LMFDB - Embedded newform 3.28.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,28,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, 28, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 28 $
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:	$13.8556672451$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{30001}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 7500 $ x^2 - x - 7500
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-86.1040$ 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)

$f(q)$	$=$	$q+21703.1 q^{2} -1.59432e6 q^{3} +3.36807e8 q^{4} -6.93920e8 q^{5} -3.46018e10 q^{6} +3.81056e11 q^{7} +4.39681e12 q^{8} +2.54187e12 q^{9} +O(q^{10})$	\(q+21703.1 q^{2} -1.59432e6 q^{3} +3.36807e8 q^{4} -6.93920e8 q^{5} -3.46018e10 q^{6} +3.81056e11 q^{7} +4.39681e12 q^{8} +2.54187e12 q^{9} -1.50602e13 q^{10} +1.26337e14 q^{11} -5.36979e14 q^{12} -1.31606e15 q^{13} +8.27009e15 q^{14} +1.10633e15 q^{15} +5.02190e16 q^{16} -3.53536e16 q^{17} +5.51664e16 q^{18} +8.65178e16 q^{19} -2.33717e17 q^{20} -6.07526e17 q^{21} +2.74191e18 q^{22} +5.10955e17 q^{23} -7.00994e18 q^{24} -6.96906e18 q^{25} -2.85626e19 q^{26} -4.05256e18 q^{27} +1.28342e20 q^{28} -2.74961e19 q^{29} +2.40109e19 q^{30} -9.77996e19 q^{31} +4.99779e20 q^{32} -2.01422e20 q^{33} -7.67282e20 q^{34} -2.64422e20 q^{35} +8.56118e20 q^{36} -1.80293e21 q^{37} +1.87770e21 q^{38} +2.09822e21 q^{39} -3.05104e21 q^{40} -5.17966e21 q^{41} -1.31852e22 q^{42} +8.74613e21 q^{43} +4.25513e22 q^{44} -1.76385e21 q^{45} +1.10893e22 q^{46} +2.51817e22 q^{47} -8.00654e22 q^{48} +7.94910e22 q^{49} -1.51250e23 q^{50} +5.63650e22 q^{51} -4.43258e23 q^{52} +2.11957e23 q^{53} -8.79530e22 q^{54} -8.76680e22 q^{55} +1.67543e24 q^{56} -1.37937e23 q^{57} -5.96750e23 q^{58} -7.00844e23 q^{59} +3.72620e23 q^{60} +1.08505e23 q^{61} -2.12256e24 q^{62} +9.68592e23 q^{63} +4.10646e24 q^{64} +9.13240e23 q^{65} -4.37149e24 q^{66} +2.46540e24 q^{67} -1.19073e25 q^{68} -8.14627e23 q^{69} -5.73878e24 q^{70} +1.29459e25 q^{71} +1.11761e25 q^{72} +7.46465e24 q^{73} -3.91291e25 q^{74} +1.11109e25 q^{75} +2.91398e25 q^{76} +4.81415e25 q^{77} +4.55380e25 q^{78} -4.94644e25 q^{79} -3.48480e25 q^{80} +6.46108e24 q^{81} -1.12415e26 q^{82} -5.54332e25 q^{83} -2.04619e26 q^{84} +2.45325e25 q^{85} +1.89818e26 q^{86} +4.38376e25 q^{87} +5.55481e26 q^{88} -1.32973e26 q^{89} -3.82811e25 q^{90} -5.01492e26 q^{91} +1.72093e26 q^{92} +1.55924e26 q^{93} +5.46521e26 q^{94} -6.00364e25 q^{95} -7.96808e26 q^{96} -1.06222e27 q^{97} +1.72520e27 q^{98} +3.21132e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9}+O(q^{10}) $ 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9	$ 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9} - 14929666656300 q^{10} + 75762335668248 q^{11} - 323015968377612 q^{12} - 103021079177588 q^{13} + 82\!\cdots\!36 q^{14}+ \cdots + 19\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9 - 14929666656300 * q^10 + 75762335668248 * q^11 - 323015968377612 * q^12 - 103021079177588 * q^13 + 8271467686583136 * q^14 + 2825054421990300 * q^15 + 68227529433700880 * q^16 + 34691611579147908 * q^17 + 54858548306996478 * q^18 + 111620476558642216 * q^19 - 89042670767082600 * q^20 - 589365730506544992 * q^21 + 2748035308851015336 * q^22 - 2892743075819387952 * q^23 - 7061766547600378152 * q^24 - 13257495997920171250 * q^25 - 28709486590882989996 * q^26 - 8105110306037952534 * q^27 + 129870778968981827392 * q^28 + 29959552473322806972 * q^29 + 23802710932472184900 * q^30 + 10367463257055494032 * q^31 + 493234742263884106464 * q^32 - 120789634289608156104 * q^33 - 775764702062031404772 * q^34 - 252142979584030920000 * q^35 + 514991787751699496676 * q^36 - 3703660908819524869316 * q^37 + 1874664150379356981528 * q^38 + 164248876017649632924 * q^39 - 3086079750063749300400 * q^40 + 1481814928479478034772 * q^41 - 13187391176476285136928 * q^42 + 9778778623457380249240 * q^43 + 49338574711945832880432 * q^44 - 4504049241230841066900 * q^45 + 11501496706538201034672 * q^46 + 89494998518809740323520 * q^47 - 108776719409326288104240 * q^48 + 13908377820361409575890 * q^49 - 150488580768890263638750 * q^50 - 55309634247701830126284 * q^51 - 606051653487262224622952 * q^52 + 425671275824601813476748 * q^53 - 87462245312455545794394 * q^54 - 33146870181194328159600 * q^55 + 1675060131754321848708480 * q^56 - 177959093048404133739768 * q^57 - 603708195922408484547804 * q^58 + 369418769643380130292824 * q^59 + 141962777985387432079800 * q^60 + 925133397428892745249420 * q^61 - 2135654804561872705821072 * q^62 + 939639339558386331280416 * q^63 + 1690192763441891790257216 * q^64 - 394447136075147294825400 * q^65 - 4381255897713277323537528 * q^66 + 4151706674555213948132968 * q^67 - 21307603540300350668680824 * q^68 + 4611966818869594057796496 * q^69 - 5740267152557252353752000 * q^70 + 9760455855870867537668784 * q^71 + 11258736827469877696431096 * q^72 + 28449956347640075157409588 * q^73 - 38898941191404112127623644 * q^74 + 21136730791892081187813750 * q^75 + 25770925690602426011538256 * q^76 + 48717589762471785388668288 * q^77 + 45772194790036341259392708 * q^78 - 49553221898675501744231120 * q^79 - 54261621238075868678378400 * q^80 + 12922163778453346597864482 * q^81 - 113221448313178537381548852 * q^82 - 120473408203228735926347736 * q^83 - 207055969938164013993095616 * q^84 - 50977978054175038499879400 * q^85 + 189693121470759531169760808 * q^86 - 47765203577925437580019956 * q^87 + 553837409674913803181095584 * q^88 + 205644052209697133056985556 * q^89 - 37949209501991851246322700 * q^90 - 515309018103795393250147648 * q^91 + 628879743331458256476717984 * q^92 - 16529085122378486411580336 * q^93 + 538732610344725656813388864 * q^94 - 87097784513216888583651600 * q^95 - 786375493990382500270003872 * q^96 - 1478339006400409594836427772 * q^97 + 1733143443943237696043598078 * q^98 + 192577692109510944264197592 * 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 $

$2$	21703.1	1.87334	0.936671	−	0.350212i	$-0.113890\pi$
$2$	21703.1	1.87334	0.936671	+	0.350212i	$0.113890\pi$
$3$	−1.59432e6	−0.577350
$3$	−1.59432e6	−0.577350
$4$	3.36807e8	2.50941
$5$	−6.93920e8	−0.254223	−0.127111	−	0.991888i	$-0.540571\pi$
$5$	−6.93920e8	−0.254223	−0.127111	+	0.991888i	$0.540571\pi$
$6$	−3.46018e10	−1.08157
$7$	3.81056e11	1.48650	0.743250	−	0.669014i	$-0.233283\pi$
$7$	3.81056e11	1.48650	0.743250	+	0.669014i	$0.233283\pi$
$8$	4.39681e12	2.82763
$9$	2.54187e12	0.333333
$10$	−1.50602e13	−0.476246
$11$	1.26337e14	1.10339	0.551697	−	0.834045i	$-0.313981\pi$
$11$	1.26337e14	1.10339	0.551697	+	0.834045i	$0.313981\pi$
$12$	−5.36979e14	−1.44881
$13$	−1.31606e15	−1.20515	−0.602574	−	0.798063i	$-0.705858\pi$
$13$	−1.31606e15	−1.20515	−0.602574	+	0.798063i	$0.705858\pi$
$14$	8.27009e15	2.78472
$15$	1.10633e15	0.146776
$16$	5.02190e16	2.78772
$17$	−3.53536e16	−0.865711	−0.432855	−	0.901463i	$-0.642494\pi$
