LMFDB - Embedded newform 3.34.a.a.1.2

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			1.2
Root			$-6131.99$ 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)

$f(q)$	$=$	$q-11418.8 q^{2} +4.30467e7 q^{3} -8.45955e9 q^{4} -6.77881e11 q^{5} -4.91541e11 q^{6} +5.88597e13 q^{7} +1.94684e14 q^{8} +1.85302e15 q^{9} +O(q^{10})$	\(q-11418.8 q^{2} +4.30467e7 q^{3} -8.45955e9 q^{4} -6.77881e11 q^{5} -4.91541e11 q^{6} +5.88597e13 q^{7} +1.94684e14 q^{8} +1.85302e15 q^{9} +7.74057e15 q^{10} -1.49196e17 q^{11} -3.64156e17 q^{12} +3.12008e18 q^{13} -6.72105e17 q^{14} -2.91806e19 q^{15} +7.04439e19 q^{16} +1.02779e20 q^{17} -2.11592e19 q^{18} -9.89896e20 q^{19} +5.73457e21 q^{20} +2.53372e21 q^{21} +1.70364e21 q^{22} +1.10512e22 q^{23} +8.38052e21 q^{24} +3.43107e23 q^{25} -3.56275e22 q^{26} +7.97664e22 q^{27} -4.97926e23 q^{28} +1.29102e24 q^{29} +3.33206e23 q^{30} -3.22272e24 q^{31} -2.47671e24 q^{32} -6.42240e24 q^{33} -1.17361e24 q^{34} -3.98999e25 q^{35} -1.56757e25 q^{36} +3.68177e25 q^{37} +1.13034e25 q^{38} +1.34309e26 q^{39} -1.31973e26 q^{40} +2.81851e26 q^{41} -2.89319e25 q^{42} +1.05360e27 q^{43} +1.26213e27 q^{44} -1.25613e27 q^{45} -1.26191e26 q^{46} -5.35397e27 q^{47} +3.03238e27 q^{48} -4.26653e27 q^{49} -3.91787e27 q^{50} +4.42430e27 q^{51} -2.63945e28 q^{52} -5.12065e27 q^{53} -9.10835e26 q^{54} +1.01137e29 q^{55} +1.14590e28 q^{56} -4.26118e28 q^{57} -1.47419e28 q^{58} -3.65874e28 q^{59} +2.46854e29 q^{60} +2.42142e29 q^{61} +3.67996e28 q^{62} +1.09068e29 q^{63} -5.76827e29 q^{64} -2.11505e30 q^{65} +7.33359e28 q^{66} +1.58257e30 q^{67} -8.69464e29 q^{68} +4.75719e29 q^{69} +4.55608e29 q^{70} -1.75986e30 q^{71} +3.60754e29 q^{72} +1.39480e29 q^{73} -4.20413e29 q^{74} +1.47696e31 q^{75} +8.37407e30 q^{76} -8.78162e30 q^{77} -1.53365e30 q^{78} +2.47706e31 q^{79} -4.77526e31 q^{80} +3.43368e30 q^{81} -3.21840e30 q^{82} +1.28430e30 q^{83} -2.14341e31 q^{84} -6.96719e31 q^{85} -1.20308e31 q^{86} +5.55742e31 q^{87} -2.90461e31 q^{88} +4.80706e31 q^{89} +1.43434e31 q^{90} +1.83647e32 q^{91} -9.34883e31 q^{92} -1.38728e32 q^{93} +6.11358e31 q^{94} +6.71032e32 q^{95} -1.06614e32 q^{96} +6.02234e32 q^{97} +4.87186e31 q^{98} -2.76463e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11418.8	−0.123204	−0.0616020	−	0.998101i	$-0.519621\pi$
$2$	−11418.8	−0.123204	−0.0616020	+	0.998101i	$0.519621\pi$
$3$	4.30467e7	0.577350
$3$	4.30467e7	0.577350
$4$	−8.45955e9	−0.984821
$5$	−6.77881e11	−1.98677	−0.993387	−	0.114815i	$-0.963373\pi$
$5$	−6.77881e11	−1.98677	−0.993387	+	0.114815i	$0.963373\pi$
$6$	−4.91541e11	−0.0711318
$7$	5.88597e13	0.669422	0.334711	−	0.942321i	$-0.391361\pi$
$7$	5.88597e13	0.669422	0.334711	+	0.942321i	$0.391361\pi$
$8$	1.94684e14	0.244538
$9$	1.85302e15	0.333333
$10$	7.74057e15	0.244778
$11$	−1.49196e17	−0.978989	−0.489494	−	0.872006i	$-0.662819\pi$
$11$	−1.49196e17	−0.978989	−0.489494	+	0.872006i	$0.662819\pi$
$12$	−3.64156e17	−0.568587
$13$	3.12008e18	1.30047	0.650236	−	0.759732i	$-0.274670\pi$
$13$	3.12008e18	1.30047	0.650236	+	0.759732i	$0.274670\pi$
$14$	−6.72105e17	−0.0824755
$15$	−2.91806e19	−1.14706
$16$	7.04439e19	0.954693
$17$	1.02779e20	0.512268	0.256134	−	0.966641i	$-0.417551\pi$
$17$	1.02779e20	0.512268	0.256134	+	0.966641i	$0.417551\pi$
$18$	−2.11592e19	−0.0410680
$19$	−9.89896e20	−0.787327	−0.393664	−	0.919255i	$-0.628793\pi$
$19$	−9.89896e20	−0.787327	−0.393664	+	0.919255i	$0.628793\pi$
$20$	5.73457e21	1.95662
$21$	2.53372e21	0.386491
$22$	1.70364e21	0.120615
$23$	1.10512e22	0.375752	0.187876	−	0.982193i	$-0.439840\pi$
$23$	1.10512e22	0.375752	0.187876	+	0.982193i	$0.439840\pi$
$24$	8.38052e21	0.141184
$25$	3.43107e23	2.94727
$26$	−3.56275e22	−0.160223
$27$	7.97664e22	0.192450
$28$	−4.97926e23	−0.659261
$29$	1.29102e24	0.958001	0.479001	−	0.877814i	$-0.340999\pi$
$29$	1.29102e24	0.958001	0.479001	+	0.877814i	$0.340999\pi$
$30$	3.33206e23	0.141323
$31$	−3.22272e24	−0.795710	−0.397855	−	0.917448i	$-0.630245\pi$
$31$	−3.22272e24	−0.795710	−0.397855	+	0.917448i	$0.630245\pi$
$32$	−2.47671e24	−0.362160
$33$	−6.42240e24	−0.565219
$34$	−1.17361e24	−0.0631135
$35$	−3.98999e25	−1.32999
$36$	−1.56757e25	−0.328274
$37$	3.68177e25	0.490600	0.245300	−	0.969447i	$-0.421114\pi$
$37$	3.68177e25	0.490600	0.245300	+	0.969447i	$0.421114\pi$
$38$	1.13034e25	0.0970018
$39$	1.34309e26	0.750828
$40$	−1.31973e26	−0.485841
$41$	2.81851e26	0.690377	0.345188	−	0.938533i	$-0.387815\pi$
$41$	2.81851e26	0.690377	0.345188	+	0.938533i	$0.387815\pi$
$42$	−2.89319e25	−0.0476172
$43$	1.05360e27	1.17610	0.588051	−	0.808824i	$-0.299895\pi$
$43$	1.05360e27	1.17610	0.588051	+	0.808824i	$0.299895\pi$
$44$	1.26213e27	0.964128
$45$	−1.25613e27	−0.662258
$46$	−1.26191e26	−0.0462941
$47$	−5.35397e27	−1.37740	−0.688702	−	0.725044i	$-0.741819\pi$
$47$	−5.35397e27	−1.37740	−0.688702	+	0.725044i	$0.741819\pi$
$48$	3.03238e27	0.551192
$49$	−4.26653e27	−0.551874
$50$	−3.91787e27	−0.363115
$51$	4.42430e27	0.295758
$52$	−2.63945e28	−1.28073
$53$	−5.12065e27	−0.181457	−0.0907285	−	0.995876i	$-0.528920\pi$
$53$	−5.12065e27	−0.181457	−0.0907285	+	0.995876i	$0.528920\pi$
$54$	−9.10835e26	−0.0237106
$55$	1.01137e29	1.94503
$56$	1.14590e28	0.163699
$57$	−4.26118e28	−0.454564
$58$	−1.47419e28	−0.118030
$59$	−3.65874e28	−0.220940	−0.110470	−	0.993879i	$-0.535236\pi$
$59$	−3.65874e28	−0.220940	−0.110470	+	0.993879i	$0.535236\pi$
$60$	2.46854e29	1.12965
$61$	2.42142e29	0.843583	0.421791	−	0.906693i	$-0.361401\pi$
$61$	2.42142e29	0.843583	0.421791	+	0.906693i	$0.361401\pi$
$62$	3.67996e28	0.0980347
$63$	1.09068e29	0.223141
$64$	−5.76827e29	−0.910073
$65$	−2.11505e30	−2.58374
$66$	7.33359e28	0.0696373
$67$	1.58257e30	1.17254	0.586271	−	0.810115i	$-0.300595\pi$
$67$	1.58257e30	1.17254	0.586271	+	0.810115i	$0.300595\pi$
$68$	−8.69464e29	−0.504492
$69$	4.75719e29	0.216940
$70$	4.55608e29	0.163860
$71$	−1.75986e30	−0.500860	−0.250430	−	0.968135i	$-0.580572\pi$
$71$	−1.75986e30	−0.500860	−0.250430	+	0.968135i	$0.580572\pi$
$72$	3.60754e29	0.0815126
$73$	1.39480e29	0.0251007	0.0125503	−	0.999921i	$-0.496005\pi$
$73$	1.39480e29	0.0251007	0.0125503	+	0.999921i	$0.496005\pi$
