LMFDB - Embedded newform 3.44.a.b.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3,44,Mod(1,3)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3.1"); S:= CuspForms(chi, 44); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 44, names="a")

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$35.1331186037$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 886516819907x^{2} - 42308083143723387x + 94580276745082867224894 $ x^4 - x^3 - 886516819907x^2 - 42308083143723387x + 94580276745082867224894
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 11 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-388484.$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.91590e6 q^{2} -1.04604e10 q^{3} -5.12540e12 q^{4} +2.05854e15 q^{5} +2.00410e16 q^{6} +1.37114e18 q^{7} +2.66723e19 q^{8} +1.09419e20 q^{9} -3.94396e21 q^{10} -2.95641e22 q^{11} +5.36135e22 q^{12} +4.85026e23 q^{13} -2.62698e24 q^{14} -2.15330e25 q^{15} -6.01799e24 q^{16} +2.08153e26 q^{17} -2.09636e26 q^{18} -1.07725e27 q^{19} -1.05508e28 q^{20} -1.43426e28 q^{21} +5.66420e28 q^{22} -2.47106e29 q^{23} -2.79001e29 q^{24} +3.10071e30 q^{25} -9.29263e29 q^{26} -1.14456e30 q^{27} -7.02766e30 q^{28} +1.39089e31 q^{29} +4.12553e31 q^{30} +1.48976e31 q^{31} -2.23082e32 q^{32} +3.09251e32 q^{33} -3.98801e32 q^{34} +2.82255e33 q^{35} -5.60816e32 q^{36} +9.02009e33 q^{37} +2.06390e33 q^{38} -5.07354e33 q^{39} +5.49059e34 q^{40} +5.58080e34 q^{41} +2.74791e34 q^{42} -2.06648e35 q^{43} +1.51528e35 q^{44} +2.25243e35 q^{45} +4.73431e35 q^{46} +6.46223e35 q^{47} +6.29503e34 q^{48} -3.03780e35 q^{49} -5.94067e36 q^{50} -2.17735e36 q^{51} -2.48595e36 q^{52} -4.21095e36 q^{53} +2.19287e36 q^{54} -6.08589e37 q^{55} +3.65715e37 q^{56} +1.12684e37 q^{57} -2.66481e37 q^{58} +4.40127e37 q^{59} +1.10366e38 q^{60} +4.53571e37 q^{61} -2.85424e37 q^{62} +1.50029e38 q^{63} +4.80338e38 q^{64} +9.98445e38 q^{65} -5.92495e38 q^{66} -1.64891e37 q^{67} -1.06687e39 q^{68} +2.58481e39 q^{69} -5.40774e39 q^{70} +6.75118e39 q^{71} +2.91845e39 q^{72} -5.28077e39 q^{73} -1.72816e40 q^{74} -3.24346e40 q^{75} +5.52132e39 q^{76} -4.05366e40 q^{77} +9.72042e39 q^{78} +1.01508e41 q^{79} -1.23883e40 q^{80} +1.19725e40 q^{81} -1.06923e41 q^{82} +2.11545e41 q^{83} +7.35118e40 q^{84} +4.28491e41 q^{85} +3.95917e41 q^{86} -1.45492e41 q^{87} -7.88542e41 q^{88} -7.34681e41 q^{89} -4.31545e41 q^{90} +6.65040e41 q^{91} +1.26652e42 q^{92} -1.55834e41 q^{93} -1.23810e42 q^{94} -2.21755e42 q^{95} +2.33351e42 q^{96} -6.37472e42 q^{97} +5.82013e41 q^{98} -3.23487e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5} - 17\!\cdots\!42 q^{6} + 11\!\cdots\!28 q^{7} + 77\!\cdots\!48 q^{8} + 43\!\cdots\!36 q^{9} + 53\!\cdots\!60 q^{10}+ \cdots + 95\!\cdots\!64 q^{99}+O(q^{100}) $ 4 * q + 1660014 * q^2 - 41841412812 * q^3 + 29333750564548 * q^4 + 1650650807536920 * q^5 - 17364332761924842 * q^6 + 114481425784209728 * q^7 + 77966588660971173048 * q^8 + 437675956526049436836 * q^9 + 5359044979781953498260 * q^10 + 8715200555107127298096 * q^11 - 306841391673872730047244 * q^12 - 1622373819341917660395496 * q^13 - 13467578670319198438149408 * q^14 - 17266390461653357662754760 * q^15 + 265331272220473559715915280 * q^16 + 293411853143037894856883976 * q^17 + 181637053824158357459968926 * q^18 - 2594414378517928782354874288 * q^19 + 8558701143076231384453792920 * q^20 - 1197516148885865015108558784 * q^21 + 74078936455805689993083157032 * q^22 - 165719576853043327961325838944 * q^23 - 815558055426773291083314072744 * q^24 + 2162829068891925341689803823900 * q^25 + 6101006421154528454709899598228 * q^26 - 4578245093723349979543798785708 * q^27 - 41688560653908286820790912158656 * q^28 + 50103930548121691368807724902264 * q^29 - 56057503319283227517121045926780 * q^30 + 153232269806257085529351412219424 * q^31 + 1375373155850513577371148105862368 * q^32 - 91164076041402217040767229401488 * q^33 + 60331877005992911765859543576156 * q^34 + 794758271825314756362531708950400 * q^35 + 3209669334208772143164043116722532 * q^36 + 19599702088800583695304816898379128 * q^37 + 30934350335669500918957603769116056 * q^38 + 16970603177616571751080292830373688 * q^39 + 196041911393456394134889832442905680 * q^40 - 9038336825299507042215563101837656 * q^41 + 140875629680727908414888757365353824 * q^42 + 57884775638210824781567117092305200 * q^43 + 1103928490692495293822086256175019824 * q^44 + 180612542769804348503301347569496280 * q^45 + 718247490543964330689612210436911024 * q^46 + 489795556049192314087538359958202240 * q^47 - 2775458823227495522551186169224641840 * q^48 - 4317642451006561098818513062358614620 * q^49 - 5579808201219996041105683525421159550 * q^50 - 3069191617822942060616583524950975128 * q^51 - 13582094185786578557618520483683206504 * q^52 - 40271515633256644720413455555285829864 * q^53 - 1899987737753018273235604899364569978 * q^54 - 47661104270181626262923295497298490080 * q^55 - 117390605534482290403396341738920952960 * q^56 + 27138490754239270731431699141143144464 * q^57 + 166036404448317657164763132092855468772 * q^58 - 31284936358538459187079576876991825232 * q^59 - 89527036915497218235540357176220722760 * q^60 - 246678251415393769778200255087667843560 * q^61 + 1447587501085892804433014348598690126576 * q^62 + 12526441883642482992216456268928185152 * q^63 + 3779239307999191671459925914328934335552 * q^64 + 3201204112021109289173748012488728936080 * q^65 - 774891840230320517264772449505033173496 * q^66 + 1029262961963280586877382927523715757776 * q^67 - 5728258265472538567897226405540492998008 * q^68 + 1733485306534536435938034199524532537632 * q^69 - 13998939704532003940217885479727831428800 * q^70 - 7158914166122718301934674138622261107872 * q^71 + 8531025317315899527338195700682675399032 * q^72 + 5436935716056938749789214886435330158696 * q^73 - 39560290302967463129010858736787279461788 * q^74 - 22623955978325158908781808861774012951700 * q^75 - 84965301579645016687884089536788004332208 * q^76 - 70649133554843036086189895413395482145024 * q^77 - 63818682059047338679179338698132672924284 * q^78 - 18459961314698254348045108075380001958560 * q^79 + 422317828506146509768424873205600266179680 * q^80 + 47890060730248079154410960106868188422724 * q^81 + 147229844429377279789779107991029019615756 * q^82 + 207863929126228047172838511060419328637008 * q^83 + 436077068964569322514102904992088933775168 * q^84 + 221112002042063917840135331898684555973680 * q^85 + 458138780643704418519204317947537057045416 * q^86 - 524104810391934279943485339472540094351592 * q^87 + 1517878779794169852250121294325123418262688 * q^88 - 442176536724138726190556195414134338798168 * q^89 + 586381284398047440622894870098903276476340 * q^90 - 241286657628373017846026300207834298513536 * q^91 - 501856507576284139621951265540431125198432 * q^92 - 1602863664270841494058395995322025177215072 * q^93 - 12731451681111622228496468053131446537940672 * q^94 - 877953040109009235535219131018818763586080 * q^95 - 14386888996121137888249277408944804185964704 * q^96 - 5068444705076967721898551548017617825231864 * q^97 + 6262356698119668842821753019159492533814046 * q^98 + 953608434818217241633690669647290773766064 * 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 $

