LMFDB - Embedded newform 3.44.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,44,Mod(1,3)]

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

lf = mfeigenbasis(mf)

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")

//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);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	3.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:	$35.1331186037$
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			1.4
Root			$904229.$ 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)

$f(q)$	$=$	$q+5.84038e6 q^{2} -1.04604e10 q^{3} +2.53139e13 q^{4} +1.12222e15 q^{5} -6.10924e16 q^{6} -1.55171e18 q^{7} +9.64704e19 q^{8} +1.09419e20 q^{9} +O(q^{10})$	\(q+5.84038e6 q^{2} -1.04604e10 q^{3} +2.53139e13 q^{4} +1.12222e15 q^{5} -6.10924e16 q^{6} -1.55171e18 q^{7} +9.64704e19 q^{8} +1.09419e20 q^{9} +6.55417e21 q^{10} +2.50474e22 q^{11} -2.64793e23 q^{12} +2.47924e23 q^{13} -9.06257e24 q^{14} -1.17388e25 q^{15} +3.40760e26 q^{16} -1.03830e26 q^{17} +6.39048e26 q^{18} -6.03963e26 q^{19} +2.84077e28 q^{20} +1.62314e28 q^{21} +1.46286e29 q^{22} -3.77076e28 q^{23} -1.00911e30 q^{24} +1.22504e29 q^{25} +1.44797e30 q^{26} -1.14456e30 q^{27} -3.92798e31 q^{28} +4.08866e31 q^{29} -6.85590e31 q^{30} +1.22125e32 q^{31} +1.14160e33 q^{32} -2.62004e32 q^{33} -6.06407e32 q^{34} -1.74135e33 q^{35} +2.76982e33 q^{36} +1.91574e33 q^{37} -3.52737e33 q^{38} -2.59338e33 q^{39} +1.08261e35 q^{40} -5.34995e34 q^{41} +9.47977e34 q^{42} -3.81616e33 q^{43} +6.34047e35 q^{44} +1.22792e35 q^{45} -2.20227e35 q^{46} -9.23813e35 q^{47} -3.56447e36 q^{48} +2.23986e35 q^{49} +7.15467e35 q^{50} +1.08610e36 q^{51} +6.27594e36 q^{52} -7.06846e36 q^{53} -6.68467e36 q^{54} +2.81086e37 q^{55} -1.49694e38 q^{56} +6.31767e36 q^{57} +2.38793e38 q^{58} -7.34591e37 q^{59} -2.97155e38 q^{60} -4.55925e38 q^{61} +7.13257e38 q^{62} -1.69786e38 q^{63} +3.67005e39 q^{64} +2.78225e38 q^{65} -1.53020e39 q^{66} +9.19424e38 q^{67} -2.62835e39 q^{68} +3.94435e38 q^{69} -1.01702e40 q^{70} -1.09989e40 q^{71} +1.05557e40 q^{72} +6.59819e39 q^{73} +1.11886e40 q^{74} -1.28143e39 q^{75} -1.52887e40 q^{76} -3.88662e40 q^{77} -1.51463e40 q^{78} -1.10389e41 q^{79} +3.82407e41 q^{80} +1.19725e40 q^{81} -3.12457e41 q^{82} -1.89663e41 q^{83} +4.10881e41 q^{84} -1.16520e41 q^{85} -2.22878e40 q^{86} -4.27688e41 q^{87} +2.41633e42 q^{88} -1.34816e41 q^{89} +7.17151e41 q^{90} -3.84707e41 q^{91} -9.54529e41 q^{92} -1.27747e42 q^{93} -5.39542e42 q^{94} -6.77778e41 q^{95} -1.19416e43 q^{96} +7.60760e42 q^{97} +1.30816e42 q^{98} +2.74066e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5}+ \cdots + 43\!\cdots\!36 q^{9}+O(q^{10}) $ 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	$ 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5}+ \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

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	5.84038e6	1.96923	0.984614	−	0.174742i	$-0.0559093\pi$
$2$	5.84038e6	1.96923	0.984614	+	0.174742i	$0.0559093\pi$
$3$	−1.04604e10	−0.577350
$3$	−1.04604e10	−0.577350
$4$	2.53139e13	2.87786
$5$	1.12222e15	1.05250	0.526250	−	0.850330i	$-0.323598\pi$
$5$	1.12222e15	1.05250	0.526250	+	0.850330i	$0.323598\pi$
$6$	−6.10924e16	−1.13693
$7$	−1.55171e18	−1.05003	−0.525016	−	0.851092i	$-0.675941\pi$
$7$	−1.55171e18	−1.05003	−0.525016	+	0.851092i	$0.675941\pi$
$8$	9.64704e19	3.69794
$9$	1.09419e20	0.333333
$10$	6.55417e21	2.07261
$11$	2.50474e22	1.02052	0.510258	−	0.860022i	$-0.329550\pi$
$11$	2.50474e22	1.02052	0.510258	+	0.860022i	$0.329550\pi$
$12$	−2.64793e23	−1.66153
$13$	2.47924e23	0.278315	0.139158	−	0.990270i	$-0.455560\pi$
$13$	2.47924e23	0.278315	0.139158	+	0.990270i	$0.455560\pi$
$14$	−9.06257e24	−2.06775
$15$	−1.17388e25	−0.607661
$16$	3.40760e26	4.40422
$17$	−1.03830e26	−0.364478	−0.182239	−	0.983254i	$-0.558334\pi$
$17$	−1.03830e26	−0.364478	−0.182239	+	0.983254i	$0.558334\pi$
$18$	6.39048e26	0.656409
$19$	−6.03963e26	−0.194003	−0.0970014	−	0.995284i	$-0.530925\pi$
$19$	−6.03963e26	−0.194003	−0.0970014	+	0.995284i	$0.530925\pi$
$20$	2.84077e28	3.02895
$21$	1.62314e28	0.606236
$22$	1.46286e29	2.00963
$23$	−3.77076e28	−0.199196	−0.0995981	−	0.995028i	$-0.531756\pi$
$23$	−3.77076e28	−0.199196	−0.0995981	+	0.995028i	$0.531756\pi$
$24$	−1.00911e30	−2.13500
$25$	1.22504e29	0.107755
$26$	1.44797e30	0.548067
$27$	−1.14456e30	−0.192450
$28$	−3.92798e31	−3.02184
$29$	4.08866e31	1.47919	0.739595	−	0.673052i	$-0.235017\pi$
$29$	4.08866e31	1.47919	0.739595	+	0.673052i	$0.235017\pi$
$30$	−6.85590e31	−1.19662
$31$	1.22125e32	1.05324	0.526621	−	0.850100i	$-0.323459\pi$
$31$	1.22125e32	1.05324	0.526621	+	0.850100i	$0.323459\pi$
$32$	1.14160e33	4.97498
$33$	−2.62004e32	−0.589195
$34$	−6.06407e32	−0.717740
$35$	−1.74135e33	−1.10516
$36$	2.76982e33	0.959287
$37$	1.91574e33	0.368128	0.184064	−	0.982914i	$-0.441075\pi$
$37$	1.91574e33	0.368128	0.184064	+	0.982914i	$0.441075\pi$
$38$	−3.52737e33	−0.382036
$39$	−2.59338e33	−0.160685
$40$	1.08261e35	3.89208
$41$	−5.34995e34	−1.13109	−0.565545	−	0.824718i	$-0.691334\pi$
$41$	−5.34995e34	−1.13109	−0.565545	+	0.824718i	$0.691334\pi$
$42$	9.47977e34	1.19382
$43$	−3.81616e33	−0.0289771	−0.0144885	−	0.999895i	$-0.504612\pi$
$43$	−3.81616e33	−0.0289771	−0.0144885	+	0.999895i	$0.504612\pi$
$44$	6.34047e35	2.93690
$45$	1.22792e35	0.350833
$46$	−2.20227e35	−0.392263
$47$	−9.23813e35	−1.03629	−0.518144	−	0.855293i	$-0.673377\pi$
$47$	−9.23813e35	−1.03629	−0.518144	+	0.855293i	$0.673377\pi$
$48$	−3.56447e36	−2.54278
$49$	2.23986e35	0.102566
$50$	7.15467e35	0.212195
$51$	1.08610e36	0.210431
$52$	6.27594e36	0.800953
$53$	−7.06846e36	−0.598954	−0.299477	−	0.954103i	$-0.596812\pi$
$53$	−7.06846e36	−0.598954	−0.299477	+	0.954103i	$0.596812\pi$
$54$	−6.68467e36	−0.378978
$55$	2.81086e37	1.07409
$56$	−1.49694e38	−3.88295
$57$	6.31767e36	0.112008
$58$	2.38793e38	2.91286
$59$	−7.34591e37	−0.620480	−0.310240	−	0.950658i	$-0.600409\pi$
$59$	−7.34591e37	−0.620480	−0.310240	+	0.950658i	$0.600409\pi$
$60$	−2.97155e38	−1.74876
$61$	−4.55925e38	−1.88062	−0.940312	−	0.340313i	$-0.889467\pi$
$61$	−4.55925e38	−1.88062	−0.940312	+	0.340313i	$0.889467\pi$
