LMFDB - Embedded newform 4025.2.a.be.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67541 q^{2} +3.24787 q^{3} +0.806990 q^{4} -5.44150 q^{6} +1.00000 q^{7} +1.99878 q^{8} +7.54864 q^{9} +O(q^{10})$	\(q-1.67541 q^{2} +3.24787 q^{3} +0.806990 q^{4} -5.44150 q^{6} +1.00000 q^{7} +1.99878 q^{8} +7.54864 q^{9} -4.71556 q^{11} +2.62100 q^{12} +3.32391 q^{13} -1.67541 q^{14} -4.96275 q^{16} +1.29098 q^{17} -12.6470 q^{18} +2.45303 q^{19} +3.24787 q^{21} +7.90049 q^{22} +1.00000 q^{23} +6.49176 q^{24} -5.56891 q^{26} +14.7734 q^{27} +0.806990 q^{28} -5.36305 q^{29} +5.21170 q^{31} +4.31707 q^{32} -15.3155 q^{33} -2.16292 q^{34} +6.09168 q^{36} +10.2179 q^{37} -4.10983 q^{38} +10.7956 q^{39} -9.56611 q^{41} -5.44150 q^{42} +6.36288 q^{43} -3.80541 q^{44} -1.67541 q^{46} -13.2443 q^{47} -16.1183 q^{48} +1.00000 q^{49} +4.19294 q^{51} +2.68236 q^{52} +7.80242 q^{53} -24.7514 q^{54} +1.99878 q^{56} +7.96713 q^{57} +8.98529 q^{58} +8.55068 q^{59} +3.86811 q^{61} -8.73173 q^{62} +7.54864 q^{63} +2.69264 q^{64} +25.6597 q^{66} -4.50444 q^{67} +1.04181 q^{68} +3.24787 q^{69} +9.57212 q^{71} +15.0880 q^{72} +2.46669 q^{73} -17.1191 q^{74} +1.97958 q^{76} -4.71556 q^{77} -18.0871 q^{78} -9.45120 q^{79} +25.3360 q^{81} +16.0271 q^{82} +6.14398 q^{83} +2.62100 q^{84} -10.6604 q^{86} -17.4185 q^{87} -9.42536 q^{88} +14.4501 q^{89} +3.32391 q^{91} +0.806990 q^{92} +16.9269 q^{93} +22.1897 q^{94} +14.0213 q^{96} -5.54746 q^{97} -1.67541 q^{98} -35.5961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 30 * q^4 + 6 * q^6 + 21 * q^7 + 6 * q^8 + 30 * q^9	$ 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9} + 7 q^{11} - 22 q^{12} - 3 q^{13} + 2 q^{14} + 56 q^{16} + 7 q^{17} + 24 q^{19} - q^{21} + 4 q^{22} + 21 q^{23} + 24 q^{24} - 2 q^{26} - 19 q^{27} + 30 q^{28} + 11 q^{29} + 46 q^{31} - 6 q^{32} - 3 q^{33} + 28 q^{34} + 58 q^{36} + 24 q^{37} - 4 q^{38} + 31 q^{39} + 14 q^{41} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 2 q^{46} - 25 q^{47} - 36 q^{48} + 21 q^{49} + 17 q^{51} - 8 q^{52} + 22 q^{53} - 6 q^{54} + 6 q^{56} + 40 q^{57} + 6 q^{58} + 10 q^{59} + 38 q^{61} - 54 q^{62} + 30 q^{63} + 100 q^{64} + 38 q^{66} + 12 q^{67} + 18 q^{68} - q^{69} + 56 q^{71} + 42 q^{72} - 40 q^{73} - 20 q^{74} + 60 q^{76} + 7 q^{77} + 38 q^{78} + 49 q^{79} + 57 q^{81} + 16 q^{82} - 2 q^{83} - 22 q^{84} + 16 q^{86} - 23 q^{87} + 12 q^{88} + 28 q^{89} - 3 q^{91} + 30 q^{92} - 30 q^{93} + 66 q^{94} + 46 q^{96} - q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) $ 21 * q + 2 * q^2 - q^3 + 30 * q^4 + 6 * q^6 + 21 * q^7 + 6 * q^8 + 30 * q^9 + 7 * q^11 - 22 * q^12 - 3 * q^13 + 2 * q^14 + 56 * q^16 + 7 * q^17 + 24 * q^19 - q^21 + 4 * q^22 + 21 * q^23 + 24 * q^24 - 2 * q^26 - 19 * q^27 + 30 * q^28 + 11 * q^29 + 46 * q^31 - 6 * q^32 - 3 * q^33 + 28 * q^34 + 58 * q^36 + 24 * q^37 - 4 * q^38 + 31 * q^39 + 14 * q^41 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 2 * q^46 - 25 * q^47 - 36 * q^48 + 21 * q^49 + 17 * q^51 - 8 * q^52 + 22 * q^53 - 6 * q^54 + 6 * q^56 + 40 * q^57 + 6 * q^58 + 10 * q^59 + 38 * q^61 - 54 * q^62 + 30 * q^63 + 100 * q^64 + 38 * q^66 + 12 * q^67 + 18 * q^68 - q^69 + 56 * q^71 + 42 * q^72 - 40 * q^73 - 20 * q^74 + 60 * q^76 + 7 * q^77 + 38 * q^78 + 49 * q^79 + 57 * q^81 + 16 * q^82 - 2 * q^83 - 22 * q^84 + 16 * q^86 - 23 * q^87 + 12 * q^88 + 28 * q^89 - 3 * q^91 + 30 * q^92 - 30 * q^93 + 66 * q^94 + 46 * q^96 - q^97 + 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.67541	−1.18469	−0.592346	−	0.805684i	$-0.701798\pi$
$2$	−1.67541	−1.18469	−0.592346	+	0.805684i	$0.701798\pi$
$3$	3.24787	1.87516	0.937578	−	0.347774i	$-0.113062\pi$
$3$	3.24787	1.87516	0.937578	+	0.347774i	$0.113062\pi$
$4$	0.806990	0.403495
$5$	0	0
$5$	0	0
$6$	−5.44150	−2.22148
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.99878	0.706675
$9$	7.54864	2.51621
$10$	0	0
$11$	−4.71556	−1.42180	−0.710898	−	0.703295i	$-0.751711\pi$
$11$	−4.71556	−1.42180	−0.710898	+	0.703295i	$0.751711\pi$
$12$	2.62100	0.756617
$13$	3.32391	0.921887	0.460944	−	0.887429i	$-0.347511\pi$
$13$	3.32391	0.921887	0.460944	+	0.887429i	$0.347511\pi$
$14$	−1.67541	−0.447771
$15$	0	0
$16$	−4.96275	−1.24069
$17$	1.29098	0.313109	0.156555	−	0.987669i	$-0.449961\pi$
$17$	1.29098	0.313109	0.156555	+	0.987669i	$0.449961\pi$
$18$	−12.6470	−2.98094
$19$	2.45303	0.562765	0.281382	−	0.959596i	$-0.409207\pi$
$19$	2.45303	0.562765	0.281382	+	0.959596i	$0.409207\pi$
$20$	0	0
$21$	3.24787	0.708743
$22$	7.90049	1.68439
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	6.49176	1.32513
$25$	0	0
$26$	−5.56891	−1.09215
$27$	14.7734	2.84314
$28$	0.806990	0.152507
$29$	−5.36305	−0.995893	−0.497946	−	0.867208i	$-0.665912\pi$
$29$	−5.36305	−0.995893	−0.497946	+	0.867208i	$0.665912\pi$
$30$	0	0
$31$	5.21170	0.936049	0.468025	−	0.883715i	$-0.344966\pi$
$31$	5.21170	0.936049	0.468025	+	0.883715i	$0.344966\pi$
$32$	4.31707	0.763157
$33$	−15.3155	−2.66609
$34$	−2.16292	−0.370938
$35$	0	0
$36$	6.09168	1.01528
$37$	10.2179	1.67981	0.839903	−	0.542737i	$-0.182612\pi$
$37$	10.2179	1.67981	0.839903	+	0.542737i	$0.182612\pi$
$38$	−4.10983	−0.666703
$39$	10.7956	1.72868
$40$	0	0
$41$	−9.56611	−1.49398	−0.746988	−	0.664838i	$-0.768501\pi$
$41$	−9.56611	−1.49398	−0.746988	+	0.664838i	$0.768501\pi$
$42$	−5.44150	−0.839642
$43$	6.36288	0.970330	0.485165	−	0.874423i	$-0.338759\pi$
$43$	6.36288	0.970330	0.485165	+	0.874423i	$0.338759\pi$
$44$	−3.80541	−0.573688
$45$	0	0
$46$	−1.67541	−0.247025
$47$	−13.2443	−1.93189	−0.965943	−	0.258753i	$-0.916688\pi$
