LMFDB - Embedded newform 3.34.a.a.1.1

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			1.1
Root			$5840.68$ 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)

$f(q)$	$=$	$q-81270.9 q^{2} +4.30467e7 q^{3} -1.98497e9 q^{4} +5.17904e11 q^{5} -3.49845e12 q^{6} -3.34870e13 q^{7} +8.59432e14 q^{8} +1.85302e15 q^{9} +O(q^{10})$	\(q-81270.9 q^{2} +4.30467e7 q^{3} -1.98497e9 q^{4} +5.17904e11 q^{5} -3.49845e12 q^{6} -3.34870e13 q^{7} +8.59432e14 q^{8} +1.85302e15 q^{9} -4.20905e16 q^{10} -8.29940e16 q^{11} -8.54466e16 q^{12} -3.31294e18 q^{13} +2.72152e18 q^{14} +2.22941e19 q^{15} -5.27961e19 q^{16} +2.58112e20 q^{17} -1.50597e20 q^{18} +1.73293e21 q^{19} -1.02802e21 q^{20} -1.44151e21 q^{21} +6.74500e21 q^{22} +3.47011e22 q^{23} +3.69957e22 q^{24} +1.51809e23 q^{25} +2.69246e23 q^{26} +7.97664e22 q^{27} +6.64708e22 q^{28} -1.23881e24 q^{29} -1.81186e24 q^{30} +4.83164e24 q^{31} -3.09168e24 q^{32} -3.57262e24 q^{33} -2.09770e25 q^{34} -1.73430e25 q^{35} -3.67819e24 q^{36} +6.61199e25 q^{37} -1.40837e26 q^{38} -1.42611e26 q^{39} +4.45103e26 q^{40} +4.65320e26 q^{41} +1.17153e26 q^{42} +4.73069e26 q^{43} +1.64741e26 q^{44} +9.59686e26 q^{45} -2.82019e27 q^{46} -2.09961e26 q^{47} -2.27270e27 q^{48} -6.60961e27 q^{49} -1.23376e28 q^{50} +1.11109e28 q^{51} +6.57609e27 q^{52} +2.04943e28 q^{53} -6.48269e27 q^{54} -4.29829e28 q^{55} -2.87798e28 q^{56} +7.45970e28 q^{57} +1.00680e29 q^{58} +5.20142e28 q^{59} -4.42531e28 q^{60} +4.57140e29 q^{61} -3.92672e29 q^{62} -6.20521e28 q^{63} +7.04779e29 q^{64} -1.71578e30 q^{65} +2.90350e29 q^{66} -2.36411e30 q^{67} -5.12346e29 q^{68} +1.49377e30 q^{69} +1.40949e30 q^{70} -1.81156e30 q^{71} +1.59255e30 q^{72} +9.48028e30 q^{73} -5.37362e30 q^{74} +6.53487e30 q^{75} -3.43982e30 q^{76} +2.77922e30 q^{77} +1.15901e31 q^{78} +5.17354e30 q^{79} -2.73433e31 q^{80} +3.43368e30 q^{81} -3.78170e31 q^{82} -4.73633e31 q^{83} +2.86135e30 q^{84} +1.33677e32 q^{85} -3.84468e31 q^{86} -5.33269e31 q^{87} -7.13277e31 q^{88} +2.98958e31 q^{89} -7.79946e31 q^{90} +1.10940e32 q^{91} -6.88807e31 q^{92} +2.07986e32 q^{93} +1.70638e31 q^{94} +8.97491e32 q^{95} -1.33087e32 q^{96} -6.56839e32 q^{97} +5.37169e32 q^{98} -1.53790e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−81270.9	−0.876880	−0.438440	−	0.898760i	$-0.644469\pi$
$2$	−81270.9	−0.876880	−0.438440	+	0.898760i	$0.644469\pi$
$3$	4.30467e7	0.577350
$3$	4.30467e7	0.577350
$4$	−1.98497e9	−0.231081
$5$	5.17904e11	1.51790	0.758951	−	0.651147i	$-0.225712\pi$
$5$	5.17904e11	1.51790	0.758951	+	0.651147i	$0.225712\pi$
$6$	−3.49845e12	−0.506267
$7$	−3.34870e13	−0.380854	−0.190427	−	0.981701i	$-0.560987\pi$
$7$	−3.34870e13	−0.380854	−0.190427	+	0.981701i	$0.560987\pi$
$8$	8.59432e14	1.07951
$9$	1.85302e15	0.333333
$10$	−4.20905e16	−1.33102
$11$	−8.29940e16	−0.544587	−0.272293	−	0.962214i	$-0.587782\pi$
$11$	−8.29940e16	−0.544587	−0.272293	+	0.962214i	$0.587782\pi$
$12$	−8.54466e16	−0.133415
$13$	−3.31294e18	−1.38085	−0.690427	−	0.723402i	$-0.742578\pi$
$13$	−3.31294e18	−1.38085	−0.690427	+	0.723402i	$0.742578\pi$
$14$	2.72152e18	0.333963
$15$	2.22941e19	0.876361
$16$	−5.27961e19	−0.715520
$17$	2.58112e20	1.28648	0.643238	−	0.765667i	$-0.277591\pi$
$17$	2.58112e20	1.28648	0.643238	+	0.765667i	$0.277591\pi$
$18$	−1.50597e20	−0.292293
$19$	1.73293e21	1.37831	0.689155	−	0.724614i	$-0.257982\pi$
$19$	1.73293e21	1.37831	0.689155	+	0.724614i	$0.257982\pi$
$20$	−1.02802e21	−0.350759
$21$	−1.44151e21	−0.219886
$22$	6.74500e21	0.477538
$23$	3.47011e22	1.17987	0.589934	−	0.807451i	$-0.299154\pi$
$23$	3.47011e22	1.17987	0.589934	+	0.807451i	$0.299154\pi$
$24$	3.69957e22	0.623256
$25$	1.51809e23	1.30403
$26$	2.69246e23	1.21084
$27$	7.97664e22	0.192450
$28$	6.64708e22	0.0880083
$29$	−1.23881e24	−0.919261	−0.459631	−	0.888110i	$-0.652018\pi$
$29$	−1.23881e24	−0.919261	−0.459631	+	0.888110i	$0.652018\pi$
$30$	−1.81186e24	−0.768464
$31$	4.83164e24	1.19296	0.596481	−	0.802628i	$-0.296565\pi$
$31$	4.83164e24	1.19296	0.596481	+	0.802628i	$0.296565\pi$
$32$	−3.09168e24	−0.452085
$33$	−3.57262e24	−0.314417
$34$	−2.09770e25	−1.12808
$35$	−1.73430e25	−0.578100
$36$	−3.67819e24	−0.0770271
$37$	6.61199e25	0.881056	0.440528	−	0.897739i	$-0.354791\pi$
$37$	6.61199e25	0.881056	0.440528	+	0.897739i	$0.354791\pi$
$38$	−1.40837e26	−1.20861
$39$	−1.42611e26	−0.797237
$40$	4.45103e26	1.63859
$41$	4.65320e26	1.13977	0.569886	−	0.821724i	$-0.306987\pi$
$41$	4.65320e26	1.13977	0.569886	+	0.821724i	$0.306987\pi$
$42$	1.17153e26	0.192814
$43$	4.73069e26	0.528074	0.264037	−	0.964513i	$-0.414946\pi$
$43$	4.73069e26	0.528074	0.264037	+	0.964513i	$0.414946\pi$
$44$	1.64741e26	0.125844
$45$	9.59686e26	0.505968
$46$	−2.82019e27	−1.03460
$47$	−2.09961e26	−0.0540163	−0.0270081	−	0.999635i	$-0.508598\pi$
$47$	−2.09961e26	−0.0540163	−0.0270081	+	0.999635i	$0.508598\pi$
$48$	−2.27270e27	−0.413106
$49$	−6.60961e27	−0.854950
$50$	−1.23376e28	−1.14348
$51$	1.11109e28	0.742747
$52$	6.57609e27	0.319090
$53$	2.04943e28	0.726243	0.363121	−	0.931742i	$-0.381711\pi$
$53$	2.04943e28	0.726243	0.363121	+	0.931742i	$0.381711\pi$
$54$	−6.48269e27	−0.168756
$55$	−4.29829e28	−0.826630
$56$	−2.87798e28	−0.411136
$57$	7.45970e28	0.795767
$58$	1.00680e29	0.806082
$59$	5.20142e28	0.314097	0.157049	−	0.987591i	$-0.449802\pi$
$59$	5.20142e28	0.314097	0.157049	+	0.987591i	$0.449802\pi$
$60$	−4.42531e28	−0.202511
$61$	4.57140e29	1.59260	0.796300	−	0.604902i	$-0.206788\pi$
$61$	4.57140e29	1.59260	0.796300	+	0.604902i	$0.206788\pi$
$62$	−3.92672e29	−1.04608
$63$	−6.20521e28	−0.126951
$64$	7.04779e29	1.11194
$65$	−1.71578e30	−2.09600
$66$	2.90350e29	0.275706
$67$	−2.36411e30	−1.75159	−0.875796	−	0.482681i	$-0.839663\pi$
$67$	−2.36411e30	−1.75159	−0.875796	+	0.482681i	$0.839663\pi$
$68$	−5.12346e29	−0.297280
$69$	1.49377e30	0.681197
$70$	1.40949e30	0.506924
$71$	−1.81156e30	−0.515571	−0.257786	−	0.966202i	$-0.582993\pi$
$71$	−1.81156e30	−0.515571	−0.257786	+	0.966202i	$0.582993\pi$
$72$	1.59255e30	0.359837
$73$	9.48028e30	1.70606	0.853030	−	0.521862i	$-0.174763\pi$
