LMFDB - Embedded newform 961.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(1,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("961.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.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:	$7.67362363425$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.2051578125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 19x^{5} + 14x^{4} - 28x^{3} - 11x^{2} + 6x + 1 $ x^8 - 2x^7 - 9x^6 + 19x^5 + 14x^4 - 28x^3 - 11x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.73366$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.689493 q^{2} -0.902401 q^{3} -1.52460 q^{4} +3.70752 q^{5} +0.622199 q^{6} +0.763394 q^{7} +2.43019 q^{8} -2.18567 q^{9} -2.55631 q^{10} -4.11562 q^{11} +1.37580 q^{12} -2.90975 q^{13} -0.526355 q^{14} -3.34567 q^{15} +1.37360 q^{16} +1.30852 q^{17} +1.50701 q^{18} -3.79954 q^{19} -5.65248 q^{20} -0.688887 q^{21} +2.83769 q^{22} -3.28296 q^{23} -2.19300 q^{24} +8.74568 q^{25} +2.00625 q^{26} +4.67956 q^{27} -1.16387 q^{28} +4.89563 q^{29} +2.30681 q^{30} -5.80746 q^{32} +3.71394 q^{33} -0.902218 q^{34} +2.83030 q^{35} +3.33228 q^{36} -10.4128 q^{37} +2.61976 q^{38} +2.62576 q^{39} +9.00995 q^{40} +0.755946 q^{41} +0.474983 q^{42} -7.15689 q^{43} +6.27468 q^{44} -8.10342 q^{45} +2.26358 q^{46} -0.876067 q^{47} -1.23954 q^{48} -6.41723 q^{49} -6.03008 q^{50} -1.18081 q^{51} +4.43621 q^{52} +3.57570 q^{53} -3.22652 q^{54} -15.2587 q^{55} +1.85519 q^{56} +3.42871 q^{57} -3.37550 q^{58} +0.927270 q^{59} +5.10080 q^{60} +2.31704 q^{61} -1.66853 q^{63} +1.25699 q^{64} -10.7879 q^{65} -2.56074 q^{66} -2.08690 q^{67} -1.99498 q^{68} +2.96254 q^{69} -1.95147 q^{70} -7.73608 q^{71} -5.31159 q^{72} -5.65748 q^{73} +7.17954 q^{74} -7.89211 q^{75} +5.79278 q^{76} -3.14184 q^{77} -1.81044 q^{78} -14.0947 q^{79} +5.09266 q^{80} +2.33418 q^{81} -0.521219 q^{82} -14.1077 q^{83} +1.05028 q^{84} +4.85137 q^{85} +4.93462 q^{86} -4.41782 q^{87} -10.0017 q^{88} -4.43481 q^{89} +5.58725 q^{90} -2.22129 q^{91} +5.00520 q^{92} +0.604042 q^{94} -14.0869 q^{95} +5.24066 q^{96} -5.27764 q^{97} +4.42463 q^{98} +8.99540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} + 8 q^{4} + 3 q^{5} - 11 q^{6} - 2 q^{7} - 9 q^{8} + 5 q^{9} - 13 q^{10} - 18 q^{11} - 8 q^{13} - 9 q^{14} - 18 q^{15} + 4 q^{16} - 14 q^{17} + 23 q^{18} - 6 q^{19} - 7 q^{20} + q^{21}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 + 8 * q^4 + 3 * q^5 - 11 * q^6 - 2 * q^7 - 9 * q^8 + 5 * q^9 - 13 * q^10 - 18 * q^11 - 8 * q^13 - 9 * q^14 - 18 * q^15 + 4 * q^16 - 14 * q^17 + 23 * q^18 - 6 * q^19 - 7 * q^20 + q^21 - 4 * q^22 - 22 * q^23 - 30 * q^24 + 13 * q^25 - 9 * q^26 - 18 * q^27 - 5 * q^28 - 12 * q^29 - 11 * q^30 - 21 * q^32 + 6 * q^33 + 7 * q^34 - 12 * q^35 - q^36 + 8 * q^37 + 7 * q^38 + q^39 + 11 * q^40 - 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 - 18 * q^46 - 18 * q^47 + q^48 - 2 * q^49 + 27 * q^50 + 2 * q^51 + q^52 - 6 * q^53 + 7 * q^54 - 28 * q^55 + 30 * q^56 + 17 * q^57 + 5 * q^58 - 4 * q^59 + 40 * q^60 - 30 * q^61 - 23 * q^63 + 9 * q^64 - 3 * q^65 + 10 * q^66 - 13 * q^67 - 30 * q^68 + 22 * q^69 - 39 * q^70 - q^71 + 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 - 33 * q^76 + 24 * q^77 - 8 * q^79 + 24 * q^80 - 28 * q^81 - 19 * q^82 - 39 * q^83 - 8 * q^84 + 26 * q^85 + 16 * q^86 - 15 * q^87 + 17 * q^88 - 27 * q^89 + 8 * q^90 - 16 * q^91 - 32 * q^92 + 22 * q^94 - 6 * q^95 + 12 * q^96 + 34 * q^97 + 10 * q^98 - 6 * q^99

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 $

$2$	−0.689493	−0.487545	−0.243772	−	0.969832i	$-0.578385\pi$
$2$	−0.689493	−0.487545	−0.243772	+	0.969832i	$0.578385\pi$
$3$	−0.902401	−0.521001	−0.260501	−	0.965474i	$-0.583888\pi$
$3$	−0.902401	−0.521001	−0.260501	+	0.965474i	$0.583888\pi$
$4$	−1.52460	−0.762300
$5$	3.70752	1.65805	0.829026	−	0.559210i	$-0.188896\pi$
$5$	3.70752	1.65805	0.829026	+	0.559210i	$0.188896\pi$
$6$	0.622199	0.254012
$7$	0.763394	0.288536	0.144268	−	0.989539i	$-0.453917\pi$
$7$	0.763394	0.288536	0.144268	+	0.989539i	$0.453917\pi$
$8$	2.43019	0.859200
$9$	−2.18567	−0.728558
$10$	−2.55631	−0.808375
$11$	−4.11562	−1.24091	−0.620453	−	0.784243i	$-0.713051\pi$
$11$	−4.11562	−1.24091	−0.620453	+	0.784243i	$0.713051\pi$
$12$	1.37580	0.397159
$13$	−2.90975	−0.807020	−0.403510	−	0.914975i	$-0.632210\pi$
$13$	−2.90975	−0.807020	−0.403510	+	0.914975i	$0.632210\pi$
$14$	−0.526355	−0.140674
$15$	−3.34567	−0.863847
$16$	1.37360	0.343401
$17$	1.30852	0.317364	0.158682	−	0.987330i	$-0.449276\pi$
$17$	1.30852	0.317364	0.158682	+	0.987330i	$0.449276\pi$
$18$	1.50701	0.355205
$19$	−3.79954	−0.871675	−0.435837	−	0.900025i	$-0.643548\pi$
$19$	−3.79954	−0.871675	−0.435837	+	0.900025i	$0.643548\pi$
$20$	−5.65248	−1.26393
$21$	−0.688887	−0.150328
$22$	2.83769	0.604998
$23$	−3.28296	−0.684544	−0.342272	−	0.939601i	$-0.611196\pi$
$23$	−3.28296	−0.684544	−0.342272	+	0.939601i	$0.611196\pi$
$24$	−2.19300	−0.447645
$25$	8.74568	1.74914
$26$	2.00625	0.393458
$27$	4.67956	0.900581
$28$	−1.16387	−0.219951
$29$	4.89563	0.909096	0.454548	−	0.890722i	$-0.349801\pi$
$29$	4.89563	0.909096	0.454548	+	0.890722i	$0.349801\pi$
$30$	2.30681	0.421164
$31$	0	0
$31$	0	0
$32$	−5.80746	−1.02662
$33$	3.71394	0.646514
$34$	−0.902218	−0.154729
$35$	2.83030	0.478407
$36$	3.33228	0.555379
$37$	−10.4128	−1.71185	−0.855925	−	0.517099i	$-0.827012\pi$
$37$	−10.4128	−1.71185	−0.855925	+	0.517099i	$0.827012\pi$
$38$	2.61976	0.424981
$39$	2.62576	0.420458
$40$	9.00995	1.42460
$41$	0.755946	0.118059	0.0590295	−	0.998256i	$-0.481199\pi$
$41$	0.755946	0.118059	0.0590295	+	0.998256i	$0.481199\pi$
$42$	0.474983	0.0732914
$43$	−7.15689	−1.09142	−0.545708	−	0.837976i	$-0.683739\pi$
$43$	−7.15689	−1.09142	−0.545708	+	0.837976i	$0.683739\pi$
$44$	6.27468	0.945943
$45$	−8.10342	−1.20799
$46$	2.26358	0.333746
$47$	−0.876067	−0.127787	−0.0638937	−	0.997957i	$-0.520352\pi$
$47$	−0.876067	−0.127787	−0.0638937	+	0.997957i	$0.520352\pi$
$48$	−1.23954	−0.178912
$49$	−6.41723	−0.916747
$50$	−6.03008	−0.852782
$51$	−1.18081	−0.165347
$52$	4.43621	0.615191
$53$	3.57570	0.491161	0.245580	−	0.969376i	$-0.421021\pi$
$53$	3.57570	0.491161	0.245580	+	0.969376i	$0.421021\pi$