$62$	7.13257e38	2.07408
$63$	−1.69786e38	−0.350011
$64$	3.67005e39	5.39265
$65$	2.78225e38	0.292927
$66$	−1.53020e39	−1.16026
$67$	9.19424e38	0.504554	0.252277	−	0.967655i	$-0.418821\pi$
$67$	9.19424e38	0.504554	0.252277	+	0.967655i	$0.418821\pi$
$68$	−2.62835e39	−1.04892
$69$	3.94435e38	0.115006
$70$	−1.01702e40	−2.17631
$71$	−1.09989e40	−1.73498	−0.867491	−	0.497452i	$-0.834269\pi$
$71$	−1.09989e40	−1.73498	−0.867491	+	0.497452i	$0.834269\pi$
$72$	1.05557e40	1.23265
$73$	6.59819e39	0.572774	0.286387	−	0.958114i	$-0.407546\pi$
$73$	6.59819e39	0.572774	0.286387	+	0.958114i	$0.407546\pi$
$74$	1.11886e40	0.724928
$75$	−1.28143e39	−0.0622125
$76$	−1.52887e40	−0.558313
$77$	−3.88662e40	−1.07157
$78$	−1.51463e40	−0.316426
$79$	−1.10389e41	−1.75365	−0.876824	−	0.480812i	$-0.840342\pi$
$79$	−1.10389e41	−1.75365	−0.876824	+	0.480812i	$0.840342\pi$
$80$	3.82407e41	4.63544
$81$	1.19725e40	0.111111
$82$	−3.12457e41	−2.22737
$83$	−1.89663e41	−1.04185	−0.520923	−	0.853604i	$-0.674412\pi$
$83$	−1.89663e41	−1.04185	−0.520923	+	0.853604i	$0.674412\pi$
$84$	4.10881e41	1.74466
$85$	−1.16520e41	−0.383613
$86$	−2.22878e40	−0.0570625
$87$	−4.27688e41	−0.854010
$88$	2.41633e42	3.77380
$89$	−1.34816e41	−0.165141	−0.0825706	−	0.996585i	$-0.526313\pi$
$89$	−1.34816e41	−0.165141	−0.0825706	+	0.996585i	$0.526313\pi$
$90$	7.17151e41	0.690871
$91$	−3.84707e41	−0.292240
$92$	−9.54529e41	−0.573259
$93$	−1.27747e42	−0.608090
$94$	−5.39542e42	−2.04069
$95$	−6.77778e41	−0.204188
$96$	−1.19416e43	−2.87231
$97$	7.60760e42	1.46439	0.732193	−	0.681097i	$-0.238497\pi$
$97$	7.60760e42	1.46439	0.732193	+	0.681097i	$0.238497\pi$
$98$	1.30816e42	0.201977
$99$	2.74066e42	0.340172
$100$	3.10104e42	0.310104
$101$	6.35457e42	0.513070	0.256535	−	0.966535i	$-0.417419\pi$
$101$	6.35457e42	0.513070	0.256535	+	0.966535i	$0.417419\pi$
$102$	6.34323e42	0.414387
$103$	1.31047e43	0.694107	0.347054	−	0.937845i	$-0.387182\pi$
$103$	1.31047e43	0.694107	0.347054	+	0.937845i	$0.387182\pi$
$104$	2.39174e43	1.02919
$105$	1.82152e43	0.638063
$106$	−4.12825e43	−1.17948
$107$	−2.81715e43	−0.657746	−0.328873	−	0.944374i	$-0.606669\pi$
$107$	−2.81715e43	−0.657746	−0.328873	+	0.944374i	$0.606669\pi$
$108$	−2.89733e43	−0.553844
$109$	8.11440e43	1.27229	0.636146	−	0.771569i	$-0.280528\pi$
$109$	8.11440e43	1.27229	0.636146	+	0.771569i	$0.280528\pi$
$110$	1.64165e44	2.11513
$111$	−2.00393e43	−0.212539
$112$	−5.28760e44	−4.62457
$113$	1.06927e43	0.0772504	0.0386252	−	0.999254i	$-0.487702\pi$
$113$	1.06927e43	0.0772504	0.0386252	+	0.999254i	$0.487702\pi$
$114$	3.68976e43	0.220569
$115$	−4.23162e43	−0.209654
$116$	1.03500e45	4.25690
$117$	2.71276e43	0.0927718
$118$	−4.29029e44	−1.22187
$119$	1.61114e44	0.382713
$120$	−1.13245e45	−2.24709
$121$	2.49702e43	0.0414511
$122$	−2.66278e45	−3.70338
$123$	5.59624e44	0.653035
$124$	3.09147e45	3.03109
$125$	−1.13834e45	−0.939087
$126$	−9.91617e44	−0.689251
$127$	−1.72579e45	−1.01206	−0.506031	−	0.862515i	$-0.668888\pi$
$127$	−1.72579e45	−1.01206	−0.506031	+	0.862515i	$0.668888\pi$
$128$	1.13928e46	5.64438
$129$	3.99184e43	0.0167299
$130$	1.62494e45	0.576840
$131$	−3.41058e45	−1.02682	−0.513411	−	0.858143i	$-0.671618\pi$
$131$	−3.41058e45	−1.02682	−0.513411	+	0.858143i	$0.671618\pi$
$132$	−6.63236e45	−1.69562
$133$	9.37175e44	0.203709
$134$	5.36978e45	0.993582
$135$	−1.28445e45	−0.202554
$136$	−1.00165e46	−1.34782
$137$	1.24997e46	1.43684	0.718419	−	0.695611i	$-0.244866\pi$
$137$	1.24997e46	1.43684	0.718419	+	0.695611i	$0.244866\pi$
$138$	2.30365e45	0.226473
$139$	−7.01821e44	−0.0590756	−0.0295378	−	0.999564i	$-0.509404\pi$
$139$	−7.01821e44	−0.0590756	−0.0295378	+	0.999564i	$0.509404\pi$
$140$	−4.40805e46	−3.18049
$141$	9.66342e45	0.598301
$142$	−6.42378e46	−3.41658
$143$	6.20986e45	0.284025
$144$	3.72856e46	1.46807
$145$	4.58836e46	1.55685
$146$	3.85359e46	1.12792
$147$	−2.34297e45	−0.0592168
$148$	4.84948e46	1.05942
$149$	1.96373e46	0.371173	0.185587	−	0.982628i	$-0.440581\pi$
$149$	1.96373e46	0.371173	0.185587	+	0.982628i	$0.440581\pi$
$150$	−7.48404e45	−0.122511
$151$	3.89180e46	0.552263	0.276132	−	0.961120i	$-0.410947\pi$
$151$	3.89180e46	0.552263	0.276132	+	0.961120i	$0.410947\pi$
$152$	−5.82646e46	−0.717410
$153$	−1.13610e46	−0.121493
$154$	−2.26993e47	−2.11017
$155$	1.37051e47	1.10854
$156$	−6.56486e46	−0.462430
$157$	1.84154e47	1.13068	0.565339	−	0.824859i	$-0.308745\pi$
$157$	1.84154e47	1.13068	0.565339	+	0.824859i	$0.308745\pi$
$158$	−6.44712e47	−3.45333
$159$	7.39386e46	0.345806
$160$	1.28113e48	5.23616
$161$	5.85113e46	0.209162
$162$	6.99240e46	0.218803
$163$	−9.31726e46	−0.255420	−0.127710	−	0.991812i	$-0.540763\pi$
$163$	−9.31726e46	−0.255420	−0.127710	+	0.991812i	$0.540763\pi$
$164$	−1.35428e48	−3.25512
$165$	−2.94026e47	−0.620127
$166$	−1.10770e48	−2.05163
$167$	8.32780e47	1.35558	0.677791	−	0.735254i	$-0.262937\pi$
$167$	8.32780e47	1.35558	0.677791	+	0.735254i	$0.262937\pi$
$168$	1.56585e48	2.24182
$169$	−7.32065e47	−0.922541
$170$	−6.80520e47	−0.755421
$171$	−6.60851e46	−0.0646676
$172$	−9.66020e46	−0.0833920
$173$	−7.91931e47	−0.603526	−0.301763	−	0.953383i	$-0.597575\pi$
$173$	−7.91931e47	−0.603526	−0.301763	+	0.953383i	$0.597575\pi$
$174$	−2.49786e48	−1.68174
$175$	−1.90090e47	−0.113146
$176$	8.53514e48	4.49457
$177$	7.68408e47	0.358234
$178$	−7.87375e47	−0.325201
$179$	5.03154e46	0.0184230	0.00921151	−	0.999958i	$-0.497068\pi$
$179$	5.03154e46	0.0184230	0.00921151	+	0.999958i	$0.497068\pi$
$180$	3.10835e48	1.00965
$181$	1.71556e48	0.494672	0.247336	−	0.968930i	$-0.420445\pi$
$181$	1.71556e48	0.494672	0.247336	+	0.968930i	$0.420445\pi$
$182$	−2.24683e48	−0.575487
$183$	4.76914e48	1.08578
$184$	−3.63767e48	−0.736615
$185$	2.14987e48	0.387455
$186$	−7.46092e48	−1.19747
$187$	−2.60067e48	−0.371955
$188$	−2.33853e49	−2.98229
$189$	1.77603e48	0.202079
$190$	−3.95848e48	−0.402093
$191$	4.46570e48	0.405202	0.202601	−	0.979261i	$-0.435061\pi$
$191$	4.46570e48	0.405202	0.202601	+	0.979261i	$0.435061\pi$
$192$	−3.83900e49	−3.11345
$193$	2.46079e49	1.78481	0.892404	−	0.451237i	$-0.149017\pi$
$193$	2.46079e49	1.78481	0.892404	+	0.451237i	$0.149017\pi$