$17$	−3.53536e16	−0.865711	−0.432855	+	0.901463i	$0.642494\pi$
$18$	5.51664e16	0.624447
$19$	8.65178e16	0.471989	0.235994	−	0.971754i	$-0.424165\pi$
$19$	8.65178e16	0.471989	0.235994	+	0.971754i	$0.424165\pi$
$20$	−2.33717e17	−0.637948
$21$	−6.07526e17	−0.858231
$22$	2.74191e18	2.06703
$23$	5.10955e17	0.211376	0.105688	−	0.994399i	$-0.466295\pi$
$23$	5.10955e17	0.211376	0.105688	+	0.994399i	$0.466295\pi$
$24$	−7.00994e18	−1.63254
$25$	−6.96906e18	−0.935371
$26$	−2.85626e19	−2.25765
$27$	−4.05256e18	−0.192450
$28$	1.28342e20	3.73023
$29$	−2.74961e19	−0.497620	−0.248810	−	0.968552i	$-0.580039\pi$
$29$	−2.74961e19	−0.497620	−0.248810	+	0.968552i	$0.580039\pi$
$30$	2.40109e19	0.274961
$31$	−9.77996e19	−0.719373	−0.359687	−	0.933073i	$-0.617116\pi$
$31$	−9.77996e19	−0.719373	−0.359687	+	0.933073i	$0.617116\pi$
$32$	4.99779e20	2.39471
$33$	−2.01422e20	−0.637044
$34$	−7.67282e20	−1.62177
$35$	−2.64422e20	−0.377902
$36$	8.56118e20	0.836469
$37$	−1.80293e21	−1.21690	−0.608450	−	0.793592i	$-0.708208\pi$
$37$	−1.80293e21	−1.21690	−0.608450	+	0.793592i	$0.708208\pi$
$38$	1.87770e21	0.884196
$39$	2.09822e21	0.695793
$40$	−3.05104e21	−0.718849
$41$	−5.17966e21	−0.874419	−0.437209	−	0.899360i	$-0.644033\pi$
$41$	−5.17966e21	−0.874419	−0.437209	+	0.899360i	$0.644033\pi$
$42$	−1.31852e22	−1.60776
$43$	8.74613e21	0.776233	0.388116	−	0.921610i	$-0.373126\pi$
$43$	8.74613e21	0.776233	0.388116	+	0.921610i	$0.373126\pi$
$44$	4.25513e22	2.76886
$45$	−1.76385e21	−0.0847409
$46$	1.10893e22	0.395980
$47$	2.51817e22	0.672611	0.336306	−	0.941753i	$-0.390823\pi$
$47$	2.51817e22	0.672611	0.336306	+	0.941753i	$0.390823\pi$
$48$	−8.00654e22	−1.60949
$49$	7.94910e22	1.20968
$50$	−1.51250e23	−1.75227
$51$	5.63650e22	0.499818
$52$	−4.43258e23	−3.02421
$53$	2.11957e23	1.11821	0.559106	−	0.829096i	$-0.311144\pi$
$53$	2.11957e23	1.11821	0.559106	+	0.829096i	$0.311144\pi$
$54$	−8.79530e22	−0.360525
$55$	−8.76680e22	−0.280508
$56$	1.67543e24	4.20328
$57$	−1.37937e23	−0.272503
$58$	−5.96750e23	−0.932212
$59$	−7.00844e23	−0.869199	−0.434600	−	0.900624i	$-0.643110\pi$
$59$	−7.00844e23	−0.869199	−0.434600	+	0.900624i	$0.643110\pi$
$60$	3.72620e23	0.368320
$61$	1.08505e23	0.0858020	0.0429010	−	0.999079i	$-0.486340\pi$
$61$	1.08505e23	0.0858020	0.0429010	+	0.999079i	$0.486340\pi$
$62$	−2.12256e24	−1.34763
$63$	9.68592e23	0.495500
$64$	4.10646e24	1.69839
$65$	9.13240e23	0.306376
$66$	−4.37149e24	−1.19340
$67$	2.46540e24	0.549387	0.274693	−	0.961532i	$-0.411424\pi$
$67$	2.46540e24	0.549387	0.274693	+	0.961532i	$0.411424\pi$
$68$	−1.19073e25	−2.17242
$69$	−8.14627e23	−0.122038
$70$	−5.73878e24	−0.707939
$71$	1.29459e25	1.31870	0.659349	−	0.751837i	$-0.270832\pi$
$71$	1.29459e25	1.31870	0.659349	+	0.751837i	$0.270832\pi$
$72$	1.11761e25	0.942545
$73$	7.46465e24	0.522577	0.261289	−	0.965261i	$-0.415853\pi$
$73$	7.46465e24	0.522577	0.261289	+	0.965261i	$0.415853\pi$
$74$	−3.91291e25	−2.27967
$75$	1.11109e25	0.540037
$76$	2.91398e25	1.18441
$77$	4.81415e25	1.64019
$78$	4.55380e25	1.30346
$79$	−4.94644e25	−1.19214	−0.596070	−	0.802933i	$-0.703272\pi$
$79$	−4.94644e25	−1.19214	−0.596070	+	0.802933i	$0.703272\pi$
$80$	−3.48480e25	−0.708701
$81$	6.46108e24	0.111111
$82$	−1.12415e26	−1.63808
$83$	−5.54332e25	−0.685828	−0.342914	−	0.939367i	$-0.611414\pi$
$83$	−5.54332e25	−0.685828	−0.342914	+	0.939367i	$0.611414\pi$
$84$	−2.04619e26	−2.15365
$85$	2.45325e25	0.220083
$86$	1.89818e26	1.45415
$87$	4.38376e25	0.287301
$88$	5.55481e26	3.11999
$89$	−1.32973e26	−0.641206	−0.320603	−	0.947214i	$-0.603886\pi$
$89$	−1.32973e26	−0.641206	−0.320603	+	0.947214i	$0.603886\pi$
$90$	−3.82811e25	−0.158749
$91$	−5.01492e26	−1.79145
$92$	1.72093e26	0.530430
$93$	1.55924e26	0.415330
$94$	5.46521e26	1.26003
$95$	−6.00364e25	−0.119990
$96$	−7.96808e26	−1.38259
$97$	−1.06222e27	−1.60249	−0.801243	−	0.598339i	$-0.795827\pi$
$97$	−1.06222e27	−1.60249	−0.801243	+	0.598339i	$0.795827\pi$
$98$	1.72520e27	2.26615
$99$	3.21132e26	0.367798
$100$	−2.34723e27	−2.34723
$101$	1.74011e27	1.52138	0.760691	−	0.649114i	$-0.224860\pi$
$101$	1.74011e27	1.52138	0.760691	+	0.649114i	$0.224860\pi$
$102$	1.22330e27	0.936330
$103$	4.99563e26	0.335187	0.167594	−	0.985856i	$-0.446400\pi$
$103$	4.99563e26	0.335187	0.167594	+	0.985856i	$0.446400\pi$
$104$	−5.78647e27	−3.40772
$105$	4.21574e26	0.218182
$106$	4.60013e27	2.09479
$107$	−1.30395e27	−0.523096	−0.261548	−	0.965190i	$-0.584233\pi$
$107$	−1.30395e27	−0.523096	−0.261548	+	0.965190i	$0.584233\pi$
$108$	−1.36493e27	−0.482936
$109$	−5.74920e27	−1.79618	−0.898089	−	0.439814i	$-0.855044\pi$
$109$	−5.74920e27	−1.79618	−0.898089	+	0.439814i	$0.855044\pi$
$110$	−1.90267e27	−0.525486
$111$	2.87445e27	0.702578
$112$	1.91362e28	4.14394
$113$	8.29240e27	1.59265	0.796326	−	0.604867i	$-0.206774\pi$
$113$	8.29240e27	1.59265	0.796326	+	0.604867i	$0.206774\pi$
$114$	−2.99367e27	−0.510491
$115$	−3.54562e26	−0.0537367
$116$	−9.26087e27	−1.24873
$117$	−3.34525e27	−0.401716
$118$	−1.52105e28	−1.62831
$119$	−1.34717e28	−1.28688
$120$	4.86434e27	0.415028
$121$	2.85111e27	0.217476
$122$	2.35490e27	0.160736
$123$	8.25805e27	0.504846
$124$	−3.29396e28	−1.80520
$125$	1.00061e28	0.492015
$126$	2.10215e28	0.928240
$127$	2.16098e27	0.0857631	0.0428815	−	0.999080i	$-0.486346\pi$
$127$	2.16098e27	0.0857631	0.0428815	+	0.999080i	$0.486346\pi$
$128$	2.20438e28	0.786957
$129$	−1.39442e28	−0.448158
$130$	1.98202e28	0.573947
$131$	7.19824e28	1.87959	0.939797	−	0.341734i	$-0.111014\pi$
$131$	7.19824e28	1.87959	0.939797	+	0.341734i	$0.111014\pi$
$132$	−6.78405e28	−1.59860
$133$	3.29681e28	0.701611
$134$	5.35069e28	1.02919
$135$	2.81215e27	0.0489252
$136$	−1.55443e29	−2.44791
$137$	−8.23477e28	−1.17469	−0.587346	−	0.809336i	$-0.699827\pi$
$137$	−8.23477e28	−1.17469	−0.587346	+	0.809336i	$0.699827\pi$
$138$	−1.76799e28	−0.228619
$139$	1.17233e29	1.37515	0.687574	−	0.726114i	$-0.258676\pi$
$139$	1.17233e29	1.37515	0.687574	+	0.726114i	$0.258676\pi$
$140$	−8.90592e28	−0.948310
$141$	−4.01478e28	−0.388332
$142$	2.80967e29	2.47037
$143$	−1.66267e29	−1.32975
$144$	1.27650e29	0.929239
$145$	1.90801e28	0.126506
$146$	1.62006e29	0.978966
$147$	−1.26734e29	−0.698410
$148$	−6.07239e29	−3.05370
$149$	−2.66795e28	−0.122508	−0.0612538	−	0.998122i	$-0.519510\pi$
$149$	−2.66795e28	−0.122508	−0.0612538	+	0.998122i	$0.519510\pi$
$150$	2.41142e29	1.01167
$151$	−4.49422e29	−1.72372	−0.861859	−	0.507149i	$-0.830699\pi$
$151$	−4.49422e29	−1.72372	−0.861859	+	0.507149i	$0.830699\pi$
$152$	3.80403e29	1.33461
$153$	−8.98640e28	−0.288570
$154$	1.04482e30	3.07264
$155$	6.78651e28	0.182881
$156$	7.06697e29	1.74603
$157$	2.00427e29	0.454268	0.227134	−	0.973864i	$-0.427065\pi$
$157$	2.00427e29	0.454268	0.227134	+	0.973864i	$0.427065\pi$
$158$	−1.07353e30	−2.23328
$159$	−3.37928e29	−0.645600
$160$	−3.46806e29	−0.608790
$161$	1.94702e29	0.314211
$162$	1.40226e29	0.208149
$163$	6.62774e29	0.905384	0.452692	−	0.891667i	$-0.350464\pi$
$163$	6.62774e29	0.905384	0.452692	+	0.891667i	$0.350464\pi$
