LMFDB - Embedded newform 4025.2.a.be.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.68001 q^{2} -3.08395 q^{3} +5.18247 q^{4} +8.26504 q^{6} +1.00000 q^{7} -8.52906 q^{8} +6.51078 q^{9} +O(q^{10})$	\(q-2.68001 q^{2} -3.08395 q^{3} +5.18247 q^{4} +8.26504 q^{6} +1.00000 q^{7} -8.52906 q^{8} +6.51078 q^{9} -1.03638 q^{11} -15.9825 q^{12} +4.03133 q^{13} -2.68001 q^{14} +12.4931 q^{16} -4.11805 q^{17} -17.4490 q^{18} -6.23865 q^{19} -3.08395 q^{21} +2.77751 q^{22} +1.00000 q^{23} +26.3032 q^{24} -10.8040 q^{26} -10.8271 q^{27} +5.18247 q^{28} -8.14422 q^{29} +10.0647 q^{31} -16.4234 q^{32} +3.19615 q^{33} +11.0364 q^{34} +33.7419 q^{36} -4.74088 q^{37} +16.7197 q^{38} -12.4325 q^{39} -4.45005 q^{41} +8.26504 q^{42} +4.71008 q^{43} -5.37101 q^{44} -2.68001 q^{46} -4.57220 q^{47} -38.5280 q^{48} +1.00000 q^{49} +12.6999 q^{51} +20.8923 q^{52} +6.63018 q^{53} +29.0167 q^{54} -8.52906 q^{56} +19.2397 q^{57} +21.8266 q^{58} +5.25847 q^{59} -0.922345 q^{61} -26.9735 q^{62} +6.51078 q^{63} +19.0289 q^{64} -8.56573 q^{66} +9.91482 q^{67} -21.3417 q^{68} -3.08395 q^{69} -3.55231 q^{71} -55.5308 q^{72} -10.3525 q^{73} +12.7056 q^{74} -32.3316 q^{76} -1.03638 q^{77} +33.3191 q^{78} +4.18977 q^{79} +13.8579 q^{81} +11.9262 q^{82} +13.7686 q^{83} -15.9825 q^{84} -12.6231 q^{86} +25.1164 q^{87} +8.83935 q^{88} +2.94290 q^{89} +4.03133 q^{91} +5.18247 q^{92} -31.0391 q^{93} +12.2536 q^{94} +50.6491 q^{96} -0.694430 q^{97} -2.68001 q^{98} -6.74764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.68001	−1.89506	−0.947528	−	0.319674i	$-0.896427\pi$
$2$	−2.68001	−1.89506	−0.947528	+	0.319674i	$0.896427\pi$
$3$	−3.08395	−1.78052	−0.890261	−	0.455451i	$-0.849478\pi$
$3$	−3.08395	−1.78052	−0.890261	+	0.455451i	$0.849478\pi$
$4$	5.18247	2.59123
$5$	0	0
$5$	0	0
$6$	8.26504	3.37419
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.52906	−3.01548
$9$	6.51078	2.17026
$10$	0	0
$11$	−1.03638	−0.312481	−0.156240	−	0.987719i	$-0.549937\pi$
$11$	−1.03638	−0.312481	−0.156240	+	0.987719i	$0.549937\pi$
$12$	−15.9825	−4.61375
$13$	4.03133	1.11809	0.559046	−	0.829137i	$-0.311168\pi$
$13$	4.03133	1.11809	0.559046	+	0.829137i	$0.311168\pi$
$14$	−2.68001	−0.716264
$15$	0	0
$16$	12.4931	3.12326
$17$	−4.11805	−0.998773	−0.499387	−	0.866379i	$-0.666441\pi$
$17$	−4.11805	−0.998773	−0.499387	+	0.866379i	$0.666441\pi$
$18$	−17.4490	−4.11276
$19$	−6.23865	−1.43125	−0.715623	−	0.698487i	$-0.753857\pi$
$19$	−6.23865	−1.43125	−0.715623	+	0.698487i	$0.753857\pi$
$20$	0	0
$21$	−3.08395	−0.672974
$22$	2.77751	0.592168
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	26.3032	5.36913
$25$	0	0
$26$	−10.8040	−2.11884
$27$	−10.8271	−2.08367
$28$	5.18247	0.979395
$29$	−8.14422	−1.51234	−0.756172	−	0.654373i	$-0.772933\pi$
$29$	−8.14422	−1.51234	−0.756172	+	0.654373i	$0.772933\pi$
$30$	0	0
$31$	10.0647	1.80767	0.903837	−	0.427876i	$-0.140738\pi$
$31$	10.0647	1.80767	0.903837	+	0.427876i	$0.140738\pi$
$32$	−16.4234	−2.90328
$33$	3.19615	0.556379
$34$	11.0364	1.89273
$35$	0	0
$36$	33.7419	5.62365
$37$	−4.74088	−0.779395	−0.389698	−	0.920943i	$-0.627420\pi$
$37$	−4.74088	−0.779395	−0.389698	+	0.920943i	$0.627420\pi$
$38$	16.7197	2.71229
$39$	−12.4325	−1.99079
$40$	0	0
$41$	−4.45005	−0.694982	−0.347491	−	0.937683i	$-0.612966\pi$
$41$	−4.45005	−0.694982	−0.347491	+	0.937683i	$0.612966\pi$
$42$	8.26504	1.27532
$43$	4.71008	0.718280	0.359140	−	0.933284i	$-0.383070\pi$
$43$	4.71008	0.718280	0.359140	+	0.933284i	$0.383070\pi$
$44$	−5.37101	−0.809711
$45$	0	0
$46$	−2.68001	−0.395146
$47$	−4.57220	−0.666924	−0.333462	−	0.942763i	$-0.608217\pi$
$47$	−4.57220	−0.666924	−0.333462	+	0.942763i	$0.608217\pi$
$48$	−38.5280	−5.56104
$49$	1.00000	0.142857
$50$	0	0
$51$	12.6999	1.77834
$52$	20.8923	2.89724
$53$	6.63018	0.910725	0.455363	−	0.890306i	$-0.349510\pi$
$53$	6.63018	0.910725	0.455363	+	0.890306i	$0.349510\pi$
$54$	29.0167	3.94867
$55$	0	0
$56$	−8.52906	−1.13974
$57$	19.2397	2.54836
$58$	21.8266	2.86598
$59$	5.25847	0.684595	0.342297	−	0.939592i	$-0.388795\pi$
$59$	5.25847	0.684595	0.342297	+	0.939592i	$0.388795\pi$
$60$	0	0
$61$	−0.922345	−0.118094	−0.0590471	−	0.998255i	$-0.518806\pi$
$61$	−0.922345	−0.118094	−0.0590471	+	0.998255i	$0.518806\pi$
$62$	−26.9735	−3.42564
$63$	6.51078	0.820281
$64$	19.0289	2.37861
$65$	0	0
$66$	−8.56573	−1.05437
$67$	9.91482	1.21129	0.605644	−	0.795735i	$-0.292915\pi$
$67$	9.91482	1.21129	0.605644	+	0.795735i	$0.292915\pi$
$68$	−21.3417	−2.58806
$69$	−3.08395	−0.371265
$70$	0	0
$71$	−3.55231	−0.421581	−0.210791	−	0.977531i	$-0.567604\pi$
$71$	−3.55231	−0.421581	−0.210791	+	0.977531i	$0.567604\pi$
$72$	−55.5308	−6.54437
$73$	−10.3525	−1.21167	−0.605833	−	0.795592i	$-0.707160\pi$
$73$	−10.3525	−1.21167	−0.605833	+	0.795592i	$0.707160\pi$
$74$	12.7056	1.47700
$75$	0	0
$76$	−32.3316	−3.70869
$77$	−1.03638	−0.118107
$78$	33.3191	3.77265
$79$	4.18977	0.471385	0.235693	−	0.971828i	$-0.424264\pi$
$79$	4.18977	0.471385	0.235693	+	0.971828i	$0.424264\pi$
$80$	0	0
$81$	13.8579	1.53976
$82$	11.9262	1.31703