$74$	−4.20413e29	−0.0604439
$75$	1.47696e31	1.70161
$76$	8.37407e30	0.775376
$77$	−8.78162e30	−0.655357
$78$	−1.53365e30	−0.0925050
$79$	2.47706e31	1.21085	0.605425	−	0.795903i	$-0.293003\pi$
$79$	2.47706e31	1.21085	0.605425	+	0.795903i	$0.293003\pi$
$80$	−4.77526e31	−1.89676
$81$	3.43368e30	0.111111
$82$	−3.21840e30	−0.0850572
$83$	1.28430e30	0.0277894	0.0138947	−	0.999903i	$-0.495577\pi$
$83$	1.28430e30	0.0277894	0.0138947	+	0.999903i	$0.495577\pi$
$84$	−2.14341e31	−0.380624
$85$	−6.96719e31	−1.01776
$86$	−1.20308e31	−0.144900
$87$	5.55742e31	0.553102
$88$	−2.90461e31	−0.239400
$89$	4.80706e31	0.328810	0.164405	−	0.986393i	$-0.447430\pi$
$89$	4.80706e31	0.328810	0.164405	+	0.986393i	$0.447430\pi$
$90$	1.43434e31	0.0815928
$91$	1.83647e32	0.870565
$92$	−9.34883e31	−0.370048
$93$	−1.38728e32	−0.459404
$94$	6.11358e31	0.169702
$95$	6.71032e32	1.56424
$96$	−1.06614e32	−0.209093
$97$	6.02234e32	0.995477	0.497739	−	0.867327i	$-0.334164\pi$
$97$	6.02234e32	0.995477	0.497739	+	0.867327i	$0.334164\pi$
$98$	4.87186e31	0.0679931
$99$	−2.76463e32	−0.326330
$100$	−2.90253e33	−2.90253
$101$	1.39729e33	1.18572	0.592862	−	0.805304i	$-0.297998\pi$
$101$	1.39729e33	1.18572	0.592862	+	0.805304i	$0.297998\pi$
$102$	−5.05201e31	−0.0364386
$103$	−7.87046e32	−0.483266	−0.241633	−	0.970368i	$-0.577683\pi$
$103$	−7.87046e32	−0.483266	−0.241633	+	0.970368i	$0.577683\pi$
$104$	6.07431e32	0.318014
$105$	−1.71756e33	−0.767870
$106$	5.84716e31	0.0223562
$107$	−1.03770e33	−0.339812	−0.169906	−	0.985460i	$-0.554346\pi$
$107$	−1.03770e33	−0.339812	−0.169906	+	0.985460i	$0.554346\pi$
$108$	−6.74788e32	−0.189529
$109$	3.76867e33	0.909182	0.454591	−	0.890700i	$-0.349785\pi$
$109$	3.76867e33	0.909182	0.454591	+	0.890700i	$0.349785\pi$
$110$	−1.15486e33	−0.239635
$111$	1.58488e33	0.283248
$112$	4.14630e33	0.639093
$113$	1.16997e34	1.55733	0.778666	−	0.627439i	$-0.215897\pi$
$113$	1.16997e34	1.55733	0.778666	+	0.627439i	$0.215897\pi$
$114$	4.86575e32	0.0560040
$115$	−7.49141e33	−0.746533
$116$	−1.09214e34	−0.943460
$117$	5.78158e33	0.433491
$118$	4.17783e32	0.0272206
$119$	6.04954e33	0.342924
$120$	−5.68099e33	−0.280501
$121$	−9.65732e32	−0.0415813
$122$	−2.76496e33	−0.103933
$123$	1.21328e34	0.398589
$124$	2.72628e34	0.783632
$125$	−1.53670e35	−3.86879
$126$	−1.24542e33	−0.0274918
$127$	4.40742e33	0.0853931	0.0426966	−	0.999088i	$-0.486405\pi$
$127$	4.40742e33	0.0853931	0.0426966	+	0.999088i	$0.486405\pi$
$128$	2.78614e34	0.474284
$129$	4.53539e34	0.679023
$130$	2.41512e34	0.318327
$131$	1.20964e35	1.40501	0.702506	−	0.711678i	$-0.252064\pi$
$131$	1.20964e35	1.40501	0.702506	+	0.711678i	$0.252064\pi$
$132$	5.43305e34	0.556640
$133$	−5.82650e34	−0.527054
$134$	−1.80710e34	−0.144462
$135$	−5.40722e34	−0.382355
$136$	2.00095e34	0.125269
$137$	−8.78206e34	−0.487200	−0.243600	−	0.969876i	$-0.578328\pi$
$137$	−8.78206e34	−0.487200	−0.243600	+	0.969876i	$0.578328\pi$
$138$	−5.43213e33	−0.0267279
$139$	2.90956e35	1.27082	0.635408	−	0.772177i	$-0.280832\pi$
$139$	2.90956e35	1.27082	0.635408	+	0.772177i	$0.280832\pi$
$140$	3.37535e35	1.30980
$141$	−2.30471e35	−0.795245
$142$	2.00955e34	0.0617079
$143$	−4.65504e35	−1.27315
$144$	1.30534e35	0.318231
$145$	−8.75158e35	−1.90333
$146$	−1.59269e33	−0.00309250
$147$	−1.83660e35	−0.318625
$148$	−3.11461e35	−0.483153
$149$	1.18398e36	1.64350	0.821752	−	0.569845i	$-0.192997\pi$
$149$	1.18398e36	1.64350	0.821752	+	0.569845i	$0.192997\pi$
$150$	−1.68651e35	−0.209645
$151$	−2.18048e35	−0.242903	−0.121452	−	0.992597i	$-0.538755\pi$
$151$	−2.18048e35	−0.242903	−0.121452	+	0.992597i	$0.538755\pi$
$152$	−1.92717e35	−0.192531
$153$	1.90452e35	0.170756
$154$	1.00275e35	0.0807425
$155$	2.18462e36	1.58090
$156$	−1.13620e36	−0.739431
$157$	1.54475e36	0.904722	0.452361	−	0.891835i	$-0.350582\pi$
$157$	1.54475e36	0.904722	0.452361	+	0.891835i	$0.350582\pi$
$158$	−2.82850e35	−0.149181
$159$	−2.20427e35	−0.104764
$160$	1.67891e36	0.719530
$161$	6.50471e35	0.251536
$162$	−3.92085e34	−0.0136893
$163$	−4.37252e36	−1.37923	−0.689614	−	0.724177i	$-0.742220\pi$
$163$	−4.37252e36	−1.37923	−0.689614	+	0.724177i	$0.742220\pi$
$164$	−2.38433e36	−0.679898
$165$	4.35362e36	1.12296
$166$	−1.46652e34	−0.00342376
$167$	−6.88704e36	−1.45617	−0.728083	−	0.685489i	$-0.759589\pi$
$167$	−6.88704e36	−1.45617	−0.728083	+	0.685489i	$0.759589\pi$
$168$	4.93274e35	0.0945117
$169$	3.97879e36	0.691227
$170$	7.95569e35	0.125392
$171$	−1.83430e36	−0.262442
$172$	−8.91295e36	−1.15825
$173$	−5.78793e36	−0.683538	−0.341769	−	0.939784i	$-0.611026\pi$
$173$	−5.78793e36	−0.683538	−0.341769	+	0.939784i	$0.611026\pi$
$174$	−6.34589e35	−0.0681444
$175$	2.01952e37	1.97297
$176$	−1.05099e37	−0.934633
$177$	−1.57497e36	−0.127560
$178$	−5.48907e35	−0.0405106
$179$	1.81644e37	1.22221	0.611107	−	0.791548i	$-0.290725\pi$
$179$	1.81644e37	1.22221	0.611107	+	0.791548i	$0.290725\pi$
$180$	1.06263e37	0.652205
$181$	4.65177e36	0.260568	0.130284	−	0.991477i	$-0.458411\pi$
$181$	4.65177e36	0.260568	0.130284	+	0.991477i	$0.458411\pi$
$182$	−2.09703e36	−0.107257
$183$	1.04234e37	0.487043
$184$	2.15150e36	0.0918855
$185$	−2.49580e37	−0.974711
$186$	1.58410e36	0.0566003
$187$	−1.53342e37	−0.501505
$188$	4.52922e37	1.35650
$189$	4.69503e36	0.128830
$190$	−7.66236e36	−0.192721
$191$	−3.12863e37	−0.721613	−0.360806	−	0.932641i	$-0.617498\pi$
$191$	−3.12863e37	−0.721613	−0.360806	+	0.932641i	$0.617498\pi$
$192$	−2.48305e37	−0.525431
$193$	−4.16584e37	−0.809110	−0.404555	−	0.914514i	$-0.632574\pi$
$193$	−4.16584e37	−0.809110	−0.404555	+	0.914514i	$0.632574\pi$
$194$	−6.87677e36	−0.122647
$195$	−9.10458e37	−1.49172
$196$	3.60929e37	0.543497
$197$	5.96505e37	0.825888	0.412944	−	0.910756i	$-0.364500\pi$
$197$	5.96505e37	0.825888	0.412944	+	0.910756i	$0.364500\pi$
$198$	3.15687e36	0.0402051
$199$	−3.35871e37	−0.393638	−0.196819	−	0.980440i	$-0.563061\pi$
$199$	−3.35871e37	−0.393638	−0.196819	+	0.980440i	$0.563061\pi$
$200$	6.67976e37	0.720719
$201$	6.81244e37	0.676967
$202$	−1.59553e37	−0.146086
$203$	7.59890e37	0.641307
$204$	−3.74276e37	−0.291269
$205$	−1.91062e38	−1.37162
