LMFDB - Embedded newform 3.20.a.b.1.2

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			1.2
Root			$-147.386$ 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)

$f(q)$	$=$	$q+1238.32 q^{2} -19683.0 q^{3} +1.00914e6 q^{4} +6.69930e6 q^{5} -2.43738e7 q^{6} +214621. q^{7} +6.00397e8 q^{8} +3.87420e8 q^{9} +O(q^{10})$	\(q+1238.32 q^{2} -19683.0 q^{3} +1.00914e6 q^{4} +6.69930e6 q^{5} -2.43738e7 q^{6} +214621. q^{7} +6.00397e8 q^{8} +3.87420e8 q^{9} +8.29585e9 q^{10} -1.30816e10 q^{11} -1.98629e10 q^{12} +1.34409e10 q^{13} +2.65768e8 q^{14} -1.31862e11 q^{15} +2.14402e11 q^{16} -3.48802e11 q^{17} +4.79749e11 q^{18} -6.20630e11 q^{19} +6.76052e12 q^{20} -4.22438e9 q^{21} -1.61991e13 q^{22} -2.65405e12 q^{23} -1.18176e13 q^{24} +2.58072e13 q^{25} +1.66441e13 q^{26} -7.62560e12 q^{27} +2.16582e11 q^{28} +1.27229e14 q^{29} -1.63287e14 q^{30} +2.32290e12 q^{31} -4.92835e13 q^{32} +2.57485e14 q^{33} -4.31927e14 q^{34} +1.43781e12 q^{35} +3.90961e14 q^{36} -7.19096e14 q^{37} -7.68535e14 q^{38} -2.64557e14 q^{39} +4.02224e15 q^{40} +1.72545e15 q^{41} -5.23112e12 q^{42} +2.48385e15 q^{43} -1.32011e16 q^{44} +2.59545e15 q^{45} -3.28655e15 q^{46} +1.39689e15 q^{47} -4.22007e15 q^{48} -1.13988e16 q^{49} +3.19574e16 q^{50} +6.86546e15 q^{51} +1.35637e16 q^{52} +1.05483e16 q^{53} -9.44290e15 q^{54} -8.76375e16 q^{55} +1.28858e14 q^{56} +1.22159e16 q^{57} +1.57550e17 q^{58} -2.80846e16 q^{59} -1.33067e17 q^{60} -3.60392e16 q^{61} +2.87648e15 q^{62} +8.31485e13 q^{63} -1.73437e17 q^{64} +9.00446e16 q^{65} +3.18848e17 q^{66} +2.91862e17 q^{67} -3.51989e17 q^{68} +5.22397e16 q^{69} +1.78046e15 q^{70} +3.20038e17 q^{71} +2.32606e17 q^{72} -3.15819e17 q^{73} -8.90467e17 q^{74} -5.07963e17 q^{75} -6.26301e17 q^{76} -2.80758e15 q^{77} -3.27605e17 q^{78} +1.83029e18 q^{79} +1.43634e18 q^{80} +1.50095e17 q^{81} +2.13665e18 q^{82} -1.64758e18 q^{83} -4.26298e15 q^{84} -2.33673e18 q^{85} +3.07579e18 q^{86} -2.50426e18 q^{87} -7.85414e18 q^{88} +5.75855e18 q^{89} +3.21398e18 q^{90} +2.88469e15 q^{91} -2.67830e18 q^{92} -4.57216e16 q^{93} +1.72979e18 q^{94} -4.15779e18 q^{95} +9.70047e17 q^{96} +6.23309e18 q^{97} -1.41154e19 q^{98} -5.06808e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1238.32	1.71020	0.855099	−	0.518465i	$-0.173496\pi$
$2$	1238.32	1.71020	0.855099	+	0.518465i	$0.173496\pi$
$3$	−19683.0	−0.577350
$3$	−19683.0	−0.577350
$4$	1.00914e6	1.92478
$5$	6.69930e6	1.53396	0.766981	−	0.641670i	$-0.221758\pi$
$5$	6.69930e6	1.53396	0.766981	+	0.641670i	$0.221758\pi$
$6$	−2.43738e7	−0.987383
$7$	214621.	0.00201021	0.00100510	−	0.999999i	$-0.499680\pi$
$7$	214621.	0.00201021	0.00100510	+	0.999999i	$0.499680\pi$
$8$	6.00397e8	1.58155
$9$	3.87420e8	0.333333
$10$	8.29585e9	2.62338
$11$	−1.30816e10	−1.67275	−0.836373	−	0.548161i	$-0.815328\pi$
$11$	−1.30816e10	−1.67275	−0.836373	+	0.548161i	$0.815328\pi$
$12$	−1.98629e10	−1.11127
$13$	1.34409e10	0.351533	0.175766	−	0.984432i	$-0.443760\pi$
$13$	1.34409e10	0.351533	0.175766	+	0.984432i	$0.443760\pi$
$14$	2.65768e8	0.00343785
$15$	−1.31862e11	−0.885633
$16$	2.14402e11	0.779990
$17$	−3.48802e11	−0.713368	−0.356684	−	0.934225i	$-0.616093\pi$
$17$	−3.48802e11	−0.713368	−0.356684	+	0.934225i	$0.616093\pi$
$18$	4.79749e11	0.570066
$19$	−6.20630e11	−0.441238	−0.220619	−	0.975360i	$-0.570808\pi$
$19$	−6.20630e11	−0.441238	−0.220619	+	0.975360i	$0.570808\pi$
$20$	6.76052e12	2.95253
$21$	−4.22438e9	−0.00116059
$22$	−1.61991e13	−2.86073
$23$	−2.65405e12	−0.307252	−0.153626	−	0.988129i	$-0.549095\pi$
$23$	−2.65405e12	−0.307252	−0.153626	+	0.988129i	$0.549095\pi$
$24$	−1.18176e13	−0.913109
$25$	2.58072e13	1.35304
$26$	1.66441e13	0.601191
$27$	−7.62560e12	−0.192450
$28$	2.16582e11	0.00386920
$29$	1.27229e14	1.62857	0.814286	−	0.580464i	$-0.197129\pi$
$29$	1.27229e14	1.62857	0.814286	+	0.580464i	$0.197129\pi$
$30$	−1.63287e14	−1.51461
$31$	2.32290e12	0.0157795	0.00788977	−	0.999969i	$-0.497489\pi$
$31$	2.32290e12	0.0157795	0.00788977	+	0.999969i	$0.497489\pi$
$32$	−4.92835e13	−0.247615
$33$	2.57485e14	0.965760
$34$	−4.31927e14	−1.22000
$35$	1.43781e12	0.00308358
$36$	3.90961e14	0.641592
$37$	−7.19096e14	−0.909642	−0.454821	−	0.890583i	$-0.650297\pi$
$37$	−7.19096e14	−0.909642	−0.454821	+	0.890583i	$0.650297\pi$
$38$	−7.68535e14	−0.754605
$39$	−2.64557e14	−0.202958
$40$	4.02224e15	2.42604
$41$	1.72545e15	0.823105	0.411553	−	0.911386i	$-0.364987\pi$
$41$	1.72545e15	0.823105	0.411553	+	0.911386i	$0.364987\pi$
$42$	−5.23112e12	−0.00198484
$43$	2.48385e15	0.753660	0.376830	−	0.926282i	$-0.377014\pi$
$43$	2.48385e15	0.753660	0.376830	+	0.926282i	$0.377014\pi$
$44$	−1.32011e16	−3.21966
$45$	2.59545e15	0.511321
$46$	−3.28655e15	−0.525462
$47$	1.39689e15	0.182067	0.0910336	−	0.995848i	$-0.470983\pi$
$47$	1.39689e15	0.182067	0.0910336	+	0.995848i	$0.470983\pi$
$48$	−4.22007e15	−0.450327
$49$	−1.13988e16	−0.999996
$50$	3.19574e16	2.31396
$51$	6.86546e15	0.411863
$52$	1.35637e16	0.676623
$53$	1.05483e16	0.439099	0.219550	−	0.975601i	$-0.429541\pi$
$53$	1.05483e16	0.439099	0.219550	+	0.975601i	$0.429541\pi$
$54$	−9.44290e15	−0.329128
$55$	−8.76375e16	−2.56593
$56$	1.28858e14	0.00317925
$57$	1.22159e16	0.254749
$58$	1.57550e17	2.78518
$59$	−2.80846e16	−0.422060	−0.211030	−	0.977480i	$-0.567682\pi$
$59$	−2.80846e16	−0.422060	−0.211030	+	0.977480i	$0.567682\pi$
$60$	−1.33067e17	−1.70465
$61$	−3.60392e16	−0.394586	−0.197293	−	0.980345i	$-0.563215\pi$
$61$	−3.60392e16	−0.394586	−0.197293	+	0.980345i	$0.563215\pi$
$62$	2.87648e15	0.0269861
$63$	8.31485e13	0.000670069 0
$64$	−1.73437e17	−1.20346
$65$	9.00446e16	0.539238
$66$	3.18848e17	1.65164
$67$	2.91862e17	1.31059	0.655296	−	0.755373i	$-0.272544\pi$
$67$	2.91862e17	1.31059	0.655296	+	0.755373i	$0.272544\pi$
$68$	−3.51989e17	−1.37308
$69$	5.22397e16	0.177392
$70$	1.78046e15	0.00527353
$71$	3.20038e17	0.828414	0.414207	−	0.910183i	$-0.364059\pi$
$71$	3.20038e17	0.828414	0.414207	+	0.910183i	$0.364059\pi$
$72$	2.32606e17	0.527184
$73$	−3.15819e17	−0.627873	−0.313936	−	0.949444i	$-0.601648\pi$
$73$	−3.15819e17	−0.627873	−0.313936	+	0.949444i	$0.601648\pi$
$74$	−8.90467e17	−1.55567