$194$	4.44313e49	2.88371
$195$	−2.91033e48	−0.169121
$196$	5.66997e48	0.295172
$197$	1.80008e49	0.839978	0.419989	−	0.907529i	$-0.362034\pi$
$197$	1.80008e49	0.839978	0.419989	+	0.907529i	$0.362034\pi$
$198$	1.60065e49	0.669876
$199$	−4.16022e49	−1.56234	−0.781169	−	0.624320i	$-0.785376\pi$
$199$	−4.16022e49	−1.56234	−0.781169	+	0.624320i	$0.785376\pi$
$200$	1.18180e49	0.398472
$201$	−9.61750e48	−0.291304
$202$	3.71131e49	1.01035
$203$	−6.34441e49	−1.55320
$204$	2.74934e49	0.605592
$205$	−6.00381e49	−1.19047
$206$	7.65364e49	1.36686
$207$	−4.12593e48	−0.0663987
$208$	8.44827e49	1.22576
$209$	−1.51277e49	−0.197983
$210$	1.06384e50	1.25649
$211$	−9.52137e49	−1.01538	−0.507688	−	0.861541i	$-0.669500\pi$
$211$	−9.52137e49	−1.01538	−0.507688	+	0.861541i	$0.669500\pi$
$212$	−1.78930e50	−1.72371
$213$	1.15052e50	1.00169
$214$	−1.64532e50	−1.29525
$215$	−4.28256e48	−0.0304984
$216$	−1.10416e50	−0.711668
$217$	−1.89503e50	−1.10594
$218$	4.73912e50	2.50543
$219$	−6.90194e49	−0.330691
$220$	7.11539e50	3.09109
$221$	−2.57420e49	−0.101440
$222$	−1.17037e50	−0.418537
$223$	−2.25626e50	−0.732547	−0.366274	−	0.930507i	$-0.619367\pi$
$223$	−2.25626e50	−0.732547	−0.366274	+	0.930507i	$0.619367\pi$
$224$	−1.77144e51	−5.22388
$225$	1.34042e49	0.0359184
$226$	6.24494e49	0.152124
$227$	3.85591e50	0.854222	0.427111	−	0.904199i	$-0.359531\pi$
$227$	3.85591e50	0.854222	0.427111	+	0.904199i	$0.359531\pi$
$228$	1.59925e50	0.322342
$229$	−4.43731e50	−0.814060	−0.407030	−	0.913415i	$-0.633436\pi$
$229$	−4.43731e50	−0.814060	−0.407030	+	0.913415i	$0.633436\pi$
$230$	−2.47142e50	−0.412856
$231$	4.06555e50	0.618673
$232$	3.94434e51	5.46995
$233$	1.01914e51	1.28849	0.644246	−	0.764818i	$-0.277171\pi$
$233$	1.01914e51	1.28849	0.644246	+	0.764818i	$0.277171\pi$
$234$	1.58436e50	0.182689
$235$	−1.03672e51	−1.09069
$236$	−1.85954e51	−1.78565
$237$	1.15471e51	1.01247
$238$	9.40966e50	0.753650
$239$	1.51135e51	1.10614	0.553070	−	0.833135i	$-0.313456\pi$
$239$	1.51135e51	1.10614	0.553070	+	0.833135i	$0.313456\pi$
$240$	−4.00011e51	−2.67627
$241$	−5.65653e50	−0.346086	−0.173043	−	0.984914i	$-0.555360\pi$
$241$	−5.65653e50	−0.346086	−0.173043	+	0.984914i	$0.555360\pi$
$242$	1.45835e50	0.0816268
$243$	−1.25237e50	−0.0641500
$244$	−1.15413e52	−5.41218
$245$	2.51361e50	0.107951
$246$	3.26841e51	1.28597
$247$	−1.49737e50	−0.0539940
$248$	1.17815e52	3.89482
$249$	1.98394e51	0.601510
$250$	−6.64832e51	−1.84928
$251$	−1.07547e51	−0.274546	−0.137273	−	0.990533i	$-0.543834\pi$
$251$	−1.07547e51	−0.274546	−0.137273	+	0.990533i	$0.543834\pi$
$252$	−4.29796e51	−1.00728
$253$	−9.44477e50	−0.203283
$254$	−1.00793e52	−1.99298
$255$	1.21884e51	0.221479
$256$	3.42562e52	5.72242
$257$	−4.15883e51	−0.638864	−0.319432	−	0.947609i	$-0.603492\pi$
$257$	−4.15883e51	−0.638864	−0.319432	+	0.947609i	$0.603492\pi$
$258$	2.33138e50	0.0329451
$259$	−2.97267e51	−0.386546
$260$	7.04297e51	0.843003
$261$	4.47377e51	0.493063
$262$	−1.99191e52	−2.02205
$263$	1.73259e52	1.62049	0.810247	−	0.586089i	$-0.199333\pi$
$263$	1.73259e52	1.62049	0.810247	+	0.586089i	$0.199333\pi$
$264$	−2.52757e52	−2.17880
$265$	−7.93235e51	−0.630399
$266$	5.47346e51	0.401150
$267$	1.41022e51	0.0953444
$268$	2.32742e52	1.45204
$269$	−3.21419e51	−0.185096	−0.0925480	−	0.995708i	$-0.529501\pi$
$269$	−3.21419e51	−0.185096	−0.0925480	+	0.995708i	$0.529501\pi$
$270$	−7.50165e51	−0.398874
$271$	−2.56205e52	−1.25820	−0.629098	−	0.777326i	$-0.716576\pi$
$271$	−2.56205e52	−1.25820	−0.629098	+	0.777326i	$0.716576\pi$
$272$	−3.53811e52	−1.60524
$273$	4.02417e51	0.168725
$274$	7.30030e52	2.82946
$275$	3.06839e51	0.109966
$276$	9.98471e51	0.330971
$277$	3.56124e52	1.09216	0.546080	−	0.837733i	$-0.316120\pi$
$277$	3.56124e52	1.09216	0.546080	+	0.837733i	$0.316120\pi$
$278$	−4.09890e51	−0.116333
$279$	1.33628e52	0.351081
$280$	−1.67989e53	−4.08680
$281$	2.80555e52	0.632168	0.316084	−	0.948731i	$-0.397632\pi$
$281$	2.80555e52	0.632168	0.316084	+	0.948731i	$0.397632\pi$
$282$	5.64380e52	1.17819
$283$	1.65450e52	0.320080	0.160040	−	0.987111i	$-0.448838\pi$
$283$	1.65450e52	0.320080	0.160040	+	0.987111i	$0.448838\pi$
$284$	−2.78426e53	−4.99304
$285$	7.08980e51	0.117888
$286$	3.62679e52	0.559310
$287$	8.30157e52	1.18768
$288$	1.24913e53	1.65833
$289$	−7.03721e52	−0.867156
$290$	2.67978e53	3.06579
$291$	−7.95782e52	−0.845464
$292$	1.67026e53	1.64836
$293$	−1.33492e53	−1.22405	−0.612026	−	0.790838i	$-0.709645\pi$
$293$	−1.33492e53	−1.22405	−0.612026	+	0.790838i	$0.709645\pi$
$294$	−1.36839e52	−0.116611
$295$	−8.24371e52	−0.653054
$296$	1.84812e53	1.36131
$297$	−2.86683e52	−0.196398
$298$	1.14689e53	0.730925
$299$	−9.34865e51	−0.0554394
$300$	−3.24380e52	−0.179039
$301$	5.92157e51	0.0304269
$302$	2.27296e53	1.08753
$303$	−6.64711e52	−0.296221
$304$	−2.05807e53	−0.854431
$305$	−5.11647e53	−1.97936
$306$	−6.63524e52	−0.239247
$307$	2.94135e53	0.988715	0.494358	−	0.869259i	$-0.335403\pi$
$307$	2.94135e53	0.988715	0.494358	+	0.869259i	$0.335403\pi$
$308$	−9.83857e53	−3.08384
$309$	−1.37080e53	−0.400743
$310$	8.00429e53	2.18296
$311$	−4.93184e53	−1.25505	−0.627525	−	0.778596i	$-0.715932\pi$
$311$	−4.93184e53	−1.25505	−0.627525	+	0.778596i	$0.715932\pi$
$312$	−2.50184e53	−0.594205
$313$	3.03044e53	0.671896	0.335948	−	0.941881i	$-0.390943\pi$
$313$	3.03044e53	0.671896	0.335948	+	0.941881i	$0.390943\pi$
$314$	1.07553e54	2.22656
$315$	−1.90537e53	−0.368386
$316$	−2.79437e54	−5.04675
$317$	1.06006e53	0.178878	0.0894391	−	0.995992i	$-0.471493\pi$
$317$	1.06006e53	0.178878	0.0894391	+	0.995992i	$0.471493\pi$
$318$	4.31829e53	0.680972
$319$	1.02410e54	1.50954
$320$	4.11859e54	5.67576
$321$	2.94684e53	0.379750
$322$	3.41728e53	0.411888
$323$	6.27095e52	0.0707097
$324$	3.03071e53	0.319762
$325$	3.03716e52	0.0299899
$326$	−5.44163e53	−0.502980
$327$	−8.48795e53	−0.734558
$328$	−5.16112e54	−4.18270
$329$	1.43349e54	1.08813
$330$	−1.71722e54	−1.22117
$331$	9.09091e53	0.605767	0.302883	−	0.953028i	$-0.402051\pi$
$331$	9.09091e53	0.605767	0.302883	+	0.953028i	$0.402051\pi$
$332$	−4.80111e54	−2.99829
$333$	2.09618e53	0.122709
$334$	4.86375e54	2.66945
$335$	1.03179e54	0.531043
$336$	5.53102e54	2.67000
