LMFDB - Embedded newform 3.20.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,20,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, 20, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 20 $
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:	$6.86450089669$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{87481}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 21870 $ x^2 - x - 21870
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$148.386$ 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)

$f(q)$	$=$	$q-536.316 q^{2} -19683.0 q^{3} -236654. q^{4} -683163. q^{5} +1.05563e7 q^{6} +1.13677e8 q^{7} +4.08105e8 q^{8} +3.87420e8 q^{9} +O(q^{10})$	\(q-536.316 q^{2} -19683.0 q^{3} -236654. q^{4} -683163. q^{5} +1.05563e7 q^{6} +1.13677e8 q^{7} +4.08105e8 q^{8} +3.87420e8 q^{9} +3.66391e8 q^{10} +6.43152e9 q^{11} +4.65805e9 q^{12} -5.75132e10 q^{13} -6.09670e10 q^{14} +1.34467e10 q^{15} -9.47984e10 q^{16} +6.85083e11 q^{17} -2.07780e11 q^{18} +1.22275e12 q^{19} +1.61673e11 q^{20} -2.23751e12 q^{21} -3.44932e12 q^{22} +5.02230e12 q^{23} -8.03273e12 q^{24} -1.86068e13 q^{25} +3.08453e13 q^{26} -7.62560e12 q^{27} -2.69022e13 q^{28} +1.53748e14 q^{29} -7.21167e12 q^{30} +3.92872e13 q^{31} -1.63123e14 q^{32} -1.26592e14 q^{33} -3.67421e14 q^{34} -7.76602e13 q^{35} -9.16844e13 q^{36} +1.35709e15 q^{37} -6.55779e14 q^{38} +1.13203e15 q^{39} -2.78802e14 q^{40} -5.75410e14 q^{41} +1.20001e15 q^{42} +3.36667e14 q^{43} -1.52204e15 q^{44} -2.64671e14 q^{45} -2.69354e15 q^{46} -6.99998e15 q^{47} +1.86592e15 q^{48} +1.52367e15 q^{49} +9.97910e15 q^{50} -1.34845e16 q^{51} +1.36107e16 q^{52} +1.69895e16 q^{53} +4.08973e15 q^{54} -4.39377e15 q^{55} +4.63923e16 q^{56} -2.40674e16 q^{57} -8.24573e16 q^{58} -2.70689e16 q^{59} -3.18221e15 q^{60} -5.11533e16 q^{61} -2.10704e16 q^{62} +4.40410e16 q^{63} +1.37187e17 q^{64} +3.92909e16 q^{65} +6.78930e16 q^{66} +2.07437e17 q^{67} -1.62127e17 q^{68} -9.88540e16 q^{69} +4.16504e16 q^{70} -2.35123e17 q^{71} +1.58108e17 q^{72} +7.43858e16 q^{73} -7.27828e17 q^{74} +3.66237e17 q^{75} -2.89368e17 q^{76} +7.31118e17 q^{77} -6.07127e17 q^{78} -6.98697e17 q^{79} +6.47627e16 q^{80} +1.50095e17 q^{81} +3.08601e17 q^{82} +3.25532e18 q^{83} +5.29515e17 q^{84} -4.68023e17 q^{85} -1.80560e17 q^{86} -3.02622e18 q^{87} +2.62473e18 q^{88} -1.43575e18 q^{89} +1.41947e17 q^{90} -6.53796e18 q^{91} -1.18855e18 q^{92} -7.73291e17 q^{93} +3.75420e18 q^{94} -8.35337e17 q^{95} +3.21074e18 q^{96} +1.66911e18 q^{97} -8.17166e17 q^{98} +2.49170e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 702 q^{2} - 39366 q^{3} + 772484 q^{4} + 6016140 q^{5} - 13817466 q^{6} + 113892064 q^{7} + 1008501624 q^{8} + 774840978 q^{9}+O(q^{10}) $ 2 * q + 702 * q^2 - 39366 * q^3 + 772484 * q^4 + 6016140 * q^5 - 13817466 * q^6 + 113892064 * q^7 + 1008501624 * q^8 + 774840978 * q^9	$ 2 q + 702 q^{2} - 39366 q^{3} + 772484 q^{4} + 6016140 q^{5} - 13817466 q^{6} + 113892064 q^{7} + 1008501624 q^{8} + 774840978 q^{9} + 8662242420 q^{10} - 6650071272 q^{11} - 15204802572 q^{12} - 44072356148 q^{13} - 60701219424 q^{14} - 118415683620 q^{15} + 119603620880 q^{16} + 336281471748 q^{17} + 271969183278 q^{18} + 602118925096 q^{19} + 6922191196440 q^{20} - 2241737495712 q^{21} - 19648459326744 q^{22} + 2368252165968 q^{23} - 19850337465192 q^{24} + 7200399078350 q^{25} + 47489309789364 q^{26} - 15251194969974 q^{27} - 26685589805888 q^{28} + 280977251970492 q^{29} - 170498917552860 q^{30} + 41610149253712 q^{31} - 212406109003296 q^{32} + 130893352846776 q^{33} - 799347349171332 q^{34} - 76222408017600 q^{35} + 299276129024676 q^{36} + 637994163989884 q^{37} - 14\!\cdots\!32 q^{38}+ \cdots - 25\!\cdots\!08 q^{99}+O(q^{100}) $ 2 * q + 702 * q^2 - 39366 * q^3 + 772484 * q^4 + 6016140 * q^5 - 13817466 * q^6 + 113892064 * q^7 + 1008501624 * q^8 + 774840978 * q^9 + 8662242420 * q^10 - 6650071272 * q^11 - 15204802572 * q^12 - 44072356148 * q^13 - 60701219424 * q^14 - 118415683620 * q^15 + 119603620880 * q^16 + 336281471748 * q^17 + 271969183278 * q^18 + 602118925096 * q^19 + 6922191196440 * q^20 - 2241737495712 * q^21 - 19648459326744 * q^22 + 2368252165968 * q^23 - 19850337465192 * q^24 + 7200399078350 * q^25 + 47489309789364 * q^26 - 15251194969974 * q^27 - 26685589805888 * q^28 + 280977251970492 * q^29 - 170498917552860 * q^30 + 41610149253712 * q^31 - 212406109003296 * q^32 + 130893352846776 * q^33 - 799347349171332 * q^34 - 76222408017600 * q^35 + 299276129024676 * q^36 + 637994163989884 * q^37 - 1424314643816232 * q^38 + 867476186061084 * q^39 + 3743437831857360 * q^40 + 1150038430280532 * q^41 + 1194782101922592 * q^42 + 2820518953538200 * q^43 - 14723164414050768 * q^44 + 2330775900692460 * q^45 - 5980094010800208 * q^46 - 5603091319500480 * q^47 - 2354158069781040 * q^48 - 9875183230193070 * q^49 + 41936530073800050 * q^50 - 6619028208415884 * q^51 + 27174417188397208 * q^52 + 27537868857647628 * q^53 - 5353169434460874 * q^54 - 92031302621896560 * q^55 + 46521172561587840 * q^56 - 11851506802664568 * q^57 + 75092921304821316 * q^58 - 55153474421835816 * q^59 - 136249489319528520 * q^60 - 87192569066205620 * q^61 - 18193883108252112 * q^62 + 44124119128099296 * q^63 - 36250046218631104 * q^64 + 129335487918703560 * q^65 + 386740624928302152 * q^66 + 499299710877878248 * q^67 - 514116238109034744 * q^68 - 46614307382748144 * q^69 + 43430850442699200 * q^70 + 84915048436970544 * q^71 + 390714192327374136 * q^72 - 241433711161728332 * q^73 - 1618295867440077564 * q^74 - 141725455059163050 * q^75 - 915668569473570224 * q^76 + 728310910203957888 * q^77 - 934732084584051612 * q^78 + 1131591466033523440 * q^79 + 1501106673028491360 * q^80 + 300189270593998242 * q^81 + 2445251486788059948 * q^82 + 1607743276003583784 * q^83 + 525252464149293504 * q^84 - 2804751519619294440 * q^85 + 2895233411994836328 * q^86 - 5530475250535194036 * q^87 - 5229410429487705696 * q^88 + 4322797626369576276 * q^89 + 3355930194192943380 * q^90 - 6535073681312344768 * q^91 - 3866849612692780896 * q^92 - 819012567760813296 * q^93 + 5483985680095257024 * q^94 - 4993123012930175760 * q^95 + 4180789443511875168 * q^96 + 7902201235299458308 * q^97 - 14932538668319232402 * q^98 - 2576373864083092008 * 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 $

$2$	−536.316	−0.740688	−0.370344	−	0.928895i	$-0.620760\pi$
$2$	−536.316	−0.740688	−0.370344	+	0.928895i	$0.620760\pi$
$3$	−19683.0	−0.577350
$3$	−19683.0	−0.577350
$4$	−236654.	−0.451381
$5$	−683163.	−0.156426	−0.0782131	−	0.996937i	$-0.524921\pi$
$5$	−683163.	−0.156426	−0.0782131	+	0.996937i	$0.524921\pi$
$6$	1.05563e7	0.427637
$7$	1.13677e8	1.06474	0.532369	−	0.846512i	$-0.321302\pi$
$7$	1.13677e8	1.06474	0.532369	+	0.846512i	$0.321302\pi$
$8$	4.08105e8	1.07502
$9$	3.87420e8	0.333333
$10$	3.66391e8	0.115863
$11$	6.43152e9	0.822400	0.411200	−	0.911545i	$-0.365110\pi$
$11$	6.43152e9	0.822400	0.411200	+	0.911545i	$0.365110\pi$
$12$	4.65805e9	0.260605
$13$	−5.75132e10	−1.50420	−0.752101	−	0.659048i	$-0.770959\pi$