$47$	−13.2443	−1.93189	−0.965943	+	0.258753i	$0.916688\pi$
$48$	−16.1183	−2.32648
$49$	1.00000	0.142857
$50$	0	0
$51$	4.19294	0.587129
$52$	2.68236	0.371977
$53$	7.80242	1.07174	0.535872	−	0.844299i	$-0.319983\pi$
$53$	7.80242	1.07174	0.535872	+	0.844299i	$0.319983\pi$
$54$	−24.7514	−3.36824
$55$	0	0
$56$	1.99878	0.267098
$57$	7.96713	1.05527
$58$	8.98529	1.17983
$59$	8.55068	1.11320	0.556602	−	0.830779i	$-0.312105\pi$
$59$	8.55068	1.11320	0.556602	+	0.830779i	$0.312105\pi$
$60$	0	0
$61$	3.86811	0.495260	0.247630	−	0.968855i	$-0.420348\pi$
$61$	3.86811	0.495260	0.247630	+	0.968855i	$0.420348\pi$
$62$	−8.73173	−1.10893
$63$	7.54864	0.951039
$64$	2.69264	0.336581
$65$	0	0
$66$	25.6597	3.15850
$67$	−4.50444	−0.550305	−0.275153	−	0.961401i	$-0.588728\pi$
$67$	−4.50444	−0.550305	−0.275153	+	0.961401i	$0.588728\pi$
$68$	1.04181	0.126338
$69$	3.24787	0.390997
$70$	0	0
$71$	9.57212	1.13600	0.568001	−	0.823028i	$-0.307717\pi$
$71$	9.57212	1.13600	0.568001	+	0.823028i	$0.307717\pi$
$72$	15.0880	1.77814
$73$	2.46669	0.288704	0.144352	−	0.989526i	$-0.453890\pi$
$73$	2.46669	0.288704	0.144352	+	0.989526i	$0.453890\pi$
$74$	−17.1191	−1.99005
$75$	0	0
$76$	1.97958	0.227073
$77$	−4.71556	−0.537388
$78$	−18.0871	−2.04796
$79$	−9.45120	−1.06334	−0.531671	−	0.846951i	$-0.678436\pi$
$79$	−9.45120	−1.06334	−0.531671	+	0.846951i	$0.678436\pi$
$80$	0	0
$81$	25.3360	2.81511
$82$	16.0271	1.76990
$83$	6.14398	0.674389	0.337194	−	0.941435i	$-0.390522\pi$
$83$	6.14398	0.674389	0.337194	+	0.941435i	$0.390522\pi$
$84$	2.62100	0.285974
$85$	0	0
$86$	−10.6604	−1.14954
$87$	−17.4185	−1.86745
$88$	−9.42536	−1.00475
$89$	14.4501	1.53171	0.765854	−	0.643014i	$-0.222316\pi$
$89$	14.4501	1.53171	0.765854	+	0.643014i	$0.222316\pi$
$90$	0	0
$91$	3.32391	0.348441
$92$	0.806990	0.0841346
$93$	16.9269	1.75524
$94$	22.1897	2.28869
$95$	0	0
$96$	14.0213	1.43104
$97$	−5.54746	−0.563259	−0.281630	−	0.959523i	$-0.590875\pi$
$97$	−5.54746	−0.563259	−0.281630	+	0.959523i	$0.590875\pi$
$98$	−1.67541	−0.169242
$99$	−35.5961	−3.57754
$100$	0	0
$101$	−12.7725	−1.27091	−0.635453	−	0.772139i	$-0.719187\pi$
$101$	−12.7725	−1.27091	−0.635453	+	0.772139i	$0.719187\pi$
$102$	−7.02488	−0.695567
$103$	−1.60594	−0.158238	−0.0791192	−	0.996865i	$-0.525211\pi$
$103$	−1.60594	−0.158238	−0.0791192	+	0.996865i	$0.525211\pi$
$104$	6.64376	0.651474
$105$	0	0
$106$	−13.0722	−1.26969
$107$	3.64251	0.352134	0.176067	−	0.984378i	$-0.443662\pi$
$107$	3.64251	0.352134	0.176067	+	0.984378i	$0.443662\pi$
$108$	11.9220	1.14719
$109$	−4.38865	−0.420357	−0.210178	−	0.977663i	$-0.567404\pi$
$109$	−4.38865	−0.420357	−0.210178	+	0.977663i	$0.567404\pi$
$110$	0	0
$111$	33.1862	3.14990
$112$	−4.96275	−0.468936
$113$	3.68000	0.346186	0.173093	−	0.984906i	$-0.444624\pi$
$113$	3.68000	0.346186	0.173093	+	0.984906i	$0.444624\pi$
$114$	−13.3482	−1.25017
$115$	0	0
$116$	−4.32793	−0.401838
$117$	25.0910	2.31966
$118$	−14.3259	−1.31880
$119$	1.29098	0.118344
$120$	0	0
$121$	11.2365	1.02150
$122$	−6.48066	−0.586731
$123$	−31.0695	−2.80144
$124$	4.20579	0.377691
$125$	0	0
$126$	−12.6470	−1.12669
$127$	−14.5388	−1.29011	−0.645054	−	0.764137i	$-0.723165\pi$
$127$	−14.5388	−1.29011	−0.645054	+	0.764137i	$0.723165\pi$
$128$	−13.1454	−1.16190
$129$	20.6658	1.81952
$130$	0	0
$131$	−5.83175	−0.509522	−0.254761	−	0.967004i	$-0.581997\pi$
$131$	−5.83175	−0.509522	−0.254761	+	0.967004i	$0.581997\pi$
$132$	−12.3595	−1.07575
$133$	2.45303	0.212705
$134$	7.54678	0.651942
$135$	0	0
$136$	2.58039	0.221266
$137$	−5.70872	−0.487729	−0.243864	−	0.969809i	$-0.578415\pi$
$137$	−5.70872	−0.487729	−0.243864	+	0.969809i	$0.578415\pi$
$138$	−5.44150	−0.463211
$139$	15.5122	1.31573	0.657864	−	0.753137i	$-0.271460\pi$
$139$	15.5122	1.31573	0.657864	+	0.753137i	$0.271460\pi$
$140$	0	0
$141$	−43.0159	−3.62259
$142$	−16.0372	−1.34581
$143$	−15.6741	−1.31074
$144$	−37.4620	−3.12183
$145$	0	0
$146$	−4.13271	−0.342025
$147$	3.24787	0.267880
$148$	8.24571	0.677793
$149$	22.5592	1.84812	0.924059	−	0.382250i	$-0.124851\pi$
$149$	22.5592	1.84812	0.924059	+	0.382250i	$0.124851\pi$
$150$	0	0
$151$	22.3893	1.82201	0.911006	−	0.412393i	$-0.135307\pi$
$151$	22.3893	1.82201	0.911006	+	0.412393i	$0.135307\pi$
$152$	4.90307	0.397692
$153$	9.74516	0.787849
$154$	7.90049	0.636640
$155$	0	0
$156$	8.71196	0.697515
$157$	−8.05876	−0.643159	−0.321580	−	0.946883i	$-0.604214\pi$
$157$	−8.05876	−0.643159	−0.321580	+	0.946883i	$0.604214\pi$
$158$	15.8346	1.25973
$159$	25.3412	2.00969
$160$	0	0
$161$	1.00000	0.0788110
$162$	−42.4481	−3.33504
$163$	−1.32876	−0.104077	−0.0520384	−	0.998645i	$-0.516572\pi$
$163$	−1.32876	−0.104077	−0.0520384	+	0.998645i	$0.516572\pi$
$164$	−7.71976	−0.602812
$165$	0	0
$166$	−10.2937	−0.798943
$167$	9.41640	0.728663	0.364332	−	0.931269i	$-0.381297\pi$
$167$	9.41640	0.728663	0.364332	+	0.931269i	$0.381297\pi$
$168$	6.49176	0.500850
$169$	−1.95161	−0.150124
$170$	0	0
$171$	18.5171	1.41604
$172$	5.13478	0.391524
$173$	−6.91314	−0.525596	−0.262798	−	0.964851i	$-0.584645\pi$
$173$	−6.91314	−0.525596	−0.262798	+	0.964851i	$0.584645\pi$
$174$	29.1830	2.21236
$175$	0	0
$176$	23.4022	1.76400
$177$	27.7715	2.08743
$178$	−24.2098	−1.81460
$179$	−12.9352	−0.966823	−0.483412	−	0.875393i	$-0.660603\pi$
$179$	−12.9352	−0.966823	−0.483412	+	0.875393i	$0.660603\pi$
$180$	0	0
$181$	13.3860	0.994971	0.497485	−	0.867472i	$-0.334257\pi$
$181$	13.3860	0.994971	0.497485	+	0.867472i	$0.334257\pi$
$182$	−5.56891	−0.412795
$183$	12.5631	0.928691
$184$	1.99878	0.147352
$185$	0	0
$186$	−28.3595	−2.07942
$187$	−6.08771	−0.445177