$337$	1.08227e54	0.490111	0.245055	−	0.969509i	$-0.421194\pi$
$337$	1.08227e54	0.490111	0.245055	+	0.969509i	$0.421194\pi$
$338$	−4.27554e54	−1.81669
$339$	−1.11849e53	−0.0446005
$340$	−2.94957e54	−1.10398
$341$	3.05891e54	1.07485
$342$	−3.85962e53	−0.127345
$343$	3.04108e54	0.942334
$344$	−3.68146e53	−0.107155
$345$	4.42642e53	0.121044
$346$	−4.62517e54	−1.18848
$347$	−7.73095e54	−1.86702	−0.933511	−	0.358550i	$-0.883271\pi$
$347$	−7.73095e54	−1.86702	−0.933511	+	0.358550i	$0.883271\pi$
$348$	−1.08265e55	−2.45772
$349$	1.87438e53	0.0400046	0.0200023	−	0.999800i	$-0.493633\pi$
$349$	1.87438e53	0.0400046	0.0200023	+	0.999800i	$0.493633\pi$
$350$	−1.11020e54	−0.222811
$351$	−2.83765e53	−0.0535618
$352$	2.85942e55	5.07704
$353$	2.76868e54	0.462505	0.231253	−	0.972894i	$-0.425718\pi$
$353$	2.76868e54	0.462505	0.231253	+	0.972894i	$0.425718\pi$
$354$	4.48780e54	0.705445
$355$	−1.23432e55	−1.82607
$356$	−3.41272e54	−0.475253
$357$	−1.68531e54	−0.220960
$358$	2.93861e53	0.0362792
$359$	−4.17292e54	−0.485187	−0.242593	−	0.970128i	$-0.577998\pi$
$359$	−4.17292e54	−0.485187	−0.242593	+	0.970128i	$0.577998\pi$
$360$	1.18458e55	1.29736
$361$	−9.32704e54	−0.962363
$362$	1.00195e55	0.974121
$363$	−2.61197e53	−0.0239318
$364$	−9.73843e54	−0.841026
$365$	7.40460e54	0.602844
$366$	2.78536e55	2.13815
$367$	2.15332e55	1.55879	0.779395	−	0.626533i	$-0.215527\pi$
$367$	2.15332e55	1.55879	0.779395	+	0.626533i	$0.215527\pi$
$368$	−1.28493e55	−0.877304
$369$	−5.85386e54	−0.377030
$370$	1.25561e55	0.762986
$371$	1.09682e55	0.628921
$372$	−3.23378e55	−1.75000
$373$	−2.85558e55	−1.45866	−0.729330	−	0.684162i	$-0.760168\pi$
$373$	−2.85558e55	−1.45866	−0.729330	+	0.684162i	$0.760168\pi$
$374$	−1.51889e55	−0.732465
$375$	1.19074e55	0.542182
$376$	−8.91207e55	−3.83213
$377$	1.01368e55	0.411681
$378$	1.03727e55	0.397939
$379$	−1.10097e55	−0.399054	−0.199527	−	0.979892i	$-0.563941\pi$
$379$	−1.10097e55	−0.399054	−0.199527	+	0.979892i	$0.563941\pi$
$380$	−1.71572e55	−0.587624
$381$	1.80523e55	0.584314
$382$	2.60814e55	0.797936
$383$	4.65254e55	1.34560	0.672801	−	0.739824i	$-0.265091\pi$
$383$	4.65254e55	1.34560	0.672801	+	0.739824i	$0.265091\pi$
$384$	−1.19173e56	−3.25878
$385$	−4.36164e55	−1.12783
$386$	1.43719e56	3.51470
$387$	−4.17560e53	−0.00965903
$388$	1.92578e56	4.21430
$389$	−4.74715e55	−0.982916	−0.491458	−	0.870901i	$-0.663536\pi$
$389$	−4.74715e55	−0.982916	−0.491458	+	0.870901i	$0.663536\pi$
$390$	−1.69974e55	−0.333039
$391$	3.91519e54	0.0726026
$392$	2.16080e55	0.379284
$393$	3.56759e55	0.592836
$394$	1.05131e56	1.65411
$395$	−1.23880e56	−1.84571
$396$	6.93768e55	0.978967
$397$	−9.79248e55	−1.30887	−0.654435	−	0.756118i	$-0.727094\pi$
$397$	−9.79248e55	−1.30887	−0.654435	+	0.756118i	$0.727094\pi$
$398$	−2.42972e56	−3.07660
$399$	−9.80318e54	−0.117612
$400$	4.17443e55	0.474578
$401$	1.75250e56	1.88822	0.944112	−	0.329626i	$-0.106923\pi$
$401$	1.75250e56	1.88822	0.944112	+	0.329626i	$0.106923\pi$
$402$	−5.61698e55	−0.573645
$403$	3.02778e55	0.293134
$404$	1.60859e56	1.47654
$405$	1.34358e55	0.116944
$406$	−3.70537e56	−3.05860
$407$	4.79842e55	0.375680
$408$	1.04776e56	0.778162
$409$	−7.29856e55	−0.514264	−0.257132	−	0.966376i	$-0.582778\pi$
$409$	−7.29856e55	−0.514264	−0.257132	+	0.966376i	$0.582778\pi$
$410$	−3.50645e56	−2.34431
$411$	−1.30751e56	−0.829559
$412$	3.31731e56	1.99754
$413$	1.13987e56	0.651523
$414$	−2.40970e55	−0.130754
$415$	−2.12843e56	−1.09654
$416$	2.83032e56	1.38461
$417$	7.34129e54	0.0341073
$418$	−8.83515e55	−0.389873
$419$	2.05799e56	0.862663	0.431331	−	0.902194i	$-0.358044\pi$
$419$	2.05799e56	0.862663	0.431331	+	0.902194i	$0.358044\pi$
$420$	4.61098e56	1.83626
$421$	1.61027e56	0.609303	0.304651	−	0.952464i	$-0.401460\pi$
$421$	1.61027e56	0.609303	0.304651	+	0.952464i	$0.401460\pi$
$422$	−5.56084e56	−1.99951
$423$	−1.01083e56	−0.345429
$424$	−6.81897e56	−2.21489
$425$	−1.27195e55	−0.0392744
$426$	6.71950e56	1.97256
$427$	7.07463e56	1.97472
$428$	−7.13131e56	−1.89290
$429$	−6.49573e55	−0.163982
$430$	−2.50118e55	−0.0600583
$431$	4.99012e55	0.113986	0.0569928	−	0.998375i	$-0.481849\pi$
$431$	4.99012e55	0.113986	0.0569928	+	0.998375i	$0.481849\pi$
$432$	−3.90021e56	−0.847592
$433$	1.70771e56	0.353122	0.176561	−	0.984290i	$-0.443503\pi$
$433$	1.70771e56	0.353122	0.176561	+	0.984290i	$0.443503\pi$
$434$	−1.10677e57	−2.17785
$435$	−4.79959e56	−0.898846
$436$	2.05407e57	3.66148
$437$	2.27740e55	0.0386446
$438$	−4.03099e56	−0.651206
$439$	8.43143e56	1.29692	0.648461	−	0.761248i	$-0.275413\pi$
$439$	8.43143e56	1.29692	0.648461	+	0.761248i	$0.275413\pi$
$440$	2.71165e57	3.97192
$441$	2.45083e55	0.0341888
$442$	−1.50343e56	−0.199758
$443$	6.70909e56	0.849149	0.424574	−	0.905393i	$-0.360424\pi$
$443$	6.70909e56	0.849149	0.424574	+	0.905393i	$0.360424\pi$
$444$	−5.07273e56	−0.611657
$445$	−1.51293e56	−0.173811
$446$	−1.31774e57	−1.44255
$447$	−2.05413e56	−0.214297
$448$	−5.69484e57	−5.66245
$449$	3.02462e56	0.286665	0.143332	−	0.989675i	$-0.454218\pi$
$449$	3.02462e56	0.286665	0.143332	+	0.989675i	$0.454218\pi$
$450$	7.82857e55	0.0707315
$451$	−1.34002e57	−1.15429
$452$	2.70674e56	0.222316
$453$	−4.07096e56	−0.318849
$454$	2.25200e57	1.68216
$455$	−4.31724e56	−0.307582
$456$	6.09468e56	0.414197
$457$	1.97429e57	1.28001	0.640004	−	0.768371i	$-0.278933\pi$
$457$	1.97429e57	1.28001	0.640004	+	0.768371i	$0.278933\pi$
$458$	−2.59155e57	−1.60307
$459$	1.18840e56	0.0701438
$460$	−1.07119e57	−0.603354
$461$	−1.53445e57	−0.824864	−0.412432	−	0.910988i	$-0.635321\pi$
$461$	−1.53445e57	−0.824864	−0.412432	+	0.910988i	$0.635321\pi$
$462$	2.37443e57	1.21831
$463$	−3.68882e57	−1.80674	−0.903370	−	0.428861i	$-0.858915\pi$
$463$	−3.68882e57	−1.80674	−0.903370	+	0.428861i	$0.858915\pi$
$464$	1.39325e58	6.51468
$465$	−1.43360e57	−0.640015
$466$	5.95217e57	2.53734
$467$	−7.85062e56	−0.319588	−0.159794	−	0.987150i	$-0.551083\pi$
$467$	−7.85062e56	−0.319588	−0.159794	+	0.987150i	$0.551083\pi$
$468$	6.86707e56	0.266984
$469$	−1.42668e57	−0.529797
$470$	−6.05483e57	−2.14782
$471$	−1.92632e57	−0.652797
$472$	−7.08663e57	−2.29449
$473$	−9.55848e55	−0.0295716
$474$	6.74392e57	1.99378