$13$	−5.75132e10	−1.50420	−0.752101	+	0.659048i	$0.770959\pi$
$14$	−6.09670e10	−0.788639
$15$	1.34467e10	0.0903127
$16$	−9.47984e10	−0.344874
$17$	6.85083e11	1.40113	0.700565	−	0.713588i	$-0.252931\pi$
$17$	6.85083e11	1.40113	0.700565	+	0.713588i	$0.252931\pi$
$18$	−2.07780e11	−0.246896
$19$	1.22275e12	0.869317	0.434658	−	0.900595i	$-0.356869\pi$
$19$	1.22275e12	0.869317	0.434658	+	0.900595i	$0.356869\pi$
$20$	1.61673e11	0.0706078
$21$	−2.23751e12	−0.614727
$22$	−3.44932e12	−0.609142
$23$	5.02230e12	0.581418	0.290709	−	0.956811i	$-0.406109\pi$
$23$	5.02230e12	0.581418	0.290709	+	0.956811i	$0.406109\pi$
$24$	−8.03273e12	−0.620664
$25$	−1.86068e13	−0.975531
$26$	3.08453e13	1.11414
$27$	−7.62560e12	−0.192450
$28$	−2.69022e13	−0.480603
$29$	1.53748e14	1.96801	0.984006	−	0.178134i	$-0.0570060\pi$
$29$	1.53748e14	1.96801	0.984006	+	0.178134i	$0.0570060\pi$
$30$	−7.21167e12	−0.0668935
$31$	3.92872e13	0.266880	0.133440	−	0.991057i	$-0.457398\pi$
$31$	3.92872e13	0.266880	0.133440	+	0.991057i	$0.457398\pi$
$32$	−1.63123e14	−0.819576
$33$	−1.26592e14	−0.474813
$34$	−3.67421e14	−1.03780
$35$	−7.76602e13	−0.166553
$36$	−9.16844e13	−0.150460
$37$	1.35709e15	1.71669	0.858346	−	0.513072i	$-0.171493\pi$
$37$	1.35709e15	1.71669	0.858346	+	0.513072i	$0.171493\pi$
$38$	−6.55779e14	−0.643893
$39$	1.13203e15	0.868451
$40$	−2.78802e14	−0.168161
$41$	−5.75410e14	−0.274493	−0.137246	−	0.990537i	$-0.543825\pi$
$41$	−5.75410e14	−0.274493	−0.137246	+	0.990537i	$0.543825\pi$
$42$	1.20001e15	0.455321
$43$	3.36667e14	0.102153	0.0510763	−	0.998695i	$-0.483735\pi$
$43$	3.36667e14	0.102153	0.0510763	+	0.998695i	$0.483735\pi$
$44$	−1.52204e15	−0.371215
$45$	−2.64671e14	−0.0521420
$46$	−2.69354e15	−0.430650
$47$	−6.99998e15	−0.912362	−0.456181	−	0.889887i	$-0.650783\pi$
$47$	−6.99998e15	−0.912362	−0.456181	+	0.889887i	$0.650783\pi$
$48$	1.86592e15	0.199113
$49$	1.52367e15	0.133668
$50$	9.97910e15	0.722564
$51$	−1.34845e16	−0.808943
$52$	1.36107e16	0.678968
$53$	1.69895e16	0.707231	0.353615	−	0.935391i	$-0.384952\pi$
$53$	1.69895e16	0.707231	0.353615	+	0.935391i	$0.384952\pi$
$54$	4.08973e15	0.142546
$55$	−4.39377e15	−0.128645
$56$	4.63923e16	1.14462
$57$	−2.40674e16	−0.501900
$58$	−8.24573e16	−1.45768
$59$	−2.70689e16	−0.406796	−0.203398	−	0.979096i	$-0.565198\pi$
$59$	−2.70689e16	−0.406796	−0.203398	+	0.979096i	$0.565198\pi$
$60$	−3.18221e15	−0.0407654
$61$	−5.11533e16	−0.560068	−0.280034	−	0.959990i	$-0.590346\pi$
$61$	−5.11533e16	−0.560068	−0.280034	+	0.959990i	$0.590346\pi$
$62$	−2.10704e16	−0.197675
$63$	4.40410e16	0.354913
$64$	1.37187e17	0.951925
$65$	3.92909e16	0.235296
$66$	6.78930e16	0.351688
$67$	2.07437e17	0.931487	0.465743	−	0.884920i	$-0.345787\pi$
$67$	2.07437e17	0.931487	0.465743	+	0.884920i	$0.345787\pi$
$68$	−1.62127e17	−0.632443
$69$	−9.88540e16	−0.335682
$70$	4.16504e16	0.123364
$71$	−2.35123e17	−0.608613	−0.304306	−	0.952574i	$-0.598425\pi$
$71$	−2.35123e17	−0.608613	−0.304306	+	0.952574i	$0.598425\pi$
$72$	1.58108e17	0.358340
$73$	7.43858e16	0.147885	0.0739423	−	0.997263i	$-0.476442\pi$
$73$	7.43858e16	0.147885	0.0739423	+	0.997263i	$0.476442\pi$
$74$	−7.27828e17	−1.27153
$75$	3.66237e17	0.563223
$76$	−2.89368e17	−0.392393
$77$	7.31118e17	0.875641
$78$	−6.07127e17	−0.643252
$79$	−6.98697e17	−0.655890	−0.327945	−	0.944697i	$-0.606356\pi$
$79$	−6.98697e17	−0.655890	−0.327945	+	0.944697i	$0.606356\pi$
$80$	6.47627e16	0.0539474
$81$	1.50095e17	0.111111
$82$	3.08601e17	0.203314
$83$	3.25532e18	1.91140	0.955701	−	0.294338i	$-0.0950992\pi$
$83$	3.25532e18	1.91140	0.955701	+	0.294338i	$0.0950992\pi$
$84$	5.29515e17	0.277476
$85$	−4.68023e17	−0.219173
$86$	−1.80560e17	−0.0756633
$87$	−3.02622e18	−1.13623
$88$	2.62473e18	0.884097
$89$	−1.43575e18	−0.434385	−0.217193	−	0.976129i	$-0.569690\pi$
$89$	−1.43575e18	−0.434385	−0.217193	+	0.976129i	$0.569690\pi$
$90$	1.41947e17	0.0386210
$91$	−6.53796e18	−1.60158
$92$	−1.18855e18	−0.262441
$93$	−7.73291e17	−0.154083
$94$	3.75420e18	0.675776
$95$	−8.35337e17	−0.135984
$96$	3.21074e18	0.473183
$97$	1.66911e18	0.222922	0.111461	−	0.993769i	$-0.464447\pi$
$97$	1.66911e18	0.222922	0.111461	+	0.993769i	$0.464447\pi$
$98$	−8.17166e17	−0.0990062
$99$	2.49170e18	0.274133
$100$	4.40336e18	0.440336
$101$	9.99068e18	0.908955	0.454477	−	0.890758i	$-0.349826\pi$
$101$	9.99068e18	0.908955	0.454477	+	0.890758i	$0.349826\pi$
$102$	7.23194e18	0.599175
$103$	1.17501e18	0.0887333	0.0443666	−	0.999015i	$-0.485873\pi$
$103$	1.17501e18	0.0887333	0.0443666	+	0.999015i	$0.485873\pi$
$104$	−2.34714e19	−1.61705
$105$	1.52859e18	0.0961594
$106$	−9.11176e18	−0.523837
$107$	−1.73164e19	−0.910568	−0.455284	−	0.890346i	$-0.650462\pi$
$107$	−1.73164e19	−0.910568	−0.455284	+	0.890346i	$0.650462\pi$
$108$	1.80462e18	0.0868683
$109$	1.57748e19	0.695685	0.347842	−	0.937553i	$-0.386914\pi$
$109$	1.57748e19	0.695685	0.347842	+	0.937553i	$0.386914\pi$
$110$	2.35645e18	0.0952857
$111$	−2.67116e19	−0.991132
$112$	−1.07764e19	−0.367201
$113$	4.78817e19	1.49942	0.749712	−	0.661764i	$-0.230192\pi$
$113$	4.78817e19	1.49942	0.749712	+	0.661764i	$0.230192\pi$
$114$	1.29077e19	0.371752
$115$	−3.43105e18	−0.0909490
$116$	−3.63850e19	−0.888323
$117$	−2.22818e19	−0.501400
$118$	1.45175e19	0.301309
$119$	7.78785e19	1.49184
$120$	5.48766e18	0.0970880
$121$	−1.97947e19	−0.323659
$122$	2.74343e19	0.414836
$123$	1.13258e19	0.158478
$124$	−9.29747e18	−0.120464
$125$	2.57418e19	0.309025
$126$	−2.36199e19	−0.262880
$127$	−1.25232e20	−1.29294	−0.646472	−	0.762938i	$-0.723756\pi$
$127$	−1.25232e20	−1.29294	−0.646472	+	0.762938i	$0.723756\pi$
$128$	1.19478e19	0.114497
$129$	−6.62661e18	−0.0589779
$130$	−2.10723e19	−0.174281
$131$	−2.09329e20	−1.60972	−0.804862	−	0.593462i	$-0.797761\pi$
$131$	−2.09329e20	−1.60972	−0.804862	+	0.593462i	$0.797761\pi$
$132$	2.99583e19	0.214321
$133$	1.38999e20	0.925595
$134$	−1.11252e20	−0.689941
$135$	5.20953e18	0.0301042
$136$	2.79586e20	1.50624
$137$	1.53205e20	0.769888	0.384944	−	0.922940i	$-0.374221\pi$
$137$	1.53205e20	0.769888	0.384944	+	0.922940i	$0.374221\pi$
$138$	5.30169e19	0.248636
$139$	−2.54374e19	−0.111386	−0.0556932	−	0.998448i	$-0.517737\pi$
$139$	−2.54374e19	−0.111386	−0.0556932	+	0.998448i	$0.517737\pi$
$140$	1.83786e19	0.0751788
$141$	1.37781e20	0.526752
$142$	1.26100e20	0.450792
$143$	−3.69897e20	−1.23705
$144$	−3.67268e19	−0.114958
$145$	−1.05035e20	−0.307849
$146$	−3.98942e19	−0.109536
$147$	−2.99903e19	−0.0771732
$148$	−3.21160e20	−0.774882
$149$	1.67659e20	0.379453	0.189727	−	0.981837i	$-0.439240\pi$
$149$	1.67659e20	0.379453	0.189727	+	0.981837i	$0.439240\pi$
$150$	−1.96419e20	−0.417173
$151$	−4.29868e20	−0.857144	−0.428572	−	0.903508i	$-0.640983\pi$
$151$	−4.29868e20	−0.857144	−0.428572	+	0.903508i	$0.640983\pi$
$152$	4.99010e20	0.934533
$153$	2.65415e20	0.467043
$154$	−3.92110e20	−0.648577
$155$	−2.68396e19	−0.0417470
$156$	−2.67900e20	−0.392002
$157$	9.16306e20	1.26181	0.630905	−	0.775860i	$-0.282684\pi$
$157$	9.16306e20	1.26181	0.630905	+	0.775860i	$0.282684\pi$
$158$	3.74722e20	0.485810
$159$	−3.34405e20	−0.408320
$160$	1.11439e20	0.128203
$161$	5.70923e20	0.619058