$188$	−10.6881	−0.779507
$189$	14.7734	1.07460
$190$	0	0
$191$	−2.88332	−0.208630	−0.104315	−	0.994544i	$-0.533265\pi$
$191$	−2.88332	−0.208630	−0.104315	+	0.994544i	$0.533265\pi$
$192$	8.74535	0.631141
$193$	6.38788	0.459810	0.229905	−	0.973213i	$-0.426159\pi$
$193$	6.38788	0.459810	0.229905	+	0.973213i	$0.426159\pi$
$194$	9.29426	0.667289
$195$	0	0
$196$	0.806990	0.0576422
$197$	13.5259	0.963683	0.481842	−	0.876258i	$-0.339968\pi$
$197$	13.5259	0.963683	0.481842	+	0.876258i	$0.339968\pi$
$198$	59.6379	4.23828
$199$	−7.09374	−0.502862	−0.251431	−	0.967875i	$-0.580901\pi$
$199$	−7.09374	−0.502862	−0.251431	+	0.967875i	$0.580901\pi$
$200$	0	0
$201$	−14.6298	−1.03191
$202$	21.3991	1.50563
$203$	−5.36305	−0.376412
$204$	3.38366	0.236904
$205$	0	0
$206$	2.69061	0.187464
$207$	7.54864	0.524667
$208$	−16.4957	−1.14377
$209$	−11.5674	−0.800137
$210$	0	0
$211$	16.7479	1.15297	0.576486	−	0.817107i	$-0.304423\pi$
$211$	16.7479	1.15297	0.576486	+	0.817107i	$0.304423\pi$
$212$	6.29647	0.432444
$213$	31.0890	2.13018
$214$	−6.10268	−0.417171
$215$	0	0
$216$	29.5287	2.00917
$217$	5.21170	0.353793
$218$	7.35278	0.497993
$219$	8.01147	0.541365
$220$	0	0
$221$	4.29111	0.288651
$222$	−55.6005	−3.73166
$223$	−5.61468	−0.375987	−0.187993	−	0.982170i	$-0.560198\pi$
$223$	−5.61468	−0.375987	−0.187993	+	0.982170i	$0.560198\pi$
$224$	4.31707	0.288446
$225$	0	0
$226$	−6.16550	−0.410123
$227$	0.810714	0.0538090	0.0269045	−	0.999638i	$-0.491435\pi$
$227$	0.810714	0.0538090	0.0269045	+	0.999638i	$0.491435\pi$
$228$	6.42940	0.425797
$229$	−10.5222	−0.695325	−0.347663	−	0.937620i	$-0.613025\pi$
$229$	−10.5222	−0.695325	−0.347663	+	0.937620i	$0.613025\pi$
$230$	0	0
$231$	−15.3155	−1.00769
$232$	−10.7195	−0.703772
$233$	−5.84919	−0.383193	−0.191597	−	0.981474i	$-0.561367\pi$
$233$	−5.84919	−0.383193	−0.191597	+	0.981474i	$0.561367\pi$
$234$	−42.0377	−2.74809
$235$	0	0
$236$	6.90032	0.449172
$237$	−30.6962	−1.99393
$238$	−2.16292	−0.140201
$239$	7.51430	0.486060	0.243030	−	0.970019i	$-0.421859\pi$
$239$	7.51430	0.486060	0.243030	+	0.970019i	$0.421859\pi$
$240$	0	0
$241$	−4.84325	−0.311981	−0.155991	−	0.987759i	$-0.549857\pi$
$241$	−4.84325	−0.311981	−0.155991	+	0.987759i	$0.549857\pi$
$242$	−18.8258	−1.21017
$243$	37.9679	2.43564
$244$	3.12153	0.199835
$245$	0	0
$246$	52.0540	3.31884
$247$	8.15367	0.518806
$248$	10.4170	0.661482
$249$	19.9548	1.26458
$250$	0	0
$251$	7.80238	0.492482	0.246241	−	0.969209i	$-0.420805\pi$
$251$	7.80238	0.492482	0.246241	+	0.969209i	$0.420805\pi$
$252$	6.09168	0.383740
$253$	−4.71556	−0.296465
$254$	24.3584	1.52838
$255$	0	0
$256$	16.6386	1.03991
$257$	−26.0999	−1.62807	−0.814035	−	0.580816i	$-0.802734\pi$
$257$	−26.0999	−1.62807	−0.814035	+	0.580816i	$0.802734\pi$
$258$	−34.6236	−2.15557
$259$	10.2179	0.634907
$260$	0	0
$261$	−40.4837	−2.50588
$262$	9.77055	0.603627
$263$	−11.3976	−0.702807	−0.351403	−	0.936224i	$-0.614295\pi$
$263$	−11.3976	−0.702807	−0.351403	+	0.936224i	$0.614295\pi$
$264$	−30.6123	−1.88406
$265$	0	0
$266$	−4.10983	−0.251990
$267$	46.9320	2.87219
$268$	−3.63504	−0.222045
$269$	−7.52881	−0.459040	−0.229520	−	0.973304i	$-0.573716\pi$
$269$	−7.52881	−0.459040	−0.229520	+	0.973304i	$0.573716\pi$
$270$	0	0
$271$	−9.58270	−0.582108	−0.291054	−	0.956707i	$-0.594006\pi$
$271$	−9.58270	−0.582108	−0.291054	+	0.956707i	$0.594006\pi$
$272$	−6.40682	−0.388470
$273$	10.7956	0.653381
$274$	9.56443	0.577808
$275$	0	0
$276$	2.62100	0.157765
$277$	−1.69971	−0.102125	−0.0510627	−	0.998695i	$-0.516261\pi$
$277$	−1.69971	−0.102125	−0.0510627	+	0.998695i	$0.516261\pi$
$278$	−25.9892	−1.55873
$279$	39.3413	2.35530
$280$	0	0
$281$	−13.3254	−0.794928	−0.397464	−	0.917618i	$-0.630110\pi$
$281$	−13.3254	−0.794928	−0.397464	+	0.917618i	$0.630110\pi$
$282$	72.0691	4.29165
$283$	0.662695	0.0393931	0.0196966	−	0.999806i	$-0.493730\pi$
$283$	0.662695	0.0393931	0.0196966	+	0.999806i	$0.493730\pi$
$284$	7.72461	0.458371
$285$	0	0
$286$	26.2605	1.55282
$287$	−9.56611	−0.564670
$288$	32.5880	1.92027
$289$	−15.3334	−0.901963
$290$	0	0
$291$	−18.0174	−1.05620
$292$	1.99059	0.116491
$293$	22.6711	1.32446	0.662229	−	0.749301i	$-0.269611\pi$
$293$	22.6711	1.32446	0.662229	+	0.749301i	$0.269611\pi$
$294$	−5.44150	−0.317355
$295$	0	0
$296$	20.4232	1.18708
$297$	−69.6648	−4.04236
$298$	−37.7958	−2.18945
$299$	3.32391	0.192227
$300$	0	0
$301$	6.36288	0.366750
$302$	−37.5111	−2.15852
$303$	−41.4832	−2.38315
$304$	−12.1738	−0.698215
$305$	0	0
$306$	−16.3271	−0.933359
$307$	−8.01273	−0.457310	−0.228655	−	0.973507i	$-0.573433\pi$
$307$	−8.01273	−0.457310	−0.228655	+	0.973507i	$0.573433\pi$
$308$	−3.80541	−0.216834
$309$	−5.21589	−0.296722
$310$	0	0
$311$	15.9732	0.905758	0.452879	−	0.891572i	$-0.350397\pi$
$311$	15.9732	0.905758	0.452879	+	0.891572i	$0.350397\pi$
$312$	21.5780	1.22162
$313$	−6.62792	−0.374632	−0.187316	−	0.982300i	$-0.559979\pi$
$313$	−6.62792	−0.374632	−0.187316	+	0.982300i	$0.559979\pi$
$314$	13.5017	0.761946
$315$	0	0
$316$	−7.62703	−0.429054
$317$	11.6010	0.651577	0.325788	−	0.945443i	$-0.394370\pi$
$317$	11.6010	0.651577	0.325788	+	0.945443i	$0.394370\pi$
$318$	−42.4568	−2.38086
$319$	25.2898	1.41596
$320$	0	0
$321$	11.8304	0.660307
$322$	−1.67541	−0.0933668
$323$	3.16682	0.176207
$324$	20.4459	1.13588
$325$	0	0
$326$	2.22622	0.123299
$327$	−14.2538	−0.788235
$328$	−19.1205	−1.05575
$329$	−13.2443	−0.730185
$330$	0	0
$331$	14.3019	0.786105	0.393053	−	0.919516i	$-0.371419\pi$
$331$	14.3019	0.786105	0.393053	+	0.919516i	$0.371419\pi$
$332$	4.95813	0.272113
$333$	77.1309	4.22675