$75$	−5.07963e17	−0.781178
$76$	−6.26301e17	−0.849286
$77$	−2.80758e15	−0.00336256
$78$	−3.27605e17	−0.347098
$79$	1.83029e18	1.71815	0.859077	−	0.511846i	$-0.171038\pi$
$79$	1.83029e18	1.71815	0.859077	+	0.511846i	$0.171038\pi$
$80$	1.43634e18	1.19647
$81$	1.50095e17	0.111111
$82$	2.13665e18	1.40767
$83$	−1.64758e18	−0.967397	−0.483698	−	0.875235i	$-0.660707\pi$
$83$	−1.64758e18	−0.967397	−0.483698	+	0.875235i	$0.660707\pi$
$84$	−4.26298e15	−0.00223388
$85$	−2.33673e18	−1.09428
$86$	3.07579e18	1.28891
$87$	−2.50426e18	−0.940256
$88$	−7.85414e18	−2.64553
$89$	5.75855e18	1.74224	0.871120	−	0.491069i	$-0.163394\pi$
$89$	5.75855e18	1.74224	0.871120	+	0.491069i	$0.163394\pi$
$90$	3.21398e18	0.874460
$91$	2.88469e15	0.000706654 0
$92$	−2.67830e18	−0.591392
$93$	−4.57216e16	−0.00911032
$94$	1.72979e18	0.311371
$95$	−4.15779e18	−0.676843
$96$	9.70047e17	0.142960
$97$	6.23309e18	0.832477	0.416238	−	0.909256i	$-0.363348\pi$
$97$	6.23309e18	0.832477	0.416238	+	0.909256i	$0.363348\pi$
$98$	−1.41154e19	−1.71019
$99$	−5.06808e18	−0.557582
$100$	2.60430e19	2.60430
$101$	8.80411e17	0.0801000	0.0400500	−	0.999198i	$-0.487248\pi$
$101$	8.80411e17	0.0801000	0.0400500	+	0.999198i	$0.487248\pi$
$102$	8.50161e18	0.704368
$103$	−1.96998e19	−1.48767	−0.743837	−	0.668361i	$-0.766996\pi$
$103$	−1.96998e19	−1.48767	−0.743837	+	0.668361i	$0.766996\pi$
$104$	8.06987e18	0.555968
$105$	−2.83004e16	−0.00178031
$106$	1.30622e19	0.750946
$107$	2.58893e19	1.36136	0.680682	−	0.732579i	$-0.261684\pi$
$107$	2.58893e19	1.36136	0.680682	+	0.732579i	$0.261684\pi$
$108$	−7.69528e18	−0.370424
$109$	−3.42533e19	−1.51060	−0.755302	−	0.655377i	$-0.772510\pi$
$109$	−3.42533e19	−1.51060	−0.755302	+	0.655377i	$0.772510\pi$
$110$	−1.08523e20	−4.38825
$111$	1.41540e19	0.525182
$112$	4.60151e16	0.00156794
$113$	5.49844e19	1.72185	0.860923	−	0.508735i	$-0.169887\pi$
$113$	5.49844e19	1.72185	0.860923	+	0.508735i	$0.169887\pi$
$114$	1.51271e19	0.435671
$115$	−1.77803e19	−0.471313
$116$	1.28392e20	3.13464
$117$	5.20727e18	0.117178
$118$	−3.47776e19	−0.721806
$119$	−7.48601e16	−0.00143402
$120$	−7.91697e19	−1.40068
$121$	1.09969e20	1.79808
$122$	−4.46279e19	−0.674821
$123$	−3.39620e19	−0.475220
$124$	2.34412e18	0.0303721
$125$	4.51110e19	0.541549
$126$	1.02964e17	0.00114595
$127$	−8.76640e19	−0.905078	−0.452539	−	0.891745i	$-0.649482\pi$
$127$	−8.76640e19	−0.905078	−0.452539	+	0.891745i	$0.649482\pi$
$128$	−1.88931e20	−1.81054
$129$	−4.88897e19	−0.435126
$130$	1.11504e20	0.922204
$131$	−1.23083e20	−0.946497	−0.473249	−	0.880929i	$-0.656919\pi$
$131$	−1.23083e20	−0.946497	−0.473249	+	0.880929i	$0.656919\pi$
$132$	2.59838e20	1.85887
$133$	−1.33200e17	−0.000886980 0
$134$	3.61418e20	2.24137
$135$	−5.10862e19	−0.295211
$136$	−2.09419e20	−1.12823
$137$	−1.10729e20	−0.556435	−0.278218	−	0.960518i	$-0.589744\pi$
$137$	−1.10729e20	−0.556435	−0.278218	+	0.960518i	$0.589744\pi$
$138$	6.46892e19	0.303376
$139$	−2.36141e20	−1.03402	−0.517012	−	0.855978i	$-0.672956\pi$
$139$	−2.36141e20	−1.03402	−0.517012	+	0.855978i	$0.672956\pi$
$140$	1.45095e18	0.00593520
$141$	−2.74949e19	−0.105117
$142$	3.96308e20	1.41675
$143$	−1.75828e20	−0.588025
$144$	8.30637e19	0.259997
$145$	8.52349e20	2.49817
$146$	−3.91084e20	−1.07379
$147$	2.24364e20	0.577348
$148$	−7.25666e20	−1.75086
$149$	2.05810e20	0.465796	0.232898	−	0.972501i	$-0.425179\pi$
$149$	2.05810e20	0.465796	0.232898	+	0.972501i	$0.425179\pi$
$150$	−6.29018e20	−1.33597
$151$	−2.24449e20	−0.447546	−0.223773	−	0.974641i	$-0.571837\pi$
$151$	−2.24449e20	−0.447546	−0.223773	+	0.974641i	$0.571837\pi$
$152$	−3.72624e20	−0.697842
$153$	−1.35133e20	−0.237789
$154$	−3.47667e18	−0.00575065
$155$	1.55618e19	0.0242052
$156$	−2.66974e20	−0.390648
$157$	3.13212e20	0.431312	0.215656	−	0.976469i	$-0.430811\pi$
$157$	3.13212e20	0.431312	0.215656	+	0.976469i	$0.430811\pi$
$158$	2.26647e21	2.93838
$159$	−2.07623e20	−0.253514
$160$	−3.30165e20	−0.379832
$161$	−5.69615e17	−0.000617640 0
$162$	1.85865e20	0.190022
$163$	2.00591e20	0.193432	0.0967160	−	0.995312i	$-0.469166\pi$
$163$	2.00591e20	0.193432	0.0967160	+	0.995312i	$0.469166\pi$
$164$	1.74122e21	1.58429
$165$	1.72497e21	1.48144
$166$	−2.04022e21	−1.65444
$167$	−2.56060e21	−1.96126	−0.980632	−	0.195860i	$-0.937250\pi$
$167$	−2.56060e21	−1.96126	−0.980632	+	0.195860i	$0.937250\pi$
$168$	−2.53631e18	−0.00183554
$169$	−1.28126e21	−0.876425
$170$	−2.89361e21	−1.87144
$171$	−2.40445e20	−0.147079
$172$	2.50655e21	1.45063
$173$	2.86308e21	1.56818	0.784089	−	0.620649i	$-0.213131\pi$
$173$	2.86308e21	1.56818	0.784089	+	0.620649i	$0.213131\pi$
$174$	−3.10106e21	−1.60802
$175$	5.53876e18	0.00271989
$176$	−2.80472e21	−1.30472
$177$	5.52789e20	0.243676
$178$	7.13090e21	2.97958
$179$	3.79065e20	0.150179	0.0750896	−	0.997177i	$-0.476076\pi$
$179$	3.79065e20	0.150179	0.0750896	+	0.997177i	$0.476076\pi$
$180$	2.61916e21	0.984178
$181$	−3.15578e21	−1.12502	−0.562510	−	0.826790i	$-0.690164\pi$
$181$	−3.15578e21	−1.12502	−0.562510	+	0.826790i	$0.690164\pi$
$182$	3.57216e18	0.00120852
$183$	7.09360e20	0.227814
$184$	−1.59348e21	−0.485935
$185$	−4.81744e21	−1.39536
$186$	−5.66178e19	−0.0155805
$187$	4.56288e21	1.19328
$188$	1.40965e21	0.350439
$189$	−1.63661e18	−0.000386864 0
$190$	−5.14865e21	−1.15754
$191$	2.79667e21	0.598170	0.299085	−	0.954226i	$-0.403319\pi$
$191$	2.79667e21	0.598170	0.299085	+	0.954226i	$0.403319\pi$
$192$	3.41376e21	0.694818
$193$	−7.34293e20	−0.142257	−0.0711287	−	0.997467i	$-0.522660\pi$
$193$	−7.34293e20	−0.142257	−0.0711287	+	0.997467i	$0.522660\pi$
$194$	7.71854e21	1.42370
$195$	−1.77235e21	−0.311329
$196$	−1.15030e22	−1.92477
$197$	−5.32518e21	−0.848995	−0.424498	−	0.905429i	$-0.639549\pi$
$197$	−5.32518e21	−0.848995	−0.424498	+	0.905429i	$0.639549\pi$
$198$	−6.27588e21	−0.953576
$199$	−2.54553e21	−0.368701	−0.184350	−	0.982861i	$-0.559018\pi$
$199$	−2.54553e21	−0.368701	−0.184350	+	0.982861i	$0.559018\pi$
$200$	1.54945e22	2.13990
$201$	−5.74472e21	−0.756670
$202$	1.09023e21	0.136987
$203$	2.73061e19	0.00327376
$204$	6.92820e21	0.792745
$205$	1.15593e22	1.26261
$206$	−2.43945e22	−2.54422
$207$	−1.02823e21	−0.102417