$162$	−8.04981e19	−0.0822987
$163$	4.50070e20	0.434008	0.217004	−	0.976171i	$-0.430372\pi$
$163$	4.50070e20	0.434008	0.217004	+	0.976171i	$0.430372\pi$
$164$	1.36173e20	0.123901
$165$	8.64827e19	0.0742731
$166$	−1.74588e21	−1.41575
$167$	−1.62414e20	−0.124399	−0.0621993	−	0.998064i	$-0.519811\pi$
$167$	−1.62414e20	−0.124399	−0.0621993	+	0.998064i	$0.519811\pi$
$168$	−9.13140e20	−0.660844
$169$	1.84585e21	1.26262
$170$	2.51008e20	0.162339
$171$	4.73718e20	0.289772
$172$	−7.96734e19	−0.0461098
$173$	−3.29538e21	−1.80496	−0.902481	−	0.430731i	$-0.858256\pi$
$173$	−3.29538e21	−1.80496	−0.902481	+	0.430731i	$0.858256\pi$
$174$	1.62301e21	0.841594
$175$	−2.11517e21	−1.03869
$176$	−6.09697e20	−0.283625
$177$	5.32797e20	0.234864
$178$	7.70017e20	0.321744
$179$	−9.81720e20	−0.388941	−0.194471	−	0.980908i	$-0.562299\pi$
$179$	−9.81720e20	−0.388941	−0.194471	+	0.980908i	$0.562299\pi$
$180$	6.26354e19	0.0235359
$181$	1.51701e20	0.0540807	0.0270403	−	0.999634i	$-0.491392\pi$
$181$	1.51701e20	0.0540807	0.0270403	+	0.999634i	$0.491392\pi$
$182$	3.50641e21	1.18627
$183$	1.00685e21	0.323355
$184$	2.04963e21	0.625037
$185$	−9.27114e20	−0.268535
$186$	4.14728e20	0.114128
$187$	4.40612e21	1.15229
$188$	1.65657e21	0.411823
$189$	−8.66858e20	−0.204909
$190$	4.48004e20	0.100722
$191$	−5.13044e21	−1.09733	−0.548666	−	0.836042i	$-0.684864\pi$
$191$	−5.13044e21	−1.09733	−0.548666	+	0.836042i	$0.684864\pi$
$192$	−2.70025e21	−0.549594
$193$	−9.72873e21	−1.88478	−0.942392	−	0.334510i	$-0.891429\pi$
$193$	−9.72873e21	−1.88478	−0.942392	+	0.334510i	$0.891429\pi$
$194$	−8.95169e20	−0.165116
$195$	−7.73363e20	−0.135848
$196$	−3.60581e20	−0.0603351
$197$	7.68506e21	1.22523	0.612616	−	0.790381i	$-0.290117\pi$
$197$	7.68506e21	1.22523	0.612616	+	0.790381i	$0.290117\pi$
$198$	−1.33634e21	−0.203047
$199$	4.55786e21	0.660172	0.330086	−	0.943951i	$-0.392922\pi$
$199$	4.55786e21	0.660172	0.330086	+	0.943951i	$0.392922\pi$
$200$	−7.59351e21	−1.04872
$201$	−4.08299e21	−0.537794
$202$	−5.35816e21	−0.673252
$203$	1.74777e22	2.09542
$204$	3.19115e21	0.365141
$205$	3.93099e20	0.0429378
$206$	−6.30174e20	−0.0657237
$207$	1.94574e21	0.193806
$208$	5.45216e21	0.518761
$209$	7.86413e21	0.714926
$210$	−8.19805e20	−0.0712241
$211$	−1.71334e22	−1.42285	−0.711426	−	0.702761i	$-0.751950\pi$
$211$	−1.71334e22	−1.42285	−0.711426	+	0.702761i	$0.751950\pi$
$212$	−4.02064e21	−0.319230
$213$	4.62793e21	0.351383
$214$	9.28707e21	0.674447
$215$	−2.29998e20	−0.0159794
$216$	−3.11204e21	−0.206888
$217$	4.46607e21	0.284157
$218$	−8.46028e21	−0.515286
$219$	−1.46414e21	−0.0853812
$220$	1.03980e21	0.0580678
$221$	−3.94014e22	−2.10758
$222$	1.43258e22	0.734120
$223$	3.17895e22	1.56095	0.780473	−	0.625189i	$-0.214978\pi$
$223$	3.17895e22	1.56095	0.780473	+	0.625189i	$0.214978\pi$
$224$	−1.85434e22	−0.872634
$225$	−7.20865e21	−0.325177
$226$	−2.56797e22	−1.11061
$227$	2.55774e22	1.06074	0.530372	−	0.847765i	$-0.322052\pi$
$227$	2.55774e22	1.06074	0.530372	+	0.847765i	$0.322052\pi$
$228$	5.69563e21	0.226548
$229$	−2.23445e22	−0.852576	−0.426288	−	0.904588i	$-0.640179\pi$
$229$	−2.23445e22	−0.852576	−0.426288	+	0.904588i	$0.640179\pi$
$230$	1.84013e21	0.0673648
$231$	−1.43906e22	−0.505551
$232$	6.27452e22	2.11565
$233$	−2.52369e21	−0.0816874	−0.0408437	−	0.999166i	$-0.513005\pi$
$233$	−2.52369e21	−0.0816874	−0.0408437	+	0.999166i	$0.513005\pi$
$234$	1.19501e22	0.371381
$235$	4.78213e21	0.142717
$236$	6.40595e21	0.183620
$237$	1.37524e22	0.378678
$238$	−4.17675e22	−1.10499
$239$	3.93020e22	0.999158	0.499579	−	0.866268i	$-0.333488\pi$
$239$	3.93020e22	0.999158	0.499579	+	0.866268i	$0.333488\pi$
$240$	−1.27472e21	−0.0311465
$241$	−1.99943e22	−0.469618	−0.234809	−	0.972042i	$-0.575447\pi$
$241$	−1.99943e22	−0.469618	−0.234809	+	0.972042i	$0.575447\pi$
$242$	1.06162e22	0.239730
$243$	−2.95431e21	−0.0641500
$244$	1.21056e22	0.252804
$245$	−1.04091e21	−0.0209091
$246$	−6.07420e21	−0.117383
$247$	−7.03242e22	−1.30763
$248$	1.60333e22	0.286901
$249$	−6.40745e22	−1.10355
$250$	−1.38057e22	−0.228891
$251$	−4.94152e22	−0.788788	−0.394394	−	0.918942i	$-0.629045\pi$
$251$	−4.94152e22	−0.788788	−0.394394	+	0.918942i	$0.629045\pi$
$252$	−1.04225e22	−0.160201
$253$	3.23010e22	0.478158
$254$	6.71638e22	0.957668
$255$	9.21211e21	0.126540
$256$	−7.83332e22	−1.03673
$257$	1.79354e22	0.228742	0.114371	−	0.993438i	$-0.463515\pi$
$257$	1.79354e22	0.228742	0.114371	+	0.993438i	$0.463515\pi$
$258$	3.55395e21	0.0436842
$259$	1.54271e23	1.82783
$260$	−9.29834e21	−0.106208
$261$	5.95650e22	0.656004
$262$	1.12266e23	1.19230
$263$	2.64384e22	0.270804	0.135402	−	0.990791i	$-0.456767\pi$
$263$	2.64384e22	0.270804	0.135402	+	0.990791i	$0.456767\pi$
$264$	−5.16626e22	−0.510434
$265$	−1.16066e22	−0.110629
$266$	−7.45473e22	−0.685577
$267$	2.82599e22	0.250792
$268$	−4.90908e22	−0.420455
$269$	−6.26512e22	−0.517944	−0.258972	−	0.965885i	$-0.583384\pi$
$269$	−6.26512e22	−0.517944	−0.258972	+	0.965885i	$0.583384\pi$
$270$	−2.79395e21	−0.0222978
$271$	−8.23488e22	−0.634525	−0.317263	−	0.948338i	$-0.602764\pi$
$271$	−8.23488e22	−0.634525	−0.317263	+	0.948338i	$0.602764\pi$
$272$	−6.49448e22	−0.483214
$273$	1.28687e23	0.924673
$274$	−8.21662e22	−0.570247
$275$	−1.19670e23	−0.802276
$276$	2.33942e22	0.151520
$277$	1.42704e23	0.893057	0.446528	−	0.894769i	$-0.352660\pi$
$277$	1.42704e23	0.893057	0.446528	+	0.894769i	$0.352660\pi$
$278$	1.36425e22	0.0825026
$279$	1.52207e22	0.0889599
$280$	−3.16935e22	−0.179048
$281$	4.36986e22	0.238648	0.119324	−	0.992855i	$-0.461927\pi$
$281$	4.36986e22	0.238648	0.119324	+	0.992855i	$0.461927\pi$
$282$	−7.38939e22	−0.390159
$283$	−2.42461e23	−1.23786	−0.618929	−	0.785447i	$-0.712433\pi$
$283$	−2.42461e23	−1.23786	−0.618929	+	0.785447i	$0.712433\pi$
$284$	5.56427e22	0.274716
$285$	1.64419e22	0.0785103
$286$	1.98382e23	0.916272
$287$	−6.54112e22	−0.292263
$288$	−6.31970e22	−0.273192
$289$	2.30266e23	0.963166
$290$	5.63318e22	0.228020
$291$	−3.28531e22	−0.128704
$292$	−1.76037e22	−0.0667522
$293$	1.65262e22	0.0606638	0.0303319	−	0.999540i	$-0.490344\pi$
$293$	1.65262e22	0.0606638	0.0303319	+	0.999540i	$0.490344\pi$
$294$	1.60843e22	0.0571613
$295$	1.84925e22	0.0636335
$296$	5.53835e23	1.84548
$297$	−4.90442e22	−0.158271
$298$	−8.99184e22	−0.281057
$299$	−2.88849e23	−0.874570
$300$	−8.66713e22	−0.254228
$301$	3.82714e22	0.108766
$302$	2.30545e23	0.634876
$303$	−1.96647e23	−0.524785
$304$	−1.15915e23	−0.299805
$305$	3.49461e22	0.0876092
$306$	−1.42346e23	−0.345934
$307$	−7.14354e23	−1.68306	−0.841528	−	0.540213i	$-0.818344\pi$
$307$	−7.14354e23	−1.68306	−0.841528	+	0.540213i	$0.818344\pi$
$308$	−1.73022e23	−0.395247
$309$	−2.31276e22	−0.0512302
$310$	1.43945e22	0.0309215
$311$	3.74882e23	0.781037	0.390518	−	0.920595i	$-0.372296\pi$
$311$	3.74882e23	0.781037	0.390518	+	0.920595i	$0.372296\pi$
$312$	4.61988e23	0.933603
$313$	−2.04132e23	−0.400166	−0.200083	−	0.979779i	$-0.564121\pi$
$313$	−2.04132e23	−0.400166	−0.200083	+	0.979779i	$0.564121\pi$
$314$	−4.91429e23	−0.934607
$315$	−3.00872e22	−0.0555176
$316$	1.65349e23	0.296056