$334$	−15.7763	−0.863241
$335$	0	0
$336$	−16.1183	−0.879328
$337$	14.7354	0.802688	0.401344	−	0.915927i	$-0.368543\pi$
$337$	14.7354	0.802688	0.401344	+	0.915927i	$0.368543\pi$
$338$	3.26974	0.177851
$339$	11.9522	0.649152
$340$	0	0
$341$	−24.5761	−1.33087
$342$	−31.0236	−1.67757
$343$	1.00000	0.0539949
$344$	12.7180	0.685708
$345$	0	0
$346$	11.5823	0.622669
$347$	−36.6256	−1.96617	−0.983084	−	0.183156i	$-0.941369\pi$
$347$	−36.6256	−1.96617	−0.983084	+	0.183156i	$0.941369\pi$
$348$	−14.0565	−0.753509
$349$	32.8614	1.75903	0.879516	−	0.475870i	$-0.157867\pi$
$349$	32.8614	1.75903	0.879516	+	0.475870i	$0.157867\pi$
$350$	0	0
$351$	49.1054	2.62105
$352$	−20.3574	−1.08505
$353$	−6.41683	−0.341533	−0.170767	−	0.985312i	$-0.554624\pi$
$353$	−6.41683	−0.341533	−0.170767	+	0.985312i	$0.554624\pi$
$354$	−46.5285	−2.47296
$355$	0	0
$356$	11.6611	0.618037
$357$	4.19294	0.221914
$358$	21.6718	1.14539
$359$	−30.5190	−1.61073	−0.805366	−	0.592777i	$-0.798031\pi$
$359$	−30.5190	−1.61073	−0.805366	+	0.592777i	$0.798031\pi$
$360$	0	0
$361$	−12.9826	−0.683296
$362$	−22.4269	−1.17873
$363$	36.4948	1.91548
$364$	2.68236	0.140594
$365$	0	0
$366$	−21.0483	−1.10021
$367$	13.7125	0.715784	0.357892	−	0.933763i	$-0.383496\pi$
$367$	13.7125	0.715784	0.357892	+	0.933763i	$0.383496\pi$
$368$	−4.96275	−0.258701
$369$	−72.2111	−3.75916
$370$	0	0
$371$	7.80242	0.405081
$372$	13.6599	0.708231
$373$	−29.1811	−1.51094	−0.755470	−	0.655183i	$-0.772591\pi$
$373$	−29.1811	−1.51094	−0.755470	+	0.655183i	$0.772591\pi$
$374$	10.1994	0.527398
$375$	0	0
$376$	−26.4725	−1.36522
$377$	−17.8263	−0.918101
$378$	−24.7514	−1.27308
$379$	22.3635	1.14874	0.574369	−	0.818597i	$-0.305248\pi$
$379$	22.3635	1.14874	0.574369	+	0.818597i	$0.305248\pi$
$380$	0	0
$381$	−47.2200	−2.41915
$382$	4.83073	0.247162
$383$	6.14680	0.314087	0.157043	−	0.987592i	$-0.449804\pi$
$383$	6.14680	0.314087	0.157043	+	0.987592i	$0.449804\pi$
$384$	−42.6946	−2.17875
$385$	0	0
$386$	−10.7023	−0.544733
$387$	48.0311	2.44156
$388$	−4.47675	−0.227272
$389$	−23.8681	−1.21016	−0.605081	−	0.796164i	$-0.706859\pi$
$389$	−23.8681	−1.21016	−0.605081	+	0.796164i	$0.706859\pi$
$390$	0	0
$391$	1.29098	0.0652878
$392$	1.99878	0.100954
$393$	−18.9407	−0.955434
$394$	−22.6615	−1.14167
$395$	0	0
$396$	−28.7257	−1.44352
$397$	11.8662	0.595550	0.297775	−	0.954636i	$-0.403756\pi$
$397$	11.8662	0.595550	0.297775	+	0.954636i	$0.403756\pi$
$398$	11.8849	0.595737
$399$	7.96713	0.398855
$400$	0	0
$401$	−33.5721	−1.67651	−0.838254	−	0.545280i	$-0.816423\pi$
$401$	−33.5721	−1.67651	−0.838254	+	0.545280i	$0.816423\pi$
$402$	24.5109	1.22249
$403$	17.3232	0.862932
$404$	−10.3072	−0.512805
$405$	0	0
$406$	8.98529	0.445932
$407$	−48.1830	−2.38834
$408$	8.38075	0.414909
$409$	−31.7257	−1.56874	−0.784368	−	0.620295i	$-0.787013\pi$
$409$	−31.7257	−1.56874	−0.784368	+	0.620295i	$0.787013\pi$
$410$	0	0
$411$	−18.5412	−0.914568
$412$	−1.29598	−0.0638484
$413$	8.55068	0.420752
$414$	−12.6470	−0.621568
$415$	0	0
$416$	14.3496	0.703545
$417$	50.3815	2.46719
$418$	19.3802	0.947916
$419$	28.5676	1.39562	0.697808	−	0.716285i	$-0.254159\pi$
$419$	28.5676	1.39562	0.697808	+	0.716285i	$0.254159\pi$
$420$	0	0
$421$	−4.26901	−0.208059	−0.104029	−	0.994574i	$-0.533174\pi$
$421$	−4.26901	−0.208059	−0.104029	+	0.994574i	$0.533174\pi$
$422$	−28.0595	−1.36592
$423$	−99.9768	−4.86104
$424$	15.5953	0.757374
$425$	0	0
$426$	−52.0867	−2.52361
$427$	3.86811	0.187191
$428$	2.93947	0.142085
$429$	−50.9075	−2.45783
$430$	0	0
$431$	20.2717	0.976452	0.488226	−	0.872717i	$-0.337644\pi$
$431$	20.2717	0.976452	0.488226	+	0.872717i	$0.337644\pi$
$432$	−73.3165	−3.52744
$433$	10.5000	0.504600	0.252300	−	0.967649i	$-0.418813\pi$
$433$	10.5000	0.504600	0.252300	+	0.967649i	$0.418813\pi$
$434$	−8.73173	−0.419136
$435$	0	0
$436$	−3.54160	−0.169612
$437$	2.45303	0.117345
$438$	−13.4225	−0.641351
$439$	2.68417	0.128108	0.0640541	−	0.997946i	$-0.479597\pi$
$439$	2.68417	0.128108	0.0640541	+	0.997946i	$0.479597\pi$
$440$	0	0
$441$	7.54864	0.359459
$442$	−7.18936	−0.341963
$443$	24.8675	1.18149	0.590745	−	0.806858i	$-0.298834\pi$
$443$	24.8675	1.18149	0.590745	+	0.806858i	$0.298834\pi$
$444$	26.7810	1.27097
$445$	0	0
$446$	9.40687	0.445428
$447$	73.2691	3.46551
$448$	2.69264	0.127215
$449$	9.70691	0.458097	0.229049	−	0.973415i	$-0.426439\pi$
$449$	9.70691	0.458097	0.229049	+	0.973415i	$0.426439\pi$
$450$	0	0
$451$	45.1096	2.12413
$452$	2.96973	0.139684
$453$	72.7173	3.41656
$454$	−1.35828	−0.0637471
$455$	0	0
$456$	15.9245	0.745734
$457$	−9.88093	−0.462210	−0.231105	−	0.972929i	$-0.574234\pi$
$457$	−9.88093	−0.462210	−0.231105	+	0.972929i	$0.574234\pi$
$458$	17.6289	0.823746
$459$	19.0722	0.890212
$460$	0	0
$461$	−39.0170	−1.81720	−0.908601	−	0.417665i	$-0.862848\pi$
$461$	−39.0170	−1.81720	−0.908601	+	0.417665i	$0.862848\pi$
$462$	25.6597	1.19380
$463$	26.6240	1.23732	0.618661	−	0.785658i	$-0.287675\pi$
$463$	26.6240	1.23732	0.618661	+	0.785658i	$0.287675\pi$
$464$	26.6154	1.23559
$465$	0	0
$466$	9.79978	0.453966
$467$	35.5199	1.64367	0.821833	−	0.569729i	$-0.192952\pi$
$467$	35.5199	1.64367	0.821833	+	0.569729i	$0.192952\pi$
$468$	20.2482	0.935973
$469$	−4.50444	−0.207996
$470$	0	0
$471$	−26.1738	−1.20602
$472$	17.0909	0.786673
$473$	−30.0046	−1.37961
$474$	51.4287	2.36220
$475$	0	0
$476$	1.04181	0.0477513
$477$	58.8976	2.69674
$478$	−12.5895	−0.575831
$479$	−28.6888	−1.31082	−0.655412	−	0.755272i	$-0.727505\pi$
$479$	−28.6888	−1.31082	−0.655412	+	0.755272i	$0.727505\pi$
$480$	0	0
$481$	33.9633	1.54859
$482$	8.11442	0.369602
