LMFDB - Embedded newform 7120.2.a.bj.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7120,2,Mod(1,7120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("7120.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7120 = 2^{4} \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7120.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:	$56.8534862392$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 8x^{5} + 6x^{4} + 19x^{3} - 10x^{2} - 12x + 6 $ x^7 - x^6 - 8x^5 + 6x^4 + 19x^3 - 10x^2 - 12*x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 445)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.26266$ of defining polynomial
Character	$\chi$	$=$	7120.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.29058 q^{3} +1.00000 q^{5} +4.83304 q^{7} +7.82788 q^{9} +O(q^{10})$	$q+3.29058 q^{3} +1.00000 q^{5} +4.83304 q^{7} +7.82788 q^{9} +2.21586 q^{11} -2.26162 q^{13} +3.29058 q^{15} -3.10920 q^{17} +5.93952 q^{19} +15.9035 q^{21} -5.79416 q^{23} +1.00000 q^{25} +15.8865 q^{27} +2.32757 q^{29} -4.47624 q^{31} +7.29145 q^{33} +4.83304 q^{35} -8.23124 q^{37} -7.44204 q^{39} -0.278075 q^{41} +0.176109 q^{43} +7.82788 q^{45} -1.91855 q^{47} +16.3583 q^{49} -10.2311 q^{51} +8.65904 q^{53} +2.21586 q^{55} +19.5444 q^{57} -5.39666 q^{59} -9.69150 q^{61} +37.8325 q^{63} -2.26162 q^{65} -8.06916 q^{67} -19.0661 q^{69} +5.00576 q^{71} -9.18909 q^{73} +3.29058 q^{75} +10.7093 q^{77} +1.78949 q^{79} +28.7921 q^{81} -13.8879 q^{83} -3.10920 q^{85} +7.65906 q^{87} +1.00000 q^{89} -10.9305 q^{91} -14.7294 q^{93} +5.93952 q^{95} -5.52008 q^{97} +17.3455 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9}+O(q^{10}) $ 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9	$ 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9} + 10 q^{11} - 7 q^{13} + 8 q^{15} - 13 q^{17} + 7 q^{19} + 16 q^{21} + 13 q^{23} + 7 q^{25} + 23 q^{27} - 4 q^{29} - q^{31} - 6 q^{33} + 16 q^{35} - 5 q^{37} + 13 q^{39} + 5 q^{41} + 31 q^{43} + 11 q^{45} + 14 q^{47} + 19 q^{49} + q^{51} - 13 q^{53} + 10 q^{55} + 21 q^{57} + 14 q^{59} + 3 q^{61} + 54 q^{63} - 7 q^{65} - q^{67} + 31 q^{69} + 8 q^{71} + 9 q^{73} + 8 q^{75} + 42 q^{77} - 9 q^{79} + 35 q^{81} + 42 q^{83} - 13 q^{85} - 6 q^{87} + 7 q^{89} - 31 q^{91} + 24 q^{93} + 7 q^{95} - 7 q^{97} - 5 q^{99}+O(q^{100}) $ 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9 + 10 * q^11 - 7 * q^13 + 8 * q^15 - 13 * q^17 + 7 * q^19 + 16 * q^21 + 13 * q^23 + 7 * q^25 + 23 * q^27 - 4 * q^29 - q^31 - 6 * q^33 + 16 * q^35 - 5 * q^37 + 13 * q^39 + 5 * q^41 + 31 * q^43 + 11 * q^45 + 14 * q^47 + 19 * q^49 + q^51 - 13 * q^53 + 10 * q^55 + 21 * q^57 + 14 * q^59 + 3 * q^61 + 54 * q^63 - 7 * q^65 - q^67 + 31 * q^69 + 8 * q^71 + 9 * q^73 + 8 * q^75 + 42 * q^77 - 9 * q^79 + 35 * q^81 + 42 * q^83 - 13 * q^85 - 6 * q^87 + 7 * q^89 - 31 * q^91 + 24 * q^93 + 7 * q^95 - 7 * q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	3.29058	1.89981	0.949907	−	0.312532i	$-0.101177\pi$
$3$	3.29058	1.89981	0.949907	+	0.312532i	$0.101177\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	4.83304	1.82672	0.913358	−	0.407157i	$-0.133480\pi$
$7$	4.83304	1.82672	0.913358	+	0.407157i	$0.133480\pi$
$8$	0	0
$9$	7.82788	2.60929
$10$	0	0
$11$	2.21586	0.668106	0.334053	−	0.942554i	$-0.391583\pi$
$11$	2.21586	0.668106	0.334053	+	0.942554i	$0.391583\pi$
$12$	0	0
$13$	−2.26162	−0.627261	−0.313631	−	0.949545i	$-0.601545\pi$
$13$	−2.26162	−0.627261	−0.313631	+	0.949545i	$0.601545\pi$
$14$	0	0
$15$	3.29058	0.849623
$16$	0	0
$17$	−3.10920	−0.754092	−0.377046	−	0.926194i	$-0.623060\pi$
$17$	−3.10920	−0.754092	−0.377046	+	0.926194i	$0.623060\pi$
$18$	0	0
$19$	5.93952	1.36262	0.681309	−	0.731996i	$-0.261411\pi$
$19$	5.93952	1.36262	0.681309	+	0.731996i	$0.261411\pi$
$20$	0	0
$21$	15.9035	3.47042
$22$	0	0
$23$	−5.79416	−1.20817	−0.604083	−	0.796921i	$-0.706460\pi$
$23$	−5.79416	−1.20817	−0.604083	+	0.796921i	$0.706460\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	15.8865	3.05736
$28$	0	0
$29$	2.32757	0.432220	0.216110	−	0.976369i	$-0.430663\pi$
$29$	2.32757	0.432220	0.216110	+	0.976369i	$0.430663\pi$
$30$	0	0
$31$	−4.47624	−0.803956	−0.401978	−	0.915649i	$-0.631677\pi$
$31$	−4.47624	−0.803956	−0.401978	+	0.915649i	$0.631677\pi$
$32$	0	0
$33$	7.29145	1.26928
$34$	0	0
$35$	4.83304	0.816932
$36$	0	0
$37$	−8.23124	−1.35321	−0.676604	−	0.736347i	$-0.736549\pi$
$37$	−8.23124	−1.35321	−0.676604	+	0.736347i	$0.736549\pi$
$38$	0	0
$39$	−7.44204	−1.19168
$40$	0	0
$41$	−0.278075	−0.0434281	−0.0217140	−	0.999764i	$-0.506912\pi$
$41$	−0.278075	−0.0434281	−0.0217140	+	0.999764i	$0.506912\pi$
$42$	0	0
$43$	0.176109	0.0268564	0.0134282	−	0.999910i	$-0.495726\pi$
$43$	0.176109	0.0268564	0.0134282	+	0.999910i	$0.495726\pi$
$44$	0	0
$45$	7.82788	1.16691
$46$	0	0
$47$	−1.91855	−0.279850	−0.139925	−	0.990162i	$-0.544686\pi$