$317$	−2.74437e23	−0.476848	−0.238424	−	0.971161i	$-0.576631\pi$
$317$	−2.74437e23	−0.476848	−0.238424	+	0.971161i	$0.576631\pi$
$318$	1.79347e23	0.302438
$319$	9.88832e23	1.61849
$320$	−9.37210e22	−0.148906
$321$	3.40839e23	0.525717
$322$	−3.06195e23	−0.458529
$323$	8.37684e23	1.21803
$324$	−3.55204e22	−0.0501534
$325$	1.07014e24	1.46739
$326$	−2.41379e23	−0.321464
$327$	−3.10496e23	−0.401654
$328$	−2.34828e23	−0.295085
$329$	−7.95740e23	−0.971427
$330$	−4.63820e22	−0.0550132
$331$	−2.31592e23	−0.266906	−0.133453	−	0.991055i	$-0.542607\pi$
$331$	−2.31592e23	−0.266906	−0.133453	+	0.991055i	$0.542607\pi$
$332$	−7.70384e23	−0.862771
$333$	5.25764e23	0.572230
$334$	8.71049e22	0.0921406
$335$	−1.41714e23	−0.145709
$336$	2.12113e23	0.212004
$337$	−1.11237e23	−0.108085	−0.0540425	−	0.998539i	$-0.517211\pi$
$337$	−1.11237e23	−0.108085	−0.0540425	+	0.998539i	$0.517211\pi$
$338$	−9.89960e23	−0.935209
$339$	−9.42456e23	−0.865693
$340$	1.10759e23	0.0989307
$341$	2.52677e23	0.219482
$342$	−2.54062e23	−0.214631
$343$	−1.12259e24	−0.922417
$344$	1.37395e23	0.109816
$345$	6.75334e22	0.0525094
$346$	1.76737e24	1.33691
$347$	2.05609e24	1.51326	0.756629	−	0.653844i	$-0.226845\pi$
$347$	2.05609e24	1.51326	0.756629	+	0.653844i	$0.226845\pi$
$348$	7.16165e23	0.512874
$349$	−1.75492e24	−1.22297	−0.611487	−	0.791255i	$-0.709428\pi$
$349$	−1.75492e24	−1.22297	−0.611487	+	0.791255i	$0.709428\pi$
$350$	1.13440e24	0.769342
$351$	4.38573e23	0.289484
$352$	−1.04913e24	−0.674019
$353$	8.21430e23	0.513702	0.256851	−	0.966451i	$-0.417315\pi$
$353$	8.21430e23	0.513702	0.256851	+	0.966451i	$0.417315\pi$
$354$	−2.85747e23	−0.173961
$355$	1.60627e23	0.0952029
$356$	3.39776e23	0.196073
$357$	−1.53288e24	−0.861313
$358$	5.26512e23	0.288084
$359$	5.29683e23	0.282240	0.141120	−	0.989992i	$-0.454930\pi$
$359$	5.29683e23	0.282240	0.141120	+	0.989992i	$0.454930\pi$
$360$	−1.08014e23	−0.0560538
$361$	−4.83305e23	−0.244289
$362$	−8.13596e22	−0.0400569
$363$	3.89618e23	0.186864
$364$	1.54723e24	0.722923
$365$	−5.08176e22	−0.0231330
$366$	−5.39990e23	−0.239505
$367$	−2.30180e24	−0.994809	−0.497404	−	0.867519i	$-0.665713\pi$
$367$	−2.30180e24	−0.994809	−0.497404	+	0.867519i	$0.665713\pi$
$368$	−4.76106e23	−0.200516
$369$	−2.22926e23	−0.0914976
$370$	4.97225e23	0.198901
$371$	1.93133e24	0.753016
$372$	1.83002e23	0.0695501
$373$	1.64953e24	0.611120	0.305560	−	0.952173i	$-0.401156\pi$
$373$	1.64953e24	0.611120	0.305560	+	0.952173i	$0.401156\pi$
$374$	−2.36307e24	−0.853487
$375$	−5.06675e23	−0.178415
$376$	−2.85673e24	−0.980808
$377$	−8.84253e24	−2.96029
$378$	4.64910e23	0.151774
$379$	3.36454e24	1.07116	0.535579	−	0.844485i	$-0.320094\pi$
$379$	3.36454e24	1.07116	0.535579	+	0.844485i	$0.320094\pi$
$380$	1.97685e23	0.0613805
$381$	2.46494e24	0.746482
$382$	2.75154e24	0.812780
$383$	1.55219e24	0.447257	0.223628	−	0.974674i	$-0.428210\pi$
$383$	1.55219e24	0.447257	0.223628	+	0.974674i	$0.428210\pi$
$384$	−2.35168e23	−0.0661046
$385$	−4.99473e23	−0.136973
$386$	5.21767e24	1.39604
$387$	1.30432e23	0.0340509
$388$	−3.95000e23	−0.100623
$389$	−1.19996e23	−0.0298295	−0.0149148	−	0.999889i	$-0.504748\pi$
$389$	−1.19996e23	−0.0298295	−0.0149148	+	0.999889i	$0.504748\pi$
$390$	4.14767e23	0.100621
$391$	3.44070e24	0.814643
$392$	6.21815e23	0.143696
$393$	4.12022e24	0.929375
$394$	−4.12162e24	−0.907515
$395$	4.77324e23	0.102598
$396$	−5.89670e23	−0.123738
$397$	−1.23812e24	−0.253661	−0.126831	−	0.991924i	$-0.540480\pi$
$397$	−1.23812e24	−0.253661	−0.126831	+	0.991924i	$0.540480\pi$
$398$	−2.44445e24	−0.488981
$399$	−2.73592e24	−0.534392
$400$	1.76389e24	0.336436
$401$	−6.55287e24	−1.22056	−0.610281	−	0.792185i	$-0.708943\pi$
$401$	−6.55287e24	−1.22056	−0.610281	+	0.792185i	$0.708943\pi$
$402$	2.18977e24	0.398338
$403$	−2.25954e24	−0.401441
$404$	−2.36433e24	−0.410285
$405$	−1.02539e23	−0.0173807
$406$	−9.37354e24	−1.55205
$407$	8.72815e24	1.41181
$408$	−5.50309e24	−0.869631
$409$	8.56848e24	1.32292	0.661458	−	0.749982i	$-0.269938\pi$
$409$	8.56848e24	1.32292	0.661458	+	0.749982i	$0.269938\pi$
$410$	−2.10825e23	−0.0318036
$411$	−3.01553e24	−0.444495
$412$	−2.78069e23	−0.0400525
$413$	−3.07712e24	−0.433131
$414$	−1.04353e24	−0.143550
$415$	−2.22392e24	−0.298993
$416$	9.38171e24	1.23281
$417$	5.00685e23	0.0643090
$418$	−4.21766e24	−0.529537
$419$	8.09987e24	0.994134	0.497067	−	0.867712i	$-0.334410\pi$
$419$	8.09987e24	0.994134	0.497067	+	0.867712i	$0.334410\pi$
$420$	−3.61745e23	−0.0434045
$421$	9.99748e24	1.17276	0.586382	−	0.810035i	$-0.300552\pi$
$421$	9.99748e24	1.17276	0.586382	+	0.810035i	$0.300552\pi$
$422$	9.18890e24	1.05389
$423$	−2.71194e24	−0.304121
$424$	6.93352e24	0.760288
$425$	−1.27472e25	−1.36685
$426$	−2.48203e24	−0.260265
$427$	−5.81498e24	−0.596326
$428$	4.09799e24	0.411013
$429$	7.28069e24	0.714214
$430$	1.23352e23	0.0118357
$431$	−4.59733e24	−0.431491	−0.215745	−	0.976450i	$-0.569218\pi$
$431$	−4.59733e24	−0.431491	−0.215745	+	0.976450i	$0.569218\pi$
$432$	7.22894e23	0.0663711
$433$	−7.51468e24	−0.674956	−0.337478	−	0.941333i	$-0.609574\pi$
$433$	−7.51468e24	−0.674956	−0.337478	+	0.941333i	$0.609574\pi$
$434$	−2.39523e24	−0.210472
$435$	2.06740e24	0.177736
$436$	−3.73317e24	−0.314019
$437$	6.14102e24	0.505436
$438$	7.85238e23	0.0632408
$439$	−2.04197e25	−1.60930	−0.804649	−	0.593751i	$-0.797647\pi$
$439$	−2.04197e25	−1.60930	−0.804649	+	0.593751i	$0.797647\pi$
$440$	−1.79312e24	−0.138296
$441$	5.90299e23	0.0445560
$442$	2.11316e25	1.56106
$443$	−1.84340e25	−1.33286	−0.666428	−	0.745569i	$-0.732178\pi$
$443$	−1.84340e25	−1.33286	−0.666428	+	0.745569i	$0.732178\pi$
$444$	6.32140e24	0.447378
$445$	9.80854e23	0.0679492
$446$	−1.70492e25	−1.15617
$447$	−3.30004e24	−0.219077
$448$	1.55951e25	1.01355
$449$	7.82616e24	0.497976	0.248988	−	0.968507i	$-0.419902\pi$
$449$	7.82616e24	0.497976	0.248988	+	0.968507i	$0.419902\pi$
$450$	3.86611e24	0.240855
$451$	−3.70076e24	−0.225743
$452$	−1.13314e25	−0.676811
$453$	8.46108e24	0.494872
$454$	−1.37176e25	−0.785681
$455$	4.46649e24	0.250529
$456$	−9.82201e24	−0.539553
$457$	2.15612e25	1.16003	0.580015	−	0.814606i	$-0.303047\pi$
$457$	2.15612e25	1.16003	0.580015	+	0.814606i	$0.303047\pi$
$458$	1.19837e25	0.631493
$459$	−5.22417e24	−0.269648
$460$	8.11971e23	0.0410526
$461$	4.52754e24	0.224235	0.112118	−	0.993695i	$-0.464237\pi$
$461$	4.52754e24	0.224235	0.112118	+	0.993695i	$0.464237\pi$
$462$	7.71791e24	0.374456
$463$	1.12552e25	0.534974	0.267487	−	0.963562i	$-0.413807\pi$
$463$	1.12552e25	0.534974	0.267487	+	0.963562i	$0.413807\pi$
$464$	−1.45750e25	−0.678717
$465$	5.28284e23	0.0241026
$466$	1.35350e24	0.0605049
$467$	1.73792e25	0.761237	0.380618	−	0.924732i	$-0.375711\pi$
$467$	1.73792e25	0.761237	0.380618	+	0.924732i	$0.375711\pi$
$468$	5.27307e24	0.226323
$469$	2.35810e25	0.991790
$470$	−2.56473e24	−0.105709
$471$	−1.80356e25	−0.728506
$472$	−1.10469e25	−0.437314
$473$	2.16528e24	0.0840104
$474$	−7.37565e24	−0.280483
$475$	−2.27514e25	−0.848045
$476$	−1.84302e25	−0.673387
$477$	6.58210e24	0.235744
$478$	−2.10783e25	−0.740065
$479$	4.26798e25	1.46904	0.734522	−	0.678585i	$-0.237407\pi$
