LMFDB - Embedded newform 3.42.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,42,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, 42, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 42 $
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:	$31.9415011369$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 14982256920x + 433388802120300 $ x^3 - x^2 - 14982256920*x + 433388802120300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-134889.$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.52221e6 q^{2} -3.48678e9 q^{3} +1.18107e11 q^{4} +2.08853e14 q^{5} -5.30763e15 q^{6} -2.54249e16 q^{7} -3.16760e18 q^{8} +1.21577e19 q^{9} +O(q^{10})$	\(q+1.52221e6 q^{2} -3.48678e9 q^{3} +1.18107e11 q^{4} +2.08853e14 q^{5} -5.30763e15 q^{6} -2.54249e16 q^{7} -3.16760e18 q^{8} +1.21577e19 q^{9} +3.17919e20 q^{10} -6.14868e20 q^{11} -4.11814e20 q^{12} +5.75265e22 q^{13} -3.87021e22 q^{14} -7.28226e23 q^{15} -5.08147e24 q^{16} -1.56294e25 q^{17} +1.85065e25 q^{18} -2.61062e26 q^{19} +2.46671e25 q^{20} +8.86513e25 q^{21} -9.35959e26 q^{22} +2.02809e27 q^{23} +1.10447e28 q^{24} -1.85508e27 q^{25} +8.75676e28 q^{26} -4.23912e28 q^{27} -3.00287e27 q^{28} -1.88071e30 q^{29} -1.10851e30 q^{30} -1.56469e30 q^{31} -7.69466e29 q^{32} +2.14391e30 q^{33} -2.37913e31 q^{34} -5.31008e30 q^{35} +1.43591e30 q^{36} -1.62226e32 q^{37} -3.97393e32 q^{38} -2.00583e32 q^{39} -6.61563e32 q^{40} -1.30947e32 q^{41} +1.34946e32 q^{42} +5.91017e32 q^{43} -7.26203e31 q^{44} +2.53917e33 q^{45} +3.08719e33 q^{46} +3.41234e34 q^{47} +1.77180e34 q^{48} -4.39212e34 q^{49} -2.82383e33 q^{50} +5.44964e34 q^{51} +6.79430e33 q^{52} +2.09230e35 q^{53} -6.45283e34 q^{54} -1.28417e35 q^{55} +8.05359e34 q^{56} +9.10269e35 q^{57} -2.86283e36 q^{58} -8.11837e35 q^{59} -8.60088e34 q^{60} -6.81541e36 q^{61} -2.38179e36 q^{62} -3.09108e35 q^{63} +1.00030e37 q^{64} +1.20146e37 q^{65} +3.26349e36 q^{66} +3.85118e37 q^{67} -1.84595e36 q^{68} -7.07152e36 q^{69} -8.08307e36 q^{70} +3.64228e37 q^{71} -3.85106e37 q^{72} +1.66046e38 q^{73} -2.46943e38 q^{74} +6.46827e36 q^{75} -3.08334e37 q^{76} +1.56330e37 q^{77} -3.05329e38 q^{78} +1.86540e38 q^{79} -1.06128e39 q^{80} +1.47809e38 q^{81} -1.99329e38 q^{82} -3.07845e38 q^{83} +1.04704e37 q^{84} -3.26425e39 q^{85} +8.99653e38 q^{86} +6.55762e39 q^{87} +1.94765e39 q^{88} +9.41198e39 q^{89} +3.86515e39 q^{90} -1.46261e39 q^{91} +2.39532e38 q^{92} +5.45573e39 q^{93} +5.19431e40 q^{94} -5.45237e40 q^{95} +2.68296e39 q^{96} -9.48812e40 q^{97} -6.68574e40 q^{98} -7.47535e39 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 36\!\cdots\!03 q^{9}+O(q^{10}) $ 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9	$ 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 26\!\cdots\!04 q^{99}+O(q^{100}) $ 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9 + 303684786396357841224 * q^10 + 2162403578017276790604 * q^11 + 7860140147941716898800 * q^12 + 44715417115247213223642 * q^13 + 320671470159767900457984 * q^14 - 134766121552486207386426 * q^15 - 5459234621059712438935296 * q^16 - 10989933423479049968718714 * q^17 - 3518185230541894056433380 * q^18 + 196397070114735534584831028 * q^19 + 531636782784591447776761824 * q^20 + 155518294615858001587027968 * q^21 - 4513503674461058254096349328 * q^22 - 4665149638066794122614978584 * q^23 - 7908141906446322929993781696 * q^24 - 4609009761244207114343812899 * q^25 + 122894273592250273312332501576 * q^26 - 127173474825648610542883299603 * q^27 - 599824891534617466777136050176 * q^28 - 941555486655490244273102003214 * q^29 - 1058883376027837523993877946824 * q^30 - 6480085319036017864686465368808 * q^31 - 9194142460916956643740243289088 * q^32 - 7539835064497227221977370568204 * q^33 - 50410977973081452147630100226760 * q^34 - 153374925211463555312750388019200 * q^35 - 27406614057517010739893935618800 * q^36 - 442820255707228186224391784737998 * q^37 - 832008681100278182323288015176048 * q^38 - 155913018881652402326915850008442 * q^39 - 830400317719830554628641188275072 * q^40 - 438132779830146983268076758934098 * q^41 - 1118112279998815693097419367107584 * q^42 - 1310999240696843410630649721463476 * q^43 - 1443247128257998435455229084014528 * q^44 + 469900410412478810682641155940826 * q^45 + 7997471516728167525889026089716512 * q^46 + 64523854533555761088559286850643968 * q^47 + 19035174118110151421625255141117696 * q^48 + 171140726678012788361144930683431723 * q^49 + 28333303327284754376413888152266724 * q^50 + 38319528429015278581227949931980314 * q^51 - 20984793566307791589805690265685024 * q^52 + 34693992770270063328682081068689946 * q^53 + 12267153381682064972966523079705380 * q^54 + 100035221507232528994896069839569896 * q^55 - 568132015233041377672136741101977600 * q^56 - 684794240478163142230784839651194228 * q^57 - 2740694640626009342372591817401518296 * q^58 - 4582685445865314260503003260089664948 * q^59 - 1853702841211138803266019258215507424 * q^60 - 8693740159306202291599355552752714662 * q^61 + 265004064722629998116825545352842464 * q^62 - 542258763736695967164682362773127168 * q^63 + 16981741764860889983034117450588819456 * q^64 + 2721360738989032295650621165564283148 * q^65 + 15737614205967000002335445187917232528 * q^66 + 32867814173503669322418795877934200116 * q^67 + 33261671085355608094778443956314848800 * q^68 + 16266370986342093542812388655640268184 * q^69 + 98543364272473044599951459881688524800 * q^70 + 149748844745311390685366673232301225496 * q^71 + 27573985840291440136110933044612124096 * q^72 + 6619123649433674932122580558210670046 * q^73 + 14490759310413784046620539770501448744 * q^74 + 16070623339563035717907230167095788499 * q^75 - 536779250932404614788199202699778310208 * q^76 - 954944421253262491346753072408971247616 * q^77 - 428505836133684487473427567420504715976 * q^78 - 1112771209183156752666617542198723627800 * q^79 - 2423764999311265237507278994973679346176 * q^80 + 443426488243037769948249630619149892803 * q^81 - 107939940778839787676218322470600048296 * q^82 - 1187635824307222104653182519688468749260 * q^83 + 2091460075134421134660653723208430104576 * q^84 + 6153092316082135211652182465439269196852 * q^85 + 2889811785377479896729751911427106623344 * q^86 + 3283000983546327044739131648688427064814 * q^87 + 11348012623814378178834124633898985613056 * q^88 - 2907470395792485617492963651915834875602 * q^89 + 3692098038012081220424316844483830692424 * q^90 + 19747616149564653802226421926044582182912 * q^91 + 10266693573432860781998326486887076136832 * q^92 + 22594660407563895447746096203786446364008 * q^93 + 34628213999509804914437049475497096849408 * q^94 - 84590150972982168777889232049326900017896 * q^95 + 32057992513296996581786794596336971916288 * q^96 - 52479807025249236413871256717456940920314 * q^97 - 268218382984038433881798894561914095373892 * q^98 + 26289779289001760785343260072210213785804 * 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 $

$2$	1.52221e6	1.02650	0.513252	−	0.858238i	$-0.328441\pi$
$2$	1.52221e6	1.02650	0.513252	+	0.858238i	$0.328441\pi$
$3$	−3.48678e9	−0.577350
$3$	−3.48678e9	−0.577350
$4$	1.18107e11	0.0537089
$5$	2.08853e14	0.979391	0.489695	−	0.871894i	$-0.337108\pi$
$5$	2.08853e14	0.979391	0.489695	+	0.871894i	$0.337108\pi$