$2$	−1.91590e6	−0.645995	−0.322997	−	0.946400i	$-0.604691\pi$
$2$	−1.91590e6	−0.645995	−0.322997	+	0.946400i	$0.604691\pi$
$3$	−1.04604e10	−0.577350
$3$	−1.04604e10	−0.577350
$4$	−5.12540e12	−0.582691
$5$	2.05854e15	1.93065	0.965326	−	0.261047i	$-0.0840678\pi$
$5$	2.05854e15	1.93065	0.965326	+	0.261047i	$0.0840678\pi$
$6$	2.00410e16	0.372965
$7$	1.37114e18	0.927844	0.463922	−	0.885876i	$-0.346442\pi$
$7$	1.37114e18	0.927844	0.463922	+	0.885876i	$0.346442\pi$
$8$	2.66723e19	1.02241
$9$	1.09419e20	0.333333
$10$	−3.94396e21	−1.24719
$11$	−2.95641e22	−1.20454	−0.602271	−	0.798292i	$-0.705737\pi$
$11$	−2.95641e22	−1.20454	−0.602271	+	0.798292i	$0.705737\pi$
$12$	5.36135e22	0.336417
$13$	4.85026e23	0.544481	0.272241	−	0.962229i	$-0.412235\pi$
$13$	4.85026e23	0.544481	0.272241	+	0.962229i	$0.412235\pi$
$14$	−2.62698e24	−0.599383
$15$	−2.15330e25	−1.11466
$16$	−6.01799e24	−0.0777807
$17$	2.08153e26	0.730686	0.365343	−	0.930873i	$-0.380952\pi$
$17$	2.08153e26	0.730686	0.365343	+	0.930873i	$0.380952\pi$
$18$	−2.09636e26	−0.215332
$19$	−1.07725e27	−0.346029	−0.173015	−	0.984919i	$-0.555351\pi$
$19$	−1.07725e27	−0.346029	−0.173015	+	0.984919i	$0.555351\pi$
$20$	−1.05508e28	−1.12497
$21$	−1.43426e28	−0.535691
$22$	5.66420e28	0.778128
$23$	−2.47106e29	−1.30537	−0.652686	−	0.757628i	$-0.726358\pi$
$23$	−2.47106e29	−1.30537	−0.652686	+	0.757628i	$0.726358\pi$
$24$	−2.79001e29	−0.590289
$25$	3.10071e30	2.72742
$26$	−9.29263e29	−0.351732
$27$	−1.14456e30	−0.192450
$28$	−7.02766e30	−0.540646
$29$	1.39089e31	0.503195	0.251597	−	0.967832i	$-0.419044\pi$
$29$	1.39089e31	0.503195	0.251597	+	0.967832i	$0.419044\pi$
$30$	4.12553e31	0.720066
$31$	1.48976e31	0.128481	0.0642406	−	0.997934i	$-0.479537\pi$
$31$	1.48976e31	0.128481	0.0642406	+	0.997934i	$0.479537\pi$
$32$	−2.23082e32	−0.972164
$33$	3.09251e32	0.695443
$34$	−3.98801e32	−0.472020
$35$	2.82255e33	1.79134
$36$	−5.60816e32	−0.194230
$37$	9.02009e33	1.73330	0.866651	−	0.498916i	$-0.166268\pi$
$37$	9.02009e33	1.73330	0.866651	+	0.498916i	$0.166268\pi$
$38$	2.06390e33	0.223533
$39$	−5.07354e33	−0.314356
$40$	5.49059e34	1.97392
$41$	5.58080e34	1.17989	0.589947	−	0.807442i	$-0.299148\pi$
$41$	5.58080e34	1.17989	0.589947	+	0.807442i	$0.299148\pi$
$42$	2.74791e34	0.346054
$43$	−2.06648e35	−1.56913	−0.784565	−	0.620047i	$-0.787113\pi$
$43$	−2.06648e35	−1.56913	−0.784565	+	0.620047i	$0.787113\pi$
$44$	1.51528e35	0.701876
$45$	2.25243e35	0.643551
$46$	4.73431e35	0.843264
$47$	6.46223e35	0.724901	0.362450	−	0.932003i	$-0.381940\pi$
$47$	6.46223e35	0.724901	0.362450	+	0.932003i	$0.381940\pi$
$48$	6.29503e34	0.0449067
$49$	−3.03780e35	−0.139105
$50$	−5.94067e36	−1.76190
$51$	−2.17735e36	−0.421862
$52$	−2.48595e36	−0.317264
$53$	−4.21095e36	−0.356820	−0.178410	−	0.983956i	$-0.557095\pi$
$53$	−4.21095e36	−0.356820	−0.178410	+	0.983956i	$0.557095\pi$
$54$	2.19287e36	0.124322
$55$	−6.08589e37	−2.32555
$56$	3.65715e37	0.948637
$57$	1.12684e37	0.199780
$58$	−2.66481e37	−0.325061
$59$	4.40127e37	0.371757	0.185879	−	0.982573i	$-0.440487\pi$
$59$	4.40127e37	0.371757	0.185879	+	0.982573i	$0.440487\pi$
$60$	1.10366e38	0.649504
$61$	4.53571e37	0.187091	0.0935457	−	0.995615i	$-0.470180\pi$
$61$	4.53571e37	0.187091	0.0935457	+	0.995615i	$0.470180\pi$
$62$	−2.85424e37	−0.0829982
$63$	1.50029e38	0.309281
$64$	4.80338e38	0.705794
$65$	9.98445e38	1.05120
$66$	−5.92495e38	−0.449252
$67$	−1.64891e37	−0.00904878	−0.00452439	−	0.999990i	$-0.501440\pi$
$67$	−1.64891e37	−0.00904878	−0.00452439	+	0.999990i	$0.501440\pi$
$68$	−1.06687e39	−0.425764
$69$	2.58481e39	0.753657
$70$	−5.40774e39	−1.15720
$71$	6.75118e39	1.06494	0.532470	−	0.846449i	$-0.321264\pi$
$71$	6.75118e39	1.06494	0.532470	+	0.846449i	$0.321264\pi$
$72$	2.91845e39	0.340803
$73$	−5.28077e39	−0.458412	−0.229206	−	0.973378i	$-0.573613\pi$
$73$	−5.28077e39	−0.458412	−0.229206	+	0.973378i	$0.573613\pi$
$74$	−1.72816e40	−1.11970
$75$	−3.24346e40	−1.57468
$76$	5.52132e39	0.201628
$77$	−4.05366e40	−1.11763
$78$	9.72042e39	0.203073
$79$	1.01508e41	1.61257	0.806286	−	0.591526i	$-0.201474\pi$
$79$	1.01508e41	1.61257	0.806286	+	0.591526i	$0.201474\pi$
$80$	−1.23883e40	−0.150167
$81$	1.19725e40	0.111111
$82$	−1.06923e41	−0.762206
$83$	2.11545e41	1.16205	0.581024	−	0.813886i	$-0.302652\pi$
$83$	2.11545e41	1.16205	0.581024	+	0.813886i	$0.302652\pi$
$84$	7.35118e40	0.312142
$85$	4.28491e41	1.41070
$86$	3.95917e41	1.01365
$87$	−1.45492e41	−0.290520
$88$	−7.88542e41	−1.23154
$89$	−7.34681e41	−0.899940	−0.449970	−	0.893044i	$-0.648565\pi$
$89$	−7.34681e41	−0.899940	−0.449970	+	0.893044i	$0.648565\pi$
$90$	−4.31545e41	−0.415730
$91$	6.65040e41	0.505194
$92$	1.26652e42	0.760629
$93$	−1.55834e41	−0.0741787
$94$	−1.23810e42	−0.468282
$95$	−2.21755e42	−0.668062
$96$	2.33351e42	0.561279
$97$	−6.37472e42	−1.22707	−0.613534	−	0.789668i	$-0.710253\pi$
$97$	−6.37472e42	−1.22707	−0.613534	+	0.789668i	$0.710253\pi$
$98$	5.82013e41	0.0898611
$99$	−3.23487e42	−0.401514
$100$	−1.58924e43	−1.58924
$101$	1.97674e43	1.59602	0.798012	−	0.602642i	$-0.205885\pi$
$101$	1.97674e43	1.59602	0.798012	+	0.602642i	$0.205885\pi$
$102$	4.17160e42	0.272521
$103$	2.37782e43	1.25944	0.629721	−	0.776821i	$-0.283169\pi$
$103$	2.37782e43	1.25944	0.629721	+	0.776821i	$0.283169\pi$
$104$	1.29367e43	0.556683
$105$	−2.95249e43	−1.03423
$106$	8.06778e42	0.230504
$107$	1.70071e41	0.00397081	0.00198541	−	0.999998i	$-0.499368\pi$
$107$	1.70071e41	0.00397081	0.00198541	+	0.999998i	$0.499368\pi$
$108$	5.86634e42	0.112139
$109$	5.49545e43	0.861656	0.430828	−	0.902434i	$-0.358222\pi$
$109$	5.49545e43	0.861656	0.430828	+	0.902434i	$0.358222\pi$
$110$	1.16600e44	1.50229
$111$	−9.43534e43	−1.00072
$112$	−8.25153e42	−0.0721683
$113$	5.69482e43	0.411427	0.205714	−	0.978612i	$-0.434048\pi$
$113$	5.69482e43	0.411427	0.205714	+	0.978612i	$0.434048\pi$
$114$	−2.15891e43	−0.129057
$115$	−5.08677e44	−2.52022
$116$	−7.12888e43	−0.293207
$117$	5.30710e43	0.181494
$118$	−8.43241e43	−0.240153
$119$	2.85408e44	0.677963
$120$	−5.74335e44	−1.13964
$121$	2.71636e44	0.450922
$122$	−8.68999e43	−0.120860
$123$	−5.83771e44	−0.681213
$124$	−7.63561e43	−0.0748648
$125$	4.04265e45	3.33504
$126$	−2.87442e44	−0.199794
$127$	−1.89728e45	−1.11263	−0.556316	−	0.830971i	$-0.687786\pi$
$127$	−1.89728e45	−1.11263	−0.556316	+	0.830971i	$0.687786\pi$
$128$	1.04197e45	0.516225
$129$	2.16161e45	0.905937
$130$	−1.91292e45	−0.679072
$131$	1.03358e45	0.311179	0.155590	−	0.987822i	$-0.450272\pi$
$131$	1.03358e45	0.311179	0.155590	+	0.987822i	$0.450272\pi$
$132$	−1.58504e45	−0.405228
$133$	−1.47706e45	−0.321061
$134$	3.15916e43	0.00584546
$135$	−2.35612e45	−0.371554
$136$	5.55191e45	0.747061
$137$	7.28740e45	0.837684	0.418842	−	0.908059i	$-0.362436\pi$
$137$	7.28740e45	0.837684	0.418842	+	0.908059i	$0.362436\pi$
$138$	−4.95226e45	−0.486859
$139$	−6.85030e44	−0.0576622	−0.0288311	−	0.999584i	$-0.509178\pi$
$139$	−6.85030e44	−0.0576622	−0.0288311	+	0.999584i	$0.509178\pi$
$140$	−1.44667e46	−1.04380
$141$	−6.75972e45	−0.418522
$142$	−1.29346e46	−0.687945
$143$	−1.43394e46	−0.655851
$144$	−6.58482e44	−0.0259269
$145$	2.86320e46	0.971494
$146$	1.01175e46	0.296132
$147$	3.17764e45	0.0803123
$148$	−4.62316e46	−1.00998
$149$	−8.50711e45	−0.160797	−0.0803984	−	0.996763i	$-0.525619\pi$