$73$	9.48028e30	1.70606	0.853030	+	0.521862i	$0.174763\pi$
$74$	−5.37362e30	−0.772581
$75$	6.53487e30	0.752881
$76$	−3.43982e30	−0.318501
$77$	2.77922e30	0.207408
$78$	1.15901e31	0.699081
$79$	5.17354e30	0.252895	0.126448	−	0.991973i	$-0.459642\pi$
$79$	5.17354e30	0.252895	0.126448	+	0.991973i	$0.459642\pi$
$80$	−2.73433e31	−1.08609
$81$	3.43368e30	0.111111
$82$	−3.78170e31	−0.999443
$83$	−4.73633e31	−1.02483	−0.512417	−	0.858737i	$-0.671250\pi$
$83$	−4.73633e31	−1.02483	−0.512417	+	0.858737i	$0.671250\pi$
$84$	2.86135e30	0.0508116
$85$	1.33677e32	1.95274
$86$	−3.84468e31	−0.463058
$87$	−5.33269e31	−0.530736
$88$	−7.13277e31	−0.587887
$89$	2.98958e31	0.204491	0.102246	−	0.994759i	$-0.467397\pi$
$89$	2.98958e31	0.204491	0.102246	+	0.994759i	$0.467397\pi$
$90$	−7.79946e31	−0.443673
$91$	1.10940e32	0.525904
$92$	−6.88807e31	−0.272645
$93$	2.07986e32	0.688756
$94$	1.70638e31	0.0473658
$95$	8.97491e32	2.09214
$96$	−1.33087e32	−0.261012
$97$	−6.56839e32	−1.08574	−0.542870	−	0.839817i	$-0.682662\pi$
$97$	−6.56839e32	−1.08574	−0.542870	+	0.839817i	$0.682662\pi$
$98$	5.37169e32	0.749689
$99$	−1.53790e32	−0.181529
$100$	−3.01336e32	−0.301336
$101$	6.25629e32	0.530902	0.265451	−	0.964124i	$-0.414479\pi$
$101$	6.25629e32	0.530902	0.265451	+	0.964124i	$0.414479\pi$
$102$	−9.02992e32	−0.651300
$103$	−1.78958e33	−1.09884	−0.549422	−	0.835545i	$-0.685152\pi$
$103$	−1.78958e33	−1.09884	−0.549422	+	0.835545i	$0.685152\pi$
$104$	−2.84725e33	−1.49065
$105$	−7.46561e32	−0.333766
$106$	−1.66559e33	−0.636828
$107$	5.95632e33	1.95050	0.975249	−	0.221110i	$-0.0709681\pi$
$107$	5.95632e33	1.95050	0.975249	+	0.221110i	$0.0709681\pi$
$108$	−1.58334e32	−0.0444716
$109$	2.52749e33	0.609750	0.304875	−	0.952392i	$-0.401385\pi$
$109$	2.52749e33	0.609750	0.304875	+	0.952392i	$0.401385\pi$
$110$	3.49326e33	0.724855
$111$	2.84624e33	0.508678
$112$	1.76798e33	0.272509
$113$	−8.07301e33	−1.07459	−0.537293	−	0.843396i	$-0.680553\pi$
$113$	−8.07301e33	−1.07459	−0.537293	+	0.843396i	$0.680553\pi$
$114$	−6.06256e33	−0.697793
$115$	1.79718e34	1.79092
$116$	2.45901e33	0.212424
$117$	−6.13894e33	−0.460285
$118$	−4.22724e33	−0.275425
$119$	−8.64341e33	−0.489959
$120$	1.91602e34	0.946042
$121$	−1.63372e34	−0.703425
$122$	−3.71522e34	−1.39652
$123$	2.00305e34	0.658048
$124$	−9.59067e33	−0.275671
$125$	1.83304e34	0.461485
$126$	5.04303e33	0.111321
$127$	−4.85654e34	−0.940947	−0.470474	−	0.882414i	$-0.655917\pi$
$127$	−4.85654e34	−0.940947	−0.470474	+	0.882414i	$0.655917\pi$
$128$	−3.07207e34	−0.522957
$129$	2.03641e34	0.304884
$130$	1.39443e35	1.83794
$131$	−1.37299e35	−1.59474	−0.797370	−	0.603491i	$-0.793776\pi$
$131$	−1.37299e35	−1.59474	−0.797370	+	0.603491i	$0.793776\pi$
$132$	7.09155e33	0.0726560
$133$	−5.80307e34	−0.524935
$134$	1.92133e35	1.53594
$135$	4.13113e34	0.292120
$136$	2.21830e35	1.38876
$137$	−2.75553e34	−0.152867	−0.0764337	−	0.997075i	$-0.524353\pi$
$137$	−2.75553e34	−0.152867	−0.0764337	+	0.997075i	$0.524353\pi$
$138$	−1.21400e35	−0.597328
$139$	−1.41702e35	−0.618916	−0.309458	−	0.950913i	$-0.600148\pi$
$139$	−1.41702e35	−0.618916	−0.309458	+	0.950913i	$0.600148\pi$
$140$	3.44255e34	0.133588
$141$	−9.03815e33	−0.0311863
$142$	1.47227e35	0.452094
$143$	2.74954e35	0.751996
$144$	−9.78322e34	−0.238507
$145$	−6.41586e35	−1.39535
$146$	−7.70471e35	−1.49601
$147$	−2.84522e35	−0.493606
$148$	−1.31246e35	−0.203596
$149$	3.75865e35	0.521745	0.260872	−	0.965373i	$-0.415990\pi$
$149$	3.75865e35	0.521745	0.260872	+	0.965373i	$0.415990\pi$
$150$	−5.31095e35	−0.660186
$151$	3.32978e34	0.0370933	0.0185467	−	0.999828i	$-0.494096\pi$
$151$	3.32978e34	0.0370933	0.0185467	+	0.999828i	$0.494096\pi$
$152$	1.48934e36	1.48790
$153$	4.78287e35	0.428825
$154$	−2.25870e35	−0.181872
$155$	2.50232e36	1.81080
$156$	2.83079e35	0.184227
$157$	−4.35698e35	−0.255177	−0.127588	−	0.991827i	$-0.540724\pi$
$157$	−4.35698e35	−0.255177	−0.127588	+	0.991827i	$0.540724\pi$
$158$	−4.20458e35	−0.221759
$159$	8.82213e35	0.419296
$160$	−1.60119e36	−0.686221
$161$	−1.16203e36	−0.449358
$162$	−2.79059e35	−0.0974311
$163$	8.76558e35	0.276494	0.138247	−	0.990398i	$-0.455853\pi$
$163$	8.76558e35	0.276494	0.138247	+	0.990398i	$0.455853\pi$
$164$	−9.23647e35	−0.263380
$165$	−1.85027e36	−0.477255
$166$	3.84926e36	0.898656
$167$	−4.42450e36	−0.935498	−0.467749	−	0.883861i	$-0.654935\pi$
$167$	−4.42450e36	−0.935498	−0.467749	+	0.883861i	$0.654935\pi$
$168$	−1.23888e36	−0.237370
$169$	5.21943e36	0.906760
$170$	−1.08641e37	−1.71232
$171$	3.21115e36	0.459436
$172$	−9.39029e35	−0.122028
$173$	1.98007e36	0.233840	0.116920	−	0.993141i	$-0.462698\pi$
$173$	1.98007e36	0.233840	0.116920	+	0.993141i	$0.462698\pi$
$174$	4.33392e36	0.465392
$175$	−5.08362e36	−0.496645
$176$	4.38176e36	0.389663
$177$	2.23904e36	0.181344
$178$	−2.42966e36	−0.179314
$179$	−9.34514e36	−0.628797	−0.314399	−	0.949291i	$-0.601803\pi$
$179$	−9.34514e36	−0.628797	−0.314399	+	0.949291i	$0.601803\pi$
$180$	−1.90495e36	−0.116920
$181$	1.54677e37	0.866423	0.433211	−	0.901292i	$-0.357380\pi$
$181$	1.54677e37	0.866423	0.433211	+	0.901292i	$0.357380\pi$
$182$	−9.01623e36	−0.461155
$183$	1.96784e37	0.919488
$184$	2.98232e37	1.27368
$185$	3.42437e37	1.33736
$186$	−1.69032e37	−0.603957
$187$	−2.14218e37	−0.700598
$188$	4.16768e35	0.0124822
$189$	−2.67114e36	−0.0732954
$190$	−7.29399e37	−1.83456
$191$	−1.92891e37	−0.444900	−0.222450	−	0.974944i	$-0.571405\pi$
$191$	−1.92891e37	−0.444900	−0.222450	+	0.974944i	$0.571405\pi$
$192$	3.03384e37	0.641982
$193$	−2.29200e37	−0.445163	−0.222581	−	0.974914i	$-0.571448\pi$
$193$	−2.29200e37	−0.445163	−0.222581	+	0.974914i	$0.571448\pi$
$194$	5.33819e37	0.952063
$195$	−7.38588e37	−1.21013
$196$	1.31199e37	0.197563
$197$	−8.27324e37	−1.14547	−0.572734	−	0.819741i	$-0.694117\pi$
$197$	−8.27324e37	−1.14547	−0.572734	+	0.819741i	$0.694117\pi$
$198$	1.24986e37	0.159179
$199$	5.86543e36	0.0687423	0.0343712	−	0.999409i	$-0.489057\pi$
$199$	5.86543e36	0.0687423	0.0343712	+	0.999409i	$0.489057\pi$
$200$	1.30469e38	1.40771
$201$	−1.01767e38	−1.01128
$202$	−5.08455e37	−0.465538
$203$	4.14842e37	0.350105