$206$	8.98710e36	0.0595403
$207$	2.04781e37	0.125251
$208$	2.19791e38	1.24155
$209$	1.47688e38	0.770784
$210$	1.96124e37	0.0946047
$211$	2.71696e38	1.21178	0.605889	−	0.795549i	$-0.292817\pi$
$211$	2.71696e38	1.21178	0.605889	+	0.795549i	$0.292817\pi$
$212$	4.33184e37	0.178703
$213$	−7.57563e37	−0.289171
$214$	1.18492e37	0.0418662
$215$	−7.14213e38	−2.33665
$216$	1.55293e37	0.0470613
$217$	−1.89688e38	−0.532666
$218$	−4.30336e37	−0.112015
$219$	6.00417e36	0.0144919
$220$	−8.55574e38	−1.91550
$221$	3.20679e38	0.666190
$222$	−1.80974e37	−0.0348973
$223$	9.01256e38	1.61368	0.806841	−	0.590769i	$-0.201175\pi$
$223$	9.01256e38	1.61368	0.806841	+	0.590769i	$0.201175\pi$
$224$	−1.45778e38	−0.242438
$225$	6.35785e38	0.982423
$226$	−1.33596e38	−0.191869
$227$	−8.88403e38	−1.18627	−0.593135	−	0.805103i	$-0.702110\pi$
$227$	−8.88403e38	−1.18627	−0.593135	+	0.805103i	$0.702110\pi$
$228$	3.60476e38	0.447664
$229$	−4.22424e37	−0.0488049	−0.0244024	−	0.999702i	$-0.507768\pi$
$229$	−4.22424e37	−0.0488049	−0.0244024	+	0.999702i	$0.507768\pi$
$230$	8.55427e37	0.0919759
$231$	−3.78020e38	−0.378370
$232$	2.51341e38	0.234268
$233$	−1.00204e39	−0.869989	−0.434995	−	0.900433i	$-0.643250\pi$
$233$	−1.00204e39	−0.869989	−0.434995	+	0.900433i	$0.643250\pi$
$234$	−6.60186e37	−0.0534078
$235$	3.62936e39	2.73659
$236$	3.09513e38	0.217586
$237$	1.06629e39	0.699084
$238$	−6.90783e37	−0.0422495
$239$	1.64429e39	0.938454	0.469227	−	0.883078i	$-0.344533\pi$
$239$	1.64429e39	0.938454	0.469227	+	0.883078i	$0.344533\pi$
$240$	−2.05559e39	−1.09509
$241$	−3.83207e39	−1.90613	−0.953065	−	0.302766i	$-0.902090\pi$
$241$	−3.83207e39	−1.90613	−0.953065	+	0.302766i	$0.902090\pi$
$242$	1.10275e37	0.00512298
$243$	1.47809e38	0.0641500
$244$	−2.04841e39	−0.830778
$245$	2.89220e39	1.09645
$246$	−1.38541e38	−0.0491078
$247$	−3.08856e39	−1.02390
$248$	−6.27413e38	−0.194581
$249$	5.52851e37	0.0160442
$250$	1.75473e39	0.476650
$251$	−1.64281e39	−0.417801	−0.208901	−	0.977937i	$-0.566989\pi$
$251$	−1.64281e39	−0.417801	−0.208901	+	0.977937i	$0.566989\pi$
$252$	−9.22667e38	−0.219754
$253$	−1.64880e39	−0.367856
$254$	−5.03273e37	−0.0105208
$255$	−2.99915e39	−0.587604
$256$	4.63677e39	0.851640
$257$	−1.07806e39	−0.185672	−0.0928359	−	0.995681i	$-0.529593\pi$
$257$	−1.07806e39	−0.185672	−0.0928359	+	0.995681i	$0.529593\pi$
$258$	−5.17886e38	−0.0836583
$259$	2.16707e39	0.328419
$260$	1.78923e40	2.54452
$261$	2.39229e39	0.319334
$262$	−1.38126e39	−0.173103
$263$	−7.17542e39	−0.844457	−0.422229	−	0.906489i	$-0.638752\pi$
$263$	−7.17542e39	−0.844457	−0.422229	+	0.906489i	$0.638752\pi$
$264$	−1.25034e39	−0.138217
$265$	3.47119e39	0.360514
$266$	6.65315e38	0.0649352
$267$	2.06928e39	0.189838
$268$	−1.33878e40	−1.15474
$269$	5.46727e39	0.443463	0.221732	−	0.975108i	$-0.428829\pi$
$269$	5.46727e39	0.443463	0.221732	+	0.975108i	$0.428829\pi$
$270$	6.17438e38	0.0471076
$271$	−1.41003e38	−0.0101212	−0.00506062	−	0.999987i	$-0.501611\pi$
$271$	−1.41003e38	−0.0101212	−0.00506062	+	0.999987i	$0.501611\pi$
$272$	7.24015e39	0.489059
$273$	7.90540e39	0.502621
$274$	1.00280e39	0.0600249
$275$	−5.11902e40	−2.88534
$276$	−4.02436e39	−0.213647
$277$	2.70637e40	1.35354	0.676769	−	0.736195i	$-0.263380\pi$
$277$	2.70637e40	1.35354	0.676769	+	0.736195i	$0.263380\pi$
$278$	−3.32236e39	−0.156570
$279$	−5.97177e39	−0.265237
$280$	−7.76787e39	−0.325233
$281$	−4.09700e40	−1.61738	−0.808690	−	0.588235i	$-0.799823\pi$
$281$	−4.09700e40	−1.61738	−0.808690	+	0.588235i	$0.799823\pi$
$282$	2.63170e39	0.0979773
$283$	1.53690e40	0.539722	0.269861	−	0.962899i	$-0.413022\pi$
$283$	1.53690e40	0.539722	0.269861	+	0.962899i	$0.413022\pi$
$284$	1.48876e40	0.493257
$285$	2.88857e40	0.903115
$286$	5.31548e39	0.156857
$287$	1.65897e40	0.462154
$288$	−4.58939e39	−0.120720
$289$	−2.96910e40	−0.737581
$290$	9.99324e39	0.234498
$291$	2.59242e40	0.574739
$292$	−1.17994e39	−0.0247197
$293$	4.40586e40	0.872398	0.436199	−	0.899850i	$-0.356324\pi$
$293$	4.40586e40	0.872398	0.436199	+	0.899850i	$0.356324\pi$
$294$	2.09718e39	0.0392558
$295$	2.48019e40	0.438957
$296$	7.16782e39	0.119970
$297$	−1.19008e40	−0.188406
$298$	−1.35196e40	−0.202486
$299$	3.44807e40	0.488654
$300$	−1.24945e41	−1.67578
$301$	6.20144e40	0.787309
$302$	2.48985e39	0.0299266
$303$	6.01487e40	0.684578
$304$	−6.97321e40	−0.751656
$305$	−1.64143e41	−1.67601
$306$	−2.17472e39	−0.0210378
$307$	−6.32712e40	−0.579993	−0.289997	−	0.957028i	$-0.593654\pi$
$307$	−6.32712e40	−0.579993	−0.289997	+	0.957028i	$0.593654\pi$
$308$	7.42885e40	0.645409
$309$	−3.38798e40	−0.279014
$310$	−2.49457e40	−0.194773
$311$	1.41606e41	1.04842	0.524210	−	0.851589i	$-0.324361\pi$
$311$	1.41606e41	1.04842	0.524210	+	0.851589i	$0.324361\pi$
$312$	2.61479e40	0.183606
$313$	3.77426e40	0.251391	0.125696	−	0.992069i	$-0.459884\pi$
$313$	3.77426e40	0.251391	0.125696	+	0.992069i	$0.459884\pi$
$314$	−1.76392e40	−0.111465
$315$	−7.39352e40	−0.443330
$316$	−2.09548e41	−1.19247
$317$	3.18839e40	0.172224	0.0861119	−	0.996285i	$-0.472556\pi$
$317$	3.18839e40	0.172224	0.0861119	+	0.996285i	$0.472556\pi$
$318$	2.51701e39	0.0129074
$319$	−1.92615e41	−0.937873
$320$	3.91020e41	1.80811
$321$	−4.46695e40	−0.196190
$322$	−7.42758e39	−0.0309903
$323$	−1.01741e41	−0.403323
$324$	−2.90474e40	−0.109425
$325$	1.07052e42	3.83284
$326$	4.99288e40	0.169926
$327$	1.62229e41	0.524917
$328$	5.48720e40	0.168823
$329$	−3.15133e41	−0.922065
$330$	−4.97130e40	−0.138353
$331$	−6.27457e41	−1.66120	−0.830600	−	0.556869i	$-0.812003\pi$
$331$	−6.27457e41	−1.66120	−0.830600	+	0.556869i	$0.812003\pi$
$332$	−1.08646e40	−0.0273676
$333$	6.82239e40	0.163533
$334$	7.86416e40	0.179406
$335$	−1.07279e42	−2.32958
$336$	1.78485e41	0.368980
$337$	−4.80273e41	−0.945356	−0.472678	−	0.881235i	$-0.656713\pi$
$337$	−4.80273e41	−0.945356	−0.472678	+	0.881235i	$0.656713\pi$
$338$	−4.54329e40	−0.0851619
$339$	5.03635e41	0.899126
$340$	5.89393e41	1.00231
$341$	4.80817e41	0.778991
$342$	2.09454e40	0.0323339
$343$	−7.06170e41	−1.03886
$344$	2.05119e41	0.287601
$345$	−3.22481e41	−0.431011
$346$	6.60911e40	0.0842146