$479$	4.26798e25	1.46904	0.734522	+	0.678585i	$0.237407\pi$
$480$	−2.19346e24	−0.0740181
$481$	−7.80506e25	−2.58225
$482$	1.07233e25	0.347841
$483$	−1.12375e25	−0.357413
$484$	4.68448e24	0.146093
$485$	−1.14027e24	−0.0348708
$486$	1.58444e24	0.0475152
$487$	−6.57071e24	−0.193236	−0.0966178	−	0.995322i	$-0.530802\pi$
$487$	−6.57071e24	−0.193236	−0.0966178	+	0.995322i	$0.530802\pi$
$488$	−2.08759e25	−0.602085
$489$	−8.85872e24	−0.250574
$490$	5.58257e23	0.0154872
$491$	5.24168e25	1.42625	0.713126	−	0.701035i	$-0.247279\pi$
$491$	5.24168e25	1.42625	0.713126	+	0.701035i	$0.247279\pi$
$492$	−2.68029e24	−0.0715342
$493$	1.05330e26	2.75744
$494$	3.77160e25	0.968544
$495$	−1.70224e24	−0.0428816
$496$	−3.72437e24	−0.0920400
$497$	−2.67282e25	−0.648013
$498$	3.43642e25	0.817386
$499$	−2.55146e25	−0.595434	−0.297717	−	0.954654i	$-0.596225\pi$
$499$	−2.55146e25	−0.595434	−0.297717	+	0.954654i	$0.596225\pi$
$500$	−6.09188e24	−0.139488
$501$	3.19679e24	0.0718216
$502$	2.65021e25	0.584246
$503$	−5.69466e25	−1.23189	−0.615945	−	0.787789i	$-0.711225\pi$
$503$	−5.69466e25	−1.23189	−0.615945	+	0.787789i	$0.711225\pi$
$504$	1.79733e25	0.381539
$505$	−6.82527e24	−0.142184
$506$	−1.73236e25	−0.354166
$507$	−3.63319e25	−0.728975
$508$	2.96366e25	0.583610
$509$	−3.26878e25	−0.631781	−0.315891	−	0.948796i	$-0.602303\pi$
$509$	−3.26878e25	−0.631781	−0.315891	+	0.948796i	$0.602303\pi$
$510$	−4.94060e24	−0.0937266
$511$	8.45598e24	0.157458
$512$	3.57472e25	0.653398
$513$	−9.32419e24	−0.167300
$514$	−9.61903e24	−0.169427
$515$	−8.02721e23	−0.0138802
$516$	1.56821e24	0.0266215
$517$	−4.50205e25	−0.750326
$518$	−8.27377e25	−1.35385
$519$	6.48630e25	1.04209
$520$	1.60348e25	0.252949
$521$	−9.30404e25	−1.44116	−0.720581	−	0.693370i	$-0.756125\pi$
$521$	−9.30404e25	−1.44116	−0.720581	+	0.693370i	$0.756125\pi$
$522$	−3.19457e25	−0.485895
$523$	4.88002e25	0.728879	0.364440	−	0.931227i	$-0.381261\pi$
$523$	4.88002e25	0.728879	0.364440	+	0.931227i	$0.381261\pi$
$524$	4.95384e25	0.726599
$525$	4.16329e25	0.599685
$526$	−1.41793e25	−0.200582
$527$	2.69150e25	0.373933
$528$	1.20007e25	0.163751
$529$	−4.93919e25	−0.661953
$530$	6.22482e24	0.0819419
$531$	−1.04870e25	−0.135599
$532$	−3.28946e25	−0.417796
$533$	3.30937e25	0.412892
$534$	−1.51562e25	−0.185759
$535$	1.18299e25	0.142437
$536$	8.46562e25	1.00137
$537$	1.93232e25	0.224555
$538$	3.36008e25	0.383635
$539$	9.79948e24	0.109928
$540$	−1.23285e24	−0.0135885
$541$	8.45858e25	0.916059	0.458030	−	0.888937i	$-0.348555\pi$
$541$	8.45858e25	0.916059	0.458030	+	0.888937i	$0.348555\pi$
$542$	4.41649e25	0.469985
$543$	−2.98593e24	−0.0312235
$544$	−1.11753e26	−1.14833
$545$	−1.07768e25	−0.108823
$546$	−6.90167e25	−0.684895
$547$	−2.08591e25	−0.203430	−0.101715	−	0.994814i	$-0.532433\pi$
$547$	−2.08591e25	−0.203430	−0.101715	+	0.994814i	$0.532433\pi$
$548$	−3.62565e25	−0.347513
$549$	−1.98179e25	−0.186689
$550$	6.41808e25	0.594237
$551$	1.87995e26	1.71083
$552$	−4.03428e25	−0.360865
$553$	−7.94260e25	−0.698352
$554$	−7.65345e25	−0.661477
$555$	1.82484e25	0.155039
$556$	6.01985e24	0.0502777
$557$	−1.19573e25	−0.0981768	−0.0490884	−	0.998794i	$-0.515632\pi$
$557$	−1.19573e25	−0.0981768	−0.0490884	+	0.998794i	$0.515632\pi$
$558$	−8.16309e24	−0.0658916
$559$	−1.93628e25	−0.153658
$560$	7.36206e24	0.0574398
$561$	−8.67257e25	−0.665274
$562$	−2.34362e25	−0.176764
$563$	−1.51109e26	−1.12063	−0.560313	−	0.828281i	$-0.689319\pi$
$563$	−1.51109e26	−1.12063	−0.560313	+	0.828281i	$0.689319\pi$
$564$	−3.26063e25	−0.237766
$565$	−3.27110e25	−0.234549
$566$	1.30036e26	0.916866
$567$	1.70624e25	0.118304
$568$	−9.59549e25	−0.654271
$569$	−1.31930e26	−0.884661	−0.442331	−	0.896852i	$-0.645848\pi$
$569$	−1.31930e26	−0.884661	−0.442331	+	0.896852i	$0.645848\pi$
$570$	−8.81806e24	−0.0581517
$571$	2.65239e26	1.72026	0.860130	−	0.510076i	$-0.170383\pi$
$571$	2.65239e26	1.72026	0.860130	+	0.510076i	$0.170383\pi$
$572$	8.75375e25	0.558383
$573$	1.00982e26	0.633544
$574$	3.50810e25	0.216476
$575$	−9.34489e25	−0.567191
$576$	5.31490e25	0.317308
$577$	−9.99355e25	−0.586880	−0.293440	−	0.955977i	$-0.594800\pi$
$577$	−9.99355e25	−0.586880	−0.293440	+	0.955977i	$0.594800\pi$
$578$	−1.23496e26	−0.713406
$579$	1.91491e26	1.08818
$580$	2.48569e25	0.138957
$581$	3.70057e26	2.03514
$582$	1.76196e25	0.0953296
$583$	1.09269e26	0.581626
$584$	3.03572e25	0.158979
$585$	1.52221e25	0.0784321
$586$	−8.86324e24	−0.0449330
$587$	−1.90494e26	−0.950209	−0.475104	−	0.879930i	$-0.657590\pi$
$587$	−1.90494e26	−0.950209	−0.475104	+	0.879930i	$0.657590\pi$
$588$	7.09732e24	0.0348345
$589$	4.80384e25	0.232003
$590$	−9.91779e24	−0.0471326
$591$	−1.51265e26	−0.707388
$592$	−1.28650e26	−0.592043
$593$	−2.37669e26	−1.07635	−0.538173	−	0.842834i	$-0.680885\pi$
$593$	−2.37669e26	−1.07635	−0.538173	+	0.842834i	$0.680885\pi$
$594$	2.63032e25	0.117229
$595$	−5.32037e25	−0.233362
$596$	−3.96772e25	−0.171278
$597$	−8.97124e25	−0.381150
$598$	1.54914e26	0.647784
$599$	−3.08975e26	−1.27165	−0.635826	−	0.771832i	$-0.719341\pi$
$599$	−3.08975e26	−1.27165	−0.635826	+	0.771832i	$0.719341\pi$
$600$	1.49463e26	0.605476
$601$	−2.61533e26	−1.04284	−0.521421	−	0.853299i	$-0.674598\pi$
$601$	−2.61533e26	−1.04284	−0.521421	+	0.853299i	$0.674598\pi$
$602$	−2.05256e25	−0.0805616
$603$	8.03655e25	0.310496
$604$	1.01730e26	0.386898
$605$	1.35230e25	0.0506287
$606$	1.05465e26	0.388702
$607$	5.37620e25	0.195067	0.0975334	−	0.995232i	$-0.468905\pi$
$607$	5.37620e25	0.195067	0.0975334	+	0.995232i	$0.468905\pi$
$608$	−1.99458e26	−0.712471
$609$	−3.44013e26	−1.20979
$610$	−1.87421e25	−0.0648911
$611$	4.02591e26	1.37238
$612$	−6.28115e25	−0.210814
$613$	3.16087e26	1.04456	0.522278	−	0.852775i	$-0.325082\pi$
$613$	3.16087e26	1.04456	0.522278	+	0.852775i	$0.325082\pi$
$614$	3.83119e26	1.24662
$615$	−7.73737e24	−0.0247902
$616$	2.98373e26	0.941332
$617$	1.98562e26	0.616862	0.308431	−	0.951247i	$-0.400196\pi$
$617$	1.98562e26	0.616862	0.308431	+	0.951247i	$0.400196\pi$
$618$	1.24037e25	0.0379456
$619$	−4.82992e26	−1.45505	−0.727527	−	0.686080i	$-0.759330\pi$
$619$	−4.82992e26	−1.45505	−0.727527	+	0.686080i	$0.759330\pi$
$620$	6.35169e24	0.0188438
$621$	−3.82981e25	−0.111894
$622$	−2.01055e26	−0.578505
$623$	−1.63213e26	−0.462507
$624$	−1.07315e26	−0.299507
$625$	3.37310e26	0.927191
$626$	1.09479e26	0.296398
$627$	−1.54790e26	−0.412763
$628$	−2.16847e26	−0.569556
$629$	9.29719e26	2.40531
$630$	1.61362e25	0.0411213
$631$	−6.27693e26	−1.57568	−0.787841	−	0.615879i	$-0.788801\pi$
$631$	−6.27693e26	−1.57568	−0.787841	+	0.615879i	$0.788801\pi$
$632$	−2.85141e26	−0.705096
$633$	3.37236e26	0.821484
$634$	1.47185e26	0.353196
$635$	8.55538e25	0.202250
$636$	7.91382e25	0.184308
$637$	−8.76310e25	−0.201063
$638$	−5.30326e26	−1.19880
$639$	−9.10915e25	−0.202871
$640$	−8.16228e24	−0.0179103
$641$	2.15915e26	0.466800	0.233400	−	0.972381i	$-0.425015\pi$
$641$	2.15915e26	0.466800	0.233400	+	0.972381i	$0.425015\pi$
$642$	−1.82797e26	−0.389392
$643$	4.68779e26	0.983929	0.491964	−	0.870615i	$-0.336279\pi$
$643$	4.68779e26	0.983929	0.491964	+	0.870615i	$0.336279\pi$