$149$	−8.50711e45	−0.160797	−0.0803984	+	0.996763i	$0.525619\pi$
$150$	6.21415e46	1.01723
$151$	8.58237e46	1.21788	0.608938	−	0.793218i	$-0.291596\pi$
$151$	8.58237e46	1.21788	0.608938	+	0.793218i	$0.291596\pi$
$152$	−2.87326e46	−0.353784
$153$	2.27759e46	0.243562
$154$	7.76643e46	0.721982
$155$	3.06673e46	0.248053
$156$	2.60039e46	0.183173
$157$	2.17438e47	1.33504	0.667519	−	0.744593i	$-0.267356\pi$
$157$	2.17438e47	1.33504	0.667519	+	0.744593i	$0.267356\pi$
$158$	−1.94480e47	−1.04171
$159$	4.40480e46	0.206010
$160$	−4.59223e47	−1.87691
$161$	−3.38818e47	−1.21118
$162$	−2.29382e46	−0.0717772
$163$	2.10328e47	0.576584	0.288292	−	0.957543i	$-0.406913\pi$
$163$	2.10328e47	0.576584	0.288292	+	0.957543i	$0.406913\pi$
$164$	−2.86038e47	−0.687514
$165$	6.36605e47	1.34266
$166$	−4.05300e47	−0.750677
$167$	4.19368e47	0.682639	0.341320	−	0.939947i	$-0.389126\pi$
$167$	4.19368e47	0.682639	0.341320	+	0.939947i	$0.389126\pi$
$168$	−3.82551e47	−0.547696
$169$	−5.58281e47	−0.703540
$170$	−8.20948e47	−0.911305
$171$	−1.17871e47	−0.115343
$172$	1.05915e48	0.914317
$173$	−2.43273e47	−0.185397	−0.0926983	−	0.995694i	$-0.529549\pi$
$173$	−2.43273e47	−0.185397	−0.0926983	+	0.995694i	$0.529549\pi$
$174$	2.78749e47	0.187674
$175$	4.25153e48	2.53062
$176$	1.77916e47	0.0936901
$177$	−4.60388e47	−0.214634
$178$	1.40758e48	0.581357
$179$	3.65334e47	0.133767	0.0668836	−	0.997761i	$-0.478694\pi$
$179$	3.65334e47	0.133767	0.0668836	+	0.997761i	$0.478694\pi$
$180$	−1.15446e48	−0.374991
$181$	−4.64912e48	−1.34054	−0.670272	−	0.742115i	$-0.733823\pi$
$181$	−4.64912e48	−1.34054	−0.670272	+	0.742115i	$0.733823\pi$
$182$	−1.27415e48	−0.326352
$183$	−4.74451e47	−0.108017
$184$	−6.59087e48	−1.33463
$185$	1.85682e49	3.34640
$186$	2.98563e47	0.0479190
$187$	−6.15386e48	−0.880143
$188$	−3.31215e48	−0.422393
$189$	−1.56936e48	−0.178564
$190$	4.24862e48	0.431565
$191$	−1.11668e49	−1.01324	−0.506621	−	0.862169i	$-0.669106\pi$
$191$	−1.11668e49	−1.01324	−0.506621	+	0.862169i	$0.669106\pi$
$192$	−5.02451e48	−0.407490
$193$	−8.49609e48	−0.616222	−0.308111	−	0.951350i	$-0.599697\pi$
$193$	−8.49609e48	−0.616222	−0.308111	+	0.951350i	$0.599697\pi$
$194$	1.22134e49	0.792680
$195$	−1.04441e49	−0.606913
$196$	1.55699e48	0.0810552
$197$	−2.47958e49	−1.15706	−0.578529	−	0.815662i	$-0.696373\pi$
$197$	−2.47958e49	−1.15706	−0.578529	+	0.815662i	$0.696373\pi$
$198$	6.19771e48	0.259376
$199$	−1.43615e49	−0.539336	−0.269668	−	0.962953i	$-0.586914\pi$
$199$	−1.43615e49	−0.539336	−0.269668	+	0.962953i	$0.586914\pi$
$200$	8.27031e49	2.78854
$201$	1.72482e47	0.00522431
$202$	−3.78724e49	−1.03102
$203$	1.90711e49	0.466886
$204$	1.11598e49	0.245815
$205$	1.14883e50	2.27797
$206$	−4.55567e49	−0.813593
$207$	−2.70381e49	−0.435124
$208$	−2.91888e48	−0.0423501
$209$	3.18478e49	0.416807
$210$	5.65669e49	0.668109
$211$	−1.63599e49	−0.174464	−0.0872322	−	0.996188i	$-0.527802\pi$
$211$	−1.63599e49	−0.174464	−0.0872322	+	0.996188i	$0.527802\pi$
$212$	2.15828e49	0.207916
$213$	−7.06197e49	−0.614843
$214$	−3.25840e47	−0.00256512
$215$	−4.25392e50	−3.02944
$216$	−3.05280e49	−0.196763
$217$	2.04267e49	0.119211
$218$	−1.05288e50	−0.556625
$219$	5.52387e49	0.264664
$220$	3.11926e50	1.35508
$221$	1.00960e50	0.397845
$222$	1.80772e50	0.646461
$223$	−3.73988e50	−1.21424	−0.607118	−	0.794612i	$-0.707674\pi$
$223$	−3.73988e50	−1.21424	−0.607118	+	0.794612i	$0.707674\pi$
$224$	−3.05877e50	−0.902017
$225$	3.39277e50	0.909139
$226$	−1.09107e50	−0.265780
$227$	8.48595e49	0.187994	0.0939972	−	0.995572i	$-0.470036\pi$
$227$	8.48595e49	0.187994	0.0939972	+	0.995572i	$0.470036\pi$
$228$	−5.77550e49	−0.116410
$229$	−7.41729e49	−0.136076	−0.0680381	−	0.997683i	$-0.521674\pi$
$229$	−7.41729e49	−0.136076	−0.0680381	+	0.997683i	$0.521674\pi$
$230$	9.74577e50	1.62805
$231$	4.24028e50	0.645263
$232$	3.70982e50	0.514471
$233$	−1.00178e51	−1.26654	−0.633269	−	0.773932i	$-0.718287\pi$
$233$	−1.00178e51	−1.26654	−0.633269	+	0.773932i	$0.718287\pi$
$234$	−1.01679e50	−0.117244
$235$	1.33028e51	1.39953
$236$	−2.25583e50	−0.216620
$237$	−1.06181e51	−0.931019
$238$	−5.46814e50	−0.437961
$239$	8.73908e50	0.639604	0.319802	−	0.947484i	$-0.396384\pi$
$239$	8.73908e50	0.639604	0.319802	+	0.947484i	$0.396384\pi$
$240$	1.29586e50	0.0866992
$241$	−3.95900e50	−0.242225	−0.121112	−	0.992639i	$-0.538646\pi$
$241$	−3.95900e50	−0.242225	−0.121112	+	0.992639i	$0.538646\pi$
$242$	−5.20428e50	−0.291293
$243$	−1.25237e50	−0.0641500
$244$	−2.32473e50	−0.109016
$245$	−6.25342e50	−0.268563
$246$	1.11845e51	0.440060
$247$	−5.22493e50	−0.188406
$248$	3.97352e50	0.131360
$249$	−2.21284e51	−0.670909
$250$	−7.74534e51	−2.15442
$251$	1.46542e51	0.374090	0.187045	−	0.982351i	$-0.440109\pi$
$251$	1.46542e51	0.374090	0.187045	+	0.982351i	$0.440109\pi$
$252$	−7.68960e50	−0.180215
$253$	7.30546e51	1.57238
$254$	3.63501e51	0.718755
$255$	−4.48217e51	−0.814469
$256$	−6.22141e51	−1.03927
$257$	1.09888e52	1.68806	0.844030	−	0.536296i	$-0.180177\pi$
$257$	1.09888e52	1.68806	0.844030	+	0.536296i	$0.180177\pi$
$258$	−4.14143e51	−0.585231
$259$	1.23678e52	1.60823
$260$	−5.11743e51	−0.612527
$261$	1.52190e51	0.167732
$262$	−1.98024e51	−0.201020
$263$	1.90424e51	0.178104	0.0890519	−	0.996027i	$-0.471616\pi$
$263$	1.90424e51	0.178104	0.0890519	+	0.996027i	$0.471616\pi$
$264$	8.24842e51	0.711028
$265$	−8.66841e51	−0.688895
$266$	2.82991e51	0.207404
$267$	7.68502e51	0.519581
$268$	8.45135e49	0.00527264
$269$	2.81599e52	1.62165	0.810826	−	0.585287i	$-0.199018\pi$
$269$	2.81599e52	1.62165	0.810826	+	0.585287i	$0.199018\pi$
$270$	4.51411e51	0.240022
$271$	−1.50188e52	−0.737558	−0.368779	−	0.929517i	$-0.620224\pi$
$271$	−1.50188e52	−0.737558	−0.368779	+	0.929517i	$0.620224\pi$
$272$	−1.25266e51	−0.0568333
$273$	−6.95655e51	−0.291674
$274$	−1.39620e52	−0.541140
$275$	−9.16699e52	−3.28529
$276$	−1.32482e52	−0.439149
$277$	−2.09522e52	−0.642561	−0.321280	−	0.946984i	$-0.604113\pi$
$277$	−2.09522e52	−0.642561	−0.321280	+	0.946984i	$0.604113\pi$
$278$	1.31245e51	0.0372495
$279$	1.63008e51	0.0428271
$280$	7.52839e52	1.83149
$281$	−1.94351e52	−0.437926	−0.218963	−	0.975733i	$-0.570267\pi$
$281$	−1.94351e52	−0.437926	−0.218963	+	0.975733i	$0.570267\pi$
$282$	1.29510e52	0.270363
$283$	5.63973e52	1.09106	0.545532	−	0.838090i	$-0.316328\pi$
$283$	5.63973e52	1.09106	0.545532	+	0.838090i	$0.316328\pi$
$284$	−3.46025e52	−0.620531
$285$	2.31964e52	0.385706
$286$	2.74728e52	0.423676
$287$	7.65207e52	1.09476
$288$	−2.44094e52	−0.324055
$289$	−3.78251e52	−0.466098
$290$	−5.48562e52	−0.627580
$291$	6.66818e52	0.708448
$292$	2.70661e52	0.267112
$293$	−1.38284e53	−1.26800	−0.633998	−	0.773334i	$-0.718587\pi$
$293$	−1.38284e53	−1.26800	−0.633998	+	0.773334i	$0.718587\pi$
$294$	−6.08806e51	−0.0518813
$295$	9.06018e52	0.717734
$296$	2.40586e53	1.77214
$297$	3.38379e52	0.231814
$298$	1.62988e52	0.103874
$299$	−1.19853e53	−0.710751
$300$	1.66240e53	0.917549
$301$	−2.83344e53	−1.45591
$302$	−1.64430e53	−0.786742
$303$	−2.06774e53	−0.921465
$304$	6.48286e51	0.0269144
$305$	9.33693e52	0.361208
$306$	−4.36364e52	−0.157340
$307$	1.55833e53	0.523822	0.261911	−	0.965092i	$-0.415647\pi$
$307$	1.55833e53	0.523822	0.261911	+	0.965092i	$0.415647\pi$
$308$	2.07767e53	0.651231
$309$	−2.48728e53	−0.727139
