LMFDB - Embedded newform 3.44.a.b.1.1

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			1.1
Root			$-837306.$ 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)

$f(q)$	$=$	$q-4.60883e6 q^{2} -1.04604e10 q^{3} +1.24452e13 q^{4} -9.11231e14 q^{5} +4.82100e16 q^{6} +3.55193e17 q^{7} -1.68183e19 q^{8} +1.09419e20 q^{9} +O(q^{10})$	\(q-4.60883e6 q^{2} -1.04604e10 q^{3} +1.24452e13 q^{4} -9.11231e14 q^{5} +4.82100e16 q^{6} +3.55193e17 q^{7} -1.68183e19 q^{8} +1.09419e20 q^{9} +4.19971e21 q^{10} +2.29922e22 q^{11} -1.30182e23 q^{12} -1.59697e24 q^{13} -1.63703e24 q^{14} +9.53179e24 q^{15} -3.19568e25 q^{16} -8.94904e25 q^{17} -5.04294e26 q^{18} -4.96731e27 q^{19} -1.13405e28 q^{20} -3.71545e27 q^{21} -1.05967e29 q^{22} -2.67276e28 q^{23} +1.75925e29 q^{24} -3.06527e29 q^{25} +7.36016e30 q^{26} -1.14456e30 q^{27} +4.42046e30 q^{28} +5.04944e30 q^{29} -4.39304e31 q^{30} -1.04250e32 q^{31} +2.95219e32 q^{32} -2.40507e32 q^{33} +4.12446e32 q^{34} -3.23663e32 q^{35} +1.36175e33 q^{36} +7.73436e33 q^{37} +2.28935e34 q^{38} +1.67049e34 q^{39} +1.53253e34 q^{40} -8.53148e34 q^{41} +1.71239e34 q^{42} +7.83235e34 q^{43} +2.86144e35 q^{44} -9.97059e34 q^{45} +1.23183e35 q^{46} +1.13573e36 q^{47} +3.34279e35 q^{48} -2.05765e36 q^{49} +1.41273e36 q^{50} +9.36102e35 q^{51} -1.98747e37 q^{52} -1.82287e37 q^{53} +5.27509e36 q^{54} -2.09512e37 q^{55} -5.97374e36 q^{56} +5.19598e37 q^{57} -2.32720e37 q^{58} +1.43137e38 q^{59} +1.18625e38 q^{60} -2.85373e38 q^{61} +4.80471e38 q^{62} +3.88649e37 q^{63} -1.07952e39 q^{64} +1.45521e39 q^{65} +1.10846e39 q^{66} -3.77513e38 q^{67} -1.11373e39 q^{68} +2.79581e38 q^{69} +1.49171e39 q^{70} +1.14161e39 q^{71} -1.84024e39 q^{72} +1.49078e40 q^{73} -3.56464e40 q^{74} +3.20638e39 q^{75} -6.18193e40 q^{76} +8.16669e39 q^{77} -7.69899e40 q^{78} +7.25526e40 q^{79} +2.91200e40 q^{80} +1.19725e40 q^{81} +3.93201e41 q^{82} +1.45212e41 q^{83} -4.62396e40 q^{84} +8.15464e40 q^{85} -3.60980e41 q^{86} -5.28189e40 q^{87} -3.86690e41 q^{88} +2.43978e41 q^{89} +4.59528e41 q^{90} -5.67233e41 q^{91} -3.32632e41 q^{92} +1.09049e42 q^{93} -5.23439e42 q^{94} +4.52636e42 q^{95} -3.08809e42 q^{96} -4.23085e42 q^{97} +9.48337e42 q^{98} +2.51579e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.60883e6	−1.55398	−0.776991	−	0.629512i	$-0.783255\pi$
$2$	−4.60883e6	−1.55398	−0.776991	+	0.629512i	$0.783255\pi$
$3$	−1.04604e10	−0.577350
$3$	−1.04604e10	−0.577350
$4$	1.24452e13	1.41486
$5$	−9.11231e14	−0.854620	−0.427310	−	0.904105i	$-0.640539\pi$
$5$	−9.11231e14	−0.854620	−0.427310	+	0.904105i	$0.640539\pi$
$6$	4.82100e16	0.897192
$7$	3.55193e17	0.240357	0.120178	−	0.992752i	$-0.461653\pi$
$7$	3.55193e17	0.240357	0.120178	+	0.992752i	$0.461653\pi$
$8$	−1.68183e19	−0.644685
$9$	1.09419e20	0.333333
$10$	4.19971e21	1.32806
$11$	2.29922e22	0.936782	0.468391	−	0.883521i	$-0.344834\pi$
$11$	2.29922e22	0.936782	0.468391	+	0.883521i	$0.344834\pi$
$12$	−1.30182e23	−0.816870
$13$	−1.59697e24	−1.79273	−0.896364	−	0.443318i	$-0.853801\pi$
$13$	−1.59697e24	−1.79273	−0.896364	+	0.443318i	$0.853801\pi$
$14$	−1.63703e24	−0.373510
$15$	9.53179e24	0.493415
$16$	−3.19568e25	−0.413032
$17$	−8.94904e25	−0.314141	−0.157071	−	0.987587i	$-0.550205\pi$
$17$	−8.94904e25	−0.314141	−0.157071	+	0.987587i	$0.550205\pi$
$18$	−5.04294e26	−0.517994
$19$	−4.96731e27	−1.59558	−0.797790	−	0.602935i	$-0.793998\pi$
$19$	−4.96731e27	−1.59558	−0.797790	+	0.602935i	$0.793998\pi$
$20$	−1.13405e28	−1.20917
$21$	−3.71545e27	−0.138770
$22$	−1.05967e29	−1.45574
$23$	−2.67276e28	−0.141193	−0.0705963	−	0.997505i	$-0.522490\pi$
$23$	−2.67276e28	−0.141193	−0.0705963	+	0.997505i	$0.522490\pi$
$24$	1.75925e29	0.372209
$25$	−3.06527e29	−0.269624
$26$	7.36016e30	2.78587
$27$	−1.14456e30	−0.192450
$28$	4.42046e30	0.340071
$29$	5.04944e30	0.182678	0.0913390	−	0.995820i	$-0.470885\pi$
$29$	5.04944e30	0.182678	0.0913390	+	0.995820i	$0.470885\pi$
$30$	−4.39304e31	−0.766758
$31$	−1.04250e32	−0.899083	−0.449541	−	0.893259i	$-0.648413\pi$
$31$	−1.04250e32	−0.899083	−0.449541	+	0.893259i	$0.648413\pi$
$32$	2.95219e32	1.28653
$33$	−2.40507e32	−0.540852
$34$	4.12446e32	0.488170
$35$	−3.23663e32	−0.205414
$36$	1.36175e33	0.471620
$37$	7.73436e33	1.48624	0.743118	−	0.669161i	$-0.233346\pi$
$37$	7.73436e33	1.48624	0.743118	+	0.669161i	$0.233346\pi$
$38$	2.28935e34	2.47950
$39$	1.67049e34	1.03503
$40$	1.53253e34	0.550961
$41$	−8.53148e34	−1.80373	−0.901865	−	0.432019i	$-0.857801\pi$
$41$	−8.53148e34	−1.80373	−0.901865	+	0.432019i	$0.857801\pi$
$42$	1.71239e34	0.215646
$43$	7.83235e34	0.594731	0.297365	−	0.954764i	$-0.403892\pi$
$43$	7.83235e34	0.594731	0.297365	+	0.954764i	$0.403892\pi$
$44$	2.86144e35	1.32542
$45$	−9.97059e34	−0.284873
$46$	1.23183e35	0.219411
$47$	1.13573e36	1.27401	0.637003	−	0.770861i	$-0.280174\pi$
$47$	1.13573e36	1.27401	0.637003	+	0.770861i	$0.280174\pi$
$48$	3.34279e35	0.238464
$49$	−2.05765e36	−0.942229
$50$	1.41273e36	0.418991
$51$	9.36102e35	0.181369
$52$	−1.98747e37	−2.53646
$53$	−1.82287e37	−1.54463	−0.772316	−	0.635238i	$-0.780902\pi$
$53$	−1.82287e37	−1.54463	−0.772316	+	0.635238i	$0.780902\pi$
$54$	5.27509e36	0.299064
$55$	−2.09512e37	−0.800593
$56$	−5.97374e36	−0.154954
$57$	5.19598e37	0.921209
$58$	−2.32720e37	−0.283878
$59$	1.43137e38	1.20902	0.604510	−	0.796597i	$-0.293369\pi$
$59$	1.43137e38	1.20902	0.604510	+	0.796597i	$0.293369\pi$
$60$	1.18625e38	0.698113
$61$	−2.85373e38	−1.17712	−0.588561	−	0.808453i	$-0.700305\pi$
$61$	−2.85373e38	−1.17712	−0.588561	+	0.808453i	$0.700305\pi$
$62$	4.80471e38	1.39716
$63$	3.88649e37	0.0801190
$64$	−1.07952e39	−1.58621
$65$	1.45521e39	1.53210
$66$	1.10846e39	0.840474
$67$	−3.77513e38	−0.207169	−0.103584	−	0.994621i	$-0.533031\pi$
$67$	−3.77513e38	−0.207169	−0.103584	+	0.994621i	$0.533031\pi$
$68$	−1.11373e39	−0.444466
$69$	2.79581e38	0.0815176
$70$	1.49171e39	0.319210
$71$	1.14161e39	0.180080	0.0900398	−	0.995938i	$-0.471301\pi$
$71$	1.14161e39	0.180080	0.0900398	+	0.995938i	$0.471301\pi$
$72$	−1.84024e39	−0.214895
$73$	1.49078e40	1.29411	0.647054	−	0.762444i	$-0.276001\pi$