$83$	13.7686	1.51129	0.755647	−	0.654979i	$-0.227322\pi$
$83$	13.7686	1.51129	0.755647	+	0.654979i	$0.227322\pi$
$84$	−15.9825	−1.74383
$85$	0	0
$86$	−12.6231	−1.36118
$87$	25.1164	2.69276
$88$	8.83935	0.942278
$89$	2.94290	0.311946	0.155973	−	0.987761i	$-0.450149\pi$
$89$	2.94290	0.311946	0.155973	+	0.987761i	$0.450149\pi$
$90$	0	0
$91$	4.03133	0.422599
$92$	5.18247	0.540310
$93$	−31.0391	−3.21860
$94$	12.2536	1.26386
$95$	0	0
$96$	50.6491	5.16935
$97$	−0.694430	−0.0705087	−0.0352544	−	0.999378i	$-0.511224\pi$
$97$	−0.694430	−0.0705087	−0.0352544	+	0.999378i	$0.511224\pi$
$98$	−2.68001	−0.270722
$99$	−6.74764	−0.678164
$100$	0	0
$101$	9.42415	0.937738	0.468869	−	0.883268i	$-0.344662\pi$
$101$	9.42415	0.937738	0.468869	+	0.883268i	$0.344662\pi$
$102$	−34.0358	−3.37005
$103$	−10.0654	−0.991770	−0.495885	−	0.868388i	$-0.665156\pi$
$103$	−10.0654	−0.991770	−0.495885	+	0.868388i	$0.665156\pi$
$104$	−34.3835	−3.37158
$105$	0	0
$106$	−17.7690	−1.72587
$107$	5.34125	0.516358	0.258179	−	0.966097i	$-0.416878\pi$
$107$	5.34125	0.516358	0.258179	+	0.966097i	$0.416878\pi$
$108$	−56.1110	−5.39928
$109$	−4.52282	−0.433207	−0.216604	−	0.976260i	$-0.569498\pi$
$109$	−4.52282	−0.433207	−0.216604	+	0.976260i	$0.569498\pi$
$110$	0	0
$111$	14.6206	1.38773
$112$	12.4931	1.18048
$113$	9.22779	0.868078	0.434039	−	0.900894i	$-0.357088\pi$
$113$	9.22779	0.868078	0.434039	+	0.900894i	$0.357088\pi$
$114$	−51.5627	−4.82929
$115$	0	0
$116$	−42.2072	−3.91884
$117$	26.2471	2.42655
$118$	−14.0928	−1.29735
$119$	−4.11805	−0.377501
$120$	0	0
$121$	−9.92591	−0.902356
$122$	2.47190	0.223795
$123$	13.7238	1.23743
$124$	52.1600	4.68411
$125$	0	0
$126$	−17.4490	−1.55448
$127$	7.22753	0.641339	0.320670	−	0.947191i	$-0.396092\pi$
$127$	7.22753	0.641339	0.320670	+	0.947191i	$0.396092\pi$
$128$	−18.1508	−1.60432
$129$	−14.5257	−1.27891
$130$	0	0
$131$	−12.5103	−1.09303	−0.546515	−	0.837450i	$-0.684046\pi$
$131$	−12.5103	−1.09303	−0.546515	+	0.837450i	$0.684046\pi$
$132$	16.5640	1.44171
$133$	−6.23865	−0.540960
$134$	−26.5719	−2.29546
$135$	0	0
$136$	35.1231	3.01178
$137$	−8.00974	−0.684318	−0.342159	−	0.939642i	$-0.611158\pi$
$137$	−8.00974	−0.684318	−0.342159	+	0.939642i	$0.611158\pi$
$138$	8.26504	0.703567
$139$	−15.4003	−1.30624	−0.653118	−	0.757256i	$-0.726539\pi$
$139$	−15.4003	−1.30624	−0.653118	+	0.757256i	$0.726539\pi$
$140$	0	0
$141$	14.1005	1.18747
$142$	9.52023	0.798920
$143$	−4.17800	−0.349382
$144$	81.3395	6.77829
$145$	0	0
$146$	27.7448	2.29617
$147$	−3.08395	−0.254360
$148$	−24.5694	−2.01960
$149$	−16.6464	−1.36373	−0.681864	−	0.731479i	$-0.738830\pi$
$149$	−16.6464	−1.36373	−0.681864	+	0.731479i	$0.738830\pi$
$150$	0	0
$151$	9.04004	0.735668	0.367834	−	0.929891i	$-0.380099\pi$
$151$	9.04004	0.735668	0.367834	+	0.929891i	$0.380099\pi$
$152$	53.2099	4.31589
$153$	−26.8117	−2.16760
$154$	2.77751	0.223818
$155$	0	0
$156$	−64.4308	−5.15859
$157$	−13.2316	−1.05600	−0.527999	−	0.849245i	$-0.677057\pi$
$157$	−13.2316	−1.05600	−0.527999	+	0.849245i	$0.677057\pi$
$158$	−11.2286	−0.893301
$159$	−20.4472	−1.62157
$160$	0	0
$161$	1.00000	0.0788110
$162$	−37.1393	−2.91794
$163$	−5.89731	−0.461913	−0.230957	−	0.972964i	$-0.574186\pi$
$163$	−5.89731	−0.461913	−0.230957	+	0.972964i	$0.574186\pi$
$164$	−23.0623	−1.80086
$165$	0	0
$166$	−36.8999	−2.86399
$167$	7.11397	0.550495	0.275248	−	0.961373i	$-0.411240\pi$
$167$	7.11397	0.550495	0.275248	+	0.961373i	$0.411240\pi$
$168$	26.3032	2.02934
$169$	3.25166	0.250128
$170$	0	0
$171$	−40.6185	−3.10617
$172$	24.4098	1.86123
$173$	−25.6483	−1.95001	−0.975004	−	0.222188i	$-0.928680\pi$
$173$	−25.6483	−1.95001	−0.975004	+	0.222188i	$0.928680\pi$
$174$	−67.3123	−5.10293
$175$	0	0
$176$	−12.9476	−0.975959
$177$	−16.2169	−1.21894
$178$	−7.88700	−0.591156
$179$	7.09135	0.530032	0.265016	−	0.964244i	$-0.414623\pi$
$179$	7.09135	0.530032	0.265016	+	0.964244i	$0.414623\pi$
$180$	0	0
$181$	7.09002	0.526997	0.263499	−	0.964660i	$-0.415124\pi$
$181$	7.09002	0.526997	0.263499	+	0.964660i	$0.415124\pi$
$182$	−10.8040	−0.800848
$183$	2.84447	0.210269
$184$	−8.52906	−0.628771
$185$	0	0
$186$	83.1852	6.09943
$187$	4.26787	0.312097
$188$	−23.6953	−1.72816
$189$	−10.8271	−0.787554
$190$	0	0
$191$	19.5891	1.41741	0.708707	−	0.705503i	$-0.249279\pi$
$191$	19.5891	1.41741	0.708707	+	0.705503i	$0.249279\pi$
$192$	−58.6842	−4.23517
$193$	12.0977	0.870811	0.435405	−	0.900235i	$-0.356605\pi$
$193$	12.0977	0.870811	0.435405	+	0.900235i	$0.356605\pi$
$194$	1.86108	0.133618
$195$	0	0
$196$	5.18247	0.370176
$197$	−2.29867	−0.163773	−0.0818866	−	0.996642i	$-0.526095\pi$
$197$	−2.29867	−0.163773	−0.0818866	+	0.996642i	$0.526095\pi$
$198$	18.0838	1.28516
$199$	16.1216	1.14283	0.571416	−	0.820661i	$-0.306394\pi$
$199$	16.1216	1.14283	0.571416	+	0.820661i	$0.306394\pi$
$200$	0	0
$201$	−30.5769	−2.15673
$202$	−25.2568	−1.77707
$203$	−8.14422	−0.571612
$204$	65.8167	4.60809
$205$	0	0
$206$	26.9753	1.87946
$207$	6.51078	0.452530
$208$	50.3637	3.49209
$209$	6.46562	0.447236
$210$	0	0
$211$	3.31907	0.228494	0.114247	−	0.993452i	$-0.463554\pi$