$483$	3.24787	0.147783
$484$	9.06779	0.412172
$485$	0	0
$486$	−63.6117	−2.88548
$487$	31.3538	1.42077	0.710387	−	0.703811i	$-0.248520\pi$
$487$	31.3538	1.42077	0.710387	+	0.703811i	$0.248520\pi$
$488$	7.73149	0.349988
$489$	−4.31565	−0.195160
$490$	0	0
$491$	−15.1255	−0.682604	−0.341302	−	0.939954i	$-0.610868\pi$
$491$	−15.1255	−0.682604	−0.341302	+	0.939954i	$0.610868\pi$
$492$	−25.0728	−1.13037
$493$	−6.92360	−0.311823
$494$	−13.6607	−0.614625
$495$	0	0
$496$	−25.8644	−1.16134
$497$	9.57212	0.429368
$498$	−33.4324	−1.49814
$499$	−30.2061	−1.35221	−0.676106	−	0.736805i	$-0.736334\pi$
$499$	−30.2061	−1.35221	−0.676106	+	0.736805i	$0.736334\pi$
$500$	0	0
$501$	30.5832	1.36636
$502$	−13.0722	−0.583439
$503$	30.6606	1.36709	0.683545	−	0.729909i	$-0.260437\pi$
$503$	30.6606	1.36709	0.683545	+	0.729909i	$0.260437\pi$
$504$	15.0880	0.672075
$505$	0	0
$506$	7.90049	0.351220
$507$	−6.33857	−0.281506
$508$	−11.7327	−0.520552
$509$	8.27053	0.366585	0.183292	−	0.983058i	$-0.441324\pi$
$509$	8.27053	0.366585	0.183292	+	0.983058i	$0.441324\pi$
$510$	0	0
$511$	2.46669	0.109120
$512$	−1.58567	−0.0700774
$513$	36.2396	1.60002
$514$	43.7280	1.92876
$515$	0	0
$516$	16.6771	0.734168
$517$	62.4546	2.74675
$518$	−17.1191	−0.752169
$519$	−22.4529	−0.985575
$520$	0	0
$521$	20.5913	0.902122	0.451061	−	0.892493i	$-0.351046\pi$
$521$	20.5913	0.902122	0.451061	+	0.892493i	$0.351046\pi$
$522$	67.8267	2.96869
$523$	7.36919	0.322232	0.161116	−	0.986935i	$-0.448491\pi$
$523$	7.36919	0.322232	0.161116	+	0.986935i	$0.448491\pi$
$524$	−4.70616	−0.205590
$525$	0	0
$526$	19.0956	0.832609
$527$	6.72822	0.293086
$528$	76.0071	3.30778
$529$	1.00000	0.0434783
$530$	0	0
$531$	64.5460	2.80106
$532$	1.97958	0.0858255
$533$	−31.7969	−1.37728
$534$	−78.6303	−3.40267
$535$	0	0
$536$	−9.00338	−0.388887
$537$	−42.0118	−1.81294
$538$	12.6138	0.543821
$539$	−4.71556	−0.203114
$540$	0	0
$541$	3.10388	0.133446	0.0667232	−	0.997772i	$-0.478746\pi$
$541$	3.10388	0.133446	0.0667232	+	0.997772i	$0.478746\pi$
$542$	16.0549	0.689618
$543$	43.4758	1.86573
$544$	5.57326	0.238952
$545$	0	0
$546$	−18.0871	−0.774055
$547$	−7.58208	−0.324186	−0.162093	−	0.986775i	$-0.551824\pi$
$547$	−7.58208	−0.324186	−0.162093	+	0.986775i	$0.551824\pi$
$548$	−4.60688	−0.196796
$549$	29.1989	1.24618
$550$	0	0
$551$	−13.1557	−0.560453
$552$	6.49176	0.276308
$553$	−9.45120	−0.401906
$554$	2.84770	0.120987
$555$	0	0
$556$	12.5182	0.530890
$557$	7.19964	0.305059	0.152529	−	0.988299i	$-0.451258\pi$
$557$	7.19964	0.305059	0.152529	+	0.988299i	$0.451258\pi$
$558$	−65.9126	−2.79030
$559$	21.1497	0.894535
$560$	0	0
$561$	−19.7721	−0.834778
$562$	22.3255	0.941745
$563$	−2.09427	−0.0882629	−0.0441314	−	0.999026i	$-0.514052\pi$
$563$	−2.09427	−0.0882629	−0.0441314	+	0.999026i	$0.514052\pi$
$564$	−34.7134	−1.46170
$565$	0	0
$566$	−1.11028	−0.0466687
$567$	25.3360	1.06401
$568$	19.1325	0.802783
$569$	−19.0948	−0.800497	−0.400248	−	0.916407i	$-0.631076\pi$
$569$	−19.0948	−0.800497	−0.400248	+	0.916407i	$0.631076\pi$
$570$	0	0
$571$	−23.3991	−0.979221	−0.489611	−	0.871941i	$-0.662861\pi$
$571$	−23.3991	−0.979221	−0.489611	+	0.871941i	$0.662861\pi$
$572$	−12.6489	−0.528876
$573$	−9.36463	−0.391213
$574$	16.0271	0.668960
$575$	0	0
$576$	20.3258	0.846908
$577$	−25.5284	−1.06276	−0.531381	−	0.847133i	$-0.678327\pi$
$577$	−25.5284	−1.06276	−0.531381	+	0.847133i	$0.678327\pi$
$578$	25.6896	1.06855
$579$	20.7470	0.862215
$580$	0	0
$581$	6.14398	0.254895
$582$	30.1865	1.25127
$583$	−36.7928	−1.52380
$584$	4.93036	0.204020
$585$	0	0
$586$	−37.9833	−1.56908
$587$	−25.7534	−1.06296	−0.531479	−	0.847071i	$-0.678364\pi$
$587$	−25.7534	−1.06296	−0.531479	+	0.847071i	$0.678364\pi$
$588$	2.62100	0.108088
$589$	12.7845	0.526776
$590$	0	0
$591$	43.9304	1.80706
$592$	−50.7086	−2.08411
$593$	−4.80602	−0.197360	−0.0986798	−	0.995119i	$-0.531462\pi$
$593$	−4.80602	−0.197360	−0.0986798	+	0.995119i	$0.531462\pi$
$594$	116.717	4.78895
$595$	0	0
$596$	18.2050	0.745707
$597$	−23.0395	−0.942945
$598$	−5.56891	−0.227730
$599$	−26.2262	−1.07157	−0.535786	−	0.844354i	$-0.679985\pi$
$599$	−26.2262	−1.07157	−0.535786	+	0.844354i	$0.679985\pi$
$600$	0	0
$601$	11.5348	0.470513	0.235256	−	0.971933i	$-0.424407\pi$
$601$	11.5348	0.470513	0.235256	+	0.971933i	$0.424407\pi$
$602$	−10.6604	−0.434486
$603$	−34.0024	−1.38468
$604$	18.0679	0.735173
$605$	0	0
$606$	69.5013	2.82330
$607$	−11.7398	−0.476503	−0.238251	−	0.971204i	$-0.576574\pi$
$607$	−11.7398	−0.476503	−0.238251	+	0.971204i	$0.576574\pi$
$608$	10.5899	0.429478
$609$	−17.4185	−0.705832
$610$	0	0
$611$	−44.0230	−1.78098
$612$	7.86425	0.317893
$613$	−35.1273	−1.41878	−0.709388	−	0.704818i	$-0.751029\pi$
$613$	−35.1273	−1.41878	−0.709388	+	0.704818i	$0.751029\pi$
$614$	13.4246	0.541772
$615$	0	0
$616$	−9.42536	−0.379759
$617$	16.4808	0.663490	0.331745	−	0.943369i	$-0.392363\pi$
$617$	16.4808	0.663490	0.331745	+	0.943369i	$0.392363\pi$
$618$	8.73875	0.351524
$619$	47.3768	1.90424	0.952118	−	0.305731i	$-0.0989010\pi$
$619$	47.3768	1.90424	0.952118	+	0.305731i	$0.0989010\pi$
$620$	0	0
$621$	14.7734	0.592835
$622$	−26.7616	−1.07304
$623$	14.4501	0.578932
$624$	−53.5759	−2.14475
$625$	0	0
$626$	11.1045	0.443824
$627$	−37.5695	−1.50038
$628$	−6.50335	−0.259512
$629$	13.1911	0.525963
$630$	0	0
$631$	31.3869	1.24949	0.624746	−	0.780828i	$-0.285203\pi$
$631$	31.3869	1.24949	0.624746	+	0.780828i	$0.285203\pi$
$632$	−18.8908	−0.751437
$633$	54.3949	2.16200
$634$	−19.4364	−0.771918
$635$	0	0
$636$	20.4501	0.810899
$637$	3.32391	0.131698
$638$	−42.3707	−1.67747