$6$	−5.30763e15	−0.592652
$7$	−2.54249e16	−0.120434	−0.0602171	−	0.998185i	$-0.519179\pi$
$7$	−2.54249e16	−0.120434	−0.0602171	+	0.998185i	$0.519179\pi$
$8$	−3.16760e18	−0.971371
$9$	1.21577e19	0.333333
$10$	3.17919e20	1.00535
$11$	−6.14868e20	−0.275570	−0.137785	−	0.990462i	$-0.543998\pi$
$11$	−6.14868e20	−0.275570	−0.137785	+	0.990462i	$0.543998\pi$
$12$	−4.11814e20	−0.0310089
$13$	5.75265e22	0.839517	0.419758	−	0.907636i	$-0.362115\pi$
$13$	5.75265e22	0.839517	0.419758	+	0.907636i	$0.362115\pi$
$14$	−3.87021e22	−0.123626
$15$	−7.28226e23	−0.565452
$16$	−5.08147e24	−1.05082
$17$	−1.56294e25	−0.932696	−0.466348	−	0.884601i	$-0.654430\pi$
$17$	−1.56294e25	−0.932696	−0.466348	+	0.884601i	$0.654430\pi$
$18$	1.85065e25	0.342168
$19$	−2.61062e26	−1.59329	−0.796647	−	0.604445i	$-0.793395\pi$
$19$	−2.61062e26	−1.59329	−0.796647	+	0.604445i	$0.793395\pi$
$20$	2.46671e25	0.0526020
$21$	8.86513e25	0.0695327
$22$	−9.35959e26	−0.282873
$23$	2.02809e27	0.246415	0.123207	−	0.992381i	$-0.460682\pi$
$23$	2.02809e27	0.246415	0.123207	+	0.992381i	$0.460682\pi$
$24$	1.10447e28	0.560821
$25$	−1.85508e27	−0.0407937
$26$	8.75676e28	0.861767
$27$	−4.23912e28	−0.192450
$28$	−3.00287e27	−0.00646840
$29$	−1.88071e30	−1.97316	−0.986579	−	0.163283i	$-0.947792\pi$
$29$	−1.88071e30	−1.97316	−0.986579	+	0.163283i	$0.947792\pi$
$30$	−1.10851e30	−0.580438
$31$	−1.56469e30	−0.418324	−0.209162	−	0.977881i	$-0.567074\pi$
$31$	−1.56469e30	−0.418324	−0.209162	+	0.977881i	$0.567074\pi$
$32$	−7.69466e29	−0.107304
$33$	2.14391e30	0.159100
$34$	−2.37913e31	−0.957415
$35$	−5.31008e30	−0.117952
$36$	1.43591e30	0.0179030
$37$	−1.62226e32	−1.15342	−0.576708	−	0.816951i	$-0.695663\pi$
$37$	−1.62226e32	−1.15342	−0.576708	+	0.816951i	$0.695663\pi$
$38$	−3.97393e32	−1.63552
$39$	−2.00583e32	−0.484695
$40$	−6.61563e32	−0.951352
$41$	−1.30947e32	−0.113508	−0.0567539	−	0.998388i	$-0.518075\pi$
$41$	−1.30947e32	−0.113508	−0.0567539	+	0.998388i	$0.518075\pi$
$42$	1.34946e32	0.0713756
$43$	5.91017e32	0.192973	0.0964865	−	0.995334i	$-0.469240\pi$
$43$	5.91017e32	0.192973	0.0964865	+	0.995334i	$0.469240\pi$
$44$	−7.26203e31	−0.0148006
$45$	2.53917e33	0.326464
$46$	3.08719e33	0.252946
$47$	3.41234e34	1.79906	0.899532	−	0.436855i	$-0.143908\pi$
$47$	3.41234e34	1.79906	0.899532	+	0.436855i	$0.143908\pi$
$48$	1.77180e34	0.606694
$49$	−4.39212e34	−0.985496
$50$	−2.82383e33	−0.0418749
$51$	5.44964e34	0.538492
$52$	6.79430e33	0.0450896
$53$	2.09230e35	0.939655	0.469827	−	0.882758i	$-0.344316\pi$
$53$	2.09230e35	0.939655	0.469827	+	0.882758i	$0.344316\pi$
$54$	−6.45283e34	−0.197551
$55$	−1.28417e35	−0.269890
$56$	8.05359e34	0.116986
$57$	9.10269e35	0.919888
$58$	−2.86283e36	−2.02545
$59$	−8.11837e35	−0.404578	−0.202289	−	0.979326i	$-0.564838\pi$
$59$	−8.11837e35	−0.404578	−0.202289	+	0.979326i	$0.564838\pi$
$60$	−8.60088e34	−0.0303698
$61$	−6.81541e36	−1.71487	−0.857433	−	0.514596i	$-0.827942\pi$
$61$	−6.81541e36	−1.71487	−0.857433	+	0.514596i	$0.827942\pi$
$62$	−2.38179e36	−0.429411
$63$	−3.09108e35	−0.0401447
$64$	1.00030e37	0.940677
$65$	1.20146e37	0.822215
$66$	3.26349e36	0.163317
$67$	3.85118e37	1.41599	0.707995	−	0.706217i	$-0.249600\pi$
$67$	3.85118e37	1.41599	0.707995	+	0.706217i	$0.249600\pi$
$68$	−1.84595e36	−0.0500941
$69$	−7.07152e36	−0.142268
$70$	−8.08307e36	−0.121078
$71$	3.64228e37	0.407922	0.203961	−	0.978979i	$-0.434618\pi$
$71$	3.64228e37	0.407922	0.203961	+	0.978979i	$0.434618\pi$
$72$	−3.85106e37	−0.323790
$73$	1.66046e38	1.05223	0.526115	−	0.850413i	$-0.323648\pi$
$73$	1.66046e38	1.05223	0.526115	+	0.850413i	$0.323648\pi$
$74$	−2.46943e38	−1.18398
$75$	6.46827e36	0.0235523
$76$	−3.08334e37	−0.0855741
$77$	1.56330e37	0.0331880
$78$	−3.05329e38	−0.497541
$79$	1.86540e38	0.234108	0.117054	−	0.993126i	$-0.462655\pi$
$79$	1.86540e38	0.234108	0.117054	+	0.993126i	$0.462655\pi$
$80$	−1.06128e39	−1.02917
$81$	1.47809e38	0.111111
$82$	−1.99329e38	−0.116516
$83$	−3.07845e38	−0.140356	−0.0701781	−	0.997534i	$-0.522357\pi$
$83$	−3.07845e38	−0.140356	−0.0701781	+	0.997534i	$0.522357\pi$
$84$	1.04704e37	0.00373453
$85$	−3.26425e39	−0.913474
$86$	8.99653e38	0.198087
$87$	6.55762e39	1.13920
$88$	1.94765e39	0.267680
$89$	9.41198e39	1.02609	0.513045	−	0.858362i	$-0.328517\pi$
$89$	9.41198e39	1.02609	0.513045	+	0.858362i	$0.328517\pi$
$90$	3.86515e39	0.335116
$91$	−1.46261e39	−0.101107
$92$	2.39532e38	0.0132347
$93$	5.45573e39	0.241520
$94$	5.19431e40	1.84675
$95$	−5.45237e40	−1.56046
$96$	2.68296e39	0.0619518
$97$	−9.48812e40	−1.77158	−0.885788	−	0.464090i	$-0.846381\pi$
$97$	−9.48812e40	−1.77158	−0.885788	+	0.464090i	$0.846381\pi$
$98$	−6.68574e40	−1.01161
$99$	−7.47535e39	−0.0918566
$100$	−2.19099e38	−0.00219099
$101$	−1.18043e41	−0.962612	−0.481306	−	0.876553i	$-0.659837\pi$
$101$	−1.18043e41	−0.962612	−0.481306	+	0.876553i	$0.659837\pi$
$102$	8.29551e40	0.552764
$103$	3.50531e41	1.91233	0.956167	−	0.292821i	$-0.0945939\pi$
$103$	3.50531e41	1.91233	0.956167	+	0.292821i	$0.0945939\pi$
$104$	−1.82221e41	−0.815482
$105$	1.85151e40	0.0680997
$106$	3.18492e41	0.964559
$107$	−3.54843e41	−0.886480	−0.443240	−	0.896403i	$-0.646171\pi$
$107$	−3.54843e41	−0.886480	−0.443240	+	0.896403i	$0.646171\pi$
$108$	−5.00670e39	−0.0103363
$109$	4.46918e41	0.763809	0.381904	−	0.924202i	$-0.375268\pi$
$109$	4.46918e41	0.763809	0.381904	+	0.924202i	$0.375268\pi$
$110$	−1.95478e41	−0.277043
$111$	5.65648e41	0.665925
$112$	1.29196e41	0.126555
$113$	−1.24716e42	−1.01816	−0.509078	−	0.860720i	$-0.670014\pi$
$113$	−1.24716e42	−1.01816	−0.509078	+	0.860720i	$0.670014\pi$
$114$	1.38562e42	0.944268
$115$	4.23573e41	0.241336
$116$	−2.22125e41	−0.105976
$117$	6.99388e41	0.279839
$118$	−1.23579e42	−0.415301
$119$	3.97377e41	0.112329
$120$	2.30673e42	0.549263
$121$	−4.60046e42	−0.924061
$122$	−1.03745e43	−1.76031
$123$	4.56583e41	0.0655338
$124$	−1.84801e41	−0.0224678
$125$	−9.88498e42	−1.01934
$126$	−4.70528e41	−0.0412087
$127$	1.07922e43	0.803774	0.401887	−	0.915689i	$-0.368355\pi$
$127$	1.07922e43	0.803774	0.401887	+	0.915689i	$0.368355\pi$
$128$	1.69187e43	1.07291
$129$	−2.06075e42	−0.111413
$130$	1.82888e43	0.844006
$131$	−1.06628e43	−0.420541	−0.210270	−	0.977643i	$-0.567434\pi$
$131$	−1.06628e43	−0.420541	−0.210270	+	0.977643i	$0.567434\pi$
$132$	2.53211e41	0.00854511
$133$	6.63750e42	0.191887
$134$	5.86231e43	1.45352
$135$	−8.85353e42	−0.188484
$136$	4.95077e43	0.905993
$137$	−1.41910e43	−0.223482	−0.111741	−	0.993737i	$-0.535643\pi$
$137$	−1.41910e43	−0.223482	−0.111741	+	0.993737i	$0.535643\pi$
$138$	−1.07644e43	−0.146038
$139$	−1.16397e44	−1.36188	−0.680939	−	0.732340i	$-0.738428\pi$
$139$	−1.16397e44	−1.36188	−0.680939	+	0.732340i	$0.738428\pi$
$140$	−6.27159e41	−0.00633509
$141$	−1.18981e44	−1.03869
$142$	5.54433e43	0.418734
$143$	−3.53712e43	−0.231345
$144$	−6.17789e43	−0.350275
$145$	−3.92791e44	−1.93249
$146$	2.52758e44	1.08012
$147$	1.53144e44	0.568976
$148$	−1.91601e43	−0.0619487
$149$	3.81054e44	1.07317	0.536584	−	0.843847i	$-0.319714\pi$
$149$	3.81054e44	1.07317	0.536584	+	0.843847i	$0.319714\pi$
$150$	9.84609e42	0.0241765
$151$	−5.66688e44	−1.21427	−0.607137	−	0.794597i	$-0.707682\pi$
$151$	−5.66688e44	−1.21427	−0.607137	+	0.794597i	$0.707682\pi$
$152$	8.26941e44	1.54768
