LMFDB - Embedded newform 3.44.a.b.1.3

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			1.3
Root			$321562.$ 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)

$f(q)$	$=$	$q+2.34437e6 q^{2} -1.04604e10 q^{3} -3.30001e12 q^{4} -6.18875e14 q^{5} -2.45230e16 q^{6} -6.01464e16 q^{7} -2.83578e19 q^{8} +1.09419e20 q^{9} +O(q^{10})$	\(q+2.34437e6 q^{2} -1.04604e10 q^{3} -3.30001e12 q^{4} -6.18875e14 q^{5} -2.45230e16 q^{6} -6.01464e16 q^{7} -2.83578e19 q^{8} +1.09419e20 q^{9} -1.45087e21 q^{10} -9.76031e21 q^{11} +3.45193e22 q^{12} -7.58355e23 q^{13} -1.41006e23 q^{14} +6.47365e24 q^{15} -3.74540e25 q^{16} +2.78579e26 q^{17} +2.56519e26 q^{18} +4.05410e27 q^{19} +2.04230e27 q^{20} +6.29153e26 q^{21} -2.28818e28 q^{22} +1.45822e29 q^{23} +2.96632e29 q^{24} -7.53862e29 q^{25} -1.77787e30 q^{26} -1.14456e30 q^{27} +1.98484e29 q^{28} -9.74099e30 q^{29} +1.51766e31 q^{30} +1.20460e32 q^{31} +1.61632e32 q^{32} +1.02096e32 q^{33} +6.53093e32 q^{34} +3.72231e31 q^{35} -3.61084e32 q^{36} +9.29506e32 q^{37} +9.50433e33 q^{38} +7.93266e33 q^{39} +1.75499e34 q^{40} +7.39680e34 q^{41} +1.47497e33 q^{42} +1.90025e35 q^{43} +3.22092e34 q^{44} -6.77167e34 q^{45} +3.41860e35 q^{46} -3.68345e35 q^{47} +3.91782e35 q^{48} -2.18020e36 q^{49} -1.76733e36 q^{50} -2.91404e36 q^{51} +2.50258e36 q^{52} -1.07634e37 q^{53} -2.68328e36 q^{54} +6.04041e36 q^{55} +1.70562e36 q^{56} -4.24074e37 q^{57} -2.28365e37 q^{58} -1.44976e38 q^{59} -2.13631e37 q^{60} +4.49263e38 q^{61} +2.82402e38 q^{62} -6.58116e36 q^{63} +7.08373e38 q^{64} +4.69327e38 q^{65} +2.39352e38 q^{66} +5.03842e38 q^{67} -9.19315e38 q^{68} -1.52534e39 q^{69} +8.72649e37 q^{70} -4.05279e39 q^{71} -3.10288e39 q^{72} -1.07882e40 q^{73} +2.17911e39 q^{74} +7.88566e39 q^{75} -1.33786e40 q^{76} +5.87048e38 q^{77} +1.85971e40 q^{78} -8.21320e40 q^{79} +2.31793e40 q^{80} +1.19725e40 q^{81} +1.73408e41 q^{82} +4.07702e40 q^{83} -2.07621e39 q^{84} -1.72406e41 q^{85} +4.45489e41 q^{86} +1.01894e41 q^{87} +2.76781e41 q^{88} +1.83342e41 q^{89} -1.58753e41 q^{90} +4.56124e40 q^{91} -4.81213e41 q^{92} -1.26005e42 q^{93} -8.63538e41 q^{94} -2.50898e42 q^{95} -1.69072e42 q^{96} -2.07049e42 q^{97} -5.11119e42 q^{98} -1.06796e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.34437e6	0.790463	0.395232	−	0.918582i	$-0.370664\pi$
$2$	2.34437e6	0.790463	0.395232	+	0.918582i	$0.370664\pi$
$3$	−1.04604e10	−0.577350
$3$	−1.04604e10	−0.577350
$4$	−3.30001e12	−0.375168
$5$	−6.18875e14	−0.580427	−0.290214	−	0.956962i	$-0.593726\pi$
$5$	−6.18875e14	−0.580427	−0.290214	+	0.956962i	$0.593726\pi$
$6$	−2.45230e16	−0.456374
$7$	−6.01464e16	−0.0407007	−0.0203504	−	0.999793i	$-0.506478\pi$
$7$	−6.01464e16	−0.0407007	−0.0203504	+	0.999793i	$0.506478\pi$
$8$	−2.83578e19	−1.08702
$9$	1.09419e20	0.333333
$10$	−1.45087e21	−0.458806
$11$	−9.76031e21	−0.397668	−0.198834	−	0.980033i	$-0.563716\pi$
$11$	−9.76031e21	−0.397668	−0.198834	+	0.980033i	$0.563716\pi$
$12$	3.45193e22	0.216603
$13$	−7.58355e23	−0.851315	−0.425658	−	0.904884i	$-0.639957\pi$
$13$	−7.58355e23	−0.851315	−0.425658	+	0.904884i	$0.639957\pi$
$14$	−1.41006e23	−0.0321724
$15$	6.47365e24	0.335110
$16$	−3.74540e25	−0.484081
$17$	2.78579e26	0.977906	0.488953	−	0.872310i	$-0.337379\pi$
$17$	2.78579e26	0.977906	0.488953	+	0.872310i	$0.337379\pi$
$18$	2.56519e26	0.263488
$19$	4.05410e27	1.30224	0.651122	−	0.758973i	$-0.274298\pi$
$19$	4.05410e27	1.30224	0.651122	+	0.758973i	$0.274298\pi$
$20$	2.04230e27	0.217758
$21$	6.29153e26	0.0234986
$22$	−2.28818e28	−0.314342
$23$	1.45822e29	0.770324	0.385162	−	0.922849i	$-0.374146\pi$
$23$	1.45822e29	0.770324	0.385162	+	0.922849i	$0.374146\pi$
$24$	2.96632e29	0.627591
$25$	−7.53862e29	−0.663104
$26$	−1.77787e30	−0.672933
$27$	−1.14456e30	−0.192450
$28$	1.98484e29	0.0152696
$29$	−9.74099e30	−0.352408	−0.176204	−	0.984354i	$-0.556382\pi$
$29$	−9.74099e30	−0.352408	−0.176204	+	0.984354i	$0.556382\pi$
$30$	1.51766e31	0.264892
$31$	1.20460e32	1.03888	0.519440	−	0.854507i	$-0.326141\pi$
$31$	1.20460e32	1.03888	0.519440	+	0.854507i	$0.326141\pi$
$32$	1.61632e32	0.704371
$33$	1.02096e32	0.229594
$34$	6.53093e32	0.772998
$35$	3.72231e31	0.0236238
$36$	−3.61084e32	−0.125056
$37$	9.29506e32	0.178614	0.0893069	−	0.996004i	$-0.471535\pi$
$37$	9.29506e32	0.178614	0.0893069	+	0.996004i	$0.471535\pi$
$38$	9.50433e33	1.02938
$39$	7.93266e33	0.491507
$40$	1.75499e34	0.630936
$41$	7.39680e34	1.56383	0.781917	−	0.623382i	$-0.214242\pi$
$41$	7.39680e34	1.56383	0.781917	+	0.623382i	$0.214242\pi$
$42$	1.47497e33	0.0185748
$43$	1.90025e35	1.44291	0.721455	−	0.692462i	$-0.243474\pi$
$43$	1.90025e35	1.44291	0.721455	+	0.692462i	$0.243474\pi$
$44$	3.22092e34	0.149192
$45$	−6.77167e34	−0.193476
$46$	3.41860e35	0.608912
$47$	−3.68345e35	−0.413191	−0.206595	−	0.978426i	$-0.566238\pi$
$47$	−3.68345e35	−0.413191	−0.206595	+	0.978426i	$0.566238\pi$
$48$	3.91782e35	0.279484
$49$	−2.18020e36	−0.998343
$50$	−1.76733e36	−0.524159
$51$	−2.91404e36	−0.564594
$52$	2.50258e36	0.319386
$53$	−1.07634e37	−0.912047	−0.456023	−	0.889968i	$-0.650727\pi$
$53$	−1.07634e37	−0.912047	−0.456023	+	0.889968i	$0.650727\pi$
$54$	−2.68328e36	−0.152125
$55$	6.04041e36	0.230818
$56$	1.70562e36	0.0442425
$57$	−4.24074e37	−0.751851
$58$	−2.28365e37	−0.278566
$59$	−1.44976e38	−1.22455	−0.612275	−	0.790645i	$-0.709745\pi$
$59$	−1.44976e38	−1.22455	−0.612275	+	0.790645i	$0.709745\pi$
$60$	−2.13631e37	−0.125722
$61$	4.49263e38	1.85314	0.926572	−	0.376117i	$-0.122741\pi$
$61$	4.49263e38	1.85314	0.926572	+	0.376117i	$0.122741\pi$
$62$	2.82402e38	0.821196
$63$	−6.58116e36	−0.0135669
$64$	7.08373e38	1.04086
$65$	4.69327e38	0.494127
$66$	2.39352e38	0.181486
$67$	5.03842e38	0.276494	0.138247	−	0.990398i	$-0.455853\pi$
$67$	5.03842e38	0.276494	0.138247	+	0.990398i	$0.455853\pi$
$68$	−9.19315e38	−0.366879
$69$	−1.52534e39	−0.444747
$70$	8.72649e37	0.0186738
$71$	−4.05279e39	−0.639293	−0.319646	−	0.947537i	$-0.603564\pi$
$71$	−4.05279e39	−0.639293	−0.319646	+	0.947537i	$0.603564\pi$
$72$	−3.10288e39	−0.362340
$73$	−1.07882e40	−0.936503	−0.468251	−	0.883595i	$-0.655116\pi$