$639$	72.2564	2.85842
$640$	0	0
$641$	30.4996	1.20466	0.602331	−	0.798246i	$-0.294239\pi$
$641$	30.4996	1.20466	0.602331	+	0.798246i	$0.294239\pi$
$642$	−19.8207	−0.782261
$643$	5.37023	0.211781	0.105891	−	0.994378i	$-0.466231\pi$
$643$	5.37023	0.211781	0.105891	+	0.994378i	$0.466231\pi$
$644$	0.806990	0.0317999
$645$	0	0
$646$	−5.30572	−0.208751
$647$	0.112636	0.00442817	0.00221408	−	0.999998i	$-0.499295\pi$
$647$	0.112636	0.00442817	0.00221408	+	0.999998i	$0.499295\pi$
$648$	50.6410	1.98937
$649$	−40.3213	−1.58275
$650$	0	0
$651$	16.9269	0.663418
$652$	−1.07230	−0.0419945
$653$	−4.15912	−0.162759	−0.0813794	−	0.996683i	$-0.525933\pi$
$653$	−4.15912	−0.162759	−0.0813794	+	0.996683i	$0.525933\pi$
$654$	23.8809	0.933816
$655$	0	0
$656$	47.4742	1.85356
$657$	18.6201	0.726440
$658$	22.1897	0.865044
$659$	−5.02617	−0.195792	−0.0978959	−	0.995197i	$-0.531211\pi$
$659$	−5.02617	−0.195792	−0.0978959	+	0.995197i	$0.531211\pi$
$660$	0	0
$661$	26.5451	1.03248	0.516242	−	0.856443i	$-0.327330\pi$
$661$	26.5451	1.03248	0.516242	+	0.856443i	$0.327330\pi$
$662$	−23.9616	−0.931292
$663$	13.9370	0.541267
$664$	12.2804	0.476573
$665$	0	0
$666$	−129.226	−5.00739
$667$	−5.36305	−0.207658
$668$	7.59895	0.294012
$669$	−18.2357	−0.705034
$670$	0	0
$671$	−18.2403	−0.704159
$672$	14.0213	0.540882
$673$	14.8480	0.572349	0.286174	−	0.958178i	$-0.407616\pi$
$673$	14.8480	0.572349	0.286174	+	0.958178i	$0.407616\pi$
$674$	−24.6878	−0.950939
$675$	0	0
$676$	−1.57493	−0.0605743
$677$	−45.2056	−1.73739	−0.868695	−	0.495347i	$-0.835041\pi$
$677$	−45.2056	−1.73739	−0.868695	+	0.495347i	$0.835041\pi$
$678$	−20.0247	−0.769045
$679$	−5.54746	−0.212892
$680$	0	0
$681$	2.63309	0.100900
$682$	41.1750	1.57667
$683$	6.82707	0.261231	0.130615	−	0.991433i	$-0.458305\pi$
$683$	6.82707	0.261231	0.130615	+	0.991433i	$0.458305\pi$
$684$	14.9431	0.571364
$685$	0	0
$686$	−1.67541	−0.0639674
$687$	−34.1746	−1.30384
$688$	−31.5774	−1.20388
$689$	25.9345	0.988027
$690$	0	0
$691$	−34.9080	−1.32796	−0.663981	−	0.747749i	$-0.731135\pi$
$691$	−34.9080	−1.32796	−0.663981	+	0.747749i	$0.731135\pi$
$692$	−5.57883	−0.212075
$693$	−35.5961	−1.35218
$694$	61.3629	2.32930
$695$	0	0
$696$	−34.8156	−1.31968
$697$	−12.3497	−0.467778
$698$	−55.0563	−2.08391
$699$	−18.9974	−0.718548
$700$	0	0
$701$	−0.266164	−0.0100529	−0.00502643	−	0.999987i	$-0.501600\pi$
$701$	−0.266164	−0.0100529	−0.00502643	+	0.999987i	$0.501600\pi$
$702$	−82.2715	−3.10514
$703$	25.0648	0.945335
$704$	−12.6973	−0.478549
$705$	0	0
$706$	10.7508	0.404612
$707$	−12.7725	−0.480357
$708$	22.4113	0.842269
$709$	52.1348	1.95796	0.978981	−	0.203952i	$-0.0653785\pi$
$709$	52.1348	1.95796	0.978981	+	0.203952i	$0.0653785\pi$
$710$	0	0
$711$	−71.3437	−2.67560
$712$	28.8826	1.08242
$713$	5.21170	0.195180
$714$	−7.02488	−0.262900
$715$	0	0
$716$	−10.4386	−0.390108
$717$	24.4054	0.911438
$718$	51.1318	1.90822
$719$	−40.8130	−1.52207	−0.761034	−	0.648712i	$-0.775308\pi$
$719$	−40.8130	−1.52207	−0.761034	+	0.648712i	$0.775308\pi$
$720$	0	0
$721$	−1.60594	−0.0598085
$722$	21.7512	0.809495
$723$	−15.7302	−0.585014
$724$	10.8023	0.401466
$725$	0	0
$726$	−61.1437	−2.26925
$727$	6.25856	0.232117	0.116059	−	0.993242i	$-0.462974\pi$
$727$	6.25856	0.232117	0.116059	+	0.993242i	$0.462974\pi$
$728$	6.64376	0.246234
$729$	47.3066	1.75210
$730$	0	0
$731$	8.21437	0.303819
$732$	10.1383	0.374722
$733$	20.2784	0.748999	0.374499	−	0.927227i	$-0.377815\pi$
$733$	20.2784	0.748999	0.374499	+	0.927227i	$0.377815\pi$
$734$	−22.9739	−0.847984
$735$	0	0
$736$	4.31707	0.159129
$737$	21.2410	0.782422
$738$	120.983	4.45345
$739$	−2.42929	−0.0893628	−0.0446814	−	0.999001i	$-0.514227\pi$
$739$	−2.42929	−0.0893628	−0.0446814	+	0.999001i	$0.514227\pi$
$740$	0	0
$741$	26.4820	0.972842
$742$	−13.0722	−0.479896
$743$	−12.4554	−0.456943	−0.228471	−	0.973551i	$-0.573373\pi$
$743$	−12.4554	−0.456943	−0.228471	+	0.973551i	$0.573373\pi$
$744$	33.8331	1.24038
$745$	0	0
$746$	48.8902	1.79000
$747$	46.3786	1.69691
$748$	−4.91272	−0.179627
$749$	3.64251	0.133094
$750$	0	0
$751$	−44.7352	−1.63241	−0.816205	−	0.577762i	$-0.803926\pi$
$751$	−44.7352	−1.63241	−0.816205	+	0.577762i	$0.803926\pi$
$752$	65.7284	2.39687
$753$	25.3411	0.923480
$754$	29.8663	1.08767
$755$	0	0
$756$	11.9220	0.433598
$757$	−9.77540	−0.355293	−0.177646	−	0.984094i	$-0.556848\pi$
$757$	−9.77540	−0.355293	−0.177646	+	0.984094i	$0.556848\pi$
$758$	−37.4680	−1.36090
$759$	−15.3155	−0.555918
$760$	0	0
$761$	−8.26912	−0.299755	−0.149878	−	0.988705i	$-0.547888\pi$
$761$	−8.26912	−0.299755	−0.149878	+	0.988705i	$0.547888\pi$
$762$	79.1128	2.86595
$763$	−4.38865	−0.158880
$764$	−2.32681	−0.0841810
$765$	0	0
$766$	−10.2984	−0.372096
$767$	28.4217	1.02625
$768$	54.0401	1.95000
$769$	−27.2698	−0.983375	−0.491688	−	0.870772i	$-0.663620\pi$
$769$	−27.2698	−0.983375	−0.491688	+	0.870772i	$0.663620\pi$
$770$	0	0
$771$	−84.7691	−3.05289
$772$	5.15496	0.185531
$773$	−9.52236	−0.342496	−0.171248	−	0.985228i	$-0.554780\pi$
$773$	−9.52236	−0.342496	−0.171248	+	0.985228i	$0.554780\pi$
$774$	−80.4716	−2.89249
$775$	0	0
$776$	−11.0881	−0.398041
$777$	33.1862	1.19055
$778$	39.9888	1.43367
$779$	−23.4660	−0.840757
$780$	0	0
$781$	−45.1379	−1.61516
$782$	−2.16292	−0.0773459
$783$	−79.2302	−2.83146
$784$	−4.96275	−0.177241
$785$	0	0
$786$	31.7335	1.13189
$787$	−7.57938	−0.270176	−0.135088	−	0.990834i	$-0.543132\pi$
$787$	−7.57938	−0.270176	−0.135088	+	0.990834i	$0.543132\pi$
$788$	10.9153	0.388842
$789$	−37.0179	−1.31787
$790$	0	0
$791$	3.68000	0.130846
$792$	−71.1487	−2.52816