$475$	−7.39876e55	−0.0209048
$476$	4.07843e57	1.10140
$477$	−7.73424e56	−0.199651
$478$	8.82686e57	2.17824
$479$	1.37087e57	0.323432	0.161716	−	0.986837i	$-0.448297\pi$
$479$	1.37087e57	0.323432	0.161716	+	0.986837i	$0.448297\pi$
$480$	−1.34011e58	−3.02310
$481$	4.74958e56	0.102456
$482$	−3.30363e57	−0.681522
$483$	−6.12049e56	−0.120760
$484$	6.32094e56	0.119291
$485$	8.53739e57	1.54127
$486$	−7.31430e56	−0.126326
$487$	−2.84405e57	−0.469963	−0.234982	−	0.972000i	$-0.575503\pi$
$487$	−2.84405e57	−0.469963	−0.234982	+	0.972000i	$0.575503\pi$
$488$	−4.39833e58	−6.95443
$489$	9.74618e56	0.147467
$490$	1.46804e57	0.212580
$491$	7.25320e57	1.00526	0.502629	−	0.864502i	$-0.332366\pi$
$491$	7.25320e57	1.00526	0.502629	+	0.864502i	$0.332366\pi$
$492$	1.41663e58	1.87934
$493$	−4.24525e57	−0.539132
$494$	−8.74522e56	−0.106327
$495$	3.07561e57	0.358031
$496$	4.16154e58	4.63871
$497$	1.70671e58	1.82179
$498$	1.15870e58	1.18451
$499$	−5.10524e57	−0.499867	−0.249934	−	0.968263i	$-0.580409\pi$
$499$	−5.10524e57	−0.499867	−0.249934	+	0.968263i	$0.580409\pi$
$500$	−2.88158e58	−2.70256
$501$	−8.71117e57	−0.782646
$502$	−6.28118e57	−0.540644
$503$	6.21015e57	0.512142	0.256071	−	0.966658i	$-0.417572\pi$
$503$	6.21015e57	0.512142	0.256071	+	0.966658i	$0.417572\pi$
$504$	−1.63794e58	−1.29432
$505$	7.13121e57	0.540006
$506$	−5.51611e57	−0.400310
$507$	7.65766e57	0.532629
$508$	−4.36865e58	−2.91257
$509$	−1.13593e58	−0.725970	−0.362985	−	0.931795i	$-0.618242\pi$
$509$	−1.13593e58	−0.725970	−0.362985	+	0.931795i	$0.618242\pi$
$510$	7.11848e57	0.436143
$511$	−1.02385e58	−0.601431
$512$	9.98570e58	5.62438
$513$	6.91273e56	0.0373359
$514$	−2.42891e58	−1.25807
$515$	1.47063e58	0.730548
$516$	1.01049e57	0.0481464
$517$	−2.31391e58	−1.05755
$518$	−1.73615e58	−0.761197
$519$	8.28387e57	0.348446
$520$	2.68405e58	1.08322
$521$	3.70604e58	1.43515	0.717577	−	0.696479i	$-0.245251\pi$
$521$	3.70604e58	1.43515	0.717577	+	0.696479i	$0.245251\pi$
$522$	2.61285e58	0.970954
$523$	−1.73713e58	−0.619506	−0.309753	−	0.950817i	$-0.600246\pi$
$523$	−1.73713e58	−0.619506	−0.309753	+	0.950817i	$0.600246\pi$
$524$	−8.63351e58	−2.95505
$525$	1.98841e57	0.0653251
$526$	1.01190e59	3.19112
$527$	−1.26803e58	−0.383884
$528$	−8.92806e58	−2.59494
$529$	−3.44123e58	−0.960321
$530$	−4.63279e58	−1.24140
$531$	−8.03782e57	−0.206827
$532$	2.37236e58	0.586247
$533$	−1.32638e58	−0.314800
$534$	8.23622e57	0.187755
$535$	−3.16145e58	−0.692278
$536$	8.86972e58	1.86581
$537$	−5.26317e56	−0.0106365
$538$	−1.87721e58	−0.364496
$539$	5.61026e57	0.104671
$540$	−3.25144e58	−0.582921
$541$	7.40944e58	1.27657	0.638284	−	0.769801i	$-0.279645\pi$
$541$	7.40944e58	1.27657	0.638284	+	0.769801i	$0.279645\pi$
$542$	−1.49634e59	−2.47768
$543$	−1.79454e58	−0.285599
$544$	−1.18533e59	−1.81327
$545$	9.10612e58	1.33909
$546$	2.35027e58	0.332258
$547$	5.02792e57	0.0683378	0.0341689	−	0.999416i	$-0.489122\pi$
$547$	5.02792e57	0.0683378	0.0341689	+	0.999416i	$0.489122\pi$
$548$	3.16417e59	4.13502
$549$	−4.98869e58	−0.626875
$550$	1.79206e58	0.216548
$551$	−2.46940e58	−0.286967
$552$	3.80513e58	0.425285
$553$	1.71291e59	1.84139
$554$	2.07990e59	2.15071
$555$	−2.24884e58	−0.223697
$556$	−1.77658e58	−0.170011
$557$	−7.96564e58	−0.733389	−0.366694	−	0.930341i	$-0.619511\pi$
$557$	−7.96564e58	−0.733389	−0.366694	+	0.930341i	$0.619511\pi$
$558$	7.80438e58	0.691359
$559$	−9.46119e56	−0.00806477
$560$	−5.93384e59	−4.86736
$561$	2.72039e58	0.214748
$562$	1.63855e59	1.24488
$563$	−1.11608e59	−0.816140	−0.408070	−	0.912951i	$-0.633798\pi$
$563$	−1.11608e59	−0.816140	−0.408070	+	0.912951i	$0.633798\pi$
$564$	2.44619e59	1.72183
$565$	1.19995e58	0.0813060
$566$	9.66292e58	0.630311
$567$	−1.85779e58	−0.116670
$568$	−1.06107e60	−6.41586
$569$	−1.60618e59	−0.935147	−0.467574	−	0.883954i	$-0.654872\pi$
$569$	−1.60618e59	−0.935147	−0.467574	+	0.883954i	$0.654872\pi$
$570$	4.14071e58	0.232148
$571$	−2.42835e59	−1.31110	−0.655549	−	0.755152i	$-0.727563\pi$
$571$	−2.42835e59	−1.31110	−0.655549	+	0.755152i	$0.727563\pi$
$572$	1.57196e59	0.817385
$573$	−4.67128e58	−0.233944
$574$	4.84843e59	2.33881
$575$	−4.61932e57	−0.0214644
$576$	4.01573e59	1.79755
$577$	3.48888e59	1.50455	0.752273	−	0.658852i	$-0.228957\pi$
$577$	3.48888e59	1.50455	0.752273	+	0.658852i	$0.228957\pi$
$578$	−4.11000e59	−1.70763
$579$	−2.57407e59	−1.03046
$580$	1.16149e60	4.48039
$581$	2.94302e59	1.09397
$582$	−4.64767e59	−1.66491
$583$	−1.77046e59	−0.611242
$584$	6.36530e59	2.11808
$585$	3.04431e58	0.0976423
$586$	−7.79641e59	−2.41044
$587$	−2.28083e59	−0.679788	−0.339894	−	0.940464i	$-0.610391\pi$
$587$	−2.28083e59	−0.679788	−0.339894	+	0.940464i	$0.610391\pi$
$588$	−5.93099e58	−0.170418
$589$	−7.37591e58	−0.204332
$590$	−4.81464e59	−1.28601
$591$	−1.88295e59	−0.484961
$592$	6.52806e59	1.62132
$593$	1.06412e59	0.254867	0.127433	−	0.991847i	$-0.459326\pi$
$593$	1.06412e59	0.254867	0.127433	+	0.991847i	$0.459326\pi$
$594$	−1.67433e59	−0.386753
$595$	1.80805e59	0.402806
$596$	4.97097e59	1.06818
$597$	4.35173e59	0.902016
$598$	−5.45996e58	−0.109173
$599$	−6.02562e59	−1.16232	−0.581160	−	0.813790i	$-0.697401\pi$
$599$	−6.02562e59	−1.16232	−0.581160	+	0.813790i	$0.697401\pi$
$600$	−1.23620e59	−0.230058
$601$	−2.73543e59	−0.491162	−0.245581	−	0.969376i	$-0.578979\pi$
$601$	−2.73543e59	−0.491162	−0.245581	+	0.969376i	$0.578979\pi$
$602$	3.45842e58	0.0599174
$603$	1.00602e59	0.168185
$604$	9.85167e59	1.58934
$605$	2.80220e58	0.0436273
$606$	−3.88216e59	−0.583327
$607$	1.04019e60	1.50853	0.754265	−	0.656570i	$-0.227993\pi$
$607$	1.04019e60	1.50853	0.754265	+	0.656570i	$0.227993\pi$
$608$	−6.89487e59	−0.965160
$609$	6.63647e59	0.896738
$610$	−2.98821e60	−3.89781
$611$	−2.29036e59	−0.288415
$612$	−2.87591e59	−0.349639
$613$	1.21215e60	1.42284	0.711419	−	0.702768i	$-0.248053\pi$
$613$	1.21215e60	1.42284	0.711419	+	0.702768i	$0.248053\pi$
$614$	1.71786e60	1.94701
$615$	6.28020e59	0.687319
$616$	−3.74944e60	−3.96261
$617$	9.18588e59	0.937540	0.468770	−	0.883320i	$-0.344697\pi$
$617$	9.18588e59	0.937540	0.468770	+	0.883320i	$0.344697\pi$
$618$	−8.00598e59	−0.789155
$619$	3.53192e58	0.0336250	0.0168125	−	0.999859i	$-0.494648\pi$