$153$	−1.90017e44	−0.310899
$154$	2.37967e43	0.0340676
$155$	−3.26790e44	−0.409703
$156$	−2.36902e43	−0.0260325
$157$	1.02109e45	0.984282	0.492141	−	0.870516i	$-0.336214\pi$
$157$	1.02109e45	0.984282	0.492141	+	0.870516i	$0.336214\pi$
$158$	2.83954e44	0.240313
$159$	−7.29539e44	−0.542510
$160$	−1.60705e44	−0.105092
$161$	−5.15641e43	−0.0296768
$162$	2.24996e44	0.114056
$163$	2.23234e45	0.997502	0.498751	−	0.866745i	$-0.333792\pi$
$163$	2.23234e45	0.997502	0.498751	+	0.866745i	$0.333792\pi$
$164$	−1.54658e43	−0.00609639
$165$	4.47763e44	0.155821
$166$	−4.68606e44	−0.144076
$167$	−3.36842e45	−0.915669	−0.457835	−	0.889037i	$-0.651375\pi$
$167$	−3.36842e45	−0.915669	−0.457835	+	0.889037i	$0.651375\pi$
$168$	−2.80811e44	−0.0675421
$169$	−1.38615e45	−0.295212
$170$	−4.96889e45	−0.937684
$171$	−3.17391e45	−0.531098
$172$	6.98034e43	0.0103644
$173$	−1.29186e46	−1.70321	−0.851607	−	0.524181i	$-0.824372\pi$
$173$	−1.29186e46	−1.70321	−0.851607	+	0.524181i	$0.824372\pi$
$174$	9.98209e45	1.16940
$175$	4.71654e43	0.00491296
$176$	3.12443e45	0.289575
$177$	2.83070e45	0.233584
$178$	1.43270e46	1.05329
$179$	1.87780e46	1.23073	0.615364	−	0.788243i	$-0.289009\pi$
$179$	1.87780e46	1.23073	0.615364	+	0.788243i	$0.289009\pi$
$180$	2.99894e44	0.0175340
$181$	4.91658e45	0.256597	0.128299	−	0.991736i	$-0.459048\pi$
$181$	4.91658e45	0.256597	0.128299	+	0.991736i	$0.459048\pi$
$182$	−2.22640e45	−0.103786
$183$	2.37638e46	0.990078
$184$	−6.42417e45	−0.239360
$185$	−3.38815e46	−1.12964
$186$	8.30478e45	0.247921
$187$	9.61002e45	0.257023
$188$	4.03022e45	0.0966258
$189$	1.07779e45	0.0231776
$190$	−8.29967e46	−1.60181
$191$	3.36912e46	0.583892	0.291946	−	0.956435i	$-0.405697\pi$
$191$	3.36912e46	0.583892	0.291946	+	0.956435i	$0.405697\pi$
$192$	−3.48783e46	−0.543100
$193$	3.07564e46	0.430538	0.215269	−	0.976555i	$-0.430937\pi$
$193$	3.07564e46	0.430538	0.215269	+	0.976555i	$0.430937\pi$
$194$	−1.44429e47	−1.81853
$195$	−4.18923e46	−0.474706
$196$	−5.18741e45	−0.0529299
$197$	1.03519e47	0.951616	0.475808	−	0.879549i	$-0.342156\pi$
$197$	1.03519e47	0.951616	0.475808	+	0.879549i	$0.342156\pi$
$198$	−1.13791e46	−0.0942911
$199$	2.57727e47	1.92607	0.963036	−	0.269374i	$-0.0868167\pi$
$199$	2.57727e47	1.92607	0.963036	+	0.269374i	$0.0868167\pi$
$200$	5.87615e45	0.0396258
$201$	−1.34282e47	−0.817522
$202$	−1.79686e47	−0.988124
$203$	4.78168e46	0.237636
$204$	6.43642e45	0.0289218
$205$	−2.73487e46	−0.111169
$206$	5.33583e47	1.96302
$207$	2.46569e46	0.0821383
$208$	−2.92319e47	−0.882184
$209$	1.60519e47	0.439063
$210$	2.81839e46	0.0699046
$211$	1.98388e47	0.446401	0.223201	−	0.974773i	$-0.428350\pi$
$211$	1.98388e47	0.446401	0.223201	+	0.974773i	$0.428350\pi$
$212$	2.47116e46	0.0504679
$213$	−1.26999e47	−0.235514
$214$	−5.40147e47	−0.909975
$215$	1.23436e47	0.188996
$216$	1.34278e47	0.186940
$217$	3.97821e46	0.0503806
$218$	6.80304e47	0.784052
$219$	−5.78968e47	−0.607505
$220$	−1.51670e46	−0.0144955
$221$	−8.99106e47	−0.783014
$222$	8.61036e47	0.683574
$223$	−9.92002e47	−0.718229	−0.359114	−	0.933294i	$-0.616921\pi$
$223$	−9.92002e47	−0.718229	−0.359114	+	0.933294i	$0.616921\pi$
$224$	1.95636e46	0.0129230
$225$	−2.25535e46	−0.0135979
$226$	−1.89844e48	−1.04514
$227$	−3.26915e48	−1.64401	−0.822004	−	0.569481i	$-0.807144\pi$
$227$	−3.26915e48	−1.64401	−0.822004	+	0.569481i	$0.807144\pi$
$228$	1.07509e47	0.0494062
$229$	1.29571e48	0.544352	0.272176	−	0.962248i	$-0.412257\pi$
$229$	1.29571e48	0.544352	0.272176	+	0.962248i	$0.412257\pi$
$230$	6.44769e47	0.247733
$231$	−5.45088e46	−0.0191611
$232$	5.95732e48	1.91667
$233$	−7.07738e47	−0.208486	−0.104243	−	0.994552i	$-0.533242\pi$
$233$	−7.07738e47	−0.208486	−0.104243	+	0.994552i	$0.533242\pi$
$234$	1.06462e48	0.287256
$235$	7.12679e48	1.76199
$236$	−9.58839e46	−0.0217295
$237$	−6.50426e47	−0.135163
$238$	6.04892e47	0.115306
$239$	−5.93274e47	−0.103776	−0.0518882	−	0.998653i	$-0.516524\pi$
$239$	−5.93274e47	−0.103776	−0.0518882	+	0.998653i	$0.516524\pi$
$240$	3.70046e48	0.594190
$241$	9.41681e47	0.138853	0.0694264	−	0.997587i	$-0.477883\pi$
$241$	9.41681e47	0.138853	0.0694264	+	0.997587i	$0.477883\pi$
$242$	−7.00287e48	−0.948552
$243$	−5.15378e47	−0.0641500
$244$	−8.04949e47	−0.0921036
$245$	−9.17309e48	−0.965185
$246$	6.95017e47	0.0672706
$247$	−1.50180e49	−1.33760
$248$	4.95630e48	0.406348
$249$	1.07339e48	0.0810347
$250$	−1.50470e49	−1.04636
$251$	−4.05119e48	−0.259580	−0.129790	−	0.991542i	$-0.541430\pi$
$251$	−4.05119e48	−0.259580	−0.129790	+	0.991542i	$0.541430\pi$
$252$	−3.65079e46	−0.00215613
$253$	−1.24701e48	−0.0679045
$254$	1.64280e49	0.825076
$255$	1.13818e49	0.527394
$256$	3.75712e48	0.160670
$257$	1.58585e49	0.626086	0.313043	−	0.949739i	$-0.398652\pi$
$257$	1.58585e49	0.626086	0.313043	+	0.949739i	$0.398652\pi$
$258$	−3.13690e48	−0.114366
$259$	4.12459e48	0.138911
$260$	1.41901e48	0.0441603
$261$	−2.28650e49	−0.657720
$262$	−1.62310e49	−0.431686
$263$	3.33765e49	0.821008	0.410504	−	0.911859i	$-0.365353\pi$
$263$	3.33765e49	0.821008	0.410504	+	0.911859i	$0.365353\pi$
$264$	−6.79104e48	−0.154545
$265$	4.36983e49	0.920289
$266$	1.01037e49	0.196973
$267$	−3.28175e49	−0.592414
$268$	4.54852e48	0.0760513
$269$	1.93141e49	0.299193	0.149597	−	0.988747i	$-0.452202\pi$
$269$	1.93141e49	0.299193	0.149597	+	0.988747i	$0.452202\pi$
$270$	−1.34770e49	−0.193479
$271$	−2.04588e49	−0.272276	−0.136138	−	0.990690i	$-0.543469\pi$
$271$	−2.04588e49	−0.272276	−0.136138	+	0.990690i	$0.543469\pi$
$272$	7.94205e49	0.980099
$273$	5.09980e48	0.0583739
$274$	−2.16018e49	−0.229405
$275$	1.14063e48	0.0112415
$276$	−8.35197e47	−0.00764105
$277$	−4.77316e48	−0.0405481	−0.0202741	−	0.999794i	$-0.506454\pi$
$277$	−4.77316e48	−0.0405481	−0.0202741	+	0.999794i	$0.506454\pi$
$278$	−1.77181e50	−1.39797
$279$	−1.90230e49	−0.139441
$280$	1.68202e49	0.114575
$281$	5.44601e49	0.344825	0.172413	−	0.985025i	$-0.444844\pi$
$281$	5.44601e49	0.344825	0.172413	+	0.985025i	$0.444844\pi$
$282$	−1.81114e50	−1.06622
$283$	−5.27820e49	−0.288977	−0.144489	−	0.989506i	$-0.546154\pi$
$283$	−5.27820e49	−0.288977	−0.144489	+	0.989506i	$0.546154\pi$
$284$	4.30180e48	0.0219091
$285$	1.90113e50	0.900930
$286$	−5.38425e49	−0.237477
$287$	3.32931e48	0.0136702
$288$	−9.35491e48	−0.0357679
$289$	−3.65268e49	−0.130079
$290$	−5.97912e50	−1.98371
$291$	3.30830e50	1.02282
$292$	1.96113e49	0.0565142
$293$	4.59364e50	1.23416	0.617079	−	0.786901i	$-0.288316\pi$
$293$	4.59364e50	1.23416	0.617079	+	0.786901i	$0.288316\pi$
$294$	2.33117e50	0.584056
$295$	−1.69555e50	−0.396240
$296$	5.13867e50	1.12039
$297$	2.60649e49	0.0530334
$298$	5.80045e50	1.10161
$299$	1.16669e50	0.206869
$300$	7.63950e47	0.00126497
$301$	−1.50266e49	−0.0232406
$302$	−8.62620e50	−1.24646
$303$	4.11590e50	0.555764
$304$	1.32658e51	1.67427
$305$	−1.42342e51	−1.67952
$306$	−2.89247e50	−0.319138
$307$	−4.69523e50	−0.484529	−0.242265	−	0.970210i	$-0.577890\pi$
$307$	−4.69523e50	−0.484529	−0.242265	+	0.970210i	$0.577890\pi$
$308$	1.84637e48	0.00178249
$309$	−1.22223e51	−1.10409
$310$	−4.97444e50	−0.420562
$311$	−1.49521e51	−1.18335	−0.591676	−	0.806176i	$-0.701533\pi$
$311$	−1.49521e51	−1.18335	−0.591676	+	0.806176i	$0.701533\pi$
$312$	6.35364e50	0.470819
$313$	−6.94871e50	−0.482220	−0.241110	−	0.970498i	$-0.577512\pi$