$73$	−1.07882e40	−0.936503	−0.468251	+	0.883595i	$0.655116\pi$
$74$	2.17911e39	0.141188
$75$	7.88566e39	0.382843
$76$	−1.33786e40	−0.488560
$77$	5.87048e38	0.0161854
$78$	1.85971e40	0.388518
$79$	−8.21320e40	−1.30476	−0.652379	−	0.757893i	$-0.726229\pi$
$79$	−8.21320e40	−1.30476	−0.652379	+	0.757893i	$0.726229\pi$
$80$	2.31793e40	0.280974
$81$	1.19725e40	0.111111
$82$	1.73408e41	1.23615
$83$	4.07702e40	0.223956	0.111978	−	0.993711i	$-0.464281\pi$
$83$	4.07702e40	0.223956	0.111978	+	0.993711i	$0.464281\pi$
$84$	−2.07621e39	−0.00881591
$85$	−1.72406e41	−0.567603
$86$	4.45489e41	1.14057
$87$	1.01894e41	0.203463
$88$	2.76781e41	0.432273
$89$	1.83342e41	0.224583	0.112292	−	0.993675i	$-0.464181\pi$
$89$	1.83342e41	0.224583	0.112292	+	0.993675i	$0.464181\pi$
$90$	−1.58753e41	−0.152935
$91$	4.56124e40	0.0346491
$92$	−4.81213e41	−0.289001
$93$	−1.26005e42	−0.599797
$94$	−8.63538e41	−0.326612
$95$	−2.50898e42	−0.755858
$96$	−1.69072e42	−0.406669
$97$	−2.07049e42	−0.398547	−0.199274	−	0.979944i	$-0.563858\pi$
$97$	−2.07049e42	−0.398547	−0.199274	+	0.979944i	$0.563858\pi$
$98$	−5.11119e42	−0.789154
$99$	−1.06796e42	−0.132556
$100$	2.48775e42	0.248775
$101$	1.86748e43	1.50781	0.753904	−	0.656985i	$-0.228169\pi$
$101$	1.86748e43	1.50781	0.753904	+	0.656985i	$0.228169\pi$
$102$	−6.83159e42	−0.446291
$103$	1.80725e43	0.957233	0.478617	−	0.878024i	$-0.341138\pi$
$103$	1.80725e43	0.957233	0.478617	+	0.878024i	$0.341138\pi$
$104$	2.15053e43	0.925396
$105$	−3.89367e41	−0.0136392
$106$	−2.52333e43	−0.720939
$107$	5.57930e43	1.30265	0.651326	−	0.758798i	$-0.274213\pi$
$107$	5.57930e43	1.30265	0.651326	+	0.758798i	$0.274213\pi$
$108$	3.77707e42	0.0722011
$109$	−9.67648e43	−1.51722	−0.758609	−	0.651546i	$-0.774121\pi$
$109$	−9.67648e43	−1.51722	−0.758609	+	0.651546i	$0.774121\pi$
$110$	1.41610e43	0.182453
$111$	−9.72296e42	−0.103123
$112$	2.25272e42	0.0197024
$113$	1.75497e44	1.26790	0.633948	−	0.773375i	$-0.281433\pi$
$113$	1.75497e44	1.26790	0.633948	+	0.773375i	$0.281433\pi$
$114$	−9.94187e43	−0.594311
$115$	−9.02453e43	−0.447117
$116$	3.21454e43	0.132212
$117$	−8.29784e43	−0.283772
$118$	−3.39877e44	−0.967961
$119$	−1.67556e43	−0.0398015
$120$	−1.83578e44	−0.364271
$121$	−5.07137e44	−0.841860
$122$	1.05324e45	1.46484
$123$	−7.73731e44	−0.902880
$124$	−3.97518e44	−0.389754
$125$	1.17013e45	0.965311
$126$	−1.54287e43	−0.0107241
$127$	2.40153e45	1.40834	0.704170	−	0.710032i	$-0.251319\pi$
$127$	2.40153e45	1.40834	0.704170	+	0.710032i	$0.251319\pi$
$128$	2.38964e44	0.118391
$129$	−1.98773e45	−0.833064
$130$	1.10028e45	0.390589
$131$	4.93252e45	1.48503	0.742516	−	0.669828i	$-0.233632\pi$
$131$	4.93252e45	1.48503	0.742516	+	0.669828i	$0.233632\pi$
$132$	−3.36919e44	−0.0861363
$133$	−2.43840e44	−0.0530023
$134$	1.18119e45	0.218558
$135$	7.08340e44	0.111703
$136$	−7.89989e45	−1.06300
$137$	−4.38206e45	−0.503716	−0.251858	−	0.967764i	$-0.581042\pi$
$137$	−4.38206e45	−0.503716	−0.251858	+	0.967764i	$0.581042\pi$
$138$	−3.57598e45	−0.351556
$139$	−1.27611e46	−1.07416	−0.537082	−	0.843530i	$-0.680473\pi$
$139$	−1.27611e46	−1.07416	−0.537082	+	0.843530i	$0.680473\pi$
$140$	−1.22837e44	−0.00886290
$141$	3.85302e45	0.238556
$142$	−9.50126e45	−0.505338
$143$	7.40178e45	0.338541
$144$	−4.09817e45	−0.161360
$145$	6.02846e45	0.204548
$146$	−2.52916e46	−0.740271
$147$	2.28056e46	0.576394
$148$	−3.06738e45	−0.0670102
$149$	6.74357e46	1.27463	0.637316	−	0.770602i	$-0.280045\pi$
$149$	6.74357e46	1.27463	0.637316	+	0.770602i	$0.280045\pi$
$150$	1.84869e46	0.302624
$151$	1.15191e47	1.63461	0.817303	−	0.576209i	$-0.195468\pi$
$151$	1.15191e47	1.63461	0.817303	+	0.576209i	$0.195468\pi$
$152$	−1.14965e47	−1.41557
$153$	3.04819e46	0.325969
$154$	1.37626e45	0.0127940
$155$	−7.45494e46	−0.602994
$156$	−2.61779e46	−0.184398
$157$	1.70621e47	1.04759	0.523795	−	0.851844i	$-0.324516\pi$
$157$	1.70621e47	1.04759	0.523795	+	0.851844i	$0.324516\pi$
$158$	−1.92548e47	−1.03136
$159$	1.12589e47	0.526570
$160$	−1.00030e47	−0.408836
$161$	−8.77065e45	−0.0313527
$162$	2.80680e46	0.0878292
$163$	2.46516e47	0.675790	0.337895	−	0.941184i	$-0.390285\pi$
$163$	2.46516e47	0.675790	0.337895	+	0.941184i	$0.390285\pi$
$164$	−2.44095e47	−0.586701
$165$	−6.31849e46	−0.133263
$166$	9.55804e46	0.177029
$167$	−1.01601e48	−1.65384	−0.826920	−	0.562319i	$-0.809909\pi$
$167$	−1.01601e48	−1.65384	−0.826920	+	0.562319i	$0.809909\pi$
$168$	−1.78414e46	−0.0255434
$169$	−2.18429e47	−0.275262
$170$	−4.04183e47	−0.448669
$171$	4.43596e47	0.434082
$172$	−6.27085e47	−0.541333
$173$	1.53528e48	1.17003	0.585015	−	0.811023i	$-0.301089\pi$
$173$	1.53528e48	1.17003	0.585015	+	0.811023i	$0.301089\pi$
$174$	2.38878e47	0.160830
$175$	4.53421e46	0.0269888
$176$	3.65562e47	0.192504
$177$	1.51650e48	0.706994
$178$	4.29822e47	0.177525
$179$	4.05033e48	1.48303	0.741515	−	0.670936i	$-0.234108\pi$
$179$	4.05033e48	1.48303	0.741515	+	0.670936i	$0.234108\pi$
$180$	2.23466e47	0.0725859
$181$	2.03822e48	0.587708	0.293854	−	0.955850i	$-0.405062\pi$
$181$	2.03822e48	0.587708	0.293854	+	0.955850i	$0.405062\pi$
$182$	1.06932e47	0.0273889
$183$	−4.69945e48	−1.06991
$184$	−4.13517e48	−0.837357
$185$	−5.75248e47	−0.103672
$186$	−2.95403e48	−0.474118
$187$	−2.71902e48	−0.388882
$188$	1.21554e48	0.155016
$189$	6.88413e46	0.00783286
$190$	−5.88199e48	−0.597478
$191$	3.56591e48	0.323559	0.161779	−	0.986827i	$-0.448277\pi$
$191$	3.56591e48	0.323559	0.161779	+	0.986827i	$0.448277\pi$
$192$	−7.40983e48	−0.600941
$193$	−2.12053e48	−0.153802	−0.0769012	−	0.997039i	$-0.524503\pi$
$193$	−2.12053e48	−0.153802	−0.0769012	+	0.997039i	$0.524503\pi$
$194$	−4.85399e48	−0.315037
$195$	−4.90933e48	−0.285284
$196$	7.19468e48	0.374546
$197$	1.79197e49	0.836192	0.418096	−	0.908403i	$-0.362698\pi$
$197$	1.79197e49	0.836192	0.418096	+	0.908403i	$0.362698\pi$
$198$	−2.50370e48	−0.104781
$199$	−7.04650e48	−0.264626	−0.132313	−	0.991208i	$-0.542240\pi$
$199$	−7.04650e48	−0.264626	−0.132313	+	0.991208i	$0.542240\pi$
$200$	2.13778e49	0.720807
$201$	−5.27036e48	−0.159634
$202$	4.37806e49	1.19187
$203$	5.85886e47	0.0143433