$47$	−1.91855	−0.279850	−0.139925	+	0.990162i	$0.544686\pi$
$48$	0	0
$49$	16.3583	2.33689
$50$	0	0
$51$	−10.2311	−1.43264
$52$	0	0
$53$	8.65904	1.18941	0.594706	−	0.803944i	$-0.297269\pi$
$53$	8.65904	1.18941	0.594706	+	0.803944i	$0.297269\pi$
$54$	0	0
$55$	2.21586	0.298786
$56$	0	0
$57$	19.5444	2.58872
$58$	0	0
$59$	−5.39666	−0.702585	−0.351292	−	0.936266i	$-0.614258\pi$
$59$	−5.39666	−0.702585	−0.351292	+	0.936266i	$0.614258\pi$
$60$	0	0
$61$	−9.69150	−1.24087	−0.620434	−	0.784258i	$-0.713044\pi$
$61$	−9.69150	−1.24087	−0.620434	+	0.784258i	$0.713044\pi$
$62$	0	0
$63$	37.8325	4.76644
$64$	0	0
$65$	−2.26162	−0.280520
$66$	0	0
$67$	−8.06916	−0.985805	−0.492903	−	0.870084i	$-0.664064\pi$
$67$	−8.06916	−0.985805	−0.492903	+	0.870084i	$0.664064\pi$
$68$	0	0
$69$	−19.0661	−2.29529
$70$	0	0
$71$	5.00576	0.594075	0.297037	−	0.954866i	$-0.404001\pi$
$71$	5.00576	0.594075	0.297037	+	0.954866i	$0.404001\pi$
$72$	0	0
$73$	−9.18909	−1.07550	−0.537751	−	0.843104i	$-0.680726\pi$
$73$	−9.18909	−1.07550	−0.537751	+	0.843104i	$0.680726\pi$
$74$	0	0
$75$	3.29058	0.379963
$76$	0	0
$77$	10.7093	1.22044
$78$	0	0
$79$	1.78949	0.201333	0.100666	−	0.994920i	$-0.467903\pi$
$79$	1.78949	0.201333	0.100666	+	0.994920i	$0.467903\pi$
$80$	0	0
$81$	28.7921	3.19912
$82$	0	0
$83$	−13.8879	−1.52439	−0.762197	−	0.647345i	$-0.775879\pi$
$83$	−13.8879	−1.52439	−0.762197	+	0.647345i	$0.775879\pi$
$84$	0	0
$85$	−3.10920	−0.337240
$86$	0	0
$87$	7.65906	0.821137
$88$	0	0
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	0	0
$91$	−10.9305	−1.14583
$92$	0	0
$93$	−14.7294	−1.52737
$94$	0	0
$95$	5.93952	0.609382
$96$	0	0
$97$	−5.52008	−0.560479	−0.280240	−	0.959930i	$-0.590414\pi$
$97$	−5.52008	−0.560479	−0.280240	+	0.959930i	$0.590414\pi$
$98$	0	0
$99$	17.3455	1.74329
$100$	0	0
$101$	−12.8409	−1.27772	−0.638860	−	0.769323i	$-0.720594\pi$
$101$	−12.8409	−1.27772	−0.638860	+	0.769323i	$0.720594\pi$
$102$	0	0
$103$	11.7697	1.15970	0.579852	−	0.814722i	$-0.303110\pi$
$103$	11.7697	1.15970	0.579852	+	0.814722i	$0.303110\pi$
$104$	0	0
$105$	15.9035	1.55202
$106$	0	0
$107$	15.4620	1.49477	0.747383	−	0.664393i	$-0.231310\pi$
$107$	15.4620	1.49477	0.747383	+	0.664393i	$0.231310\pi$
$108$	0	0
$109$	−7.88060	−0.754824	−0.377412	−	0.926045i	$-0.623186\pi$
$109$	−7.88060	−0.754824	−0.377412	+	0.926045i	$0.623186\pi$
$110$	0	0
$111$	−27.0855	−2.57084
$112$	0	0
$113$	−2.01004	−0.189088	−0.0945442	−	0.995521i	$-0.530139\pi$
$113$	−2.01004	−0.189088	−0.0945442	+	0.995521i	$0.530139\pi$
$114$	0	0
$115$	−5.79416	−0.540308
$116$	0	0
$117$	−17.7037	−1.63671
$118$	0	0
$119$	−15.0269	−1.37751
$120$	0	0
$121$	−6.08997	−0.553634
$122$	0	0
$123$	−0.915028	−0.0825053
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	12.0158	1.06623	0.533113	−	0.846044i	$-0.321022\pi$
$127$	12.0158	1.06623	0.533113	+	0.846044i	$0.321022\pi$
$128$	0	0
$129$	0.579500	0.0510221
$130$	0	0
$131$	20.6066	1.80040	0.900202	−	0.435472i	$-0.143419\pi$
$131$	20.6066	1.80040	0.900202	+	0.435472i	$0.143419\pi$
$132$	0	0
$133$	28.7059	2.48912
$134$	0	0
$135$	15.8865	1.36729
$136$	0	0
$137$	10.9369	0.934400	0.467200	−	0.884152i	$-0.345263\pi$
$137$	10.9369	0.934400	0.467200	+	0.884152i	$0.345263\pi$
$138$	0	0
$139$	0.432073	0.0366479	0.0183240	−	0.999832i	$-0.494167\pi$
$139$	0.432073	0.0366479	0.0183240	+	0.999832i	$0.494167\pi$
$140$	0	0
$141$	−6.31314	−0.531663
$142$	0	0
$143$	−5.01144	−0.419077
$144$	0	0
$145$	2.32757	0.193294
$146$	0	0
$147$	53.8281	4.43966
$148$	0	0
$149$	−13.6417	−1.11757	−0.558785	−	0.829313i	$-0.688732\pi$
$149$	−13.6417	−1.11757	−0.558785	+	0.829313i	$0.688732\pi$
$150$	0	0
$151$	−22.3825	−1.82146	−0.910730	−	0.413002i	$-0.864480\pi$
$151$	−22.3825	−1.82146	−0.910730	+	0.413002i	$0.864480\pi$
$152$	0	0
$153$	−24.3385	−1.96765
$154$	0	0
$155$	−4.47624	−0.359540
$156$	0	0
$157$	11.7366	0.936683	0.468342	−	0.883547i	$-0.344852\pi$
$157$	11.7366	0.936683	0.468342	+	0.883547i	$0.344852\pi$
$158$	0	0
$159$	28.4932	2.25966
$160$	0	0
$161$	−28.0034	−2.20698
$162$	0	0
$163$	−1.49678	−0.117237	−0.0586184	−	0.998280i	$-0.518670\pi$
$163$	−1.49678	−0.117237	−0.0586184	+	0.998280i	$0.518670\pi$
$164$	0	0
$165$	7.29145	0.567638
$166$	0	0
$167$	0.555849	0.0430129	0.0215064	−	0.999769i	$-0.493154\pi$
$167$	0.555849	0.0430129	0.0215064	+	0.999769i	$0.493154\pi$
$168$	0	0
$169$	−7.88506	−0.606543
$170$	0	0
$171$	46.4939	3.55547
$172$	0	0
$173$	14.0371	1.06722	0.533611	−	0.845730i	$-0.320835\pi$
$173$	14.0371	1.06722	0.533611	+	0.845730i	$0.320835\pi$
$174$	0	0
$175$	4.83304	0.365343
$176$	0	0
$177$	−17.7581	−1.33478
$178$	0	0
$179$	−9.22570	−0.689561	−0.344780	−	0.938683i	$-0.612047\pi$
$179$	−9.22570	−0.689561	−0.344780	+	0.938683i	$0.612047\pi$
$180$	0	0
$181$	−10.4704	−0.778259	−0.389129	−	0.921183i	$-0.627224\pi$
