LMFDB - Embedded newform 3.34.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,34,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, 34, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 34 $
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:	$20.6948486643$
Analytic rank:	$0$
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} - 35900150x + 10469144400 $ x^3 - x^2 - 35900150*x + 10469144400
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6}\cdot 5\cdot 7\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$292.312$ 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)

$f(q)$	$=$	$q+133892. q^{2} +4.30467e7 q^{3} +9.33705e9 q^{4} +2.11239e11 q^{5} +5.76360e12 q^{6} +5.07411e13 q^{7} +1.00033e14 q^{8} +1.85302e15 q^{9} +O(q^{10})$	\(q+133892. q^{2} +4.30467e7 q^{3} +9.33705e9 q^{4} +2.11239e11 q^{5} +5.76360e12 q^{6} +5.07411e13 q^{7} +1.00033e14 q^{8} +1.85302e15 q^{9} +2.82832e16 q^{10} +1.28666e17 q^{11} +4.01929e17 q^{12} +2.10827e18 q^{13} +6.79381e18 q^{14} +9.09316e18 q^{15} -6.68111e19 q^{16} -3.77843e20 q^{17} +2.48104e20 q^{18} +1.88735e21 q^{19} +1.97235e21 q^{20} +2.18424e21 q^{21} +1.72273e22 q^{22} +3.37815e22 q^{23} +4.30608e21 q^{24} -7.17933e22 q^{25} +2.82280e23 q^{26} +7.97664e22 q^{27} +4.73772e23 q^{28} +1.12019e24 q^{29} +1.21750e24 q^{30} -3.33906e24 q^{31} -9.80473e24 q^{32} +5.53866e24 q^{33} -5.05900e25 q^{34} +1.07185e25 q^{35} +1.73017e25 q^{36} -7.98655e25 q^{37} +2.52700e26 q^{38} +9.07540e25 q^{39} +2.11308e25 q^{40} -3.19623e26 q^{41} +2.92451e26 q^{42} -5.95015e26 q^{43} +1.20136e27 q^{44} +3.91431e26 q^{45} +4.52306e27 q^{46} -3.19407e27 q^{47} -2.87600e27 q^{48} -5.15634e27 q^{49} -9.61253e27 q^{50} -1.62649e28 q^{51} +1.96850e28 q^{52} -2.72657e28 q^{53} +1.06801e28 q^{54} +2.71793e28 q^{55} +5.07577e27 q^{56} +8.12441e28 q^{57} +1.49985e29 q^{58} +1.14251e29 q^{59} +8.49033e28 q^{60} -3.38193e29 q^{61} -4.47072e29 q^{62} +9.40242e28 q^{63} -7.38868e29 q^{64} +4.45349e29 q^{65} +7.41580e29 q^{66} +7.65727e29 q^{67} -3.52793e30 q^{68} +1.45418e30 q^{69} +1.43512e30 q^{70} -3.08052e30 q^{71} +1.85363e29 q^{72} +7.89884e30 q^{73} -1.06933e31 q^{74} -3.09047e30 q^{75} +1.76223e31 q^{76} +6.52866e30 q^{77} +1.21512e31 q^{78} +1.70954e31 q^{79} -1.41131e31 q^{80} +3.43368e30 q^{81} -4.27948e31 q^{82} -6.36922e31 q^{83} +2.03943e31 q^{84} -7.98152e31 q^{85} -7.96676e31 q^{86} +4.82207e31 q^{87} +1.28708e31 q^{88} +2.03754e32 q^{89} +5.24093e31 q^{90} +1.06976e32 q^{91} +3.15420e32 q^{92} -1.43736e32 q^{93} -4.27659e32 q^{94} +3.98682e32 q^{95} -4.22061e32 q^{96} +8.71102e32 q^{97} -6.90391e32 q^{98} +2.38421e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 41202 q^{2} + 129140163 q^{3} - 1107467772 q^{4} + 51261823890 q^{5} + 1773610998642 q^{6} + 76113734015256 q^{7} + 11\!\cdots\!92 q^{8}+ \cdots + 55\!\cdots\!23 q^{9}+O(q^{10}) $ 3 * q + 41202 * q^2 + 129140163 * q^3 - 1107467772 * q^4 + 51261823890 * q^5 + 1773610998642 * q^6 + 76113734015256 * q^7 + 1154149348489992 * q^8 + 5559060566555523 * q^9	$ 3 q + 41202 q^{2} + 129140163 q^{3} - 1107467772 q^{4} + 51261823890 q^{5} + 1773610998642 q^{6} + 76113734015256 q^{7} + 11\!\cdots\!92 q^{8}+ \cdots - 19\!\cdots\!80 q^{99}+O(q^{100}) $ 3 * q + 41202 * q^2 + 129140163 * q^3 - 1107467772 * q^4 + 51261823890 * q^5 + 1773610998642 * q^6 + 76113734015256 * q^7 + 1154149348489992 * q^8 + 5559060566555523 * q^9 - 6066746915652180 * q^10 - 103523748885455580 * q^11 - 47672856197775612 * q^12 + 1915412601357848490 * q^13 + 8843223974387917968 * q^14 + 2206653430943964690 * q^15 - 49163291855293757424 * q^16 - 16951254031996646346 * q^17 + 76348137821073552882 * q^18 + 2630380764132092623164 * q^19 + 6678893290406160608280 * q^20 + 3276446672422934775576 * q^21 + 25675959809490476752728 * q^22 + 79533787326189199888968 * q^23 + 49682344996780456916232 * q^24 + 423122978202020785717725 * q^25 + 515897524308539260240956 * q^26 + 239299329230617529590083 * q^27 + 42316840140910701529632 * q^28 + 1172400205292105207396058 * q^29 - 261153561855689925501780 * q^30 - 1730146178193885575522976 * q^31 - 15373118219420180766165984 * q^32 - 4456357935146267310153180 * q^33 - 72740605403522266308053244 * q^34 - 46524388137754256582413680 * q^35 - 2052160140018767590368252 * q^36 + 23072071636478902337811186 * q^37 + 123166602227885110273091304 * q^38 + 82452231850535525109301290 * q^39 + 334261243758638084780401200 * q^40 + 427548398123528287702034814 * q^41 + 380671795165987850539382928 * q^42 + 931650906163677813302061444 * q^43 + 2628232920146985471809839152 * q^44 + 94989194585537614644281490 * q^45 + 1576684767863897418449809584 * q^46 - 8758003298318968412560605552 * q^47 - 2116318507936402748872606704 * q^48 - 16032483885040282346174924373 * q^49 - 25868038199816062069548246450 * q^50 - 729695902915484708191931466 * q^51 - 133394982794577721290532296 * q^52 - 11892082156717187440623348702 * q^53 + 3286536987653301151390199922 * q^54 + 85333548015142237994905073880 * q^55 - 12245006589032410415460987840 * q^56 + 113229266877360998295498845244 * q^57 + 235922229903297044437282825308 * q^58 + 129677501466859357385715960756 * q^59 + 287504456060885972385819449880 * q^60 + 361088280985963126642141896762 * q^61 - 802944337692828230733430911168 * q^62 + 141040285779168467285417686296 * q^63 - 610917178484121070749024145344 * q^64 - 3385479539558515212808386273540 * q^65 + 1105265878326349704931668204888 * q^66 - 15812977239651397801356345396 * q^67 - 4909744547418540815627091775416 * q^68 + 3423668753103802480833636473928 * q^69 + 3300211942819681129760102456160 * q^70 - 6651937250528040326415493209384 * q^71 + 2138662043702154227125559275272 * q^72 + 17518600058904527629736361597918 * q^73 - 16487357564767645293733531370772 * q^74 + 18214056791351470398991692829725 * q^75 + 22556505117012105673290504564816 * q^76 + 526258013649190142100618876192 * q^77 + 22207696793500407453138825705276 * q^78 + 47039564834071071994823399481840 * q^79 - 89208987985140435656381122400160 * q^80 + 10301051460877537453973547267843 * q^81 - 83830191778687263739261116864588 * q^82 - 109771167143400749356291310773764 * q^83 + 1821601211147383654660341936672 * q^84 - 15809846025180808515314622875580 * q^85 - 130145119975743665925790272902760 * q^86 + 50467984537551976365425245225818 * q^87 - 87502984757959105129975772457888 * q^88 + 281720374074160857951628988116494 * q^89 - 11241804515358126485585908663380 * q^90 + 401563251462740776922902836239184 * q^91 + 153050732902924794873793215390816 * q^92 - 74477119821928476275461976961696 * q^93 - 349459814745766324819266344330400 * q^94 + 1967204571038464419732100554685800 * q^95 - 661762330891397303210713352938464 * q^96 + 816496586052591264484966840489254 * q^97 - 104502643082987555680827083473950 * q^98 - 191831596710377463091584406722780 * 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 $

$2$	133892.	1.44464	0.722318	−	0.691561i	$-0.243077\pi$
$2$	133892.	1.44464	0.722318	+	0.691561i	$0.243077\pi$
$3$	4.30467e7	0.577350
$3$	4.30467e7	0.577350
$4$	9.33705e9	1.08698
$5$	2.11239e11	0.619112	0.309556	−	0.950881i	$-0.399820\pi$