$73$	1.49078e40	1.29411	0.647054	+	0.762444i	$0.276001\pi$
$74$	−3.56464e40	−2.30958
$75$	3.20638e39	0.155668
$76$	−6.18193e40	−2.25752
$77$	8.16669e39	0.225162
$78$	−7.69899e40	−1.60842
$79$	7.25526e40	1.15258	0.576289	−	0.817246i	$-0.304500\pi$
$79$	7.25526e40	1.15258	0.576289	+	0.817246i	$0.304500\pi$
$80$	2.91200e40	0.352985
$81$	1.19725e40	0.111111
$82$	3.93201e41	2.80296
$83$	1.45212e41	0.797668	0.398834	−	0.917023i	$-0.369415\pi$
$83$	1.45212e41	0.797668	0.398834	+	0.917023i	$0.369415\pi$
$84$	−4.62396e40	−0.196340
$85$	8.15464e40	0.268471
$86$	−3.60980e41	−0.924201
$87$	−5.28189e40	−0.105469
$88$	−3.86690e41	−0.603929
$89$	2.43978e41	0.298859	0.149429	−	0.988772i	$-0.452256\pi$
$89$	2.43978e41	0.298859	0.149429	+	0.988772i	$0.452256\pi$
$90$	4.59528e41	0.442688
$91$	−5.67233e41	−0.430895
$92$	−3.32632e41	−0.199768
$93$	1.09049e42	0.519086
$94$	−5.23439e42	−1.97978
$95$	4.52636e42	1.36362
$96$	−3.08809e42	−0.742777
$97$	−4.23085e42	−0.814395	−0.407197	−	0.913340i	$-0.633494\pi$
$97$	−4.23085e42	−0.814395	−0.407197	+	0.913340i	$0.633494\pi$
$98$	9.48337e42	1.46421
$99$	2.51579e42	0.312261
$100$	−3.81480e42	−0.381480
$101$	−1.68235e43	−1.35833	−0.679166	−	0.733985i	$-0.737658\pi$
$101$	−1.68235e43	−1.35833	−0.679166	+	0.733985i	$0.737658\pi$
$102$	−4.31433e42	−0.281845
$103$	−1.99312e43	−1.05568	−0.527842	−	0.849343i	$-0.676999\pi$
$103$	−1.99312e43	−1.05568	−0.527842	+	0.849343i	$0.676999\pi$
$104$	2.68583e43	1.15574
$105$	3.38563e42	0.118596
$106$	8.40132e43	2.40033
$107$	2.25305e43	0.526040	0.263020	−	0.964790i	$-0.415281\pi$
$107$	2.25305e43	0.526040	0.263020	+	0.964790i	$0.415281\pi$
$108$	−1.42443e43	−0.272290
$109$	3.06480e42	0.0480544	0.0240272	−	0.999711i	$-0.492351\pi$
$109$	3.06480e42	0.0480544	0.0240272	+	0.999711i	$0.492351\pi$
$110$	9.65607e43	1.24411
$111$	−8.09042e43	−0.858078
$112$	−1.13508e43	−0.0992750
$113$	−2.22799e43	−0.160963	−0.0804817	−	0.996756i	$-0.525646\pi$
$113$	−2.22799e43	−0.160963	−0.0804817	+	0.996756i	$0.525646\pi$
$114$	−2.39474e44	−1.43154
$115$	2.43550e43	0.120666
$116$	6.28415e43	0.258464
$117$	−1.74739e44	−0.597576
$118$	−6.59694e44	−1.87880
$119$	−3.17864e43	−0.0755060
$120$	−1.60309e44	−0.318097
$121$	−7.37572e43	−0.122439
$122$	1.31524e45	1.82923
$123$	8.92423e44	1.04138
$124$	−1.29742e45	−1.27208
$125$	1.31527e45	1.08505
$126$	−1.79122e44	−0.124503
$127$	2.11747e45	1.24176	0.620881	−	0.783905i	$-0.286775\pi$
$127$	2.11747e45	1.24176	0.620881	+	0.783905i	$0.286775\pi$
$128$	2.37855e45	1.17841
$129$	−8.19292e44	−0.343368
$130$	−6.70681e45	−2.38086
$131$	3.36973e45	1.01452	0.507262	−	0.861792i	$-0.330658\pi$
$131$	3.36973e45	1.01452	0.507262	+	0.861792i	$0.330658\pi$
$132$	−2.99317e45	−0.765229
$133$	−1.76435e45	−0.383509
$134$	1.73990e45	0.321936
$135$	1.04296e45	0.164472
$136$	1.50508e45	0.202522
$137$	4.40626e45	0.506498	0.253249	−	0.967401i	$-0.418501\pi$
$137$	4.40626e45	0.506498	0.253249	+	0.967401i	$0.418501\pi$
$138$	−1.28854e45	−0.126677
$139$	1.29461e46	1.08973	0.544867	−	0.838522i	$-0.316580\pi$
$139$	1.29461e46	1.08973	0.544867	+	0.838522i	$0.316580\pi$
$140$	−4.02806e45	−0.290632
$141$	−1.18801e46	−0.735548
$142$	−5.26150e45	−0.279840
$143$	−3.67179e46	−1.67940
$144$	−3.49668e45	−0.137677
$145$	−4.60120e45	−0.156120
$146$	−6.87073e46	−2.01102
$147$	2.15238e46	0.543996
$148$	9.62560e46	2.10281
$149$	5.88212e46	1.11181	0.555903	−	0.831247i	$-0.312373\pi$
$149$	5.88212e46	1.11181	0.555903	+	0.831247i	$0.312373\pi$
$150$	−1.47777e46	−0.241905
$151$	−5.76594e45	−0.0818211	−0.0409106	−	0.999163i	$-0.513026\pi$
$151$	−5.76594e45	−0.0818211	−0.0409106	+	0.999163i	$0.513026\pi$
$152$	8.35417e46	1.02865
$153$	−9.79195e45	−0.104714
$154$	−3.76389e46	−0.349898
$155$	9.49958e46	0.768375
$156$	2.07896e47	1.46443
$157$	1.78729e46	0.109737	0.0548683	−	0.998494i	$-0.482526\pi$
$157$	1.78729e46	0.109737	0.0548683	+	0.998494i	$0.482526\pi$
$158$	−3.34383e47	−1.79108
$159$	1.90679e47	0.891794
$160$	−2.69012e47	−1.09949
$161$	−9.49348e45	−0.0339366
$162$	−5.51793e46	−0.172665
$163$	6.64718e46	0.182223	0.0911117	−	0.995841i	$-0.470958\pi$
$163$	6.64718e46	0.182223	0.0911117	+	0.995841i	$0.470958\pi$
$164$	−1.06176e48	−2.55202
$165$	2.19157e47	0.462223
$166$	−6.69256e47	−1.23956
$167$	−7.48013e45	−0.0121760	−0.00608801	−	0.999981i	$-0.501938\pi$
$167$	−7.48013e45	−0.0121760	−0.00608801	+	0.999981i	$0.501938\pi$
$168$	6.24875e46	0.0894630
$169$	1.75678e48	2.21388
$170$	−3.75834e47	−0.417200
$171$	−5.43518e47	−0.531860
$172$	9.74755e47	0.841461
$173$	2.18826e48	1.66766	0.833829	−	0.552022i	$-0.186144\pi$
$173$	2.18826e48	1.66766	0.833829	+	0.552022i	$0.186144\pi$
$174$	2.43434e47	0.163897
$175$	−1.08876e47	−0.0648060
$176$	−7.34758e47	−0.386921
$177$	−1.49726e48	−0.698028
$178$	−1.12446e48	−0.464421
$179$	−6.25704e47	−0.229102	−0.114551	−	0.993417i	$-0.536543\pi$
$179$	−6.25704e47	−0.229102	−0.114551	+	0.993417i	$0.536543\pi$
$180$	−1.24086e48	−0.403056
$181$	4.05524e48	1.16930	0.584651	−	0.811285i	$-0.301231\pi$
$181$	4.05524e48	1.16930	0.584651	+	0.811285i	$0.301231\pi$
$182$	2.61428e48	0.669603
$183$	2.98510e48	0.679612
$184$	4.49513e47	0.0910248
$185$	−7.04779e48	−1.27017
$186$	−5.02589e48	−0.806650
$187$	−2.05759e48	−0.294282
$188$	1.41344e49	1.80254
$189$	−4.06540e47	−0.0462567
$190$	−2.08613e49	−2.11903
$191$	5.44465e48	0.494029	0.247014	−	0.969012i	$-0.420550\pi$
$191$	5.44465e48	0.494029	0.247014	+	0.969012i	$0.420550\pi$
$192$	1.12921e49	0.915799
$193$	−1.22005e49	−0.884904	−0.442452	−	0.896792i	$-0.645891\pi$
$193$	−1.22005e49	−0.884904	−0.442452	+	0.896792i	$0.645891\pi$
$194$	1.94993e49	1.26555
$195$	−1.52220e49	−0.884560
$196$	−2.56080e49	−1.33312
$197$	3.57228e48	0.166695	0.0833474	−	0.996521i	$-0.473439\pi$
$197$	3.57228e48	0.166695	0.0833474	+	0.996521i	$0.473439\pi$
$198$	−1.15948e49	−0.485248
$199$	−3.16418e49	−1.18828	−0.594142	−	0.804360i	$-0.702508\pi$
$199$	−3.16418e49	−1.18828	−0.594142	+	0.804360i	$0.702508\pi$
$200$	5.15526e48	0.173823
$201$	3.94892e48	0.119609
$202$	7.75365e49	2.11082
$203$	1.79353e48	0.0439079