$54$	−3.22652	−0.439074
$55$	−15.2587	−2.05749
$56$	1.85519	0.247910
$57$	3.42871	0.454144
$58$	−3.37550	−0.443225
$59$	0.927270	0.120720	0.0603601	−	0.998177i	$-0.480775\pi$
$59$	0.927270	0.120720	0.0603601	+	0.998177i	$0.480775\pi$
$60$	5.10080	0.658511
$61$	2.31704	0.296666	0.148333	−	0.988937i	$-0.452609\pi$
$61$	2.31704	0.296666	0.148333	+	0.988937i	$0.452609\pi$
$62$	0	0
$63$	−1.66853	−0.210215
$64$	1.25699	0.157124
$65$	−10.7879	−1.33808
$66$	−2.56074	−0.315205
$67$	−2.08690	−0.254955	−0.127478	−	0.991841i	$-0.540688\pi$
$67$	−2.08690	−0.254955	−0.127478	+	0.991841i	$0.540688\pi$
$68$	−1.99498	−0.241926
$69$	2.96254	0.356648
$70$	−1.95147	−0.233245
$71$	−7.73608	−0.918104	−0.459052	−	0.888409i	$-0.651811\pi$
$71$	−7.73608	−0.918104	−0.459052	+	0.888409i	$0.651811\pi$
$72$	−5.31159	−0.625977
$73$	−5.65748	−0.662158	−0.331079	−	0.943603i	$-0.607413\pi$
$73$	−5.65748	−0.662158	−0.331079	+	0.943603i	$0.607413\pi$
$74$	7.17954	0.834604
$75$	−7.89211	−0.911302
$76$	5.79278	0.664477
$77$	−3.14184	−0.358046
$78$	−1.81044	−0.204992
$79$	−14.0947	−1.58578	−0.792890	−	0.609365i	$-0.791424\pi$
$79$	−14.0947	−1.58578	−0.792890	+	0.609365i	$0.791424\pi$
$80$	5.09266	0.569377
$81$	2.33418	0.259354
$82$	−0.521219	−0.0575590
$83$	−14.1077	−1.54852	−0.774261	−	0.632866i	$-0.781878\pi$
$83$	−14.1077	−1.54852	−0.774261	+	0.632866i	$0.781878\pi$
$84$	1.05028	0.114595
$85$	4.85137	0.526205
$86$	4.93462	0.532114
$87$	−4.41782	−0.473640
$88$	−10.0017	−1.06619
$89$	−4.43481	−0.470089	−0.235045	−	0.971985i	$-0.575524\pi$
$89$	−4.43481	−0.470089	−0.235045	+	0.971985i	$0.575524\pi$
$90$	5.58725	0.588948
$91$	−2.22129	−0.232854
$92$	5.00520	0.521828
$93$	0	0
$94$	0.604042	0.0623021
$95$	−14.0869	−1.44528
$96$	5.24066	0.534872
$97$	−5.27764	−0.535863	−0.267932	−	0.963438i	$-0.586340\pi$
$97$	−5.27764	−0.535863	−0.267932	+	0.963438i	$0.586340\pi$
$98$	4.42463	0.446955
$99$	8.99540	0.904072
$100$	−13.3337	−1.33337
$101$	3.80743	0.378853	0.189427	−	0.981895i	$-0.439337\pi$
$101$	3.80743	0.378853	0.189427	+	0.981895i	$0.439337\pi$
$102$	0.814162	0.0806141
$103$	−6.24569	−0.615406	−0.307703	−	0.951482i	$-0.599560\pi$
$103$	−6.24569	−0.615406	−0.307703	+	0.951482i	$0.599560\pi$
$104$	−7.07124	−0.693392
$105$	−2.55406	−0.249251
$106$	−2.46542	−0.239463
$107$	2.32738	0.224997	0.112498	−	0.993652i	$-0.464115\pi$
$107$	2.32738	0.224997	0.112498	+	0.993652i	$0.464115\pi$
$108$	−7.13445	−0.686513
$109$	1.47683	0.141454	0.0707272	−	0.997496i	$-0.477468\pi$
$109$	1.47683	0.141454	0.0707272	+	0.997496i	$0.477468\pi$
$110$	10.5208	1.00312
$111$	9.39650	0.891877
$112$	1.04860	0.0990835
$113$	6.38055	0.600231	0.300116	−	0.953903i	$-0.402975\pi$
$113$	6.38055	0.600231	0.300116	+	0.953903i	$0.402975\pi$
$114$	−2.36407	−0.221415
$115$	−12.1716	−1.13501
$116$	−7.46388	−0.693004
$117$	6.35976	0.587960
$118$	−0.639346	−0.0588566
$119$	0.998919	0.0915708
$120$	−8.13059	−0.742218
$121$	5.93835	0.539850
$122$	−1.59758	−0.144638
$123$	−0.682166	−0.0615089
$124$	0	0
$125$	13.8872	1.24211
$126$	1.15044	0.102489
$127$	−1.43201	−0.127071	−0.0635354	−	0.997980i	$-0.520238\pi$
$127$	−1.43201	−0.127071	−0.0635354	+	0.997980i	$0.520238\pi$
$128$	10.7482	0.950019
$129$	6.45838	0.568629
$130$	7.43821	0.652374
$131$	6.29290	0.549813	0.274907	−	0.961471i	$-0.411353\pi$
$131$	6.29290	0.549813	0.274907	+	0.961471i	$0.411353\pi$
$132$	−5.66227	−0.492838
$133$	−2.90055	−0.251509
$134$	1.43890	0.124302
$135$	17.3495	1.49321
$136$	3.17996	0.272679
$137$	12.7499	1.08930	0.544649	−	0.838664i	$-0.316663\pi$
$137$	12.7499	1.08930	0.544649	+	0.838664i	$0.316663\pi$
$138$	−2.04265	−0.173882
$139$	18.7137	1.58728	0.793640	−	0.608388i	$-0.208184\pi$
$139$	18.7137	1.58728	0.793640	+	0.608388i	$0.208184\pi$
$140$	−4.31507	−0.364690
$141$	0.790563	0.0665774
$142$	5.33397	0.447617
$143$	11.9754	1.00144
$144$	−3.00225	−0.250187
$145$	18.1506	1.50733
$146$	3.90079	0.322832
$147$	5.79091	0.477627
$148$	15.8753	1.30494
$149$	−20.1353	−1.64955	−0.824774	−	0.565462i	$-0.808698\pi$
$149$	−20.1353	−1.64955	−0.824774	+	0.565462i	$0.808698\pi$
$150$	5.44155	0.444301
$151$	15.3725	1.25099	0.625497	−	0.780227i	$-0.284896\pi$
$151$	15.3725	1.25099	0.625497	+	0.780227i	$0.284896\pi$
$152$	−9.23359	−0.748943
$153$	−2.86001	−0.231218
$154$	2.16628	0.174564
$155$	0	0
$156$	−4.00324	−0.320515
$157$	15.1473	1.20888	0.604442	−	0.796649i	$-0.293396\pi$
$157$	15.1473	1.20888	0.604442	+	0.796649i	$0.293396\pi$
$158$	9.71821	0.773139
$159$	−3.22672	−0.255895
$160$	−21.5313	−1.70220
$161$	−2.50619	−0.197515
$162$	−1.60940	−0.126447
$163$	−1.04487	−0.0818405	−0.0409202	−	0.999162i	$-0.513029\pi$
$163$	−1.04487	−0.0818405	−0.0409202	+	0.999162i	$0.513029\pi$
$164$	−1.15251	−0.0899963
$165$	13.7695	1.07195
$166$	9.72717	0.754975
$167$	−11.2894	−0.873600	−0.436800	−	0.899559i	$-0.643888\pi$
$167$	−11.2894	−0.873600	−0.436800	+	0.899559i	$0.643888\pi$
$168$	−1.67412	−0.129161
$169$	−4.53335	−0.348719
$170$	−3.34499	−0.256549
$171$	8.30455	0.635065
$172$	10.9114	0.831986
$173$	−20.6527	−1.57019	−0.785097	−	0.619373i	$-0.787387\pi$
$173$	−20.6527	−1.57019	−0.785097	+	0.619373i	$0.787387\pi$
$174$	3.04606	0.230921
$175$	6.67640	0.504688
$176$	−5.65324	−0.426129
$177$	−0.836769	−0.0628954
$178$	3.05777	0.229190
$179$	−0.131662	−0.00984091	−0.00492045	−	0.999988i	$-0.501566\pi$
$179$	−0.131662	−0.00984091	−0.00492045	+	0.999988i	$0.501566\pi$
$180$	12.3545	0.920848
$181$	7.73199	0.574714	0.287357	−	0.957824i	$-0.407223\pi$
$181$	7.73199	0.574714	0.287357	+	0.957824i	$0.407223\pi$
$182$	1.53156	0.113527
$183$	−2.09090	−0.154564
$184$	−7.97820	−0.588161
$185$	−38.6056	−2.83834
$186$	0	0
$187$	−5.38539	−0.393819
$188$	1.33565	0.0974124
$189$	3.57234	0.259850
$190$	9.71279	0.704640
$191$	−21.1027	−1.52694	−0.763468	−	0.645846i	$-0.776505\pi$
$191$	−21.1027	−1.52694	−0.763468	+	0.645846i	$0.776505\pi$
$192$	−1.13431	−0.0818620
$193$	5.66324	0.407649	0.203824	−	0.979007i	$-0.434663\pi$
$193$	5.66324	0.407649	0.203824	+	0.979007i	$0.434663\pi$
$194$	3.63889	0.261257
$195$	9.73506	0.697142
$196$	9.78371	0.698836
$197$	15.9148	1.13388	0.566941	−	0.823758i	$-0.308127\pi$