$310$	−5.87556e52	−0.160241
$311$	3.09503e53	0.787620	0.393810	−	0.919192i	$-0.371157\pi$
$311$	3.09503e53	0.787620	0.393810	+	0.919192i	$0.371157\pi$
$312$	−1.35323e53	−0.321401
$313$	−6.06624e53	−1.34498	−0.672490	−	0.740106i	$-0.734775\pi$
$313$	−6.06624e53	−1.34498	−0.672490	+	0.740106i	$0.734775\pi$
$314$	−4.16591e53	−0.862428
$315$	3.08841e53	0.597115
$316$	−5.20271e53	−0.939631
$317$	7.12220e53	1.20182	0.600911	−	0.799316i	$-0.294805\pi$
$317$	7.12220e53	1.20182	0.600911	+	0.799316i	$0.294805\pi$
$318$	−8.43919e52	−0.133081
$319$	−4.11204e53	−0.606119
$320$	9.88795e53	1.36264
$321$	−1.77900e51	−0.00229255
$322$	6.49142e53	0.782418
$323$	−2.24232e53	−0.252839
$324$	−6.13640e52	−0.0647434
$325$	1.50393e54	1.48503
$326$	−4.02968e53	−0.372470
$327$	−5.74844e53	−0.497477
$328$	1.48852e54	1.20634
$329$	8.86065e53	0.672595
$330$	−1.21968e54	−0.867350
$331$	−2.21005e53	−0.147265	−0.0736325	−	0.997285i	$-0.523459\pi$
$331$	−2.21005e53	−0.147265	−0.0736325	+	0.997285i	$0.523459\pi$
$332$	−1.08425e54	−0.677115
$333$	9.86970e53	0.577767
$334$	−8.03469e53	−0.440981
$335$	−3.39435e52	−0.0174700
$336$	8.63139e52	0.0416664
$337$	−9.92988e53	−0.449678	−0.224839	−	0.974396i	$-0.572186\pi$
$337$	−9.92988e53	−0.449678	−0.224839	+	0.974396i	$0.572186\pi$
$338$	1.06961e54	0.454483
$339$	−5.95698e53	−0.237538
$340$	−2.19619e54	−0.822002
$341$	−4.40434e53	−0.154761
$342$	2.25830e53	0.0745110
$343$	−3.41085e54	−1.05691
$344$	−5.51176e54	−1.60429
$345$	5.32094e54	1.45505
$346$	4.66087e53	0.119765
$347$	−2.14712e53	−0.0518530	−0.0259265	−	0.999664i	$-0.508254\pi$
$347$	−2.14712e53	−0.0518530	−0.0259265	+	0.999664i	$0.508254\pi$
$348$	7.45706e53	0.169283
$349$	2.01754e53	0.0430601	0.0215300	−	0.999768i	$-0.493146\pi$
$349$	2.01754e53	0.0430601	0.0215300	+	0.999768i	$0.493146\pi$
$350$	−8.14552e54	−1.63477
$351$	−5.55142e53	−0.104785
$352$	6.59521e54	1.17101
$353$	7.42627e54	1.24055	0.620275	−	0.784384i	$-0.287021\pi$
$353$	7.42627e54	1.24055	0.620275	+	0.784384i	$0.287021\pi$
$354$	8.82060e53	0.138653
$355$	1.38976e55	2.05603
$356$	3.76554e54	0.524387
$357$	−2.98547e54	−0.391422
$358$	−6.99945e53	−0.0864129
$359$	−8.85340e54	−1.02939	−0.514694	−	0.857374i	$-0.672095\pi$
$359$	−8.85340e54	−1.02939	−0.514694	+	0.857374i	$0.672095\pi$
$360$	6.00775e54	0.657973
$361$	−8.53135e54	−0.880264
$362$	8.90727e54	0.865985
$363$	−2.84141e54	−0.260340
$364$	−3.40860e54	−0.294372
$365$	−1.08707e55	−0.885034
$366$	9.09003e53	0.0697786
$367$	2.72584e55	1.97324	0.986620	−	0.163035i	$-0.0521283\pi$
$367$	2.72584e55	1.97324	0.986620	+	0.163035i	$0.0521283\pi$
$368$	1.48708e54	0.101533
$369$	6.10645e54	0.393298
$370$	−3.55749e55	−2.16176
$371$	−5.77382e54	−0.331073
$372$	7.98712e53	0.0432232
$373$	−2.12458e55	−1.08526	−0.542628	−	0.839973i	$-0.682571\pi$
$373$	−2.12458e55	−1.08526	−0.542628	+	0.839973i	$0.682571\pi$
$374$	1.17902e55	0.568567
$375$	−4.22876e55	−1.92549
$376$	1.72362e55	0.741146
$377$	6.74618e54	0.273980
$378$	3.00674e54	0.115351
$379$	2.08438e55	0.755499	0.377750	−	0.925908i	$-0.376698\pi$
$379$	2.08438e55	0.755499	0.377750	+	0.925908i	$0.376698\pi$
$380$	1.13659e55	0.389274
$381$	1.98462e55	0.642379
$382$	2.13946e55	0.654549
$383$	−1.15099e55	−0.332889	−0.166444	−	0.986051i	$-0.553229\pi$
$383$	−1.15099e55	−0.332889	−0.166444	+	0.986051i	$0.553229\pi$
$384$	−1.08993e55	−0.298043
$385$	−8.34463e55	−2.15775
$386$	1.62777e55	0.398076
$387$	−2.26112e55	−0.523043
$388$	3.26730e55	0.715001
$389$	2.58934e54	0.0536132	0.0268066	−	0.999641i	$-0.491466\pi$
$389$	2.58934e54	0.0536132	0.0268066	+	0.999641i	$0.491466\pi$
$390$	2.00099e55	0.392062
$391$	−5.14358e55	−0.953818
$392$	−8.10249e54	−0.142222
$393$	−1.08116e55	−0.179659
$394$	4.75065e55	0.747453
$395$	2.08959e56	3.11331
$396$	1.65800e55	0.233959
$397$	−4.99618e55	−0.667793	−0.333897	−	0.942610i	$-0.608364\pi$
$397$	−4.99618e55	−0.667793	−0.333897	+	0.942610i	$0.608364\pi$
$398$	2.75153e55	0.348408
$399$	1.54506e55	0.185365
$400$	−1.86601e55	−0.212140
$401$	5.05004e55	0.544115	0.272058	−	0.962281i	$-0.412296\pi$
$401$	5.05004e55	0.544115	0.272058	+	0.962281i	$0.412296\pi$
$402$	−3.30460e53	−0.00337488
$403$	7.22572e54	0.0699556
$404$	−1.01316e56	−0.929988
$405$	2.46459e55	0.214517
$406$	−3.65384e55	−0.301606
$407$	−2.66671e56	−2.08783
$408$	−5.80750e55	−0.431316
$409$	2.15446e56	1.51806	0.759028	−	0.651058i	$-0.225674\pi$
$409$	2.15446e56	1.51806	0.759028	+	0.651058i	$0.225674\pi$
$410$	−2.20105e56	−1.47155
$411$	−7.62288e55	−0.483637
$412$	−1.21873e56	−0.733866
$413$	6.03477e55	0.344933
$414$	5.18024e55	0.281088
$415$	4.35474e56	2.24351
$416$	−1.08200e56	−0.529325
$417$	7.16566e54	0.0332913
$418$	−6.10174e55	−0.269255
$419$	−3.43101e56	−1.43820	−0.719102	−	0.694904i	$-0.755447\pi$
$419$	−3.43101e56	−1.43820	−0.719102	+	0.694904i	$0.755447\pi$
$420$	1.51327e56	0.602638
$421$	−4.45367e56	−1.68521	−0.842603	−	0.538536i	$-0.818978\pi$
$421$	−4.45367e56	−1.68521	−0.842603	+	0.538536i	$0.818978\pi$
$422$	3.13439e55	0.112703
$423$	7.07091e55	0.241634
$424$	−1.12316e56	−0.364816
$425$	6.45423e56	1.99289
$426$	1.35301e56	0.397185
$427$	6.21911e55	0.173592
$428$	−8.71683e53	−0.00231376
$429$	1.49995e56	0.378656
$430$	8.15011e56	1.95700
$431$	−1.15170e56	−0.263074	−0.131537	−	0.991311i	$-0.541991\pi$
$431$	−1.15170e56	−0.263074	−0.131537	+	0.991311i	$0.541991\pi$
$432$	6.88796e54	0.0149689
$433$	2.47297e56	0.511362	0.255681	−	0.966761i	$-0.417700\pi$
$433$	2.47297e56	0.511362	0.255681	+	0.966761i	$0.417700\pi$
$434$	−3.91357e55	−0.0770094
$435$	−2.99501e56	−0.560892
$436$	−2.81664e56	−0.502079
$437$	2.66194e56	0.451697
$438$	−1.05832e56	−0.170972
$439$	4.99561e55	0.0768424	0.0384212	−	0.999262i	$-0.487767\pi$
$439$	4.99561e55	0.0768424	0.0384212	+	0.999262i	$0.487767\pi$
$440$	−1.62324e57	−2.37767
$441$	−3.32393e55	−0.0463683
$442$	−1.93429e56	−0.257006
$443$	1.10930e57	1.40401	0.702003	−	0.712174i	$-0.252289\pi$
$443$	1.10930e57	1.40401	0.702003	+	0.712174i	$0.252289\pi$
$444$	4.83599e56	0.583111
$445$	−1.51237e57	−1.73747
$446$	7.16525e56	0.784389
$447$	8.89874e55	0.0928360
$448$	6.58613e56	0.654866
$449$	−4.08332e55	−0.0387005	−0.0193503	−	0.999813i	$-0.506160\pi$
$449$	−4.08332e55	−0.0387005	−0.0193503	+	0.999813i	$0.506160\pi$
$450$	−6.50023e56	−0.587299
$451$	−1.64991e57	−1.42123
$452$	−2.91882e56	−0.239735
$453$	−8.97747e56	−0.703141
$454$	−1.62583e56	−0.121443
$455$	1.36901e57	0.975353
$456$	3.00553e56	0.204257
$457$	−1.23487e57	−0.800611	−0.400305	−	0.916382i	$-0.631096\pi$
$457$	−1.23487e57	−0.800611	−0.400305	+	0.916382i	$0.631096\pi$
$458$	1.42108e56	0.0879045
$459$	−2.38244e56	−0.140621
$460$	2.60717e57	1.46851
$461$	1.83528e57	0.986580	0.493290	−	0.869865i	$-0.335794\pi$
$461$	1.83528e57	0.986580	0.493290	+	0.869865i	$0.335794\pi$
$462$	−8.12396e56	−0.416836
$463$	8.87478e56	0.434677	0.217338	−	0.976096i	$-0.430262\pi$
$463$	8.87478e56	0.434677	0.217338	+	0.976096i	$0.430262\pi$
$464$	−8.37036e55	−0.0391388
$465$	−3.20790e56	−0.143213
$466$	1.91931e57	0.818177
$467$	−9.54635e56	−0.388620	−0.194310	−	0.980940i	$-0.562247\pi$
$467$	−9.54635e56	−0.388620	−0.194310	+	0.980940i	$0.562247\pi$
$468$	−2.72010e56	−0.105755
$469$	−2.26090e55	−0.00839586
$470$	−2.54868e57	−0.904090
$471$	−2.27448e57	−0.770785