$347$	−1.32573e42	−1.61071	−0.805356	−	0.592791i	$-0.798026\pi$
$347$	−1.32573e42	−1.61071	−0.805356	+	0.592791i	$0.798026\pi$
$348$	−4.70133e41	−0.544707
$349$	9.12206e41	1.00803	0.504015	−	0.863695i	$-0.331856\pi$
$349$	9.12206e41	1.00803	0.504015	+	0.863695i	$0.331856\pi$
$350$	−2.30604e41	−0.243078
$351$	2.48878e41	0.250276
$352$	3.69515e41	0.354550
$353$	1.18898e42	1.08866	0.544331	−	0.838871i	$-0.316784\pi$
$353$	1.18898e42	1.08866	0.544331	+	0.838871i	$0.316784\pi$
$354$	1.79842e40	0.0157158
$355$	1.19298e42	0.995095
$356$	−4.06655e41	−0.323818
$357$	2.60413e41	0.197987
$358$	−2.07416e41	−0.150582
$359$	2.16487e42	1.50098	0.750488	−	0.660884i	$-0.229819\pi$
$359$	2.16487e42	1.50098	0.750488	+	0.660884i	$0.229819\pi$
$360$	−2.44548e41	−0.161947
$361$	−6.00876e41	−0.380116
$362$	−5.31175e40	−0.0321030
$363$	−4.15716e40	−0.0240070
$364$	−1.55357e42	−0.857350
$365$	−9.45510e40	−0.0498694
$366$	−1.19023e41	−0.0600056
$367$	−2.03646e42	−0.981489	−0.490744	−	0.871304i	$-0.663275\pi$
$367$	−2.03646e42	−0.981489	−0.490744	+	0.871304i	$0.663275\pi$
$368$	7.78491e41	0.358727
$369$	5.22276e41	0.230126
$370$	2.84990e41	0.120088
$371$	−3.01400e41	−0.121471
$372$	1.17357e42	0.452430
$373$	−2.43891e41	−0.0899497	−0.0449748	−	0.998988i	$-0.514321\pi$
$373$	−2.43891e41	−0.0899497	−0.0449748	+	0.998988i	$0.514321\pi$
$374$	1.75098e41	0.0617874
$375$	−6.61500e42	−2.23364
$376$	−1.04233e42	−0.336827
$377$	4.02809e42	1.24585
$378$	−5.36115e40	−0.0158724
$379$	−6.65700e41	−0.188683	−0.0943413	−	0.995540i	$-0.530074\pi$
$379$	−6.65700e41	−0.188683	−0.0943413	+	0.995540i	$0.530074\pi$
$380$	−5.67663e42	−1.54050
$381$	1.89725e41	0.0493017
$382$	3.57252e41	0.0889056
$383$	3.05351e42	0.727814	0.363907	−	0.931435i	$-0.381443\pi$
$383$	3.05351e42	0.727814	0.363907	+	0.931435i	$0.381443\pi$
$384$	1.19934e42	0.273828
$385$	5.95290e42	1.30205
$386$	4.75688e41	0.0996855
$387$	1.95234e42	0.392034
$388$	−5.09462e42	−0.980367
$389$	7.29960e42	1.34627	0.673133	−	0.739522i	$-0.264948\pi$
$389$	7.29960e42	1.34627	0.673133	+	0.739522i	$0.264948\pi$
$390$	1.03963e42	0.183786
$391$	1.13583e42	0.192485
$392$	−8.30627e41	−0.134954
$393$	5.20711e42	0.811184
$394$	−6.81136e41	−0.101753
$395$	−1.67915e43	−2.40568
$396$	2.33875e42	0.321376
$397$	7.44559e41	0.0981422	0.0490711	−	0.998795i	$-0.484374\pi$
$397$	7.44559e41	0.0981422	0.0490711	+	0.998795i	$0.484374\pi$
$398$	3.83524e41	0.0484978
$399$	−2.50812e42	−0.304295
$400$	2.41698e43	2.81374
$401$	4.66871e42	0.521572	0.260786	−	0.965397i	$-0.416018\pi$
$401$	4.66871e42	0.521572	0.260786	+	0.965397i	$0.416018\pi$
$402$	−7.77897e41	−0.0834050
$403$	−1.00552e43	−1.03480
$404$	−1.18204e43	−1.16772
$405$	−2.32763e42	−0.220753
$406$	−8.67702e41	−0.0790116
$407$	−5.49304e42	−0.480292
$408$	8.61341e41	0.0723240
$409$	−1.94142e43	−1.56561	−0.782807	−	0.622264i	$-0.786213\pi$
$409$	−1.94142e43	−1.56561	−0.782807	+	0.622264i	$0.786213\pi$
$410$	2.18169e42	0.168989
$411$	−3.78039e42	−0.281285
$412$	6.65805e42	0.475930
$413$	−2.15352e42	−0.147902
$414$	−2.33835e41	−0.0154314
$415$	−8.70605e41	−0.0552112
$416$	−7.72754e42	−0.470978
$417$	1.25247e43	0.733706
$418$	−1.68642e42	−0.0949637
$419$	5.88836e42	0.318759	0.159380	−	0.987217i	$-0.449051\pi$
$419$	5.88836e42	0.318759	0.159380	+	0.987217i	$0.449051\pi$
$420$	1.45298e43	0.756215
$421$	2.13517e41	0.0106851	0.00534255	−	0.999986i	$-0.498299\pi$
$421$	2.13517e41	0.0106851	0.00534255	+	0.999986i	$0.498299\pi$
$422$	−3.10244e42	−0.149296
$423$	−9.92102e42	−0.459135
$424$	−9.96910e41	−0.0443731
$425$	3.52642e43	1.50979
$426$	8.65045e41	0.0356271
$427$	1.42524e43	0.564713
$428$	8.77845e42	0.334654
$429$	−2.00384e43	−0.735052
$430$	8.15544e42	0.287884
$431$	1.10857e43	0.376606	0.188303	−	0.982111i	$-0.439701\pi$
$431$	1.10857e43	0.376606	0.188303	+	0.982111i	$0.439701\pi$
$432$	5.61906e42	0.183731
$433$	2.66960e43	0.840225	0.420112	−	0.907472i	$-0.361991\pi$
$433$	2.66960e43	0.840225	0.420112	+	0.907472i	$0.361991\pi$
$434$	2.16601e42	0.0656266
$435$	−3.76727e43	−1.09889
$436$	−3.18812e43	−0.895382
$437$	−1.09396e43	−0.295839
$438$	−6.85603e40	−0.00178546
$439$	−3.38880e43	−0.849927	−0.424963	−	0.905211i	$-0.639713\pi$
$439$	−3.38880e43	−0.849927	−0.424963	+	0.905211i	$0.639713\pi$
$440$	1.96898e43	0.475633
$441$	−7.90597e42	−0.183958
$442$	−3.66176e42	−0.0820773
$443$	1.65855e43	0.358152	0.179076	−	0.983835i	$-0.442689\pi$
$443$	1.65855e43	0.358152	0.179076	+	0.983835i	$0.442689\pi$
$444$	−1.34074e43	−0.278949
$445$	−3.25861e43	−0.653270
$446$	−1.02912e43	−0.198812
$447$	5.09664e43	0.948877
$448$	−3.39519e43	−0.609223
$449$	1.08981e44	1.88488	0.942442	−	0.334371i	$-0.108524\pi$
$449$	1.08981e44	1.88488	0.942442	+	0.334371i	$0.108524\pi$
$450$	−7.25989e42	−0.121038
$451$	−4.20511e43	−0.675871
$452$	−9.89743e43	−1.53369
$453$	−9.38626e42	−0.140240
$454$	1.01445e43	0.146153
$455$	−1.24491e44	−1.72962
$456$	−8.29584e42	−0.111158
$457$	1.14820e44	1.48389	0.741946	−	0.670460i	$-0.233903\pi$
$457$	1.14820e44	1.48389	0.741946	+	0.670460i	$0.233903\pi$
$458$	4.82357e41	0.00601295
$459$	8.19832e42	0.0985860
$460$	6.33739e43	0.735202
$461$	1.07382e43	0.120190	0.0600950	−	0.998193i	$-0.480860\pi$
$461$	1.07382e43	0.120190	0.0600950	+	0.998193i	$0.480860\pi$
$462$	4.31653e42	0.0466167
$463$	6.75739e43	0.704195	0.352097	−	0.935963i	$-0.385469\pi$
$463$	6.75739e43	0.704195	0.352097	+	0.935963i	$0.385469\pi$
$464$	9.09445e43	0.914597
$465$	9.40408e43	0.912731
$466$	1.14421e43	0.107186
$467$	5.13120e42	0.0463971	0.0231985	−	0.999731i	$-0.492615\pi$
$467$	5.13120e42	0.0463971	0.0231985	+	0.999731i	$0.492615\pi$
$468$	−4.89095e43	−0.426911
$469$	9.31494e43	0.784925
$470$	−4.14428e43	−0.337159
$471$	6.64966e43	0.522341
$472$	−7.12299e42	−0.0540281
$473$	−1.57192e44	−1.15139
$474$	−1.21758e43	−0.0861300
$475$	−3.39641e44	−2.32047
$476$	−5.11763e43	−0.337718
$477$	−9.48867e42	−0.0604856
$478$	−1.87758e43	−0.115621
$479$	1.87816e44	1.11737	0.558684	−	0.829380i	$-0.311306\pi$
$479$	1.87816e44	1.11737	0.558684	+	0.829380i	$0.311306\pi$
$480$	7.22717e43	0.415421
$481$	1.14874e44	0.638012
$482$	4.37576e43	0.234843