$204$	−2.20548e37	−0.171635
$205$	2.40991e38	1.73006
$206$	1.45440e38	0.963554
$207$	6.43018e37	0.393289
$208$	1.74910e38	0.988030
$209$	−1.43823e38	−0.750609
$210$	6.06737e37	0.292673
$211$	−1.77543e38	−0.791849	−0.395924	−	0.918283i	$-0.629576\pi$
$211$	−1.77543e38	−0.791849	−0.395924	+	0.918283i	$0.629576\pi$
$212$	−4.06807e37	−0.167821
$213$	−7.79815e37	−0.297665
$214$	−4.84075e38	−1.71035
$215$	2.45004e38	0.801565
$216$	6.85539e37	0.207752
$217$	−1.61797e38	−0.454344
$218$	−2.05411e38	−0.534678
$219$	4.08095e38	0.984994
$220$	8.53199e37	0.191019
$221$	−8.55110e38	−1.77644
$222$	−2.31317e38	−0.446050
$223$	1.69223e38	0.302991	0.151496	−	0.988458i	$-0.451591\pi$
$223$	1.69223e38	0.302991	0.151496	+	0.988458i	$0.451591\pi$
$224$	1.03531e38	0.172179
$225$	2.81305e38	0.434676
$226$	6.56101e38	0.942283
$227$	1.08500e38	0.144878	0.0724389	−	0.997373i	$-0.476922\pi$
$227$	1.08500e38	0.144878	0.0724389	+	0.997373i	$0.476922\pi$
$228$	−1.48073e38	−0.183887
$229$	1.12197e39	1.29628	0.648138	−	0.761523i	$-0.275548\pi$
$229$	1.12197e39	1.29628	0.648138	+	0.761523i	$0.275548\pi$
$230$	−1.46059e39	−1.57043
$231$	1.19636e38	0.119747
$232$	−1.06468e39	−0.992352
$233$	1.10275e39	0.957425	0.478712	−	0.877972i	$-0.341104\pi$
$233$	1.10275e39	0.957425	0.478712	+	0.877972i	$0.341104\pi$
$234$	4.98917e38	0.403615
$235$	−1.08740e38	−0.0819915
$236$	−1.03247e38	−0.0725819
$237$	2.22704e38	0.146009
$238$	7.02458e38	0.429636
$239$	5.37006e38	0.306488	0.153244	−	0.988188i	$-0.451028\pi$
$239$	5.37006e38	0.306488	0.153244	+	0.988188i	$0.451028\pi$
$240$	−1.17704e39	−0.627054
$241$	3.01700e39	1.50070	0.750349	−	0.661042i	$-0.229885\pi$
$241$	3.01700e39	1.50070	0.750349	+	0.661042i	$0.229885\pi$
$242$	1.32774e39	0.616819
$243$	1.47809e38	0.0641500
$244$	−9.07410e38	−0.368020
$245$	−3.42314e39	−1.29773
$246$	−1.62790e39	−0.577029
$247$	−5.74109e39	−1.90325
$248$	4.15246e39	1.28781
$249$	−2.03883e39	−0.591688
$250$	−1.48973e39	−0.404667
$251$	−1.87895e39	−0.477859	−0.238930	−	0.971037i	$-0.576796\pi$
$251$	−1.87895e39	−0.477859	−0.238930	+	0.971037i	$0.576796\pi$
$252$	1.23172e38	0.0293361
$253$	−2.87998e39	−0.642541
$254$	3.94695e39	0.825098
$255$	5.75437e39	1.12742
$256$	−3.55731e39	−0.653374
$257$	6.73154e39	1.15936	0.579680	−	0.814844i	$-0.303178\pi$
$257$	6.73154e39	1.15936	0.579680	+	0.814844i	$0.303178\pi$
$258$	−1.65501e39	−0.267347
$259$	−2.21416e39	−0.335554
$260$	3.40578e39	0.484347
$261$	−2.29555e39	−0.306420
$262$	1.11584e40	1.39840
$263$	5.65348e38	0.0665344	0.0332672	−	0.999446i	$-0.489409\pi$
$263$	5.65348e38	0.0665344	0.0332672	+	0.999446i	$0.489409\pi$
$264$	−3.07042e39	−0.339417
$265$	1.06141e40	1.10237
$266$	4.71620e39	0.460305
$267$	1.28692e39	0.118063
$268$	4.69269e39	0.404760
$269$	−1.75035e40	−1.41975	−0.709877	−	0.704326i	$-0.751249\pi$
$269$	−1.75035e40	−1.41975	−0.709877	+	0.704326i	$0.751249\pi$
$270$	−3.35741e39	−0.256155
$271$	−1.20904e40	−0.867857	−0.433929	−	0.900947i	$-0.642873\pi$
$271$	−1.20904e40	−0.867857	−0.433929	+	0.900947i	$0.642873\pi$
$272$	−1.36273e40	−0.920499
$273$	4.77562e39	0.303631
$274$	2.23944e39	0.134046
$275$	−1.25992e40	−0.710157
$276$	−2.96509e39	−0.157412
$277$	3.57007e39	0.178550	0.0892752	−	0.996007i	$-0.471545\pi$
$277$	3.57007e39	0.178550	0.0892752	+	0.996007i	$0.471545\pi$
$278$	1.15162e40	0.542715
$279$	8.95312e39	0.397654
$280$	−1.49052e40	−0.624065
$281$	−3.74483e40	−1.47835	−0.739175	−	0.673513i	$-0.764785\pi$
$281$	−3.74483e40	−1.47835	−0.739175	+	0.673513i	$0.764785\pi$
$282$	7.34539e38	0.0273467
$283$	3.35021e40	1.17651	0.588254	−	0.808676i	$-0.299815\pi$
$283$	3.35021e40	1.17651	0.588254	+	0.808676i	$0.299815\pi$
$284$	3.59589e39	0.119139
$285$	3.86340e40	1.20790
$286$	−2.23458e40	−0.659410
$287$	−1.55822e40	−0.434087
$288$	−5.72895e39	−0.150695
$289$	2.63674e40	0.655018
$290$	5.21423e40	1.22355
$291$	−2.82748e40	−0.626852
$292$	−1.88181e40	−0.394238
$293$	1.15254e40	0.228213	0.114106	−	0.993469i	$-0.463599\pi$
$293$	1.15254e40	0.228213	0.114106	+	0.993469i	$0.463599\pi$
$294$	2.31234e40	0.432833
$295$	2.69384e40	0.476769
$296$	5.68256e40	0.951110
$297$	−6.62013e39	−0.104806
$298$	−3.05469e40	−0.457507
$299$	−1.14962e41	−1.62923
$300$	−1.29715e40	−0.173977
$301$	−1.58417e40	−0.201119
$302$	−2.70614e39	−0.0325264
$303$	2.69313e40	0.306517
$304$	−9.14919e40	−0.986208
$305$	2.36754e41	2.41741
$306$	−3.88708e40	−0.376028
$307$	1.08038e41	0.990357	0.495179	−	0.868791i	$-0.335103\pi$
$307$	1.08038e41	0.990357	0.495179	+	0.868791i	$0.335103\pi$
$308$	−5.51668e39	−0.0479282
$309$	−7.70354e40	−0.634418
$310$	−2.03366e41	−1.58785
$311$	−1.74640e41	−1.29300	−0.646499	−	0.762915i	$-0.723768\pi$
$311$	−1.74640e41	−1.29300	−0.646499	+	0.762915i	$0.723768\pi$
$312$	−1.22565e41	−0.860626
$313$	1.84552e41	1.22924	0.614621	−	0.788823i	$-0.289309\pi$
$313$	1.84552e41	1.22924	0.614621	+	0.788823i	$0.289309\pi$
$314$	3.54096e40	0.223759
$315$	−3.21370e40	−0.192700
$316$	−1.02693e40	−0.0584393
$317$	−2.48316e41	−1.34130	−0.670652	−	0.741772i	$-0.733985\pi$
$317$	−2.48316e41	−1.34130	−0.670652	+	0.741772i	$0.733985\pi$
$318$	−7.16983e40	−0.367673
$319$	1.02814e41	0.500618
$320$	3.65007e41	1.68782
$321$	2.56400e41	1.12612
$322$	9.44396e40	0.394033
$323$	4.47291e41	1.77316
$324$	−6.81577e39	−0.0256757
$325$	−5.02933e41	−1.80067
$326$	−7.12387e40	−0.242452
$327$	1.08800e41	0.352039
$328$	3.99911e41	1.23040
$329$	7.03098e39	0.0205723
$330$	1.50373e41	0.418495
$331$	−4.31549e41	−1.14253	−0.571266	−	0.820765i	$-0.693548\pi$
$331$	−4.31549e41	−1.14253	−0.571266	+	0.820765i	$0.693548\pi$
$332$	9.40148e40	0.236820
$333$	1.22521e41	0.293685
$334$	3.59583e41	0.820319
$335$	−1.22438e42	−2.65875
$336$	7.61059e40	0.157333
$337$	1.26028e40	0.0248070	0.0124035	−	0.999923i	$-0.496052\pi$
$337$	1.26028e40	0.0248070	0.0124035	+	0.999923i	$0.496052\pi$
$338$	−4.24188e41	−0.795120
$339$	−3.47517e41	−0.620413
$340$	−2.65346e41	−0.451243
$341$	−4.00997e41	−0.649671
$342$	−2.60974e41	−0.402871
$343$	4.80224e41	0.706465
$344$	4.06571e41	0.570062
$345$	7.73627e41	1.03399
$346$	−1.60922e41	−0.205050