$313$	−6.94871e50	−0.482220	−0.241110	+	0.970498i	$0.577512\pi$
$314$	1.55431e51	1.01037
$315$	−6.45582e49	−0.0393174
$316$	2.20317e49	0.0125737
$317$	−1.60924e51	−0.860809	−0.430404	−	0.902636i	$-0.641629\pi$
$317$	−1.60924e51	−0.860809	−0.430404	+	0.902636i	$0.641629\pi$
$318$	−1.11051e51	−0.556888
$319$	1.15639e51	0.543743
$320$	2.08916e51	0.921290
$321$	1.23726e51	0.511810
$322$	−7.84915e49	−0.0304633
$323$	4.08026e51	1.48606
$324$	1.74573e49	0.00596766
$325$	−1.06716e50	−0.0342470
$326$	3.39809e51	1.02394
$327$	−1.55831e51	−0.440985
$328$	4.14787e50	0.110258
$329$	−8.67586e50	−0.216669
$330$	6.81590e50	0.159951
$331$	−6.95098e51	−1.53311	−0.766553	−	0.642181i	$-0.778030\pi$
$331$	−6.95098e51	−1.53311	−0.766553	+	0.642181i	$0.778030\pi$
$332$	−3.63588e49	−0.00753839
$333$	−1.97229e51	−0.384472
$334$	−5.12745e51	−0.939937
$335$	8.04331e51	1.38681
$336$	−4.50479e50	−0.0730667
$337$	6.12109e51	0.934148	0.467074	−	0.884218i	$-0.345308\pi$
$337$	6.12109e51	0.934148	0.467074	+	0.884218i	$0.345308\pi$
$338$	−2.11002e51	−0.303036
$339$	4.34858e51	0.587833
$340$	−3.85532e50	−0.0490617
$341$	9.62076e50	0.115278
$342$	−4.83137e51	−0.545174
$343$	2.24982e51	0.239122
$344$	−1.87210e51	−0.187448
$345$	−1.47691e51	−0.139336
$346$	−1.96648e52	−1.74835
$347$	−8.85024e51	−0.741653	−0.370826	−	0.928702i	$-0.620926\pi$
$347$	−8.85024e51	−0.741653	−0.370826	+	0.928702i	$0.620926\pi$
$348$	7.74502e50	0.0611854
$349$	1.47646e52	1.09977	0.549884	−	0.835241i	$-0.314672\pi$
$349$	1.47646e52	1.09977	0.549884	+	0.835241i	$0.314672\pi$
$350$	7.17957e49	0.00504317
$351$	−2.43862e51	−0.161565
$352$	4.73120e50	0.0295697
$353$	−1.58824e52	−0.936559	−0.468280	−	0.883580i	$-0.655126\pi$
$353$	−1.58824e52	−0.936559	−0.468280	+	0.883580i	$0.655126\pi$
$354$	4.30893e51	0.239774
$355$	7.60702e51	0.399515
$356$	1.11162e51	0.0551102
$357$	−1.38557e51	−0.0648529
$358$	2.85841e52	1.26335
$359$	−3.40525e52	−1.42139	−0.710694	−	0.703501i	$-0.751619\pi$
$359$	−3.40525e52	−1.42139	−0.710694	+	0.703501i	$0.751619\pi$
$360$	−8.04306e51	−0.317117
$361$	4.13065e52	1.53858
$362$	7.48408e51	0.263398
$363$	1.60408e52	0.533507
$364$	−1.72745e50	−0.00543033
$365$	3.46793e52	1.03054
$366$	3.61736e52	1.01632
$367$	−8.17353e51	−0.217148	−0.108574	−	0.994088i	$-0.534628\pi$
$367$	−8.17353e51	−0.217148	−0.108574	+	0.994088i	$0.534628\pi$
$368$	−1.03057e52	−0.258939
$369$	−1.59201e51	−0.0378359
$370$	−5.15748e52	−1.15958
$371$	−5.31965e51	−0.113167
$372$	6.44361e50	0.0129718
$373$	1.25113e52	0.238382	0.119191	−	0.992871i	$-0.461970\pi$
$373$	1.25113e52	0.238382	0.119191	+	0.992871i	$0.461970\pi$
$374$	1.46285e52	0.263835
$375$	3.44668e52	0.588518
$376$	−1.08089e53	−1.74756
$377$	−1.08190e53	−1.65650
$378$	1.64063e51	0.0237919
$379$	−1.18800e52	−0.163198	−0.0815988	−	0.996665i	$-0.526003\pi$
$379$	−1.18800e52	−0.163198	−0.0815988	+	0.996665i	$0.526003\pi$
$380$	−6.43965e51	−0.0838105
$381$	−3.76301e52	−0.464059
$382$	5.12852e52	0.599367
$383$	3.04741e52	0.337563	0.168782	−	0.985653i	$-0.446017\pi$
$383$	3.04741e52	0.337563	0.168782	+	0.985653i	$0.446017\pi$
$384$	−5.89920e52	−0.619446
$385$	3.26499e51	0.0325041
$386$	4.68178e52	0.441948
$387$	7.18538e51	0.0643243
$388$	−1.12062e52	−0.0951495
$389$	3.81054e52	0.306916	0.153458	−	0.988155i	$-0.450959\pi$
$389$	3.81054e52	0.306916	0.153458	+	0.988155i	$0.450959\pi$
$390$	−6.37690e52	−0.487287
$391$	−3.16979e52	−0.229830
$392$	1.39125e53	0.957282
$393$	3.71787e52	0.242799
$394$	1.57578e53	0.976836
$395$	3.89595e52	0.229284
$396$	−8.82893e50	−0.00493352
$397$	6.52535e52	0.346257	0.173129	−	0.984899i	$-0.444612\pi$
$397$	6.52535e52	0.346257	0.173129	+	0.984899i	$0.444612\pi$
$398$	3.92316e53	1.97712
$399$	−2.31435e52	−0.110786
$400$	9.42656e51	0.0428670
$401$	−3.27270e53	−1.41399	−0.706995	−	0.707219i	$-0.749950\pi$
$401$	−3.27270e53	−1.41399	−0.706995	+	0.707219i	$0.749950\pi$
$402$	−2.04406e53	−0.839189
$403$	−9.00111e52	−0.351190
$404$	−1.39417e52	−0.0517009
$405$	3.08703e52	0.108821
$406$	7.27874e52	0.243934
$407$	9.97476e52	0.317846
$408$	−1.72623e53	−0.523076
$409$	−4.10159e53	−1.18202	−0.591009	−	0.806665i	$-0.701270\pi$
$409$	−4.10159e53	−1.18202	−0.591009	+	0.806665i	$0.701270\pi$
$410$	−4.16305e52	−0.114115
$411$	4.94811e52	0.129027
$412$	4.14003e52	0.102709
$413$	2.06409e52	0.0487251
$414$	3.75330e52	0.0843152
$415$	−6.42945e52	−0.137464
$416$	−4.42647e52	−0.0900833
$417$	4.05851e53	0.786280
$418$	2.44344e53	0.450700
$419$	−4.77579e53	−0.838798	−0.419399	−	0.907802i	$-0.637759\pi$
$419$	−4.77579e53	−0.838798	−0.419399	+	0.907802i	$0.637759\pi$
$420$	2.18677e51	0.00365756
$421$	−4.69403e53	−0.747761	−0.373880	−	0.927477i	$-0.621973\pi$
$421$	−4.69403e53	−0.747761	−0.373880	+	0.927477i	$0.621973\pi$
$422$	3.01989e53	0.458232
$423$	4.14861e53	0.599688
$424$	−6.62756e53	−0.912753
$425$	2.89939e52	0.0380481
$426$	−1.93319e53	−0.241756
$427$	1.73281e53	0.206529
$428$	−4.19095e52	−0.0476119
$429$	1.23332e53	0.133567
$430$	1.87895e53	0.194005
$431$	−1.40100e54	−1.37928	−0.689641	−	0.724151i	$-0.742232\pi$
$431$	−1.40100e54	−1.37928	−0.689641	+	0.724151i	$0.742232\pi$
$432$	2.15410e53	0.202231
$433$	1.75852e54	1.57451	0.787257	−	0.616625i	$-0.211501\pi$
$433$	1.75852e54	1.57451	0.787257	+	0.616625i	$0.211501\pi$
$434$	6.05568e52	0.0517158
$435$	1.36958e54	1.11573
$436$	5.27842e52	0.0410234
$437$	−5.29459e53	−0.392611
$438$	−8.81312e53	−0.623606
$439$	2.74897e54	1.85630	0.928148	−	0.372213i	$-0.121401\pi$
$439$	2.74897e54	1.85630	0.928148	+	0.372213i	$0.121401\pi$
$440$	4.06773e53	0.262164
$441$	−5.33979e53	−0.328499
$442$	−1.36863e54	−0.803766
$443$	1.68192e54	0.943036	0.471518	−	0.881856i	$-0.343706\pi$
$443$	1.68192e54	0.943036	0.471518	+	0.881856i	$0.343706\pi$
$444$	6.68071e52	0.0357661
$445$	1.96572e54	1.00494
$446$	−1.51004e54	−0.737264
$447$	−1.32865e54	−0.619594
$448$	−2.54325e53	−0.113290
$449$	−3.75457e54	−1.59775	−0.798877	−	0.601495i	$-0.794572\pi$
$449$	−3.75457e54	−1.59775	−0.798877	+	0.601495i	$0.794572\pi$
$450$	−3.43312e52	−0.0139583
$451$	8.05149e52	0.0312793
$452$	−1.47299e53	−0.0546841
$453$	1.97592e54	0.701062
$454$	−4.97633e54	−1.68758
$455$	−3.05470e53	−0.0990228
$456$	−2.88336e54	−0.893553
$457$	−6.18127e54	−1.83145	−0.915726	−	0.401802i	$-0.868384\pi$
$457$	−6.18127e54	−1.83145	−0.915726	+	0.401802i	$0.868384\pi$
$458$	1.97234e54	0.558779
$459$	6.62549e53	0.179497
$460$	5.00271e52	0.0129619
$461$	3.58199e54	0.887678	0.443839	−	0.896107i	$-0.353616\pi$
$461$	3.58199e54	0.887678	0.443839	+	0.896107i	$0.353616\pi$
$462$	−8.29739e52	−0.0196690
$463$	5.07064e54	1.14988	0.574940	−	0.818196i	$-0.305026\pi$
$463$	5.07064e54	1.14988	0.574940	+	0.818196i	$0.305026\pi$
$464$	9.55676e54	2.07344
$465$	1.13945e54	0.236542
$466$	−1.07733e54	−0.214011
$467$	−6.01143e54	−1.14283	−0.571415	−	0.820661i	$-0.693606\pi$
$467$	−6.01143e54	−1.14283	−0.571415	+	0.820661i	$0.693606\pi$
$468$	8.26028e52	0.0150299
$469$	−9.79160e53	−0.170534
$470$	1.08485e55	1.80869
$471$	−3.56031e54	−0.568275
$472$	2.57157e54	0.392996
$473$	−3.63397e53	−0.0531775
$474$	−9.90086e53	−0.138745
$475$	4.84293e53	0.0649963
$476$	4.69331e52	0.00603305
$477$	2.54375e54	0.313218
$478$	−9.03089e53	−0.106527
$479$	5.39762e54	0.609993	0.304996	−	0.952354i	$-0.401345\pi$