$204$	1.16500e49	0.256612
$205$	7.77414e49	1.54150
$206$	9.18597e49	1.64051
$207$	−2.92451e48	−0.0470642
$208$	5.10340e49	0.740453
$209$	−1.14210e50	−1.49471
$210$	−1.56038e49	−0.184296
$211$	5.97577e49	0.637267	0.318633	−	0.947878i	$-0.396776\pi$
$211$	5.97577e49	0.637267	0.318633	+	0.947878i	$0.396776\pi$
$212$	−2.26861e50	−2.18544
$213$	−1.19417e49	−0.103969
$214$	−1.03839e50	−0.817457
$215$	−7.13708e49	−0.508269
$216$	1.92496e49	0.124070
$217$	−3.70289e49	−0.216101
$218$	−1.41252e49	−0.0746756
$219$	−1.55940e50	−0.747154
$220$	−2.60743e50	−1.13273
$221$	1.42913e50	0.563170
$222$	3.72874e50	1.33344
$223$	3.45413e50	1.12146	0.560731	−	0.827998i	$-0.310520\pi$
$223$	3.45413e50	1.12146	0.560731	+	0.827998i	$0.310520\pi$
$224$	1.04860e50	0.309226
$225$	−3.35399e49	−0.0898747
$226$	1.02684e50	0.250134
$227$	−7.06592e50	−1.56535	−0.782677	−	0.622428i	$-0.786146\pi$
$227$	−7.06592e50	−1.56535	−0.782677	+	0.622428i	$0.786146\pi$
$228$	6.46652e50	1.30338
$229$	1.50809e50	0.276672	0.138336	−	0.990385i	$-0.455825\pi$
$229$	1.50809e50	0.276672	0.138336	+	0.990385i	$0.455825\pi$
$230$	−1.12248e50	−0.187513
$231$	−8.54265e49	−0.129997
$232$	−8.49230e49	−0.117770
$233$	2.74035e50	0.346461	0.173230	−	0.984881i	$-0.444579\pi$
$233$	2.74035e50	0.346461	0.173230	+	0.984881i	$0.444579\pi$
$234$	8.05342e50	0.928622
$235$	−1.03491e51	−1.08879
$236$	1.78137e51	1.71059
$237$	−7.58925e50	−0.665441
$238$	1.46498e50	0.117335
$239$	−2.50602e51	−1.83413	−0.917064	−	0.398741i	$-0.869447\pi$
$239$	−2.50602e51	−1.83413	−0.917064	+	0.398741i	$0.869447\pi$
$240$	−3.04605e50	−0.203796
$241$	1.93392e51	1.18324	0.591618	−	0.806219i	$-0.298490\pi$
$241$	1.93392e51	1.18324	0.591618	+	0.806219i	$0.298490\pi$
$242$	3.39934e50	0.190268
$243$	−1.25237e50	−0.0641500
$244$	−3.55154e51	−1.66546
$245$	1.87500e51	0.805248
$246$	−4.11303e51	−1.61829
$247$	7.93264e51	2.86044
$248$	1.75331e51	0.579625
$249$	−1.51896e51	−0.460534
$250$	−6.06184e51	−1.68614
$251$	4.48391e50	0.114465	0.0572323	−	0.998361i	$-0.481772\pi$
$251$	4.48391e50	0.114465	0.0572323	+	0.998361i	$0.481772\pi$
$252$	4.83683e50	0.113357
$253$	−6.14529e50	−0.132267
$254$	−9.75908e51	−1.92967
$255$	−8.53004e50	−0.155002
$256$	−1.46678e51	−0.245023
$257$	2.58564e51	0.397197	0.198598	−	0.980081i	$-0.436361\pi$
$257$	2.58564e51	0.397197	0.198598	+	0.980081i	$0.436361\pi$
$258$	3.77598e51	0.533588
$259$	2.74719e51	0.357227
$260$	1.81104e52	2.16771
$261$	5.52505e50	0.0608927
$262$	−1.55305e52	−1.57655
$263$	2.04714e52	1.91469	0.957344	−	0.288950i	$-0.0933062\pi$
$263$	2.04714e52	1.91469	0.957344	+	0.288950i	$0.0933062\pi$
$264$	4.04492e51	0.348679
$265$	1.66106e52	1.32007
$266$	8.13161e51	0.595966
$267$	−2.55210e51	−0.172546
$268$	−4.69824e51	−0.293115
$269$	−2.30210e52	−1.32571	−0.662857	−	0.748746i	$-0.730656\pi$
$269$	−2.30210e52	−1.32571	−0.662857	+	0.748746i	$0.730656\pi$
$270$	−4.80682e51	−0.255586
$271$	−2.53971e52	−1.24722	−0.623611	−	0.781735i	$-0.714335\pi$
$271$	−2.53971e52	−1.24722	−0.623611	+	0.781735i	$0.714335\pi$
$272$	2.85983e51	0.129750
$273$	5.93345e51	0.248777
$274$	−2.03077e52	−0.787088
$275$	−7.04775e51	−0.252579
$276$	3.47945e51	0.115336
$277$	6.05395e51	0.185662	0.0928312	−	0.995682i	$-0.470408\pi$
$277$	6.05395e51	0.185662	0.0928312	+	0.995682i	$0.470408\pi$
$278$	−5.96664e52	−1.69343
$279$	−1.14069e52	−0.299694
$280$	5.44346e51	0.132427
$281$	−7.32071e52	−1.64956	−0.824779	−	0.565456i	$-0.808700\pi$
$281$	−7.32071e52	−1.64956	−0.824779	+	0.565456i	$0.808700\pi$
$282$	5.47536e52	1.14303
$283$	8.02189e52	1.55192	0.775958	−	0.630785i	$-0.217267\pi$
$283$	8.02189e52	1.55192	0.775958	+	0.630785i	$0.217267\pi$
$284$	1.42076e52	0.254787
$285$	−4.73474e52	−0.787284
$286$	1.69227e53	2.60975
$287$	−3.03032e52	−0.433539
$288$	3.23025e52	0.428843
$289$	−7.31443e52	−0.901315
$290$	2.12062e52	0.242608
$291$	4.42561e52	0.470191
$292$	1.85531e53	1.83098
$293$	6.96756e52	0.638891	0.319445	−	0.947605i	$-0.396503\pi$
$293$	6.96756e52	0.638891	0.319445	+	0.947605i	$0.396503\pi$
$294$	−9.91994e52	−0.845360
$295$	−1.30431e53	−1.03325
$296$	−1.30079e53	−0.958153
$297$	−2.63160e52	−0.180284
$298$	−2.71097e53	−1.72773
$299$	4.26832e52	0.253120
$300$	3.99042e52	0.220248
$301$	2.78200e52	0.142948
$302$	2.65742e52	0.127149
$303$	1.75979e53	0.784233
$304$	1.58739e53	0.659025
$305$	2.60041e53	1.00599
$306$	4.51295e52	0.162723
$307$	−3.43634e53	−1.15510	−0.577551	−	0.816355i	$-0.695992\pi$
$307$	−3.43634e53	−1.15510	−0.577551	+	0.816355i	$0.695992\pi$
$308$	1.01636e53	0.318573
$309$	2.08488e53	0.609499
$310$	−4.37820e53	−1.19404
$311$	−2.49528e53	−0.634996	−0.317498	−	0.948259i	$-0.602843\pi$
$311$	−2.49528e53	−0.634996	−0.317498	+	0.948259i	$0.602843\pi$
$312$	−2.80947e53	−0.667269
$313$	−6.77102e53	−1.50124	−0.750621	−	0.660733i	$-0.770246\pi$
$313$	−6.77102e53	−1.50124	−0.750621	+	0.660733i	$0.770246\pi$
$314$	−8.23730e52	−0.170529
$315$	−3.54149e52	−0.0684713
$316$	9.02934e53	1.63074
$317$	3.07400e53	0.518715	0.259358	−	0.965781i	$-0.416489\pi$
$317$	3.07400e53	0.518715	0.259358	+	0.965781i	$0.416489\pi$
$318$	−8.78807e53	−1.38583
$319$	1.16098e53	0.171130
$320$	9.83690e53	1.35561
$321$	−2.35677e53	−0.303709
$322$	4.37538e52	0.0527369
$323$	4.44527e53	0.501238
$324$	1.49001e53	0.157207
$325$	4.89514e53	0.483363
$326$	−3.06358e53	−0.283172
$327$	−3.20589e52	−0.0277442
$328$	1.43485e54	1.16284
$329$	4.03404e53	0.306216
$330$	−1.01006e54	−0.718286
$331$	−4.66089e53	−0.310575	−0.155288	−	0.987869i	$-0.549630\pi$
$331$	−4.66089e53	−0.310575	−0.155288	+	0.987869i	$0.549630\pi$
$332$	1.80719e54	1.12859
$333$	8.46286e53	0.495412
$334$	3.44747e52	0.0189213
$335$	3.44002e53	0.177051
$336$	1.18734e53	0.0573165
$337$	−2.50903e53	−0.113622	−0.0568110	−	0.998385i	$-0.518093\pi$
$337$	−2.50903e53	−0.113622	−0.0568110	+	0.998385i	$0.518093\pi$
$338$	−8.09670e54	−3.44032
$339$	2.33056e53	0.0929323
$340$	1.01486e54	0.379849
$341$	−2.39694e54	−0.842245
$342$	2.50498e54	0.826501
$343$	−1.50654e54	−0.466828
$344$	−1.31727e54	−0.383414
$345$	−2.54762e53	−0.0696666