$208$	2.88175e21	0.274192
$209$	8.11882e21	0.738080
$210$	−3.50448e19	−0.00304467
$211$	7.77610e21	0.645771	0.322886	−	0.946438i	$-0.395347\pi$
$211$	7.77610e21	0.645771	0.322886	+	0.946438i	$0.395347\pi$
$212$	1.06447e22	0.845168
$213$	−6.29931e21	−0.478285
$214$	3.20591e22	2.32820
$215$	1.66401e22	1.15609
$216$	−4.57838e21	−0.304370
$217$	4.98543e17	3.17201e−5 0
$218$	−4.24164e22	−2.58343
$219$	6.21627e21	0.362503
$220$	−8.84383e22	−4.93884
$221$	−4.68820e21	−0.250772
$222$	1.75271e22	0.898165
$223$	−1.89249e22	−0.929259	−0.464629	−	0.885505i	$-0.653812\pi$
$223$	−1.89249e22	−0.929259	−0.464629	+	0.885505i	$0.653812\pi$
$224$	−1.05773e19	−0.000497757 0
$225$	9.99823e21	0.451013
$226$	6.80881e22	2.94470
$227$	2.42145e22	1.00422	0.502111	−	0.864803i	$-0.332557\pi$
$227$	2.42145e22	1.00422	0.502111	+	0.864803i	$0.332557\pi$
$228$	1.23275e22	0.490335
$229$	−3.29966e22	−1.25902	−0.629510	−	0.776992i	$-0.716744\pi$
$229$	−3.29966e22	−1.25902	−0.629510	+	0.776992i	$0.716744\pi$
$230$	−2.20176e22	−0.806039
$231$	5.52616e19	0.00194138
$232$	7.63882e22	2.57567
$233$	−8.99479e21	−0.291145	−0.145573	−	0.989348i	$-0.546502\pi$
$233$	−8.99479e21	−0.291145	−0.145573	+	0.989348i	$0.546502\pi$
$234$	6.44825e21	0.200397
$235$	9.35817e21	0.279284
$236$	−2.83412e22	−0.812371
$237$	−3.60256e22	−0.991977
$238$	−9.27005e19	−0.00245245
$239$	1.22851e22	0.312319	0.156159	−	0.987732i	$-0.450089\pi$
$239$	1.22851e22	0.312319	0.156159	+	0.987732i	$0.450089\pi$
$240$	−2.82716e22	−0.690785
$241$	−4.48313e22	−1.05298	−0.526489	−	0.850182i	$-0.676492\pi$
$241$	−4.48313e22	−1.05298	−0.526489	+	0.850182i	$0.676492\pi$
$242$	1.36176e23	3.07507
$243$	−2.95431e21	−0.0641500
$244$	−3.63685e22	−0.759491
$245$	−7.63643e22	−1.53396
$246$	−4.20557e22	−0.812720
$247$	−8.34181e21	−0.155110
$248$	1.39466e21	0.0249562
$249$	3.24293e22	0.558527
$250$	5.58617e22	0.926155
$251$	3.85123e22	0.614750	0.307375	−	0.951588i	$-0.400549\pi$
$251$	3.85123e22	0.614750	0.307375	+	0.951588i	$0.400549\pi$
$252$	8.39083e19	0.00128973
$253$	3.47192e22	0.513955
$254$	−1.08556e23	−1.54786
$255$	4.59938e22	0.631783
$256$	−1.43025e23	−1.89292
$257$	9.07321e22	1.15717	0.578584	−	0.815623i	$-0.303606\pi$
$257$	9.07321e22	1.15717	0.578584	+	0.815623i	$0.303606\pi$
$258$	−6.05408e22	−0.744151
$259$	−1.54333e20	−0.00182857
$260$	9.08674e22	1.03791
$261$	4.92913e22	0.542857
$262$	−1.52415e23	−1.61870
$263$	−2.56086e21	−0.0262305	−0.0131152	−	0.999914i	$-0.504175\pi$
$263$	−2.56086e21	−0.0262305	−0.0131152	+	0.999914i	$0.504175\pi$
$264$	1.54593e23	1.52740
$265$	7.06664e22	0.673561
$266$	−1.64944e20	−0.00151691
$267$	−1.13346e23	−1.00588
$268$	2.94529e23	2.52260
$269$	3.82577e22	0.316281	0.158140	−	0.987417i	$-0.449450\pi$
$269$	3.82577e22	0.316281	0.158140	+	0.987417i	$0.449450\pi$
$270$	−6.32608e22	−0.504869
$271$	3.64857e22	0.281135	0.140567	−	0.990071i	$-0.455107\pi$
$271$	3.64857e22	0.281135	0.140567	+	0.990071i	$0.455107\pi$
$272$	−7.47838e22	−0.556420
$273$	−5.67794e19	−0.000407987 0
$274$	−1.37117e23	−0.951615
$275$	−3.37599e23	−2.26329
$276$	5.27170e22	0.341440
$277$	1.78571e23	1.11752	0.558758	−	0.829331i	$-0.311278\pi$
$277$	1.78571e23	1.11752	0.558758	+	0.829331i	$0.311278\pi$
$278$	−2.92417e23	−1.76839
$279$	8.99939e20	0.00525985
$280$	8.63257e20	0.00487684
$281$	−2.28261e23	−1.24659	−0.623293	−	0.781989i	$-0.714205\pi$
$281$	−2.28261e23	−1.24659	−0.623293	+	0.781989i	$0.714205\pi$
$282$	−3.40474e22	−0.179770
$283$	1.87538e23	0.957453	0.478727	−	0.877964i	$-0.341098\pi$
$283$	1.87538e23	0.957453	0.478727	+	0.877964i	$0.341098\pi$
$284$	3.22962e23	1.59451
$285$	8.18377e22	0.390775
$286$	−2.17731e23	−1.00564
$287$	3.70317e20	0.00165461
$288$	−1.90934e22	−0.0825383
$289$	−1.17410e23	−0.491106
$290$	1.05548e24	4.27236
$291$	−1.22686e23	−0.480631
$292$	−3.18705e23	−1.20852
$293$	2.82617e23	1.03742	0.518711	−	0.854950i	$-0.326412\pi$
$293$	2.82617e23	1.03742	0.518711	+	0.854950i	$0.326412\pi$
$294$	2.77833e23	0.987379
$295$	−1.88147e23	−0.647424
$296$	−4.31743e23	−1.43865
$297$	9.97549e22	0.321920
$298$	2.54857e23	0.796604
$299$	−3.56728e22	−0.108009
$300$	−5.12604e23	−1.50359
$301$	5.33087e20	0.00151501
$302$	−2.77939e23	−0.765392
$303$	−1.73291e22	−0.0462457
$304$	−1.33064e23	−0.344162
$305$	−2.41438e23	−0.605280
$306$	−1.67337e23	−0.406667
$307$	−2.47019e23	−0.581991	−0.290996	−	0.956724i	$-0.593986\pi$
$307$	−2.47019e23	−0.581991	−0.290996	+	0.956724i	$0.593986\pi$
$308$	−2.83324e21	−0.00647219
$309$	3.87751e23	0.858909
$310$	1.92704e22	0.0413957
$311$	3.27126e23	0.681539	0.340770	−	0.940147i	$-0.389312\pi$
$311$	3.27126e23	0.681539	0.340770	+	0.940147i	$0.389312\pi$
$312$	−1.58839e23	−0.320988
$313$	3.73412e23	0.732011	0.366005	−	0.930613i	$-0.380725\pi$
$313$	3.73412e23	0.732011	0.366005	+	0.930613i	$0.380725\pi$
$314$	3.87855e23	0.737628
$315$	5.57037e20	0.00102786
$316$	1.84701e24	3.30706
$317$	−5.83518e22	−0.101389	−0.0506945	−	0.998714i	$-0.516143\pi$
$317$	−5.83518e22	−0.101389	−0.0506945	+	0.998714i	$0.516143\pi$
$318$	−2.57102e23	−0.433559
$319$	−1.66436e24	−2.72419
$320$	−1.16191e24	−1.84606
$321$	−5.09579e23	−0.785984
$322$	−7.05363e20	−0.00105629
$323$	2.16477e23	0.314766
$324$	1.51466e23	0.213864
$325$	3.46871e23	0.475638
$326$	2.48394e23	0.330807
$327$	6.74208e23	0.872148
$328$	1.03595e24	1.30178
$329$	2.99801e20	0.000365993 0
$330$	2.13606e24	2.53355
$331$	3.84253e23	0.442845	0.221422	−	0.975178i	$-0.428930\pi$
$331$	3.84253e23	0.442845	0.221422	+	0.975178i	$0.428930\pi$
$332$	−1.66263e24	−1.86202
$333$	−2.78592e23	−0.303214
$334$	−3.17084e24	−3.35415
$335$	1.95527e24	2.01040
$336$	−9.05716e20	−0.000905251 0
$337$	1.30128e24	1.26440	0.632202	−	0.774803i	$-0.282151\pi$
$337$	1.30128e24	1.26440	0.632202	+	0.774803i	$0.282151\pi$
$338$	−1.58661e24	−1.49886
$339$	−1.08226e24	−0.994109
$340$	−2.35808e24	−2.10624
$341$	−3.03872e22	−0.0263952
$342$	−2.97746e23	−0.251535
$343$	−4.89287e21	−0.00402040
$344$	1.49130e24	1.19195
$345$	3.49970e23	0.272113
$346$	3.54539e24	2.68189
$347$	−8.56826e22	−0.0630613	−0.0315306	−	0.999503i	$-0.510038\pi$
$347$	−8.56826e22	−0.0630613	−0.0315306	+	0.999503i	$0.510038\pi$