$619$	3.53192e58	0.0336250	0.0168125	+	0.999859i	$0.494648\pi$
$620$	3.46930e60	3.19022
$621$	4.31587e58	0.0383353
$622$	−2.88038e60	−2.47148
$623$	2.09195e59	0.173404
$624$	−8.83719e59	−0.707694
$625$	−1.41673e60	−1.09614
$626$	1.76989e60	1.32312
$627$	1.58241e59	0.114305
$628$	4.66166e60	3.25393
$629$	−1.98911e59	−0.134174
$630$	−1.11281e60	−0.725436
$631$	2.71946e59	0.171337	0.0856686	−	0.996324i	$-0.472697\pi$
$631$	2.71946e59	0.171337	0.0856686	+	0.996324i	$0.472697\pi$
$632$	−1.06492e61	−6.48488
$633$	9.95969e59	0.586227
$634$	6.19117e59	0.352252
$635$	−1.93671e60	−1.06520
$636$	1.87168e60	0.995182
$637$	5.55316e58	0.0285458
$638$	5.98114e60	2.97262
$639$	−1.20349e60	−0.578328
$640$	1.27852e61	5.94071
$641$	1.40756e60	0.632441	0.316221	−	0.948686i	$-0.397586\pi$
$641$	1.40756e60	0.632441	0.316221	+	0.948686i	$0.397586\pi$
$642$	1.72106e60	0.747815
$643$	−4.39184e60	−1.84549	−0.922743	−	0.385417i	$-0.874058\pi$
$643$	−4.39184e60	−1.84549	−0.922743	+	0.385417i	$0.874058\pi$
$644$	1.48115e60	0.601940
$645$	4.47971e58	0.0176082
$646$	3.66247e59	0.139244
$647$	−4.47537e60	−1.64584	−0.822918	−	0.568160i	$-0.807655\pi$
$647$	−4.47537e60	−1.64584	−0.822918	+	0.568160i	$0.807655\pi$
$648$	1.15499e60	0.410882
$649$	−1.83996e60	−0.633209
$650$	1.77382e59	0.0590570
$651$	1.98226e60	0.638514
$652$	−2.35856e60	−0.735062
$653$	2.47480e60	0.746287	0.373144	−	0.927774i	$-0.378280\pi$
$653$	2.47480e60	0.746287	0.373144	+	0.927774i	$0.378280\pi$
$654$	−4.95728e60	−1.44651
$655$	−3.82741e60	−1.08073
$656$	−1.82305e61	−4.98157
$657$	7.21967e59	0.190925
$658$	8.37212e60	2.14279
$659$	−1.36885e60	−0.339093	−0.169546	−	0.985522i	$-0.554230\pi$
$659$	−1.36885e60	−0.339093	−0.169546	+	0.985522i	$0.554230\pi$
$660$	−7.44295e60	−1.78464
$661$	6.52007e60	1.51329	0.756643	−	0.653828i	$-0.226838\pi$
$661$	6.52007e60	1.51329	0.756643	+	0.653828i	$0.226838\pi$
$662$	5.30943e60	1.19289
$663$	2.69270e59	0.0585663
$664$	−1.82969e61	−3.85268
$665$	1.05171e60	0.214404
$666$	1.22425e60	0.241643
$667$	−1.54174e60	−0.294649
$668$	2.10809e61	3.90118
$669$	2.36013e60	0.422936
$670$	6.02606e60	1.04574
$671$	−1.14197e61	−1.91921
$672$	1.85299e61	3.01601
$673$	4.62327e60	0.728829	0.364414	−	0.931237i	$-0.381269\pi$
$673$	4.62327e60	0.728829	0.364414	+	0.931237i	$0.381269\pi$
$674$	6.32089e60	0.965140
$675$	−1.40213e59	−0.0207375
$676$	−1.85314e61	−2.65494
$677$	2.55010e60	0.353916	0.176958	−	0.984218i	$-0.443374\pi$
$677$	2.55010e60	0.353916	0.176958	+	0.984218i	$0.443374\pi$
$678$	−6.53243e59	−0.0878287
$679$	−1.18048e61	−1.53765
$680$	−1.12407e61	−1.41858
$681$	−4.03342e60	−0.493185
$682$	1.78652e61	2.11663
$683$	4.71795e60	0.541636	0.270818	−	0.962631i	$-0.412706\pi$
$683$	4.71795e60	0.541636	0.270818	+	0.962631i	$0.412706\pi$
$684$	−1.67287e60	−0.186104
$685$	1.40274e61	1.51227
$686$	1.77611e61	1.85567
$687$	4.64158e60	0.469998
$688$	−1.30039e60	−0.127621
$689$	−1.75244e60	−0.166698
$690$	2.58520e60	0.238363
$691$	2.07448e61	1.85409	0.927046	−	0.374948i	$-0.122339\pi$
$691$	2.07448e61	1.85409	0.927046	+	0.374948i	$0.122339\pi$
$692$	−2.00469e61	−1.73686
$693$	−4.25270e60	−0.357191
$694$	−4.51517e61	−3.67659
$695$	−7.87595e59	−0.0621770
$696$	−4.12592e61	−3.15808
$697$	5.55486e60	0.412257
$698$	1.09471e60	0.0787782
$699$	−1.06606e61	−0.743912
$700$	−4.81192e60	−0.325620
$701$	−5.96323e59	−0.0391331	−0.0195666	−	0.999809i	$-0.506229\pi$
$701$	−5.96323e59	−0.0391331	−0.0195666	+	0.999809i	$0.506229\pi$
$702$	−1.65729e60	−0.105475
$703$	−1.15703e60	−0.0714179
$704$	9.19250e61	5.50328
$705$	1.08445e61	0.629711
$706$	1.61701e61	0.910779
$707$	−9.86045e60	−0.538740
$708$	1.94514e61	1.03095
$709$	3.39528e61	1.74575	0.872874	−	0.487946i	$-0.162254\pi$
$709$	3.39528e61	1.74575	0.872874	+	0.487946i	$0.162254\pi$
$710$	−7.20888e61	−3.59595
$711$	−1.20786e61	−0.584549
$712$	−1.30057e61	−0.610682
$713$	−4.60505e60	−0.209802
$714$	−9.84284e60	−0.435120
$715$	6.96881e60	0.298936
$716$	1.27368e60	0.0530189
$717$	−1.58093e61	−0.638631
$718$	−2.43714e61	−0.955444
$719$	−5.59707e59	−0.0212956	−0.0106478	−	0.999943i	$-0.503389\pi$
$719$	−5.59707e59	−0.0212956	−0.0106478	+	0.999943i	$0.503389\pi$
$720$	4.18426e61	1.54515
$721$	−2.03347e61	−0.728835
$722$	−5.44734e61	−1.89511
$723$	5.91693e60	0.199813
$724$	4.34276e61	1.42360
$725$	5.00875e60	0.159390
$726$	−1.52549e60	−0.0471272
$727$	−5.23685e61	−1.57065	−0.785327	−	0.619081i	$-0.787505\pi$
$727$	−5.23685e61	−1.57065	−0.785327	+	0.619081i	$0.787505\pi$
$728$	−3.71128e61	−1.08068
$729$	1.31002e60	0.0370370
$730$	4.32457e61	1.18714
$731$	3.96232e59	0.0105615
$732$	1.20726e62	3.12472
$733$	9.78635e60	0.245972	0.122986	−	0.992408i	$-0.460753\pi$
$733$	9.78635e60	0.245972	0.122986	+	0.992408i	$0.460753\pi$
$734$	1.25762e62	3.06961
$735$	−2.62933e60	−0.0623256
$736$	−4.30472e61	−0.990996
$737$	2.30292e61	0.514905
$738$	−3.41888e61	−0.742458
$739$	−5.80837e61	−1.22518	−0.612589	−	0.790402i	$-0.709872\pi$
$739$	−5.80837e61	−1.22518	−0.612589	+	0.790402i	$0.709872\pi$
$740$	5.44217e61	1.11504
$741$	1.56631e60	0.0311734
$742$	6.40584e61	1.23849
$743$	8.10359e61	1.52201	0.761005	−	0.648745i	$-0.224706\pi$
$743$	8.10359e61	1.52201	0.761005	+	0.648745i	$0.224706\pi$
$744$	−1.23238e62	−2.24868
$745$	2.20373e61	0.390660
$746$	−1.66777e62	−2.87244
$747$	−2.07527e61	−0.347282
$748$	−6.58331e61	−1.07043
$749$	4.37139e61	0.690654
$750$	6.95438e61	1.06768
$751$	3.71783e61	0.554665	0.277332	−	0.960774i	$-0.410550\pi$
$751$	3.71783e61	0.554665	0.277332	+	0.960774i	$0.410550\pi$
$752$	−3.14799e62	−4.56404
$753$	1.12498e61	0.158509
$754$	5.92026e61	0.810694
$755$	4.36745e61	0.581257
$756$	4.49582e61	0.581554
$757$	1.55778e61	0.195859	0.0979296	−	0.995193i	$-0.468778\pi$
$757$	1.55778e61	0.195859	0.0979296	+	0.995193i	$0.468778\pi$
$758$	−6.43007e61	−0.785829
$759$	9.87957e60	0.117365
$760$	−6.53855e61	−0.755074
$761$	−3.67288e61	−0.412322	−0.206161	−	0.978518i	$-0.566097\pi$
$761$	−3.67288e61	−0.412322	−0.206161	+	0.978518i	$0.566097\pi$
$762$	1.05433e62	1.15065
$763$	−1.25912e62	−1.33595
$764$	1.13044e62	1.16612
$765$	−1.27495e61	−0.127871
$766$	2.71726e62	2.64980