$644$	−1.35111e26	−0.279431
$645$	4.52706e24	0.00922568
$646$	−4.49263e26	−0.902177
$647$	−2.10829e26	−0.417196	−0.208598	−	0.978001i	$-0.566890\pi$
$647$	−2.10829e26	−0.417196	−0.208598	+	0.978001i	$0.566890\pi$
$648$	6.12543e25	0.119447
$649$	−1.74094e26	−0.334549
$650$	−5.73931e26	−1.08688
$651$	−8.79057e25	−0.164058
$652$	−1.06511e26	−0.195903
$653$	2.88194e26	0.522408	0.261204	−	0.965284i	$-0.415880\pi$
$653$	2.88194e26	0.522408	0.261204	+	0.965284i	$0.415880\pi$
$654$	1.66524e26	0.297500
$655$	1.43006e26	0.251803
$656$	5.45480e25	0.0946656
$657$	2.88186e25	0.0492948
$658$	4.26768e26	0.719524
$659$	−7.36091e26	−1.22326	−0.611632	−	0.791143i	$-0.709486\pi$
$659$	−7.36091e26	−1.22326	−0.611632	+	0.791143i	$0.709486\pi$
$660$	−2.04664e25	−0.0335255
$661$	3.05440e25	0.0493187	0.0246594	−	0.999696i	$-0.492150\pi$
$661$	3.05440e25	0.0493187	0.0246594	+	0.999696i	$0.492150\pi$
$662$	1.24207e26	0.197694
$663$	7.75537e26	1.21681
$664$	1.32851e27	2.05480
$665$	−9.49589e25	−0.144787
$666$	−2.81976e26	−0.423844
$667$	7.72168e26	1.14424
$668$	3.84357e25	0.0561512
$669$	−6.25713e26	−0.901213
$670$	7.60032e25	0.107925
$671$	−3.28994e26	−0.460600
$672$	3.64989e26	0.503816
$673$	−9.62645e26	−1.31016	−0.655078	−	0.755561i	$-0.727364\pi$
$673$	−9.62645e26	−1.31016	−0.655078	+	0.755561i	$0.727364\pi$
$674$	5.96582e25	0.0800573
$675$	1.41888e26	0.187741
$676$	−4.36828e26	−0.569923
$677$	1.18974e27	1.53059	0.765295	−	0.643680i	$-0.222593\pi$
$677$	1.18974e27	1.53059	0.765295	+	0.643680i	$0.222593\pi$
$678$	5.05454e26	0.641208
$679$	1.89740e26	0.237354
$680$	−1.91003e26	−0.235616
$681$	−5.03440e26	−0.612421
$682$	−1.35514e26	−0.162568
$683$	−1.51240e27	−1.78925	−0.894624	−	0.446819i	$-0.852557\pi$
$683$	−1.51240e27	−1.78925	−0.894624	+	0.446819i	$0.852557\pi$
$684$	−1.12107e26	−0.130798
$685$	−1.04664e26	−0.120431
$686$	6.02063e26	0.683224
$687$	4.39806e26	0.492235
$688$	−3.19155e25	−0.0352299
$689$	−9.77124e26	−1.06382
$690$	−3.62192e25	−0.0388931
$691$	−1.40247e27	−1.48543	−0.742716	−	0.669606i	$-0.766463\pi$
$691$	−1.40247e27	−1.48543	−0.742716	+	0.669606i	$0.766463\pi$
$692$	7.79864e26	0.814725
$693$	2.83250e26	0.291880
$694$	−1.10272e27	−1.12085
$695$	1.73779e25	0.0174238
$696$	−1.23501e27	−1.22147
$697$	−3.94204e26	−0.384600
$698$	9.41194e26	0.905842
$699$	4.96738e25	0.0471622
$700$	5.00563e26	0.468843
$701$	6.64167e26	0.613700	0.306850	−	0.951758i	$-0.400725\pi$
$701$	6.64167e26	0.613700	0.306850	+	0.951758i	$0.400725\pi$
$702$	−2.35213e26	−0.214417
$703$	1.65938e27	1.49235
$704$	8.82320e26	0.782863
$705$	−9.41266e25	−0.0823978
$706$	−4.40546e26	−0.380493
$707$	1.13572e27	0.967799
$708$	−1.26088e26	−0.106013
$709$	1.03445e27	0.858163	0.429081	−	0.903266i	$-0.358837\pi$
$709$	1.03445e27	0.858163	0.429081	+	0.903266i	$0.358837\pi$
$710$	−8.61470e25	−0.0705157
$711$	−2.70689e26	−0.218630
$712$	−5.85938e26	−0.466973
$713$	1.97313e26	0.155169
$714$	8.22109e26	0.637964
$715$	2.52700e26	0.193508
$716$	2.32328e26	0.175561
$717$	−7.73581e26	−0.576864
$718$	−2.84077e26	−0.209052
$719$	−1.59383e26	−0.115749	−0.0578744	−	0.998324i	$-0.518432\pi$
$719$	−1.59383e26	−0.115749	−0.0578744	+	0.998324i	$0.518432\pi$
$720$	2.50904e25	0.0179825
$721$	1.33572e26	0.0944777
$722$	2.59204e26	0.180942
$723$	3.93548e26	0.271134
$724$	−3.59006e25	−0.0244110
$725$	−2.86075e27	−1.91986
$726$	−2.08958e26	−0.138408
$727$	1.66059e27	1.08564	0.542819	−	0.839850i	$-0.317357\pi$
$727$	1.66059e27	1.08564	0.542819	+	0.839850i	$0.317357\pi$
$728$	−2.66817e27	−1.72173
$729$	5.81497e25	0.0370370
$730$	2.72543e25	0.0171343
$731$	2.30645e26	0.143129
$732$	−2.38275e26	−0.145956
$733$	−1.36074e27	−0.822786	−0.411393	−	0.911458i	$-0.634958\pi$
$733$	−1.36074e27	−0.822786	−0.411393	+	0.911458i	$0.634958\pi$
$734$	1.23449e27	0.736843
$735$	2.04883e25	0.0120719
$736$	−8.19251e26	−0.476517
$737$	1.33414e27	0.766054
$738$	1.19559e26	0.0677712
$739$	9.59784e26	0.537095	0.268548	−	0.963266i	$-0.413456\pi$
$739$	9.59784e26	0.537095	0.268548	+	0.963266i	$0.413456\pi$
$740$	2.19405e26	0.121212
$741$	1.38419e27	0.754959
$742$	−1.03580e27	−0.557750
$743$	−1.18287e27	−0.628846	−0.314423	−	0.949283i	$-0.601811\pi$
$743$	−1.18287e27	−0.628846	−0.314423	+	0.949283i	$0.601811\pi$
$744$	−3.15584e26	−0.165643
$745$	−1.14539e26	−0.0593564
$746$	−8.84670e26	−0.452650
$747$	1.26118e27	0.637134
$748$	−1.04273e27	−0.520121
$749$	−1.96849e27	−0.969516
$750$	2.71738e26	0.132150
$751$	−1.02382e27	−0.491637	−0.245819	−	0.969316i	$-0.579057\pi$
$751$	−1.02382e27	−0.491637	−0.245819	+	0.969316i	$0.579057\pi$
$752$	6.63587e26	0.314650
$753$	9.72639e26	0.455407
$754$	4.74239e27	2.19265
$755$	2.93670e26	0.134080
$756$	2.05145e26	0.0924920
$757$	2.74415e25	0.0122179	0.00610897	−	0.999981i	$-0.498055\pi$
$757$	2.74415e25	0.0122179	0.00610897	+	0.999981i	$0.498055\pi$
$758$	−1.80446e27	−0.793394
$759$	−6.35781e26	−0.276065
$760$	−3.40905e26	−0.146185
$761$	1.89240e27	0.801416	0.400708	−	0.916206i	$-0.368764\pi$
$761$	1.89240e27	0.801416	0.400708	+	0.916206i	$0.368764\pi$
$762$	−1.32199e27	−0.552910
$763$	1.79324e27	0.740722
$764$	1.21414e27	0.495314
$765$	−1.81322e26	−0.0730578
$766$	−8.32465e26	−0.331278
$767$	1.55682e27	0.611902
$768$	1.54183e27	0.598557
$769$	−1.93865e27	−0.743359	−0.371679	−	0.928361i	$-0.621218\pi$
$769$	−1.93865e27	−0.743359	−0.371679	+	0.928361i	$0.621218\pi$
$770$	2.67875e26	0.101454
$771$	−3.53022e26	−0.132064
$772$	2.30234e27	0.850756
$773$	−7.63732e24	−0.00278764	−0.00139382	−	0.999999i	$-0.500444\pi$
$773$	−7.63732e24	−0.00278764	−0.00139382	+	0.999999i	$0.500444\pi$
$774$	−6.99525e25	−0.0252211
$775$	−7.31009e26	−0.260349
$776$	6.81171e26	0.239646
$777$	−3.03651e27	−1.05530
$778$	6.43559e25	0.0220944
$779$	−7.03582e26	−0.238621
$780$	1.83019e26	0.0613194
$781$	−1.51220e27	−0.500523
$782$	−1.84530e27	−0.603396
$783$	−1.17242e27	−0.378744
$784$	−1.44441e26	−0.0460986
$785$	−6.25986e26	−0.197380
$786$	−2.20974e27	−0.688377
$787$	−4.61341e27	−1.41991	−0.709956	−	0.704246i	$-0.751285\pi$
$787$	−4.61341e27	−1.41991	−0.709956	+	0.704246i	$0.751285\pi$
$788$	−1.81870e27	−0.553046
$789$	−5.20387e26	−0.156349
$790$	−2.55996e26	−0.0759934
$791$	5.44307e27	1.59649
$792$	1.01688e27	0.294699
$793$	2.94199e27	0.842455
$794$	6.64025e26	0.187884
$795$	2.28453e26	0.0638719
$796$	−1.07863e27	−0.297989
$797$	1.01219e27	0.276316	0.138158	−	0.990410i	$-0.455882\pi$
$797$	1.01219e27	0.276316	0.138158	+	0.990410i	$0.455882\pi$
$798$	1.46731e27	0.395818
$799$	−4.79557e27	−1.27834
$800$	3.03519e27	0.799522
$801$	−5.56240e26	−0.144795
$802$	3.51440e27	0.904056
$803$	4.78413e26	0.121620
$804$	9.66255e26	0.242750
$805$	−3.90033e26	−0.0968369
$806$	1.21183e27	0.297343
$807$	1.23316e27	0.299035
$808$	4.07725e27	0.977145
$809$	3.00853e27	0.712597	0.356298	−	0.934372i	$-0.384039\pi$
$809$	3.00853e27	0.712597	0.356298	+	0.934372i	$0.384039\pi$
$810$	5.49933e25	0.0128737
$811$	3.54753e27	0.820782	0.410391	−	0.911910i	$-0.365392\pi$
$811$	3.54753e27	0.820782	0.410391	+	0.911910i	$0.365392\pi$
$812$	−4.13615e27	−0.945832
$813$	1.62087e27	0.366343