$472$	1.17392e57	0.380089
$473$	6.10935e57	1.89008
$474$	2.03433e57	0.601433
$475$	−3.34024e57	−0.943766
$476$	−1.46283e57	−0.395043
$477$	−4.60758e56	−0.118940
$478$	−1.67432e57	−0.413181
$479$	1.34733e57	0.317877	0.158939	−	0.987288i	$-0.449193\pi$
$479$	1.34733e57	0.317877	0.158939	+	0.987288i	$0.449193\pi$
$480$	4.80363e57	1.08363
$481$	4.37498e57	0.943750
$482$	7.58506e56	0.156476
$483$	3.54415e57	0.699277
$484$	−1.39224e57	−0.262748
$485$	−1.31226e58	−2.36904
$486$	2.39942e56	0.0414406
$487$	−9.08466e57	−1.50119	−0.750596	−	0.660762i	$-0.770233\pi$
$487$	−9.08466e57	−1.50119	−0.750596	+	0.660762i	$0.770233\pi$
$488$	1.20978e57	0.191284
$489$	−2.20010e57	−0.332891
$490$	1.19810e57	0.173491
$491$	−8.89699e57	−1.23308	−0.616540	−	0.787324i	$-0.711466\pi$
$491$	−8.89699e57	−1.23308	−0.616540	+	0.787324i	$0.711466\pi$
$492$	2.99206e57	0.396936
$493$	2.89518e57	0.367677
$494$	1.00105e57	0.121710
$495$	−6.65912e57	−0.775184
$496$	−8.96535e55	−0.00999335
$497$	9.25683e57	0.988098
$498$	4.23958e57	0.433404
$499$	−7.85254e56	−0.0768862	−0.0384431	−	0.999261i	$-0.512240\pi$
$499$	−7.85254e56	−0.0768862	−0.0384431	+	0.999261i	$0.512240\pi$
$500$	−2.07202e58	−1.94330
$501$	−4.38674e57	−0.394122
$502$	−2.80760e57	−0.241660
$503$	2.18276e58	1.80009	0.900044	−	0.435800i	$-0.143534\pi$
$503$	2.18276e58	1.80009	0.900044	+	0.435800i	$0.143534\pi$
$504$	4.00162e57	0.316212
$505$	4.06919e58	3.08137
$506$	−1.39966e58	−1.01575
$507$	5.83982e57	0.406189
$508$	9.72433e57	0.648321
$509$	−9.01858e57	−0.576376	−0.288188	−	0.957574i	$-0.593053\pi$
$509$	−9.01858e57	−0.576376	−0.288188	+	0.957574i	$0.593053\pi$
$510$	8.58741e57	0.526142
$511$	−7.24069e57	−0.425335
$512$	2.75439e57	0.155139
$513$	1.23297e57	0.0665934
$514$	−2.10535e58	−1.09048
$515$	4.89483e58	2.43155
$516$	−1.10791e58	−0.527881
$517$	−1.91050e58	−0.873174
$518$	−2.36956e58	−1.03891
$519$	2.54472e57	0.107039
$520$	2.66308e58	1.07476
$521$	−4.86422e57	−0.188366	−0.0941829	−	0.995555i	$-0.530024\pi$
$521$	−4.86422e57	−0.188366	−0.0941829	+	0.995555i	$0.530024\pi$
$522$	−2.91581e57	−0.108354
$523$	−4.83195e58	−1.72320	−0.861601	−	0.507586i	$-0.830538\pi$
$523$	−4.83195e58	−1.72320	−0.861601	+	0.507586i	$0.830538\pi$
$524$	−5.29750e57	−0.181321
$525$	−4.44725e58	−1.46105
$526$	−3.64834e57	−0.115054
$527$	3.10098e57	0.0938795
$528$	−1.86107e57	−0.0540920
$529$	2.52272e58	0.703998
$530$	1.66078e58	0.445023
$531$	4.81582e57	0.123919
$532$	7.57053e57	0.187079
$533$	2.70683e58	0.642430
$534$	−1.47238e58	−0.335647
$535$	3.50098e56	0.00766626
$536$	−4.39803e56	−0.00925156
$537$	−3.82152e57	−0.0772305
$538$	−5.39517e58	−1.04758
$539$	8.98097e57	0.167558
$540$	1.20761e58	0.216501
$541$	−8.31551e58	−1.43267	−0.716337	−	0.697754i	$-0.754183\pi$
$541$	−8.31551e58	−1.43267	−0.716337	+	0.697754i	$0.754183\pi$
$542$	2.87746e58	0.476458
$543$	4.86314e58	0.773964
$544$	−4.64351e58	−0.710347
$545$	1.13126e59	1.66356
$546$	1.33281e58	0.188420
$547$	−1.45905e58	−0.198310	−0.0991548	−	0.995072i	$-0.531614\pi$
$547$	−1.45905e58	−0.198310	−0.0991548	+	0.995072i	$0.531614\pi$
$548$	−3.73508e58	−0.488111
$549$	4.96293e57	0.0623638
$550$	1.75631e59	2.12228
$551$	−1.49833e58	−0.174120
$552$	6.89428e58	0.770547
$553$	1.39182e59	1.49622
$554$	4.01424e58	0.415091
$555$	−1.94230e59	−1.93205
$556$	3.51105e57	0.0335992
$557$	−1.75662e59	−1.61730	−0.808650	−	0.588290i	$-0.799801\pi$
$557$	−1.75662e59	−1.61730	−0.808650	+	0.588290i	$0.799801\pi$
$558$	−3.12308e57	−0.0276661
$559$	−1.00229e59	−0.854361
$560$	−1.69861e58	−0.139332
$561$	6.43715e58	0.508151
$562$	3.72358e58	0.282898
$563$	−1.51361e59	−1.10684	−0.553418	−	0.832903i	$-0.686677\pi$
$563$	−1.51361e59	−1.10684	−0.553418	+	0.832903i	$0.686677\pi$
$564$	3.46463e58	0.243869
$565$	1.17230e59	0.794323
$566$	−1.08052e59	−0.704821
$567$	1.64160e58	0.103094
$568$	1.80069e59	1.08880
$569$	2.44840e59	1.42550	0.712752	−	0.701417i	$-0.247449\pi$
$569$	2.44840e59	1.42550	0.712752	+	0.701417i	$0.247449\pi$
$570$	−4.44421e58	−0.249164
$571$	−2.27586e59	−1.22877	−0.614384	−	0.789007i	$-0.710595\pi$
$571$	−2.27586e59	−1.22877	−0.614384	+	0.789007i	$0.710595\pi$
$572$	7.34950e58	0.382158
$573$	1.16809e59	0.584995
$574$	−1.46606e59	−0.707208
$575$	−7.66205e59	−3.56030
$576$	5.25581e58	0.235265
$577$	−5.18881e58	−0.223763	−0.111881	−	0.993722i	$-0.535688\pi$
$577$	−5.18881e58	−0.223763	−0.111881	+	0.993722i	$0.535688\pi$
$578$	7.24693e58	0.301097
$579$	8.88721e58	0.355776
$580$	−1.46751e59	−0.566081
$581$	2.90059e59	1.07820
$582$	−1.27756e59	−0.457654
$583$	1.24493e59	0.429805
$584$	−1.40850e59	−0.468685
$585$	1.09249e59	0.350401
$586$	2.64939e59	0.819119
$587$	2.57601e59	0.767764	0.383882	−	0.923382i	$-0.374587\pi$
$587$	2.57601e59	0.767764	0.383882	+	0.923382i	$0.374587\pi$
$588$	−1.62867e58	−0.0467973
$589$	−1.60484e58	−0.0444583
$590$	−1.73585e59	−0.463653
$591$	2.59373e59	0.668028
$592$	−5.42828e58	−0.134817
$593$	3.64832e59	0.873810	0.436905	−	0.899508i	$-0.356075\pi$
$593$	3.64832e59	0.873810	0.436905	+	0.899508i	$0.356075\pi$
$594$	−6.48303e58	−0.149751
$595$	5.87523e59	1.30891
$596$	4.36023e58	0.0936948
$597$	1.50227e59	0.311386
$598$	2.29626e59	0.459141
$599$	−3.13536e58	−0.0604798	−0.0302399	−	0.999543i	$-0.509627\pi$
$599$	−3.13536e58	−0.0604798	−0.0302399	+	0.999543i	$0.509627\pi$
$600$	−8.65103e59	−1.60996
$601$	−5.61238e59	−1.00773	−0.503867	−	0.863781i	$-0.668090\pi$
$601$	−5.61238e59	−1.00773	−0.503867	+	0.863781i	$0.668090\pi$
$602$	5.42859e59	0.940509
$603$	−1.80423e57	−0.00301626
$604$	−4.39881e59	−0.709645
$605$	5.59173e59	0.870574
$606$	3.96159e59	0.595261
$607$	−4.58204e59	−0.664511	−0.332255	−	0.943189i	$-0.607810\pi$
$607$	−4.58204e59	−0.664511	−0.332255	+	0.943189i	$0.607810\pi$
$608$	2.40314e59	0.336397
$609$	−1.99491e59	−0.269557
$610$	−1.78887e59	−0.233339
$611$	3.13435e59	0.394695
$612$	−1.16736e59	−0.141921
$613$	−1.17245e60	−1.37624	−0.688118	−	0.725599i	$-0.741563\pi$
$613$	−1.17245e60	−1.37624	−0.688118	+	0.725599i	$0.741563\pi$
$614$	−2.98561e59	−0.338387
$615$	−1.20172e60	−1.31518
$616$	−1.08120e60	−1.14267
$617$	−1.43564e60	−1.46526	−0.732628	−	0.680629i	$-0.761707\pi$
$617$	−1.43564e60	−1.46526	−0.732628	+	0.680629i	$0.761707\pi$
$618$	4.76540e59	0.469728
$619$	1.66096e60	1.58129	0.790644	−	0.612276i	$-0.209746\pi$
$619$	1.66096e60	1.58129	0.790644	+	0.612276i	$0.209746\pi$
$620$	−1.57182e59	−0.144538
$621$	2.82828e59	0.251219
$622$	−5.92978e59	−0.508798
$623$	−1.00735e60	−0.835005
$624$	3.05325e58	0.0244508
$625$	4.79686e60	3.71139
$626$	1.16223e60	0.868850
$627$	−3.33140e59	−0.240644
$628$	−1.11446e60	−0.777914
$629$	1.87756e60	1.26650
$630$	−5.91710e59	−0.385733
$631$	−5.47413e59	−0.344892	−0.172446	−	0.985019i	$-0.555167\pi$
$631$	−5.47413e59	−0.344892	−0.172446	+	0.985019i	$0.555167\pi$
$632$	2.70745e60	1.64871
$633$	1.71130e59	0.100727
$634$	−1.36455e60	−0.776371
$635$	−3.90563e60	−2.14811
$636$	−2.25764e59	−0.120040
$637$	−1.47341e59	−0.0757401
$638$	7.87829e59	0.391550
$639$	7.38707e59	0.354980
$640$	2.14493e60	0.996651
$641$	−3.66398e59	−0.164628	−0.0823142	−	0.996606i	$-0.526231\pi$
$641$	−3.66398e59	−0.164628	−0.0823142	+	0.996606i	$0.526231\pi$
$642$	3.40840e57	0.00148098
$643$	−2.84143e60	−1.19399	−0.596995	−	0.802245i	$-0.703639\pi$