$767$	−1.82123e61	−0.172689
$768$	−3.58332e62	−3.30384
$769$	−1.62546e62	−1.45734	−0.728670	−	0.684865i	$-0.759861\pi$
$769$	−1.62546e62	−1.45734	−0.728670	+	0.684865i	$0.759861\pi$
$770$	−2.54736e62	−2.22096
$771$	4.35028e61	0.368849
$772$	6.22921e62	5.13643
$773$	−1.56394e61	−0.125418	−0.0627090	−	0.998032i	$-0.519974\pi$
$773$	−1.56394e61	−0.125418	−0.0627090	+	0.998032i	$0.519974\pi$
$774$	−2.43871e60	−0.0190208
$775$	1.49608e61	0.113492
$776$	7.33909e62	5.41521
$777$	3.10951e61	0.223172
$778$	−2.77251e62	−1.93559
$779$	3.23117e61	0.219435
$780$	−7.36720e61	−0.486708
$781$	−2.75494e62	−1.77058
$782$	2.28662e61	0.142971
$783$	−4.67972e61	−0.284670
$784$	7.63255e61	0.451725
$785$	2.06661e62	1.19004
$786$	2.08361e62	1.16743
$787$	8.01741e61	0.437097	0.218548	−	0.975826i	$-0.429868\pi$
$787$	8.01741e61	0.437097	0.218548	+	0.975826i	$0.429868\pi$
$788$	4.55671e62	2.41734
$789$	−1.81235e62	−0.935593
$790$	−7.23507e62	−3.63463
$791$	−1.65920e61	−0.0811154
$792$	2.64392e62	1.25793
$793$	−1.13035e62	−0.523407
$794$	−5.71918e62	−2.57746
$795$	8.29752e61	0.363961
$796$	−1.05311e63	−4.49619
$797$	−3.70582e62	−1.54004	−0.770018	−	0.638022i	$-0.779753\pi$
$797$	−3.70582e62	−1.54004	−0.770018	+	0.638022i	$0.779753\pi$
$798$	−5.72543e61	−0.231604
$799$	9.59196e61	0.377704
$800$	1.39851e62	0.536080
$801$	−1.47514e61	−0.0550471
$802$	1.02352e63	3.71834
$803$	1.65267e62	0.584525
$804$	−2.43457e62	−0.838333
$805$	6.56624e61	0.220143
$806$	1.76834e62	0.577247
$807$	3.36215e61	0.106865
$808$	6.13028e62	1.89730
$809$	3.31262e62	0.998340	0.499170	−	0.866504i	$-0.333638\pi$
$809$	3.31262e62	0.998340	0.499170	+	0.866504i	$0.333638\pi$
$810$	7.84700e61	0.230290
$811$	5.37292e62	1.53554	0.767771	−	0.640724i	$-0.221366\pi$
$811$	5.37292e62	1.53554	0.767771	+	0.640724i	$0.221366\pi$
$812$	−1.60602e63	−4.46988
$813$	2.68000e62	0.726420
$814$	2.80246e62	0.739800
$815$	−1.04560e62	−0.268829
$816$	3.70099e62	0.926786
$817$	2.30482e60	0.00562164
$818$	−4.26264e62	−1.01270
$819$	−4.20942e61	−0.0974133
$820$	−1.51980e63	−3.42601
$821$	6.93889e62	1.52375	0.761873	−	0.647727i	$-0.224280\pi$
$821$	6.93889e62	1.52375	0.761873	+	0.647727i	$0.224280\pi$
$822$	−7.63638e62	−1.63359
$823$	−1.99591e61	−0.0415953	−0.0207977	−	0.999784i	$-0.506621\pi$
$823$	−1.99591e61	−0.0415953	−0.0207977	+	0.999784i	$0.506621\pi$
$824$	1.26422e63	2.56676
$825$	−3.20965e61	−0.0634888
$826$	6.65728e62	1.28300
$827$	1.08641e62	0.203998	0.101999	−	0.994785i	$-0.467476\pi$
$827$	1.08641e62	0.203998	0.101999	+	0.994785i	$0.467476\pi$
$828$	−1.04444e62	−0.191086
$829$	−2.63199e62	−0.469203	−0.234602	−	0.972092i	$-0.575379\pi$
$829$	−2.63199e62	−0.469203	−0.234602	+	0.972092i	$0.575379\pi$
$830$	−1.24308e63	−2.15934
$831$	−3.72518e62	−0.630559
$832$	9.09894e62	1.50086
$833$	−2.32565e61	−0.0373832
$834$	4.28759e61	0.0671650
$835$	9.34560e62	1.42675
$836$	−3.82941e62	−0.569767
$837$	−1.39780e62	−0.202697
$838$	1.20194e63	1.69878
$839$	−1.30446e62	−0.179700	−0.0898501	−	0.995955i	$-0.528639\pi$
$839$	−1.30446e62	−0.179700	−0.0898501	+	0.995955i	$0.528639\pi$
$840$	1.75723e63	2.35952
$841$	9.07676e62	1.18800
$842$	9.40458e62	1.19986
$843$	−2.93470e62	−0.364982
$844$	−2.41023e63	−2.92211
$845$	−8.21536e62	−0.970973
$846$	−5.90361e62	−0.680229
$847$	−3.87465e61	−0.0435250
$848$	−2.40865e63	−2.63793
$849$	−1.73067e62	−0.184798
$850$	−7.42869e61	−0.0773402
$851$	−7.22379e61	−0.0733297
$852$	2.91243e63	2.88273
$853$	−1.52650e63	−1.47330	−0.736651	−	0.676273i	$-0.763594\pi$
$853$	−1.52650e63	−1.47330	−0.736651	+	0.676273i	$0.763594\pi$
$854$	4.13185e63	3.88867
$855$	−7.41618e61	−0.0680626
$856$	−2.71771e63	−2.43230
$857$	−2.04521e63	−1.78505	−0.892525	−	0.450997i	$-0.851068\pi$
$857$	−2.04521e63	−1.78505	−0.892525	+	0.450997i	$0.851068\pi$
$858$	−3.79375e62	−0.322918
$859$	1.90624e63	1.58243	0.791214	−	0.611539i	$-0.209449\pi$
$859$	1.90624e63	1.58243	0.791214	+	0.611539i	$0.209449\pi$
$860$	−1.08408e62	−0.0877701
$861$	−8.68373e62	−0.685707
$862$	2.91442e62	0.224464
$863$	−2.73667e62	−0.205584	−0.102792	−	0.994703i	$-0.532778\pi$
$863$	−2.73667e62	−0.205584	−0.102792	+	0.994703i	$0.532778\pi$
$864$	−1.30664e63	−0.957435
$865$	−8.88718e62	−0.635211
$866$	9.97369e62	0.695378
$867$	7.36118e62	0.500653
$868$	−4.79706e63	−3.18274
$869$	−2.76495e63	−1.78962
$870$	−2.80314e63	−1.77003
$871$	2.27948e62	0.140425
$872$	7.82799e63	4.70485
$873$	8.32416e62	0.488129
$874$	1.33009e62	0.0761001
$875$	1.76637e63	0.986071
$876$	−1.74715e63	−0.951683
$877$	−2.23947e62	−0.119029	−0.0595147	−	0.998227i	$-0.518955\pi$
$877$	−2.23947e62	−0.119029	−0.0595147	+	0.998227i	$0.518955\pi$
$878$	4.92427e63	2.55394
$879$	1.39637e63	0.706707
$880$	9.57829e63	4.73054
$881$	−3.58209e63	−1.72645	−0.863227	−	0.504816i	$-0.831560\pi$
$881$	−3.58209e63	−1.72645	−0.863227	+	0.504816i	$0.831560\pi$
$882$	1.43138e62	0.0673256
$883$	−1.72878e63	−0.793568	−0.396784	−	0.917912i	$-0.629874\pi$
$883$	−1.72878e63	−0.793568	−0.396784	+	0.917912i	$0.629874\pi$
$884$	−6.51631e62	−0.291930
$885$	8.62321e62	0.377041
$886$	3.91836e63	1.67217
$887$	−4.06149e62	−0.169172	−0.0845858	−	0.996416i	$-0.526957\pi$
$887$	−4.06149e62	−0.169172	−0.0845858	+	0.996416i	$0.526957\pi$
$888$	−1.93320e63	−0.785955
$889$	2.67792e63	1.06270
$890$	−8.83606e62	−0.342274
$891$	2.99880e62	0.113391
$892$	−5.71149e63	−2.10817
$893$	5.57949e62	0.201043
$894$	−1.19969e63	−0.422000
$895$	5.64649e61	0.0193902
$896$	−1.76783e64	−5.92678
$897$	9.77902e61	0.0320079
$898$	1.76649e63	0.564509
$899$	4.99328e63	1.55795
$900$	3.39313e62	0.103368
$901$	7.33918e62	0.218306
$902$	−7.82624e63	−2.27307
$903$	−6.19417e61	−0.0175670
$904$	1.03153e63	0.285667
$905$	1.92523e63	0.520642
$906$	−2.37759e63	−0.627887
$907$	−7.47218e62	−0.192704	−0.0963520	−	0.995347i	$-0.530717\pi$
$907$	−7.47218e62	−0.192704	−0.0963520	+	0.995347i	$0.530717\pi$
$908$	9.76082e63	2.45833
$909$	6.95311e62	0.171023
$910$	−2.52143e63	−0.605700
$911$	1.73959e63	0.408134	0.204067	−	0.978957i	$-0.434584\pi$
$911$	1.73959e63	0.408134	0.204067	+	0.978957i	$0.434584\pi$
$912$	2.15281e63	0.493306
$913$	−4.75056e63	−1.06322
$914$	1.15306e64	2.52063
$915$	5.35201e63	1.14278