$204$	9.61636e48	0.211818
$205$	−4.57769e49	−0.907693
$206$	4.23687e49	0.756658
$207$	1.59556e49	0.256775
$208$	2.84034e49	0.412106
$209$	−3.95693e49	−0.517861
$210$	−9.12822e47	−0.0107813
$211$	−1.48444e50	−1.58303	−0.791516	−	0.611149i	$-0.790708\pi$
$211$	−1.48444e50	−1.58303	−0.791516	+	0.611149i	$0.790708\pi$
$212$	3.55193e49	0.342171
$213$	4.23936e49	0.369096
$214$	1.30799e50	1.02970
$215$	−1.17602e50	−0.837504
$216$	3.24572e49	0.209197
$217$	−7.24522e48	−0.0422831
$218$	−2.26853e50	−1.19930
$219$	1.12849e50	0.540690
$220$	−1.99334e49	−0.0865954
$221$	−2.11262e50	−0.832506
$222$	−2.27942e49	−0.0815147
$223$	−8.53574e49	−0.277132	−0.138566	−	0.990353i	$-0.544249\pi$
$223$	−8.53574e49	−0.277132	−0.138566	+	0.990353i	$0.544249\pi$
$224$	−9.72157e48	−0.0286684
$225$	−8.24868e49	−0.221035
$226$	4.11431e50	1.00223
$227$	−4.48691e50	−0.994012	−0.497006	−	0.867747i	$-0.665567\pi$
$227$	−4.48691e50	−0.994012	−0.497006	+	0.867747i	$0.665567\pi$
$228$	1.39945e50	0.282071
$229$	7.28299e50	1.33612	0.668062	−	0.744106i	$-0.267124\pi$
$229$	7.28299e50	1.33612	0.668062	+	0.744106i	$0.267124\pi$
$230$	−2.11569e50	−0.353429
$231$	−6.14073e48	−0.00934464
$232$	2.76233e50	0.383075
$233$	9.17803e50	1.16037	0.580186	−	0.814484i	$-0.302980\pi$
$233$	9.17803e50	1.16037	0.580186	+	0.814484i	$0.302980\pi$
$234$	−1.94532e50	−0.224311
$235$	2.27959e50	0.239827
$236$	4.78421e50	0.459412
$237$	8.59130e50	0.753303
$238$	−3.92813e49	−0.0314616
$239$	−1.09851e50	−0.0803990	−0.0401995	−	0.999192i	$-0.512799\pi$
$239$	−1.09851e50	−0.0803990	−0.0401995	+	0.999192i	$0.512799\pi$
$240$	−2.42464e50	−0.162220
$241$	−1.97410e51	−1.20782	−0.603910	−	0.797052i	$-0.706391\pi$
$241$	−1.97410e51	−1.20782	−0.603910	+	0.797052i	$0.706391\pi$
$242$	−1.18892e51	−0.665459
$243$	−1.25237e50	−0.0641500
$244$	−1.48257e51	−0.695240
$245$	1.34927e51	0.579466
$246$	−1.81391e51	−0.713694
$247$	−3.07445e51	−1.10862
$248$	−3.41597e51	−1.12928
$249$	−4.26470e50	−0.129301
$250$	2.74321e51	0.763043
$251$	6.49802e51	1.65881	0.829404	−	0.558650i	$-0.188680\pi$
$251$	6.49802e51	1.65881	0.829404	+	0.558650i	$0.188680\pi$
$252$	2.17179e49	0.00508987
$253$	−1.42326e51	−0.306333
$254$	5.63007e51	1.11324
$255$	1.80343e51	0.327706
$256$	−5.67070e51	−0.947277
$257$	6.62733e51	1.01807	0.509033	−	0.860747i	$-0.330003\pi$
$257$	6.62733e51	1.01807	0.509033	+	0.860747i	$0.330003\pi$
$258$	−4.65998e51	−0.658507
$259$	−5.59065e49	−0.00726971
$260$	−1.54878e51	−0.185380
$261$	−1.06585e51	−0.117469
$262$	1.15637e52	1.17386
$263$	2.00645e51	0.187663	0.0938315	−	0.995588i	$-0.470088\pi$
$263$	2.00645e51	0.187663	0.0938315	+	0.995588i	$0.470088\pi$
$264$	−2.89522e51	−0.249573
$265$	6.66118e51	0.529377
$266$	−5.71652e50	−0.0418964
$267$	−1.91782e51	−0.129663
$268$	−1.66268e51	−0.103732
$269$	−1.18548e52	−0.682686	−0.341343	−	0.939939i	$-0.610882\pi$
$269$	−1.18548e52	−0.682686	−0.341343	+	0.939939i	$0.610882\pi$
$270$	1.66061e51	0.0882973
$271$	1.04772e52	0.514522	0.257261	−	0.966342i	$-0.417180\pi$
$271$	1.04772e52	0.514522	0.257261	+	0.966342i	$0.417180\pi$
$272$	−1.04339e52	−0.473386
$273$	−4.77121e50	−0.0200047
$274$	−1.02732e52	−0.398169
$275$	7.35793e51	0.263695
$276$	5.03366e51	0.166855
$277$	−2.05756e52	−0.631012	−0.315506	−	0.948924i	$-0.602174\pi$
$277$	−2.05756e52	−0.631012	−0.315506	+	0.948924i	$0.602174\pi$
$278$	−2.99168e52	−0.849087
$279$	1.31806e52	0.346293
$280$	−1.05557e51	−0.0256795
$281$	−4.36534e52	−0.983631	−0.491816	−	0.870699i	$-0.663667\pi$
$281$	−4.36534e52	−0.983631	−0.491816	+	0.870699i	$0.663667\pi$
$282$	9.03291e51	0.188570
$283$	−5.12915e51	−0.0992286	−0.0496143	−	0.998768i	$-0.515799\pi$
$283$	−5.12915e51	−0.0992286	−0.0496143	+	0.998768i	$0.515799\pi$
$284$	1.33743e52	0.239842
$285$	2.62449e52	0.436395
$286$	1.73525e52	0.267604
$287$	−4.44891e51	−0.0636492
$288$	1.76856e52	0.234790
$289$	−3.54642e51	−0.0437005
$290$	1.41330e52	0.161687
$291$	2.16580e52	0.230101
$292$	3.56013e52	0.351346
$293$	−1.29030e52	−0.118314	−0.0591571	−	0.998249i	$-0.518841\pi$
$293$	−1.29030e52	−0.118314	−0.0591571	+	0.998249i	$0.518841\pi$
$294$	5.34649e52	0.455618
$295$	8.97217e52	0.710762
$296$	−2.63587e52	−0.194157
$297$	1.11713e52	0.0765313
$298$	1.58094e53	1.00755
$299$	−1.10584e53	−0.655788
$300$	−2.60228e52	−0.143631
$301$	−1.14293e52	−0.0587275
$302$	2.70050e53	1.29210
$303$	−1.95345e53	−0.870533
$304$	−1.51842e53	−0.630392
$305$	−2.78038e53	−1.07562
$306$	7.14608e52	0.257666
$307$	−2.82932e53	−0.951058	−0.475529	−	0.879700i	$-0.657743\pi$
$307$	−2.82932e53	−0.951058	−0.475529	+	0.879700i	$0.657743\pi$
$308$	−1.93727e51	−0.00607224
$309$	−1.89045e53	−0.552659
$310$	−1.74772e53	−0.476644
$311$	−2.02380e53	−0.515014	−0.257507	−	0.966276i	$-0.582901\pi$
$311$	−2.02380e53	−0.515014	−0.257507	+	0.966276i	$0.582901\pi$
$312$	−2.24953e53	−0.534278
$313$	−4.97243e52	−0.110247	−0.0551234	−	0.998480i	$-0.517555\pi$
$313$	−4.97243e52	−0.110247	−0.0551234	+	0.998480i	$0.517555\pi$
$314$	4.00000e53	0.828081
$315$	4.07292e51	0.00787460
$316$	2.71037e53	0.489504
$317$	1.06498e54	1.79708	0.898540	−	0.438893i	$-0.144629\pi$
$317$	1.06498e54	1.79708	0.898540	+	0.438893i	$0.144629\pi$
$318$	2.63950e53	0.416235
$319$	9.50751e52	0.140142
$320$	−4.38394e53	−0.604144
$321$	−5.83614e53	−0.752086
$322$	−2.05617e52	−0.0247832
$323$	1.12939e54	1.27347
$324$	−3.95094e52	−0.0416853
$325$	5.71695e53	0.564511
$326$	5.77925e53	0.534187
$327$	1.01219e54	0.875966
$328$	−2.09757e54	−1.69992
$329$	2.21546e52	0.0168172
$330$	−1.48129e53	−0.105339
$331$	3.46154e51	0.00230657	0.00115329	−	0.999999i	$-0.499633\pi$
$331$	3.46154e51	0.00230657	0.00115329	+	0.999999i	$0.499633\pi$
$332$	−1.34542e53	−0.0840213
$333$	1.01706e53	0.0595379
$334$	−2.38190e54	−1.30730
$335$	−3.11815e53	−0.160485
$336$	−2.35643e52	−0.0113752
$337$	3.36356e54	1.52320	0.761599	−	0.648048i	$-0.224414\pi$
$337$	3.36356e54	1.52320	0.761599	+	0.648048i	$0.224414\pi$
$338$	−5.12080e53	−0.217585
$339$	−1.83576e54	−0.732021
$340$	5.68941e53	0.212947
$341$	−1.17572e54	−0.413129
$342$	1.03995e54	0.343125
$343$	2.62480e53	0.0813340