$346$	−1.00853e55	−2.59151
$347$	5.24694e54	1.26713	0.633567	−	0.773688i	$-0.281590\pi$
$347$	5.24694e54	1.26713	0.633567	+	0.773688i	$0.281590\pi$
$348$	−6.57344e53	−0.149224
$349$	2.37990e54	0.507940	0.253970	−	0.967212i	$-0.418264\pi$
$349$	2.37990e54	0.507940	0.253970	+	0.967212i	$0.418264\pi$
$350$	5.01793e53	0.100707
$351$	1.82783e54	0.345011
$352$	6.78774e54	1.20520
$353$	5.53664e54	0.924889	0.462445	−	0.886648i	$-0.346972\pi$
$353$	5.53664e54	0.924889	0.462445	+	0.886648i	$0.346972\pi$
$354$	6.90064e54	1.08472
$355$	−1.04027e54	−0.153900
$356$	3.03637e54	0.422843
$357$	3.32497e53	0.0435934
$358$	2.88376e54	0.356020
$359$	−3.21985e53	−0.0374373	−0.0187187	−	0.999825i	$-0.505959\pi$
$359$	−3.21985e53	−0.0374373	−0.0187187	+	0.999825i	$0.505959\pi$
$360$	1.67688e54	0.183654
$361$	1.49824e55	1.54588
$362$	−1.86899e55	−1.81707
$363$	7.71526e53	0.0706900
$364$	−7.05934e54	−0.609656
$365$	−1.35844e55	−1.10597
$366$	−1.37578e55	−1.05610
$367$	−8.35527e54	−0.604840	−0.302420	−	0.953175i	$-0.597794\pi$
$367$	−8.35527e54	−0.604840	−0.302420	+	0.953175i	$0.597794\pi$
$368$	8.54129e53	0.0583170
$369$	−9.33506e54	−0.601243
$370$	3.24821e55	1.97382
$371$	−6.47472e54	−0.371263
$372$	1.35714e55	0.734434
$373$	1.03829e55	0.530371	0.265186	−	0.964197i	$-0.414567\pi$
$373$	1.03829e55	0.530371	0.265186	+	0.964197i	$0.414567\pi$
$374$	9.48307e54	0.457309
$375$	−1.37581e55	−0.626452
$376$	−1.91011e55	−0.821332
$377$	−8.06380e54	−0.327492
$378$	1.87368e54	0.0718821
$379$	−2.96294e55	−1.07394	−0.536969	−	0.843602i	$-0.680431\pi$
$379$	−2.96294e55	−1.07394	−0.536969	+	0.843602i	$0.680431\pi$
$380$	5.63317e55	1.92932
$381$	−2.21495e55	−0.716931
$382$	−2.50935e55	−0.767712
$383$	1.85318e55	0.535974	0.267987	−	0.963423i	$-0.413642\pi$
$383$	1.85318e55	0.535974	0.267987	+	0.963423i	$0.413642\pi$
$384$	−2.48805e55	−0.680357
$385$	−7.44174e54	−0.192428
$386$	5.62301e55	1.37512
$387$	8.57008e54	0.198244
$388$	−5.26539e55	−1.15225
$389$	−3.65114e55	−0.755983	−0.377992	−	0.925809i	$-0.623385\pi$
$389$	−3.65114e55	−0.755983	−0.377992	+	0.925809i	$0.623385\pi$
$390$	7.01556e55	1.37459
$391$	2.39187e54	0.0443544
$392$	3.46062e55	0.607440
$393$	−3.52485e55	−0.585735
$394$	−1.64640e55	−0.259041
$395$	−6.61121e55	−0.985016
$396$	3.13096e55	0.441805
$397$	2.90269e55	0.387976	0.193988	−	0.981004i	$-0.437858\pi$
$397$	2.90269e55	0.387976	0.193988	+	0.981004i	$0.437858\pi$
$398$	1.45832e56	1.84657
$399$	1.84558e55	0.221419
$400$	9.79562e54	0.111363
$401$	6.83973e55	0.736944	0.368472	−	0.929639i	$-0.379881\pi$
$401$	6.83973e55	0.736944	0.368472	+	0.929639i	$0.379881\pi$
$402$	−1.81999e55	−0.185870
$403$	1.66484e56	1.61181
$404$	−2.09372e56	−1.92185
$405$	−1.09097e55	−0.0949578
$406$	−8.26606e54	−0.0682321
$407$	1.77830e56	1.39228
$408$	−1.57436e55	−0.116926
$409$	−8.27249e55	−0.582888	−0.291444	−	0.956588i	$-0.594136\pi$
$409$	−8.27249e55	−0.582888	−0.291444	+	0.956588i	$0.594136\pi$
$410$	−3.58297e56	−2.39547
$411$	−4.60910e55	−0.292427
$412$	−2.48049e56	−1.49364
$413$	5.08413e55	0.290597
$414$	1.34786e55	0.0731370
$415$	−1.32321e56	−0.681703
$416$	−4.71455e56	−2.30640
$417$	−1.35421e56	−0.629158
$418$	5.26373e56	2.32276
$419$	2.20061e56	0.922449	0.461224	−	0.887284i	$-0.347410\pi$
$419$	2.20061e56	0.922449	0.461224	+	0.887284i	$0.347410\pi$
$420$	4.21349e55	0.167796
$421$	3.68461e56	1.39421	0.697103	−	0.716971i	$-0.254472\pi$
$421$	3.68461e56	1.39421	0.697103	+	0.716971i	$0.254472\pi$
$422$	−2.75413e56	−0.990301
$423$	1.24271e56	0.424669
$424$	3.06576e56	0.995801
$425$	2.74312e55	0.0847000
$426$	5.50372e55	0.161566
$427$	−1.01363e56	−0.282930
$428$	2.80397e56	0.744273
$429$	3.84082e56	0.969600
$430$	3.28936e56	0.789841
$431$	−3.10101e56	−0.708339	−0.354170	−	0.935181i	$-0.615236\pi$
$431$	−3.10101e56	−0.708339	−0.354170	+	0.935181i	$0.615236\pi$
$432$	3.65765e55	0.0794880
$433$	−6.81278e56	−1.40875	−0.704376	−	0.709827i	$-0.748773\pi$
$433$	−6.81278e56	−1.40875	−0.704376	+	0.709827i	$0.748773\pi$
$434$	1.70660e56	0.335817
$435$	4.81302e55	0.0901361
$436$	3.81422e55	0.0679902
$437$	1.32764e56	0.225284
$438$	7.18703e56	1.16106
$439$	−9.51612e56	−1.46377	−0.731885	−	0.681428i	$-0.761359\pi$
$439$	−9.51612e56	−1.46377	−0.731885	+	0.681428i	$0.761359\pi$
$440$	3.52364e56	0.516130
$441$	−2.25146e56	−0.314076
$442$	−6.58664e56	−0.875156
$443$	1.38132e57	1.74829	0.874146	−	0.485663i	$-0.161422\pi$
$443$	1.38132e57	1.74829	0.874146	+	0.485663i	$0.161422\pi$
$444$	−1.00687e57	−1.21406
$445$	−2.22321e56	−0.255411
$446$	−1.59195e57	−1.74273
$447$	−6.15290e56	−0.641901
$448$	−3.83438e56	−0.381257
$449$	1.19466e57	1.13227	0.566134	−	0.824313i	$-0.308438\pi$
$449$	1.19466e57	1.13227	0.566134	+	0.824313i	$0.308438\pi$
$450$	1.54580e56	0.139664
$451$	−1.96158e57	−1.68970
$452$	−2.77279e56	−0.227741
$453$	6.03137e55	0.0472395
$454$	3.25656e57	2.43253
$455$	5.16880e56	0.368251
$456$	−8.73875e56	−0.593889
$457$	1.76193e57	1.14233	0.571163	−	0.820837i	$-0.306493\pi$
$457$	1.76193e57	1.14233	0.571163	+	0.820837i	$0.306493\pi$
$458$	−6.95055e56	−0.429943
$459$	1.02427e56	0.0604565
$460$	3.03104e56	0.170726
$461$	1.04730e57	0.562991	0.281496	−	0.959562i	$-0.409169\pi$
$461$	1.04730e57	0.562991	0.281496	+	0.959562i	$0.409169\pi$
$462$	3.93716e56	0.202014
$463$	3.90864e56	0.191441	0.0957203	−	0.995408i	$-0.469485\pi$
$463$	3.90864e56	0.191441	0.0957203	+	0.995408i	$0.469485\pi$
$464$	−1.61364e56	−0.0754518
$465$	−9.93690e56	−0.443621
$466$	−1.26298e57	−0.538394
$467$	−3.62485e57	−1.47563	−0.737815	−	0.675003i	$-0.764142\pi$
$467$	−3.62485e57	−1.47563	−0.737815	+	0.675003i	$0.764142\pi$
$468$	−2.17467e57	−0.845486
$469$	−1.34090e56	−0.0497944
$470$	4.76974e57	1.69196
$471$	−1.86956e56	−0.0633564
$472$	−2.40732e57	−0.779437
$473$	1.80083e57	0.557133
$474$	3.49776e57	1.03408
$475$	1.52261e57	0.430207
$476$	−3.95589e56	−0.106830
$477$	−1.99457e57	−0.514878
$478$	1.15498e58	2.85020
$479$	5.28083e57	1.24591	0.622957	−	0.782256i	$-0.285931\pi$
$479$	5.28083e57	1.24591	0.622957	+	0.782256i	$0.285931\pi$
$480$	2.81396e57	0.634793
$481$	−1.23515e58	−2.66442