$181$	−10.4704	−0.778259	−0.389129	+	0.921183i	$0.627224\pi$
$182$	0	0
$183$	−31.8906	−2.35742
$184$	0	0
$185$	−8.23124	−0.605173
$186$	0	0
$187$	−6.88955	−0.503814
$188$	0	0
$189$	76.7801	5.58493
$190$	0	0
$191$	4.73905	0.342906	0.171453	−	0.985192i	$-0.445154\pi$
$191$	4.73905	0.342906	0.171453	+	0.985192i	$0.445154\pi$
$192$	0	0
$193$	1.48587	0.106955	0.0534775	−	0.998569i	$-0.482969\pi$
$193$	1.48587	0.106955	0.0534775	+	0.998569i	$0.482969\pi$
$194$	0	0
$195$	−7.44204	−0.532936
$196$	0	0
$197$	−4.51312	−0.321547	−0.160773	−	0.986991i	$-0.551399\pi$
$197$	−4.51312	−0.321547	−0.160773	+	0.986991i	$0.551399\pi$
$198$	0	0
$199$	−7.28028	−0.516085	−0.258043	−	0.966134i	$-0.583077\pi$
$199$	−7.28028	−0.516085	−0.258043	+	0.966134i	$0.583077\pi$
$200$	0	0
$201$	−26.5522	−1.87285
$202$	0	0
$203$	11.2493	0.789543
$204$	0	0
$205$	−0.278075	−0.0194216
$206$	0	0
$207$	−45.3560	−3.15246
$208$	0	0
$209$	13.1611	0.910374
$210$	0	0
$211$	−14.0051	−0.964154	−0.482077	−	0.876129i	$-0.660117\pi$
$211$	−14.0051	−0.964154	−0.482077	+	0.876129i	$0.660117\pi$
$212$	0	0
$213$	16.4718	1.12863
$214$	0	0
$215$	0.176109	0.0120105
$216$	0	0
$217$	−21.6338	−1.46860
$218$	0	0
$219$	−30.2374	−2.04325
$220$	0	0
$221$	7.03184	0.473013
$222$	0	0
$223$	8.76611	0.587022	0.293511	−	0.955956i	$-0.405176\pi$
$223$	8.76611	0.587022	0.293511	+	0.955956i	$0.405176\pi$
$224$	0	0
$225$	7.82788	0.521859
$226$	0	0
$227$	21.8527	1.45042	0.725209	−	0.688529i	$-0.241743\pi$
$227$	21.8527	1.45042	0.725209	+	0.688529i	$0.241743\pi$
$228$	0	0
$229$	−20.0211	−1.32303	−0.661514	−	0.749932i	$-0.730086\pi$
$229$	−20.0211	−1.32303	−0.661514	+	0.749932i	$0.730086\pi$
$230$	0	0
$231$	35.2398	2.31861
$232$	0	0
$233$	15.3296	1.00428	0.502139	−	0.864787i	$-0.332547\pi$
$233$	15.3296	1.00428	0.502139	+	0.864787i	$0.332547\pi$
$234$	0	0
$235$	−1.91855	−0.125153
$236$	0	0
$237$	5.88844	0.382495
$238$	0	0
$239$	−7.27188	−0.470379	−0.235190	−	0.971950i	$-0.575571\pi$
$239$	−7.27188	−0.470379	−0.235190	+	0.971950i	$0.575571\pi$
$240$	0	0
$241$	4.02887	0.259522	0.129761	−	0.991545i	$-0.458579\pi$
$241$	4.02887	0.259522	0.129761	+	0.991545i	$0.458579\pi$
$242$	0	0
$243$	47.0831	3.02038
$244$	0	0
$245$	16.3583	1.04509
$246$	0	0
$247$	−13.4329	−0.854718
$248$	0	0
$249$	−45.6992	−2.89607
$250$	0	0
$251$	6.99410	0.441464	0.220732	−	0.975335i	$-0.429155\pi$
$251$	6.99410	0.441464	0.220732	+	0.975335i	$0.429155\pi$
$252$	0	0
$253$	−12.8390	−0.807183
$254$	0	0
$255$	−10.2311	−0.640694
$256$	0	0
$257$	−19.3582	−1.20753	−0.603767	−	0.797161i	$-0.706334\pi$
$257$	−19.3582	−1.20753	−0.603767	+	0.797161i	$0.706334\pi$
$258$	0	0
$259$	−39.7819	−2.47193
$260$	0	0
$261$	18.2200	1.12779
$262$	0	0
$263$	5.73446	0.353602	0.176801	−	0.984247i	$-0.443425\pi$
$263$	5.73446	0.353602	0.176801	+	0.984247i	$0.443425\pi$
$264$	0	0
$265$	8.65904	0.531921
$266$	0	0
$267$	3.29058	0.201380
$268$	0	0
$269$	5.07725	0.309565	0.154783	−	0.987949i	$-0.450532\pi$
$269$	5.07725	0.309565	0.154783	+	0.987949i	$0.450532\pi$
$270$	0	0
$271$	−14.8909	−0.904557	−0.452278	−	0.891877i	$-0.649389\pi$
$271$	−14.8909	−0.904557	−0.452278	+	0.891877i	$0.649389\pi$
$272$	0	0
$273$	−35.9677	−2.17686
$274$	0	0
$275$	2.21586	0.133621
$276$	0	0
$277$	−30.6930	−1.84417	−0.922083	−	0.386993i	$-0.873514\pi$
$277$	−30.6930	−1.84417	−0.922083	+	0.386993i	$0.873514\pi$
$278$	0	0
$279$	−35.0395	−2.09776
$280$	0	0
$281$	19.5982	1.16913	0.584564	−	0.811348i	$-0.301266\pi$
$281$	19.5982	1.16913	0.584564	+	0.811348i	$0.301266\pi$
$282$	0	0
$283$	−32.1638	−1.91194	−0.955968	−	0.293469i	$-0.905190\pi$
$283$	−32.1638	−1.91194	−0.955968	+	0.293469i	$0.905190\pi$
$284$	0	0
$285$	19.5444	1.15771
$286$	0	0
$287$	−1.34395	−0.0793308
$288$	0	0
$289$	−7.33286	−0.431345
$290$	0	0
$291$	−18.1642	−1.06481
$292$	0	0
$293$	−22.7569	−1.32947	−0.664737	−	0.747077i	$-0.731457\pi$
$293$	−22.7569	−1.32947	−0.664737	+	0.747077i	$0.731457\pi$
$294$	0	0
$295$	−5.39666	−0.314205
$296$	0	0
$297$	35.2023	2.04264
$298$	0	0
$299$	13.1042	0.757836
$300$	0	0
$301$	0.851142	0.0490590
$302$	0	0
$303$	−42.2541	−2.42743
$304$	0	0
$305$	−9.69150	−0.554933
$306$	0	0
$307$	−0.883192	−0.0504064	−0.0252032	−	0.999682i	$-0.508023\pi$
$307$	−0.883192	−0.0504064	−0.0252032	+	0.999682i	$0.508023\pi$
$308$	0	0
$309$	38.7291	2.20322
$310$	0	0
$311$	2.98323	0.169163	0.0845816	−	0.996417i	$-0.473045\pi$
$311$	2.98323	0.169163	0.0845816	+	0.996417i	$0.473045\pi$
$312$	0	0
$313$	6.07859	0.343582	0.171791	−	0.985133i	$-0.445045\pi$
$313$	6.07859	0.343582	0.171791	+	0.985133i	$0.445045\pi$
$314$	0	0
$315$	37.8325	2.13162
$316$	0	0
$317$	2.02998	0.114015	0.0570075	−	0.998374i	$-0.481844\pi$
$317$	2.02998	0.114015	0.0570075	+	0.998374i	$0.481844\pi$
$318$	0	0
$319$	5.15757	0.288769
$320$	0	0
$321$	50.8788	2.83978
$322$	0	0
$323$	−18.4672	−1.02754
$324$	0	0