$348$	−2.52714e24	−1.80978
$349$	−1.11294e24	−0.775586	−0.387793	−	0.921746i	$-0.626763\pi$
$349$	−1.11294e24	−0.775586	−0.387793	+	0.921746i	$0.626763\pi$
$350$	6.85873e21	0.00465155
$351$	−1.02495e23	−0.0676526
$352$	6.44706e23	0.414197
$353$	−2.23748e24	−1.39926	−0.699631	−	0.714505i	$-0.746652\pi$
$353$	−2.23748e24	−1.39926	−0.699631	+	0.714505i	$0.746652\pi$
$354$	6.84527e23	0.416735
$355$	2.14403e24	1.27076
$356$	5.81117e24	3.35343
$357$	1.47347e21	0.000827930 0
$358$	4.69402e23	0.256836
$359$	2.02884e24	1.08106	0.540531	−	0.841324i	$-0.318223\pi$
$359$	2.02884e24	1.08106	0.540531	+	0.841324i	$0.318223\pi$
$360$	1.55830e24	0.808680
$361$	−1.59324e24	−0.805309
$362$	−3.90785e24	−1.92401
$363$	−2.16452e24	−1.03812
$364$	2.91105e21	0.00136015
$365$	−2.11577e24	−0.963133
$366$	8.78412e23	0.389608
$367$	−2.03395e24	−0.879049	−0.439525	−	0.898230i	$-0.644853\pi$
$367$	−2.03395e24	−0.879049	−0.439525	+	0.898230i	$0.644853\pi$
$368$	−5.69034e23	−0.239654
$369$	6.68474e23	0.274368
$370$	−5.96551e24	−2.38633
$371$	2.26389e21	0.000882680 0
$372$	−4.61394e22	−0.0175353
$373$	−7.78333e23	−0.288358	−0.144179	−	0.989552i	$-0.546054\pi$
$373$	−7.78333e23	−0.288358	−0.144179	+	0.989552i	$0.546054\pi$
$374$	5.65029e24	2.04075
$375$	−8.87920e23	−0.312663
$376$	8.38687e23	0.287949
$377$	1.71008e24	0.572497
$378$	−2.02664e21	−0.000661615 0
$379$	3.15677e24	1.00501	0.502505	−	0.864575i	$-0.332412\pi$
$379$	3.15677e24	1.00501	0.502505	+	0.864575i	$0.332412\pi$
$380$	−4.19578e24	−1.30277
$381$	1.72549e24	0.522547
$382$	3.46316e24	1.02299
$383$	−3.09305e24	−0.891249	−0.445625	−	0.895220i	$-0.647018\pi$
$383$	−3.09305e24	−0.891249	−0.445625	+	0.895220i	$0.647018\pi$
$384$	3.71873e24	1.04532
$385$	−1.88088e22	−0.00515804
$386$	−9.09286e23	−0.243288
$387$	9.62295e23	0.251220
$388$	6.29005e24	1.60233
$389$	−4.58505e24	−1.13978	−0.569892	−	0.821719i	$-0.693015\pi$
$389$	−4.58505e24	−1.13978	−0.569892	+	0.821719i	$0.693015\pi$
$390$	−2.19473e24	−0.532435
$391$	9.25738e23	0.219184
$392$	−6.84383e24	−1.58155
$393$	2.42263e24	0.546460
$394$	−6.59426e24	−1.45195
$395$	1.22617e25	2.63558
$396$	−5.11439e24	−1.07322
$397$	5.62169e24	1.15175	0.575873	−	0.817539i	$-0.304662\pi$
$397$	5.62169e24	1.15175	0.575873	+	0.817539i	$0.304662\pi$
$398$	−3.15217e24	−0.630551
$399$	2.62178e21	0.000512098 0
$400$	5.53311e24	1.05536
$401$	−8.34521e24	−1.55441	−0.777206	−	0.629247i	$-0.783364\pi$
$401$	−8.34521e24	−1.55441	−0.777206	+	0.629247i	$0.783364\pi$
$402$	−7.11378e24	−1.29406
$403$	3.12218e22	0.00554703
$404$	8.88456e23	0.154175
$405$	1.00553e24	0.170440
$406$	3.38136e22	0.00559878
$407$	9.40691e24	1.52160
$408$	4.12200e24	0.651383
$409$	−1.09120e25	−1.68474	−0.842370	−	0.538900i	$-0.818840\pi$
$409$	−1.09120e25	−1.68474	−0.842370	+	0.538900i	$0.818840\pi$
$410$	1.43141e25	2.15932
$411$	2.17947e24	0.321258
$412$	−1.98798e25	−2.86344
$413$	−6.02754e21	−0.000848427 0
$414$	−1.27328e24	−0.175154
$415$	−1.10376e25	−1.48395
$416$	−6.62414e23	−0.0870448
$417$	4.64796e24	0.596994
$418$	1.00537e25	1.26226
$419$	−1.35175e25	−1.65906	−0.829529	−	0.558463i	$-0.811391\pi$
$419$	−1.35175e25	−1.65906	−0.829529	+	0.558463i	$0.811391\pi$
$420$	−2.85590e22	−0.00342669
$421$	9.91185e24	1.16272	0.581360	−	0.813647i	$-0.302521\pi$
$421$	9.91185e24	1.16272	0.581360	+	0.813647i	$0.302521\pi$
$422$	9.62927e24	1.10440
$423$	5.41183e23	0.0606891
$424$	6.33318e24	0.694458
$425$	−9.00159e24	−0.965215
$426$	−7.80053e24	−0.817962
$427$	−7.73477e21	−0.000793200 0
$428$	2.61259e25	2.62032
$429$	3.46083e24	0.339497
$430$	2.06057e25	1.97714
$431$	1.91272e24	0.179522	0.0897610	−	0.995963i	$-0.471390\pi$
$431$	1.91272e24	0.179522	0.0897610	+	0.995963i	$0.471390\pi$
$432$	−1.63494e24	−0.150109
$433$	5.77174e24	0.518408	0.259204	−	0.965823i	$-0.416540\pi$
$433$	5.77174e24	0.518408	0.259204	+	0.965823i	$0.416540\pi$
$434$	6.17353e20	5.42477e−5 0
$435$	−1.67768e25	−1.44232
$436$	−3.45663e25	−2.90758
$437$	1.64718e24	0.135571
$438$	7.69771e24	0.619951
$439$	8.11473e21	0.000639530 0	0.000319765	−	1.00000i	$-0.499898\pi$
$439$	8.11473e21	0.000639530 0	0.000319765		1.00000i	$0.499898\pi$
$440$	−5.26173e25	−4.05815
$441$	−4.41615e24	−0.333332
$442$	−5.80548e24	−0.428871
$443$	2.51728e24	0.182010	0.0910051	−	0.995850i	$-0.470992\pi$
$443$	2.51728e24	0.182010	0.0910051	+	0.995850i	$0.470992\pi$
$444$	1.42833e25	1.01086
$445$	3.85783e25	2.67253
$446$	−2.34350e25	−1.58922
$447$	−4.05095e24	−0.268928
$448$	−3.72232e22	−0.00241920
$449$	−1.07451e25	−0.683706	−0.341853	−	0.939753i	$-0.611055\pi$
$449$	−1.07451e25	−0.683706	−0.341853	+	0.939753i	$0.611055\pi$
$450$	1.23810e25	0.771322
$451$	−2.25716e25	−1.37685
$452$	5.54869e25	3.31417
$453$	4.41784e24	0.258391
$454$	2.99852e25	1.71742
$455$	1.93254e22	0.00108398
$456$	7.33436e24	0.402899
$457$	8.09140e24	0.435331	0.217665	−	0.976023i	$-0.430156\pi$
$457$	8.09140e24	0.435331	0.217665	+	0.976023i	$0.430156\pi$
$458$	−4.08603e25	−2.15317
$459$	2.65982e24	0.137288
$460$	−1.79428e25	−0.907173
$461$	1.48075e25	0.733368	0.366684	−	0.930346i	$-0.380493\pi$
$461$	1.48075e25	0.733368	0.366684	+	0.930346i	$0.380493\pi$
$462$	6.84313e22	0.00332014
$463$	−2.65292e25	−1.26097	−0.630485	−	0.776202i	$-0.717144\pi$
$463$	−2.65292e25	−1.26097	−0.630485	+	0.776202i	$0.717144\pi$
$464$	2.72783e25	1.27027
$465$	−3.06303e23	−0.0139749
$466$	−1.11384e25	−0.497916
$467$	3.57468e25	1.56576	0.782882	−	0.622170i	$-0.213749\pi$
$467$	3.57468e25	1.56576	0.782882	+	0.622170i	$0.213749\pi$
$468$	5.25486e24	0.225541
$469$	6.26397e22	0.00263456
$470$	1.15884e25	0.477631
$471$	−6.16494e24	−0.249018
$472$	−1.68619e25	−0.667510
$473$	−3.24927e25	−1.26068
$474$	−4.46110e25	−1.69648
$475$	−1.60167e25	−0.597013
$476$	−7.55442e22	−0.00276016
$477$	4.08664e24	0.146366
$478$	1.52128e25	0.534127
$479$	−2.88220e24	−0.0992056	−0.0496028	−	0.998769i	$-0.515796\pi$
$479$	−2.88220e24	−0.0992056	−0.0496028	+	0.998769i	$0.515796\pi$
$480$	6.49864e24	0.219296
$481$	−9.66528e24	−0.319769
$482$	−5.55152e25	−1.80080
$483$	1.12117e22	0.000356595 0
$484$	1.10974e26	3.46090
$485$	4.17574e25	1.27699
$486$	−3.65837e24	−0.109709
