\pi$
$827$	7.58265i	0.263674i	−0.991271	+	0.131837i	$0.957912\pi$
$828$	0.955823i	0.0332171i
$829$	24.5064	0.851141	0.425570	−	0.904925i	$-0.360073\pi$
$829$	24.5064	0.851141	0.425570	+	0.904925i	$0.360073\pi$
$830$	7.24243i	0.251388i
$831$	−0.758589	−0.0263152
$832$	43.4508	1.50639
$833$	0	0
$834$	−2.09508	−0.0725467
$835$	5.70603	0.197465
$836$	0.777324i	0.0268843i
$837$	4.36456	0.150861
$838$	50.3761i	1.74021i
$839$	− 13.9747i	− 0.482462i	−0.970468	−	0.241231i	$-0.922449\pi$
$839$	− 13.9747i	− 0.482462i	0.970468	−	0.241231i	$-0.0775511\pi$
$840$	− 0.212190i	− 0.00732127i
$841$	−13.3304	−0.459669
$842$	14.4172	0.496850
$843$	− 1.03099i	− 0.0355093i
$844$	− 0.888437i	− 0.0305813i
$845$	18.7989i	0.646703i
$846$	−21.2184	−0.729505
$847$	− 8.71017i	− 0.299285i
$848$	49.5423	1.70129
$849$	2.26154	0.0776158
$850$	0	0
$851$	0.550047	0.0188554
$852$	−0.0355504	−0.00121794
$853$	7.40009i	0.253374i	0.991943	+	0.126687i	$0.0404344\pi$
$853$	7.40009i	0.253374i	−0.991943	+	0.126687i	$0.959566\pi$
$854$	1.60262	0.0548404
$855$	6.94010i	0.237347i
$856$	46.1834i	1.57852i
$857$	− 48.3185i	− 1.65053i	−0.564748	−	0.825264i	$-0.691027\pi$
$857$	− 48.3185i	− 1.65053i	0.564748	−	0.825264i	$-0.308973\pi$
$858$	4.32445	0.147634
$859$	5.21085	0.177792	0.0888959	−	0.996041i	$-0.471666\pi$
$859$	5.21085	0.177792	0.0888959	+	0.996041i	$0.471666\pi$
$860$	0.0442299i	0.00150823i
$861$	− 0.0824119i	− 0.00280859i
$862$	− 34.1563i	− 1.16337i
$863$	7.90307	0.269024	0.134512	−	0.990912i	$-0.457053\pi$
$863$	7.90307	0.269024	0.134512	+	0.990912i	$0.457053\pi$
$864$	0.256725i	0.00873396i
$865$	−4.53754	−0.154281
$866$	−46.4483	−1.57838
$867$	0	0
$868$	0.318026	0.0107945
$869$	−72.0063	−2.44265
$870$	− 1.02856i	− 0.0348715i
$871$	−16.8840	−0.572091
$872$	− 29.4419i	− 0.997027i
$873$	8.06979i	0.273121i
$874$	− 15.4917i	− 0.524016i
$875$	0.695085	0.0234982
$876$	0.0416967	0.00140880
$877$	− 27.5064i	− 0.928824i	−0.885619	−	0.464412i	$-0.846266\pi$
$877$	− 27.5064i	− 0.928824i	0.885619	−	0.464412i	$-0.153734\pi$
$878$	30.6766i	1.03528i
$879$	− 2.57775i	− 0.0869452i
$880$	20.0498	0.675878
$881$	19.7314i	0.664769i	0.943144	+	0.332384i	$0.107853\pi$
$881$	19.7314i	0.664769i	−0.943144	+	0.332384i	$0.892147\pi$
$882$	−28.0083	−0.943088
$883$	21.8566	0.735534	0.367767	−	0.929918i	$-0.380122\pi$
$883$	21.8566	0.735534	0.367767	+	0.929918i	$0.380122\pi$
$884$	0	0
$885$	−1.09009	−0.0366429
$886$	19.8768	0.667774
$887$	− 2.77874i	− 0.0933011i	−0.998911	−	0.0466505i	$-0.985145\pi$