$479$	5.39762e54	0.609993	0.304996	+	0.952354i	$0.401345\pi$
$480$	5.60345e53	0.0606750
$481$	−9.33231e54	−0.968311
$482$	1.43344e54	0.142533
$483$	1.79793e53	0.0171339
$484$	−5.43347e53	−0.0496304
$485$	−1.98162e55	−1.73506
$486$	−7.84514e53	−0.0658502
$487$	1.62965e54	0.131145	0.0655723	−	0.997848i	$-0.479113\pi$
$487$	1.62965e54	0.131145	0.0655723	+	0.997848i	$0.479113\pi$
$488$	2.15885e55	1.66577
$489$	−7.78368e54	−0.575908
$490$	−1.39634e55	−0.990766
$491$	−2.75266e55	−1.87319	−0.936596	−	0.350410i	$-0.886042\pi$
$491$	−2.75266e55	−1.87319	−0.936596	+	0.350410i	$0.886042\pi$
$492$	5.39258e52	0.00351975
$493$	2.93944e55	1.84036
$494$	−2.28606e55	−1.37305
$495$	−1.56125e54	−0.0899635
$496$	7.95093e54	0.439585
$497$	−9.26048e53	−0.0491278
$498$	1.63393e54	0.0831824
$499$	3.11535e55	1.52211	0.761055	−	0.648688i	$-0.224682\pi$
$499$	3.11535e55	1.52211	0.761055	+	0.648688i	$0.224682\pi$
$500$	−1.16749e54	−0.0547479
$501$	1.17450e55	0.528662
$502$	−6.16677e54	−0.266460
$503$	−3.69063e54	−0.153093	−0.0765467	−	0.997066i	$-0.524389\pi$
$503$	−3.69063e54	−0.153093	−0.0765467	+	0.997066i	$0.524389\pi$
$504$	9.79129e53	0.0389954
$505$	−2.46536e55	−0.942773
$506$	−1.89821e54	−0.0697042
$507$	4.83322e54	0.170441
$508$	1.27464e54	0.0431698
$509$	3.79605e54	0.123486	0.0617430	−	0.998092i	$-0.480334\pi$
$509$	3.79605e54	0.123486	0.0617430	+	0.998092i	$0.480334\pi$
$510$	1.73254e55	0.541372
$511$	−4.22172e54	−0.126725
$512$	−3.14856e55	−0.907983
$513$	1.10667e55	0.306629
$514$	2.41401e55	0.642679
$515$	7.32096e55	1.87292
$516$	−2.43389e53	−0.00598387
$517$	−2.09814e55	−0.495768
$518$	6.27850e54	0.142592
$519$	4.50443e55	0.983351
$520$	−3.80574e55	−0.798676
$521$	−5.60913e55	−1.13168	−0.565838	−	0.824516i	$-0.691447\pi$
$521$	−5.60913e55	−1.13168	−0.565838	+	0.824516i	$0.691447\pi$
$522$	−3.48054e55	−0.675151
$523$	2.10936e55	0.393429	0.196714	−	0.980461i	$-0.436973\pi$
$523$	2.10936e55	0.393429	0.196714	+	0.980461i	$0.436973\pi$
$524$	−1.25935e54	−0.0225868
$525$	−1.64455e53	−0.00283650
$526$	5.08061e55	0.842768
$527$	2.44552e55	0.390169
$528$	−1.08942e55	−0.167186
$529$	−6.36262e55	−0.939280
$530$	6.65181e55	0.944680
$531$	−9.87005e54	−0.134859
$532$	7.83936e53	0.0103061
$533$	−7.53291e54	−0.0952917
$534$	−4.99552e55	−0.608115
$535$	−7.41101e55	−0.868210
$536$	−1.21990e56	−1.37545
$537$	−6.54748e55	−0.710561
$538$	2.94001e55	0.307123
$539$	2.70057e55	0.271573
$540$	−1.04567e54	−0.0101233
$541$	−7.29358e55	−0.679825	−0.339912	−	0.940457i	$-0.610397\pi$
$541$	−7.29358e55	−0.679825	−0.339912	+	0.940457i	$0.610397\pi$
$542$	−3.11427e55	−0.279493
$543$	−1.71431e55	−0.148147
$544$	1.20263e55	0.100082
$545$	9.33403e55	0.748067
$546$	7.76297e54	0.0599210
$547$	1.99029e56	1.47971	0.739854	−	0.672767i	$-0.234894\pi$
$547$	1.99029e56	1.47971	0.739854	+	0.672767i	$0.234894\pi$
$548$	−1.67606e54	−0.0120030
$549$	−8.28594e55	−0.571622
$550$	1.73628e54	0.0115394
$551$	4.90982e56	3.14382
$552$	2.23997e55	0.138195
$553$	−4.74277e54	−0.0281947
$554$	−7.26576e54	−0.0416228
$555$	1.18137e56	0.652200
$556$	−1.37473e55	−0.0731450
$557$	−8.80376e55	−0.451478	−0.225739	−	0.974188i	$-0.572480\pi$
$557$	−8.80376e55	−0.451478	−0.225739	+	0.974188i	$0.572480\pi$
$558$	−2.89570e55	−0.143137
$559$	3.39991e55	0.162004
$560$	2.69830e55	0.123947
$561$	−3.35081e55	−0.148392
$562$	8.28998e55	0.353964
$563$	−2.45378e56	−1.01021	−0.505107	−	0.863057i	$-0.668547\pi$
$563$	−2.45378e56	−1.01021	−0.505107	+	0.863057i	$0.668547\pi$
$564$	−1.40525e55	−0.0557870
$565$	−2.60474e56	−0.997173
$566$	−8.03454e55	−0.296636
$567$	−3.75803e54	−0.0133816
$568$	−1.15373e56	−0.396244
$569$	−2.70768e56	−0.897008	−0.448504	−	0.893781i	$-0.648043\pi$
$569$	−2.70768e56	−0.897008	−0.448504	+	0.893781i	$0.648043\pi$
$570$	2.89392e56	0.924808
$571$	−2.46500e56	−0.759936	−0.379968	−	0.925000i	$-0.624065\pi$
$571$	−2.46500e56	−0.759936	−0.379968	+	0.925000i	$0.624065\pi$
$572$	−4.17759e54	−0.0124253
$573$	−1.17474e56	−0.337110
$574$	5.06792e54	0.0140325
$575$	−3.76228e54	−0.0100522
$576$	1.21613e56	0.313559
$577$	7.01788e54	0.0174623	0.00873116	−	0.999962i	$-0.497221\pi$
$577$	7.01788e54	0.0174623	0.00873116	+	0.999962i	$0.497221\pi$
$578$	−5.56015e55	−0.133526
$579$	−1.07241e56	−0.248571
$580$	−4.63915e55	−0.103792
$581$	7.82695e54	0.0169037
$582$	5.03594e56	1.04993
$583$	−1.28649e56	−0.258940
$584$	−5.25968e56	−1.02211
$585$	1.46069e56	0.274072
$586$	6.99250e56	1.26687
$587$	2.53642e56	0.443753	0.221876	−	0.975075i	$-0.428782\pi$
$587$	2.53642e56	0.443753	0.221876	+	0.975075i	$0.428782\pi$
$588$	1.80874e55	0.0305591
$589$	4.08482e56	0.666513
$590$	−2.58098e56	−0.406742
$591$	−3.60948e56	−0.549415
$592$	8.24348e56	1.21204
$593$	−7.95609e56	−1.13000	−0.565000	−	0.825091i	$-0.691124\pi$
$593$	−7.95609e56	−1.13000	−0.565000	+	0.825091i	$0.691124\pi$
$594$	3.96764e55	0.0544390
$595$	8.29934e55	0.110014
$596$	4.50052e55	0.0576387
$597$	−8.98640e56	−1.11202
$598$	1.77595e56	0.212352
$599$	1.10237e57	1.27373	0.636863	−	0.770977i	$-0.280232\pi$
$599$	1.10237e57	1.27373	0.636863	+	0.770977i	$0.280232\pi$
$600$	−2.04889e55	−0.0228780
$601$	2.50520e56	0.270343	0.135172	−	0.990822i	$-0.456841\pi$
$601$	2.50520e56	0.270343	0.135172	+	0.990822i	$0.456841\pi$
$602$	−2.28736e55	−0.0238565
$603$	4.68213e56	0.471997
$604$	−6.69300e55	−0.0652174
$605$	−9.60820e56	−0.905017
$606$	6.26527e56	0.570494
$607$	9.00711e56	0.792898	0.396449	−	0.918057i	$-0.370242\pi$
$607$	9.00711e56	0.792898	0.396449	+	0.918057i	$0.370242\pi$
$608$	2.00879e56	0.170966
$609$	−1.66727e56	−0.137199
$610$	−2.16675e57	−1.72404
$611$	1.96300e57	1.51034
$612$	−2.24424e55	−0.0166980
$613$	−2.25023e57	−1.61915	−0.809576	−	0.587015i	$-0.800303\pi$
$613$	−2.25023e57	−1.61915	−0.809576	+	0.587015i	$0.800303\pi$
$614$	−7.14713e56	−0.497371
$615$	9.53589e55	0.0641832
$616$	−4.95189e55	−0.0322379
$617$	1.83076e57	1.15289	0.576443	−	0.817138i	$-0.304440\pi$
$617$	1.83076e57	1.15289	0.576443	+	0.817138i	$0.304440\pi$
$618$	−1.86049e57	−1.13335
$619$	1.01118e57	0.595899	0.297949	−	0.954582i	$-0.403697\pi$
$619$	1.01118e57	0.595899	0.297949	+	0.954582i	$0.403697\pi$
$620$	−3.85963e55	−0.0220047
$621$	−8.59731e55	−0.0474226
$622$	−2.27603e57	−1.21471
$623$	−2.39299e56	−0.123576
$624$	1.01926e57	0.509329
$625$	−1.98015e57	−0.957542
$626$	−1.05774e57	−0.495001
$627$	−5.59695e56	−0.253493
$628$	1.20598e56	0.0528647
$629$	2.53550e57	1.07579
$630$	−9.82712e55	−0.0403594
$631$	3.65269e57	1.45215	0.726074	−	0.687616i	$-0.241343\pi$
$631$	3.65269e57	1.45215	0.726074	+	0.687616i	$0.241343\pi$
$632$	−5.90884e56	−0.227406
$633$	−6.91736e56	−0.257730
$634$	−2.44961e57	−0.883623
$635$	2.25399e57	0.787208
$636$	−8.61639e55	−0.0291376
$637$	−2.52663e57	−0.827340
$638$	1.76026e57	0.558154
$639$	4.42816e56	0.135974
$640$	3.53353e57	1.05080
$641$	−2.19802e57	−0.633056	−0.316528	−	0.948583i	$-0.602517\pi$
$641$	−2.19802e57	−0.633056	−0.316528	+	0.948583i	$0.602517\pi$
$642$	1.88337e57	0.525374
$643$	2.64051e57	0.713448	0.356724	−	0.934210i	$-0.383894\pi$
$643$	2.64051e57	0.713448	0.356724	+	0.934210i	$0.383894\pi$
$644$	−6.09009e54	−0.00159391
$645$	−4.30394e56	−0.109117
$646$	6.21102e57	1.52544
$647$	4.31568e57	1.02686	0.513431	−	0.858131i	$-0.328374\pi$