$197$	15.9148	1.13388	0.566941	+	0.823758i	$0.308127\pi$
$198$	−6.20227	−0.440776
$199$	−4.26145	−0.302086	−0.151043	−	0.988527i	$-0.548263\pi$
$199$	−4.26145	−0.302086	−0.151043	+	0.988527i	$0.548263\pi$
$200$	21.2536	1.50286
$201$	1.88322	0.132832
$202$	−2.62520	−0.184708
$203$	3.73730	0.262307
$204$	1.80027	0.126044
$205$	2.80268	0.195748
$206$	4.30636	0.300038
$207$	7.17547	0.498730
$208$	−3.99685	−0.277131
$209$	15.6375	1.08167
$210$	1.76101	0.121521
$211$	−11.5083	−0.792263	−0.396131	−	0.918194i	$-0.629648\pi$
$211$	−11.5083	−0.792263	−0.396131	+	0.918194i	$0.629648\pi$
$212$	−5.45152	−0.374412
$213$	6.98105	0.478334
$214$	−1.60471	−0.109696
$215$	−26.5343	−1.80962
$216$	11.3722	0.773780
$217$	0	0
$218$	−1.01826	−0.0689654
$219$	5.10531	0.344985
$220$	23.2635	1.56842
$221$	−3.80748	−0.256119
$222$	−6.47882	−0.434830
$223$	9.42391	0.631072	0.315536	−	0.948914i	$-0.397816\pi$
$223$	9.42391	0.631072	0.315536	+	0.948914i	$0.397816\pi$
$224$	−4.43338	−0.296218
$225$	−19.1152	−1.27435
$226$	−4.39934	−0.292640
$227$	21.7630	1.44446	0.722231	−	0.691652i	$-0.243117\pi$
$227$	21.7630	1.44446	0.722231	+	0.691652i	$0.243117\pi$
$228$	−5.22741	−0.346194
$229$	16.9559	1.12048	0.560238	−	0.828331i	$-0.310709\pi$
$229$	16.9559	1.12048	0.560238	+	0.828331i	$0.310709\pi$
$230$	8.39224	0.553368
$231$	2.83520	0.186542
$232$	11.8973	0.781096
$233$	−9.83611	−0.644385	−0.322192	−	0.946674i	$-0.604420\pi$
$233$	−9.83611	−0.644385	−0.322192	+	0.946674i	$0.604420\pi$
$234$	−4.38501	−0.286657
$235$	−3.24803	−0.211878
$236$	−1.41372	−0.0920250
$237$	12.7191	0.826193
$238$	−0.688748	−0.0446449
$239$	0.590635	0.0382050	0.0191025	−	0.999818i	$-0.493919\pi$
$239$	0.590635	0.0382050	0.0191025	+	0.999818i	$0.493919\pi$
$240$	−4.59562	−0.296646
$241$	15.3704	0.990097	0.495049	−	0.868865i	$-0.335150\pi$
$241$	15.3704	0.990097	0.495049	+	0.868865i	$0.335150\pi$
$242$	−4.09445	−0.263201
$243$	−16.1450	−1.03570
$244$	−3.53256	−0.226149
$245$	−23.7920	−1.52001
$246$	0.470349	0.0299883
$247$	11.0557	0.703459
$248$	0	0
$249$	12.7308	0.806783
$250$	−9.57510	−0.605582
$251$	−6.05150	−0.381967	−0.190984	−	0.981593i	$-0.561168\pi$
$251$	−6.05150	−0.381967	−0.190984	+	0.981593i	$0.561168\pi$
$252$	2.54384	0.160247
$253$	13.5114	0.849455
$254$	0.987363	0.0619527
$255$	−4.37788	−0.274154
$256$	−9.92482	−0.620301
$257$	−4.52784	−0.282439	−0.141219	−	0.989978i	$-0.545102\pi$
$257$	−4.52784	−0.282439	−0.141219	+	0.989978i	$0.545102\pi$
$258$	−4.45301	−0.277232
$259$	−7.94906	−0.493930
$260$	16.4473	1.02002
$261$	−10.7002	−0.662329
$262$	−4.33891	−0.268059
$263$	−2.50886	−0.154703	−0.0773516	−	0.997004i	$-0.524646\pi$
$263$	−2.50886	−0.154703	−0.0773516	+	0.997004i	$0.524646\pi$
$264$	9.02557	0.555485
$265$	13.2570	0.814370
$266$	1.99991	0.122622
$267$	4.00198	0.244917
$268$	3.18168	0.194352
$269$	13.3398	0.813340	0.406670	−	0.913575i	$-0.366690\pi$
$269$	13.3398	0.813340	0.406670	+	0.913575i	$0.366690\pi$
$270$	−11.9624	−0.728007
$271$	13.8242	0.839759	0.419879	−	0.907580i	$-0.362072\pi$
$271$	13.8242	0.839759	0.419879	+	0.907580i	$0.362072\pi$
$272$	1.79739	0.108983
$273$	2.00449	0.121317
$274$	−8.79097	−0.531082
$275$	−35.9939	−2.17051
$276$	−4.51669	−0.271873
$277$	11.5707	0.695219	0.347609	−	0.937639i	$-0.386994\pi$
$277$	11.5707	0.695219	0.347609	+	0.937639i	$0.386994\pi$
$278$	−12.9030	−0.773870
$279$	0	0
$280$	6.87814	0.411048
$281$	−15.3993	−0.918648	−0.459324	−	0.888269i	$-0.651908\pi$
$281$	−15.3993	−0.918648	−0.459324	+	0.888269i	$0.651908\pi$
$282$	−0.545088	−0.0324595
$283$	−22.6957	−1.34912	−0.674560	−	0.738220i	$-0.735667\pi$
$283$	−22.6957	−1.34912	−0.674560	+	0.738220i	$0.735667\pi$
$284$	11.7944	0.699871
$285$	12.7120	0.752994
$286$	−8.25698	−0.488245
$287$	0.577084	0.0340642
$288$	12.6932	0.747955
$289$	−15.2878	−0.899280
$290$	−12.5147	−0.734890
$291$	4.76255	0.279185
$292$	8.62539	0.504763
$293$	12.4009	0.724466	0.362233	−	0.932088i	$-0.382014\pi$
$293$	12.4009	0.724466	0.362233	+	0.932088i	$0.382014\pi$
$294$	−3.99279	−0.232864
$295$	3.43787	0.200160
$296$	−25.3050	−1.47082
$297$	−19.2593	−1.11754
$298$	13.8831	0.804229
$299$	9.55259	0.552441
$300$	12.0323	0.694685
$301$	−5.46353	−0.314912
$302$	−10.5992	−0.609915
$303$	−3.43583	−0.197383
$304$	−5.21907	−0.299334
$305$	8.59046	0.491888
$306$	1.97195	0.112729
$307$	30.7200	1.75328	0.876641	−	0.481145i	$-0.159779\pi$
$307$	30.7200	1.75328	0.876641	+	0.481145i	$0.159779\pi$
$308$	4.79005	0.272938
$309$	5.63612	0.320628
$310$	0	0
$311$	2.38141	0.135037	0.0675187	−	0.997718i	$-0.478492\pi$
$311$	2.38141	0.135037	0.0675187	+	0.997718i	$0.478492\pi$
$312$	6.38109	0.361258
$313$	10.7456	0.607377	0.303688	−	0.952771i	$-0.401782\pi$
$313$	10.7456	0.607377	0.303688	+	0.952771i	$0.401782\pi$
$314$	−10.4439	−0.589385
$315$	−6.18610	−0.348547
$316$	21.4888	1.20884
$317$	8.74635	0.491244	0.245622	−	0.969366i	$-0.421008\pi$
$317$	8.74635	0.491244	0.245622	+	0.969366i	$0.421008\pi$
$318$	2.22480	0.124761
$319$	−20.1486	−1.12810
$320$	4.66033	0.260520
$321$	−2.10023	−0.117224
$322$	1.72800	0.0962977
$323$	−4.97179	−0.276638
$324$	−3.55869	−0.197705
$325$	−25.4477	−1.41159
$326$	0.720430	0.0399009
$327$	−1.33269	−0.0736979
$328$	1.83709	0.101436
$329$	−0.668784	−0.0368713
$330$	−9.49397	−0.522626
$331$	−32.3691	−1.77917	−0.889583	−	0.456773i	$-0.849005\pi$
$331$	−32.3691	−1.77917	−0.889583	+	0.456773i	$0.849005\pi$
$332$	21.5086	1.18044
$333$	22.7589	1.24718
$334$	7.78396	0.425919
$335$	−7.73721	−0.422729
$336$	−0.946258	−0.0516226
$337$	27.7338	1.51076	0.755378	−	0.655289i	$-0.227453\pi$
$337$	27.7338	1.51076	0.755378	+	0.655289i	$0.227453\pi$
$338$	3.12571	0.170016
$339$	−5.75781	−0.312721
$340$	−7.39640	−0.401126
$341$	0	0
$342$	−5.72593	−0.309623
$343$	−10.2426	−0.553050
$344$	−17.3926	−0.937745
$345$	10.9837	0.591342
$346$	14.2399	0.765540
$347$	−25.9161	−1.39125	−0.695624	−	0.718407i	$-0.744872\pi$
$347$	−25.9161	−1.39125	−0.695624	+	0.718407i	$0.744872\pi$
$348$	6.73541	0.361056
$349$	5.59393	0.299436	0.149718	−	0.988729i	$-0.452163\pi$
$349$	5.59393	0.299436	0.149718	+	0.988729i	$0.452163\pi$
$350$	−4.60333	−0.246058
$351$	−13.6163	−0.726787
$352$	23.9013	1.27394