$887$	− 2.77874i	− 0.0933011i	0.998911	−	0.0466505i	$-0.0148547\pi$
$888$	0.0362130	0.00121523
$889$	0.346526i	0.0116221i
$890$	3.38969i	0.113623i
$891$	43.1313i	1.44495i
$892$	−1.40882	−0.0471709
$893$	11.4673	0.383740
$894$	2.75934i	0.0922861i
$895$	18.3756i	0.614227i
$896$	− 8.24615i	− 0.275485i
$897$	−2.87379	−0.0959530
$898$	− 9.51328i	− 0.317462i
$899$	−43.1486	−1.43909
$900$	−0.206136	−0.00687119
$901$	0	0
$902$	7.52710	0.250625
$903$	−0.0489771	−0.00162986
$904$	− 32.0521i	− 1.06604i
$905$	−10.7182	−0.356286
$906$	− 1.78191i	− 0.0592000i
$907$	42.4769i	1.41042i	0.708998	+	0.705210i	$0.249147\pi$
$907$	42.4769i	1.41042i	−0.708998	+	0.705210i	$0.750853\pi$
$908$	0.0841875i	0.00279386i
$909$	42.7347	1.41742
$910$	5.63798	0.186897
$911$	− 59.0680i	− 1.95701i	−0.206223	−	0.978505i	$-0.566117\pi$
$911$	− 59.0680i	− 1.95701i	0.206223	−	0.978505i	$-0.433883\pi$
$912$	− 1.05514i	− 0.0349392i
$913$	− 24.4245i	− 0.808333i
$914$	7.20694	0.238384
$915$	− 0.176172i	− 0.00582407i
$916$	−0.242805	−0.00802251
$917$	−13.5778	−0.448380
$918$	0	0
$919$	26.5657	0.876323	0.438161	−	0.898896i	$-0.355630\pi$
$919$	26.5657	0.876323	0.438161	+	0.898896i	$0.355630\pi$
$920$	−12.8792	−0.424614
$921$	3.34402i	0.110189i
$922$	23.5641	0.776042
$923$	26.4388i	0.870245i
$924$	− 0.0255663i	0 0.000841069i
$925$	0.118625i	0.00390036i
$926$	39.3787	1.29406
$927$	−32.5574	−1.06932
$928$	− 2.53801i	− 0.0833144i
$929$	− 38.9968i	− 1.27944i	−0.768606	−	0.639722i	$-0.779049\pi$
$929$	− 38.9968i	− 1.27944i	0.768606	−	0.639722i	$-0.220951\pi$
$930$	− 1.04844i	− 0.0343797i
$931$	15.1368	0.496090
$932$	2.00088i	0.0655410i
$933$	−0.118687	−0.00388563
$934$	−0.929695	−0.0304206
$935$	0	0
$936$	46.7993	1.52968
$937$	−9.80514	−0.320320	−0.160160	−	0.987091i	$-0.551201\pi$
$937$	−9.80514	−0.320320	−0.160160	+	0.987091i	$0.551201\pi$
$938$	2.99354i	0.0977425i
$939$	0.398471	0.0130036
$940$	0.340604i	0.0111093i
$941$	− 49.2240i	− 1.60466i	−0.596884	−	0.802328i	$-0.703595\pi$
$941$	− 49.2240i	− 1.60466i	0.596884	−	0.802328i	$-0.296405\pi$
$942$	0.971527i	0.0316540i
$943$	−5.00209	−0.162890
$944$	−40.9945	−1.33426
$945$	− 0.457444i	− 0.0148807i
$946$	− 4.47333i	− 0.145441i
$947$	− 18.1975i	− 0.591339i	−0.955290	−	0.295669i	$-0.904457\pi$
$947$	− 18.1975i	− 0.591339i	0.955290	−	0.295669i	$-0.0955426\pi$
$948$	−0.112553	−0.00365556
$949$	− 31.0098i	− 1.00662i
$950$	3.34100	0.108396
$951$	−0.966612	−0.0313445
$952$	0	0