$164$	−1.74455e30	−2.19427
$165$	1.39771e29	0.161951
$166$	−1.20307e30	−1.28479
$167$	1.07500e30	1.05861	0.529307	−	0.848431i	$-0.322452\pi$
$167$	1.07500e30	1.05861	0.529307	+	0.848431i	$0.322452\pi$
$168$	−2.67118e30	−2.42676
$169$	5.39481e29	0.452382
$170$	5.32432e29	0.412291
$171$	2.19917e29	0.157330
$172$	2.94576e30	1.94788
$173$	8.13189e29	0.497244	0.248622	−	0.968601i	$-0.420022\pi$
$173$	8.13189e29	0.497244	0.248622	+	0.968601i	$0.420022\pi$
$174$	9.51413e29	0.538213
$175$	−2.65560e30	−1.39043
$176$	6.34454e30	3.07595
$177$	1.11737e30	0.501832
$178$	−2.88592e30	−1.20120
$179$	1.37936e30	0.532305	0.266152	−	0.963931i	$-0.414248\pi$
$179$	1.37936e30	0.532305	0.266152	+	0.963931i	$0.414248\pi$
$180$	−5.94077e29	−0.212649
$181$	−1.97778e30	−0.656927	−0.328464	−	0.944517i	$-0.606531\pi$
$181$	−1.97778e30	−0.656927	−0.328464	+	0.944517i	$0.606531\pi$
$182$	−1.08839e31	−3.35600
$183$	−1.72992e29	−0.0495378
$184$	2.24657e30	0.597695
$185$	1.25109e30	0.309364
$186$	3.38404e30	0.778056
$187$	−4.46647e30	−0.955219
$188$	8.48137e30	1.68785
$189$	−1.54425e30	−0.286077
$190$	−1.30298e30	−0.224783
$191$	8.23146e30	1.32290	0.661449	−	0.749990i	$-0.269942\pi$
$191$	8.23146e30	1.32290	0.661449	+	0.749990i	$0.269942\pi$
$192$	−6.54702e30	−0.980567
$193$	−2.63632e30	−0.368107	−0.184054	−	0.982916i	$-0.558922\pi$
$193$	−2.63632e30	−0.368107	−0.184054	+	0.982916i	$0.558922\pi$
$194$	−2.30534e31	−3.00200
$195$	−1.45600e30	−0.176886
$196$	2.67731e31	3.03558
$197$	9.66937e30	1.02354	0.511769	−	0.859123i	$-0.328990\pi$
$197$	9.66937e30	1.02354	0.511769	+	0.859123i	$0.328990\pi$
$198$	6.96957e30	0.689011
$199$	−8.33709e30	−0.770012	−0.385006	−	0.922914i	$-0.625801\pi$
$199$	−8.33709e30	−0.770012	−0.385006	+	0.922914i	$0.625801\pi$
$200$	−3.06416e31	−2.64489
$201$	−3.93065e30	−0.317189
$202$	3.77658e31	2.85007
$203$	−1.04775e31	−0.739712
$204$	1.89841e31	1.25425
$205$	3.59427e30	0.222297
$206$	1.08421e31	0.627920
$207$	1.29878e30	0.0704588
$208$	−6.60913e31	−3.35961
$209$	1.09304e31	0.520789
$210$	9.14947e30	0.408729
$211$	1.34579e31	0.563850	0.281925	−	0.959437i	$-0.409027\pi$
$211$	1.34579e31	0.563850	0.281925	+	0.959437i	$0.409027\pi$
$212$	7.13887e31	2.80605
$213$	−2.06400e31	−0.761351
$214$	−2.82998e31	−0.979937
$215$	−6.06912e30	−0.197336
$216$	−1.78183e31	−0.544178
$217$	−3.72671e31	−1.06935
$218$	−1.24775e32	−3.36485
$219$	−1.19011e31	−0.301710
$220$	−2.95272e31	−0.703908
$221$	4.65274e31	1.04331
$222$	6.23845e31	1.31617
$223$	7.20166e30	0.142994	0.0714969	−	0.997441i	$-0.477222\pi$
$223$	7.20166e30	0.142994	0.0714969	+	0.997441i	$0.477222\pi$
$224$	1.90443e32	3.55974
$225$	−1.77144e31	−0.311790
$226$	1.79971e32	2.98358
$227$	−1.24397e32	−1.94294	−0.971472	−	0.237153i	$-0.923786\pi$
$227$	−1.24397e32	−1.94294	−0.971472	+	0.237153i	$0.923786\pi$
$228$	−4.64582e31	−0.683821
$229$	1.14944e32	1.59481	0.797403	−	0.603447i	$-0.206206\pi$
$229$	1.14944e32	1.59481	0.797403	+	0.603447i	$0.206206\pi$
$230$	−7.69509e30	−0.100667
$231$	−7.67531e31	−0.946966
$232$	−1.20895e32	−1.40709
$233$	1.39267e32	1.52948	0.764741	−	0.644337i	$-0.222867\pi$
$233$	1.39267e32	1.52948	0.764741	+	0.644337i	$0.222867\pi$
$234$	−7.26023e31	−0.752551
$235$	−1.74741e31	−0.170993
$236$	−2.36049e32	−2.18117
$237$	7.88622e31	0.688282
$238$	−2.92377e32	−2.41076
$239$	1.18142e32	0.920517	0.460259	−	0.887785i	$-0.347757\pi$
$239$	1.18142e32	0.920517	0.460259	+	0.887785i	$0.347757\pi$
$240$	5.55590e31	0.409169
$241$	1.39602e32	0.971991	0.485996	−	0.873961i	$-0.338457\pi$
$241$	1.39602e32	0.971991	0.485996	+	0.873961i	$0.338457\pi$
$242$	6.18779e31	0.407407
$243$	−1.03011e31	−0.0641500
$244$	3.65453e31	0.215312
$245$	−5.51604e31	−0.307528
$246$	1.79225e32	0.945748
$247$	−1.13863e32	−0.568817
$248$	−4.30007e32	−2.03412
$249$	8.83784e31	0.395963
$250$	2.17163e32	0.921712
$251$	9.88006e31	0.397342	0.198671	−	0.980066i	$-0.436338\pi$
$251$	9.88006e31	0.397342	0.198671	+	0.980066i	$0.436338\pi$
$252$	3.26229e32	1.24341
$253$	6.45526e31	0.233231
$254$	4.69000e31	0.160664
$255$	−3.91128e31	−0.127065
$256$	−7.27415e31	−0.224152
$257$	−8.60649e31	−0.251611	−0.125805	−	0.992055i	$-0.540151\pi$
$257$	−8.60649e31	−0.251611	−0.125805	+	0.992055i	$0.540151\pi$
$258$	−3.02631e32	−0.839553
$259$	−6.87016e32	−1.80892
$260$	3.07586e32	0.768822
$261$	−6.98913e31	−0.165873
$262$	1.56224e33	3.52112
$263$	−2.80912e32	−0.601405	−0.300703	−	0.953718i	$-0.597221\pi$
$263$	−2.80912e32	−0.601405	−0.300703	+	0.953718i	$0.597221\pi$
$264$	−8.85617e32	−1.80133
$265$	−1.47081e32	−0.284275
$266$	7.15510e32	1.31436
$267$	2.12002e32	0.370200
$268$	8.30365e32	1.37864
$269$	−1.02703e32	−0.162153	−0.0810767	−	0.996708i	$-0.525836\pi$
$269$	−1.02703e32	−0.162153	−0.0810767	+	0.996708i	$0.525836\pi$
$270$	6.10324e31	0.0916536
$271$	−1.27505e33	−1.82155	−0.910775	−	0.412903i	$-0.864515\pi$
$271$	−1.27505e33	−1.82155	−0.910775	+	0.412903i	$0.864515\pi$
$272$	−1.77542e33	−2.41336
$273$	7.99540e32	1.03430
$274$	−1.78720e33	−2.20060
$275$	−8.80451e32	−1.03208
$276$	−2.74372e32	−0.306244
$277$	1.09712e33	1.16621	0.583107	−	0.812396i	$-0.301837\pi$
$277$	1.09712e33	1.16621	0.583107	+	0.812396i	$0.301837\pi$
$278$	2.54432e33	2.57612
$279$	−2.48594e32	−0.239791
$280$	−1.16261e33	−1.06857
$281$	1.35684e33	1.18849	0.594244	−	0.804285i	$-0.297451\pi$
$281$	1.35684e33	1.18849	0.594244	+	0.804285i	$0.297451\pi$
$282$	−8.71331e32	−0.727479
$283$	2.13864e33	1.70224	0.851120	−	0.524972i	$-0.175924\pi$
$283$	2.13864e33	1.70224	0.851120	+	0.524972i	$0.175924\pi$
$284$	4.36028e33	3.30915
$285$	9.57174e31	0.0692764
$286$	−3.60852e33	−2.49108
$287$	−1.97374e33	−1.29982
$288$	1.27037e33	0.798237
$289$	−4.17837e32	−0.250545
$290$	4.14097e32	0.236989
$291$	1.69351e33	0.925195
$292$	2.51414e33	1.31136
$293$	4.30088e32	0.214212	0.107106	−	0.994248i	$-0.465842\pi$
$293$	4.30088e32	0.214212	0.107106	+	0.994248i	$0.465842\pi$
$294$	−2.75053e33	−1.30836
$295$	4.86330e32	0.220970
$296$	−7.92714e33	−3.44095
$297$	−5.11989e32	−0.212348
$298$	−5.79028e32	−0.229499
$299$	−6.72447e32	−0.254740
$300$	3.74224e33	1.35517
$301$	3.33276e33	1.15387
$302$	−9.75386e33	−3.22911
$303$	−2.77430e33	−0.878370
$304$	4.34484e33	1.31577
$305$	−7.52938e31	−0.0218128
$306$	−1.95033e33	−0.540591
$307$	−5.70033e32	−0.151193	−0.0755966	−	0.997138i	$-0.524086\pi$
$307$	−5.70033e32	−0.151193	−0.0755966	+	0.997138i	$0.524086\pi$
$308$	1.62144e34	4.11591
$309$	−7.96464e32	−0.193520
$310$	1.47288e33	0.342599
$311$	−4.65284e33	−1.03622	−0.518111	−	0.855313i	$-0.673365\pi$
$311$	−4.65284e33	−1.03622	−0.518111	+	0.855313i	$0.673365\pi$
$312$	9.22550e33	1.96745
$313$	4.33109e33	0.884604	0.442302	−	0.896866i	$-0.354162\pi$
$313$	4.33109e33	0.884604	0.442302	+	0.896866i	$0.354162\pi$
$314$	4.34990e33	0.850998
$315$	−6.72126e32	−0.125967
$316$	−1.66600e34	−2.99156
$317$	−2.47386e33	−0.425671	−0.212836	−	0.977088i	$-0.568270\pi$
$317$	−2.47386e33	−0.425671	−0.212836	+	0.977088i	$0.568270\pi$