$482$	−8.91309e57	−1.83873
$483$	9.93051e55	0.0195933
$484$	−9.17926e56	−0.173234
$485$	3.85528e57	0.695998
$486$	5.77195e56	0.0996880
$487$	−2.42806e57	−0.401224	−0.200612	−	0.979671i	$-0.564293\pi$
$487$	−2.42806e57	−0.401224	−0.200612	+	0.979671i	$0.564293\pi$
$488$	4.79949e57	0.758873
$489$	−6.95319e56	−0.105207
$490$	−8.64154e57	−1.25134
$491$	−8.39260e57	−1.16317	−0.581587	−	0.813484i	$-0.697568\pi$
$491$	−8.39260e57	−1.16317	−0.581587	+	0.813484i	$0.697568\pi$
$492$	1.11064e58	1.47341
$493$	−4.51877e56	−0.0573867
$494$	−3.65602e58	−4.44508
$495$	−2.29246e57	−0.266864
$496$	3.33149e57	0.371350
$497$	4.05493e56	0.0432834
$498$	7.00065e57	0.715661
$499$	7.51378e57	0.735693	0.367847	−	0.929886i	$-0.380095\pi$
$499$	7.51378e57	0.735693	0.367847	+	0.929886i	$0.380095\pi$
$500$	1.63688e58	1.53519
$501$	7.82448e55	0.00702982
$502$	−2.06656e57	−0.177876
$503$	1.17094e58	0.965660	0.482830	−	0.875714i	$-0.339609\pi$
$503$	1.17094e58	0.965660	0.482830	+	0.875714i	$0.339609\pi$
$504$	−6.53641e56	−0.0516515
$505$	1.53301e58	1.16086
$506$	2.83226e57	0.205540
$507$	−1.83765e58	−1.27818
$508$	2.63525e58	1.75692
$509$	9.33395e57	0.596531	0.298266	−	0.954483i	$-0.403592\pi$
$509$	9.33395e57	0.596531	0.298266	+	0.954483i	$0.403592\pi$
$510$	3.93135e57	0.240870
$511$	5.29513e57	0.311048
$512$	−1.41618e58	−0.797652
$513$	5.68539e57	0.307070
$514$	−1.19168e58	−0.617237
$515$	1.81619e58	0.902209
$516$	−1.01963e58	−0.485818
$517$	2.61130e58	1.19347
$518$	−1.26614e58	−0.555124
$519$	−2.28899e58	−0.962823
$520$	−2.44741e58	−0.987723
$521$	−3.80596e58	−1.47385	−0.736924	−	0.675975i	$-0.763723\pi$
$521$	−3.80596e58	−1.47385	−0.736924	+	0.675975i	$0.763723\pi$
$522$	−2.54640e57	−0.0946261
$523$	2.57459e58	0.918167	0.459083	−	0.888393i	$-0.348178\pi$
$523$	2.57459e58	0.918167	0.459083	+	0.888393i	$0.348178\pi$
$524$	4.19371e58	1.43541
$525$	1.13888e57	0.0374158
$526$	−9.43490e58	−2.97539
$527$	9.32938e57	0.282439
$528$	7.68583e57	0.223389
$529$	−3.51198e58	−0.980065
$530$	−7.65554e58	−2.05137
$531$	1.56619e58	0.403007
$532$	−2.19578e58	−0.542611
$533$	1.36245e59	3.23360
$534$	1.17622e58	0.268134
$535$	−2.05304e58	−0.449565
$536$	6.34913e57	0.133558
$537$	6.54509e57	0.132272
$538$	1.06100e59	2.06014
$539$	−4.73101e58	−0.882663
$540$	1.29799e58	0.232704
$541$	−2.90048e58	−0.499723	−0.249861	−	0.968282i	$-0.580385\pi$
$541$	−2.90048e58	−0.499723	−0.249861	+	0.968282i	$0.580385\pi$
$542$	1.17051e59	1.93816
$543$	−4.24192e58	−0.675097
$544$	−2.64192e58	−0.404151
$545$	−2.79274e57	−0.0410682
$546$	−2.73463e58	−0.386595
$547$	−1.06891e59	−1.45283	−0.726416	−	0.687255i	$-0.758816\pi$
$547$	−1.06891e59	−1.45283	−0.726416	+	0.687255i	$0.758816\pi$
$548$	5.48369e58	0.716623
$549$	−3.12252e58	−0.392374
$550$	3.24819e58	0.392503
$551$	−2.50821e58	−0.291477
$552$	−4.70207e57	−0.0525532
$553$	2.57702e58	0.277030
$554$	−2.79017e58	−0.288516
$555$	7.37224e58	0.733331
$556$	1.61117e59	1.54182
$557$	−3.59735e58	−0.331204	−0.165602	−	0.986193i	$-0.552957\pi$
$557$	−3.59735e58	−0.331204	−0.165602	+	0.986193i	$0.552957\pi$
$558$	5.25726e58	0.465720
$559$	−1.25080e59	−1.06619
$560$	1.03432e58	0.0848424
$561$	2.15231e58	0.169904
$562$	3.37399e59	2.56338
$563$	−1.77021e59	−1.29448	−0.647239	−	0.762287i	$-0.724076\pi$
$563$	−1.77021e59	−1.29448	−0.647239	+	0.762287i	$0.724076\pi$
$564$	−1.47851e59	−1.04070
$565$	2.03022e58	0.137563
$566$	−3.69715e59	−2.41165
$567$	4.25256e57	0.0267063
$568$	−1.92000e58	−0.116094
$569$	1.92114e59	1.11852	0.559261	−	0.828992i	$-0.311085\pi$
$569$	1.92114e59	1.11852	0.559261	+	0.828992i	$0.311085\pi$
$570$	2.18216e59	1.22342
$571$	4.64275e58	0.250668	0.125334	−	0.992115i	$-0.460000\pi$
$571$	4.64275e58	0.250668	0.125334	+	0.992115i	$0.460000\pi$
$572$	−4.56963e59	−2.37611
$573$	−5.69529e58	−0.285228
$574$	1.39662e59	0.673712
$575$	8.19275e57	0.0380690
$576$	−1.18120e59	−0.528737
$577$	−1.55024e59	−0.668528	−0.334264	−	0.942480i	$-0.608488\pi$
$577$	−1.55024e59	−0.668528	−0.334264	+	0.942480i	$0.608488\pi$
$578$	3.37110e59	1.40063
$579$	1.27622e59	0.510900
$580$	−5.72631e58	−0.220888
$581$	5.15781e58	0.191725
$582$	−2.03969e59	−0.730668
$583$	−4.19120e59	−1.44698
$584$	−2.50723e59	−0.834292
$585$	1.59227e59	0.510701
$586$	−3.21123e59	−0.992825
$587$	−3.75482e58	−0.111910	−0.0559551	−	0.998433i	$-0.517820\pi$
$587$	−3.75482e58	−0.111910	−0.0559551	+	0.998433i	$0.517820\pi$
$588$	2.67868e59	0.769678
$589$	5.17842e59	1.43456
$590$	6.01134e59	1.60566
$591$	−3.73673e58	−0.0962412
$592$	−2.47165e59	−0.613862
$593$	4.26058e58	0.102045	0.0510226	−	0.998697i	$-0.483752\pi$
$593$	4.26058e58	0.102045	0.0510226	+	0.998697i	$0.483752\pi$
$594$	1.21286e59	0.280158
$595$	2.89647e58	0.0645290
$596$	7.32043e59	1.57305
$597$	3.30985e59	0.686056
$598$	−1.96720e59	−0.393344
$599$	5.38127e59	1.03803	0.519013	−	0.854766i	$-0.326300\pi$
$599$	5.38127e59	1.03803	0.519013	+	0.854766i	$0.326300\pi$
$600$	−5.39259e58	−0.100356
$601$	8.97834e59	1.61211	0.806055	−	0.591840i	$-0.201598\pi$
$601$	8.97834e59	1.61211	0.806055	+	0.591840i	$0.201598\pi$
$602$	−1.28218e59	−0.222138
$603$	−4.13071e58	−0.0690562
$604$	−7.17585e58	−0.115765
$605$	6.72098e58	0.104639
$606$	−8.11059e59	−1.21868
$607$	−6.27059e59	−0.909392	−0.454696	−	0.890647i	$-0.650252\pi$
$607$	−6.27059e59	−0.909392	−0.454696	+	0.890647i	$0.650252\pi$
$608$	−1.46644e60	−2.05276
$609$	−1.87609e58	−0.0253503
$610$	−1.19848e60	−1.56329
$611$	−1.81373e60	−2.28395
$612$	−1.21863e59	−0.148155
$613$	7.05913e59	0.828611	0.414306	−	0.910138i	$-0.364025\pi$
$613$	7.05913e59	0.828611	0.414306	+	0.910138i	$0.364025\pi$
$614$	1.58375e60	1.79501
$615$	−8.13203e59	−0.889988
$616$	−1.37350e59	−0.145159
$617$	3.52675e58	0.0359951	0.0179975	−	0.999838i	$-0.494271\pi$
$617$	3.52675e58	0.0359951	0.0179975	+	0.999838i	$0.494271\pi$
$618$	−9.60885e59	−0.947151
$619$	3.13527e59	0.298488	0.149244	−	0.988800i	$-0.452316\pi$
$619$	3.13527e59	0.298488	0.149244	+	0.988800i	$0.452316\pi$
$620$	1.18225e60	1.08714
$621$	3.05914e58	0.0271725
$622$	1.15003e60	0.986772
$623$	8.66594e58	0.0718328