$793$	12.8572	0.456574
$794$	−19.8808	−0.705543
$795$	0	0
$796$	−5.72458	−0.202902
$797$	16.0716	0.569285	0.284643	−	0.958634i	$-0.408125\pi$
$797$	16.0716	0.569285	0.284643	+	0.958634i	$0.408125\pi$
$798$	−13.3482	−0.472521
$799$	−17.0982	−0.604892
$800$	0	0
$801$	109.079	3.85410
$802$	56.2469	1.98615
$803$	−11.6318	−0.410478
$804$	−11.8061	−0.416370
$805$	0	0
$806$	−29.0235	−1.02231
$807$	−24.4526	−0.860771
$808$	−25.5293	−0.898117
$809$	−10.8485	−0.381412	−0.190706	−	0.981647i	$-0.561078\pi$
$809$	−10.8485	−0.381412	−0.190706	+	0.981647i	$0.561078\pi$
$810$	0	0
$811$	3.22362	0.113197	0.0565984	−	0.998397i	$-0.481975\pi$
$811$	3.22362	0.113197	0.0565984	+	0.998397i	$0.481975\pi$
$812$	−4.32793	−0.151880
$813$	−31.1233	−1.09154
$814$	80.7261	2.82945
$815$	0	0
$816$	−20.8085	−0.728443
$817$	15.6084	0.546068
$818$	53.1535	1.85847
$819$	25.0910	0.876751
$820$	0	0
$821$	47.4934	1.65753	0.828765	−	0.559597i	$-0.189044\pi$
$821$	47.4934	1.65753	0.828765	+	0.559597i	$0.189044\pi$
$822$	31.0640	1.08348
$823$	−23.9905	−0.836256	−0.418128	−	0.908388i	$-0.637314\pi$
$823$	−23.9905	−0.836256	−0.418128	+	0.908388i	$0.637314\pi$
$824$	−3.20992	−0.111823
$825$	0	0
$826$	−14.3259	−0.498461
$827$	36.4023	1.26583	0.632916	−	0.774220i	$-0.281858\pi$
$827$	36.4023	1.26583	0.632916	+	0.774220i	$0.281858\pi$
$828$	6.09168	0.211700
$829$	−25.8329	−0.897212	−0.448606	−	0.893730i	$-0.648079\pi$
$829$	−25.8329	−0.897212	−0.448606	+	0.893730i	$0.648079\pi$
$830$	0	0
$831$	−5.52042	−0.191501
$832$	8.95011	0.310289
$833$	1.29098	0.0447299
$834$	−84.4096	−2.92287
$835$	0	0
$836$	−9.33482	−0.322851
$837$	76.9944	2.66132
$838$	−47.8623	−1.65338
$839$	27.1877	0.938623	0.469311	−	0.883033i	$-0.344502\pi$
$839$	27.1877	0.938623	0.469311	+	0.883033i	$0.344502\pi$
$840$	0	0
$841$	−0.237738	−0.00819788
$842$	7.15232	0.246485
$843$	−43.2792	−1.49061
$844$	13.5154	0.465219
$845$	0	0
$846$	167.502	5.75883
$847$	11.2365	0.386092
$848$	−38.7214	−1.32970
$849$	2.15235	0.0738683
$850$	0	0
$851$	10.2179	0.350264
$852$	25.0885	0.859518
$853$	−29.0731	−0.995444	−0.497722	−	0.867337i	$-0.665830\pi$
$853$	−29.0731	−0.995444	−0.497722	+	0.867337i	$0.665830\pi$
$854$	−6.48066	−0.221764
$855$	0	0
$856$	7.28056	0.248844
$857$	−29.9372	−1.02264	−0.511318	−	0.859392i	$-0.670842\pi$
$857$	−29.9372	−1.02264	−0.511318	+	0.859392i	$0.670842\pi$
$858$	85.2907	2.91178
$859$	6.51948	0.222442	0.111221	−	0.993796i	$-0.464524\pi$
$859$	6.51948	0.222442	0.111221	+	0.993796i	$0.464524\pi$
$860$	0	0
$861$	−31.0695	−1.05884
$862$	−33.9633	−1.15679
$863$	3.36951	0.114699	0.0573497	−	0.998354i	$-0.481735\pi$
$863$	3.36951	0.114699	0.0573497	+	0.998354i	$0.481735\pi$
$864$	63.7776	2.16976
$865$	0	0
$866$	−17.5918	−0.597795
$867$	−49.8007	−1.69132
$868$	4.20579	0.142754
$869$	44.5677	1.51186
$870$	0	0
$871$	−14.9724	−0.507319
$872$	−8.77194	−0.297055
$873$	−41.8758	−1.41728
$874$	−4.10983	−0.139017
$875$	0	0
$876$	6.46518	0.218438
$877$	−16.4862	−0.556701	−0.278350	−	0.960480i	$-0.589788\pi$
$877$	−16.4862	−0.556701	−0.278350	+	0.960480i	$0.589788\pi$
$878$	−4.49707	−0.151769
$879$	73.6326	2.48357
$880$	0	0
$881$	9.75479	0.328647	0.164324	−	0.986406i	$-0.447456\pi$
$881$	9.75479	0.328647	0.164324	+	0.986406i	$0.447456\pi$
$882$	−12.6470	−0.425848
$883$	−2.42333	−0.0815516	−0.0407758	−	0.999168i	$-0.512983\pi$
$883$	−2.42333	−0.0815516	−0.0407758	+	0.999168i	$0.512983\pi$
$884$	3.46289	0.116469
$885$	0	0
$886$	−41.6632	−1.39970
$887$	−27.7278	−0.931009	−0.465504	−	0.885046i	$-0.654127\pi$
$887$	−27.7278	−0.931009	−0.465504	+	0.885046i	$0.654127\pi$
$888$	66.3319	2.22595
$889$	−14.5388	−0.487615
$890$	0	0
$891$	−119.474	−4.00252
$892$	−4.53099	−0.151709
$893$	−32.4888	−1.08720
$894$	−122.756	−4.10556
$895$	0	0
$896$	−13.1454	−0.439157
$897$	10.7956	0.360455
$898$	−16.2630	−0.542704
$899$	−27.9506	−0.932205
$900$	0	0
$901$	10.0728	0.335573
$902$	−75.5770	−2.51644
$903$	20.6658	0.687714
$904$	7.35551	0.244641
$905$	0	0
$906$	−121.831	−4.04757
$907$	−30.6564	−1.01793	−0.508965	−	0.860787i	$-0.669972\pi$
$907$	−30.6564	−1.01793	−0.508965	+	0.860787i	$0.669972\pi$
$908$	0.654239	0.0217117
$909$	−96.4146	−3.19787
$910$	0	0
$911$	−2.28984	−0.0758657	−0.0379329	−	0.999280i	$-0.512077\pi$
$911$	−2.28984	−0.0758657	−0.0379329	+	0.999280i	$0.512077\pi$
$912$	−39.5389	−1.30926
$913$	−28.9723	−0.958844
$914$	16.5546	0.547577
$915$	0	0
$916$	−8.49130	−0.280560
$917$	−5.83175	−0.192581
$918$	−31.9536	−1.05463
$919$	17.4859	0.576807	0.288404	−	0.957509i	$-0.406876\pi$
$919$	17.4859	0.576807	0.288404	+	0.957509i	$0.406876\pi$
$920$	0	0
$921$	−26.0243	−0.857529
$922$	65.3693	2.15282
$923$	31.8169	1.04727
$924$	−12.3595	−0.406597
$925$	0	0
$926$	−44.6061	−1.46585
$927$	−12.1227	−0.398161
$928$	−23.1526	−0.760023
$929$	33.0959	1.08584	0.542921	−	0.839784i	$-0.317318\pi$
$929$	33.0959	1.08584	0.542921	+	0.839784i	$0.317318\pi$
$930$	0	0
$931$	2.45303	0.0803950
$932$	−4.72024	−0.154617
$933$	51.8789	1.69844
$934$	−59.5103	−1.94724
$935$	0	0
$936$	50.1513	1.63925
$937$	−34.9436	−1.14156	−0.570779	−	0.821104i	$-0.693359\pi$
$937$	−34.9436	−1.14156	−0.570779	+	0.821104i	$0.693359\pi$
$938$	7.54678	0.246411
$939$	−21.5266	−0.702494
$940$	0	0
$941$	5.57317	0.181680	0.0908401	−	0.995865i	$-0.471045\pi$
$941$	5.57317	0.181680	0.0908401	+	0.995865i	$0.471045\pi$
$942$	43.8518	1.42877
$943$	−9.56611	−0.311515
$944$	−42.4349	−1.38114
$945$	0	0
$946$	50.2699	1.63442
$947$	−55.5601	−1.80546	−0.902730	−	0.430208i	$-0.858440\pi$
$947$	−55.5601	−1.80546	−0.902730	+	0.430208i	$0.858440\pi$