$353$	11.6690	0.621077	0.310538	−	0.950561i	$-0.399491\pi$
$353$	11.6690	0.621077	0.310538	+	0.950561i	$0.399491\pi$
$354$	0.576946	0.0306643
$355$	−28.6817	−1.52226
$356$	6.76131	0.358349
$357$	−0.901426	−0.0477085
$358$	0.0907803	0.00479789
$359$	26.1998	1.38278	0.691388	−	0.722484i	$-0.257000\pi$
$359$	26.1998	1.38278	0.691388	+	0.722484i	$0.257000\pi$
$360$	−19.6928	−1.03790
$361$	−4.56348	−0.240183
$362$	−5.33115	−0.280199
$363$	−5.35877	−0.281263
$364$	3.38657	0.177505
$365$	−20.9752	−1.09789
$366$	1.44166	0.0753567
$367$	27.0146	1.41015	0.705076	−	0.709132i	$-0.250913\pi$
$367$	27.0146	1.41015	0.705076	+	0.709132i	$0.250913\pi$
$368$	−4.50948	−0.235073
$369$	−1.65225	−0.0860127
$370$	26.6183	1.38382
$371$	2.72967	0.141717
$372$	0	0
$373$	−12.4058	−0.642351	−0.321175	−	0.947020i	$-0.604078\pi$
$373$	−12.4058	−0.642351	−0.321175	+	0.947020i	$0.604078\pi$
$374$	3.71319	0.192004
$375$	−12.5318	−0.647139
$376$	−2.12900	−0.109795
$377$	−14.2451	−0.733658
$378$	−2.46311	−0.126688
$379$	−4.63901	−0.238290	−0.119145	−	0.992877i	$-0.538015\pi$
$379$	−4.63901	−0.238290	−0.119145	+	0.992877i	$0.538015\pi$
$380$	21.4768	1.10174
$381$	1.29225	0.0662040
$382$	14.5501	0.744450
$383$	−5.02133	−0.256578	−0.128289	−	0.991737i	$-0.540949\pi$
$383$	−5.02133	−0.256578	−0.128289	+	0.991737i	$0.540949\pi$
$384$	−9.69922	−0.494961
$385$	−11.6484	−0.593659
$386$	−3.90476	−0.198747
$387$	15.6426	0.795159
$388$	8.04629	0.408488
$389$	18.6018	0.943151	0.471575	−	0.881826i	$-0.343686\pi$
$389$	18.6018	0.943151	0.471575	+	0.881826i	$0.343686\pi$
$390$	−6.71225	−0.339888
$391$	−4.29583	−0.217249
$392$	−15.5951	−0.787670
$393$	−5.67872	−0.286453
$394$	−10.9731	−0.552819
$395$	−52.2564	−2.62930
$396$	−13.7144	−0.689174
$397$	32.5588	1.63408	0.817040	−	0.576581i	$-0.195614\pi$
$397$	32.5588	1.63408	0.817040	+	0.576581i	$0.195614\pi$
$398$	2.93824	0.147281
$399$	2.61746	0.131037
$400$	12.0131	0.600655
$401$	−12.3903	−0.618740	−0.309370	−	0.950942i	$-0.600118\pi$
$401$	−12.3903	−0.618740	−0.309370	+	0.950942i	$0.600118\pi$
$402$	−1.29847	−0.0647616
$403$	0	0
$404$	−5.80481	−0.288800
$405$	8.65402	0.430022
$406$	−2.57684	−0.127886
$407$	42.8551	2.12425
$408$	−2.86960	−0.142066
$409$	−3.44808	−0.170497	−0.0852484	−	0.996360i	$-0.527168\pi$
$409$	−3.44808	−0.170497	−0.0852484	+	0.996360i	$0.527168\pi$
$410$	−1.93243	−0.0954358
$411$	−11.5055	−0.567526
$412$	9.52218	0.469124
$413$	0.707872	0.0348321
$414$	−4.94744	−0.243153
$415$	−52.3046	−2.56753
$416$	16.8983	0.828506
$417$	−16.8873	−0.826975
$418$	−10.7819	−0.527361
$419$	−40.0471	−1.95643	−0.978216	−	0.207592i	$-0.933437\pi$
$419$	−40.0471	−1.95643	−0.978216	+	0.207592i	$0.933437\pi$
$420$	3.89392	0.190004
$421$	21.6844	1.05683	0.528417	−	0.848985i	$-0.322786\pi$
$421$	21.6844	1.05683	0.528417	+	0.848985i	$0.322786\pi$
$422$	7.93488	0.386264
$423$	1.91479	0.0931005
$424$	8.68963	0.422006
$425$	11.4439	0.555112
$426$	−4.81338	−0.233209
$427$	1.76881	0.0855989
$428$	−3.54833	−0.171515
$429$	−10.8066	−0.521750
$430$	18.2952	0.882273
$431$	−11.6207	−0.559748	−0.279874	−	0.960037i	$-0.590293\pi$
$431$	−11.6207	−0.559748	−0.279874	+	0.960037i	$0.590293\pi$
$432$	6.42786	0.309260
$433$	24.5964	1.18203	0.591015	−	0.806661i	$-0.298728\pi$
$433$	24.5964	1.18203	0.591015	+	0.806661i	$0.298728\pi$
$434$	0	0
$435$	−16.3791	−0.785320
$436$	−2.25157	−0.107831
$437$	12.4737	0.596700
$438$	−3.52008	−0.168196
$439$	18.1932	0.868316	0.434158	−	0.900837i	$-0.357046\pi$
$439$	18.1932	0.868316	0.434158	+	0.900837i	$0.357046\pi$
$440$	−37.0816	−1.76779
$441$	14.0260	0.667903
$442$	2.62523	0.124869
$443$	17.7603	0.843819	0.421909	−	0.906638i	$-0.361360\pi$
$443$	17.7603	0.843819	0.421909	+	0.906638i	$0.361360\pi$
$444$	−14.3259	−0.679878
$445$	−16.4421	−0.779432
$446$	−6.49772	−0.307676
$447$	18.1701	0.859417
$448$	0.959582	0.0453360
$449$	−9.19857	−0.434107	−0.217054	−	0.976160i	$-0.569645\pi$
$449$	−9.19857	−0.434107	−0.217054	+	0.976160i	$0.569645\pi$
$450$	13.1798	0.621301
$451$	−3.11119	−0.146500
$452$	−9.72778	−0.457556
$453$	−13.8721	−0.651769
$454$	−15.0054	−0.704241
$455$	−8.23545	−0.386084
$456$	8.33240	0.390200
$457$	−31.1999	−1.45947	−0.729735	−	0.683730i	$-0.760356\pi$
$457$	−31.1999	−1.45947	−0.729735	+	0.683730i	$0.760356\pi$
$458$	−11.6910	−0.546283
$459$	6.12331	0.285812
$460$	18.5568	0.865218
$461$	−6.66847	−0.310582	−0.155291	−	0.987869i	$-0.549631\pi$
$461$	−6.66847	−0.310582	−0.155291	+	0.987869i	$0.549631\pi$
$462$	−1.95485	−0.0909479
$463$	35.3185	1.64139	0.820694	−	0.571368i	$-0.193587\pi$
$463$	35.3185	1.64139	0.820694	+	0.571368i	$0.193587\pi$
$464$	6.72466	0.312184
$465$	0	0
$466$	6.78192	0.314167
$467$	35.9434	1.66326	0.831632	−	0.555327i	$-0.187407\pi$
$467$	35.9434	1.66326	0.831632	+	0.555327i	$0.187407\pi$
$468$	−9.69609	−0.448202
$469$	−1.59312	−0.0735637
$470$	2.23949	0.103300
$471$	−13.6689	−0.629830
$472$	2.25344	0.103723
$473$	29.4551	1.35434
$474$	−8.76972	−0.402806
$475$	−33.2296	−1.52468
$476$	−1.52295	−0.0698044
$477$	−7.81532	−0.357839
$478$	−0.407239	−0.0186267
$479$	33.2444	1.51898	0.759488	−	0.650521i	$-0.225450\pi$
$479$	33.2444	1.51898	0.759488	+	0.650521i	$0.225450\pi$
$480$	19.4298	0.886846
$481$	30.2986	1.38150
$482$	−10.5978	−0.482717
$483$	2.26159	0.102906
$484$	−9.05361	−0.411528
$485$	−19.5669	−0.888489
$486$	11.1319	0.504953
$487$	28.5154	1.29215	0.646077	−	0.763272i	$-0.276408\pi$
$487$	28.5154	1.29215	0.646077	+	0.763272i	$0.276408\pi$
$488$	5.63084	0.254896
$489$	0.942891	0.0426390
$490$	16.4044	0.741075
$491$	−27.9636	−1.26198	−0.630991	−	0.775790i	$-0.717351\pi$
$491$	−27.9636	−1.26198	−0.630991	+	0.775790i	$0.717351\pi$
$492$	1.04003	0.0468882
$493$	6.40605	0.288514
$494$	−7.62284	−0.342968
$495$	33.3506	1.49900
$496$	0	0
$497$	−5.90568	−0.264906
$498$	−8.77780	−0.393343
$499$	−41.3050	−1.84906	−0.924532	−	0.381104i	$-0.875544\pi$
$499$	−41.3050	−1.84906	−0.924532	+	0.381104i	$0.875544\pi$
$500$	−21.1724	−0.946857
$501$	10.1876	0.455147
$502$	4.17247	0.186226
$503$	−25.5860	−1.14082	−0.570412	−	0.821358i	$-0.693217\pi$
$503$	−25.5860	−1.14082	−0.570412	+	0.821358i	$0.693217\pi$
$504$	−4.05484	−0.180617
$505$	14.1161	0.628159