$483$	2.80006e43	0.145225
$484$	8.16966e42	0.0409501
$485$	−4.08243e44	−1.97779
$486$	−1.68780e42	−0.00790354
$487$	1.39466e44	0.631307	0.315654	−	0.948874i	$-0.397776\pi$
$487$	1.39466e44	0.631307	0.315654	+	0.948874i	$0.397776\pi$
$488$	4.71412e43	0.206288
$489$	−1.88222e44	−0.796297
$490$	−3.30254e43	−0.135087
$491$	−3.20414e44	−1.26726	−0.633631	−	0.773635i	$-0.718436\pi$
$491$	−3.20414e44	−1.26726	−0.633631	+	0.773635i	$0.718436\pi$
$492$	−1.02638e44	−0.392539
$493$	1.32690e44	0.490754
$494$	3.52676e43	0.126148
$495$	1.87409e44	0.648343
$496$	−2.27021e44	−0.759659
$497$	−1.03585e44	−0.335287
$498$	−6.31288e41	−0.00197671
$499$	3.67146e44	1.11219	0.556096	−	0.831118i	$-0.312299\pi$
$499$	3.67146e44	1.11219	0.556096	+	0.831118i	$0.312299\pi$
$500$	1.29998e45	3.81006
$501$	−2.96465e44	−0.840718
$502$	1.87588e43	0.0514748
$503$	4.42864e44	1.17598	0.587989	−	0.808869i	$-0.299920\pi$
$503$	4.42864e44	1.17598	0.587989	+	0.808869i	$0.299920\pi$
$504$	2.12338e43	0.0545663
$505$	−9.47195e44	−2.35576
$506$	1.88272e43	0.0453214
$507$	1.71274e44	0.399080
$508$	−3.72848e43	−0.0840969
$509$	1.56192e43	0.0341047	0.0170524	−	0.999855i	$-0.494572\pi$
$509$	1.56192e43	0.0341047	0.0170524	+	0.999855i	$0.494572\pi$
$510$	3.42466e43	0.0723952
$511$	8.20976e42	0.0168030
$512$	−2.92274e44	−0.579210
$513$	−7.89605e43	−0.151521
$514$	1.23101e43	0.0228755
$515$	5.33524e44	0.960140
$516$	−3.83673e44	−0.668716
$517$	7.98791e44	1.34846
$518$	−2.47453e43	−0.0404625
$519$	−2.49151e44	−0.394641
$520$	−4.11766e44	−0.631823
$521$	−9.13574e44	−1.35807	−0.679033	−	0.734107i	$-0.737601\pi$
$521$	−9.13574e44	−1.35807	−0.679033	+	0.734107i	$0.737601\pi$
$522$	−2.73170e43	−0.0393432
$523$	−5.82078e43	−0.0812275	−0.0406138	−	0.999175i	$-0.512931\pi$
$523$	−5.82078e43	−0.0812275	−0.0406138	+	0.999175i	$0.512931\pi$
$524$	−1.02330e45	−1.38369
$525$	8.69337e44	1.13909
$526$	8.19346e43	0.104040
$527$	−3.31228e44	−0.407617
$528$	−4.52419e44	−0.539611
$529$	−7.42876e44	−0.858811
$530$	−3.96368e43	−0.0444167
$531$	−6.77972e43	−0.0736465
$532$	4.92895e44	0.519054
$533$	8.79399e44	0.897816
$534$	−2.36287e43	−0.0233888
$535$	7.03436e44	0.675129
$536$	3.08101e44	0.286731
$537$	7.81920e44	0.705646
$538$	−6.24295e43	−0.0546364
$539$	6.36549e44	0.540278
$540$	4.57426e44	0.376551
$541$	−5.45279e44	−0.435375	−0.217688	−	0.976018i	$-0.569851\pi$
$541$	−5.45279e44	−0.435375	−0.217688	+	0.976018i	$0.569851\pi$
$542$	1.61008e42	0.00124698
$543$	2.00243e44	0.150439
$544$	−2.54554e44	−0.185523
$545$	−2.55471e45	−1.80634
$546$	−9.02701e43	−0.0619249
$547$	2.26359e45	1.50663	0.753317	−	0.657658i	$-0.228453\pi$
$547$	2.26359e45	1.50663	0.753317	+	0.657658i	$0.228453\pi$
$548$	7.42922e44	0.479804
$549$	4.48694e44	0.281194
$550$	5.84530e44	0.355486
$551$	−1.27798e45	−0.754261
$552$	9.26149e43	0.0530501
$553$	1.45799e45	0.810570
$554$	−3.09034e44	−0.166761
$555$	−1.07436e45	−0.562750
$556$	−2.46135e45	−1.25153
$557$	2.87891e45	1.42108	0.710539	−	0.703658i	$-0.248451\pi$
$557$	2.87891e45	1.42108	0.710539	+	0.703658i	$0.248451\pi$
$558$	6.81903e43	0.0326782
$559$	3.28731e45	1.52949
$560$	−2.81070e45	−1.26973
$561$	−6.60087e44	−0.289544
$562$	4.67828e44	0.199268
$563$	−2.82468e45	−1.16837	−0.584185	−	0.811621i	$-0.698586\pi$
$563$	−2.82468e45	−1.16837	−0.584185	+	0.811621i	$0.698586\pi$
$564$	1.94968e45	0.783174
$565$	−7.93102e45	−3.09407
$566$	−1.75495e44	−0.0664959
$567$	2.02105e44	0.0743802
$568$	−3.42618e44	−0.122479
$569$	1.95632e45	0.679340	0.339670	−	0.940545i	$-0.389685\pi$
$569$	1.95632e45	0.679340	0.339670	+	0.940545i	$0.389685\pi$
$570$	−3.29840e44	−0.111267
$571$	−1.92656e45	−0.631373	−0.315687	−	0.948864i	$-0.602235\pi$
$571$	−1.92656e45	−0.631373	−0.315687	+	0.948864i	$0.602235\pi$
$572$	3.93795e45	1.25382
$573$	−1.34677e45	−0.416623
$574$	−1.89434e44	−0.0569392
$575$	3.79175e45	1.10744
$576$	−1.06887e45	−0.303358
$577$	−1.91570e45	−0.528356	−0.264178	−	0.964474i	$-0.585101\pi$
$577$	−1.91570e45	−0.528356	−0.264178	+	0.964474i	$0.585101\pi$
$578$	3.39035e44	0.0908730
$579$	−1.79326e45	−0.467140
$580$	7.40344e45	1.87444
$581$	7.55937e43	0.0186028
$582$	−2.96023e44	−0.0708102
$583$	7.63981e44	0.177644
$584$	2.71546e43	0.00613807
$585$	−3.91922e45	−0.861248
$586$	−5.03095e44	−0.107483
$587$	8.50088e45	1.76577	0.882887	−	0.469585i	$-0.155596\pi$
$587$	8.50088e45	1.76577	0.882887	+	0.469585i	$0.155596\pi$
$588$	1.55368e45	0.313788
$589$	3.19016e45	0.626484
$590$	−2.83208e44	−0.0540812
$591$	2.56776e45	0.476827
$592$	2.59358e45	0.468372
$593$	−3.73193e45	−0.655437	−0.327719	−	0.944775i	$-0.606280\pi$
$593$	−3.73193e45	−0.655437	−0.327719	+	0.944775i	$0.606280\pi$
$594$	1.35893e44	0.0232124
$595$	−4.10087e45	−0.681312
$596$	−1.00159e46	−1.61856
$597$	−1.44582e45	−0.227267
$598$	−3.93728e44	−0.0602041
$599$	5.52400e45	0.821696	0.410848	−	0.911704i	$-0.365233\pi$
$599$	5.52400e45	0.821696	0.410848	+	0.911704i	$0.365233\pi$
$600$	2.87542e45	0.416107
$601$	−1.23464e46	−1.73825	−0.869124	−	0.494595i	$-0.835316\pi$
$601$	−1.23464e46	−1.73825	−0.869124	+	0.494595i	$0.835316\pi$
$602$	−7.08128e44	−0.0969996
$603$	2.93253e45	0.390847
$604$	1.84459e45	0.239216
$605$	6.54652e44	0.0826127
$606$	−6.86824e44	−0.0843427
$607$	2.45129e45	0.292942	0.146471	−	0.989215i	$-0.453209\pi$
$607$	2.45129e45	0.292942	0.146471	+	0.989215i	$0.453209\pi$
$608$	2.45168e45	0.285138
$609$	3.27108e45	0.370259
$610$	1.87432e45	0.206491
$611$	−1.67048e46	−1.79128
$612$	−1.61113e45	−0.168164
$613$	−6.68046e44	−0.0678748	−0.0339374	−	0.999424i	$-0.510805\pi$
$613$	−6.68046e44	−0.0678748	−0.0339374	+	0.999424i	$0.510805\pi$
$614$	7.22480e44	0.0714575
$615$	−8.22458e45	−0.791907
$616$	−1.70964e45	−0.160259
$617$	6.12997e45	0.559440	0.279720	−	0.960082i	$-0.409758\pi$
$617$	6.12997e45	0.559440	0.279720	+	0.960082i	$0.409758\pi$
$618$	3.86865e44	0.0343756
$619$	−3.79910e45	−0.328689	−0.164344	−	0.986403i	$-0.552551\pi$
$619$	−3.79910e45	−0.328689	−0.164344	+	0.986403i	$0.552551\pi$
$620$	−1.84809e46	−1.55690
$621$	8.81516e44	0.0723134
$622$	−1.61697e45	−0.129170
$623$	2.82942e45	0.220112
$624$	9.46127e45	0.716810