$318$	−7.33410e33	−1.20943
$319$	−3.47378e33	−0.549070
$320$	−2.84955e33	−0.431770
$321$	2.07892e33	0.302010
$322$	4.22564e33	0.588624
$323$	−3.05871e33	−0.408606
$324$	2.17614e33	0.278823
$325$	9.17170e33	1.12726
$326$	1.43842e34	1.69609
$327$	9.16607e33	1.03702
$328$	−2.27740e34	−2.47254
$329$	9.59563e33	0.999836
$330$	3.03347e33	0.303390
$331$	−2.93911e33	−0.282188	−0.141094	−	0.989996i	$-0.545062\pi$
$331$	−2.93911e33	−0.282188	−0.141094	+	0.989996i	$0.545062\pi$
$332$	−1.86703e34	−1.72102
$333$	−4.58280e33	−0.405633
$334$	2.33309e34	1.98314
$335$	−1.71079e33	−0.139667
$336$	−3.05094e34	−2.39250
$337$	−1.57199e34	−1.18426	−0.592128	−	0.805844i	$-0.701712\pi$
$337$	−1.57199e34	−1.18426	−0.592128	+	0.805844i	$0.701712\pi$
$338$	1.17084e34	0.847466
$339$	−1.32208e34	−0.919518
$340$	8.26273e33	0.552279
$341$	−1.23557e34	−0.793752
$342$	4.77287e33	0.294732
$343$	5.25043e33	0.311691
$344$	3.84551e34	2.19490
$345$	5.65286e32	0.0310249
$346$	1.76487e34	0.931507
$347$	2.55505e34	1.29703	0.648516	−	0.761201i	$-0.275390\pi$
$347$	2.55505e34	1.29703	0.648516	+	0.761201i	$0.275390\pi$
$348$	1.47648e34	0.720955
$349$	−3.50116e34	−1.64463	−0.822316	−	0.569031i	$-0.807319\pi$
$349$	−3.50116e34	−1.64463	−0.822316	+	0.569031i	$0.807319\pi$
$350$	−5.76347e34	−2.60475
$351$	5.33341e33	0.231931
$352$	6.31407e34	2.64231
$353$	−6.64200e33	−0.267510	−0.133755	−	0.991014i	$-0.542704\pi$
$353$	−6.64200e33	−0.267510	−0.133755	+	0.991014i	$0.542704\pi$
$354$	2.42504e34	0.940103
$355$	−8.98343e33	−0.335243
$356$	−4.47861e34	−1.60905
$357$	2.14782e34	0.742980
$358$	2.99363e34	0.997188
$359$	4.11061e34	1.31865	0.659327	−	0.751856i	$-0.270841\pi$
$359$	4.11061e34	1.31865	0.659327	+	0.751856i	$0.270841\pi$
$360$	−7.75533e33	−0.239616
$361$	−2.61153e34	−0.777227
$362$	−4.29240e34	−1.23065
$363$	−4.54559e33	−0.125560
$364$	−1.68906e35	−4.49548
$365$	−5.17987e33	−0.132851
$366$	−3.75447e33	−0.0928012
$367$	−3.04370e33	−0.0725121	−0.0362560	−	0.999343i	$-0.511543\pi$
$367$	−3.04370e33	−0.0725121	−0.0362560	+	0.999343i	$0.511543\pi$
$368$	2.56597e34	0.589258
$369$	−1.31660e34	−0.291473
$370$	2.71525e34	0.579544
$371$	8.07675e34	1.66222
$372$	5.25164e34	1.04223
$373$	4.11966e34	0.788483	0.394242	−	0.919007i	$-0.371007\pi$
$373$	4.11966e34	0.788483	0.394242	+	0.919007i	$0.371007\pi$
$374$	−9.69363e34	−1.78945
$375$	−1.59529e34	−0.284065
$376$	1.10719e35	1.90190
$377$	3.61865e34	0.599706
$378$	−3.35150e34	−0.535920
$379$	8.35010e34	1.28843	0.644217	−	0.764842i	$-0.277183\pi$
$379$	8.35010e34	1.28843	0.644217	+	0.764842i	$0.277183\pi$
$380$	−2.02207e34	−0.301104
$381$	−3.44530e33	−0.0495153
$382$	1.78648e35	2.47824
$383$	−5.20579e34	−0.697113	−0.348557	−	0.937288i	$-0.613328\pi$
$383$	−5.20579e34	−0.697113	−0.348557	+	0.937288i	$0.613328\pi$
$384$	−3.51449e34	−0.454350
$385$	−3.34064e34	−0.416974
$386$	−5.72163e34	−0.689591
$387$	2.22315e34	0.258744
$388$	−3.57761e35	−4.02129
$389$	−3.57703e34	−0.388332	−0.194166	−	0.980969i	$-0.562200\pi$
$389$	−3.57703e34	−0.388332	−0.194166	+	0.980969i	$0.562200\pi$
$390$	−3.15997e34	−0.331368
$391$	−1.80641e34	−0.182991
$392$	3.49507e35	3.42054
$393$	−1.14763e35	−1.08518
$394$	2.09855e35	1.91744
$395$	3.43243e34	0.303069
$396$	1.08160e35	0.922954
$397$	−7.79828e34	−0.643172	−0.321586	−	0.946880i	$-0.604216\pi$
$397$	−7.79828e34	−0.643172	−0.321586	+	0.946880i	$0.604216\pi$
$398$	−1.80941e35	−1.44250
$399$	−5.25618e34	−0.405075
$400$	−3.49979e35	−2.60755
$401$	−2.28761e34	−0.164791	−0.0823955	−	0.996600i	$-0.526257\pi$
$401$	−2.28761e34	−0.164791	−0.0823955	+	0.996600i	$0.526257\pi$
$402$	−8.53073e34	−0.594203
$403$	1.28710e35	0.866952
$404$	5.86081e35	3.81777
$405$	−4.48347e33	−0.0282470
$406$	−2.27395e35	−1.38573
$407$	−2.27777e35	−1.34272
$408$	2.47826e35	1.41330
$409$	−1.15859e34	−0.0639243	−0.0319621	−	0.999489i	$-0.510176\pi$
$409$	−1.15859e34	−0.0639243	−0.0319621	+	0.999489i	$0.510176\pi$
$410$	7.80068e34	0.416438
$411$	1.31289e35	0.678209
$412$	1.68256e35	0.841121
$413$	−2.67061e35	−1.29206
$414$	2.81875e34	0.131993
$415$	3.84662e34	0.174353
$416$	−6.57739e35	−2.88598
$417$	−1.86907e35	−0.793942
$418$	2.37224e35	0.975616
$419$	6.19060e34	0.246515	0.123258	−	0.992375i	$-0.460666\pi$
$419$	6.19060e34	0.246515	0.123258	+	0.992375i	$0.460666\pi$
$420$	1.41989e35	0.547507
$421$	−8.53227e33	−0.0318608	−0.0159304	−	0.999873i	$-0.505071\pi$
$421$	−8.53227e33	−0.0318608	−0.0159304	+	0.999873i	$0.505071\pi$
$422$	2.92078e35	1.05628
$423$	6.40085e34	0.224204
$424$	9.31937e35	3.16190
$425$	2.46381e35	0.809761
$426$	−4.47952e35	−1.42627
$427$	4.13465e34	0.127545
$428$	−4.39181e35	−1.31266
$429$	2.65084e35	0.767733
$430$	−1.31719e35	−0.369678
$431$	4.08719e35	1.11169	0.555843	−	0.831288i	$-0.312396\pi$
$431$	4.08719e35	1.11169	0.555843	+	0.831288i	$0.312396\pi$
$432$	−2.03515e35	−0.536496
$433$	1.44666e35	0.369642	0.184821	−	0.982772i	$-0.440830\pi$
$433$	1.44666e35	0.369642	0.184821	+	0.982772i	$0.440830\pi$
$434$	−8.08812e35	−2.00325
$435$	−3.04198e34	−0.0730385
$436$	−1.93637e36	−4.50734
$437$	4.42067e34	0.0997673
$438$	−2.58290e35	−0.565206
$439$	2.97115e34	0.0630454	0.0315227	−	0.999503i	$-0.489964\pi$
$439$	2.97115e34	0.0630454	0.0315227	+	0.999503i	$0.489964\pi$
$440$	−3.85460e35	−0.793173
$441$	2.02055e35	0.403227
$442$	1.00979e36	1.95448
$443$	−1.94735e35	−0.365589	−0.182795	−	0.983151i	$-0.558514\pi$
$443$	−1.94735e35	−0.365589	−0.182795	+	0.983151i	$0.558514\pi$
$444$	9.68134e35	1.76305
$445$	9.22725e34	0.163009
$446$	1.56298e35	0.267876
$447$	4.25357e34	0.0707298
$448$	1.56479e36	2.52466
$449$	−3.89051e35	−0.609089	−0.304544	−	0.952498i	$-0.598504\pi$
$449$	−3.89051e35	−0.609089	−0.304544	+	0.952498i	$0.598504\pi$
$450$	−3.84458e35	−0.584090
$451$	−6.54384e35	−0.964827
$452$	2.79294e36	3.99661
$453$	7.16525e35	0.995188
$454$	−2.69980e36	−3.63980
$455$	3.47995e35	0.455428
$456$	−6.06485e35	−0.770538
$457$	−7.79952e35	−0.962053	−0.481027	−	0.876706i	$-0.659736\pi$
$457$	−7.79952e35	−0.962053	−0.481027	+	0.876706i	$0.659736\pi$
$458$	2.49465e36	2.98762
$459$	1.43272e35	0.166606
$460$	−1.19419e35	−0.134847
$461$	−1.33828e36	−1.46752	−0.733760	−	0.679408i	$-0.762236\pi$
$461$	−1.33828e36	−1.46752	−0.733760	+	0.679408i	$0.762236\pi$
$462$	−1.66578e36	−1.77399
$463$	3.79932e35	0.392973	0.196486	−	0.980507i	$-0.437047\pi$
$463$	3.79932e35	0.392973	0.196486	+	0.980507i	$0.437047\pi$
$464$	−1.38083e36	−1.38722
$465$	−1.08199e35	−0.105586
$466$	3.02253e36	2.86524
$467$	−7.20473e35	−0.663499	−0.331749	−	0.943368i	$-0.607639\pi$
$467$	−7.20473e35	−0.663499	−0.331749	+	0.943368i	$0.607639\pi$
$468$	−1.12670e36	−1.00807
$469$	9.39456e35	0.816664
$470$	−3.79242e35	−0.320328
$471$	−3.19546e35	−0.262271
$472$	−3.08148e36	−2.45778
$473$	1.10496e36	0.856490
$474$	1.71156e36	1.28939
$475$	−6.02947e35	−0.441485
$476$	−4.53735e36	−3.22930
$477$	5.38767e35	0.372737
$478$	2.56404e36	1.72444
$479$	−4.56900e34	−0.0298739	−0.0149370	−	0.999888i	$-0.504755\pi$