$647$	4.31568e57	1.02686	0.513431	+	0.858131i	$0.328374\pi$
$648$	−4.68199e56	−0.107930
$649$	4.99172e56	0.111490
$650$	−1.62445e56	−0.0351546
$651$	−1.38712e56	−0.0290872
$652$	2.63655e56	0.0535748
$653$	−9.50604e57	−1.87189	−0.935943	−	0.352151i	$-0.885450\pi$
$653$	−9.50604e57	−1.87189	−0.935943	+	0.352151i	$0.885450\pi$
$654$	−2.37207e57	−0.452673
$655$	−2.22695e57	−0.411874
$656$	6.65403e56	0.119277
$657$	2.01874e57	0.350743
$658$	−1.32065e57	−0.222411
$659$	−1.08623e58	−1.77325	−0.886623	−	0.462492i	$-0.846955\pi$
$659$	−1.08623e58	−1.77325	−0.886623	+	0.462492i	$0.846955\pi$
$660$	5.28840e55	0.00836900
$661$	−1.84350e57	−0.282821	−0.141411	−	0.989951i	$-0.545164\pi$
$661$	−1.84350e57	−0.282821	−0.141411	+	0.989951i	$0.545164\pi$
$662$	−1.05809e58	−1.57374
$663$	3.13499e57	0.452073
$664$	9.75130e56	0.136338
$665$	1.38626e57	0.187932
$666$	−3.00225e57	−0.394662
$667$	−3.81424e57	−0.486216
$668$	−3.97835e56	−0.0491796
$669$	3.45890e57	0.414670
$670$	1.22436e58	1.42356
$671$	4.19057e57	0.472565
$672$	−6.82141e55	−0.00746112
$673$	−9.72288e57	−1.03154	−0.515770	−	0.856727i	$-0.672494\pi$
$673$	−9.72288e57	−1.03154	−0.515770	+	0.856727i	$0.672494\pi$
$674$	9.31759e57	0.958906
$675$	7.86391e55	0.00785075
$676$	−1.63715e56	−0.0158555
$677$	−9.24153e57	−0.868313	−0.434157	−	0.900837i	$-0.642954\pi$
$677$	−9.24153e57	−0.868313	−0.434157	+	0.900837i	$0.642954\pi$
$678$	6.61947e57	0.603412
$679$	2.41235e57	0.213358
$680$	1.03398e58	0.887322
$681$	1.13988e58	0.949169
$682$	1.46448e57	0.118333
$683$	6.23415e57	0.488824	0.244412	−	0.969671i	$-0.421405\pi$
$683$	6.23415e57	0.488824	0.244412	+	0.969671i	$0.421405\pi$
$684$	−3.74862e56	−0.0285247
$685$	−2.96384e57	−0.218876
$686$	3.42471e57	0.245459
$687$	−4.51785e57	−0.314282
$688$	−3.00324e57	−0.202781
$689$	1.20363e58	0.788856
$690$	−2.24817e57	−0.143029
$691$	−1.96245e57	−0.121199	−0.0605995	−	0.998162i	$-0.519301\pi$
$691$	−1.96245e57	−0.121199	−0.0605995	+	0.998162i	$0.519301\pi$
$692$	−1.52578e57	−0.0914778
$693$	1.90060e56	0.0110627
$694$	−1.34719e58	−0.761309
$695$	−2.43099e58	−1.33381
$696$	−2.07719e58	−1.10659
$697$	2.04662e57	0.105868
$698$	2.24749e58	1.12892
$699$	2.46773e57	0.120369
$700$	5.57057e54	0.000263870 0
$701$	4.83883e57	0.222598	0.111299	−	0.993787i	$-0.464499\pi$
$701$	4.83883e57	0.222598	0.111299	+	0.993787i	$0.464499\pi$
$702$	−3.71209e57	−0.165847
$703$	4.23512e58	1.83773
$704$	−6.15051e57	−0.259222
$705$	−2.48496e58	−1.01728
$706$	−2.41764e58	−0.961381
$707$	3.00123e57	0.115931
$708$	3.34326e56	0.0125455
$709$	2.85115e58	1.03937	0.519687	−	0.854357i	$-0.326049\pi$
$709$	2.85115e58	1.03937	0.519687	+	0.854357i	$0.326049\pi$
$710$	1.15795e58	0.410104
$711$	2.26789e57	0.0780362
$712$	−2.98133e58	−0.996714
$713$	−3.17333e57	−0.103081
$714$	−2.10913e57	−0.0665717
$715$	−7.38739e57	−0.226578
$716$	2.21782e57	0.0661011
$717$	2.06862e57	0.0599153
$718$	−5.18351e58	−1.45906
$719$	−4.02434e58	−1.10091	−0.550456	−	0.834864i	$-0.685546\pi$
$719$	−4.02434e58	−1.10091	−0.550456	+	0.834864i	$0.685546\pi$
$720$	−1.29027e58	−0.343056
$721$	−8.91224e57	−0.230311
$722$	6.28773e58	1.57936
$723$	−3.28344e57	−0.0801667
$724$	5.80684e56	0.0137816
$725$	3.48887e57	0.0804924
$726$	2.44175e58	0.547647
$727$	6.63952e57	0.144771	0.0723854	−	0.997377i	$-0.476939\pi$
$727$	6.63952e57	0.144771	0.0723854	+	0.997377i	$0.476939\pi$
$728$	4.63295e57	0.0982120
$729$	1.79701e57	0.0370370
$730$	5.27893e58	1.05786
$731$	−9.23725e57	−0.179985
$732$	2.80668e57	0.0531760
$733$	8.47264e58	1.56094	0.780472	−	0.625191i	$-0.214979\pi$
$733$	8.47264e58	1.56094	0.780472	+	0.625191i	$0.214979\pi$
$734$	−1.24419e58	−0.222903
$735$	3.19846e58	0.557250
$736$	−1.56055e57	−0.0264412
$737$	−2.36797e58	−0.390204
$738$	−2.42337e57	−0.0388387
$739$	−8.89009e58	−1.38578	−0.692891	−	0.721042i	$-0.743663\pi$
$739$	−8.89009e58	−1.38578	−0.692891	+	0.721042i	$0.743663\pi$
$740$	−4.00165e57	−0.0606720
$741$	5.23646e58	0.772261
$742$	−8.09764e57	−0.116166
$743$	5.64085e58	0.787180	0.393590	−	0.919286i	$-0.371233\pi$
$743$	5.64085e58	0.787180	0.393590	+	0.919286i	$0.371233\pi$
$744$	−1.72816e58	−0.234605
$745$	7.95843e58	1.05105
$746$	1.90449e58	0.244699
$747$	−3.74268e57	−0.0467854
$748$	1.13501e57	0.0138044
$749$	9.02186e57	0.106763
$750$	5.24658e58	0.604116
$751$	−6.08485e58	−0.681760	−0.340880	−	0.940107i	$-0.610725\pi$
$751$	−6.08485e58	−0.681760	−0.340880	+	0.940107i	$0.610725\pi$
$752$	−1.73397e59	−1.89050
$753$	1.41256e58	0.149868
$754$	−1.64689e59	−1.70040
$755$	−1.18355e59	−1.18925
$756$	1.27295e56	0.00124484
$757$	2.27854e58	0.216866	0.108433	−	0.994104i	$-0.465417\pi$
$757$	2.27854e58	0.216866	0.108433	+	0.994104i	$0.465417\pi$
$758$	−1.80839e58	−0.167523
$759$	4.34805e57	0.0392047
$760$	1.72709e59	1.51578
$761$	−1.11747e59	−0.954666	−0.477333	−	0.878723i	$-0.658396\pi$
$761$	−1.11747e59	−0.954666	−0.477333	+	0.878723i	$0.658396\pi$
$762$	−5.72810e58	−0.476358
$763$	−1.13629e58	−0.0919887
$764$	3.97917e57	0.0313602
$765$	−3.96857e58	−0.304491
$766$	4.63880e58	0.346510
$767$	−4.67022e58	−0.339650
$768$	−1.31003e58	−0.0927631
$769$	1.36814e59	0.943277	0.471638	−	0.881792i	$-0.343663\pi$
$769$	1.36814e59	0.943277	0.471638	+	0.881792i	$0.343663\pi$
$770$	4.97002e57	0.0333655
$771$	−5.52953e58	−0.361471
$772$	3.63256e57	0.0231237
$773$	9.09293e58	0.563669	0.281835	−	0.959463i	$-0.409057\pi$
$773$	9.09293e58	0.563669	0.281835	+	0.959463i	$0.409057\pi$
$774$	1.09377e58	0.0660291
$775$	2.90263e57	0.0170650
$776$	3.00545e59	1.72086
$777$	−1.43816e58	−0.0802001
$778$	5.80045e58	0.315050
$779$	3.41853e58	0.180851
$780$	−4.94778e57	−0.0254960
$781$	−2.23952e58	−0.112411
$782$	−4.82509e58	−0.235921
$783$	7.97253e58	0.379735
$784$	2.23185e59	1.03558
$785$	2.13257e59	0.963997
$786$	5.65939e58	0.249234
$787$	−3.17394e59	−1.36181	−0.680906	−	0.732371i	$-0.738414\pi$
$787$	−3.17394e59	−1.36181	−0.680906	+	0.732371i	$0.738414\pi$
$788$	1.22263e58	0.0511103
$789$	−1.16377e59	−0.474009
$790$	5.93047e58	0.235360
$791$	3.17090e58	0.122621
$792$	2.36789e58	0.0892268
$793$	−3.92066e59	−1.43966
$794$	9.93297e58	0.355434
$795$	−1.52367e59	−0.531329
$796$	3.04395e58	0.103447
$797$	3.02927e59	1.00333	0.501663	−	0.865063i	$-0.332722\pi$
$797$	3.02927e59	1.00333	0.501663	+	0.865063i	$0.332722\pi$
$798$	−3.52293e58	−0.113722
$799$	−5.33330e59	−1.67798
$800$	1.42742e57	0.00437732
$801$	1.14428e59	0.342030
$802$	−4.98174e59	−1.45146
$803$	−1.02097e59	−0.289963
$804$	−1.58597e58	−0.0439083
$805$	−1.07693e58	−0.0290652
$806$	−1.37016e59	−0.360498
$807$	−6.73440e58	−0.172739
$808$	3.73912e59	0.935053
$809$	−1.21835e59	−0.297049	−0.148525	−	0.988909i	$-0.547452\pi$
$809$	−1.21835e59	−0.297049	−0.148525	+	0.988909i	$0.547452\pi$
$810$	4.69912e58	0.111705
$811$	4.77973e59	1.10784	0.553919	−	0.832571i	$-0.313132\pi$
$811$	4.77973e59	1.10784	0.553919	+	0.832571i	$0.313132\pi$
$812$	5.64751e57	0.0127632
$813$	7.13355e58	0.157199
$814$	1.51837e59	0.326270
$815$	4.66231e59	0.976945
$816$	−2.76922e59	−0.565861
$817$	−1.54292e59	−0.307463
$818$	−6.24349e59	−1.21335
$819$	−1.77819e58	−0.0337022
$820$	−3.23007e57	−0.00597074
$821$	9.72831e59	1.75389	0.876946	−	0.480589i	$-0.159577\pi$
$821$	9.72831e59	1.75389	0.876946	+	0.480589i	$0.159577\pi$
$822$	7.53207e58	0.132447