$347$	−3.74663e41	−0.455203	−0.227601	−	0.973754i	$-0.573088\pi$
$347$	−3.74663e41	−0.455203	−0.227601	+	0.973754i	$0.573088\pi$
$348$	1.05852e41	0.122643
$349$	9.31275e41	1.02910	0.514551	−	0.857460i	$-0.327959\pi$
$349$	9.31275e41	1.02910	0.514551	+	0.857460i	$0.327959\pi$
$350$	4.13151e41	0.435498
$351$	−2.64261e41	−0.265746
$352$	2.56591e41	0.246200
$353$	5.48298e41	0.502035	0.251017	−	0.967983i	$-0.419235\pi$
$353$	5.48298e41	0.502035	0.251017	+	0.967983i	$0.419235\pi$
$354$	−1.81969e41	−0.159017
$355$	−9.38211e41	−0.782587
$356$	−5.93423e40	−0.0472541
$357$	−3.72070e41	−0.282878
$358$	7.59488e41	0.551380
$359$	1.35776e41	0.0941378	0.0470689	−	0.998892i	$-0.485012\pi$
$359$	1.35776e41	0.0941378	0.0470689	+	0.998892i	$0.485012\pi$
$360$	8.24785e41	0.546197
$361$	1.42228e42	0.899737
$362$	−1.25708e42	−0.759749
$363$	−7.03261e41	−0.406123
$364$	−2.20214e41	−0.121527
$365$	4.90987e42	2.58963
$366$	−1.59928e42	−0.806281
$367$	−2.75920e42	−1.32982	−0.664909	−	0.746924i	$-0.731530\pi$
$367$	−2.75920e42	−1.32982	−0.664909	+	0.746924i	$0.731530\pi$
$368$	−1.83208e42	−0.844220
$369$	8.62247e41	0.379924
$370$	−2.78302e42	−1.17270
$371$	−6.86294e41	−0.276592
$372$	−4.12847e41	−0.159159
$373$	−2.85732e41	−0.105381	−0.0526907	−	0.998611i	$-0.516780\pi$
$373$	−2.85732e41	−0.105381	−0.0526907	+	0.998611i	$0.516780\pi$
$374$	1.74097e42	0.614340
$375$	7.89065e41	0.266439
$376$	−1.80448e41	−0.0583112
$377$	4.10411e42	1.26937
$378$	2.17086e41	0.0642713
$379$	−4.89498e42	−1.38741	−0.693704	−	0.720260i	$-0.744023\pi$
$379$	−4.89498e42	−1.38741	−0.693704	+	0.720260i	$0.744023\pi$
$380$	−1.78150e42	−0.483454
$381$	−2.09058e42	−0.543256
$382$	1.56765e42	0.390124
$383$	−9.26621e41	−0.220863	−0.110431	−	0.993884i	$-0.535223\pi$
$383$	−9.26621e41	−0.220863	−0.110431	+	0.993884i	$0.535223\pi$
$384$	−1.32242e42	−0.301929
$385$	1.43937e42	0.314825
$386$	1.86273e42	0.390354
$387$	8.76607e41	0.176025
$388$	1.30381e42	0.250894
$389$	−3.04785e42	−0.562114	−0.281057	−	0.959691i	$-0.590685\pi$
$389$	−3.04785e42	−0.562114	−0.281057	+	0.959691i	$0.590685\pi$
$390$	6.00257e42	1.06114
$391$	8.95677e42	1.51787
$392$	−5.68052e42	−0.922928
$393$	−5.91026e42	−0.920723
$394$	6.72374e42	1.00444
$395$	2.67939e42	0.383870
$396$	3.05268e41	0.0419479
$397$	1.35863e43	1.79085	0.895425	−	0.445212i	$-0.146872\pi$
$397$	1.35863e43	1.79085	0.895425	+	0.445212i	$0.146872\pi$
$398$	−4.76689e41	−0.0602788
$399$	−2.49803e42	−0.303071
$400$	−8.01491e42	−0.933058
$401$	−4.45094e42	−0.497244	−0.248622	−	0.968601i	$-0.579978\pi$
$401$	−4.45094e42	−0.497244	−0.248622	+	0.968601i	$0.579978\pi$
$402$	8.27071e42	0.886774
$403$	−1.60069e43	−1.64731
$404$	−1.24186e42	−0.122682
$405$	1.77832e42	0.168656
$406$	−3.37146e42	−0.307000
$407$	−5.48755e42	−0.479812
$408$	9.54906e42	0.801803
$409$	−1.72623e42	−0.139208	−0.0696040	−	0.997575i	$-0.522174\pi$
$409$	−1.72623e42	−0.139208	−0.0696040	+	0.997575i	$0.522174\pi$
$410$	−1.95855e43	−1.51706
$411$	−1.18616e42	−0.0882581
$412$	3.55226e42	0.253922
$413$	−1.74180e42	−0.119625
$414$	−5.22586e42	−0.344868
$415$	−2.45296e43	−1.55560
$416$	1.02426e43	0.624264
$417$	−6.09980e42	−0.357331
$418$	1.16886e43	0.658194
$419$	3.17161e42	0.171692	0.0858458	−	0.996308i	$-0.472641\pi$
$419$	3.17161e42	0.171692	0.0858458	+	0.996308i	$0.472641\pi$
$420$	1.48190e42	0.0771270
$421$	2.93978e43	1.47116	0.735581	−	0.677437i	$-0.236909\pi$
$421$	2.93978e43	1.47116	0.735581	+	0.677437i	$0.236909\pi$
$422$	1.44291e43	0.694356
$423$	−3.89063e41	−0.0180054
$424$	1.76135e43	0.783987
$425$	3.91837e43	1.67760
$426$	6.33763e42	0.261017
$427$	−1.53082e43	−0.606548
$428$	−1.18231e43	−0.450723
$429$	1.18359e43	0.434165
$430$	−1.99117e43	−0.702877
$431$	−1.58221e43	−0.537514	−0.268757	−	0.963208i	$-0.586613\pi$
$431$	−1.58221e43	−0.537514	−0.268757	+	0.963208i	$0.586613\pi$
$432$	−4.21135e42	−0.137702
$433$	−2.09797e43	−0.660310	−0.330155	−	0.943927i	$-0.607101\pi$
$433$	−2.09797e43	−0.660310	−0.330155	+	0.943927i	$0.607101\pi$
$434$	1.31494e43	0.398405
$435$	−2.76182e43	−0.805605
$436$	−5.01699e42	−0.140902
$437$	6.01345e43	1.62622
$438$	−3.31663e43	−0.863721
$439$	−2.43485e43	−0.610671	−0.305335	−	0.952245i	$-0.598769\pi$
$439$	−2.43485e43	−0.610671	−0.305335	+	0.952245i	$0.598769\pi$
$440$	−3.69409e43	−0.892356
$441$	−1.22477e43	−0.284983
$442$	6.94956e43	1.55772
$443$	1.69015e42	0.0364974	0.0182487	−	0.999833i	$-0.494191\pi$
$443$	1.69015e42	0.0364974	0.0182487	+	0.999833i	$0.494191\pi$
$444$	−5.64972e42	−0.117546
$445$	1.54831e43	0.310398
$446$	−1.37529e43	−0.265687
$447$	1.61797e43	0.301229
$448$	−2.36009e43	−0.423489
$449$	−4.20978e43	−0.728106	−0.364053	−	0.931378i	$-0.618607\pi$
$449$	−4.20978e43	−0.728106	−0.364053	+	0.931378i	$0.618607\pi$
$450$	−2.28619e43	−0.381159
$451$	−3.86187e43	−0.620705
$452$	1.60247e43	0.248317
$453$	1.43336e42	0.0214159
$454$	−8.81787e42	−0.127041
$455$	5.74564e43	0.798272
$456$	6.41111e43	0.859039
$457$	−2.83335e43	−0.366170	−0.183085	−	0.983097i	$-0.558608\pi$
$457$	−2.83335e43	−0.366170	−0.183085	+	0.983097i	$0.558608\pi$
$458$	−9.11838e43	−1.13668
$459$	2.05887e43	0.247582
$460$	−3.56735e43	−0.413849
$461$	7.85165e43	0.878812	0.439406	−	0.898289i	$-0.355189\pi$
$461$	7.85165e43	0.878812	0.439406	+	0.898289i	$0.355189\pi$
$462$	−9.72295e42	−0.105004
$463$	1.07156e44	1.11668	0.558342	−	0.829611i	$-0.311438\pi$
$463$	1.07156e44	1.11668	0.558342	+	0.829611i	$0.311438\pi$
$464$	6.54045e43	0.657750
$465$	1.07717e44	1.04547
$466$	−8.96216e43	−0.839547
$467$	−1.40278e44	−1.26841	−0.634207	−	0.773163i	$-0.718673\pi$
$467$	−1.40278e44	−1.26841	−0.634207	+	0.773163i	$0.718673\pi$
$468$	1.21856e43	0.106363
$469$	7.91669e43	0.667101
$470$	8.83738e42	0.0718967
$471$	−1.87554e43	−0.147326
$472$	4.47027e43	0.339071
$473$	−3.92619e43	−0.287582
$474$	−1.80993e43	−0.128032
$475$	2.63074e44	1.79735
$476$	1.71569e43	0.113220
$477$	3.79764e43	0.242081
$478$	−4.36430e43	−0.268753
$479$	−8.38081e43	−0.498598	−0.249299	−	0.968427i	$-0.580200\pi$
$479$	−8.38081e43	−0.498598	−0.249299	+	0.968427i	$0.580200\pi$
$480$	−6.89261e43	−0.396190