$487$	6.03233e25	1.77403	0.887014	−	0.461743i	$-0.152776\pi$
$487$	6.03233e25	1.77403	0.887014	+	0.461743i	$0.152776\pi$
$488$	−2.16378e25	−0.624059
$489$	−3.94822e24	−0.111678
$490$	−9.45632e25	−2.62337
$491$	4.20599e25	1.14444	0.572222	−	0.820099i	$-0.306082\pi$
$491$	4.20599e25	1.14444	0.572222	+	0.820099i	$0.306082\pi$
$492$	−3.42723e25	−0.914693
$493$	−4.43779e25	−1.16177
$494$	−1.03298e25	−0.265269
$495$	−3.39526e25	−0.855310
$496$	4.98034e23	0.0123079
$497$	6.86869e22	0.00166528
$498$	4.01577e25	0.955191
$499$	−3.96358e25	−0.924979	−0.462490	−	0.886625i	$-0.653044\pi$
$499$	−3.96358e25	−0.924979	−0.462490	+	0.886625i	$0.653044\pi$
$500$	4.55232e25	1.04236
$501$	5.04004e25	1.13234
$502$	4.76904e25	1.05134
$503$	5.09940e25	1.10312	0.551561	−	0.834135i	$-0.314032\pi$
$503$	5.09940e25	1.10312	0.551561	+	0.834135i	$0.314032\pi$
$504$	4.99221e22	0.00105975
$505$	5.89814e24	0.122870
$506$	4.29933e25	0.878965
$507$	2.52191e25	0.506004
$508$	−8.84651e25	−1.74207
$509$	−4.45056e25	−0.860193	−0.430096	−	0.902783i	$-0.641520\pi$
$509$	−4.45056e25	−0.860193	−0.430096	+	0.902783i	$0.641520\pi$
$510$	5.69549e25	1.08047
$511$	−6.77814e22	−0.00126215
$512$	−7.80561e25	−1.42673
$513$	4.73267e24	0.0849164
$514$	1.12355e26	1.97899
$515$	−1.31975e26	−2.28204
$516$	−4.93364e25	−0.837520
$517$	−1.82735e25	−0.304552
$518$	−1.91113e23	−0.00312721
$519$	−5.63540e25	−0.905388
$520$	5.40625e25	0.852833
$521$	−1.65819e24	−0.0256847	−0.0128424	−	0.999918i	$-0.504088\pi$
$521$	−1.65819e24	−0.0256847	−0.0128424	+	0.999918i	$0.504088\pi$
$522$	6.10382e25	0.928393
$523$	−4.69898e25	−0.701839	−0.350920	−	0.936406i	$-0.614131\pi$
$523$	−4.69898e25	−0.701839	−0.350920	+	0.936406i	$0.614131\pi$
$524$	−1.24207e26	−1.82180
$525$	−1.09019e23	−0.00157033
$526$	−3.17115e24	−0.0448593
$527$	−8.10231e23	−0.0112566
$528$	5.52053e25	0.753283
$529$	−6.75715e25	−0.905596
$530$	8.75073e25	1.15192
$531$	−1.08805e25	−0.140687
$532$	−1.34417e23	−0.00170724
$533$	2.31916e25	0.289349
$534$	−1.40358e26	−1.72026
$535$	1.73440e26	2.08828
$536$	1.75233e26	2.07277
$537$	−7.46114e24	−0.0867060
$538$	4.73752e25	0.540903
$539$	1.49115e26	1.67274
$540$	−5.15530e25	−0.568216
$541$	6.20242e25	0.671718	0.335859	−	0.941912i	$-0.390973\pi$
$541$	6.20242e25	0.671718	0.335859	+	0.941912i	$0.390973\pi$
$542$	4.51808e25	0.480796
$543$	6.21152e25	0.649531
$544$	1.71902e25	0.176641
$545$	−2.29473e26	−2.31721
$546$	−7.03109e22	−0.000697738 0
$547$	7.76624e25	0.757410	0.378705	−	0.925517i	$-0.376370\pi$
$547$	7.76624e25	0.757410	0.378705	+	0.925517i	$0.376370\pi$
$548$	−1.11740e26	−1.07101
$549$	−1.39623e25	−0.131529
$550$	−4.18054e26	−3.87068
$551$	−7.89624e25	−0.718588
$552$	3.13646e25	0.280555
$553$	3.92818e23	0.00345384
$554$	2.21128e26	1.91117
$555$	9.48217e25	0.805609
$556$	−2.38299e26	−1.99027
$557$	3.67420e25	0.301675	0.150837	−	0.988559i	$-0.451803\pi$
$557$	3.67420e25	0.301675	0.150837	+	0.988559i	$0.451803\pi$
$558$	1.11441e24	0.00899538
$559$	3.33852e25	0.264936
$560$	3.08269e23	0.00240516
$561$	−8.98112e25	−0.688943
$562$	−2.82659e26	−2.13191
$563$	1.24531e26	0.923526	0.461763	−	0.887003i	$-0.347217\pi$
$563$	1.24531e26	0.923526	0.461763	+	0.887003i	$0.347217\pi$
$564$	−2.77462e25	−0.202326
$565$	3.68357e26	2.64125
$566$	2.32231e26	1.63743
$567$	3.22134e22	0.000223356 0
$568$	1.92150e26	1.31018
$569$	−5.63513e25	−0.377866	−0.188933	−	0.981990i	$-0.560503\pi$
$569$	−5.63513e25	−0.377866	−0.188933	+	0.981990i	$0.560503\pi$
$570$	1.01341e26	0.668303
$571$	−1.23813e26	−0.803012	−0.401506	−	0.915856i	$-0.631513\pi$
$571$	−1.23813e26	−0.803012	−0.401506	+	0.915856i	$0.631513\pi$
$572$	−1.77435e26	−1.13182
$573$	−5.50469e25	−0.345354
$574$	4.58570e23	0.00282971
$575$	−6.84936e25	−0.415724
$576$	−6.71930e25	−0.401153
$577$	−3.01722e26	−1.77189	−0.885945	−	0.463790i	$-0.846489\pi$
$577$	−3.01722e26	−1.77189	−0.885945	+	0.463790i	$0.846489\pi$
$578$	−1.45390e26	−0.839888
$579$	1.44531e25	0.0821323
$580$	8.60137e26	4.80841
$581$	−3.53605e23	−0.00194467
$582$	−1.51924e26	−0.821974
$583$	−1.37989e26	−0.734501
$584$	−1.89617e26	−0.993014
$585$	3.48851e25	0.179746
$586$	3.49968e26	1.77420
$587$	−6.00743e25	−0.299659	−0.149829	−	0.988712i	$-0.547872\pi$
$587$	−6.00743e25	−0.299659	−0.149829	+	0.988712i	$0.547872\pi$
$588$	2.26414e26	1.11127
$589$	−1.44166e24	−0.00696254
$590$	−2.32986e26	−1.10722
$591$	1.04816e26	0.490168
$592$	−1.54176e26	−0.709511
$593$	−9.94196e25	−0.450248	−0.225124	−	0.974330i	$-0.572279\pi$
$593$	−9.94196e25	−0.450248	−0.225124	+	0.974330i	$0.572279\pi$
$594$	1.23528e26	0.550547
$595$	−5.01511e23	−0.00219973
$596$	2.07690e26	0.896554
$597$	5.01037e25	0.212869
$598$	−4.41742e25	−0.184717
$599$	−1.95677e26	−0.805350	−0.402675	−	0.915343i	$-0.631920\pi$
$599$	−1.95677e26	−0.805350	−0.402675	+	0.915343i	$0.631920\pi$
$600$	−3.04979e26	−1.23547
$601$	−4.73445e26	−1.88782	−0.943912	−	0.330197i	$-0.892885\pi$
$601$	−4.73445e26	−1.88782	−0.943912	+	0.330197i	$0.892885\pi$
$602$	6.60129e23	0.00259097
$603$	1.13073e26	0.436864
$604$	−2.26500e26	−0.861426
$605$	7.36715e26	2.75818
$606$	−2.14589e25	−0.0790894
$607$	−1.22707e26	−0.445222	−0.222611	−	0.974907i	$-0.571458\pi$
$607$	−1.22707e26	−0.445222	−0.222611	+	0.974907i	$0.571458\pi$
$608$	3.05868e25	0.109257
$609$	−5.37466e23	−0.00189011
$610$	−2.98976e26	−1.03515
$611$	1.87754e25	0.0640026
$612$	−1.36368e26	−0.457692
$613$	3.20354e26	1.05866	0.529329	−	0.848417i	$-0.322444\pi$
$613$	3.20354e26	1.05866	0.529329	+	0.848417i	$0.322444\pi$
$614$	−3.05888e26	−0.995320
$615$	−2.27522e26	−0.728969
$616$	−1.68566e24	−0.00531807
$617$	9.79781e25	0.304383	0.152191	−	0.988351i	$-0.451367\pi$
$617$	9.79781e25	0.304383	0.152191	+	0.988351i	$0.451367\pi$
$618$	4.80158e26	1.46890
$619$	−1.22713e25	−0.0369682	−0.0184841	−	0.999829i	$-0.505884\pi$
$619$	−1.22713e25	−0.0369682	−0.0184841	+	0.999829i	$0.505884\pi$
$620$	1.57040e25	0.0465896
$621$	2.02387e25	0.0591307
$622$	4.05085e26	1.16557
$623$	1.23591e24	0.00350226
$624$	−5.67215e25	−0.158305
$625$	−1.90020e26	−0.522324
$626$	4.62402e26	1.25188
$627$	−1.59803e26	−0.426131
$628$	3.16074e26	0.830179