$5$	2.11239e11	0.619112	0.309556	+	0.950881i	$0.399820\pi$
$6$	5.76360e12	0.834062
$7$	5.07411e13	0.577088	0.288544	−	0.957467i	$-0.406829\pi$
$7$	5.07411e13	0.577088	0.288544	+	0.957467i	$0.406829\pi$
$8$	1.00033e14	0.125648
$9$	1.85302e15	0.333333
$10$	2.82832e16	0.894393
$11$	1.28666e17	0.844277	0.422139	−	0.906531i	$-0.361280\pi$
$11$	1.28666e17	0.844277	0.422139	+	0.906531i	$0.361280\pi$
$12$	4.01929e17	0.627566
$13$	2.10827e18	0.878740	0.439370	−	0.898306i	$-0.355202\pi$
$13$	2.10827e18	0.878740	0.439370	+	0.898306i	$0.355202\pi$
$14$	6.79381e18	0.833683
$15$	9.09316e18	0.357445
$16$	−6.68111e19	−0.905459
$17$	−3.77843e20	−1.88323	−0.941616	−	0.336690i	$-0.890693\pi$
$17$	−3.77843e20	−1.88323	−0.941616	+	0.336690i	$0.890693\pi$
$18$	2.48104e20	0.481546
$19$	1.88735e21	1.50113	0.750563	−	0.660799i	$-0.229782\pi$
$19$	1.88735e21	1.50113	0.750563	+	0.660799i	$0.229782\pi$
$20$	1.97235e21	0.672960
$21$	2.18424e21	0.333182
$22$	1.72273e22	1.21967
$23$	3.37815e22	1.14860	0.574301	−	0.818644i	$-0.305274\pi$
$23$	3.37815e22	1.14860	0.574301	+	0.818644i	$0.305274\pi$
$24$	4.30608e21	0.0725432
$25$	−7.17933e22	−0.616700
$26$	2.82280e23	1.26946
$27$	7.97664e22	0.192450
$28$	4.73772e23	0.627281
$29$	1.12019e24	0.831239	0.415620	−	0.909539i	$-0.363565\pi$
$29$	1.12019e24	0.831239	0.415620	+	0.909539i	$0.363565\pi$
$30$	1.21750e24	0.516378
$31$	−3.33906e24	−0.824435	−0.412217	−	0.911086i	$-0.635246\pi$
$31$	−3.33906e24	−0.824435	−0.412217	+	0.911086i	$0.635246\pi$
$32$	−9.80473e24	−1.43371
$33$	5.53866e24	0.487444
$34$	−5.05900e25	−2.72059
$35$	1.07185e25	0.357282
$36$	1.73017e25	0.362325
$37$	−7.98655e25	−1.06422	−0.532109	−	0.846676i	$-0.678600\pi$
$37$	−7.98655e25	−1.06422	−0.532109	+	0.846676i	$0.678600\pi$
$38$	2.52700e26	2.16858
$39$	9.07540e25	0.507341
$40$	2.11308e25	0.0777905
$41$	−3.19623e26	−0.782896	−0.391448	−	0.920200i	$-0.628026\pi$
$41$	−3.19623e26	−0.782896	−0.391448	+	0.920200i	$0.628026\pi$
$42$	2.92451e26	0.481327
$43$	−5.95015e26	−0.664199	−0.332100	−	0.943244i	$-0.607757\pi$
$43$	−5.95015e26	−0.664199	−0.332100	+	0.943244i	$0.607757\pi$
$44$	1.20136e27	0.917709
$45$	3.91431e26	0.206371
$46$	4.52306e27	1.65931
$47$	−3.19407e27	−0.821731	−0.410866	−	0.911696i	$-0.634773\pi$
$47$	−3.19407e27	−0.821731	−0.410866	+	0.911696i	$0.634773\pi$
$48$	−2.87600e27	−0.522767
$49$	−5.15634e27	−0.666969
$50$	−9.61253e27	−0.890907
$51$	−1.62649e28	−1.08728
$52$	1.96850e28	0.955169
$53$	−2.72657e28	−0.966197	−0.483098	−	0.875566i	$-0.660489\pi$
$53$	−2.72657e28	−0.966197	−0.483098	+	0.875566i	$0.660489\pi$
$54$	1.06801e28	0.278021
$55$	2.71793e28	0.522702
$56$	5.07577e27	0.0725102
$57$	8.12441e28	0.866676
$58$	1.49985e29	1.20084
$59$	1.14251e29	0.689923	0.344962	−	0.938617i	$-0.387892\pi$
$59$	1.14251e29	0.689923	0.344962	+	0.938617i	$0.387892\pi$
$60$	8.49033e28	0.388534
$61$	−3.38193e29	−1.17821	−0.589105	−	0.808056i	$-0.700520\pi$
$61$	−3.38193e29	−1.17821	−0.589105	+	0.808056i	$0.700520\pi$
$62$	−4.47072e29	−1.19101
$63$	9.40242e28	0.192363
$64$	−7.38868e29	−1.16573
$65$	4.45349e29	0.544039
$66$	7.41580e29	0.704179
$67$	7.65727e29	0.567335	0.283668	−	0.958923i	$-0.408449\pi$
$67$	7.65727e29	0.567335	0.283668	+	0.958923i	$0.408449\pi$
$68$	−3.52793e30	−2.04703
$69$	1.45418e30	0.663146
$70$	1.43512e30	0.516143
$71$	−3.08052e30	−0.876720	−0.438360	−	0.898799i	$-0.644441\pi$
$71$	−3.08052e30	−0.876720	−0.438360	+	0.898799i	$0.644441\pi$
$72$	1.85363e29	0.0418828
$73$	7.89884e30	1.42146	0.710732	−	0.703463i	$-0.248364\pi$
$73$	7.89884e30	1.42146	0.710732	+	0.703463i	$0.248364\pi$
$74$	−1.06933e31	−1.53741
$75$	−3.09047e30	−0.356052
$76$	1.76223e31	1.63169
$77$	6.52866e30	0.487222
$78$	1.21512e31	0.732923
$79$	1.70954e31	0.835665	0.417832	−	0.908524i	$-0.362790\pi$
$79$	1.70954e31	0.835665	0.417832	+	0.908524i	$0.362790\pi$
$80$	−1.41131e31	−0.560581
$81$	3.43368e30	0.111111
$82$	−4.27948e31	−1.13100
$83$	−6.36922e31	−1.37815	−0.689077	−	0.724688i	$-0.741984\pi$
$83$	−6.36922e31	−1.37815	−0.689077	+	0.724688i	$0.741984\pi$
$84$	2.03943e31	0.362161
$85$	−7.98152e31	−1.16593
$86$	−7.96676e31	−0.959527
$87$	4.82207e31	0.479916
$88$	1.28708e31	0.106082
$89$	2.03754e32	1.39371	0.696853	−	0.717214i	$-0.254583\pi$
$89$	2.03754e32	1.39371	0.696853	+	0.717214i	$0.254583\pi$
$90$	5.24093e31	0.298131
$91$	1.06976e32	0.507110
$92$	3.15420e32	1.24850
$93$	−1.43736e32	−0.475988
$94$	−4.27659e32	−1.18710
$95$	3.98682e32	0.929366
$96$	−4.22061e32	−0.827752
$97$	8.71102e32	1.43991	0.719955	−	0.694020i	$-0.244162\pi$
$97$	8.71102e32	1.43991	0.719955	+	0.694020i	$0.244162\pi$
$98$	−6.90391e32	−0.963529
$99$	2.38421e32	0.281426
$100$	−6.70338e32	−0.670338
$101$	1.56455e32	0.132766	0.0663828	−	0.997794i	$-0.478854\pi$
$101$	1.56455e32	0.132766	0.0663828	+	0.997794i	$0.478854\pi$
$102$	−2.17773e33	−1.57073
$103$	1.68985e33	1.03761	0.518804	−	0.854893i	$-0.326377\pi$
$103$	1.68985e33	1.03761	0.518804	+	0.854893i	$0.326377\pi$
$104$	2.10896e32	0.110412
$105$	4.61397e32	0.206277
$106$	−3.65066e33	−1.39580
$107$	3.74884e33	1.22762	0.613811	−	0.789453i	$-0.289636\pi$
$107$	3.74884e33	1.22762	0.613811	+	0.789453i	$0.289636\pi$
$108$	7.44783e32	0.209189
$109$	−4.06931e33	−0.981710	−0.490855	−	0.871241i	$-0.663315\pi$
$109$	−4.06931e33	−0.981710	−0.490855	+	0.871241i	$0.663315\pi$
$110$	3.63909e33	0.755115
$111$	−3.43795e33	−0.614426
$112$	−3.39007e33	−0.522530
$113$	−8.91272e32	−0.118636	−0.0593179	−	0.998239i	$-0.518893\pi$
$113$	−8.91272e32	−0.118636	−0.0593179	+	0.998239i	$0.518893\pi$
$114$	1.08779e34	1.25203
$115$	7.13598e33	0.711114
$116$	1.04593e34	0.903537
$117$	3.90666e33	0.292913
$118$	1.52972e34	0.996688
$119$	−1.91721e34	−1.08679
$120$	9.09613e32	0.0449124
$121$	−6.67018e33	−0.287196
$122$	−4.52813e34	−1.70209
$123$	−1.37587e34	−0.452005
$124$	−3.11770e34	−0.896141
$125$	−3.97570e34	−1.00092
$126$	1.25891e34	0.277894
$127$	8.42089e34	1.63154	0.815768	−	0.578379i	$-0.196315\pi$
$127$	8.42089e34	1.63154	0.815768	+	0.578379i	$0.196315\pi$
$128$	−1.47064e34	−0.250346
$129$	−2.56134e34	−0.383476
$130$	5.96285e34	0.785939
$131$	4.08668e32	0.00474673	0.00237337	−	0.999997i	$-0.499245\pi$
$131$	4.08668e32	0.00474673	0.00237337	+	0.999997i	$0.499245\pi$
$132$	5.17147e34	0.529839
$133$	9.57660e34	0.866282
$134$	1.02524e35	0.819593
$135$	1.68498e34	0.119148
$136$	−3.77966e34	−0.236625
$137$	−1.67972e35	−0.931852	−0.465926	−	0.884824i	$-0.654279\pi$
$137$	−1.67972e35	−0.931852	−0.465926	+	0.884824i	$0.654279\pi$
$138$	1.94703e35	0.958005
$139$	−3.56236e35	−1.55594	−0.777972	−	0.628299i	$-0.783752\pi$
$139$	−3.56236e35	−1.55594	−0.777972	+	0.628299i	$0.783752\pi$
$140$	1.00079e35	0.388357
$141$	−1.37494e35	−0.474427
$142$	−4.12456e35	−1.26654
$143$	2.71263e35	0.741900
$144$	−1.23802e35	−0.301820
$145$	2.36629e35	0.514631
$146$	1.05759e36	2.05350
$147$	−2.21963e35	−0.385075
$148$	−7.45708e35	−1.15678
$149$	−9.09973e35	−1.26315	−0.631575	−	0.775315i	$-0.717591\pi$
$149$	−9.09973e35	−1.26315	−0.631575	+	0.775315i	$0.717591\pi$
$150$	−4.13788e35	−0.514366
$151$	6.64477e35	0.740219	0.370110	−	0.928988i	$-0.379320\pi$
$151$	6.64477e35	0.740219	0.370110	+	0.928988i	$0.379320\pi$