$625$	6.42272e46	4.73913
$626$	−4.30975e44	−0.0309724
$627$	6.35750e45	0.445013
$628$	−1.30679e46	−0.890989
$629$	3.78408e45	0.251319
$630$	8.44250e44	0.0546200
$631$	−1.99452e46	−1.25705	−0.628527	−	0.777788i	$-0.716342\pi$
$631$	−1.99452e46	−1.25705	−0.628527	+	0.777788i	$0.716342\pi$
$632$	4.82245e45	0.296098
$633$	1.16956e46	0.699621
$634$	−3.64075e44	−0.0212187
$635$	−2.98770e45	−0.169657
$636$	1.86472e45	0.103174
$637$	−1.33119e46	−0.717696
$638$	2.19943e45	0.115550
$639$	−3.26106e45	−0.166953
$640$	−1.88867e46	−0.942296
$641$	−7.09519e45	−0.344990	−0.172495	−	0.985010i	$-0.555183\pi$
$641$	−7.09519e45	−0.344990	−0.172495	+	0.985010i	$0.555183\pi$
$642$	5.10071e44	0.0241714
$643$	1.44723e46	0.668430	0.334215	−	0.942497i	$-0.391529\pi$
$643$	1.44723e46	0.668430	0.334215	+	0.942497i	$0.391529\pi$
$644$	−5.50269e45	−0.247718
$645$	−3.07445e46	−1.34906
$646$	1.16175e45	0.0496909
$647$	4.07680e46	1.69980	0.849902	−	0.526940i	$-0.176661\pi$
$647$	4.07680e46	1.69980	0.849902	+	0.526940i	$0.176661\pi$
$648$	6.68484e44	0.0271709
$649$	5.45869e45	0.216297
$650$	−1.22241e46	−0.472221
$651$	−8.16546e45	−0.307535
$652$	3.69895e46	1.35829
$653$	−1.54475e46	−0.553085	−0.276543	−	0.961002i	$-0.589189\pi$
$653$	−1.54475e46	−0.553085	−0.276543	+	0.961002i	$0.589189\pi$
$654$	−1.85246e45	−0.0646718
$655$	−8.19993e46	−2.79144
$656$	1.98547e46	0.659098
$657$	2.58460e44	0.00836689
$658$	3.59843e45	0.113602
$659$	−1.48126e46	−0.456058	−0.228029	−	0.973654i	$-0.573228\pi$
$659$	−1.48126e46	−0.456058	−0.228029	+	0.973654i	$0.573228\pi$
$660$	−3.68296e46	−1.10592
$661$	−8.93529e45	−0.261689	−0.130844	−	0.991403i	$-0.541769\pi$
$661$	−8.93529e45	−0.261689	−0.130844	+	0.991403i	$0.541769\pi$
$662$	7.16479e45	0.204667
$663$	1.38042e46	0.384625
$664$	2.50034e44	0.00679556
$665$	3.94967e46	1.04714
$666$	−7.79033e44	−0.0201480
$667$	1.42673e46	0.359971
$668$	5.82613e46	1.43406
$669$	3.87961e46	0.931660
$670$	1.22500e46	0.287013
$671$	−3.61266e46	−0.825858
$672$	−6.27527e45	−0.139972
$673$	−1.06117e46	−0.230960	−0.115480	−	0.993310i	$-0.536841\pi$
$673$	−1.06117e46	−0.230960	−0.115480	+	0.993310i	$0.536841\pi$
$674$	5.48414e45	0.116472
$675$	2.73685e46	0.567202
$676$	−3.36588e46	−0.680734
$677$	4.27203e46	0.843183	0.421591	−	0.906786i	$-0.361472\pi$
$677$	4.27203e46	0.843183	0.421591	+	0.906786i	$0.361472\pi$
$678$	−5.75089e45	−0.110776
$679$	3.54473e46	0.666395
$680$	−1.35640e46	−0.248881
$681$	−3.82428e46	−0.684893
$682$	−5.49034e45	−0.0959748
$683$	−6.43002e46	−1.09716	−0.548581	−	0.836098i	$-0.684832\pi$
$683$	−6.43002e46	−1.09716	−0.548581	+	0.836098i	$0.684832\pi$
$684$	1.55173e46	0.258459
$685$	5.95319e46	0.967956
$686$	8.06360e45	0.127992
$687$	−1.81840e45	−0.0281775
$688$	7.42195e46	1.12282
$689$	−1.59769e46	−0.235980
$690$	3.68233e45	0.0531023
$691$	−5.26382e46	−0.741163	−0.370581	−	0.928800i	$-0.620842\pi$
$691$	−5.26382e46	−0.741163	−0.370581	+	0.928800i	$0.620842\pi$
$692$	4.89633e46	0.673162
$693$	−1.62725e46	−0.218452
$694$	1.51382e46	0.198446
$695$	−1.97233e47	−2.52482
$696$	1.08194e46	0.135254
$697$	2.89684e46	0.353658
$698$	−1.04163e46	−0.124193
$699$	−4.31347e46	−0.502289
$700$	−1.70842e47	−1.94302
$701$	−1.00489e47	−1.11628	−0.558140	−	0.829747i	$-0.688485\pi$
$701$	−1.00489e47	−1.11628	−0.558140	+	0.829747i	$0.688485\pi$
$702$	−2.84188e45	−0.0308350
$703$	−3.64457e46	−0.386263
$704$	8.60603e46	0.890951
$705$	1.56232e47	1.57997
$706$	−1.35767e46	−0.134127
$707$	8.22439e46	0.793749
$708$	1.33235e46	0.125623
$709$	7.15848e46	0.659414	0.329707	−	0.944083i	$-0.393050\pi$
$709$	7.15848e46	0.659414	0.329707	+	0.944083i	$0.393050\pi$
$710$	−1.36223e46	−0.122600
$711$	4.59005e46	0.403617
$712$	9.35859e45	0.0804064
$713$	−3.56150e46	−0.298989
$714$	−2.97360e45	−0.0243928
$715$	3.15556e47	2.52946
$716$	−1.53663e47	−1.20366
$717$	7.07813e46	0.541817
$718$	−2.47202e46	−0.184926
$719$	−9.57451e46	−0.699987	−0.349993	−	0.936752i	$-0.613816\pi$
$719$	−9.57451e46	−0.699987	−0.349993	+	0.936752i	$0.613816\pi$
$720$	−8.84865e46	−0.632253
$721$	−4.63253e46	−0.323509
$722$	6.86127e45	0.0468318
$723$	−1.64958e47	−1.10050
$724$	−3.93518e46	−0.256613
$725$	4.42959e47	2.82349
$726$	4.74697e44	0.00295776
$727$	1.95428e46	0.119034	0.0595168	−	0.998227i	$-0.481044\pi$
$727$	1.95428e46	0.119034	0.0595168	+	0.998227i	$0.481044\pi$
$728$	3.57532e46	0.212886
$729$	6.36269e45	0.0370370
$730$	1.07966e45	0.00614411
$731$	1.08288e47	0.602479
$732$	−8.81774e46	−0.479650
$733$	−1.03780e47	−0.551948	−0.275974	−	0.961165i	$-0.589000\pi$
$733$	−1.03780e47	−0.551948	−0.275974	+	0.961165i	$0.589000\pi$
$734$	2.32539e46	0.120923
$735$	1.24500e47	0.633035
$736$	−2.73706e46	−0.136082
$737$	−2.36113e47	−1.14790
$738$	−5.96375e45	−0.0283524
$739$	−1.43435e47	−0.666841	−0.333420	−	0.942778i	$-0.608203\pi$
$739$	−1.43435e47	−0.666841	−0.333420	+	0.942778i	$0.608203\pi$
$740$	2.11133e47	0.959916
$741$	−1.32952e47	−0.591147
$742$	3.44162e45	0.0149657
$743$	1.25170e47	0.532334	0.266167	−	0.963927i	$-0.414243\pi$
$743$	1.25170e47	0.532334	0.266167	+	0.963927i	$0.414243\pi$
$744$	−2.70081e46	−0.112342
$745$	−8.02597e47	−3.26527
$746$	2.78493e45	0.0110822
$747$	2.37984e45	0.00926313
$748$	1.29720e47	0.493892
$749$	−6.10785e46	−0.227478
$750$	7.55352e46	0.275194
$751$	5.16112e47	1.83944	0.919718	−	0.392579i	$-0.128417\pi$
$751$	5.16112e47	1.83944	0.919718	+	0.392579i	$0.128417\pi$
$752$	−3.77155e47	−1.31500
$753$	−7.07174e46	−0.241218
$754$	−4.59959e46	−0.153494
$755$	1.47811e47	0.482594
$756$	−3.97178e46	−0.126875
$757$	8.94121e46	0.279457	0.139728	−	0.990190i	$-0.455377\pi$
$757$	8.94121e46	0.279457	0.139728	+	0.990190i	$0.455377\pi$
$758$	7.60149e45	0.0232464
$759$	−7.09753e46	−0.212382
$760$	1.30639e47	0.382516
$761$	1.08123e47	0.309793	0.154896	−	0.987931i	$-0.450496\pi$
$761$	1.08123e47	0.309793	0.154896	+	0.987931i	$0.450496\pi$
$762$	−2.16643e45	−0.00607417
$763$	2.21823e47	0.608627
$764$	2.64668e47	0.710659
$765$	−1.29104e47	−0.339254
$766$	−3.48674e46	−0.0896695
$767$	−1.14156e47	−0.287326
$768$	1.99598e47	0.491694
$769$	4.35551e47	1.05016	0.525079	−	0.851054i	$-0.324036\pi$