$506$	−9.31602	−0.414148
$507$	4.09090	0.181683
$508$	2.18325	0.0968660
$509$	−24.4678	−1.08452	−0.542258	−	0.840212i	$-0.682430\pi$
$509$	−24.4678	−1.08452	−0.542258	+	0.840212i	$0.682430\pi$
$510$	3.01852	0.133662
$511$	−4.31888	−0.191056
$512$	−14.6534	−0.647594
$513$	−17.7802	−0.785014
$514$	3.12191	0.137702
$515$	−23.1560	−1.02038
$516$	−9.84645	−0.433466
$517$	3.60556	0.158572
$518$	5.48082	0.240813
$519$	18.6370	0.818073
$520$	−26.2167	−1.14968
$521$	14.9656	0.655654	0.327827	−	0.944738i	$-0.393684\pi$
$521$	14.9656	0.655654	0.327827	+	0.944738i	$0.393684\pi$
$522$	7.37774	0.322915
$523$	−20.9656	−0.916763	−0.458381	−	0.888756i	$-0.651571\pi$
$523$	−20.9656	−0.916763	−0.458381	+	0.888756i	$0.651571\pi$
$524$	−9.59415	−0.419123
$525$	−6.02479	−0.262943
$526$	1.72984	0.0754247
$527$	0	0
$528$	5.10148	0.222014
$529$	−12.2222	−0.531399
$530$	−9.14059	−0.397042
$531$	−2.02671	−0.0879517
$532$	4.42217	0.191726
$533$	−2.19961	−0.0952759
$534$	−2.75933	−0.119408
$535$	8.62882	0.373056
$536$	−5.07155	−0.219058
$537$	0.118812	0.00512713
$538$	−9.19768	−0.396540
$539$	26.4109	1.13760
$540$	−26.4511	−1.13827
$541$	1.73130	0.0744345	0.0372172	−	0.999307i	$-0.488151\pi$
$541$	1.73130	0.0744345	0.0372172	+	0.999307i	$0.488151\pi$
$542$	−9.53167	−0.409420
$543$	−6.97735	−0.299427
$544$	−7.59920	−0.325813
$545$	5.47536	0.234539
$546$	−1.38208	−0.0591476
$547$	−13.1214	−0.561032	−0.280516	−	0.959849i	$-0.590506\pi$
$547$	−13.1214	−0.561032	−0.280516	+	0.959849i	$0.590506\pi$
$548$	−19.4385	−0.830372
$549$	−5.06429	−0.216139
$550$	24.8175	1.05822
$551$	−18.6012	−0.792436
$552$	7.19953	0.306432
$553$	−10.7598	−0.457554
$554$	−7.97795	−0.338950
$555$	34.8377	1.47878
$556$	−28.5310	−1.20998
$557$	−28.0246	−1.18744	−0.593721	−	0.804671i	$-0.702342\pi$
$557$	−28.0246	−1.18744	−0.593721	+	0.804671i	$0.702342\pi$
$558$	0	0
$559$	20.8248	0.880794
$560$	3.88770	0.164286
$561$	4.85978	0.205180
$562$	10.6177	0.447882
$563$	22.6519	0.954662	0.477331	−	0.878723i	$-0.341604\pi$
$563$	22.6519	0.954662	0.477331	+	0.878723i	$0.341604\pi$
$564$	−1.20529	−0.0507520
$565$	23.6560	0.995215
$566$	15.6485	0.657757
$567$	1.78190	0.0748328
$568$	−18.8001	−0.788836
$569$	−46.4420	−1.94695	−0.973475	−	0.228792i	$-0.926522\pi$
$569$	−46.4420	−1.94695	−0.973475	+	0.228792i	$0.926522\pi$
$570$	−8.76483	−0.367118
$571$	−12.4984	−0.523040	−0.261520	−	0.965198i	$-0.584224\pi$
$571$	−12.4984	−0.523040	−0.261520	+	0.965198i	$0.584224\pi$
$572$	−18.2577	−0.763395
$573$	19.0431	0.795536
$574$	−0.397896	−0.0166078
$575$	−28.7117	−1.19736
$576$	−2.74738	−0.114474
$577$	−30.4843	−1.26908	−0.634539	−	0.772891i	$-0.718810\pi$
$577$	−30.4843	−1.26908	−0.634539	+	0.772891i	$0.718810\pi$
$578$	10.5408	0.438440
$579$	−5.11051	−0.212385
$580$	−27.6725	−1.14904
$581$	−10.7697	−0.446804
$582$	−3.28374	−0.136115
$583$	−14.7162	−0.609485
$584$	−13.7487	−0.568926
$585$	23.5789	0.974869
$586$	−8.55030	−0.353210
$587$	33.6581	1.38922	0.694609	−	0.719387i	$-0.255577\pi$
$587$	33.6581	1.38922	0.694609	+	0.719387i	$0.255577\pi$
$588$	−8.82883	−0.364095
$589$	0	0
$590$	−2.37039	−0.0975872
$591$	−14.3615	−0.590754
$592$	−14.3030	−0.587851
$593$	−44.8879	−1.84333	−0.921663	−	0.387992i	$-0.873169\pi$
$593$	−44.8879	−1.84333	−0.921663	+	0.387992i	$0.873169\pi$
$594$	13.2791	0.544850
$595$	3.70351	0.151829
$596$	30.6983	1.25745
$597$	3.84554	0.157387
$598$	−6.58644	−0.269340
$599$	−19.5846	−0.800206	−0.400103	−	0.916470i	$-0.631026\pi$
$599$	−19.5846	−0.800206	−0.400103	+	0.916470i	$0.631026\pi$
$600$	−19.1793	−0.782991
$601$	30.4595	1.24247	0.621234	−	0.783625i	$-0.286632\pi$
$601$	30.4595	1.24247	0.621234	+	0.783625i	$0.286632\pi$
$602$	3.76706	0.153534
$603$	4.56127	0.185749
$604$	−23.4368	−0.953632
$605$	22.0165	0.895099
$606$	2.36898	0.0962332
$607$	−13.3746	−0.542857	−0.271428	−	0.962459i	$-0.587496\pi$
$607$	−13.3746	−0.542857	−0.271428	+	0.962459i	$0.587496\pi$
$608$	22.0657	0.894882
$609$	−3.37254	−0.136662
$610$	−5.92306	−0.239818
$611$	2.54914	0.103127
$612$	4.36036	0.176257
$613$	−5.19521	−0.209832	−0.104916	−	0.994481i	$-0.533457\pi$
$613$	−5.19521	−0.209832	−0.104916	+	0.994481i	$0.533457\pi$
$614$	−21.1812	−0.854804
$615$	−2.52914	−0.101985
$616$	−7.63526	−0.307633
$617$	−30.0131	−1.20828	−0.604140	−	0.796878i	$-0.706483\pi$
$617$	−30.0131	−1.20828	−0.604140	+	0.796878i	$0.706483\pi$
$618$	−3.88606	−0.156320
$619$	18.3260	0.736584	0.368292	−	0.929710i	$-0.379943\pi$
$619$	18.3260	0.736584	0.368292	+	0.929710i	$0.379943\pi$
$620$	0	0
$621$	−15.3628	−0.616487
$622$	−1.64197	−0.0658369
$623$	−3.38551	−0.135638
$624$	3.60676	0.144386
$625$	7.75849	0.310339
$626$	−7.40901	−0.296123
$627$	−14.1113	−0.563550
$628$	−23.0935	−0.921532
$629$	−13.6254	−0.543279
$630$	4.26527	0.169932
$631$	10.3352	0.411438	0.205719	−	0.978611i	$-0.434047\pi$
$631$	10.3352	0.411438	0.205719	+	0.978611i	$0.434047\pi$
$632$	−34.2528	−1.36250
$633$	10.3851	0.412770
$634$	−6.03054	−0.239503
$635$	−5.30922	−0.210690
$636$	4.91945	0.195069
$637$	18.6725	0.739833
$638$	13.8923	0.550001
$639$	16.9085	0.668892
$640$	39.8493	1.57518
$641$	0.101252	0.00399921	0.00199961	−	0.999998i	$-0.499364\pi$
$641$	0.101252	0.00399921	0.00199961	+	0.999998i	$0.499364\pi$
$642$	1.44810	0.0571518
$643$	−13.7118	−0.540742	−0.270371	−	0.962756i	$-0.587146\pi$
$643$	−13.7118	−0.540742	−0.270371	+	0.962756i	$0.587146\pi$
$644$	3.82094	0.150566
$645$	23.9446	0.942816
$646$	3.42801	0.134873
$647$	−10.8344	−0.425943	−0.212971	−	0.977058i	$-0.568314\pi$
$647$	−10.8344	−0.425943	−0.212971	+	0.977058i	$0.568314\pi$
$648$	5.67250	0.222837
$649$	−3.81629	−0.149803
$650$	17.5460	0.688212
$651$	0	0
$652$	1.59301	0.0623870
$653$	−24.2522	−0.949061	−0.474531	−	0.880239i	$-0.657382\pi$
$653$	−24.2522	−0.949061	−0.474531	+	0.880239i	$0.657382\pi$
$654$	0.918880	0.0359310
$655$	23.3310	0.911619
$656$	1.03837	0.0405415
$657$	12.3654	0.482420
$658$	0.461122	0.0179764
$659$	−8.53349	−0.332418	−0.166209	−	0.986091i	$-0.553153\pi$
$659$	−8.53349	−0.332418	−0.166209	+	0.986091i	$0.553153\pi$
$660$	−20.9930	−0.817150
$661$	37.8842	1.47352	0.736762	−	0.676152i	$-0.236354\pi$
$661$	37.8842	1.47352	0.736762	+	0.676152i	$0.236354\pi$