$344$	−5.38869e54	−1.56847
$345$	9.43998e53	0.258143
$346$	3.59927e54	0.924865
$347$	−1.72459e54	−0.416487	−0.208244	−	0.978077i	$-0.566775\pi$
$347$	−1.72459e54	−0.416487	−0.208244	+	0.978077i	$0.566775\pi$
$348$	−3.36252e53	−0.0763328
$349$	−9.94419e53	−0.212238	−0.106119	−	0.994353i	$-0.533842\pi$
$349$	−9.94419e53	−0.212238	−0.106119	+	0.994353i	$0.533842\pi$
$350$	1.06299e53	0.0213337
$351$	8.67984e53	0.163836
$352$	−1.57757e54	−0.280106
$353$	−5.27615e54	−0.881375	−0.440687	−	0.897661i	$-0.645265\pi$
$353$	−5.27615e54	−0.881375	−0.440687	+	0.897661i	$0.645265\pi$
$354$	3.55523e54	0.558853
$355$	2.50817e54	0.371063
$356$	−6.05031e53	−0.0842564
$357$	1.75269e53	0.0229794
$358$	9.49547e54	1.17228
$359$	3.67568e54	0.427372	0.213686	−	0.976902i	$-0.431453\pi$
$359$	3.67568e54	0.427372	0.213686	+	0.976902i	$0.431453\pi$
$360$	1.92029e54	0.210312
$361$	6.74396e54	0.695841
$362$	4.77835e54	0.464562
$363$	5.30483e54	0.486048
$364$	−1.50521e53	−0.0129992
$365$	6.67657e54	0.543572
$366$	−1.10173e55	−0.845727
$367$	−1.91563e55	−1.38673	−0.693364	−	0.720587i	$-0.743872\pi$
$367$	−1.91563e55	−1.38673	−0.693364	+	0.720587i	$0.743872\pi$
$368$	−5.46159e54	−0.372899
$369$	8.09350e54	0.521278
$370$	−1.34860e54	−0.0819492
$371$	6.47379e53	0.0371210
$372$	4.15818e54	0.225025
$373$	−2.66201e55	−1.35978	−0.679891	−	0.733313i	$-0.737973\pi$
$373$	−2.66201e55	−1.35978	−0.679891	+	0.733313i	$0.737973\pi$
$374$	−6.37440e54	−0.307397
$375$	−1.22399e55	−0.557323
$376$	1.04454e55	0.449147
$377$	7.38713e54	0.300011
$378$	1.61390e53	0.00619159
$379$	−2.91659e55	−1.05714	−0.528570	−	0.848890i	$-0.677271\pi$
$379$	−2.91659e55	−1.05714	−0.528570	+	0.848890i	$0.677271\pi$
$380$	8.27968e54	0.283574
$381$	−2.51208e55	−0.813105
$382$	8.35983e54	0.255761
$383$	8.50754e54	0.246054	0.123027	−	0.992403i	$-0.460740\pi$
$383$	8.50754e54	0.246054	0.123027	+	0.992403i	$0.460740\pi$
$384$	−2.49964e54	−0.0683529
$385$	−3.63309e53	−0.00939444
$386$	−4.97132e54	−0.121575
$387$	2.07923e55	0.480970
$388$	6.83263e54	0.149522
$389$	4.01341e55	0.830993	0.415497	−	0.909595i	$-0.363608\pi$
$389$	4.01341e55	0.830993	0.415497	+	0.909595i	$0.363608\pi$
$390$	−1.15093e55	−0.225507
$391$	4.06229e55	0.753304
$392$	6.18255e55	1.08522
$393$	−5.15959e55	−0.857384
$394$	4.20103e55	0.660979
$395$	5.08295e55	0.757318
$396$	3.52429e54	0.0497308
$397$	3.05288e54	0.0408051	0.0204026	−	0.999792i	$-0.493505\pi$
$397$	3.05288e54	0.0408051	0.0204026	+	0.999792i	$0.493505\pi$
$398$	−1.65196e55	−0.209177
$399$	2.55065e54	0.0306009
$400$	2.82351e55	0.320996
$401$	−6.81054e55	−0.733800	−0.366900	−	0.930260i	$-0.619581\pi$
$401$	−6.81054e55	−0.733800	−0.366900	+	0.930260i	$0.619581\pi$
$402$	−1.23557e55	−0.126185
$403$	−9.13511e55	−0.884414
$404$	−6.16270e55	−0.565681
$405$	−7.40949e54	−0.0644919
$406$	1.37354e54	0.0113378
$407$	−9.07227e54	−0.0710291
$408$	8.26356e55	0.613725
$409$	−7.81408e55	−0.550588	−0.275294	−	0.961360i	$-0.588775\pi$
$409$	−7.81408e55	−0.550588	−0.275294	+	0.961360i	$0.588775\pi$
$410$	−1.07318e56	−0.717498
$411$	4.58379e55	0.290821
$412$	−5.96395e55	−0.359123
$413$	8.71976e54	0.0498401
$414$	3.74060e55	0.202971
$415$	−2.52316e55	−0.129990
$416$	−1.22574e56	−0.599642
$417$	1.33486e56	0.620169
$418$	−9.27652e55	−0.409350
$419$	2.00491e56	0.840413	0.420207	−	0.907428i	$-0.361958\pi$
$419$	2.00491e56	0.840413	0.420207	+	0.907428i	$0.361958\pi$
$420$	1.28492e54	0.00511700
$421$	2.87650e56	1.08843	0.544214	−	0.838946i	$-0.316828\pi$
$421$	2.87650e56	1.08843	0.544214	+	0.838946i	$0.316828\pi$
$422$	−3.48008e56	−1.25133
$423$	−4.03039e55	−0.137730
$424$	3.05225e56	0.991413
$425$	−2.10010e56	−0.648453
$426$	9.93865e55	0.291757
$427$	−2.70216e55	−0.0754243
$428$	−1.84117e56	−0.488713
$429$	−7.74252e55	−0.195457
$430$	−2.75702e56	−0.662016
$431$	4.69093e56	1.07151	0.535757	−	0.844372i	$-0.320026\pi$
$431$	4.69093e56	1.07151	0.535757	+	0.844372i	$0.320026\pi$
$432$	4.28683e55	0.0931614
$433$	4.37174e56	0.903993	0.451996	−	0.892020i	$-0.350712\pi$
$433$	4.37174e56	0.903993	0.451996	+	0.892020i	$0.350712\pi$
$434$	−1.69855e55	−0.0334233
$435$	−6.30598e55	−0.118096
$436$	3.19325e56	0.569211
$437$	5.91176e56	1.00315
$438$	2.64559e56	0.427396
$439$	3.15508e56	0.485314	0.242657	−	0.970112i	$-0.421981\pi$
$439$	3.15508e56	0.485314	0.242657	+	0.970112i	$0.421981\pi$
$440$	−1.71293e56	−0.250903
$441$	−2.38555e56	−0.332781
$442$	−4.95277e56	−0.658065
$443$	−8.23492e56	−1.04227	−0.521134	−	0.853475i	$-0.674491\pi$
$443$	−8.23492e56	−1.04227	−0.521134	+	0.853475i	$0.674491\pi$
$444$	3.20859e55	0.0386883
$445$	−1.13466e56	−0.130354
$446$	−2.00110e56	−0.219063
$447$	−7.05401e56	−0.735909
$448$	−4.26061e55	−0.0423638
$449$	8.61086e56	0.816113	0.408057	−	0.912957i	$-0.366207\pi$
$449$	8.61086e56	0.816113	0.408057	+	0.912957i	$0.366207\pi$
$450$	−1.93380e56	−0.174720
$451$	−7.21951e56	−0.621888
$452$	−5.79143e56	−0.475674
$453$	−1.20493e57	−0.943740
$454$	−1.05190e57	−0.785730
$455$	−2.82283e55	−0.0201113
$456$	1.20258e57	0.817277
$457$	−1.34211e57	−0.870141	−0.435070	−	0.900396i	$-0.643277\pi$
$457$	−1.34211e57	−0.870141	−0.435070	+	0.900396i	$0.643277\pi$
$458$	1.70740e57	1.05616
$459$	−3.18851e56	−0.188198
$460$	2.97811e56	0.167744
$461$	2.56415e57	1.37840	0.689198	−	0.724573i	$-0.257963\pi$
$461$	2.56415e57	1.37840	0.689198	+	0.724573i	$0.257963\pi$
$462$	−1.43962e55	−0.00738659
$463$	−1.67394e57	−0.819875	−0.409937	−	0.912114i	$-0.634449\pi$
$463$	−1.67394e57	−0.819875	−0.409937	+	0.912114i	$0.634449\pi$
$464$	3.64839e56	0.170594
$465$	7.79813e56	0.348139
$466$	2.15167e57	0.917231
$467$	2.78817e57	1.13503	0.567514	−	0.823364i	$-0.307905\pi$
$467$	2.78817e57	1.13503	0.567514	+	0.823364i	$0.307905\pi$
$468$	2.73830e56	0.106462
$469$	−3.03043e55	−0.0112535
$470$	5.34422e56	0.189575
$471$	−1.78476e57	−0.604826
$472$	4.11118e57	1.33111
$473$	−1.85470e57	−0.573799
$474$	2.01412e57	0.595458
$475$	−3.05624e57	−0.863524
$476$	5.52935e55	0.0149322
$477$	−1.17772e57	−0.304016
$478$	−2.57533e56	−0.0635525
$479$	−3.93113e57	−0.927478	−0.463739	−	0.885972i	$-0.653493\pi$