$325$	−2.26162	−0.125452
$326$	0	0
$327$	−25.9317	−1.43403
$328$	0	0
$329$	−9.27244	−0.511206
$330$	0	0
$331$	12.3999	0.681559	0.340779	−	0.940143i	$-0.389309\pi$
$331$	12.3999	0.681559	0.340779	+	0.940143i	$0.389309\pi$
$332$	0	0
$333$	−64.4332	−3.53092
$334$	0	0
$335$	−8.06916	−0.440866
$336$	0	0
$337$	27.1425	1.47855	0.739274	−	0.673405i	$-0.235169\pi$
$337$	27.1425	1.47855	0.739274	+	0.673405i	$0.235169\pi$
$338$	0	0
$339$	−6.61418	−0.359233
$340$	0	0
$341$	−9.91871	−0.537128
$342$	0	0
$343$	45.2288	2.44213
$344$	0	0
$345$	−19.0661	−1.02649
$346$	0	0
$347$	17.0635	0.916019	0.458009	−	0.888947i	$-0.348563\pi$
$347$	17.0635	0.916019	0.458009	+	0.888947i	$0.348563\pi$
$348$	0	0
$349$	25.3297	1.35587	0.677933	−	0.735124i	$-0.262876\pi$
$349$	25.3297	1.35587	0.677933	+	0.735124i	$0.262876\pi$
$350$	0	0
$351$	−35.9293	−1.91776
$352$	0	0
$353$	15.3713	0.818132	0.409066	−	0.912505i	$-0.365854\pi$
$353$	15.3713	0.818132	0.409066	+	0.912505i	$0.365854\pi$
$354$	0	0
$355$	5.00576	0.265678
$356$	0	0
$357$	−49.4471	−2.61702
$358$	0	0
$359$	4.81197	0.253966	0.126983	−	0.991905i	$-0.459471\pi$
$359$	4.81197	0.253966	0.126983	+	0.991905i	$0.459471\pi$
$360$	0	0
$361$	16.2779	0.856730
$362$	0	0
$363$	−20.0395	−1.05180
$364$	0	0
$365$	−9.18909	−0.480979
$366$	0	0
$367$	−23.4281	−1.22294	−0.611468	−	0.791269i	$-0.709421\pi$
$367$	−23.4281	−1.22294	−0.611468	+	0.791269i	$0.709421\pi$
$368$	0	0
$369$	−2.17674	−0.113317
$370$	0	0
$371$	41.8495	2.17272
$372$	0	0
$373$	10.4886	0.543078	0.271539	−	0.962427i	$-0.412467\pi$
$373$	10.4886	0.543078	0.271539	+	0.962427i	$0.412467\pi$
$374$	0	0
$375$	3.29058	0.169925
$376$	0	0
$377$	−5.26409	−0.271115
$378$	0	0
$379$	20.6495	1.06069	0.530347	−	0.847781i	$-0.322062\pi$
$379$	20.6495	1.06069	0.530347	+	0.847781i	$0.322062\pi$
$380$	0	0
$381$	39.5388	2.02563
$382$	0	0
$383$	−11.8529	−0.605654	−0.302827	−	0.953046i	$-0.597930\pi$
$383$	−11.8529	−0.605654	−0.302827	+	0.953046i	$0.597930\pi$
$384$	0	0
$385$	10.7093	0.545798
$386$	0	0
$387$	1.37856	0.0700762
$388$	0	0
$389$	−11.8172	−0.599157	−0.299578	−	0.954072i	$-0.596846\pi$
$389$	−11.8172	−0.599157	−0.299578	+	0.954072i	$0.596846\pi$
$390$	0	0
$391$	18.0152	0.911068
$392$	0	0
$393$	67.8075	3.42043
$394$	0	0
$395$	1.78949	0.0900388
$396$	0	0
$397$	36.5070	1.83223	0.916116	−	0.400912i	$-0.131307\pi$
$397$	36.5070	1.83223	0.916116	+	0.400912i	$0.131307\pi$
$398$	0	0
$399$	94.4590	4.72886
$400$	0	0
$401$	1.45221	0.0725197	0.0362599	−	0.999342i	$-0.488456\pi$
$401$	1.45221	0.0725197	0.0362599	+	0.999342i	$0.488456\pi$
$402$	0	0
$403$	10.1236	0.504291
$404$	0	0
$405$	28.7921	1.43069
$406$	0	0
$407$	−18.2393	−0.904086
$408$	0	0
$409$	32.3981	1.60198	0.800992	−	0.598674i	$-0.204306\pi$
$409$	32.3981	1.60198	0.800992	+	0.598674i	$0.204306\pi$
$410$	0	0
$411$	35.9886	1.77519
$412$	0	0
$413$	−26.0822	−1.28342
$414$	0	0
$415$	−13.8879	−0.681730
$416$	0	0
$417$	1.42177	0.0696242
$418$	0	0
$419$	10.4032	0.508227	0.254114	−	0.967174i	$-0.418216\pi$
$419$	10.4032	0.508227	0.254114	+	0.967174i	$0.418216\pi$
$420$	0	0
$421$	1.28300	0.0625297	0.0312648	−	0.999511i	$-0.490046\pi$
$421$	1.28300	0.0625297	0.0312648	+	0.999511i	$0.490046\pi$
$422$	0	0
$423$	−15.0182	−0.730211
$424$	0	0
$425$	−3.10920	−0.150818
$426$	0	0
$427$	−46.8394	−2.26672
$428$	0	0
$429$	−16.4905	−0.796169
$430$	0	0
$431$	2.37582	0.114439	0.0572195	−	0.998362i	$-0.481777\pi$
$431$	2.37582	0.114439	0.0572195	+	0.998362i	$0.481777\pi$
$432$	0	0
$433$	31.3903	1.50852	0.754262	−	0.656574i	$-0.227995\pi$
$433$	31.3903	1.50852	0.754262	+	0.656574i	$0.227995\pi$
$434$	0	0
$435$	7.65906	0.367224
$436$	0	0
$437$	−34.4145	−1.64627
$438$	0	0
$439$	8.32745	0.397448	0.198724	−	0.980056i	$-0.436320\pi$
$439$	8.32745	0.397448	0.198724	+	0.980056i	$0.436320\pi$
$440$	0	0
$441$	128.051	6.09764
$442$	0	0
$443$	27.1908	1.29188	0.645938	−	0.763390i	$-0.276466\pi$
$443$	27.1908	1.29188	0.645938	+	0.763390i	$0.276466\pi$
$444$	0	0
$445$	1.00000	0.0474045
$446$	0	0
$447$	−44.8890	−2.12318
$448$	0	0
$449$	−20.2755	−0.956861	−0.478430	−	0.878126i	$-0.658794\pi$
$449$	−20.2755	−0.956861	−0.478430	+	0.878126i	$0.658794\pi$
$450$	0	0
$451$	−0.616176	−0.0290146
$452$	0	0
$453$	−73.6512	−3.46044
$454$	0	0
$455$	−10.9305	−0.512430
$456$	0	0
$457$	−27.8204	−1.30138	−0.650691	−	0.759343i	$-0.725521\pi$
$457$	−27.8204	−1.30138	−0.650691	+	0.759343i	$0.725521\pi$
$458$	0	0
$459$	−49.3944	−2.30553
$460$	0	0
$461$	3.25129	0.151428	0.0757138	−	0.997130i	$-0.475876\pi$
$461$	3.25129	0.151428	0.0757138	+	0.997130i	$0.475876\pi$
$462$	0	0
$463$	13.8292	0.642699	0.321349	−	0.946961i	$-0.395864\pi$
$463$	13.8292	0.642699	0.321349	+	0.946961i	$0.395864\pi$
$464$	0	0
$465$	−14.7294	−0.683059
$466$	0	0
$467$	19.5627	0.905253	0.452626	−	0.891700i	$-0.350487\pi$
$467$	19.5627	0.905253	0.452626	+	0.891700i	$0.350487\pi$