$624$	−5.33833e59	−0.427501
$625$	−8.50030e59	−0.657679
$626$	3.12065e60	2.33290
$627$	1.19467e60	0.862972
$628$	2.22432e59	0.155262
$629$	−6.92152e59	−0.466888
$630$	1.63221e59	0.106403
$631$	9.96673e59	0.627945	0.313972	−	0.949432i	$-0.398340\pi$
$631$	9.96673e59	0.627945	0.313972	+	0.949432i	$0.398340\pi$
$632$	−1.22021e60	−0.743049
$633$	−6.25087e59	−0.367926
$634$	−1.41675e60	−0.806074
$635$	−1.92951e60	−1.06123
$636$	2.37305e60	1.26176
$637$	3.28601e60	1.68916
$638$	−5.35076e59	−0.265932
$639$	1.24914e59	0.0600265
$640$	−2.16741e60	−1.00710
$641$	1.42679e60	0.641081	0.320540	−	0.947235i	$-0.396136\pi$
$641$	1.42679e60	0.641081	0.320540	+	0.947235i	$0.396136\pi$
$642$	1.08619e60	0.471959
$643$	−1.52594e60	−0.641212	−0.320606	−	0.947213i	$-0.603887\pi$
$643$	−1.52594e60	−0.641212	−0.320606	+	0.947213i	$0.603887\pi$
$644$	−1.18149e59	−0.0480156
$645$	7.46564e59	0.293449
$646$	−2.04875e60	−0.778914
$647$	−1.67275e60	−0.615162	−0.307581	−	0.951522i	$-0.599519\pi$
$647$	−1.67275e60	−0.615162	−0.307581	+	0.951522i	$0.599519\pi$
$648$	−2.01357e59	−0.0716316
$649$	3.29104e60	1.13259
$650$	−2.25609e60	−0.751137
$651$	3.87335e59	0.124766
$652$	8.27258e59	0.257821
$653$	−1.56884e60	−0.473091	−0.236546	−	0.971620i	$-0.576015\pi$
$653$	−1.56884e60	−0.473091	−0.236546	+	0.971620i	$0.576015\pi$
$654$	1.47754e59	0.0431140
$655$	−3.07060e60	−0.867032
$656$	2.72638e60	0.744997
$657$	1.63119e60	0.431369
$658$	−1.85922e60	−0.475854
$659$	−3.59936e60	−0.891638	−0.445819	−	0.895123i	$-0.647087\pi$
$659$	−3.59936e60	−0.891638	−0.445819	+	0.895123i	$0.647087\pi$
$660$	2.72747e60	0.653980
$661$	3.79640e60	0.881130	0.440565	−	0.897721i	$-0.354778\pi$
$661$	3.79640e60	0.881130	0.440565	+	0.897721i	$0.354778\pi$
$662$	2.14813e60	0.482629
$663$	−1.49493e60	−0.325146
$664$	−2.44221e60	−0.514244
$665$	1.60773e60	0.327755
$666$	−3.90039e60	−0.769861
$667$	−1.34960e59	−0.0257928
$668$	−9.30920e58	−0.0172273
$669$	−3.61314e60	−0.647476
$670$	−1.58545e60	−0.275133
$671$	−6.56137e60	−1.10271
$672$	−1.09687e60	−0.178532
$673$	−4.09984e59	−0.0646314	−0.0323157	−	0.999478i	$-0.510288\pi$
$673$	−4.09984e59	−0.0646314	−0.0323157	+	0.999478i	$0.510288\pi$
$674$	1.15637e60	0.176567
$675$	3.50839e59	0.0518892
$676$	2.18635e61	3.13232
$677$	−1.26931e61	−1.76161	−0.880807	−	0.473476i	$-0.842999\pi$
$677$	−1.26931e61	−1.76161	−0.880807	+	0.473476i	$0.842999\pi$
$678$	−1.07412e60	−0.144415
$679$	−1.50277e60	−0.195745
$680$	−1.37147e60	−0.173079
$681$	7.39120e60	0.903758
$682$	1.10471e61	1.30883
$683$	8.67303e59	0.0995694	0.0497847	−	0.998760i	$-0.484146\pi$
$683$	8.67303e59	0.0995694	0.0497847	+	0.998760i	$0.484146\pi$
$684$	−6.76421e60	−0.752508
$685$	−4.01511e60	−0.432863
$686$	6.94339e60	0.725443
$687$	−1.57752e60	−0.159737
$688$	−2.50297e60	−0.245643
$689$	2.91107e61	2.76911
$690$	1.17416e60	0.108261
$691$	−8.54208e60	−0.763459	−0.381729	−	0.924274i	$-0.624671\pi$
$691$	−8.54208e60	−0.763459	−0.381729	+	0.924274i	$0.624671\pi$
$692$	2.72334e61	2.35950
$693$	8.93591e59	0.0750541
$694$	−2.41823e61	−1.96910
$695$	−1.17969e61	−0.931309
$696$	8.88324e59	0.0679944
$697$	7.63486e60	0.566626
$698$	−1.09686e61	−0.789329
$699$	−2.86651e60	−0.200029
$700$	−1.35499e60	−0.0916915
$701$	2.76955e61	1.81749	0.908745	−	0.417351i	$-0.137041\pi$
$701$	2.76955e61	1.81749	0.908745	+	0.417351i	$0.137041\pi$
$702$	−8.42416e60	−0.536140
$703$	−3.84190e61	−2.37141
$704$	−2.48206e61	−1.48593
$705$	1.08256e61	0.628614
$706$	−2.55174e61	−1.43726
$707$	−5.97558e60	−0.326484
$708$	−1.86338e61	−0.987612
$709$	3.69130e60	0.189795	0.0948976	−	0.995487i	$-0.469748\pi$
$709$	3.69130e60	0.189795	0.0948976	+	0.995487i	$0.469748\pi$
$710$	4.79444e60	0.239157
$711$	7.93863e60	0.384193
$712$	−4.10330e60	−0.192670
$713$	2.78636e60	0.126944
$714$	−1.53242e60	−0.0677434
$715$	3.34585e61	1.43525
$716$	−7.78704e60	−0.324147
$717$	2.62138e61	1.05893
$718$	1.48397e60	0.0581769
$719$	3.31674e61	1.26194	0.630971	−	0.775806i	$-0.282657\pi$
$719$	3.31674e61	1.26194	0.630971	+	0.775806i	$0.282657\pi$
$720$	3.18628e60	0.117662
$721$	−7.07944e60	−0.253741
$722$	−6.90511e61	−2.40227
$723$	−2.02294e61	−0.683141
$724$	5.04684e61	1.65440
$725$	−1.54779e60	−0.0492544
$726$	−3.55583e60	−0.109851
$727$	5.21486e61	1.56406	0.782028	−	0.623243i	$-0.214185\pi$
$727$	5.21486e61	1.56406	0.782028	+	0.623243i	$0.214185\pi$
$728$	9.53989e60	0.277791
$729$	1.31002e60	0.0370370
$730$	6.26082e61	1.71866
$731$	−7.00921e60	−0.186829
$732$	3.71503e61	0.961556
$733$	−1.84311e61	−0.463252	−0.231626	−	0.972805i	$-0.574404\pi$
$733$	−1.84311e61	−0.463252	−0.231626	+	0.972805i	$0.574404\pi$
$734$	3.85080e61	0.939910
$735$	−1.96131e61	−0.464910
$736$	−7.89050e60	−0.181648
$737$	−8.67988e60	−0.194072
$738$	4.30237e61	0.934321
$739$	−3.99109e61	−0.841854	−0.420927	−	0.907095i	$-0.638295\pi$
$739$	−3.99109e61	−0.841854	−0.420927	+	0.907095i	$0.638295\pi$
$740$	−8.77114e61	−1.79711
$741$	−8.29782e61	−1.65148
$742$	2.98409e61	0.576936
$743$	−7.25446e60	−0.136253	−0.0681264	−	0.997677i	$-0.521702\pi$
$743$	−7.25446e60	−0.136253	−0.0681264	+	0.997677i	$0.521702\pi$
$744$	−1.83402e61	−0.334647
$745$	−5.35996e61	−0.950172
$746$	−4.78532e61	−0.824188
$747$	1.58889e61	0.265889
$748$	−2.56072e61	−0.416368
$749$	8.00267e60	0.126437
$750$	6.34090e61	0.973495
$751$	−1.53386e61	−0.228837	−0.114418	−	0.993433i	$-0.536500\pi$
$751$	−1.53386e61	−0.228837	−0.114418	+	0.993433i	$0.536500\pi$
$752$	−3.62943e61	−0.526205
$753$	−4.69032e60	−0.0660862
$754$	3.71647e61	0.508917
$755$	5.25410e60	0.0699260
$756$	−5.05949e60	−0.0654468
$757$	9.79211e61	1.23116	0.615580	−	0.788074i	$-0.288922\pi$
$757$	9.79211e61	1.23116	0.615580	+	0.788074i	$0.288922\pi$
$758$	1.36557e62	1.66888
$759$	6.42819e60	0.0763643
$760$	−7.61257e61	−0.879102
$761$	−2.66266e61	−0.298913	−0.149457	−	0.988768i	$-0.547752\pi$
$761$	−2.66266e61	−0.298913	−0.149457	+	0.988768i	$0.547752\pi$
$762$	1.02083e62	1.11410
$763$	1.08860e60	0.0115502
$764$	6.77599e61	0.698982
$765$	8.92273e60	0.0894905
$766$	−8.54099e61	−0.832894
$767$	−2.28585e62	−2.16745