$814$	−4.68104e27	−1.04571
$815$	−3.07471e26	−0.0678901
$816$	1.27831e27	0.278984
$817$	4.11659e26	0.0888030
$818$	−4.59541e27	−0.979869
$819$	−2.53294e27	−0.533860
$820$	−9.30283e25	−0.0193813
$821$	−4.28797e27	−0.883063	−0.441532	−	0.897246i	$-0.645565\pi$
$821$	−4.28797e27	−0.883063	−0.441532	+	0.897246i	$0.645565\pi$
$822$	1.61728e27	0.329232
$823$	3.20459e27	0.644874	0.322437	−	0.946591i	$-0.395498\pi$
$823$	3.20459e27	0.644874	0.322437	+	0.946591i	$0.395498\pi$
$824$	4.79526e26	0.0953901
$825$	2.35546e27	0.463194
$826$	1.65031e27	0.320815
$827$	−4.02192e27	−0.772914	−0.386457	−	0.922308i	$-0.626301\pi$
$827$	−4.02192e27	−0.772914	−0.386457	+	0.922308i	$0.626301\pi$
$828$	−4.60467e26	−0.0874803
$829$	−1.58908e27	−0.298455	−0.149227	−	0.988803i	$-0.547679\pi$
$829$	−1.58908e27	−0.298455	−0.149227	+	0.988803i	$0.547679\pi$
$830$	1.19272e27	0.221461
$831$	−2.80885e27	−0.515607
$832$	−7.89006e27	−1.43189
$833$	1.04384e27	0.187286
$834$	−2.68525e26	−0.0476329
$835$	1.10955e26	0.0194592
$836$	−1.86107e27	−0.322704
$837$	−2.99589e26	−0.0513610
$838$	−4.34409e27	−0.736343
$839$	−5.31813e27	−0.891293	−0.445646	−	0.895209i	$-0.647026\pi$
$839$	−5.31813e27	−0.891293	−0.445646	+	0.895209i	$0.647026\pi$
$840$	6.23823e26	0.103373
$841$	1.75351e28	2.87307
$842$	−5.36180e27	−0.868652
$843$	−8.60120e26	−0.137783
$844$	4.05467e27	0.642248
$845$	−1.26102e27	−0.197507
$846$	1.45445e27	0.225259
$847$	−2.25021e27	−0.344612
$848$	−1.61058e27	−0.243906
$849$	4.77236e27	0.714677
$850$	6.83652e27	1.01241
$851$	6.81572e27	0.998115
$852$	−1.09522e27	−0.158607
$853$	−1.60722e27	−0.230176	−0.115088	−	0.993355i	$-0.536715\pi$
$853$	−1.60722e27	−0.230176	−0.115088	+	0.993355i	$0.536715\pi$
$854$	3.11867e27	0.441691
$855$	−3.23627e26	−0.0453279
$856$	−7.06692e27	−0.978879
$857$	8.25782e27	1.13122	0.565611	−	0.824672i	$-0.308641\pi$
$857$	8.25782e27	1.13122	0.565611	+	0.824672i	$0.308641\pi$
$858$	−3.90475e27	−0.529010
$859$	−9.31408e27	−1.24797	−0.623986	−	0.781436i	$-0.714488\pi$
$859$	−9.31408e27	−1.24797	−0.623986	+	0.781436i	$0.714488\pi$
$860$	5.44299e25	0.00721277
$861$	1.28749e27	0.168738
$862$	2.46562e27	0.319600
$863$	6.65457e27	0.853134	0.426567	−	0.904456i	$-0.359723\pi$
$863$	6.65457e27	0.853134	0.426567	+	0.904456i	$0.359723\pi$
$864$	1.24391e27	0.157728
$865$	2.25128e27	0.282343
$866$	4.03024e27	0.499932
$867$	−4.53234e27	−0.556084
$868$	−1.05691e27	−0.128263
$869$	−4.49368e27	−0.539404
$870$	−1.10878e27	−0.131647
$871$	−1.19304e28	−1.40114
$872$	6.43778e27	0.747876
$873$	6.46647e26	0.0743074
$874$	−3.29352e27	−0.374371
$875$	2.92626e27	0.329030
$876$	3.46493e26	0.0385394
$877$	−1.08073e27	−0.118911	−0.0594554	−	0.998231i	$-0.518936\pi$
$877$	−1.08073e27	−0.118911	−0.0594554	+	0.998231i	$0.518936\pi$
$878$	1.09514e28	1.19199
$879$	−3.25285e26	−0.0350243
$880$	4.16523e26	0.0443663
$881$	−1.38540e28	−1.45983	−0.729916	−	0.683536i	$-0.760441\pi$
$881$	−1.38540e28	−1.45983	−0.729916	+	0.683536i	$0.760441\pi$
$882$	−3.16587e26	−0.0330021
$883$	6.76336e27	0.697487	0.348743	−	0.937218i	$-0.386608\pi$
$883$	6.76336e27	0.697487	0.348743	+	0.937218i	$0.386608\pi$
$884$	9.32447e27	0.951322
$885$	−3.63987e26	−0.0367388
$886$	9.88642e27	0.987231
$887$	−1.60903e28	−1.58960	−0.794802	−	0.606869i	$-0.792425\pi$
$887$	−1.60903e28	−1.58960	−0.794802	+	0.606869i	$0.792425\pi$
$888$	−1.09011e28	−1.06549
$889$	−1.42360e28	−1.37665
$890$	−5.26047e26	−0.0503292
$891$	9.65336e26	0.0913777
$892$	−7.52311e27	−0.704581
$893$	−8.55921e27	−0.793131
$894$	1.76986e27	0.162268
$895$	6.70675e26	0.0608406
$896$	1.35819e27	0.121909
$897$	5.68541e27	0.504933
$898$	−4.19729e27	−0.368845
$899$	6.04033e27	0.525223
$900$	1.70595e27	0.146779
$901$	1.16393e28	0.990922
$902$	1.98478e27	0.167205
$903$	−7.53296e26	−0.0627960
$904$	1.95408e28	1.61191
$905$	−1.03636e26	−0.00845963
$906$	−4.53781e27	−0.366546
$907$	−4.87731e26	−0.0389862	−0.0194931	−	0.999810i	$-0.506205\pi$
$907$	−4.87731e26	−0.0389862	−0.0194931	+	0.999810i	$0.506205\pi$
$908$	−6.05299e27	−0.478800
$909$	3.87060e27	0.302985
$910$	−2.39545e27	−0.185564
$911$	2.04975e28	1.57136	0.785680	−	0.618634i	$-0.212313\pi$
$911$	2.04975e28	1.57136	0.785680	+	0.618634i	$0.212313\pi$
$912$	2.28155e27	0.173093
$913$	2.09367e28	1.57194
$914$	−1.15636e28	−0.859221
$915$	−6.87844e26	−0.0505812
$916$	5.28790e27	0.384836
$917$	−2.37960e28	−1.71394
$918$	2.80180e27	0.199725
$919$	7.36209e27	0.519402	0.259701	−	0.965689i	$-0.416376\pi$
$919$	7.36209e27	0.519402	0.259701	+	0.965689i	$0.416376\pi$
$920$	−1.40023e27	−0.0977720
$921$	1.40606e28	0.971713
$922$	−2.42819e27	−0.166088
$923$	1.35227e28	0.915476
$924$	3.40559e27	0.228196
$925$	−2.52511e28	−1.67469
$926$	−6.03632e27	−0.396249
$927$	4.55222e26	0.0295778
$928$	−2.50797e28	−1.61294
$929$	−9.18844e27	−0.584915	−0.292457	−	0.956279i	$-0.594473\pi$
$929$	−9.18844e27	−0.584915	−0.292457	+	0.956279i	$0.594473\pi$
$930$	−2.83327e26	−0.0178525
$931$	1.86306e27	0.116200
$932$	5.97241e26	0.0368721
$933$	−7.37881e27	−0.450932
$934$	−9.32074e27	−0.563839
$935$	−3.01010e27	−0.180248
$936$	−9.09331e27	−0.539016
$937$	1.55615e28	0.913113	0.456557	−	0.889694i	$-0.349083\pi$
$937$	1.55615e28	0.913113	0.456557	+	0.889694i	$0.349083\pi$
$938$	−1.26468e28	−0.734607
$939$	4.01793e27	0.231036
$940$	−1.13171e27	−0.0644198
$941$	−4.21264e27	−0.237385	−0.118693	−	0.992931i	$-0.537870\pi$
$941$	−4.21264e27	−0.237385	−0.118693	+	0.992931i	$0.537870\pi$
$942$	9.67280e27	0.539596
$943$	−2.88989e27	−0.159595
$944$	2.56609e27	0.140293
$945$	5.92206e26	0.0320531
$946$	−1.16127e27	−0.0622255
$947$	1.60906e27	0.0853584	0.0426792	−	0.999089i	$-0.486411\pi$
$947$	1.60906e27	0.0853584	0.0426792	+	0.999089i	$0.486411\pi$
$948$	−3.25456e27	−0.170928
$949$	−4.27817e27	−0.222448
$950$	1.22019e28	0.628137
$951$	5.40175e27	0.275308
$952$	3.17826e28	1.60376
$953$	2.00721e28	1.00279	0.501396	−	0.865218i	$-0.332820\pi$
$953$	2.00721e28	1.00279	0.501396	+	0.865218i	$0.332820\pi$
$954$	−3.53008e27	−0.174612
$955$	3.50493e27	0.171651
$956$	−9.30095e27	−0.451001
$957$	−1.94632e28	−0.934437
$958$	−2.28898e28	−1.08810
$959$	1.74160e28	0.819729
$960$	1.84471e27	0.0859709
$961$	−2.01272e28	−0.928775
$962$	4.18598e28	1.91264
$963$	−6.70874e27	−0.303523
$964$	4.73173e27	0.211977
$965$	6.64631e27	0.294830
$966$	6.02683e27	0.264732
$967$	3.69606e28	1.60764	0.803818	−	0.594876i	$-0.202799\pi$
$967$	3.69606e28	1.60764	0.803818	+	0.594876i	$0.202799\pi$
$968$	−8.07830e27	−0.347940
$969$	−1.64881e28	−0.703228
$970$	6.11546e26	0.0258284
$971$	−2.54073e28	−1.06261	−0.531306	−	0.847180i	$-0.678299\pi$
$971$	−2.54073e28	−1.06261	−0.531306	+	0.847180i	$0.678299\pi$
$972$	6.99149e26	0.0289561
$973$	−2.89166e27	−0.118597
$974$	3.52397e27	0.143127
$975$	−2.10635e28	−0.847201
$976$	4.84925e27	0.193153
$977$	8.52403e27	0.336238	0.168119	−	0.985767i	$-0.446231\pi$
$977$	8.52403e27	0.336238	0.168119	+	0.985767i	$0.446231\pi$
$978$	4.75107e27	0.185598
$979$	−9.23408e27	−0.357238
$980$	2.46336e26	0.00943799
$981$	6.11149e27	0.231895
$982$	−2.81120e28	−1.05641