$481$	−2.19051e44	−1.21661
$482$	−2.45194e44	−1.31593
$483$	−5.00218e43	−0.259437
$484$	3.24288e43	0.162548
$485$	−3.40179e44	−1.64805
$486$	−1.20126e43	−0.0562519
$487$	−3.03323e43	−0.137302	−0.0686510	−	0.997641i	$-0.521870\pi$
$487$	−3.03323e43	−0.137302	−0.0686510	+	0.997641i	$0.521870\pi$
$488$	3.92881e44	1.71923
$489$	3.77330e43	0.159634
$490$	2.78202e44	1.13795
$491$	−2.37164e44	−0.938003	−0.469002	−	0.883197i	$-0.655386\pi$
$491$	−2.37164e44	−0.938003	−0.469002	+	0.883197i	$0.655386\pi$
$492$	−3.97600e43	−0.152062
$493$	−3.19753e44	−1.18261
$494$	4.66584e44	1.66892
$495$	−7.96481e43	−0.275543
$496$	−2.55091e44	−0.853588
$497$	6.06636e43	0.196358
$498$	1.65698e44	0.518839
$499$	9.10376e43	0.275779	0.137890	−	0.990448i	$-0.455968\pi$
$499$	9.10376e43	0.275779	0.137890	+	0.990448i	$0.455968\pi$
$500$	−3.63854e43	−0.106641
$501$	−1.90460e44	−0.540110
$502$	1.52704e44	0.419025
$503$	6.97448e44	1.85199	0.925997	−	0.377530i	$-0.123226\pi$
$503$	6.97448e44	1.85199	0.925997	+	0.377530i	$0.123226\pi$
$504$	−5.33296e43	−0.137045
$505$	3.24016e44	0.805858
$506$	2.34059e44	0.563431
$507$	2.24679e44	0.523518
$508$	9.64009e43	0.217435
$509$	2.47285e43	0.0539951	0.0269976	−	0.999635i	$-0.491405\pi$
$509$	2.47285e43	0.0539951	0.0269976	+	0.999635i	$0.491405\pi$
$510$	−4.67663e44	−0.988610
$511$	−3.17466e44	−0.649760
$512$	5.52994e44	1.09589
$513$	1.38230e44	0.265256
$514$	−5.47079e44	−1.01662
$515$	−9.26828e44	−1.66794
$516$	−4.04221e43	−0.0704529
$517$	1.74255e43	0.0294166
$518$	1.79947e44	0.294241
$519$	8.52354e43	0.135008
$520$	−1.47460e45	−2.26266
$521$	−5.68488e44	−0.845083	−0.422541	−	0.906344i	$-0.638862\pi$
$521$	−5.68488e44	−0.845083	−0.422541	+	0.906344i	$0.638862\pi$
$522$	1.86561e44	0.268694
$523$	4.69149e44	0.654686	0.327343	−	0.944906i	$-0.393847\pi$
$523$	4.69149e44	0.654686	0.327343	+	0.944906i	$0.393847\pi$
$524$	2.72534e44	0.368514
$525$	−2.18833e44	−0.286738
$526$	−4.59463e43	−0.0583427
$527$	1.24710e45	1.53471
$528$	1.88620e44	0.224972
$529$	3.39159e44	0.392089
$530$	−8.62616e44	−0.966642
$531$	9.63834e43	0.104699
$532$	1.15189e44	0.121303
$533$	−1.54158e45	−1.57386
$534$	−1.04589e44	−0.103527
$535$	3.08480e45	2.96067
$536$	−2.03179e45	−1.89086
$537$	−4.02277e44	−0.363036
$538$	1.42253e45	1.24495
$539$	5.48558e44	0.465595
$540$	−8.20019e43	−0.0675036
$541$	−8.09047e44	−0.645980	−0.322990	−	0.946402i	$-0.604688\pi$
$541$	−8.09047e44	−0.645980	−0.322990	+	0.946402i	$0.604688\pi$
$542$	9.82600e44	0.761007
$543$	6.65835e44	0.500229
$544$	−7.98001e44	−0.581596
$545$	1.30900e45	0.925541
$546$	−3.88119e44	−0.266248
$547$	−1.56788e45	−1.04357	−0.521785	−	0.853077i	$-0.674734\pi$
$547$	−1.56788e45	−1.04357	−0.521785	+	0.853077i	$0.674734\pi$
$548$	5.46964e43	0.0353248
$549$	8.47089e44	0.530867
$550$	1.02395e45	0.622722
$551$	−2.14678e45	−1.26703
$552$	1.28379e45	0.735360
$553$	−1.73246e44	−0.0963162
$554$	−2.90143e44	−0.156567
$555$	1.47408e45	0.772124
$556$	2.81275e44	0.143020
$557$	−5.87364e44	−0.289932	−0.144966	−	0.989437i	$-0.546307\pi$
$557$	−5.87364e44	−0.289932	−0.144966	+	0.989437i	$0.546307\pi$
$558$	−7.27628e44	−0.348695
$559$	−1.56725e45	−0.729194
$560$	9.15645e44	0.413642
$561$	−9.22137e44	−0.404490
$562$	3.04346e45	1.29634
$563$	3.47988e45	1.43938	0.719691	−	0.694295i	$-0.244284\pi$
$563$	3.47988e45	1.43938	0.719691	+	0.694295i	$0.244284\pi$
$564$	1.79405e43	0.00720657
$565$	−4.18104e45	−1.63112
$566$	−2.72274e45	−1.03166
$567$	−1.14984e44	−0.0423171
$568$	−1.55691e45	−0.556565
$569$	−1.84148e45	−0.639462	−0.319731	−	0.947508i	$-0.603592\pi$
$569$	−1.84148e45	−0.639462	−0.319731	+	0.947508i	$0.603592\pi$
$570$	−3.13982e45	−1.05918
$571$	−3.82958e45	−1.25503	−0.627517	−	0.778603i	$-0.715929\pi$
$571$	−3.82958e45	−1.25503	−0.627517	+	0.778603i	$0.715929\pi$
$572$	−5.45776e44	−0.173772
$573$	−8.30335e44	−0.256863
$574$	1.26638e45	0.380642
$575$	5.26793e45	1.53858
$576$	1.30597e45	0.370648
$577$	4.49659e45	1.24017	0.620087	−	0.784533i	$-0.287097\pi$
$577$	4.49659e45	1.24017	0.620087	+	0.784533i	$0.287097\pi$
$578$	−2.14291e45	−0.574373
$579$	−9.86631e44	−0.257015
$580$	1.27353e45	0.322439
$581$	1.58605e45	0.390312
$582$	2.29792e45	0.549674
$583$	−1.70091e45	−0.395502
$584$	8.14766e45	1.84171
$585$	−3.17938e45	−0.698668
$586$	−9.36680e44	−0.200115
$587$	4.44787e45	0.923897	0.461949	−	0.886907i	$-0.347150\pi$
$587$	4.44787e45	0.923897	0.461949	+	0.886907i	$0.347150\pi$
$588$	5.64769e44	0.114063
$589$	8.37289e45	1.64427
$590$	−2.18930e45	−0.418069
$591$	−3.56136e45	−0.661336
$592$	−3.49087e45	−0.630414
$593$	−1.98733e45	−0.349034	−0.174517	−	0.984654i	$-0.555836\pi$
$593$	−1.98733e45	−0.349034	−0.174517	+	0.984654i	$0.555836\pi$
$594$	5.38024e44	0.0919021
$595$	−4.47645e45	−0.743711
$596$	−7.46081e44	−0.120565
$597$	2.52488e44	0.0396884
$598$	9.34311e45	1.42864
$599$	−4.92255e45	−0.732230	−0.366115	−	0.930570i	$-0.619312\pi$
$599$	−4.92255e45	−0.732230	−0.366115	+	0.930570i	$0.619312\pi$
$600$	5.61628e45	0.812743
$601$	−1.08800e46	−1.53179	−0.765897	−	0.642964i	$-0.777705\pi$
$601$	−1.08800e46	−1.53179	−0.765897	+	0.642964i	$0.777705\pi$
$602$	1.28747e45	0.176358
$603$	−4.38074e45	−0.583864
$604$	−6.60952e43	−0.00857158
$605$	−8.46107e45	−1.06773
$606$	−2.18873e45	−0.268778
$607$	1.54173e46	1.84244	0.921221	−	0.389040i	$-0.127193\pi$
$607$	1.54173e46	1.84244	0.921221	+	0.389040i	$0.127193\pi$
$608$	−5.35767e45	−0.623113
$609$	1.78576e45	0.202133
$610$	−1.92412e46	−2.11978
$611$	6.95589e44	0.0745887
$612$	−9.49387e44	−0.0990934
$613$	−1.21132e46	−1.23073	−0.615365	−	0.788242i	$-0.710991\pi$
$613$	−1.21132e46	−1.23073	−0.615365	+	0.788242i	$0.710991\pi$
$614$	−8.78032e45	−0.868424
$615$	1.03739e46	0.998852
$616$	2.38855e45	0.223899
$617$	1.84533e46	1.68411	0.842054	−	0.539394i	$-0.181347\pi$
$617$	1.84533e46	1.68411	0.842054	+	0.539394i	$0.181347\pi$
$618$	6.26074e45	0.556308
$619$	9.86703e45	0.853671	0.426836	−	0.904329i	$-0.359628\pi$
$619$	9.86703e45	0.853671	0.426836	+	0.904329i	$0.359628\pi$
$620$	−4.96704e45	−0.418442
$621$	2.76798e45	0.227066
$622$	1.41932e46	1.13380