$152$	1.88796e35	0.188614
$153$	−7.00150e35	−0.627744
$154$	8.74133e35	0.703859
$155$	−7.05341e35	−0.510418
$156$	8.47375e35	0.551467
$157$	1.61643e36	0.946699	0.473350	−	0.880875i	$-0.343045\pi$
$157$	1.61643e36	0.946699	0.473350	+	0.880875i	$0.343045\pi$
$158$	2.28893e36	1.20723
$159$	−1.17370e36	−0.557834
$160$	−2.07114e36	−0.887627
$161$	1.71411e36	0.662845
$162$	4.59742e35	0.160515
$163$	4.95505e36	1.56298	0.781488	−	0.623920i	$-0.214461\pi$
$163$	4.95505e36	1.56298	0.781488	+	0.623920i	$0.214461\pi$
$164$	−2.98433e36	−0.850989
$165$	1.16998e36	0.301782
$166$	−8.52785e36	−1.99093
$167$	9.75378e35	0.206230	0.103115	−	0.994669i	$-0.467119\pi$
$167$	9.75378e35	0.206230	0.103115	+	0.994669i	$0.467119\pi$
$168$	2.18495e35	0.0418638
$169$	−1.31134e36	−0.227816
$170$	−1.06866e37	−1.68435
$171$	3.49729e36	0.500375
$172$	−5.55569e36	−0.721969
$173$	3.61074e35	0.0426418	0.0213209	−	0.999773i	$-0.493213\pi$
$173$	3.61074e35	0.0426418	0.0213209	+	0.999773i	$0.493213\pi$
$174$	6.45634e36	0.693305
$175$	−3.64287e36	−0.355890
$176$	−8.59633e36	−0.764459
$177$	4.91812e36	0.398327
$178$	2.72810e37	2.01340
$179$	5.03498e36	0.338784	0.169392	−	0.985549i	$-0.445820\pi$
$179$	5.03498e36	0.338784	0.169392	+	0.985549i	$0.445820\pi$
$180$	3.65481e36	0.224320
$181$	2.77751e37	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$181$	2.77751e37	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$182$	1.43232e37	0.732590
$183$	−1.45581e37	−0.680240
$184$	3.37926e36	0.144320
$185$	−1.68707e37	−0.658871
$186$	−1.92450e37	−0.687629
$187$	−4.86155e37	−1.58997
$188$	−2.98232e37	−0.893202
$189$	4.04744e36	0.111061
$190$	5.33802e37	1.34260
$191$	−8.30582e36	−0.191572	−0.0957859	−	0.995402i	$-0.530536\pi$
$191$	−8.30582e36	−0.191572	−0.0957859	+	0.995402i	$0.530536\pi$
$192$	−3.18059e37	−0.673034
$193$	−4.49959e37	−0.873932	−0.436966	−	0.899478i	$-0.643947\pi$
$193$	−4.49959e37	−0.873932	−0.436966	+	0.899478i	$0.643947\pi$
$194$	1.16633e38	2.08015
$195$	1.91708e37	0.314101
$196$	−4.81450e37	−0.724980
$197$	−1.87245e37	−0.259250	−0.129625	−	0.991563i	$-0.541377\pi$
$197$	−1.87245e37	−0.259250	−0.129625	+	0.991563i	$0.541377\pi$
$198$	3.19226e37	0.406558
$199$	−8.00618e37	−0.938317	−0.469159	−	0.883114i	$-0.655443\pi$
$199$	−8.00618e37	−0.938317	−0.469159	+	0.883114i	$0.655443\pi$
$200$	−7.18168e36	−0.0774874
$201$	3.29620e37	0.327551
$202$	2.09480e37	0.191798
$203$	5.68398e37	0.479698
$204$	−1.51866e38	−1.18185
$205$	−6.75169e37	−0.484701
$206$	2.26257e38	1.49897
$207$	6.25978e37	0.382867
$208$	−1.40856e38	−0.795663
$209$	2.42838e38	1.26737
$210$	6.17772e37	0.297995
$211$	1.62623e38	0.725308	0.362654	−	0.931924i	$-0.381871\pi$
$211$	1.62623e38	0.725308	0.362654	+	0.931924i	$0.381871\pi$
$212$	−2.54582e38	−1.05023
$213$	−1.32606e38	−0.506175
$214$	5.01938e38	1.77347
$215$	−1.25691e38	−0.411214
$216$	7.97925e36	0.0241811
$217$	−1.69428e38	−0.475771
$218$	−5.44846e38	−1.41821
$219$	3.40019e38	0.820683
$220$	2.53775e38	0.568165
$221$	−7.96593e38	−1.65487
$222$	−4.60312e38	−0.887623
$223$	−1.70871e38	−0.305941	−0.152971	−	0.988231i	$-0.548884\pi$
$223$	−1.70871e38	−0.305941	−0.152971	+	0.988231i	$0.548884\pi$
$224$	−4.97502e38	−0.827376
$225$	−1.33034e38	−0.205567
$226$	−1.19334e38	−0.171386
$227$	2.91898e38	0.389767	0.194884	−	0.980826i	$-0.437567\pi$
$227$	2.91898e38	0.389767	0.194884	+	0.980826i	$0.437567\pi$
$228$	7.58580e38	0.942056
$229$	9.12257e38	1.05398	0.526989	−	0.849872i	$-0.323321\pi$
$229$	9.12257e38	1.05398	0.526989	+	0.849872i	$0.323321\pi$
$230$	9.55449e38	1.02730
$231$	2.81037e38	0.281298
$232$	1.12056e38	0.104444
$233$	4.65481e38	0.404138	0.202069	−	0.979371i	$-0.435233\pi$
$233$	4.65481e38	0.404138	0.202069	+	0.979371i	$0.435233\pi$
$234$	5.23070e38	0.423153
$235$	−6.74713e38	−0.508744
$236$	1.06676e39	0.749930
$237$	7.35900e38	0.482471
$238$	−2.56699e39	−1.57002
$239$	−5.50749e38	−0.314332	−0.157166	−	0.987572i	$-0.550236\pi$
$239$	−5.50749e38	−0.314332	−0.157166	+	0.987572i	$0.550236\pi$
$240$	−6.07524e38	−0.323652
$241$	2.21345e39	1.10101	0.550503	−	0.834833i	$-0.314436\pi$
$241$	2.21345e39	1.10101	0.550503	+	0.834833i	$0.314436\pi$
$242$	−8.93081e38	−0.414894
$243$	1.47809e38	0.0641500
$244$	−3.15773e39	−1.28069
$245$	−1.08922e39	−0.412929
$246$	−1.84218e39	−0.652983
$247$	3.97903e39	1.31910
$248$	−3.34015e38	−0.103589
$249$	−2.74174e39	−0.795677
$250$	−5.32314e39	−1.44596
$251$	−7.60543e38	−0.193423	−0.0967113	−	0.995312i	$-0.530832\pi$
$251$	−7.60543e38	−0.193423	−0.0967113	+	0.995312i	$0.530832\pi$
$252$	8.77909e38	0.209094
$253$	4.34654e39	0.969739
$254$	1.12749e40	2.35698
$255$	−3.43578e39	−0.673151
$256$	4.37777e39	0.804069
$257$	−3.77129e38	−0.0649521	−0.0324760	−	0.999473i	$-0.510339\pi$
$257$	−3.77129e38	−0.0649521	−0.0324760	+	0.999473i	$0.510339\pi$
$258$	−3.42943e39	−0.553983
$259$	−4.05246e39	−0.614147
$260$	4.15825e39	0.591357
$261$	2.07574e39	0.277080
$262$	5.47173e37	0.00685730
$263$	−1.24860e40	−1.46944	−0.734722	−	0.678368i	$-0.762687\pi$
$263$	−1.24860e40	−1.46944	−0.734722	+	0.678368i	$0.762687\pi$
$264$	5.54047e38	0.0612465
$265$	−5.75960e39	−0.598185
$266$	1.28223e40	1.25146
$267$	8.77094e39	0.804656
$268$	7.14963e39	0.616680
$269$	−1.86286e40	−1.51101	−0.755503	−	0.655145i	$-0.772608\pi$
$269$	−1.86286e40	−1.51101	−0.755503	+	0.655145i	$0.772608\pi$
$270$	2.25605e39	0.172126
$271$	8.36782e39	0.600647	0.300323	−	0.953837i	$-0.402905\pi$
$271$	8.36782e39	0.600647	0.300323	+	0.953837i	$0.402905\pi$
$272$	2.52441e40	1.70519
$273$	4.60496e39	0.292780
$274$	−2.24900e40	−1.34619
$275$	−9.23737e39	−0.520665
$276$	1.35778e40	0.720824
$277$	−7.36738e39	−0.368466	−0.184233	−	0.982883i	$-0.558980\pi$
$277$	−7.36738e39	−0.368466	−0.184233	+	0.982883i	$0.558980\pi$
$278$	−4.76971e40	−2.24777
$279$	−6.18735e39	−0.274812
$280$	1.07220e39	0.0448920
$281$	2.17290e40	0.857799	0.428899	−	0.903352i	$-0.358902\pi$
$281$	2.17290e40	0.857799	0.428899	+	0.903352i	$0.358902\pi$
$282$	−1.84093e40	−0.685374
$283$	−3.48750e40	−1.22472	−0.612362	−	0.790577i	$-0.709781\pi$
$283$	−3.48750e40	−1.22472	−0.612362	+	0.790577i	$0.709781\pi$
$284$	−2.87630e40	−0.952974
$285$	1.71619e40	0.536570
$286$	3.63198e40	1.07178
$287$	−1.62180e40	−0.451800
$288$	−1.81684e40	−0.477903
$289$	1.02510e41	2.54656
$290$	3.16826e40	0.743454
$291$	3.74981e40	0.831333
$292$	7.37518e40	1.54510
$293$	−4.11914e40	−0.815625	−0.407813	−	0.913066i	$-0.633708\pi$
$293$	−4.11914e40	−0.815625	−0.407813	+	0.913066i	$0.633708\pi$
$294$	−2.97191e40	−0.556294
$295$	2.41342e40	0.427140
$296$	−7.98916e39	−0.133717
$297$	1.02632e40	0.162481
$298$	−1.21838e41	−1.82479
$299$	7.12205e40	1.00932
$300$	−2.88558e40	−0.387020
$301$	−3.01917e40	−0.383301
$302$	8.89679e40	1.06935
$303$	6.73485e39	0.0766522
$304$	−1.26096e41	−1.35921
$305$	−7.14397e40	−0.729445
$306$	−9.37442e40	−0.906862
$307$	−7.43649e40	−0.681686	−0.340843	−	0.940120i	$-0.610713\pi$
$307$	−7.43649e40	−0.681686	−0.340843	+	0.940120i	$0.610713\pi$
$308$	6.09584e40	0.529599
$309$	7.27424e40	0.599063
$310$	−9.44392e40	−0.737368
$311$	−1.87725e40	−0.138988	−0.0694939	−	0.997582i	$-0.522138\pi$