$916$	−1.12326e64	−2.34275
$917$	5.29223e63	1.07820
$918$	6.94069e62	0.138129
$919$	−5.38688e63	−1.04726	−0.523629	−	0.851946i	$-0.675422\pi$
$919$	−5.38688e63	−1.04726	−0.523629	+	0.851946i	$0.675422\pi$
$920$	−4.08226e63	−0.775286
$921$	−3.07675e63	−0.570835
$922$	−8.96176e63	−1.62435
$923$	−2.72690e63	−0.482873
$924$	1.02915e64	1.78045
$925$	2.34685e62	0.0396677
$926$	−2.15441e64	−3.55788
$927$	1.43390e63	0.231369
$928$	4.66763e64	7.35894
$929$	−7.61471e63	−1.17305	−0.586524	−	0.809932i	$-0.699504\pi$
$929$	−7.61471e63	−1.17305	−0.586524	+	0.809932i	$0.699504\pi$
$930$	−8.37277e63	−1.26033
$931$	−1.35279e62	−0.0198982
$932$	2.57985e64	3.70810
$933$	5.15888e63	0.724603
$934$	−4.58506e63	−0.629343
$935$	−2.91852e63	−0.391483
$936$	2.61701e63	0.343064
$937$	5.74325e63	0.735795	0.367898	−	0.929866i	$-0.380078\pi$
$937$	5.74325e63	0.735795	0.367898	+	0.929866i	$0.380078\pi$
$938$	−8.33234e63	−1.04329
$939$	−3.16994e63	−0.387919
$940$	−2.62434e64	−3.13886
$941$	3.32937e63	0.389211	0.194605	−	0.980882i	$-0.437657\pi$
$941$	3.32937e63	0.389211	0.194605	+	0.980882i	$0.437657\pi$
$942$	−1.12504e64	−1.28551
$943$	2.01734e63	0.225309
$944$	−2.50319e64	−2.73273
$945$	1.99309e63	0.212688
$946$	−5.58251e62	−0.0582332
$947$	−8.50061e62	−0.0866814	−0.0433407	−	0.999060i	$-0.513800\pi$
$947$	−8.50061e62	−0.0866814	−0.0433407	+	0.999060i	$0.513800\pi$
$948$	2.92301e64	2.91374
$949$	1.63585e63	0.159412
$950$	−4.32116e62	−0.0411664
$951$	−1.10886e63	−0.103275
$952$	1.55427e64	1.41525
$953$	−1.75369e63	−0.156119	−0.0780594	−	0.996949i	$-0.524872\pi$
$953$	−1.75369e63	−0.156119	−0.0780594	+	0.996949i	$0.524872\pi$
$954$	−4.51709e63	−0.393159
$955$	5.01148e63	0.426475
$956$	3.82582e64	3.18332
$957$	−1.07125e64	−0.871531
$958$	8.00640e63	0.636911
$959$	−1.93959e64	−1.50873
$960$	−4.30819e64	−3.27690
$961$	1.46979e63	0.109321
$962$	2.77393e63	0.201759
$963$	−3.08249e63	−0.219249
$964$	−1.43189e64	−0.995987
$965$	2.76154e64	1.87851
$966$	−3.57460e63	−0.237804
$967$	−4.52883e63	−0.294657	−0.147329	−	0.989088i	$-0.547067\pi$
$967$	−4.52883e63	−0.294657	−0.147329	+	0.989088i	$0.547067\pi$
$968$	2.40889e63	0.153284
$969$	−6.55964e62	−0.0408243
$970$	4.98616e64	3.03510
$971$	2.53970e63	0.151206	0.0756030	−	0.997138i	$-0.475912\pi$
$971$	2.53970e63	0.151206	0.0756030	+	0.997138i	$0.475912\pi$
$972$	−3.17023e63	−0.184615
$973$	1.08902e63	0.0620312
$974$	−1.66103e64	−0.925465
$975$	−3.17698e62	−0.0173147
$976$	−1.55361e65	−8.28268
$977$	−2.95562e63	−0.154140	−0.0770700	−	0.997026i	$-0.524556\pi$
$977$	−2.95562e63	−0.154140	−0.0770700	+	0.997026i	$0.524556\pi$
$978$	5.69214e63	0.290396
$979$	−3.37678e63	−0.168529
$980$	6.36294e63	0.310668
$981$	8.87869e63	0.424097
$982$	4.23614e64	1.97958
$983$	1.18645e64	0.542436	0.271218	−	0.962518i	$-0.412574\pi$
$983$	1.18645e64	0.542436	0.271218	+	0.962518i	$0.412574\pi$
$984$	5.39871e64	2.41488
$985$	2.02008e64	0.884076
$986$	−2.47939e64	−1.06167
$987$	−1.49948e64	−0.628235
$988$	−3.79044e63	−0.155387
$989$	1.43898e62	0.00577212
$990$	1.79628e64	0.705044
$991$	2.27045e64	0.872023	0.436012	−	0.899941i	$-0.356391\pi$
$991$	2.27045e64	0.872023	0.436012	+	0.899941i	$0.356391\pi$
$992$	1.39419e65	5.23986
$993$	−9.50941e63	−0.349740
$994$	9.96784e64	3.58751
$995$	−4.66867e64	−1.64436
$996$	5.02213e64	1.73106
$997$	−4.07400e64	−1.37428	−0.687140	−	0.726525i	$-0.741134\pi$
$997$	−4.07400e64	−1.37428	−0.687140	+	0.726525i	$0.741134\pi$
$998$	−2.98165e64	−0.984353
$999$	−2.19268e63	−0.0708463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.44.a.b.1.4	✓	4
3.2	odd	2		9.44.a.c.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.44.a.b.1.4	✓	4	1.1	even	1	trivial
9.44.a.c.1.1		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+5.84038e6 q^{2} -1.04604e10 q^{3} +2.53139e13 q^{4} +1.12222e15 q^{5} -6.10924e16 q^{6} -1.55171e18 q^{7} +9.64704e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\)	\(q+5.84038e6 q^{2} -1.04604e10 q^{3} +2.53139e13 q^{4} +1.12222e15 q^{5} -6.10924e16 q^{6} -1.55171e18 q^{7} +9.64704e19 q^{8} +1.09419e20 q^{9} +6.55417e21 q^{10} +2.50474e22 q^{11} -2.64793e23 q^{12} +2.47924e23 q^{13} -9.06257e24 q^{14} -1.17388e25 q^{15} +3.40760e26 q^{16} -1.03830e26 q^{17} +6.39048e26 q^{18} -6.03963e26 q^{19} +2.84077e28 q^{20} +1.62314e28 q^{21} +1.46286e29 q^{22} -3.77076e28 q^{23} -1.00911e30 q^{24} +1.22504e29 q^{25} +1.44797e30 q^{26} -1.14456e30 q^{27} -3.92798e31 q^{28} +4.08866e31 q^{29} -6.85590e31 q^{30} +1.22125e32 q^{31} +1.14160e33 q^{32} -2.62004e32 q^{33} -6.06407e32 q^{34} -1.74135e33 q^{35} +2.76982e33 q^{36} +1.91574e33 q^{37} -3.52737e33 q^{38} -2.59338e33 q^{39} +1.08261e35 q^{40} -5.34995e34 q^{41} +9.47977e34 q^{42} -3.81616e33 q^{43} +6.34047e35 q^{44} +1.22792e35 q^{45} -2.20227e35 q^{46} -9.23813e35 q^{47} -3.56447e36 q^{48} +2.23986e35 q^{49} +7.15467e35 q^{50} +1.08610e36 q^{51} +6.27594e36 q^{52} -7.06846e36 q^{53} -6.68467e36 q^{54} +2.81086e37 q^{55} -1.49694e38 q^{56} +6.31767e36 q^{57} +2.38793e38 q^{58} -7.34591e37 q^{59} -2.97155e38 q^{60} -4.55925e38 q^{61} +7.13257e38 q^{62} -1.69786e38 q^{63} +3.67005e39 q^{64} +2.78225e38 q^{65} -1.53020e39 q^{66} +9.19424e38 q^{67} -2.62835e39 q^{68} +3.94435e38 q^{69} -1.01702e40 q^{70} -1.09989e40 q^{71} +1.05557e40 q^{72} +6.59819e39 q^{73} +1.11886e40 q^{74} -1.28143e39 q^{75} -1.52887e40 q^{76} -3.88662e40 q^{77} -1.51463e40 q^{78} -1.10389e41 q^{79} +3.82407e41 q^{80} +1.19725e40 q^{81} -3.12457e41 q^{82} -1.89663e41 q^{83} +4.10881e41 q^{84} -1.16520e41 q^{85} -2.22878e40 q^{86} -4.27688e41 q^{87} +2.41633e42 q^{88} -1.34816e41 q^{89} +7.17151e41 q^{90} -3.84707e41 q^{91} -9.54529e41 q^{92} -1.27747e42 q^{93} -5.39542e42 q^{94} -6.77778e41 q^{95} -1.19416e43 q^{96} +7.60760e42 q^{97} +1.30816e42 q^{98} +2.74066e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5}+ \cdots + 43\!\cdots\!36 q^{9}+O(q^{10}) \) 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	\( 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5}+ \cdots + 95\!\cdots\!64 q^{99}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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