$629$	2.50822e26	0.648909
$630$	6.89788e23	0.00175784
$631$	4.30803e26	1.08143	0.540716	−	0.841205i	$-0.318153\pi$
$631$	4.30803e26	1.08143	0.540716	+	0.841205i	$0.318153\pi$
$632$	1.09890e27	2.71735
$633$	−1.53057e26	−0.372836
$634$	−7.22579e25	−0.173395
$635$	−5.87288e26	−1.38836
$636$	−2.09520e26	−0.487958
$637$	−1.53211e26	−0.351532
$638$	−2.06101e27	−4.65890
$639$	1.23989e26	0.276138
$640$	−1.26571e27	−2.77730
$641$	5.54923e26	1.19972	0.599862	−	0.800104i	$-0.295222\pi$
$641$	5.54923e26	1.19972	0.599862	+	0.800104i	$0.295222\pi$
$642$	−6.31020e26	−1.34419
$643$	6.72911e26	1.41239	0.706193	−	0.708019i	$-0.250411\pi$
$643$	6.72911e26	1.41239	0.706193	+	0.708019i	$0.250411\pi$
$644$	−5.74820e23	−0.00118882
$645$	−3.27527e26	−0.667466
$646$	2.68066e26	0.538311
$647$	−3.57860e26	−0.708146	−0.354073	−	0.935218i	$-0.615204\pi$
$647$	−3.57860e26	−0.708146	−0.354073	+	0.935218i	$0.615204\pi$
$648$	9.01163e25	0.175728
$649$	3.67391e26	0.705999
$650$	4.29536e26	0.813435
$651$	−9.81282e21	−1.83136e−5 0
$652$	2.02423e26	0.372313
$653$	5.10990e26	0.926269	0.463135	−	0.886288i	$-0.346725\pi$
$653$	5.10990e26	0.926269	0.463135	+	0.886288i	$0.346725\pi$
$654$	8.34882e26	1.49155
$655$	−8.24568e26	−1.45189
$656$	3.69940e26	0.642014
$657$	−1.22355e26	−0.209291
$658$	3.71249e23	0.000625920 0
$659$	−6.67000e26	−1.10844	−0.554222	−	0.832369i	$-0.686984\pi$
$659$	−6.67000e26	−1.10844	−0.554222	+	0.832369i	$0.686984\pi$
$660$	1.74073e27	2.85144
$661$	2.27178e26	0.366819	0.183410	−	0.983037i	$-0.441287\pi$
$661$	2.27178e26	0.366819	0.183410	+	0.983037i	$0.441287\pi$
$662$	4.75827e26	0.757352
$663$	9.22779e25	0.144784
$664$	−9.89202e26	−1.52999
$665$	−8.92348e23	−0.00136059
$666$	−3.44985e26	−0.518556
$667$	−3.37674e26	−0.500382
$668$	−2.58400e27	−3.77500
$669$	3.72498e26	0.536508
$670$	2.42125e27	3.43818
$671$	4.71450e26	0.660043
$672$	2.08192e23	0.000287380 0
$673$	2.72017e26	0.370214	0.185107	−	0.982718i	$-0.440737\pi$
$673$	2.72017e26	0.370214	0.185107	+	0.982718i	$0.440737\pi$
$674$	1.61139e27	2.16238
$675$	−1.96795e26	−0.260393
$676$	−1.29297e27	−1.68692
$677$	4.27674e26	0.550200	0.275100	−	0.961416i	$-0.411289\pi$
$677$	4.27674e26	0.550200	0.275100	+	0.961416i	$0.411289\pi$
$678$	−1.34018e27	−1.70012
$679$	1.33775e24	0.00167345
$680$	−1.40296e27	−1.73066
$681$	−4.76614e26	−0.579788
$682$	−3.76290e25	−0.0451409
$683$	−1.11866e26	−0.132344	−0.0661719	−	0.997808i	$-0.521079\pi$
$683$	−1.11866e26	−0.132344	−0.0661719	+	0.997808i	$0.521079\pi$
$684$	−2.42642e26	−0.283095
$685$	−7.41805e26	−0.853551
$686$	−6.05892e24	−0.00687569
$687$	6.49473e26	0.726896
$688$	5.32543e26	0.587847
$689$	1.41779e26	0.154358
$690$	4.33373e26	0.465367
$691$	1.82536e27	1.93333	0.966667	−	0.256037i	$-0.0824171\pi$
$691$	1.82536e27	1.93333	0.966667	+	0.256037i	$0.0824171\pi$
$692$	2.88924e27	3.01839
$693$	−1.08771e24	−0.00112085
$694$	−1.06102e26	−0.107847
$695$	−1.58198e27	−1.58615
$696$	−1.50355e27	−1.48706
$697$	−6.01839e26	−0.587177
$698$	−1.37817e27	−1.32641
$699$	1.77045e26	0.168093
$700$	5.58937e24	0.00523518
$701$	−2.03227e27	−1.87785	−0.938924	−	0.344125i	$-0.888176\pi$
$701$	−2.03227e27	−1.87785	−0.938924	+	0.344125i	$0.888176\pi$
$702$	−1.26921e26	−0.115699
$703$	4.46292e26	0.401369
$704$	2.26883e27	2.01308
$705$	−1.84197e26	−0.161245
$706$	−2.77070e27	−2.39301
$707$	1.88955e23	0.000161017 0
$708$	5.57840e26	0.469023
$709$	−1.86039e27	−1.54335	−0.771675	−	0.636017i	$-0.780581\pi$
$709$	−1.86039e27	−1.54335	−0.771675	+	0.636017i	$0.780581\pi$
$710$	2.65499e27	2.17324
$711$	7.09091e26	0.572718
$712$	3.45742e27	2.75544
$713$	−6.16510e24	−0.00484830
$714$	1.82462e24	0.00141592
$715$	−1.17793e27	−0.902009
$716$	3.82529e26	0.289062
$717$	−2.41807e26	−0.180317
$718$	2.51234e27	1.84883
$719$	1.92780e27	1.40003	0.700014	−	0.714129i	$-0.253177\pi$
$719$	1.92780e27	1.40003	0.700014	+	0.714129i	$0.253177\pi$
$720$	5.56469e26	0.398825
$721$	−4.22798e24	−0.00299053
$722$	−1.97293e27	−1.37724
$723$	8.82414e26	0.607937
$724$	−3.18462e27	−2.16541
$725$	3.28343e27	2.20352
$726$	−2.68036e27	−1.77539
$727$	−1.11559e27	−0.729339	−0.364670	−	0.931137i	$-0.618818\pi$
$727$	−1.11559e27	−0.729339	−0.364670	+	0.931137i	$0.618818\pi$
$728$	1.73196e24	0.00111761
$729$	5.81497e25	0.0370370
$730$	−2.61999e27	−1.64715
$731$	−8.66372e26	−0.537637
$732$	7.15842e26	0.438492
$733$	2.04762e27	1.23812	0.619059	−	0.785344i	$-0.287514\pi$
$733$	2.04762e27	1.23812	0.619059	+	0.785344i	$0.287514\pi$
$734$	−2.51868e27	−1.50335
$735$	1.50308e27	0.885630
$736$	1.30801e26	0.0760802
$737$	−3.81802e27	−2.19229
$738$	8.27782e26	0.469224
$739$	1.50373e27	0.841486	0.420743	−	0.907180i	$-0.361769\pi$
$739$	1.50373e27	0.841486	0.420743	+	0.907180i	$0.361769\pi$
$740$	−4.86146e27	−2.68575
$741$	1.64192e26	0.0895527
$742$	2.80341e24	0.00150956
$743$	1.88836e27	1.00390	0.501950	−	0.864897i	$-0.332616\pi$
$743$	1.88836e27	1.00390	0.501950	+	0.864897i	$0.332616\pi$
$744$	−2.74511e25	−0.0144084
$745$	1.37878e27	0.714514
$746$	−9.63821e26	−0.493149
$747$	−6.38306e26	−0.322466
$748$	4.60457e27	2.29681
$749$	5.55638e24	0.00273662
$750$	−1.09953e27	−0.534716
$751$	8.19244e26	0.393400	0.196700	−	0.980464i	$-0.436978\pi$
$751$	8.19244e26	0.393400	0.196700	+	0.980464i	$0.436978\pi$
$752$	2.99495e26	0.142011
$753$	−7.58037e26	−0.354926
$754$	2.11762e27	0.979082
$755$	−1.50365e27	−0.686518
$756$	−1.65157e24	−0.000744628 0
$757$	1.94096e27	0.864184	0.432092	−	0.901829i	$-0.357776\pi$
$757$	1.94096e27	0.864184	0.432092	+	0.901829i	$0.357776\pi$
$758$	3.90907e27	1.71876
$759$	−6.83378e26	−0.296732
$760$	−2.49632e27	−1.07046
$761$	2.40135e27	1.01695	0.508477	−	0.861076i	$-0.330209\pi$
$761$	2.40135e27	1.01695	0.508477	+	0.861076i	$0.330209\pi$
$762$	2.13670e27	0.893659
$763$	−7.35147e24	−0.00303663
$764$	2.82223e27	1.15134
$765$	−9.05296e26	−0.364760
$766$	−3.83018e27	−1.52421
$767$	−3.77482e26	−0.148368
$768$	2.81516e27	1.09288
$769$	−3.49979e27	−1.34197	−0.670984	−	0.741472i	$-0.734128\pi$
$769$	−3.49979e27	−1.34197	−0.670984	+	0.741472i	$0.734128\pi$
$770$	−2.32913e25	−0.00882128
$771$	−1.78588e27	−0.668091
$772$	−7.41002e26	−0.273814