$479$	−3.93113e57	−0.927478	−0.463739	+	0.885972i	$0.653493\pi$
$480$	1.04635e57	0.236042
$481$	−7.04895e56	−0.152057
$482$	−4.62802e57	−0.954737
$483$	9.17441e55	0.0181015
$484$	1.67356e57	0.315839
$485$	1.28137e57	0.231328
$486$	−2.93602e56	−0.0507082
$487$	4.59837e57	0.759855	0.379928	−	0.925016i	$-0.375949\pi$
$487$	4.59837e57	0.759855	0.379928	+	0.925016i	$0.375949\pi$
$488$	−1.27401e58	−2.01440
$489$	−2.57865e57	−0.390168
$490$	3.16319e57	0.458046
$491$	5.46081e57	0.756842	0.378421	−	0.925634i	$-0.376467\pi$
$491$	5.46081e57	0.756842	0.378421	+	0.925634i	$0.376467\pi$
$492$	2.55332e57	0.338732
$493$	−2.71364e57	−0.344622
$494$	−7.20766e57	−0.876324
$495$	6.60936e56	0.0769392
$496$	−4.51169e57	−0.502902
$497$	2.43761e56	0.0260197
$498$	−9.99805e56	−0.102208
$499$	4.19230e57	0.410478	0.205239	−	0.978712i	$-0.434203\pi$
$499$	4.19230e57	0.410478	0.205239	+	0.978712i	$0.434203\pi$
$500$	−3.86143e57	−0.362154
$501$	1.06278e58	0.954845
$502$	1.52338e58	1.31123
$503$	8.78676e57	0.724631	0.362316	−	0.932056i	$-0.381986\pi$
$503$	8.78676e57	0.724631	0.362316	+	0.932056i	$0.381986\pi$
$504$	1.86627e56	0.0147475
$505$	−1.15574e58	−0.875173
$506$	−3.33666e57	−0.242145
$507$	2.28485e57	0.158923
$508$	−7.92507e57	−0.528364
$509$	2.23159e58	1.42620	0.713102	−	0.701060i	$-0.247290\pi$
$509$	2.23159e58	1.42620	0.713102	+	0.701060i	$0.247290\pi$
$510$	4.22790e57	0.259039
$511$	6.48874e56	0.0381163
$512$	−1.53962e58	−0.867178
$513$	−4.64017e57	−0.250617
$514$	1.55369e58	0.804744
$515$	−1.11846e58	−0.555604
$516$	6.55953e57	0.312539
$517$	3.59516e57	0.164313
$518$	−1.31066e56	−0.00574644
$519$	−1.60596e58	−0.675517
$520$	−1.33091e58	−0.537125
$521$	4.83482e58	1.87227	0.936136	−	0.351638i	$-0.114375\pi$
$521$	4.83482e58	1.87227	0.936136	+	0.351638i	$0.114375\pi$
$522$	−2.49875e57	−0.0928553
$523$	−3.33314e58	−1.18869	−0.594343	−	0.804212i	$-0.702588\pi$
$523$	−3.33314e58	−1.18869	−0.594343	+	0.804212i	$0.702588\pi$
$524$	−1.62774e58	−0.557137
$525$	−4.74295e56	−0.0155820
$526$	4.70386e57	0.148341
$527$	3.35575e58	1.01593
$528$	−3.82391e57	−0.111142
$529$	−1.45702e58	−0.406602
$530$	1.56163e58	0.418453
$531$	−1.58631e58	−0.408183
$532$	8.04675e56	0.0198848
$533$	−5.60940e58	−1.33132
$534$	−4.49609e57	−0.102494
$535$	−3.45289e58	−0.756095
$536$	−1.42878e58	−0.300554
$537$	−4.23678e58	−0.856228
$538$	−2.77921e58	−0.539638
$539$	2.12794e58	0.397010
$540$	−2.33753e57	−0.0419075
$541$	6.69687e58	1.15380	0.576900	−	0.816815i	$-0.304262\pi$
$541$	6.69687e58	1.15380	0.576900	+	0.816815i	$0.304262\pi$
$542$	2.45624e58	0.406711
$543$	−2.13205e58	−0.339313
$544$	4.50272e58	0.688809
$545$	5.98853e58	0.880635
$546$	−1.11855e57	−0.0158130
$547$	5.70829e58	0.775852	0.387926	−	0.921691i	$-0.373192\pi$
$547$	5.70829e58	0.775852	0.387926	+	0.921691i	$0.373192\pi$
$548$	1.44608e58	0.188978
$549$	4.91579e58	0.617715
$550$	1.72497e58	0.208442
$551$	−3.94910e58	−0.458922
$552$	4.32554e58	0.483448
$553$	4.93995e57	0.0531046
$554$	−4.82369e58	−0.498792
$555$	6.01730e57	0.0598553
$556$	4.21118e58	0.402992
$557$	1.85005e59	1.70332	0.851661	−	0.524093i	$-0.175596\pi$
$557$	1.85005e59	1.70332	0.851661	+	0.524093i	$0.175596\pi$
$558$	3.09002e58	0.273732
$559$	−1.44106e59	−1.22837
$560$	−1.39415e57	−0.0114358
$561$	2.84419e58	0.224521
$562$	−1.02340e59	−0.777524
$563$	−2.39144e59	−1.74875	−0.874377	−	0.485247i	$-0.838730\pi$
$563$	−2.39144e59	−1.74875	−0.874377	+	0.485247i	$0.838730\pi$
$564$	−1.27150e58	−0.0894985
$565$	−1.08611e59	−0.735922
$566$	−1.20246e58	−0.0784366
$567$	−7.20104e56	−0.00452230
$568$	1.14928e59	0.694924
$569$	−2.48333e59	−1.44584	−0.722921	−	0.690930i	$-0.757201\pi$
$569$	−2.48333e59	−1.44584	−0.722921	+	0.690930i	$0.757201\pi$
$570$	6.15277e58	0.344954
$571$	5.26109e57	0.0284053	0.0142027	−	0.999899i	$-0.495479\pi$
$571$	5.26109e57	0.0284053	0.0142027	+	0.999899i	$0.495479\pi$
$572$	−2.44260e58	−0.127010
$573$	−3.73007e58	−0.186807
$574$	−1.04299e58	−0.0503124
$575$	−1.09929e59	−0.510805
$576$	7.75095e58	0.346954
$577$	1.90433e59	0.821224	0.410612	−	0.911810i	$-0.365315\pi$
$577$	1.90433e59	0.821224	0.410612	+	0.911810i	$0.365315\pi$
$578$	−8.31412e57	−0.0345436
$579$	2.21815e58	0.0887979
$580$	−1.98940e58	−0.0767397
$581$	−2.45218e57	−0.00911519
$582$	5.07744e58	0.181887
$583$	1.05054e59	0.362692
$584$	3.05930e59	1.01800
$585$	5.13533e58	0.164709
$586$	−3.02494e58	−0.0935231
$587$	−5.30546e59	−1.58126	−0.790630	−	0.612294i	$-0.790247\pi$
$587$	−5.30546e59	−1.58126	−0.790630	+	0.612294i	$0.790247\pi$
$588$	−7.52589e58	−0.216245
$589$	4.88356e59	1.35287
$590$	2.10341e59	0.561831
$591$	−1.87446e59	−0.482775
$592$	−3.48137e58	−0.0864636
$593$	3.29065e59	0.788144	0.394072	−	0.919080i	$-0.371066\pi$
$593$	3.29065e59	0.788144	0.394072	+	0.919080i	$0.371066\pi$
$594$	2.61896e58	0.0604952
$595$	1.03696e58	0.0231019
$596$	−2.22539e59	−0.478201
$597$	7.37089e58	0.152782
$598$	−2.59251e59	−0.518376
$599$	4.73910e59	0.914154	0.457077	−	0.889427i	$-0.348896\pi$
$599$	4.73910e59	0.914154	0.457077	+	0.889427i	$0.348896\pi$
$600$	−2.23620e59	−0.416158
$601$	6.03771e59	1.08410	0.542052	−	0.840345i	$-0.317648\pi$
$601$	6.03771e59	1.08410	0.542052	+	0.840345i	$0.317648\pi$
$602$	−2.67946e58	−0.0464219
$603$	5.51298e58	0.0921647
$604$	−3.80131e59	−0.613252
$605$	3.13854e59	0.488639
$606$	−4.57961e59	−0.688124
$607$	−1.12859e60	−1.63674	−0.818370	−	0.574692i	$-0.805122\pi$
$607$	−1.12859e60	−1.63674	−0.818370	+	0.574692i	$0.805122\pi$
$608$	6.55271e59	0.917264
$609$	−6.12858e57	−0.00828110
$610$	−6.51824e59	−0.850234
$611$	2.79336e59	0.351756
$612$	−1.00591e59	−0.122293
$613$	5.36469e59	0.629716	0.314858	−	0.949139i	$-0.398043\pi$
$613$	5.36469e59	0.629716	0.314858	+	0.949139i	$0.398043\pi$
$614$	−6.63298e59	−0.751776
$615$	4.78843e59	0.524057
$616$	−1.66474e58	−0.0175938
$617$	5.39956e58	0.0551096	0.0275548	−	0.999620i	$-0.491228\pi$
$617$	5.39956e58	0.0551096	0.0275548	+	0.999620i	$0.491228\pi$
$618$	−4.43191e59	−0.436857
$619$	−8.54808e59	−0.813803	−0.406902	−	0.913472i	$-0.633391\pi$
$619$	−8.54808e59	−0.813803	−0.406902	+	0.913472i	$0.633391\pi$