$468$	0	0
$469$	−38.9986	−1.80079
$470$	0	0
$471$	38.6202	1.77952
$472$	0	0
$473$	0.390233	0.0179429
$474$	0	0
$475$	5.93952	0.272524
$476$	0	0
$477$	67.7820	3.10352
$478$	0	0
$479$	−26.2070	−1.19743	−0.598714	−	0.800963i	$-0.704321\pi$
$479$	−26.2070	−1.19743	−0.598714	+	0.800963i	$0.704321\pi$
$480$	0	0
$481$	18.6160	0.848815
$482$	0	0
$483$	−92.1473	−4.19285
$484$	0	0
$485$	−5.52008	−0.250654
$486$	0	0
$487$	−28.8600	−1.30777	−0.653887	−	0.756592i	$-0.726863\pi$
$487$	−28.8600	−1.30777	−0.653887	+	0.756592i	$0.726863\pi$
$488$	0	0
$489$	−4.92526	−0.222728
$490$	0	0
$491$	27.5737	1.24438	0.622192	−	0.782865i	$-0.286242\pi$
$491$	27.5737	1.24438	0.622192	+	0.782865i	$0.286242\pi$
$492$	0	0
$493$	−7.23690	−0.325933
$494$	0	0
$495$	17.3455	0.779621
$496$	0	0
$497$	24.1930	1.08521
$498$	0	0
$499$	−32.9455	−1.47484	−0.737422	−	0.675432i	$-0.763957\pi$
$499$	−32.9455	−1.47484	−0.737422	+	0.675432i	$0.763957\pi$
$500$	0	0
$501$	1.82906	0.0817165
$502$	0	0
$503$	25.6894	1.14543	0.572717	−	0.819753i	$-0.305890\pi$
$503$	25.6894	1.14543	0.572717	+	0.819753i	$0.305890\pi$
$504$	0	0
$505$	−12.8409	−0.571414
$506$	0	0
$507$	−25.9464	−1.15232
$508$	0	0
$509$	27.1811	1.20478	0.602390	−	0.798202i	$-0.294215\pi$
$509$	27.1811	1.20478	0.602390	+	0.798202i	$0.294215\pi$
$510$	0	0
$511$	−44.4112	−1.96464
$512$	0	0
$513$	94.3582	4.16602
$514$	0	0
$515$	11.7697	0.518635
$516$	0	0
$517$	−4.25124	−0.186969
$518$	0	0
$519$	46.1902	2.02752
$520$	0	0
$521$	0.901023	0.0394745	0.0197373	−	0.999805i	$-0.493717\pi$
$521$	0.901023	0.0394745	0.0197373	+	0.999805i	$0.493717\pi$
$522$	0	0
$523$	−0.0126235	−0.000551986 0	−0.000275993	−	1.00000i	$-0.500088\pi$
$523$	−0.0126235	−0.000551986 0	−0.000275993		1.00000i	$0.500088\pi$
$524$	0	0
$525$	15.9035	0.694084
$526$	0	0
$527$	13.9175	0.606257
$528$	0	0
$529$	10.5723	0.459665
$530$	0	0
$531$	−42.2444	−1.83325
$532$	0	0
$533$	0.628902	0.0272408
$534$	0	0
$535$	15.4620	0.668480
$536$	0	0
$537$	−30.3578	−1.31004
$538$	0	0
$539$	36.2476	1.56129
$540$	0	0
$541$	9.28499	0.399193	0.199596	−	0.979878i	$-0.436037\pi$
$541$	9.28499	0.399193	0.199596	+	0.979878i	$0.436037\pi$
$542$	0	0
$543$	−34.4536	−1.47855
$544$	0	0
$545$	−7.88060	−0.337568
$546$	0	0
$547$	12.6475	0.540770	0.270385	−	0.962752i	$-0.412849\pi$
$547$	12.6475	0.540770	0.270385	+	0.962752i	$0.412849\pi$
$548$	0	0
$549$	−75.8639	−3.23779
$550$	0	0
$551$	13.8247	0.588951
$552$	0	0
$553$	8.64865	0.367778
$554$	0	0
$555$	−27.0855	−1.14972
$556$	0	0
$557$	−1.89455	−0.0802747	−0.0401374	−	0.999194i	$-0.512780\pi$
$557$	−1.89455	−0.0802747	−0.0401374	+	0.999194i	$0.512780\pi$
$558$	0	0
$559$	−0.398292	−0.0168460
$560$	0	0
$561$	−22.6706	−0.957153
$562$	0	0
$563$	39.9171	1.68231	0.841153	−	0.540797i	$-0.181877\pi$
$563$	39.9171	1.68231	0.841153	+	0.540797i	$0.181877\pi$
$564$	0	0
$565$	−2.01004	−0.0845629
$566$	0	0
$567$	139.153	5.84389
$568$	0	0
$569$	−12.8214	−0.537499	−0.268750	−	0.963210i	$-0.586610\pi$
$569$	−12.8214	−0.537499	−0.268750	+	0.963210i	$0.586610\pi$
$570$	0	0
$571$	24.0157	1.00503	0.502513	−	0.864570i	$-0.332409\pi$
$571$	24.0157	1.00503	0.502513	+	0.864570i	$0.332409\pi$
$572$	0	0
$573$	15.5942	0.651457
$574$	0	0
$575$	−5.79416	−0.241633
$576$	0	0
$577$	−28.5046	−1.18666	−0.593331	−	0.804959i	$-0.702187\pi$
$577$	−28.5046	−1.18666	−0.593331	+	0.804959i	$0.702187\pi$
$578$	0	0
$579$	4.88935	0.203195
$580$	0	0
$581$	−67.1207	−2.78464
$582$	0	0
$583$	19.1872	0.794653
$584$	0	0
$585$	−17.7037	−0.731959
$586$	0	0
$587$	2.40697	0.0993462	0.0496731	−	0.998766i	$-0.484182\pi$
$587$	2.40697	0.0993462	0.0496731	+	0.998766i	$0.484182\pi$
$588$	0	0
$589$	−26.5867	−1.09549
$590$	0	0
$591$	−14.8508	−0.610879
$592$	0	0
$593$	10.4715	0.430013	0.215006	−	0.976613i	$-0.431023\pi$
$593$	10.4715	0.430013	0.215006	+	0.976613i	$0.431023\pi$
$594$	0	0
$595$	−15.0269	−0.616042
$596$	0	0
$597$	−23.9563	−0.980466
$598$	0	0
$599$	−9.28858	−0.379521	−0.189760	−	0.981830i	$-0.560771\pi$
$599$	−9.28858	−0.379521	−0.189760	+	0.981830i	$0.560771\pi$
$600$	0	0
$601$	−18.0877	−0.737814	−0.368907	−	0.929466i	$-0.620268\pi$
$601$	−18.0877	−0.737814	−0.368907	+	0.929466i	$0.620268\pi$
$602$	0	0
$603$	−63.1645	−2.57226
$604$	0	0
$605$	−6.08997	−0.247593
$606$	0	0
$607$	4.08445	0.165783	0.0828914	−	0.996559i	$-0.473585\pi$
$607$	4.08445	0.165783	0.0828914	+	0.996559i	$0.473585\pi$
$608$	0	0
$609$	37.0165	1.49998
$610$	0	0
$611$	4.33904	0.175539
$612$	0	0
$613$	20.2800	0.819101	0.409551	−	0.912287i	$-0.365685\pi$
$613$	20.2800	0.819101	0.409551	+	0.912287i	$0.365685\pi$
$614$	0	0
$615$	−0.915028	−0.0368975
$616$	0	0
$617$	3.23902	0.130398	0.0651990	−	0.997872i	$-0.479232\pi$
$617$	3.23902	0.130398	0.0651990	+	0.997872i	$0.479232\pi$
$618$	0	0
$619$	−2.62101	−0.105347	−0.0526737	−	0.998612i	$-0.516774\pi$