$311$	−1.87725e40	−0.138988	−0.0694939	+	0.997582i	$0.522138\pi$
$312$	9.07837e39	0.0637466
$313$	−1.40866e41	−0.938265	−0.469133	−	0.883128i	$-0.655433\pi$
$313$	−1.40866e41	−0.938265	−0.469133	+	0.883128i	$0.655433\pi$
$314$	2.16426e41	1.36764
$315$	1.98616e40	0.119094
$316$	1.59621e41	0.908347
$317$	3.03770e41	1.64084	0.820421	−	0.571761i	$-0.193739\pi$
$317$	3.03770e41	1.64084	0.820421	+	0.571761i	$0.193739\pi$
$318$	−1.57149e41	−0.805868
$319$	1.44131e41	0.701796
$320$	−1.56078e41	−0.721717
$321$	1.61375e41	0.708767
$322$	2.29505e41	0.957570
$323$	−7.13120e41	−2.82697
$324$	3.20605e40	0.120775
$325$	−1.51359e41	−0.541919
$326$	6.63440e41	2.25793
$327$	−1.75170e41	−0.566790
$328$	−3.19727e40	−0.0983697
$329$	−1.62071e41	−0.474211
$330$	1.56651e41	0.435966
$331$	4.31930e41	1.14354	0.571770	−	0.820414i	$-0.306257\pi$
$331$	4.31930e41	1.14354	0.571770	+	0.820414i	$0.306257\pi$
$332$	−5.94697e41	−1.49802
$333$	−1.47992e41	−0.354739
$334$	1.30595e41	0.297927
$335$	1.61752e41	0.351244
$336$	−1.45931e41	−0.301683
$337$	7.02963e41	1.38369	0.691845	−	0.722046i	$-0.256798\pi$
$337$	7.02963e41	1.38369	0.691845	+	0.722046i	$0.256798\pi$
$338$	−1.75577e41	−0.329111
$339$	−3.83663e40	−0.0684944
$340$	−7.45238e41	−1.26734
$341$	−4.29624e41	−0.696051
$342$	4.68258e41	0.722861
$343$	−6.53917e41	−0.961988
$344$	−5.95210e40	−0.0834556
$345$	3.07181e41	0.410562
$346$	4.83448e40	0.0616019
$347$	−9.44052e41	−1.14699	−0.573495	−	0.819209i	$-0.694413\pi$
$347$	−9.44052e41	−1.14699	−0.573495	+	0.819209i	$0.694413\pi$
$348$	4.50239e41	0.521657
$349$	5.66950e41	0.626506	0.313253	−	0.949670i	$-0.398581\pi$
$349$	5.66950e41	0.626506	0.313253	+	0.949670i	$0.398581\pi$
$350$	−4.87750e41	−0.514132
$351$	1.68169e41	0.169114
$352$	−1.26154e42	−1.21045
$353$	1.43677e42	1.31554	0.657770	−	0.753219i	$-0.271500\pi$
$353$	1.43677e42	1.31554	0.657770	+	0.753219i	$0.271500\pi$
$354$	6.58495e41	0.575438
$355$	−6.50727e41	−0.542789
$356$	1.90246e42	1.51492
$357$	−8.25298e41	−0.627459
$358$	6.74141e41	0.489419
$359$	−1.53962e42	−1.06747	−0.533736	−	0.845651i	$-0.679212\pi$
$359$	−1.53962e42	−1.06747	−0.533736	+	0.845651i	$0.679212\pi$
$360$	3.91559e40	0.0259302
$361$	1.98131e42	1.25338
$362$	3.71886e42	2.24759
$363$	−2.87129e41	−0.165813
$364$	9.98838e41	0.551217
$365$	1.66854e42	0.880046
$366$	−1.94921e42	−0.982700
$367$	−1.54570e42	−0.744963	−0.372481	−	0.928040i	$-0.621493\pi$
$367$	−1.54570e42	−0.744963	−0.372481	+	0.928040i	$0.621493\pi$
$368$	−2.25698e42	−1.04001
$369$	−5.92267e41	−0.260965
$370$	−2.25885e42	−0.951829
$371$	−1.38349e42	−0.557581
$372$	−1.34207e42	−0.517387
$373$	1.17940e41	0.0434976	0.0217488	−	0.999763i	$-0.493077\pi$
$373$	1.17940e41	0.0434976	0.0217488	+	0.999763i	$0.493077\pi$
$374$	−6.50922e42	−2.29693
$375$	−1.71141e42	−0.577881
$376$	−3.19511e41	−0.103249
$377$	2.36167e42	0.730443
$378$	5.41918e41	0.160442
$379$	1.44566e42	0.409750	0.204875	−	0.978788i	$-0.434321\pi$
$379$	1.44566e42	0.409750	0.204875	+	0.978788i	$0.434321\pi$
$380$	3.72251e42	1.01020
$381$	3.62492e42	0.941968
$382$	−1.11208e42	−0.276752
$383$	6.89721e42	1.64397	0.821985	−	0.569510i	$-0.192867\pi$
$383$	6.89721e42	1.64397	0.821985	+	0.569510i	$0.192867\pi$
$384$	−6.33062e41	−0.144538
$385$	1.37911e42	0.301645
$386$	−6.02458e42	−1.26251
$387$	−1.10257e42	−0.221400
$388$	8.13353e42	1.56515
$389$	6.54747e42	1.20755	0.603775	−	0.797155i	$-0.293662\pi$
$389$	6.54747e42	1.20755	0.603775	+	0.797155i	$0.293662\pi$
$390$	2.56681e42	0.453762
$391$	−1.27641e43	−2.16308
$392$	−5.15802e41	−0.0838037
$393$	1.75918e40	0.00274053
$394$	−2.50706e42	−0.374522
$395$	3.61122e42	0.517370
$396$	2.22615e42	0.305903
$397$	1.63597e42	0.215641	0.107821	−	0.994170i	$-0.465613\pi$
$397$	1.63597e42	0.215641	0.107821	+	0.994170i	$0.465613\pi$
$398$	−1.07196e43	−1.35553
$399$	4.12241e42	0.500148
$400$	4.79659e42	0.558397
$401$	−7.21743e42	−0.806308	−0.403154	−	0.915132i	$-0.632086\pi$
$401$	−7.21743e42	−0.806308	−0.403154	+	0.915132i	$0.632086\pi$
$402$	4.41334e42	0.473192
$403$	−7.03963e42	−0.724464
$404$	1.46082e42	0.144313
$405$	7.25329e41	0.0687903
$406$	7.61038e42	0.692990
$407$	−1.02760e43	−0.898495
$408$	−1.62702e42	−0.136616
$409$	2.87628e42	0.231951	0.115975	−	0.993252i	$-0.463001\pi$
$409$	2.87628e42	0.231951	0.115975	+	0.993252i	$0.463001\pi$
$410$	−9.03995e42	−0.700216
$411$	−7.23064e42	−0.538005
$412$	1.57782e43	1.12785
$413$	5.79720e42	0.398146
$414$	8.38133e42	0.553105
$415$	−1.34543e43	−0.853232
$416$	−2.06710e43	−1.25986
$417$	−1.53348e43	−0.898325
$418$	3.25139e43	1.83088
$419$	−1.47936e43	−0.800833	−0.400416	−	0.916333i	$-0.631135\pi$
$419$	−1.47936e43	−0.800833	−0.400416	+	0.916333i	$0.631135\pi$
$420$	4.30808e42	0.224218
$421$	−9.12939e42	−0.456864	−0.228432	−	0.973560i	$-0.573360\pi$
$421$	−9.12939e42	−0.456864	−0.228432	+	0.973560i	$0.573360\pi$
$422$	2.17739e43	1.04781
$423$	−5.91868e42	−0.273910
$424$	−2.72747e42	−0.121401
$425$	2.71266e43	1.16139
$426$	−1.77549e43	−0.731239
$427$	−1.71603e43	−0.679931
$428$	3.50031e43	1.33439
$429$	1.16770e43	0.428336
$430$	−1.68289e43	−0.594055
$431$	2.61125e43	0.887100	0.443550	−	0.896250i	$-0.353719\pi$
$431$	2.61125e43	0.887100	0.443550	+	0.896250i	$0.353719\pi$
$432$	−5.32928e42	−0.174256
$433$	2.30519e43	0.725532	0.362766	−	0.931880i	$-0.381832\pi$
$433$	2.30519e43	0.725532	0.362766	+	0.931880i	$0.381832\pi$
$434$	−2.26849e43	−0.687317
$435$	1.01861e43	0.297122
$436$	−3.79953e43	−1.06709
$437$	6.37574e43	1.72420
$438$	4.55257e43	1.18559
$439$	1.92949e43	0.483924	0.241962	−	0.970286i	$-0.422209\pi$
$439$	1.92949e43	0.483924	0.241962	+	0.970286i	$0.422209\pi$
$440$	2.71882e42	0.0656768
$441$	−9.55480e42	−0.222323
$442$	−1.06657e44	−2.39069
$443$	−7.10349e43	−1.53395	−0.766974	−	0.641679i	$-0.778238\pi$
$443$	−7.10349e43	−1.53395	−0.766974	+	0.641679i	$0.778238\pi$
$444$	−3.21003e43	−0.667867
$445$	4.30408e43	0.862860
$446$	−2.28782e43	−0.441974
$447$	−3.91714e43	−0.729280
$448$	−3.74910e43	−0.672728
$449$	8.96271e42	0.155015	0.0775077	−	0.996992i	$-0.475304\pi$
$449$	8.96271e42	0.155015	0.0775077	+	0.996992i	$0.475304\pi$
$450$	−1.78122e43	−0.296969
$451$	−4.11246e43	−0.660981
$452$	−8.32185e42	−0.128954
$453$	2.86036e43	0.427366
$454$	3.90828e43	0.563072
$455$	2.25975e43	0.313958
$456$	8.12707e42	0.108896
$457$	6.47355e43	0.836615	0.418307	−	0.908306i	$-0.362624\pi$
$457$	6.47355e43	0.836615	0.418307	+	0.908306i	$0.362624\pi$
$458$	1.22144e44	1.52262
$459$	−3.01392e43	−0.362428
$460$	6.66290e43	0.772964
$461$	−1.18390e44	−1.32510	−0.662550	−	0.749018i	$-0.730526\pi$
$461$	−1.18390e44	−1.32510	−0.662550	+	0.749018i	$0.730526\pi$
$462$	3.76286e43	0.406373
$463$	1.63898e44	1.70800	0.853999	−	0.520275i	$-0.174170\pi$
$463$	1.63898e44	1.70800	0.853999	+	0.520275i	$0.174170\pi$
$464$	−7.48414e43	−0.752653
$465$	−3.03626e43	−0.294690
$466$	6.23241e43	0.583833
$467$	4.36528e43	0.394715	0.197358	−	0.980332i	$-0.436764\pi$
$467$	4.36528e43	0.394715	0.197358	+	0.980332i	$0.436764\pi$
$468$	3.64767e43	0.318390
$469$	3.88538e43	0.327402
$470$	−9.03385e43	−0.734950
$471$	6.95819e43	0.546577
$472$	1.14288e43	0.0866878
$473$	−7.65583e43	−0.560768
$474$	9.85310e43	0.696996