$620$	2.46014e59	0.226224
$621$	−1.66902e59	−0.148249
$622$	−4.74454e59	−0.407100
$623$	−1.10274e58	−0.00914069
$624$	−2.97109e59	−0.237929
$625$	1.32880e59	0.102811
$626$	−1.16572e59	−0.0871460
$627$	4.13909e59	0.298987
$628$	−5.63053e59	−0.393022
$629$	2.58941e59	0.174667
$630$	9.54844e57	0.00622458
$631$	−1.08863e60	−0.685883	−0.342942	−	0.939357i	$-0.611423\pi$
$631$	−1.08863e60	−0.685883	−0.342942	+	0.939357i	$0.611423\pi$
$632$	2.32908e60	1.41830
$633$	1.55278e60	0.913963
$634$	2.49671e60	1.42052
$635$	−1.48624e60	−0.817439
$636$	−3.71544e59	−0.197552
$637$	1.65336e60	0.849905
$638$	2.22892e59	0.110777
$639$	−4.43453e59	−0.213098
$640$	−1.47889e59	−0.0687172
$641$	−5.75414e59	−0.258543	−0.129271	−	0.991609i	$-0.541264\pi$
$641$	−5.75414e59	−0.258543	−0.129271	+	0.991609i	$0.541264\pi$
$642$	−1.36821e60	−0.594496
$643$	2.44929e60	1.02921	0.514605	−	0.857427i	$-0.327939\pi$
$643$	2.44929e60	1.02921	0.514605	+	0.857427i	$0.327939\pi$
$644$	2.89432e58	0.0117625
$645$	1.23016e60	0.483533
$646$	2.64771e60	1.00663
$647$	−4.54713e60	−1.67223	−0.836113	−	0.548557i	$-0.815177\pi$
$647$	−4.54713e60	−1.67223	−0.836113	+	0.548557i	$0.815177\pi$
$648$	−3.39514e59	−0.120780
$649$	1.41501e60	0.486965
$650$	1.34027e60	0.446225
$651$	7.57875e58	0.0244122
$652$	−8.13506e59	−0.253535
$653$	−9.46384e59	−0.285387	−0.142693	−	0.989767i	$-0.545576\pi$
$653$	−9.46384e59	−0.285387	−0.142693	+	0.989767i	$0.545576\pi$
$654$	2.37296e60	0.692419
$655$	−3.05261e60	−0.861954
$656$	−2.77039e60	−0.757023
$657$	−1.18044e60	−0.312168
$658$	5.19387e58	0.0132934
$659$	−7.05783e60	−1.74837	−0.874187	−	0.485589i	$-0.838605\pi$
$659$	−7.05783e60	−1.74837	−0.874187	+	0.485589i	$0.838605\pi$
$660$	2.08511e59	0.0499959
$661$	−4.92212e60	−1.14241	−0.571204	−	0.820808i	$-0.693523\pi$
$661$	−4.92212e60	−1.14241	−0.571204	+	0.820808i	$0.693523\pi$
$662$	8.11513e57	0.00182326
$663$	2.20987e60	0.480648
$664$	−1.15615e60	−0.243445
$665$	1.50906e59	0.0307640
$666$	2.38436e59	0.0470626
$667$	−1.42045e60	−0.271469
$668$	3.35284e60	0.620468
$669$	8.92869e59	0.160002
$670$	−7.31011e59	−0.126857
$671$	−4.38495e60	−0.736937
$672$	1.01691e59	0.0165517
$673$	9.64075e60	1.51980	0.759901	−	0.650039i	$-0.225248\pi$
$673$	9.64075e60	1.51980	0.759901	+	0.650039i	$0.225248\pi$
$674$	7.88544e60	1.20403
$675$	8.62841e59	0.127614
$676$	7.20820e59	0.103270
$677$	9.30646e60	1.29160	0.645800	−	0.763506i	$-0.276524\pi$
$677$	9.30646e60	1.29160	0.645800	+	0.763506i	$0.276524\pi$
$678$	−4.30371e60	−0.578635
$679$	1.24532e59	0.0162212
$680$	4.88904e60	0.616996
$681$	4.69347e60	0.573893
$682$	−2.75633e60	−0.326563
$683$	−1.08277e60	−0.124306	−0.0621530	−	0.998067i	$-0.519797\pi$
$683$	−1.08277e60	−0.124306	−0.0621530	+	0.998067i	$0.519797\pi$
$684$	−1.46387e60	−0.162853
$685$	2.71195e60	0.292371
$686$	6.15350e59	0.0642916
$687$	−7.61826e60	−0.771412
$688$	−7.11719e60	−0.698485
$689$	8.16246e60	0.776439
$690$	2.21308e60	0.204053
$691$	−1.51050e61	−1.35003	−0.675014	−	0.737804i	$-0.735863\pi$
$691$	−1.51050e61	−1.35003	−0.675014	+	0.737804i	$0.735863\pi$
$692$	−5.06645e60	−0.438958
$693$	6.42342e58	0.00539513
$694$	−4.04308e60	−0.329218
$695$	7.89754e60	0.623474
$696$	−2.88949e60	−0.221168
$697$	2.06059e61	1.52928
$698$	−2.33129e60	−0.167766
$699$	−9.60054e60	−0.669941
$700$	−1.49630e59	−0.0101253
$701$	−2.93153e60	−0.192379	−0.0961893	−	0.995363i	$-0.530665\pi$
$701$	−2.93153e60	−0.192379	−0.0961893	+	0.995363i	$0.530665\pi$
$702$	2.03488e60	0.129506
$703$	3.76831e60	0.232599
$704$	−6.91394e60	−0.413917
$705$	−2.38454e60	−0.138464
$706$	−1.23693e61	−0.696694
$707$	−1.12322e60	−0.0613688
$708$	−5.00445e60	−0.265242
$709$	2.90358e60	0.149293	0.0746465	−	0.997210i	$-0.476217\pi$
$709$	2.90358e60	0.149293	0.0746465	+	0.997210i	$0.476217\pi$
$710$	5.88009e60	0.293312
$711$	−8.98680e60	−0.434920
$712$	−5.19917e60	−0.244126
$713$	1.75656e61	0.800273
$714$	4.10896e59	0.0181644
$715$	−4.58078e60	−0.196499
$716$	−1.33661e61	−0.556385
$717$	1.14908e60	0.0464184
$718$	8.61715e60	0.337822
$719$	−3.54815e61	−1.34999	−0.674995	−	0.737822i	$-0.735854\pi$
$719$	−3.54815e61	−1.34999	−0.674995	+	0.737822i	$0.735854\pi$
$720$	2.53626e60	0.0936580
$721$	−1.08700e60	−0.0389601
$722$	1.58103e61	0.550037
$723$	2.06498e61	0.697335
$724$	−6.72615e60	−0.220489
$725$	7.34337e60	0.233684
$726$	1.24365e61	0.384203
$727$	1.03918e61	0.311674	0.155837	−	0.987783i	$-0.450193\pi$
$727$	1.03918e61	0.311674	0.155837	+	0.987783i	$0.450193\pi$
$728$	−1.29346e60	−0.0376643
$729$	1.31002e60	0.0370370
$730$	1.56524e61	0.429673
$731$	5.29370e61	1.41103
$732$	1.55082e61	0.401397
$733$	−1.42956e61	−0.359308	−0.179654	−	0.983730i	$-0.557498\pi$
$733$	−1.42956e61	−0.359308	−0.179654	+	0.983730i	$0.557498\pi$
$734$	−4.49095e61	−1.09616
$735$	−1.41138e61	−0.334555
$736$	2.35694e61	0.542594
$737$	−4.91765e60	−0.109953
$738$	1.89742e61	0.412051
$739$	3.23314e61	0.681975	0.340988	−	0.940068i	$-0.389239\pi$
$739$	3.23314e61	0.681975	0.340988	+	0.940068i	$0.389239\pi$
$740$	1.89833e60	0.0388945
$741$	3.21598e61	0.640062
$742$	1.51770e60	0.0293428
$743$	−4.05119e61	−0.760893	−0.380446	−	0.924803i	$-0.624230\pi$
$743$	−4.05119e61	−0.760893	−0.380446	+	0.924803i	$0.624230\pi$
$744$	3.57322e61	0.651991
$745$	−4.17343e61	−0.739832
$746$	−6.24073e61	−1.07486
$747$	4.46103e60	0.0746521
$748$	8.97280e60	0.145896
$749$	−3.35575e60	−0.0530189
$750$	−2.86950e61	−0.440543
$751$	−3.19198e61	−0.476214	−0.238107	−	0.971239i	$-0.576527\pi$
$751$	−3.19198e61	−0.476214	−0.238107	+	0.971239i	$0.576527\pi$
$752$	1.37960e61	0.200018
$753$	−6.79716e61	−0.957713
$754$	1.73182e61	0.237147
$755$	−7.12886e61	−0.948770
$756$	−2.27177e59	−0.00293864
$757$	−2.67158e61	−0.335898	−0.167949	−	0.985796i	$-0.553714\pi$
$757$	−2.67158e61	−0.335898	−0.167949	+	0.985796i	$0.553714\pi$
$758$	−6.83757e61	−0.835630
$759$	1.48878e61	0.176862
$760$	7.11492e61	0.821633
$761$	4.67073e61	0.524342	0.262171	−	0.965021i	$-0.415562\pi$
$761$	4.67073e61	0.524342	0.262171	+	0.965021i	$0.415562\pi$
$762$	−5.88925e61	−0.642730
$763$	5.82006e60	0.0617519