$953$	−5.23591	−0.169608	−0.0848039	−	0.996398i	$-0.527026\pi$
$953$	−5.23591	−0.169608	−0.0848039	+	0.996398i	$0.527026\pi$
$954$	51.5153	1.66787
$955$	18.5397i	0.599930i
$956$	0.543041	0.0175632
$957$	3.46874i	0.112128i
$958$	− 19.5117i	− 0.630395i
$959$	− 2.65331i	− 0.0856797i
$960$	−0.846868	−0.0273326
$961$	−12.9826	−0.418793
$962$	0.962191i	0.0310223i
$963$	49.6811i	1.60095i
$964$	− 0.802141i	− 0.0258352i
$965$	−9.88591	−0.318239
$966$	0.509525i	0.0163937i
$967$	−3.19462	−0.102732	−0.0513661	−	0.998680i	$-0.516358\pi$
$967$	−3.19462	−0.102732	−0.0513661	+	0.998680i	$0.516358\pi$
$968$	−34.8059	−1.11870
$969$	0	0
$970$	3.88483	0.124734
$971$	27.2613	0.874856	0.437428	−	0.899253i	$-0.355890\pi$
$971$	27.2613	0.874856	0.437428	+	0.899253i	$0.355890\pi$
$972$	0.203628i	0.00653136i
$973$	9.21160	0.295310
$974$	− 41.7623i	− 1.33815i
$975$	− 0.619770i	− 0.0198485i
$976$	− 6.62524i	− 0.212069i
$977$	−8.00610	−0.256138	−0.128069	−	0.991765i	$-0.540878\pi$
$977$	−8.00610	−0.256138	−0.128069	+	0.991765i	$0.540878\pi$
$978$	1.77079	0.0566236
$979$	− 11.4315i	− 0.365351i
$980$	0.449596i	0.0143618i
$981$	− 31.6716i	− 1.01120i
$982$	18.8859	0.602674
$983$	10.9464i	0.349137i	0.984645	+	0.174569i	$0.0558531\pi$
$983$	10.9464i	0.349137i	−0.984645	+	0.174569i	$0.944147\pi$
$984$	−0.329318	−0.0104983
$985$	−13.9534	−0.444592
$986$	0	0
$987$	−0.377162	−0.0120052
$988$	0.903624	0.0287481
$989$	2.97273i	0.0945273i
$990$	20.8482	0.662600
$991$	− 29.0834i	− 0.923863i	−0.886915	−	0.461932i	$-0.847157\pi$
$991$	− 29.0834i	− 0.923863i	0.886915	−	0.461932i	$-0.152843\pi$
$992$	− 2.58707i	− 0.0821395i
$993$	− 3.86470i	− 0.122642i
$994$	4.68762	0.148682
$995$	12.7366	0.403778
$996$	− 0.0381780i	− 0.00120972i
$997$	− 13.6956i	− 0.433745i	−0.976200	−	0.216873i	$-0.930414\pi$
$997$	− 13.6956i	− 0.433745i	0.976200	−	0.216873i	$-0.0695856\pi$
$998$	− 16.3128i	− 0.516373i
$999$	0.0780686	0.00246998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.j.866.6		24
17.4	even	4		1445.2.a.p.1.10		12
17.5	odd	16		85.2.l.a.26.5	✓	24
17.10	odd	16		85.2.l.a.36.5	yes	24
17.13	even	4		1445.2.a.q.1.10		12
17.16	even	2	inner	1445.2.d.j.866.5		24
51.5	even	16		765.2.be.b.451.2		24
51.44	even	16		765.2.be.b.631.2		24
85.4	even	4		7225.2.a.bs.1.3		12
85.22	even	16		425.2.n.f.349.5		24
85.27	even	16		425.2.n.c.274.2		24
85.39	odd	16		425.2.m.b.26.2		24
85.44	odd	16		425.2.m.b.376.2		24
85.64	even	4		7225.2.a.bq.1.3		12
85.73	even	16		425.2.n.c.349.2		24