$773$	−3.84483e27	−1.40337	−0.701685	−	0.712487i	$-0.747569\pi$
$773$	−3.84483e27	−1.40337	−0.701685	+	0.712487i	$0.747569\pi$
$774$	1.19163e27	0.429636
$775$	5.99475e25	0.0213503
$776$	3.74233e27	1.31661
$777$	3.03774e24	0.00105572
$778$	−5.67774e27	−1.94926
$779$	−1.07086e27	−0.363186
$780$	−1.78854e27	−0.599240
$781$	−4.18661e27	−1.38573
$782$	1.14636e27	0.374848
$783$	−9.70201e26	−0.313419
$784$	−2.44394e27	−0.779987
$785$	2.09830e27	0.661615
$786$	2.99999e27	0.934556
$787$	4.22212e27	1.29948	0.649741	−	0.760155i	$-0.274877\pi$
$787$	4.22212e27	1.29948	0.649741	+	0.760155i	$0.274877\pi$
$788$	−5.37384e27	−1.63413
$789$	5.04054e25	0.0151442
$790$	1.51838e28	4.50737
$791$	1.18008e25	0.00346127
$792$	−3.04286e27	−0.881845
$793$	−4.84399e26	−0.138710
$794$	6.96142e27	1.96971
$795$	−1.39093e27	−0.388881
$796$	−2.56879e27	−0.709667
$797$	−2.10706e27	−0.575205	−0.287602	−	0.957750i	$-0.592858\pi$
$797$	−2.10706e27	−0.575205	−0.287602	+	0.957750i	$0.592858\pi$
$798$	3.24659e24	0.000875789 0
$799$	−4.87237e26	−0.129881
$800$	−1.27187e27	−0.335033
$801$	2.23098e27	0.580747
$802$	−1.03340e28	−2.65835
$803$	4.13142e27	1.05027
$804$	−5.79722e27	−1.45642
$805$	−3.81602e24	−0.000947436 0
$806$	3.86625e25	0.00948652
$807$	−7.53027e26	−0.182605
$808$	5.28596e26	0.126682
$809$	2.31386e27	0.548056	0.274028	−	0.961722i	$-0.411644\pi$
$809$	2.31386e27	0.548056	0.274028	+	0.961722i	$0.411644\pi$
$810$	1.24516e27	0.291487
$811$	2.32427e27	0.537760	0.268880	−	0.963174i	$-0.413347\pi$
$811$	2.32427e27	0.537760	0.268880	+	0.963174i	$0.413347\pi$
$812$	2.75556e25	0.00630127
$813$	−7.18148e26	−0.162313
$814$	1.16487e28	2.60224
$815$	1.34382e27	0.296717
$816$	1.47197e27	0.321249
$817$	−1.54155e27	−0.332544
$818$	−1.35125e28	−2.88124
$819$	1.11759e24	0.000235551 0
$820$	1.16649e28	2.43025
$821$	6.08231e27	1.25259	0.626295	−	0.779587i	$-0.284571\pi$
$821$	6.08231e27	1.25259	0.626295	+	0.779587i	$0.284571\pi$
$822$	2.69888e27	0.549415
$823$	−3.84390e27	−0.773523	−0.386762	−	0.922180i	$-0.626406\pi$
$823$	−3.84390e27	−0.773523	−0.386762	+	0.922180i	$0.626406\pi$
$824$	−1.18277e28	−2.35283
$825$	6.64496e27	1.30671
$826$	−7.46400e24	−0.00145098
$827$	5.47093e27	1.05138	0.525689	−	0.850677i	$-0.323807\pi$
$827$	5.47093e27	1.05138	0.525689	+	0.850677i	$0.323807\pi$
$828$	−1.03763e27	−0.197131
$829$	8.53655e26	0.160330	0.0801649	−	0.996782i	$-0.474455\pi$
$829$	8.53655e26	0.160330	0.0801649	+	0.996782i	$0.474455\pi$
$830$	−1.36681e28	−2.53785
$831$	−3.51482e27	−0.645198
$832$	−2.33115e27	−0.423056
$833$	3.97594e27	0.713365
$834$	5.75564e27	1.02098
$835$	−1.71543e28	−3.00850
$836$	8.19301e27	1.42064
$837$	−1.77135e25	−0.00303677
$838$	−1.67389e28	−2.83732
$839$	−8.76504e27	−1.46898	−0.734489	−	0.678621i	$-0.762578\pi$
$839$	−8.76504e27	−1.46898	−0.734489	+	0.678621i	$0.762578\pi$
$840$	−1.69915e25	−0.00281565
$841$	1.00841e28	1.65224
$842$	1.22740e28	1.98848
$843$	4.49287e27	0.719716
$844$	7.84716e27	1.24297
$845$	−8.58357e27	−1.34440
$846$	6.70155e26	0.103790
$847$	2.36016e25	0.00361451
$848$	2.26158e27	0.342493
$849$	−3.69131e27	−0.552786
$850$	−1.11468e28	−1.65071
$851$	1.90852e27	0.279489
$852$	−6.35687e27	−0.920592
$853$	4.55754e27	0.652702	0.326351	−	0.945249i	$-0.394181\pi$
$853$	4.55754e27	0.652702	0.326351	+	0.945249i	$0.394181\pi$
$854$	−9.57809e24	−0.00135653
$855$	−1.61081e27	−0.225614
$856$	1.55438e28	2.15307
$857$	8.72531e27	1.19526	0.597631	−	0.801771i	$-0.296109\pi$
$857$	8.72531e27	1.19526	0.597631	+	0.801771i	$0.296109\pi$
$858$	4.28559e27	0.580606
$859$	−6.82608e27	−0.914610	−0.457305	−	0.889310i	$-0.651185\pi$
$859$	−6.82608e27	−0.914610	−0.457305	+	0.889310i	$0.651185\pi$
$860$	1.67921e28	2.22521
$861$	−7.28895e24	−0.000955290 0
$862$	2.36855e27	0.307018
$863$	1.70088e27	0.218058	0.109029	−	0.994039i	$-0.465226\pi$
$863$	1.70088e27	0.218058	0.109029	+	0.994039i	$0.465226\pi$
$864$	3.75816e26	0.0476535
$865$	1.91806e28	2.40552
$866$	7.14723e27	0.886580
$867$	2.31098e27	0.283540
$868$	5.03098e23	6.10542e−5 0
$869$	−2.39431e28	−2.87404
$870$	−2.07750e28	−2.46665
$871$	3.92289e27	0.460716
$872$	−2.05656e28	−2.38910
$873$	2.41483e27	0.277492
$874$	2.03973e27	0.231854
$875$	9.68176e24	0.00108862
$876$	6.27308e27	0.697737
$877$	−9.69466e27	−1.06669	−0.533343	−	0.845899i	$-0.679064\pi$
$877$	−9.69466e27	−1.06669	−0.533343	+	0.845899i	$0.679064\pi$
$878$	1.00486e25	0.00109372
$879$	−5.56274e27	−0.598955
$880$	−1.87897e28	−2.00140
$881$	−2.20901e27	−0.232769	−0.116385	−	0.993204i	$-0.537131\pi$
$881$	−2.20901e27	−0.232769	−0.116385	+	0.993204i	$0.537131\pi$
$882$	−5.46858e27	−0.570064
$883$	−5.45945e27	−0.563018	−0.281509	−	0.959559i	$-0.590835\pi$
$883$	−5.45945e27	−0.563018	−0.281509	+	0.959559i	$0.590835\pi$
$884$	−4.73104e27	−0.482681
$885$	3.70330e27	0.373790
$886$	3.11718e27	0.311273
$887$	1.69664e28	1.67616	0.838081	−	0.545546i	$-0.183678\pi$
$887$	1.69664e28	1.67616	0.838081	+	0.545546i	$0.183678\pi$
$888$	8.49799e27	0.830602
$889$	−1.88145e25	−0.00181939
$890$	4.77721e28	4.57056
$891$	−1.96348e27	−0.185861
$892$	−1.90978e28	−1.78862
$893$	−8.66950e26	−0.0803351
$894$	−5.01636e27	−0.459920
$895$	2.53947e27	0.230369
$896$	−4.05485e25	−0.00363956
$897$	7.02148e26	0.0623592
$898$	−1.33058e28	−1.16927
$899$	2.95541e26	0.0256981
$900$	1.00896e28	0.868100
$901$	−3.67927e27	−0.313239
$902$	−2.79508e28	−2.35468
$903$	−1.04927e25	−0.000874692 0
$904$	3.30125e28	2.72319
$905$	−2.11415e28	−1.72574
$906$	5.47068e27	0.441899
$907$	1.06963e28	0.854996	0.427498	−	0.904016i	$-0.359395\pi$
$907$	1.06963e28	0.854996	0.427498	+	0.904016i	$0.359395\pi$
$908$	2.44357e28	1.93290
$909$	3.41089e26	0.0267000
$910$	2.39310e25	0.00185382
$911$	−2.36272e28	−1.81129	−0.905645	−	0.424036i	$-0.860613\pi$
$911$	−2.36272e28	−1.81129	−0.905645	+	0.424036i	$0.860613\pi$
$912$	2.61910e27	0.198702
$913$	2.15530e28	1.61821
$914$	1.00197e28	0.744502
$915$	4.75222e27	0.349459
$916$	−3.32982e28	−2.42333
$917$	−2.64161e25	−0.00190265
$918$	3.29370e27	0.234789
$919$	4.79736e27	0.338458	0.169229	−	0.985577i	$-0.445872\pi$
$919$	4.79736e27	0.338458	0.169229	+	0.985577i	$0.445872\pi$