$764$	−1.17676e61	−0.121389
$765$	−1.88645e61	−0.189201
$766$	1.99448e61	0.194497
$767$	1.09943e62	1.04248
$768$	5.93175e61	0.546911
$769$	−3.41657e61	−0.306319	−0.153159	−	0.988202i	$-0.548945\pi$
$769$	−3.41657e61	−0.306319	−0.153159	+	0.988202i	$0.548945\pi$
$770$	−8.51733e59	−0.00742596
$771$	−6.93242e61	−0.587781
$772$	6.99779e60	0.0577017
$773$	6.37216e61	0.511008	0.255504	−	0.966808i	$-0.417759\pi$
$773$	6.37216e61	0.511008	0.255504	+	0.966808i	$0.417759\pi$
$774$	4.87450e61	0.380189
$775$	−9.08099e61	−0.688885
$776$	5.87144e61	0.433229
$777$	5.84802e59	0.00419717
$778$	9.40894e61	0.656870
$779$	2.99874e62	2.03650
$780$	1.62008e61	0.107029
$781$	3.95565e61	0.254227
$782$	9.52351e61	0.595459
$783$	1.11492e61	0.0678210
$784$	8.16570e61	0.483279
$785$	−1.05593e62	−0.608050
$786$	−1.20960e62	−0.677731
$787$	−2.17767e62	−1.18723	−0.593614	−	0.804750i	$-0.702300\pi$
$787$	−2.17767e62	−1.18723	−0.593614	+	0.804750i	$0.702300\pi$
$788$	−5.91351e61	−0.313712
$789$	−2.09881e61	−0.108347
$790$	1.19163e62	0.598632
$791$	−1.05555e61	−0.0516043
$792$	3.02851e61	0.144091
$793$	−3.40701e62	−1.57761
$794$	7.15710e60	0.0322549
$795$	−6.96783e61	−0.305636
$796$	2.32535e61	0.0992791
$797$	7.92440e61	0.329316	0.164658	−	0.986351i	$-0.447348\pi$
$797$	7.92440e61	0.329316	0.164658	+	0.986351i	$0.447348\pi$
$798$	5.97968e60	0.0241889
$799$	−1.02613e62	−0.404062
$800$	−1.21848e62	−0.467072
$801$	2.00611e61	0.0748610
$802$	−1.59664e62	−0.580042
$803$	1.05297e62	0.372417
$804$	1.73923e61	0.0598895
$805$	5.42794e60	0.0181980
$806$	−2.14161e62	−0.699096
$807$	1.24006e62	0.394149
$808$	−5.29575e62	−1.63902
$809$	3.01193e62	0.907719	0.453860	−	0.891073i	$-0.350047\pi$
$809$	3.01193e62	0.907719	0.453860	+	0.891073i	$0.350047\pi$
$810$	−1.73706e61	−0.0509785
$811$	4.60520e62	1.31613	0.658067	−	0.752959i	$-0.271374\pi$
$811$	4.60520e62	1.31613	0.658067	+	0.752959i	$0.271374\pi$
$812$	−1.93343e60	−0.00538114
$813$	−1.09595e62	−0.297059
$814$	−2.12688e61	−0.0561459
$815$	−1.52563e62	−0.392247
$816$	1.09142e62	0.273309
$817$	7.70381e62	1.87902
$818$	−1.83191e62	−0.435220
$819$	4.99086e60	0.0115497
$820$	1.51064e62	0.340537
$821$	−6.21732e62	−1.36529	−0.682646	−	0.730749i	$-0.739171\pi$
$821$	−6.21732e62	−1.36529	−0.682646	+	0.730749i	$0.739171\pi$
$822$	1.07461e62	0.229883
$823$	4.56107e62	0.950539	0.475270	−	0.879840i	$-0.342350\pi$
$823$	4.56107e62	0.950539	0.475270	+	0.879840i	$0.342350\pi$
$824$	−5.12496e62	−1.04053
$825$	−7.69665e61	−0.152245
$826$	2.04424e61	0.0393967
$827$	6.18607e62	1.16157	0.580786	−	0.814056i	$-0.302745\pi$
$827$	6.18607e62	1.16157	0.580786	+	0.814056i	$0.302745\pi$
$828$	−5.26538e61	−0.0963336
$829$	2.44434e62	0.435751	0.217876	−	0.975977i	$-0.430087\pi$
$829$	2.44434e62	0.435751	0.217876	+	0.975977i	$0.430087\pi$
$830$	−5.91524e61	−0.102753
$831$	2.15228e62	0.364315
$832$	−5.37198e62	−0.886101
$833$	−6.07358e62	−0.976286
$834$	3.12940e62	0.490221
$835$	6.28783e62	0.959934
$836$	1.30579e62	0.194285
$837$	−1.37873e62	−0.199932
$838$	4.70025e62	0.664316
$839$	−4.81900e62	−0.663858	−0.331929	−	0.943304i	$-0.607699\pi$
$839$	−4.81900e62	−0.663858	−0.331929	+	0.943304i	$0.607699\pi$
$840$	1.10416e61	0.0148261
$841$	−6.69149e62	−0.875808
$842$	6.74359e62	0.860362
$843$	4.56630e62	0.567900
$844$	4.89867e62	0.593903
$845$	1.35180e62	0.159770
$846$	−9.44874e61	−0.108871
$847$	3.05025e61	0.0342643
$848$	4.03131e62	0.441505
$849$	5.36527e61	0.0572897
$850$	−4.92342e62	−0.512578
$851$	1.35542e62	0.137590
$852$	−1.39900e62	−0.138473
$853$	−1.38529e63	−1.33702	−0.668510	−	0.743703i	$-0.733068\pi$
$853$	−1.38529e63	−1.33702	−0.668510	+	0.743703i	$0.733068\pi$
$854$	−6.33486e61	−0.0596201
$855$	−2.74531e62	−0.251953
$856$	−1.58216e63	−1.41601
$857$	−2.18315e63	−1.90545	−0.952723	−	0.303840i	$-0.901731\pi$
$857$	−2.18315e63	−1.90545	−0.952723	+	0.303840i	$0.901731\pi$
$858$	−1.81514e62	−0.154501
$859$	−3.10254e62	−0.257552	−0.128776	−	0.991674i	$-0.541105\pi$
$859$	−3.10254e62	−0.257552	−0.128776	+	0.991674i	$0.541105\pi$
$860$	3.88087e62	0.314205
$861$	4.65372e61	0.0367479
$862$	1.09973e63	0.846993
$863$	3.22226e62	0.242063	0.121032	−	0.992649i	$-0.461380\pi$
$863$	3.22226e62	0.242063	0.121032	+	0.992649i	$0.461380\pi$
$864$	−1.84997e62	−0.135556
$865$	−9.50148e62	−0.679117
$866$	1.02490e63	0.714573
$867$	3.70968e61	0.0252305
$868$	2.39093e61	0.0158633
$869$	8.01634e62	0.518861
$870$	−1.47836e62	−0.0933502
$871$	−3.82091e62	−0.235384
$872$	2.74404e63	1.64925
$873$	−2.26550e62	−0.132849
$874$	1.38594e63	0.792953
$875$	−7.03789e61	−0.0392889
$876$	−3.72402e62	−0.202850
$877$	9.37907e62	0.498504	0.249252	−	0.968439i	$-0.419815\pi$
$877$	9.37907e62	0.498504	0.249252	+	0.968439i	$0.419815\pi$
$878$	7.39667e62	0.383623
$879$	1.34970e62	0.0683088
$880$	−2.26237e62	−0.111734
$881$	−1.19604e63	−0.576452	−0.288226	−	0.957562i	$-0.593065\pi$
$881$	−1.19604e63	−0.576452	−0.288226	+	0.957562i	$0.593065\pi$
$882$	−5.59262e62	−0.263051
$883$	3.71532e63	1.70546	0.852728	−	0.522355i	$-0.174946\pi$
$883$	3.71532e63	1.70546	0.852728	+	0.522355i	$0.174946\pi$
$884$	6.97167e62	0.312330
$885$	−9.38521e62	−0.410359
$886$	−1.93057e63	−0.823875
$887$	3.17967e63	1.32442	0.662208	−	0.749320i	$-0.269620\pi$
$887$	3.17967e63	1.32442	0.662208	+	0.749320i	$0.269620\pi$
$888$	2.75721e62	0.112096
$889$	−1.44443e62	−0.0573204
$890$	−2.66006e62	−0.103040
$891$	−1.16855e62	−0.0441854
$892$	2.81681e62	0.103971
$893$	−1.49331e63	−0.538076
$894$	−1.65372e63	−0.581709
$895$	−2.50665e63	−0.860791
$896$	−1.43728e61	−0.00481859
$897$	1.15675e63	0.378620
$898$	2.01871e63	0.645107
$899$	−1.17340e63	−0.366110
$900$	2.72208e62	0.0829251
$901$	−2.99845e63	−0.891896
$902$	−1.69252e63	−0.491579
$903$	1.19555e62	0.0339063
$904$	−4.97671e63	−1.37823
$905$	−1.26140e63	−0.341122
$906$	−2.82482e63	−0.745992
$907$	6.50266e63	1.67700	0.838502	−	0.544899i	$-0.183432\pi$
$907$	6.50266e63	1.67700	0.838502	+	0.544899i	$0.183432\pi$
$908$	1.48069e63	0.372921
$909$	2.04337e63	0.502602
$910$	−6.61777e61	−0.0158973
$911$	−7.52857e63	−1.76631	−0.883156	−	0.469079i	$-0.844586\pi$