$479$	−4.56900e34	−0.0298739	−0.0149370	+	0.999888i	$0.504755\pi$
$480$	5.52921e35	0.351485
$481$	2.37276e36	1.46655
$482$	3.02980e36	1.82087
$483$	−3.10418e35	−0.181410
$484$	9.60274e35	0.545736
$485$	7.37092e35	0.407388
$486$	−2.23565e35	−0.120175
$487$	−2.25055e36	−1.17665	−0.588326	−	0.808624i	$-0.700213\pi$
$487$	−2.25055e36	−1.17665	−0.588326	+	0.808624i	$0.700213\pi$
$488$	4.77077e35	0.242617
$489$	−1.05668e36	−0.522723
$490$	−1.19715e36	−0.576106
$491$	−3.36099e36	−1.57350	−0.786751	−	0.617271i	$-0.788238\pi$
$491$	−3.36099e36	−1.57350	−0.786751	+	0.617271i	$0.788238\pi$
$492$	2.78137e36	1.26686
$493$	9.72085e35	0.430795
$494$	−2.47117e36	−1.06559
$495$	−2.22840e35	−0.0935025
$496$	−4.91140e36	−2.00541
$497$	4.93312e36	1.96024
$498$	1.91808e36	0.741774
$499$	1.11121e35	0.0418253	0.0209127	−	0.999781i	$-0.493343\pi$
$499$	1.11121e35	0.0418253	0.0209127	+	0.999781i	$0.493343\pi$
$500$	3.37012e36	1.23467
$501$	−1.71390e36	−0.611191
$502$	2.14428e36	0.744357
$503$	−1.49384e36	−0.504818	−0.252409	−	0.967621i	$-0.581223\pi$
$503$	−1.49384e36	−0.504818	−0.252409	+	0.967621i	$0.581223\pi$
$504$	4.25872e36	1.40109
$505$	−1.20750e36	−0.386770
$506$	1.40099e36	0.436922
$507$	−8.60107e35	−0.261183
$508$	7.27833e35	0.215215
$509$	−5.00593e36	−1.44143	−0.720717	−	0.693230i	$-0.756187\pi$
$509$	−5.00593e36	−1.44143	−0.720717	+	0.693230i	$0.756187\pi$
$510$	−8.48869e35	−0.238036
$511$	2.84445e36	0.776811
$512$	−4.53738e36	−1.20687
$513$	−3.50618e35	−0.0908343
$514$	−1.86788e36	−0.471352
$515$	−3.46657e35	−0.0852122
$516$	−4.69649e36	−1.12461
$517$	3.18139e36	0.742154
$518$	−1.49104e37	−3.38873
$519$	−1.29649e36	−0.287084
$520$	4.01535e36	0.866319
$521$	3.77205e36	0.792990	0.396495	−	0.918037i	$-0.370226\pi$
$521$	3.77205e36	0.792990	0.396495	+	0.918037i	$0.370226\pi$
$522$	−1.51686e36	−0.310737
$523$	−7.85298e35	−0.156770	−0.0783848	−	0.996923i	$-0.524976\pi$
$523$	−7.85298e35	−0.156770	−0.0783848	+	0.996923i	$0.524976\pi$
$524$	2.42442e37	4.71666
$525$	4.23388e36	0.802764
$526$	−6.09666e36	−1.12664
$527$	3.45757e36	0.622769
$528$	−1.01152e37	−1.77590
$529$	−5.58214e36	−0.955320
$530$	−3.19212e36	−0.532544
$531$	−1.78145e36	−0.289733
$532$	1.11039e37	1.76063
$533$	6.81675e36	1.05380
$534$	4.60109e36	0.693512
$535$	9.04840e35	0.132983
$536$	1.08399e37	1.55347
$537$	−2.19914e36	−0.307326
$538$	−2.22897e36	−0.303769
$539$	1.00427e37	1.33475
$540$	9.47151e35	0.122773
$541$	6.90432e36	0.872887	0.436444	−	0.899732i	$-0.356238\pi$
$541$	6.90432e36	0.872887	0.436444	+	0.899732i	$0.356238\pi$
$542$	−2.76725e37	−3.41238
$543$	3.15322e36	0.379277
$544$	−1.76690e37	−2.07313
$545$	3.98948e36	0.456629
$546$	1.73525e37	1.93759
$547$	−4.90777e36	−0.534632	−0.267316	−	0.963609i	$-0.586137\pi$
$547$	−4.90777e36	−0.534632	−0.267316	+	0.963609i	$0.586137\pi$
$548$	−2.77353e37	−2.94778
$549$	2.75805e35	0.0286007
$550$	−1.91085e37	−1.93344
$551$	−2.37890e36	−0.234871
$552$	−3.58176e36	−0.345080
$553$	−1.88487e37	−1.77211
$554$	2.38109e37	2.18471
$555$	−1.99464e36	−0.178611
$556$	3.94848e37	3.45081
$557$	−8.37169e36	−0.714115	−0.357058	−	0.934082i	$-0.616220\pi$
$557$	−8.37169e36	−0.714115	−0.357058	+	0.934082i	$0.616220\pi$
$558$	−5.39525e36	−0.449211
$559$	−1.15104e37	−0.935475
$560$	−1.32790e37	−1.05348
$561$	7.12100e36	0.551496
$562$	2.94477e37	2.22644
$563$	1.53607e37	1.13383	0.566913	−	0.823778i	$-0.308138\pi$
$563$	1.53607e37	1.13383	0.566913	+	0.823778i	$0.308138\pi$
$564$	−1.35220e37	−0.974484
$565$	−5.75426e36	−0.404889
$566$	4.64151e37	3.18887
$567$	2.46203e36	0.165167
$568$	5.69208e37	3.72879
$569$	−2.56048e37	−1.63797	−0.818986	−	0.573814i	$-0.805463\pi$
$569$	−2.56048e37	−1.63797	−0.818986	+	0.573814i	$0.805463\pi$
$570$	2.07737e36	0.129778
$571$	−1.84375e37	−1.12490	−0.562450	−	0.826831i	$-0.690141\pi$
$571$	−1.84375e37	−1.12490	−0.562450	+	0.826831i	$0.690141\pi$
$572$	−5.60000e37	−3.33689
$573$	−1.31236e37	−0.763775
$574$	−4.28363e37	−2.43501
$575$	−3.56087e36	−0.197715
$576$	1.04381e37	0.566131
$577$	2.60648e37	1.38096	0.690479	−	0.723352i	$-0.257400\pi$
$577$	2.60648e37	1.38096	0.690479	+	0.723352i	$0.257400\pi$
$578$	−9.06835e36	−0.469356
$579$	4.20315e36	0.212527
$580$	6.42630e36	0.317456
$581$	−2.11231e37	−1.01948
$582$	3.67545e37	1.73321
$583$	2.67781e37	1.23383
$584$	3.28207e37	1.47766
$585$	2.32133e36	0.102125
$586$	9.33423e36	0.401292
$587$	1.64116e37	0.689505	0.344752	−	0.938694i	$-0.387963\pi$
$587$	1.64116e37	0.689505	0.344752	+	0.938694i	$0.387963\pi$
$588$	−4.26850e37	−1.75259
$589$	−8.46141e36	−0.339536
$590$	1.05549e37	0.413953
$591$	−1.54161e37	−0.590940
$592$	−9.05413e37	−3.39237
$593$	6.39232e35	0.0234110	0.0117055	−	0.999931i	$-0.496274\pi$
$593$	6.39232e35	0.0234110	0.0117055	+	0.999931i	$0.496274\pi$
$594$	−1.11117e37	−0.397800
$595$	9.34827e36	0.327154
$596$	−8.98584e36	−0.307421
$597$	1.32920e37	0.444567
$598$	−1.45942e37	−0.477215
$599$	3.67500e37	1.17488	0.587442	−	0.809266i	$-0.300135\pi$
$599$	3.67500e37	1.17488	0.587442	+	0.809266i	$0.300135\pi$
$600$	4.88527e37	1.52703
$601$	4.35901e36	0.133224	0.0666120	−	0.997779i	$-0.478781\pi$
$601$	4.35901e36	0.133224	0.0666120	+	0.997779i	$0.478781\pi$
$602$	7.23313e37	2.16159
$603$	6.26673e36	0.183129
$604$	−1.51369e38	−4.32551
$605$	−1.97844e36	−0.0552874
$606$	−6.02109e37	−1.64549
$607$	4.98438e37	1.33218	0.666092	−	0.745870i	$-0.267966\pi$
$607$	4.98438e37	1.33218	0.666092	+	0.745870i	$0.267966\pi$
$608$	4.32397e37	1.13028
$609$	1.67046e37	0.427073
$610$	−1.63411e36	−0.0408628
$611$	−3.31406e37	−0.810596
$612$	−3.02668e37	−0.724140
$613$	2.09778e37	0.490958	0.245479	−	0.969402i	$-0.421055\pi$
$613$	2.09778e37	0.490958	0.245479	+	0.969402i	$0.421055\pi$
$614$	−1.23715e37	−0.283236
$615$	−5.73043e36	−0.128343
$616$	2.11669e38	4.63787
$617$	−9.28596e37	−1.99057	−0.995284	−	0.0970039i	$-0.969074\pi$
$617$	−9.28596e37	−1.99057	−0.995284	+	0.0970039i	$0.969074\pi$
$618$	−1.72857e37	−0.362530
$619$	4.21148e37	0.864194	0.432097	−	0.901827i	$-0.357774\pi$
$619$	4.21148e37	0.864194	0.432097	+	0.901827i	$0.357774\pi$
$620$	2.28574e37	0.458923
$621$	−2.07067e36	−0.0406794
$622$	−1.00981e38	−1.94120
$623$	−5.06700e37	−0.953153
$624$	1.05371e38	1.93967
$625$	4.49801e37	0.810289
$626$	9.39981e37	1.65716
$627$	−1.74266e37	−0.300678
$628$	6.75053e37	1.13994
$629$	6.37399e37	1.05348
$630$	−1.45872e37	−0.235980
$631$	−1.60405e37	−0.253993	−0.126997	−	0.991903i	$-0.540534\pi$
$631$	−1.60405e37	−0.253993	−0.126997	+	0.991903i	$0.540534\pi$
$632$	−2.17486e38	−3.37093
$633$	−2.14562e37	−0.325539
$634$	−5.36903e37	−0.797427
$635$	−1.49955e36	−0.0218029
$636$	−1.13817e38	−1.62007
$637$	−1.04615e38	−1.45784
$638$	−7.53918e37	−1.02860
$639$	3.29068e37	0.439566
$640$	−1.52966e37	−0.200062
$641$	−4.27881e37	−0.547948	−0.273974	−	0.961737i	$-0.588338\pi$
$641$	−4.27881e37	−0.547948	−0.273974	+	0.961737i	$0.588338\pi$
$642$	4.51191e37	0.565767
$643$	6.44875e36	0.0791821	0.0395911	−	0.999216i	$-0.487394\pi$