$475$	−1.35499e44	−0.925744
$476$	−1.79011e44	−1.18131
$477$	−5.05240e43	−0.322066
$478$	−7.37407e43	−0.454095
$479$	−2.46140e44	−1.46435	−0.732177	−	0.681115i	$-0.761495\pi$
$479$	−2.46140e44	−1.46435	−0.732177	+	0.681115i	$0.761495\pi$
$480$	−8.91559e43	−0.512472
$481$	−1.68378e44	−0.935171
$482$	2.96363e44	1.59055
$483$	7.37868e43	0.382694
$484$	−6.22798e43	−0.312175
$485$	1.84011e44	0.891467
$486$	1.97904e43	0.0926735
$487$	1.23117e44	0.557300	0.278650	−	0.960393i	$-0.410113\pi$
$487$	1.23117e44	0.557300	0.278650	+	0.960393i	$0.410113\pi$
$488$	−3.38304e43	−0.148040
$489$	2.13299e44	0.902385
$490$	−1.45838e44	−0.596533
$491$	1.33486e44	0.527949	0.263974	−	0.964530i	$-0.414967\pi$
$491$	1.33486e44	0.527949	0.263974	+	0.964530i	$0.414967\pi$
$492$	−1.28466e44	−0.491319
$493$	−4.23257e44	−1.56542
$494$	5.32759e44	1.90562
$495$	5.03639e43	0.174234
$496$	2.23086e44	0.746492
$497$	−1.56309e44	−0.505945
$498$	−3.67096e44	−1.14946
$499$	1.73789e44	0.526456	0.263228	−	0.964734i	$-0.415213\pi$
$499$	1.73789e44	0.526456	0.263228	+	0.964734i	$0.415213\pi$
$500$	−3.71214e44	−1.08797
$501$	4.19868e43	0.119067
$502$	−1.01830e44	−0.279426
$503$	−2.41822e44	−0.642131	−0.321065	−	0.947057i	$-0.604041\pi$
$503$	−2.41822e44	−0.642131	−0.321065	+	0.947057i	$0.604041\pi$
$504$	9.40550e42	0.0241701
$505$	3.30493e43	0.0821968
$506$	5.81965e44	1.40092
$507$	−5.64488e43	−0.131530
$508$	7.86263e44	1.77344
$509$	−1.65916e44	−0.362281	−0.181141	−	0.983457i	$-0.557979\pi$
$509$	−1.65916e44	−0.362281	−0.181141	+	0.983457i	$0.557979\pi$
$510$	−4.60023e44	−0.972459
$511$	4.00796e44	0.820310
$512$	7.12474e44	1.41193
$513$	1.50547e44	0.288892
$514$	−5.04944e43	−0.0938321
$515$	3.56962e44	0.642396
$516$	−2.39154e44	−0.416829
$517$	−4.10969e44	−0.693769
$518$	−5.42591e44	−0.887220
$519$	1.55431e43	0.0246193
$520$	4.45495e43	0.0683577
$521$	−8.60802e44	−1.27962	−0.639810	−	0.768533i	$-0.720987\pi$
$521$	−8.60802e44	−1.27962	−0.639810	+	0.768533i	$0.720987\pi$
$522$	2.77924e44	0.400280
$523$	−7.87580e44	−1.09905	−0.549524	−	0.835478i	$-0.685191\pi$
$523$	−7.87580e44	−1.09905	−0.549524	+	0.835478i	$0.685191\pi$
$524$	3.81576e42	0.00515958
$525$	−1.56814e44	−0.205473
$526$	−1.67177e45	−2.12281
$527$	1.26164e45	1.55260
$528$	−3.70044e44	−0.441360
$529$	2.76185e44	0.319288
$530$	−7.71162e44	−0.864159
$531$	2.11709e44	0.229974
$532$	8.94172e44	0.941628
$533$	−6.73850e44	−0.687962
$534$	1.17436e45	1.16244
$535$	7.91902e44	0.760036
$536$	7.65977e43	0.0712848
$537$	2.16739e44	0.195597
$538$	−2.49421e45	−2.18286
$539$	−6.63446e44	−0.563107
$540$	1.57327e44	0.129511
$541$	6.87521e44	0.548948	0.274474	−	0.961595i	$-0.411496\pi$
$541$	6.87521e44	0.548948	0.274474	+	0.961595i	$0.411496\pi$
$542$	1.12038e45	0.867716
$543$	1.19563e45	0.898253
$544$	3.70464e45	2.70000
$545$	−8.59597e44	−0.607789
$546$	6.16565e44	0.422961
$547$	1.66250e45	1.10655	0.553273	−	0.833000i	$-0.313379\pi$
$547$	1.66250e45	1.10655	0.553273	+	0.833000i	$0.313379\pi$
$548$	−1.56836e45	−1.01290
$549$	−6.26679e44	−0.392737
$550$	−1.23681e45	−0.752172
$551$	2.11419e45	1.24780
$552$	1.45466e44	0.0833233
$553$	8.67439e44	0.482252
$554$	−9.86431e44	−0.532299
$555$	−7.26229e44	−0.380399
$556$	−3.32620e45	−1.69127
$557$	−7.21644e42	−0.00356215	−0.00178108	−	0.999998i	$-0.500567\pi$
$557$	−7.21644e42	−0.00356215	−0.00178108	+	0.999998i	$0.500567\pi$
$558$	−8.28434e44	−0.397003
$559$	−1.25445e45	−0.583659
$560$	−7.16115e44	−0.323505
$561$	−2.09274e45	−0.917969
$562$	2.90933e45	1.23921
$563$	−8.87912e44	−0.367266	−0.183633	−	0.982995i	$-0.558786\pi$
$563$	−8.87912e44	−0.367266	−0.183633	+	0.982995i	$0.558786\pi$
$564$	−1.28379e45	−0.515690
$565$	−1.88272e44	−0.0734489
$566$	−4.66948e45	−1.76928
$567$	1.74229e44	0.0641209
$568$	−3.08153e44	−0.110159
$569$	2.28043e45	0.791888	0.395944	−	0.918275i	$-0.370417\pi$
$569$	2.28043e45	0.791888	0.395944	+	0.918275i	$0.370417\pi$
$570$	2.29784e45	0.775148
$571$	3.59225e45	1.17725	0.588627	−	0.808405i	$-0.299669\pi$
$571$	3.59225e45	1.17725	0.588627	+	0.808405i	$0.299669\pi$
$572$	2.53279e45	0.806427
$573$	−3.57538e44	−0.110604
$574$	−2.17146e45	−0.652687
$575$	−2.42529e45	−0.708343
$576$	−1.36914e45	−0.388576
$577$	−2.49209e45	−0.687326	−0.343663	−	0.939093i	$-0.611668\pi$
$577$	−2.49209e45	−0.687326	−0.343663	+	0.939093i	$0.611668\pi$
$578$	1.37253e46	3.67885
$579$	−1.93693e45	−0.504565
$580$	2.20942e45	0.559391
$581$	−3.23181e45	−0.795316
$582$	5.02068e45	1.20097
$583$	−3.50818e45	−0.815738
$584$	7.90142e44	0.178605
$585$	8.25240e44	0.181346
$586$	−5.51519e45	−1.17828
$587$	9.89410e44	0.205517	0.102758	−	0.994706i	$-0.467233\pi$
$587$	9.89410e44	0.205517	0.102758	+	0.994706i	$0.467233\pi$
$588$	−2.07248e45	−0.418567
$589$	−6.30196e45	−1.23758
$590$	3.23137e45	0.617062
$591$	−8.06030e44	−0.149678
$592$	5.33590e45	0.963606
$593$	5.52950e45	0.971143	0.485571	−	0.874197i	$-0.338612\pi$
$593$	5.52950e45	0.971143	0.485571	+	0.874197i	$0.338612\pi$
$594$	1.37416e45	0.234726
$595$	−4.04991e45	−0.672845
$596$	−8.49646e45	−1.37301
$597$	−3.44640e45	−0.541738
$598$	9.53583e45	1.45811
$599$	1.10536e46	1.64423	0.822113	−	0.569325i	$-0.192795\pi$
$599$	1.10536e46	1.64423	0.822113	+	0.569325i	$0.192795\pi$
$600$	−3.09148e44	−0.0447374
$601$	−1.03350e46	−1.45506	−0.727531	−	0.686075i	$-0.759332\pi$
$601$	−1.03350e46	−1.45506	−0.727531	+	0.686075i	$0.759332\pi$
$602$	−4.04242e45	−0.553731
$603$	1.41891e45	0.189112
$604$	6.20426e45	0.804600
$605$	−1.40900e45	−0.177807
$606$	9.01741e44	0.110735
$607$	1.28551e46	1.53626	0.768128	−	0.640297i	$-0.221189\pi$
$607$	1.28551e46	1.53626	0.768128	+	0.640297i	$0.221189\pi$
$608$	−1.85049e46	−2.15218
$609$	2.44677e45	0.276954
$610$	−9.56518e45	−1.05378
$611$	−6.73395e45	−0.722088
$612$	−6.53733e45	−0.682342
$613$	1.79735e46	1.82614	0.913070	−	0.407803i	$-0.133705\pi$
$613$	1.79735e46	1.82614	0.913070	+	0.407803i	$0.133705\pi$
$614$	−9.95684e45	−0.984789
$615$	−2.90638e45	−0.279842
$616$	6.53079e44	0.0612187
$617$	−4.75429e45	−0.433891	−0.216945	−	0.976184i	$-0.569609\pi$
$617$	−4.75429e45	−0.433891	−0.216945	+	0.976184i	$0.569609\pi$
$618$	9.73960e45	0.865429
$619$	−6.09300e45	−0.527151	−0.263576	−	0.964639i	$-0.584902\pi$
$619$	−6.09300e45	−0.527151	−0.263576	+	0.964639i	$0.584902\pi$
$620$	−6.58580e45	−0.554812
$621$	2.69463e45	0.221049
$622$	−2.51349e45	−0.200787
$623$	1.03387e46	0.804291
$624$	−6.06338e45	−0.459376
$625$	−4.04098e43	−0.00298172
$626$	−1.88608e46	−1.35545
$627$	1.04534e46	0.731714
$628$	1.50927e46	1.02904
$629$	3.01766e46	2.00417
$630$	2.65930e45	0.172048
$631$	−1.32006e46	−0.831972	−0.415986	−	0.909371i	$-0.636564\pi$
$631$	−1.32006e46	−0.831972	−0.415986	+	0.909371i	$0.636564\pi$
$632$	1.71010e45	0.105000
$633$	7.00041e45	0.418757
$634$	4.06722e46	2.37042
$635$	1.77882e46	1.01010
$636$	−1.09589e46	−0.606352
$637$	−1.08709e46	−0.586093
$638$	1.92979e46	1.01384
$639$	−5.70826e45	−0.292240
$640$	−3.10657e45	−0.154993
$641$	−1.67470e46	−0.814289	−0.407144	−	0.913364i	$-0.633475\pi$
$641$	−1.67470e46	−0.814289	−0.407144	+	0.913364i	$0.633475\pi$
$642$	2.16068e46	1.02391
$643$	−3.15271e46	−1.45614	−0.728070	−	0.685503i	$-0.759583\pi$