$211$	3.31907	0.228494	0.114247	+	0.993452i	$0.463554\pi$
$212$	34.3607	2.35990
$213$	10.9552	0.750635
$214$	−14.3146	−0.978526
$215$	0	0
$216$	92.3448	6.28327
$217$	10.0647	0.683237
$218$	12.1212	0.820952
$219$	31.9266	2.15740
$220$	0	0
$221$	−16.6012	−1.11672
$222$	−39.1835	−2.62983
$223$	7.85449	0.525975	0.262988	−	0.964799i	$-0.415292\pi$
$223$	7.85449	0.525975	0.262988	+	0.964799i	$0.415292\pi$
$224$	−16.4234	−1.09734
$225$	0	0
$226$	−24.7306	−1.64506
$227$	−23.7425	−1.57585	−0.787923	−	0.615774i	$-0.788844\pi$
$227$	−23.7425	−1.57585	−0.787923	+	0.615774i	$0.788844\pi$
$228$	99.7093	6.60341
$229$	−1.09061	−0.0720696	−0.0360348	−	0.999351i	$-0.511473\pi$
$229$	−1.09061	−0.0720696	−0.0360348	+	0.999351i	$0.511473\pi$
$230$	0	0
$231$	3.19615	0.210291
$232$	69.4626	4.56044
$233$	−19.7955	−1.29684	−0.648422	−	0.761281i	$-0.724571\pi$
$233$	−19.7955	−1.29684	−0.648422	+	0.761281i	$0.724571\pi$
$234$	−70.3426	−4.59844
$235$	0	0
$236$	27.2519	1.77395
$237$	−12.9210	−0.839312
$238$	11.0364	0.715385
$239$	17.1731	1.11083	0.555417	−	0.831572i	$-0.312559\pi$
$239$	17.1731	1.11083	0.555417	+	0.831572i	$0.312559\pi$
$240$	0	0
$241$	−26.4098	−1.70121	−0.850604	−	0.525807i	$-0.823763\pi$
$241$	−26.4098	−1.70121	−0.850604	+	0.525807i	$0.823763\pi$
$242$	26.6016	1.71001
$243$	−10.2558	−0.657912
$244$	−4.78003	−0.306010
$245$	0	0
$246$	−36.7799	−2.34500
$247$	−25.1501	−1.60026
$248$	−85.8425	−5.45100
$249$	−42.4616	−2.69089
$250$	0	0
$251$	−15.0483	−0.949837	−0.474919	−	0.880030i	$-0.657522\pi$
$251$	−15.0483	−0.949837	−0.474919	+	0.880030i	$0.657522\pi$
$252$	33.7419	2.12554
$253$	−1.03638	−0.0651567
$254$	−19.3699	−1.21537
$255$	0	0
$256$	10.5866	0.661665
$257$	18.6447	1.16303	0.581513	−	0.813537i	$-0.302461\pi$
$257$	18.6447	1.16303	0.581513	+	0.813537i	$0.302461\pi$
$258$	38.9290	2.42361
$259$	−4.74088	−0.294584
$260$	0	0
$261$	−53.0252	−3.28218
$262$	33.5277	2.07135
$263$	2.26355	0.139576	0.0697882	−	0.997562i	$-0.477768\pi$
$263$	2.26355	0.139576	0.0697882	+	0.997562i	$0.477768\pi$
$264$	−27.2602	−1.67775
$265$	0	0
$266$	16.7197	1.02515
$267$	−9.07576	−0.555427
$268$	51.3833	3.13873
$269$	2.42234	0.147692	0.0738462	−	0.997270i	$-0.476473\pi$
$269$	2.42234	0.147692	0.0738462	+	0.997270i	$0.476473\pi$
$270$	0	0
$271$	−1.07451	−0.0652718	−0.0326359	−	0.999467i	$-0.510390\pi$
$271$	−1.07451	−0.0652718	−0.0326359	+	0.999467i	$0.510390\pi$
$272$	−51.4470	−3.11943
$273$	−12.4325	−0.752446
$274$	21.4662	1.29682
$275$	0	0
$276$	−15.9825	−0.962034
$277$	18.3660	1.10351	0.551753	−	0.834008i	$-0.313959\pi$
$277$	18.3660	1.10351	0.551753	+	0.834008i	$0.313959\pi$
$278$	41.2730	2.47539
$279$	65.5290	3.92312
$280$	0	0
$281$	23.7585	1.41731	0.708656	−	0.705554i	$-0.249302\pi$
$281$	23.7585	1.41731	0.708656	+	0.705554i	$0.249302\pi$
$282$	−37.7894	−2.25033
$283$	−24.6469	−1.46511	−0.732553	−	0.680710i	$-0.761671\pi$
$283$	−24.6469	−1.46511	−0.732553	+	0.680710i	$0.761671\pi$
$284$	−18.4097	−1.09242
$285$	0	0
$286$	11.1971	0.662098
$287$	−4.45005	−0.262678
$288$	−106.929	−6.30087
$289$	−0.0416824	−0.00245191
$290$	0	0
$291$	2.14159	0.125542
$292$	−53.6514	−3.13971
$293$	−4.83385	−0.282396	−0.141198	−	0.989981i	$-0.545095\pi$
$293$	−4.83385	−0.282396	−0.141198	+	0.989981i	$0.545095\pi$
$294$	8.26504	0.482027
$295$	0	0
$296$	40.4352	2.35025
$297$	11.2210	0.651107
$298$	44.6126	2.58434
$299$	4.03133	0.233138
$300$	0	0
$301$	4.71008	0.271484
$302$	−24.2274	−1.39413
$303$	−29.0637	−1.66966
$304$	−77.9398	−4.47016
$305$	0	0
$306$	71.8557	4.10772
$307$	9.95089	0.567927	0.283964	−	0.958835i	$-0.408350\pi$
$307$	9.95089	0.567927	0.283964	+	0.958835i	$0.408350\pi$
$308$	−5.37101	−0.306042
$309$	31.0411	1.76587
$310$	0	0
$311$	17.1140	0.970444	0.485222	−	0.874391i	$-0.338739\pi$
$311$	17.1140	0.970444	0.485222	+	0.874391i	$0.338739\pi$
$312$	106.037	6.00317
$313$	−14.7785	−0.835331	−0.417666	−	0.908601i	$-0.637152\pi$
$313$	−14.7785	−0.835331	−0.417666	+	0.908601i	$0.637152\pi$
$314$	35.4609	2.00117
$315$	0	0
$316$	21.7133	1.22147
$317$	−12.6932	−0.712919	−0.356460	−	0.934311i	$-0.616016\pi$
$317$	−12.6932	−0.712919	−0.356460	+	0.934311i	$0.616016\pi$
$318$	54.7987	3.07296
$319$	8.44051	0.472578
$320$	0	0
$321$	−16.4722	−0.919386
$322$	−2.68001	−0.149351
$323$	25.6911	1.42949
$324$	71.8180	3.98989
$325$	0	0
$326$	15.8049	0.875351
$327$	13.9482	0.771335
$328$	37.9548	2.09570
$329$	−4.57220	−0.252074
$330$	0	0
$331$	27.3143	1.50133	0.750665	−	0.660683i	$-0.229733\pi$
$331$	27.3143	1.50133	0.750665	+	0.660683i	$0.229733\pi$
$332$	71.3551	3.91612
$333$	−30.8668	−1.69149
$334$	−19.0655	−1.04322
$335$	0	0
$336$	−38.5280	−2.10188
$337$	13.6129	0.741541	0.370771	−	0.928725i	$-0.379094\pi$
$337$	13.6129	0.741541	0.370771	+	0.928725i	$0.379094\pi$
$338$	−8.71449	−0.474006
$339$	−28.4581	−1.54563
$340$	0	0
$341$	−10.4309	−0.564863
$342$	108.858	5.88637
$343$	1.00000	0.0539949
$344$	−40.1725	−2.16596
$345$	0	0
$346$	68.7379	3.69537
$347$	−21.5633	−1.15758	−0.578788	−	0.815478i	$-0.696474\pi$
$347$	−21.5633	−1.15758	−0.578788	+	0.815478i	$0.696474\pi$