$769$	4.35551e47	1.05016	0.525079	+	0.851054i	$0.324036\pi$
$770$	−6.79748e46	−0.160417
$771$	−4.64069e46	−0.107198
$772$	3.52411e47	0.796828
$773$	3.21313e47	0.711160	0.355580	−	0.934646i	$-0.384283\pi$
$773$	3.21313e47	0.711160	0.355580	+	0.934646i	$0.384283\pi$
$774$	−2.22933e46	−0.0483001
$775$	−1.10574e48	−2.34517
$776$	1.17245e47	0.243432
$777$	9.32855e46	0.189613
$778$	−8.33525e46	−0.165865
$779$	−2.79003e47	−0.543553
$780$	7.70206e47	1.46908
$781$	2.62564e47	0.490336
$782$	−1.29698e46	−0.0237150
$783$	1.02980e47	0.184367
$784$	−3.00551e47	−0.526870
$785$	−1.04716e48	−1.79748
$786$	−5.94588e46	−0.0999411
$787$	7.30394e46	0.120219	0.0601096	−	0.998192i	$-0.480855\pi$
$787$	7.30394e46	0.120219	0.0601096	+	0.998192i	$0.480855\pi$
$788$	−5.04616e47	−0.813352
$789$	−3.08878e47	−0.487548
$790$	1.91739e47	0.296390
$791$	6.88642e47	1.04251
$792$	−5.38230e46	−0.0797999
$793$	7.55503e47	1.09706
$794$	−8.50195e45	−0.0120915
$795$	1.49424e47	0.208143
$796$	2.84132e47	0.387663
$797$	−1.40362e48	−1.87581	−0.937903	−	0.346897i	$-0.887235\pi$
$797$	−1.40362e48	−1.87581	−0.937903	+	0.346897i	$0.887235\pi$
$798$	2.86396e46	0.0374903
$799$	−5.50276e47	−0.705600
$800$	−8.49777e47	−1.06738
$801$	8.90758e46	0.109603
$802$	−5.33109e46	−0.0642597
$803$	−2.08099e46	−0.0245733
$804$	−5.76301e47	−0.666691
$805$	−4.40942e47	−0.499746
$806$	1.14818e47	0.127491
$807$	2.35348e47	0.256034
$808$	2.72030e47	0.289954
$809$	1.34731e48	1.40708	0.703538	−	0.710658i	$-0.251603\pi$
$809$	1.34731e48	1.40708	0.703538	+	0.710658i	$0.251603\pi$
$810$	2.65787e46	0.0271976
$811$	7.02588e47	0.704460	0.352230	−	0.935913i	$-0.385423\pi$
$811$	7.02588e47	0.704460	0.352230	+	0.935913i	$0.385423\pi$
$812$	−6.42833e47	−0.631573
$813$	−6.06970e45	−0.00584350
$814$	6.27238e46	0.0591739
$815$	2.96405e48	2.74021
$816$	3.11665e47	0.282358
$817$	−1.04295e48	−0.925977
$818$	2.21686e47	0.192890
$819$	3.40302e47	0.290188
$820$	1.61629e48	1.35080
$821$	1.77985e48	1.45788	0.728940	−	0.684577i	$-0.240013\pi$
$821$	1.77985e48	1.45788	0.728940	+	0.684577i	$0.240013\pi$
$822$	4.31674e46	0.0346554
$823$	−2.28638e48	−1.79908	−0.899541	−	0.436836i	$-0.856099\pi$
$823$	−2.28638e48	−1.79908	−0.899541	+	0.436836i	$0.856099\pi$
$824$	−1.53225e47	−0.118177
$825$	−2.20357e48	−1.66585
$826$	2.45906e46	0.0182221
$827$	−6.13384e47	−0.445545	−0.222772	−	0.974870i	$-0.571511\pi$
$827$	−6.13384e47	−0.445545	−0.222772	+	0.974870i	$0.571511\pi$
$828$	−1.73236e47	−0.123349
$829$	−7.48733e47	−0.522609	−0.261305	−	0.965256i	$-0.584153\pi$
$829$	−7.48733e47	−0.522609	−0.261305	+	0.965256i	$0.584153\pi$
$830$	9.94125e45	0.00680224
$831$	1.16500e48	0.781466
$832$	−1.79975e48	−1.18352
$833$	−4.38510e47	−0.282707
$834$	−1.43017e47	−0.0903955
$835$	4.66860e48	2.89307
$836$	−1.24938e48	−0.759084
$837$	−2.57065e47	−0.153135
$838$	−6.72378e46	−0.0392724
$839$	1.37346e48	0.786579	0.393290	−	0.919415i	$-0.371337\pi$
$839$	1.37346e48	0.786579	0.393290	+	0.919415i	$0.371337\pi$
$840$	−3.34381e47	−0.187773
$841$	−1.49342e47	−0.0822332
$842$	−2.43811e45	−0.00131645
$843$	−1.76363e48	−0.933795
$844$	−2.29843e48	−1.19338
$845$	−2.69715e48	−1.37331
$846$	1.13286e47	0.0565672
$847$	−5.68427e46	−0.0278355
$848$	−3.60719e47	−0.173236
$849$	6.61586e47	0.311609
$850$	−4.02675e47	−0.186012
$851$	4.06880e47	0.184344
$852$	6.40864e47	0.284782
$853$	−2.14688e48	−0.935728	−0.467864	−	0.883800i	$-0.654976\pi$
$853$	−2.14688e48	−0.935728	−0.467864	+	0.883800i	$0.654976\pi$
$854$	−1.62745e47	−0.0695749
$855$	1.24344e48	0.521414
$856$	−2.02023e47	−0.0830968
$857$	2.75329e48	1.11088	0.555442	−	0.831555i	$-0.312549\pi$
$857$	2.75329e48	1.11088	0.555442	+	0.831555i	$0.312549\pi$
$858$	2.28814e47	0.0905613
$859$	−1.51878e48	−0.589668	−0.294834	−	0.955548i	$-0.595264\pi$
$859$	−1.51878e48	−0.589668	−0.294834	+	0.955548i	$0.595264\pi$
$860$	6.04192e48	2.30118
$861$	7.14131e47	0.266825
$862$	−1.26585e47	−0.0463994
$863$	−3.14172e48	−1.12977	−0.564884	−	0.825170i	$-0.691079\pi$
$863$	−3.14172e48	−1.12977	−0.564884	+	0.825170i	$0.691079\pi$
$864$	−1.97558e47	−0.0696977
$865$	3.92353e48	1.35804
$866$	−3.04835e47	−0.103519
$867$	−1.27810e48	−0.425843
$868$	1.60468e48	0.524581
$869$	−3.69568e48	−1.18541
$870$	4.30176e47	0.135388
$871$	4.93775e48	1.52486
$872$	7.33701e47	0.222329
$873$	1.11595e48	0.331826
$874$	1.24916e47	0.0364486
$875$	−9.04498e48	−2.58985
$876$	−5.07925e46	−0.0142719
$877$	−3.02912e48	−0.835264	−0.417632	−	0.908616i	$-0.637140\pi$
$877$	−3.02912e48	−0.835264	−0.417632	+	0.908616i	$0.637140\pi$
$878$	3.86960e47	0.104714
$879$	1.89658e48	0.503679
$880$	7.12449e48	1.85691
$881$	5.13893e48	1.31453	0.657264	−	0.753660i	$-0.271714\pi$
$881$	5.13893e48	1.31453	0.657264	+	0.753660i	$0.271714\pi$
$882$	9.02766e46	0.0226644
$883$	2.39286e48	0.589612	0.294806	−	0.955557i	$-0.404745\pi$
$883$	2.39286e48	0.589612	0.294806	+	0.955557i	$0.404745\pi$
$884$	−2.71280e48	−0.656078
$885$	1.06764e48	0.253432
$886$	−1.89386e47	−0.0441257
$887$	−7.19496e48	−1.64547	−0.822733	−	0.568429i	$-0.807552\pi$
$887$	−7.19496e48	−1.64547	−0.822733	+	0.568429i	$0.807552\pi$
$888$	3.08551e47	0.0692649
$889$	2.59419e47	0.0571640
$890$	3.72094e47	0.0804855
$891$	−5.12292e47	−0.108777
$892$	−7.62422e48	−1.58919
$893$	5.29988e48	1.08447
$894$	−5.81974e47	−0.116905
$895$	−1.23133e49	−2.42826
$896$	1.63991e48	0.317496
$897$	1.48428e48	0.282125
$898$	−1.24442e48	−0.232225
$899$	−4.16060e48	−0.762292
$900$	−5.37845e48	−0.967511
$901$	−5.26296e47	−0.0929546
$902$	4.80172e47	0.0832700
$903$	2.66951e48	0.454553
$904$	2.27775e48	0.380826
$905$	−3.15334e48	−0.517690
$906$	1.07180e47	0.0172781
$907$	7.83294e48	1.23995	0.619976	−	0.784621i	$-0.287143\pi$
$907$	7.83294e48	1.23995	0.619976	+	0.784621i	$0.287143\pi$
$908$	7.51549e48	1.16826
$909$	2.58920e48	0.395241
$910$	1.42153e48	0.213095
$911$	1.04724e49	1.54167	0.770835	−	0.637034i	$-0.219839\pi$
$911$	1.04724e49	1.54167	0.770835	+	0.637034i	$0.219839\pi$
$912$	−3.00174e48	−0.433969
$913$	−1.91613e47	−0.0272055
$914$	−1.31111e48	−0.182821
$915$	−7.06584e48	−0.967644
$916$	3.57352e47	0.0480640
$917$	7.11991e48	0.940547