$643$	−3.15271e46	−1.45614	−0.728070	+	0.685503i	$0.759583\pi$
$644$	1.60047e46	0.720496
$645$	−5.41057e45	−0.237415
$646$	−9.54808e46	−4.08394
$647$	−3.81482e46	−1.59057	−0.795287	−	0.606234i	$-0.792680\pi$
$647$	−3.81482e46	−1.59057	−0.795287	+	0.606234i	$0.792680\pi$
$648$	3.43481e44	0.0139609
$649$	1.47002e46	0.582486
$650$	−2.02658e46	−0.782876
$651$	−7.29330e45	−0.274687
$652$	4.62656e46	1.69892
$653$	1.73839e46	0.622413	0.311207	−	0.950342i	$-0.399267\pi$
$653$	1.73839e46	0.622413	0.311207	+	0.950342i	$0.399267\pi$
$654$	−2.34538e46	−0.818806
$655$	8.63268e43	0.00293876
$656$	2.13543e46	0.708880
$657$	1.46367e46	0.473821
$658$	−2.16999e46	−0.685063
$659$	−3.23587e46	−0.996282	−0.498141	−	0.867096i	$-0.665984\pi$
$659$	−3.23587e46	−0.996282	−0.498141	+	0.867096i	$0.665984\pi$
$660$	1.09242e46	0.328030
$661$	2.97533e46	0.871386	0.435693	−	0.900095i	$-0.356503\pi$
$661$	2.97533e46	0.871386	0.435693	+	0.900095i	$0.356503\pi$
$662$	5.78318e46	1.65200
$663$	−3.42907e46	−0.955440
$664$	−6.37130e45	−0.173163
$665$	2.02295e46	0.536326
$666$	−1.98149e46	−0.512469
$667$	3.78418e46	0.954763
$668$	9.10716e45	0.224167
$669$	−7.35543e45	−0.176635
$670$	2.16572e46	0.507420
$671$	−4.35140e46	−0.994736
$672$	−2.14158e46	−0.477686
$673$	2.44628e46	0.532424	0.266212	−	0.963914i	$-0.414228\pi$
$673$	2.44628e46	0.532424	0.266212	+	0.963914i	$0.414228\pi$
$674$	9.41209e46	1.99893
$675$	−5.72670e45	−0.118684
$676$	−1.22440e46	−0.247630
$677$	−2.92966e45	−0.0578234	−0.0289117	−	0.999582i	$-0.509204\pi$
$677$	−2.92966e45	−0.0578234	−0.0289117	+	0.999582i	$0.509204\pi$
$678$	−5.13693e45	−0.0989496
$679$	4.42007e46	0.830955
$680$	−7.98413e45	−0.146498
$681$	1.25653e46	0.225032
$682$	−5.75231e46	−1.00554
$683$	−2.24947e46	−0.383829	−0.191915	−	0.981412i	$-0.561470\pi$
$683$	−2.24947e46	−0.383829	−0.191915	+	0.981412i	$0.561470\pi$
$684$	3.26544e46	0.543896
$685$	−3.54822e46	−0.576921
$686$	−8.75541e46	−1.38972
$687$	3.92697e46	0.608515
$688$	3.97536e46	0.601406
$689$	−5.74835e46	−0.849036
$690$	4.11289e46	0.593113
$691$	−3.46278e46	−0.487571	−0.243785	−	0.969829i	$-0.578389\pi$
$691$	−3.46278e46	−0.487571	−0.243785	+	0.969829i	$0.578389\pi$
$692$	3.37137e45	0.0463506
$693$	1.20977e46	0.162407
$694$	−1.26401e47	−1.65698
$695$	−7.52511e46	−0.963304
$696$	4.82364e45	0.0603007
$697$	1.20767e47	1.47437
$698$	7.59098e46	0.905073
$699$	2.00374e46	0.233329
$700$	−3.40137e46	−0.386844
$701$	9.56443e46	1.06246	0.531229	−	0.847228i	$-0.321730\pi$
$701$	9.56443e46	1.06246	0.531229	+	0.847228i	$0.321730\pi$
$702$	2.25164e46	0.244308
$703$	−1.50734e47	−1.59753
$704$	−9.50674e46	−0.984198
$705$	−2.90442e46	−0.293723
$706$	1.92371e47	1.90048
$707$	7.93867e45	0.0766174
$708$	4.59207e46	0.432972
$709$	−1.35107e46	−0.124456	−0.0622278	−	0.998062i	$-0.519821\pi$
$709$	−1.35107e46	−0.124456	−0.0622278	+	0.998062i	$0.519821\pi$
$710$	−8.71269e46	−0.784132
$711$	3.16781e46	0.278555
$712$	2.03821e46	0.175117
$713$	−1.12798e47	−0.946948
$714$	−1.10501e47	−0.906450
$715$	5.73013e46	0.459320
$716$	4.70118e46	0.368250
$717$	−2.37079e46	−0.181479
$718$	−2.06143e47	−1.54211
$719$	−2.83412e46	−0.207201	−0.103600	−	0.994619i	$-0.533036\pi$
$719$	−2.83412e46	−0.207201	−0.103600	+	0.994619i	$0.533036\pi$
$720$	−2.61519e46	−0.186860
$721$	8.57447e46	0.598791
$722$	2.65281e47	1.81068
$723$	9.52820e46	0.635666
$724$	2.59338e47	1.69114
$725$	−8.04224e46	−0.512625
$726$	−3.84442e46	−0.239539
$727$	1.28209e47	0.780909	0.390454	−	0.920622i	$-0.372318\pi$
$727$	1.28209e47	0.780909	0.390454	+	0.920622i	$0.372318\pi$
$728$	1.07011e46	0.0637176
$729$	6.36269e45	0.0370370
$730$	2.23404e47	1.27135
$731$	2.24822e47	1.25084
$732$	−1.35930e47	−0.739404
$733$	−4.19929e46	−0.223337	−0.111668	−	0.993746i	$-0.535619\pi$
$733$	−4.19929e46	−0.223337	−0.111668	+	0.993746i	$0.535619\pi$
$734$	−2.06956e47	−1.07620
$735$	−4.68874e46	−0.238405
$736$	−3.31218e47	−1.64676
$737$	9.85231e46	0.478988
$738$	−7.92997e46	−0.377000
$739$	1.15341e47	0.536229	0.268115	−	0.963387i	$-0.413599\pi$
$739$	1.15341e47	0.536229	0.268115	+	0.963387i	$0.413599\pi$
$740$	−1.57523e47	−0.716176
$741$	1.71284e47	0.761583
$742$	−1.85238e47	−0.805502
$743$	−3.47051e46	−0.147597	−0.0737986	−	0.997273i	$-0.523512\pi$
$743$	−3.47051e46	−0.147597	−0.0737986	+	0.997273i	$0.523512\pi$
$744$	−1.43783e46	−0.0598071
$745$	−1.92222e47	−0.782032
$746$	1.57912e46	0.0628382
$747$	−1.18023e47	−0.459385
$748$	−4.53926e47	−1.72826
$749$	1.90220e47	0.708446
$750$	−2.29144e47	−0.834828
$751$	−3.73630e47	−1.33163	−0.665814	−	0.746117i	$-0.731916\pi$
$751$	−3.73630e47	−1.33163	−0.665814	+	0.746117i	$0.731916\pi$
$752$	2.13399e47	0.744044
$753$	−3.27389e46	−0.111673
$754$	3.16208e47	1.05523
$755$	1.40364e47	0.458279
$756$	3.77911e46	0.120720
$757$	−2.59029e47	−0.809591	−0.404796	−	0.914407i	$-0.632657\pi$
$757$	−2.59029e47	−0.809591	−0.404796	+	0.914407i	$0.632657\pi$
$758$	1.93562e47	0.591939
$759$	1.87104e47	0.559879
$760$	3.98812e46	0.116773
$761$	2.00203e47	0.573619	0.286809	−	0.957988i	$-0.407405\pi$
$761$	2.00203e47	0.573619	0.286809	+	0.957988i	$0.407405\pi$
$762$	4.85346e47	1.36080
$763$	−2.06481e47	−0.566533
$764$	−7.75518e46	−0.208234
$765$	−1.47899e47	−0.388644
$766$	9.23479e47	2.37494
$767$	2.40871e47	0.606263
$768$	1.88449e47	0.464230
$769$	2.91716e47	0.703357	0.351679	−	0.936121i	$-0.385611\pi$
$769$	2.91716e47	0.703357	0.351679	+	0.936121i	$0.385611\pi$
$770$	1.84651e47	0.435768
$771$	−1.62342e46	−0.0375001
$772$	−4.20129e47	−0.949942
$773$	−7.37093e47	−1.63140	−0.815701	−	0.578474i	$-0.803648\pi$
$773$	−7.37093e47	−1.63140	−0.815701	+	0.578474i	$0.803648\pi$
$774$	−1.47626e47	−0.319842
$775$	2.39722e47	0.508429
$776$	8.71387e46	0.180923
$777$	−1.74445e47	−0.354578
$778$	8.76652e47	1.74447
$779$	−6.03239e47	−1.17523
$780$	1.78999e47	0.341420
$781$	−3.96358e47	−0.740195
$782$	−1.70901e48	−3.12487
$783$	8.93538e46	0.159972
$784$	3.44501e47	0.603914
$785$	3.41453e47	0.586113
$786$	2.35540e45	0.00395907
$787$	6.09892e46	0.100385	0.0501926	−	0.998740i	$-0.484016\pi$
$787$	6.09892e46	0.100385	0.0501926	+	0.998740i	$0.484016\pi$
$788$	−1.74832e47	−0.281798
$789$	−5.37481e47	−0.848384
$790$	4.83512e47	0.747412
$791$	−4.52241e46	−0.0684633
$792$	2.38499e46	0.0353607
$793$	−7.13002e47	−1.03534
$794$	2.19043e47	0.311523
$795$	−2.47932e47	−0.345362
$796$	−7.47541e47	−1.01993
$797$	8.14237e46	0.108815	0.0544075	−	0.998519i	$-0.482673\pi$
$797$	8.14237e46	0.108815	0.0544075	+	0.998519i	$0.482673\pi$
$798$	5.51957e47	0.722533
$799$	1.20686e48	1.54751
$800$	7.03914e47	0.884168
$801$	3.77560e47	0.464568
$802$	−9.66355e47	−1.16482
$803$	1.01631e48	1.20011
$804$	3.07768e47	0.356040
$805$	3.62087e47	0.410375
$806$	−9.42548e47	−1.04659
$807$	−8.01898e47	−0.872380
$808$	1.56506e46	0.0166818
$809$	−1.76833e48	−1.84677	−0.923386	−	0.383872i	$-0.874590\pi$
$809$	−1.76833e48	−1.84677	−0.923386	+	0.383872i	$0.874590\pi$
$810$	9.71155e46	0.0993770
$811$	6.28234e47	0.629908	0.314954	−	0.949107i	$-0.398011\pi$
$811$	6.28234e47	0.629908	0.314954	+	0.949107i	$0.398011\pi$
$812$	5.30716e47	0.521420
$813$	3.60207e47	0.346784
$814$	−1.37587e48	−1.29800
$815$	1.04670e48	0.967659
$816$	1.08667e48	0.984492