$643$	−2.84143e60	−1.19399	−0.596995	+	0.802245i	$0.703639\pi$
$644$	1.73658e60	0.705745
$645$	4.44975e60	1.74905
$646$	4.29608e59	0.163333
$647$	−1.01042e60	−0.371585	−0.185793	−	0.982589i	$-0.559485\pi$
$647$	−1.01042e60	−0.371585	−0.185793	+	0.982589i	$0.559485\pi$
$648$	3.19334e59	0.113601
$649$	−1.30120e60	−0.447798
$650$	−2.88138e60	−0.959320
$651$	−2.13671e59	−0.0688262
$652$	−1.07801e60	−0.335970
$653$	−4.87378e59	−0.146971	−0.0734857	−	0.997296i	$-0.523412\pi$
$653$	−4.87378e59	−0.146971	−0.0734857	+	0.997296i	$0.523412\pi$
$654$	1.10135e60	0.321368
$655$	2.12766e60	0.600779
$656$	−3.35852e59	−0.0917730
$657$	−5.77816e59	−0.152804
$658$	−1.69762e60	−0.434493
$659$	−7.34783e60	−1.82022	−0.910108	−	0.414371i	$-0.864002\pi$
$659$	−7.34783e60	−1.82022	−0.910108	+	0.414371i	$0.864002\pi$
$660$	−3.26286e60	−0.782355
$661$	6.39610e60	1.48451	0.742256	−	0.670116i	$-0.233756\pi$
$661$	6.39610e60	1.48451	0.742256	+	0.670116i	$0.233756\pi$
$662$	4.23424e59	0.0951324
$663$	−1.05607e60	−0.229696
$664$	5.64239e60	1.18809
$665$	−3.04059e60	−0.619858
$666$	−1.89094e60	−0.373234
$667$	−3.43697e60	−0.656857
$668$	−2.14943e60	−0.397768
$669$	3.91204e60	0.701039
$670$	6.50326e58	0.0112856
$671$	−1.34094e60	−0.225359
$672$	3.19958e60	0.520780
$673$	−5.66196e60	−0.892571	−0.446285	−	0.894891i	$-0.647253\pi$
$673$	−5.66196e60	−0.892571	−0.446285	+	0.894891i	$0.647253\pi$
$674$	1.90247e60	0.290489
$675$	−3.54896e60	−0.524892
$676$	2.86142e60	0.409946
$677$	8.79026e60	1.21996	0.609980	−	0.792417i	$-0.291177\pi$
$677$	8.79026e60	1.21996	0.609980	+	0.792417i	$0.291177\pi$
$678$	1.14130e60	0.153448
$679$	−8.74065e60	−1.13853
$680$	1.14288e61	1.44231
$681$	−8.87661e59	−0.108539
$682$	8.43830e59	0.0999748
$683$	1.82024e60	0.208969	0.104485	−	0.994526i	$-0.466681\pi$
$683$	1.82024e60	0.208969	0.104485	+	0.994526i	$0.466681\pi$
$684$	6.04138e59	0.0672093
$685$	1.50014e61	1.61728
$686$	6.53486e60	0.682760
$687$	7.75875e59	0.0785636
$688$	1.24360e60	0.122048
$689$	−2.04242e60	−0.194282
$690$	−1.01944e61	−0.939955
$691$	−9.14476e60	−0.817324	−0.408662	−	0.912686i	$-0.634005\pi$
$691$	−9.14476e60	−0.817324	−0.408662	+	0.912686i	$0.634005\pi$
$692$	1.24687e60	0.108029
$693$	−4.43548e60	−0.372543
$694$	4.11369e59	0.0334967
$695$	−1.41016e60	−0.111326
$696$	−3.88060e60	−0.297030
$697$	1.16166e61	0.862133
$698$	−3.86541e59	−0.0278166
$699$	1.04789e61	0.731236
$700$	−2.17908e61	−1.47457
$701$	1.07211e61	0.703560	0.351780	−	0.936083i	$-0.385577\pi$
$701$	1.07211e61	0.703560	0.351780	+	0.936083i	$0.385577\pi$
$702$	1.06360e60	0.0676908
$703$	−9.71687e60	−0.599773
$704$	−1.42008e61	−0.850158
$705$	−1.39152e61	−0.808020
$706$	−1.42280e61	−0.801389
$707$	2.71039e61	1.48086
$708$	2.35968e60	0.125065
$709$	6.45364e60	0.331826	0.165913	−	0.986140i	$-0.446943\pi$
$709$	6.45364e60	0.331826	0.165913	+	0.986140i	$0.446943\pi$
$710$	−2.66264e61	−1.32818
$711$	1.11069e61	0.537524
$712$	−1.95956e61	−0.920108
$713$	−3.68128e60	−0.167716
$714$	5.71987e60	0.252857
$715$	−2.95181e61	−1.26622
$716$	−1.87248e60	−0.0779449
$717$	−9.14139e60	−0.369275
$718$	1.69623e61	0.664980
$719$	−4.63987e60	−0.176537	−0.0882683	−	0.996097i	$-0.528133\pi$
$719$	−4.63987e60	−0.176537	−0.0882683	+	0.996097i	$0.528133\pi$
$720$	−1.35551e60	−0.0500558
$721$	3.26033e61	1.16857
$722$	1.63452e61	0.568646
$723$	4.14125e60	0.139849
$724$	2.38286e61	0.781123
$725$	4.31276e61	1.37242
$726$	5.44387e60	0.168178
$727$	1.44955e61	0.434753	0.217376	−	0.976088i	$-0.430250\pi$
$727$	1.44955e61	0.434753	0.217376	+	0.976088i	$0.430250\pi$
$728$	1.77381e61	0.516515
$729$	1.31002e60	0.0370370
$730$	2.08272e61	0.571727
$731$	−4.30143e61	−1.14654
$732$	2.43175e60	0.0629406
$733$	2.28885e61	0.575282	0.287641	−	0.957738i	$-0.407129\pi$
$733$	2.28885e61	0.575282	0.287641	+	0.957738i	$0.407129\pi$
$734$	−5.22245e61	−1.27470
$735$	6.54130e60	0.155055
$736$	5.51248e61	1.26904
$737$	4.87487e59	0.0108996
$738$	−1.16994e61	−0.254069
$739$	−1.52004e61	−0.320628	−0.160314	−	0.987066i	$-0.551251\pi$
$739$	−1.52004e61	−0.320628	−0.160314	+	0.987066i	$0.551251\pi$
$740$	−9.51696e61	−1.94992
$741$	5.46546e60	0.108776
$742$	1.10621e61	0.213872
$743$	−7.23666e61	−1.35919	−0.679593	−	0.733589i	$-0.737844\pi$
$743$	−7.23666e61	−1.35919	−0.679593	+	0.733589i	$0.737844\pi$
$744$	−4.15645e60	−0.0758410
$745$	−1.75122e61	−0.310443
$746$	4.07049e61	0.701070
$747$	2.31471e61	0.387349
$748$	3.15410e61	0.512851
$749$	2.33192e59	0.00368430
$750$	8.10190e61	1.24385
$751$	−1.13301e62	−1.69034	−0.845171	−	0.534496i	$-0.820502\pi$
$751$	−1.13301e62	−1.69034	−0.845171	+	0.534496i	$0.820502\pi$
$752$	−3.88896e60	−0.0563833
$753$	−1.53288e61	−0.215981
$754$	−1.29250e61	−0.176990
$755$	1.76672e62	2.35129
$756$	8.04359e60	0.104047
$757$	−1.15154e62	−1.44783	−0.723916	−	0.689888i	$-0.757660\pi$
$757$	−1.15154e62	−1.44783	−0.723916	+	0.689888i	$0.757660\pi$
$758$	−3.99348e61	−0.488049
$759$	−7.64177e61	−0.907812
$760$	−5.91472e61	−0.683033
$761$	−1.34334e62	−1.50805	−0.754025	−	0.656845i	$-0.771890\pi$
$761$	−1.34334e62	−1.50805	−0.754025	+	0.656845i	$0.771890\pi$
$762$	−3.80235e61	−0.414973
$763$	7.53505e61	0.799482
$764$	5.72346e61	0.590407
$765$	4.68851e61	0.470234
$766$	2.20519e61	0.215044
$767$	2.13473e61	0.202415
$768$	6.50781e61	0.600024
$769$	9.50818e61	0.852474	0.426237	−	0.904612i	$-0.359839\pi$
$769$	9.50818e61	0.852474	0.426237	+	0.904612i	$0.359839\pi$
$770$	1.59875e62	1.39390
$771$	−1.14947e62	−0.974602
$772$	4.35459e61	0.359067
$773$	2.61737e61	0.209897	0.104949	−	0.994478i	$-0.466532\pi$
$773$	2.61737e61	0.209897	0.104949	+	0.994478i	$0.466532\pi$
$774$	4.33209e61	0.337883
$775$	4.61932e61	0.350422
$776$	−1.70028e62	−1.25457
$777$	−1.29372e62	−0.928514
$778$	−4.96092e60	−0.0346339
$779$	−6.01190e61	−0.408278
$780$	5.35301e61	0.353642
$781$	−1.99593e62	−1.28276
$782$	9.85461e61	0.616161
$783$	−1.59196e61	−0.0968399
$784$	1.82814e60	0.0108197
$785$	4.47605e62	2.57749
$786$	2.07140e61	0.116059
$787$	3.01082e62	1.64145	0.820726	−	0.571322i	$-0.193569\pi$
$787$	3.01082e62	1.64145	0.820726	+	0.571322i	$0.193569\pi$
$788$	1.27089e62	0.674207
$789$	−1.99190e61	−0.102828
$790$	−4.00345e62	−2.01118
$791$	7.80841e61	0.381741
$792$	−8.62814e61	−0.410512
$793$	2.19994e61	0.101868
$794$	9.57220e61	0.431391
$795$	9.06746e61	0.397734
$796$	7.36086e61	0.314266
$797$	−2.40878e62	−1.00102	−0.500511	−	0.865730i	$-0.666855\pi$
$797$	−2.40878e62	−1.00102	−0.500511	+	0.865730i	$0.666855\pi$
$798$	−2.96018e61	−0.119745
$799$	1.34513e62	0.529675
$800$	−6.91713e62	−2.65150
$801$	−8.03881e61	−0.299980
$802$	−9.67540e61	−0.351496
$803$	1.56121e62	0.552176
$804$	−8.84041e59	−0.00304416
$805$	−6.97469e62	−2.33837
$806$	−1.38438e61	−0.0451909
$807$	−2.94563e62	−0.936261
$808$	5.27240e62	1.63179
$809$	−1.56406e62	−0.471369	−0.235685	−	0.971830i	$-0.575733\pi$
$809$	−1.56406e62	−0.471369	−0.235685	+	0.971830i	$0.575733\pi$
$810$	−4.72192e61	−0.138577
$811$	1.12549e62	0.321656	0.160828	−	0.986982i	$-0.448584\pi$
$811$	1.12549e62	0.321656	0.160828	+	0.986982i	$0.448584\pi$
$812$	−9.77471e61	−0.272050
$813$	1.57102e62	0.425829
$814$	5.10916e62	1.34873
$815$	4.32967e62	1.11318
$816$	1.31033e61	0.0328127
$817$	2.22611e62	0.542965
$818$	−4.12775e62	−0.980657