$623$	−1.00112e45	−0.0778814
$624$	7.52931e45	0.570439
$625$	−8.17948e45	−0.603539
$626$	−1.49987e46	−1.07790
$627$	−6.19110e45	−0.433365
$628$	8.64848e44	0.0589665
$629$	1.70664e46	1.13346
$630$	2.61180e45	0.168975
$631$	4.19804e45	0.264583	0.132291	−	0.991211i	$-0.457767\pi$
$631$	4.19804e45	0.264583	0.132291	+	0.991211i	$0.457767\pi$
$632$	4.44631e45	0.273003
$633$	−7.64263e45	−0.457174
$634$	2.01809e46	1.17616
$635$	−2.51522e46	−1.42827
$636$	−1.75117e45	−0.0968915
$637$	2.18972e46	1.18056
$638$	−8.35579e45	−0.438982
$639$	−3.35685e45	−0.171857
$640$	−1.59103e46	−0.793798
$641$	4.61654e45	0.224470	0.112235	−	0.993682i	$-0.464199\pi$
$641$	4.61654e45	0.224470	0.112235	+	0.993682i	$0.464199\pi$
$642$	−2.08379e46	−0.987473
$643$	2.40828e46	1.11231	0.556155	−	0.831078i	$-0.312276\pi$
$643$	2.40828e46	1.11231	0.556155	+	0.831078i	$0.312276\pi$
$644$	2.30661e45	0.103838
$645$	1.05466e46	0.462784
$646$	−3.63517e46	−1.55485
$647$	−1.82163e46	−0.759521	−0.379760	−	0.925085i	$-0.623994\pi$
$647$	−1.82163e46	−0.759521	−0.379760	+	0.925085i	$0.623994\pi$
$648$	2.95102e45	0.119946
$649$	−4.31687e45	−0.171053
$650$	4.08739e46	1.57897
$651$	−6.96483e45	−0.262316
$652$	−1.73994e45	−0.0638925
$653$	2.56540e46	0.918516	0.459258	−	0.888303i	$-0.348115\pi$
$653$	2.56540e46	0.918516	0.459258	+	0.888303i	$0.348115\pi$
$654$	−8.84228e45	−0.308696
$655$	−7.11075e46	−2.42066
$656$	−2.45671e46	−0.815530
$657$	1.75672e46	0.568686
$658$	−5.71414e44	−0.0180395
$659$	3.46081e46	1.06554	0.532768	−	0.846262i	$-0.321152\pi$
$659$	3.46081e46	1.06554	0.532768	+	0.846262i	$0.321152\pi$
$660$	3.67274e45	0.110285
$661$	4.34316e46	1.27198	0.635992	−	0.771695i	$-0.280591\pi$
$661$	4.34316e46	1.27198	0.635992	+	0.771695i	$0.280591\pi$
$662$	3.50724e46	1.00186
$663$	−3.68097e46	−1.02563
$664$	−4.07055e46	−1.10632
$665$	−3.00543e46	−0.796800
$666$	−9.95743e45	−0.257527
$667$	−4.29882e46	−1.08461
$668$	8.78252e45	0.216176
$669$	7.28451e45	0.174932
$670$	9.95065e46	2.33140
$671$	−3.79398e46	−0.867309
$672$	4.45668e45	0.0994073
$673$	−1.33190e46	−0.289884	−0.144942	−	0.989440i	$-0.546300\pi$
$673$	−1.33190e46	−0.289884	−0.144942	+	0.989440i	$0.546300\pi$
$674$	−1.02424e45	−0.0217527
$675$	1.21093e46	0.250960
$676$	−1.03604e46	−0.209535
$677$	7.51587e46	1.48343	0.741714	−	0.670717i	$-0.234013\pi$
$677$	7.51587e46	1.48343	0.741714	+	0.670717i	$0.234013\pi$
$678$	2.82430e46	0.544028
$679$	2.19956e46	0.413508
$680$	1.14887e47	2.10801
$681$	4.67056e45	0.0836453
$682$	3.25894e46	0.569684
$683$	−6.21215e46	−1.05999	−0.529994	−	0.848002i	$-0.677806\pi$
$683$	−6.21215e46	−1.05999	−0.529994	+	0.848002i	$0.677806\pi$
$684$	−6.37406e45	−0.106167
$685$	−1.42710e46	−0.232038
$686$	−3.90283e46	−0.619486
$687$	4.82973e46	0.748405
$688$	−2.49762e46	−0.377848
$689$	−6.78964e46	−1.00284
$690$	−6.28734e46	−0.906686
$691$	−1.00092e47	−1.40932	−0.704660	−	0.709545i	$-0.748901\pi$
$691$	−1.00092e47	−1.40932	−0.704660	+	0.709545i	$0.748901\pi$
$692$	−3.93038e45	−0.0540361
$693$	5.14995e45	0.0691361
$694$	3.04492e46	0.399158
$695$	−7.33880e46	−0.939454
$696$	−4.58308e46	−0.572935
$697$	1.20105e47	1.46629
$698$	−7.56856e46	−0.902399
$699$	4.74698e46	0.552769
$700$	1.00909e46	0.114765
$701$	−1.45114e47	−1.61199	−0.805997	−	0.591919i	$-0.798370\pi$
$701$	−1.45114e47	−1.61199	−0.805997	+	0.591919i	$0.798370\pi$
$702$	2.14768e46	0.233027
$703$	1.14581e47	1.21437
$704$	−5.84924e46	−0.605551
$705$	−4.68089e45	−0.0473378
$706$	−4.45607e46	−0.440224
$707$	−2.09505e46	−0.202196
$708$	−4.44444e45	−0.0419052
$709$	−8.80696e46	−0.811265	−0.405633	−	0.914036i	$-0.632949\pi$
$709$	−8.80696e46	−0.811265	−0.405633	+	0.914036i	$0.632949\pi$
$710$	7.62493e46	0.686235
$711$	9.58667e45	0.0842984
$712$	2.56934e46	0.220751
$713$	1.67663e47	1.40754
$714$	3.02385e46	0.248050
$715$	1.42400e47	1.14146
$716$	1.85498e46	0.145303
$717$	2.31163e46	0.176951
$718$	−1.10346e46	−0.0825475
$719$	2.08060e47	1.52112	0.760558	−	0.649270i	$-0.224926\pi$
$719$	2.08060e47	1.52112	0.760558	+	0.649270i	$0.224926\pi$
$720$	−5.06676e46	−0.362030
$721$	5.99276e46	0.418499
$722$	−1.15590e47	−0.788961
$723$	1.29872e47	0.866429
$724$	−3.07030e46	−0.200214
$725$	−1.88063e47	−1.19874
$726$	5.71547e46	0.356121
$727$	−2.27614e47	−1.38638	−0.693189	−	0.720756i	$-0.743795\pi$
$727$	−2.27614e47	−1.38638	−0.693189	+	0.720756i	$0.743795\pi$
$728$	9.53458e46	0.567719
$729$	6.36269e45	0.0370370
$730$	−3.99030e47	−2.27080
$731$	1.22105e47	0.679354
$732$	−3.90610e46	−0.212476
$733$	2.76398e47	1.47001	0.735004	−	0.678063i	$-0.237180\pi$
$733$	2.76398e47	1.47001	0.735004	+	0.678063i	$0.237180\pi$
$734$	2.24242e47	1.16609
$735$	−1.47355e47	−0.749245
$736$	−1.07285e47	−0.533401
$737$	1.96207e47	0.953895
$738$	−7.00756e46	−0.333148
$739$	−6.98734e46	−0.324847	−0.162423	−	0.986721i	$-0.551931\pi$
$739$	−6.98734e46	−0.324847	−0.162423	+	0.986721i	$0.551931\pi$
$740$	−6.79729e46	−0.309038
$741$	−2.47135e47	−1.09884
$742$	5.57757e46	0.242538
$743$	−2.67820e47	−1.13901	−0.569505	−	0.821988i	$-0.692865\pi$
$743$	−2.67820e47	−1.13901	−0.569505	+	0.821988i	$0.692865\pi$
$744$	1.78750e47	0.743520
$745$	1.94662e47	0.791957
$746$	2.32217e46	0.0924068
$747$	−8.77651e46	−0.341611
$748$	4.25216e46	0.161895
$749$	−1.99459e47	−0.742855
$750$	−6.41281e46	−0.233635
$751$	4.75386e46	0.169429	0.0847144	−	0.996405i	$-0.473002\pi$
$751$	4.75386e46	0.169429	0.0847144	+	0.996405i	$0.473002\pi$
$752$	1.10851e46	0.0386498
$753$	−8.08828e46	−0.275892
$754$	−3.33545e47	−1.11308
$755$	1.72451e46	0.0563041
$756$	5.30214e45	0.0169372
$757$	−2.78767e47	−0.871282	−0.435641	−	0.900121i	$-0.643478\pi$
$757$	−2.78767e47	−0.871282	−0.435641	+	0.900121i	$0.643478\pi$
$758$	3.97820e47	1.21659
$759$	−1.23974e47	−0.370971
$760$	7.71333e47	2.25849
$761$	1.74435e47	0.499790	0.249895	−	0.968273i	$-0.419604\pi$
$761$	1.74435e47	0.499790	0.249895	+	0.968273i	$0.419604\pi$
$762$	1.69903e47	0.476370
$763$	−8.46380e46	−0.232226
$764$	3.82884e46	0.102808
$765$	2.47707e47	0.650915
$766$	7.53073e46	0.193670
$767$	−1.72320e47	−0.433723
$768$	−1.53130e47	−0.377226