$920$	−1.06752e28	−0.745406
$921$	4.86208e27	0.336013
$922$	1.83363e28	1.25420
$923$	4.30160e27	0.291215
$924$	5.57666e25	0.00373672
$925$	−1.85578e28	−1.23078
$926$	−3.28515e28	−2.15651
$927$	−7.63210e27	−0.495891
$928$	−6.27031e27	−0.403258
$929$	−4.77499e27	−0.303965	−0.151982	−	0.988383i	$-0.548566\pi$
$929$	−4.77499e27	−0.303965	−0.151982	+	0.988383i	$0.548566\pi$
$930$	−3.79300e26	−0.0238998
$931$	7.07446e27	0.441237
$932$	−9.07699e27	−0.560390
$933$	−6.43881e27	−0.393487
$934$	4.42658e28	2.67777
$935$	3.05681e28	1.83045
$936$	3.12643e27	0.185323
$937$	−3.08658e27	−0.181114	−0.0905568	−	0.995891i	$-0.528865\pi$
$937$	−3.08658e27	−0.181114	−0.0905568	+	0.995891i	$0.528865\pi$
$938$	7.75677e25	0.00450562
$939$	−7.34987e27	−0.422627
$940$	9.44368e27	0.537560
$941$	2.51804e27	0.141893	0.0709466	−	0.997480i	$-0.477398\pi$
$941$	2.51804e27	0.141893	0.0709466	+	0.997480i	$0.477398\pi$
$942$	−7.63414e27	−0.425870
$943$	−4.57943e27	−0.252901
$944$	−6.02139e27	−0.329202
$945$	−1.09642e25	−0.000593435 0
$946$	−4.02363e28	−2.15602
$947$	8.85552e27	0.469774	0.234887	−	0.972023i	$-0.424528\pi$
$947$	8.85552e27	0.469774	0.234887	+	0.972023i	$0.424528\pi$
$948$	−3.63547e28	−1.90933
$949$	−4.24489e27	−0.220718
$950$	−1.98337e28	−1.02101
$951$	1.14854e27	0.0585370
$952$	−4.49458e25	−0.00226797
$953$	1.35516e28	0.677030	0.338515	−	0.940961i	$-0.390075\pi$
$953$	1.35516e28	0.677030	0.338515	+	0.940961i	$0.390075\pi$
$954$	5.06055e27	0.250315
$955$	1.87358e28	0.917570
$956$	1.23973e28	0.601144
$957$	3.27597e28	1.57281
$958$	−3.56907e27	−0.169661
$959$	−2.37647e25	−0.00111855
$960$	2.28698e28	1.06582
$961$	−2.16653e28	−0.999751
$962$	−1.19687e28	−0.546868
$963$	1.00300e28	0.453788
$964$	−4.52409e28	−2.02675
$965$	−4.91925e27	−0.218217
$966$	1.38837e25	0.000609848 0
$967$	5.51108e27	0.239710	0.119855	−	0.992791i	$-0.461757\pi$
$967$	5.51108e27	0.239710	0.119855	+	0.992791i	$0.461757\pi$
$968$	6.60250e28	2.84376
$969$	−4.26091e27	−0.181730
$970$	5.17088e28	2.18390
$971$	2.37023e28	0.991308	0.495654	−	0.868520i	$-0.334928\pi$
$971$	2.37023e28	0.991308	0.495654	+	0.868520i	$0.334928\pi$
$972$	−2.98131e27	−0.123475
$973$	−5.06808e25	−0.00207860
$974$	7.46993e28	3.03394
$975$	−6.82747e27	−0.274610
$976$	−7.72688e27	−0.307773
$977$	−6.97540e27	−0.275151	−0.137575	−	0.990491i	$-0.543931\pi$
$977$	−6.97540e27	−0.275151	−0.137575	+	0.990491i	$0.543931\pi$
$978$	−4.88915e27	−0.190992
$979$	−7.53310e28	−2.91433
$980$	−7.70621e28	−2.95252
$981$	−1.32704e28	−0.503535
$982$	5.20835e28	1.95722
$983$	1.96330e28	0.730683	0.365341	−	0.930874i	$-0.380952\pi$
$983$	1.96330e28	0.730683	0.365341	+	0.930874i	$0.380952\pi$
$984$	−2.03907e28	−0.751585
$985$	−3.56750e28	−1.30233
$986$	−5.49538e28	−1.98686
$987$	−5.90099e24	−0.000211306 0
$988$	−8.41804e27	−0.298552
$989$	−6.59227e27	−0.231564
$990$	−4.20440e28	−1.46275
$991$	4.20556e28	1.44918	0.724592	−	0.689178i	$-0.242028\pi$
$991$	4.20556e28	1.44918	0.724592	+	0.689178i	$0.242028\pi$
$992$	−1.14481e26	−0.00390725
$993$	−7.56325e27	−0.255676
$994$	8.50560e25	0.00284796
$995$	−1.70533e28	−0.565573
$996$	3.27256e28	1.07504
$997$	−1.15418e28	−0.375551	−0.187776	−	0.982212i	$-0.560128\pi$
$997$	−1.15418e28	−0.375551	−0.187776	+	0.982212i	$0.560128\pi$
$998$	−4.90816e28	−1.58190
$999$	5.48353e27	0.175061

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.20.a.b.1.2	✓	2
3.2	odd	2		9.20.a.c.1.1		2
4.3	odd	2		48.20.a.j.1.2		2
5.2	odd	4		75.20.b.b.49.4		4
5.3	odd	4		75.20.b.b.49.1		4
5.4	even	2		75.20.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.20.a.b.1.2	✓	2	1.1	even	1	trivial
9.20.a.c.1.1		2	3.2	odd	2
48.20.a.j.1.2		2	4.3	odd	2
75.20.a.b.1.1		2	5.4	even	2
75.20.b.b.49.1		4	5.3	odd	4
75.20.b.b.49.4		4	5.2	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)

\(f(q)\)	\(=\)	\(q+1238.32 q^{2} -19683.0 q^{3} +1.00914e6 q^{4} +6.69930e6 q^{5} -2.43738e7 q^{6} +214621. q^{7} +6.00397e8 q^{8} +3.87420e8 q^{9} +O(q^{10})\)	\(q+1238.32 q^{2} -19683.0 q^{3} +1.00914e6 q^{4} +6.69930e6 q^{5} -2.43738e7 q^{6} +214621. q^{7} +6.00397e8 q^{8} +3.87420e8 q^{9} +8.29585e9 q^{10} -1.30816e10 q^{11} -1.98629e10 q^{12} +1.34409e10 q^{13} +2.65768e8 q^{14} -1.31862e11 q^{15} +2.14402e11 q^{16} -3.48802e11 q^{17} +4.79749e11 q^{18} -6.20630e11 q^{19} +6.76052e12 q^{20} -4.22438e9 q^{21} -1.61991e13 q^{22} -2.65405e12 q^{23} -1.18176e13 q^{24} +2.58072e13 q^{25} +1.66441e13 q^{26} -7.62560e12 q^{27} +2.16582e11 q^{28} +1.27229e14 q^{29} -1.63287e14 q^{30} +2.32290e12 q^{31} -4.92835e13 q^{32} +2.57485e14 q^{33} -4.31927e14 q^{34} +1.43781e12 q^{35} +3.90961e14 q^{36} -7.19096e14 q^{37} -7.68535e14 q^{38} -2.64557e14 q^{39} +4.02224e15 q^{40} +1.72545e15 q^{41} -5.23112e12 q^{42} +2.48385e15 q^{43} -1.32011e16 q^{44} +2.59545e15 q^{45} -3.28655e15 q^{46} +1.39689e15 q^{47} -4.22007e15 q^{48} -1.13988e16 q^{49} +3.19574e16 q^{50} +6.86546e15 q^{51} +1.35637e16 q^{52} +1.05483e16 q^{53} -9.44290e15 q^{54} -8.76375e16 q^{55} +1.28858e14 q^{56} +1.22159e16 q^{57} +1.57550e17 q^{58} -2.80846e16 q^{59} -1.33067e17 q^{60} -3.60392e16 q^{61} +2.87648e15 q^{62} +8.31485e13 q^{63} -1.73437e17 q^{64} +9.00446e16 q^{65} +3.18848e17 q^{66} +2.91862e17 q^{67} -3.51989e17 q^{68} +5.22397e16 q^{69} +1.78046e15 q^{70} +3.20038e17 q^{71} +2.32606e17 q^{72} -3.15819e17 q^{73} -8.90467e17 q^{74} -5.07963e17 q^{75} -6.26301e17 q^{76} -2.80758e15 q^{77} -3.27605e17 q^{78} +1.83029e18 q^{79} +1.43634e18 q^{80} +1.50095e17 q^{81} +2.13665e18 q^{82} -1.64758e18 q^{83} -4.26298e15 q^{84} -2.33673e18 q^{85} +3.07579e18 q^{86} -2.50426e18 q^{87} -7.85414e18 q^{88} +5.75855e18 q^{89} +3.21398e18 q^{90} +2.88469e15 q^{91} -2.67830e18 q^{92} -4.57216e16 q^{93} +1.72979e18 q^{94} -4.15779e18 q^{95} +9.70047e17 q^{96} +6.23309e18 q^{97} -1.41154e19 q^{98} -5.06808e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 702 q^{2} - 39366 q^{3} + 772484 q^{4} + 6016140 q^{5} - 13817466 q^{6} + 113892064 q^{7} + 1008501624 q^{8} + 774840978 q^{9}+O(q^{10}) \) 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

Modular forms

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