$819$	7.27680e61	0.168398
$820$	−5.88821e62	−1.32735
$821$	5.96819e61	0.131058	0.0655291	−	0.997851i	$-0.479126\pi$
$821$	5.96819e61	0.131058	0.0655291	+	0.997851i	$0.479126\pi$
$822$	1.46047e62	0.312427
$823$	−4.06781e62	−0.847743	−0.423872	−	0.905722i	$-0.639329\pi$
$823$	−4.06781e62	−0.847743	−0.423872	+	0.905722i	$0.639329\pi$
$824$	6.34218e62	1.28767
$825$	9.58899e62	1.89676
$826$	−1.15620e62	−0.222825
$827$	−4.41980e61	−0.0829915	−0.0414958	−	0.999139i	$-0.513212\pi$
$827$	−4.41980e61	−0.0829915	−0.0414958	+	0.999139i	$0.513212\pi$
$828$	1.38581e62	0.253543
$829$	1.49177e62	0.265937	0.132969	−	0.991120i	$-0.457549\pi$
$829$	1.49177e62	0.265937	0.132969	+	0.991120i	$0.457549\pi$
$830$	−8.34327e62	−1.44930
$831$	2.19167e62	0.370983
$832$	2.32976e62	0.384291
$833$	−6.32326e61	−0.101642
$834$	−1.37287e61	−0.0215060
$835$	8.63286e62	1.31794
$836$	−1.63233e62	−0.242870
$837$	−1.70512e61	−0.0247262
$838$	6.57349e62	0.929072
$839$	1.09602e62	0.150986	0.0754930	−	0.997146i	$-0.475947\pi$
$839$	1.09602e62	0.150986	0.0754930	+	0.997146i	$0.475947\pi$
$840$	−7.87496e62	−1.05741
$841$	−5.70578e62	−0.746795
$842$	8.53281e62	1.08863
$843$	2.03298e62	0.252837
$844$	8.38508e61	0.101659
$845$	−1.14924e63	−1.35829
$846$	−1.35472e62	−0.156094
$847$	3.72452e62	0.418386
$848$	2.53415e61	0.0277537
$849$	−5.89936e62	−0.629926
$850$	−1.23657e63	−1.28739
$851$	−2.22892e63	−2.26260
$852$	3.61954e62	0.358263
$853$	−5.00803e61	−0.0483351	−0.0241675	−	0.999708i	$-0.507694\pi$
$853$	−5.00803e61	−0.0483351	−0.0241675	+	0.999708i	$0.507694\pi$
$854$	−1.19152e62	−0.112139
$855$	−2.42643e62	−0.222687
$856$	4.53618e60	0.00405980
$857$	1.37674e63	1.20161	0.600805	−	0.799396i	$-0.294847\pi$
$857$	1.37674e63	1.20161	0.600805	+	0.799396i	$0.294847\pi$
$858$	−2.87376e62	−0.244609
$859$	1.75498e62	0.145687	0.0728434	−	0.997343i	$-0.476793\pi$
$859$	1.75498e62	0.145687	0.0728434	+	0.997343i	$0.476793\pi$
$860$	2.18031e63	1.76523
$861$	−8.00434e62	−0.632059
$862$	2.20655e62	0.169944
$863$	2.82644e62	0.212328	0.106164	−	0.994349i	$-0.466143\pi$
$863$	2.82644e62	0.212328	0.106164	+	0.994349i	$0.466143\pi$
$864$	2.55331e62	0.187093
$865$	−5.00786e62	−0.357936
$866$	−4.73797e62	−0.330337
$867$	3.95664e62	0.269102
$868$	−1.04695e62	−0.0694629
$869$	−3.00100e63	−1.94241
$870$	5.73816e62	0.362333
$871$	−7.99766e60	−0.00492689
$872$	1.46576e63	0.880965
$873$	−6.97515e62	−0.409023
$874$	−5.10002e62	−0.291794
$875$	5.54306e63	3.09440
$876$	−2.83121e62	−0.154217
$877$	−6.64060e62	−0.352952	−0.176476	−	0.984305i	$-0.556470\pi$
$877$	−6.64060e62	−0.352952	−0.176476	+	0.984305i	$0.556470\pi$
$878$	−9.57111e61	−0.0496398
$879$	1.44650e63	0.732078
$880$	3.66248e62	0.180883
$881$	3.34334e62	0.161138	0.0805690	−	0.996749i	$-0.474326\pi$
$881$	3.34334e62	0.161138	0.0805690	+	0.996749i	$0.474326\pi$
$882$	6.36832e61	0.0299537
$883$	2.18835e63	1.00453	0.502263	−	0.864715i	$-0.332501\pi$
$883$	2.18835e63	1.00453	0.502263	+	0.864715i	$0.332501\pi$
$884$	−5.17459e62	−0.231821
$885$	−9.47727e62	−0.414384
$886$	−2.12531e63	−0.906980
$887$	−1.17168e63	−0.488034	−0.244017	−	0.969771i	$-0.578465\pi$
$887$	−1.17168e63	−0.488034	−0.244017	+	0.969771i	$0.578465\pi$
$888$	−2.51662e63	−1.02315
$889$	−2.60144e63	−1.03235
$890$	2.89756e63	1.12240
$891$	−3.53957e62	−0.133838
$892$	1.91684e63	0.707524
$893$	−6.96142e62	−0.250837
$894$	−1.70491e62	−0.0599716
$895$	7.52054e62	0.258258
$896$	1.42868e63	0.478977
$897$	1.25370e63	0.410352
$898$	7.82325e61	0.0250003
$899$	2.07209e62	0.0646511
$900$	−1.73893e63	−0.529747
$901$	−8.76523e62	−0.260723
$902$	3.16108e63	0.918109
$903$	2.96387e63	0.840569
$904$	1.51894e63	0.420647
$905$	−9.57039e63	−2.58813
$906$	1.72000e63	0.454225
$907$	−1.34194e63	−0.346081	−0.173041	−	0.984915i	$-0.555359\pi$
$907$	−1.34194e63	−0.346081	−0.173041	+	0.984915i	$0.555359\pi$
$908$	−4.34939e62	−0.109543
$909$	2.16293e63	0.532008
$910$	−2.62289e63	−0.630073
$911$	−4.78106e63	−1.12171	−0.560853	−	0.827915i	$-0.689527\pi$
$911$	−4.78106e63	−1.12171	−0.560853	+	0.827915i	$0.689527\pi$
$912$	−6.78130e61	−0.0155390
$913$	−6.25414e63	−1.39974
$914$	2.36588e63	0.517190
$915$	−9.76676e62	−0.208544
$916$	3.80166e62	0.0792904
$917$	1.41718e63	0.288726
$918$	4.56453e62	0.0908402
$919$	3.81921e63	0.742489	0.371245	−	0.928535i	$-0.378931\pi$
$919$	3.81921e63	0.742489	0.371245	+	0.928535i	$0.378931\pi$
$920$	−1.35676e64	−2.57670
$921$	−1.63007e63	−0.302429
$922$	−3.51622e63	−0.637326
$923$	3.27450e63	0.579840
$924$	−2.17331e63	−0.375989
$925$	2.79687e64	4.72744
$926$	−1.70032e63	−0.280799
$927$	2.60178e63	0.419814
$928$	−3.10282e63	−0.489188
$929$	6.39575e63	0.985266	0.492633	−	0.870237i	$-0.336035\pi$
$929$	6.39575e63	0.985266	0.492633	+	0.870237i	$0.336035\pi$
$930$	6.14604e62	0.0925150
$931$	3.27246e62	0.0481344
$932$	5.13450e63	0.738000
$933$	−3.23751e63	−0.454732
$934$	1.82899e63	0.251046
$935$	−1.26680e64	−1.69925
$936$	1.41552e63	0.185561
$937$	1.49402e64	1.91405	0.957027	−	0.290000i	$-0.0936554\pi$
$937$	1.49402e64	1.91405	0.957027	+	0.290000i	$0.0936554\pi$
$938$	4.33167e61	0.00542368
$939$	6.34550e63	0.776525
$940$	−6.81820e63	−0.815494
$941$	3.85740e63	0.450939	0.225469	−	0.974250i	$-0.427608\pi$
$941$	3.85740e63	0.450939	0.225469	+	0.974250i	$0.427608\pi$
$942$	4.35769e63	0.497923
$943$	−1.37905e64	−1.54020
$944$	−2.64868e62	−0.0289155
$945$	−3.23058e63	−0.344744
$946$	−1.17049e64	−1.22098
$947$	1.02507e64	1.04527	0.522633	−	0.852558i	$-0.324950\pi$
$947$	1.02507e64	1.04527	0.522633	+	0.852558i	$0.324950\pi$
$948$	5.44222e63	0.542496
$949$	−2.56131e63	−0.249597
$950$	6.39957e63	0.609668
$951$	−7.45008e63	−0.693872
$952$	7.61247e63	0.693156
$953$	−1.69549e63	−0.150938	−0.0754689	−	0.997148i	$-0.524045\pi$
$953$	−1.69549e63	−0.150938	−0.0754689	+	0.997148i	$0.524045\pi$
$954$	8.82769e62	0.0768346
$955$	−2.29874e64	−1.95622
$956$	−4.47913e63	−0.372691
$957$	4.30134e63	0.349943
$958$	−2.58135e63	−0.205347
$959$	9.99207e63	0.777240
$960$	−1.03431e64	−0.786722
$961$	−1.32228e64	−0.983493
$962$	−8.38204e63	−0.609657
$963$	1.86090e61	0.00132360
$964$	2.02915e63	0.141142
$965$	−1.74895e64	−1.18971
$966$	−6.79026e63	−0.451729
$967$	4.59701e63	0.299093	0.149546	−	0.988755i	$-0.452219\pi$
$967$	4.59701e63	0.299093	0.149546	+	0.988755i	$0.452219\pi$
$968$	7.24514e63	0.461027
$969$	2.34555e63	0.145977
$970$	2.51417e64	1.53039
$971$	−3.19574e63	−0.190265	−0.0951324	−	0.995465i	$-0.530327\pi$
$971$	−3.19574e63	−0.190265	−0.0951324	+	0.995465i	$0.530327\pi$
$972$	6.41889e62	0.0373796
$973$	−9.39274e62	−0.0535016
$974$	1.74053e64	0.969762
$975$	−1.57316e64	−0.857381
$976$	−2.72958e62	−0.0145521
$977$	5.68464e63	0.296462	0.148231	−	0.988953i	$-0.452642\pi$
$977$	5.68464e63	0.296462	0.148231	+	0.988953i	$0.452642\pi$
$978$	4.21518e63	0.215046
$979$	2.17202e64	1.08402
$980$	3.20513e63	0.156489
$981$	6.01307e63	0.287219
$982$	1.70458e64	0.796563
$983$	2.85765e64	1.30650	0.653249	−	0.757143i	$-0.273406\pi$
$983$	2.85765e64	1.30650	0.653249	+	0.757143i	$0.273406\pi$
$984$	−1.55705e64	−0.696479
$985$	−5.10432e64	−2.23388
$986$	−5.54689e63	−0.237518
$987$	−9.26855e63	−0.388323
$988$	2.67798e63	0.109783
$989$	5.10638e64	2.04830
$990$	1.27582e64	0.500765
$991$	−3.67835e64	−1.41276	−0.706381	−	0.707832i	$-0.749674\pi$