$768$	1.53431e61	0.141464
$769$	−1.71538e62	−1.53795	−0.768977	−	0.639276i	$-0.779234\pi$
$769$	−1.71538e62	−1.53795	−0.768977	+	0.639276i	$0.779234\pi$
$770$	3.42977e61	0.299030
$771$	−2.70467e61	−0.229322
$772$	−1.51838e62	−1.25202
$773$	1.24612e62	0.999311	0.499655	−	0.866224i	$-0.333460\pi$
$773$	1.24612e62	0.999311	0.499655	+	0.866224i	$0.333460\pi$
$774$	−3.94981e61	−0.308067
$775$	3.19555e61	0.242414
$776$	7.11556e61	0.525028
$777$	−2.87366e61	−0.206245
$778$	1.68275e62	1.17478
$779$	4.23785e62	2.87800
$780$	−1.89441e62	−1.25153
$781$	2.62482e61	0.168695
$782$	−1.10237e61	−0.0689260
$783$	−5.77939e60	−0.0351564
$784$	6.57559e61	0.389170
$785$	−1.62863e61	−0.0937831
$786$	1.62455e62	0.910222
$787$	−4.54644e61	−0.247865	−0.123932	−	0.992291i	$-0.539551\pi$
$787$	−4.54644e61	−0.247865	−0.123932	+	0.992291i	$0.539551\pi$
$788$	4.44579e61	0.235850
$789$	−2.14138e62	−1.10545
$790$	3.04700e62	1.53070
$791$	−7.91368e60	−0.0386887
$792$	−4.23113e61	−0.201310
$793$	4.55732e62	2.11026
$794$	−1.33780e62	−0.602907
$795$	−1.73753e62	−0.762145
$796$	−3.93790e62	−1.68126
$797$	−1.24938e62	−0.519205	−0.259603	−	0.965716i	$-0.583592\pi$
$797$	−1.24938e62	−0.519205	−0.259603	+	0.965716i	$0.583592\pi$
$798$	−8.50595e61	−0.344081
$799$	−1.01637e62	−0.400218
$800$	−9.04925e61	−0.346879
$801$	2.66959e61	0.0996196
$802$	−3.15231e62	−1.14520
$803$	3.42763e62	1.21230
$804$	4.91453e61	0.169230
$805$	8.65075e60	0.0290029
$806$	−7.67297e62	−2.50473
$807$	2.40808e62	0.765401
$808$	2.82942e62	0.875695
$809$	−3.18031e62	−0.958466	−0.479233	−	0.877688i	$-0.659085\pi$
$809$	−3.18031e62	−0.958466	−0.479233	+	0.877688i	$0.659085\pi$
$810$	5.02811e61	0.147563
$811$	8.37352e61	0.239309	0.119655	−	0.992816i	$-0.461821\pi$
$811$	8.37352e61	0.239309	0.119655	+	0.992816i	$0.461821\pi$
$812$	2.23209e61	0.0621236
$813$	2.65662e62	0.720084
$814$	−8.19591e62	−2.16358
$815$	−6.05712e61	−0.155732
$816$	−2.99148e61	−0.0749113
$817$	−3.89057e62	−0.948941
$818$	3.81265e62	0.905797
$819$	−6.20660e61	−0.143632
$820$	9.67511e62	2.18101
$821$	8.31504e61	0.182594	0.0912969	−	0.995824i	$-0.470899\pi$
$821$	8.31504e61	0.182594	0.0912969	+	0.995824i	$0.470899\pi$
$822$	2.12426e62	0.454426
$823$	3.58911e61	0.0747981	0.0373991	−	0.999300i	$-0.488093\pi$
$823$	3.58911e61	0.0747981	0.0373991	+	0.999300i	$0.488093\pi$
$824$	3.35209e62	0.680583
$825$	7.37219e61	0.145827
$826$	−2.34319e62	−0.451582
$827$	4.47535e62	0.840348	0.420174	−	0.907444i	$-0.361969\pi$
$827$	4.47535e62	0.840348	0.420174	+	0.907444i	$0.361969\pi$
$828$	−3.63962e61	−0.0665893
$829$	−3.66788e62	−0.653872	−0.326936	−	0.945046i	$-0.606016\pi$
$829$	−3.66788e62	−0.653872	−0.326936	+	0.945046i	$0.606016\pi$
$830$	6.09846e62	1.05935
$831$	−6.33265e61	−0.107192
$832$	1.72396e63	2.84364
$833$	1.84140e62	0.295993
$834$	6.24131e62	0.977701
$835$	6.81612e60	0.0104059
$836$	−1.42137e63	−2.11481
$837$	1.19321e62	0.173029
$838$	−1.01423e63	−1.43347
$839$	5.88661e62	0.810929	0.405465	−	0.914111i	$-0.367110\pi$
$839$	5.88661e62	0.810929	0.405465	+	0.914111i	$0.367110\pi$
$840$	−5.69405e61	−0.0764569
$841$	−7.38539e62	−0.966629
$842$	−1.69818e63	−2.16657
$843$	7.65772e62	0.952372
$844$	7.43699e62	0.901643
$845$	−1.60083e63	−1.89202
$846$	−5.72742e62	−0.659927
$847$	−2.61980e61	−0.0294290
$848$	5.82531e62	0.637982
$849$	−8.39118e62	−0.895999
$850$	−1.26426e62	−0.131622
$851$	−2.06721e62	−0.209846
$852$	−1.48617e62	−0.147102
$853$	3.01212e62	0.290715	0.145358	−	0.989379i	$-0.453567\pi$
$853$	3.01212e62	0.290715	0.145358	+	0.989379i	$0.453567\pi$
$854$	4.67163e62	0.439667
$855$	4.95270e62	0.454539
$856$	−3.78924e62	−0.339130
$857$	4.36183e62	0.380698	0.190349	−	0.981716i	$-0.439038\pi$
$857$	4.36183e62	0.380698	0.190349	+	0.981716i	$0.439038\pi$
$858$	−1.77017e63	−1.50674
$859$	1.95589e63	1.62365	0.811825	−	0.583901i	$-0.198475\pi$
$859$	1.95589e63	1.62365	0.811825	+	0.583901i	$0.198475\pi$
$860$	−8.88227e62	−0.719130
$861$	3.16982e62	0.250304
$862$	1.42920e63	1.10075
$863$	−1.38066e63	−1.03718	−0.518589	−	0.855023i	$-0.673543\pi$
$863$	−1.38066e63	−1.03718	−0.518589	+	0.855023i	$0.673543\pi$
$864$	−3.37896e62	−0.247592
$865$	−1.99401e63	−1.42522
$866$	3.13989e63	2.18917
$867$	7.65115e62	0.520375
$868$	−4.60833e62	−0.305752
$869$	1.66815e63	1.07971
$870$	−2.21824e62	−0.140070
$871$	6.02877e62	0.371397
$872$	−5.15447e61	−0.0309799
$873$	−4.62935e62	−0.271465
$874$	−6.11889e62	−0.350088
$875$	4.67174e62	0.260799
$876$	−1.94071e63	−1.05712
$877$	−1.10853e63	−0.589191	−0.294596	−	0.955622i	$-0.595185\pi$
$877$	−1.10853e63	−0.589191	−0.294596	+	0.955622i	$0.595185\pi$
$878$	4.38582e63	2.27467
$879$	−7.28831e62	−0.368864
$880$	6.69534e62	0.330670
$881$	−1.87933e63	−0.905775	−0.452888	−	0.891568i	$-0.649606\pi$
$881$	−1.87933e63	−0.905775	−0.452888	+	0.891568i	$0.649606\pi$
$882$	1.03766e63	0.488069
$883$	−1.17140e63	−0.537713	−0.268857	−	0.963180i	$-0.586646\pi$
$883$	−1.17140e63	−0.537713	−0.268857	+	0.963180i	$0.586646\pi$
$884$	1.77859e63	0.796806
$885$	1.36435e63	0.596549
$886$	−6.36627e63	−2.71681
$887$	7.10638e62	0.295999	0.148000	−	0.988987i	$-0.452717\pi$
$887$	7.10638e62	0.295999	0.148000	+	0.988987i	$0.452717\pi$
$888$	1.36067e63	0.553190
$889$	7.52112e62	0.298466
$890$	1.02464e63	0.396904
$891$	2.75275e62	0.104087
$892$	4.29875e63	1.58671
$893$	−5.64153e63	−2.03278
$894$	2.83577e63	0.997503
$895$	5.70161e62	0.195795
$896$	8.44844e62	0.283240
$897$	−4.46482e62	−0.146139
$898$	−5.50600e63	−1.75952
$899$	−5.26404e62	−0.164243
$900$	−4.17412e62	−0.127160
$901$	1.63130e63	0.485233
$902$	9.04059e63	2.62577
$903$	−2.91007e62	−0.0825309
$904$	3.74711e62	0.103771
$905$	−3.69525e63	−0.999309
$906$	−2.77976e62	−0.0734093
$907$	4.63671e63	1.19579	0.597893	−	0.801576i	$-0.296005\pi$
$907$	4.63671e63	1.19579	0.597893	+	0.801576i	$0.296005\pi$
$908$	−8.79370e63	−2.21476
$909$	−1.84081e63	−0.452777
$910$	−2.38221e63	−0.572256
$911$	4.42595e62	0.103839	0.0519197	−	0.998651i	$-0.483466\pi$
$911$	4.42595e62	0.103839	0.0519197	+	0.998651i	$0.483466\pi$
$912$	−1.66047e63	−0.380488
$913$	3.33874e63	0.747241