$983$	3.09592e28	1.15221	0.576105	−	0.817376i	$-0.304572\pi$
$983$	3.09592e28	1.15221	0.576105	+	0.817376i	$0.304572\pi$
$984$	4.62211e27	0.170368
$985$	−5.25015e27	−0.191658
$986$	−5.64901e28	−2.04240
$987$	1.56625e28	0.560853
$988$	1.66425e28	0.590238
$989$	1.69084e27	0.0593934
$990$	9.12937e26	0.0317619
$991$	−2.94856e28	−1.01604	−0.508020	−	0.861345i	$-0.669622\pi$
$991$	−2.94856e28	−1.01604	−0.508020	+	0.861345i	$0.669622\pi$
$992$	−6.40864e27	−0.218728
$993$	4.55843e27	0.154098
$994$	1.43347e28	0.479976
$995$	−3.11376e27	−0.103268
$996$	1.51635e28	0.498121
$997$	−3.29038e28	−1.07064	−0.535318	−	0.844650i	$-0.679808\pi$
$997$	−3.29038e28	−1.07064	−0.535318	+	0.844650i	$0.679808\pi$
$998$	1.36839e28	0.441031
$999$	−1.03486e28	−0.330377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.20.a.b.1.1	✓	2
3.2	odd	2		9.20.a.c.1.2		2
4.3	odd	2		48.20.a.j.1.1		2
5.2	odd	4		75.20.b.b.49.2		4
5.3	odd	4		75.20.b.b.49.3		4
5.4	even	2		75.20.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.20.a.b.1.1	✓	2	1.1	even	1	trivial
9.20.a.c.1.2		2	3.2	odd	2
48.20.a.j.1.1		2	4.3	odd	2
75.20.a.b.1.2		2	5.4	even	2
75.20.b.b.49.2		4	5.2	odd	4
75.20.b.b.49.3		4	5.3	odd	4

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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-536.316 q^{2} -19683.0 q^{3} -236654. q^{4} -683163. q^{5} +1.05563e7 q^{6} +1.13677e8 q^{7} +4.08105e8 q^{8} +3.87420e8 q^{9} +O(q^{10})\)	\(q-536.316 q^{2} -19683.0 q^{3} -236654. q^{4} -683163. q^{5} +1.05563e7 q^{6} +1.13677e8 q^{7} +4.08105e8 q^{8} +3.87420e8 q^{9} +3.66391e8 q^{10} +6.43152e9 q^{11} +4.65805e9 q^{12} -5.75132e10 q^{13} -6.09670e10 q^{14} +1.34467e10 q^{15} -9.47984e10 q^{16} +6.85083e11 q^{17} -2.07780e11 q^{18} +1.22275e12 q^{19} +1.61673e11 q^{20} -2.23751e12 q^{21} -3.44932e12 q^{22} +5.02230e12 q^{23} -8.03273e12 q^{24} -1.86068e13 q^{25} +3.08453e13 q^{26} -7.62560e12 q^{27} -2.69022e13 q^{28} +1.53748e14 q^{29} -7.21167e12 q^{30} +3.92872e13 q^{31} -1.63123e14 q^{32} -1.26592e14 q^{33} -3.67421e14 q^{34} -7.76602e13 q^{35} -9.16844e13 q^{36} +1.35709e15 q^{37} -6.55779e14 q^{38} +1.13203e15 q^{39} -2.78802e14 q^{40} -5.75410e14 q^{41} +1.20001e15 q^{42} +3.36667e14 q^{43} -1.52204e15 q^{44} -2.64671e14 q^{45} -2.69354e15 q^{46} -6.99998e15 q^{47} +1.86592e15 q^{48} +1.52367e15 q^{49} +9.97910e15 q^{50} -1.34845e16 q^{51} +1.36107e16 q^{52} +1.69895e16 q^{53} +4.08973e15 q^{54} -4.39377e15 q^{55} +4.63923e16 q^{56} -2.40674e16 q^{57} -8.24573e16 q^{58} -2.70689e16 q^{59} -3.18221e15 q^{60} -5.11533e16 q^{61} -2.10704e16 q^{62} +4.40410e16 q^{63} +1.37187e17 q^{64} +3.92909e16 q^{65} +6.78930e16 q^{66} +2.07437e17 q^{67} -1.62127e17 q^{68} -9.88540e16 q^{69} +4.16504e16 q^{70} -2.35123e17 q^{71} +1.58108e17 q^{72} +7.43858e16 q^{73} -7.27828e17 q^{74} +3.66237e17 q^{75} -2.89368e17 q^{76} +7.31118e17 q^{77} -6.07127e17 q^{78} -6.98697e17 q^{79} +6.47627e16 q^{80} +1.50095e17 q^{81} +3.08601e17 q^{82} +3.25532e18 q^{83} +5.29515e17 q^{84} -4.68023e17 q^{85} -1.80560e17 q^{86} -3.02622e18 q^{87} +2.62473e18 q^{88} -1.43575e18 q^{89} +1.41947e17 q^{90} -6.53796e18 q^{91} -1.18855e18 q^{92} -7.73291e17 q^{93} +3.75420e18 q^{94} -8.35337e17 q^{95} +3.21074e18 q^{96} +1.66911e18 q^{97} -8.17166e17 q^{98} +2.49170e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 702 q^{2} - 39366 q^{3} + 772484 q^{4} + 6016140 q^{5} - 13817466 q^{6} + 113892064 q^{7} + 1008501624 q^{8} + 774840978 q^{9}+O(q^{10}) \) 2 * q + 702 * q^2 - 39366 * q^3 + 772484 * q^4 + 6016140 * q^5 - 13817466 * q^6 + 113892064 * q^7 + 1008501624 * q^8 + 774840978 * q^9	\( 2 q + 702 q^{2} - 39366 q^{3} + 772484 q^{4} + 6016140 q^{5} - 13817466 q^{6} + 113892064 q^{7} + 1008501624 q^{8} + 774840978 q^{9} + 8662242420 q^{10} - 6650071272 q^{11} - 15204802572 q^{12} - 44072356148 q^{13} - 60701219424 q^{14} - 118415683620 q^{15} + 119603620880 q^{16} + 336281471748 q^{17} + 271969183278 q^{18} + 602118925096 q^{19} + 6922191196440 q^{20} - 2241737495712 q^{21} - 19648459326744 q^{22} + 2368252165968 q^{23} - 19850337465192 q^{24} + 7200399078350 q^{25} + 47489309789364 q^{26} - 15251194969974 q^{27} - 26685589805888 q^{28} + 280977251970492 q^{29} - 170498917552860 q^{30} + 41610149253712 q^{31} - 212406109003296 q^{32} + 130893352846776 q^{33} - 799347349171332 q^{34} - 76222408017600 q^{35} + 299276129024676 q^{36} + 637994163989884 q^{37} - 14\!\cdots\!32 q^{38}+ \cdots - 25\!\cdots\!08 q^{99}+O(q^{100}) \) 2 * q + 702 * q^2 - 39366 * q^3 + 772484 * q^4 + 6016140 * q^5 - 13817466 * q^6 + 113892064 * q^7 + 1008501624 * q^8 + 774840978 * q^9 + 8662242420 * q^10 - 6650071272 * q^11 - 15204802572 * q^12 - 44072356148 * q^13 - 60701219424 * q^14 - 118415683620 * q^15 + 119603620880 * q^16 + 336281471748 * q^17 + 271969183278 * q^18 + 602118925096 * q^19 + 6922191196440 * q^20 - 2241737495712 * q^21 - 19648459326744 * q^22 + 2368252165968 * q^23 - 19850337465192 * q^24 + 7200399078350 * q^25 + 47489309789364 * q^26 - 15251194969974 * q^27 - 26685589805888 * q^28 + 280977251970492 * q^29 - 170498917552860 * q^30 + 41610149253712 * q^31 - 212406109003296 * q^32 + 130893352846776 * q^33 - 799347349171332 * q^34 - 76222408017600 * q^35 + 299276129024676 * q^36 + 637994163989884 * q^37 - 1424314643816232 * q^38 + 867476186061084 * q^39 + 3743437831857360 * q^40 + 1150038430280532 * q^41 + 1194782101922592 * q^42 + 2820518953538200 * q^43 - 14723164414050768 * q^44 + 2330775900692460 * q^45 - 5980094010800208 * q^46 - 5603091319500480 * q^47 - 2354158069781040 * q^48 - 9875183230193070 * q^49 + 41936530073800050 * q^50 - 6619028208415884 * q^51 + 27174417188397208 * q^52 + 27537868857647628 * q^53 - 5353169434460874 * q^54 - 92031302621896560 * q^55 + 46521172561587840 * q^56 - 11851506802664568 * q^57 + 75092921304821316 * q^58 - 55153474421835816 * q^59 - 136249489319528520 * q^60 - 87192569066205620 * q^61 - 18193883108252112 * q^62 + 44124119128099296 * q^63 - 36250046218631104 * q^64 + 129335487918703560 * q^65 + 386740624928302152 * q^66 + 499299710877878248 * q^67 - 514116238109034744 * q^68 - 46614307382748144 * q^69 + 43430850442699200 * q^70 + 84915048436970544 * q^71 + 390714192327374136 * q^72 - 241433711161728332 * q^73 - 1618295867440077564 * q^74 - 141725455059163050 * q^75 - 915668569473570224 * q^76 + 728310910203957888 * q^77 - 934732084584051612 * q^78 + 1131591466033523440 * q^79 + 1501106673028491360 * q^80 + 300189270593998242 * q^81 + 2445251486788059948 * q^82 + 1607743276003583784 * q^83 + 525252464149293504 * q^84 - 2804751519619294440 * q^85 + 2895233411994836328 * q^86 - 5530475250535194036 * q^87 - 5229410429487705696 * q^88 + 4322797626369576276 * q^89 + 3355930194192943380 * q^90 - 6535073681312344768 * q^91 - 3866849612692780896 * q^92 - 819012567760813296 * q^93 + 5483985680095257024 * q^94 - 4993123012930175760 * q^95 + 4180789443511875168 * q^96 + 7902201235299458308 * q^97 - 14932538668319232402 * q^98 - 2576373864083092008 * q^99

Introduction

L-functions

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