$643$	6.44875e36	0.0791821	0.0395911	+	0.999216i	$0.487394\pi$
$644$	6.55770e37	0.788483
$645$	9.67613e36	0.113932
$646$	−6.63835e37	−0.765458
$647$	1.16912e38	1.32024	0.660118	−	0.751162i	$-0.270506\pi$
$647$	1.16912e38	1.32024	0.660118	+	0.751162i	$0.270506\pi$
$648$	2.84082e37	0.314182
$649$	−8.85427e37	−0.959068
$650$	1.99054e38	2.11174
$651$	5.94158e37	0.617389
$652$	2.23227e38	2.27198
$653$	−7.34409e37	−0.732167	−0.366083	−	0.930582i	$-0.619301\pi$
$653$	−7.34409e37	−0.732167	−0.366083	+	0.930582i	$0.619301\pi$
$654$	1.98932e38	1.94270
$655$	−4.99500e37	−0.477835
$656$	−2.60118e38	−2.43763
$657$	1.89741e37	0.174192
$658$	2.08255e38	1.87303
$659$	3.42254e37	0.301575	0.150788	−	0.988566i	$-0.451819\pi$
$659$	3.42254e37	0.301575	0.150788	+	0.988566i	$0.451819\pi$
$660$	4.70759e37	0.406401
$661$	−1.89312e37	−0.160125	−0.0800625	−	0.996790i	$-0.525512\pi$
$661$	−1.89312e37	−0.160125	−0.0800625	+	0.996790i	$0.525512\pi$
$662$	−6.37878e37	−0.528634
$663$	−7.41797e37	−0.602355
$664$	−2.43729e38	−1.93927
$665$	−2.28772e37	−0.178366
$666$	−9.94610e37	−0.759890
$667$	−1.40493e37	−0.105185
$668$	3.62068e38	2.65649
$669$	−1.14818e37	−0.0825575
$670$	−3.71295e37	−0.261643
$671$	1.37082e37	0.0946733
$672$	−3.03628e38	−2.05521
$673$	2.43532e38	1.61567	0.807835	−	0.589409i	$-0.200639\pi$
$673$	2.43532e38	1.61567	0.807835	+	0.589409i	$0.200639\pi$
$674$	−3.41170e38	−2.21852
$675$	2.82425e37	0.180012
$676$	1.81701e38	1.13521
$677$	2.58654e38	1.58406	0.792032	−	0.610479i	$-0.209023\pi$
$677$	2.58654e38	1.58406	0.792032	+	0.610479i	$0.209023\pi$
$678$	−2.86931e38	−1.72257
$679$	−4.04763e38	−2.38209
$680$	1.07865e38	0.622315
$681$	1.98329e38	1.12176
$682$	−2.68158e38	−1.48697
$683$	5.72592e37	0.311290	0.155645	−	0.987813i	$-0.450254\pi$
$683$	5.72592e37	0.311290	0.155645	+	0.987813i	$0.450254\pi$
$684$	7.40694e37	0.394804
$685$	5.71427e37	0.298633
$686$	1.13951e38	0.583903
$687$	−1.83258e38	−0.920762
$688$	4.39222e38	2.16392
$689$	−2.78949e38	−1.34761
$690$	1.22685e37	0.0581202
$691$	−1.45765e38	−0.677175	−0.338588	−	0.940935i	$-0.609949\pi$
$691$	−1.45765e38	−0.677175	−0.338588	+	0.940935i	$0.609949\pi$
$692$	2.73888e38	1.24779
$693$	1.22369e38	0.546731
$694$	5.54524e38	2.42978
$695$	−8.13502e37	−0.349594
$696$	1.92746e38	0.812382
$697$	1.83120e38	0.756994
$698$	−7.59861e38	−3.08096
$699$	−2.22037e38	−0.883047
$700$	−8.94424e38	−3.48915
$701$	−5.69328e37	−0.217856	−0.108928	−	0.994050i	$-0.534742\pi$
$701$	−5.69328e37	−0.217856	−0.108928	+	0.994050i	$0.534742\pi$
$702$	1.15751e38	0.434486
$703$	−1.55985e38	−0.574363
$704$	5.18799e38	1.87399
$705$	2.78593e37	0.0987229
$706$	−1.44152e38	−0.501138
$707$	6.63079e38	2.26153
$708$	3.76339e38	1.25930
$709$	2.15586e38	0.707776	0.353888	−	0.935288i	$-0.384859\pi$
$709$	2.15586e38	0.707776	0.353888	+	0.935288i	$0.384859\pi$
$710$	−1.94968e38	−0.628024
$711$	−1.25732e38	−0.397380
$712$	−5.84656e38	−1.81310
$713$	−4.99712e37	−0.152059
$714$	4.66144e38	1.39185
$715$	1.15376e38	0.338053
$716$	4.64577e38	1.33577
$717$	−1.88356e38	−0.531461
$718$	8.92129e38	2.47029
$719$	2.25632e38	0.613141	0.306571	−	0.951848i	$-0.400818\pi$
$719$	2.25632e38	0.613141	0.306571	+	0.951848i	$0.400818\pi$
$720$	−8.85789e37	−0.236234
$721$	1.90361e38	0.498256
$722$	−5.66783e38	−1.45601
$723$	−2.22571e38	−0.561179
$724$	−6.66130e38	−1.64850
$725$	1.91622e38	0.465459
$726$	−9.86534e37	−0.235217
$727$	3.26448e38	0.764010	0.382005	−	0.924160i	$-0.375234\pi$
$727$	3.26448e38	0.764010	0.382005	+	0.924160i	$0.375234\pi$
$728$	−2.20497e39	−5.06557
$729$	1.64232e37	0.0370370
$730$	−1.12419e38	−0.248875
$731$	−3.09207e38	−0.671993
$732$	−5.82649e37	−0.124310
$733$	3.51091e38	0.735387	0.367694	−	0.929947i	$-0.380147\pi$
$733$	3.51091e38	0.735387	0.367694	+	0.929947i	$0.380147\pi$
$734$	−6.60578e37	−0.135840
$735$	8.79435e37	0.177552
$736$	2.55364e38	0.506185
$737$	3.11472e38	0.606190
$738$	−2.85743e38	−0.546028
$739$	−5.12467e38	−0.961537	−0.480768	−	0.876848i	$-0.659642\pi$
$739$	−5.12467e38	−0.961537	−0.480768	+	0.876848i	$0.659642\pi$
$740$	4.21375e38	0.776320
$741$	1.81534e38	0.328406
$742$	1.75291e39	3.11391
$743$	−6.94450e38	−1.21141	−0.605706	−	0.795688i	$-0.707109\pi$
$743$	−6.94450e38	−1.21141	−0.605706	+	0.795688i	$0.707109\pi$
$744$	6.85570e38	1.17440
$745$	1.85134e37	0.0311442
$746$	8.94095e38	1.47710
$747$	−1.40904e38	−0.228609
$748$	−1.50434e39	−2.39703
$749$	−4.96879e38	−0.777582
$750$	−3.46228e38	−0.532151
$751$	5.87337e38	0.886642	0.443321	−	0.896363i	$-0.353800\pi$
$751$	5.87337e38	0.886642	0.443321	+	0.896363i	$0.353800\pi$
$752$	1.26460e39	1.87505
$753$	−1.57520e38	−0.229405
$754$	7.85359e38	1.12345
$755$	3.11863e38	0.438208
$756$	−5.20114e38	−0.717884
$757$	1.01202e38	0.137212	0.0686062	−	0.997644i	$-0.478145\pi$
$757$	1.01202e38	0.137212	0.0686062	+	0.997644i	$0.478145\pi$
$758$	1.81223e39	2.41368
$759$	−1.02918e38	−0.134656
$760$	−2.63969e38	−0.339289
$761$	−1.48838e39	−1.87941	−0.939705	−	0.341987i	$-0.888900\pi$
$761$	−1.48838e39	−1.87941	−0.939705	+	0.341987i	$0.888900\pi$
$762$	−7.47737e37	−0.0927591
$763$	−2.19076e39	−2.67002
$764$	2.77241e39	3.31969
$765$	6.23585e37	0.0733611
$766$	−1.12982e39	−1.30593
$767$	9.22353e38	1.04751
$768$	1.15973e38	0.129414
$769$	−1.63286e39	−1.79037	−0.895186	−	0.445692i	$-0.852958\pi$
$769$	−1.63286e39	−1.79037	−0.895186	+	0.445692i	$0.852958\pi$
$770$	−7.25022e38	−0.781135
$771$	1.37215e38	0.145267
$772$	−8.87931e38	−0.923731
$773$	9.47969e36	0.00969105	0.00484552	−	0.999988i	$-0.498458\pi$
$773$	9.47969e36	0.00969105	0.00484552	+	0.999988i	$0.498458\pi$
$774$	4.82492e38	0.484716
$775$	6.81571e38	0.672881
$776$	−4.67036e39	−4.53124
$777$	1.09532e39	1.04438
$778$	−7.76327e38	−0.727479
$779$	−4.48133e38	−0.412716
$780$	−4.90391e38	−0.443880
$781$	1.63555e39	1.45504
$782$	−3.92046e38	−0.342804
$783$	1.11429e38	0.0957670
$784$	3.99196e39	3.37225
$785$	−1.39081e38	−0.115485
$786$	−2.49072e39	−2.03292
$787$	1.01258e39	0.812401	0.406201	−	0.913784i	$-0.366853\pi$
$787$	1.01258e39	0.812401	0.406201	+	0.913784i	$0.366853\pi$
$788$	3.25671e39	2.56847
$789$	4.47864e38	0.347222
$790$	7.44945e38	0.567752
$791$	3.15986e39	2.36748
$792$	1.41196e39	1.04000
$793$	−1.42799e38	−0.103404
$794$	−1.69247e39	−1.20488
$795$	2.34495e38	0.164126
$796$	−2.80799e39	−1.93227
$797$	−1.64542e39	−1.11324	−0.556620	−	0.830767i	$-0.687902\pi$
$797$	−1.64542e39	−1.11324	−0.556620	+	0.830767i	$0.687902\pi$
$798$	−1.14075e39	−0.758844
$799$	−8.90263e38	−0.582287
$800$	−3.48298e39	−2.23994
$801$	−3.37999e38	−0.213735
$802$	−4.96483e38	−0.308710
$803$	9.43063e38	0.576608
$804$	−1.32387e39	−0.795956
$805$	−1.35108e38	−0.0798796
$806$	2.79341e39	1.62410
$807$	1.63741e38	0.0936193
$808$	7.65094e39	4.30191
$809$	−3.76453e38	−0.208164	−0.104082	−	0.994569i	$-0.533190\pi$
$809$	−3.76453e38	−0.208164	−0.104082	+	0.994569i	$0.533190\pi$
$810$	−9.73053e37	−0.0529162
$811$	1.84807e39	0.988408	0.494204	−	0.869346i	$-0.335460\pi$
$811$	1.84807e39	0.988408	0.494204	+	0.869346i	$0.335460\pi$