$914$	−8.12043e63	−1.77515
$915$	−2.72012e63	−0.580810
$916$	1.87686e63	0.391452
$917$	1.19690e63	0.243848
$918$	−4.72070e62	−0.0939483
$919$	1.37688e63	0.267678	0.133839	−	0.991003i	$-0.457270\pi$
$919$	1.37688e63	0.267678	0.133839	+	0.991003i	$0.457270\pi$
$920$	−4.09610e62	−0.0777916
$921$	3.59453e63	0.666899
$922$	−4.82684e63	−0.874878
$923$	−1.82312e63	−0.322834
$924$	−1.06315e63	−0.183928
$925$	−2.37079e63	−0.400725
$926$	−1.80143e63	−0.297495
$927$	−2.18086e63	−0.351895
$928$	1.49069e63	0.235020
$929$	−8.40170e62	−0.129428	−0.0647141	−	0.997904i	$-0.520614\pi$
$929$	−8.40170e62	−0.129428	−0.0647141	+	0.997904i	$0.520614\pi$
$930$	4.57975e63	0.689379
$931$	1.02210e64	1.50340
$932$	3.41043e63	0.490194
$933$	2.61015e63	0.366615
$934$	1.67063e64	2.29310
$935$	1.87494e63	0.251499
$936$	2.93881e63	0.385248
$937$	1.44074e64	1.84580	0.922899	−	0.385042i	$-0.125813\pi$
$937$	1.44074e64	1.84580	0.922899	+	0.385042i	$0.125813\pi$
$938$	6.17999e62	0.0773797
$939$	7.08272e63	0.866742
$940$	−1.28797e64	−1.54049
$941$	5.65255e63	0.660796	0.330398	−	0.943842i	$-0.392817\pi$
$941$	5.65255e63	0.660796	0.330398	+	0.943842i	$0.392817\pi$
$942$	8.61651e62	0.0984548
$943$	2.28026e63	0.254673
$944$	−4.57420e63	−0.499364
$945$	3.70452e62	0.0395319
$946$	−8.29974e63	−0.865775
$947$	−4.18520e63	−0.426768	−0.213384	−	0.976968i	$-0.568449\pi$
$947$	−4.18520e63	−0.426768	−0.213384	+	0.976968i	$0.568449\pi$
$948$	−9.44501e63	−0.941506
$949$	−2.38072e64	−2.31998
$950$	−7.01748e63	−0.668534
$951$	−3.21551e63	−0.299480
$952$	5.34593e62	0.0486776
$953$	1.28551e64	1.14440	0.572201	−	0.820114i	$-0.306090\pi$
$953$	1.28551e64	1.14440	0.572201	+	0.820114i	$0.306090\pi$
$954$	9.19263e63	0.800110
$955$	−4.96133e63	−0.422207
$956$	−3.11880e64	−2.59503
$957$	−1.21443e63	−0.0988017
$958$	−2.43384e64	−1.93613
$959$	1.56507e63	0.121740
$960$	−1.02897e64	−0.782660
$961$	−2.57668e63	−0.191650
$962$	5.69262e64	4.14045
$963$	2.46526e63	0.175347
$964$	2.40680e64	1.67411
$965$	1.11175e64	0.756257
$966$	−4.57681e62	−0.0304477
$967$	−2.87160e64	−1.86833	−0.934167	−	0.356837i	$-0.883855\pi$
$967$	−2.87160e64	−1.86833	−0.934167	+	0.356837i	$0.883855\pi$
$968$	1.24047e63	0.0789344
$969$	−4.64991e63	−0.289390
$970$	−1.77683e64	−1.08157
$971$	−1.65066e64	−0.982755	−0.491378	−	0.870947i	$-0.663507\pi$
$971$	−1.65066e64	−0.982755	−0.491378	+	0.870947i	$0.663507\pi$
$972$	−1.55860e63	−0.0907633
$973$	4.59836e63	0.261925
$974$	1.11905e64	0.623495
$975$	−5.12049e63	−0.279070
$976$	9.11960e63	0.486189
$977$	4.23828e63	0.221033	0.110516	−	0.993874i	$-0.464750\pi$
$977$	4.23828e63	0.221033	0.110516	+	0.993874i	$0.464750\pi$
$978$	3.20461e63	0.163489
$979$	5.60961e63	0.279966
$980$	2.33348e64	1.13931
$981$	3.35348e62	0.0160181
$982$	3.86801e64	1.80755
$983$	−3.13044e64	−1.43121	−0.715607	−	0.698503i	$-0.753850\pi$
$983$	−3.13044e64	−1.43121	−0.715607	+	0.698503i	$0.753850\pi$
$984$	−1.50090e64	−0.671364
$985$	−3.25517e63	−0.142461
$986$	2.08262e63	0.0891779
$987$	−4.21975e63	−0.176794
$988$	9.87236e64	4.04713
$989$	−2.09340e63	−0.0839717
$990$	1.05656e64	0.414702
$991$	−5.07278e64	−1.94833	−0.974165	−	0.225836i	$-0.927489\pi$
$991$	−5.07278e64	−1.94833	−0.974165	+	0.225836i	$0.927489\pi$
$992$	−3.07766e64	−1.15670
$993$	4.87546e63	0.179311
$994$	−1.86885e63	−0.0672616
$995$	2.88330e64	1.01553
$996$	−1.89039e64	−0.651591
$997$	1.59932e64	0.539496	0.269748	−	0.962931i	$-0.413060\pi$
$997$	1.59932e64	0.539496	0.269748	+	0.962931i	$0.413060\pi$
$998$	−3.46297e64	−1.14325
$999$	−8.85245e63	−0.286026

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.44.a.b.1.1	✓	4	1.1	even	1	trivial
9.44.a.c.1.4		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)

\(f(q)\)	\(=\)	\(q-4.60883e6 q^{2} -1.04604e10 q^{3} +1.24452e13 q^{4} -9.11231e14 q^{5} +4.82100e16 q^{6} +3.55193e17 q^{7} -1.68183e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\)	\(q-4.60883e6 q^{2} -1.04604e10 q^{3} +1.24452e13 q^{4} -9.11231e14 q^{5} +4.82100e16 q^{6} +3.55193e17 q^{7} -1.68183e19 q^{8} +1.09419e20 q^{9} +4.19971e21 q^{10} +2.29922e22 q^{11} -1.30182e23 q^{12} -1.59697e24 q^{13} -1.63703e24 q^{14} +9.53179e24 q^{15} -3.19568e25 q^{16} -8.94904e25 q^{17} -5.04294e26 q^{18} -4.96731e27 q^{19} -1.13405e28 q^{20} -3.71545e27 q^{21} -1.05967e29 q^{22} -2.67276e28 q^{23} +1.75925e29 q^{24} -3.06527e29 q^{25} +7.36016e30 q^{26} -1.14456e30 q^{27} +4.42046e30 q^{28} +5.04944e30 q^{29} -4.39304e31 q^{30} -1.04250e32 q^{31} +2.95219e32 q^{32} -2.40507e32 q^{33} +4.12446e32 q^{34} -3.23663e32 q^{35} +1.36175e33 q^{36} +7.73436e33 q^{37} +2.28935e34 q^{38} +1.67049e34 q^{39} +1.53253e34 q^{40} -8.53148e34 q^{41} +1.71239e34 q^{42} +7.83235e34 q^{43} +2.86144e35 q^{44} -9.97059e34 q^{45} +1.23183e35 q^{46} +1.13573e36 q^{47} +3.34279e35 q^{48} -2.05765e36 q^{49} +1.41273e36 q^{50} +9.36102e35 q^{51} -1.98747e37 q^{52} -1.82287e37 q^{53} +5.27509e36 q^{54} -2.09512e37 q^{55} -5.97374e36 q^{56} +5.19598e37 q^{57} -2.32720e37 q^{58} +1.43137e38 q^{59} +1.18625e38 q^{60} -2.85373e38 q^{61} +4.80471e38 q^{62} +3.88649e37 q^{63} -1.07952e39 q^{64} +1.45521e39 q^{65} +1.10846e39 q^{66} -3.77513e38 q^{67} -1.11373e39 q^{68} +2.79581e38 q^{69} +1.49171e39 q^{70} +1.14161e39 q^{71} -1.84024e39 q^{72} +1.49078e40 q^{73} -3.56464e40 q^{74} +3.20638e39 q^{75} -6.18193e40 q^{76} +8.16669e39 q^{77} -7.69899e40 q^{78} +7.25526e40 q^{79} +2.91200e40 q^{80} +1.19725e40 q^{81} +3.93201e41 q^{82} +1.45212e41 q^{83} -4.62396e40 q^{84} +8.15464e40 q^{85} -3.60980e41 q^{86} -5.28189e40 q^{87} -3.86690e41 q^{88} +2.43978e41 q^{89} +4.59528e41 q^{90} -5.67233e41 q^{91} -3.32632e41 q^{92} +1.09049e42 q^{93} -5.23439e42 q^{94} +4.52636e42 q^{95} -3.08809e42 q^{96} -4.23085e42 q^{97} +9.48337e42 q^{98} +2.51579e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1660014 q^{2} - 41841412812 q^{3} + 29333750564548 q^{4} + 16\!\cdots\!20 q^{5}+ \cdots + 43\!\cdots\!36 q^{9}+O(q^{10}) \) 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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