$348$	130.165	6.97758
$349$	25.6897	1.37514	0.687570	−	0.726118i	$-0.258677\pi$
$349$	25.6897	1.37514	0.687570	+	0.726118i	$0.258677\pi$
$350$	0	0
$351$	−43.6476	−2.32973
$352$	17.0209	0.907218
$353$	10.8774	0.578946	0.289473	−	0.957186i	$-0.406520\pi$
$353$	10.8774	0.578946	0.289473	+	0.957186i	$0.406520\pi$
$354$	43.4615	2.30995
$355$	0	0
$356$	15.2515	0.808326
$357$	12.6999	0.672149
$358$	−19.0049	−1.00444
$359$	20.6570	1.09024	0.545118	−	0.838359i	$-0.316485\pi$
$359$	20.6570	1.09024	0.545118	+	0.838359i	$0.316485\pi$
$360$	0	0
$361$	19.9208	1.04846
$362$	−19.0014	−0.998689
$363$	30.6111	1.60666
$364$	20.8923	1.09505
$365$	0	0
$366$	−7.62322	−0.398472
$367$	29.7267	1.55172	0.775860	−	0.630905i	$-0.217316\pi$
$367$	29.7267	1.55172	0.775860	+	0.630905i	$0.217316\pi$
$368$	12.4931	0.651245
$369$	−28.9733	−1.50829
$370$	0	0
$371$	6.63018	0.344222
$372$	−160.859	−8.34016
$373$	30.3763	1.57283	0.786413	−	0.617701i	$-0.211936\pi$
$373$	30.3763	1.57283	0.786413	+	0.617701i	$0.211936\pi$
$374$	−11.4379	−0.591442
$375$	0	0
$376$	38.9966	2.01110
$377$	−32.8321	−1.69094
$378$	29.0167	1.49246
$379$	−1.07829	−0.0553881	−0.0276940	−	0.999616i	$-0.508816\pi$
$379$	−1.07829	−0.0553881	−0.0276940	+	0.999616i	$0.508816\pi$
$380$	0	0
$381$	−22.2894	−1.14192
$382$	−52.4989	−2.68608
$383$	−7.58719	−0.387688	−0.193844	−	0.981032i	$-0.562095\pi$
$383$	−7.58719	−0.387688	−0.193844	+	0.981032i	$0.562095\pi$
$384$	55.9763	2.85653
$385$	0	0
$386$	−32.4220	−1.65023
$387$	30.6663	1.55885
$388$	−3.59886	−0.182705
$389$	19.8445	1.00616	0.503079	−	0.864241i	$-0.332201\pi$
$389$	19.8445	1.00616	0.503079	+	0.864241i	$0.332201\pi$
$390$	0	0
$391$	−4.11805	−0.208259
$392$	−8.52906	−0.430783
$393$	38.5812	1.94616
$394$	6.16046	0.310359
$395$	0	0
$396$	−34.9695	−1.75728
$397$	−12.9874	−0.651818	−0.325909	−	0.945401i	$-0.605670\pi$
$397$	−12.9874	−0.651818	−0.325909	+	0.945401i	$0.605670\pi$
$398$	−43.2062	−2.16573
$399$	19.2397	0.963191
$400$	0	0
$401$	10.2632	0.512519	0.256259	−	0.966608i	$-0.417510\pi$
$401$	10.2632	0.512519	0.256259	+	0.966608i	$0.417510\pi$
$402$	81.9464	4.08712
$403$	40.5742	2.02114
$404$	48.8404	2.42990
$405$	0	0
$406$	21.8266	1.08324
$407$	4.91335	0.243546
$408$	−108.318	−5.36254
$409$	23.4909	1.16155	0.580775	−	0.814064i	$-0.302750\pi$
$409$	23.4909	1.16155	0.580775	+	0.814064i	$0.302750\pi$
$410$	0	0
$411$	24.7017	1.21844
$412$	−52.1635	−2.56991
$413$	5.25847	0.258753
$414$	−17.4490	−0.857570
$415$	0	0
$416$	−66.2083	−3.24613
$417$	47.4938	2.32578
$418$	−17.3279	−0.847538
$419$	−10.2429	−0.500398	−0.250199	−	0.968194i	$-0.580496\pi$
$419$	−10.2429	−0.500398	−0.250199	+	0.968194i	$0.580496\pi$
$420$	0	0
$421$	23.9872	1.16907	0.584533	−	0.811370i	$-0.301278\pi$
$421$	23.9872	1.16907	0.584533	+	0.811370i	$0.301278\pi$
$422$	−8.89514	−0.433009
$423$	−29.7686	−1.44740
$424$	−56.5492	−2.74627
$425$	0	0
$426$	−29.3600	−1.42249
$427$	−0.922345	−0.0446354
$428$	27.6808	1.33800
$429$	12.8848	0.622082
$430$	0	0
$431$	16.6824	0.803564	0.401782	−	0.915735i	$-0.368391\pi$
$431$	16.6824	0.803564	0.401782	+	0.915735i	$0.368391\pi$
$432$	−135.263	−6.50785
$433$	5.02449	0.241462	0.120731	−	0.992685i	$-0.461476\pi$
$433$	5.02449	0.241462	0.120731	+	0.992685i	$0.461476\pi$
$434$	−26.9735	−1.29477
$435$	0	0
$436$	−23.4394	−1.12254
$437$	−6.23865	−0.298435
$438$	−85.5636	−4.08839
$439$	−19.9912	−0.954126	−0.477063	−	0.878869i	$-0.658299\pi$
$439$	−19.9912	−0.954126	−0.477063	+	0.878869i	$0.658299\pi$
$440$	0	0
$441$	6.51078	0.310037
$442$	44.4915	2.11625
$443$	6.40997	0.304547	0.152273	−	0.988338i	$-0.451341\pi$
$443$	6.40997	0.304547	0.152273	+	0.988338i	$0.451341\pi$
$444$	75.7711	3.59594
$445$	0	0
$446$	−21.0501	−0.996753
$447$	51.3368	2.42815
$448$	19.0289	0.899030
$449$	−20.1421	−0.950565	−0.475282	−	0.879833i	$-0.657654\pi$
$449$	−20.1421	−0.950565	−0.475282	+	0.879833i	$0.657654\pi$
$450$	0	0
$451$	4.61195	0.217168
$452$	47.8228	2.24939
$453$	−27.8791	−1.30987
$454$	63.6302	2.98632
$455$	0	0
$456$	−164.097	−7.68454
$457$	12.9762	0.607001	0.303500	−	0.952831i	$-0.401845\pi$
$457$	12.9762	0.607001	0.303500	+	0.952831i	$0.401845\pi$
$458$	2.92285	0.136576
$459$	44.5864	2.08112
$460$	0	0
$461$	−23.4048	−1.09007	−0.545036	−	0.838413i	$-0.683484\pi$
$461$	−23.4048	−1.09007	−0.545036	+	0.838413i	$0.683484\pi$
$462$	−8.56573	−0.398514
$463$	15.1716	0.705083	0.352541	−	0.935796i	$-0.385318\pi$
$463$	15.1716	0.705083	0.352541	+	0.935796i	$0.385318\pi$
$464$	−101.746	−4.72345
$465$	0	0
$466$	53.0521	2.45759
$467$	−6.97074	−0.322568	−0.161284	−	0.986908i	$-0.551563\pi$
$467$	−6.97074	−0.322568	−0.161284	+	0.986908i	$0.551563\pi$
$468$	136.025	6.28775
$469$	9.91482	0.457824
$470$	0	0
$471$	40.8057	1.88023
$472$	−44.8498	−2.06438
$473$	−4.88143	−0.224449
$474$	34.6286	1.59054
$475$	0	0
$476$	−21.3417	−0.978193
$477$	43.1676	1.97651
$478$	−46.0240	−2.10509
$479$	3.49742	0.159801	0.0799006	−	0.996803i	$-0.474540\pi$
$479$	3.49742	0.159801	0.0799006	+	0.996803i	$0.474540\pi$
$480$	0	0
$481$	−19.1121	−0.871435
$482$	70.7787	3.22388