$812$	−3.52891e39	−1.85624
$813$	2.03284e39	1.05167
$814$	−4.94347e39	−2.51537
$815$	−4.59912e38	−0.230169
$816$	2.83060e39	1.39335
$817$	7.56696e38	0.366373
$818$	−2.51450e38	−0.119752
$819$	−1.27473e39	−0.597151
$820$	1.21058e39	0.557834
$821$	−4.29041e39	−1.94476	−0.972380	−	0.233401i	$-0.925014\pi$
$821$	−4.29041e39	−1.94476	−0.972380	+	0.233401i	$0.925014\pi$
$822$	2.84938e39	1.27052
$823$	−1.74258e39	−0.764355	−0.382177	−	0.924089i	$-0.624826\pi$
$823$	−1.74258e39	−0.764355	−0.382177	+	0.924089i	$0.624826\pi$
$824$	2.19648e39	0.947787
$825$	1.40372e39	0.595873
$826$	−5.79604e39	−2.42048
$827$	3.90760e39	1.60541	0.802704	−	0.596378i	$-0.203394\pi$
$827$	3.90760e39	1.60541	0.802704	+	0.596378i	$0.203394\pi$
$828$	4.37438e38	0.176810
$829$	1.05175e39	0.418243	0.209121	−	0.977890i	$-0.432940\pi$
$829$	1.05175e39	0.418243	0.209121	+	0.977890i	$0.432940\pi$
$830$	8.34836e38	0.326623
$831$	−1.74917e39	−0.673313
$832$	−5.40435e39	−2.04681
$833$	−2.81029e39	−1.04723
$834$	−4.05646e39	−1.48732
$835$	−7.45966e38	−0.269124
$836$	3.68144e39	1.30687
$837$	3.96338e38	0.138443
$838$	1.34355e39	0.461807
$839$	−9.84534e38	−0.333000	−0.166500	−	0.986041i	$-0.553247\pi$
$839$	−9.84534e38	−0.333000	−0.166500	+	0.986041i	$0.553247\pi$
$840$	1.85358e39	0.616938
$841$	−2.29710e39	−0.752374
$842$	−1.85177e38	−0.0596861
$843$	−2.16325e39	−0.686173
$844$	4.53270e39	1.41493
$845$	−3.74357e38	−0.115006
$846$	1.38918e39	0.420010
$847$	1.08643e39	0.323278
$848$	1.06443e40	3.11726
$849$	−3.40968e39	−0.982788
$850$	5.34723e39	1.51696
$851$	−9.21214e38	−0.257224
$852$	−6.95169e39	−1.91054
$853$	2.30350e39	0.623125	0.311563	−	0.950226i	$-0.399148\pi$
$853$	2.30350e39	0.623125	0.311563	+	0.950226i	$0.399148\pi$
$854$	8.97347e38	0.238935
$855$	−1.52605e38	−0.0399968
$856$	−5.73324e39	−1.47912
$857$	−1.77038e39	−0.449600	−0.224800	−	0.974405i	$-0.572173\pi$
$857$	−1.77038e39	−0.449600	−0.224800	+	0.974405i	$0.572173\pi$
$858$	5.75314e39	1.43823
$859$	5.46881e39	1.34581	0.672907	−	0.739727i	$-0.265046\pi$
$859$	5.46881e39	1.34581	0.672907	+	0.739727i	$0.265046\pi$
$860$	−2.04412e39	−0.495196
$861$	3.14678e39	0.750453
$862$	8.87047e39	2.08257
$863$	5.53394e39	1.27905	0.639526	−	0.768769i	$-0.279130\pi$
$863$	5.53394e39	1.27905	0.639526	+	0.768769i	$0.279130\pi$
$864$	−2.02538e39	−0.460862
$865$	−5.64288e38	−0.126411
$866$	3.13971e39	0.692465
$867$	6.66166e38	0.144652
$868$	−1.25518e40	−2.68343
$869$	−6.24920e39	−1.31540
$870$	−6.60204e38	−0.136826
$871$	−3.24462e39	−0.662093
$872$	−2.52781e40	−5.07893
$873$	−2.70001e39	−0.534162
$874$	9.59422e38	0.186898
$875$	3.81287e39	0.731380
$876$	−4.00836e39	−0.757114
$877$	7.58578e39	1.41093	0.705466	−	0.708744i	$-0.250738\pi$
$877$	7.58578e39	1.41093	0.705466	+	0.708744i	$0.250738\pi$
$878$	6.44831e38	0.118106
$879$	−6.85699e38	−0.123675
$880$	−4.40260e39	−0.781976
$881$	−5.97063e38	−0.104435	−0.0522174	−	0.998636i	$-0.516629\pi$
$881$	−5.97063e38	−0.104435	−0.0522174	+	0.998636i	$0.516629\pi$
$882$	4.38523e39	0.755382
$883$	−7.85839e39	−1.33310	−0.666552	−	0.745459i	$-0.732230\pi$
$883$	−7.85839e39	−1.33310	−0.666552	+	0.745459i	$0.732230\pi$
$884$	1.56708e40	2.61809
$885$	−7.75367e38	−0.127577
$886$	−4.22635e39	−0.684874
$887$	5.04306e39	0.804869	0.402434	−	0.915449i	$-0.368164\pi$
$887$	5.04306e39	0.804869	0.402434	+	0.915449i	$0.368164\pi$
$888$	1.26384e40	1.98663
$889$	8.23453e38	0.127487
$890$	2.00260e39	0.305372
$891$	8.16275e38	0.122599
$892$	2.42557e39	0.358829
$893$	2.17866e39	0.317465
$894$	9.23157e38	0.132501
$895$	−9.57163e38	−0.135324
$896$	8.39990e39	1.16981
$897$	1.07210e39	0.147074
$898$	−8.44360e39	−1.14103
$899$	2.68911e39	0.357975
$900$	−5.96633e39	−0.782409
$901$	−7.49345e39	−0.968048
$902$	−1.42022e40	−1.80745
$903$	−5.31350e39	−0.666187
$904$	3.64601e40	4.50344
$905$	1.37242e39	0.167006
$906$	1.55508e40	1.86433
$907$	−7.33863e39	−0.866796	−0.433398	−	0.901203i	$-0.642686\pi$
$907$	−7.33863e39	−0.866796	−0.433398	+	0.901203i	$0.642686\pi$
$908$	−4.18977e40	−4.87564
$909$	4.42313e39	0.507127
$910$	7.55258e39	0.853172
$911$	7.23054e39	0.804771	0.402386	−	0.915470i	$-0.368181\pi$
$911$	7.23054e39	0.804771	0.402386	+	0.915470i	$0.368181\pi$
$912$	−6.92708e39	−0.759661
$913$	−7.00327e39	−0.756738
$914$	−1.69274e40	−1.80225
$915$	1.20043e38	0.0125936
$916$	3.87140e40	4.00202
$917$	2.74293e40	2.79401
$918$	3.10945e39	0.312110
$919$	−1.06263e40	−1.05105	−0.525523	−	0.850780i	$-0.676130\pi$
$919$	−1.06263e40	−1.05105	−0.525523	+	0.850780i	$0.676130\pi$
$920$	−1.55894e39	−0.151948
$921$	9.08817e38	0.0872914
$922$	−2.90448e40	−2.74917
$923$	−1.70376e40	−1.58923
$924$	−2.58510e40	−2.37632
$925$	1.25647e40	1.13825
$926$	8.24570e39	0.736172
$927$	1.26982e39	0.111729
$928$	−1.37419e40	−1.19166
$929$	−9.62717e39	−0.822785	−0.411392	−	0.911458i	$-0.634957\pi$
$929$	−9.62717e39	−0.822785	−0.411392	+	0.911458i	$0.634957\pi$
$930$	−2.34825e39	−0.197799
$931$	6.87738e39	0.570956
$932$	4.69062e40	3.83809
$933$	7.41813e39	0.598263
$934$	−1.56365e40	−1.24296
$935$	3.09938e39	0.242838
$936$	−1.47084e40	−1.13591
$937$	1.21318e40	0.923509	0.461755	−	0.887008i	$-0.347220\pi$
$937$	1.21318e40	0.923509	0.461755	+	0.887008i	$0.347220\pi$
$938$	2.03891e40	1.52989
$939$	−6.90516e39	−0.510726
$940$	−5.88539e39	−0.429091
$941$	−5.05393e38	−0.0363219	−0.0181610	−	0.999835i	$-0.505781\pi$
$941$	−5.05393e38	−0.0363219	−0.0181610	+	0.999835i	$0.505781\pi$
$942$	−6.93514e39	−0.491324
$943$	−2.64657e39	−0.184831
$944$	−3.51957e40	−2.42308
$945$	1.07159e39	0.0727273
$946$	2.39811e40	1.60450
$947$	8.58094e39	0.565992	0.282996	−	0.959121i	$-0.408672\pi$
$947$	8.58094e39	0.565992	0.282996	+	0.959121i	$0.408672\pi$
$948$	2.65613e40	1.72718
$949$	−9.82392e39	−0.629783
$950$	−1.30858e40	−0.827051
$951$	3.94413e39	0.245761
$952$	−5.92324e40	−3.63882
$953$	−2.53482e39	−0.153530	−0.0767649	−	0.997049i	$-0.524459\pi$
$953$	−2.53482e39	−0.153530	−0.0767649	+	0.997049i	$0.524459\pi$
$954$	1.16929e40	0.698264
$955$	−5.71197e39	−0.336311
$956$	3.97910e40	2.30995
$957$	5.53833e39	0.317006
$958$	−9.91616e38	−0.0559640
$959$	−3.13791e40	−1.74618
$960$	4.54311e39	0.249282
$961$	−8.91794e39	−0.482502
$962$	5.14963e40	2.74734
$963$	−3.31448e39	−0.174365
$964$	4.70190e40	2.43912
$965$	1.82940e39	0.0935813
$966$	−6.73704e39	−0.339842
$967$	−2.17064e39	−0.107977	−0.0539884	−	0.998542i	$-0.517193\pi$
$967$	−2.17064e39	−0.107977	−0.0539884	+	0.998542i	$0.517193\pi$
$968$	1.25358e40	0.614943
$969$	4.87658e39	0.235909
$970$	1.59972e40	0.763177
$971$	2.71062e40	1.27529	0.637645	−	0.770330i	$-0.279909\pi$
$971$	2.71062e40	1.27529	0.637645	+	0.770330i	$0.279909\pi$
$972$	−3.46947e39	−0.160979
$973$	4.46722e40	2.04416
$974$	−4.88440e40	−2.20427
$975$	−1.46226e40	−0.650824
$976$	5.44902e39	0.239192
$977$	−4.41710e40	−1.91232	−0.956161	−	0.292841i	$-0.905399\pi$
$977$	−4.41710e40	−1.91232	−0.956161	+	0.292841i	$0.905399\pi$
$978$	−2.29331e40	−0.979239
$979$	−1.67994e40	−0.707502