$662$	22.3183	0.867424
$663$	3.43587	0.133438
$664$	−34.2844	−1.33049
$665$	−10.7538	−0.417015
$666$	−15.6921	−0.608057
$667$	−16.0722	−0.622316
$668$	17.2118	0.665945
$669$	−8.50414	−0.328789
$670$	5.33475	0.206099
$671$	−9.53606	−0.368136
$672$	4.00069	0.154330
$673$	7.12011	0.274460	0.137230	−	0.990539i	$-0.456180\pi$
$673$	7.12011	0.274460	0.137230	+	0.990539i	$0.456180\pi$
$674$	−19.1223	−0.736562
$675$	40.9259	1.57524
$676$	6.91154	0.265829
$677$	48.0610	1.84713	0.923567	−	0.383438i	$-0.125260\pi$
$677$	48.0610	1.84713	0.923567	+	0.383438i	$0.125260\pi$
$678$	3.96997	0.152466
$679$	−4.02892	−0.154616
$680$	11.7897	0.452116
$681$	−19.6390	−0.752567
$682$	0	0
$683$	32.5731	1.24638	0.623188	−	0.782072i	$-0.285837\pi$
$683$	32.5731	1.24638	0.623188	+	0.782072i	$0.285837\pi$
$684$	−12.6611	−0.484110
$685$	47.2705	1.80611
$686$	7.06222	0.269637
$687$	−15.3010	−0.583770
$688$	−9.83073	−0.374793
$689$	−10.4044	−0.396376
$690$	−7.57317	−0.288306
$691$	27.2531	1.03676	0.518378	−	0.855152i	$-0.326536\pi$
$691$	27.2531	1.03676	0.518378	+	0.855152i	$0.326536\pi$
$692$	31.4871	1.19696
$693$	6.86704	0.260857
$694$	17.8689	0.678296
$695$	69.3815	2.63179
$696$	−10.7361	−0.406952
$697$	0.989173	0.0374676
$698$	−3.85698	−0.145989
$699$	8.87611	0.335725
$700$	−10.1788	−0.384724
$701$	8.48915	0.320631	0.160315	−	0.987066i	$-0.448749\pi$
$701$	8.48915	0.320631	0.160315	+	0.987066i	$0.448749\pi$
$702$	9.38837	0.354341
$703$	39.5638	1.49218
$704$	−5.17332	−0.194977
$705$	2.93103	0.110389
$706$	−8.04567	−0.302803
$707$	2.90657	0.109313
$708$	1.27574	0.0479452
$709$	−23.3861	−0.878283	−0.439142	−	0.898418i	$-0.644717\pi$
$709$	−23.3861	−0.878283	−0.439142	+	0.898418i	$0.644717\pi$
$710$	19.7758	0.742172
$711$	30.8064	1.15533
$712$	−10.7774	−0.403901
$713$	0	0
$714$	0.621526	0.0232600
$715$	44.3991	1.66043
$716$	0.200732	0.00750172
$717$	−0.532990	−0.0199049
$718$	−18.0646	−0.674165
$719$	12.9769	0.483956	0.241978	−	0.970282i	$-0.422204\pi$
$719$	12.9769	0.483956	0.241978	+	0.970282i	$0.422204\pi$
$720$	−11.1309	−0.414824
$721$	−4.76792	−0.177567
$722$	3.14649	0.117100
$723$	−13.8703	−0.515842
$724$	−11.7882	−0.438104
$725$	42.8156	1.59013
$726$	3.69483	0.137128
$727$	−12.4230	−0.460744	−0.230372	−	0.973103i	$-0.573994\pi$
$727$	−12.4230	−0.460744	−0.230372	+	0.973103i	$0.573994\pi$
$728$	−5.39814	−0.200068
$729$	7.56675	0.280250
$730$	14.4622	0.535272
$731$	−9.36496	−0.346376
$732$	3.18778	0.117824
$733$	−34.1573	−1.26163	−0.630815	−	0.775933i	$-0.717279\pi$
$733$	−34.1573	−1.26163	−0.630815	+	0.775933i	$0.717279\pi$
$734$	−18.6264	−0.687512
$735$	21.4699	0.791929
$736$	19.0657	0.702769
$737$	8.58888	0.316376
$738$	1.13921	0.0419351
$739$	−12.3749	−0.455219	−0.227610	−	0.973752i	$-0.573091\pi$
$739$	−12.3749	−0.455219	−0.227610	+	0.973752i	$0.573091\pi$
$740$	58.8580	2.16366
$741$	−9.97669	−0.366503
$742$	−1.88209	−0.0690936
$743$	−16.2455	−0.595990	−0.297995	−	0.954567i	$-0.596318\pi$
$743$	−16.2455	−0.595990	−0.297995	+	0.954567i	$0.596318\pi$
$744$	0	0
$745$	−74.6520	−2.73504
$746$	8.55374	0.313175
$747$	30.8348	1.12819
$748$	8.21057	0.300208
$749$	1.77671	0.0649196
$750$	8.64058	0.315509
$751$	−10.7883	−0.393670	−0.196835	−	0.980437i	$-0.563066\pi$
$751$	−10.7883	−0.393670	−0.196835	+	0.980437i	$0.563066\pi$
$752$	−1.20337	−0.0438823
$753$	5.46088	0.199006
$754$	9.82187	0.357691
$755$	56.9936	2.07421
$756$	−5.44640	−0.198083
$757$	41.1017	1.49387	0.746933	−	0.664900i	$-0.231526\pi$
$757$	41.1017	1.49387	0.746933	+	0.664900i	$0.231526\pi$
$758$	3.19857	0.116177
$759$	−12.1927	−0.442568
$760$	−34.2337	−1.24179
$761$	19.6605	0.712693	0.356347	−	0.934354i	$-0.384022\pi$
$761$	19.6605	0.712693	0.356347	+	0.934354i	$0.384022\pi$
$762$	−0.890998	−0.0322774
$763$	1.12740	0.0408146
$764$	32.1731	1.16398
$765$	−10.6035	−0.383371
$766$	3.46217	0.125093
$767$	−2.69812	−0.0974236
$768$	8.95617	0.323178
$769$	3.78834	0.136611	0.0683055	−	0.997664i	$-0.478241\pi$
$769$	3.78834	0.136611	0.0683055	+	0.997664i	$0.478241\pi$
$770$	8.03151	0.289435
$771$	4.08593	0.147151
$772$	−8.63417	−0.310750
$773$	−25.3696	−0.912480	−0.456240	−	0.889857i	$-0.650804\pi$
$773$	−25.3696	−0.912480	−0.456240	+	0.889857i	$0.650804\pi$
$774$	−10.7855	−0.387676
$775$	0	0
$776$	−12.8256	−0.460414
$777$	7.17323	0.257338
$778$	−12.8258	−0.459828
$779$	−2.87225	−0.102909
$780$	−14.8421	−0.531431
$781$	31.8388	1.13928
$782$	2.96194	0.105919
$783$	22.9094	0.818714
$784$	−8.81473	−0.314812
$785$	56.1588	2.00439
$786$	3.91543	0.139659
$787$	−25.9466	−0.924896	−0.462448	−	0.886646i	$-0.653029\pi$
$787$	−25.9466	−0.924896	−0.462448	+	0.886646i	$0.653029\pi$
$788$	−24.2637	−0.864359
$789$	2.26400	0.0806006
$790$	36.0304	1.28190
$791$	4.87087	0.173188
$792$	21.8605	0.776779
$793$	−6.74201	−0.239416
$794$	−22.4491	−0.796687
$795$	−11.9631	−0.424288
$796$	6.49701	0.230280
$797$	−18.5026	−0.655396	−0.327698	−	0.944782i	$-0.606273\pi$
$797$	−18.5026	−0.655396	−0.327698	+	0.944782i	$0.606273\pi$
$798$	−1.80472	−0.0638863
$799$	−1.14635	−0.0405551
$800$	−50.7902	−1.79570
$801$	9.69305	0.342487
$802$	8.54300	0.301664
$803$	23.2840	0.821676
$804$	−2.87115	−0.101258
$805$	−9.29174	−0.327491
$806$	0	0
$807$	−12.0378	−0.423751
$808$	9.25276	0.325511
$809$	36.7478	1.29199	0.645993	−	0.763344i	$-0.276444\pi$
$809$	36.7478	1.29199	0.645993	+	0.763344i	$0.276444\pi$
$810$	−5.96688	−0.209655
$811$	−39.4301	−1.38458	−0.692289	−	0.721620i	$-0.743398\pi$
$811$	−39.4301	−1.38458	−0.692289	+	0.721620i	$0.743398\pi$
$812$	−5.69788	−0.199956
$813$	−12.4749	−0.437515
$814$	−29.5483	−1.03567
$815$	−3.87387	−0.135696
$816$	−1.62197	−0.0567803
$817$	27.1929	0.951359
$818$	2.37743	0.0831248
$819$	4.85500	0.169648
$820$	−4.27297	−0.149218
$821$	1.48058	0.0516727	0.0258363	−	0.999666i	$-0.491775\pi$
$821$	1.48058	0.0516727	0.0258363	+	0.999666i	$0.491775\pi$
$822$	7.93298	0.276694
$823$	−38.8652	−1.35476	−0.677378	−	0.735635i	$-0.736884\pi$
$823$	−38.8652	−1.35476	−0.677378	+	0.735635i	$0.736884\pi$
$824$	−15.1782	−0.528758
$825$	32.4809	1.13084
$826$	−0.488073	−0.0169822
$827$	33.9363	1.18008	0.590040	−	0.807374i	$-0.299112\pi$