$483$	−3.08395	−0.140325
$484$	−51.4408	−2.33822
$485$	0	0
$486$	27.4858	1.24678
$487$	1.57825	0.0715174	0.0357587	−	0.999360i	$-0.488615\pi$
$487$	1.57825	0.0715174	0.0357587	+	0.999360i	$0.488615\pi$
$488$	7.86674	0.356110
$489$	18.1870	0.822447
$490$	0	0
$491$	−34.0732	−1.53770	−0.768852	−	0.639427i	$-0.779172\pi$
$491$	−34.0732	−1.53770	−0.768852	+	0.639427i	$0.779172\pi$
$492$	71.1230	3.20647
$493$	33.5383	1.51049
$494$	67.4026	3.03259
$495$	0	0
$496$	125.739	5.64584
$497$	−3.55231	−0.159343
$498$	113.798	5.09939
$499$	−21.5769	−0.965913	−0.482956	−	0.875644i	$-0.660437\pi$
$499$	−21.5769	−0.965913	−0.482956	+	0.875644i	$0.660437\pi$
$500$	0	0
$501$	−21.9391	−0.980169
$502$	40.3295	1.79999
$503$	4.91991	0.219368	0.109684	−	0.993967i	$-0.465016\pi$
$503$	4.91991	0.219368	0.109684	+	0.993967i	$0.465016\pi$
$504$	−55.5308	−2.47354
$505$	0	0
$506$	2.77751	0.123476
$507$	−10.0280	−0.445358
$508$	37.4564	1.66186
$509$	14.1012	0.625027	0.312513	−	0.949913i	$-0.398829\pi$
$509$	14.1012	0.625027	0.312513	+	0.949913i	$0.398829\pi$
$510$	0	0
$511$	−10.3525	−0.457967
$512$	7.92928	0.350428
$513$	67.5464	2.98224
$514$	−49.9681	−2.20400
$515$	0	0
$516$	−75.2788	−3.31396
$517$	4.73854	0.208401
$518$	12.7056	0.558252
$519$	79.0983	3.47203
$520$	0	0
$521$	29.8650	1.30841	0.654204	−	0.756318i	$-0.273004\pi$
$521$	29.8650	1.30841	0.654204	+	0.756318i	$0.273004\pi$
$522$	142.108	6.21991
$523$	−22.7170	−0.993345	−0.496672	−	0.867938i	$-0.665445\pi$
$523$	−22.7170	−0.993345	−0.496672	+	0.867938i	$0.665445\pi$
$524$	−64.8342	−2.83230
$525$	0	0
$526$	−6.06634	−0.264505
$527$	−41.4469	−1.80546
$528$	39.9297	1.73772
$529$	1.00000	0.0434783
$530$	0	0
$531$	34.2367	1.48575
$532$	−32.3316	−1.40175
$533$	−17.9397	−0.777053
$534$	24.3231	1.05257
$535$	0	0
$536$	−84.5641	−3.65261
$537$	−21.8694	−0.943734
$538$	−6.49189	−0.279885
$539$	−1.03638	−0.0446401
$540$	0	0
$541$	−30.9193	−1.32932	−0.664661	−	0.747145i	$-0.731424\pi$
$541$	−30.9193	−1.32932	−0.664661	+	0.747145i	$0.731424\pi$
$542$	2.87970	0.123694
$543$	−21.8653	−0.938330
$544$	67.6325	2.89972
$545$	0	0
$546$	33.3191	1.42593
$547$	19.4587	0.831992	0.415996	−	0.909366i	$-0.363433\pi$
$547$	19.4587	0.831992	0.415996	+	0.909366i	$0.363433\pi$
$548$	−41.5102	−1.77323
$549$	−6.00518	−0.256295
$550$	0	0
$551$	50.8090	2.16453
$552$	26.3032	1.11954
$553$	4.18977	0.178167
$554$	−49.2211	−2.09120
$555$	0	0
$556$	−79.8115	−3.38476
$557$	7.00008	0.296603	0.148302	−	0.988942i	$-0.452619\pi$
$557$	7.00008	0.296603	0.148302	+	0.988942i	$0.452619\pi$
$558$	−175.619	−7.43453
$559$	18.9879	0.803102
$560$	0	0
$561$	−13.1619	−0.555696
$562$	−63.6731	−2.68589
$563$	−5.32058	−0.224236	−0.112118	−	0.993695i	$-0.535763\pi$
$563$	−5.32058	−0.224236	−0.112118	+	0.993695i	$0.535763\pi$
$564$	73.0752	3.07702
$565$	0	0
$566$	66.0540	2.77646
$567$	13.8579	0.581976
$568$	30.2979	1.27127
$569$	−40.4405	−1.69535	−0.847676	−	0.530514i	$-0.821999\pi$
$569$	−40.4405	−1.69535	−0.847676	+	0.530514i	$0.821999\pi$
$570$	0	0
$571$	15.3192	0.641090	0.320545	−	0.947233i	$-0.396134\pi$
$571$	15.3192	0.641090	0.320545	+	0.947233i	$0.396134\pi$
$572$	−21.6523	−0.905330
$573$	−60.4118	−2.52374
$574$	11.9262	0.497790
$575$	0	0
$576$	123.893	5.16220
$577$	−5.49935	−0.228941	−0.114470	−	0.993427i	$-0.536517\pi$
$577$	−5.49935	−0.228941	−0.114470	+	0.993427i	$0.536517\pi$
$578$	0.111709	0.00464650
$579$	−37.3087	−1.55050
$580$	0	0
$581$	13.7686	0.571216
$582$	−5.73949	−0.237910
$583$	−6.87139	−0.284584
$584$	88.2969	3.65375
$585$	0	0
$586$	12.9548	0.535157
$587$	32.7728	1.35268	0.676338	−	0.736591i	$-0.263566\pi$
$587$	32.7728	1.35268	0.676338	+	0.736591i	$0.263566\pi$
$588$	−15.9825	−0.659107
$589$	−62.7902	−2.58723
$590$	0	0
$591$	7.08898	0.291602
$592$	−59.2280	−2.43426
$593$	31.2505	1.28330	0.641652	−	0.766996i	$-0.278249\pi$
$593$	31.2505	1.28330	0.641652	+	0.766996i	$0.278249\pi$
$594$	−30.0723	−1.23388
$595$	0	0
$596$	−86.2695	−3.53374
$597$	−49.7184	−2.03484
$598$	−10.8040	−0.441810
$599$	25.6017	1.04606	0.523028	−	0.852316i	$-0.324802\pi$
$599$	25.6017	1.04606	0.523028	+	0.852316i	$0.324802\pi$
$600$	0	0
$601$	33.3933	1.36214	0.681071	−	0.732217i	$-0.261514\pi$
$601$	33.3933	1.36214	0.681071	+	0.732217i	$0.261514\pi$
$602$	−12.6231	−0.514478
$603$	64.5532	2.62881
$604$	46.8497	1.90629
$605$	0	0
$606$	77.8910	3.16410
$607$	−39.6763	−1.61041	−0.805205	−	0.592996i	$-0.797945\pi$
$607$	−39.6763	−1.61041	−0.805205	+	0.592996i	$0.797945\pi$
$608$	102.460	4.15530
$609$	25.1164	1.01777
$610$	0	0
$611$	−18.4321	−0.745682
$612$	−138.951	−5.61675
$613$	−29.2538	−1.18155	−0.590776	−	0.806836i	$-0.701178\pi$
$613$	−29.2538	−1.18155	−0.590776	+	0.806836i	$0.701178\pi$
$614$	−26.6685	−1.07625
$615$	0	0
$616$	8.83935	0.356148
$617$	15.0304	0.605101	0.302550	−	0.953133i	$-0.402162\pi$
$617$	15.0304	0.605101	0.302550	+	0.953133i	$0.402162\pi$
$618$	−83.1907	−3.34642
$619$	18.7893	0.755207	0.377604	−	0.925967i	$-0.376748\pi$
$619$	18.7893	0.755207	0.377604	+	0.925967i	$0.376748\pi$
$620$	0	0
$621$	−10.8271	−0.434476