$619$	−2.62101	−0.105347	−0.0526737	+	0.998612i	$0.516774\pi$
$620$	0	0
$621$	−92.0490	−3.69380
$622$	0	0
$623$	4.83304	0.193632
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	43.3077	1.72954
$628$	0	0
$629$	25.5926	1.02044
$630$	0	0
$631$	4.84085	0.192711	0.0963557	−	0.995347i	$-0.469281\pi$
$631$	4.84085	0.192711	0.0963557	+	0.995347i	$0.469281\pi$
$632$	0	0
$633$	−46.0850	−1.83171
$634$	0	0
$635$	12.0158	0.476831
$636$	0	0
$637$	−36.9962	−1.46584
$638$	0	0
$639$	39.1845	1.55012
$640$	0	0
$641$	−41.4377	−1.63669	−0.818344	−	0.574728i	$-0.805108\pi$
$641$	−41.4377	−1.63669	−0.818344	+	0.574728i	$0.805108\pi$
$642$	0	0
$643$	26.2789	1.03634	0.518168	−	0.855279i	$-0.326614\pi$
$643$	26.2789	1.03634	0.518168	+	0.855279i	$0.326614\pi$
$644$	0	0
$645$	0.579500	0.0228178
$646$	0	0
$647$	−32.8680	−1.29218	−0.646088	−	0.763263i	$-0.723596\pi$
$647$	−32.8680	−1.29218	−0.646088	+	0.763263i	$0.723596\pi$
$648$	0	0
$649$	−11.9582	−0.469401
$650$	0	0
$651$	−71.1877	−2.79007
$652$	0	0
$653$	34.0840	1.33381	0.666904	−	0.745143i	$-0.267619\pi$
$653$	34.0840	1.33381	0.666904	+	0.745143i	$0.267619\pi$
$654$	0	0
$655$	20.6066	0.805165
$656$	0	0
$657$	−71.9311	−2.80630
$658$	0	0
$659$	22.3303	0.869864	0.434932	−	0.900463i	$-0.356772\pi$
$659$	22.3303	0.869864	0.434932	+	0.900463i	$0.356772\pi$
$660$	0	0
$661$	−4.90059	−0.190611	−0.0953055	−	0.995448i	$-0.530383\pi$
$661$	−4.90059	−0.190611	−0.0953055	+	0.995448i	$0.530383\pi$
$662$	0	0
$663$	23.1388	0.898637
$664$	0	0
$665$	28.7059	1.11317
$666$	0	0
$667$	−13.4863	−0.522193
$668$	0	0
$669$	28.8455	1.11523
$670$	0	0
$671$	−21.4750	−0.829032
$672$	0	0
$673$	17.8142	0.686689	0.343344	−	0.939210i	$-0.388440\pi$
$673$	17.8142	0.686689	0.343344	+	0.939210i	$0.388440\pi$
$674$	0	0
$675$	15.8865	0.611472
$676$	0	0
$677$	−2.59037	−0.0995561	−0.0497780	−	0.998760i	$-0.515851\pi$
$677$	−2.59037	−0.0995561	−0.0497780	+	0.998760i	$0.515851\pi$
$678$	0	0
$679$	−26.6788	−1.02384
$680$	0	0
$681$	71.9081	2.75552
$682$	0	0
$683$	−24.9388	−0.954257	−0.477128	−	0.878834i	$-0.658322\pi$
$683$	−24.9388	−0.954257	−0.477128	+	0.878834i	$0.658322\pi$
$684$	0	0
$685$	10.9369	0.417876
$686$	0	0
$687$	−65.8808	−2.51351
$688$	0	0
$689$	−19.5835	−0.746072
$690$	0	0
$691$	29.1377	1.10845	0.554226	−	0.832366i	$-0.313014\pi$
$691$	29.1377	1.10845	0.554226	+	0.832366i	$0.313014\pi$
$692$	0	0
$693$	83.8314	3.18449
$694$	0	0
$695$	0.432073	0.0163894
$696$	0	0
$697$	0.864593	0.0327488
$698$	0	0
$699$	50.4433	1.90794
$700$	0	0
$701$	−37.5559	−1.41847	−0.709233	−	0.704974i	$-0.750958\pi$
$701$	−37.5559	−1.41847	−0.709233	+	0.704974i	$0.750958\pi$
$702$	0	0
$703$	−48.8896	−1.84391
$704$	0	0
$705$	−6.31314	−0.237767
$706$	0	0
$707$	−62.0607	−2.33403
$708$	0	0
$709$	−16.0916	−0.604334	−0.302167	−	0.953255i	$-0.597710\pi$
$709$	−16.0916	−0.604334	−0.302167	+	0.953255i	$0.597710\pi$
$710$	0	0
$711$	14.0079	0.525337
$712$	0	0
$713$	25.9360	0.971312
$714$	0	0
$715$	−5.01144	−0.187417
$716$	0	0
$717$	−23.9287	−0.893633
$718$	0	0
$719$	3.86290	0.144062	0.0720310	−	0.997402i	$-0.477052\pi$
$719$	3.86290	0.144062	0.0720310	+	0.997402i	$0.477052\pi$
$720$	0	0
$721$	56.8834	2.11845
$722$	0	0
$723$	13.2573	0.493044
$724$	0	0
$725$	2.32757	0.0864439
$726$	0	0
$727$	10.4042	0.385871	0.192935	−	0.981211i	$-0.438199\pi$
$727$	10.4042	0.385871	0.192935	+	0.981211i	$0.438199\pi$
$728$	0	0
$729$	68.5541	2.53904
$730$	0	0
$731$	−0.547558	−0.0202522
$732$	0	0
$733$	−16.9908	−0.627569	−0.313784	−	0.949494i	$-0.601597\pi$
$733$	−16.9908	−0.627569	−0.313784	+	0.949494i	$0.601597\pi$
$734$	0	0
$735$	53.8281	1.98548
$736$	0	0
$737$	−17.8801	−0.658623
$738$	0	0
$739$	−10.1630	−0.373854	−0.186927	−	0.982374i	$-0.559853\pi$
$739$	−10.1630	−0.373854	−0.186927	+	0.982374i	$0.559853\pi$
$740$	0	0
$741$	−44.2021	−1.62381
$742$	0	0
$743$	25.6666	0.941617	0.470809	−	0.882235i	$-0.343962\pi$
$743$	25.6666	0.941617	0.470809	+	0.882235i	$0.343962\pi$
$744$	0	0
$745$	−13.6417	−0.499793
$746$	0	0
$747$	−108.713	−3.97759
$748$	0	0
$749$	74.7284	2.73051
$750$	0	0
$751$	1.88134	0.0686510	0.0343255	−	0.999411i	$-0.489072\pi$
$751$	1.88134	0.0686510	0.0343255	+	0.999411i	$0.489072\pi$
$752$	0	0
$753$	23.0146	0.838699
$754$	0	0
$755$	−22.3825	−0.814582
$756$	0	0
$757$	11.6427	0.423161	0.211580	−	0.977361i	$-0.432139\pi$
$757$	11.6427	0.423161	0.211580	+	0.977361i	$0.432139\pi$
$758$	0	0
$759$	−42.2478	−1.53350
$760$	0	0
$761$	20.9113	0.758035	0.379017	−	0.925390i	$-0.376262\pi$
$761$	20.9113	0.758035	0.379017	+	0.925390i	$0.376262\pi$
$762$	0	0
$763$	−38.0872	−1.37885
$764$	0	0
$765$	−24.3385	−0.879959
$766$	0	0
$767$	12.2052	0.440704
$768$	0	0
$769$	−21.0699	−0.759800	−0.379900	−	0.925028i	$-0.624042\pi$
$769$	−21.0699	−0.759800	−0.379900	+	0.925028i	$0.624042\pi$
$770$	0	0
$771$	−63.6997	−2.29409
$772$	0	0