$827$	33.9363	1.18008	0.590040	+	0.807374i	$0.299112\pi$
$828$	−10.9397	−0.380182
$829$	16.5307	0.574135	0.287067	−	0.957910i	$-0.407320\pi$
$829$	16.5307	0.574135	0.287067	+	0.957910i	$0.407320\pi$
$830$	36.0636	1.25179
$831$	−10.4415	−0.362210
$832$	−3.65754	−0.126802
$833$	−8.39710	−0.290942
$834$	11.6437	0.403187
$835$	−41.8556	−1.44847
$836$	−23.8409	−0.824555
$837$	0	0
$838$	27.6122	0.953848
$839$	−54.0781	−1.86698	−0.933491	−	0.358600i	$-0.883254\pi$
$839$	−54.0781	−1.86698	−0.933491	+	0.358600i	$0.883254\pi$
$840$	−6.20684	−0.214156
$841$	−5.03279	−0.173545
$842$	−14.9512	−0.515254
$843$	13.8964	0.478617
$844$	17.5455	0.603942
$845$	−16.8075	−0.578194
$846$	−1.32024	−0.0453907
$847$	4.53330	0.155766
$848$	4.91160	0.168665
$849$	20.4806	0.702894
$850$	−7.89051	−0.270642
$851$	34.1847	1.17184
$852$	−10.6433	−0.364634
$853$	39.5762	1.35506	0.677532	−	0.735493i	$-0.263050\pi$
$853$	39.5762	1.35506	0.677532	+	0.735493i	$0.263050\pi$
$854$	−1.21958	−0.0417333
$855$	30.7893	1.05297
$856$	5.65598	0.193317
$857$	12.7250	0.434679	0.217340	−	0.976096i	$-0.430262\pi$
$857$	12.7250	0.434679	0.217340	+	0.976096i	$0.430262\pi$
$858$	7.45110	0.254376
$859$	−21.1543	−0.721777	−0.360888	−	0.932609i	$-0.617526\pi$
$859$	−21.1543	−0.721777	−0.360888	+	0.932609i	$0.617526\pi$
$860$	40.4542	1.37948
$861$	−0.520762	−0.0177475
$862$	8.01237	0.272902
$863$	9.33974	0.317928	0.158964	−	0.987284i	$-0.449185\pi$
$863$	9.33974	0.317928	0.158964	+	0.987284i	$0.449185\pi$
$864$	−27.1763	−0.924558
$865$	−76.5702	−2.60346
$866$	−16.9591	−0.576292
$867$	13.7957	0.468526
$868$	0	0
$869$	58.0085	1.96780
$870$	11.2933	0.382879
$871$	6.07235	0.205754
$872$	3.58896	0.121538
$873$	11.5352	0.390407
$874$	−8.60055	−0.290918
$875$	10.6014	0.358392
$876$	−7.78356	−0.262982
$877$	22.4353	0.757585	0.378792	−	0.925482i	$-0.376339\pi$
$877$	22.4353	0.757585	0.378792	+	0.925482i	$0.376339\pi$
$878$	−12.5441	−0.423343
$879$	−11.1905	−0.377448
$880$	−20.9595	−0.706543
$881$	−46.4315	−1.56432	−0.782158	−	0.623080i	$-0.785881\pi$
$881$	−46.4315	−1.56432	−0.782158	+	0.623080i	$0.785881\pi$
$882$	−9.67080	−0.325633
$883$	36.5396	1.22965	0.614827	−	0.788662i	$-0.289226\pi$
$883$	36.5396	1.22965	0.614827	+	0.788662i	$0.289226\pi$
$884$	5.80488	0.195239
$885$	−3.10234	−0.104284
$886$	−12.2456	−0.411400
$887$	28.6850	0.963150	0.481575	−	0.876405i	$-0.340065\pi$
$887$	28.6850	0.963150	0.481575	+	0.876405i	$0.340065\pi$
$888$	22.8353	0.766301
$889$	−1.09319	−0.0366644
$890$	11.3367	0.380008
$891$	−9.60662	−0.321834
$892$	−14.3677	−0.481066
$893$	3.32865	0.111389
$894$	−12.5282	−0.419005
$895$	−0.488140	−0.0163167
$896$	8.20514	0.274114
$897$	−8.62027	−0.287822
$898$	6.34235	0.211647
$899$	0	0
$900$	29.1430	0.971434
$901$	4.67889	0.155877
$902$	2.14514	0.0714254
$903$	4.93029	0.164070
$904$	15.5059	0.515719
$905$	28.6665	0.952906
$906$	9.56473	0.317767
$907$	−22.1896	−0.736794	−0.368397	−	0.929669i	$-0.620093\pi$
$907$	−22.1896	−0.736794	−0.368397	+	0.929669i	$0.620093\pi$
$908$	−33.1799	−1.10111
$909$	−8.32179	−0.276017
$910$	5.67829	0.188233
$911$	−28.8324	−0.955261	−0.477631	−	0.878561i	$-0.658504\pi$
$911$	−28.8324	−0.955261	−0.477631	+	0.878561i	$0.658504\pi$
$912$	4.70969	0.155953
$913$	58.0620	1.92157
$914$	21.5121	0.711557
$915$	−7.75204	−0.256275
$916$	−25.8510	−0.854139
$917$	4.80396	0.158641
$918$	−4.22198	−0.139346
$919$	48.0623	1.58543	0.792715	−	0.609592i	$-0.208667\pi$
$919$	48.0623	1.58543	0.792715	+	0.609592i	$0.208667\pi$
$920$	−29.5793	−0.975201
$921$	−27.7217	−0.913463
$922$	4.59786	0.151423
$923$	22.5101	0.740928
$924$	−4.32255	−0.142201
$925$	−91.0668	−2.99426
$926$	−24.3518	−0.800251
$927$	13.6510	0.448359
$928$	−28.4312	−0.933300
$929$	7.01617	0.230193	0.115097	−	0.993354i	$-0.463282\pi$
$929$	7.01617	0.230193	0.115097	+	0.993354i	$0.463282\pi$
$930$	0	0
$931$	24.3825	0.799105
$932$	14.9961	0.491214
$933$	−2.14899	−0.0703547
$934$	−24.7827	−0.810916
$935$	−19.9664	−0.652972
$936$	15.4554	0.505176
$937$	−12.8807	−0.420793	−0.210396	−	0.977616i	$-0.567475\pi$
$937$	−12.8807	−0.420793	−0.210396	+	0.977616i	$0.567475\pi$
$938$	1.09845	0.0358656
$939$	−9.69683	−0.316444
$940$	4.95195	0.161515
$941$	−50.0392	−1.63123	−0.815616	−	0.578593i	$-0.803602\pi$
$941$	−50.0392	−1.63123	−0.815616	+	0.578593i	$0.803602\pi$
$942$	9.42462	0.307071
$943$	−2.48174	−0.0808165
$944$	1.27370	0.0414555
$945$	13.2445	0.430844
$946$	−20.3090	−0.660304
$947$	51.8679	1.68548	0.842741	−	0.538320i	$-0.180941\pi$
$947$	51.8679	1.68548	0.842741	+	0.538320i	$0.180941\pi$
$948$	−19.3915	−0.629807
$949$	16.4619	0.534374
$950$	22.9115	0.743349
$951$	−7.89271	−0.255939
$952$	2.42756	0.0786777
$953$	18.7352	0.606893	0.303447	−	0.952848i	$-0.401863\pi$
$953$	18.7352	0.606893	0.303447	+	0.952848i	$0.401863\pi$
$954$	5.38861	0.174463
$955$	−78.2385	−2.53174
$956$	−0.900482	−0.0291237
$957$	18.1821	0.587743
$958$	−22.9218	−0.740569
$959$	9.73320	0.314301
$960$	−4.20549	−0.135731
$961$	0	0
$962$	−20.8907	−0.673542
$963$	−5.08690	−0.163923
$964$	−23.4338	−0.754751
$965$	20.9965	0.675902
$966$	−1.55935	−0.0501712
$967$	−47.7846	−1.53665	−0.768324	−	0.640061i	$-0.778909\pi$
$967$	−47.7846	−1.53665	−0.768324	+	0.640061i	$0.778909\pi$
$968$	14.4313	0.463839
$969$	4.48655	0.144129
$970$	13.4913	0.433178
$971$	−31.1007	−0.998068	−0.499034	−	0.866583i	$-0.666312\pi$
$971$	−31.1007	−0.998068	−0.499034	+	0.866583i	$0.666312\pi$
$972$	24.6147	0.789517
$973$	14.2860	0.457987
$974$	−19.6611	−0.629983
$975$	22.9641	0.735439
$976$	3.18269	0.101876
$977$	−22.0791	−0.706375	−0.353187	−	0.935553i	$-0.614902\pi$
$977$	−22.0791	−0.706375	−0.353187	+	0.935553i	$0.614902\pi$
$978$	−0.650117	−0.0207884
$979$	18.2520	0.583337
$980$	36.2733	1.15871
$981$	−3.22786	−0.103058
$982$	19.2807	0.615273
$983$	−37.5769	−1.19852	−0.599258	−	0.800556i	$-0.704538\pi$
$983$	−37.5769	−1.19852	−0.599258	+	0.800556i	$0.704538\pi$
$984$	−1.65779	−0.0528484
$985$	59.0044	1.88004
$986$	−4.41693	−0.140664
$987$	0.603511	0.0192100
$988$	−16.8555	−0.536246
$989$	23.4958	0.747122
$990$	−22.9950	−0.730829
$991$	−6.77397	−0.215182	−0.107591	−	0.994195i	$-0.534314\pi$
$991$	−6.77397	−0.215182	−0.107591	+	0.994195i	$0.534314\pi$