$622$	−45.8656	−1.83904
$623$	2.94290	0.117905
$624$	−155.319	−6.21775
$625$	0	0
$626$	39.6066	1.58300
$627$	−19.9397	−0.796314
$628$	−68.5724	−2.73634
$629$	19.5232	0.778439
$630$	0	0
$631$	−18.7280	−0.745548	−0.372774	−	0.927922i	$-0.621593\pi$
$631$	−18.7280	−0.745548	−0.372774	+	0.927922i	$0.621593\pi$
$632$	−35.7348	−1.42145
$633$	−10.2358	−0.406838
$634$	34.0179	1.35102
$635$	0	0
$636$	−105.967	−4.20186
$637$	4.03133	0.159727
$638$	−22.6207	−0.895562
$639$	−23.1283	−0.914941
$640$	0	0
$641$	24.4090	0.964098	0.482049	−	0.876144i	$-0.339893\pi$
$641$	24.4090	0.964098	0.482049	+	0.876144i	$0.339893\pi$
$642$	44.1456	1.74229
$643$	−19.3762	−0.764121	−0.382060	−	0.924137i	$-0.624785\pi$
$643$	−19.3762	−0.764121	−0.382060	+	0.924137i	$0.624785\pi$
$644$	5.18247	0.204218
$645$	0	0
$646$	−68.8524	−2.70896
$647$	16.9974	0.668238	0.334119	−	0.942531i	$-0.391561\pi$
$647$	16.9974	0.668238	0.334119	+	0.942531i	$0.391561\pi$
$648$	−118.195	−4.64312
$649$	−5.44978	−0.213923
$650$	0	0
$651$	−31.0391	−1.21652
$652$	−30.5626	−1.19693
$653$	1.42934	0.0559344	0.0279672	−	0.999609i	$-0.491097\pi$
$653$	1.42934	0.0559344	0.0279672	+	0.999609i	$0.491097\pi$
$654$	−37.3813	−1.46172
$655$	0	0
$656$	−55.5948	−2.17061
$657$	−67.4026	−2.62963
$658$	12.2536	0.477694
$659$	−25.6190	−0.997976	−0.498988	−	0.866609i	$-0.666295\pi$
$659$	−25.6190	−0.997976	−0.498988	+	0.866609i	$0.666295\pi$
$660$	0	0
$661$	−33.2265	−1.29236	−0.646181	−	0.763184i	$-0.723635\pi$
$661$	−33.2265	−1.29236	−0.646181	+	0.763184i	$0.723635\pi$
$662$	−73.2027	−2.84510
$663$	51.1974	1.98834
$664$	−117.433	−4.55728
$665$	0	0
$666$	82.7234	3.20547
$667$	−8.14422	−0.315346
$668$	36.8679	1.42646
$669$	−24.2229	−0.936511
$670$	0	0
$671$	0.955901	0.0369021
$672$	50.6491	1.95383
$673$	33.5144	1.29188	0.645942	−	0.763386i	$-0.276465\pi$
$673$	33.5144	1.29188	0.645942	+	0.763386i	$0.276465\pi$
$674$	−36.4827	−1.40526
$675$	0	0
$676$	16.8516	0.648140
$677$	−20.9404	−0.804807	−0.402403	−	0.915462i	$-0.631825\pi$
$677$	−20.9404	−0.804807	−0.402403	+	0.915462i	$0.631825\pi$
$678$	76.2681	2.92906
$679$	−0.694430	−0.0266498
$680$	0	0
$681$	73.2208	2.80583
$682$	27.9549	1.07045
$683$	15.3782	0.588430	0.294215	−	0.955739i	$-0.404942\pi$
$683$	15.3782	0.588430	0.294215	+	0.955739i	$0.404942\pi$
$684$	−210.504	−8.04882
$685$	0	0
$686$	−2.68001	−0.102323
$687$	3.36340	0.128322
$688$	58.8432	2.24338
$689$	26.7285	1.01827
$690$	0	0
$691$	21.2733	0.809273	0.404637	−	0.914478i	$-0.367398\pi$
$691$	21.2733	0.809273	0.404637	+	0.914478i	$0.367398\pi$
$692$	−132.922	−5.05293
$693$	−6.74764	−0.256322
$694$	57.7898	2.19367
$695$	0	0
$696$	−214.219	−8.11996
$697$	18.3255	0.694129
$698$	−68.8489	−2.60597
$699$	61.0483	2.30906
$700$	0	0
$701$	8.49681	0.320920	0.160460	−	0.987042i	$-0.448702\pi$
$701$	8.49681	0.320920	0.160460	+	0.987042i	$0.448702\pi$
$702$	116.976	4.41498
$703$	29.5767	1.11551
$704$	−19.7212	−0.743270
$705$	0	0
$706$	−29.1516	−1.09714
$707$	9.42415	0.354432
$708$	−84.0435	−3.15855
$709$	−20.2759	−0.761477	−0.380739	−	0.924683i	$-0.624330\pi$
$709$	−20.2759	−0.761477	−0.380739	+	0.924683i	$0.624330\pi$
$710$	0	0
$711$	27.2786	1.02303
$712$	−25.1001	−0.940667
$713$	10.0647	0.376926
$714$	−34.0358	−1.27376
$715$	0	0
$716$	36.7507	1.37344
$717$	−52.9610	−1.97786
$718$	−55.3611	−2.06606
$719$	31.2522	1.16551	0.582754	−	0.812648i	$-0.301975\pi$
$719$	31.2522	1.16551	0.582754	+	0.812648i	$0.301975\pi$
$720$	0	0
$721$	−10.0654	−0.374854
$722$	−53.3880	−1.98690
$723$	81.4468	3.02904
$724$	36.7438	1.36557
$725$	0	0
$726$	−82.0381	−3.04472
$727$	−32.3133	−1.19844	−0.599218	−	0.800586i	$-0.704522\pi$
$727$	−32.3133	−1.19844	−0.599218	+	0.800586i	$0.704522\pi$
$728$	−34.3835	−1.27434
$729$	−9.94509	−0.368337
$730$	0	0
$731$	−19.3963	−0.717399
$732$	14.7414	0.544857
$733$	−30.4247	−1.12376	−0.561881	−	0.827218i	$-0.689922\pi$
$733$	−30.4247	−1.12376	−0.561881	+	0.827218i	$0.689922\pi$
$734$	−79.6679	−2.94060
$735$	0	0
$736$	−16.4234	−0.605376
$737$	−10.2755	−0.378504
$738$	77.6488	2.85829
$739$	39.6163	1.45731	0.728654	−	0.684882i	$-0.240146\pi$
$739$	39.6163	1.45731	0.728654	+	0.684882i	$0.240146\pi$
$740$	0	0
$741$	77.5618	2.84930
$742$	−17.7690	−0.652319
$743$	−14.2833	−0.524003	−0.262001	−	0.965068i	$-0.584382\pi$
$743$	−14.2833	−0.524003	−0.262001	+	0.965068i	$0.584382\pi$
$744$	264.734	9.70563
$745$	0	0
$746$	−81.4089	−2.98059
$747$	89.6440	3.27990
$748$	22.1181	0.808717
$749$	5.34125	0.195165
$750$	0	0
$751$	32.3361	1.17996	0.589980	−	0.807418i	$-0.299136\pi$
$751$	32.3361	1.17996	0.589980	+	0.807418i	$0.299136\pi$
$752$	−57.1208	−2.08298
$753$	46.4081	1.69121
$754$	87.9904	3.20442
$755$	0	0
$756$	−56.1110	−2.04074
$757$	17.4509	0.634263	0.317131	−	0.948382i	$-0.397280\pi$
$757$	17.4509	0.634263	0.317131	+	0.948382i	$0.397280\pi$
$758$	2.88983	0.104963
$759$	3.19615	0.116013
$760$	0	0
$761$	10.2059	0.369962	0.184981	−	0.982742i	$-0.440778\pi$
$761$	10.2059	0.369962	0.184981	+	0.982742i	$0.440778\pi$
$762$	59.7358	2.16400
$763$	−4.52282	−0.163737
$764$	101.520	3.67285
$765$	0	0