$911$	−7.52857e63	−1.76631	−0.883156	+	0.469079i	$0.844586\pi$
$912$	1.58832e63	0.363957
$913$	−3.97930e62	−0.0890604
$914$	−3.14640e63	−0.687814
$915$	2.90837e63	0.621007
$916$	−2.40340e63	−0.501271
$917$	−2.96674e62	−0.0604419
$918$	−7.47505e62	−0.148764
$919$	2.17512e63	0.422864	0.211432	−	0.977393i	$-0.432187\pi$
$919$	2.17512e63	0.422864	0.211432	+	0.977393i	$0.432187\pi$
$920$	2.55916e63	0.486025
$921$	2.95957e63	0.549093
$922$	6.01133e63	1.08957
$923$	3.07346e63	0.544240
$924$	2.02645e61	0.00350581
$925$	−7.00719e62	−0.118440
$926$	−3.92433e63	−0.648081
$927$	1.97747e63	0.319078
$928$	−1.57445e63	−0.248226
$929$	7.86465e63	1.21155	0.605775	−	0.795636i	$-0.292863\pi$
$929$	7.86465e63	1.21155	0.605775	+	0.795636i	$0.292863\pi$
$930$	1.82817e63	0.275191
$931$	−8.83875e63	−1.30009
$932$	−3.02876e63	−0.435334
$933$	2.11696e63	0.297343
$934$	6.53651e63	0.897198
$935$	1.68273e63	0.225718
$936$	2.35308e63	0.308465
$937$	1.79538e63	0.230015	0.115007	−	0.993365i	$-0.463311\pi$
$937$	1.79538e63	0.230015	0.115007	+	0.993365i	$0.463311\pi$
$938$	−7.10445e61	−0.00889548
$939$	5.20134e62	0.0636510
$940$	−7.52269e62	−0.0899755
$941$	−1.29813e64	−1.51754	−0.758771	−	0.651358i	$-0.774200\pi$
$941$	−1.29813e64	−1.51754	−0.758771	+	0.651358i	$0.774200\pi$
$942$	−4.18414e63	−0.478093
$943$	1.07861e64	1.20466
$944$	5.42991e63	0.592781
$945$	−4.26042e61	−0.00454641
$946$	−4.34812e63	−0.453567
$947$	3.48486e63	0.355353	0.177677	−	0.984089i	$-0.443142\pi$
$947$	3.48486e63	0.355353	0.177677	+	0.984089i	$0.443142\pi$
$948$	−2.83514e63	−0.282615
$949$	8.18131e63	0.797259
$950$	−7.16495e63	−0.682584
$951$	−1.11401e64	−1.03754
$952$	4.75150e62	0.0432650
$953$	3.62975e63	0.323131	0.161566	−	0.986862i	$-0.448346\pi$
$953$	3.62975e63	0.323131	0.161566	+	0.986862i	$0.448346\pi$
$954$	−2.76101e63	−0.240313
$955$	−2.20685e63	−0.187802
$956$	3.62511e62	0.0301631
$957$	−9.94520e62	−0.0809108
$958$	−9.21603e63	−0.733137
$959$	2.63565e62	0.0205016
$960$	4.58576e63	0.348803
$961$	1.06576e63	0.0792697
$962$	−1.65254e63	−0.120195
$963$	6.10481e63	0.434217
$964$	6.51455e63	0.453135
$965$	1.31235e63	0.0892711
$966$	2.15082e62	0.0143086
$967$	−2.78438e64	−1.81159	−0.905794	−	0.423719i	$-0.860724\pi$
$967$	−2.78438e64	−1.81159	−0.905794	+	0.423719i	$0.860724\pi$
$968$	1.43813e64	0.915118
$969$	−1.18138e64	−0.735240
$970$	3.00401e63	0.182856
$971$	−2.13572e64	−1.27154	−0.635770	−	0.771878i	$-0.719317\pi$
$971$	−2.13572e64	−1.27154	−0.635770	+	0.771878i	$0.719317\pi$
$972$	4.13283e62	0.0240670
$973$	7.67536e62	0.0437192
$974$	1.07803e64	0.600638
$975$	−5.98013e63	−0.325920
$976$	−1.68267e64	−0.897072
$977$	3.39336e64	1.76969	0.884843	−	0.465889i	$-0.154266\pi$
$977$	3.39336e64	1.76969	0.884843	+	0.465889i	$0.154266\pi$
$978$	−6.04530e63	−0.308413
$979$	−1.78948e63	−0.0893096
$980$	−4.45261e63	−0.217397
$981$	−1.05879e64	−0.505739
$982$	1.28022e64	0.598255
$983$	8.51968e63	0.389514	0.194757	−	0.980852i	$-0.437608\pi$
$983$	8.51968e63	0.389514	0.194757	+	0.980852i	$0.437608\pi$
$984$	2.19413e64	0.981449
$985$	−1.10900e64	−0.485348
$986$	−6.36178e63	−0.272411
$987$	−2.31745e62	−0.00970940
$988$	1.01457e64	0.415919
$989$	2.77097e64	1.11151
$990$	1.54948e63	0.0608176
$991$	4.90354e63	0.188333	0.0941664	−	0.995556i	$-0.469981\pi$
$991$	4.90354e63	0.188333	0.0941664	+	0.995556i	$0.469981\pi$
$992$	1.94701e64	0.731757
$993$	−3.62089e61	−0.00133170
$994$	5.71467e62	0.0205676
$995$	4.36090e63	0.153596
$996$	1.40736e63	0.0485097
$997$	4.69596e64	1.58409	0.792043	−	0.610465i	$-0.209017\pi$
$997$	4.69596e64	1.58409	0.792043	+	0.610465i	$0.209017\pi$
$998$	9.82831e63	0.324468
$999$	−1.06388e63	−0.0343742

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.44.a.b.1.3	✓	4	1.1	even	1	trivial
9.44.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+2.34437e6 q^{2} -1.04604e10 q^{3} -3.30001e12 q^{4} -6.18875e14 q^{5} -2.45230e16 q^{6} -6.01464e16 q^{7} -2.83578e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\)	\(q+2.34437e6 q^{2} -1.04604e10 q^{3} -3.30001e12 q^{4} -6.18875e14 q^{5} -2.45230e16 q^{6} -6.01464e16 q^{7} -2.83578e19 q^{8} +1.09419e20 q^{9} -1.45087e21 q^{10} -9.76031e21 q^{11} +3.45193e22 q^{12} -7.58355e23 q^{13} -1.41006e23 q^{14} +6.47365e24 q^{15} -3.74540e25 q^{16} +2.78579e26 q^{17} +2.56519e26 q^{18} +4.05410e27 q^{19} +2.04230e27 q^{20} +6.29153e26 q^{21} -2.28818e28 q^{22} +1.45822e29 q^{23} +2.96632e29 q^{24} -7.53862e29 q^{25} -1.77787e30 q^{26} -1.14456e30 q^{27} +1.98484e29 q^{28} -9.74099e30 q^{29} +1.51766e31 q^{30} +1.20460e32 q^{31} +1.61632e32 q^{32} +1.02096e32 q^{33} +6.53093e32 q^{34} +3.72231e31 q^{35} -3.61084e32 q^{36} +9.29506e32 q^{37} +9.50433e33 q^{38} +7.93266e33 q^{39} +1.75499e34 q^{40} +7.39680e34 q^{41} +1.47497e33 q^{42} +1.90025e35 q^{43} +3.22092e34 q^{44} -6.77167e34 q^{45} +3.41860e35 q^{46} -3.68345e35 q^{47} +3.91782e35 q^{48} -2.18020e36 q^{49} -1.76733e36 q^{50} -2.91404e36 q^{51} +2.50258e36 q^{52} -1.07634e37 q^{53} -2.68328e36 q^{54} +6.04041e36 q^{55} +1.70562e36 q^{56} -4.24074e37 q^{57} -2.28365e37 q^{58} -1.44976e38 q^{59} -2.13631e37 q^{60} +4.49263e38 q^{61} +2.82402e38 q^{62} -6.58116e36 q^{63} +7.08373e38 q^{64} +4.69327e38 q^{65} +2.39352e38 q^{66} +5.03842e38 q^{67} -9.19315e38 q^{68} -1.52534e39 q^{69} +8.72649e37 q^{70} -4.05279e39 q^{71} -3.10288e39 q^{72} -1.07882e40 q^{73} +2.17911e39 q^{74} +7.88566e39 q^{75} -1.33786e40 q^{76} +5.87048e38 q^{77} +1.85971e40 q^{78} -8.21320e40 q^{79} +2.31793e40 q^{80} +1.19725e40 q^{81} +1.73408e41 q^{82} +4.07702e40 q^{83} -2.07621e39 q^{84} -1.72406e41 q^{85} +4.45489e41 q^{86} +1.01894e41 q^{87} +2.76781e41 q^{88} +1.83342e41 q^{89} -1.58753e41 q^{90} +4.56124e40 q^{91} -4.81213e41 q^{92} -1.26005e42 q^{93} -8.63538e41 q^{94} -2.50898e42 q^{95} -1.69072e42 q^{96} -2.07049e42 q^{97} -5.11119e42 q^{98} -1.06796e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5}+ \cdots + 43\!\cdots\!36 q^{9}+O(q^{10}) \) 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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