85.78	even	16		425.2.n.f.274.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.5	✓	24	17.5	odd	16
85.2.l.a.36.5	yes	24	17.10	odd	16
425.2.m.b.26.2		24	85.39	odd	16
425.2.m.b.376.2		24	85.44	odd	16
425.2.n.c.274.2		24	85.27	even	16
425.2.n.c.349.2		24	85.73	even	16
425.2.n.f.274.5		24	85.78	even	16
425.2.n.f.349.5		24	85.22	even	16
765.2.be.b.451.2		24	51.5	even	16
765.2.be.b.631.2		24	51.44	even	16
1445.2.a.p.1.10		12	17.4	even	4
1445.2.a.q.1.10		12	17.13	even	4
1445.2.d.j.866.5		24	17.16	even	2	inner
1445.2.d.j.866.6		24	1.1	even	1	trivial
7225.2.a.bq.1.3		12	85.64	even	4
7225.2.a.bs.1.3		12	85.4	even	4

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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.43840 q^{2} +0.109907i q^{3} +0.0689897 q^{4} +1.00000i q^{5} -0.158090i q^{6} +0.695085i q^{7} +2.77756 q^{8} +2.98792 q^{9} -1.43840i q^{10} +4.85089i q^{11} +0.00758244i q^{12} +5.63906 q^{13} -0.999809i q^{14} -0.109907 q^{15} -4.13322 q^{16} -4.29782 q^{18} +2.32272 q^{19} +0.0689897i q^{20} -0.0763945 q^{21} -6.97750i q^{22} +4.63686i q^{23} +0.305273i q^{24} -1.00000 q^{25} -8.11121 q^{26} +0.658113i q^{27} +0.0479537i q^{28} -6.50618i q^{29} +0.158090 q^{30} -6.63194i q^{31} +0.390093 q^{32} -0.533145 q^{33} -0.695085 q^{35} +0.206136 q^{36} -0.118625i q^{37} -3.34100 q^{38} +0.619770i q^{39} +2.77756i q^{40} +1.07877i q^{41} +0.109886 q^{42} +0.641108 q^{43} +0.334661i q^{44} +2.98792i q^{45} -6.66965i q^{46} +4.93703 q^{47} -0.454269i q^{48} +6.51686 q^{49} +1.43840 q^{50} +0.389037 q^{52} -11.9864 q^{53} -0.946629i q^{54} -4.85089 q^{55} +1.93064i q^{56} +0.255283i q^{57} +9.35848i q^{58} +9.91829 q^{59} -0.00758244 q^{60} +1.60292i q^{61} +9.53937i q^{62} +2.07686i q^{63} +7.70533 q^{64} +5.63906i q^{65} +0.766875 q^{66} -2.99411 q^{67} -0.509622 q^{69} +0.999809 q^{70} +4.68852i q^{71} +8.29913 q^{72} -5.49911i q^{73} +0.170630i q^{74} -0.109907i q^{75} +0.160244 q^{76} -3.37178 q^{77} -0.891477i q^{78} +14.8439i q^{79} -4.13322i q^{80} +8.89143 q^{81} -1.55170i q^{82} -5.03506 q^{83} -0.00527044 q^{84} -0.922169 q^{86} +0.715073 q^{87} +13.4736i q^{88} -2.35657 q^{89} -4.29782i q^{90} +3.91962i q^{91} +0.319896i q^{92} +0.728895 q^{93} -7.10141 q^{94} +2.32272i q^{95} +0.0428738i q^{96} +2.70080i q^{97} -9.37384 q^{98} +14.4941i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43}+ \cdots - 120 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

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