$766$	20.3338	0.734689
$767$	21.1987	0.765439
$768$	−32.6487	−1.17811
$769$	28.8172	1.03917	0.519587	−	0.854418i	$-0.326086\pi$
$769$	28.8172	1.03917	0.519587	+	0.854418i	$0.326086\pi$
$770$	0	0
$771$	−57.4995	−2.07080
$772$	62.6959	2.25648
$773$	3.93807	0.141642	0.0708212	−	0.997489i	$-0.477438\pi$
$773$	3.93807	0.141642	0.0708212	+	0.997489i	$0.477438\pi$
$774$	−82.1860	−2.95411
$775$	0	0
$776$	5.92284	0.212617
$777$	14.6206	0.524513
$778$	−53.1836	−1.90672
$779$	27.7623	0.994689
$780$	0	0
$781$	3.68154	0.131736
$782$	11.0364	0.394662
$783$	88.1781	3.15123
$784$	12.4931	0.446181
$785$	0	0
$786$	−103.398	−3.68809
$787$	30.9868	1.10456	0.552281	−	0.833658i	$-0.313758\pi$
$787$	30.9868	1.10456	0.552281	+	0.833658i	$0.313758\pi$
$788$	−11.9128	−0.424375
$789$	−6.98068	−0.248519
$790$	0	0
$791$	9.22779	0.328103
$792$	57.5511	2.04499
$793$	−3.71828	−0.132040
$794$	34.8063	1.23523
$795$	0	0
$796$	83.5499	2.96135
$797$	32.8018	1.16190	0.580949	−	0.813940i	$-0.302681\pi$
$797$	32.8018	1.16190	0.580949	+	0.813940i	$0.302681\pi$
$798$	−51.5627	−1.82530
$799$	18.8285	0.666106
$800$	0	0
$801$	19.1605	0.677004
$802$	−27.5055	−0.971252
$803$	10.7291	0.378622
$804$	−158.464	−5.58858
$805$	0	0
$806$	−108.739	−3.83018
$807$	−7.47038	−0.262970
$808$	−80.3792	−2.82773
$809$	3.96801	0.139508	0.0697539	−	0.997564i	$-0.477779\pi$
$809$	3.96801	0.139508	0.0697539	+	0.997564i	$0.477779\pi$
$810$	0	0
$811$	−50.1963	−1.76263	−0.881315	−	0.472528i	$-0.843341\pi$
$811$	−50.1963	−1.76263	−0.881315	+	0.472528i	$0.843341\pi$
$812$	−42.2072	−1.48118
$813$	3.31374	0.116218
$814$	−13.1679	−0.461533
$815$	0	0
$816$	158.660	5.55422
$817$	−29.3845	−1.02803
$818$	−62.9559	−2.20120
$819$	26.2471	0.917149
$820$	0	0
$821$	26.7036	0.931963	0.465982	−	0.884794i	$-0.345701\pi$
$821$	26.7036	0.931963	0.465982	+	0.884794i	$0.345701\pi$
$822$	−66.2008	−2.30902
$823$	−52.5717	−1.83253	−0.916267	−	0.400567i	$-0.868813\pi$
$823$	−52.5717	−1.83253	−0.916267	+	0.400567i	$0.868813\pi$
$824$	85.8482	2.99066
$825$	0	0
$826$	−14.0928	−0.490350
$827$	12.2541	0.426116	0.213058	−	0.977040i	$-0.431658\pi$
$827$	12.2541	0.426116	0.213058	+	0.977040i	$0.431658\pi$
$828$	33.7419	1.17261
$829$	−31.4723	−1.09308	−0.546540	−	0.837433i	$-0.684055\pi$
$829$	−31.4723	−1.09308	−0.546540	+	0.837433i	$0.684055\pi$
$830$	0	0
$831$	−56.6399	−1.96482
$832$	76.7118	2.65950
$833$	−4.11805	−0.142682
$834$	−127.284	−4.40748
$835$	0	0
$836$	33.5079	1.15889
$837$	−108.971	−3.76660
$838$	27.4511	0.948283
$839$	−48.5824	−1.67725	−0.838625	−	0.544710i	$-0.816640\pi$
$839$	−48.5824	−1.67725	−0.838625	+	0.544710i	$0.816640\pi$
$840$	0	0
$841$	37.3283	1.28718
$842$	−64.2861	−2.21545
$843$	−73.2701	−2.52356
$844$	17.2010	0.592081
$845$	0	0
$846$	79.7802	2.74290
$847$	−9.92591	−0.341058
$848$	82.8312	2.84443
$849$	76.0099	2.60865
$850$	0	0
$851$	−4.74088	−0.162515
$852$	56.7748	1.94507
$853$	−32.3500	−1.10764	−0.553821	−	0.832636i	$-0.686831\pi$
$853$	−32.3500	−1.10764	−0.553821	+	0.832636i	$0.686831\pi$
$854$	2.47190	0.0845866
$855$	0	0
$856$	−45.5558	−1.55707
$857$	−43.0385	−1.47017	−0.735084	−	0.677976i	$-0.762857\pi$
$857$	−43.0385	−1.47017	−0.735084	+	0.677976i	$0.762857\pi$
$858$	−34.5313	−1.17888
$859$	21.0942	0.719726	0.359863	−	0.933005i	$-0.382824\pi$
$859$	21.0942	0.719726	0.359863	+	0.933005i	$0.382824\pi$
$860$	0	0
$861$	13.7238	0.467705
$862$	−44.7091	−1.52280
$863$	−8.34066	−0.283919	−0.141960	−	0.989872i	$-0.545340\pi$
$863$	−8.34066	−0.283919	−0.141960	+	0.989872i	$0.545340\pi$
$864$	177.818	6.04948
$865$	0	0
$866$	−13.4657	−0.457583
$867$	0.128547	0.00436568
$868$	52.1600	1.77043
$869$	−4.34219	−0.147299
$870$	0	0
$871$	39.9700	1.35433
$872$	38.5754	1.30633
$873$	−4.52128	−0.153022
$874$	16.7197	0.565551
$875$	0	0
$876$	165.458	5.59032
$877$	11.4469	0.386534	0.193267	−	0.981146i	$-0.438092\pi$
$877$	11.4469	0.386534	0.193267	+	0.981146i	$0.438092\pi$
$878$	53.5765	1.80812
$879$	14.9074	0.502813
$880$	0	0
$881$	−26.5224	−0.893562	−0.446781	−	0.894643i	$-0.647430\pi$
$881$	−26.5224	−0.893562	−0.446781	+	0.894643i	$0.647430\pi$
$882$	−17.4490	−0.587537
$883$	2.39513	0.0806025	0.0403012	−	0.999188i	$-0.487168\pi$
$883$	2.39513	0.0806025	0.0403012	+	0.999188i	$0.487168\pi$
$884$	−86.0354	−2.89368
$885$	0	0
$886$	−17.1788	−0.577133
$887$	40.1901	1.34945	0.674726	−	0.738068i	$-0.264262\pi$
$887$	40.1901	1.34945	0.674726	+	0.738068i	$0.264262\pi$
$888$	−124.700	−4.18467
$889$	7.22753	0.242403
$890$	0	0
$891$	−14.3620	−0.481146
$892$	40.7057	1.36293
$893$	28.5244	0.954532
$894$	−137.583	−4.60147
$895$	0	0
$896$	−18.1508	−0.606376
$897$	−12.4325	−0.415108
$898$	53.9811	1.80137
$899$	−81.9692	−2.73383
$900$	0	0
$901$	−27.3034	−0.909608
$902$	−12.3601	−0.411546
$903$	−14.5257	−0.483384
$904$	−78.7044	−2.61767
$905$	0	0
$906$	74.7163	2.48228
$907$	59.7687	1.98459	0.992294	−	0.123907i	$-0.0395425\pi$
$907$	59.7687	1.98459	0.992294	+	0.123907i	$0.0395425\pi$
$908$	−123.045	−4.08339
$909$	61.3585	2.03513
$910$	0	0
$911$	−8.52185	−0.282341	−0.141171	−	0.989985i	$-0.545087\pi$