$817$	−1.12300e48	−0.997047
$818$	3.85109e47	0.335085
$819$	1.98228e47	0.169037
$820$	−6.30408e47	−0.526858
$821$	1.56380e48	1.28091	0.640455	−	0.767996i	$-0.278746\pi$
$821$	1.56380e48	1.28091	0.640455	+	0.767996i	$0.278746\pi$
$822$	−9.68122e47	−0.777222
$823$	9.59054e47	0.754650	0.377325	−	0.926081i	$-0.376844\pi$
$823$	9.59054e47	0.754650	0.377325	+	0.926081i	$0.376844\pi$
$824$	1.69040e47	0.130374
$825$	−3.97638e47	−0.300606
$826$	7.76197e47	0.575177
$827$	1.93418e48	1.40493	0.702467	−	0.711716i	$-0.252082\pi$
$827$	1.93418e48	1.40493	0.702467	+	0.711716i	$0.252082\pi$
$828$	5.84479e47	0.416168
$829$	7.19795e47	0.502411	0.251205	−	0.967934i	$-0.419173\pi$
$829$	7.19795e47	0.502411	0.251205	+	0.967934i	$0.419173\pi$
$830$	−1.80142e48	−1.23261
$831$	−3.17142e47	−0.212734
$832$	−1.55773e48	−1.02437
$833$	1.94828e48	1.25606
$834$	−2.05320e48	−1.29775
$835$	2.06038e47	0.127679
$836$	2.26739e48	1.37760
$837$	−2.66345e47	−0.158663
$838$	−1.98074e48	−1.15691
$839$	−2.53702e48	−1.45295	−0.726476	−	0.687192i	$-0.758843\pi$
$839$	−2.53702e48	−1.45295	−0.726476	+	0.687192i	$0.758843\pi$
$840$	4.61548e46	0.0259184
$841$	−5.61242e47	−0.309041
$842$	−1.22235e48	−0.660003
$843$	9.35362e47	0.495250
$844$	1.51842e48	0.788393
$845$	−2.77006e47	−0.141044
$846$	−7.92461e47	−0.395701
$847$	−3.38452e47	−0.165738
$848$	1.82166e48	0.874852
$849$	−1.50126e48	−0.707095
$850$	3.63202e48	1.67778
$851$	−2.69798e48	−1.22236
$852$	−1.23815e48	−0.550200
$853$	−8.62674e47	−0.376000	−0.188000	−	0.982169i	$-0.560200\pi$
$853$	−8.62674e47	−0.376000	−0.188000	+	0.982169i	$0.560200\pi$
$854$	−2.29762e48	−0.982253
$855$	7.38765e47	0.309789
$856$	3.75006e47	0.154249
$857$	−2.78552e48	−1.12389	−0.561943	−	0.827176i	$-0.689946\pi$
$857$	−2.78552e48	−1.12389	−0.561943	+	0.827176i	$0.689946\pi$
$858$	1.56345e48	0.618790
$859$	−2.05191e48	−0.796656	−0.398328	−	0.917243i	$-0.630409\pi$
$859$	−2.05191e48	−0.796656	−0.398328	+	0.917243i	$0.630409\pi$
$860$	−1.17358e48	−0.446980
$861$	−6.98132e47	−0.260847
$862$	3.49624e48	1.28154
$863$	2.04429e48	0.735129	0.367564	−	0.929998i	$-0.380192\pi$
$863$	2.04429e48	0.735129	0.367564	+	0.929998i	$0.380192\pi$
$864$	−7.82088e47	−0.275917
$865$	7.62730e46	0.0264001
$866$	3.08646e48	1.04813
$867$	4.41274e48	1.47026
$868$	−1.58195e48	−0.517152
$869$	2.19960e48	0.705532
$870$	1.36383e48	0.429234
$871$	1.61436e48	0.498540
$872$	−4.07064e47	−0.123350
$873$	1.61417e48	0.479970
$874$	8.53659e48	2.49084
$875$	−2.01732e48	−0.577618
$876$	3.17477e48	0.892062
$877$	−3.91822e48	−1.08043	−0.540214	−	0.841528i	$-0.681657\pi$
$877$	−3.91822e48	−1.08043	−0.540214	+	0.841528i	$0.681657\pi$
$878$	2.58342e48	0.699095
$879$	−1.77315e48	−0.470902
$880$	−1.81588e48	−0.473286
$881$	2.83055e48	0.724050	0.362025	−	0.932168i	$-0.382085\pi$
$881$	2.83055e48	0.724050	0.362025	+	0.932168i	$0.382085\pi$
$882$	−1.27931e48	−0.321176
$883$	−7.31883e48	−1.80339	−0.901695	−	0.432372i	$-0.857677\pi$
$883$	−7.31883e48	−1.80339	−0.901695	+	0.432372i	$0.857677\pi$
$884$	−7.43783e48	−1.79880
$885$	1.03890e48	0.246609
$886$	−9.51099e48	−2.21600
$887$	−3.20297e48	−0.732510	−0.366255	−	0.930514i	$-0.619360\pi$
$887$	−3.20297e48	−0.732510	−0.366255	+	0.930514i	$0.619360\pi$
$888$	−3.43907e47	−0.0772017
$889$	4.27285e48	0.941540
$890$	5.76281e48	1.24652
$891$	4.41799e47	0.0938086
$892$	−1.59543e48	−0.332551
$893$	−6.02832e48	−1.23352
$894$	−5.24472e48	−1.05355
$895$	1.06358e48	0.209745
$896$	−7.46218e47	−0.144472
$897$	3.06581e48	0.582733
$898$	1.20003e48	0.223941
$899$	−3.74039e48	−0.685302
$900$	−1.24215e48	−0.223446
$901$	1.03022e49	1.81957
$902$	−5.50625e48	−0.954878
$903$	−1.29965e48	−0.221299
$904$	−8.91563e46	−0.0149064
$905$	5.86719e48	0.963227
$906$	3.82978e48	0.617388
$907$	4.90212e48	0.776003	0.388001	−	0.921659i	$-0.373166\pi$
$907$	4.90212e48	0.776003	0.388001	+	0.921659i	$0.373166\pi$
$908$	2.72547e48	0.423667
$909$	2.89913e47	0.0442552
$910$	3.02562e48	0.453556
$911$	1.14051e48	0.167899	0.0839493	−	0.996470i	$-0.473247\pi$
$911$	1.14051e48	0.167899	0.0839493	+	0.996470i	$0.473247\pi$
$912$	−5.42801e48	−0.784740
$913$	−8.19503e48	−1.16354
$914$	8.66755e48	1.20860
$915$	−3.07525e48	−0.421145
$916$	8.51779e48	1.14565
$917$	2.07363e46	0.00273928
$918$	−4.03538e48	−0.523577
$919$	5.91264e48	0.753486	0.376743	−	0.926318i	$-0.377044\pi$
$919$	5.91264e48	0.753486	0.376743	+	0.926318i	$0.377044\pi$
$920$	7.13831e47	0.0893504
$921$	−3.20116e48	−0.393572
$922$	−1.58514e49	−1.91429
$923$	−6.49456e48	−0.770409
$924$	2.62406e48	0.305764
$925$	5.73380e48	0.656303
$926$	2.19446e49	2.46744
$927$	3.13132e48	0.345869
$928$	−1.09832e49	−1.19175
$929$	2.22429e48	0.237100	0.118550	−	0.992948i	$-0.462175\pi$
$929$	2.22429e48	0.237100	0.118550	+	0.992948i	$0.462175\pi$
$930$	−4.06530e48	−0.425720
$931$	−9.73179e48	−1.00121
$932$	4.34622e48	0.439288
$933$	−8.08096e47	−0.0802447
$934$	5.84475e48	0.570220
$935$	−1.02695e49	−0.984370
$936$	3.90794e47	0.0368041
$937$	8.79742e48	0.814052	0.407026	−	0.913417i	$-0.366566\pi$
$937$	8.79742e48	0.814052	0.407026	+	0.913417i	$0.366566\pi$
$938$	5.20220e48	0.472977
$939$	−6.06383e48	−0.541708
$940$	−6.29983e48	−0.552992
$941$	1.05576e49	0.910619	0.455309	−	0.890333i	$-0.349529\pi$
$941$	1.05576e49	0.910619	0.455309	+	0.890333i	$0.349529\pi$
$942$	9.31644e48	0.789605
$943$	−1.07973e49	−0.899236
$944$	−7.63322e48	−0.624697
$945$	8.54977e47	0.0687590
$946$	−1.02505e49	−0.810107
$947$	−3.99538e48	−0.310302	−0.155151	−	0.987891i	$-0.549586\pi$
$947$	−3.99538e48	−0.310302	−0.155151	+	0.987891i	$0.549586\pi$
$948$	6.87114e48	0.524434
$949$	1.66529e49	1.24910
$950$	−1.81422e49	−1.33736
$951$	1.30763e49	0.947340
$952$	−1.91784e48	−0.136554
$953$	1.09387e49	0.765480	0.382740	−	0.923856i	$-0.374981\pi$
$953$	1.09387e49	0.765480	0.382740	+	0.923856i	$0.374981\pi$
$954$	−6.76474e48	−0.465268
$955$	−1.75451e48	−0.118605
$956$	−5.14237e48	−0.341671
$957$	6.20437e48	0.405182
$958$	−3.29561e49	−2.11546
$959$	−8.52307e48	−0.537761
$960$	−6.71865e48	−0.416684
$961$	−5.25416e48	−0.320307
$962$	−2.25444e49	−1.35098
$963$	6.94667e48	0.409207
$964$	2.06671e49	1.19677
$965$	−9.50490e48	−0.541062
$966$	9.87944e48	0.552853
$967$	3.02159e49	1.66226	0.831129	−	0.556080i	$-0.187695\pi$
$967$	3.02159e49	1.66226	0.831129	+	0.556080i	$0.187695\pi$
$968$	−6.67236e47	−0.0360858
$969$	−3.06975e49	−1.63215
$970$	2.46375e49	1.28785
$971$	4.99356e48	0.256621	0.128311	−	0.991734i	$-0.459045\pi$
$971$	4.99356e48	0.256621	0.128311	+	0.991734i	$0.459045\pi$
$972$	1.38010e48	0.0697295
$973$	−1.80758e49	−0.897917
$974$	1.64843e49	0.805096
$975$	−6.51553e48	−0.312877
$976$	2.25951e49	1.06682
$977$	2.61319e49	1.21314	0.606570	−	0.795030i	$-0.292545\pi$
$977$	2.61319e49	1.21314	0.606570	+	0.795030i	$0.292545\pi$
$978$	2.85589e49	1.30362
$979$	2.62162e49	1.17667
$980$	−1.01701e49	−0.448844
$981$	−7.54051e48	−0.327237
$982$	1.78727e49	0.762694
$983$	3.57124e48	0.149860	0.0749301	−	0.997189i	$-0.476127\pi$
$983$	3.57124e48	0.149860	0.0749301	+	0.997189i	$0.476127\pi$
$984$	−1.37632e48	−0.0567938
$985$	−3.95536e48	−0.160505
$986$	−5.66706e49	−2.26146
$987$	−6.97661e48	−0.273786
$988$	3.71524e49	1.43383