$991$	−3.67835e64	−1.41276	−0.706381	+	0.707832i	$0.749674\pi$
$992$	−3.32338e63	−0.124905
$993$	2.31179e63	0.0850234
$994$	−1.77352e64	−0.638306
$995$	−2.95638e64	−1.04127
$996$	1.13417e64	0.390932
$997$	2.35927e64	0.795850	0.397925	−	0.917418i	$-0.369730\pi$
$997$	2.35927e64	0.795850	0.397925	+	0.917418i	$0.369730\pi$
$998$	1.50447e63	0.0496681
$999$	−1.03241e64	−0.333574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.44.a.b.1.2	✓	4
3.2	odd	2		9.44.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.44.a.b.1.2	✓	4	1.1	even	1	trivial
9.44.a.c.1.3		4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-1.91590e6 q^{2} -1.04604e10 q^{3} -5.12540e12 q^{4} +2.05854e15 q^{5} +2.00410e16 q^{6} +1.37114e18 q^{7} +2.66723e19 q^{8} +1.09419e20 q^{9} -3.94396e21 q^{10} -2.95641e22 q^{11} +5.36135e22 q^{12} +4.85026e23 q^{13} -2.62698e24 q^{14} -2.15330e25 q^{15} -6.01799e24 q^{16} +2.08153e26 q^{17} -2.09636e26 q^{18} -1.07725e27 q^{19} -1.05508e28 q^{20} -1.43426e28 q^{21} +5.66420e28 q^{22} -2.47106e29 q^{23} -2.79001e29 q^{24} +3.10071e30 q^{25} -9.29263e29 q^{26} -1.14456e30 q^{27} -7.02766e30 q^{28} +1.39089e31 q^{29} +4.12553e31 q^{30} +1.48976e31 q^{31} -2.23082e32 q^{32} +3.09251e32 q^{33} -3.98801e32 q^{34} +2.82255e33 q^{35} -5.60816e32 q^{36} +9.02009e33 q^{37} +2.06390e33 q^{38} -5.07354e33 q^{39} +5.49059e34 q^{40} +5.58080e34 q^{41} +2.74791e34 q^{42} -2.06648e35 q^{43} +1.51528e35 q^{44} +2.25243e35 q^{45} +4.73431e35 q^{46} +6.46223e35 q^{47} +6.29503e34 q^{48} -3.03780e35 q^{49} -5.94067e36 q^{50} -2.17735e36 q^{51} -2.48595e36 q^{52} -4.21095e36 q^{53} +2.19287e36 q^{54} -6.08589e37 q^{55} +3.65715e37 q^{56} +1.12684e37 q^{57} -2.66481e37 q^{58} +4.40127e37 q^{59} +1.10366e38 q^{60} +4.53571e37 q^{61} -2.85424e37 q^{62} +1.50029e38 q^{63} +4.80338e38 q^{64} +9.98445e38 q^{65} -5.92495e38 q^{66} -1.64891e37 q^{67} -1.06687e39 q^{68} +2.58481e39 q^{69} -5.40774e39 q^{70} +6.75118e39 q^{71} +2.91845e39 q^{72} -5.28077e39 q^{73} -1.72816e40 q^{74} -3.24346e40 q^{75} +5.52132e39 q^{76} -4.05366e40 q^{77} +9.72042e39 q^{78} +1.01508e41 q^{79} -1.23883e40 q^{80} +1.19725e40 q^{81} -1.06923e41 q^{82} +2.11545e41 q^{83} +7.35118e40 q^{84} +4.28491e41 q^{85} +3.95917e41 q^{86} -1.45492e41 q^{87} -7.88542e41 q^{88} -7.34681e41 q^{89} -4.31545e41 q^{90} +6.65040e41 q^{91} +1.26652e42 q^{92} -1.55834e41 q^{93} -1.23810e42 q^{94} -2.21755e42 q^{95} +2.33351e42 q^{96} -6.37472e42 q^{97} +5.82013e41 q^{98} -3.23487e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5} - 17\!\cdots\!42 q^{6} + 11\!\cdots\!28 q^{7} + 77\!\cdots\!48 q^{8} + 43\!\cdots\!36 q^{9} + 53\!\cdots\!60 q^{10}+ \cdots + 95\!\cdots\!64 q^{99}+O(q^{100}) \) 4 * q + 1660014 * q^2 - 41841412812 * q^3 + 29333750564548 * q^4 + 1650650807536920 * q^5 - 17364332761924842 * q^6 + 114481425784209728 * q^7 + 77966588660971173048 * q^8 + 437675956526049436836 * q^9 + 5359044979781953498260 * q^10 + 8715200555107127298096 * q^11 - 306841391673872730047244 * q^12 - 1622373819341917660395496 * q^13 - 13467578670319198438149408 * q^14 - 17266390461653357662754760 * q^15 + 265331272220473559715915280 * q^16 + 293411853143037894856883976 * q^17 + 181637053824158357459968926 * q^18 - 2594414378517928782354874288 * q^19 + 8558701143076231384453792920 * q^20 - 1197516148885865015108558784 * q^21 + 74078936455805689993083157032 * q^22 - 165719576853043327961325838944 * q^23 - 815558055426773291083314072744 * q^24 + 2162829068891925341689803823900 * q^25 + 6101006421154528454709899598228 * q^26 - 4578245093723349979543798785708 * q^27 - 41688560653908286820790912158656 * q^28 + 50103930548121691368807724902264 * q^29 - 56057503319283227517121045926780 * q^30 + 153232269806257085529351412219424 * q^31 + 1375373155850513577371148105862368 * q^32 - 91164076041402217040767229401488 * q^33 + 60331877005992911765859543576156 * q^34 + 794758271825314756362531708950400 * q^35 + 3209669334208772143164043116722532 * q^36 + 19599702088800583695304816898379128 * q^37 + 30934350335669500918957603769116056 * q^38 + 16970603177616571751080292830373688 * q^39 + 196041911393456394134889832442905680 * q^40 - 9038336825299507042215563101837656 * q^41 + 140875629680727908414888757365353824 * q^42 + 57884775638210824781567117092305200 * q^43 + 1103928490692495293822086256175019824 * q^44 + 180612542769804348503301347569496280 * q^45 + 718247490543964330689612210436911024 * q^46 + 489795556049192314087538359958202240 * q^47 - 2775458823227495522551186169224641840 * q^48 - 4317642451006561098818513062358614620 * q^49 - 5579808201219996041105683525421159550 * q^50 - 3069191617822942060616583524950975128 * q^51 - 13582094185786578557618520483683206504 * q^52 - 40271515633256644720413455555285829864 * q^53 - 1899987737753018273235604899364569978 * q^54 - 47661104270181626262923295497298490080 * q^55 - 117390605534482290403396341738920952960 * q^56 + 27138490754239270731431699141143144464 * q^57 + 166036404448317657164763132092855468772 * q^58 - 31284936358538459187079576876991825232 * q^59 - 89527036915497218235540357176220722760 * q^60 - 246678251415393769778200255087667843560 * q^61 + 1447587501085892804433014348598690126576 * q^62 + 12526441883642482992216456268928185152 * q^63 + 3779239307999191671459925914328934335552 * q^64 + 3201204112021109289173748012488728936080 * q^65 - 774891840230320517264772449505033173496 * q^66 + 1029262961963280586877382927523715757776 * q^67 - 5728258265472538567897226405540492998008 * q^68 + 1733485306534536435938034199524532537632 * q^69 - 13998939704532003940217885479727831428800 * q^70 - 7158914166122718301934674138622261107872 * q^71 + 8531025317315899527338195700682675399032 * q^72 + 5436935716056938749789214886435330158696 * q^73 - 39560290302967463129010858736787279461788 * q^74 - 22623955978325158908781808861774012951700 * q^75 - 84965301579645016687884089536788004332208 * q^76 - 70649133554843036086189895413395482145024 * q^77 - 63818682059047338679179338698132672924284 * q^78 - 18459961314698254348045108075380001958560 * q^79 + 422317828506146509768424873205600266179680 * q^80 + 47890060730248079154410960106868188422724 * q^81 + 147229844429377279789779107991029019615756 * q^82 + 207863929126228047172838511060419328637008 * q^83 + 436077068964569322514102904992088933775168 * q^84 + 221112002042063917840135331898684555973680 * q^85 + 458138780643704418519204317947537057045416 * q^86 - 524104810391934279943485339472540094351592 * q^87 + 1517878779794169852250121294325123418262688 * q^88 - 442176536724138726190556195414134338798168 * q^89 + 586381284398047440622894870098903276476340 * q^90 - 241286657628373017846026300207834298513536 * q^91 - 501856507576284139621951265540431125198432 * q^92 - 1602863664270841494058395995322025177215072 * q^93 - 12731451681111622228496468053131446537940672 * q^94 - 877953040109009235535219131018818763586080 * q^95 - 14386888996121137888249277408944804185964704 * q^96 - 5068444705076967721898551548017617825231864 * q^97 + 6262356698119668842821753019159492533814046 * q^98 + 953608434818217241633690669647290773766064 * q^99

Introduction

L-functions

Modular forms

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