$911$	−8.52185	−0.282341	−0.141171	+	0.989985i	$0.545087\pi$
$912$	240.363	7.95921
$913$	−14.2695	−0.472250
$914$	−34.7764	−1.15030
$915$	0	0
$916$	−5.65206	−0.186749
$917$	−12.5103	−0.413126
$918$	−119.492	−3.94383
$919$	7.32586	0.241658	0.120829	−	0.992673i	$-0.461445\pi$
$919$	7.32586	0.241658	0.120829	+	0.992673i	$0.461445\pi$
$920$	0	0
$921$	−30.6881	−1.01121
$922$	62.7253	2.06575
$923$	−14.3205	−0.471366
$924$	16.5640	0.544914
$925$	0	0
$926$	−40.6600	−1.33617
$927$	−65.5334	−2.15240
$928$	133.756	4.39076
$929$	31.8080	1.04359	0.521793	−	0.853072i	$-0.325263\pi$
$929$	31.8080	1.04359	0.521793	+	0.853072i	$0.325263\pi$
$930$	0	0
$931$	−6.23865	−0.204464
$932$	−102.589	−3.36043
$933$	−52.7787	−1.72790
$934$	18.6817	0.611283
$935$	0	0
$936$	−223.863	−7.31720
$937$	16.9706	0.554405	0.277203	−	0.960811i	$-0.410593\pi$
$937$	16.9706	0.554405	0.277203	+	0.960811i	$0.410593\pi$
$938$	−26.5719	−0.867602
$939$	45.5763	1.48733
$940$	0	0
$941$	45.6926	1.48954	0.744769	−	0.667323i	$-0.232560\pi$
$941$	45.6926	1.48954	0.744769	+	0.667323i	$0.232560\pi$
$942$	−109.360	−3.56313
$943$	−4.45005	−0.144914
$944$	65.6944	2.13817
$945$	0	0
$946$	13.0823	0.425342
$947$	18.3647	0.596771	0.298386	−	0.954445i	$-0.403552\pi$
$947$	18.3647	0.596771	0.298386	+	0.954445i	$0.403552\pi$
$948$	−66.9629	−2.17485
$949$	−41.7343	−1.35475
$950$	0	0
$951$	39.1452	1.26937
$952$	35.1231	1.13835
$953$	32.2793	1.04563	0.522815	−	0.852446i	$-0.324882\pi$
$953$	32.2793	1.04563	0.522815	+	0.852446i	$0.324882\pi$
$954$	−115.690	−3.74559
$955$	0	0
$956$	88.9989	2.87843
$957$	−26.0302	−0.841436
$958$	−9.37313	−0.302832
$959$	−8.00974	−0.258648
$960$	0	0
$961$	70.2983	2.26769
$962$	51.2206	1.65142
$963$	34.7757	1.12063
$964$	−136.868	−4.40823
$965$	0	0
$966$	8.26504	0.265923
$967$	−17.5358	−0.563913	−0.281956	−	0.959427i	$-0.590983\pi$
$967$	−17.5358	−0.563913	−0.281956	+	0.959427i	$0.590983\pi$
$968$	84.6587	2.72103
$969$	−79.2301	−2.54524
$970$	0	0
$971$	39.8737	1.27961	0.639804	−	0.768538i	$-0.279016\pi$
$971$	39.8737	1.27961	0.639804	+	0.768538i	$0.279016\pi$
$972$	−53.1506	−1.70481
$973$	−15.4003	−0.493711
$974$	−4.22974	−0.135529
$975$	0	0
$976$	−11.5229	−0.368839
$977$	4.11183	0.131549	0.0657745	−	0.997835i	$-0.479048\pi$
$977$	4.11183	0.131549	0.0657745	+	0.997835i	$0.479048\pi$
$978$	−48.7415	−1.55858
$979$	−3.04996	−0.0974772
$980$	0	0
$981$	−29.4471	−0.940172
$982$	91.3167	2.91403
$983$	−2.63477	−0.0840360	−0.0420180	−	0.999117i	$-0.513379\pi$
$983$	−2.63477	−0.0840360	−0.0420180	+	0.999117i	$0.513379\pi$
$984$	−117.051	−3.73144
$985$	0	0
$986$	−89.8831	−2.86246
$987$	14.1005	0.448823
$988$	−130.340	−4.14666
$989$	4.71008	0.149772
$990$	0	0
$991$	−1.03819	−0.0329790	−0.0164895	−	0.999864i	$-0.505249\pi$
$991$	−1.03819	−0.0329790	−0.0164895	+	0.999864i	$0.505249\pi$
$992$	−165.297	−5.24818
$993$	−84.2361	−2.67315
$994$	9.52023	0.301963
$995$	0	0
$996$	−220.056	−6.97274
$997$	28.6033	0.905875	0.452938	−	0.891542i	$-0.350376\pi$
$997$	28.6033	0.905875	0.452938	+	0.891542i	$0.350376\pi$
$998$	57.8263	1.83046
$999$	51.3298	1.62400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.be.1.2		21
5.2	odd	4		805.2.c.c.484.4	✓	42
5.3	odd	4		805.2.c.c.484.39	yes	42
5.4	even	2		4025.2.a.bd.1.20		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.4	✓	42	5.2	odd	4
805.2.c.c.484.39	yes	42	5.3	odd	4
4025.2.a.bd.1.20		21	5.4	even	2
4025.2.a.be.1.2		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)

\(f(q)\)	\(=\)	\(q-2.68001 q^{2} -3.08395 q^{3} +5.18247 q^{4} +8.26504 q^{6} +1.00000 q^{7} -8.52906 q^{8} +6.51078 q^{9} +O(q^{10})\)	\(q-2.68001 q^{2} -3.08395 q^{3} +5.18247 q^{4} +8.26504 q^{6} +1.00000 q^{7} -8.52906 q^{8} +6.51078 q^{9} -1.03638 q^{11} -15.9825 q^{12} +4.03133 q^{13} -2.68001 q^{14} +12.4931 q^{16} -4.11805 q^{17} -17.4490 q^{18} -6.23865 q^{19} -3.08395 q^{21} +2.77751 q^{22} +1.00000 q^{23} +26.3032 q^{24} -10.8040 q^{26} -10.8271 q^{27} +5.18247 q^{28} -8.14422 q^{29} +10.0647 q^{31} -16.4234 q^{32} +3.19615 q^{33} +11.0364 q^{34} +33.7419 q^{36} -4.74088 q^{37} +16.7197 q^{38} -12.4325 q^{39} -4.45005 q^{41} +8.26504 q^{42} +4.71008 q^{43} -5.37101 q^{44} -2.68001 q^{46} -4.57220 q^{47} -38.5280 q^{48} +1.00000 q^{49} +12.6999 q^{51} +20.8923 q^{52} +6.63018 q^{53} +29.0167 q^{54} -8.52906 q^{56} +19.2397 q^{57} +21.8266 q^{58} +5.25847 q^{59} -0.922345 q^{61} -26.9735 q^{62} +6.51078 q^{63} +19.0289 q^{64} -8.56573 q^{66} +9.91482 q^{67} -21.3417 q^{68} -3.08395 q^{69} -3.55231 q^{71} -55.5308 q^{72} -10.3525 q^{73} +12.7056 q^{74} -32.3316 q^{76} -1.03638 q^{77} +33.3191 q^{78} +4.18977 q^{79} +13.8579 q^{81} +11.9262 q^{82} +13.7686 q^{83} -15.9825 q^{84} -12.6231 q^{86} +25.1164 q^{87} +8.83935 q^{88} +2.94290 q^{89} +4.03133 q^{91} +5.18247 q^{92} -31.0391 q^{93} +12.2536 q^{94} +50.6491 q^{96} -0.694430 q^{97} -2.68001 q^{98} -6.74764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9}+O(q^{10}) \) 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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