$980$	−1.85784e40	−0.771714
$981$	−1.46137e40	−0.598726
$982$	−7.29439e40	−2.94770
$983$	−2.40915e40	−0.960266	−0.480133	−	0.877196i	$-0.659412\pi$
$983$	−2.40915e40	−0.960266	−0.480133	+	0.877196i	$0.659412\pi$
$984$	3.63091e40	1.42752
$985$	−6.70977e39	−0.260207
$986$	2.10972e40	0.807026
$987$	−1.52985e40	−0.577256
$988$	−3.83497e40	−1.42739
$989$	4.46888e39	0.164077
$990$	−4.83632e39	−0.175162
$991$	−1.16541e39	−0.0416376	−0.0208188	−	0.999783i	$-0.506627\pi$
$991$	−1.16541e39	−0.0416376	−0.0208188	+	0.999783i	$0.506627\pi$
$992$	−4.88782e40	−1.72269
$993$	4.68589e39	0.162921
$994$	1.07064e41	3.67221
$995$	5.78527e39	0.195755
$996$	2.97664e40	0.993633
$997$	5.76017e40	1.89693	0.948463	−	0.316888i	$-0.102638\pi$
$997$	5.76017e40	1.89693	0.948463	+	0.316888i	$0.102638\pi$
$998$	2.41167e39	0.0783531
$999$	7.30646e39	0.234193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.28.a.b.1.2	✓	2
3.2	odd	2		9.28.a.b.1.1		2
4.3	odd	2		48.28.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.28.a.b.1.2	✓	2	1.1	even	1	trivial
9.28.a.b.1.1		2	3.2	odd	2
48.28.a.e.1.2		2	4.3	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:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+21703.1 q^{2} -1.59432e6 q^{3} +3.36807e8 q^{4} -6.93920e8 q^{5} -3.46018e10 q^{6} +3.81056e11 q^{7} +4.39681e12 q^{8} +2.54187e12 q^{9} +O(q^{10})\)	\(q+21703.1 q^{2} -1.59432e6 q^{3} +3.36807e8 q^{4} -6.93920e8 q^{5} -3.46018e10 q^{6} +3.81056e11 q^{7} +4.39681e12 q^{8} +2.54187e12 q^{9} -1.50602e13 q^{10} +1.26337e14 q^{11} -5.36979e14 q^{12} -1.31606e15 q^{13} +8.27009e15 q^{14} +1.10633e15 q^{15} +5.02190e16 q^{16} -3.53536e16 q^{17} +5.51664e16 q^{18} +8.65178e16 q^{19} -2.33717e17 q^{20} -6.07526e17 q^{21} +2.74191e18 q^{22} +5.10955e17 q^{23} -7.00994e18 q^{24} -6.96906e18 q^{25} -2.85626e19 q^{26} -4.05256e18 q^{27} +1.28342e20 q^{28} -2.74961e19 q^{29} +2.40109e19 q^{30} -9.77996e19 q^{31} +4.99779e20 q^{32} -2.01422e20 q^{33} -7.67282e20 q^{34} -2.64422e20 q^{35} +8.56118e20 q^{36} -1.80293e21 q^{37} +1.87770e21 q^{38} +2.09822e21 q^{39} -3.05104e21 q^{40} -5.17966e21 q^{41} -1.31852e22 q^{42} +8.74613e21 q^{43} +4.25513e22 q^{44} -1.76385e21 q^{45} +1.10893e22 q^{46} +2.51817e22 q^{47} -8.00654e22 q^{48} +7.94910e22 q^{49} -1.51250e23 q^{50} +5.63650e22 q^{51} -4.43258e23 q^{52} +2.11957e23 q^{53} -8.79530e22 q^{54} -8.76680e22 q^{55} +1.67543e24 q^{56} -1.37937e23 q^{57} -5.96750e23 q^{58} -7.00844e23 q^{59} +3.72620e23 q^{60} +1.08505e23 q^{61} -2.12256e24 q^{62} +9.68592e23 q^{63} +4.10646e24 q^{64} +9.13240e23 q^{65} -4.37149e24 q^{66} +2.46540e24 q^{67} -1.19073e25 q^{68} -8.14627e23 q^{69} -5.73878e24 q^{70} +1.29459e25 q^{71} +1.11761e25 q^{72} +7.46465e24 q^{73} -3.91291e25 q^{74} +1.11109e25 q^{75} +2.91398e25 q^{76} +4.81415e25 q^{77} +4.55380e25 q^{78} -4.94644e25 q^{79} -3.48480e25 q^{80} +6.46108e24 q^{81} -1.12415e26 q^{82} -5.54332e25 q^{83} -2.04619e26 q^{84} +2.45325e25 q^{85} +1.89818e26 q^{86} +4.38376e25 q^{87} +5.55481e26 q^{88} -1.32973e26 q^{89} -3.82811e25 q^{90} -5.01492e26 q^{91} +1.72093e26 q^{92} +1.55924e26 q^{93} +5.46521e26 q^{94} -6.00364e25 q^{95} -7.96808e26 q^{96} -1.06222e27 q^{97} +1.72520e27 q^{98} +3.21132e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9}+O(q^{10}) \) 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9	\( 2 q + 21582 q^{2} - 3188646 q^{3} + 202603844 q^{4} - 1771946100 q^{5} - 34408678986 q^{6} + 369665199904 q^{7} + 4429319872824 q^{8} + 5083731656658 q^{9} - 14929666656300 q^{10} + 75762335668248 q^{11} - 323015968377612 q^{12} - 103021079177588 q^{13} + 82\!\cdots\!36 q^{14}+ \cdots + 19\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q + 21582 * q^2 - 3188646 * q^3 + 202603844 * q^4 - 1771946100 * q^5 - 34408678986 * q^6 + 369665199904 * q^7 + 4429319872824 * q^8 + 5083731656658 * q^9 - 14929666656300 * q^10 + 75762335668248 * q^11 - 323015968377612 * q^12 - 103021079177588 * q^13 + 8271467686583136 * q^14 + 2825054421990300 * q^15 + 68227529433700880 * q^16 + 34691611579147908 * q^17 + 54858548306996478 * q^18 + 111620476558642216 * q^19 - 89042670767082600 * q^20 - 589365730506544992 * q^21 + 2748035308851015336 * q^22 - 2892743075819387952 * q^23 - 7061766547600378152 * q^24 - 13257495997920171250 * q^25 - 28709486590882989996 * q^26 - 8105110306037952534 * q^27 + 129870778968981827392 * q^28 + 29959552473322806972 * q^29 + 23802710932472184900 * q^30 + 10367463257055494032 * q^31 + 493234742263884106464 * q^32 - 120789634289608156104 * q^33 - 775764702062031404772 * q^34 - 252142979584030920000 * q^35 + 514991787751699496676 * q^36 - 3703660908819524869316 * q^37 + 1874664150379356981528 * q^38 + 164248876017649632924 * q^39 - 3086079750063749300400 * q^40 + 1481814928479478034772 * q^41 - 13187391176476285136928 * q^42 + 9778778623457380249240 * q^43 + 49338574711945832880432 * q^44 - 4504049241230841066900 * q^45 + 11501496706538201034672 * q^46 + 89494998518809740323520 * q^47 - 108776719409326288104240 * q^48 + 13908377820361409575890 * q^49 - 150488580768890263638750 * q^50 - 55309634247701830126284 * q^51 - 606051653487262224622952 * q^52 + 425671275824601813476748 * q^53 - 87462245312455545794394 * q^54 - 33146870181194328159600 * q^55 + 1675060131754321848708480 * q^56 - 177959093048404133739768 * q^57 - 603708195922408484547804 * q^58 + 369418769643380130292824 * q^59 + 141962777985387432079800 * q^60 + 925133397428892745249420 * q^61 - 2135654804561872705821072 * q^62 + 939639339558386331280416 * q^63 + 1690192763441891790257216 * q^64 - 394447136075147294825400 * q^65 - 4381255897713277323537528 * q^66 + 4151706674555213948132968 * q^67 - 21307603540300350668680824 * q^68 + 4611966818869594057796496 * q^69 - 5740267152557252353752000 * q^70 + 9760455855870867537668784 * q^71 + 11258736827469877696431096 * q^72 + 28449956347640075157409588 * q^73 - 38898941191404112127623644 * q^74 + 21136730791892081187813750 * q^75 + 25770925690602426011538256 * q^76 + 48717589762471785388668288 * q^77 + 45772194790036341259392708 * q^78 - 49553221898675501744231120 * q^79 - 54261621238075868678378400 * q^80 + 12922163778453346597864482 * q^81 - 113221448313178537381548852 * q^82 - 120473408203228735926347736 * q^83 - 207055969938164013993095616 * q^84 - 50977978054175038499879400 * q^85 + 189693121470759531169760808 * q^86 - 47765203577925437580019956 * q^87 + 553837409674913803181095584 * q^88 + 205644052209697133056985556 * q^89 - 37949209501991851246322700 * q^90 - 515309018103795393250147648 * q^91 + 628879743331458256476717984 * q^92 - 16529085122378486411580336 * q^93 + 538732610344725656813388864 * q^94 - 87097784513216888583651600 * q^95 - 786375493990382500270003872 * q^96 - 1478339006400409594836427772 * q^97 + 1733143443943237696043598078 * q^98 + 192577692109510944264197592 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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