$773$	4.26541	0.153416	0.0767080	−	0.997054i	$-0.475559\pi$
$773$	4.26541	0.153416	0.0767080	+	0.997054i	$0.475559\pi$
$774$	0	0
$775$	−4.47624	−0.160791
$776$	0	0
$777$	−130.905	−4.69620
$778$	0	0
$779$	−1.65163	−0.0591759
$780$	0	0
$781$	11.0921	0.396905
$782$	0	0
$783$	36.9770	1.32145
$784$	0	0
$785$	11.7366	0.418898
$786$	0	0
$787$	−46.9571	−1.67384	−0.836920	−	0.547325i	$-0.815646\pi$
$787$	−46.9571	−1.67384	−0.836920	+	0.547325i	$0.815646\pi$
$788$	0	0
$789$	18.8697	0.671778
$790$	0	0
$791$	−9.71458	−0.345411
$792$	0	0
$793$	21.9185	0.778349
$794$	0	0
$795$	28.4932	1.01055
$796$	0	0
$797$	−36.9401	−1.30849	−0.654243	−	0.756284i	$-0.727013\pi$
$797$	−36.9401	−1.30849	−0.654243	+	0.756284i	$0.727013\pi$
$798$	0	0
$799$	5.96517	0.211033
$800$	0	0
$801$	7.82788	0.276585
$802$	0	0
$803$	−20.3617	−0.718549
$804$	0	0
$805$	−28.0034	−0.986990
$806$	0	0
$807$	16.7071	0.588116
$808$	0	0
$809$	17.3676	0.610613	0.305306	−	0.952254i	$-0.401241\pi$
$809$	17.3676	0.610613	0.305306	+	0.952254i	$0.401241\pi$
$810$	0	0
$811$	44.5363	1.56388	0.781941	−	0.623352i	$-0.214230\pi$
$811$	44.5363	1.56388	0.781941	+	0.623352i	$0.214230\pi$
$812$	0	0
$813$	−48.9996	−1.71849
$814$	0	0
$815$	−1.49678	−0.0524299
$816$	0	0
$817$	1.04600	0.0365950
$818$	0	0
$819$	−85.5628	−2.98980
$820$	0	0
$821$	−17.7581	−0.619761	−0.309880	−	0.950776i	$-0.600289\pi$
$821$	−17.7581	−0.619761	−0.309880	+	0.950776i	$0.600289\pi$
$822$	0	0
$823$	27.7787	0.968304	0.484152	−	0.874984i	$-0.339128\pi$
$823$	27.7787	0.968304	0.484152	+	0.874984i	$0.339128\pi$
$824$	0	0
$825$	7.29145	0.253856
$826$	0	0
$827$	28.8725	1.00400	0.501998	−	0.864869i	$-0.332599\pi$
$827$	28.8725	1.00400	0.501998	+	0.864869i	$0.332599\pi$
$828$	0	0
$829$	41.4440	1.43941	0.719704	−	0.694281i	$-0.244277\pi$
$829$	41.4440	1.43941	0.719704	+	0.694281i	$0.244277\pi$
$830$	0	0
$831$	−100.998	−3.50357
$832$	0	0
$833$	−50.8611	−1.76223
$834$	0	0
$835$	0.555849	0.0192360
$836$	0	0
$837$	−71.1118	−2.45798
$838$	0	0
$839$	15.0790	0.520583	0.260292	−	0.965530i	$-0.416181\pi$
$839$	15.0790	0.520583	0.260292	+	0.965530i	$0.416181\pi$
$840$	0	0
$841$	−23.5824	−0.813186
$842$	0	0
$843$	64.4892	2.22113
$844$	0	0
$845$	−7.88506	−0.271254
$846$	0	0
$847$	−29.4331	−1.01133
$848$	0	0
$849$	−105.837	−3.63233
$850$	0	0
$851$	47.6931	1.63490
$852$	0	0
$853$	36.1724	1.23852	0.619260	−	0.785186i	$-0.287433\pi$
$853$	36.1724	1.23852	0.619260	+	0.785186i	$0.287433\pi$
$854$	0	0
$855$	46.4939	1.59006
$856$	0	0
$857$	14.1138	0.482117	0.241058	−	0.970511i	$-0.422505\pi$
$857$	14.1138	0.482117	0.241058	+	0.970511i	$0.422505\pi$
$858$	0	0
$859$	3.04904	0.104032	0.0520159	−	0.998646i	$-0.483435\pi$
$859$	3.04904	0.104032	0.0520159	+	0.998646i	$0.483435\pi$
$860$	0	0
$861$	−4.42237	−0.150714
$862$	0	0
$863$	44.3700	1.51037	0.755187	−	0.655510i	$-0.227546\pi$
$863$	44.3700	1.51037	0.755187	+	0.655510i	$0.227546\pi$
$864$	0	0
$865$	14.0371	0.477276
$866$	0	0
$867$	−24.1293	−0.819475
$868$	0	0
$869$	3.96525	0.134512
$870$	0	0
$871$	18.2494	0.618358
$872$	0	0
$873$	−43.2105	−1.46246
$874$	0	0
$875$	4.83304	0.163386
$876$	0	0
$877$	−39.0474	−1.31854	−0.659268	−	0.751908i	$-0.729134\pi$
$877$	−39.0474	−1.31854	−0.659268	+	0.751908i	$0.729134\pi$
$878$	0	0
$879$	−74.8834	−2.52575
$880$	0	0
$881$	8.96712	0.302110	0.151055	−	0.988525i	$-0.451733\pi$
$881$	8.96712	0.302110	0.151055	+	0.988525i	$0.451733\pi$
$882$	0	0
$883$	−6.30062	−0.212033	−0.106016	−	0.994364i	$-0.533810\pi$
$883$	−6.30062	−0.212033	−0.106016	+	0.994364i	$0.533810\pi$
$884$	0	0
$885$	−17.7581	−0.596932
$886$	0	0
$887$	−51.6559	−1.73443	−0.867217	−	0.497931i	$-0.834093\pi$
$887$	−51.6559	−1.73443	−0.867217	+	0.497931i	$0.834093\pi$
$888$	0	0
$889$	58.0726	1.94769
$890$	0	0
$891$	63.7993	2.13736
$892$	0	0
$893$	−11.3953	−0.381329
$894$	0	0
$895$	−9.22570	−0.308381
$896$	0	0
$897$	43.1204	1.43975
$898$	0	0
$899$	−10.4188	−0.347486
$900$	0	0
$901$	−26.9227	−0.896926
$902$	0	0
$903$	2.80075	0.0932030
$904$	0	0
$905$	−10.4704	−0.348048
$906$	0	0
$907$	30.5492	1.01437	0.507185	−	0.861837i	$-0.330686\pi$
$907$	30.5492	1.01437	0.507185	+	0.861837i	$0.330686\pi$
$908$	0	0
$909$	−100.517	−3.33395
$910$	0	0
$911$	−13.9379	−0.461784	−0.230892	−	0.972979i	$-0.574164\pi$
$911$	−13.9379	−0.461784	−0.230892	+	0.972979i	$0.574164\pi$
$912$	0	0
$913$	−30.7736	−1.01846
$914$	0	0
$915$	−31.8906	−1.05427
$916$	0	0
$917$	99.5923	3.28883
$918$	0	0
$919$	−21.5909	−0.712217	−0.356108	−	0.934445i	$-0.615897\pi$
$919$	−21.5909	−0.712217	−0.356108	+	0.934445i	$0.615897\pi$
$920$	0	0
$921$	−2.90621	−0.0957628
$922$	0	0
$923$	−11.3211	−0.372640
$924$	0	0
$925$	−8.23124	−0.270641
$926$	0	0
$927$	92.1319	3.02601
$928$	0	0
$929$	−34.8126	−1.14216	−0.571082	−	0.820893i	$-0.693476\pi$
$929$	−34.8126	−1.14216	−0.571082	+	0.820893i	$0.693476\pi$
$930$	0	0