$823$	2.82742e59	0.484946	0.242473	−	0.970158i	$-0.422041\pi$
$823$	2.82742e59	0.484946	0.242473	+	0.970158i	$0.422041\pi$
$824$	−1.11034e60	−1.85759
$825$	−3.97713e57	−0.00649029
$826$	3.14198e58	0.0500165
$827$	−9.08676e59	−1.41106	−0.705531	−	0.708679i	$-0.749291\pi$
$827$	−9.08676e59	−1.41106	−0.705531	+	0.708679i	$0.749291\pi$
$828$	2.91215e57	0.00441156
$829$	5.79734e59	0.856764	0.428382	−	0.903598i	$-0.359084\pi$
$829$	5.79734e59	0.856764	0.428382	+	0.903598i	$0.359084\pi$
$830$	−9.78699e58	−0.141107
$831$	1.66430e58	0.0234105
$832$	5.75437e59	0.789714
$833$	6.86463e59	0.919168
$834$	6.17791e59	0.807119
$835$	−7.03505e59	−0.896798
$836$	1.89584e58	0.0235816
$837$	6.63290e58	0.0805066
$838$	−7.26976e59	−0.861029
$839$	5.21809e59	0.603102	0.301551	−	0.953450i	$-0.402496\pi$
$839$	5.21809e59	0.603102	0.301551	+	0.953450i	$0.402496\pi$
$840$	−5.86483e58	−0.0661501
$841$	2.62857e60	2.89336
$842$	−7.14531e59	−0.767579
$843$	−1.89891e59	−0.199085
$844$	2.34311e58	0.0239757
$845$	−2.89502e59	−0.289128
$846$	6.31507e59	0.615582
$847$	1.16966e59	0.111289
$848$	−1.06320e60	−0.987412
$849$	1.84039e59	0.166841
$850$	4.41348e58	0.0390565
$851$	−3.29010e59	−0.284219
$852$	−1.49994e58	−0.0126492
$853$	−1.72551e60	−1.42057	−0.710284	−	0.703915i	$-0.751434\pi$
$853$	−1.72551e60	−1.42057	−0.710284	+	0.703915i	$0.751434\pi$
$854$	2.63771e59	0.212002
$855$	−6.62881e59	−0.520152
$856$	1.12400e60	0.861101
$857$	−6.30064e59	−0.471279	−0.235639	−	0.971841i	$-0.575718\pi$
$857$	−6.30064e59	−0.471279	−0.235639	+	0.971841i	$0.575718\pi$
$858$	1.87737e59	0.137107
$859$	−1.34196e60	−0.956929	−0.478465	−	0.878107i	$-0.658807\pi$
$859$	−1.34196e60	−0.956929	−0.478465	+	0.878107i	$0.658807\pi$
$860$	1.45787e58	0.0101508
$861$	−1.16086e58	−0.00789251
$862$	−2.13261e60	−1.41584
$863$	−8.68966e59	−0.563354	−0.281677	−	0.959509i	$-0.590891\pi$
$863$	−8.68966e59	−0.563354	−0.281677	+	0.959509i	$0.590891\pi$
$864$	3.26185e58	0.0206506
$865$	−2.69808e60	−1.66811
$866$	2.67685e60	1.61624
$867$	1.27361e59	0.0751009
$868$	4.69855e57	0.00270589
$869$	−1.14698e59	−0.0645132
$870$	2.08479e60	1.14530
$871$	2.21545e60	1.18875
$872$	−1.41566e60	−0.741942
$873$	−1.15353e60	−0.590525
$874$	−8.05948e59	−0.403017
$875$	2.51325e59	0.122764
$876$	−6.83803e58	−0.0326285
$877$	−1.21007e59	−0.0564051	−0.0282026	−	0.999602i	$-0.508978\pi$
$877$	−1.21007e59	−0.0564051	−0.0282026	+	0.999602i	$0.508978\pi$
$878$	4.18451e60	1.90549
$879$	−1.60170e60	−0.712542
$880$	6.52548e59	0.283607
$881$	4.09203e60	1.73753	0.868767	−	0.495222i	$-0.164913\pi$
$881$	4.09203e60	1.73753	0.868767	+	0.495222i	$0.164913\pi$
$882$	−8.12830e59	−0.337205
$883$	3.03135e60	1.22869	0.614343	−	0.789039i	$-0.289421\pi$
$883$	3.03135e60	1.22869	0.614343	+	0.789039i	$0.289421\pi$
$884$	−1.06191e59	−0.0420548
$885$	5.91201e59	0.228770
$886$	2.56023e60	0.968029
$887$	2.05975e59	0.0760991	0.0380496	−	0.999276i	$-0.487886\pi$
$887$	2.05975e59	0.0760991	0.0380496	+	0.999276i	$0.487886\pi$
$888$	−1.79174e60	−0.646860
$889$	−2.74391e59	−0.0968019
$890$	2.99224e60	1.03158
$891$	−9.08829e58	−0.0306189
$892$	−1.17163e59	−0.0385753
$893$	−8.90835e60	−2.86644
$894$	−2.02249e60	−0.636015
$895$	3.92184e60	1.20536
$896$	−4.30158e59	−0.129215
$897$	−4.06800e59	−0.119436
$898$	−5.71525e60	−1.64010
$899$	2.94272e60	0.825420
$900$	−2.66373e57	−0.000730329 0
$901$	−3.27014e60	−0.876412
$902$	1.22561e59	0.0321083
$903$	5.23944e58	0.0134179
$904$	3.95050e60	0.989008
$905$	1.02684e60	0.251309
$906$	3.00777e60	0.719642
$907$	−6.46152e60	−1.51142	−0.755711	−	0.654906i	$-0.772708\pi$
$907$	−6.46152e60	−1.51142	−0.755711	+	0.654906i	$0.772708\pi$
$908$	−3.86110e59	−0.0882980
$909$	−1.43512e60	−0.320871
$910$	−4.64991e59	−0.101647
$911$	2.85638e60	0.610506	0.305253	−	0.952271i	$-0.401259\pi$
$911$	2.85638e60	0.610506	0.305253	+	0.952271i	$0.401259\pi$
$912$	−4.62551e60	−0.966641
$913$	1.89284e59	0.0386779
$914$	−9.40921e60	−1.87999
$915$	4.96316e60	0.969673
$916$	1.53032e59	0.0292366
$917$	2.71100e59	0.0506475
$918$	1.00854e60	0.184255
$919$	−4.07197e60	−0.727507	−0.363753	−	0.931495i	$-0.618505\pi$
$919$	−4.07197e60	−0.727507	−0.363753	+	0.931495i	$0.618505\pi$
$920$	−1.34171e60	−0.234427
$921$	1.63712e60	0.279743
$922$	5.45255e60	0.911204
$923$	2.09528e60	0.342458
$924$	−6.43788e57	−0.00102912
$925$	3.00943e59	0.0470521
$926$	7.71859e60	1.18035
$927$	4.26164e60	0.637445
$928$	1.44714e60	0.211727
$929$	−1.03310e61	−1.47850	−0.739249	−	0.673433i	$-0.764819\pi$
$929$	−1.03310e61	−1.47850	−0.739249	+	0.673433i	$0.764819\pi$
$930$	1.73448e60	0.242811
$931$	1.14662e61	1.57018
$932$	−8.35890e58	−0.0111975
$933$	5.21347e60	0.683208
$934$	−9.15068e60	−1.17312
$935$	2.00708e60	0.251726
$936$	−2.21538e60	−0.271827
$937$	8.10591e59	0.0973061	0.0486531	−	0.998816i	$-0.484507\pi$
$937$	8.10591e59	0.0973061	0.0486531	+	0.998816i	$0.484507\pi$
$938$	−1.49049e60	−0.175053
$939$	2.42287e60	0.278410
$940$	8.41725e59	0.0946345
$941$	−1.30342e60	−0.143383	−0.0716914	−	0.997427i	$-0.522840\pi$
$941$	−1.30342e60	−0.143383	−0.0716914	+	0.997427i	$0.522840\pi$
$942$	−5.41954e60	−0.583337
$943$	−2.65572e59	−0.0279700
$944$	4.12533e60	0.425141
$945$	2.25100e59	0.0226999
$946$	−5.53168e59	−0.0545869
$947$	−1.33812e61	−1.29217	−0.646086	−	0.763265i	$-0.723595\pi$
$947$	−1.33812e61	−1.29217	−0.646086	+	0.763265i	$0.723595\pi$
$948$	−7.68200e58	−0.00725944
$949$	9.55207e60	0.883364
$950$	7.37196e59	0.0667189
$951$	5.61108e60	0.496988
$952$	−1.25873e60	−0.109113
$953$	−6.00792e59	−0.0509706	−0.0254853	−	0.999675i	$-0.508113\pi$
$953$	−6.00792e59	−0.0509706	−0.0254853	+	0.999675i	$0.508113\pi$
$954$	3.87212e60	0.321520
$955$	7.03652e60	0.571858
$956$	−7.00700e58	−0.00557372
$957$	−4.03207e60	−0.313930
$958$	8.21633e60	0.626159
$959$	3.60806e59	0.0269149
$960$	−7.28444e60	−0.531907
$961$	−1.15421e61	−0.825005
$962$	−1.42058e61	−0.993975
$963$	−4.31406e60	−0.295493
$964$	1.11219e59	0.00745763
$965$	6.42358e60	0.421665
$966$	2.73683e59	0.0175880
$967$	−1.43503e60	−0.0902854	−0.0451427	−	0.998981i	$-0.514374\pi$
$967$	−1.43503e60	−0.0902854	−0.0451427	+	0.998981i	$0.514374\pi$
$968$	1.45724e61	0.897606
$969$	−1.42270e61	−0.857976
$970$	−3.01645e61	−1.78105
$971$	6.25825e60	0.361792	0.180896	−	0.983502i	$-0.442100\pi$
$971$	6.25825e60	0.361792	0.180896	+	0.983502i	$0.442100\pi$
$972$	−6.08698e58	−0.00344543
$973$	2.95938e60	0.164017
$974$	2.48067e60	0.134620
$975$	3.72097e59	0.0197725
$976$	3.46323e61	1.80202
$977$	−2.80135e61	−1.42734	−0.713671	−	0.700481i	$-0.752969\pi$
$977$	−2.80135e61	−1.42734	−0.713671	+	0.700481i	$0.752969\pi$
$978$	−1.18484e61	−0.591172
$979$	−5.78712e60	−0.282760
$980$	−1.08341e60	−0.0518391
$981$	5.43348e60	0.254603
$982$	−4.19014e61	−1.92284
$983$	1.57447e61	0.707598	0.353799	−	0.935321i	$-0.384890\pi$
$983$	1.57447e61	0.707598	0.353799	+	0.935321i	$0.384890\pi$
$984$	−1.44627e60	−0.0636576
$985$	2.16202e61	0.932003
$986$	4.47444e61	1.88913
$987$	3.02509e60	0.125094
$988$	−1.77374e60	−0.0718409
$989$	1.19864e60	0.0475514
$990$	−2.37656e60	−0.0923478
$991$	−9.61235e60	−0.365864	−0.182932	−	0.983126i	$-0.558559\pi$
$991$	−9.61235e60	−0.365864	−0.182932	+	0.983126i	$0.558559\pi$
$992$	1.20397e60	0.0448878
$993$	2.42366e61	0.885139