$989$	−2.01005e49	−0.762901
$990$	6.74330e48	0.251705
$991$	−2.36062e49	−0.866585	−0.433293	−	0.901253i	$-0.642648\pi$
$991$	−2.36062e49	−0.866585	−0.433293	+	0.901253i	$0.642648\pi$
$992$	3.27386e49	1.18200
$993$	1.85932e49	0.660223
$994$	−2.09285e49	−0.730907
$995$	−1.69122e49	−0.580924
$996$	−2.55998e49	−0.864882
$997$	−4.27804e49	−1.42159	−0.710796	−	0.703399i	$-0.751665\pi$
$997$	−4.27804e49	−1.42159	−0.710796	+	0.703399i	$0.751665\pi$
$998$	2.32689e49	0.760538
$999$	−6.37058e48	−0.204809

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.34.a.a.1.3	✓	3
3.2	odd	2		9.34.a.d.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.34.a.a.1.3	✓	3	1.1	even	1	trivial
9.34.a.d.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:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+133892. q^{2} +4.30467e7 q^{3} +9.33705e9 q^{4} +2.11239e11 q^{5} +5.76360e12 q^{6} +5.07411e13 q^{7} +1.00033e14 q^{8} +1.85302e15 q^{9} +O(q^{10})\)	\(q+133892. q^{2} +4.30467e7 q^{3} +9.33705e9 q^{4} +2.11239e11 q^{5} +5.76360e12 q^{6} +5.07411e13 q^{7} +1.00033e14 q^{8} +1.85302e15 q^{9} +2.82832e16 q^{10} +1.28666e17 q^{11} +4.01929e17 q^{12} +2.10827e18 q^{13} +6.79381e18 q^{14} +9.09316e18 q^{15} -6.68111e19 q^{16} -3.77843e20 q^{17} +2.48104e20 q^{18} +1.88735e21 q^{19} +1.97235e21 q^{20} +2.18424e21 q^{21} +1.72273e22 q^{22} +3.37815e22 q^{23} +4.30608e21 q^{24} -7.17933e22 q^{25} +2.82280e23 q^{26} +7.97664e22 q^{27} +4.73772e23 q^{28} +1.12019e24 q^{29} +1.21750e24 q^{30} -3.33906e24 q^{31} -9.80473e24 q^{32} +5.53866e24 q^{33} -5.05900e25 q^{34} +1.07185e25 q^{35} +1.73017e25 q^{36} -7.98655e25 q^{37} +2.52700e26 q^{38} +9.07540e25 q^{39} +2.11308e25 q^{40} -3.19623e26 q^{41} +2.92451e26 q^{42} -5.95015e26 q^{43} +1.20136e27 q^{44} +3.91431e26 q^{45} +4.52306e27 q^{46} -3.19407e27 q^{47} -2.87600e27 q^{48} -5.15634e27 q^{49} -9.61253e27 q^{50} -1.62649e28 q^{51} +1.96850e28 q^{52} -2.72657e28 q^{53} +1.06801e28 q^{54} +2.71793e28 q^{55} +5.07577e27 q^{56} +8.12441e28 q^{57} +1.49985e29 q^{58} +1.14251e29 q^{59} +8.49033e28 q^{60} -3.38193e29 q^{61} -4.47072e29 q^{62} +9.40242e28 q^{63} -7.38868e29 q^{64} +4.45349e29 q^{65} +7.41580e29 q^{66} +7.65727e29 q^{67} -3.52793e30 q^{68} +1.45418e30 q^{69} +1.43512e30 q^{70} -3.08052e30 q^{71} +1.85363e29 q^{72} +7.89884e30 q^{73} -1.06933e31 q^{74} -3.09047e30 q^{75} +1.76223e31 q^{76} +6.52866e30 q^{77} +1.21512e31 q^{78} +1.70954e31 q^{79} -1.41131e31 q^{80} +3.43368e30 q^{81} -4.27948e31 q^{82} -6.36922e31 q^{83} +2.03943e31 q^{84} -7.98152e31 q^{85} -7.96676e31 q^{86} +4.82207e31 q^{87} +1.28708e31 q^{88} +2.03754e32 q^{89} +5.24093e31 q^{90} +1.06976e32 q^{91} +3.15420e32 q^{92} -1.43736e32 q^{93} -4.27659e32 q^{94} +3.98682e32 q^{95} -4.22061e32 q^{96} +8.71102e32 q^{97} -6.90391e32 q^{98} +2.38421e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 41202 q^{2} + 129140163 q^{3} - 1107467772 q^{4} + 51261823890 q^{5} + 1773610998642 q^{6} + 76113734015256 q^{7} + 11\!\cdots\!92 q^{8}+ \cdots + 55\!\cdots\!23 q^{9}+O(q^{10}) \) 3 * q + 41202 * q^2 + 129140163 * q^3 - 1107467772 * q^4 + 51261823890 * q^5 + 1773610998642 * q^6 + 76113734015256 * q^7 + 1154149348489992 * q^8 + 5559060566555523 * q^9	\( 3 q + 41202 q^{2} + 129140163 q^{3} - 1107467772 q^{4} + 51261823890 q^{5} + 1773610998642 q^{6} + 76113734015256 q^{7} + 11\!\cdots\!92 q^{8}+ \cdots - 19\!\cdots\!80 q^{99}+O(q^{100}) \) 3 * q + 41202 * q^2 + 129140163 * q^3 - 1107467772 * q^4 + 51261823890 * q^5 + 1773610998642 * q^6 + 76113734015256 * q^7 + 1154149348489992 * q^8 + 5559060566555523 * q^9 - 6066746915652180 * q^10 - 103523748885455580 * q^11 - 47672856197775612 * q^12 + 1915412601357848490 * q^13 + 8843223974387917968 * q^14 + 2206653430943964690 * q^15 - 49163291855293757424 * q^16 - 16951254031996646346 * q^17 + 76348137821073552882 * q^18 + 2630380764132092623164 * q^19 + 6678893290406160608280 * q^20 + 3276446672422934775576 * q^21 + 25675959809490476752728 * q^22 + 79533787326189199888968 * q^23 + 49682344996780456916232 * q^24 + 423122978202020785717725 * q^25 + 515897524308539260240956 * q^26 + 239299329230617529590083 * q^27 + 42316840140910701529632 * q^28 + 1172400205292105207396058 * q^29 - 261153561855689925501780 * q^30 - 1730146178193885575522976 * q^31 - 15373118219420180766165984 * q^32 - 4456357935146267310153180 * q^33 - 72740605403522266308053244 * q^34 - 46524388137754256582413680 * q^35 - 2052160140018767590368252 * q^36 + 23072071636478902337811186 * q^37 + 123166602227885110273091304 * q^38 + 82452231850535525109301290 * q^39 + 334261243758638084780401200 * q^40 + 427548398123528287702034814 * q^41 + 380671795165987850539382928 * q^42 + 931650906163677813302061444 * q^43 + 2628232920146985471809839152 * q^44 + 94989194585537614644281490 * q^45 + 1576684767863897418449809584 * q^46 - 8758003298318968412560605552 * q^47 - 2116318507936402748872606704 * q^48 - 16032483885040282346174924373 * q^49 - 25868038199816062069548246450 * q^50 - 729695902915484708191931466 * q^51 - 133394982794577721290532296 * q^52 - 11892082156717187440623348702 * q^53 + 3286536987653301151390199922 * q^54 + 85333548015142237994905073880 * q^55 - 12245006589032410415460987840 * q^56 + 113229266877360998295498845244 * q^57 + 235922229903297044437282825308 * q^58 + 129677501466859357385715960756 * q^59 + 287504456060885972385819449880 * q^60 + 361088280985963126642141896762 * q^61 - 802944337692828230733430911168 * q^62 + 141040285779168467285417686296 * q^63 - 610917178484121070749024145344 * q^64 - 3385479539558515212808386273540 * q^65 + 1105265878326349704931668204888 * q^66 - 15812977239651397801356345396 * q^67 - 4909744547418540815627091775416 * q^68 + 3423668753103802480833636473928 * q^69 + 3300211942819681129760102456160 * q^70 - 6651937250528040326415493209384 * q^71 + 2138662043702154227125559275272 * q^72 + 17518600058904527629736361597918 * q^73 - 16487357564767645293733531370772 * q^74 + 18214056791351470398991692829725 * q^75 + 22556505117012105673290504564816 * q^76 + 526258013649190142100618876192 * q^77 + 22207696793500407453138825705276 * q^78 + 47039564834071071994823399481840 * q^79 - 89208987985140435656381122400160 * q^80 + 10301051460877537453973547267843 * q^81 - 83830191778687263739261116864588 * q^82 - 109771167143400749356291310773764 * q^83 + 1821601211147383654660341936672 * q^84 - 15809846025180808515314622875580 * q^85 - 130145119975743665925790272902760 * q^86 + 50467984537551976365425245225818 * q^87 - 87502984757959105129975772457888 * q^88 + 281720374074160857951628988116494 * q^89 - 11241804515358126485585908663380 * q^90 + 401563251462740776922902836239184 * q^91 + 153050732902924794873793215390816 * q^92 - 74477119821928476275461976961696 * q^93 - 349459814745766324819266344330400 * q^94 + 1967204571038464419732100554685800 * q^95 - 661762330891397303210713352938464 * q^96 + 816496586052591264484966840489254 * q^97 - 104502643082987555680827083473950 * q^98 - 191831596710377463091584406722780 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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