$992$	0	0
$993$	29.2099	0.926948
$994$	4.07192	0.129154
$995$	−15.7994	−0.500875
$996$	−19.4094	−0.615010
$997$	−29.5733	−0.936595	−0.468298	−	0.883571i	$-0.655132\pi$
$997$	−29.5733	−0.936595	−0.468298	+	0.883571i	$0.655132\pi$
$998$	28.4795	0.901502
$999$	−48.7272	−1.54166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.a.i.1.3		8
3.2	odd	2		8649.2.a.bf.1.6		8
31.2	even	5		961.2.d.p.531.1		16
31.3	odd	30		961.2.g.m.846.1		16
31.4	even	5		961.2.d.o.388.4		16
31.5	even	3		961.2.c.j.521.3		16
31.6	odd	6		961.2.c.i.439.3		16
31.7	even	15		31.2.g.a.18.2	✓	16
31.8	even	5		961.2.d.o.374.4		16
31.9	even	15		31.2.g.a.19.2	yes	16
31.10	even	15		961.2.g.s.844.1		16
31.11	odd	30		961.2.g.j.338.2		16
31.12	odd	30		961.2.g.n.547.1		16
31.13	odd	30		961.2.g.n.448.1		16
31.14	even	15		961.2.g.k.816.2		16
31.15	odd	10		961.2.d.q.628.1		16
31.16	even	5		961.2.d.p.628.1		16
31.17	odd	30		961.2.g.j.816.2		16
31.18	even	15		961.2.g.t.448.1		16
31.19	even	15		961.2.g.t.547.1		16
31.20	even	15		961.2.g.k.338.2		16
31.21	odd	30		961.2.g.m.844.1		16
31.22	odd	30		961.2.g.l.732.2		16
31.23	odd	10		961.2.d.n.374.4		16
31.24	odd	30		961.2.g.l.235.2		16
31.25	even	3		961.2.c.j.439.3		16
31.26	odd	6		961.2.c.i.521.3		16
31.27	odd	10		961.2.d.n.388.4		16
31.28	even	15		961.2.g.s.846.1		16
31.29	odd	10		961.2.d.q.531.1		16
31.30	odd	2		961.2.a.j.1.3		8
93.38	odd	30		279.2.y.c.235.1		16
93.71	odd	30		279.2.y.c.19.1		16
93.92	even	2		8649.2.a.be.1.6		8
124.7	odd	30		496.2.bg.c.49.1		16
124.71	odd	30		496.2.bg.c.81.1		16
155.7	odd	60		775.2.ck.a.49.3		32
155.9	even	30		775.2.bl.a.701.1		16
155.38	odd	60		775.2.ck.a.49.2		32
155.69	even	30		775.2.bl.a.576.1		16
155.102	odd	60		775.2.ck.a.174.2		32
155.133	odd	60		775.2.ck.a.174.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.7	even	15
31.2.g.a.19.2	yes	16	31.9	even	15
279.2.y.c.19.1		16	93.71	odd	30
279.2.y.c.235.1		16	93.38	odd	30
496.2.bg.c.49.1		16	124.7	odd	30
496.2.bg.c.81.1		16	124.71	odd	30
775.2.bl.a.576.1		16	155.69	even	30
775.2.bl.a.701.1		16	155.9	even	30
775.2.ck.a.49.2		32	155.38	odd	60
775.2.ck.a.49.3		32	155.7	odd	60
775.2.ck.a.174.2		32	155.102	odd	60
775.2.ck.a.174.3		32	155.133	odd	60
961.2.a.i.1.3		8	1.1	even	1	trivial
961.2.a.j.1.3		8	31.30	odd	2
961.2.c.i.439.3		16	31.6	odd	6
961.2.c.i.521.3		16	31.26	odd	6
961.2.c.j.439.3		16	31.25	even	3
961.2.c.j.521.3		16	31.5	even	3
961.2.d.n.374.4		16	31.23	odd	10
961.2.d.n.388.4		16	31.27	odd	10
961.2.d.o.374.4		16	31.8	even	5
961.2.d.o.388.4		16	31.4	even	5
961.2.d.p.531.1		16	31.2	even	5
961.2.d.p.628.1		16	31.16	even	5
961.2.d.q.531.1		16	31.29	odd	10
961.2.d.q.628.1		16	31.15	odd	10
961.2.g.j.338.2		16	31.11	odd	30
961.2.g.j.816.2		16	31.17	odd	30
961.2.g.k.338.2		16	31.20	even	15
961.2.g.k.816.2		16	31.14	even	15
961.2.g.l.235.2		16	31.24	odd	30
961.2.g.l.732.2		16	31.22	odd	30
961.2.g.m.844.1		16	31.21	odd	30
961.2.g.m.846.1		16	31.3	odd	30
961.2.g.n.448.1		16	31.13	odd	30
961.2.g.n.547.1		16	31.12	odd	30
961.2.g.s.844.1		16	31.10	even	15
961.2.g.s.846.1		16	31.28	even	15
961.2.g.t.448.1		16	31.18	even	15
961.2.g.t.547.1		16	31.19	even	15
8649.2.a.be.1.6		8	93.92	even	2
8649.2.a.bf.1.6		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q-0.689493 q^{2} -0.902401 q^{3} -1.52460 q^{4} +3.70752 q^{5} +0.622199 q^{6} +0.763394 q^{7} +2.43019 q^{8} -2.18567 q^{9} -2.55631 q^{10} -4.11562 q^{11} +1.37580 q^{12} -2.90975 q^{13} -0.526355 q^{14} -3.34567 q^{15} +1.37360 q^{16} +1.30852 q^{17} +1.50701 q^{18} -3.79954 q^{19} -5.65248 q^{20} -0.688887 q^{21} +2.83769 q^{22} -3.28296 q^{23} -2.19300 q^{24} +8.74568 q^{25} +2.00625 q^{26} +4.67956 q^{27} -1.16387 q^{28} +4.89563 q^{29} +2.30681 q^{30} -5.80746 q^{32} +3.71394 q^{33} -0.902218 q^{34} +2.83030 q^{35} +3.33228 q^{36} -10.4128 q^{37} +2.61976 q^{38} +2.62576 q^{39} +9.00995 q^{40} +0.755946 q^{41} +0.474983 q^{42} -7.15689 q^{43} +6.27468 q^{44} -8.10342 q^{45} +2.26358 q^{46} -0.876067 q^{47} -1.23954 q^{48} -6.41723 q^{49} -6.03008 q^{50} -1.18081 q^{51} +4.43621 q^{52} +3.57570 q^{53} -3.22652 q^{54} -15.2587 q^{55} +1.85519 q^{56} +3.42871 q^{57} -3.37550 q^{58} +0.927270 q^{59} +5.10080 q^{60} +2.31704 q^{61} -1.66853 q^{63} +1.25699 q^{64} -10.7879 q^{65} -2.56074 q^{66} -2.08690 q^{67} -1.99498 q^{68} +2.96254 q^{69} -1.95147 q^{70} -7.73608 q^{71} -5.31159 q^{72} -5.65748 q^{73} +7.17954 q^{74} -7.89211 q^{75} +5.79278 q^{76} -3.14184 q^{77} -1.81044 q^{78} -14.0947 q^{79} +5.09266 q^{80} +2.33418 q^{81} -0.521219 q^{82} -14.1077 q^{83} +1.05028 q^{84} +4.85137 q^{85} +4.93462 q^{86} -4.41782 q^{87} -10.0017 q^{88} -4.43481 q^{89} +5.58725 q^{90} -2.22129 q^{91} +5.00520 q^{92} +0.604042 q^{94} -14.0869 q^{95} +5.24066 q^{96} -5.27764 q^{97} +4.42463 q^{98} +8.99540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} + 8 q^{4} + 3 q^{5} - 11 q^{6} - 2 q^{7} - 9 q^{8} + 5 q^{9} - 13 q^{10} - 18 q^{11} - 8 q^{13} - 9 q^{14} - 18 q^{15} + 4 q^{16} - 14 q^{17} + 23 q^{18} - 6 q^{19} - 7 q^{20} + q^{21}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 + 8 * q^4 + 3 * q^5 - 11 * q^6 - 2 * q^7 - 9 * q^8 + 5 * q^9 - 13 * q^10 - 18 * q^11 - 8 * q^13 - 9 * q^14 - 18 * q^15 + 4 * q^16 - 14 * q^17 + 23 * q^18 - 6 * q^19 - 7 * q^20 + q^21 - 4 * q^22 - 22 * q^23 - 30 * q^24 + 13 * q^25 - 9 * q^26 - 18 * q^27 - 5 * q^28 - 12 * q^29 - 11 * q^30 - 21 * q^32 + 6 * q^33 + 7 * q^34 - 12 * q^35 - q^36 + 8 * q^37 + 7 * q^38 + q^39 + 11 * q^40 - 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 - 18 * q^46 - 18 * q^47 + q^48 - 2 * q^49 + 27 * q^50 + 2 * q^51 + q^52 - 6 * q^53 + 7 * q^54 - 28 * q^55 + 30 * q^56 + 17 * q^57 + 5 * q^58 - 4 * q^59 + 40 * q^60 - 30 * q^61 - 23 * q^63 + 9 * q^64 - 3 * q^65 + 10 * q^66 - 13 * q^67 - 30 * q^68 + 22 * q^69 - 39 * q^70 - q^71 + 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 - 33 * q^76 + 24 * q^77 - 8 * q^79 + 24 * q^80 - 28 * q^81 - 19 * q^82 - 39 * q^83 - 8 * q^84 + 26 * q^85 + 16 * q^86 - 15 * q^87 + 17 * q^88 - 27 * q^89 + 8 * q^90 - 16 * q^91 - 32 * q^92 + 22 * q^94 - 6 * q^95 + 12 * q^96 + 34 * q^97 + 10 * q^98 - 6 * q^99

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