$769$	−6.02112e47	−1.45175	−0.725877	−	0.687825i	$-0.758566\pi$
$769$	−6.02112e47	−1.45175	−0.725877	+	0.687825i	$0.758566\pi$
$770$	−1.16979e47	−0.276064
$771$	2.89771e47	0.669357
$772$	4.54956e46	0.102869
$773$	−3.48813e46	−0.0772024	−0.0386012	−	0.999255i	$-0.512290\pi$
$773$	−3.48813e46	−0.0772024	−0.0386012	+	0.999255i	$0.512290\pi$
$774$	−7.12426e46	−0.154353
$775$	7.33485e47	1.55565
$776$	−5.64509e47	−1.17207
$777$	−9.53122e46	−0.193732
$778$	2.47701e47	0.492907
$779$	8.06367e47	1.57096
$780$	1.46608e47	0.279638
$781$	1.50348e47	0.280774
$782$	−7.27925e47	−1.33099
$783$	−9.88158e46	−0.176912
$784$	3.48962e47	0.611734
$785$	−2.25649e47	−0.387333
$786$	4.80332e47	0.807364
$787$	−3.81267e47	−0.627546	−0.313773	−	0.949498i	$-0.601593\pi$
$787$	−3.81267e47	−0.627546	−0.313773	+	0.949498i	$0.601593\pi$
$788$	1.64222e47	0.264696
$789$	2.43364e46	0.0384136
$790$	−2.17757e47	−0.336608
$791$	2.70341e47	0.409261
$792$	−1.32172e47	−0.195962
$793$	−1.51448e48	−2.19915
$794$	−1.10417e48	−1.57036
$795$	4.56901e47	0.636451
$796$	−1.16427e46	−0.0158851
$797$	−3.54905e47	−0.474297	−0.237148	−	0.971473i	$-0.576213\pi$
$797$	−3.54905e47	−0.474297	−0.237148	+	0.971473i	$0.576213\pi$
$798$	2.03017e47	0.265757
$799$	−5.41936e46	−0.0694906
$800$	−4.69345e47	−0.589532
$801$	5.53975e46	0.0681638
$802$	3.61732e47	0.436024
$803$	−7.86806e47	−0.929098
$804$	2.02005e47	0.233688
$805$	−6.01822e47	−0.682081
$806$	1.30090e48	1.44449
$807$	−7.53470e47	−0.819695
$808$	5.37686e47	0.573115
$809$	8.95740e47	0.935473	0.467736	−	0.883868i	$-0.345070\pi$
$809$	8.95740e47	0.935473	0.467736	+	0.883868i	$0.345070\pi$
$810$	−1.44525e47	−0.147891
$811$	1.69350e48	1.69802	0.849008	−	0.528380i	$-0.177200\pi$
$811$	1.69350e48	1.69802	0.849008	+	0.528380i	$0.177200\pi$
$812$	−8.23449e46	−0.0809026
$813$	−5.20453e47	−0.501058
$814$	4.45978e47	0.420737
$815$	4.53973e47	0.419691
$816$	−5.86611e47	−0.531450
$817$	8.19796e47	0.727850
$818$	1.40292e47	0.122069
$819$	2.05575e47	0.175301
$820$	−4.78360e47	−0.399785
$821$	1.61425e48	1.32223	0.661116	−	0.750283i	$-0.270083\pi$
$821$	1.61425e48	1.32223	0.661116	+	0.750283i	$0.270083\pi$
$822$	9.64006e46	0.0773917
$823$	1.91494e48	1.50681	0.753404	−	0.657557i	$-0.228410\pi$
$823$	1.91494e48	1.50681	0.753404	+	0.657557i	$0.228410\pi$
$824$	−1.53802e48	−1.18621
$825$	−5.42355e47	−0.410009
$826$	1.41558e47	0.104897
$827$	1.00878e48	0.732753	0.366376	−	0.930467i	$-0.380598\pi$
$827$	1.00878e48	0.732753	0.366376	+	0.930467i	$0.380598\pi$
$828$	−1.27637e47	−0.0908818
$829$	−2.11059e48	−1.47317	−0.736587	−	0.676343i	$-0.763564\pi$
$829$	−2.11059e48	−1.47317	−0.736587	+	0.676343i	$0.763564\pi$
$830$	1.99354e48	1.36407
$831$	1.53680e47	0.103086
$832$	−2.33489e48	−1.53543
$833$	−1.70602e48	−1.09987
$834$	4.95737e47	0.313337
$835$	−2.29147e48	−1.41999
$836$	2.85484e47	0.173452
$837$	3.85402e47	0.229585
$838$	−2.57760e47	−0.150553
$839$	6.29564e47	0.360552	0.180276	−	0.983616i	$-0.442301\pi$
$839$	6.29564e47	0.360552	0.180276	+	0.983616i	$0.442301\pi$
$840$	−6.41619e47	−0.360304
$841$	−2.81416e47	−0.154958
$842$	−2.38919e48	−1.29003
$843$	−1.61203e48	−0.853526
$844$	3.52417e47	0.182981
$845$	2.70316e48	1.37637
$846$	3.16195e46	0.0157886
$847$	5.47082e47	0.267902
$848$	−1.08202e48	−0.519641
$849$	1.44215e48	0.679258
$850$	−3.18450e48	−1.47105
$851$	2.29443e48	1.03953
$852$	1.54791e47	0.0687849
$853$	1.62291e48	0.707350	0.353675	−	0.935368i	$-0.384932\pi$
$853$	1.62291e48	0.707350	0.353675	+	0.935368i	$0.384932\pi$
$854$	1.24411e48	0.531870
$855$	1.66307e48	0.697380
$856$	5.11905e48	2.10558
$857$	−2.42272e48	−0.977506	−0.488753	−	0.872422i	$-0.662548\pi$
$857$	−2.42272e48	−0.977506	−0.488753	+	0.872422i	$0.662548\pi$
$858$	−9.61912e47	−0.380711
$859$	−4.05624e48	−1.57484	−0.787421	−	0.616416i	$-0.788584\pi$
$859$	−4.05624e48	−1.57484	−0.787421	+	0.616416i	$0.788584\pi$
$860$	−4.86327e47	−0.185227
$861$	−6.70761e47	−0.250620
$862$	1.28588e48	0.471335
$863$	−5.06827e48	−1.82256	−0.911279	−	0.411790i	$-0.864904\pi$
$863$	−5.06827e48	−1.82256	−0.911279	+	0.411790i	$0.864904\pi$
$864$	−2.46613e47	−0.0870038
$865$	1.02548e48	0.354947
$866$	1.70504e48	0.579013
$867$	1.13503e48	0.378175
$868$	3.21163e47	0.104990
$869$	−4.29372e47	−0.137723
$870$	2.24455e48	0.706419
$871$	7.83215e48	2.41870
$872$	2.17220e48	0.658232
$873$	−1.21714e48	−0.361913
$874$	−4.88719e48	−1.42600
$875$	−6.13832e47	−0.175759
$876$	−8.10058e47	−0.227614
$877$	5.06152e47	0.139569	0.0697843	−	0.997562i	$-0.477769\pi$
$877$	5.06152e47	0.139569	0.0697843	+	0.997562i	$0.477769\pi$
$878$	1.97882e48	0.535485
$879$	4.96131e47	0.131759
$880$	2.26933e48	0.591470
$881$	−6.99658e48	−1.78971	−0.894856	−	0.446355i	$-0.852722\pi$
$881$	−6.99658e48	−1.78971	−0.894856	+	0.446355i	$0.852722\pi$
$882$	9.95386e47	0.249896
$883$	2.10243e47	0.0518048	0.0259024	−	0.999664i	$-0.491754\pi$
$883$	2.10243e47	0.0518048	0.0259024	+	0.999664i	$0.491754\pi$
$884$	1.69737e48	0.410501
$885$	1.15961e48	0.275263
$886$	−1.37360e47	−0.0320039
$887$	−5.10566e48	−1.16765	−0.583824	−	0.811880i	$-0.698444\pi$
$887$	−5.10566e48	−1.16765	−0.583824	+	0.811880i	$0.698444\pi$
$888$	2.44615e48	0.549123
$889$	1.62631e48	0.358364
$890$	−1.25833e48	−0.272182
$891$	−2.84975e47	−0.0605097
$892$	−3.35904e47	−0.0700156
$893$	−3.63848e47	−0.0744512
$894$	−1.31494e48	−0.264142
$895$	−4.83988e48	−0.954453
$896$	1.02874e48	0.199170
$897$	−4.94876e48	−0.940635
$898$	3.42132e48	0.638461
$899$	−5.98550e48	−1.09664
$900$	−5.58383e47	−0.100445
$901$	5.28984e48	0.934293
$902$	3.13858e48	0.544284
$903$	−6.81932e47	−0.116116
$904$	−6.93821e48	−1.16003
$905$	8.01079e48	1.31515
$906$	−1.16491e47	−0.0187791
$907$	−1.01583e49	−1.60805	−0.804027	−	0.594593i	$-0.797313\pi$
$907$	−1.01583e49	−1.60805	−0.804027	+	0.594593i	$0.797313\pi$
$908$	−2.15369e47	−0.0334786
$909$	1.15930e48	0.176967
$910$	−4.66954e48	−0.699988
$911$	9.92594e47	0.146123	0.0730614	−	0.997327i	$-0.476723\pi$
$911$	9.92594e47	0.146123	0.0730614	+	0.997327i	$0.476723\pi$
$912$	−3.93843e48	−0.569388
$913$	3.93087e48	0.558111
$914$	2.30269e48	0.321087