$918$	−9.36148e46	−0.0121462
$919$	−5.79471e48	−0.738458	−0.369229	−	0.929339i	$-0.620378\pi$
$919$	−5.79471e48	−0.738458	−0.369229	+	0.929339i	$0.620378\pi$
$920$	−1.45846e48	−0.182556
$921$	−2.72362e48	−0.334859
$922$	−1.22618e47	−0.0148079
$923$	−5.49092e48	−0.651354
$924$	3.19788e48	0.372627
$925$	1.26324e49	1.44593
$926$	−7.71612e47	−0.0867596
$927$	−1.45841e48	−0.161089
$928$	−3.19748e48	−0.346950
$929$	2.97562e48	0.317189	0.158595	−	0.987344i	$-0.449304\pi$
$929$	2.97562e48	0.317189	0.158595	+	0.987344i	$0.449304\pi$
$930$	−1.07383e48	−0.112452
$931$	4.22343e48	0.434505
$932$	8.47684e48	0.856784
$933$	6.09568e48	0.605306
$934$	−5.85920e46	−0.00571630
$935$	1.03948e49	0.996376
$936$	1.12558e48	0.106005
$937$	−5.85538e48	−0.541816	−0.270908	−	0.962605i	$-0.587324\pi$
$937$	−5.85538e48	−0.541816	−0.270908	+	0.962605i	$0.587324\pi$
$938$	−1.06365e48	−0.0967059
$939$	1.62470e48	0.145141
$940$	−3.07027e49	−2.69505
$941$	−2.05174e48	−0.176968	−0.0884839	−	0.996078i	$-0.528202\pi$
$941$	−2.05174e48	−0.176968	−0.0884839	+	0.996078i	$0.528202\pi$
$942$	−7.59310e47	−0.0643545
$943$	3.11480e48	0.259410
$944$	−2.57736e48	−0.210929
$945$	−3.18267e48	−0.255957
$946$	1.79494e48	0.141856
$947$	−1.52950e49	−1.18789	−0.593944	−	0.804506i	$-0.702430\pi$
$947$	−1.52950e49	−1.18789	−0.593944	+	0.804506i	$0.702430\pi$
$948$	−9.02037e48	−0.688473
$949$	4.35190e47	0.0326427
$950$	3.87828e48	0.285891
$951$	1.37250e48	0.0994335
$952$	1.17775e48	0.0838578
$953$	−1.07701e49	−0.753682	−0.376841	−	0.926278i	$-0.622990\pi$
$953$	−1.07701e49	−0.753682	−0.376841	+	0.926278i	$0.622990\pi$
$954$	1.08349e47	0.00745207
$955$	2.12084e49	1.43368
$956$	−1.39099e49	−0.924209
$957$	−8.29144e48	−0.541481
$958$	−2.14463e48	−0.137664
$959$	−5.16909e48	−0.326142
$960$	1.68321e49	1.04391
$961$	−6.01753e48	−0.366845
$962$	−1.31172e48	−0.0786056
$963$	−1.92287e48	−0.113271
$964$	3.24176e49	1.87720
$965$	2.82395e49	1.60752
$966$	−3.19733e47	−0.0178922
$967$	−2.22373e49	−1.22334	−0.611668	−	0.791114i	$-0.709501\pi$
$967$	−2.22373e49	−1.22334	−0.611668	+	0.791114i	$0.709501\pi$
$968$	−1.88013e47	−0.0101682
$969$	−4.37960e48	−0.232858
$970$	4.66163e48	0.243671
$971$	−3.59347e49	−1.84670	−0.923351	−	0.383958i	$-0.874561\pi$
$971$	−3.59347e49	−1.84670	−0.923351	+	0.383958i	$0.874561\pi$
$972$	−1.25040e48	−0.0631763
$973$	1.71255e49	0.850712
$974$	−1.59253e48	−0.0777796
$975$	4.60825e49	2.21289
$976$	1.70574e49	0.805362
$977$	2.70035e49	1.25360	0.626801	−	0.779180i	$-0.284364\pi$
$977$	2.70035e49	1.25360	0.626801	+	0.779180i	$0.284364\pi$
$978$	2.14927e48	0.0981070
$979$	−7.17194e48	−0.321901
$980$	−2.44667e49	−1.07981
$981$	6.98342e48	0.303061
$982$	3.65873e48	0.156132
$983$	−1.06598e49	−0.447318	−0.223659	−	0.974667i	$-0.571800\pi$
$983$	−1.06598e49	−0.447318	−0.223659	+	0.974667i	$0.571800\pi$
$984$	2.36206e48	0.0974702
$985$	−4.04359e49	−1.64085
$986$	−1.51516e48	−0.0604628
$987$	−1.35654e49	−0.532355
$988$	2.61278e49	1.00835
$989$	1.16435e49	0.441922
$990$	−2.13998e48	−0.0798784
$991$	−3.50891e49	−1.28812	−0.644061	−	0.764974i	$-0.722752\pi$
$991$	−3.50891e49	−1.28812	−0.644061	+	0.764974i	$0.722752\pi$
$992$	7.98174e48	0.288174
$993$	−2.70100e49	−0.959095
$994$	1.18281e48	0.0413086
$995$	2.27681e49	0.782070
$996$	−4.67686e47	−0.0158007
$997$	5.09100e49	1.69174	0.845869	−	0.533391i	$-0.179083\pi$
$997$	5.09100e49	1.69174	0.845869	+	0.533391i	$0.179083\pi$
$998$	−4.19235e48	−0.137026
$999$	2.93681e48	0.0944160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.34.a.a.1.2	✓	3
3.2	odd	2		9.34.a.d.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.34.a.a.1.2	✓	3	1.1	even	1	trivial
9.34.a.d.1.2		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)

\(f(q)\)	\(=\)	\(q-11418.8 q^{2} +4.30467e7 q^{3} -8.45955e9 q^{4} -6.77881e11 q^{5} -4.91541e11 q^{6} +5.88597e13 q^{7} +1.94684e14 q^{8} +1.85302e15 q^{9} +O(q^{10})\)	\(q-11418.8 q^{2} +4.30467e7 q^{3} -8.45955e9 q^{4} -6.77881e11 q^{5} -4.91541e11 q^{6} +5.88597e13 q^{7} +1.94684e14 q^{8} +1.85302e15 q^{9} +7.74057e15 q^{10} -1.49196e17 q^{11} -3.64156e17 q^{12} +3.12008e18 q^{13} -6.72105e17 q^{14} -2.91806e19 q^{15} +7.04439e19 q^{16} +1.02779e20 q^{17} -2.11592e19 q^{18} -9.89896e20 q^{19} +5.73457e21 q^{20} +2.53372e21 q^{21} +1.70364e21 q^{22} +1.10512e22 q^{23} +8.38052e21 q^{24} +3.43107e23 q^{25} -3.56275e22 q^{26} +7.97664e22 q^{27} -4.97926e23 q^{28} +1.29102e24 q^{29} +3.33206e23 q^{30} -3.22272e24 q^{31} -2.47671e24 q^{32} -6.42240e24 q^{33} -1.17361e24 q^{34} -3.98999e25 q^{35} -1.56757e25 q^{36} +3.68177e25 q^{37} +1.13034e25 q^{38} +1.34309e26 q^{39} -1.31973e26 q^{40} +2.81851e26 q^{41} -2.89319e25 q^{42} +1.05360e27 q^{43} +1.26213e27 q^{44} -1.25613e27 q^{45} -1.26191e26 q^{46} -5.35397e27 q^{47} +3.03238e27 q^{48} -4.26653e27 q^{49} -3.91787e27 q^{50} +4.42430e27 q^{51} -2.63945e28 q^{52} -5.12065e27 q^{53} -9.10835e26 q^{54} +1.01137e29 q^{55} +1.14590e28 q^{56} -4.26118e28 q^{57} -1.47419e28 q^{58} -3.65874e28 q^{59} +2.46854e29 q^{60} +2.42142e29 q^{61} +3.67996e28 q^{62} +1.09068e29 q^{63} -5.76827e29 q^{64} -2.11505e30 q^{65} +7.33359e28 q^{66} +1.58257e30 q^{67} -8.69464e29 q^{68} +4.75719e29 q^{69} +4.55608e29 q^{70} -1.75986e30 q^{71} +3.60754e29 q^{72} +1.39480e29 q^{73} -4.20413e29 q^{74} +1.47696e31 q^{75} +8.37407e30 q^{76} -8.78162e30 q^{77} -1.53365e30 q^{78} +2.47706e31 q^{79} -4.77526e31 q^{80} +3.43368e30 q^{81} -3.21840e30 q^{82} +1.28430e30 q^{83} -2.14341e31 q^{84} -6.96719e31 q^{85} -1.20308e31 q^{86} +5.55742e31 q^{87} -2.90461e31 q^{88} +4.80706e31 q^{89} +1.43434e31 q^{90} +1.83647e32 q^{91} -9.34883e31 q^{92} -1.38728e32 q^{93} +6.11358e31 q^{94} +6.71032e32 q^{95} -1.06614e32 q^{96} +6.02234e32 q^{97} +4.87186e31 q^{98} -2.76463e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 41202 q^{2} + 129140163 q^{3} - 1107467772 q^{4} + 51261823890 q^{5} + 1773610998642 q^{6} + 76113734015256 q^{7} + 11\!\cdots\!92 q^{8}+ \cdots + 55\!\cdots\!23 q^{9}+O(q^{10}) \) 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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