$931$	97.1601	3.18429
$932$	0	0
$933$	9.81653	0.321379
$934$	0	0
$935$	−6.88955	−0.225312
$936$	0	0
$937$	29.3529	0.958918	0.479459	−	0.877564i	$-0.340833\pi$
$937$	29.3529	0.958918	0.479459	+	0.877564i	$0.340833\pi$
$938$	0	0
$939$	20.0021	0.652743
$940$	0	0
$941$	39.9726	1.30307	0.651534	−	0.758619i	$-0.274126\pi$
$941$	39.9726	1.30307	0.651534	+	0.758619i	$0.274126\pi$
$942$	0	0
$943$	1.61121	0.0524683
$944$	0	0
$945$	76.7801	2.49766
$946$	0	0
$947$	−57.0642	−1.85434	−0.927168	−	0.374646i	$-0.877764\pi$
$947$	−57.0642	−1.85434	−0.927168	+	0.374646i	$0.877764\pi$
$948$	0	0
$949$	20.7822	0.674620
$950$	0	0
$951$	6.67980	0.216607
$952$	0	0
$953$	47.9488	1.55321	0.776607	−	0.629985i	$-0.216939\pi$
$953$	47.9488	1.55321	0.776607	+	0.629985i	$0.216939\pi$
$954$	0	0
$955$	4.73905	0.153352
$956$	0	0
$957$	16.9714	0.548607
$958$	0	0
$959$	52.8583	1.70688
$960$	0	0
$961$	−10.9633	−0.353655
$962$	0	0
$963$	121.035	3.90029
$964$	0	0
$965$	1.48587	0.0478317
$966$	0	0
$967$	22.9873	0.739222	0.369611	−	0.929187i	$-0.379491\pi$
$967$	22.9873	0.739222	0.369611	+	0.929187i	$0.379491\pi$
$968$	0	0
$969$	−60.7676	−1.95214
$970$	0	0
$971$	−4.86938	−0.156266	−0.0781330	−	0.996943i	$-0.524896\pi$
$971$	−4.86938	−0.156266	−0.0781330	+	0.996943i	$0.524896\pi$
$972$	0	0
$973$	2.08822	0.0669454
$974$	0	0
$975$	−7.44204	−0.238336
$976$	0	0
$977$	5.28623	0.169121	0.0845607	−	0.996418i	$-0.473051\pi$
$977$	5.28623	0.169121	0.0845607	+	0.996418i	$0.473051\pi$
$978$	0	0
$979$	2.21586	0.0708191
$980$	0	0
$981$	−61.6884	−1.96956
$982$	0	0
$983$	−21.4830	−0.685202	−0.342601	−	0.939481i	$-0.611308\pi$
$983$	−21.4830	−0.685202	−0.342601	+	0.939481i	$0.611308\pi$
$984$	0	0
$985$	−4.51312	−0.143800
$986$	0	0
$987$	−30.5117	−0.971197
$988$	0	0
$989$	−1.02040	−0.0324470
$990$	0	0
$991$	39.9796	1.26999	0.634997	−	0.772514i	$-0.281001\pi$
$991$	39.9796	1.26999	0.634997	+	0.772514i	$0.281001\pi$
$992$	0	0
$993$	40.8027	1.29484
$994$	0	0
$995$	−7.28028	−0.230800
$996$	0	0
$997$	−40.8157	−1.29265	−0.646323	−	0.763064i	$-0.723694\pi$
$997$	−40.8157	−1.29265	−0.646323	+	0.763064i	$0.723694\pi$
$998$	0	0
$999$	−130.766	−4.13724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7120.2.a.bj.1.7		7
4.3	odd	2		445.2.a.f.1.7	✓	7
12.11	even	2		4005.2.a.o.1.1		7
20.19	odd	2		2225.2.a.k.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.a.f.1.7	✓	7	4.3	odd	2
2225.2.a.k.1.1		7	20.19	odd	2
4005.2.a.o.1.1		7	12.11	even	2
7120.2.a.bj.1.7		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7120 = 2^{4} \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7120.a (trivial)

\(f(q)\)	\(=\)	\(q+3.29058 q^{3} +1.00000 q^{5} +4.83304 q^{7} +7.82788 q^{9} +O(q^{10})\)	\(q+3.29058 q^{3} +1.00000 q^{5} +4.83304 q^{7} +7.82788 q^{9} +2.21586 q^{11} -2.26162 q^{13} +3.29058 q^{15} -3.10920 q^{17} +5.93952 q^{19} +15.9035 q^{21} -5.79416 q^{23} +1.00000 q^{25} +15.8865 q^{27} +2.32757 q^{29} -4.47624 q^{31} +7.29145 q^{33} +4.83304 q^{35} -8.23124 q^{37} -7.44204 q^{39} -0.278075 q^{41} +0.176109 q^{43} +7.82788 q^{45} -1.91855 q^{47} +16.3583 q^{49} -10.2311 q^{51} +8.65904 q^{53} +2.21586 q^{55} +19.5444 q^{57} -5.39666 q^{59} -9.69150 q^{61} +37.8325 q^{63} -2.26162 q^{65} -8.06916 q^{67} -19.0661 q^{69} +5.00576 q^{71} -9.18909 q^{73} +3.29058 q^{75} +10.7093 q^{77} +1.78949 q^{79} +28.7921 q^{81} -13.8879 q^{83} -3.10920 q^{85} +7.65906 q^{87} +1.00000 q^{89} -10.9305 q^{91} -14.7294 q^{93} +5.93952 q^{95} -5.52008 q^{97} +17.3455 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9}+O(q^{10}) \) 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9	\( 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9} + 10 q^{11} - 7 q^{13} + 8 q^{15} - 13 q^{17} + 7 q^{19} + 16 q^{21} + 13 q^{23} + 7 q^{25} + 23 q^{27} - 4 q^{29} - q^{31} - 6 q^{33} + 16 q^{35} - 5 q^{37} + 13 q^{39} + 5 q^{41} + 31 q^{43} + 11 q^{45} + 14 q^{47} + 19 q^{49} + q^{51} - 13 q^{53} + 10 q^{55} + 21 q^{57} + 14 q^{59} + 3 q^{61} + 54 q^{63} - 7 q^{65} - q^{67} + 31 q^{69} + 8 q^{71} + 9 q^{73} + 8 q^{75} + 42 q^{77} - 9 q^{79} + 35 q^{81} + 42 q^{83} - 13 q^{85} - 6 q^{87} + 7 q^{89} - 31 q^{91} + 24 q^{93} + 7 q^{95} - 7 q^{97} - 5 q^{99}+O(q^{100}) \) 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9 + 10 * q^11 - 7 * q^13 + 8 * q^15 - 13 * q^17 + 7 * q^19 + 16 * q^21 + 13 * q^23 + 7 * q^25 + 23 * q^27 - 4 * q^29 - q^31 - 6 * q^33 + 16 * q^35 - 5 * q^37 + 13 * q^39 + 5 * q^41 + 31 * q^43 + 11 * q^45 + 14 * q^47 + 19 * q^49 + q^51 - 13 * q^53 + 10 * q^55 + 21 * q^57 + 14 * q^59 + 3 * q^61 + 54 * q^63 - 7 * q^65 - q^67 + 31 * q^69 + 8 * q^71 + 9 * q^73 + 8 * q^75 + 42 * q^77 - 9 * q^79 + 35 * q^81 + 42 * q^83 - 13 * q^85 - 6 * q^87 + 7 * q^89 - 31 * q^91 + 24 * q^93 + 7 * q^95 - 7 * q^97 - 5 * q^99

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