$915$	1.01915e49	1.39569
$916$	−2.22709e48	−0.299545
$917$	4.59772e48	0.607363
$918$	−1.67326e48	−0.217100
$919$	7.48597e47	0.0953986	0.0476993	−	0.998862i	$-0.484811\pi$
$919$	7.48597e47	0.0953986	0.0476993	+	0.998862i	$0.484811\pi$
$920$	1.54456e49	1.93332
$921$	4.65067e48	0.571783
$922$	−6.38111e48	−0.770613
$923$	6.00157e48	0.711929
$924$	−2.37475e47	−0.0276713
$925$	1.00376e49	1.14892
$926$	−8.70868e48	−0.979199
$927$	−3.31612e48	−0.366281
$928$	3.83002e48	0.415584
$929$	1.49889e49	1.59776	0.798878	−	0.601493i	$-0.205427\pi$
$929$	1.49889e49	1.59776	0.798878	+	0.601493i	$0.205427\pi$
$930$	−8.75424e48	−0.916748
$931$	−1.14540e49	−1.17839
$932$	−2.18893e48	−0.221243
$933$	−7.51769e48	−0.746513
$934$	1.14005e49	1.11225
$935$	−1.10944e49	−1.06344
$936$	−5.27601e48	−0.496883
$937$	4.11649e48	0.380911	0.190455	−	0.981696i	$-0.439004\pi$
$937$	4.11649e48	0.380911	0.190455	+	0.981696i	$0.439004\pi$
$938$	−6.43397e48	−0.584968
$939$	7.94436e48	0.709703
$940$	2.15845e47	0.0189467
$941$	1.69570e48	0.146258	0.0731292	−	0.997322i	$-0.476701\pi$
$941$	1.69570e48	0.146258	0.0731292	+	0.997322i	$0.476701\pi$
$942$	1.52427e48	0.129188
$943$	1.61471e49	1.34478
$944$	−2.74615e48	−0.224743
$945$	−1.38339e48	−0.111255
$946$	3.19085e48	0.252175
$947$	−1.73372e49	−1.34649	−0.673246	−	0.739419i	$-0.735100\pi$
$947$	−1.73372e49	−1.34649	−0.673246	+	0.739419i	$0.735100\pi$
$948$	−4.42061e47	−0.0337400
$949$	−3.14076e49	−2.35582
$950$	−2.13803e49	−1.57606
$951$	−1.06892e49	−0.774402
$952$	−7.42842e48	−0.528916
$953$	2.13426e49	1.49353	0.746767	−	0.665086i	$-0.231605\pi$
$953$	2.13426e49	1.49353	0.746767	+	0.665086i	$0.231605\pi$
$954$	−3.08638e48	−0.212276
$955$	−9.98992e48	−0.675315
$956$	−1.06594e48	−0.0708237
$957$	4.42581e48	0.289032
$958$	6.81116e48	0.437210
$959$	9.22743e47	0.0582202
$960$	1.57124e49	0.974466
$961$	6.94123e48	0.423156
$962$	1.78025e49	1.06682
$963$	1.10372e49	0.650166
$964$	−5.98865e48	−0.346783
$965$	−1.18703e49	−0.675714
$966$	4.06532e48	0.227495
$967$	3.11384e49	1.71301	0.856504	−	0.516141i	$-0.172632\pi$
$967$	3.11384e49	1.71301	0.856504	+	0.516141i	$0.172632\pi$
$968$	−1.40407e49	−0.759355
$969$	1.92544e49	1.02373
$970$	2.76467e49	1.44514
$971$	8.15863e47	0.0419276	0.0209638	−	0.999780i	$-0.493327\pi$
$971$	8.15863e47	0.0419276	0.0209638	+	0.999780i	$0.493327\pi$
$972$	−2.93397e47	−0.0148239
$973$	4.74518e48	0.235717
$974$	2.46513e48	0.120397
$975$	−2.16496e49	−1.03962
$976$	−2.41352e49	−1.13954
$977$	−1.51181e49	−0.701836	−0.350918	−	0.936406i	$-0.614130\pi$
$977$	−1.51181e49	−0.701836	−0.350918	+	0.936406i	$0.614130\pi$
$978$	−3.06659e48	−0.139980
$979$	−2.48117e48	−0.111363
$980$	6.79485e48	0.299881
$981$	4.68349e48	0.203250
$982$	1.92745e49	0.822517
$983$	−2.56714e49	−1.07725	−0.538626	−	0.842545i	$-0.681056\pi$
$983$	−2.56714e49	−1.07725	−0.538626	+	0.842545i	$0.681056\pi$
$984$	1.72149e49	0.710369
$985$	−4.28474e49	−1.73871
$986$	2.59866e49	1.03700
$987$	3.02661e47	0.0118774
$988$	1.13959e49	0.439804
$989$	1.64160e49	0.623058
$990$	6.47308e48	0.241618
$991$	−9.23991e47	−0.0339197	−0.0169599	−	0.999856i	$-0.505399\pi$
$991$	−9.23991e47	−0.0339197	−0.0169599	+	0.999856i	$0.505399\pi$
$992$	−1.49379e49	−0.539320
$993$	−1.85768e49	−0.659641
$994$	−4.93018e48	−0.172182
$995$	3.03773e48	0.104344
$996$	4.04703e48	0.136728
$997$	−9.11625e48	−0.302933	−0.151466	−	0.988462i	$-0.548400\pi$
$997$	−9.11625e48	−0.302933	−0.151466	+	0.988462i	$0.548400\pi$
$998$	−7.39871e48	−0.241826
$999$	5.27415e48	0.169559

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.34.a.a.1.1	✓	3	1.1	even	1	trivial
9.34.a.d.1.3		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)

\(f(q)\)	\(=\)	\(q-81270.9 q^{2} +4.30467e7 q^{3} -1.98497e9 q^{4} +5.17904e11 q^{5} -3.49845e12 q^{6} -3.34870e13 q^{7} +8.59432e14 q^{8} +1.85302e15 q^{9} +O(q^{10})\)	\(q-81270.9 q^{2} +4.30467e7 q^{3} -1.98497e9 q^{4} +5.17904e11 q^{5} -3.49845e12 q^{6} -3.34870e13 q^{7} +8.59432e14 q^{8} +1.85302e15 q^{9} -4.20905e16 q^{10} -8.29940e16 q^{11} -8.54466e16 q^{12} -3.31294e18 q^{13} +2.72152e18 q^{14} +2.22941e19 q^{15} -5.27961e19 q^{16} +2.58112e20 q^{17} -1.50597e20 q^{18} +1.73293e21 q^{19} -1.02802e21 q^{20} -1.44151e21 q^{21} +6.74500e21 q^{22} +3.47011e22 q^{23} +3.69957e22 q^{24} +1.51809e23 q^{25} +2.69246e23 q^{26} +7.97664e22 q^{27} +6.64708e22 q^{28} -1.23881e24 q^{29} -1.81186e24 q^{30} +4.83164e24 q^{31} -3.09168e24 q^{32} -3.57262e24 q^{33} -2.09770e25 q^{34} -1.73430e25 q^{35} -3.67819e24 q^{36} +6.61199e25 q^{37} -1.40837e26 q^{38} -1.42611e26 q^{39} +4.45103e26 q^{40} +4.65320e26 q^{41} +1.17153e26 q^{42} +4.73069e26 q^{43} +1.64741e26 q^{44} +9.59686e26 q^{45} -2.82019e27 q^{46} -2.09961e26 q^{47} -2.27270e27 q^{48} -6.60961e27 q^{49} -1.23376e28 q^{50} +1.11109e28 q^{51} +6.57609e27 q^{52} +2.04943e28 q^{53} -6.48269e27 q^{54} -4.29829e28 q^{55} -2.87798e28 q^{56} +7.45970e28 q^{57} +1.00680e29 q^{58} +5.20142e28 q^{59} -4.42531e28 q^{60} +4.57140e29 q^{61} -3.92672e29 q^{62} -6.20521e28 q^{63} +7.04779e29 q^{64} -1.71578e30 q^{65} +2.90350e29 q^{66} -2.36411e30 q^{67} -5.12346e29 q^{68} +1.49377e30 q^{69} +1.40949e30 q^{70} -1.81156e30 q^{71} +1.59255e30 q^{72} +9.48028e30 q^{73} -5.37362e30 q^{74} +6.53487e30 q^{75} -3.43982e30 q^{76} +2.77922e30 q^{77} +1.15901e31 q^{78} +5.17354e30 q^{79} -2.73433e31 q^{80} +3.43368e30 q^{81} -3.78170e31 q^{82} -4.73633e31 q^{83} +2.86135e30 q^{84} +1.33677e32 q^{85} -3.84468e31 q^{86} -5.33269e31 q^{87} -7.13277e31 q^{88} +2.98958e31 q^{89} -7.79946e31 q^{90} +1.10940e32 q^{91} -6.88807e31 q^{92} +2.07986e32 q^{93} +1.70638e31 q^{94} +8.97491e32 q^{95} -1.33087e32 q^{96} -6.56839e32 q^{97} +5.37169e32 q^{98} -1.53790e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 41202 q^{2} + 129140163 q^{3} - 1107467772 q^{4} + 51261823890 q^{5} + 1773610998642 q^{6} + 76113734015256 q^{7} + 11\!\cdots\!92 q^{8}+ \cdots + 55\!\cdots\!23 q^{9}+O(q^{10}) \) 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

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