$948$	−24.7716	−0.804543
$949$	8.19905	0.266153
$950$	0	0
$951$	37.6785	1.22181
$952$	2.58039	0.0836308
$953$	−23.0666	−0.747201	−0.373600	−	0.927590i	$-0.621877\pi$
$953$	−23.0666	−0.747201	−0.373600	+	0.927590i	$0.621877\pi$
$954$	−98.6775	−3.19480
$955$	0	0
$956$	6.06397	0.196123
$957$	82.1379	2.65514
$958$	48.0654	1.55292
$959$	−5.70872	−0.184344
$960$	0	0
$961$	−3.83816	−0.123811
$962$	−56.9023	−1.83460
$963$	27.4960	0.886045
$964$	−3.90846	−0.125883
$965$	0	0
$966$	−5.44150	−0.175077
$967$	−10.2089	−0.328296	−0.164148	−	0.986436i	$-0.552487\pi$
$967$	−10.2089	−0.328296	−0.164148	+	0.986436i	$0.552487\pi$
$968$	22.4594	0.721871
$969$	10.2854	0.330415
$970$	0	0
$971$	48.3068	1.55024	0.775120	−	0.631814i	$-0.217690\pi$
$971$	48.3068	1.55024	0.775120	+	0.631814i	$0.217690\pi$
$972$	30.6397	0.982769
$973$	15.5122	0.497298
$974$	−52.5303	−1.68318
$975$	0	0
$976$	−19.1964	−0.614463
$977$	−39.0156	−1.24822	−0.624109	−	0.781337i	$-0.714538\pi$
$977$	−39.0156	−1.24822	−0.624109	+	0.781337i	$0.714538\pi$
$978$	7.23047	0.231205
$979$	−68.1404	−2.17778
$980$	0	0
$981$	−33.1284	−1.05771
$982$	25.3414	0.808676
$983$	−45.4731	−1.45037	−0.725183	−	0.688556i	$-0.758245\pi$
$983$	−45.4731	−1.45037	−0.725183	+	0.688556i	$0.758245\pi$
$984$	−62.1009	−1.97971
$985$	0	0
$986$	11.5998	0.369414
$987$	−43.0159	−1.36921
$988$	6.57993	0.209336
$989$	6.36288	0.202328
$990$	0	0
$991$	21.9955	0.698711	0.349355	−	0.936990i	$-0.386401\pi$
$991$	21.9955	0.698711	0.349355	+	0.936990i	$0.386401\pi$
$992$	22.4993	0.714353
$993$	46.4508	1.47407
$994$	−16.0372	−0.508669
$995$	0	0
$996$	16.1033	0.510254
$997$	8.33601	0.264004	0.132002	−	0.991249i	$-0.457859\pi$
$997$	8.33601	0.264004	0.132002	+	0.991249i	$0.457859\pi$
$998$	50.6075	1.60195
$999$	150.952	4.77592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.be.1.5		21
5.2	odd	4		805.2.c.c.484.10	✓	42
5.3	odd	4		805.2.c.c.484.33	yes	42
5.4	even	2		4025.2.a.bd.1.17		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.10	✓	42	5.2	odd	4
805.2.c.c.484.33	yes	42	5.3	odd	4
4025.2.a.bd.1.17		21	5.4	even	2
4025.2.a.be.1.5		21	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67541 q^{2} +3.24787 q^{3} +0.806990 q^{4} -5.44150 q^{6} +1.00000 q^{7} +1.99878 q^{8} +7.54864 q^{9} +O(q^{10})\)	\(q-1.67541 q^{2} +3.24787 q^{3} +0.806990 q^{4} -5.44150 q^{6} +1.00000 q^{7} +1.99878 q^{8} +7.54864 q^{9} -4.71556 q^{11} +2.62100 q^{12} +3.32391 q^{13} -1.67541 q^{14} -4.96275 q^{16} +1.29098 q^{17} -12.6470 q^{18} +2.45303 q^{19} +3.24787 q^{21} +7.90049 q^{22} +1.00000 q^{23} +6.49176 q^{24} -5.56891 q^{26} +14.7734 q^{27} +0.806990 q^{28} -5.36305 q^{29} +5.21170 q^{31} +4.31707 q^{32} -15.3155 q^{33} -2.16292 q^{34} +6.09168 q^{36} +10.2179 q^{37} -4.10983 q^{38} +10.7956 q^{39} -9.56611 q^{41} -5.44150 q^{42} +6.36288 q^{43} -3.80541 q^{44} -1.67541 q^{46} -13.2443 q^{47} -16.1183 q^{48} +1.00000 q^{49} +4.19294 q^{51} +2.68236 q^{52} +7.80242 q^{53} -24.7514 q^{54} +1.99878 q^{56} +7.96713 q^{57} +8.98529 q^{58} +8.55068 q^{59} +3.86811 q^{61} -8.73173 q^{62} +7.54864 q^{63} +2.69264 q^{64} +25.6597 q^{66} -4.50444 q^{67} +1.04181 q^{68} +3.24787 q^{69} +9.57212 q^{71} +15.0880 q^{72} +2.46669 q^{73} -17.1191 q^{74} +1.97958 q^{76} -4.71556 q^{77} -18.0871 q^{78} -9.45120 q^{79} +25.3360 q^{81} +16.0271 q^{82} +6.14398 q^{83} +2.62100 q^{84} -10.6604 q^{86} -17.4185 q^{87} -9.42536 q^{88} +14.4501 q^{89} +3.32391 q^{91} +0.806990 q^{92} +16.9269 q^{93} +22.1897 q^{94} +14.0213 q^{96} -5.54746 q^{97} -1.67541 q^{98} -35.5961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 30 * q^4 + 6 * q^6 + 21 * q^7 + 6 * q^8 + 30 * q^9	\( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9} + 7 q^{11} - 22 q^{12} - 3 q^{13} + 2 q^{14} + 56 q^{16} + 7 q^{17} + 24 q^{19} - q^{21} + 4 q^{22} + 21 q^{23} + 24 q^{24} - 2 q^{26} - 19 q^{27} + 30 q^{28} + 11 q^{29} + 46 q^{31} - 6 q^{32} - 3 q^{33} + 28 q^{34} + 58 q^{36} + 24 q^{37} - 4 q^{38} + 31 q^{39} + 14 q^{41} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 2 q^{46} - 25 q^{47} - 36 q^{48} + 21 q^{49} + 17 q^{51} - 8 q^{52} + 22 q^{53} - 6 q^{54} + 6 q^{56} + 40 q^{57} + 6 q^{58} + 10 q^{59} + 38 q^{61} - 54 q^{62} + 30 q^{63} + 100 q^{64} + 38 q^{66} + 12 q^{67} + 18 q^{68} - q^{69} + 56 q^{71} + 42 q^{72} - 40 q^{73} - 20 q^{74} + 60 q^{76} + 7 q^{77} + 38 q^{78} + 49 q^{79} + 57 q^{81} + 16 q^{82} - 2 q^{83} - 22 q^{84} + 16 q^{86} - 23 q^{87} + 12 q^{88} + 28 q^{89} - 3 q^{91} + 30 q^{92} - 30 q^{93} + 66 q^{94} + 46 q^{96} - q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 30 * q^4 + 6 * q^6 + 21 * q^7 + 6 * q^8 + 30 * q^9 + 7 * q^11 - 22 * q^12 - 3 * q^13 + 2 * q^14 + 56 * q^16 + 7 * q^17 + 24 * q^19 - q^21 + 4 * q^22 + 21 * q^23 + 24 * q^24 - 2 * q^26 - 19 * q^27 + 30 * q^28 + 11 * q^29 + 46 * q^31 - 6 * q^32 - 3 * q^33 + 28 * q^34 + 58 * q^36 + 24 * q^37 - 4 * q^38 + 31 * q^39 + 14 * q^41 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 2 * q^46 - 25 * q^47 - 36 * q^48 + 21 * q^49 + 17 * q^51 - 8 * q^52 + 22 * q^53 - 6 * q^54 + 6 * q^56 + 40 * q^57 + 6 * q^58 + 10 * q^59 + 38 * q^61 - 54 * q^62 + 30 * q^63 + 100 * q^64 + 38 * q^66 + 12 * q^67 + 18 * q^68 - q^69 + 56 * q^71 + 42 * q^72 - 40 * q^73 - 20 * q^74 + 60 * q^76 + 7 * q^77 + 38 * q^78 + 49 * q^79 + 57 * q^81 + 16 * q^82 - 2 * q^83 - 22 * q^84 + 16 * q^86 - 23 * q^87 + 12 * q^88 + 28 * q^89 - 3 * q^91 + 30 * q^92 - 30 * q^93 + 66 * q^94 + 46 * q^96 - q^97 + 2 * q^98 - 2 * q^99

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