$994$	−1.40964e60	−0.0504299
$995$	5.38272e61	1.88638
$996$	1.26775e59	0.00435229
$997$	−4.03169e61	−1.35593	−0.677964	−	0.735095i	$-0.737138\pi$
$997$	−4.03169e61	−1.35593	−0.677964	+	0.735095i	$0.737138\pi$
$998$	4.74223e61	1.56245
$999$	6.87696e60	0.221975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.42.a.a.1.3	✓	3
3.2	odd	2		9.42.a.a.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.a.1.3	✓	3	1.1	even	1	trivial
9.42.a.a.1.1		3	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:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+1.52221e6 q^{2} -3.48678e9 q^{3} +1.18107e11 q^{4} +2.08853e14 q^{5} -5.30763e15 q^{6} -2.54249e16 q^{7} -3.16760e18 q^{8} +1.21577e19 q^{9} +O(q^{10})\)	\(q+1.52221e6 q^{2} -3.48678e9 q^{3} +1.18107e11 q^{4} +2.08853e14 q^{5} -5.30763e15 q^{6} -2.54249e16 q^{7} -3.16760e18 q^{8} +1.21577e19 q^{9} +3.17919e20 q^{10} -6.14868e20 q^{11} -4.11814e20 q^{12} +5.75265e22 q^{13} -3.87021e22 q^{14} -7.28226e23 q^{15} -5.08147e24 q^{16} -1.56294e25 q^{17} +1.85065e25 q^{18} -2.61062e26 q^{19} +2.46671e25 q^{20} +8.86513e25 q^{21} -9.35959e26 q^{22} +2.02809e27 q^{23} +1.10447e28 q^{24} -1.85508e27 q^{25} +8.75676e28 q^{26} -4.23912e28 q^{27} -3.00287e27 q^{28} -1.88071e30 q^{29} -1.10851e30 q^{30} -1.56469e30 q^{31} -7.69466e29 q^{32} +2.14391e30 q^{33} -2.37913e31 q^{34} -5.31008e30 q^{35} +1.43591e30 q^{36} -1.62226e32 q^{37} -3.97393e32 q^{38} -2.00583e32 q^{39} -6.61563e32 q^{40} -1.30947e32 q^{41} +1.34946e32 q^{42} +5.91017e32 q^{43} -7.26203e31 q^{44} +2.53917e33 q^{45} +3.08719e33 q^{46} +3.41234e34 q^{47} +1.77180e34 q^{48} -4.39212e34 q^{49} -2.82383e33 q^{50} +5.44964e34 q^{51} +6.79430e33 q^{52} +2.09230e35 q^{53} -6.45283e34 q^{54} -1.28417e35 q^{55} +8.05359e34 q^{56} +9.10269e35 q^{57} -2.86283e36 q^{58} -8.11837e35 q^{59} -8.60088e34 q^{60} -6.81541e36 q^{61} -2.38179e36 q^{62} -3.09108e35 q^{63} +1.00030e37 q^{64} +1.20146e37 q^{65} +3.26349e36 q^{66} +3.85118e37 q^{67} -1.84595e36 q^{68} -7.07152e36 q^{69} -8.08307e36 q^{70} +3.64228e37 q^{71} -3.85106e37 q^{72} +1.66046e38 q^{73} -2.46943e38 q^{74} +6.46827e36 q^{75} -3.08334e37 q^{76} +1.56330e37 q^{77} -3.05329e38 q^{78} +1.86540e38 q^{79} -1.06128e39 q^{80} +1.47809e38 q^{81} -1.99329e38 q^{82} -3.07845e38 q^{83} +1.04704e37 q^{84} -3.26425e39 q^{85} +8.99653e38 q^{86} +6.55762e39 q^{87} +1.94765e39 q^{88} +9.41198e39 q^{89} +3.86515e39 q^{90} -1.46261e39 q^{91} +2.39532e38 q^{92} +5.45573e39 q^{93} +5.19431e40 q^{94} -5.45237e40 q^{95} +2.68296e39 q^{96} -9.48812e40 q^{97} -6.68574e40 q^{98} -7.47535e39 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 36\!\cdots\!03 q^{9}+O(q^{10}) \) 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9	\( 3 q - 289380 q^{2} - 10460353203 q^{3} - 2254266178800 q^{4} + 38650546192026 q^{5} + 10\!\cdots\!80 q^{6}+ \cdots + 26\!\cdots\!04 q^{99}+O(q^{100}) \) 3 * q - 289380 * q^2 - 10460353203 * q^3 - 2254266178800 * q^4 + 38650546192026 * q^5 + 1009005669961380 * q^6 - 44602211301408768 * q^7 + 2268032948689999296 * q^8 + 36472996377170786403 * q^9 + 303684786396357841224 * q^10 + 2162403578017276790604 * q^11 + 7860140147941716898800 * q^12 + 44715417115247213223642 * q^13 + 320671470159767900457984 * q^14 - 134766121552486207386426 * q^15 - 5459234621059712438935296 * q^16 - 10989933423479049968718714 * q^17 - 3518185230541894056433380 * q^18 + 196397070114735534584831028 * q^19 + 531636782784591447776761824 * q^20 + 155518294615858001587027968 * q^21 - 4513503674461058254096349328 * q^22 - 4665149638066794122614978584 * q^23 - 7908141906446322929993781696 * q^24 - 4609009761244207114343812899 * q^25 + 122894273592250273312332501576 * q^26 - 127173474825648610542883299603 * q^27 - 599824891534617466777136050176 * q^28 - 941555486655490244273102003214 * q^29 - 1058883376027837523993877946824 * q^30 - 6480085319036017864686465368808 * q^31 - 9194142460916956643740243289088 * q^32 - 7539835064497227221977370568204 * q^33 - 50410977973081452147630100226760 * q^34 - 153374925211463555312750388019200 * q^35 - 27406614057517010739893935618800 * q^36 - 442820255707228186224391784737998 * q^37 - 832008681100278182323288015176048 * q^38 - 155913018881652402326915850008442 * q^39 - 830400317719830554628641188275072 * q^40 - 438132779830146983268076758934098 * q^41 - 1118112279998815693097419367107584 * q^42 - 1310999240696843410630649721463476 * q^43 - 1443247128257998435455229084014528 * q^44 + 469900410412478810682641155940826 * q^45 + 7997471516728167525889026089716512 * q^46 + 64523854533555761088559286850643968 * q^47 + 19035174118110151421625255141117696 * q^48 + 171140726678012788361144930683431723 * q^49 + 28333303327284754376413888152266724 * q^50 + 38319528429015278581227949931980314 * q^51 - 20984793566307791589805690265685024 * q^52 + 34693992770270063328682081068689946 * q^53 + 12267153381682064972966523079705380 * q^54 + 100035221507232528994896069839569896 * q^55 - 568132015233041377672136741101977600 * q^56 - 684794240478163142230784839651194228 * q^57 - 2740694640626009342372591817401518296 * q^58 - 4582685445865314260503003260089664948 * q^59 - 1853702841211138803266019258215507424 * q^60 - 8693740159306202291599355552752714662 * q^61 + 265004064722629998116825545352842464 * q^62 - 542258763736695967164682362773127168 * q^63 + 16981741764860889983034117450588819456 * q^64 + 2721360738989032295650621165564283148 * q^65 + 15737614205967000002335445187917232528 * q^66 + 32867814173503669322418795877934200116 * q^67 + 33261671085355608094778443956314848800 * q^68 + 16266370986342093542812388655640268184 * q^69 + 98543364272473044599951459881688524800 * q^70 + 149748844745311390685366673232301225496 * q^71 + 27573985840291440136110933044612124096 * q^72 + 6619123649433674932122580558210670046 * q^73 + 14490759310413784046620539770501448744 * q^74 + 16070623339563035717907230167095788499 * q^75 - 536779250932404614788199202699778310208 * q^76 - 954944421253262491346753072408971247616 * q^77 - 428505836133684487473427567420504715976 * q^78 - 1112771209183156752666617542198723627800 * q^79 - 2423764999311265237507278994973679346176 * q^80 + 443426488243037769948249630619149892803 * q^81 - 107939940778839787676218322470600048296 * q^82 - 1187635824307222104653182519688468749260 * q^83 + 2091460075134421134660653723208430104576 * q^84 + 6153092316082135211652182465439269196852 * q^85 + 2889811785377479896729751911427106623344 * q^86 + 3283000983546327044739131648688427064814 * q^87 + 11348012623814378178834124633898985613056 * q^88 - 2907470395792485617492963651915834875602 * q^89 + 3692098038012081220424316844483830692424 * q^90 + 19747616149564653802226421926044582182912 * q^91 + 10266693573432860781998326486887076136832 * q^92 + 22594660407563895447746096203786446364008 * q^93 + 34628213999509804914437049475497096849408 * q^94 - 84590150972982168777889232049326900017896 * q^95 + 32057992513296996581786794596336971916288 * q^96 - 52479807025249236413871256717456940920314 * q^97 - 268218382984038433881798894561914095373892 * q^98 + 26289779289001760785343260072210213785804 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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